Enhanced oil recovery, Volume 13: Proceedings of the third European Symposium on Enhanced Oil Recovery, held in Bournemouth, U.K., September 21-23, 1981 (Developments in Petroleum Science)

Developments in Petroleum Science, 13

enhanced oil recovery

FURTHER TITLES IN THIS SERIES

1A, GENE COLLINS GEOCHEMISTRY O F OILFIELD WATERS 2 W.H. FERTL ABNORMAL FORMATION PRESSURES 3 A.P. SZILAS PRODUCTION AND TRANSPORT O F OIL AND GAS 4 C.E.B. CONYBEARE GEOMORPHOLOGY O F OIL AND GAS FIELDS IN SANDSTONE BODIES

5 T.F. YEN and G.V. CHILINGARIAN (Editors) OIL SHALE 6 D.W. PEACEMAN FUNDAMENTALS O F NUMERICAL RESERVOIR SIMULATION

7 G.V. CHILINGARIAN and T.F. YEN (Editors) BITUMENS, ASPHALTS AND TAR SANDS 8 L.P. DAKE FUNDAMENTALS OF RESERVOIR ENGINEERING

9 K. MAGARA COMPACTION AND FLUID MIGRATION 10 M.T. SILVIA and E.A. ROBINSON DECONVOLUTION O F GEOPHYSICAL TIME SERIES IN THE EXPLORATION FOR OIL AND NATURAL GAS 11G.V. CHILINGARIAN and P. VORABUTR DRILLING AND DRILLING FLUIDS 1 2 T. VAN GOLF-RACHT FRACTURED HYDROCARBON-RESERVOIR ENGINEERING

Developments in Petroleum Science, 1 3

Proceedings of the third European Symposium on Enhanced Oil Recovery, held in Bournemouth, U.K., September 21-23,1981

Edited by

EJOHN FAYERS Atomic Energy Establishment, Winfrith, Dorchester, England

ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM -OXFORD -NEW YORK 1981

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Molenwerf 1 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

Distributors for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

ISBN 0-444-42033-9 (Vol. 13) ISBN 0-444-41625-0 (Series) 0 Elsevier Scientific Publishing Company, 1981

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands Printed in The Netherlands

V

TABLE OF CONTENTS

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

CHEMICAL FLOODING 1.

2.

Keynote Paper: “Fundamental Aspects of Surfactant-Polymer Flooding Process” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. 0. SHAH, University of Florida, USA Surfactants for EOR Processes in High-Salinity Systems; Product Selection and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. H. AKSTINAT, Institute of Petroleum Engineering, Clausthal, West Germany

1

43

3. Preliminary Studies of the Behaviour or Some Commercially Available Surfactants in Hydrocarbon-Brine-Mineral Systems . . . . . . . . . . . . . . . . . 63 C. ANDREWS, N. COLLEY and R. THAVER, British Gas Corporation, London Research Station, UK 4. The Provision of Laboratory Data for EOR Simulation. . . . . . . . . . . . . . . . 81 C. E. BROWN and G. 0. LANGLEY, BP Research Centre, Sunbury, UK

5. Experimental Study and Interpretation of Surfactant Retention in Porous 101 Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. NOVOSAD, Petroleum Recovery Institute, Calgary, Canada 6. The EACN of a Crude Oil: Variations with Cosurfactant and Water Oil Ratio 123 MIN KWAN THAM and P. B. LORENZ, US Department of Energy, Bartlesville, OK, USA 7.

Dynamic Interfacial Phenomena Related to EOR. . . . . . . . . . . . . . . . . . . . 135 J. H. CLINT, E. L. NEUSTADTER and T. J. JONES, BP Research Centre, Sunbury, UK

8. Behaviour of Surfactants in EOR Applications at High Temperatures . . . . . . 149 L. L. HANDY, University of Southern California, Los Angeles, CA, USA 9. Surfactant Slug Displacement Efficiency in Reservoirs . . . . . . . . . . . . . . . . 161 R. J. WRIGHT and R. A. DAWE, Imperial College, University of London, UK 10. Some Aspects of the Injectivity of Non-Newtonian Fluids in Porous Media. . . 179 P. VOGEL and G. PUSCH, Institute. of Petroleum Engineering, Clausthal, West Germany

vi 11.

Basic Rheological Behaviour of Xanthan Polysaccharide Solutions in Porous Media: Effects of Pore Size and Polymer Concentration . . . . . . . . . . . . . . . 197 G. CHAUVETEAU and A. ZAITOUN, Institut Franqais du PCtrole, RueilMalmaison, France

12.

The Chateaurenard (France) Polymer Flood Field Test. . . . . . . . . . . . . . . . 213 A. LABASTIE, Elf Aquitaine, Boussens, Saint-Martory, France L. VIO, Elf Aquitaine, Centre de Recherche de Lacq, Artix, France

13.

Caustic Flooding in the Wilmington Field, California, Laboratory Modelling and Field Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 V. S. BREIT, Scientific Software Corp., Denver, TX, USA E. H. MAYER, THUMS Long Beach Co, CA, USA J. D. CARMICHAEL, City of Long Beach Department of Oil Properties

MISCIBLE GAS DISPLACEMENT 14.

Keynote Paper: “Miscible Displacement: Its Potential for Enhanced Oil 237 Recovery” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. J. BLACKWELL, Exxon Production Research, Houston, TX, USA

15.

Theoretical Aspects of Calculating the Performance of COz as an EOR 247 Process in North Sea Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S. HUGHES, J. D. MATTHEWS and R. E. MOTT, AEE Winfrith, DorChester, Dorset, UK

16.

A New Linear Displacement Model with Mass Transfer Between Phases, n.a. Adapted to C 0 2 Injection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. JAIN, Institut Franqais du PCtrole, Rued-Malmaison, France (This paper will be distributed at the Conference)

17.

Oil Recovery by Carbon Dioxide, the results of Scaled Physical Models and 267 Field Pilots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. M. DOSCHER, M. EL ARABI, S. GHARIB and R. OYEKAN, University of Southern California, Los Angeles, CA, USA

18.

Laboratory Testing Procedures for Miscible Floods . . . . . . . . . . . . . . . . . . 285 S. G. SAYEGH and F. G. MCCAFFERY, Petroleum Recovery Institute, Calgary, Canada

19.

299 Complex Study of C 0 2 Flooding in Hungary . . . . . . . . . . . . . . . . . . . . . . s. DOLESCHALL, G. ACS, v. BALINT, z. BIRO, E. FARKAS, T. PAAL, J. TOROK, Hungarian Hydrocarbon Inst., Szazhalombatta, Hungary

20.

An Iterative Method for Phase Equilibria Calculations with Particular Appli313 cation t o Multicomponent Miscible Systems . . . . . . . . . . . . . . . . . . . . . . . N. VAROTSIS, A. C. TODD and G. STEWART, Heriot-Watt University, Edinburgh, UK

vii 2 1.

Phase Equilibrium Calculations in the Near-Critical Region . . . . . . . . . . . . . 329 R. RISNES, Norsk Agip, Norway V. DALEN, J. I. JENSEN, Continental Shelf Institute, Trondheim, Norway

22.

The Effect of Simulated COz Flooding on the Permeability of Reservoir Rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 G. D. ROSS, A. C. TODD and J . A. TWEEDIE, Heriot-Watt University, Edinburgh, UK

NUMERICAL METHODS

.............

23.

Keynote Paper: “Computer Modelling of EOR Processes”. K. AZIZ, University of Calgary, Canada

24.

Three-Dimensional Numerical Simulation of Steam Injection. . . . . . . . . . . . 379 P. LEMONNIER, Institut Frangais du PCtrole, Rueil-Malmaison, France

25.

Special Techniques for Fully Implicit Simulators. . . . . . . . . . . . . . . . . . . . 395 J. R. APPLEYARD, I. M. CHESHIRE and R. K. POLLARD, Operatings Research Group, AERE Harwell, UK

26.

Some Considerations Concerning the Efficiency of Chemical Flood Simulators 409 R. W. S. FOULSER, AEE Winfrith, Dorchester, Dorset, UK

27.

Control of Numerical Dispersion in Compositional Simulation. . . . . . . . . . . 425 D. C. WILSON, T. C. TAN and P. C. CASINADER, Imperial College, University of London, UK

28.

Interphase Mass Transfer Effects in Implicit Black Oil Simulators. D. BANKS and D.K. PONTING, AERE Harwell, Oxfordshire, UK

........

367

441

EXPERIMENTAL TECHNIQUES 29.

45 1 A Novel Device for COz Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. MEYN, Institute of Petroleum Engineering, Clausthal, West Germany

30.

The Use of Slim Tube Displacement Experiments in the Assessment of Miscible Gas Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 B. J. SKILLERNE DE BRISTOWE, BP Research Centre, Sunbury, UK

31.

Nuclear Measurements of Fluid Saturations in EOR Flood Experiments 483 N. A. BAILEY, P. R. ROWLAND and D. P. ROBINSON, AEE Winfrith, Dorchester, Dorset, UK

32.

Characterisation of EOR Polymers as to Size in Solution . . . . . . . . . . . . . . 499 R. DIETZ, National Physical Laboratory, Teddington, UK

viii 33.

Visualization of the Behaviour of EOR Reagents in Displacements in Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 E. G. MAHERS, R. J. WRIGHT and R. A. DAWE, Imperial College, University of London, UK

THERMAL RECOVERY METHODS 34.

Keynote Paper: “The Interplay Between Research and Field Operations in the Development of Thermal Recovery Methods” . . . . . . . . . . . . . . . . . . . 527 J. OFFERINGA, R. BARTHEL and J. WEIJDEMA, Shell Exploration and Production Laboratories, Rijswijk, Holland

35.

U.S. Department of Energy R & D on Downhole Steam Generator for the Recovery of Heavy Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 R. L. FOX, Sandia Laboratories, NM, USA J. J. STOSUR, U.S. Department of Energy, Washington, DC, USA

36.

Steam Drive - The Successful Enhanced Oil Recovery Technology. . . . . . . . 549 T. M. DOSCHER and F. GHASSEMI, University of California, Los Angeles, CA, USA

37.

Down Hole Steam Generation using a Pulsed Burner . . . . . . . . . . . . . . . . . 563 D. A. CHESTERS, C. J. CLARK, F. A. RIDDIFORD, BP Research Centre, Sunbury, UK

38.

Hot Caustic Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 R. JANSSEN-VAN ROSMALEN and F. Th. HESSELINK, Shell Exploration and Production Laboratories, Rijswijk, Holland

UNITED STATES RESEARCH PROGRAMME 39.

Enhanced Oil Recovery Research and Development in the United States and in the U.S. Department of Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 J. J. G. STOSUR, U.S. Department of Energy, Washington, DC, USA

AUTHORINDEX

............................................

595

ix

FOREWORD

T h i s r e s i d e n t i a l symposium i s t h e t h i r d i n t h e series of symposia which have been h e l d on t h e s u b j e c t of enhanced o i l r e c o v e r y i r , t h e United Kingdom; t h e o t h e r two b e i n g h e l d a t B r i t a n n i c House of BP i n London i n May 1977, and a t Heriot-Watt U n i v e r s i t y i n Edinburgh i n J u l y 1978. S i n c e 1977, when t h e f i r s t symposium was h e l d i n London, t h e a n n u a l p r o d u c t i o n and t h e number o f f i e l d s i n o p e r a t i o n i n t h e UK s e c t o r o f t h e North Sea h a s roughly doubled and i t i s perhaps r i g h t t o r e - i t e r a t e t h e remarks of t h e Chairman of t h e o r g a n i s i n g committee of t h e f i r s t meeting. H e s a i d t h a t , "There i s an u r g e n t need t o d e c i d e which enhanced o i l r e c o v e r y t e c h n i q u e s a r e s u i t a b l e f o r u s e i n t h e North Sea. Once t h i s d e c i s i o n i s made, t h e s e l e c t e d R&D g o a l s s h o u l d b e v i g o r o u s l y p u r s u e d , l e a d i n g , h o p e f u l l y , t o t h e development of s p e c i f i c t a i l o r - m a d e t e c h n i q u e s e f f e c t i v e i n t h e i n d i v i d u a l f i e l d s i n t h e North Sea a r e a " . Although t h e s e remarks a r e s t i l l v a l i d t o d a y , i n t h e i n t e r vening p e r i o d t h r o u g h o u t Europe s i g n i f i c a n t p r o g r e s s has been made. W e have s e e n an i n c r e a s e i n t h e number o f p i l o t f i e l d experiments u n d e r t a k e n by t h e o i l i n d u s t r y , an i n c r e a s e i n t h e r e s e a r c h work c a r r i e d o u t a t u n i v e r s i t i e s , r e s e a r c h i n s t i t u t e s and o i l company laboratories. A number of Government programmes have been i n i t i a t e d o r expanded. A g a i n s t t h i s background of an i n c r e a s e d R&D a c t i v i t y , some s i g n i f i c a n t , a l b e i t t e n t a t i v e , s t e p s i n t h e a p p l i c a t i o n of enhanced o i l r e c o v e r y o f f s h o r e have been t a k e n . The c o n t i n u i n g i n c r e a s e i n t h e p r i c e of o i l o v e r t h e p a s t few y e a r s r e n d e r s t h e t i m i n g of t h e p r e s e n t symposium t o be p a r t i c u l a r l y r e l e v a n t t o t h e q u e s t i o n of improvement i n o i l recovery i n a l l t h e s e c t o r s of t h e North Sea and f o r t h e p r o v i s i o n of f u t u r e s u p p l i e s of e n e r g y t o Europe. The o c c a s i o n of t h e p r e s e n t c o n f e r e n c e p r o v i d e s an i n t e r n a t i o n a l forum f o r r e s e a r c h workers ins enhanced o i l r e c o v e r y t o exchange i n f o r m a t i o n and t o develop an i n c r e a s e d awareness of t h e r e s e a r c h s t u d i e s c u r r e n t l y b e i n g pursued e l s e w h e r e . I t i s hoped t h a t new d i r e c t i o n s f o r r e s e a r c h , a p p l i c a b l e t o t h e European C o n t i n e n t a l S h e l f , may become a p p a r e n t and t h e f u t u r e a d o p t i o n of enhanced o i l r e c o v e r y t e c h n i q u e s i n t h i s a r e a advanced. T h i s volume i s a c o l l e c t i o n of t h e p a p e r s t o b e p r e s e n t e d and d i s c u s s e d a t t h e Symposium.

F J FAYERS

Chairman, O r g a n i s i n g Committee September 1981

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CHEMICAL FLOODING

1

FUNDAMENTAL ASPECTS OF SURFACTANT-POLYMER FLOODING PROCESS

D.0.SHAH Department of Chemical Engineering and Anesthesiology, University of Florida, Gainesville, Florida 3261 I ABSTRACT Surfactant-polymer f l o o d i n g process o f f e r s a promising approach t o recover a d d i t i o n a l o i l from the water flooded r e s e r v o i r s which may conThe c a p i l l a r y number, t a i n as much as 70% o f o r i g i n a l o i l - i n - p l a c e . which determines the microscopic displacement e f f i c i e n c y o f o i l , can be increased b y 3 t o 4 orders o f magnitude by reducing the i n t e r f a c i a l tension (IFT) of o i l ganglia below 10-3 dynes/cm. Conceptual events involved i n the m o b i l i z a t i o n and displacement o f o i l ganglia are described i n c l u d i n g the r o l e o f u l t r a l o w i n t e r f a c i a l tension, t h e r o l e o f i n t e r f a c i a l v i s c o s i t y i n coalescence o f o i l ganglia and formation o f t h e o i l bank, the propagation o f the o i l bank, the surfactant-polymer incomp a t i b i l i t y , the formation and f l o w o f emulsions i n porous media, the r o l e o f w e t t a b i l i t y as well as the i n f l u e n c e o f surface charge d e n s i t y o f the r o c k / f l u i d i n t e r f a c e and o i l - b r i n e i n t e r f a c e i n o i l displacement e f f i ciency. It i s shown t h a t t h e r e are two regions o f u l t r a - l o w IFT; 1) i n the low surfactant concentration (0.1-0.2%) and the other i n t h e high s u r f a c t a n t concentration region (2.0%-10.0%). I n t h e low concentration systems, the u l t r a - l o w i n t e r f a c i a l tension occurs when t h e aqueous phase of the surfactant s o l u t i o n i s about the apparent c r i t i c a l m i c e l l e concent r a t i o n . And, the s a l i n i t y i s a t the c r i t i c a l e l e c t r o l y t e concentration for the coacervation process. The m i g r a t i o n o f surfactant from the aqueous phase t o the o i l phase v i a coacervation process appears t o be r e sponsible f o r the u l t r a l o w i n t e r f a c i a l tension. I n high surfactant concentration systems, a middle phase microemuls i o n i n e q u i l i b r i u m w i t h excess o i l and b r i n e forms i n a narrow s a l i n i t y range. T h e ' s a l i n i t y a t which equal volumes o f o i l and b r i n e are s o l u b i l i z e d i n the middle phase microemulsion i s r e f e r r e d t o as the optimal s a l i n i t y o f the system. A t t h e optimal s a l i n i t y , t h e i n t e r f a c i a l tension a t both i n t e r f a c e s i s equal. Evidence i s presented t h a t the middle phase microemulsion a t the optimal s a l i n i t y i s a water external microemulsion formed due t o coacervation and subsequent phase separation o f m i c e l l e s f r a n t h e aqueous phase. The optimal s a l i n i t y can be s h i f t e d t o a desired value by varying t h e s t r u c t u r e and 'concentration o f alcohol. The s h i f t i n optimal s a l i n i t y can be c o r r e l a t e d w i t h t h e b r i n e s o l u b i l i t y o f the alcohol used i n a given s u r f a c t a n t formulation. It was f u r t h e r observed t h a t the optimal s a l i n i t y increases w i t h the o i l chain length. I n order t o form middle phase microemulsions at very high s a l i n i t y , ethoxylated surfactants o r alcohols can be incorporated i n t o a s u r f a c t a n t formulation which can s h i f t the optimal s a l i n i t y t o as high as 32% NaCl concentration. Such high s a l i n i t y formulations c o n s i s t i n g o f petroleum sulfonates and ethoxylated sulfonates are r e l a t i v e l y i n s e n s i t i v e t o diva1ent c a t ions.

2

The coalescence r a t e o r the phase separation time was minimum at optimal s a l i n i t y . I t was also observed t h a t the apparent v i s c o s i t y was minimal a t the optimal s a l i n i t y f o r the f l o w o f microemulsions through porous media. The r a t e o f f l a t t e n i n g o f an o i l drop i n a surfactant f o r mulation increases s t r i k i n g l y i n the presence o f alcohol. I t appears t h a t the presence o f alcohol promotes the mass t r a n s f e r o f s u r f a c t a n t from the aqueous phase t o the i n t e r f a c e . The a d d i t i o n o f alcohol also promotes the coalescence o f o i l drops, presumably due t o a decrease i n the i n t e r f a c i a l v i s c o s i t y . The surfactant-polymer i n c o m p a t i b i l i t y can lead t o a phase separat i o n o f a surfactant and polymer even i n the absence o f o i l . I n the presence o f o i l , the formation o f middle phase microemulsion i s promoted by the presence o f polymer i n the aqueous phase. The surfactant-polymer i n c o m p a t i b i l i t y i s explained i n terms o f excluded volume e f f e c t s and the maximization o f solvent f o r polymer molecules. Some novel concepts f o r surfactant-polymer f l o o d i n g process have been discussed i n c l u d i n g the use o f tm, d i f f e r e n t s u r f a c t a n t slugs, two d i f f e r e n t polymer slugs, s a l i n i t y gradient design and the i n j e c t i o n o f an o i l bank t o promote o i l recovery.

PRODUCTION

BANK

PRODUCTION

WATER

WELLS

A

Fig. 1

B

C

D

Schematic diagram o f an o i l r e s e r v o i r and the displacement of o i l by water o r chemical flooding.

3 A.

INTRODUCTION

I t i s well recognized t h a t the energy consumption per c a p i t a and the standard of. l i v i n g o f a s o c i e t y are i n t e r r e l a t e d . Among various sources o f energy, f o s s i l f u e l s o r crude o i l s p l a y an important r o l e i n providing the energy supply o f t h e world. It also serves as a raw m a t e r i a l f o r feed stocks i n chemical industry. I n view o f the worldwide energy c r i sis, the importance o f enhanced o i l recovery t o increase t h e supply o f crude o i l i s obvious and various enhanced o i l recovery processes have been proposed and tested both on a l a b o r a t o r y scale and i n the f i e l d . For heavy o i l s , thermal processes have been used e x t e n s i v e l y whereas f o r l i g h t o i l s , chemical processes such as polymer flooding, caustic f l o o d ing , m i s c i b l e f 1ood ing and s u r f act ant-pol ymer f 1oodi ng have a t t r a c t e d great i n t e r e s t . The major research f i n d i n g s i n the enhanced o i l recovery area have been reported i n recent l i t e r a t u r e and the symposia proceedings of various conferences during the l a s t decade (1-11). The present paper focuses on the fundamental aspects o f the surfactant-polymer f l o o d i n g process and r e 1ated phenomena.

Figure 1 schematically shows a three-dimensional view o f a petroleum reservoir. A t the end o f water-flooding, t h e o i l t h a t remains i n the r e s e r v o i r i s believed t o be i n the form o f o i l ganglia trapped i n t h e pore s t r u c t u r e o f the rock as shown i n Figure 1A. These o i l ganglia are entrapped due t o c a p i l l a r y forces. However, i f a s u r f a c t a n t s o l u t i o n i s i n j e c t e d t o lower the i n t e r f a c i a l tension o f the o i l ganglia from i t s value o f 20-30 dynes/cm t o 10-3 dyneslcm, the o i l ganglia can be mobilized and can move through narrow necks o f t h e pores. Such mobilized o i l ganglia form an o i l bank as shown i n Figure 16. Figures 1C and 1D schematically show the o i l bank approaching the production well and the subsequent breakthrough o f t h e d r i v e water. Figure 2 schematically i l l u s t r a t e s a twodimensional view o f the surfactant-polymer f l o o d i n g process.

S URFACTANT SLUG

INJECTION

---- - - ---

PRODUCTION

-

THICKENED FRESH WATER

Fig. 2

Schematic diagram o f the surfactant-polymer f l o o d i n g process.

The s u r f a c t a n t slug i s followed by a polymer slug f o r a proper m o b i l i t y c o n t r o l o f the process.

4

B.

CAPILLARY NUMBER AND CONCEPTUAL ASPECTS OF THE PROCESS

Recently, i n an excellent review a r t i c l e , Taber (12) has summarized various emperical dimensionless numbers proposed by several i n v e s t i g a t o r s t o c o r r e l a t e t h e o i l displacement e f f i c i e n c y i n porous media. F i g u r e 3 shows such a c o r r e l a t i o n reported by Foster (13) between t h e c a p i l l a r y number and r e s i d u a l o i l i n porous media.

I10 ~ 1 0 2 0 3 00 4 0 5 0 6 0

l

RESIDUAL OIL, PERCENT PORE VOLUME Fig. 3

Dependence o f r e s i d u a l o i l s a t u r a t i o n on C a p i l l a r y Number (Foster, W.R., J. Pet. Tech., p. 206, Feb. 1973).

The c a p i l l a r y number represents the r a t i o o f viscous t o c a p i l l a r y forces uv/u+ where 11 and v are the v i s c o s i t y and v e l o c i t y of ! k e i i $ ? l i n g f l u i d , u i s the i n t e r f a c i a l tension and 4 i s t h e pore volume). A t the end o f water flooding, the c a p i l l a r y number i s around 10-6 and t h i s number has t o be increased by 3 t o 4 orders o f magnitude f o r t e r t i a r y o i l recovery processes (14). Under p r a c t i c a l r e s e r v o i r conditions, the reduc i o n i n ' n t e r f a c i a l tension from a high value of 20 o r 30 dyneslcm t o 1 0 - i o r 10-4 dynes/cm o f f e r s such a p o s s i b i l i ty. Therefore, the main f u n c t i o n o f t h e s u r f a c t a n t i s t o produce such an u l t r a - l o w i n t e r f a c i a l tension a t the o i l ganglia/surfactant formulation i n t e r f a c e . Figure 4 schematically shows the r o l e o f u l t r a l o w i n t e r f a c i a l tension i n promoting the m o b i l i z a t i o n o f o i l ganglia i n porous media. Subsequently, t h e displaced o i l ganglia must coalesce t o form an o i l bank. For t h i s a very low i n t e r f a c i a l v i s c o s i t y i s d e s i r a b l e (Figure 5). I t i s known t h a t h i g h i n t e r f a c i a l v i s c o s i t y r e s u l t s i n the formatin o f s t a b l e emulsion (15).

5 FOR THE MOVEMENT OF OIL THROUGH NARROW NECK OF PORES, A VERY LOW OIL / WATER INTERFACIAL TENSION IS DESIRABLE z .OOl DYNES/CM

Fig. 4

Schematic diagran of the role of low interfacial tension in the surf actant-pol ymer flooding process.

SURFACTANT SLUG

4

DISPLACED OIL GANGLIA MUST COALESCE TO FORM A CONTINUOUS OIL BANK : FOR THIS A VERY LOW INTERFACIAL VISCOSITY IS DESIRABLE

Fig. 5

Schematic diagran of the role of low interfacial viscosity in the surfactant-polymer flooding process.

Once an o i l bank is formed i n the porous medium, i t has to be propagated through the porous medium without increasing the entrapment of o i l at the t r a i l i n g edge of the oil bank. As shown in Figure 6 , the maintenance of ultralow interfacial tension at the o i l bank/surfactant/ slug interface i s essential for minimizing the entrapment of the oil i n the porous medium whereas the leading edge will coalesce with the o i l gang1 i a.

SURFACTANT " Yd SLUG

COALESCENCE OF OIL GANGLIA WITH OIL BANK CAUSES FURTHER DISPLACEMENT OF OIL Fig. 6

Schematic diagran of the role of coalescence of o i l ganglia i n the surf act ant-pol ymer flooding process.

6 Figure 7 schematically i l l u s t r a t e s the movement o f the o i l bank, surfactant s l u g and the m o b i l i t y c o n t r o l polymer slug i n the porous med ium

.

INTERFACES

t Since the f l o w i s through porous m e d i a , t h e e f f e c t o f dispersion for emulsification should b e minimized a t a l l 3 interfaces. A l s o a v o i d t h e formation of high v i s c o s i t y structures i n the o i l - water - surfactant dispersions i n

SURFACTANT SLUG

Fig. 7

OIL

Schematic i l l u s t r a t i o n o f t h e e f f e c t s o f dispersion and emulsif i c a t i o n between the various slugs during the surfactant-polymer f l o a d i n g process.

Since the f l o w through the porous mediun causes dispersion o f these f l u i d s , emulsions w i l l be formed a t the o i l bank/surfactant slug i n t e r face and a mixed surfactant-polymer zone w i l l occur a t t h e s u r f a c t a n t polymer s o l u t i o n i n t e r f a c e . High v i s c o s i t y - s t r u c t u r e s a t both these i n t e r f a c e s should be avoided i n order t o improve the e f f i c i e n c y o f t h e process. The mass t r a n s f e r o f s u r f a c t a n t t o t h e o i l bank can i n f l u e n c e the magnitude o f i n t e r f a c i a l tension (16). Trushenski (17) has shown t h a t surfactant-polymer i n c o m p a t i b i l i t y leading t o a phase separation o f surfactant and polymer s t r i k i n g l y reduces t h e e f f i c i e n c y o f t h e process.

PROPER CHOICE

Fig. 8

OF SURFACTANT CAN CHANGE@TO@

The r o l e o f w e t t a b i l i t y and contact angle on o i l displacement.

7 Figure 8 schematically i l l u s t r a t e s the r o l e o f w e t t a b i l i t y o f s o l i d surface on the o i l ganglia. The choice o f s u r f a c t a n t can i n f l u e n c e the w e t t a b i l i t y o f t h e rock surface t o o i l and b r i n e (12). Another parameter t h a t we have found (18, 19) t h a t influences the i n t e r f a c i a l tension and i n t e r f a c i a l v i s c o s i t y and o i l recovery i s t h e surface charge a t the o i l - b r i n e as well as rock-brine i n t e r f a c e s . We found t h a t a high surface charge d e n s i t y leads t o a lower i n t e r f a c i a l tension, lower i n t e r f a c i a l v i s c o s i t y and higher o i l recovery (Figure 9).

High Surface Charge Densky -Low Interfacial Tenslon Low Interfacial Vicorlty High Electrkal Repulsion Between Oil Droplets (i Sand

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Fig. 9

Schematic diagran o f the r o l e o f surface charge i n the o i l d i s placement process.

The conceptual processes described i n Figures 3 t o 9 are supported by t h e r e s u l t s o f our studies described i n the following sections.

C. LOW SURFACTANT CONCENTRATION SYSTEMS

Figure 10 shows the i n t e r f a c i a l tension as a f u n c t i o n o f s u r f a c t a n t concentration i n a dodecane/brine system. ' I t i s evident t h a t there are two regions o f u l t r a - l o w i n t e r f a c i a l tension (IFT). A t low surfactant concentrations, the system appears t o be a two-phase system, namely, o i l and b r i n e i n e q u i l i b r i u m w i t h each other, whereas a t high s u r f a c t a n t concentration systems (around 4 t o 8% s u r f a c t a n t concentration), a middle phase microemulsion e x i s t s i n e q u i l i b r i u n w i t h excess o i l and brine. The formation o f middle phase microemulsion and r e l a t e d phenomena w i l l be discussed i n section D.

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9 For low s u r f a c t a n t concentration systems, we have show t h a t t h e u l t r a l o w IFT occurs when s u r f a c t a n t molecules migrate from t h e aqueous phase t o the o i l phase (19-21). Figure 11 shows t h e i n t e r f a c i a l t e n s i o n and t h e p a r t i t i o n c o e f f i c i e n t o f a s u r f a c t a n t i n an octane/brine system. The u l t r a low IFT occurred around a p a r t i t i o n c o e f f i c i e n t o f u n i t y i n t h i s system (19,ZO). However, i t should be emphasized t h a t since t h e p a r t i t i o n c o e f f i c i e n t changes a b r u p t l y i n t h i s region the exact value o f p a r t i t i o n c o e f f i c i e n t can vary s i g n i f i c a n t l y around u l t r a l o w IFT. We bel i e v e t h a t a reasonable conclusion i s t h a t lowering o f i n t e r f a c i a l tension i s observed when m i c e l l e s leave the aqueous phase due t o coacervat i o n process (19-23). I(

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Fig. 11

E f f e c t o f added e l e c t r o l y t e on i n t e r f a c i a l tension and surfact a n t p a r t i t i o n c o e f f i c i e n t o f t h e system O.TXTRS 10-80 + b r i n e + octane.

Since c m e r c i a l petroleum sulfonates i n v o l v e a d i s t r i b u t i o n o f molecular weights and isomeric s t r u c t u r e s we also Investigated t h e i n t e r f a c i a l tension using i s o m e r i c a l l y pure sulfonates. Figure 12 shows the IFT behavior as a f u n c t i o n o f s a l i n i t y , o i l 'chain length and s u r f a c t a n t concentration using petroleum sulfonates (TRS 10-80 o r TRS 10-410 and an It i s evident t h a t both t h e s a l i n l t y i s o m e r i c a l l y pure s u r f a c t a n t UT-1). and o i l chain length e f f e c t s were s i m i l a r f o r both these classes o f sur-

10 PETROLEUM SULFONATES:

ISOMERICALLY PURE ALKYL BENZENE SULFONATES:

Fig. 12

Schematic diagram o f the e f f e c t o f s a l t concentration, o i l chain length and s u r f a c t a n t concentration on t h e i n t e r f a c i a l tension o f pure and impure a1 k y l benzene sulfonates.

factants, namely, t h e r e i s a s p e c i f i c s a l i n i t y and s p e c i f i c o i l chain length where we o b t a i n an u l t r a l o w IFT. However, the e f f e c t o f surfact a n t concentration on IFT was d i f f e r e n t f o r commercial and i s o m e r i c a l l y pure surfactants. For low surfactant concentration systems, we also observed t h a t the u l t r a low IFT appears when the aqueous phase i s a t t h e apparent anc f o r the surfactant remaining i n t h e aqueous phase. These conclusions were i n aggreement w i t h osmotic pressure, l i g h t s c a t t e r i n g and spectroscopic measurements on t h e e q u i l i b r a t e d aqueous phase (22). Figure 13 i s a generalized diagran showing t h e IFT, phase behavior and the two c r i t i c a l e l e c t r o l y t e concentrations f o r both pure and ctmwnerc i a 1 surfactants a t low as w e l l as high s u r f a c t a n t concentrations. By d i r e c t analysis o f surfactant concentrations i n each phase, we found (21) t h a t t h e s a l i n i t y a t which s u r f a c t a n t molecules leave t h e aqueous phase i s lower than the s a l i n i t y at which they enter t h e o i l phase. Thus, we d e f i n e two c r i t i c a l e l e c t r o l y t e concentrations, namely, CEC1, and CEC2, t o represent the e l e c t r o l y t e concentrations a t which t h e surf a c t a n t concentration begins t o decrease i n t h e aqueous phase and begin t o increase i n t h e o i l phase respectively. We f u r t h e r observed t h a t t h e minimun i n t e r f a c i a l tension occurs i n the v i c i n i t y o f t h e f i r s t c r i t i c a l I n between CECl and CEC2, t h e s u r f a c t a n t e l e c t r o l y t e concentration. m a y p r e c i p i t a t e o r may form a coacervate phase below t h e aqueous phase o r i n between the aqueous and the o i l phase depending upon i t s d e n s i t y (21).

11 I n low concentration systems, i t i s possible t h a t an extremely small volume o f middle phase may e x i s t between the o i l and b r i n e phases even though i t may not be v i s i b l e . This suggestion i s i n agreement w i t h observation t h a t the volume o f the middle phase microemulsion increases l i n e a r l y w i t h the surfactant concentration and the s t r a i g h t l i n e passes through the o r i g i n (24). It should be emphasized t h a t the general behavior and i n t e r - r e l a t i o n s h i p shown i n Figure 13 i s v a l i d f o r both commercial and i s o m e r i c a l l y pure surfactants (21).

NaCl Fig.

CONCENTRATION

Generalized d i a g r m o f the e f f e c t o f s a l t concentration on surf a c t a n t p a r t i t i o n i n g , phase behavior and i n t e r f a c i a l tension.

Figure 14 shows the e f f e c t o f o i l chain length on CEC and CEC2 i n Aerosol OT/brine/oil systems. I t i s evident t h a t the EEC! i n creases w i t h o i l chain length u n t i l i t reaches the c r i t i c a l o i l chain length (C11) above which the value o f CECl remains constant. On t h e other hand, CEC2 continues t o increase w i t h the o i l chain length. I n t e r e s t i n g l y , we observed t h a t the u l t r a l o w IFT o n l y occurs f o r o i l chain lengths below the c r i t i c a l o i l chain length (< C11), whereas the i n t e r f a c i a l tension remains high for o i l s above t h e c r i t i c a l o i l chain length (21). We propose t h a t a l l the o i l s below the c r i t i c a l o i l chain length are able t o s o l u b i l i z e i n the m i c e l l e s whereas the o i l s having chain length above the c r i t i c a l o i l chain length are unable t o s o l u b i l i z e i n the m i c e l l a r s o l u t i o n . Thus, i t appears t h a t s o l u b i l i z a t j o n o f o i l w i t h i n the m i c e l l e s i s an important requirement f o r producing u l t r a l o w IFT. From our extensive studies on i n t e r f a c i a l tension and p a r t i t i o n i n g o f surfactant i n r e l a t i o n t o many parameters, we have proposed the f o l l o w i n g 5 necessar y conditions t o achieve u l t r a l o w IFT's.

12

Fig. 14

E f f e c t of o i l chain length on the f i r s t and second c r i t i c a l e l e c t r o l y t e concentrations of Aerosol OT.

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E f f e c t of o i l chain length on the i n t e r f a c i a l tension o f t h e systems 1.0% AOT/brine/oil

.

13 The t o t a l surfactant concentration should be appreciably above the apparent anc i n the aqueous phase. The surfactant should be soluble i n both the aqueous and the hydrocarbon phase. Micelles i n the aqueous phase should be able t o s o l u b i l i z e o i l from the hydrocarbon phase. The aqueous phase s a l i n i t y should be near the f i r s t c r i t i c a l electrol y t e concentration (CECI). There should be a large slope i n the surfactant p a r t i t i o n c o e f f i c i e n t curve i n the region o f the ultralow IFT. (i.e. a steep p a r t i t i o n coe f f i c i e n t curve f o r surfactant).

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A correlation between i n t e r f a c i a l tension and electrophoretic m o b i l i t y f o r crude oil-NaOH solutions.

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Figure 16 shows the correlation of interfacial tension with electrophoretic mobility in crude oil/caustic systems (18,19,25,26). We have observed for several crude o i l s that the u l t r a low IFT occurs in the r e gion where the electrophoretic mobility is maximum. This suggests that the maximun in surface charge density coincides w i t h the m i n i m u m i n i n terfacial tension. T h i s correlation was also observed for the effect of s a l i n i t y and surfactant concentration (19). Figure 17 schematically i l l u s t r a t e s 3 components of the interfacial tension, namely, 1 ) surface concentration of the surfactant, 2) surface charge density, and 3) mutual solubilization of o i l and brine. W e propose that by a d j u s t i n g any of these variables one can influence the magnitude of interfacial tension. Using the conceptual approach shown i n Figure 17, we were able to broaden and lower the magnitude of interfacial tension as well as increase the s a l t tolerance limit of the surfactant formulation;

dyneskm

Fig. 17

A schematic i l l u s t r a t i o n of the factors affecting the magnitude of the interfacial tension.

Figure 18 shows the interfacial tension of a petroleum sulfonate TRS 10-410/n-octane/brine system when gradually the petroleum sulfonate i s replaced w i t h an ethoxylated phosphate e s t e r (Klearfac AA-270). The Klearfac AA-270 containing a phosphate group possesses two ionic oxygen atoms and hence can generate a high surface charge density a t the interface. This presumably i s responsible for lowering the magnitude of IFT and broadening the s a l i n i t y range over which the ultralow IFT occurs for the mixed surfactant systems (27).

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16 D.

HIGH SURFACTANT CONCENTRATION SYSTEMS AND THE OPTIMAL SALINITY

Many s u r f a c t a n t formulations e x h i b i t extreme flow o r s t a t i c b i r e f r i n g e n c e i n a given s a l i n i t y range o r i n a given temperature range. Often these o p t i c a l l y a n i s o t r o p i c formulations e x h i b i t u l t r a l o w IFT w i t h o i l . The m i c r o s t r u c t u r e o f such b i r e f r i n g e n t formulations should be o f i n t e r e s t i n understanding the changes i n molecular associations o c c u r r i n g i n these systems. Figures 19-21 i l l u s t r a t e the m i c r o s t r u c t u r e o f a b i r e f r i n g e n t surfactant formulation c o n s i s t i n g o f 5% TRS 10-410 + 3% isobutanol and 2% NaCl brine.

Fig. 19

Freeze-fracture e l e c t r o n micrograph o f t h e a n i s o t r o p i c system 5% TRS 10-410 + 3% Isobutanol + 2% NaCl ( 8 5 5 0 1x).

The freeze-fracture e l e c t r o n microscopic technique used t o o b t a i n these p i c t u r e s i s believed t o preserve the m i c r o s t r u c t u r e o f the sanples due t o the very r a p i d c o o l i n g r a t e (24). These e l e c t r o n micrographs c l e a r l y i n d i c a t e t h a t the b i r e f r i n g e n t formulations c o n s i s t o f bubbles f i l l e d w i t h ' b r i n e and separated f r a n each other by a t h i n s u r f a c t a n t membrane. Figure 21 c l e a r l y shows the s t r u c t u r e o f t h i s membrane c o n s i s t i n g o f several t h i n layers. The dimension o f each l a y e r i s close t o a surfact a n t b i l a y e r (approximately 70A). Therefore, I t appears t h a t when t h e s a l i n i t y i s increased i n the s u r f a c t a n t formulation, t h e s u r f a c t a n t molecules form the m u l t i l a y e r s t r u c t u r e w h i l e keeping t h e i r p o l a r groups i n contact with b r i n e and form such c e l l s o r f o m l i k e s t a b l e s t r u c t u r e . We have c a l l e d these s t r u c t u r e s b i r e f r i n g e n t c e l l u l a r f l u i d s (24).

17

Fig. 20

Fig. 21

Freeze-fracture electron micrograph o f the above system at 18,OOOX.

Freeze-fracture electron micrograph of the above system at 30, OOOX

.

18 Figure 22 shows the s i m i l a r i t y between coacervation o f a m i c e l l a r s o l u t i o n i n the absence o f o i l and the formation o f a middle phase microemulsion i n t h e presence o f o i l . The lower p a r t o f F i g u r e 22 shows t h e t r a n s i t i o n o f a b i r e f r i n g e n t s u r f a c t a n t formulation t o an i s o t r o p i c coacervate phase upon a d d i t i o n o f s a l t . (x, the other hand, t h e same formulation i n the presence o f an equal volume o f dodecane shows the formation o f lower phase, middle phase and upper phase microemulsions. We propose t h a t the middle phase microemulsion i s s i m i l a r t o t h e coacervated phase containing some s o l u b i l i z e d o i l . Additional studies i n support o f these models have been reported elsewhere (21, 23, 24).

Fig. 22

A comparison o f coacervation i n aqueous s o l u t i o n with middle phase format i o n i n s u r f act a n t / o i 1/ b r i ne/al coho1 systems.

19 Figure 23 schematically shows the mechanism o f formation o f middle phase microemulsions as s a l i n i t y i s increased.

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A schematic i l l u s t r a t i o n o f t h e l + m + u t r a n s i t i o n f o r t h e TRS 10-410/Isobutano1/0il /Brine System.

As one increases the s a l i n i t y , t h e anc decreases, the aggregation number o f the m i c e l l e s increases and the s o l u b i l i z a t i o n o f o i l w i t h i n m i c e l l e s increases. The compression o f the e l e c t r i c a l double l a y e r around m i c e l l e s w i l l occur, hence reducing the r e p u l s i v e forces between the m i c e l l e s . Thus t h e reduction i n the r e p u l s i v e forces and increase i n the a t t r a c t i v e forces between t h e m i c e l l e s w i l l b r i n g t h e m i c e l l e s c l o s e r and u l t i m a t e l y lead t o a separation o f a m i c e l l e r i c h phase forming the middle phase microemulsion. Upon f u r t h e r increase i n s a l i n i t y , the solub i l i z a t i o n o f o i l i n t h i s middle phase increases whereas t h a t o f b r i n e decreases. The magnitude o f i n t e r f a c i a l tension o f t h e middle phase w i t h o i l o r b r i n e depends upon the extent o f s o l u b i l i z a t i o n o f o i l and b r i n e i n the middle phase. I n general, t h e higher t h e s o l u b i l i z a t i o n o f oi.1 o r b r i n e i n the middle phase microemulsion, t h e lower i s t h e i n t e r f a c i a l tension w i t h respect t o these excess phases (28). The s a l i n i t y a t which equal volumes o f o i l and b r i n e are s o l u b i l i z e d i n the middle phase microemulsion i s r e f e r r e d t o as optimal s a l i n i t y f o r the s u r f a c t a n t - o i l - b r i n e systems under given physical chemical conditions (29, 30).

Figure 24 shows the f r e e z e - f r a c t u r e e l e c t r o n micrograph o f a middle phase microemulsion formed i n the system e x t e n s i v e l y studied by Reed and Healy (28-30). It c l e a r l y shows t h e d i s c r e t e spherical s t r u c t u r e s embedded i n a continuous aqueous phase consistent w i t h the mechanism proposed i n Figure 23. It should be pointed out t h a t other i q v e s t i g a t o r s (40-47) have proposed the p o s s i b i l i t y o f bicontinuous s t r u c t u r e o r t h e coexistance o f o i l external and water external microemulsions i n the middle phase. I n very high s u r f a c t a n t concentration systems, (15-20%) the existence o f anamalous s t r u c t u r e which are n e i t h e r conventional water external o r o i l ext e r n a l microemulsions have been proposed t o a.ccount f o r some unusual prop e r t i e s o f these systems (43-46). Figure 25 shows t h a t the t r a n s i t i o n l + m - c u i s not o n l y achieved by increasing the s a l i n i t y but i s also possible by changing any o f t h e other 8 variables.

7

20

Fig. 24

Freeze-fracture electron micrograph of the middle phase o f the Exxon system at the optimal salinity.

Oil

U

m

m

m

Brine

-

D

Parameter Increasing

The transition I

m --c u occurs by:

1. Increasing Salinity

2. 3. 4. 5. 6. 7. 8.

Fig. 25

Decreasing oil chain length Increasing alcohol concentration (C,, C,, C, ) Decreasing temperature Increasing total surfactant concentration Increasing brine/oil ratio Increasing surfactant solution/oil ratio Increasing molecular weight of surfactanf

Schematic illustration of the factors influencing the l + m + u transit ion in surf act ant /oi 1 /bri ne/al coho1 systems.

21

Thus, by choice of a suitable parameter, one can obtain the transition i n the structure of these microemulsions. A t optimal s a l i n i t y , the partition coefficient of surfactant i n the excess o i l and brine phases i s found to be near unity and the interfacial tension between the excess oil and excess brine is also m i n i m u n (19).

The importance of the optimal s a l i n i t y concept for enhanced oil recovery i s shown in the data i l l u s t r a t e d in Figure 26.

SURFACTANT SLUG =O.OS P.V. FLOODING RATEm2.3 ft/day DOW PUSHER 700:

SALINITY, NaCl w t 70

Fig. 26

Effect of s a l i n i t y on the capillary number and t e r t i a r y oil recovery i n sand packs.

I t i s evident that the o i l recovery is maximum at optimal s a l i n i t y f o r the systems reported here. An excellent correlation between the capillary number and oil recovery i s also evident from Figure 26 (48). In view of this observation, the surfactant formulation for a practical application should be designed such that the reservoir s a l i n i t y becomes the optimal s a l i n i t y under the given reservoir conditions. Figure 27 shows the effect of o i l chain length on optimal s a l i n i t y of the TRS 10-410 + isobutanol systems (49) and the corresponding interfacial tension at the optimal s a l i n i t y for dach o i l chain length. I t was observed that as the o i l chain length increases, the optimal s a l i n i t y i n creases and the volume of the middle phase decreases. The range over which the middle phase microemulsion exists also increases as the o i l

22

FFig. i g . 27 27

E f f e c t o f o i l chain length on t h e optimal s a l i n i t y and i n t e r f a c i a l tension a t t h e optimal s a l i n i t y .

chain length increases. It should be pointed out t h a t from extensive studies on mixed a1 kanes, the concept o f -Equivalent A1 kane Carbon Number (EACN) has been proposed t o c o r r e l a t e the i n t e r f a c i a l tension o f pure alkanes w i t h those o f the mixtures (50). Many l i g h t crude o i l s have been simulated by the mixtures o f pure hydrocarbons (51). Most l i g h t o i l s o r t h e EACN f o r most l i g h t crude o i l s were found t o be between C7 and c11. Figure 28 shows t h e c o r r e l a t i o n o f optimal s a l i n i t y i n t h e presence o f various alcohols w i t h t h e i r s o l u b i l i t y i n brine. F i g u r e 28 sumnarizes the data obtained by three research groups (49,52, 53). It i s i n t e r e s t i n g t h a t the optimal s a l i n i t y o f a given o i l and surf a c t a n t formulation l i e s near t h e i n t e r s e c t i o n o f the b r i n e s o l u b i l i t y . This c o r r e l a t i o n suggests t h a t i f one determines t h e optimal s a l i n i t y i n the presence o f 2 o r 3 alcohols, one can p r e d i c t the optimal s a l i n i t y i n t h e presence o f other alcohols from t h e i r b r i n e s o l u b i l i t y data. This i s a very useful c o r r e l a t i o n and eliminates t h e t i m e consuming and laborious procedure o f o b t a i n i n g t h e optimal s a l i n i t y i n t h e presence o f each alcohol.

E. TRANSIENT PROCESSES There are several t r a n s i e n t processes, such as the formation and coalescence o f drops as w e l l as t h e i r f l o w through porous media, t h a t a r e l i k e l y t o occur i n the surfactant-polymer f l o o d i n g process. Figure 29 shows the coalescence o r phase separation t i m e o f handshaken and sonicated macroemulsions as a f u n c t i o n o f s a l i n i t y .

Surfoclont

5 0 % TRS 10-410

40%

Alcohol

30%

0 7%

Brine

Variable

Vorioble

NoCl

01I

Dodecone

Wyomlng

Crude

WOR

I0

I0

Ref

Shah ond Hsleh, SPE 6594

Salter. SPE

BRINE SALINITY

(wt % NoCl 1

F i g . 28

NoCl

BRINE

Amoco

A A - Sulfonate

1.5 %

Xylene

Sulfonate

0. 5 % Variable

Oil

NaCl

90/10 lsopor

M/HAN

I .o

6843

SALINITY

(wt%

Puerto and Gale,

doc1 I

BRINE

SALINITY

A c o r r e l a t i o n o f optimal s a l i n i t y i n t h e presence of various alcohols w i t h t h e i r s o l u b i l i t y i n b r i n e .

SPE 5 8 1 4

( u t % No CI I

N W

24

16C

12c

8C E w

E l-

4c SONICATEO

C

0

2

4

6

SODIUM CHLORIDE CONCENTRATION, (b1T.X)

F i g . 29

E f f e c t o f s a l i n i t y on t h e phase separation o r coalescence r a t e o f sonicated and hand-shaken emulsions.

8

25

I t i s obvious that minimal phase separation time or the f a s t e s t coalescence r a t e occurs at the optimal s a l i n i t y (54). The rapid coalescence could contribute significantly to the formation of an oil bank from the mobilized oil ganglia. This also suggest that at the optimal s a l i n i t y the interfacial viscosity must be very low to promote the rapid coalescence. Figure 30 shows the pressure drop across a porous medium hhen emulsions prepared at various s a l i n i t i e s flow through i t . I t is evident that the minimum pressure drop occurs at and around the optimal s a l i n i t y of the surfactant formulation. T h i s also suggests that the interfacial tension is an important factor influencing the pressure drop across porous media ( 5 4 ) .

L

t

SONICATED EMULSION CONTAINING EQUAL VOLUME OF DODECANE AND AQUEOUS PHASE : TRS 10 -410 + IBA (5:3W/W) + NaCl +WATER

/

EMULSION FLOW RATE QE (rnl/rnin)

Fig. 30

Effect of s a l i n i t y on the pressure drop-flow r a t e curves of soni cated emu1 sions.

26

Figure 31 shows a very interesting and important correlation between the coalescence r a t e in enulsions and the apparent viscosity i n the flow through porous media. The minimun apparent viscosity for the flow of emulsions in porous media coincides with minimum phase separation time a t the optimal s a l i n i t y .

SYSTEM: SONICATED EMULSION CONTAINING TRS 10-410

30

1

0 1 0

t

IBA(5:3 W/W)

t

WATER

+ NaCl (x%) AND EQUAL VOLUME OF DODECANE

I

I

2

I

I

4

I

I

I

6

NaCl CONCENTRATiON (WT. %)

F i g . 31

A correlation between the apparent viscosity and coalescence r a t e of sonicated emulsions.

This correlation between the phenomena occurring in porous media and outside the porous medium allows us to use coalescence measurements as a screening criterion for many surfactant formulations for their possible behavior i n porous media. I t i s l i k e l y that a rapidly coalescing m u l sion will give a lower apparent viscosity for the flow i n porous media (54).

27

Figure 32 sumnarizes a l l the phenomena occurring a t t h e optimal s a l i n i t y i n r e l a t i o n t o enhanced o i l recovery by surfactant-polymer flooding.

yp

Oi I Recovery Efficiency

I

Apporent viscosity (or AP) of emulsions in porous media Coolescence or phase-seporotion time of emulsions

v

*VW

Surfoctont loss in Porous Media

vo

x

v

Solubilirotion of Oil and Brine in m+ microemulsions

w

lnterfociol tension

Ymo

-

OPTIMAL SALINITY

I/ Fig. 32

SALl NlTY A sumnary o f various phenomena occurring a t t h e optimal s a l i n i t y i n r e l a t i o n t o enhanced o i l recovery by surfactant-polymer flooding

.

It i s evident t h a t the maximum i n o i l recovery e f f i c i e n c y c o r r e l a t e s w e l l with t r a n s i e n t and equilibrium p r o p e r t i e s o f s u r f a c t a n t - o i l - b r i n e systems. I n our p r e l i m i n a r y studies, we have found t h a t t h e s u r f a c t a n t l o s s i n porous media i s also minimum a t t h e optimal s a l i h , i t y presumably due t o r e d u c t i o n i n the entrapment process f o r the surfactant phase. Therefore, the maximum i n o i l recovery at optimal s a l i n i t y might be a combined e f f e c t o f a l l these processes t a k i n g place a t the optimal s a l i n i t y .

Since optimal s a l i n i t y leads t o favorable conditions f o r optimal o i l recovery, one would l i k e t o design approaches t o a l t e r the optimal s a l i Figure 33 shows the n i t y o f a given s u r f a c t a n t formulation (55-57). optimal s a l i n i t y of a mixed s u r f a c t a n t formulation c o n s i s t i n g of a petroleum sutfonate and ethoxylated s u l f o n a t e (EOR-200).

28 I

1

I

SURFACTANT FORMULATION: TRS 10-410 t EOR-200

5.00/0

t

ISOBUTANOL

3.0%

4

2 I

I

TRSIO-410 €OR-200 I

Fig. 33.

5 C '0

4

1

1

I

2 3 4 3 2 I SURFACTANT CONCENTRATION wt.%

Increase i n the optimal s a l i n i t y o f surfactant formulation by a d d i t i o n o f EOR-200.

As one replaces petroleum sulfonates w i t h the ethoxylated s u l f o n a t e t h e optimal s a l i n i t y increases and can reach as h i g h as 32% NaCl brine. I n t e r e s t i n g l y , these formulations when e q u i l i b r a t e d with o i l produced middle phase microemulsions having very low i n t e r f a c i a l tension. Thus, the mixed s u r f a c t a n t formulations containing p e t r o l e m sulfonates and ethoxylated sulfonates o r alcohol are promising candidates f o r h i g h s a l i n i t y formulations ( 5 5 , 5 6 ) . Figure 34 shows t h e shape o f an o i l drop upon contacting a surfact a n t formulation c o n s i s t i n g o f 0.05% TRS 10-80 i n 1% NaCl. It i s e v i dent t h a t as s u r f a c t a n t molecules migrate from t h e aqueous phase t o the i n t e r f a c e and subsequently t o the o i l phase the i n t e r f a c i a l tension decreases and the spherical drop g r a d u a l l y f l a t t e n s out. This f l a t t e n i n g

29

Fig. 34.

An i l l u s t r a t i o n o f t h e drop f l a t t e n i n g phenomenon f o r a drop of octane i n an e q u i l i b r a t e d s o l u t r i o n o f 0.05% TRS 10-80 I n 1% NaCl

.

time r e f l e c t s the r a t e a t which molecules accumulate a t the o i l - b r i n e i n t e r f a c e . As shown i n Table 1, there i s a good c o r r e l a t i o n between the f l a t t e n i n g time, IFT and the o i l recovery. The reduction i n t h e f l a t t e n i n g time leads t o favorable o i l recovery efficiency (16,48).

30 TABLE 1

IFT, Flattening Time,and O i l Recovery Efficiency of 0. 052TRS 10-80 in I%NaCl vs. n-octane at 25OC

SYSTEM

IFT i m)

FLATTENING TIME*

1. II.

Ii1. IV.

Fresh Oilll% NaCl ~50.8* * FreshOillEquilibrated Surfactant 0.731 Solution Fresh OillFresh 0.627 Surfactant Solution EquilibratedOill% a 121 NaCl

V.

VI.

OILRECOVERY+

(seconds)

(m

(%OIP)

00

61-63

6600

44-52

480

15-11

900

83

w

EquilibratedOil/ Equilibrated Surfactant Solution

0.0267

240

EquilibratedOill Fresh Surfactant Solution

aOO209

15

*Flattening time i s defined as the time required for the n-octane drop to gradually flatten out

* *OctanelH@, 20'

C, IFT = 50.8 mNlm, "Interfacial Phenomenb', Davies and Rideal, Chapter 1, p. 17 Table I, Academic Press, N.Y. 1963.

+ San@ckdimension9 1. W'dia

x 7" long: Permeability= 3 darcy: flow rate:

2.3 f t /day.

I n general, a s u r f a c t a n t formulation f o r enhanced o i l recovery i n cludes a short chain alcohol. The p o s s i b l e e f f e c t o f alcohol can be t h e change i n v i s c o s i t y , lowering o f the i n t e r f a c i a l tension, r e d u c t i o n i n i n t e r f a c i a l v i s c o s i t y o r change i n s u r f a c t a n t p a r t i t i o n i n g and modifying the s o l u b i l i t y o f s u r f a c t a n t i n o i l o r b r i n e phase. I n t e r e s t i n g l y , we have observed t h a t the presence o f alcohol has a much more s t r i k i n g effect on the f l a t t e n i n g t i m e o f an o i l drop i n the presence o f a surfact a n t formulation. As shown i n Table 2 i t compares t h e many i n t e r f a c i a l properties, f l a t t e n i n g t i m e and o i l recovery e f f i c i e n c y i n the presence and absence o f alcohol (16). It i s evident t h a t the f l a t t e n i n g time decreases s t r i k i n g l y i n t h e presence o f alcohol suggesting t h a t t h e alcohol promotes the mass t r a n s f e r t o the i n t e r f a c e and a r a p i d r e d u c t i o n i n t h e magnitude o f the i n t e r f a c i a l tension. There are also time dependent changes i n the surface p r o p e r t i e s of a surfactant formulation. This include the chemical degradation (58,59), o r changes i n the aggregation process o f m i c e l l e s (60). Several i n v e s t i gators have show t h a t the i n t e r f a c i a l tension changes w i t h t i m e (61). We have also shown t h a t using several physical techniques t h a t molecular association also changes w i t h t i m e leading t o t h e aging e f f e c t s o f the surfactant formulation (58). The aging processes may occur over a period o f months o r years.

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32 F. SURFACTANT-POLYMER INCOMPATIBILITY Trushenski (17) has shown t h a t surfactant-polymer i n c o m p a t i b i l i t y can lead t o a considerable r e d u c t i o n i n the e f f i c i e n c y o f the process. The surfactant-polymer i n c o m p a t i b i l i t y manifests i t s e l f as a phase separ a t i o n and a l t e r a t i o n o f the v i s c o s i t y o f t h e separated phases. The entrapment o f the h i g h v i s c o s i t y phase w i l l e f f e c t i v e l y remove t h a t component from the f l o o d i n g process. The mixing o f the surfactant and polymer i n the porous medium occurs due t o both dispersion e f f e c t s as w e l l as excluded volume e f f e c t s f o r the f l o w o f polymer molecules i n porous media. Figure 35 shows the e f f e c t o f mixing surfactant and a polymer solut i o n i n the absence o f o i l .

Fig. 35.

E f f e c t o f a d d i t i o n o f polymer on t h e phase behavior o f aqueous s u r f actant solutions.

I t i s evident t h a t there are tho regions o f phase separation, one a t low s a l i n i t y and the other a t h i g h s a l i n i t y separated by a metastable c o l l o i d a l dispersion. We r e f e r t o the separation a t the lower s a l i n i t y as r e gion 1 and those a t h i g h s a l i n i t y as region 2. The separation o f a surf a c t a n t - r i c h phase i n r e g i o n 2 i s s i m i l a r t o t h a t i n coacervation process, h e r e a s t h e separation o f m i c e l l e s i n region 1 i s induced by the presence o f p o lymer molecules. The s u r f act ant -polymer incompat ib i 1it y shows up s t r i k i n g l y i n t h e formation o f region 1 (62).

The a d d i t i o n o f polymer t o an oillbrinelsurfactantlalcohol system shows t h a t the formation o f middle phase microemulsion i s promoted by the presence o f polymer (Figure 36). However, the t r a n s i t i o n middle phase t o upper phase microemulsion i s not influenced a t a l l by t h e presence o f polymer. We have f u r t h e r s h o w (62,63) t h a t t h e optimal s a l i n i t y i s n o t s i g n i f i c a n t l y influenced by the presence o f polymer i n t h e o i l l b r i n e l s u r f a c t a n t l a l c o h o l system.

33

1.0

-

0.8 -

0.6

-

0.4

-

0.2

0.0

5%

Polymer Concentration

W/V TRS 10-410

3% w/v IBA O i l : n-dodecane (MOR=l .O)

2500 ppm

-

1500 ppm

1.0 0.8

0.6 0.4 0.2 0.0

I

Fig. 36.

I

I

I

1

I

I

Effect of polymer concentration on the s a l i n i t y range f o r formation of middle-phase microemulsion.

Figure 37 shows the schematic explanation of the surfactant polymer incompati b i 1 it y and concomittant phase separation.

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36 surfactant slug i n porous media i s l a r g e l y determined by the s a l i n i t y o f t h e polymer s o l u t i o n (65). For b e t t e r m o b i l i t y c o n t r o l and minimal surfactant loss a two-slug design o f a s u r f a c t a n t formulation was employed (23). In t h i s design, the f i r s t surfactant s l u q has an optimal s a l i n i t y close t o the connate water s a l i n i t y and the second s u r f a c t a n t slug has a much lower optimal s a l i n i t y . The polymer s o l u t i o n s a l i n i t y i s made equal t o the optimal s a l i n i t y o f the second s u r f a c t a n t slug. With t h i s design, high o i l recovery i n berea cores can be obtained even i n the presence of h i g h s a l i n i t y (6% NaCl + 1% calcium c h l o r i d e ) connate water. The optimal s a l i n i t y concept i s f u r t h e r extended t o include t h e e f f e c t o f m o b i l i t y c o n t r o l and s u r f a c t a n t dispersion and entrappment i n porous media (65). The proposed s a l i n i t y shock design o f m o b i l i t y polymer s o l u t i o n s employs two slugs o f polymer s o l u t i o n s i n which t h e f i r s t polymer slug i s a t the optimal s a l i n i t y o f the preceeding s u r f a c t a n t f o r mulation and the second polymer slug i s at a much lower s a l i n i t y . INJECTION

PRODUCTION

c n

21

0

FLOW

A

c t

OPTIMAL SALINITY

Fig. 39.

SALINITY, %NaCI

Schematic representation o f the g r a d e d - s a l i n i t y design o f polymer b u f f e r s o l u t i o n f o r enhanced o i l recovery.

With t h i s unique design h i g h o i l recovery and h i g h s u r f a c t a n t recovery can be obtained f o r soluble o i l f l o o d i n g i n sandpacks, while t h e polymer consumption can be g r e a t l y reduced. Figure 40 schematically shows our r e s u l t s obtained using t h e s a l i n i ty shock design. The optimal s a l i n i t y f o r t h e s u r f a c t a n t f o r m u l a t i o n used was 2.1% NaCl and t h e r e s e r v o i r b r i n e was 3% NaCl p l u s 1% calcium c h l o r i d e . By the use o f two polymer slugs we were able t o o b t a i n i n berea cores 88% t e r t i a r y o i l recovery and 48% s u r f a c t a n t recovery. For aqueous micellar-polymer f l o o d i n g w i t h crude o i l i n Berea cores, i t has been shown (66-69) t h a t a c o n t r a s t s a l i n i t y design o f t h e p r e f l u s h micellar-polymer f l o o d i n g process may produce a b e t t e r o i l recovery than t h a t obtained from a constant s a l i n i t y process. In t h e c o n t r a s t s a l i n i t y design, the s a l i n i t y o f the p r e f l u s h water i s made higher while t h e s a l i n i t y o f the polyner s o l u t i o n i s made lower than the optimal s a l i n i t y o f the s u r f a c t a n t formulation. The r a t i o n a l e o f t h i s design i s t h a t an opt i m a l s a l i n i t y p r o f i l e can be established i n t h e v i c i n i t y o f the surfact a n t slug upon mixing o f t h e i n j e c t e d f l u i d s i n t h e porous medium.

37

1

CHASE WATER

~

~

~

a

~

L

u

G

.prrRI

'IiASE

POLYMER SLUG 0.05% NaCl

42 %

88 x

Fig. 40.

25 %

48 x

The e f f e c t o f s a l i n i t y shock o f polymer buffer s o l u t i o n an o i l displacement e f f i c i e n c y and surfactant loss.

I t i s hoped t h a t the experimental r e s u l t s presented i n t h i s paper c o n t r i b u t e i n a small way t o increasing our understanding of phenomena occurring i n porous media. It should be enphasized t h a t r e s u l t s we have obtained using laboratory scale experiments are n e i t h e r conducted nor intended t o be extrapolated t o the o i l f i e l d processes. It i s recognized t h a t the processes occurlng i n petroleun r e s e r v o i r s are f a r more complex than those t h a t we can design and c o n t r o l using a laboratory setup.

ACKNOWLEDGEMENTS The author wishes t o express h i s sincere thanks and appreciation t o the National Science Foundation RANN, ERDA and t h e Department of Energy (Grant No: DE-AC1979BC10075) and the consortium o f the f o l l o w i n g Indust r i a l Associates f o r t h e i r generous support o f t h e U n i v e r s i t y o f F l o r i d a Enhanced O i l Recovery Research Program during the past seven years: 1) A l b e r t a Research Council, Canada, 2) Pmerican Cyananid Co., 3 ) Ammo Production Co., 4) A t l a n t i c - R i c h f i e l d Co., 5 ) BASF-Wyandotte Co., 6 ) B r i t i s h Petroleum Co., England, 7) Calgon Corp., 8) C i t i e s Service O i l Co., 9) Continental O i l Co., 10) E t h y l Corp., 11) Exxon Production Research Co., 12) Getty O i l Co., 13) Gulf Research and Development Co., 14) Marathon O i l Co., 15) Mobil Research and Development Co., 16) Nalco Chemical Co., 17) P h i l l i p s Petroleum Co., 18) Shell Development Co., 19) Standard O i l o f Ohio Co., 20) Stepan Chemical Co., 21) Sun O i l Chemical Co. 22) Texaco, Inc., 23) Union Carbide Corp., 24) Union O i l Co., 25) Westvaco, Inc., 26) Witco Chemical Co., and the U n i v e r s i t y o f Florida. He also wishes t o convey h i s sincere thanks t o h i s Colleagues i n Chemical Engineering, Petroleum Engineering and I n s t i t u t e f o r Energy Studies o f Stanf o r d U n i v e r s i t y f o r t h e i r c o l l a b o r a t i o n during h i s s t a y a t Stanford University.

-

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40

38.

Chou, S. I.and Shah, D.O., ( 1981 )

J. C o l l o i d I n t e r f a c e Sci.,

39.

Chou, S. I. and Shah, D.O., (1981).

J. C o l l o i d I n t e r f a c e Sci

40.

Scriven, L.E.,

41.

Scriven, L.E., i n "Mice1 1i z a t i o n , Sol u b i l i z a t i o n and Microemulsions" ed. K.L. M i t t a l , Vol. 11, pp. 877, Plenum Press, N.Y. (1977).

42.

Ranachandran, C., 1561 (1980).

43.

Hwan, R., M i l l e r , C.A. 68, 221 (1979).

44.

Shinoda, K. J. C o l l o i d I n t e r f a c e Sci.,

45.

Shinoda, K. and Saito, H.,

46.

Friberg, S., Lapczynska, I. and Gilberg, G., Sci., 56, 19 (1976).

47.

M i l l e r , C.A., Hwan,.R., Benton, W.J. and Fort, T. Jr., J. C o l l o i d I n t e r f a c e Sci , 61 (3), 554 ( 1977).

48.

Chiang, M.Y.,

49.

"The E f f e c t o f Chain Length o f O i l and Hsieh, W.C. and Shah, D.O., Alcohol as w e l l as Surfactant t o Alcohol R a t i o on t h e S o l u b i l i z a tion, Phase Behavior and I n t e r f a c i a l Tension o f Oil/Brine/Surfactant/Alcohol Systems",SPE 6594, presented a t t h e 1977 SPE-AIME I n t l . Symposiun on O i l f i e l d and Geothermal Chemistry, LaJolla, CA, June 27-28, 1977.

50.

Morgan, J.C., Schechter, R.S. and Wade, W.H., i n "Improved O i l Recovery by Surfactant and Polymer Flooding", D.O. Shah and R.S. Schechter, eds., Acad. Press, Inc., N.Y. (1977).

51.

Cash, R.L., Cayias, J.L., Fournier, G., Jacobson, J.K., Schares, T., Schechter, R.S. and Wade, W.H., "Modeling Crude O i l s f o r Low I n t g r f a c i a l Tension", SPE 5813, presented a t t h e SPE Symposium on I m proved O i l Recovery, Tulsa, OK, March 22-24, 1979.

52.

Satter, S.J., "The I n f l u e n c e o f Type and Amount o f Alcohol on Surfact a n t - O i l - B r i n e Phase Behavior and Properties," SPE 6843, presented a t the 52nd Annual F a l l Conference and E x h i b i t i o n o f SPE-AIME, Denver Co., Oct. 9-12, 1977.

53.

"Estimation o f O p t i m a l S a l i n i t y and SolPuerto, M.C. and Gale, W.W., u b i l i z a t i o n Parameters f o r A l k y l Orthoxylene Sulfonate Mixtures", SPE 5814, presented a t the SPE Improved O i l Recovery Symposium, Tulsa, OK March 27-24, 1976.

54.

Vijayan, S., Ramachandran, C., Doshi, H. and D.O. Shah, i n "Surface Phenomena i n Enhanced O i l Recovery", D.O. Shah ed., pp. 327-376, Plenum Publishing Co., N.Y. ( i n press).

.

Nature,

-

263,

80(1), 49

., 80(2),

311

123 (1976).

Vijayan, S. and Shah, D.O., and Fort, T.

J. Phys. Chem.,

,

84,

Jr., J. C o l l o i d I n t e r f a c e Sci.,

24, 4

(1967).

J. C o l l o i d I n t e r f a c e Sci.,

g,70

(1968).

J. C o l l o i d I n t e r f a c e

.

Ph.D.

Dissertation, l k r i v e r s i t y o f F i o r i d a (1978).

41

650,451

55.

Bansal, V.K. (1978).

and Shah, D.O.,

J. C o l l o i d I n t e r f a c e Sci.,

56.

Bansal, V.K.

and Shah, D.O.,

SPE J.,

57.

Bansal, V.K. (1978).

and Shah, D.O.,

J. h. O i l Chemists SOC.,

58.

Vijayan, S., SOC.,

Ramachandran, C., (1981).

59.

Vijayan, S., SOC.,

Ramachandran, C. and Shah, D.O., (1981).

60.

Vijayan, S., Ramachandran, C. and Doshi, H., " U n i v e r s i t y of F l o r i d a Research on Chemical O i l Recovery Systems Semi-Annual Report", pp. Bl l -857, June, 1978.

61.

Cash, R.L., Cayias, J.L., Hayes, M., M c A l l i s t e r , D.J. %hares, J. Pet. Tech., 985 (Sept. 1976). Wade, W.H.,

62.

i n " U n i v e r s i t y o f F l o r i d a Research on Surfactant-Polymer Desai, N.N.; O i l Recovery Systems-Annual Report", pp. 127-149, Dec. 1979.

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Desai, N.N., i n " U n i v e r s i t y o f F l o r i d a Research on Surfactant-Polymer O i l Recovery Systems-Annual Report", pp. 135-1-48, Dec. 1980.

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Hesselink, F. Th. and Faber, M.J., i n "Surface Phenomena i n Enhanced O i l Recovery," D.O. Shah, ed., pp. 861-869, Plenum Publishing Co., N.Y. ( i n press).

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Chou, S . I . and Shah, D.O., covery", D.O. Shah, ed., ( i n press)

66.

Paul, G.W.

67.

Gupta, S.P.

68.

Nelson, R.C., "The S a l i n i t y Requirement Diagram-A Useful Tool i n Chemical Flooding Research Development1', SPE 8824, presented a t t h e SPE Improved O i l Recovery Symposium, Tulsa, OK, A p r i l 20-23, 1980.

69.

Hirasaki, G.J., Van Dmselaar, H.R. and Nelson, R.C., "Evaluation o f . t h e S a l i n i t y Gradient Concept i n Surfactant Flooding", SPE 8825, presented a t t h e SPE Improved O i l Recovery Symposium, Tulsa, OK, A p r i l 20-23, 1980.

167 (June, 1978).

and Shah, D.O.,

580,566

580,746

and Froning, H.R.,

55 (3), 367

J. h . O i l Chemists J. An. O i l Chemists

T. and

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and Trushenski, S.P..

SPE J.,

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2, 116

(1973).

(1979)i

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This Page Intentionally Left Blank

44

The c h a r a c t e r i s t i c d a t a p e r t a i n i n g t o a s p e c i f i c g r o u p of res e r v o i r s must be e v a l u a t e d i n o r d e r t o p r o v i d e a r e p r e s e n t a t i v e s u r v e y o f t h e boundary c o n d i t i o n s r e q u i r e d f o r b o t h t h e r a p i d t e s t methods and t h e p r e l i m i n a r y f l o o d i n g e x p e r i m e n t s . C o n c l u s i o n s w i t h t h e most g e n e r a l a p p l i c a b i l i t y : S i n c e t h e r e s h o u l d be n o r e s t r i c t i o n t o one o i l r e s e r v o i r o n l y , t h e r e s u l t s s h o u l d be of t h e most g e n e r a l p o s s i b l e v a l i d i t y , and s u r f a c t a n t s o l u t i o n s w i t h a b r o a d r a n g e of a p p l i c a t i o n s h o u l d be s o u g h t . Hence, maximal demands s h o u l d be imposed on t h e f l o o d i n g media, i n o r d e r t o e n s u r e t e s t r e s u l t s which a r e a p p l i c a b l e t o a s many o i l r e s e r v o i r s a s p o s s i b l e . TEST PROGRAM/STANDARDIZATION Reproducible t e s t c o n d i t i o n s a r e always r e q u i r e d f o r i n v e s t i g a t i n g s u r f a c t a n t s , i n o r d e r t h a t v a r i o u s p r o d u c t s be a p p r a i s e d and compared. Such c o n d i t i o n s c a n be f u l f i l l e d o n l y by model s y s t e m s , s i n c e t h e p r o p e r t i e s of r e a l s y s t e m s ( r e s e r v o i r w a t e r , c r u d e o i l , reservoir rock) are usually subject t o variations. Hence a t e s t program r e q u i r e s t h e d e s i g n i n g of model s y s t e m s , i n which a s many p a r a m e t e r s of r e a l s y s t e m s a s p o s s i b l e a r e c o n s i d e red. S i n c e s u r f a c t a n t s a r e generally d i s s o l v e d i n w a t e r , t h e t o t a l s a l i n i t y and t h e c o m p o s i t i o n of r e s e r v o i r b r i n e a r e of u t m o s t i m p o r t a n c e f o r t h e s e l e c t i o n of s u i t a b l e s u r f a c t a n t s . Based on s e v e r a l hundred c h e m i c a l a n a l y s e s o f . w a t e r s a m p l e s from German o i l r e s e r v o i r s , a c l a s s i f i c a t i o n i n t o t h r e e b r i n e c a t e g o ries was p o s s i b l e : 1 t y p e AM ( l o w s a l i n i t y ) TDS < l o g.11 t y p e BM ( i n t e r m e d i a t e s a l i n i t y ) 1 0 .g-l-’C TDS (165 g.1t y p e CM ( h i g h l y s a l i n e ) TDS > 1 6 5 g.1-1

-

Observed s i g n i f i c a n t c h a r a c t e r i s t i c s of h i g h l y s a l i n e r e s e r v o i r brines are that many s a l t s o c c u r i n t h e d i s s o l v e d s t a t e a t c o n c e n t r a t i o n s exceeding t h e i r usual s o l u b i l i t y products 2+ a l l w a t e r s a m p l e s c o n t a i n heavy m e t a l i o n s , s u c h a s Fe t h e pH-values of b r i n e s BM and CM l i e i n a r e l a t i v e l y a c i d i c range (3,0-6,5) a l l b r i n e s show c o m p a r a t i v e l y h i g h s u l f a t e c o n t e n t s a l l b r i n e s c o n t a i n large q u a n t i t i e s of Ca2+ and Mg2+ i o n s and lower c o n c e n t r a t i o n s of Sr2+ and Ba2+.

-

T r a c e e l e m e n t s 0 1 0 mg.1-l) were n o t c o n s i d e r e d . A t r e s e r v o i r p r e s s u r e bgtween 50 and 100 b a r and r e s e r v o i r t e m p e r a t u r e s between 4 0 and 80 C a b o u t 4 g of C 0 2 d i s s o l v e s i n 100 g of w a t e r . However, above 6 b a r t h e pH-value of w a t e r c o n t a i n i n g CO a l r e a d y t e n d s t o ward a c o n s t a n t v a l u e of 3 , 3 / 1 5 / , which p r o b a b l y a l s o d o m i n a t e s i n most r e s e r v o i r b r i n e s of t y p e CM. For t h e s u r f a c t a n t i n v e s t i g a t i o n s a s t a t i s t i c a l c o m p o s i t i o n was a s c e r t a i n e d f o r a h i g h l y s a l i n e model r e s e r v o i r w a t e r CM ( t a b l e 1 ) . T h i s s t a n d a r d i z e d b r i n e CM was employed f e r a l l s u b s e q u e n t t e s t s , unless otherwise indicated. The p r i m a r y s c r e e n i n g c r i t e r i a of s u r f a c t a n t s f o r EOR p r o c e s s e s i n h i g h l y s a l i n e s y s t e m s may be l i s t e d a s f o l l o w s / l o / : s o l u b i l i t y i n r e s e r v o i r b r i n e (TDS >165 g . 1 - l ) long-term s t a b i l i t y i n t h e t e m p e r a t u r e r a n g e of 30-80°C low i n t e r f a c i a l t e n s i o n s i n t h e s y s t e m b r i n e / c ? u d e o i l (v< 1 mN.m-l)

-

45 Table 1: Composition of synthetic reservoir brine CM Salt

Concentrations in mg.1-l

NaCl CaC12

165 000 49 349 ( 2 5 O O O ) * 12 810 ( 6 O O O ) * 750 400 20 100

MgC12 KC1 KBr KJ LiCl NH4Cl SrC12 BaC12 NaHC03 Na2S04

. 6H20

. 6H20

350 1 681 ( 1 O O O ) * 58 ( SO)*

. 6H20 . 2H20 . 10H20

C02 injected for at least 1 h NaCQ3 4H20 FeS04 9H20

.

.

650 680 (

300)*

523 (

250)*

366 (

200)*

TDS: 200 070 mg.1-' *The concentration in parentheses refers to the quantity without water of crystallization Based on these fundamental requirements a standard test program for surfactants was developed (see fig. 1).

.solubility stobility wrfoctont in brine CM

ogoinst oil

,- nwhthenic

'T

swfoctont water soluble

interfociol tension Y e 1 mN.rn-1

1: 3a51.0 Y.

30 C' 60 'C

L poroninic

'1:

80 'C Figure 1: Test program for water-soluble surfactants

Besides the aforementioned criteria suitable surfactants should show further, - low adsorption on reservoir rock - favourable partition coefficients and. broad range of application.

-

'

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47

T a b l e 2 : Commercially a v a i l a b l e s u r f a c t a n t g r o u p s Structure

Des isnation

Ionic surfactants Na-salts of fatty acids Alkylbenzenesulfonate

R-CH,-COONa R-C,H,-S0,Na

Alkane sulfonate a-olefinsulfonate Hydroxyalkanesulfonate as byproduct

:)CH-SO,N~ R -CH,--CH=CH-CH,-SO,Na

+

R'-CH,-CH-(CH,)n-CH,-SO,Na OH

a-sulfa fatty acid ester

R-CH-C~' $O,Na'OCH' R-CH,-0-S0,Na

Fatty alcohol sulfate Fatty alcohol ether sulfate*

R; R,CH -O-(C,H,O),-SO,Nn

R -CH,-O-(C,H,O),

R',

+ /R'

-CH,COONa

Fatty alcohol ethoxylate acetate**

CP

(luaternary ammonium salts

R'/ N\R,

N o n I o n i c Surfadants R'

H

1. R=C,,, bei R'=H

R y - ~ - t ~ , ~ , ~ ) , - ~

n=3-15 2. R+R=C,,,, n=3-12

Primary or secondary alcohol ethoxylates

R-C,H.-O-(C,H.O)n-H

R=C,,,

Alkylphenol ethoxylates

n=7-10 YH, CA-Y+C' CH,

Amine oxides

h p l m l y t i c Surfactants R'

Sulfobetains R'

R' - m N -CH,-COO~ R'

Betains

* Fatty alcohol polyethylene glycol ether sulfate, Na-salt ** Fatty alcohol polyethylene glycol ether carboxymethylate,Na-salt

-

-

-

t y p e of c r u d e ( p a r a f f i n i c , n a p h t h e n i c , a r o m a t i c o r mixed t y p e ) c o l l o i d a l c h e m i s t r y of c r u d e ( c o n t e n t of a s p h a l t e n e s , r e s i n s , etc.) a d s o r p t i o n phenomena ( c o m p o s i t i o n of r e s e r v o i r r o c k ) c h a r a c t e r i s t i c s of r e s e r v o i r e n v i r o n m e n t (pH, t e m p e r a t u r e , wetting conditions, s a l i n i t y ) d i f f u s i o n phenomena ( r a p i d d i f f u s i o n t o t h e O / W - i n t e r f a c e ) .

The i m p o r t a n c e of t h e i n d i v i d u a l p a r a m e t e r s c a n v a r y g r e a t l y dep e n d i n g on t h e c o n d i t i o n s of a p p l i c a t i o n , and c a n n o t be g e n e r a l i z e d . For t h i s r e a s o n , two complex p a r a m e t e r s w i l l be d i s c u s s e d i n detai1. DIFFUSION PHENOMENA I t i s known from s t u d i e s on O/W s y s t e m s t h a t t h e d i f f u s i o n i s dep e n d e n t , among o t h e r s , on t h e s t r u c t u r e of s u r f a c t a n t s /l/. Y e t , t h e d i f f u s i o n c o e f f i c i e n t of s u r f a c t a n t s i t s e l f i s of d e c i s i v e imvortance. I n g e n e r a l , t h e following r e l a t i o n s h i p s apply:

48

-

t h e d i f f u s i o n c o e f f i c i e n t decreases w i t h i n c r e a s i n g d e g r e e of alkoxylation the d i f f u s i o n c o e f f i c i e n t increases with increasing concentrat i o n of s u r f a c t a n t ( u p t o c.m.c.) t h e d i f f u s i o n c o e f f i c i e n t i s d i r e c t l y p r o p o r t i o n a l t o temperature t h e d i f f u s i o n c o e f f i c i e n t f o r d i s s o l v e d s u r f a c t a n t s is i n v e r s e l v p r o p o r t i o n a l t o t h e v i s c o s i t y of t h e s o l v e n t branched b l o c k copolymers d i f f u s e more r e a d i l y t h a n l o n g - c h a i n l i n e a r types.

The s t r u c t u r e of t h e p o l y e t h e r c h a i n s of s y n t h e t i c s u r f a c t a n t s c a n a l s o be of i m p o r t a n c e f o r d i f f u s i o n p r o c e s s e s . I t is w e l l known t h a t p o l y e t h e r c h a i n s , depending on t h e d e g r e e of a l k o x y l a t i o n , c a n e x i s t i n t h e s o - c a l l e d z i g - z a g form o r i n t h e meander form ( s e e fig. 3 /2/).

Zig-zag form

Meander form

- F i g u r e 3 : Shapes of p o l y e t h e r c h a i n s / 2 / With i n c r e a s i n g EO number, t h e w i d t h / l e n g t h c o e f f i c i e n t of t h e noni o n i c s i n c r e a s e s , and d i f f u s i o n c o e f f i c i e n t t h u s d e c r e a s e s . By b l o c k i n g t h e p o l y e t h e r oxygen f o r h y d r a t i o n a s a r e s u l t of 0 4 H 2 d i p o l e f o r c e s , a change c a n a l s o o c c u r i n t h e c l o u d p o i n t s , t h e c r i t i c a l micelle f o r m a t i o n c o n c e n t r a t i o n (c.m.c.), and t h u s t h e i n t e r f a c i a l a c t i v i t y o r s o l u b i l i t y behavior / 3 / . ADSORPTION For t h e q u e s t i o n of a d s o r p t i o n phenomena a s a f u n c t i o n of s u r f a c t a n t s t r u c t u r e o r r e s e r v o i r r o c k , numerous f i n d i n g s a r e of importance /l, 9,12, l 4 / . GENERAL C R I T E R I A Swf aetants

-

Amphiphatic s u r f a c t a n t s a r e r e a d i l y a d s o r b e d on h y d r o p h o b i c r o c k s u r f a c e s , d e p e n d i n g on t h e i r s t r u c t u r e The g r e a t e r t h e s o l u b i l i t y of a s u r f a c t a n t , t h e s m a l l e r i s i t s a d s o r p t i o n ( g r e a t e s t a d s o r p t i o n of s u r f a c t a n t o c c u r s i n h i g h s a l i n i t y w a t e r b e c a u s e of diminished s o l u b i l i t y ) With i n c r e a s i n g t e m p e r a t u r e and v i s c o s i t y of t h e s o l v e n t a d s o r p tion decreases With i n c r e a s i n g s u r f a c t a n t c o n c e n t r a t i o n a d s o r p t i o n i n c r e a s e s

AIM:

Low t o t a l a d s o r p t i o n b u t h i g h r a t e of a d s o r p t i o n u p t o t h e s a turation concentration

R e s e r v o i r system

-

-

Hydrophilic e a s i l y water-wettable rocks: quartz, c l a y Hydrophobic, p o o r l y w a t e r - w e t t a b l e r o c k s : c a r b o n a t e s

49 SPECIAL CRITERIA Surf a c t a n t s

-

-

T o t a l a d s o r p t i o n d e c r e a s e s w i t h i n c r e a s i n g m o l e c u l a r mass of s u r f a c t a n t ( t h e t o t a l a r e a a c c e s s i b l e t o a d s o r p t i o n becomes smaller) Nonionic s u r f a c t a n t s / 9 / a r e adsorbed mostly i n unimolecular l a y e r s , a d s o r p t i o n d e c r e a s e s w i t h increasing EO d e g r e e , b u t a d s o r p t i o n i n c r e a s e s w i t h i n c r e a s i n g l e n g t h of t h e h y d r o c a r b o n c h a i n ; d e r i v a t i v e s w i t h an a l i p h a t i c h y d r o c a r b o n c h a i n a r e more s t r o n g l y a d s o r b e d t h a n d e r i v a t i v e s w i t h an a r o m a t i c h y d r o c a r b o n c h a i n I o n i c s u r f a c t a n t s a r e a d s o r b e d f o r t h e most p a r t i n polymolecul a r l a y e r s ( c a t i o n i c s : a b o u t 250 l a y e r s ) . Limiting concentration: s y n t h e t i c s u r f a c t a n t s (0.05-0.07 %) a r o m a t i c s > n a p h t h e n a t e s > a l k a n e s . C a t i o n i c s >>nonionics > anionics. S i l i c a t e s : s l i g h t a d s o r p t i o n of n o n i o n i c s ( o i l - w e t t e d > w a t e r w e t t e d ) , a d s o r p t i o n i n c r e a s e s with temperature; s t r o n g adsorpt i o n of c a t i o n i c s on q u a r t z ( l o w e r e d by a d d i t i o n of n o n i o n i c s ) .

The i n c r e a s e d a d s o r p t i o n of c a t i o n i c s , i n d e p e n d e n t of t h e reserv o i r r o c k i s t h s c l e a r l y e v i d e n t . A s a g u i d e , v a l u e s of a b o u t l o d 4 mg/cm c a n be g i v e n f o r t h e a d m i s s i b l e a d s o r p t i o n on 0,s quartz surfaces.

.

Y

PHYSICOCHEMICAL P R O P E R T I E S OF SURFACTANTS

P r i o r t o t e s t i n g , a f e w g e n e r a l l y - k n o w n r u l e s and some e m p i r i c a l d a t a from t h e c h e m i s t r y of s u r f a c t a n t s c a n be u s e d :

,:

range ( < C s m a l l m i c e l l e s , low Good w e t t i n g a c t i o n : C -C s u r f ace a c f i v $ $ y ) B r a n c h e a and s o l v a t a b l e g r o u p s s h o u l d l i e close t o t h e c e n t r e of t h e m o l e c u l e .

.

H y d r o p h i l i c c h a r a c t e r : 3 CH2 g r o u p s P 1 OH-group -$-NH-group P -0-group ( h y d r o g e n b r i d g i n g ) 3 CHp-groups

-

beginning water s o l u b i l i t y S o l u b i l i t y : n / 3 EO n / 2 EO -medium w a t e r s o l u b i l i t y 1 - 1 , 5 n EO-good water s o l u b i l i t y ( n = number of c a r b o n atoms i n h y d r o p h o b i c c h a i n ) Solubility decreases with r i s i n g temperature ( - c l o u d point/through dehydration and i n c r e a s i n g e l e c t r o l y t e c o n t e n t (see f i g . 4 / l / ) . HLB v a l u e : W/O e m u l s i f i e r s

3 -6

Wetting a g e n t s 7-9 O/W e m u l s i f i e r s 8-12 O/W d i s p e r s i n g a g e n t s , W/O demuls i f i e r s , solubilizing agents

/13

-18/

50

rurtactont nonylphsnol/l5 EO in water

0

1.o 2.0 3.0 electrolyte concentration /ma1 1-1

F i g u r e 4 : E f f e c t o f e l e c t r o l y t e c o n c e n t r a t i o n and t y p e o n c l o u d p o i n t TP / 7 / On t h e b a s i s o f t h i s p r e l i m i n a r y i n f o r m a t i o n , i t i s now a l r e a d y p o s s i b l e t o g e t the most i m p o r t a n t r e q u i r e m e n t s o n s u r f a c t a n t s f o r EOR p r o c e s s e s / 4 , 5 / : - Enrichment a t t h e i n t e r f a c e - Formation of o r i e n t e d monolayers - Permanent l o w e r i n g of i n t e r f a c i a l t e n s i o n i n t h e s y s t e m o i l / w a t e r t o (1 m N . m - 1 a t low s u r f a c t a n t c o n c e n t r a t i o n / 1 3 / - Tendency t o m i c e l l e f o r m a t i o n - Partial o i l solubility - S t a b i l i z a t i o n of O/W e m u l s i o n s Solubility or d i s p e r s a b i l i t y i n highly s a l i n e formation water - Long-term s t a b i l i t y ( 1 - 2 y e a r s ) u n d e r r e s e r v o i r c o n d i t i o n s - Low a d s o r p t i o n on r e s e r v o i r r o c k - Low c o s t c o u p l e d w i t h h i g h e f f e c t i v e n e s s

-

A l i s t of p o s s i b l e b u i l d i n g s t o n e s a v a i l a b l e c o m m e r c i a l l y f o r t h e s y n t h e s i s of s u r f a c t a n t s i s g i v e n i n t a b l e 3 . These c o n s i d e r a t i o n s t h e n l e a d t o classes of p r o m i s i n g p r o d u c t s , which i n p a r t s h o u l d e x h i b i t v e r y s t r o n g i n t e r f a c i a l a c t i v i t y and a r e described i n t h e U S - l i t e r a t u r e a s e f f e c t i v e f o r EOR p r o c e s s e s ( s e e t a b l e 4 and 5 ) .

T h e s e known s u r f a c t a n t s a r e s u i t a b l e p r i m a r i l y f o r low s a l i n i t i e s (1 % N a C l w i t h a b o u t 100-200 ppm Ca2+ and Mg2+ o n l y ) . W i t h o u t a p o l y e t h e r c h a i n w i t h s u f f i c i e n t d i s p e r s i n g power, however, t h e sol u b i l i t y i n h i g h s a l i n i t y s y s t e m s ( 1 5 - 2 5 % NaC1, 20 000-40 000 ppm C a 2 + and Mg2+) i s f o r t h e m o s t p a r t t o o low o r t h e e l e c t r o l y t e s e n s i t i v i t y t o a l k a l i n e e a r t h i o n s t o o h i g h . Even i n t h e case o f pol y e t h o x y l a t e s t h e e l e c t r o l y t e c o n t e n t of t h e r e s e r v o i r w a t e r c a n l o w e r t h e c l o u d p o i n t s t r o n g l y ( f i g . 4 ) and t h u s c a n b r i n g a b o u t a d e c r e a s e d s o l u b i l i t y as w e l l a s i n c r e a s e d a d s o r p t i o n and a p a r t i a l p a s s a g e o f t h e s u r f a c t a n t i n t o t h e o i l p h a s e /6/. I n g e n e r a l t h e i n t e r f a c i a l a c t i v i t y o f t h e anionics i s l i k e w i s e r e d u c e d s t r o n g l y i n water w i t h a h i g h e l e c t r o l y t e c o n t e n t / 5 / , F r e q u e n t l y a l s o s u r f a c t a n t m i x t u r e s f o r EOR p r o c e s s e s h a v e b e e n d e s c r i b e d and a p p l i e d . T h e r e r e m a i n s u n c l e a r t h e q u e s t i o n o f c h r o m a t o g r a p h i c phenomena i n t h e u s e of c o m p l i c a t e d s u r f a c t a n t m i x t u r e s i n r e s e r v o i r , i n which t h e q u i t e d i f f e r e n t components of t h e m i x t u r e c a n e x h i b i t c o m p l e t e l y d i f f e r e n t r a t e s of m i g r a t i o n .

51 T a b l e 3 : Possible b u i l d i n g s t o n e s f o r s u r f a c t a n t s Surfactant building stones a-olefins oligomeric alkenes fatty acids (saturated and unsaturated) and derivatives, natural oils alkanols (alfols, 0x0-alcohols, fatty alcohols) alkylaromatics isoalkylphenols alkylamines (fatty amines) polyalkylene glycol ethers polybutylene oxide (polypropylene oxide)

SO,, ( ~ O , ) , C I S O , H , , H,NSO,H,Na,SO,,NaHSO,

8 8-

),

HOC,H,SO,Na, ( C H , ) , < P ,

(CH2)(_So2\0

c'

H,O, (N), CICHFO,H, (HNO,) 1

0

/o\

(Formaldehyde, epichlorohydrin, RO-CHSH-CH,, aliphatic oligoamines, polyols, etc.)

A n i o n i c s u r f a c t a n t s f o r EOR p r o c e s s e s ( i n t e r n a t i o n a l literature)

Table 4 :

Anionic surfactants Chemical constitution

Designation

structural type

R'-FH-CO,R' SO,H (Na)

a-Sulfo fatty acid esters OH fatty acid sulfates

--T

R-CH,-CH-R-COONa OS0,Na R ~ C O N ~ ~ '

7

Sulfated amide oils

S0,Na R 2

Didecyldiphenyl ether disulfonates H H R-C -C,H,-N-CH,SO,Na bH N + S O , N ~

'c P %

R

R-N -R'-(OC,H,)xOSO,Na R PH R-CH,

RG@-o(c.H,,o)~R S0,Na (rnFXAC0) ,C,H,O-C-R HN' -C,H,O-C-R \ d H C,H,(OC,H,),OC-~-CH,-CO.Na

p

b sop

P

R-0-(CH,-CH,-0)"-P-ONa ONa

Hydroxyalkylaminosulfonic acids Alkenylsuccin-N-(alkyl)phenylimidesulfonates Dialkylamino polyether sulfates Alkenyl-, OH-Alkane sulfonates

7x -77 ).wv,

Sulfates of iosalkylphenyl polyether sulfonates Bisfatty acid esters of triethanolamine polyglycol ether sulfocarboxy lates Alkanol polyether phos-

-

52 T a b l e 5 : Amphoteric s u r f a c t a n t s f o r EOR p r o c e s s e s ( i n t e r n a t i o n a l literature) Amphoteric Surfactants Chemical constitution

Structural type Sulfobetains

R’ H R - ~ C H , - C -cH,-so,~

R’

Sulfobetains

4

Betain

--f.)

Alkylimidazoliniumbetains

-79

Amidoalkylbetains

-.-a

OH

YH’ H,,.,,c,,,:-I]I-cH,-coo~

CH,

R-&

HO-CH,~CH,/N\CH,~COO~ CH;

H,,,,-c,-co-NH-(cH,):-$-cH,-coo

e

CH,

O t h e r w i s e i t is p r o b a b l y p o s s i b l e t o i n c r e a s e , by t h e u s e of s u c h s u r f a c t a n t m i x t u r e s , t h e p a c k i n g d e n s i t y a t t h e i n t e r f a c e and t h u s t h e d e g r e e of w e t t i n g ( s e e f i g . 5 / l o / ) ; f u r t h e r , a l s o t h e format i o n of mixed micelles i s p o s s i b l e ( f i g . 6 /4/).

lipophilic port of molecule surfactant molecule

0 hydrophtlic part of mokcuie

F i g u r e 5 : I n c r e a s e d p a c k i n g d e n s i t y by s u r f a c t a n t m i x t u r e s a t O/W i n t e r f a c e s

When p u r e n o n i o n i c s a r e u s e d , s u c h a s i s o a l k y l p h e n o l e t h o x y l a t e s , a t t a i n m e n t of s a t i s f a c t o r y i n t e r f a c i a l a c t i v i t i e s demands a h i g h e r d e g r e e of a l k o x y l a t i o n . These p r o d u c t s a r e n o t e l e c t r o l y t e - s e n s i t i v e and h a v e a good s o l u b i l i t y i n b r i n e ( a r u l e of thumb i s t h a t a t 5OoC, o n l y n o n i o n i c s w i t h a d e g r e e of e t h o x y l a t i o n n of 1 0 o r more a r e s o l u b l e i n 1 0 % NaC1).

53 oure onionic surfoctont oil

011

transitional interface

L1

water

transitional interface

water

11 : 12

- 1.1

surfoctont mixture (anionics/nonionics I

F i g u r e 6 : a ) p a c k i n g d e n s i t y of p u r e a n i o n i c s u r f a c t a n t a t i n t e r face b ) p a c k i n g d e n s i t y of a n i o n i c - n o n i o n i c s u r f a c t a n t a t interface

EXPERIMENTAL

Under c o n s i d e r a t i o n of a s many s e l e c t i o n c r i t e r i a , physico-chemic a l p r o p e r t i e s and p o s s i b i l i t i e s of s u r f a c t a n t s y n t h e s i s a s poss i b l e more t h a n 1 2 0 0 s u r f a c t a n t s were t e s t e d f o r t h e i r a p p l i c a b i l i t y t o EOR p r o c e s s e s . The s c r e e n i n g of t h e s u r f a c t a n t s was c a r r i e d o u t a c c o r d i n g t o t h e r a p i d s c r e e n i n g program a l r e a d y i n troduced. F u r t h e r t e s t s on a s u r f a c t a n t w e r e proposed o n l y , i f i t had pass e d t h e s c r e e n i n g program. SOLUBILITY I N BRINE CM A l l e x p e c t a t i o n s on t h e s o l u b i l i t y of s u r f a c t a n t s i n h i g h - s a l i n i t y b r i n e s were c o n f i r m e d i n a l l r e s p e c t s . E s p e c i a l l y t h e s u r f a c t a n t s w i t h p o l y e t h e r c h a i n s and a n i o n i c g r o u p s have shown good s o l u b i l i t i e s up t o t h e mark. T a b l e 6 p r e s e n t s some t y p i c a l p r o d u c t s , which were s e l e c t e d on t h e b a s i s of t h e a b o v e - d e s c r i b e d s o l u b i l i ty criteriaa.

INTERFACIAL ACTIVITY

During t h e measurements of t h e i n t e r f a c i a l a c t i v i t y (Lecomte du Nouy) a s t r o n g dependence of t h e i n t e r f a c i a l t e n s i o n on t h e temper a t u r e and s a l i n i t y was e s t a b l i s h e d i n t h e system o i l / w a t e r w i t h o u t a d d i t i o n of any s u r f a c t a n t s ( s e e f i g . 7 ) . The e x p e r i m e n t s have shown t h a t a l l s t a n d a r d o i l s a r e c h a r a c t e r i z e d by a t y p i c a l i n t e r f a c i a l t e n sion - relationship - i n t e r f a c i a l t e n s i o n depends s t r o n g l y on t h e o i l c o m p o s i t i o n - n a p h t h e n i c o i l shows t h e h i g h e s t v a l u e s of i n t e r f a c i a l t e n s i o n against high-salinity brines - i n g e n e r a l an i n c r e a s e i n s a l i n i t y is accompanied by a d e c r e a s e i n i n t e r f a c i a l t e n s i o n / A minimum i n i n t e r f a c i a l t e n s i o n w i l l be passed. T h e r e s u l t s a r e summarized i n f i g u r e 7 .

-

54

T a b l e 6 : Some s u r f a c t a n t s w i t h good s o l u b i l i t y , t e s t e d i n h i g h salinity brine Chem. constitution

Designation

I-C,H,,~(C,H.OJ.,CH,CD,N~

Isoalkylphenylpolyether acetates Diisoalkylphenylpolyether sulfates

SO, Na

IC,H,.~O(C,H.OI,. l-C,Ha,

Rj-N/(C,H,O)x '(C,H,O), (2 x = 5 )

SO,Na S0,Na

Acylamidopolyether sulfates

fl

(R-C-~,H,-N/(C1H40)y ( 2 y t 1= 2 X I

'(C,H,Oly

(Esteramine polyether sulfates)

S0,Na)

i-C,,H,,~-CH,-~-CH,~(OC.H,.Jx SO,N~

Structural type-

( W n H x n)x O R

x-0-20 R'= H, SO,Na,

OR'

N

(Sulfone/sulfate-isoalkylphenylpolyethoxyglycerol ether)

-CH,COONa n=2,3

Ditert.-alkylphenyl polyethers

Isoalkylphenylpolyethers

I f s u r f a c t a n t s were added t o t h e s t a n d a r d o i l s , c h a r a c t e r i s t i c c u r ves r e s u l t e d f o r t h e f u n c t i o n i n t e r f a c i a l t e n s i o n y = f ( s u r f a c t a n t concentration CT). T h e s h a p e of t h e c u r v e s d e p e n d on - t y p e of o i l ( c o m p o s i t i o n ) - temper a t u r e - salinity - t y p e of s u r f a c t a n t and c o n c e n t r a t i o n of s u r f a c t a n t . T y p i c a l d i a g r a m s of s u r f a c t a n t m i x t u r e s ( a n i o n i c s - n o n i o n i c s ) a r e presented i n f i g u r e 8 a/b. -1 I f t h e i n t e r f a c i a l t e n s i o n r e a c h v a l u e s of < 1 mN.m , t h e accur a c y of t h e method of Lecomte d u Nouy i s no l o n g e r s u f f i c i e n t . Furt h e r t e s t s on " s u c c e s s f u l " s u r f a c t a n t s makes t h e a p p l i c a t i o n of a spinning-drop-tensiometer (SITE) n e c e s s a r y . A " s u c c e s s f u l " s u r f a c t a n t m u s t comely w i t h t h e f o l l o w i n q c r i t e r i o n : The i n t r f a c i a l t e n s i o n of a s u c c e s s f u l s u r f a c t a n t must be < 1 mN.m-f against a l l three standard o i l s i n the temperature range of 30-80°C. On t h e b a s i s of t h i s c r i t e r i o n a g e n e r a l t e m p e r a t u r e i n t e r f a c i a l t e n s i o n - r e l a t i o n s h i p was d e r i v e d f o r t h e s u r f a c t a n t s t e s t e d ( s e e fig. 9). By t h i s i t was e v i d e n t , t h a t a n i o n i c s ( w i t h an o p t i m a l c o n t e n t of nonionics) w i l l e x h i b i t the lowest i n t e r f a c i a l tension. TEMPERATURE STABILITY

For t h e i n v e s t i g a t i q n of t h e t e m p e r a t u r e s t a b i l i t y , s u r f a c t a n t s o l u t i o n s of v a r i o u s c o n c e n t r a t i o n s i n b r i n e CM were k e p t f o r

55

"I

Figure 7 : I n t e r f a c i a l tens i o n a s a f u n c t i o n o f temp e r a t u r e , s a l i n i t y and o i l composition (naphthenic, aromatic, p a r a f f i n i c )

N

20

Y ogoinst dist woter

6 month a t a t e m p e r a t u r e o f 8OoC. After t h i s t i m e the interf a c i a l a c t i v i t y was comp a r e d t o t h a t of a s t a n d a r d solution On t h e b a s i s of t h e s e e x periments, the following s t a t e m e n t was p o s s i b l e : ether Ether phosphates s u l f a t e s - e t h e r carboximethylates -ether sulfonates a r r o w i n d i r e c t i o n of increasing s t a b i l i t y

-

0

60

30

80

temperature 9/"C

20t

\:I y

= f(8.011 comp

1

Y against brine EM

s

12 10

5 8 .-

N

.-I

0 : .

0

20

t

1

v

.

I

.

I

.

,

80 temperot ure 8 / "C

30

60

-

SPECIAL FINDINGS

, -

P o l y e t h e r s u l f a t e s , -carbo x i m e t h y l a t e s and - s u l f o n a t e s of t h e f o l l o w i n g s t r u c ture are particularly suita b l e f o r EOR g r o c e s s e s : R(OC2H4)xY-Me (Fig.10).

y = t(;t.oil comp I

Numerous s u r f a c t a n t s w i t h e s p e c i a l l y low v a l u e s of t h e i n t e r f a c i a l t e n s i o n may be c l a s s i f i e d a s m i x e d s u r f a c t a n t s (Mischtenside) (ani o n i c / n o n i o n i c ) . The compos i t i o n of t h e m i x e d s u r f a c t a n t i s u s u a l l y g o v e r n e d by t h e manufacturing process o r t h e d e g r e e of c o n v e r s i o n . I n t h i s r e s p e c t i t was ob30 60 eo s e r v e d t h a t a d e g r e e of contemperature ;t/'C v e r s i o n o f 50 t o 8 0 p e r c e n t N naphthenic oil nonionic t o anionic surfacA aromottc oil t a n t g i v e s rise t o p a r t i c u P poroffinic oil l a r l y favourable surfactant p r o p e r t i e s . A t y p i c a l homoloaue d i s t r i b u t i o n f o r f o r s u c h a s u r f a c t a n t i s shown i n f i g u r e 11

Y agoinst brine CM

.

The f o l l o w i n g i m p o r t a n t d a t a and r e s e a r c h r e s u l t s a r e w o r t h mentioning: - The d i s t r i b u t i o n c u r v e f o r t h e s u r f a c t a n t homologs ( a l k o x i l a t e s ) s h o u l d be a s b r o a d a s p o s s i b l e (more p d l d i s p e r s e ) i . e . , a l k a l i catalyzed alkoxilation (not Lewis-acid catalyzed). - The d e g r e e of a l k o x i l a t i o n n m u s t be a d j u s t e d a c c o r d i n g t o t h e c r u d e type (and Y - ) . General r u l e s a r e HLB: 8-10 p a r a f f i n i c c r u d e s : n = 4 5 2 EO (partial o i l solubility) n a p h t h e n i c c r u d e s : n = 6 5 2 EO

56 rn namlhanic oil

oil

y = f (c,,

A poraflinic oil

type)

x ommolic oil suiodoni 63 tenpirniure ’ 30.C surfuianl in brine CM

Figure 8 a : I n t e r f a c i a l tension a s a funct i o n of o i l composition, surf a c t a n t concent r a t i o n and temp e r a t u r e (30°C) surfactant: C12/14-fatty alkohol-polyglycolether-(4,5 EO)-carboxmet h y l a t e , Na-salt

naphthanic oil

y = f (cT, oil type 1

10

A poraflinic oil

x oromalic oil surfactant 63 impKa1ua:I0.C surfoclani in brina CM

I

Figure 8 b: same a s f i g . 7a t e m p e r a t u r e 80 C

6

1n

1 A h htypical

onionics and mixed surfactants

high content of 1 nonionics

/

temperoture

area of spontaneous

a/

0;

emulsification

Figure 9 : Temperature/ i n t e r f a c i a l tension-rel a t i o n s h i p f o r some i m portant s u r f a c t a n t groups

57

hydrophobic chain

R

Polyether group

-+X+

fatty OlCOhd tatty ocid nonylphenol naphthenic ocid tatty ornines

ethyleneoxide propyleneoxide etc

polar hydrophilic group

counter ion

YQ

Z@

car boxylote sulfate sulphonate phosphate propionate etc

OlkOll earth alkali ornines etc

F i g u r e l o : S u r f a c t a n t s s u i t a b l e f o r EOR p r o c e s s e s

nonionic port

anionic part

Hal EO

Hol EO

F i g u r e 11: Q u a n t i t a t i v e a n a l y s i s of i-nonylphenol-polyglycole t h e r (6 E O ) - c a r b o x i m e t h y l a t e , Na s a l t , by HPLC aromatic crudes:

-

n

= 8 & 2 EO

( P r o p o x i l a t e s a r e i n g e n e r a l less e f f e c t i v e , a s a r e EO-PO ducts) The h y d r o p h o b i c c h a i n R must be t a i l o r e d w i t h p r e c i s i o n . p a r a f f i n i c c r u d e s : C14 5 4 ( s a t u r a t e d , u n b r a n c h e d ) naphthenic crudes: C,, + 2 arbmatic rudes: a k y l r o m a t i c s iiso-C8-12-alkyl). C a t i o n ( 2I) : Na', ,'K i'R4 o r NH4

ad-

The l e n g t h of t h e h y d r o p h o b i c and h y d r o p h i l i c m o l e c u l a r p a r t s s h o u l d be r o u g h l y i n t h e 1 : 1 r a t i o ( p a r t i a l o i l s o l u b i l i t y ) .

58 Example: C 1 2 , 1 4 - a l k y l p o l y g l y c o l

e t h e r s u l f a t e - ( 4 , 5 EO), N a - s a l t

( h y d r o p h o b i c : h y d r o p h i l i c c h a i n l e n g t h = 2 , 2 nm: 2 , 3 n m ) o r f o r n o n y l p h e n o l p o l y g l y c o l e t h e r s u l f a t e - ( 4 EO), Na-salt (hydrophobic: hydrophilic chain l e n g t h = 2,O: 2 , l nm ( s e e f i g . 1 2 ) .

oil

transitional interface

hydrophobic part A

water

hydrophilic port B

~~~

ratio at optimum A B - 1 1

-

F i g u r e 1 2 : Optimal c h a i n r a t i o of s u i t a b l e s u r f a c t a n t s f o r EOR p r o c e s s e s

The d e g r e e of c o n v e r s i o n of n o n i o n i c s i n t o s u l f a t e s , c a r b o x i m e t h y l a t e s , s u l f o n a t e s , e t c . , s h o u l d be 50-80 % ( m i x e d s u r f a c t a n t f o r m a t i o n f r o m n o n i o n i c s and a n i o n i c s ) .

The c a r a c t e r i s t i c b e h a v i o u r of a n i o n i c - n o n i o n i c m i x e d s u r f a c t a n t s w i t h t e m p e r a t u r e (minimum of i n t e r f a c i a l t e n s i o n ) c a n be e x p l a i n e d w i t h t h e h e l p of t h e p h a s e d i a g r a m f o r s u c h s y s t e m s ( s e e f i g u r e 13), w h e r e b y t h e o c c u r r e n c e o f a m i s c i b i l i t y g a p is d e c i s i v e .

A aI L aI

11 MST=T?

0% 100%

-nonionic surfnctant + c a n i o n i c surfactant -

100% 0%

MSTK

=

CK

= critical splitting -concentration of mixed micelles at MSTk

CX

= composition of mixed micelles

lower critical micell- splitting - temperature

MST=T2= splitting - temperature of mixed micelles

AT

=

a,p

= coexistent phases with concentrations c, and c ,

11 -12

F i g u r e 1 3 : Schematic p h a s e d i a g r a m f o r mixed surf actant (anionicn o n i o n i c ) w i t h miscib i l i t y gap

59

A s e p a r a t i o n i n t o w a t e r - / o i l - s o l u b l e s u r f a c t a n t s o c c u r s when t h e m i x e d m i c e l l e s formed from anionics & nonionics reach the micelle s p l i t t i n g t e m p e r a t u r e ( M S T ) . When t h e MST i s e x c e e d e d , v a r i o u s i n t e r e s t i n g phenomena may be o b s e r v e d ( s e e f i g u r e 1 4 ) ; t h e s e a r e accompanied by t r a n s p o r t p r o c e s s e s a t t h e i n t e r f a c e s .

t F i g u r e 1 4 : Phenomena a t the micelle-splitting t e m p e r a t u r e (MST) f o r m i x e d s u r f a c t a n t (nonionic-anionic)

CONCLUSIONS

With t h e t e c h n o l o g i c a l p o s s i b i l i t i e s t a k e n i n t o c o n s i d e r a t i o n , and w i t h t h e h e l p of a r a p i d t e s t p r o c e d u r e , i t was p o s s i b l e t o s e l e c t s u r f a c t a n t s s u i t e d f o r EOR p r o c e s s e s i n h i g h - s a l i n i t y s y s t e m s from a l a r g e number of p r o d u c t s . The s e l e c t e d s u r f a c t a n t s a r e ani o n i c s and b e l o n g t o t h e c l a s s e s of polyglycolethercarboximethyl a t e s and polyglycolethersulfonates. As a r e s u l t of t h e manufact u r i n g p r o c e s s , t h e s e p r o d u c t s may be c l a s s i f i e d a s mixed s u r f a c t a n t s ( n o n i o n i c - a n i o n i c ) . S i n c e m i x e d micelles a r e formed, t h e s e p r o d u c t s p o s s e s s s p e c i a l t e m p e r a t u r e - d e p e n d e n t p r o p e r t i e s which a r e i n t e r e s t i n g f o r EOR p r o c e s s e s . I n t h e long term, tailor-made p r o d u c t s , e s p e c i a l l y s u r f a c t a n t mixt u r e s o r mixed s u r f a c t a n t s , o f f e r s p e c i a l p r o m i s e from t h e economic p o i n t of view.

60

Nomenclature c .m .c CS

EO EOR

.

-

TDS

-

W/O

-

HLB HC OOIP O/W PO ppm

0

-

critical micelle formation concentration salinity/concentration of salts dissolved; g. 1-1 ethylene oxide enhanced oil recovery tertiary oil recovery phase) hydrophilic/lipophilic balance hydrocarbons original oil in place, % oil/water propylene oxide parts per million iota1 dissolved solids, % water-in-oil temperature, OC

Abbreviations for fiqures CT A1 # A 2

-

Au

-

L1 L2 Y

surfactant concentration in ppm or % distance between surfactant molecules at interface, nm thickness of transitional interface length of hydrophilic chain, nm length of hydrophobic chain, nm interfacial tension, mN.m-1

61 LITERATURE 1

Babalyan, G.A.:

Physicochemical p r o c e s s e s i n o i l prod u c t i o n , " P u b l i s h i n g House " N e d r a " , Moscow, 1974 ( i n R u s s i a n )

2

Rosch. M . :

The c o n f i g u r a t i o n of t h e p o l y e t h y l e n e o x i d e c h a i n of n o n i o n i c s u r f a c t a n t s ( p a r t 1 ti 2 ) ( i n German) Tenside Detergents ( 1 9 7 1 ) , pp. 302313 T e n s i d e D e t e r g e n t s 9 ( 1 9 7 2 ) , pp. 23-28

3

Schonfeldt, N.:

" G r e n z f l a c h e n a k t i v e E t h y l e n o x i d -Adduk-

t e " ( I n t e r f a c e - A c t i v e E t h y l e n e Oxide

Adducts) , Wiss. V e r l a g s GmbH, S t u t t g a r t Schick, M. J. :

"Nonionics Surf a c t a n t s " , M a r c e l Dekker, I n c . ,. N e w York, 1 9 6 7 / C h a p t e r 22

4

A k s t i n a t , M.H.:

V i s c o u s f l o o d i n g media f o r t e r t i a r y o i l recovery i n h i g h l y s a l i n e systems s e l e c t i o n c r i t e r i a , t e s t i n g methods and e x p e r i m e n t a l r e s u l t s ( i n German) Ph. D. t h e s i s , TU C l a u s t h a l 1 9 7 8

5

Gutscho, S.J.:

" S u r f a c t a n t s and S e q u e s t r a n t s " , Noyes Data Corp., Park Ridge, N . J . , 1977,

6

B a l z e r , D.; Kosswig , K . :

The p h a s e - i n v e r s i o n - t e m p e r a t u r e a s a c r i t e r i a f o r s e l e c t i o n of s u r f a c t a n t s f o r EOR ( i n German) T e n s i d e D e t e r g e n t s 16 ( 1 9 7 9 ) , pp. 256 261

7

Schick, M.J.:

-

-

S u r f a c e f i l m s of n o n i o n i c d e t e r g e n t s I. Surface tension study J. C o l l . Sci. ( 1 9 6 2 ) , p p . 801-813

17

8

Crook, E.H. ; F o r d y c e , D. B. ; T r e b b i , G.F.:

M o l e c u l a r w e i g h t d i s t r i b u t i o n of noni o n i c s u r f a c t a n t s / I I . P a r t i t i o n coeffic i e n t s o f n o r m a l d i s t r i b u t i o n and homogeneous p , t - Octylphenoxyethoxie t h a n o l s (OPES) J . C o l l . S c i . 20 ( 1 9 6 5 ) , p p . 191-204

9

Kravchenko, J . J . :

E f f e c t of t e m p e r a t u r e on t h e a d s o r p t i o n of n o n i o n i c s u r f a c e - a c t i v e subs t a n c e s on s o l i d a d s o r b e n t s C o l l . J. USRR 33. ( 1 9 7 1 ) , pp. 379-381

10

A k s t i n a t , M.H.:

Surface-active agents f o r t e r t i a r y

o i l r e c o v e r y : s e l e c t i o n c r i t e r i a and s e l e c t i o n m e t h o d s ( i n German) T e n s i d e D e t e r g e n t s 14 ( 1 9 7 7 ) , p p . 5763

62 11

Rieckmann, M . :

T e r t i a r y o i l r e c o v e r y methods ( i n German) Erdo14rdgas-Z. 91 ( 1 9 7 5 1 , pp. 348359

12

R u d i , V.P.; S o b k i v , E.R. :

I n f l u e n c e o f s u r f a c t a n t s on t h e p r o p e r t i e s of c l a y s ( i n R u s s i a n ) ( 1 9 6 6 ) , pp. 119-122 K o l l o i d Zh.

et al.:

S

Surfactant aging: a possible detriment t o t e r t i a r y o i l recovery 5 0 . SPE of AIME Ann. F a l l Mtg., 28.3.1.10.1975, Dallas/Tx. SPE-Paper 5564

13

Cash, R.L.

14

Trogus, F.J.

15

W r i g h t , C.C.:

The u s e o f C a r b o n D i o x i d e i n w a t e r floods A P I P r o d . D i v . P a c i f i c Coast D i s t r . Mtg., 2 1 . - 2 3 . 5 . 1 9 6 3 , Los A n g e l e s P r e p r i n t 801-39 k

16

Oppenlander , K. ; A k s t i n a t , M.H.; Murtada, H.:

S u r f a c t a n t s f o r enhanced o i l recovery i n hiqh-salinity systems - c r i t e r i a f o r t h e s u r f a c t a n t s e l e c t i o n and a p p l i cation Tenside Detergents 1 7 ( 1 9 8 0 ) , p p . 5767

et al.

A d s o r p t i o n of m i x e d s u r f a c t a n t s y s t e m s 5 2 . SPE of AIME A n n . F a l 1 Techn. Conf. & Exh., 9.-12.10.1977, Denver/Col. SPE-Paper 6845

63

CHEMICAL FLOODING

PRELIMINARY STUDIES OF THE BEHAVIOUR OF SOME COMMERCIALLY AVAILABLE SURFACTANTS IN HYDROCARBON-BRINE-MINERAL SYSTEMS C. ANDREWS, N. M. COLLEY and R. THAVER British Gas Corporation, London Research Station ABSTRACT Some commercial surfactants have been studied with a view to their usefulness for enhanced oil recovery applications. The following aspects of their behaviour have been assessed. 1.

Their interfacial tension behaviour with crude oil and pure alkanes.

2.

The variation of phase inversion temperature with different variables.

3.

Their adsorption onto rock surfaces

The interfacial tensions were measured by the spinning drop technique. As the temperature varies, the interfacial tension of a surfactant-brine- hydrocarbon mixture passes through a minimum. Some surfactants have given interfacial tensions approaching 10-3 dynes cm-1. We have found: 1.

The phase inversion temperature decreases with increasing salinity, the hydrocarbon and the surfactant concentration and composition remaining constant.

2.

For constant salinity and surfactant concentration phase inversion temperature increases with increasing equivalent alkane carbon number.

3.

The phase inversion temperature increases with ethylene oxide content of the surfactant, salinity and hydrocarbon remaining constant.

4.

The phase inversion temperature decreases with increasing lipophilic alcohol content of the systems.

5.

Static adsorption tests on reservoir rock show Langmuir adsorption isotherms.

Introduction London Research Station, the corporate laboratory of British Gas became involved in enhanced oil recovery after an invitation by the Department of Energy to take part in its research programme coordinated by A.E.E. Winfrith. After a review of information available to us on the reservoirs operated by British Gas Corporation

64

we decided that our resources would be most usefully employed studying micellar/polymer and miscible flooding. This paper describes the work we have performed so far to identify commercially available surfactants with interfacial tensions-lowering properties to suit the conditions prevailing in our reservoirs, and to assess their sensitivity to changes in reservoir variables, lack of sensitivity being a desirable (but attainable?) ideal. Measurements of phase inversion temperature (PIT), interfacial tensions and adsorption onto mineral surfaces have been made.

The Reservoir Conditions in the target reservoir are similar to those listed below: Oil type E.A.C.N.

7-a 10 43oc

(Reservoir) (Stock tank)

Temperature Formation water

90,000 mgNaCl/litre 1,300 mgCa/litre 500 mgMg/litre 30,000 mgNaCl/litre 400 mgCa/litre 1,200 mgMg/litre

Flood water (sea water)

Chemicals Surfactants. AG

.

Samples of the surfactants listed below were obtained from Hoeschst

Anionics: Hostapal" BV., an alkylaryl polyglycol ether sulphate

- Na

salt.

( 7 ethylene oxide (e.oJunits, 50% w/w active).

Surfactant A straight chain alkyl phenol ether acetate, 4 ethylene oxide units.

.

Surfactant B

Non ionics: units ) TlOO" "

.

1.

6 ethylene oxide units.

Sapogenate* T80 tri-butyl phenylpolyglycol ether(8 ethyleae oxide "(10 ethylene oxide units.) T110

'*

T130

'*

"

.- (11

ethylene

(13

ethylene

oxide units.) '*

oxide units.) Arkopal* NO60 Nonyl phenylpolyglycol ether (All 100% active).

(6 ethylene oxide units.)

Hydrocarbons used in this work were specified to be greater than 99% pure.

*

Hostapal, Sapogenate and Arkopal are trade marks of Hoechst AG.

65

Phase Inversion Temperature The phase inversion temperature, PIT, of a hydrocarbon/brine/ surfactant system indicates the existence of a minimum interfacial tension at that temperature. Since the lowering of interfacial tension is a requirement for the mobilisation of oil trapped in constricted capillaries and all oil reservoirs are essentially isothermal, PIT represents a useful parameter for the selection of surfactant for a given reservoir. For nonionic surfactants below the PIT the surfactant partitions preferentially into the aqueous phase and the emulsion formed between the two phases is predominately 'oil-in-water'. Above the PIT, it partitions mainly into the oleic phase and forms a 'water-in-oil' emulsion (Balzer and Kosswig,l979). Balzer and Kosswig (1979) have carried out some parametric studies of PIT with a range of anionic carboxy methylated nonyl phenol ethyoxylate surfactants. They found: 1. PIT increases with increasing equivalent alkane carbon number (EACN) of the oil and that aromatic hydrocarbons show very low values of EACN. Mixtures of aromatic compounds and alkanes give intermediate PITS. 2.

PIT increases with decreasing salinity.

3. PIT increases with increasing number of ethylene oxide groups in ethoxylated surfactants

We have extended this work to nonionic surfactants in studying the following variables on PIT. The effects of these variables must be considered if a surfactant flood is to maintain its oil mobilising properties as it passes through the reservoir. The parameters studied in this work are: 1. 2. 3.

4. 5. 6.

Oil type expressed as EACN. Surfactant type and concentration Salinity Co-surfactant type and concentration Phase ratio Number of ethylene oxide units in surfactant molecule.

1. The EACN for a given reservoir oil should be constant. The EACN of our reservoir crude has been assessed from measured EACN 6f stock tank crude and calculated from a well stream analysis. 2. The concentration of surfactant at some point away from the injection well is likely to change because of adsorption onto the reservoir rock surfaces. Adsorption measurements are therefore important.

3. The salinity of the brine in contact with residual crude in a waterflooded reservoir may vary from pure injection water to pure formation water.

4.

Co-surfactant effectiveness may change with concentration and type.

5. Variable oil/brine ratios will occur in a reservoir as a flood proceeds. must be taken into account when performing laboratory tests.

This

6 . The hydrophilic/lipophylic balance of a surfactant will depend upon its ethylene oxide content,(Shinoda 1965). Commercial surfactants are usually assigned a nominal ethylene oxide content, but actually contain a distribution of e.0. chain lengths. If PIT is dependent upon the number of e.0. units, then selective adsorbtion by reservoir rock will change PIT.

66 Interfacial Tension It is necessary to augment the data obtained from PIT measurements. The inversion of emulsions occurs over a small temperature range. For this to occur with minimum energy an interfacial tension minimum is implied. A typical plot of I.F.T. against temperature is sketched in Fig.1.

IFT, 10-L dynes/cm t0-L

V t I

lo-&

I I

J

PIT

T°C

Measurements have been made to determine the way IFT changes with temperature. Methods Phase Inversion Temperature was determined by means of electrical conductivity measurements (Baker and Kosswig 1979). For an oil-in- water emulsion with a non-ionic surfactant initially below the PIT the conductivity slowly increased with temperature but fell rapidly as the emulsions inverts and the aqueous phase became discontinuous and therefore non-conducting. Figure 2 shows a typical curve. More than one 'minimum' may occur for impure surfactants.

:tivity

T°C

Temperature

4'

(I

$ 4

*I

Figure 2 Adsorption The investigation consisted of a series of experiments to measure A, the adsorptive capacity of the reservoir rock for surfactant material. The method used was based on that of Somasundaran & Hannah (1979). The method of analysis for surface-active material was the titration procedure of Reid et al., (1967). Interfacial Tension Measurements were made at ambient pressure with the University of Texas spinning drop tensiometer.

67 TESTS, RESULTS AND DISCUSSION

Variation of PIT with EACN and determination of EACN value of the p h e n y u cyclohexyl groups.

1.

PITS were determined on the following mixtures at the phase ratios stated (brine/oil).

Brine

Hydrocarbons

10

Seawater

A+B

5 of each

T80

10

Surfactant

Concentration /litre

Phase Ratio brine/oil

Results

n-alkanes C7-C10

5: 1

Fig 3 line A

Seawater

n-heptane-toluene mixtures EACN 4 to 7

5:l

Fig 3 line B

Seawater

N-alkanes c6 to cll methylcyclohexane

5:l

~

A

T80

Fig 4 line A Fig 4 line B

As above after storage for 3 months at room temperature

T80

10

T80

50

30g /NaClI n-alkanes litre cg-cl1 11

**

1.

4: 1

Fig 5 line A Fig 5 line B

I.

TlOO

Fig 5 line C

TlOO

Fig 5 line D

TlOO

50

. . . I,

*.

.

butyl cyclohexane

4:l

Table 1

phenyl heptane

Table 1

phenyl octane

Table 1

Results and Discussion The results presented in Figs 3 to 5 show a linear relationship between EACN and PIT over the EACN range studied.

68

3

4

5

7

6

9

8

10 EACN

Figure 3: Variation of PIT with EACN for two different surfactant solutions.

PIT "C

70

60 50 40

30 20

I

I

4

I

I

I

I

6

5

7

I

I

8

9

I

I

1 0 1 1

12 EACN

Figure 4 :

Variation of PIT with EACN for log /1 Sapogenate T80 in seawater.

PIT "C

70

Line D

60 50 40

Line A

30 20 6

7

8

9

10

11

12

EACN Figure 5:

Variation of PIT with EACN; pure n-alkanes, 30 g /litre NaCl

69 The EACN of butyl cyclohexane was determined relative to the Fig 5 line B and line C, phenyl heptane and phenyl octane were determined relative to Fig 5 line C. The values found are listed in Table 1. TABLE I EACN found

Assigned EACN of ring

butylcyclohexane

6.5 (Fig 5 Line C) 6.75 fig 5 line B

phenyl heptane

5.0("

phenyl octane

6.0("

'.

")

"

")

-

2.6 -2.0 -2.0

Thus we are able to assign an EACN of 3.6 to methyl cyclohexane. This may enable us to dilute stocktank crude with hydrocarbons with rings to obtain mixtures of hydrocarbon at ambient pressures having EACNs more representative of reservoir crudes. A shift of PIT of 2 to 30C was observed on storage at room temperature for 3 months of the stock 50 gms TlO/litre solution from which line B fig 4 was obtained. No further change was observed on storage for a further 5 months, nor on a freshly prepared solution stored at 40OC for 3 weeks. At the higher concentration of T80 the dependance of PIT on EACN is reduced. affect is not as marked in the case of T100.

The

The difference in slopes shown between lines A and B, Fig 3 suggest the possibility of modifying the sensitivity of a system to change in temperature by the addition of another surfactant. Differential adsorption within a reservoir could cause problems in practice. PIT can change rapidly with EACN. Rates of change of PIT of up to 140C/EACN unit (line B Fig 3) are possible and the slope can change with surfactant concentration. Rates of change of PIT as low as 30C/EACN unit are possible (line A Fig 3).

2.

Variation of PIT with surfactant concentration

Tests

h e effect of increasing surfactant concentration was studied on the following mixtures.

Surfactant T80 T80 TlOO TlOO

Concentration 8 hitre Various 10 to 70

Brine g

Hydrocarbon

NaC111 30

Phase ratio brineloil

Results

heptane

4:1

Fig 6 Curve 1A

I.

*I

octane

4:1

Fig 6 Curve 1B

.*

I.

heptane

4:l

Fig 6 Curve 2A

I,

.I

octane

4:l

Fig 6 Curve 2B

I0

Results and Discussion The results are shown in Fig 6 . Both surfactants exhibit a non-linear relationship, with PIT increasing with decreasing surfactant concentration. This The rate of change of is in agreement with the work of Shinoda and Arai (1964). PIT is lower at high surfactant concentrations which indicates that a high concentration flood could be less susceptible to concentration changes.

PIT *C

60

50

40

30

20

I

'

16

o i

Figure 6:

3.

40 4b o;'

Qo 7 b ad Surfactant concentration, g /litre

Variation of PIT with concentration of Sapogenate T80 and T100.

Variation of PIT with Salinity Tests -

PIT'S were determined on the following mixtures.

Surfactant

Concentration g /litre

Brine

Hydrocarbon

Phase ratio brine/oil

Results

5:l

Fig 7 line A

hexane

4:l

Fig 7 line B

10

heptane

4:l

Fig 7 line C

10

octane

4:l

Fig 7

Ta0

10

T80

10

Ta0 T80

NaCl only Stock Tank (various Crude EACN 10 concentrations)

line D

71 Results and discussion For all hydrocarbons tested, the rate of change of The results are shown in Fig 7. PIT with salinity is independent of the hydrocarbon used. The decrease in PIT with increasing salinity is to be expected as the surfactant partitions more readily into the oleic phase as salinity increases (Knickerbocker et al, 1979).

60

.

50

-

40

-

PIT OC

\

Line A

30

2o

1 10

20

30 40

50

60

70

80

90

Brine concentration, NaCl/litre. Figure 7:,,Variation of PIT with brine salinity; 10 g /litre Sapogenate T80 solution.

g

4.

Variation of PIT with Alcohol (Cosurfactant) type and concentration

Tests -

Measurements were made on 50 g T100flitre brine. Brine concentration was 30 g /NaCl/litre and oil EACN 7.5 at a phase ratio of 4 : l . Alcohols studied were: (a)' iso-butanol (lipophilic) (b) is0 pentanol( " 1 (c) isopropanol (hydrophilic)

Results and discussion. The results shown in Fig 8 agree with trends predicted in the literature, (Knickerbocker et al, 1979), in that increasing the concentration of a lipophilic alcohol (lines A and B) will increase the partitioning of the surfactant into the oleic phase and tend to lower the PIT. The hydrophilic alcohol (line C) has the opposite affect but less pronounced. Increasing the concentration of hydrophilic alcohols has the opposite effect on PIT as increasing surfactant concentration. If an alcohol has to be used as a viscosity modifier then hydrophilic alcohols may be more manageable with respect to their effect on PIT than lipophilic alcohols.

72 PIT OC

60 50 g 30 g EACN

50

/litre Sapogenate TlOO /litre NaCl 7.5

40

30

10

20

40

30

50

Alcohol concentration, g /litre. Figure 8: Variation of PIT with alcohol concentration

5.

Variation of PIT with brine/oil phase ratio

Tests PITs were measured on the following mixtures to find out if PIT varied with phase ratio. Surfactant T80

50 g

/litre

T80

10 g

/litre

T80

.

T80

Brine

Concentration

I.

I.

.

. .

Hydrocarbon

Results

n heptane

Fig 9 line A

n hexane

Fig 9 line B

"

n heptane

Fig 9 line C

**

n octane

Fig. 9 line D

30 g Nacl /litre "

"

*.

"

*.

. .

Results and Discussions The possibility that PIT would depend upon phase ratio was indicated when PITs obtained from the measurements in the spinning drop tensiometer did not correspond exactly to those made by the conductivity measurements. The results show that PIT increases as the proportion of oleic phase increases. This is contrary to the findings of Balzer and Kosswig (1979) who reported smaller changes with the opposite slope. Arai (1965) reports the same effect as Balzer and Kosswig (op.cit.)

73

Line D '

PIT

60

Line C Line B

"C

50

40

Line A 30 20 10

20

30

40

50

Volume I hydrocarbon Figure 9: Variation of PIT with phase ratio.

6.

Variation of PIT with Ethylene Oxide (eo) content of surfactant

Tests

-

PITS were measured using a mixture of pure normal ,alkanes,EACN 7.5 with 30 g NaCl/litre brine containing 50 g of surfactant/litre. The surfactants used were Sapogenate T80,TlOO,T110 and T130 which contain (nominally) 8, 10, 11 and 13 ethylene oxide units respectively. Intermediate eo contents were obtained from mixtures of the adjacent surfactants as supplied and were calculated on a molar basis.

Results and Discussion

-

The results presented in Fig 10 show a linear relationship between PIT and the number of eo units per molecule. The deviation from linearity above eo 11 is probably due to evaporation of the hydrocarbon during the test. The change The findings are in agreement with those of Bourell et a1,(1980). in PIT is explained by the increased hydrophilic properties with increased eo content (Shinoda, 1965). The Arkopal series of surfactants probably exhibits a similar trend but only These gave PITS of two have been tried i.e. NO60 ( 6 eo's) and N080(8 eo's). about 30C and 70-75OC respectively at a concentration of 50 g /litre in the same brine/hydrocarbon system. The effect of the number of eo units is greater with the Arkopal series than the Sapogenates. Where a surfactant contains a spectrum of eo contents, selective adsorption by the reservoir rock may change its effective eo value and thus affect the PIT of the system.

74

PIT "C.

tion = 50 g

-

7.5

'Surfactant ethylene oxide number. Figure 10:

7.

Variation of PIT with surfactant ethylene oxide number

Variation of IFT with temperature

Tests Interfacial tension measurements were made between the upper and lower phases obtained from mixtures whose PIT'S had been determined in an attempt to confirm the presence of an IFT minimum at fhe PIT. Tests were performed with the following mixtures. ~~~

Concentration

Brine

T80

10 g /litre

T80

.

30 gm NAClf litre

Surfactants

NO60

1.

. .

I.

1.

*.

.

I.

*I

Hydrocarbons Phase ratio

PIT

Results Fig 11

n hexane

4: 1

39

**

n octane

4: 1

49.5

Fig 12

*'

Crude EACN =10 '

5: 1

23.5

Fig 13

Results and Discussion The results obtained are shown in Figs 11 to 13. The PITS obtained from conductivity measurements are included in the above table. Repeat determinations of 1.F.T. were usually found to agree within 2 5%. Figs 11 and 12 indicate that a minimum does occur at the PIT but that more than one 'minimum' can occur. This is supported by conductivity traces made during PIT measurements and is probably due to a proportion of surfactant having a different number of eo units than the stated nominal value. The equipment available only allowed for the transfer of phases into the tensiometer at room temperature. Measurements were made at various temperatures after heating

75

Oil : n-hexane Brine : 30g /litre NaCl Surfactant : Sapogenate T80, 1Og /litre

dynes/cm

30

34

38

42

46

Temperature, 'c Figure 11: Variation of IFT with temperature.

Oil : n-octane Brine : 30 g /litre NaCl Surfactant : Sapogenate T80,log /litre.

38

42

46

50

54

Temperature OC Figure 12:

Variation of IFT with temperature.

from room temperature. As one increases the temperature of the sample tube a third phase (microemulsion) begins to develop as the equilibrium is disturbed. In order to make meaningful measurements the middle phase is separated from the remaining oil drop. This was achieved with some difficulty especially in the case of colourless oils. Ideally, equilbratlon, sampling and measurements should be carried out at the same temperature.

16

d y n e s ; : 10-2

1

Oil : Dead crude Brine : 30 g /litre NaCl Surfactant : Arkopal N 6 0 , l O g /litre

J

lo-?

10-4

15

Figure 13:

20

25

30

Temperature ,OC Variation of IFT with temperature

Adsorption of Surfactants Tests This section describes the results obtained for adsorption of Hostapal BV on reservoir material in various states of disaggregation. Although work on Hostapal BV was terminated, (because optimal salinity falls outside the range of our interest), the results showed some of the-limitationsof static adsorption tests. Samples of reservoir rock were taken from cores and crushed in a ball mill 2 5 g of sample were taken and until the powder passed 180 sieve. equilibrated with 50 cm3 o various concentrations of Hostapal BV in The suspension was stirred constantly for 4 distilled water or sea-water. hours 40OC. The aqueous portion ws then decanted and centrifuged for 30 minutes, by which time, the supernatant liquid was clear. Analysis of this Hence the liquid then gave the remaining concentration of Hostapal BV. amount abstracted by the solids was calculated.

r

soo51 I

AdsorDtive

Adsorptive capacity,A

e o o 5 1

0.5 1 .o 0.5 1.0 Equilibrium concn., c,g / I Equilibrium concn,c,g /1 Figure 1 4 : Adsorption of Hostapal BV Figure 15: Adsorption of Hostapal BV Onto reservoir rock, Sample 1. onto reservoir rock,Sample 2.

Results and Discussion The tests performed are listed below and the results presented in Figs 14 to 18. Table 2 shows a typical sets of results. er a ."

water

0.5 1 .o Equilibrium concn., c,gr /I. Figure 16:

Adsorption of Hostapal BV onto reservoir rock,Sample 3.

TABLE 2 (SAMPLE 3) Initial surfactant concentration g /litre

Final (equilibrium) surfactant concentration,C g /litre

Adsorptive capacity A, g surfactantlg rock

0.25

0.0078

0.00048

0.50

0.033

0.00092

1.0

0.098

0.0018

1.75

0.164

0.0033

2.0

0.184

0.0036

2.5

0.193

0.0046

3.3

0.352

0.0059

5.0

0.957

0.0080

18

Adsorptive capacity A, g lg

.003

I

i

0.5

Figure 17:

-4

I

1 .o Equilibrium concn., c, g 11

Adsorption of Hostapal BV onto reservoir rock, sample 4.

-

1nA

-5

-

-6

-

-7

-

1

I

I

I

In c Figure 18:

Data from Figure 16 plotted logarithmically

79

All the figures show the tendency for A to tend towards a constant for a given Portions of Sample 3 (Fig 16) sample as the equilibrium concentration increases. were also equilibrated with the surfactant in seawater and the results appear to Sample 3 has similar permeability and show a much higher adsorptive capacity. porosity characteristics to the other samples. The curves have the same general form as the classical adsorption isotherms. A= adsorptive capacity A = Kc where c= final concentration K and n are constants or In A = In K + In C The data in Table 2 (sample 3 ) are plotted as In A against In C in Fig 18. There are indications in Fig 1 4 and 15 that adsorption may be proceeding in layers. A qualitative test of the effect of particle size on the equilibrium adsorption of surfactant was performed in a similar manner to those described above. The results obtained are shown in Table 3. Table 3 A g lg

-lng Chromosorb S packing and t h e thermal c o n d u c t i v i t y d e t e c t o r (Hewlett-Packard Instrument). Divalent Ions

- I o n i c Flame Spectrophometry - Chelatometric t i t r a t i o n

(Perkin-Elnrer

Instrument)

E i T e r i n e n t a l Procedures Berea a r e s (2.5 x 2.5 cm2 c r o s s - s e c t i o n ) were c u t t o 30 CGI l e n g t h s and d r i e d i n a vacuum oven a t ll0'C f o r 24 hours. They were t h e n s a t u r a t e d under vacuum w i t h degassed b r i n e , o i l flooded t o a connate water s a t u r a t i o n , and t h e n waterf l o o d e d t o a r e s i d u a l o i l s a t u r a t i o n u s u a l l y i n t h e range o f 30 t o 35% o f pore volume.

A s u r f a c t a n t s l u g w a s i n j e c t e d i n t o t h e cores a t r e s i d u a l o i l s a t u r a t i o n

a t c o n s t a n t rates of 2 ml/hour so that t h e a p p a r e n t f r o n t a l advance rate of the f l u i d d i d not exceed 30 cmlday. I n o r d e r t o eliminate e v a p o r a t i v e l o s s e s of v o l a t i l e components, t h e o u t l e t l i n e w a s f e d through a s y r i n g e n e e d l e p i e r c i n g t h e septum o f a c o l l e c t i o n tube. Synchronized movements of a f r a c t i o n c o l l e c t o r and t h e s y r i n g e n e e d l e were automated, t h u s a l l o w i n g u n i n t e r r u p t e d f l o o d i n g i n experiments l a s t i n g s e v e r a l days. S u r f a c t a n t f l o o d s were performed a s follows. During t h e s u r f a c t a n t flood and t h e subsequent b r i n e flood (no polymers o r v i s c o s i t y improving a g e n t s have been used i n t h i s work), t h e samples were c o l l e c t e d a t two-hour i n t e r v a l s which r e s u l t e d i n 5 t o 10% o f pore volume being c o l l e c t e d i n each sample. E f f l u e n t f l u i d s were t h e n analyzed f o r o i l , b r i n e , s u r f a c t a n t , and c o s u r f a c t a n t c o n t e n t . When t h e production of o i l , s u r f a c t a n t , and c o s u r f a c t a n t ceased, s e v e r a l pore volumes of a hydrocarbon phase were i n j e c t e d i n t o t h e c o r e i n a n a t t e m p t t o recover s u r f a c t a n t s trapped i n o i l remaining i n t h e c o r e . Liquid produced by t h i s hydrocarbon flood was analyzed f o r a l l components and recovered s u r f a c t a n t s were considered t o be s u r f a c t a n t s trapped i n t h e hydrocarbon phase d u r i n g t h e s u r f a c t a n t flood. I n some f l o o d s , o c t a n e w a s d i s p l a c e d by nonane o r decane so that a complete displacement of r e s i d u a l cil could be v e r i f i e d and a material balance 011 o i l c l o s e d . A f t e r a l l s u r f a c t a n t s trapped i n t h e o i l were d i s p l a c e d , t h e c o r e w a s flooded w i t h a s t r o n g s o l v e n t such a s e t h y l a l c o h o l o r i s o n r o p y l a l c o h o l i n a mixture w i t h b r i n e t o remove a l l remaining s u r f a c t a n t s from t h e core. This r e q u i r e d i n j e c t i o n o f 5 t o 1 0 pore volumes and t h e material balance on s u r f a c t a n t c l o s e d u s u a l l y between 90 t o 100% of i n j e c t e d s u r f a c t a n t . S u r f a c t a n t removed from t h e c o r e by a l c o h o l s o l v e n t s is considered t o be s u r f a c t a n t adsorbed on t h e rock d u r i n g t h e f l o o d . The f l o o d i n g sequence d e s c r i b e d above a l l o w s a d e t e r m i n a t i o n of t h e o v e r a l l s u r f a c t a n t r e t e n t i o n ( i . e . t h e amount o f s u r f a c t a n t l o s t d u r i n g t h e f l o o d ) from t h e d i f f e r e n c e between t h e amounts o f s u r f a c t a n t i n j e c t e d and recovered d u r i n g t h e s u r f a c t a n t and subsequent b r i n e i n j e c t i o n . The hydrocarbon flood g i v e s a amount of s u r f a c t a n t trapped i n t h e o i l phase due t o unfavorable phase behavior, and t h e adsorbed s u r f a c t a n t recovered i n t h e f i n a l s o l v e n t f l o o d completes t h e m a t e r i a l balance. This procedure i m p l i c i t l y assumes t h a t t h e hydrocarbon phase does n o t remove adsorbed s u r f a c t a n t from t h e core. This assumption was v e r i f i e d i n t h e following way: X 75X PV of 3% s u r f a c t a n t s l u g was i n j e c t e d i n a b r i n e - s a t u r a t e d c o r e and followed w i t h t h r e e a d d i t i o n a l pore volumes of b r i n e . S u r f a c t a n t l o s s was determined a t 0.6 mg/g. Then, o c t a n e was continuously i n j e c t e d and an e f f l u e n t was analyzed f o r s u r f a c t a n t s . A f t e r w r e than 5 P P o f throughput o n l y 0.06 mg of s u r f a c t a n t p e r one gram of rock w a s recovered. This i n d i c a t e s that a minor amount of adsorbed s u r f a c t a n t can be recovered by t h e o i l , and that t h e bulk of adsorbed s u r f a c t a n t w i l l n o t be desorbed. However, even c h i s small amount of adsorbed s u r f a c t a n t recovered by o i l is s u f f i c i e n t t o q u a l i f y t h i s method f o r d e t e r m i n a t i o n of trapped s u r f a c t a n t as q u a l i t a t i v e .

I n g e n e r a l , t h e b e s t m a t e r i a l balances were obtained i n f l o o d s w i t h TRS 10-80, a n d u s u a l l y t h e most i n a c c u r a t e results were obtained w i t h PDM 337. It seems reasonable t o suggest t h a t a degree of s u r f a c t a n t s o l u b i l i t y i n a l c o h o l s o l v e n t s could e x p l a i n t h i s t r e n d , however, no measurements of s u r f a c t a n t s o l u b i l i t i e s have been made.

109 I n o r d e r t o avoid experimental complications due t o t h e p o s s i b l e p r e c i p i t a t i o n of s u r f a c t a n t s by d i v a l e n t i o n s , sodium c h l o r i d e b r i n e s were used throughout t h i s study. Berea c o r e s were p r e f l u e h e d w i t h 5 t o 7 pore volumes of sodium c h l o r i d e b r i n e s i n o r d e r t o d i s p l a c e most of t h e exchangeable d i v a l e n t ions. Even w i t h t h e s e p r e c a u t i o n s , t h e r e i s a n i n c r e a s e i n d i v a l e n t c a t i o n c o n c e n t r a t i o n i n t h e propagating s u r f a c t a n t s l u g (Figure 3). I n our experiments, t h e s e l e v e l s have n o t exceeded 90 ppm. S e p a r a t e phase behavior experiments i n d i c a t e d that such low d i v a l e n t i o n c o n c e n t r a t i o n s a f f e c t e d t h e phase behavior o f s u r f a c t a n t s o l u t i o n s i n that a minor s h i f t toward upper phase microemulsions w a s n o t i c e d , but no s u r f a c t a n t p r e c i p i t a t i o n was observed.

loot

7 2

OO

1

PORE VOLUME F i g u r e 3:

DivaleDt Ions Content i n t h e E f f l u e n t ( I n j e c t i o n of 75% PV of 2% 110.5 TRS 10-8OlSBA i n 1%N a C l )

It should be noted h e r e that t h i s procedure f o r d i f f e r e n t i a t i n g trapped s u r f a c t a n t i n t h e hydrocarbon phase from t h e adsorbed s u r f a c t a n t is not a p p l i c a b l e t o a l l s i t u a t i o n s . For example, i n s u r f a c t a n t systems i n which t h e s u r f a c t a n t d i s t r i b u t i o n c o e f f i c i e n t is not a t extreme l e v e l s ( i . e . K = [ ( c s ) o i l / ( c s ) b r i n e l f o r upper phase microtends t o zero f o r lower phase microemulsions o r K + emulsions) t h e c h a s e b r i n e would b l e e d s u r f a c t a n t from t h e o i l phase and no s u r f a c t a n t would e v e r be found trapped i n the o i l .

-

RESLZTS Ah?) DISCUSSION

S t u d i e s of o i l recovery e f f i c i e n c y and s u r f a c t a n t r e t e n t i o n i n d i c a t e that b e t t e r , performing p r o c e s s e s a r e u s u a l l y accompanied by lower s u r f a c t a n t r e t e n t i o n even though lower r e t e n t i o n does n o t n e c e s s a r i l y mean higher o i l recoverp.14 Since our experimental technique can d i s t i n g u i s h between s u r f a c t a n t l o s s e s due t o a d s o r p t i o n and l o s s e s due t o unfavorable phase behavior, i t Qas thought t o be of i n t e r e s t t o perform s e v e r a l series of similar experiments and then o b s e r v e how t h e s e i n d i v i d u a l c o n t r i b u t i o n s t o t o t a l s u r f a c t a n t r e t e n t i o n are affected

.

110 E f f e c t of C o s u r f a c t a n t on S u r f a c t a n t R e t e n t i o n I t has been shown t h a n , i n systems c o n t a i n i n g no o i l ( i . e . systems c o n t a i n i n g o n l y s u r f a c t a n t , c o s u r f a c t a n t , and b r i n e ) , poor s u r f a c t a n t solub i l i t y may r e s u l t i n very high s u r f a c t a n t r e t e n t i o n i n Berea c o r e s . An a d d i t i o n a l c o s u r f a c t a n t helped t o d i s s o l v e t h e s u r f a c t a n t i n t h e b r i n e and t h e s u r f a c t a n t r e t e n t i o n w a s reduced by one o r d e r of m a g n i t ~ d e . ~I n systems c o n t a i n i n g o i l , poor s u r f a c t a n t s o l u b i l i t y may n o t r e s u l t i n s u r f a c t a n t molecule a g g r e g a t i o n b u t may l e a d t o a change in phase behavior i n which c a s e t h e s u r f a c t a n t d i s s o l v e s i n t h e upper hydrocarbon phase. I n that case t h e s u r f a c t a n t r e t e n t i o n would increase even though s u r f a c t a n t a d s o r p t i o n may e i t h e r not change a t a l l o r may even d e c r e a s e .

The PDM 337 s u r f a c t a n t w i t h secondary b u t y l a l c o h o l . a s a c o s u r f a c t a n t w a s s e l e c t e d f o r t h i s p a r t of t h e study. An i n c r e a s i n g c o s u r f a c t a n t c o n t e n t makes t h e s u r f a c t a n t s l i g h t l y -re b r i n e s o l u b l e and t h e phase behavior changes from a n upper t o a middle phase (Figure 4 ) .

SURFACTANT CONTAINING PHASE

VO.1

F i g u r e 4:

1/0.5

1/1.0

1/50

Phase Behavior of 3X PDM 337 S u r f a c t a n t (80120 volumetric r a t i o of 1.5% k C 1 / octane f o r d i f f e r e n t surfactantlsecondary butyl alcohol r a t i o s )

S u r f a c t a n t l c o s u r f a c t a n t r a t i o s of l:O.l, 1:0.5, 1:1, and 1:s were i n j e c t e d i n f o u r f l o o d s on Berea c o r e s t h a t had been waterflooded t o r e s i d u a l o i l s a t u r a t i o n s . The e f f l u e n t s were analyzed f o r s u r f a c t a n t , c o s u r f a c t a n t and o i l c o n t e n t . Typical examples of t h e d a t a c o l l e c t e d a r e shown i n F i g u r e s 5 t o 7 and t h e r e s u l t s of t h e s e f l o o d s are summarized i n Table 1. This series of f l o o d s c l e a r l y shows a l l of t h e d i f f i c u l t i e s which can be encountered when an a t t e m p t is made t o compare a d s o r p t i o n d a t a obtained from d i f f e r e n t displacement experiments.

111

PORE VOLUME Figure 5:

Surfactant and Cosurfactant Breakthrouzh Curves (Flood 112: 50% PV I n j e c t i o n o f 3%, 1:5 PDM 337lSBA i n 1.5% NaCl Brine)

6

-

0 MICROEMULSION f$jOIL

0 BRINE 5

4

s

Y

g3 3 J

0

' 2

I

0 0

I

2

PORE VOLUME Figure 6 :

Effluent Phase Behavior (Flood 112)

3

112

0.3

w

z u

k

0.2

LL

0

z

0 I-

2

0.1

K LL

0.0

PORE VOLUME F i g u r e 7:

F r a c t i o n a l Flow of O i l (Flood 1 1 2 )

Oil Recover).

Surfacuat co-surfacunc

Surfacunr Refention

u~uhtratio

4 1

lJO.1

1.2

110.5

1.2

111

1.0

115

0.7

losses Due to Adsorption ?hse BeUhvior

ulr

-

-

(c/c0)-

I MI?

Ull

z

(SorIf-

z

(foul2

52

15

17

1.2

.02

66

10

19

1.0

0.10

85

5

22

0.7

0.21

70

8

21

1.2

0

F i r s t , i t should be noted that, i n t h e f l o o d s w i t h s u r f a c t a n t r a t i o s of 1 : O . l and 1:0.5, e s s e n t i a l l y no s u r f a c t a n t is contained i n t h e e f f l u e n t . T h i s means t h a t n o t enough s u r f a c t a n t was i n j e c t e d t o s a t i s f y t h e a d s o r p t i o n c a p a c i t y o f t h e r o c k and t h a t t h e s u r f a c e s n e a r t h e end of the c o r e are probably n o t completely adsorbed w i t h s u r f a c t a n t . Floods w i t h the 1:l and 1:5 s u r f a c t a n t l c o s u r f a c t a n t r a t i o s have l e d t o t h e production of some s u r f a c t a n t ,

113 b u t t h e c o n c e n t r a t i o n peaks a t t h e c o r e o u t l e t s a r e s u b s t a n t i a l l y d i f f e r e n t

from each o t h e r and, consepuently, t h e a d s o r p t i o n v a l u e s f o r t h e two d i f f e r e n t average s u r f a c t a n t c o n c e n t r a t i o n s a r e n o t d i r e c t l y comparable. A l s o , as Figure 8 shows, t h e normalized r a t i o s of s u r f a c t a n t and c o s u r f a c t a n t concent r a t i o n s are q u i t e d i f f e r e n t f o r t h e two f l o o d s . Therefore, even though i t may b e tempting t o suggest t h a t t h e r e is enough d a t a i n Table 1 t o a s c e r t a i n t h e dependence of s u r f a c t a n t a d s o r p t i o n on a l c o h o l c o n t e n t , a c l o s e r l o o k shows that a comparison o f s u r f a c t a n t a d s o r p t i o n f o r t h e f o u r d i f f e r e n t systems cannot be nade w i t h o u t conducting a d d i t i o n a l experiments. The l a s t three c o l u m s of Table 1 c o n t a i n t h r e e i n d i c a t o r s o f t h e o i l recovery of each s u r f a c t a n t f l o o d . Results show that e f f i c i e n c y i n i t i a l l y i n c r e a s e s w i t h c o s u r f a c t a n t c o n t e n t , h w e v e r , t h e f i n a l f l o o d performs less e f f i c i e n t l y t h a n t h e p r e v i o u s one. This confirms a conclusion r e p o r t e d p r e v i o u s l y that lower s u r f a c t a n t r e t e n t i o n does n o t n e c e s s a r i l y l e a d t o t h e b e s t o i l recovery e f f i c i ~ n c y . ' ~

I

? I

I

5.0

I

I I I

4.0 Y

I I

,*olF; I I

I

0.0 0

Figure 8:

0.5

2.0 PORE VOLUME

1.0

3.0

>!ormalized C o s u r f a c t a n t / S u r f a c t a n t R a t i o s a t Core O u t l e t s

The E f f e c t of Slug S i z e on S u r f a c t a n t R e t e n t i o n The A similar series o f experiments w a s performed w i t h TRS 10-80. s u r f a c t a n t l c o s u r f a c t a n t r a t i o w a s v a r i e d from 1:O.S t o 1 : l O . Typical flooding r e s u l t s a r e shown i n F i g u r e s 9 t o 11, and Table 2 s u m a r i z e s t h e d a t a obtained i n t h e s e f i v e floods.

114

L

0 SURFACTANT

A

COSURFACTANT

1

PORE VOLUME Figure 9:

Surfactant and Cosurfactant Breakthrough Curves (Flood 69: 75% PV Injection of 2%, 1:0.5 TRS 10-80/ SBA in 1.0%NaC1)

0

2

PORE VOLUME Figure 10:

Effluent Phase Behavior

4

115

0.3

1

0 0.2 LL

0

z 2

5a

0.1

4

0.0 PORE VOLUME Figure 11:

Table 2:

Surf acUnc cesurfaeunt

Fractional Flow of O i l (Flood 69)

Summary of Flooding Results with 3% TRS 10-80/SBA i n 1.0% NaCl/Octane System

W

Injected

Retantien

x

nyh

Trapped Surfacunt =&It

Wl

1110

80

0.35

0.2

.1s

.so

115

94

0.50

0.4

0.10

0.95

113

150

0.2

-

0.15

1.0

113

75

0.3

0.1

0.20

0.85

Ill

75

0.5

0.48

0.8

110.5

75

0.6

0.55

1.0

-

Adsorption

(dc,),

116 It is i n t e r e s t i n g t o compare t h e s u r f a c t a n t r e t e n t i o n v a l u e s observed i n f l o o d s using a s u r f a c t a n t / c o s u r f a c t a n t r a t i o o f 1 : 3 i n which d i f f e r e n t s i z e s l u g s of i d e n t i c a l composition were i n j e c t e d . A 150% PV s l u g w a s s u f f i c i e n t l y l a r g e t o enable t h e e f f l u e n t c o n c e n t r a t i o n t o r e a c h t h e l e v e l of t h e i n j e c t e d concentration. The i n j e c t i o n volume i n t h e o t h e r comparable f l o o d w a s halved so t h a t t h e e f f l u e n t c o n c e n t r a t i o n reached o n l y 85% o f t h e i n j e c t e d concent r a t i o n . While t h e r e is a d i f f e r e n c e i n r e t e n t i o n , t h e d i f f e r e n c e i n adsorpt i o n i s smaller. This apparent discrepancy can b e explained i n terms o f t h e amount of o i l trapped i n t h e hydrocarbon phase. In t h e f i r s t f l o o d , t h e r e is no trapped s u r f a c t a n t , w h i l e i n t h e second about one-third of the s u r f a c t a n t l o s s i s due t o unfavorable phase behavior. T h i s example shows c l e a r l y that i n f o r n a t i o n r e f l e c t i n g o n l y o v e r a l l s u r f a c t a n t r e t e n t i o n may be very misleading.

Another series o f experiments w a s performed w i t h t h e pure Texas #I s u r f a c t a n t . F i g u r e s 12 t o 1 4 show a n example of t h e experimental d a t a and Table 3 p r e s e n t s a summary of t h e r e s u l t s . I n t h i s c a s e , even though b o t h o v e r a l l r e t e n t i o n and a d s o r p t i o n i n c r e a s e w i t h i n c r e a s i n g s l u g s i z e , they do so a t d i f f e r e n t rates. Again, i t is t h e 106s due t o t h e phase behavior which is a f f e c t e d more by t h e s i z e o f t h e s u r f a c t a n t s l u g .

0 SURFACTANT

A COSURFACTANT

/ 0.8 '*OI

p'

\ \ \

0.6

c'co 0.4

0.2 0.0 0

I

2

3

PORE VOLUME Figure 12:

S u r f a c t a n t and Cosurfactant Breakthrough Curves (Flood 99: 100% PV I n j e c t i o n of 2X, 1:6 Texas
117

0 MXROEMLILSION fQOIL

6

BRINE

5

-

- 4 E Y

g 3 J

0

>

2

1

I

L

0 0

Figure 13:

0.31

I

PORE VOLUME

Effluent Phase Behavior (Flood 99)

nn

PORE VOLUME Figure 14:

Fractional Flow of O i l (Flood 99)

118 Table 3:

Summary o f Flooding Experiments with 2 X , 1:6 Texas $l/n-Propanol in 1.5% ?;aCl/Octane I

011 Recovery

PV Injected

Rerention

bsses h e LO Phase Behavior

Adsorption 4

6

(c/co)ux

8

(fol*

ZROIP

(Sor)fLnal

x

x

2

22

.6/6

d

0.50

0.7

0.24

0.4

0.05

38

18

0.75

1.0

0.5

0.5

0.25

55

14

22

1.0

1.1

0.14

0.54

0.60

74

7

27

Experiments have beer? performed t o e v a l u a t e t h e e f f e c t o f c o s u r f a c t a n t p r e s e n c e w i t h i n t h e chase b r i n e o n t h e r e t e n t i o n o f s u r f a c t a n t s . Table 4 summarizes t h e r e s u l t s . Table 4:

Summary of Flooding R e s u l t s w i t h 3%, 1:1.75 PDM 337lSBA i n 1.5% NaCl/Octane System

Flood

Flood

I

Oewription

Retention WlK

lasses Due co M i o r p t i o n (clco)Phase k h v i o r ~

oil i n the core

86A

ti0

1.2

85

Surfacunr slug o n l y

0.8

82

Surfacunr

followed by one PV of 3Z S M in brlne 83

w/a

ma18 ~~~~~

~~~

~

1.2

0.65

0.15

0.5

1.0

0.5

0.20

0.3

0.5

0.8

0.L

0.4

1.0

79

5

36

I

s.U

am 85 bur at SLoyEll INJJLCTION

RATE

Flood 86A c o n t a i n e d no o i l , and a d s o r p t i o n of 1 . 2 mglg w a s observed. Flood 85 contained o i l a t r e s i d u a l o i l s a t u r a t i o n and a d s o r p t i o n of 0.5 mgfg was determined. I n a d d i t i o n , t h e r e was a l o s s of 0.15 mgfg s u r f a c t a n t due t o p h a s e behavior. The procedure used i n Flood 82 was t h e same a s f o r Flood 85 except t h a t i n Flood 82 t h e one PV o f t h e b r i n e t h a t followed t h e s u r f a c t a n t s l u g cont a i n e d 3% secondary b u t y l a l c o h o l . A s e x p e c t e d , t h e r e t e n t i o n and a d s o r p t i o n l e v e l s a r e both lower, however, t h e amount o f s u r f a c t a n t trapped in t h e oil phase d i d n o t change a p p r e c i a b l y . The o i l r e c o v e r y w a s b e t t e r a s t h e f i n a l o i l s a t u r a t i o n i s lowered from 1 4 % PI’ i n Flood 85 t o 5% PV i n Flood 82. Another i n t e r e s t i n g a s p e c t observed i n t h i s experiment was t h e s h a p e o f t h e s u r f a c t a n t breakthrough c u r v e s ( s e e F i g u r e 15). Even though t h e f l o o d s were r u n a t t h e same i n j e c t i o n rates, t h e shape of t h e curve in Flood 82 g i v e s t h e i m p r e s s i o n o f a much h i g h e r l e v e l of d i s p e r s i o n t h a n t h a t i n Flood 85. S e v e r a l e x p l a n a t i o n s are p o s s i b l e , b u t t h e l i m i t e d d a t a a v a i l a b l e do n o t a l l o w f o r a unique i n t e r p r e t a t i o n and

119 t h e r e f o r e none i s o f f e r e d . However, i t i s observed t h a t d a t a such a s t h e s e should be o f concern t o people d e a l i n g w i t h numerical models f o r chemical f l o o d i n g s i n c e t h e d a t a s u g g e s t t h a t t h e chemical composition of t h e s u r f a c t a n t s l u g may s u b s t a n t i a l l y a f f e c t t h e a p p a r e n t d i s p e r s i o n .

t-

0

I

I

2

3

4

PORE VOLUME F i g u r e 15:

S u r f a c t a n t Breakthrough Curves

A r e c e n t l y p u b l i s h e d paper d e s c r i b i n g s t a t i c a d s o r p t i o n e x p e r i m e n t s , among o t h e r r e s u l t s , i n d i c a t e d t h a n a n attainment of adsorption equilibrium required a l m o s t two weeks o f c o n t a c t between a s u r f a c t a n t s o l u t i o n and a s o l i d a d s 0 r b e n t . l An a t t e m p t has been made t o f i n d o u t i f similar phenomenon t a k e s p l a c e d u r i n g d i s p l a c e m e n t t e s t s i n Berea c o r e s . T h e r e f o r e , Flood 85 w a s r e p e a t e d b u t a t a n i n j e c t i o n r a t e t h a t w a s t e n times lower and e q u a l t o a n a p p a r e n t f r o n t a l v e l o c i t y of 3 cm/day. It took more t h a n 1 0 d a y s f o r t h e surf a c t a n t s l u g t o p r o p a g a t e through t h e c o r e . The o i l recovery was b e t t e r and a n a d d i t i o n a l 4% PV o f o i l was recovered which i s i n agreement w i t h t h e p r e v i o u s l y p u b l i s h e d d a t a o n t h i s t y p e of w p e r i m e n t . 1 5 The r e t e n t i o n l e v e l w a s t h e s a m e b u t t h e l o s s o f s u r f a c t a n t by t h e phase t r a p p i n g mechanism i n c r e a s e d s u b s t a n t i a l l y w h i l e t h e a d s o r p t i o n l o s s w a s s l i g h t l y lower. It t h e r e f o r e seems r e a s o n a b l e t o s u g g e s t t h a t t h e a d d i t i o n a l r e s i d e n c e time f o r t h e s u r f a c t a n t i n t h e c o r e allowed i t t o be more c o n c e n t r a t e d i n t h e o i l phase, b u t t h a n a n i n c r e a s e i n a d s o r p t i o n w a s n o t observed. I t has been noted b e f o r e t h a t , f o r s u r f a c t a n t systems which a r e n o t a t o p t i m a l f o r m u l a t i o n ( i . e . n o t a t a middle phase c o n f i g u r a t i o n ) , t h e time r e q u i r e d f o r a t t a i n m e n t o f phase e q u i l i b r i u m may b e s u b s t a n t i a l . Our experiments e n a b l e t h e s u g g e s t i o n that t h i s p r o c e s s ofs u r f a c t a n t r e d i s t r i b u t i o n among t h e p h a s e s may be more r e s p o n s i b l e f o r t h e time dependence o f r e t e n t i o n t h a n is t h e slow a t t a i n m e n t o f a d s o r p t i o n e q u i l i b r i u m a t the solid-liquid interface. T h i s s u g g e s t i o n i s supported by p r e v i o u s l y r e p o r t e d r e s u l t s o n a d s o r p t i o n measurements i n b a t c h experiments i n which, i n t h e absence of o i l , t h e a d s o r p t i o n always reached e q u i l i b r i u m w i t h i n 24 hours.4

120 SUIPlARY

Based upon more than one hundred displacement experiments w i t h t h r e e t y p e s of s u r f a c t a n t s i n Berea c o r e s , t h e following conclusions may be made:

1.

Thermodynamically v a l i d s u r f a c t a n t a d s o r p t i o n isotherms should be determined i n b a t c h experiments.

2.

Displacement experiments y i e l d s u r f a c t a n t r e t e n t i o n v a l u e s which i n v o l v e averaging s e v e r a l v a r i a b l e s . I f any theory developed f o r a d s o r p t i o n is a p p l i e d t o r e t e n t i o n d a t a obtained from displacement experiments, t h e o t h e r causes of s u r f a c t a n t l o s s e s must be accounted f o r so o n l y a d s o r p t i o n d a t a are used.

3.

Experimental procedures that permit d i f f e r e n t i a t i n g between s u r f a c t a n t l o s s e s due t o a d s o r p t i o n and t h o s c due t o unfavorable phase behavior have been developed and t e s t e d .

4.

Pure s u r f a c t a n t (Texas # 1 ) , s y n t h e t i c s u l f o n a t e (PDY 3 7 ) , and petroleum s u l f o n a t e (TRS 1@-80) g i v e comparable r e s u l t s f o r r e t e n t i o n and a d s o r p t i o n i n Berea cores.

5.

Adsorption of s u r f a c t a n t s can be reduced by t h e s d d i t i o n o f low molecular weight a l c o h o l s (sec-butyl a l c o h o l , n-propano'.?

6.

For t h e t h r e e s u r f a c t a n t s s t u d i e d , a d s o r p t i o n l e v e l s d i d not exceed 1.2 mg/g. I f t h e o v e r a l l r e t e n t i o n i s h i g h e r , s u r f a c t a n t l o s s e s due t o unfavorable phase behavior o r some o t h e r mechanism should be suspected.

.

ACKNOWLEDGEMENTS The a u t h o r wishes t o acknowledge t h e a s s i s t a n c e and d e d i c a t i o n of L a u r i e Baxter and G a i l Parker who performed t h e p r e c i s e experiments necessary f o r t h i s paper. S i n c e r e l y acknowledged a r e Bev Moore and G a i l Donaldson f o r t y p i n g t h i s manuscript.

REFERENCES

1.

MEYERS, K. 0. and SALTER, S. J.; "The E f f e c t of Oil-Brine R a t i o on S u r f a c t a n t Adsorption from Microemulsion", paper SPE 8989 presented a t t h e SPE 55th Annual F a l l Meeting, Dallas, Texas (September 21-24, 1980).

2.

CELIK, M. S., GOYAL, A., MANEV, E. and SOMASUNDURAN, P.; "The Role of S u r f a c t a n t P r e c i p i t a t i o n and R e d i s s o l u t i o n i n t h e Adsorption of S u l f o n a t e on Minerals", paper SPE 8263 presented a t t h e SPE 5 4 t h Annual F a l l Meeting, Las Vegas, Nevada, (September 23-26, 1979).

3.

KRUMRINE, P. A., CAMPBELL, T. C. and FALCONER, J. S.; "Surfactant Flooding I: The E f f e c t of A l k a l i n e Additives on IFT, S u r f a c t a n t Adsorption, and Recovery Efficiency", paper SPE 8298 p r e s e n t e d a t the 5 t h Symposium on O i l f i e l d and Geothermal Chemistry, Stanford, C a l i f o r n i a (May 28-30, 1980).

1 21 4.

NOVOSAD, J.; "Adsorption of P u r e S u r f a c t a n t and Petroleum Sulfonate a t t h e Solid-Liquid I n t e r f a c e " , P r o c e e d i n g s o f t h e 3 r d I n t e r n a t i o n a l Conference on S u r f a c e and C o l l o i d S c i e n c e s h e l d i n Stockholm, Sweden, (August 20-25, 1 9 7 9 ) , Plenum P u b l i s h i n g , New York (1981).

5.

GLOVER, C. J., PUERTO, M. C., MAERTER, J. M. and SANDVIK, E. I.; " S u r f a c t a n t Phase Behavior and R e t e n t i o n i n Porous Media", (June 1979) SPEJ 2, 183-193.

6.

"A h'ew I n t e r p r e t a t i o n TROGUS, F. J . , SCHECHTER, R. S. and WADE, W. H.; of A d s o r p t i o n Maxima and Minima", (June 1979) J. C o l l o i d S c i . 70, 293-305.

7.

GALE. W. W. and SANDVIK. E. I.: Petroleum S u l f o n a t e Composition 191-199.

8.

SOMASUNDARAN, P. and HANNA, H. S.; "Adsorption of S u l f o n a t e s on Reservoir Rocks", p a p e r SPE 7059 p r e s e n t e d a t t h e 5 t h Symposium on Improved Methods f o r O i l Recovery h e l d i n Tulsa, Oklahoma,(April 16-19, 1978).

9.

"Adsorption from Liquid SIRCAR, S., NOVOSAD, J. and MYERS, A. L.; M i x t u r e s on S o l i d s : Thermodynamics of Excess P r o p e r t i e s and T h e i r Temp e r a t u r e C o e f f i c i e n t s " , (May 1572) I & EC Fundamentals ll, 249-254.

" T e r t i a r v S u r f a c t a n t Floodinn: S t u d i e s " , (1973) SPEJ

- Efficac;

2,

10.

GILLILAND, W. E. and CONLEY, F. R. ; " S u r f a c t a n t Waterflooding".

11.

FRANCES, E. I . , DAVIS, H. T., MILLER, W. G . and SCRIVEN, L. E.; "Phase Behavior of a P u r e Alkyl A r y l S u l f o n a t e S u r f a c t a n t " , p r e s e n t e d a t t h e 1 7 5 t h ACS N a t i o n a l Meeting, Anaheim, C a l i f o r n i a (March 13-17, 1978).

12.

"Research on Chemical O i l Recovery SHAH, D. 0. and WALKER, R. D.; Systems", Semi-Annual Report, U n i v e r s i t y of F l o r i d a , G a i n e s v i l l e (June 1977).

13.

ZORNES, D. R., WILLHITE, G. P. and MICHXICK, M. J . ; "An Experimental I n v e s t i g a t i o n I n t o t h e Use of HPLC f o r t h e D e t e r m i n a t i o n of Petroleum S u l f o n a t e s " , (June 1978) SPEJ 18,207-218.

14.

TRUSHENSKI, S. P . , DAUBEN, D. L. and PARRISH, E. R.; %Micellar Flooding - F l u i d P r o p a g a t i o n , I n t e r a c t i o n and M o b i l i t y " , (1974) SPEJ l4, 633-644.

15.

HEALY', R. N., REED, R. L. and CARPENTER, C. W.; Nicroemulsion Flooding", (1975) SPEJ 15,87-100.

"A Laboratory Study of

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123

CHEMICAL FLOODING

THE EACN OF A CRUDE OIL: VARIATIONS WITH COSURFACTANT AND WATER OIL RATIO MIN KWAN THAM and PHILIP BOALT LORENZ

U.S.Department of Energy Bartlesville Energy Technology Center

ABSTRACT

The EACN concept, which allows the s u b s t i t u t i o n of a crude o i l by an alkane o r an alkane mixture f o r phase volume or i n t e r f a c i a l tension studies, has been gene r a l l y accepted. I n t h i s paper, i t was shown t h a t such parameters as alcohol type, crude o i l composition, and water-oil-ratio could have an e f f e c t on the EACN of a crude o i l . The p a r t i t i o n behavior of the alcohol was traced as one of the causes f o r t h i s aberration. Interaction of surfactant with heavy crude o i l components was thought t o be another. Experiments t e s t i n g the l a t e r hypothesis is i n progress.

INTRODUCTION

The term Equivalent Alkaf_e3Carbon Number (EACN), w a s coined by the researcn &--.up from University of Texas This concept a r i s e s from the observation t h a t the i n t e r f a c i a l properties of any o i l with a surfactant can be modeled by the behavi o r of alkanes. Thus, heptane, heptylbenzene, and butyl cyclohexane a l l exhibit "optimum" conditions, i.e., minimum i n t e r f a c i a l tension (IFT) f o r the same combinations of surfactant, cosurfactant, and s a l t concentration. I n general, the benzene r i n g appeared t o have EACN = 0 , and the cyclohexane r i n g EACN = 3. Inl-3 addition, the EACN of a mixture of hydrocarbons follows the simple mixing r u l e ,

.

(Em)mixture

=

11

xi

EACNi,

---(l)

i

where X i s the mole f r a c t i o n of component i. i

4

This concept was later found t o be applicable t o crude o i l s and pseudo crudes , whereby an alkane or alkane mixture can be found t o model the IFT behavior of a crude o i l . An important finding of t h e i r s is t h a t the EACN of an o i l (crude, pseudocrude, o r hydrocarbon) is independent of the surfactant formulation, and t h a t t h i s equivalence always holds. Crude o i l , being dark i n color and usually q u i t e viscous, can make equilibrium attainment very slow and phase volume observat i o n d i f f i c u l t . Replacing the crude with hydrocarbon w i l l f a c i l i t a t e screening of surfactant formulation, and therefore, the EACN concept is a very valuable one. Recently, the Texas group and Glinsmann5, extended t h e concept of equivalent optimal s a l i n i t y t o high concentration surfactant systems (> 2%). Here, also, the EACN of a crude o i l i s independent of the alcohols and surfactants i n the formulations.

124 As p a r t of our s u p p o r t i n g reseagch program f o r t h e DOE micellar-polymer

pilot test i n Nowata County, Oklahoma , w e determined t h e EACN of t h e Delaware-Childers (D.C.) o i l from t h a t f i e l d , u s i n g s e v e r a l s u r f a c t a n t systems, and a t e r - o i l r a t i o s (WOR). It w a s found t h a t t h e EACN w a s n o t a c o n s t a n t v a l u e This paper r e p o r t s t h e r e s u l t s i n our i n v e s t i g a t i o n on t h e p r o b a b l e c a u s e s f o r t h i s v a r i a tion.

Y.

5 Glinsmann's method of measuring t h e EACN of a n o i l was followed, i n which t h e o p t i m a l s a l i n i t i e s of a s u r f a c t a n t system w i t h a series of a l k a n e s w e r e d e t e r mined. By comparing t h e o p t i m a l s a l i n i t y of t h e c r u d e o i l w i t h t h e same s u r CN w a s determined. Of t h e d i f f e r e n t c r i t e r i a o d e f i n i n g f a c t a n t system, optimal s a l i n i t i ~ ! " ~ t h e one used h e r e w a s t h e e q u a l s o l u b i l i z a t i o n from phase volume measurements.

6

Various s u r f a c t a n t systems were s t u d i e d f i r s t , w i t h s p e c i a l emphasis on t h e e f f e c t of a l c o h o l type, becay&213tudies have shown t h e s t r o n g i n f l u e n c e of a l c o h o l s on phase behavior and IFT The e f f e c t of c r u d e o i l components w a s t h e n s t u d i e d . F i n a l l y , t h e e f f e c t of WOR w a s a l s o s t u d i e d .

.

EXPERIMENTAL Materials The s u r f a c t a n t s used (and t h e i r p r o p e r t i e s ) a r e l i s t e d i n Table I. used w i t h o u t p u r i f i c a t i o n .

They were

The a l k a n e s were pure-grade hydrocarbon from P h i l l i p s Chemical Company. phenyl dodecane w a s from Eastman Kodak Company.

The

Procedure For phase-volume s t u d i e s , s u r f a c t a n t s o l u t i o n s were mixed w i t h o i l i n g l a s s t u b e s ( p r e c i s i o n b o r e t o 0.474 5 0.001 cm i . d . ) , and shaken f o r one minute i n a mecha n i c a l s h a k e r (40 Hz). Except where noted o t h e r w i s e , t h e WOR w a s set a t u n i t y . The t u b e s were k e p t i n a n a i r b a t h a t 30' f o r e q u i l i b r a t i o n . Usually, one week t o s i x months were r e q u i r e d f o r complete e q u i l i b r a t i o n . Some of t h e s o l u t i o n s - e s p e c i a l l y t h o s e w i t h h i g h viscosity--were shaken a second t i m e t o e n s u r e thorough mixing. Table I.

P r o p e r t i e s of S u r f a c t a n t s TRS 10-410(a)

Suntech I (b)

Blend of petroleum s u l f o n a t e s mixed w i t h C o s u r f a c t a n t 122

Petroleum sulfonate

S u l f o n a t e s of mixed x y l e n e s and propylene tetramer

% Active

45

62

65

Equivalent WeAght

450

418

372

wide

400-450

344-390 (92%)

Floodaid 1 4 1

TY Pe

93"

Equivalent Weight Distribution

(80%)

(a) (b)

An e x p e r i m e n t a l s u l f p g a t e (Sample No. I , Suntech Lot 768511) prepared by

Witco Chemical Company.

(c)

Suntech Tech, Inc. Amoco C o s u r f a c t a n t 122 i s a m i x t u r e of e t h o x y l a t e d a l c o h o l s .

125 Phase volumes were measured with a cathetometer. Standard correction for the round-bottom end of the glass tubes, and for the oil and water menisci, were obtained by weight measurements. Solubilization calculations were fashioned after the work of Glinsmann. The following assumptions were made in the calculations: (a) all the surfactant and cosurfactant is in the surfactant phase (this is an incorrect assumption as can be seen later, but the effect on the phase volumes is negligible); (b) the volumes are additive. In the present work, surfactant and electrolyte concentrations refer to the concentration in the aqueous phase. Some experiments were performed with crude oil components. Distillation of crude oil into distillates and heavy ends were done at 400°F and 10 -Egg. Vacuum.

.

Asphatene Analysis for acids and bases was by column liquid chromatography determination was by pentane precipitation. Alcohol concentrations were measured with a gas chromatograph. RESULTS AND DISCUSSION

Optimal Salinities The optimal salinities for a number of systems with normal alkanes are plotted in The observed behavior is the same a8 that reported in the literature that is, the optimal salinity increases with increases in (1) hydrocarbon chain length, (2) water solubility of the cosurfactant (the solubilities are in the order IBA < TAA < Amoco 122), and (3) concentration of the water soluble cosurfactant.

I 000

'

I-

/ 5 7 0 T i3s 10- 410, 1.8% Amoco 122 ( E l

0

4% Suntech

z

-

\ U

600 8

o

o

G

.

I, 2%

TAA (A) %Amoco 122 (D)

0

!i i400 c I z

YZYO

FA 141 ( F )

U v)

-I

U

200

I

I ooc;' ,

80

*

I

7

I

8

I I I I 9 10 II 12 A L K A N E CARBON NUMBER

-

I

13

I

14

Figure 1. Optimal salinity of surfactant systems with normal alkanes. TAA = tertiary amyl alcohol; IBA = isobutyl alcohol: Amoco 122 Amoco Cosurfactant 122.

126

*

The observed l i n e a r re1 t nship of I n (S ) versus alkane carbon number (ACN) w a s reported by SalagergYfg, who found t h t t t h e s l o p e s f o r a l l t h e s u l f o n a t e systems were 0.16 5 0.01. The value f o r t h e 5 percent TRS 10-410 3 percent i s o b u t y l alcohol (IBA) system obtained by least square f i t is 0.17, which is i n good agreement with h i s values. However, t h e s l o p e s were 0.11 f o r t e r t i a r y amyl alcohol and 1.8 percent f o r c o s u r f a c t a n t 122, and 0.14 with 1.0 percent cosur-, f a c t a n t 122. This i s i n c o n t r a d i c t i o n t o t h e p r e d i c t i o n of S a l a g e r ' s equation , which p r e d i c t s s l o p e independent of t h e alcohol. The s l o p e s f o r t h e Suntech and Floodaid s u r f a c t a n t were 0.12 and 0.28, r e s p e c t i v e l y .

-

E f f e c t of S u r f a c t a n t Formulations on t h e EACN of Delaware-Childers O i l The EACN of D. C. o i l w a s determined by comparing i t s optimal s a l i n i t y with t h a t of t h e alkanes f o r a given s u r f a c t a n t formulation. The s e v e r a l s u r f a c t a n t systems w e r e used t o determine t h e constancy of i t s EACN. Table I1 shows t h e results. Table 11.

The optimal s a l i n i t y and EACN of D. C. o i l with d i f f e r e n t s u r f a c t a n t formulations

Surfactant system

Optimal s a l i n i t y meq/l N a C l

EACN

A

4% Suntech I 2% T e r t i a r y amyl alcohol (TW

680

9.5

B

5% TRS 10-410 3% TAA

197

9.3

C

5% TRS 10-410 3% I s o b u t y l alcohol

193

10.9

D

5% TRS 10-410 1% Amoco 122

410

6.15

E

5% TRS 10-410

590

6.2

222

7.7

1.8% Amoco 1 2 2 F

*

12% FA 141*

Sulfonate content equivalent t o 7.6% TRS 10-410 o r Suntech I

The spread of 4.7 u n i t s i n t h e values i n d i c a t e s t h a t EACN as u s u a l l y determined i s n o t a constant quantity. From Figure 1 and Table 11, i t is necessary t o conclude t h a t t h e c u r r e n t l y accepted concept apply only over a narrow range of

conditions. Thus, Systems A and B y with f a i r l y s i m i l a r s u r f a c t a n t s , g i v e n e a r l y i d e n t i c a l Also, i n Systems D and E , a twofold v a r i a t i o n i n alcohol concent r a t i o n has no i n f l u e n c e on EACN. But t h e t r a n s i t i o n from C t o B t o D (with a s i g n i f i c a n t i n c r e a s e i n water s o l u b i l i t y of t h e c o s u r f a c t a n t a t each s t e p ) shows t h a t t h e cosurfactant s p e c i e s has a major i n f l u e n c e on t h e r e s u l t s . There are two p r o p e r t i e s of System F t h a t could c o n t r i b u t e t o i t s d i f f e r e n t EACN value: a wide d i s t r i b u t i o n of equivalent weight and a d i f f e r e n t type of alcohol.

EACN values.

The EACN of an o i l w a s determined by comparing t h e optimal s a l i n i t y of t h e o i l with those of alkanes. The v a r i a t i o n i n EACN observed above, n e c e s s a r i l y r e f l e c t s d i f f e r e n c e s i n p r o p e r t i e s between t h e o i l and alkanes. It is t h e r e f o r e of i n t e r e s t t o study t h e e f f e c t of s u r f a c t a n t formulation on t h e EACN of a number of oils.

127 EACN of Several o i l s With Systems C and F S u r f a c t a n t s Systems C and F were used t o compare t h e b h of d i f f e r e n t o i l s . System C was chosen because i t has been widely s t u d i e d and because t h e optimal s a l i n i t i e s , phase behavior and EACN of most of t h e o i l s s t u d i e d with t h i s system followed a "regular" p a t t e r n . On t h e o t h e r hand, System F w a s chosen f o r its "irregularities". Table 111 lists t h e optimal s a l i n i t i e s and EACN of t h e s e systems with a number of o i l s . The E l Dorado o i l r e s u l t s show d i f f e r e n c e s i n t h e EACN between t h e two systems, even though t h e d e v i a t i o n i s n o t as l a r g e as t h e D. C. o i l case. Bradford o i l shows an even smaller difference. These v a r i a t i o n s among t h e various crude o i l s may be compared w i t h t h e d i f f e r e n c e s i n t h e crude o i l composition (Table I V ) . Bradford o i l i s high i n p a r a f f i n , and D. C . o i l contains a l a r g e r q u a n t i t y of heavy b28es and a c i d s . These heavy cornpounds are known t o complex with t h e s u l f o n a t e s

5*artna,

.

Table 111.

Optimal s a l i n i t i e s and EACN of crude o i l s and crude oil f r a c t i o n s System F

System C .

EACN

S*

EACN

S*

E l Dorado o i l

169

10.0

261

8.3

Bradford o i l

196

11.0

425

10.1

Bradford D i s tillates

130

8.2

197

7.3

Bradford heavyends + decanea D.

c.

Oil

D. C . digtillate

238

12.4 (20)

615

11.4 (15.8)

193

10.9

222

7.7

103

6.7

132.5

5.8

295

8.7 (4.6)

D. C. heavy-

ends + decanea

185

10.6 (12.5)

(a) Equal weight r a t i o of heavy ends and decane The behavior of t h e components of t h e s e crude o i l s is q u i t e revealing. The dist i l l a t e s show a downward s h i f t i n EACN as compared with t h a t of t h e whole crudes, as expected. I n t e r e s t i n g l y , t h e l a r g e d i f f e r e n c e s between Bradford and D. C. o i l s with r e s p e c t t o t h e s u r f a c t a n t Systems C and P disappeared. Both show a d i f f e r ence of 0.9 u n i t s w i t h t h e two systems, as compared t o 0.9 and 3.2 f o r t h e whole Bradford and D. C. o i l s , respectively. Y e t , t h e f a c t t h a t t h e d i s t i l l a t e s having d i f f e r e n t EACN with d i f f e r e n t s u r f a c t a n t systems i n d i c a t e s t h a t t h e r e are c e r t a i n components i n t h e d i s t i l l a t e s behaving d i f f e r e n t l y from t h e alkanes, which are t h e standards. Actually, i t has been recognized tQat t h e equivalence between There are d e v i a t i o n s i n t h e alkanes and o t h e r series of compounds i s n o t exact a l k y l benzene and a l k y l cyclohexane series t h a t are g r e a t e r , t h e f a r t h e r one m o v e s away from EACN of 8. Table V p r e s e n t s some f u r t h e r d a t a on t h i s , showing t h a t t h e d e v i a t i o n can be q u i t e l a r g e when less conventional materials are used. The mixing of benzene with phenyl dodecane ( t o g i v e an EACN of 8) shows normal EACN with System C. A downward s h i f t i n EACN w i t h System E, similar t o t h a t

.

1 28 Table I V .

Crude o i l p r o p e r t i e s

Delaware-Chllders o i l G r a v ity "AP I

Bradford o i l

31.9

44.3

E l Dorado o i l

36.0

Nitrogen, percent

0.07

0.01

0.07

X Aromatic through f r a c t i o n lza

4.04

3.82

5.50

X Acids17

2.17

0.13

-

17 X Bases

1.58

0.3

X T o t a l Asphaltenes

1.46

0.02

X P a r a f f i n through c u t 7

64.0

34.6

55.3

(a) Cut temperature 437°F a t 40 nun Hg. (corresponding t o molecular weight of 280). (b) Cut temperature 392°F (corresponding t o molecular weight of 150). Table V.

Optimal s a l i n i t i e s and EACN of a k y l benzenes .System C EACN

s,

-

*System E

s,

EACN

Benzene phenyl dodecane mixture, 1:2 molar r a t i o

110

7.9

360

1.9

Phenyl dodecane

145

9.0

557

5.9

with crude o i l s was ob e ved. On t h e o t h e r hand, phenyl dodecane does n o t observe the simple s c a l i n g l a w g s g f o r both s u r f a c t a n t systems. Under t h i s l a w , phenyl dodecane should have an EACN of 12. The observed EACN d i f f e r s g r e a t l y from this value and cannot be explained t o t a l y by t h e smaller d e v i a t i o n previously reported f o r t h e case without alcohol

€.

For p r a c t i The d a t a on t h e heavy ends in Table 111 are a l o t more "irregular". cal experlmental purposes, i t was necessary t o c u t t h e v i s c o s i t y by mixing with equal weights of decane. To g e t t h e EACN of t h e heavy ends by themselves from No v a l u e Equation ( l ) , an assumption was necessary on t h e molecular weight (MU). of MU could be found t h a t was c o n s i s t e n t with t h e EACN v a l u e s , even f o r "regular" System C. The d i s t i l l a t i o n temperature suggested a M J of 450, which corresponds t o an alkane of carbon No. 32, b u t gave EACN 20 f o r t h e Bradford heavy ends and 12.5 f o r those from D. C. The weight f r a c t i o n s of d i s t i l l a t e s and heavy ends from D. C. o i l (which l o s t only 4 wt-X I n d i s t i l l a t i o n ) required MW 254 (EACN 18) €or consistency with t h e whole-oil EACN. The EACN of t h e decane mixture obeyed equation (1) only w i t h MW = 160 (EACN 11.3) f o r heavy ends. It is obvious t h a t heavy ends are n o t equivalent a t a l l t o alkanes even with System C; and t h e d i s crepancy between Systems C and E are very large.

-

Alcohol P a r t i t i o n i n g and Its E f f e c t on EACN W e have shown earlier t h a t r e p l a c i n g i s o b u t y l alcohol w i t h Amoco 122 i n a s u r f a c t a n t formulation causes a downward s h i f t i n EACN. It is t h e r e f o r e of i n t e r e s t t o study the p a r t i t i o n i n g behavior of these alcohols, because alcohol p a r t i t i o n i n g is known t o be t h e prime determlnant of t h e phajts-&h2yior, i n t e r f a c i a l tension, and optimal s a l i n i t y of a s u r f a c t a n t - o i l system '

.

129 Since determination of alcohol concentrations in crude oil poses considerable problem due to its wide boiling range--choosing the right column is difficult-only the partition coefficients in hydrocarbons were measured. It was suspected that the large differences in behavior of alkanes and allcyl benzenes would be reflected in the alcohol partitioning and suggest one cause for the difference between alkanes and crude oils. The results of the partitioning experiments are listed in Table VI. The numbers are relevant only at optimal salinity, but data under other conditions are given for illustration. Partition coefficients are not very sensitive to salinity up to 3 percent; the table shows that the same value was obtained for Co-surfactant 122 in pure water and in System E at optimal salinity of 3.4 percent. The differences between the partition coefficients of Amoco 122 in octane and phenyl dodecane is striking. In addition, there is a strong preferential partitioning of the heavier alcohol compounds (components 2 and 3) into the oleic phase of the phenyl dodecane system (Table VII). Thus, in comparison with octane, the aqueous alcohol concentration in phenyl dodecane is lowered. It is not known what will be the effect of this change of alcohol composition and concentration on the optimal salinity and EACN. It is certain, however, such changes will make the effort to estimate a "true EACN" impossible. That is, it is not possible to modify the definition of EACN to account for thig2 change in alcohol concentration. In agreement with the findings of Tosh, s & , the presence of surfactant did not affect the alcohol partitioning behavior for the systems studied. Table VI.

Partition coefficients of alcohols ~

Octane

~~~~~

Phenyl dodecane

3% IBA

0.3ga

0.32b'd

1.8% Amoco 122

0.6aaSd

5.5C'd

-

a = alcohol originally in alcohol originally in b c = alcohol originally in d in the presence of 5%

-

Table VII.

deionized water. 0.9% NaC1. 3.3% NaC1. TRS 10-410 at optimal salinity.

Distribution of alcohol components, System E Alcohol concentration, %

Phase Octane

Upper Middle Lower

Component 1 0.26 0.5 0.3

Component 2 0.25 0.84 0.24

Partition coefficient

component 3

-

0.15 0.53 0.25 0.8

Alcohol concentration, % Phase Upper Phenyl Middle dodecane Lower

Component 1 0.26 0.6 0.19

Component 2 0.44 0.69

\

2.05 % TRS. 10-410

Y

I

I

- 3% IBA I

I

I

I

I

4

Figure 3 I s a similar p l o t f o r System F. Again a l i n e a r relationship f o r alkanes w a s observed. I n f a c t , Systems D and E a l s o give t h i s l i n e a r r e l a t i o n with alkanes (not shown), which shows t h a t t h i s relationship is q u i t e general. I n t h i s case, the crude o i l s and d i s t i l l a t e s do not f a l l on the line. I f the EACN values-

131 determined with System C are used, t h e f i t is much b e t t e r . This suggests t h a t degree of s o l u b i l i z a t i o n might give mre c o n s i s t e n t values of EACN than optimal s a l i n i t y . Even so, D. C. o i l does n o t f i t t h e c o r r e l a t i o n very w e l l , perhaps due t o i t s high content of a c i d s , bases, and asphaltenes.

"."

+'.

\

0-

8.0.

---

\

\

Alkane Bradford oil A D.C. oil Bradford - light ends 0 D. C. -light ends o

D

7 . 0. 6 . 0 .-

5 . 0 .-

\

4.0.

\

\

\

\

\ \

3.0.

2.0' 12% FA 141 I.

I

I

I

I

I

I

I

EACN Figure 3.

(V/Vs)s* versus equivalent alkane carbon number

Q Effect of Water-Oil-Ratio

on EACN

The e f f e c t of water-oil-ratio (WOR) can be seen from Figure 4. It is noted t h a t by i n c r e a s i n g t h e WOR from 1 t o 2, t h e p o s i t i o n of t h e octane and D. C. o i l l i n e s are interchanged. That is t h e EACN of crude o i l changed from 7.7 t o higher than 8, by simply i n c r e a s i n g t h e WOR. It is p l a u s i b l e t h a t t h e WOR e f f e c t is r e l a t e d t o alcohol p a r t i t i o n i n g . Consider t h e case of phenyl dodecane, with the d a t a of Table V I I . Increase of WOR reduces t h e proportion of t h e o i l phase, which would mean t h a t less of component l w o u l d b e e x t r a c t e d from t h e aqueous phase. The proportion of water-soluble component i n t h e aqueous phase,would Since increase. According t o Figure 1, t h i s should l e a d t o an i n c r e a s e i n S

4 .

t h e r e i s no such f r a c t i o n a t i o n with octane, and presumably w i t h o t h e r alkanes, the i n c r e a s e i n EACN is as expected.

132

30C

*,"

20c

A Octane o D.C. oil

I oc

I

0

2

3

WOR Figure 4.

Variation of optimal s a l i n i t y with water-oil-ratio CONCLUSIONS

The EACN concept was found t o be i n e r r o r +hen s y s t e m involving ethoxylated alcohols and/or aromatics were used. Alcohol p a r t i t i o n i n g is found t o be an important f a c t o r causing t h i s deviation. The higher boiling, non-hydrocarbon components of the crude o i l might have contributed p a r t i a l l y t o t h i s "abnormal" behavior. This is under investigation. W e would l i k e t o advise caution when applying the EACN concept. ACKNOWLEDGMENT The authors wish t o acknowlege the help of J. B. Green and J. Lacina f o r the analyses on crude o i l s components. NOMWCLATURe

Am

Alkane carbon number.

EACN

Equivalent alkane carbon number.

S*

Optimal s a l i n i t y f o r phase behavior, meq/l NaC1.

0

vO

vs vW

Volume of o i l solubilized i n the surfactant phase. Volume of surfactant i n the surfactant phase. Volume of water solubilized i n the surfactant phase. Volume of water o r o i l solubilized per u n i t volume of surfactant a t optimal s a l i n i t y .

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"ERDA's Walker, C. J., Burtch, F. W., Thomas, R. D., and Lorenz, P. B.: Micellar Polymer Flood P r o j e c t i n Nowata County." O i l and Gas J., 74, 6068 (1976). "Calcium E f f e c t i n t h e DOE SurfactantLorenz, P. B., and Tham, M. K.: Polymer P i l o t Test." O i l and G a s J. To be published. "Physicochemical Aspects of Microemulsion Reed, R. L. and Healy, R. N.: Flooding A Review," i n Improved O i l Recwery by S u r f a c t a n t and Polymer Flooding. Shah, D. 0. and Schechter, R. S., eds., Academic P r e s s (1977).

-

"OptiSalager, J. L., Morgan, J. C., Schechter, R. S., and Wade, W. H.: mum Formulation of SurfactantfWaterfOil Systems f o r Minimum I n t e r f a c i a l SPE J., 2,107-115 (1979). Tension o r Phase Behavior."

"Cosurfactants i n Micellar System Used (10) Jones, S. C. and Dreher, K. D.: SPE J., l6, 161-167 (1976). f o r T e r t i a r y O i l Recwery." (11) Salteli, S. J.: "The Influence of Type and Amount of Alcohol on SurfactantOil-Brine Phase Behavior and Properties." Paper 6843, presented a t t h e 52nd Annual F a l l Technical Conference and Exhibit of t h e SPE-AIME, i n Denver, Colorado, October 9-12, 1977. (12) Hsieh, W. C. and Shah, D. 0.: "The E f f e c t of Chain Length of O i l and Alcohol As W e l l Aa S u r f a c t a n t t o Alcohol Ratio on t h e S o l u b i l i z a t i o n , Phase Behavior, and I n t e r f a c i a l Tension of OilfBrinefSurf actantfAlcoho1 Systems." Paper SPE 6594, presented a t t h e SPE-AIME I n t e r n a t i o n a l S p p o sium on O i l f i e l d and Geothermal Chemistry, La J o l l a , C a l i f o r n i a , June 2728, 1977. (13) Wade, W. H., Morgan, J. C., Jacobson, J. K., Salager, J. L., and Schechter, R. S.: " I n t e r f a c i a l Tension and Phase Behavior of S u r f a c t a n t Systems." SPE J., la, 242-252 (1978). "The Influence of Alcohols (14) Baviere, M., Schechter, R., and Wade, W. H.: J. Coll. I n t . Sci., &&,266-279 (1981). on Microemulaion Composition."

134 (15) Dominguez, J. G., Willhite, G. P., and Green, D. W.: "Phase Behavior of Microemulsion Systems with Emphasis on Effects of Paraffinic Hydrocarbon and Alcohols," in Solution Chemistry of Surfactants. Vol. 2, Gttal, K. L., ed., Plenum, New York, pp. 673-697 (1979). (16) Malmberg, E. W.: "Large-Scale Samples of Sulfonates for Laboratory Studies in Tertiary Oil Recovery, Preparation and Related Studies," Report No. FE-2605-20, National Technical Information Service, U. S. Department of Commerce, Springfield, Virginia (1979). (17) Green, J. B. and Hoff, R. J.: "Liquid Chrometography on Silica Using Mobile Phases Containing Aliphatic Carboxylic Acids I1 Applications in Fossil Fuel Characterization," J. Chrom. 2,231-250 (1981).

-

(18) Salager, J. L.: "Physico-Chemical Properties of Surfactant-Water-Oil Mixtures---Phase Behavior, Microemulsion Formation and Interfacial Tension." Ph.D. Dissertation, The University of Texas at Austin, 1977. (19) Miller, C. A. and Fort, T. Jr.: "Low Interfacial Tension and Miscibility Studies for Surfactant Tertiary Oil Recovery Processes." Report No. DOE/BC/10007-4, National Technical Information Service, U.S. Department of Commerce, Springfield, Virginia 22161 (1979). (20) Clementz, D. M. and Gerbacia, W. E.: "Deactivation of Petroleum Sulfonates by Crude Oils." J. Pet. Tech., pp. 1091-1093, September 1977. (21) Puerto, M. C. and Gale, W. W.: "Estimation of Optimal Salinity and Solubilization Parameters for Alkylorthoxylene Sulfonate Mixtures." SPE J., 17, 193-200 (1977).

-

(22) Tosch, W. C., Jones, S. C., and Adamson, A. W.: "Distribution Equilibria in a Micellar Solution System." J. Coll. Int. Sci., 31, 297-306 (1969). (23) Healy, R. N., Reed, R. L., and Stenmark, D. G.: Systems." SPE J., 2,147-160 (1976).

"Multiphase Microemulsion

(24) Huh, C.: "Interfacial Tensions and Solubilizing Ability of a Microemulsion Phase That Co-exists With Oil and Brine." J. Coll. Int. Sci., 2, 408-426 (1979). (25) Fleming, P. D., 111, Vinatieri, J. E., and Glinsmann, G. R.: "Theory of Interfacial Tension in Multicomponent Systems." J. Phys. Chem., 84,15261531 (1980). (26) Klevens, H. B.:

"Solubilization."

Chem. Rev., 1-74, 1950.

135

CHEMICAL FLOODING

DYNAMIC INTERFACIAL PHENOMENA RELATED TO EOR J. H. CLINT, E. L. NEUSTADTER and T. J. JONES The British Petroleum Company Limited, BP Research Centre, Chertsey Road, Sunbutyen-Tharnes, Middlesex, TWI 6 7 WV

ABSTRACT The relevance of dynamic interfacial tension and interfacial rheology to EOR is discussed. A technique developed by BP, the "Drop Volume Dynamic Tensiometer" allows dynamic interfacial tension to be determined over a wide range of rate of fractional area change. The behaviour of aqueous surfactant systems against crude oil is very different for fresh systems compared with systems where the phases have been pre-equilibrated. The application of these measurements to EOR systems is illustrated with examples of surfactants which give widely different oil displacement profiles. new method for the measurement of interfacial dilatational rheological parameters of oil/water interfaces is described. This is the pulsed drop experiment which has experimental advantages over the interfacial trough method and allows parameters to be determined over a wider range of frequencies. The effect of interfacial dilatational rheology on coalescence phenomena is illustrated with data for water-in-oil demulsifiers.

A

The ease of oil bank formation is influenced by the kinetics of coalescence, which in turn is controlled by film drainage from between colliding droplets. For crude oil films in water, increasing interfacial shear viscosity greatly reduces the rate of thinning. For the reverse system, increasing interfacial shear viscosity can reduce coalescence rates for oil drops in water almost to zero. This would have a very adverse effect on oil bank formation.

INTRODUCTION

In an enhanced oil recovery process, oil ganglia which have been trapped at small pore throats are released by lowering the interfacial tension, prevented from being retrapped by maintaining a low tension (dynamic) and encouraged to coalesce to form an oil bank. In all except the initial release it could be argued that it is the dynamic properties of the interface such as the dynamic interfacial tension and the interfacial rheology which will govern each individual and hence the overall process. This paper reports some novel methods for measuring dynamic interfacial tension and interfacial dilatational rheology which work very well for crude oil-water systems. Techniques will be illustrated with results for pure oils as well as crude oils, and the significance of these data for EOR processes will be discussed.

136 DYNAMIC INTERFACIAL TENSION This technique is essentially an extension of the drop volume method for interfacial tension and is illustrated in Figure 1.

WATER JACKET

'k

(I

SYRINGE PUMP

SEPTUM CAP

FIGURE 1

- DROP VOLUME DYNAMIC TENSIOMETER

Oil from a syringe pump is pumped at an accurately known volume flow rate to a syringe needle inserted through a septum cap into a small glass cell surrounded by a water jacket. The tip'of the syringe needle is ground flat and the inside and outside diameters determined accurately. For convenience of observation an image of the tip and drops formed is obtained using a microscope and TV camera and displayed on a monitor screen. The experiment consists very simply of measuring the number of drops formed in a fixed period of time and repeating at a whole range of volume flow rates Q. If n is the number of drops per unit time then the volume of each drop I

Q

v = -

... (1)

n The interfacial tension y can then be calculated using the usual formula

...

(2)

137

-

where P P ' is the density difference between the oil and water phases, and R is the radius of the tip to which the drop is attached. The latter may be the inside or outside tip radius depending on the wetting conditions. If we make the assumption that the drops are spherical then the rate of fractional area change at the time when the drop detaches can be shown to be

...

(3)

Hence we are able to estimate both the interfacial tension and the rate of fractional area change simply by measuring the rate of formation of drops at a known volume flow rate. Figures 2 and 3 illustrate the type of results obtained using Forties crude oil against two different surfactant systems. The crude oil used was a well head sample free of any additives such as demulsifiers or corrosion inhibitors. All aqueous solutions were made up in filtered sea water. There were large differences in the results depending on whether the oil/water systems were preequilibrated or whether they were fresh. Figure 2 shows the dependence of dynamic interfacial tension on rate of fractional area change for a surfactant system "A" at 7OOC.

d

I

E

FIGURE 2

- DYNAMIC INTERFACIAL TENSION

-FORTIES CRUDE/SOOO PPM

SURFACTANT "A" AT 7OoC

138 The difference between fresh andpre-equilibrated systems is immediately apparent. The preequilibrated tension rises rapidly at moderate rates of area increase whereas the tension of the fresh system stays remarkably low until very high rates of area change are reached where the area is roughly doubling every second. In contrast to this is the behaviour of the surfactant system "B" shown in Figure 3.

6

5 d

I

E

0

1

FIGURE 3

- DYNAMIC INTERFACIAL TENSION I FORTIES CRUDE/50OO

PPM

SURFACTANT "B" AT 70OC

This time the pre-equilibrated system gave interfacial tensions which were very small and at time9 unmeasurably so (only the one which could be measured is shown). The dashed line indicates that the tension remains low even at high rates of area change. The tensions for the fresh system showed the normal dynamic effect rising rapidly with modest rates of area increase. The interesting point about these two systems is that they give totally different oil removal profiles when tested in a model sand column test. For surfactant "A" which gave low fresh tension but high equilibrium tensions, removal of oil was rapid but incomplete. About 35 per cent of residual crude oil was removed in less than 2 pore volumes (PV). For surfactant "B", which gave high fresh tensions but very low equilibrium tensions, removal of residual oil was Complete but required a very large number (15) of PV.

139 Admittedly the shape and duration of the oil displacement curve will be dependent on more than just the dynamic tension behaviour. Surface wettability and the degree of adsorption will also be important factors. However, the distinction between the two systems above is clear and the oil displacement behaviour is logically related to the dynamic tension properties.

INTERFACIAL DILATATIONAL RHEOLOGY For the measurement of interfacial dilatational rheology the method employed in the past has been that of dilatational modulus measurements at various frequencies using an interfacial film balance (1). The method involves propagation of longitudinal waves of the frequency of interest and measuring changes of interfacial tension with a Wilhelmy plate. These changes, together with the phase differences between them and the area changes, allow calculation of Ed# the dilatational elasticity and nd, and dilatational viscosity, at each frequency. This technique suffers from a number of disadvantages including (a) Measurements are reliable only at fairly low frequencies where the wavelength of longitudinal waves is long compared with the distance between oscillating barrier and Wilhelmy Plate. (b) Good results depend on the rapid response of the Wilhelmy plate and the maintenance of a well defined contact angle. (c) The method uses large quantities of oil with a large area exposed to air allowing loss of light ends. Also the apparatus is not easily used at temperatures much above ambient. We have developed a new technique which uses a small drop of oil pulsed in water. Area changes are calculated from drop diameters and the tip diameter, and tension is calculated by measuring the excess pressure inside the drop with a sensitive pressure transducer. The experimental arrangement is shown in Figure 4.

CHART RECORDER

SYRINGE PUMP

SENSITIVE PRESSURE TRANSDUCER

WATER FROM THERMOSTAT

FIGURE 4

-

PULSED DROP METHOD FOR INTERFACIAL DILATATIONAL RHWlLOGY

140 The oil drop is formed at a ground glass or stainless steel tip. The radius of tip needed depends on the region of interfacial tension being investigated. the excess pressure inside the drop was measured using a transducer from SE Labs (EMI) Ltd, type SE 1150/WG. Output from the transducer is displayed on a chart recorder. Instead of the conventional oscillatory method for dilatational modulus measurements, the single pulse Fourier transform method was used (2). When the cell containing the aqueous solution of interest is sufficiently well thermostatted the drop radius (rl) is measured, a fixed volume pulse is injected from the syringe pump over a short period of time which increases the radius to r2 and then the variation of pressure with time is followed on the chart recorder. The shape of a typical pressure trace is shown in Figure 5.

TIME/MINS

E'fGURE 5

- TRANSIENT PRESSURE INSIDE DROP FOLLOWING SUDDEN EXPANSION

The equilibrium pressure after the experiment is lower than that at the beginning because the drop radius is larger. All of the pressure trace after the rapid rise is assumed to take place at a constant drop radius, the final radius r ~ . Then the interfacial tension at any time Y (t) is given by

... (4)

141 The interfacial modulus is usually written:-

t*

=

dy/dlnA

=

t'

+

it"

...

(5)

Taking Fourier transforms of the numerator and denominator coverts the perturbation time function AA(t)/A and the response time function y(t), to the frequency function. Thus:-

€*(W) =

...

(6)

...

(7)

...

(8)

...

(9)

...

(10)

For a perfect step function (instantaneous area change):-

Therefore:-

~ A / A1, iw

t*(w)

=

f-

Ay(t) [cos wt

-

i sin otldt

The real part gives us the dilatational elasticity:-

=

Ed(w) =

[ :

Ay(t) sin wt dt

AA/A

The lmaginary part gives the dilatational viscosity:-

E"

= *wnd(w) =

w J:

m

AY(t) cos wt dt

W A where w = angular frequency (radians per second).

Equations 9 and 10 can be used to calculate td and n at any frequency from the decay curve. A desk top microcomputer is adequate afthough a little slow. It is convenient to take approximately 100 readings ffom the.decay curve for use in these computations. The method was evaluated using a model system of 10 ppm stearic acid dissolved in n-decane against distilled water adjusted to pH 2.5 to prevent ionisation of the acid. Results are shown in Figure6 for the real (elasticr damponent of the modulus and in Figure 7 for the imaginary (frequency x viscosity) component.

142

d

I

20

-

15

-

10

-

I I I I1111

I I I11111~

I

I111111

I I iiiirr

-

E

2

\

5 -

W

010-3

10-2

10-1

1

FREQUENCY/Hz FIGURE 6 - REAL PART OF INTERFACIAL DILATATIONAL MODULUS FOR 10 PPM STEARIC ACID IN n-DECANE/DISTIUED WATER pH 2.5 AT 25OC. OPEN CIRCLES - TROUGH METHOD. FILLED CIRCLES DROP METHOD

-

10

8

6 d

I

E

a

4

W

2

0 10-1

FREQUENCY/Hz

FIGURE 7

-

IMAGINARY PART OF INTERFACIAL DILATATIONALMDDULUS. SYSTEM AND SYMBOLS AS FOR FIGURE 6

1

143 In each case the results are shown in comparison with data obtained previously using the interfacial trough technique, also using the Fourier transform method. Each set of data is the average of three separate runs. Agreement between the drop and trough methods is very good over most of the frequency range except possibly for the values of E " at intermediate frequencies. The shapes of the curves of E ' and E" are very close to those expected for a single relaxation mechanism. This is illustrated more strikingly in Figure 8 where a Cole-Cole plot ( E " against E l ) is shown. A single relaxation mechanism has a semi-circular Cole-Cole plot and the data from interfacial trough experiments clearly follow a semi-circle quite closely. Again agreement with pulsed drop data is encouragingly good considering the great difference between the two techniques. The implication is that the techniques measure real dilatational parameters and not artefacts.

4

I

E

5

0

10 E ' / ~ N

15

20

m-l

-

COLE-COLE PLOT FOR INTERFACIAL DILATATIONAL MODULUS. FIGURE 8 10 PPM STEARIC ACID IN n-DECANE/DISTILLED WATER pH 2.5. OPEN CIRCLES TROUGH METHOD. FILLED CIRCLES DROP METHOD

-

-

The single relaxation mechanism implied by Figures 6 , 7 and 8 is presumably diffusion of the stearic acid from the interface into the bulk decane phase. The maximum in C'' which corresponds to the inflection point in E ' occurs at U = 0 . 0 0 2 5 Hz which is an angular frequency w = 2nu = 0.0157 s ' . This is the characteristic frequency of the relaxation process. The relaxation time 'I = l/w = 64 sec. This would seem to be a very reasonable relaxation time for a diffusion controlled mechanism in a dilute system [c = 10 p p = 3.5 x 10-5 mol am-31.

144 The main advantages of the drop method over the trough method are (a) The system can be enclosed so that loss of light ends from crude oils is avoided. (b) The system can easily be thermostatted at high temperatures. (c) The system is compact and very small quantities of materials are used.

EFFECT OF INTERFACIAL RHEOLCGY ON COALESCENCE PHENOMENA The pulsed drop method has not yet been used to investigate coalescence phenomena. However, as an illustration of how interfacial dilatational rheology is involved in coalescence processes which are essential to oil bank formation, dilatational parameters for the Forties crude oil/formation water interface can be quoted which were determined by the trough method. The influence of various water-in oil demulsifiers was investigated. Results are shown in Figure 9 for E " as a function of frequency and as a Cole-Cole plot in Figure 10.

6

0

5

A

4 rl

Ei

w

0

3

-

FORTIES/FORMATION WAT

-

+10 PPM DEM 1113

-

+10 PPM RP 968

-

+ 5 PPM CC

6601

2

1

0

1 FREQUENCY/Hz

FIGURE 9

- EFFECT OF VARIOUS DEMULSIFIERS ON

IMAGINARY (VISCOUS)

COMPONENT OF INTERFACI~RILATATIONAtMODULUS

FORTIES CRUDE/FORMATION WATER AT 25OC

145

4

2

0

6 E'/~N

FIGURE 10

8

10

12

m-l

- COLE-COLE

PLOT FOR SYSTBMS IN FIGURE 9. SYMBOLS AS IN FIGURE 9.

The interface without additives gives two separate peaks indicating two different relaxation mechanisms are involved. From the positions of the peak maxima we can calculate relaxation times for the two processes of 87 sec and 4 sec. These are compared with relaxation times for systems with low concentrations of three water-in-oil demulsifiers in the table below. Relaxation Time (Seconds) Forties crude/formation water 87 4

+ 5

ppn CC 6601

+10 ppm RP 968 +10 ppn DEM 1113

1

4.5 22 9

The major effect of the &emulsifiers is to remove the relaxation process characterised by a long relaxation time. Shorter relaxation times are expected to mean more rapid film drainage (3) and therefore more rapid coalescence. These demulsifiers are also found to reduce the interfacial shear viscosity of the crude oil/water interface. However, from Figure 9 it can be seen that at some frequencies the dilatational viscosity is reduced whereas at other, normally higher, frequencies the dilatational viscosity can be greatly increased. At this stage the mechanistic implications of these observations are not fully understood. Further work on this topic is planned.

146 MEASUREMENT OF DRAINAGE RATES FOR SINGLE OIL FILMS IN WATER Direct evidence for the influence of interfacial shear rheology on the kinetics of drainage of thin films has been obtained by measuring the thickness of crude oil films in distilled water. The technique was the same as that used to measure thickness of oil films in air ( 3 ) , but having the whole cell filled with water. Measurements of the intensity of light reflected from the single oil film were used to calculate film thickness as a function of time. Results for Iranian Heavy crude and for Forties crude in distilled water are shown in Figure 11.

4

0

0

0.5

1 .o

1.5

2.0

(t/min)-4 FIGURE 11

-

FILM DRAINAGE

-

CRUDE OIL FILMS IN DISTILLED WATER AT 25OC

For the Iranian Heavy case the thickness is proportional to t-+ in accordance with the Stephan-Reynolds equation indicating that drainage is essentially from between two rigid interfaces. In contrast the Forties crude in water film drainage curve is not a straight line and indicates much more rapid drainage of the film than can be accounted for by the lower bulk viscosity of Forties oil. This implies that the Forties crude/distilled water interface is much more fluid compared with the Iranian Heavy case. These implications are borne out by measurements of interfacial shear viscosity at the crude oil/water interface. Using the biconical bob shear rheometer the results shown in Figure 12 were obtained. Over a period of hours the shear viscosity of the Iranian Heavy/distilled water interface builds up to quite high values whereas that for the Forties/distilled water interface remains low. The reverse system, drainage of water films from between colliding oil droplets, is relevant to oil bank formation. Because crude oil is opaque it is not possible to perform experiments analogous to the single oil film drainage measurements outlined above. However, there is clear evidence in the literature for the reduction of coalescence rates for crude oil drops in water when interfacial shear viscosity is increased ( 4 ) .

4

E

P*

.6

\

E v)

8 v)

H

.4

3

3w X

v)

a

.2

H

V

2

FORTIES

a B

z H 0

1

2

3

I

I

4

5

INTERFACE AGE/HOURS FIGURE 12

- CRUDE OIL/WATER

INTERFACIAL, SHEAR VISCOSITIES AT 25OC

Clearly an important quality of an EOR surfactant will be the maintenance of low interfacial shear viscosity as an aid to oil bank formation.

CONCLUSIONS 1.

A dynamic drop volume technique can be used to determine dynamic

interfacial tension in crude oil/water systems as a function of rate of fractional area change. 2.

For different surfactant systems which have markedly different oil removal profiles from sand columns, dynamic interfacial tension behaviour can be completely different.

3.

A pulsing drop method has been devised which can measure the

interfacial dilatational rheological parameters for oil/water systems. The results agree well with those determined using an interfacial trough. Both systems can be used with the single step pulse Fourier transform method. 4.

For a pure system of stearic acid in n-decane against distilled water at pH 2.5, the complex dilatational modulus gives a semi-circular ColeCole plot indicating that relaxation at the interface is due to a single mechanism, presumably diffusion to and from the interface.

5.

For a Forties crude/oil formation water interface, two separate relaxation processes are detected, presumably diffusion and molecular rearrangement. Water in crude oil demulsifiers remove the mechanism with the longer relaxation time.

6.

Drainage of crude oils films in water can be followed by reflectance measurements of thickness. Drainage rate depends critically on interfacial shear viscosity.

148 NOMENCLATURE A

Q R V 9

n

AP t Y €*

E ' € "

Ed Ild U

P 'I

w

Area of interface (ma) Volumetric flow rate (m3 s-1) Tip radius (m) Volume of drop (m3) Acceleration due to gravity (m s - ~ ) Number of drops per unit time (s-l) Excess pressure inside drop (Nm-2) Time (s) Interfacial tension (Nrn-l) -1 Complex interfacial dilatational modulus (Nm ) Real part of dilatational modulus (Nm-1) Imaginary part of dilatational modulus (Nm-l) Interfacial dilatational elasticity (Nm-1) Interfacial dilatational viscosity (Ns m-l) Frequency (cyclic) (Hz) Density (kg N 3 ) Relaxation time ( 8 ) Angular frequency (s-1)

ACKNOWLEDGEMENT Permission to publish this paper has been glven by The British Petroleum Company Limited.

REFERENCES GRAHAM, D.E., JONES, T.J., NEUSTADTER, E.L. AND WHITTINGHAM, K.P. "Interfacial Rheological Properties of Crude Oil Water Systems", 3rd International Conference on Surface and Colloid Science, Stockholm, 1979, Plenum Press, in the press. LOGLIO, G., TESEI, U. AND CINI, R "Spectral Data of Surface Viscoelastic Modulus Acquired Via Digital Fourier Transformation" J. Colloid Interface Sci, (1979), 71, 316. CALLAGHAN, I.C. AND NEUSTADTER, E.L. "Foaming of Crude Oils: A Study of Non-Aqueous Foam Stability" Chemistry and Industry, 17.1.81, p 53. WASAN, D.T., McNAMARA, J.J., SHAH, S.M., SAMPATH, K. AND ADERANGI, N. "The Role of Coalescence Phenomena and Interfacial Rheological Properties in Enhanced Oil Recovery: An Overview" J. Rheology, (19791, 23, 181.

149

CHEMICAL FLOODING

BEHAVIOR OF SURFACTANTS IN EOR APPLICATIONS AT HIGH TEMPERATURES LYMAN L. HANDY Department of Petroleum Engineering University of Southern carifornrb

ABSTRACT Temperature sepsitive properties of some anionic and nonionic surfactants used in EOR operations have been measured. Of particular interest is the thermal stability. Those surfactants we investigated decomposed by first order kinetics. The stability can, therefore, be quantitatively expressed in terms of the half-life of the surfactant. At 180°C half-lifes for petroleum sulfonates varied from 1 to 11 days. Activation energies were measured and these data can be used to predict half-lifes at other temperatures. Solubility of nonionics is known to be affected by temperature. At the cloud point they dehydrate and become less soluble. Anionics appear to form precipitates with rock minerals. This problem increases with increasing temperature. Adsorption is temperature dependent although the experimental results for the anionics were obscured by precipitation. Adsorption of nonionics were observed to decrease with increasing temperature at low concentrations but to increase with temperature at high concentrations. Interfacial tensions have a l s o been measured as a function of temperature. The results vary with the surfactant. Mixtures of sulfonates, however, have all s h a m an order of magnitude reduction in interfacial tension at temperatures in excess of 120%.

INTRODUCTION Much of the unrecovered oil in the United States occurs in heavy oil deposits, mostly in California. Large accumulations of heavy oil are also known to occur in Venezuela, Mexico, Canada and elsewhere. To recover this oil the viscosity must be reduced by orders of magnitude. The only feasible way to accomplish this objective is to heat the oil in-place. This can be done by either steamflooding or in situ combustion. Steam injection is the most frequently used process. This has given rise to the investigation of various chemical additives which will improve the process. One of the problem with steam is that it tends to finger through the formation and to override the oil. Various organic chemicals have been investigated for use with steam as flow diverters to minimize gravity override. Surfactants are being evaluated as possible additives which will reduce the residual oil saturation in that portion of the reservoir which is flooded only with hot water during steam drive. Although the temperature requirements for chemicals to be used at steam tempiratures are much more rigorous, high temperatures are also encountered in the deeper reservoirs which are currently being considered for enhanced oil recovery. This has introduced additional requirements with respect to the temperature compatibility of chemicals used in these reservoirs.

150 In the present paper we are concerned, primarily, with surfactants, but problems are also encountered with polymers at high reservoir temperatures. Four aspects of the effect of temperature are considered: the effect on the stability of the surfactants, the effect on solubility, the effect on water-oil interfacial tensions and, finally, the effect on adsorption onto the solid matrix.

THERMAL STABILITY A limited number of studies have been reported in the literature on the stability of surfactants suitable for oilfield operations at temperatures in excess of 100°C. The most extensive of these is that of Handy et al.’ Data have also been reported by others for the petroleum sulfonate, TRS 10-80, but no temperatures were stated for those experiments.2 In our earlier report results were presented for anionic and nonionic surfactants. The anionics included sodium dodecylbenzene sulfonate, an acidic Dowfax sulfonate and several petroleum sulfonates. The petroleum sulfonates included TRS 10-80 manufactured by Witco and Petrostep 465 manufactured by Stepan Chemical Corporation. Dowfax 240 was from Dow Chemical Company. The nonionic was an alkylphenoxypolyethanol manufactured under the trademark of Igepal CO-850 by GAF.

The surfactants were mixed at various concentrations without salt and aged at elevated temperatures in Teflon containers in Parr Acid Digestion bombs. Particular care was taken to eliminate air from the bombs. Long term aging tests were conducted in sealed borosilicate glass vials. In comparing our work with that of others, a major factor is the method used for chemically analyzing for the active surfactant. The most common procedure is the Epton titration, which involves a dye transfer between two phases. We found the end points difficult to detect in this procedure. We used instead W spectrophotometry. The bond which ruptures during high temperature aging is the sulfur-aromatic ring bond. Disubstituted aromatic rings have a characteristic absorption wave lengths at 220-240 nm and 260-280 nm. When the sulfur-aromatic ring bond ruptures, the absorption at these characteristic wavelengths is decreased. The decrease in the concentration of the active surfactant can be measured quantitatively from the change in the peak heights. Concentrations were determined from a comparison of peak heights with those observed for solutions of known concentration. The alkylphenoxypolyethanols could also be analyzed by W absorption because these compounds also have a disubstituted aromatic ring. A modification of the Epton titration has been proposed by Mukerjee which is reported to be more quantitative than the original method. We have not tested that procedure. The decomposition reaction for the petroleum sulfonates is the following: ArSO;

+ 2H20

ArH

+ SO;

+ H30=

It would be possible, therefore, to monitor the reaction from a measurement of the pH. Representative data from reference 1 are given on Figures 1 and 2. The plot of the logarithm of concentration versus time was linear. pH versus time was also observed to be linear. The other anionic surfactants gave similar behavior. These results indicate that the decomposition reaction for the anionics is first order. The decomposition rate for a reaction following first order kinetics is

-

dC/dt = kt

151 c

=

c0c-kt

or log

c

=

-kt + 2.303

log co

In these equations C is concentration in moles per liter; C is the initial 0 concentration; t is time in days and k is the rate constant in days-'. The rate constant is determined from the slope of the semilog plot. One can also show that when C/Co 4, the elapsed time is equal to the half-life of the surfactant.

-

TRS 10-a0 C, = 243 x IU3M

70

I

0

99

OI 144 Ism HEATING TIME (HRS)

240

Fig. 1-Concentration of TKS 10-80 as function of heating time at 149°C and 204°C

Fig. 2 - pH of TRS 10-80 as function of heating time at 140'C

If one has rate constants at several different temperatures one can determine the activation energy for the reaction. With the activation energy one can determine rate constants and half-lifes at other temperatures. This is particularly useful in estimating the stability of surfactants at lower temperatures for which the decomposition rates are low and long times would be required to measure the half-lifes. Figure 3 is a plot of the log of the rate constant versus the reciprocal of the absolute temperature for TRS 10-80. This plot is typical of those obtained for the surfactants which were tested. In the equation log

a

-E a 2.303 RT +

Ea is the activation energy in cals/mole; R is 1.987 cals and T I s the absolute temperature in OK. From the slope of the plot one can determine the activation energy.

152 A summary of decomposition data for several surfactants is given in Table 1. At 180°C Petrostep 465 is the most stable of the surfactants we investigated. Because of its high activation energy relative to the other surfactants, this surfactant would have a half-life of about 16 years at 100°C. None of the surfactants have adequate stability for use at normal steam temperatures. These results would be expected to be representative for aryl sulfonates, but better stabilities have been informally reported for alkyl sulfonates.

I

1

I

1

TRS 10-80

I

w

0.7 0.5

SOLUBILITY 0.21 I 1 1 I I Quantitative data on the effect 2.0 21 ?A? 2.3 2.4 28 of temperature on the solubility of f IO~PK-IJ petroleum sulfonates have not been reported, but evidence has been cited Fig,. 3 - The rate constant (k) by several authors that precipitation 1 of the sulfonates occurs at the a s tunction of -(OK-') for T higher temperatures in natural sand'IKS 10-80 stones. * s 5 , This occurs not as a result of a direct temperature effect on the solubility of the surfactants but, apparently, as a result of an interaction with minerals in the porous media. Reed has measured a significant increase in the solubility of rock minerals at steam temperatures.' The petroleum sulfonate ions form precipitates with divalent cations. These precipitates are likely to decrease in solubility with increasing temperature. In general, the presence of salt in the solutions decreases the solubility of the sulfonates.

TABLE 1 SUMMARY OF DECOMPOSITION DATA FOR SURFACTANTS Surfactant

Mol. Wt.

Temp. "C

NaDDBS

348.5

130 180 150 180

Dowfax 2AO

500

177

TRS 10-80

415

149 204.5 180

Petrostep 465

465

130 157 180

Igepal CO-850

1100

130 180

t$(days) 6.13 .22 13.6 1.75 5.6(W) 6.9(pH) 17.4 3.0 7.0 444 108 11 .75 .22

Ea(kcals) 24.0 24.0 26.0 26.0 NA 12.4 12.4 12.4 25.2 25.2 25.2

8.84

8.84

Ziegler observed turbidity in the produced fluid from a Berea sand pack when sodium dodecylbenzene sulfonate solutions were injected at a concentration of 1400 pmols/liter. However, data in Figure 4 show that surfactant precipitated out of a 0.2 molar salt solution could be redissolved when distilled water was injected and when the temperature was increased. In this experiment the sand pack was flushed with 1374 pmols/liter surfactant In 0.2 M NaC1. Then the pack was flushed with salt solution only, with distilled water and. finallv. Fig. 4-Desorotion curve for NaDDBS with distilled wate; at 180'C. Distilled water redissolved sulfonate precipitated out of, brine and an increase in temperature to 180'C did redissolve sulfonate still precipitated at 40°C after the distilled waterflood. The solubility of nonionic surfactants is not as sensitive to salt concentration as that of the anionic surfactants. On the other hand, the solubility of the alkylphenoxypolyethanols shows a marked sensitivity to temperatures. At very specific temperatures called the cloud points, the ethoxy groups in these compounds lose associated water and the solubility decreases abruptly to form precipitates. The cloud point is a function of the molecular weight of the surfactant, the electrolyte composition and the concentration of the surfactant. Cloud points as a function of concentration for Igepal CO-850 are shown in Table 2. TABLE 2

SUMMARY OF PHYSICAL AND SORPTION PROPERTIES FOR IGEPAL CO-850 Molecular Weight

-

CMC = 100 w l / L

1,100

Cloud Points

cn trunOl/L)

Cloud Point ("C)

73

>180 113 106

366 640

Sorption Properties Temperature ("C)

Keq (dm'/pmol)

A (pmol/m2)

kl (dm'/pmol.h)

k2

(hours-')

45

5.78~

0.524

1.2 x

0.21

70

2.09 x lo-'

0.705

1.5 x

0.72

95

7.34 x lo-'

0.831

2.5x10-'

3.41

AHo (Id). -40.2

154 EFFECT OF TEMPERATURE ON SURFACTANT ADSORPTION If low concentration surfactants are to be used in combination with steamflooding or hot waterflooding in a reservoir. the effect of temperature on adsorption becomes a matter of considerable importance. Surfactant transport could be combined with heat transport through the reservoir. The surfactant concentration shock could either lead or trail the temperature shock. Data will be presented later which shows that interfacial tensions are reduced at higher temperatures. If this is the case, one would prefer to have the surfactant front remain in the heated portion of the reservoir. In steamflooding, however, it is well-established that the steam overrides the oil. The water transporting the surfactant is likely to be moving primarily in a heated region immediately below the steam zone. In that case the surfactant will be moving in a hot portion of the reservoir under isothermal conditions. Whichever mechanism prevails in the reservoir, adsorption isotherms will be required for the prevailing temperature at which the surfactant is being transported. Consequently, we have made an initial effort to determine adsorption Isotherms as a function of temperature for an anionic and a nonionic surfactant. An abundance of data exists in the literature for adsorption of surfactants onto various substrates at room temperature. These data normally obtained by equilibrating the surfactant solutions with the surfaces. Measuring adsorption isotherms at steam temperatures is a difficult problem.

various were solid much more

Ziegler et al. obtained data using a dynamic, chromatographic transport procedure. The porous medium was a disaggregated. fired Berea sandstone, packed in a core holder. The core was saturated with brine or distilled water and placed in an oven to maintain the temperature at the desired value. Surfactant solution was injected, starting at low concentrations. The pore volumes of solution required to move the surfactant through the core were measured. From chromatographic transport theory the quantity of surfactant adsorbed at this concentration could be calculated.

'

The surfactant concentration in the injected solution was increased stepwise and the volumes required to move each concentration step through the core was measured. The surface area of the sand had been measured by a variation of the BET method. From these data the adsorption isotherm

-

isotherms were also measured E 28' by the conventional static method at 25OC and 95OC. -24Dynamic and static adsorption data were obtained for sodium o 20dodecylbenzene sulfonate x (NaDDBS) and Igepal CO-850. 16: As discussed earlier, the NaDDBS has a low solubility in 0.2 molar NaCl and also tended to precipitate at the higher temperatures when in contact with the Berea sandstone. Consequently, only adsorption isotherms obtained by the static method are reported for NaDDBS. These data are shown at 25OC and 9SoC for concentrations up to 70 pmols/L on Figure 5. The results show

9 $

I

I

I

I

I

NoCl

=

I

02 Y

0

I

I

I

--

'

---

155 that adsorption decreases with increasing temperature as one would expect. Data obtained in the absence ot salt show less temperature dependence. Because of the precipitation problem, no dynamic data are reported for NaDDRS. 'Thc results o t desorption experimenLs are shown in Figure 4, but the slugs of surfactant being produced after reducing Lhe salt Concentration or after increasing the temperature had been explained earlier as being more the result of dissolving precipitated surlactant than desorption or adsorbed surfactant. The slug produced after increasing Llie temperature, however, may have resulted in part from decreased adsorption at elevated temperatures. This would be consistent with the limited static data showing a decrease in adsorption with temperature. The experiments with Igepal CO-850 were complicated by the cloud point, which is characteristic of this class of surfactants, and by the instability of this surfactant at high temperatures. Static results are given in Figure 6 . 28 Equilibration time for the ' 1 1 1 1 1 1 1 1 95OC curve was limited to E three hours. Degradation NeCl :O O M was a serious problem if significantly longer times were used. The results show a slight temperature depend- i ence. Figure 7 is an example I! 16 of results obtained by the dynamic method for Igepal CO-850. Surfactant was LEGEND injected at an initial con- ;oa + 25% centration of 67 pmols/L 2 -9- 95% and at two incremental coni~ centration higher than the initial. Consistent with a 2 1 1 1 1 1 1 1 ~ Langmuir-type isotherm, the O0 0 20 40 60 80 m pore volumes of injected SURFACTAM CONCENTRATION, M I 1 O6 surfactant required to produce the incremental step Fig. 6 - Static adsorption isotherms f o r in concentration decreased Igepal CO-830 with increasing concentration. Dynamic data were obtained at 45°C. 70°C and 95°C. Data were not obtained at higher I 1 I I I I I I I temperatures because of the 0 0 0 0 0 limit established by the cloud point's. Degradation of Igepal is not a problem in the dynamic procedure because the surfactant is LEGENO at an elevated temperaCo = 6?uM, v = 139 m/h ture only while moving -c- CO = 331uM, v 1 137 m/h through the core. 0

'

(v

-

-

-




Y

1

0.02 0.I

.

0.5 ID 20 30 NoCl CONCENTRATION (WT %)

-

Fig. 12 Interfacial tensions as functions of NaCl and TKS 10-80 concentrations at 177OC

CONCLUSIONS The results of our experimental work and data reported by others suggests conclusions about

159 t h e behavior or surfacLants a t elevated temperature. Some ol these conclusions are quite specific and dependable for the systems to which they apply. Many are tentative. Certainly more work is required to extend the nuinber of sureactants wtiicla liavc been evaluated at high tempcratures.

I .o

as

1

I

1

1

1

I

MIXTURE OF ANIONIC SURFACTANT VS N-OOD€W

4a2

a5

Ei 1

05

-

1. The surfactants investigated 02 SURFACTANT were observed to decompose by Y TRS 10-80 first order kinetics. Therefore, & I)I PETROSTEP 465 . a quantitative measure of the E PETROSTEP 450 . stability of a surfactant at a f oo( NeCI CONC g/L given temperature is its Iialf0 2 0 life. Activation energies were rn determined for several surfactants. Stabilities can be estimated from these energies at 00; higher or lower temperatures than those used in the experiments. FIR. 13- Interfacial tensions as Ciinc2 . The anionic petroleum sulfotions o f temperature and salt concennates were observed to be more tration for lsurfactant mixtures against stable than the nonionics. The n- dodccanc stabilitv of the best sulfonate would be only marginally acceptable at temperatures to 180°C but other surfactants need,to be evaluated. All of the surfactants tested would be adequately stable at normal reservoir temperatures

.

3. Evidence suggests that the sulfonates may be precipitated at steam temperatures as a result of an interaction with solubilized rock minerals which show limited solubility at elevated temperatures. The solubility of the nonionics decreases abruptly at the characteristic cloud point. This limits the concentration at which these surfactants can hr uscad at higher temperatures.

4. Dynamic and static methods were used for evaluating the temperature effect on adsorption. The data suggest that adsorption decreases for both sodium dodecylbenzene sulfonate and for Igepal CO-850, but the effect is not as substantial as one might have expected. Additional data are required with other surfactants in consolidated sandstones.

5. A substantial amount of data is being accumulated relating interfacial tension and temperature. For specific types of petroleum sulfonates some data indicate little effect of temperature on interfacial tensions. On the other hand, pendent drop data do suggest a significant decrease in interfacial tension with temperature for optimum salt and surfactant concentrations. Other results show a decrease in interfacial tension with temperature for mixtures of sulfonates against pure hydrocarbon or mineral oil. The nonionic, Igepal DM-730, showed a sharp minimum in the int'erfacial tension at a specific temperature. That temperature appears to be related to the cloud point.

160 REFEKENCES 1.

HANDY, L. L., AMAEFULE, J. O., ZIECLER, V. M., and ERSHAGHI, I.; "Thermal Stability of Surfactants for Reservoir Application", paper SPE 7867 presented at SPE Fourth Intl. Symposium on Oilfield and Geothermal Chemistry, Houston, Jan. 22-24, 1979.

2.

ISAACS, E. E., PROWSE. D. R., and RANKINE, J. P.; "The Role of Surfactant Additives in the In Situ Recovery of Bitumen from Oil Sands", Paper No. 81-32-13, presented at the 32nd Annual Technical Meeting of the Petroleum Society of ClM, Calgary, May 3-6, 1981.

3.

MUKERJEE, P.; "Use of Ionic Dyes for the Analysis of Ionic Surfactants and Other Ionic Organic Compounds", Analytical Chemistry (May 1956) 2 (5) 870.

4.

ZIECLER, V. M. and HANDY, L. L.; "Effect of Temperature on Surfactant Adsorption In Porous Media", SOC. Pet. Engr. Jour. (April 1981) 21 (2) 218-226.

5.

CELIK, M., GOYAL, A., MANEV, E., and SOMASUNDARAN, P.; "The Role of Surfactant Precipitation and Redissolution in the Adsorption of Sulfonate on Minerals", paper SPE 8263 presented at the SPE 54th Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26, 1979.

6.

REED, M. G . ; "Gravel Pack and Formation Sandstone Dissolution During Steam Injection," J. Pet. Tech. (June 1980) 941-949.

7.

GOPALAKRISHNAN, P., BOREIS, S. A., and CAMBARNOUS, M.; "An Enhanced Oil Recovery Method -- Injection of Steam with Surfactant Solutions", Report of Group d'Etude IFP-IMF Sur lee Milieux Poreux Toulouse (1977).

8.

SANDVIK. E. I., GALE, W. W.. and DENEKAS, M. 0 . ; "Characterization of Petroleum Sulfonates", SOC. Pet. Engr. Jour. (June 1977) 184-192.

9.

McCAFFERY, F. G.; "Measurement of Interfacial Tensions and Contact Angles at High Temperature and Pressure", J. of Canadian Petroleum Technology (July 1972).

10.

GASH, B., and PARRISH, D. R.; "A Simple Spinning-Drop Interfacial Tensiometer", J. Pet. Technology (January 1977) 30-31.

11.

BURKOUSKY, M. and MAX. C.; "Applications for the Spinning Drop Technique for Determining Low Interfacial Tension", Tenside Detergents (1978) 15 (5) 247-251.

12.

NELSON, W. L. ; "Petroleum Refinery Engineering", (1958) 157-161.

13.

HANDY, L. L., EL-GASSIER, M. and ERSHAGHI, I.; "Interfacial Tension Properties of Surfactant-Oil Systems Measured by a Modified Spinning Drop Method at High Temperatures", paper SPE 9003 presented SPE Fifth Intl. SvaDosium on Oilfield and Geothermal Chemistry, Stanford University, May 28-30, 1980.

14.

ZEKRI, A.;

15.

JACOBSON, J. K., MORGEN, J. C., SCHECHTEX, R. S., and WADE, W. H.; "Low Interfacial Tensions Involving Mixtures of Surfactants", SOC. Pet. Engr. Jour. (1976) 122-128.

Personal Communication.

CHEMICAL FLOODING

161

SURFACTANT SLUG DISPLACEMENT EFFICIENCY IN RESERVOIRS; TRACER STUDIES IN 2-D LAYERED MODELS

ROBERT J. WRIGHT, RICHARD A. DAWE and COLIN G. WALL

Petroleum Engineering Section, Imperial College, London SW7 2AZ

ABSTRACT

The e f f e c t s of layering within porous material with regard t o basic flow mechanisms and chemical dispersion have been investigated. have been performed within unconsolidated g l a s s bead packs.

Experiments The

variables controlled were layer permeability and dimensions, f l u i d v i s c o s i t y and flow r a t e ; gravity and c a p i l l a r y pressure influences were eliminated by using model f l u i d s of matched density and complete miscibility.

The importance of channeling and crossflow e f f e c t s a r e emph-

asized by t h e r e s u l t s , and the behaviour of non-unit mobility r a t i o displacements i s predictable using r e l a t i v e l y simple conceptual/mathema t i c a l models.

The dispersion of chemical t r a c e r s between layers has

a l s o been modelled mathematically and t h e r e s u l t s have been applied t o laboratory t e s t s on heterogeneous cores.

162 INTRODUCTION

,

I t is well known that t h e n a t u r a l heterogeneity of petroleum reservoir material is one of the major problems i n chemical E.O.R. processes. Of p a r t i c u l a r consequence are the non-random v a r i a t i o n s i n permeability to be found within porous rocks. Layering s t r u c t u r e s a r e a common feature of sandstones and their e f f e c t s have been reviewed i n recent l i t e r a t u r e w i t h reference to f l u i d flow (1) and dispersion mechanism ( 2 ) . The efficiency of s u r f a c t a n t slugs is probably the most l i k e l y application of these considerations; however the fundamental problems a r e ocnmnon to a l l E.O.R. processes. We have investigated layered models, both conceptual/ mathematical and physical ( v i s u a l ) . Experimentally, flow mechanisms and dispersion e f f e c t s have been monitored using dye tracers. Displacements have been of an i d e a l miscible type and therefore represent p e r f e c t microscopic displacement efficiency. The properties peculiar t o surfactants such as adsorption, phase equilibrium and emulsification characte r i s t i c s have been excluded i n t h e present work. W e a r e taking the approach t h a t the gross f l u i d flow and dispersion e f f e c t s w i t h i n heterogeneous media shoald be b e t t e r understood before laboratory core-flood r e s u l t s and data from l i n e a r homogeneous packs can be applied t o the reservoir system. W e have attempted t o view miscible and immiscible displacement mechanisms on a common b a s i s s i n c e the two concepts merge i n ultra-low-tension systems.

The experimental work discussed here involved idealized layered models of packed Ballotini. The flow mechanics of displacements a t various (favourable and unfavourable) mobility r a t i o s were recorded by photographing dye t r a c e r boundaries under conditions of flow r a t e f o r which diffusion/dispersion e f f e c t s were small. To quantify dispersion phenomena we have considered equiviscous miscible displacements, and we describe here numerical predictions w i t h one example application. Conceptual models were developed, based on simple two layer-channel interactions. This approach follows contributions within the l i t e r a t u r e on dispersion ( 2 ) & (3) and crossflow ( 4 ) & ( 5 ) i n such model systems.

FLOW PATTERNS I N LAYERED MEDIA

I t has been found useful t o consider simple two-channel conceptual m o d e l s

i n order t o account f o r crossflow behauiour i n multilayered and s t r i a t e d media. CrosSflow d i r e c t i o n s and approximate magnitudes can be demons t r a t e d mathematically by considering t h e v a r i a t i o n of flow p o t e n t i a l along the axes of the channels. Figure l ( i )i l l u s t r a t e s two p a r a l l e l channels composed of homogeneous and continuous porous media; a high permeability channel ( a ) and a less permeable channel ( b ) . The displacement of f l u i d (1) by f l u i d ( 2 ) within this model ( i n t h e x direction) has resulted i n two displacement boundaries ( a t Xa and q). The instantaneous pressure p r o f i l e s a r e p l o t t e d f o r two d i f f e r e n t viscosity r a t i o s ; displacing f l u i d t h e more viscous i n F i g . l ( i i ) and the l e s s viscous i n F i g . l ( i i i ) .

163

t

(i) Displacement i n dual channel m o d e l

Y

1

P

ii

(ii) P r e s s u r e P r o f i l e s f o r !J2 > p1

0 1

P -

(iii) P r e s s u r e P r o f i l e s f o r

R

p2 < p 1

0 X+

L

x4

Figure 1.

This assumes no c a p i l l a r y p r e s s u r e , d i s p e r s i o n , g r a v i t y o r c c m p r e s s i b i l i t y e f f e c t s ; also f o r t h e moment, no crossflow between t h e channels (as i f s e p a r a t e d by a n i m p e r m e a b l e b a r r i e r ) . I t is, however, a u s e f u l method for r e p r e s e n t i n g local croltsflow tendencies as i n d i c a t e d by pressure drops ( a t f i x e d x) between the channel axes. C r o s s f l o w would therefore be s t r o n g e s t around t h e displacement f r o n t s a n d o c c u r s i n t h e d i r e c t i o n s i n d i c a t e d i n Table 1.

Table 1. Fig.

p2

Location.

l(iii)

>1

0.1 and p2/p1 < 0.1, a s a general guide.

167 Experimental Results. Flow v i s u a l i z a t i o n experiments were conducted with matched d e n s i t y f l u i d p a i r s having " adverse" v i s c o s i t y ratios. The packed bead models were as described above. Experiments were d i s t i n g u i s h e d by t h e parameters given below:-

Experiment

0

1

*

3

*

2

0

4

kakD

d/L

1 1.:

1'/2'

}

0.33

2.8

0.22

.IS

-L xb

Figure 6. .I

R e l a t i v e Front Positions.

45

a a

"Mean f r o n t " p o s i t i o n s were e s t i m a t e d from c o l o u r photcgraphs t a k i n g i n t o account d i s p e r s i o n and local f i n g e r i n g . When p l o t t e d v e r s u s time,approxi m a t e l y s t r a i g h t l i n e t r a c k s were obtained; data scatter being n o t too serious. The r e s u l t s i n terms o f t h e l e a d i n g f r o n t displacement (xa) and are p l o t t e d on Fig. 6, along w i t h t h e numerically t h e main f r o n t (a) p r e d i c t e d curves using t h e parameters given i n Table 2. The c o r r e l a t i o n o f experiment and c d l c u l a t i o n s is encouraging. However, t h e s e p r e d i c t i o n s are based on equating xb/L to t h e dimensionldss t i m e (of Figs.3 - 5 ) which is n o t expected t o be a good approximation i n a l l cases. I t is n o t i c e a b l e t h a t t h e r e is a s i g n i f i c a n t dependence on v i s c o s i t y ratio: An i n t e r e s t i n g f e a t u r e o f m o s t experiments is the r e l a t i v e l y f a s t i n i t i a l p e n e t r a t i o n i n t o t h e high p e r m e a b i l i t y l a y e r , a d e t a i l c o n t r a d i c t e d by t h e n m e r i c a l r e s u l t s . S i m i l a r f i n d i n g s are d e s c r i b e d by Peaceman and Rachford (6) f o r vtscous f i n g e r i n g i n randomly v a r i a b l e porous media.

168 Discussion of Analytical Methods. I t is useful t o consider a t t h i s point the effectiveness of an a n a l y t i c a l solution method based on 1-dimensional flow theory and "pseudo" r e l a t i v e permeability functions ( 7 ) . These a r e b e t t e r described a s synthetic functions since they a r e derived by adding together t h e e f f e c t s of the individual layer properties. The r e l a t i v e permeabiliw t o displacing ( 2 ) and displaced (1) phases a r e p l o t t e d versus s a t u r a t i o n of phase ( 2 ) on Fig. 7 f o r the model parameters of experiments 3 and 4. Use of these functions is i d e a l l y r e s t r i c t e d to immiscible (no diffusion) processes; however they can be applied to miscible processes when the e f f e c t of dispersion is negligible. A useful feature of t h e present displacements is t h a t they should give r e s u l t s which a r e similar t o p e r f e c t ultra-lowtension displacements (having negligible c a p i l l a r y pressures and 100% microscopic displacement e f f i c i e n c y ) .

Predicted saturation/distance p r o f i l e s based on the above functions using the v i s c o s i t y r a t i o s of i n t e r e s t a r e given on Fig. 8 . These extended d i s t r i b u t i o n s a r e not found i n p r a c t i c e even when l o c a l fingering is taken i n t o account: however i t is only t h e averaged displacements w i t h i n 1.0) flowing regimes the f a s t (S2 = 0 0.14) and s l o w (S2 = 0.14 which w i l l be considered (dotted l i n e s ) . The r a t i o of displacement r a t e s

-

-

1.0

0.5

t 5,

0

s,

1

Fig. 7. Relative permeabilities.

0

-

0 X/L 0.5 Fig. 8 . Theoretical saturation distributions.

1.0

a r e predicted t o be 8.5 f o r a viscosity r a t i o of 0.33 and 12.9 f o r a These r e l a t i v e r a t e s a r e about a f a c t o r of two viscosity r a t i o of 0.22. g r e a t e r than those indicated i n Fig. 6 . I t is thought therefore t h a t 1dimensional flow theory exaggerates the e f f e c t of mobility r a t i o f o r reasons concerning crossflow mechanism. I t may therefore be possible, using convenient approrimations,to obtain predictions f o r miscible and low tension displacements w i t h i n layered media which a r e s i g n i f i c a n t l y b e t t e r than those provided by a n a l y t i c a l 1-dimensional methods. m t i u t i v e & s u i t s : Favourable Mobility Ratio Continuous Displacement. Crossflow is the p r i n c i p l e mechanism by which a displacement f r o n t may be s t a b i l i z e d against the influence of l o c a l permeability variations. The dual-channel pressure p r o f i l e s discussed above can be used to explain t h i s flow mechanism and t h e "shock front" concept of 1-dimensional displacement theory ( 5 ) .

169 I n sane preliminary work we used a packed bead model containing four f a s t flow channels (permeability r a t i o 13:l) of d i f f e r e n t width. The r e s u l t s r e f l e c t a considerable influence of g r a v i t y since t h e displacing f l u i d was more dense and was flowed v e r t i c a l l y upward. Pig. 9 i l l u s t r a t e s traced displacement f r o n t s ( f u l l l i n e s ) i n r e l a t i o n to t h e layer bounda r i e s (dashed) f o r three s t a g e s ( f r a c t i o n a l pore volrrmes i n j e c t e d indicated). Here l.12/l.11 = 5, Ap = 0.113 g/cm3; while on Fig. 10 are the observations f o r p2/p1 = 10,Ap = 0.149 9/cm3. Predictions based on s y n t h e t i c r e l a t i v e permeabilities f o r t h i s model lead t o the s i n g l e shock f r o n t s shown ( d o t t e d ) . The s u p e r f i c i a l flow r a t e was greater i n t h e l a t t e r case (1.8 x 10-3cm/sec, a s compared with 0.91 xlO-’an/sec) and the e f f e c t of t h i s is t o compensate t o some e x t e n t f o r the e f f e c t of a higher v i s c o s i t y r a t i o .

Fig. 9.

Fig. 10

Shock f r o n t formation is c l e a r l y not observed. The o s c i l l a t i o n s of f r o n t a l boundary appear t o increase i n amplitude with increase i n channel diameter ( t h e f a r r i g h t channel is r e a l l y a half-channel since there is a no-flow boundary a t i t s s i d e ) . I n t h e case of t h e higher v i s c o s i t y r a t i o displacement t h e r e is l i t t l e change i n t h e f r o n t a l shape with time. I t has been found t h a t the basic c h a r a c t e r i s t i c s of such s t a b i l i z e d displacement p a t t e r n s can be approximated by considering dual-channel pressure p r o f i l e s . Figure 11 i l l u s t r a t e s the form of such p r o f i l e s when viscous crossflow (but not gravity) is allowed f o r . The S t a b i l i z a t i o n

Figure 11. Pressure p r o f i l e s f o r favourable m o b i l i t i e s with crossflow.

Phenanenon, which tends t o discourage channeling i n t o the high permeability zone) depends upon the crossflow which i t s e l f i s governed by the region between t h e two p r o f i l e s . The geometry of t h i s region can be approximated by a t r i a n g l e enabling an expression t o be derived f o r a s t a b i l i z e d q),assuming the v e l o k i t i e s of the two f m n t e are separation “6”( = x a

-

170

IT. E . DANFORTM

I’aye 193 (2). Thermal Activation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 (3). Decay of Enhanced Emission.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 (4). Activation by Reverse Current.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 (5). Effects of Products from Nearby Cathodes.. . . . . . . . . . . . . . . . . . . 198 3. Mechanisms of Disappearance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 a. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 b. Electrolysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 c. S p u t t e r i n g , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 d. vapora at ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 4. Optical Phenomena in Crystalline Thorium Oxide., . . . . . . . . . . . . . . . . . . 202 5. Electrical Conductivity of Thorium Oxide.. . . . . . . . . . . . . . . . . . . . . . . . . 204 a. Powdered or Sintered Specimens.. . . . . . . . . . . . . . . . . . b. Crystalline Specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 210 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1). Three “Stateu of Activation”. . . . . . . . . . . . . . . . . . . . . . . . . .

I. INTRODUCTION The appearance of thorium oxide on the scene of high-powered tube engineering has been gradual over the past three decades, and was naturally accelerated by World War 11. I n general, it may be said t o be used in applications where barium-strontium oxide falls short in some aspect of ruggedness and where the extra heating power required by the thoria cathode is not impracticable. The present paper describes certain practical applications of thorium oxide emitters, outlines the outstanding problems and the types of research and development which are under way, and presents those rather fragmentary theoretical developments which research workers have succeeded in achieving a t the present writing. Even more than with barium oxide, the theory is still only semiquantitative, and decisive experiments are lacking. Comparing the thorium oxide situation with that of barium oxide one finds that less work with theoretical intent has been done in the former case. This is due to the fact that the latter has occupied a far more important commercial position for over a quarter of a century. Actually it may appear that, as a subject of research in semiconductor thermionics, the thorium oxide system is more amenable to quantitative understanding than is the barium oxide emitter. OXIDEAND PRACTICAL ELECTRONICS 11. THORIUM 1. Preliminary

The introduction of thorium oxide into the field of practical electronics came about because of its metallurgical as well as its thermionic properties.’ As a refractory material, insoluble in tungsten, quantities of the order of one percent are added t o tungsten t o control recrystallization

171 maxima covering t h e scatter of d a t a are p l o t t e d on Figure 13,along with crosses i n d i c a t i n g t h e s e p a r a t i o n s based on t h e p o s i t i o n a t which t h e channel is completely occupied by d i s p l a c i n g f l u i d . T h e o r e t i c a l curves applying to o u r model, and o t h e r p e r m e a b i l i t y ratios ( i n d i c a t e d on t h e curves) are included. These g i v e t h e e q u i l i b r i u m s t a b i l i z e d f r o n t a l s e p a r a t i o n s p r e d i c t e d using t h e above equations. Assuming t h e b a r s t o be a c c e p t a b l e a s an experimental estimate of t h i s parameter (remembering t h a t no p i s t o n - l i k e f r o n t is observed i n t h e high p e r m e a b i l i t y channel) then the u s e f u l n e s s of t h e mathematical approximation is supported. This should be viewed i n r e l a t i o n to the p r e d i c t i o n s o f 1-dimensional flow theory based on t h e s y n t h e t i c r e l a t i v e permeability f u n c t i o n s f o r t h e s e The a n a l y t i c a l models, Fig. 7 shows t h e s e f o r experiments 7 and 8 . s o l u t i o n i n d i c a t e s a s i n g l e shock f r o n t through t h e whole system f o r v i s c o s i t y ratios g r e a t e r than 2.82, i.e. 6 = 0. Our experimental r e s u l t s c l e a r l y demonstrate t h a t t h i s is n o t t h e case and w i l l be of more serious consequence t o displacement e f f i c i e n c y as Layer (or other channel) diameters i n c r e a s e .

5

b b

b

+

.

b

b m

8

b.

3

I

b.

.

Figure 12. F r o n t a l S e p a r a t i o n s , Experiment NOS. 0 5 , 0 6 ,

+ 7,

Figure 13. V i s c o s i t y R a t i o E f f e c t , experimental ( b a r s ) and theoretical ( l i n e s ) .

08.

172 SLUG DISPLACEMENTS I t has been found t h a t continuous i n j e c t i o n t e s t s model well t h e development of displacement boundaries a t f r o n t and rear of a "slug" up t o t h e time when overtaking occurs. P l a t e 4 shows a low v i s c o s i t y s l u g f i n g e r i n g and channelling ahead i n a similar way t o the displacements discussed abbve involving continuous i n j e c t i o n . Behind t h e slug we have a favourable r m b i l i t y r a t i o displacement of t y p i c a l pattern. The high v i s c o s i t y slug of P l a t e 5 shows a s t a b i l i z e d form a t i t s f r o n t . I t is pushed by a s i m i l a r liquid,without dye,exhibiting a t y p i c a l equiviscous displacement.

Plate 4

Plate 5

The permeability r a t i o was a s before (2.8) and the v i s c o s i t y r a t i o s involved i n t h e displacement of f l u i d (1) by f l u i d ( 2 ) by f l u i d (3) were f o r P l a t e 4, p3:p2:p1 = 3:1:3, and f o r P l a t e 5 , 4.6:4.6:1. Although the volumes of these s l u g s a r e about 20% of t h e pore volume, l o s s of slug i n t e g r i t y occurs. The low v i s c o s i t y slug ( P l a t e 6) is continuing to be squeezed from the low permeability medium i n t o t h e f a s t flow channel; however the slug is 'near being divided i n t o t h r e e portions. The high v i s c o s i t y slug ( P l a t e 7) has been s p l i t by t h e chase f l u i d which has channelled through and is crossflowing o u t of the high permeability layer, p a r t i c u l a r l y near the f r o n t o f t h e slug.

P l a t e 6.

Plate 7.

The breakdown of s l u g i n t e g r i t y could possibly be r e s i s t e d by chemicals, added t o t h e chase fluid.designed s p e c i f i c a l l y t o r e s i s t c e r t a i n crossflow processes and t h e mixing of out-of-sequence f l u i d s . An example could be the i n - s i t u g e l l i n g polymers which a r e s e n s i t i v e to s a l i n i t y environment ( 8 ) . This is a p o s s i b i l i t y which w i l l be i n v e s t i g a t e d i n f u t u r e modelling work. For s u r f a c t a h t s l u g s the f l u i a r e d i s t r i b u t i o n s discussed above w i l l be combined oith considerable adsorption, dispersion, mass-transfer and g r a v i t y e f f e c t s . Capillary pressure e f f e c t s could a l s o be important even though i n t e r f a c i a l tensions may be low, since mobilized o i l banks w i l l be p a r t l y o r wholly composed of discontinuous o i l whose flow w i l l be highly non-Newtonian. ( 9 ) .

173 DISPERSION I N LAYERED MEDIA

The s t a b i l i t y of chemical slugs w i t h i n channelled porous media can be strongly affected by diffusion/dispersion processes. Eere we consider a two-layer mode1,following the approach of Lake and IiraSaki ( 2 ) and Koonce and Blackwell ( 3 ) for chemical dispersion and Satman and Zolotukhin (10) for the analogous problem i n heat transfer. To scale these effects it is useful t o define a transverse dispersion number ( 2 ) :

14G. N~~

=

3 ,

d2 V

where L and d are the length and width of the system, Kt is the Mansverse dispersion doefficient, V is the superficial flow rate i n the high permeability layer. Lateral dispersion is insignificant when N T D < 0 . 2 , while when N T D > ~ composition is practically constant over any cross-section through the system and the behaviour can be represented by a single effective longitudinal dispersion coefficient ( 2 ) . W e examine here the intermediate range of NTD, between 0 . 2 and 5 , which could apply t o comon f i e l d conditions i f d is of the order of lm and to laboratory core tests i f layers of a few mrn width are present within the porous m e d i u m . W e consider flow parallel t o the layers and tracer dispersion normal t o t h i s direction (longitudinal dispersion coefficient is zero). The l a t e r a l dispersion coefficient has been taken to be constant,independent of concentration, position and flow rate. For reservoir r a t e s , i t is generally found to be of the order of the molecular diffusion coefficient (11). Figure 1 4 shows computed isoconcentration contours .(at 0..1 intervals) within a two layer system, the upper one (between Y values 0.5 and 1.0) flowing from l e f t t o right, the lower is stagnant but receives injected tracer by l a t e r a l dispersion from the permeable layer. Tracer injected a t u n i t concentration is dispersed as shown a t three values of the dimensionless t i m e : T Kt

t - -

d2

=

NTD

_.

14

where T is the absolute time from the s t a r t of the displacement. It is of i n t e r e s t to obtain convenient analytical approximations to the mean tracer concentration within a given cross-section of the flow channel (and of the non-flowing matrix). Figure 15 shows numerical points and analytical curves representing the distribution of average concentration w i t h distance i n the flow direction (normalized for t = 0 . 2 ) The analytical approximations were derived wing solutions t o the zeroconcentration-boundary-condition case ( 1 2 ) , evaluated for short dimensionless times. Expressions of s i d l a r form are applicable t o other channel geanetries (e.g. cylindrical) provided times are short. The approximations derived f o r the heat transfer problem (10) involve also a square root of time dependence; however these integral solutions are very complex because they are intended t o cope w i t h a large time range. Our approximation is:-

T I t l E = O -05 S

I?

I I.-,

?-

I I

-m

0-1

1.2

0.9

I

I

0.4

0.5

1

0.8

FRRCTIONAL OISTRNCE I N FLOY

0.7

0-1

0.)

I

OlRECTlON

-

I

T I t l E = O 10

I

I?

S

>

I *3 ‘

m

Z

t

a

O Z

25 N I 5

0.1

Figure 14.

0.2

0.s 0.a FRRCTIONAL OISTRNCE I N FLOY 0.9

0.4

0.1

0.m

0.)

OlRECTlON

Isoconcentration contours i n two layer system.

I

175 COnPUlEO

0 T=O.OS

A 1.0.10 1=0.15

.?

+

0

f 0

.

lu

0

_I

FITTED

-c; 1-2l'"I 1-1 I - x

I

I

a.1

-1

I

11-3

I

1

0.1

0.3

O.?

I

I

04

0.6

0.1

I

0.a

0-S

I I

FRRCTIONRL OISTRNCL

Figure 15.

E

=

Cross-sectional averaged concentrations i n flow channel.

1

-

2 . 0 t + (1

-

(1

- XI+)

where is t h e average i n j e c t e d tracer concentration w i t h i n t h e cross s e c t i o n ( a t X) of t h e flowing channel; X is t h e f r a c t i o n a l d i s t a n c e e q u a l t o x/V.i

.

similar method can be used t o approximate t h e averaged Concentrations w i t h i n t h e non-flowing matrix (Em) f o r the t w o equal-capacity l a y e r s h e r e considered:-

A

Em

=

2 . 0 t+ (1 -

x% .

Applications to a Multichannel Problem. One approach t o a multichannel problem is to consider each i n d i v i d u a l channel as i n t e r a c t i n g with a surrounding matrix which possesses t h e s u i t a b l y averaged p r o p e r t i e s o f t h e rest of t h e porous body. Generally a non-zero flow rate w i l l apply to t h e e x t e r n a l matrix i n c o n t r a s t t o t h e s t a g n a n t case as above. This n e c e s s i t a t e s c o n s i d e r a t i o n of the problem as one of r e l a t i v e flow rates using moving co-ordinate methods. Tracer e f f l u e n t p r o f i l e s have been analysed i n terms o f v a r i o u s models intended t o account f o r heterogeneity (13) ,(141, (15). Laboratory tracer tests on layered r e s e r v o i r materials are o f i n t e r e s t f o r t w o reasons; f i r s t , conventional methods f o r c h a r a c t e r i z i n g d i s p e r s i o n coe f f i c i e n t s f o r miscible displacement and r e l a t i v e p e r m e a b i l i t y f u n c t i o n s for l o w t e n s i o n immiscible d i s p l a c e m n t may be u n r e l i a b l e ; second, such l a b o r a t o r y Systems can model similar problems on t h e reservoir scale. To estimate mass t r a n s f e r rates f o r t h e channels (e.g.

layers) within a heterogeneous core sample displacement flow tests of d i f f e r e n t rates have t o be compared. Unfortunately, very l i t t l e r a w d a t a of this kind is to be found w i t h i n t h e petroleum l i t e r a t u r e . Our main source is t h e high q u a l i t y r e c e n t work o f Spence and WatJcins (16). Handy (17) has used d u a l tracers to e v a l u a t e d i f f u s i o n e f f e c t s and w e have begun tests on l a y e r e d sands t o n e s using u l t r a - v i o l e t a b s o r p t i o n monitoring techniques.

176 Using the above approximations, and the assumption t h a t flow within the matrix surrounding any given channel-"i" is approximated by the mean velocity oif the whole displacement (v), a method of effluent curve analy s i s has been derived (18). Thus i f the fractions of displacing fluid a t its moment of breakthrough a t the effluent end of the single channel j", (f (1) and f j ( 2 ) ) , a r e known from t w o experiments (1 and 2) performed :t difgerent rates, we can estimate the fractional cross section of the channel (6jS) and i t s effective mass transfer coefficient (M ) thus:j

= Vj

L/T,, L being the length of the test core.

W T j (1) M t = 4Kt/d2

= v

j ( 2 P j (2)

for a l a y e r .

These expressions can be applied to effluent eanposition values measured shortly a f t e r the f i r s t detected breakthrough of displacing phase from the multichannel system. This characterizes the f a s t e s t flow channel(s) of the sample. Subsequent tracer measurenmnts have t o be processed to allow for the ( t i m e dependent) contitbutions from a l l the faster-flowing channels. The gross composktion measured i n one experiment is F(a functibn of'.-) and the individual ("breakthrough") channel "j" contribution can be obtained using the following h1gorithm:-

The effluent profile is analyzed forward i n time as presented above for T C Lfi ; while for T > L f i s u p s are taken backward I n time redbfining F as the concentration of displaced fluid. Asatisfactory analysis can be performed with a proQramable calculator (a program suitable for an "BP 41C" Is available from the authors). Small t i m e steps should be avoided since errors due mainly to intralayer longitudinal dispersion, ignored i n the present analybls w i l l become impartant; ten t o twenty steps for each effluent curve have been found t o be satisfactory.

177 Example r e s u l t s based on some of the t r a c e r composition p r o f i l e s of Spence and Watkins a r e indicated on Figures 16 18. Mass t r a n s f e r coefficient d i s t r i b u t i o n over the cross section of t h e samples is given on Figure 16 f o r a sandstone and a carbonate. M values of lo-' and 1 0 - 4 could be i n t e r p r e t e d i n terms of layers of & o u t 2 . 0 cm and 0 . 5 an width respectively. Figure 1 7 gives the "no dispersion" velocity p r o f i l e s of the porous media. The l a t t e r can be represented as r e l a t i v e permeability functions (Fig. 18) applying to the i d e a l "no dispersion" case o r t o the i d e a l near-zero-interfacial tension immiscible displacement case. Predi c t i o n s of mobility r a t i o e f f e c t s could therefore be made using conventional 1-dimensional displacement theory. However, f o r Righly heterogeneous media allowance f o r crossflow e f f e c t s , as discussed above, should be included.

-

-

Figure 17.

Figure 16.

Mass t r a n s f e r coeffkcient d i s t r i b u t i o n s ~ ~ lines:"Sandstone 1 1 SS2" Dashed l i n e s : "Carbonate B 17"

Velocity d i s t r i b u t i o n s .

Figure 18. Miscible type r e l a t i v e penneabilities .

coNcLus10Ns Surfactant E.O.R. slugs w i l l be susceptible t o layer and streak permeabi l i t y heterogeneities found within reservoirs due t o disturbance of flow p a t t e r n s and increased dispersion. Mathematical approximations have been found which a r e capable of modelling the channelling and crossflow e f f e c t s present i n non-unit mobility ratio displacements. Experimentally, l o s s of i n t e g r i t y due to flow mechanism has been observed in slugs of around 20% pore volume. Diffusion/disper$ion e f f e c t s can be large, depending on the width of layers. For s h o r t dimensionless times it is possible to model khese phenamena a n a l y t i c a l l y to match numerical simulations and to analyze tracer t e s t data.

178 ACKNOWLEDGEMENTS Dr. M. Allmen is thanked f o r performing t h e d i s p e r s i o n computations and Mr. M. Hughes f o r t e c h n i c a l help. W e are g r a t e f u l t o t h e Department o f

Energy f o r f i n a n c i a l support.

REFERENCES

L.

WEBBER, K., Influence On F l u i d Flow of Conrmon Sedimentary S t r u c t u r e s I n Sand Bodies., S.P.E. Paper 9247

2.

LAKE, 11. & HIRASAKI. G. S.P.E. Paper 8436.

3.

KCONCE. T. & BLAQCWELL, R., I d e a l i z e d Behaviour of S o l v e n t Banks i n S t r a t i f i e d Reservoirs., S0c.Pet.Eng.J. (Dec. 1965) 2 , ( 6 ) , 318 - 328.

4.

HAWTWORNE, R.,

5.

WRIGHT, R. & DAWE.R., An Examination Of The Multiphase Darcy Model Of F l u i d Displacement I n Porous Media. Rev.Inst.Fr.du P e t r o l e (Nov-Dec 1980) 35, (N0.6) 1011 - 1024.

, Taylor's

Dispersion I n S t r a t i f i e d Porous Media.,

The E f f e c t of C a p i l l a r y P r e s s u r e I n a Multilayer Model of Porous Media. S0c.Pet.Eng.J. (Dec. 1975) Is, 467 476.

-

6.

PEACEMAN. D. & RACZiFORD, H., Numerical C a l c u l a t i o n of Multidimensional (Dec 1962) 2, 327 340. Miscible Displacement. S0c.Pet.Eng.J.

7.

€EARN. C.,

8. 9.

-

Simulation O f S t r a t i f i e d Waterflooding By Pseudo Relative Permeability Curves, ( J u l y 19711, 805 813.

g,

-

MACK, J., Process Technology Improves Oil Recovery, O i l & G a s J.(Oct.1979) No. 40, 67 - 71.

77, -

EGBOGAII, E. , WRIGHT, R. & DAWE, R., Porous Media, S.P.E. Paper 10115.

A Model Of O i l Ganglion Movement I n

10.

SATMAN, A. & Z O L O T W H I N , A., Application of the Time-Dependent O v e r a l l Heat T r a n s f e r C o e f f i c i e n t Concept t o Heat T r a n s f e r Problems I n Porous Media, S.P.E. Paper 8909.

11.

PERKINS, T. & JOHNSON, O., A Review o f Diffusion and Dispersion i n POrOUS Media, S0c.Pet.Eng.J. (March 1963) 2, 70 - 84.

12.

CRANK, J., The Mathematics o f Diffusion, Oxford Univ. Press.

13.

KOVAL, E., A Method For P r e d i c t i n g The Performance Of Unstable Miscible (June 196312,145-154. Displacements I n Heterogeneous Media, S0c.Pet.Eng.J.

14.

JOHNSON, C. & SWEENEY, S . , Q u a n t i t a t i v e Measurements Of Flow Heterogene i t y I n Laboratory Core Samples And Its E f f e c t On F l u i d Flow Characteris t i c s , S.P.E. Paper 3610:

15.

ROSMAN, A. & SIMON, R., Paper 5631.

16.

SPENCE, A.

17.

HANDY, L., An Evaluation O f Diffusion E f f e c t s I n Miscible Displacement, 65. Trans. AIME (1959) 216, 6 1

18.

WRICBT, R. et. a l . , Heterogeneous Porous Media; A Miscible Displacement Model;- t o be submitted f o r p u b l i c a t i o n .

1975,Sec.4.3.

Flow Heterogeneity I n Reservoir Rocks, S.P.E.

& WATKINS, R., The E f f e c t o f Miscfoscopic Core Heterogeneity On Miscible Flood Residual O i l S a t u r a t i o n , S.P.E. Paper 9229.

-

CHEMICAL FLOODING

179

SOME ASPECTS OF THE INJECTIVITY OF NON-NEWTONIAN FLUIDS IN POROUS MEDIA PETER VOGEL and GUNTER PUSCH Institut fur Tiefbohrkunde und Erdolgewinnung, Technical University Clausthal. West Germany

ABSTRACT In existing numerical models, the rheological behaviour of polymer solutions is commonly described by the power law, which is not satisfactory at very low shear rates and at relatively high shear rates. An improvement of the mathematical description was achieved by using the Carreau viscosity equation and deriving a filter law for porous media. The validity over a wide range of shear rates was proven by experimental results obtained from flood tests in sand packs with one typical product each of the three polymer classes (PAA, HEC, BPS) used in enhanced oil recovery. On the basis of typical reservoir data, the behaviour of an injection well during polymer injection is investigated by calculating the pressure profile around a wellbore. From these data, conclusions are drawn for the selection of polymers according to their rheological properties.

180

I NTRODUCTI ON Flooding with viscous media has aroused increasing interest in the field of enhanced o i l recovery. Numerous pilot projects are currently in progress or have already been terminated / 1 , 2 / . The importance which is at present attached to this field of research is thus evident. Chiefly aqueous polymer solutions are employed as viscous flooding media. A characteristic feature of these polymer solutions is that the decisive parameter for the description of their flow properties, the viscosity, varies as' a function of the shear rate. In general, the solutions exhibit pseudoplastic behaviour, that is, a decrease of the viscosity with augmenting shear stress. In the field of enhanced oil recovery, the viscous behaviour of polymer solutions in porous media has become of vital importance as far as their injectivity is concerned. The investigations were initiated by the following two questions:

-

-

How can the viscosity values indicated in a rheogramme be applied to flow processes in porous media? Can these polymer solutions be injected into the reservoir without exceeding the fracturing pressure of the rock?

In the following, a method which allows a calculation of the injectivity of polymer solutions on the basis of the rheogrammes and of the knowledge of the characteristic reservoir data is presented.

CHARACTERIZATION OF THE POLYMERS EMPLOYED

Information about the flow behaviour of non-NEWTONian fluids is provided by their rheogramme, that is, the plot of the viscosity as a function of the shear rate; this is both important and experimentally easy to obtain. All of the considerations discussed in the following are based exclusively on the information gained therefrom. To begin, the rheogrammes of the polymer solutions used here are presented. The liquids employed are aqueous solutions

181

Figure 1:

Figure 2:

Viscosity behaviour of a polysaccharide solution

viocosity behaviour of a hydroxyethylcelluloae solution

182

I

100

Figure 3:

Viscosity behaviour of a polyacrylamide solution

(original brine with a salt concentration of 1 0 0 g/l; reservoir temperature of 5OoC) of a typical, representative product in each of the three classes of polymers used in enhanced oil recovery. Polymer solutions which yield a mutually comparable additional oil recovery (p' of additional oil per m 3 of polymer solution consumed) in flooding tests were thereby selected. Figure 1 shows the rheogramme for a polysaccharide, figure 2 that for a hydroxyethylcellulose, and figure 3 that for a polyacrylamide solution. A double logarithmic scale has been chosen for the graphic representation. The three curves display characteristic features in common: A plateau occurs in the range of low shear rate; a linear decrease is observed at higher values. For the calculation of the flow behaviour of these nonNEWTONian fluids, an analytical expression for the dependence of the viscosity on the shear rate, which represents the experimental values of the rheogramme over a wide range of shear rate, is of special importance. The preceding figures show that the four-parameter equation found by CARREAU /3/

183 (1)

provides a good fit to the experimentally determined rheogramme for the polymer solutions under investigation here. The significance of the parameters in the CARREAU equation, as well as a simple method for determining them, are briefly explained. n o denotes the viscosity at the shear rate 0 = 0, and can be determined directly from the horizontal portion of the curve in the range of very low shear rates. By means of supplementary measurements performed in the range of high shear rates, values indicative of rl- are obtained. n-1 is the slope of the linearly decreasing part of the curve. The plateau for the range of low shear rate and the linearly decreasing part of the curve intersect at a point whose abscissa is approximately equal to 1/X. In the following, the essential steps in the development of a filter law for CARREAU fluids m d e s c r i h e d . The power law frequently employed in previous publications is considerably simpler to handle analytically, and is therefore preferred for the treatment of concrete problems. For the polymer solutions investigated in this work, however, a power-law dependence of the viscosity on the shear rate does not describe the experimentally observed behaviour with sufficient accuracy. Consequently, sizable errors can result in the description of the flow processes in porous media, as will be shown by means of an example. For a wide range of shear rates, an extension, as described in this work with respect to the viscosity model, is indispensable.

A F I LTER LAW FOR CARREAU FLUIDS Filter laws for non-NEWTONian fluids are known only for a few special cases / 4 , 5, 6, 7/. The procedure common to their derivations is as follows: First the capillary flow is treated analytically for the liquid in question, in order to obtain a filter law with the use of an appropriate capillary bundle model. This procedure is adopted in the following as well; a filter

184 law is thereby derived for CARREAU fluids, and the porous medium is replaced by a capillary bundle which is hydrodynamically equivalent with respect to porosity and permeabi 1ity

.

0

Figure 4:

Straight capillaric model of a porous medium

The simplest capillary model of a porous medium /a, 9 / consists of a bundle of circular cylindrical capillaries of equal radius R. Figure 4 illustrates this concept. A comparison of the DARCY filter law with the law of HAGEN-

POISEUILLE yields the "hydraulic equivalenceradius" for this simple model:

By means of this concept, the flow through a porous medium is related to the capillary flow of the liquid in question and can be treated accordingly. On the basis of can be derived. results. In the remarkable that

this theory, a filter law for CARREAU fluids The procedure is justified by experimental following considerations, it is no empirical corrections are required.

It is necessary first to calculate the flow behaviour of CARREAU fluids in capillaries; for this purpose the velocity profile and the averaqe velocity of the capillary flow must be known. For the derivation, a circular cylindrical capillary

185

.

1

Figure 5:

Flow throuqh a circular tube

of radius R and lensth L is considered - Figure 5 - and a cylindrical coordinate system is introduced. The z-axis and the capillary axis are identical; the direction of .flow is taken to be that of the positive z-axis. The differential equation for the radial velocity distribution v(r) is

(3)

whereby po - pL denotes the applied pressure difference. This differential equation is transcendental in the derivative of the function being souqht, v(r); this fact proved to be a considerable problem in the further course of the calculations. The introduction of the wall shear rate 0 , as a parameter is decisive for the solution of this problem. The calculation / l o / finally yields an analytical expression for the average velocity during capillary flow. By means of the hydraulic equivalence radius, this expression can be easily transformed to a filter law. In the case of the capillary bundle model used, the one-dimensional filter law takes the following form :

186

In order to save space, the following substitutions have been made :

With the exception of a correction factor, the external form of this filter law is identical to that of the DARCY law. This factor depends on the parameters of the CARREAU equation and on the maximal shear rate 9, occurring in the capillary bundle model. The maximal shear rate is obtained from the transcendental equation

which admits an iterative solution according to the BANACH fixed-point theorem. The algorithm necessary for the numerical solution of equations (4) and ( 6 ) requires the following steps: After the parameters of the CARREAU equation, as well as the permeability and porosity of the porous medium have been determined, q R is calculated from ( 6 ) for predetermined values of the pressure gradient, and the corresponding filter velocity is determined from ( 4 ) . COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS

The theoretical results are verified by experiment; no empirical correction factors are thereby required. In order to carry out the required flood experiments, an apparatus similar to that already used by DARCY was employed. Sand packs of 50 percent porosity and 5 D permeability, compacted by vibration, served as porous media. If the DARCY equation is solved for the viscosity, the result is (7)

With the use of the present results, the effective viscosity in the porous medium was determined directly from the measured data according to ( 7 ) on the one hand, and by means of the previously derived filter law, on the other hand.

188

For comparison, polysaccharide and hydroxyethylcellulose, which exhibit a dominantly linear, decreasing range in their rheourammes, were treated as power-law fluids.

A OBSERVED VALUES CALCULATE0 - C A R R E N MODEL ----- CALCULATED-POWER -LAW MODEL o

10080.

-

I

c

u

10

D

.

.Z

.e

.'s

.4

t A

400. 300.

0

- ---

\ \

\

\

i'.z

t i

1:s

*

Effective viscosity for flow of polysaccharide solution in porous media'

Figure 6:

500.

1'.

VELOCITY Im/d)

\

OBSERVED VALUES CALCULATED - CARREAU MODEL CALCULATED -POWER -LAW-MODEL

'.

\

\

W

L

t

u

K

w

100 Figure 7:

-

VELOCITY ( m/dl

.Z

.C

.6

.8

1.

1.2

Effective viscosity for flow of hydroxyethylcellulose solution in porous media

189

t

100

Figure 8:

0

OBSERVED VALUES

- CALCULATED -CARREAU HODEL

Effective viscosity for flow of polyacrylamide solution in porous media

From the filter law for power-law fluids, the effective viscosity in a porous medium was likewise calculated. Figures 6, 7, and 8 show the dependence of the viscosity on the filter velocity and compare the experimental and theoretical results. For the CARREAU model, the deviation between the experimental and theoretical results is less than 10 percent for the polysaccharide and polyacrylamide solutions, and less than 15 percent for the hydroxyethylcellulose solution. Hence the agreement between theory and experiment can be regarded as qood. The power-law model describes the dependence of the viscosity on the filter velocity with sufficient accuracy in the case of polysaccharide, whereaa considerable deviation occurs for hydroxyethylcellulose. These examples demonstrate the advantages of the new filter law for the questions under investigation. CALCULATION OF THE INJECTIVITY BEHAVIOUR

During enhanced oil recovery, the pseudoplastic behaviour of the polymer solutions used exerts a pronounced influence on their injectivity. Once the questions concerning filtration .

190

adsorption, stability, etc. have been clarified for a given reservoir in the course of the product selection procedure, the question of the injectivity of the polymer solution involved remains to be answered by the reservoir engineer. A t this juncture, an important decision of whether or not a selected product is suitable for field application must be made; this is a vital cirterion because of the high financial risk involved. A method must be provided for predicting the behaviour in the field on the basis of laboratory data; thus a criterion for decision must be established. In the following, the flowing pressure and radial distribution of pressure around the injection well are calculated for an injector in a radially symmetric reservoir and for a predetermined injection rate, with the use of the filter law just presented. The multitude of influential parameters necessitates a restriction to a typical case encountered in practice. The following, realistic, qeometrical and physical reservoir data are employed for the model calculations: Reservoir: Permeability Porosity Effective reservoir thickness

K = 1000 d = 0.24 h = 4

mD m

Well : Cased with 7" diameter and ideally perforated in the reservoir zone Wellbore radius 0.069 m rW = Injection rate q = 100 m3/d Depth = 1000 m

FORMULATIONOF THE SELECTION C R I T E R I O N From the standpoint of reservoir engineering, the essential criterion for the injectivity of a polymer solution is that the fracturing pressure of the rock must not be exceeded during the injection. The predetermined injection rate and the average reservoir pressure also affect the decision. For a depth of 1000 m and under the assumption that the average reservoir pressure corresponds to the hydrostatic pressure ,

191

a value of 5 = 100 bar results. The order of magnitude of the fracturinu qradient typical for sedimentary rocks lies between 0.18 and 0.24 bar per metre of depth. For the injector under consideration here, this results in a maximal bottom-hole flowing pressure of 180 to 240 bar: hence the bottom hole flowing pressure may exceed the average reservoir pressure by a maximum of 80 to 140 bar durinq polymer injection. Furthermore, a radially symmetric reservoir is thereby assumed. The ranue of influence of the injector is selected at re = 200 m; the reservoir pressure of 100 bar is assumed to prevail at the outer boundary. Thus, the following criterion for decision is obtained: The polymer solution is injectable provided the pressure drop over a distance of 200 m from the bore hole does not exceed 80 to 140 bar.

CALCULAT IONAL PROCEDURE The object of the calculation is to determine the relationship between the pressure gradient and the distance from the well. This function is subsequently integrated. Because of the complicated structure of the filter law previously derived, the entire calculation is performed numerically. As a result of its structure, the filter law just developed

allows only the determination of the corresponding filter velocity for given values of the pressure gradient. With reference to / l l / , the following procedure is adopted for determining the locally prevailing pressure gradient. From the equation of continuity the following expression is obtained for the radial velocity distribution:

whereby r denotes the distance from the wellbore axis. This provides a possibility of determining the distance from the well corresponding to given values of the pressure gradient by means of the filter law and equation ( 8 ) . The calculation starts with the determination of the pressure

192 gradient at the bore hole. For this purpose, two values of the pressure gradient, of which one is smaller and one larqer than that prevailing at the well, are initially assumed. By nesting of intervals a sequence of pressure gradient values is constructed in such a way'that the values of the radius determined from the filter law and equatisn ( 8 ) converge toward the wellbore radius. The procedure is truncated as soon as the wellbore radius has been approached with the required accuracy. The value of the pressure gradient corresponding to the radius thus determined is then taken as the pressure gradient at the well. Subsequently, this value is decreased stepwise, and the corresponding values of the radius are determined from the filter law and equation ( 8 ) . Thus, a tabular representation of the pressure gradient as a function of the distance from the well is obtained. .The calculation of the total pressure drop is subsequently performed by means of numerical integration.

400.

1 POLYSACCHARIOE 2 POLYACRYLAMIDE 3mi 3 HYDROXYETHYLCELLULOSE 360.-

32 0-

-

200: 2(O:

0. Figure 9:

30.

60.

90. 120. 150. DISTANCE (M 1

180. 210.

Calculated pressure profile during polymer injection

193

RESULTS OF THE MODEL CALCULATION In figure 9, the pressure difference occurring during injection, as referred to the pressure at the injection well, is plotted as a function of the distance from the well for the three polymer solutions under investigation. Moreover, the maximal values of 80 and 140 bar for the injection overpressure are indicated. According to the criterion formulated here, the polymer solutions are suitable for injection provided the pressure difference remains less than 80 to 140 bar over a distance up to 200 m from the injection well. This condition is fulfilled for the polysaccharide, and partially fulfilled for the polyacrylamide in this case. In contrast, the hydroxyethylcellulose exhibits a decidedly deviating behaviour. The pressure difference, as referred to the well, already amounts to 140 bar at a distance of about 20 m, and increases to more than 350 bar over a distance of 200 m. It must be emphasized that this is a model calculation, whereby the effects described are attributed solely to the dependence of the viscosity on the filtration velocity. If, in a practically relevant case, the model calculations indicate that the maximal permissible injection pressure will be exceeded, the concentration of the polymer solution to be used must be reduced; the viscosity is thus decreased. The parameters of the CARREAU equation are then determined from the rheogramme, and the calculation is repeated with the use of these values.

is the purely theoretical plotting of rheogrammes for injectable fluids by the variation of parameters in the CARREAU equation.

A further possibility

CONCLUSIONS The rheological behaviour of aqueous polymer solutions is well described by the CARREAU model. A filter law derived for such fluids is described and experimentally verified. With.the use of the new filter law, the radial pressure distribution around the injection well during the injection

19 4

of polymer solution is calculated. A polymer solution is judged as suitable for injection as far as the bottom hole flowing pressure does not exceed the fracturing pressure of the rock at the bottom of the hole. Among the products investigated here, the polysaccharide solution fully, and the polyacrylamide solution conditionally satisfies this criterion under the given conditions.

NOMENCLATURE h K L n

-

P

Po q

r re rW

R V V

f

P YR ‘1 ‘10

1 ‘,

h

d

-

PL

Formation thickness Permeability Length Power-law index Average pressure Pressure drop Injection rate Radial coordinate External boundary radius Wellbore radius Radius of the tube Velocity Filtration velocity Shear rate Shear rate at the tube wall viscosity Zero-shear-rate viscosity Infinite-shear-rate viscosity Time constant Porosity

REFERENCES 1

CHANG, H. L.; Polymer Flooding Technology Yesterday and Tomorrow J. Pet. Tech. (Aug. 197818 1113 1128

-

-

195 2.

GRODDE, K.H., SCHAEFER, W.; "Experience with the Application of Polymer to Improve Water Flood Efficiency in Dogger Reservoirs of the Gifhorn Trough, Germany" Erdoel-Erdgas-Zeitschrift 94 (July 1978) 7 , 252 259

-

3.

CARREAU, J.P.; 'Rheological Equations from Molecular Network Theories" Ph.D. Thesis, Univ. of Wisconsin, Madison 1968

4.

BIRD, R.B., STEWART, W.E., LIGHTFOOT, E.N.; "Transport Phenomena" 207 J. Wiley a. Sons, New York ( 1 9 6 0 1 , 206

-

5.

SADOWSKI, T.J.; "Non-Newtonian Flow Through Porous Media" 271 Trans. SOC. Rheol. 9 ( 1 9 6 5 ) 2, 251

-

6.

SADOWSKI, T.J., BIRD, R.B.; "Non-Newtonian Flow Through Porous Media" Trans. SOC. Rheol. 9 ( 1 9 6 5 ) 2 , 243 250

-

7.

PARK, H.C., HAWLEY, M a c . , BLANKS, R.F.; "The Flow of Non-Newtonian Solutions Through Packed Beds" 773 Polym. Eng. Scie. (1975) 15, 761

-

8.

9.

SCHEIDEGGER, A.E.; "Theoretical Models of Porous Matter" Producers Monthly 17 (Aug. 1953) 10. 17

-

23

SCHEIDEGGER, A.E.; "The Physics of Flow Through Porous Media" University of Toronto Press ( 1 9 6 3 1 , 115 117

-

10. VOGEL, P.;

"Untersuchungen zur Berechnung des FlieSverhaltens wlSriger Polymerl6sungen in Sandpackungen" Ph.D. Thesis, TU Clausthal 1980, West Germany 11. BONDOR, P.L.,

HIRASAKI, G.J.r T H A M r M . J . ; "Mathematical Simulation of Polymer Flooding in Complex

Re servoirs" SOC. Pet. Eng. J. (Oct. 19721, 369

-

382

This Page Intentionally Left Blank

19 I

CHEMICAL FLOODING

BASIC RHEOLOGICAL BEHAVIOR OF XANTHAN POLYSACCHARIDE SOLUTIONS IN POROUS MEDIA: EFFECTS OF PORE SIZE AND POLYMER CONCENTRATION G. CHAWETEAU and A. ZAITOUN

Institut Francais du Pktrole, B.P. 31 I , 92500 Rueil Malmaison - France ABSTRACT

The b a s i c r h e o l o g i c a l behavior of xanthan polysaccharide s o l u t i o n s has been extensively i n v e s t i g a t e d by varying polymer concentration, pore s i z e and t h e chemical n a t u r e of porous media. The r h e o l o g i c a l c h a r a c t e r i z a t i o n of s o l u t i o n s h a s s h a m t h a t xanthan macromolecules behave l i k e r i g i d rods i n the s a l i n i t y conditions selected. A l l microgels were c a r e f u l l y removed from s o l u t i o n s i n order t o study t h e behavior f a r away from i n j e c t i o n wells. I n f i n e c y l i n d r i c a l pores, mobility reduction a t low shear r a t e s was found t o be constant and lower than the Newtonian v i s c o s i t y a t low shear r a t e s , except f o r pore diameters smaller than macromolecule length. Water permeability was not reduced a f t e r polymer flow, showing t h a t the r h e o l o g i c a l behavior was not influenced by r e t e n t i o n o r adsorption phenomena. The r a t i o between mobility reduction and r e l a t i v e v i s c o s i t y decreases a s pore s i z e decreases and polymer concentration increases. This i s explained by t h e e x i s t e n c e near t h e pore w a l l of a depleted l a y e r i n which polymer concentration and thus v i r c o s i t y i s smaller than i n t h e bulk. This d e p l e t i o n i s due t o s t e r i c e f f e c t s and does not depend on chemical n a t u r e and pore shape. A model based on t h i s physical hypothesis i s proposed f o r c a l c u l a t i n g mobility reduction a s a function of pore s i z e and polymer s o l u t i o n p r o p e r t i e s . The model's p r e d i c t i o n s a r e i n agreement with experimental r e s u l t s . I n various unconsolidated porous media, such as packs of g l a s s beads, carborundum p a r t i c l e s and.sand g r a i n s , t h e same behavior i s observed. The mobility reduction i r l e s s than i n l a r g e c a p i l l a r i e s and decreases with pore size. Moreover, the depleted l a y e r e f f e c t decreases with shear r a t e u n t i l i t vanishes a t high f l o w r a t e s . A comparison between flow curves and rheograms gives an estimation of e f f e c t i v e shear r a t e s i n pore t h r o a t s of porous media a s a f u n c t i o n of average velocity. The experiments c a r r i e d out i n Fontainebleau sandstones having d i f f e r e n t permeab i l i t i e s confirm t h i s observation and show t h a t pore t h r o a t diameters i n consolidated porous media a r e l a r g e r than predicted by the usual c a p i l l a r y models. I n a l l types of porous media, no d i l a t a n t behavior was detected even a t the highest flow r a t e s . The p r a c t i c a l a p p l i c a t i o n s of t h i s study f o r EOR a r e 1) w t h a n s o l u t i o n s a r e b e t t e r sweeping f l u i d s i n heterogeneous r e s e r v o i r s than conventional f l u i d s h v i n g the same average v i s c o r i t y ; 2) they can be ured i n l e s s permeable format i o n s than previously claimed; 3) very good i n j e c t a b i l i t y i s expected f o r microgelfree solutions.

198 INTRODUCTION Both hydrolyzed polyacrylamide and xanthan polysaccharide solutions are candidates for enhancing oil recovery. Up to now, hydrolyzed polyacrylamides have undoubtedly been more extensively studied in the laboratory and used in field applications. However, the macromolecular flexibility of this type of polymer causes several detrimental effects (1): 1) The viscosity decreases sharply as salinity increases, due to the screening of charged groups, particularly in the presence of bivalent ions. 2 ) The dilatant behavior at high flow rates which decreases injectability. This behavior isdue to the coil-stretch transition of macromolecules in converging zones of porous media ( 2 ) . 3 ) The mechanical degradation which occurs when hydrodynamic forces on the stretched molecules overcome the strength of carbon-carbon bonds ( 3 ) . Moreover, the hydrolysis of acrylamide groups at high temperatures, observed even in neutral conditions ( 4 1 , can lead to precipitation in the presence of calcium ions. So their use is limited to low salinity and temperature reservoirs. The rigid rodlike conformation of xanthan polysaccharide molecules in most reservoir conditions enables the problems mentioned above to be avoided. The viscosity is almost insensitive to salinity, except in a very low salinity range, and neither dilatant behavior nor mechanical degradation has been observed in oil recovery conditions. So this polymer is potentially very attractive, particularly for high salinity reservoirs. But, up to now, the poor quality of most industrial products available on the market has excluded xanthan polysaccharides from many field applications. The poor solubility of some products and the existence of both microgels and cellular debris, particularly in powders, is well documented (5). The influence of these microgels on their flow behavior has been extensively studied in well-defined porous media (6). However, recent improvements in manufacturing processes, particularly for fermentation broths, reduce to a great extent the risks of well plugging, so that xaqthan solutions could be widely used in the near future. These newly manufactured polymers contain so few microgels that they will be adsorbed or retained at a short distance from the injection well. In these conditions, most of the oil to be recovered which is located far from the injection well will be swept by a polymer solution without microgels. Thus knowing the basic rheological properties of such a solution in porous media is very important from a practical point of view. The first experiments carried out in porous media with a microgel-free solution (7) showed that the apparent viscosity or mobility reduction is less than the viscosity determined in a viscometer, mainly at the lowest shear rates in the Newtonian regime, Further experiments, performed with a well-characterized polymer solution and well-defined porous medium, showed that this phenomenon was related to the existence of a depleted layer near the wall, due to steric effects (8). The present investigation aims to study the influence of polymer concentration and rock permeability in order to estimate the effects of this depleted-layer phenomenon on the sweeping properties of xanthan solutions. POLYMER SOLUTIONS The xanthan polymer used is a sample manufactured in a fermentation-broth form by RhBne-Poulenc laboratories with a fermentation process specially designed to avoid microgel formation. Its molecular weight should be close to 0.8 x lo6. All solutions were obtained by dilution with salted water, clarified and filtered at very low shear rate to remove any possible remaining microgel with a method previously described (6). The addition of 400 ppm NaNg protected solutions against bacterial attack. In the conditions chosen (salinity = 5 g/l NaC1, pH = 7,

-

199 8 = 30°C), t h e polymer molecule was shown t o behave l i k e a r i g i d rod having a

0.62 pm length and 16.5

1 diameter

(8).

BULK RHEOLOGICAL PROPERTIES

Shear flow V i s c o s i t y measurements were performed with a s e r i e s o f g l a s s c a p i l l a r y viscometers, previously d e s c r i b e d , over a wide shear r a t e range ( 0 . 1 t o 3000 s-1) f o r various polymer concentrations (25 t o 2400 ppm) using Rabinowitch-Mooney c o r r e c t i o n f o r power-law f l u i d s . The p l o t s of shear v i s c o s i t y versus shear r a t e i n log-log coordinates (Fig.1) show how s o l u t i o n s behave i n pure shear flow. The following can be observed:

1) A Newtonian regime, a t very low shear r a t e s , i n which r e l a t i v e v i s c o s i t y 7, which i s t h e r a t i o between polymer s o l u t i o n and b r i n e v i s c o s i t i e s i s independent of shear r a t e and equal t o q r o . 2) A t r a n s i t i o n zone, c h a r a c t e r i z e d by a c r i t i c a l shear r a t e , equal t o the inverse of a r o t a t i o n a l r e l a x a t i o h time ir.

3 ) A shear-thinning regime, i n which r e l a t i v e v i s c o s i t y decreases with shear r a t e according t o a power l a w whose exponent is 2 m. Over t h e shear r a t e range t e s t e d , t h e experimental d a t a f i t very w e l l with the Cerreau model A ( 9 ) . '1 r o I

7r

= [1+ (

TrX

Y)

'3"

100: 50-

20+

lo: 5-

2

'L 1

Figure 1. Viscosity-shear r a t e curves f o r v a r i o u s polymer concentration

200

Converging flow An estimate of viscous f r i c t i o n i n converging flows can be made by measuring the apparent r e l a t i v e v i s c o s i t y i n a model c o n s i s t i n g of successive s h o r t c a p i l l a r i e s separated by c y l i n d r i c a l expansionsfm! which the geometry is shown i n Figure 2 .

Figure 2. Influence of converging flow zones on apparent v i s c o s i t y

The c a p i l l a r y r a d i u s was chosen s u f f i c i e n t l y small so a s t o avoid any i n e r t i a e f f e c t i n our expe imental conditions. For shear r a t e s l e s s than a c r i t i c a l value 600 s-i, t h e apparent v i s c o s i t y i n the model was found t o be equal t o the shear v i s c o s i t y , meaning t h a t r e l a t i v e v i s c o s i t i e s a r e equal i n both converging and shear flow. ForY > yf, t h e apparent v i s c o s i t y becomes g r e a t e r than shear v i s c o s i t y . This increased viscous f r i c t i o n occurring i n converging flow near the entrance t o t h e c a p i l l a r y is explained by t h e s t r o n g o r i e n t a t i o n of the rods i n t h e flow d i r e c t i o n when t h e product of r e l a x a t i o n time by elongat i o n r a t e is s u f f i c i e n t l y high (2) (10). However, this i n c r e a s e i n apparent v i s c o s i t y is very s m a l l , compared t o t h a t obtained with polyacrylamide s o l u t i o n Indeed, t h e polyacrylamide molecule is both with t h e same flow conditions ( 2 ) . s t r e t c h e d and o r i e n t a t e d i n the flow d i r e c t i o n by t h e converging flow. The high s t r e t c h i n g degree ( t h e s t r e t c h e d length may be ;O times t h e i n i t i a l c o i l diameter) explains t h e magnitude of t h e viscous f r i c t i o n i n c r e a s e with polyacrylamide, thus involving d i l a t a n t behavior.

o*=

201 WALL EFFECT I N FLOW THROUGH FINE CAPILLARIES The e f f e c t s of pore s i z e on apparent v i s c o s i t y were f i r s t i n v e s t i g a t e d i n a very simple system, namelywith a well-characterized r o d l i k e polymer s o l u t i o n flowing through f i n e c y l i n d r i c a l c a p i l l a r i e s , in order t o make t h e i n t e r p r e t a t i o n e a s i e r . Experimental f a c i l i t y Nuclepore membranes were s e l e c t e d f o r these experiments because t h e i r pores have a well-defined c y l i n d r i c a l shape. The average diameters and a r e a l pore d e n s i t i e s corresponding t o nominal diameters (ranging between 0.4 and 12 pm) were determined by e l e c t r o n microscopy (81, and the average diameters a r e given i n Figure 3.

4--+

3-

-3

2-

-2

_____ 500prn Copillories

-Nuclepore Membmnes

A s e r i e s of six f i l t e r holders, each one containing f i v e membranes separated by nylon g r i d s , was used t o o b t a i n s u f f i c i e n t pressure drops measured by oil-water manometers. The thickness of the Nuclepore membranes is constant and approximately equal t o 10 p m , so that t h e c a p i l l a r y length t o r a d i u s r a t i o l / r given i n Figure 3 depends on pore diameter. Results and discussion The r e s u l t s of flow experiments a r e shown i n Figure 3. Bulk r e l a t i v e v i s c o s i t y versus shear r a t e i s p l o t t e d a s a dashed l i n e . The s o l i d - l i n e curves show the v a r i a t i o n s of r e l a t i v e apparent v i s c o s i t y measured during flow through membranes having d i f f e r e n t pore diameters. The most importcmt r e s u l t is t h a t i n t h e Newtonian regime the apparent v i s c o s i t y in f i n e pores is found t o be lower than i n bulk s o l u t i o n s and decreases with pore

202 diameter, except f o r t h e s m a l l e s t one whose diameter (0.28 pm) i s l e s s than molecule length (0.62 pm). In t h i s l a s t case t h e macromolecules a r e r e t a i n e d on the upstream s i d e of t h e membrane, causing an extra-pressure drop and thus a curve upturn i n low shear range. A t t h e h i g h e s t shear r a t e s , t h e macromoleby hydrodynamic f o r c e s and can e a s i l y pass through t h e memcules are oriented branes. In a l l experiments, t h e water permeability was unchanged a f t e r polymer flow, showing t h a t flow p r o p e r t i e s were not d i s t u r b e d by a d s o r p t i o n o r r e t e n t i o n phenomena. It must be noted t h a t a comparison between apparent v i s c o s i t i e s i s v a l i d i n t h e Newtonian regime even f o r c y l i n d r i c a l pores having d i f f e r e n t length to-radius r a t i o s . A t higher shear r a t e s , t h e entrance e f f e c t s can i n c r e a s e apparent v i s c o s i t y i n r e l a t i v e l y s h o r t c a p i l l a r i e s (111, and t h e shear r a t e dependence must be s t u d i e d with models having s i m i l a r geometric shapes such as g l a s s bead packs ( s e e below). This decrease i n apparent v i s c o s i t y a s pore diameter decreases has been i n t e r preted ( 8 ) by t h e e x i s t e n c e of a depleted l a y e r near t h e pore.wal1. This deplet i o n i s due t o t h e s t e r i c hindrances which reduce t h e p r o b a b i l i t y t h a t t h e macromolecular c e n t e r of mass may be a t a d i s t a n c e less than one macromolecular h a l f length from t h e w a l l a s shown i n Figure 4. Thus, t h e polymer concentration w i l l i n c r e a s e from zero a t w a l l c o n t a c t up t o bulk c o n c e n t r a t i o n a t a d i s t a n c e c l o s e t o h a l f t h e l e n g t h of a macromolecule. Such a depleted-layer h a s been t h e o r e t i c a l l y p r e d i c t e d f o r both c o i l polymers (12) and r o d l i k e p a r t i c l e s (131, and i t p h y s i c a l l y explains t h e apparent s l i p a t t h e w a l l p r e d i c t e d f o r concentrated s o l u t i o n s (14). A s a consequence of t h i s d e p l e t e d l a y e r , the i n c r e a s e i n v i s c o s i t y due t o t h e polymer i s l e s s near t h e w a l l than i n t h e bulk, causing a lower o v e r a l l apparent v i s c o s i t y i n f i n e pores than i n t h e bulk. This e f f e c t i n c r e a s e s a s pore diameter decreases. A c o a x i a l two-fluid flow model has been proposed t o schematize polymer s o l u t i o n flow (Fig. 4 ) . The bulk s o l u t i o n with a r e l a t i v e v i s c o s i t y q r b flows i n t h e A depleted s o l u t i o n center of the c a p i l l a r y i n s i d e a r a d i u s equal t o ( r - 5 ) . having a r e l a t i v e v i s c o s i t y 'Iw flows i n an annulus having t h i c k n e s s 5 surrounding t h e bulk s o l u t i o n . The v e l o c i t y i s zero a t t h e w a l l and equal i n both

Allowed hsitiom of Rods

Ir Figure 4 Schemetic v i e w of polymer s o l u t i o n flow through f i n e pores w i t h a depleted l a y e r e f f e c t

203 the bulk solution and the depleted solution at a distance r - 6 from the axis. From this model, an analytical equation has been derived to calculate apparent relative viscosity 'Irp as a function of pore diameter 2 r:

rlrw

rlrFJ = where

p'

1

-

(1- 1/p ) (1- 6/r )

(2)

4

Trb' 1 ,'

Very good agreement between the experimental apparent relative viscosity in the Newtonian zone (Fig. 3) and the predictions of this model was found in choosing the following values for depleted layer characteristics:

I , '

8 = 0.3 pm

1.77

The value of 6 is close to half the length of a macromolecule (L/2 = 0.31pm), and the value of qrw is consistent with the physical hypothesis proposed. Moreover W B E R T and TIRRELL (15) have recently proposed a calculation based on the finitely extendable nonlinear elastic dumbbell as a molecular model and the exclusion of all molecule configurations intersecting the walls. Good agreement is found between their calculations and our experimental findings. Thus, the relation between the diameter dependence of apparent viscosity and the depleted- layer phenomenon seems to be very well established. Moreover, the same behavior was recently observed with polyacrylamide solutions when there are no effects of adsorption on flow properties ( 1 ) . FLOW THROUGH UNCONSOLIDATED POROVS MEDIA Pore size dependence Calibrated glass beads having different diameters (see Table 1) were packed to obtain porous media having similar pore shapes but different pore sizes. The flow experiments were performed with a 400 ppm xanthan solution, and the absence TABLE I

diameter

200-250

I

&I

Permeability k km2)

Apparent viscosity

tY

0

index

rP

137

0.40

36

0.40

I

3.90

0.185

3.75

0.180

8.4

0.175

40-50

2.4

0.160

20-3.0

0.66

10-20

0.21 0.11

0.41

I

2.97

1

1

1.7

I

43

0.130

1

0.110 0.080

of permeability reduction after polymer flow was checked for .very ascertain the absence of any adsorbed layer effect.

I

bead pack to

204

The flow-experiment r e s u l t s a r e q u i t e s i m i l a r t o those observed i n flow through c y l i n d r i c a l pores (Fig. 5 ) . The apparent v i s c o s i t y i n the Newtoqian zone is

XP5gA NoCl

4.

.

-4

1lSl 1361 1841

Glass Beod Pocks

12 41

3'

.3

I0161 IOZ1

10 111

2-

. -Apparent

Viscosity

(k) Permeobilily m

I,

-2

- - - .Bulk Sheor Vscosity .

.

.

a * . . .

\

prn' 8

,

'..--

,....''

. -1

Figure 5. Pore s i z e dependence of apparent v i s c o s i t y i n flow through glass-bead packs

found t o be lower than the bulk v i s c o s i t y and decreases with average pore s i z e evaluated by pack permeability a s shown i n Figure 5. The maximum w a l l shear r a t e i n the average pore t h r o a t diameter was c a l c u l a t e d by: -0.5 ? = 4 x 4 v (8 k 0 - 5 (3 1 Where a is a shape parameter c h a r a c t e r i s t i c o f t h e pore s t r u c t u r e . The value of a should be one f o r a bundle of c a p i l l a r i e s having the same diameters. For porous media, the value of P i s experimentally determined as being t h a t which gives t h e same c r i t i c a l y c corresponding t o the onset of shear-thinning behavior f o r both the shear viscosity-shear r a t e curve and the apparent viscosity-shear r a t e curve i n the porous medium under consideration. The a value was found t o be equal t o 1 . 7 f o r packs of l a r g e spheres having the same diameter (8). It decreases with the pore size-molecule length r a t i o and i n c r e a s e s a s pore s t r u c t u r e heterogeneity increases. This i s the case when t h e bead-diameter d i s t r i b u t i o n becomes wider o r when t h e consolidation degree of sands giving sandstones i n c r e a s e s (8). Due t o the s t a t i s t i c a l homothety of bead packs, t h e shear r a t e dependence of t h e depleted-layer e f f e c t can be deduced from flow experiments i n t h i s type of porous media. As expected, t h e rod o r i e n t a t i o n with $hear decreases t h e depleted l a y e r e f f e c t a s the flow r a t e i n c r e a s e s , and apparent v i s c o s i t y becomes independent of pore s i z e a t high shear r a t e s ( y 7 3000 s-1). A t t h e highest flow r a t e s , the apparent v i s c o s i t y overcomes t h e shear v i s c o s i t y . This can be explained by t h e . l n c r e a s e i n viscous f r i c t i o n i n converging zones of porous media where the macromolecules a r e o r i e n t a t e d i n t h e d i r e c t i o n of flow (Fig. 2).

205 As shown by results obtained with polymer flow through Nuclepore membranes, Equation (2) gives the relation between apparent viscosity and pore diameter. Thus an effective diameter can be calculated for each glass bead pack from the apparent viscosity measured. This effective diameter corresponds to an average hydrodynamic diameter of pore throats where polymer flows. On the other hand the mean pore size is proportional to the square root of the permeability for homothetic porous media. In Figure 9, the effective pore-throat diameter deduced ore diameter calculated from the polymer apparent viscosity is plotted versu from the simplest capillary model, 2 r = 2 ( 8 k 0-1)8". All the points corresponding to experiments performed with glass-bead packs are lined-up on the first bissectrix. So the average hydrodynamic diameter of pore throats is approxirmrtely equal to 2 ( 8 k 0-1)0.5 for homogeneous bead packs. Additional points deduced from experiments carried out in sand packs (8) are also lined-up on the same curve. polymer concentration effects The influence of polymer concentration was systematically studied by using a Carborundum pack having a permeability equal to 0.1 p m 2 , a porosity equal to 0.48 and an effective pore diameter of 2.6pm. The polymer concentration was varied from 200 ppm to 1600 ppm, and the absence of permeability reduction was checked after every polymer flow experiment.

7rP

r)r

10 -10

I

1

lo

'"%2

. .

'

..'

Figure 6. y'(seC-'1 The depleted-layer effect as a function of shear rate at different polymer concentrations incarborundum packs

206 Both shear v i s c o s i t i e s i n dashed l i n e s and apparent v i s c o s i t i e s i n s o l i d l i n e s a r e p l o t t e d i n Figure 6. The f i r s t observation i s t h a t t h e general behavior i s q u i t e s i m i l a r t o t h a t observed i n glass-bead packs. The depleted-layer e f f e c t appears t c be insens i t i v e t o t h e pore shape and chemical n a t u r e of porous media. This r e s u l t i s c o n s i s t e n t with t h e s t e r i c o r i g i n of t h e phenomenon. Moreover, t h e magnitude of the e f f e c t , i . e . t h e r a t i o between apparent v i s c o s i t y and shear v i s c o s i t y , i n c r e a s e s sharply with t h e polymer concentration, a t low shear r a t e s (Fig. 7 ) .

'7r

'7rP I

60-

1

I

I

XP 5911 NaCl pH=7 8 = 3 0 ° C

Corborundum Packs 40-

-40 / / 1

20-

0 0

400

800

1200

1600

C ( ppml Figure 7. The i n f l u e n c e of polymer concentration on t h e magnitude of depleted l a y e r e f f e c t

A t the h i g h e s t concentration t e s t e d ( c = 1600 ppm), t h e apparent v i s c o s i t y = 17.5) i s less than one t h i r d of bulk shear v i s c o s i t y ( 'Irb = 62). ( tlrp

This polymer concentration e f f e c t could a l s o be predicted. Indeed, a f t e r both d i v i s i o n by V r b and i n v e r s i o n , Equation (2) can be w r i t t e n :

207 For dilute solutions, the thickness of the depleted layer 6 is expected to be constant so that: (5) qrb’ qrp = k + (1 k ) P

-

-6

where k = (1 l 4 is a positive constant, always less than 1 for a given porous medium. &As a consequence , the depleted-layer effect incresses iinearly with p = ‘lrb . rlw In the concentration range tested, the Cb/Cw ratio is expected to be constant (13). Since the viscosity of these polymer solutions is roughly an exponential function of polymer concentration (81, the qrb/f)r,ratio increases very sharply with polymer concentration, thus explaining the concentration dependence observed for the depleted-layer effect. FLOW THROUGH SANDSTONES Permeability effects As shown above, the depleted-layer effect depends only on pore size for a given polymer solution. However, the well-known relation between pore size and permeability deduced from the simplest capillary model -1 0.5 (6) 2rc= 2 (8 k 0 is valid only for homothetic unconsolidated packs. For and are the

natural porous media such as sandstones, this relation is no longer valid, electron microscopy observations (16)hsve shown that pore throat diameters generally larger than those calculated by Equation (6). As a consequence, influence of permeability cannot be predicted by a simple model. TABLE I1

Flow through sand packs and sandstones (XP solution, 9, = 4.0, 2 m = 0.22) Perme-

Grain diameter Dg(pLm)

I

porosity

Apparent viscosity rP

abi1i3

k ( p

I

8 0 - 1 ~ ~ 5.0 Sand

I

0.38

I

3.5

Shearthinning

1

~

~~

I

Shear-rate Pore-thros;] constant diameter

0.165

2.5

21

0.165

1.4

15.7

Sand 2

I I I

I

0.087

0.119 Ssnd;tone

Sand:tone

I I I

I

0.0373 0.0206 0.0096 0.0033

1 I I

I

0.084 0.075 0.056 0.056

I I

I

I

2.95

0.062

2.83

0.060

2.69

0.056

2.49

-

I

4.2

I

13.6

I

I

9.1

I

6.0

I

14.3

4.4

208

some cores of quartzitic Fontainebleau sandstones having permeabilities ranging from 3x10'3 t o 0.4p1d (Table 11) were selected t o obtain a quantitative evaluation of the depleted-layer effects. A l l the cores were preflushed by a hydrochloric acid solution t o remove the slight quantity of iron contained i n the sample i n order t o avoid possible interaction8 with the polymer. After polymer flow experiments, the i n i t i a l permeability of each core was exactly restored, even for the l e s s permeable sample (3.3 x 10-3)Id).

The experimental r e s u l t s shown i n Figure 8 are similar t o those observed i n unconsolidated porous media. The apparent viscosity t s l e s s than in the bulk i n the Newtonian zone, which indicater a depleted-layer effect that increases as permeability decreases.

%

7)r

4

4

3

3

2

2

1

loo

1

10'

103

104

y(sec-1) Figure 8.

The depleted layer e f f e c t s in flow through Fontainebleau Sandrtoner

using polymersolution characteristics in the bulk ( '1 b = 4) and near the wall ( 8 = 0.3 p and q d l . 7 7 1 , deduced from experimantr vfth Nuclepore membranes, Equation (2) giver the effective diameter of pore throats 2 r am a fuoction of permability for Fontainebleau sandstones (Table 11). A8 e d c t e d , t U a e f + r-tive diameter 2 rp is always larger than 2 rc; and the r a t i o rp/rc increaaes a s $-me.b i l i t y &creaser, as shown in Figure 9, in which experimental point8 corresponding t o 8andrtones are plotted as solid circler. This trend is w r u i s t e n t with the secondary crystallization process which explains the decrease in permeability for Fontainebleau sandrtoner. The r a t i o rp/rc should be no l y one for Fontainebleau rand Pack8 having the same grain diameter (10
P

209

I

I

-

--I

/

I

(8.4)

0.3601, / p . 0 )

Sandpacks I 1. Sandstones I (k)Permeability in p m 2

i

i

I

Fontainebieau Sandstones 2r~=35(2r,)~~’

20-1

1 V

I

I

I

30.11)

2

5

16

. I

20 5‘ 100 2r or 2&mi

Figure 9 . Comparison of pore throat diameters detenrdned by polymer injection method with measured or calculated pore diameter i n various porous media

From a practical point of view, these r e s u l t s show t h a t xanthan solutions can pass very e a s i l y through even the low permeability zones of reservoirs. The lowest limit for use of such xanthan solutions should correspond t o pore throat diameters equal to_ycromolecular length ( k O . 6 pm) , i . e . t o permeability much lower than 10 p d f o r sandstones having a structure similar t o Fontainebleau sandstones. Practically, the use of such polymers is never limited by polymer dimensions.

Ddrodvnamic retention The f i r s t type of hydrodynamic retention, which is related to thermodpamic effects (17) and thus does not depend on pore-molecule r e l a t i v e dimensions, was found t o be almost negligible for these u n t h a n solutions having rodlibe molecules. As theoretically expected, the entropy difference. due t o molecular alignment are too small to induce large concentration differences between the different zones

2 10

of the porous medium. In high permeability sandstones, the concentration differences observed after sudden flow-rate changes (from Newtonian to shear-thinning regimes,namely from 6 to 700 sec’l) werE very small (m/q

,/f,f'

0 2

B

-

O,'/ , /

/2'

12-

0 m

-50

A

-

,

,

,

.O

f.0

12

.I1

h

0 .PI

,

f.4

# *r.H.I .I1

C,..ll,

,

,

,

l.6

18

2.0

'

279 F. The E f f e c t of S l u g S i z e The e f f e c t of u s i n g s l u g s of c a r b o n d i o x i d e on t h e recovery of r e s i d u a l c r u d e oil was s t u d i e d , a n d t h e r e s u l t s a r e p r e s e n t e d i n F i g u r e s 18 a n d 19. The 4 5 O c r u d e w a s u s e d i n a l l t h e s e e x p e r i m e n t s , a n d t h e r e s i d u a l o i l s a t u r a t i o n w a s c o n s i s t e n t l y brought down t o 0.21 p.v. b e f o r e i n i t i a t i n g t h e test. I t is i m p o r t a n t t o n o t e i n t h e f o l l o w i n g d i s c u s s i o n , t h a t t h e comparis o n s t h a t w i l l b e made on t h e e f f i c i e n c y of t h e v a r i o u s s l u g s w i l l be f o r a ----l i m i t e d volume of t o t a l f l u i d i n j e c t e d , carbon d i o x i d e o r carbon d i o x i d e and water. F o r o p e r a t i n g c o n d i t i o n s of 1000 p s i . a n d 73OF. t h e oil r e c o v e r y i n c r e a s e s l i n e a r l y w i t h a n i n c r e s e i n s l u g s i z e f r o m 0.11 t o 0.22 p o r e volume f o r a t o t a l i n j e c t i o n of 1.0 t o 1.2 p o r e volumes. However, when t h e s i z e o f t h e s l u g i s i n c r e a s e d a b o v e 0.22 p o r e v o l u m e , a n d t h e t o t a l f l u i d i n j e c t e d i s k e p t c o n s t a n t a t a b o u t one p o r e volume, t h e recovery does n o t i n c r e a s e a n y f u r t h e r . A s a m a t t e r of f a c t , a s l o n g a s t h e t o t a l f l u i d i n j e c t e d is l i m i t e d t o 1.2 P.v., t h e r e c o v e r y a c t u a l l y d e c r e a s e s as t h e s l u g s i z e is i n c r e a s e d above a v a l u e of 0.22.

;1 L

3

o

at

FLUID INJLCTED. PV

Fig. 18. THE EFFECT OF SLUG SIZE ON THE RECOVERY OF RESIDUAL CRUDE O I L 1400 P S I , 73OF.

0.1

0.2

a3

as

0.6 0.7 FLUID INJECTED, PV

0.4

ae

-

a9

11)

Fig. 19 THE EFFECT OF SLUG SIZE ON THE RECOVERY OF RESIDUAL CRUDE O I L 18 PSI, 130°F*

2 80 Over t h e range of t e m p e r a t u r e s and p r e s s u r e s i n v e s t i g a t e d i n t h e s t u d y of t h e s l u g s of c a r b o n d i o x i d e , 7 3 O t o 130°F., a n d f r o m 1 0 0 0 p s i t o 1800 psi., t h e optimum s l u g s i z e showed no c o n s i s t e n t change; i t ranged from 0.20 t o 0.26 p o r e volume. I t i s h y p o t h e s i z e d t h a t t h e o p t i m u m s l u g s i z e i s t h a t v o l u m e of c a r b o n d i o x i d e w h i c h c a n b e i n j e c t e d i n t o t h e s y s t e m w i t h o u t e s t a b l i s h i n g a f r e e and c o n t i n u o u s s a t u r a t i o n throughout t h e e n t i r e model. Once such a mobile g a s s a t u r a t i o n is e s t a b l i s h e d , any f u r t h e r i n j e c t i o n of carbon d i o x i d e r e s u l t s i n t h e development of a (dense) gas d r i v e , which is r e l a t i v e l y i n e f f i c i e n t i n d i s p l a c i n g t h e s w o l l e n c r u d e o i l . On t h e o t h e r hand, i f carbon d i o x i d e i n j e c t i o n is h a l t e d b e f o r e a f r e e gas phase s a t u r a t i o n i s e s t a b l i s h e d throughout t h e model, t h e n t h e s w o l l e n crude o i l phase, rendered mobile by t h e i n c r e a s e i n i t s p o r e volume s a t u r a t i o n , w i l l be much more e f f i c i e n t l y d i s p l a c e d by a r e l a t i v e l y v i s c o u s f l u i d , v i z , water. The i n c r e a s e d e f f i c i e n c y of s l u g s o f c a r b o n d i o x i d e i n r e c o v e r i n g r e s i d u a l crude o i l is w e l l i l l u s t r a t e d by t h e r e s u l t s of t h i s work which are p l o t t e d i n F i g u r e 20. Again, i t m u s t be n o t e d t h a t t h e r e s e r v o l r p r o t o t y p e m o d e l l e d i n t h i s work i s o n e w h i c h s h o u l d show up c a r b o n d i o x i d e a t i t s very best. The e f f i c i e n c y of t h e u l t i m a t e d i s p l a c e m e n t c a n be i n c r e a s e d s l i g h t l y i f t h e v i s c o s i t y of t h e c h a s e w a t e r i s i n c r e a s e d by t h e a d d i t i o n of a g l y c o l o r a polymer. I f , f o l l o w i n g t h e i n j e c t i o n of a n optimum s l u g of c a r b o n d i o x i d e , n i t r o g e n is i n j e c t e d ; t h e n t h e r e s u l t i n g r e c o v e r y o f o i l is markedly reduced. The n i t r o g e n i s a n i n e f f i c i e n t d i s p l a c i n g f l u i d ; moreover It s t r i p s some of t h e d i s s o l v e d c a r b o n d i o x i d e f r om s o l u t i o n I n t h e c r u d e o i l , t h e r e b y d e f e a t i n g t h e e n t i r e p r o c e s s , see F i g u r e 21. 4

L

0

I

I

I

0.1

0.2

0.3

I

I (LEI

1

(L6 FLUID INJECTED. PV 0.4

I

1

I

0.7

0.8

0.9

I

Fig. 20. THE EFFICIENCY OF SLUGS OF CARBON DIOXIDE I N RECOVERING RESIDUAL CRUDE O I L G. N i t r o u s Oxide

r n o r d e r t o g a i n f u r t h e r c o r r o b o r a t i o n f o r t h e h y p o t h e s i s t h a t i t is t h e s w e l l i n g of t h e r e s i d u a l c r u d e o i l is t h e key f a c t o r i n t h e recovery of t h e l a t t e r by t h e i n j e c t i o n of carbon d i o x i d e , a s e a r c h . w a s made f o r o t h e r s u b s t a n c e s t h a t w o u l d d i s s o l v e t o t h e same e x t e n t a n d s w e l l t h e c r u d e o i l e q u i v a l e n t l y : n i t r o u s oxide h a s been d e s c r i b e d t o b e v i r t u a l l y e q u i v a l e n t t o c a r b o n d i o x i d e i n many p h y s i c a l p r o p e r t i e s 1 8 . Experiments proved t h a t n i t r o u s o x i d e performed i n t h e p h y s i c a l models i n a v i r t u a l l y i d e n t i c a l manner t o carbon dioxide. ( I t is a f a r more e x p e n s i v e substance.)

281 72

I

I

I

,

I

64-

---

-

56-

CO;, riuq size * 0 3 PV Pmssun 2500 psi

s P

48-

-

-

-

d

-

-c

-

s

-

U W

Tmp.mhn * 150.F S T oll = 2 3 e - ~ ~ i hi * 335 SCF/BbI

Y

0

A%=OOm

I.-------

=--

____ ____----I-

01

07

03

04

05

06

07

08

09

---

./--

AS0 * 0060

I

-

.=

24-

U

00

I

AaSOlO

0

$

I

I

Nitrogen S, * 37 PV Water Sa s 28 Pv

,

I

I0

It

I2

Fig. 21. THE INEFFICIENCY OF NITROGEN AS A CHASE FLUID AFTER A C02 SLUG

IV. CONCLUSIONS P h y s i c a l l y s c a l e d m o d e l s t u d i e s of t h e d i s p l a c e m e n t a n d r e c o v e r y of c r u d e O i l by c a r b o n d i o x i d e y i e l d r e s u l t s w h i c h a r e c o n s i s t e n t w i t h t h e r e s u l t s of f i e l d d e m o n s t r t i o n and p i l o t p r o j e c t s . and c o n s i s t e n t w i t h t h e p r i n c i p l e s of f l u i d f l o w and phase behavior. Continuous i n j e c t i o n of c a r b o n d i o x i d e w i l l r e c o v e r a s i g n i f i c a n t f r a c t i o n of a w a t e r f l o o d r e s i d u a l o i l s a t u r a t i o n , b u t t h e r e s u l t i n g carbon d i o x i d e / o i l r a t i o s w i l l b e above 20 MSCF/B, and may b e as high as 30. The u s e of s l u g s of carbon d i o x i d e f o l l o w e d by water w i l l e f f e c t i v e l y reduce t h e r e s u l t i n g carbon d i o x i d e / o i l r a t i o w i t h o u t s e r i o u s l y a f f e c t i n g t h e amount of o i l t h a t can be r e c o v e r e d by t h e i n j e c t i o n of a t o t a l of about o n e p o r e v o l u m e o f f l u i d . A l t h o u g h v a l u e s a p p r o a c h i n g 5 MSCF/B h a v e b e e n a c h i e v e d i n t h e s e model s t u d i e s , i t is c a u t i o n e d t h a t t h e model used was a v e r y f a v o r a b l e one, viz., l o w p e r m e a b i l i t y , uniform and l i n e a r . Even minor h e t e r o g e n e i t y i n a f i e l d o p e r a t i o n w i l l encourage channeling, and t h e d e c r e a s e i n t h e v i s c o u s t o g r a v i t y f o r c e s encountered I n r a d i a l f l o w away from t h e w e l l b o r e s w i l l encourage g r a v i t y s e g r e g a t i o n . The performance of t h e d i s p l a c e m e n t e x p e r i m e n t s l e a d s t o t h e conclusion t h a t t h e mechanism by which carbon d i o x i d e d i s p l a c e s r e s i d u a l crude o i l is comprised of t h r e e s e q u e n t i a l s t e p s : 1) t h e i m m i s c i b l e d i s p l a c e m e n t of t h e o i l - o c c l u d i n g , mobile water, 2) t h e s o l u t i o n of carbon d i o x i d e i n t h e crude o i l and i t s subsequent s w e l l i n g t h a t develops o i l phase m o b i l i t y , and 3) t h e i m m i s c i b l e d i s p l a c e m e n t of t h e mobile s o l u t i o n of carbon d i o x i d e i n o i l by t h e c o n t i n u i n g f l o w of carbon d i o x i d e or water. Although t h e r e s i d u a l s a t u r a t i o n of t h e o i l phase ( a s o l u t i o n of carbon d i o x i d e i n o i l ) c a n b e l o w e r e d by c o n t i n u i n g t h e f l o w of c a r b o n d i o x i d e , r e s u l t i n g i n some c o n t i n u i n g e v a p o r a t i o n o f c r u d e o i l f r a c t i o n s , t h e

282 r e s u l t i n g i n c r e m e n t a l c a r b o n d i o x i d e / p r o d u c e d o i l r a t i o s w i l l b e v e r y high. The more p r a c t i c a l l i m i t t o t h e r e c o v e r y i s r e a c h e d when t h e r e s i d u a l s a t u r a t i o n of t h e low v i s c o s i t y o i l p h a s e t o t h e s u b s e q u e n t g a s o r water d r i v e i s approached. N i t r o u s o x i d e , which d i s s o l v e s i n a n d swells c r u d e o i l s s i m i l a r l y , i s as e f f e c t i v e as c a r b o n d i o x i d e i n r e c o v e r i n g c r u d e o i l . The s u b s t i t u t i o n of n i t r o g e n f o r water as a c h a s e f l u i d i n j u r e s t h e r e c o v e r y b e c a u s e t h e g a s i s n o t as good a d i s p l a c i n g a g e n t f o r t h e s w o l l e n c r u d e . The complex p h a s e b e h a v i o r of c a r b o n d i o x i d e w i t h c r u d e o i l a p p e a r s t o c o n t r i b u t e l i t t l e t o t h e r e c o v e r y p r o c e s s ; t h e e f f e c t of t h e f r a c t i o n a t i o n of t h e c r u d e i n t h e p r e s e n c e o f c a r b o n d i o x i d e r e s u l t s i n s o m e s l i g h t a d d i t i o n a l r e c o v e r y a t t h e t a i l e n d of t h e f l o o d . S l i m t u b e e x p e r i m e n t s s i n c e t h e y do n o t c o r r e c t l y model t h e d i s p e r s i o n c o e f f i c i e n t s a n d t h e r e l a t i o n s b e t w e e n g r a v i t y a n d v i s c o u s f o r c e s do n o t provide adequate i n s i g h t i n t o a r e s e r v o i r recovery process. The s o - c a l l e d minimum m i s c i b i l i t y p r e s s u r e a s i n t e r p r e t e d f r o m s u c h e x p e r i m e n t s i s a c t u a l l y t h e p r e s s u r e above w h i c h no s i g n i f i c a n t i n c r e a s e i n r e c o v e r y w i l l b e achieved. The r e c o v e r y mechanism is s t i l l e f f e c t i v e a t l o w e r p r e s s u r e s . ACKNOWLEDGEMENTS The work on t h i s p r o j e c t w a s s u p p o r t e d by t h e U n i t e d S t a t e s Department o f E n e r g y , G a r y E n e r g y Co., a n d e n d o w m e n t f u n d s a t t h e U n i v e r s i t y o f Southern C a l i f o r n i a .

REFERENCES

1. Beeson, D. M., a n d O r t l o f f , C.D., '!Laboratory I n v e s t i g a t i o n of t h e WaterD r i v e n Carbon D i o x i d e P r o c e s s f o r O i l Recovery", TRANS AIME (1959) 216, 38891 2. Holm, Law., "Carbon D i o x i d e f o r S o l v e n t F l o o d i n g f o r I n c r e a s e d O i l Recovery", TRANS AIME (1959) 216, 225-231 3. R a t h m e l l , J.J., S t a l k u p , F.I., a n d H a s s i n g e r , R.C., "A L a b o r a t o r y I n v e s t i g a t i o n o f M i s c i b l e D i s p l a c e m e n t b y C02", SPE 3 4 8 3 , 4 6 t h A n n u a l Meeting of SPE of AIME (1971) 4. Holm, L.W., and J o s e n d a h l , V.A., "Mechanism of O i l D i s p l a c e m e n t by Carbon Dioxide", JPT ( 1 9 7 4 ) , 1417-1438. 5. D u n n y s h k i n , I.I., a n d N a m o i t , A., " S t u d y o f C o n d i t i o n s o f P e t r o l e u m M i s c i b i l i t y w i t h Carbon Dioxide", N e f t . Khoz., ( 1 9 7 8 ) , v. 3, 59-61 6. N a t i o n a l P e t r o l e u m C o u n c i l , "Enhanced O i l Recovery An A n a l y s i s of t h e P o t e n t i a l f o r Enhanced O i l Recovery f r o m Known F i e l d s i n t h e U n i t e d S t a t e s 1976 t o 2000, Washington, D.C., (1976) 7. Y e l l i g , W.F. a n d M e t c a l f e , R.S., " D e t e r m i n a t i o n a n d P r e d i c t i o n o f C O P Minimum M i s c i b i l i t y P r e s s u r e " , JPT, ( 1 9 8 0 ) , 160-168. 8. G a r d n e r , J.W., Orr, P.M., a n d P a t e l , P.D., "The E f f e c t of P h a s e B e h a v i o r on CO2 Flood D i s p l a c e m e n t E f f i c i e n c y " , SPE 8367, 5 4 t h Annual M e e t i n g of SPE of AIME, L a s Vegas, (1979) 9. E l A r a b i , M., PbD. D i s s e r t a t i o n , U n i v e r s i t y of S o u t h e r n C a l i f o r n i a , J u n e 1981. 10. O f f e r i n g a , J., a n d v a n d e r P o e l , C., " D i s p l a c e m e n t o f O i l F r o m P o r o u s Media by M i s c i b l e L i q u i d s " , TRANS AIME (1954) 201, 310-317 11. W a r n e r , H. R., Jr., "An E v a l u a t i o n o f W i s c i b l e C02 F l o o d i n g i n W a t e r f l o o d e d S a n d s t o n e R e s e r v o i r s " , JPT, (1979), 1339-1347

-

-

283 12. C l a r i d g e , E.L., " D i s c u s s i o n of t h e Use of C a p i l l a r y T u b e N e t w o r k s i n R e s e r v o i r Peformance S t u d i e s " , SPEJ ( 1 9 7 2 ) , 352-61 13. G l a s s t o n e , S., T e x t Book of P h y s i c a l C h e m i s t r y , p. 713, D. Van Nostrand, New York, 1940. 14. D o s c h e r , T. a n d G h a r i b , S., " P h y s i c a l l y S c a l e d M o d e l s S i m u l a t i n g t h e D i s p l a c e m e n t of R e s d i u a l Oil by M i s c i b l e CO2 i n L i n e a r Geometry", SPE 8896. 5 0 t h Annual C a l i f o r n i a R e g i o n a l M e e t i n g of SPE of AIME (1980) 1 5 , K a n e , A.V., " P e r f o r m a n c e Review o f a L a r g e S c a l e C a r b o n Dioxide-WAG P r o j e c t , SACROC U n i t - K e l l y S n i d e r F i e l d , SPE 7 0 9 1 , SPE I m p r o v e d O i l F i e l d Recovery Symposium, T u l s a 1978 16. G r u y F e d e r a l , Inc., " T a r g e t R e s e r v o i r s f o r C O P M i s c i b l e F l o o d i n g " , U.S.Department of Energy, Washington, D.C., (1980) 17. K a m a t h , K.I., C o m b e r i a t i , J.R., a n d Z a m m e r i l l i , A.M., "The R o l e of R e s e r v o i r T e m p e r a t u r e i n Carbon D i o x i d e F l o o d i n g " , P a p e r N4, p r e s e n t e d a t t h e U.S.Department of Energy Symposium, T u l s a , Oklahoma 1979 18. G e r r a r d , W., S o l u b i l i t y of Gases a n d L i q u i d s , A G r a p h i c A n a l y s i s , Plenum P r e s s , N e w Y o r k ( 1 9 7 6 ) . S e e a l s o , H i l d e b r a n d , J.H., a n d S c o t t , R.L., T h e S o l u b i l i t y of N o n - E l e c t r o l y t e s , R e i n h o l d , New York (1950).

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MISCIBLE GAS DISPLACEMENT

285

LABORATORY TESTING PROCEDURES FOR MISCIBLE FLOODS S. G. SAYEGH and F. G. McCAFFERY*

Petroleum Recovery Institute, Chlgury.Alberta, Gnuah T2L 2A6

ABSTRACT

The o b j e c t i v e of t h i s paper is t o provide a s t a t e - o f - t h e - a r t review and c r i t i q u e of l a b o r a t o r y t e s t i n g procedures f o r m i s c i b l e f l o o d i n g f o r r e s e a r c h e r s irr t h e f i e l d . An a d d i t i o n a l a i m of t h e paper is t o give r e s e r v o i r and production e n g i n e e r s i n s i g h t i n t o t h o s e procedures, 80 t h a t they may a p p r e c i a t e t h e i r p o t e n t i a l s and l i m i t a t i o n s , and be b e t t e r a b l e t o e v a l u a t e l a b o r a t o r y results i n l i g h t of t h e i r f i e l d experience. The t o p i c s t r e a t e d include s i n g l e - and multiple-contact phase behavior and p h y s i c a l p r o p e r t i e s measurements, and involve slim-tube and c o r e displacement t e s t s . General o b j e c t i v e s f o r each type of test are l i s t e d , recommended p r a c t i c e s are o u t l i n e d , and many examples from t h e l i t e r a t u r e are referenced. I n a d d i t i o n , g e n e r a l s c r e e n i n g criteria are presented f o r the s e l e c t i o n of s u i t a b l e candidate r e s e r v o i r s f o r m i s c i b l e flooding.

IXTRODUCTIOY One of t h e p r i n c i p a l enhanced recovery methods c u r r e n t l y under consideration f o r l i g h t o i l r e s e r v o i r s is miscible f l o o d i n g w i t h carbon dioxide and/or hydrocarbon s o l v e n t s . The process is complex and involves many parameters t h a t have t o be optimized so t h a t a flood can l e a d t o a t e c h n i c a l and economic success. Some of t h e f a c t o r s that have t o be s t u d i e d are t h e reservoir geology, o i l and o i l - s o l v e n t phase behavior, o i l solvent displacement characteristics, waterflood performance, as w e l l as r e s e r v o i r engineering a s p e c t s such as s o l v e n t production and o i l i n j e c t i o n s t r a t e g i e s , expected performance under b o t h water and solvent f l o o d i n g , apd economics. In t h i s paper, l a b o r a t o r y t e s t i n g procedures f o r m i s c i b l e flooding w i l l be d i s c u s s e d . These w i l l i n c l u d e t h e measurement of t h e phase behavior and d i s placenent d a t a of r e s e r v o i r crude o i l - s o l v e n t systems, and how such d a t a may be used in e v a l u a t i n g t h e s u i t a b i l i t y of a solvent flood f o r a p a r t i c u l a r a p p l i c a t i o n . The o b j e c t i v e of t h i s paper is t o provide a state-of-the-art review and c r i t i q u e f o r r e s e a r c h e r s i n the f i e l d . An a d d i t i o n a l aim of t h e paper is t o g i v e r e s e r v o i r and production engineers i n s i g h t i n t o l a b o r a t o r y t e s t i n g procedures SO that they may a p p r e c i a t e t h e i r p o t e n t i a l s and l i m i t a t i o n s and t h u s be b e t t e r a b l e t o e v a l u a t e l a b o r a t o r y results i n l i g h t of t h e i r f i e l d experience. For o t h e r

*

P r e s e n t address:

Occidental Research Cozporation, I r v i n e , C a l i f . 92713, U.S .A.

286 ze.:irvs of t h e E i s c i b l e f l o o d i n g process and i t s f i e l d a p p l i c a t i o n s , the reader is r s f e r r e d t o t h e works by Holm’, Stalkup2, Dosher e t a1.3, and M~ngan‘’~.

Burnett and DamC have reviewed s c r e e n i n g tests f o r a v a r i e t y of enhanced o i l recover:* p r o c e s s e s , PROCESS DESCRIPTION AND GENERAL SCREENING CRITERIA I n a m i s c i b l e f l o o d t h e s o l v e n t c o n t a c t s t h e o i l and a mixing zone is formed. I n t h e mixing zone, t h e r e is a gradual change in composition from o i l t o s o l v e n t , w i t h o u t a n i n t e r f a c e . For economic r e a s o n s , t h e s o l v e n t i s u s u a l l y n o t i n j e c t e d c o n t i n u o u s l y , b u t o f t e n i n the form of a s l u g t y p i c a l l y about 20-30% o f t h e hydrocarbon pore volume (HCPV). The s l u g is t h e n followed by a chase f l u i d , u s u a l l y water o r l e a n gas, t o d r i v e i t through t h e r e s e r v o i r towards t h e production w e l l s . The s l u g may be i n j e c t e d i n small p o r t i o n s a l t e r n a t i n g w i t h water, c o m n l y c a l l e d t h e water-alternating-gas (WAG) process. A l t e r n a t i v e l y , w a t e r may be co-injected w i t h t h e s o l v e n t . These latter i n j e c t i o n modes h e l p c o n t r o l t h e h i g h m o b i l i t y of t h e s o l v e n t . I t i s r a r e l y t e c h n i c a l l y or economically f e a s i b l e t o i n j e c t a s o l v e n t that i s d i r e c t l y m i s c i b l e w i t h t h e o i l . I n s t e a d , m i s c i b i l i t y is g e n e r a l l y achieved through what are known a s t h e m l t i p l e - c o n t a c t m i s c i b i l i t y (MCM) mechanisms7-13. Two such mechanisms can occur when gaseous or s u p e r c r i t i c a l s o l v e n t s a r e used: a condensation mechanism and a v a p o r i z a t i o n mechanism. When s u b c r i t i c a l s o l v e n t s a r e used a t p r e s s u r e s above t h e i r bubble p o i n t , t h e p r o c e s s is one of l i q u i d l i q u il e x t r a c t ion1 ’ 1 5 .

The high o i l recovery i n m i s c i b l e f l o o d s i s a t t r i b u t e d t o t h e following factors:

- high microscopic displacement - o i l e x t r a c t i o n by s o l v e n t - l o r i n t e r f a c i a l tension - o i l swelling - o i l viscosity reduction - blowdown recovery

efficiency

The s o l v e n t s used (C02 and hydrocarbons) are g e n e r a l l y less dense and v i s c o u s t h a n the o i l s . This c a u s e s t h e s o l v e n t t o o v e r r i d e t h e o i l and f i n g e r through i t . These are a d v e r s e f a c t o r s i n h o r i z o n t a l f l o o d s and lead t o e a r l y s o l v e n t breakthrough, poor sweep e f f i c i e n c y , and low o i l recovery. I n g e n e r a l , a good c a n d i d a t e r e s e r v o i r f o r h o r i z o n t a l m i s c i b l e f l o o d i n g should have t h e f o l l o v i n g characteristics:

- t h i n pay zone, up t o 5 m - good h o r i z o n t a l c o n t i n u i t y - r e l a t i v e l y homogeneous - low v e r t i c a l - t o - h o r i z o n t a l p e r m e a b i l i t y - Zot f r a c t u r e d - contains undersaturated o i l - c o n t a i n s no f r e e g a s s a t u r a t i o n - c o n t a i n s no mobile water

ratio

?ins s o l v e n t should be chosen such that i t :

- achieves m i s c i b i l i t y w i t h - is cheap - is readily available

t h e o i l a t r e s e r v o i r conditions

287 For v e r t i c a l downward displacements, t h e requirements a r e somewhat l e s s constraining:

- the - the

r e s e r v o i r should not c o n t a i n p e r m e a b i l i t y b a r r i e r s t o v e r t i c a l flow displacement should be c a r r i e d o u t a t a s u i t a b l e r a t e such that t h e flood is g r a v i t y s t a b l e

PHASE BEHAVIOR MEASUREMENTS Phase behavior measurements are c a r r i e d o u t f o r s e v e r a l purposes:

- to - to - to

c h a r a c t e r i z e t h e o i l - s o l v e n t system determine t h e mechanism by which m i s c i b i l i t y is achieved f i n e - t u n e t h e phase behavior packages i n compositional s i r m l a t o r s

I n g e n e r a l , t h e phase behavior s t u d i e s i n v o l v e t h e f o l l o w i n g measurements:

- solubilities - m u l t i p l e phase - densities - o i l swelling - viscosities

formation, i n c l u d i n g both l i q u i d and s o l i d phases

Phase Behavior Measurement Equipment High p r e s s u r e phase e q u i l i b r i u m experimental techniques f o r a v a r i e t y of a p p l i c a t i o n s have r e c e n t l y been reviewed by Eubank e t a1.16 Apparatuses used i n connection w i t h C02 and hydrocarbon systems were described by o t h e r , r e s e a r c h e r s . 17-26 A connuon t y p e o f a p p a r a t u s c o n s i s t s o f a windowed c e l l whose volume may be manipulated by means of a p i s t o n o r mercury from a p o s i t i v e displacement pump. The c e l l i s placed i n a t h e n m s t a t e d oven f o r temperature c o n t r o l . The d e s i r e d components of t h e mixture are loaded i n t o t h e cell and t h e n mixed. Mixing is u s u a l l y done w i t h a magnetically-coupled stirrer, by rocking t h e c e l l , o r by c i r c u l a t i n g t h e f l u i d s . Once e q u i l i b r i u m has been reached, v i s u a l o b s e r v a t i o n s of t h e c o e x i s t i n g phases may be c a r r i e d o u t . Samples of t h e s e phases may a l s o be withdrawn f o r d e n s i t y and v i s c o s i t y measurements, and f o r compositional a n a l y s e s . Constant composition expansions may a l s o be c a r r i e d o u t t o determine bubble and dew p o i n t s , and volumetric p r o p o r t i o n s of c o e x i s t i n g phases as f u n c t i o n s of p r e s s u r e .

The a p p a r a t u s d e s c r i b e d by LeeP3 and Sayegh e t a1.26 has two interconnected This g i v e s a greater f l e x i b i l i t y of o p e r a t i o n and p e r m i t s t h e measurement of v i s c o s i t y w i t h o u t using a s e p a r a t e viscometer. D. Robinson (personal communication) a t t h e U n i v e r s i t y of A l b e r t a has t h e c e l l constructed e n t i r e l y from sapphire. This p e r m i t s unhindered v i s u a l o b s e r v a t i o n o f t h e e n t i r e cont e n t s of the c e l l . The a p p a r a t u s e s of Orr e t a l . 2 4 , of Connor and Pope25, and of D. Robinson have t h e i r sampling l i n e s d i r e c t l y connected t o gas chromatographs f o r analysis. The a p p a r a t u s described by Orr e t a l . 2 4 d i f f e r s from t h e o t h e r s i n t h a t i t resembles a continuously s t i r r e d t a n k r e a c t o r .

cells.

288 Phase Behavior T e s t s t o C h a r a c t e r i z e t h e Crude O i l Typical t e s t s f o r t h e c h a r a c t e r i z a t i o n of t h e crude o i l involve t h e measurement of i t s composition, molecular weight, d e n s i t y , v i s c o s i t y , compressib i l i t y , bubble p o i n t , formation volume f a c t o r , g a s - o i l r a t i o , d i s t i l l a t i o n curve, d i f f e r e n t i a l l i b e r a t i o n , c o n s t a n t volume d e p l e t i o n , and c o n s t a n t composition expansion charac t e r i s tics. These tests are g e n e r a l l y c a r r i e d o u t a t r e s e r v o i r temperature using, f o r example, ASTM s t a n d a r d procedures and are p r e f e r a b l y c a r r i e d o u t w i t h bottomh o l e samples. T e s t i n g of o i l p r o p e r t i e s should b e p e r i o d i c a l l y repeated d u r i n g t h e production l i f e t i m e o f a r e s e r v o i r , and be c a r r i e d o u t on samples from t h e d i f f e r e n t producing zones o r horizons o f a pool t o determine i f t h e r e are any v a r i a t i o n s i n o i l p r o p e r t i e s . This is e s p e c i a l l y Important where t h e r e s e r v o i r p r e s s u r e f a l l s below t h e o r i g i n a l bubble p o i n t o f t h e o i l . Standingl’l and Henry e t a1.28 presented d e s c r i p t i o n s of bottomhole sampling procedures. I n g e n e r a l , t h e sampling w e l l should be s e l e c t e d so that i t is r e p r e s e n t a t i v e o f t h e average r e s e r v o i r c o n d i t i o n s . The w e l l should be produced a t a slow r a t e d u r i n g sampling t o minimize p r e s s u r e drawdown e f f e c t s and t h e r e s u l t a n t phase changes. Also, s u f f i c i e n t sampling time should be allowed t o ensure t h a t t h e sample bomb i s f i l l e d w i t h f r e s h oil. Large volumes of r e s e r v o i r f l u i d s a r e necessary t o c a r r y o u t a complete l a b o r a t o r y study of a m i s c i b l e flood. Thus, i t i s unreasonable t o u s e bottomhole samples f o r a l l t h e s e tests. The normal procedure i s t o t a k e l a r g e samples of s e p a r a t o r o i l and gas, then recombine them t o n a t c h t h e p r o p e r t i e s o f t h e bottomhole sample. 25

Phase Behavior Tests t o C h a r a c t e r i z e t h e Crude Oil-Solvent System The g e n e r a l phase behavior of hydrocarbon f l u i d s have been w e l l re~ i e w e d . ~ ”Data ~ ~ f o r hydrocarbon f l o o d s o f r e s e r v o i r crudes were presented by s e v e r a l author^^'^'^^'^^, w h i l e most of t h e r e c e n t l y published s t u d i e s have d e a l t with t h e phase behavior o f C02-011 systems.ll p12’14p18’23’24’26p30-38 This r e f l e c t s t h e growing i n t e r e s t i n u s i n g C02 as a m i s c i b l e f l o o d i n g a g e n t . The following d i s c u s s i o n w i l l c o n c e n t r a t e on C02-reservoir crude o i l systems s i n c e t h e s e are o f most i n t e r e s t t o t h e i n d u s t r y . The phase diagrams of C02crude o i l s stems a r e o f t e n presented i n t h e form o f t e r n a r y phase d i a g r a n s . 9 p 1 2 y Y 4 y 2 4Such a r e p r e s e n t a t i o n provides a convenient form f o r t h e v i s u a l i z a t i o n of t h e com o s i t i o n a l p a t h d u r i n g a c o n s t a n t temperature and p r e s s u r e d i s lacementl 11g7 and f o r determining t h e mechanism of a c h i e v i n g m i s c i b i l i t y . % It should, however, b e remembered t h a t t h e t e r n a r y r e p r e s e n t a t i o n is n o t thermodynamically r i g o r o u s and hence should n o t be i n t e r p r e t e d l i t e r a l l y . Nore a c c u r a t e p r e d i c t i o n s of t h e displacement p a t h may be made u s i n g a q u a t e r n a r y diagram. ’ A second type o f test is t h e c o n s t a n t c o n p o s i t i o n e ~ p a n s i o n . ~ ’ ~ ~ ’ ~ ~ ’ ~ ~ T n i s provides information on t h e phase b e t a v i o r of t h e C02-011 s y s t e m i n t h e v a r i o u s l o c a t i o n s of t h e r e s e r v o i r where t h e p r e s s u r e may vary. For example, a t c o c i i t i o n s where m l t i p l e l i q u i d phases appear. t h e s l u g could break down, while asp;laltene p r e c i p i t a t i o n could leqd t o a r e d u c t i o n i n r e s e r v o i r permeability.

289 The d e n s i t y , s w e l l i n g f a c t o r , and v i s c o s i t y of t h e C02-saturated 0 i 1 1 8 ’ 2 6 ’ 3 1 a r e u s u a l l y measured i n g a r a l l e l w i t h t h e phase-envelope measurements d e s c r i b e d above. Connor and Pope2 r e c e n t l y p r e s e n t e d such d a t a f o r h y d r o c a r b o n - o i l systems. I n g e n e r a l , as t h e p r e s s u r e i n c r e a s e s , more s o l v e n t g a s d i s s o l v e s i n t o t h e o i l c a u s i n g i t t o swell and t h u s t o reduce i t s d e n s i t y and v i s c o s i t y . Carbon d i o x i d e i s g e n e r a l l y more e f f e c t i v e i n t h i s r e g a r d t h a n hydrocarbon s o l v e n t g a s e s . j 6 A t v e r y h i g h p r e s s u r e s , t h e d e n s i t y and v i s c o s i t y curves could s t a r t i n c r e a s i n g because the e f f e c t o f p r e s s u r e on t h e f l u i d p r o p e r t i e s predominates o v e r t h e e f f e c t o f s o l v e n t d i s s o l u t i o n . Phase Behavior T e s t s t o Determine t h e Mechanism o f M u l t i p l e Contact M i s c i b i l i t y The tests mentioned p r e v i o u s l y are a l l s t a t i c , s i n g l e - c o n t a c t tests. The tests d e s c r i b e d i n t h i s s e c t i o n are designed t o s i m u l a t e t h e dynamic, m u l t i p l e c o n t a c t p r o c e s s o c c u r r i n g i n a r e s e r v o i r between t h e i n j e c t e d s o l v e n t and the r e s e r v o i r crude o i l . These tests are c a r r i e d o u t i n a c o n t r o l l e d manner i n a PVT c e l l , t h u s t h e p r o c e s s p a r a m e t e r s a r e w e l l d e f i n e d . The f i r s t t y p e o f t e s t is t h e g e n e r a t i o n o f a Benham p l o t by a stagewise approximation o f t h e continuous m u l t i p l e - c o n t a c t process.’ 2’ 9’ 24’2 5 ’ 39 I n t h i s procedure, a c e r t a i n p r o p o r t i o n o f o i l and s o l v e n t are mixed i n a PVT c e l l and allowed t o reach e q u i l i b r i u m . The p r o p o r t i o n s and p r o p e r t i e s o f t h e r e s u l t a n t vapor and l i q u i d a r e t h e n measured. I f a condensation p r o c e s s o c c u r s , t h e vapor phase is t h e n purged and a f r e s h b a t c h o f s o l v e n t is i n t r o d u c e d i n t o t h e c e l l . On t h e o t h e r hand, t h e l i q u i d phase i s purged i f , based on changes i n phase volume, a v a p o r i z a t i o n p r o c e s s is involved, and a f r e s h b a t c h o f o i l is i n t r o duced i n t o t h e c e l l . The e n t i r e p r o c e s s i s r e p e a t e d u n t i l o n l y one phase appears i n t h e c e l l , a t which p o i n t MCM h a s been a t t a i n e d .

’

The drawback o f t h i s method is t h a t i t is a s t a g e w i s e p r o c e s s , which o n l y approximates t h e continuous c o n t a c t s i n a r e s e r v o i r . As such, i t i s i m p l i c i t l y assumed t h a t t h e o i l and s o l v e n t i n t h e r e s e r v o i r have enough time t o reach e q u i l i b r i u m . T h i s is probably a r e a s o n a b l e assumption i n many cases s i n c e r e s e r v o i r flow rates a r e q u i t e low, b u t i f s e v e r e c h a n n e l l i n g , f i n g e r i n g , o r g r a v i t y s e g r e g a t i o n o c c u r i n t h e r e s e r v o i r , t r u e e q u i l i b r i u m may n o t be a t t a i n e d and t h e p r e d i c t i o n w i l l be o p t i m i s t i c . Another problem a s s o c i a t e d w i t h d e s i g n i n g t h i s t y p e o f batchwise experiment is t h e c h o i c e o f v o l u m e t r i c r a t i o s o f gas-to-liquid c o n t a c t e d i n each s t e p . R e s e n r o i r parameters such as t h e m o b i l i t i e s o f t h e h a s e s and flow rates should be taken i n t o account t o determine a realistic ratio. 39 The procedure d e s c r i b e d by O r r et a1.24 i s a v a r i a t i o n o f t h e above method i n t h a t t h e n u l t i p l e c o n t a c t s are c a r r i e d o u t c o n t i n u o u s l y . I n such a n e x p e r i ment, t h e rate o f s o l v e n t i n j e c t i o n i n t o t h e c e l l would have t o be c a r e f u l l y s e l e c t e d t o o b t a i n meaningful r e s u l t s .

LABORATORY DISPLACEMENT TESTS Laboratory displacement tests p r o v i d e i m p o r t a n t i n f o r m a t i o n on t h e behavior of r e s e r v o i r f l u i d / s o l v e n t systems under dynamic displacement c o n d i t i o n s . These tests a r e o f two t y p e s : slim-tube and c o r e d i s p l a c e m e n t s . It i s important t o c a r r y o u t b o t h t y p e s o f tests i n a l a b o r a t o r y s t u d y s i n c e each one p r o v i d e s d i f f e r e n t i n f o r m a t i o n n e c e s s a r y f o r t h e e v a l u a t i o n o f a f i e l d a p p l i c a t i o n . Each t y p e of t e s t w i l l now be d i s c u s s e d i n f u r t h e r d e t a i l .

Slim-Tube Displacement Tests Slim-tube displacement tests are l a b o r a t o r y tests that are c a r r i e d o u t i n a n i d e a l i z e d porous medium. As such, t h e y may be thought of a s b e i n g a n i n t e r mediate approximation t o r e s e r v o i r f l o o d s , l y i n g between t h e wre r e a l i s t i c c o r e f l o o d s and t h e more i d e a l i s t i c m u l t i p l e - c o n t a c t PVT c e l l tests. A s l i m tube t est is c a r r i e d o u t p r i m a r i l y t o determine i f a s o l v e n t a c h i e v e s m i s c i b i l i t y w i t h a n o i l a t a c e r t a i n temperature and p r e s s u r e . A l a b o r a t o r y i n v e s t i g a t i o n i n v o l v i n g a series o f r u n s ' c o u l d be done w i t h e i t h e r o r b o t h o f t h e f o l l o w i n g objectives :

- minimum m i s c i b i l i t y - solvent screening

p r e s s u r e (ME')d e t e r m i n a t i o n

Orr et al.24 have made a summary o f slim-tube displacement a p p a r a t u s e s used by v a r i o u s i n v e s t i g a t o r s . The s l i m t u b e is normally c o n s t r u c t e d from h o r i z o n t a l l y c o i l e d s t a i n l e s s steel t u b i n g . The t u b e i s 10-20 m l o n g , about 5 mu i n t e r n a l d i a m e t e r , and packed w i t h f i n e g l a s s beads o r s a n d s t o a p o r o s i t y o f about 30% and t o a p e r m e a b i l i t y of 3-15 urn2. The c o i l is f i r s t s a t u r a t e d w i t h o i l , t h e n flooded w i t h C O P . The e f f l u e n t from t h e slim-tube p a s s e s through a s i g h t g l a s s f o r visual o b s e r v a t i o n , i s sampled f o r a n a l y s i s , and is t h e n f l a s h e d t o a t m s p h e r i c p r e s s u r e through a b a c k p r e s s u r e r e g u l a t o r . Produced l i q u i d and gas phases are metered s e p a r a t e l y . The d a t a o b t a i n e d from t h e test i n c l u d e e f f l u e n t c o l o r , number o f p h a s e s , composition and g a s - o i l r a t i o , a s w e l l a s o i l recovery and p r e s s u r e drop a c r o s s t h e coil--each as a f u n c t i o n o f t h e volume o f solvent injected. The b a s i c assumption i n slim-tube tests i s that t h e displacement i s p i s t o n l i k e and t h a t l i t t l e o r no f i n g e r i n g o c c u r s . - T h i s i s due i n p a r t to t h e uniformi t y o f t h e packing and t h e dampening e f f e c t o f t h e t u b e ' s w a l l s . Accordingly, t h e c r i t e r i a f o r m i s c i b i l i t y b e i n g achieved i n a carbon d i o x i d e f l o o d a r e :

- no appearance o f -

-

a methane bank p r i o r t o . breakthrough l a t e s o l v e n t b r e a k t h r o u g h ( a t around 0.8 pore volumes o f s o l v e n t i n j e c t e d , or later) a s m o t h t r a n s i t i o n from o i l t o s o l v e n t i n t h e mixing zone w i t h o u t t h e a m e a r a n c e of a n i n t e r f a c e h i g h u l t i m a t e recovery ( g r e a t e r t h a n 95% o f t h e o r i g i n a l o i l - i n - p l a c e , . OOIP)

..

On t h e o t h e r hand, a n i m i s c i b l e displacement is c h a r a c t e r i z e d by:

- t h e appearance of a methane bank p r i o r t o s o l v e n t breakthrough - e a r l y breakthrough - t h e o b s e r v a t i o n o f a n i n t e r f a c e between t h e o i l - r i c h and s o l v e n t - r i c h p h a s e s i n t h e mixing zone - low u l t i m a t e r e c o v e r y A l l o f t h e above-noted symptoms o f a n immiscible displacement should appear i f t h e p r e s s u r e is w e l l below t h e MEip. This a l s o depends t o some e x t e n t on t h e c h a r a c t e r i s t i c s o f t h e s l i m t u b e i t s e l f ( t u b e d i a m e t e r , u n i f o r m i t y of bead s i z e and packing). I t would be i n s t r u c t i v e t o c a r r y o u t two i n i t i a l d i s p l a c e m e n t s t o c h a r a c t e r i z e t h e p a r t i c u l a r s l i m tube b e i n g used. The f i r s t f l o o d could be conducted under d e f i n i t e l y immiscible c o n d i t i o n s u s i n g n i t r o g e n , f o r example, a s t h e f l o o d i n g a g e n t , w h i l e t h e second f l o o d would i n v o l v e f i r s t - c o n t a c t m i s c i b l e c o n d i t i o n s u s i n g benzene, f o r example, as the d i s p l a c i n g a g e n t . For f u r t h e r d i s c u s s i o n s , t h e r e a d e r is r e f e r r e d t o o t h e r p u b l i s h e d works.24' 31'40'41 y 4 2

291 A v a r i e t y of s l i m t u b e l e n g t h s have been used by v a r i o u s researcher^.^^ I t would appear t h a t m u l t i p l e - c o n t a c t m i s c i b i l i t y i s achieved f a i r l y e a r l y i n t h e l i f e of t h e displacement ( w i t h i n t h e f i r s t two m e t e r s ) , o t h e r w i s e a high o i l recovery would not be o b t a i n e d . This is supported by t h e lower number of c o n t a c t s (about 1 0 ) r e q u i r e d i n PVT c e l l , m u l t i p l e - c o n t a c t experiments12’19’25 although, as mentioned p r e v i o u s l y , such experiments are open t o i n t e r p r e t a t i o n . On t h e o t h e r hand, Y e l l i g 1 5 concluded t h a t l o n g e r l e n g t h s (2.5 5 m) were required t o develop m i s c i b i l i t y when carbon d i o x i d e was i n the l i q u i d form. Thus, a s l i m tube l e n g t h between 10-20 1 is recommended. The r a t e a t which slim-tube d i s placements are r u n a f f e c t s t h e s t a b i l i t y o f t h e displacement f r o n t and t h e time allowed f o r c o n t a c t between t h e o i l and s o l v e n t . For t h i s reason, displacement rates are b e s t kept a t less t h a n 1 0 m/day. The u s e o f r e l a t i v e l y low rates a l s o minimizes t h e p r e s s u r e drop a c r o s s t h e slim tube, which provides f o r good d e f i n i t i o n o f t h e minimum m i s c i b i l i t y p r e s s u r e .

-

Benham e t a1.8 have presented c o r r e l a t i o n s f o r t h e minimum enrichment of d r y gas (by LPG) r e q u i r e d t o a c h i e v e m i s c i b i l i t y , w h i l e Jacobson43 s t u d i e d t h e c o n t r i b u t i o n o f a c i d g a s e s t o m i s c i b i l i t y . Other r e s e a r c h e r s 1 O S 3 l ’40’41 ’42’44 have i n v e s t i g a t e d t h e e f f e c t of t h e d i f f e r e n t p r o c e s s v a r i a b l e s on t h e carbon d i o x i d e MMP. I n g e n e r a l , t h e ME’ i n c r e a s e s w i t h d e c r e a s i n g o i l g r a v i t y and i t s C5 t o C30 c o n t e n t , and w i t h i n c r e a s i n g temperature and molecular weight of t h e o i l C5+ f r a c t i o n . Hydrogen s u l f i d e and LPG i n t h e carbon d i o x i d e decrease t h e I W , w h i l e n i t r o g e n and methane i n c r e a s e i t . I n a d d i t i o n t o studying dynamic m i s c i b i l i t y c o n d i t i o n s , t h e r e s u l t s of slim-tube experiments may be used t o c a l i b r a t e compositional s i m u l a t o r s . 39’45’46 Wang and L ~ c h ei n ~ v e~s t i g a t e d t h e r e l a t i v e e f f i c i e n c y of d i f f e r e n t watera l t e r n a t i n g - g a s c y c l e s and concluded t h a t t h e t o t a l o i l recovery w a s i n s i g n i f i c a n t l y a f f e c t e d by t h e i n j e c t i o n sequence provided t h a t t h e t o t a l amount of carbon d i o x i d e i n j e c t e d remained t h e same. I n summary, slim-tube displacement tests are an extremely u s e f u l t o o l f o r studying t h e m i s c i b i l i t y r e l a t i o n s h i p between o i l and s o l v e n t systems under c o n t r o l l e d dynamic c o n d i t i o n s . Caution must be e x e r c i s e d when t r a n s p o s i n g t h e r e s u l t s of such s t u d i e s t o r e s e r v o i r systems s i n c e t h e e f f e c t s of t h e r e s e r v o i r rock p r o p e r t i e s (homogeneity, r e l a t i v e p e r m e a b i l i t y , w e t t a b i l i t y , and pore geometry) have n o t been t a k e n i n t o account, hence displacement tests on r e s e r v o i r rocks must follow. The following s e c t i o n d e a l s w i t h c o r e displacement tests i n a n attempt t o provide more d e t a i l e d i n s i g h t i n t o t h e displacement behavior as i t may occur i n t h e r e s e r v o i r i n r e g i o n s contacted by t h e s o l v e n t . Core Displacement Tests Following slim-tube displacement t e s t s t o confirm t h e establishment of m i s c i b i l i t y w i t h t h e o i l f o r a given s o l v e n t a t a p p r o p r i a t e r e s e r v o i r c o n d i t i o n s of temperature and p r e s s u r e , c o r e f l o o d i n g measurements are g e n e r a l l y recommended. Such tests c a n be used t o e v a l u a t e a v a r i e t y of displacement phenomena t h a t have b e a r i n g o n t h e m i s c i b l e f l o o d i n g process. These i n c l u d e .

- recovery mechanisms9’1 9 - d i f f u s i o n and d i s p e r s i o n c o e f f i c i e n t s , and dead-end pore volume^^^-^^ - m i s c i b l e and compositional s i m u l a t o r tuning48’ 6 4 - chromatographic s e p a r a t i o n of components1 ’48 - water, o i l , and gas r e l a t i v e p e r r n e a b i l i t i e ~ ~ ” ~ ~ - r o c k i n t e r a c t i o n s w i t h gas and b r i n e - dynamic o i l - s o l v e n t phase behavior 5 8 - e f f e c t of t h e following f a c t o r s on displacement e f f i c i e n c y o r o i l recovery:

292

.. rsoocl vk e n t type’ 4’60

. water s a t u r a t i o n (secondary o r t e r t i a r y f l o o d i n g mode)59’60’63rC5 . phase behavior ( m u l t i l e l i q u i d and s o l i d phases)32 .. displacement p r e s s u r e ” ’’ solvent injection ratel5’6’

. water-solvent f l o o d i n g mode ( c o n t i n u o u s s o l v e n t i n j e c t i o n , s o l v e n t s l u g s i z e WAG, c o i n j e c t i o n , C02-foam and C02-polymer i n j e c t i o n ) b 2 ’ 6 3 . blowdown . low i n t e r f a c i a l

tension66

A c o r e d i s p l a c e m e n t a p p a r a t u s c o n s i s t s of a c o r e h o l d e r i n which t h e c o r e is placed under a c o n f i n i n g p r e s s u r e . The c o r e is connected t o r e s e r v o i r o i l and b r i n e , i n j e c t i o n water, and s o l v e n t c o n t a i n e r s . The. c o r e i s flooded a t r e s e r v o i r t e m p e r a t u r e and p r e s s u r e w i t h t h e s e f l u i d s i n t h e p r o p e r sequence, and t h e f l u i d p r o d u c t i o n and p r e s s u r e d r o p s are monitored. V i s u a l o b s e r v a t i o n o f t h e c o r e ’ s e f f l u e n t s c a n b e made through a s i g h t g l a s s .

It is recommended that c o r e from t h e a c t u a l r e s e r v o i r be used i n t h e d i s placement tests. Although o u t c r o p c o r e s may a l s o be used f o r c e r t a i n m e c h a n i s t i c s t u d i e s . The s e l e c t i o n of r e s e r v o i r c o r e s f o r t h e s e tests is a n important procedure which r e q u i r e s a n u n d e r s t a n d i n g o f t h e geology o f t h e e n t i r e r e s e r v o i r . The c o r e s should be sampled from t h e pay zone of i n t e r e s t and chosen t o p r o p e r l y r e p r e s e n t t h e main r o c k t y p e s o c c u r r i n g i n t h e r e s e r v o i r . Cores w i t h l a r g e h e t e r o g e n e i t i e s s u c h as f r a c t u t e s , vugs, and l a m i n a t i o n s would tend t o g i v e r e s u l t s that e x a g g e r a t e t h e e f f e c t s o f t h e h e t e r ~ g e n e i t i e s . ~S~t u d i e s of Rosman and Simon66, and Eatycky e t a1.67 have, however, shown t h a t t h e h e t e r o g e n e i t y e x h i b i t e d by i n d i v i d u a l c o r e segments d e c r e a s e s when t h e segments are b u t t e d t o g e t h e r t o form a l o n g e r c o r e assembly.

F u l l d i a m e t e r , v e r t i c a l c o r e s may be used f o r e v a l u a t i n g v e r t i c a l f l o o d s w h i l e , f o r h o r i z o n t a l f l o o d s , h o r i z o n t a l p l u g s have t o be d r i l l e d o u t of t h e f u l l d i a m e t e r c o r e . These p l u g s a r e t y p i c a l l y 2-3 cm i n d i a m e t e r and 6-10 cm long. About 20 p l u g s should be b u t t e d t o g e t h e r i n a c o r e h o l d e r t o g i v e a s u f f i c i e n t l y l o n g assembly f o r t h e d i s p l a c e m e n t t e s t , p a r t i c u l a r l y i f t h e development o f m u l t i p l e c o n t a c t m i s c i b i l i t y i s i n v o l v e d . To a c h i e v e good c a p i l l a r y c o n t a c t between t h e c o r e s , t h e c o r e f a c e s c a n be machined s q u a r e on a l a t h e , and t h e r e is t h e o p t i o n o f p l a c i n g f i l t e r paper between t h e c o r e f a c e s p r i o r .to mounting them i n a tiraxial c o r e h o l d e r . It i s recommended t h a t t h e plugs b e chosen s u c h that t h e y come from t h e same f a c i e s i n t h e r e s e r v o i r , and t h a t t h e y have similar and r e p r e s e n t a t i v e p o r o s i t y - p e r m e a b i l i t y c h a r a c t e r i s t i c s Combining p l u g s from d i f f e r e n t f a c i e s and w i t h w i d e l y v a r y i n g p r o p e r t i e s makes t h e i n t e r p r e t a t i o n of t h e d i s p l a c e m e n t r e s u l t s d i f f i c u l t and o f q u e s t i o n a b l e v a l u e a s i n p u t d a t a f o r s i m u l a t o r p r e d i c t i o n s of f i e l d performance. The c o r e s a v a i l a b l e f o r t e s t i n g may b e i n t h e preserved state o r , more l i k e l y , are i n a n aged c o n d i t i o n . I f p r e s e r v e d , t h e c o r e s can be used d i r e c t l y i n t h e displacement experiments. Non-preserved c o r e needs t o be cleaned thoroughly by e x t r a c t i o n or displacement w i t h s o l v e n t s such a s toluene-methano166, mounted d r y i n a c o r e h o l d e r , and t h e n have i t s w e t t a b i l i t y and i n i t i a : o i l s a t u r a t i o n r e - e s t a b l i s h e d by c o n t a c t w i t h t h e r e s e r v o i r f l u i d s . A t y p i c a l t e s t procedure u t i l i z e d w i t h c l e a n e d , non-preserved c o r e i n v o l v e s e v a c u a t i n g , s a t u r a t i n g w i t h r e s e r v o i r lsrine, and t h e n f l o o d i n g w i t h c r u d e o i l u n t i l t h e water s a t u r a t i o n approaches t h e connate water s a t u r a t i o n . I f t h i s procedure cannot p r o v i d e a s u f f i c i e n t l y low i n i t i a l water s a t u r a t i o n , t h e n methods u t i l i z i n g gas flow a n d / o r e v a p o r a t i o n c a n be Following placement of crude o i l i n t h e c o r e , i t is l e f t t o a g e f o r s e v e r a l d a y s f o r t h e purpose of

293 re-establishing t h e o r i g i n a l ~ e t t a b i l i t y ~A ~ f.t e r a g i n g , t h e c o r e is waterflooded w i t h i n j e c t i o n water down t o r e s i d u a l o i l s a t u r a t i o n . The w a t e r - o i l r e l a t i v e p e r m e a b i l i t y may be c a l c u l a t e d from t h e p r e s s u r e drop and production h i s t o r y o f t h e waterflood. F i n a l l y , t h e core i s s o l v e n t flooded. I f t h e s o l vent f l o o d is t o be a secondary one, t h e waterflood s t e p is then n a t u r a l l y omitted

.

The d i s t i n c t advantages of u s i n g non-preserved c o r e are its ease of handling d u r i n g t h e d r i l l i n g of p l u g s , and t h e a b i l i t y t o examine t h e cores and measure t h e i r p r o p e r t i e s (such as a i r p e r m e a b i l i t y and p o r o s i t y ) p r i o r t o t h e f l o o d tests. The disadvantage of u s i n g aged c o r e i s t h a t one is seldom s u r e of t h e adequacy o f t h e measures t a k e n t o r e s t o r e t h e c o r e t o its o r i g i n a l state. A prime r e a s o n f o r a t t e m p t i n g t o r e s t o r e t h e r e s e r v o i r w e t t i n g c o n d i t i o n i n t h e c o r e relates t o t h e r e p o r t e d t r a p p i n g o r s h i e l d i n g o f o i l by mobile water i n water-wet It is g e n e r a l l y b e l i e v e d that mixed o r i n t e r m e d i a t e l y w e t systems provide optimum t e r t i a r y recovery e f f i c i e n c i e s w i t h s o l v e n t floods. RECAPITULATION

The f i r s t s t e p i n t h e implementation of a f i e l d - s c a l e m i s c i b l e flood is t h e s e l e c t i o n o f s u i t a b l e c a n d i d a t e r e s e r v o i r s and s o l v e n t s . A set of t e c h n i c a l s c r e e n i n g criteria has been provided t o a i d i n t h e s e l e c t i o n . These should be augmented by o t h e r l i m i t a t i o n s and/or i n c e n t i v e s (e.g. economic) s p e c i f i c t o each locale. Once t h e p r e l i m i n a r y s e l e c t i o n has been made, l a b o r a t o r y tests can be c a r r i e d o u t t o reduce t h e t e c h n i c a l and economic u n c e r t a i n t i e s a s s o c i a t e d with f i e l d tests. The l a b o r a t o r y t e s t s should be supplemented w i t h g e o l o g i c a l ( r e s e r v o i r d e s c r i p t i o n ) and computer s i m u l a t i o n studies'. Laboratory t e s t s have been c a t e g o r i z e d i n t o s t a t i c and dynamic measurements, and d i f f e r e n t t y p e s of tests that may be c a r r i e d o u t under each category have been l i s t e d . S t a t i c phase behavior tests e n a b l e t h e measurement o f t h e p r o p e r t i e s of t h e o i l , s o l v e n t , and t h e i r m i x t u r e s under c o n t r o l l e d c o n d i t i o n s . Slim tube tests determine t h e dynamic m i s c i b i l i t y c h a r a c t e r i s t i c s of t h e o i l - s o l v e n t system. F i n a l l y , c o r e displacement tests h e l p determine t h e e f f e c t of t h e process c o n d i t i o n s and rock p r o p e r t i e s o n t h e displacement e f f i c i e n c y i n t h e swept zone of the reservoir. ACKNOIJLEDQ4ENI'S The a u t h o r s wish t o e x p r e s s t h e i r thanks t o P.M. Sigmund f o r c o n s u l t a t i o n s , and t o B. Moore f o r . t y p i n g t h e manuscript. REFERENCES 1.

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HOLM, L.W. and JOSENDAL, V.A.; " E f f e c t o f O i l Composition o n Miscible-Type Displacement by Carbon Dioxide", paper SPE 8814, p r e s e n t e d a t t h e F i r s t J o i n t SPE/DOE Symp. on Enhanced O i l Recovery, T u l s a , Oklahoma ( A p r i l 20-23, 1980),

11. METCALFE, R.S. and YARBOROUGH, L.; "The E f f e c t of Phase E q u i l i b r i a on t h e C 0 2 Displacement Mechanism", SOC. P e t . Eng. J. (August 1979), 242. 12.

GARDNER, J.W., ORR, F.M., and PATEL, P.D.; 'The E f f e c t o f Phase Behavior on Cog Flood Displacement E f f i c i e n c y " , paper SPE 8367, p r e s e n t e d a t t h e 5 4 t h Annual F a l l T e c h n i c a l Conference and E x h i b i t i o n o f t h e SOC. o f P e t . Eng. o f AIME, Las Vegas, Nevada (September 23-26, 1979).

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.;

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27 .* HENRY, R.L., FEATHER, G.L., SMITH, L.R., and FUSSELL, D.D.; " U t i l i z a t i o n of Composition O b s e r v a t i o n Wells i n a West Texas C02 P i l o t Flood", paper SPE/WE 9786, p r e s e n t e d a t t h e 1981 SPE/DOE Second J o i n t Symp. on Enhanced O i l Recovery o f t h e Soc. o f P e t . h g . , T u l s a , Oklahoma ( A p r i l 5-8, 1981).

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37.

ORR, JR., F.M., W, A.D., and LIEN, C.L.; 'Thase Behavior o f C02 and Crude O i l i n Low Temperature Reservoirs", p a p e r SPE 8813, - p r e s e n t e d a t t h e F i r s t J o i n t SPEIDOE Symp. on Enhanced O i l Recovery, T u l s a , Oklahoma ( A p r i l 20-23, 1980).

38.

TUREK, E.A., METCALFE, R.S., YARBOROUGH, L., and ROBINSON, J R . , R.L.; "Phase E q u i l i b r i a i n Carbon Dioxide-Multicomponent Hydrocarbon Systems: Experimental Data and a n Improved P r e d i c t i o n Technique", paper SPE 9231, p r e s e n t e d a t t h e 5 5 t h Annual F a l l T e c h n i c a l Conference and E x h i b i t i o n o f t h e SPE o f AIME, Dallas, Texas (September 21-24, 1 9 8 0 ) .

39.

and SHELTON, J.L.; "A M u l t i c e l l E q u i l i b r i u m METCALFE, R.S., FUSSELL, D.D., S e p a r a t i o n Model f o r t h e Study o f M u l t i p l e C o n t a c t M i s c i b i l i t y i n Rich Gas Drives", SOC. P e t . Eng. J . (June 1 9 7 3 ) , 147.

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YELLIG, W.F. and METCALFE, R.S.; ''Determination and P r e d i c t i o n of COP Minimum M i s c i b i l i t y P r e s s u r e s " , p a p e r SPE 7477, p r e s e n t e d a t t h e 53rd Annual F a l l T e c h n i c a l Conference and E x h i b i t i o n of t h e SOC. of P e t . Eng. of A m , Houston, Texas (October 1-3, 1978).

41.

" E f f e c t o f I m p u r i t i e s o n Minimum M i s c i b i l i t y P r e s s u r e s and IETCALFE, R.S Minirmm Enrichment L e v e l s f o r CO2 and Rich Gas Displacement". paper SPE 9230, p r e s e n t e d a t t h e 5 5 t h Annual F a l l Technical Conference and E x h i b i t i o n o f t h e SOC. o f P e t . Eng. o f AIME, Dallas, Texas (September 21-24, 1980).

42.

JOHNSON, J.P. and WLLIN, J.S.; '?leasurement and C o r r e l a t i o n o f CO2 M i s c i b i l i t y P r e s s u r e s " , p a p e r SPE 9790, p r e s e n t e d a t t h e 1 9 8 1 SPEIDOE Second J o i n t Symposium o n Enhanced O i l Recovery o f t h e SOC. of P e t . Eng. of AIME, T u l s a , Oklahoma ( A p r i l 5-8, 1981).

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45.

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59.

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299

MISCIBLE GAS DISPLACEMENT

COMPLEX STUDY OF COZ FJBODING IN HUNGARY

SANDOR DOLESCHALL, GABOR ACS, &VA FARKAS, TIBOR PAAL, JANOS TOROK Hungarian Hydrocarbon Institute

V A L ~ RBALINT General Contractingand Designing Office for the Oil Industry, “Olajterv”

ZOLTAN B I R ~ lhznsdanubian Oil and Gas Roduction Company

ABSTRACT A systematic program o f carbonated n a t u r a l gas f l o o d i n g has been c a r r i e d o u t i n Hungary, based on l a b o r a t o r y PVT and displacement studies, followed by composit i o n a l mathematical s i m u l a t i o n and. f i e l d experiment on depleted r e s e r v o i r . PVT s t u d i e s have proved t h a t gas c o n t a i n i n g 81 mole % carbon d i o x i d e can be used f o r EOR purposes. The s t u d i e s covered t h e v o l u m e t r i c and phase behaviour o f carbonated n a t u r a l gas f l o o d i n g under f i e l d c o n d i t i o n s and t h e r e s u l t s proved t h a t such f l o o d i n g was e f f i c i e n t even i f t h e gas i s n o t pure carbon dioxide. Based upon t h e o r e t i c a l c o n s i d e r a t i o n s a t e c h n o l o g i c a l scheme has been developed t o increase t h e sweep e f f i c i e n c y . A ten-component, three-phase mathematical model developed t o simulate carbon d i o x i d e f l o o d i n g i s s u i t a b l e f o r t r e a t i n g s i n g l e - and multi-phase systems. The d i f f e r e n c e equations handle t h e systems w i t h d i f f e r e n t number o f phases I n a u n i f o r m way, t h u s t h e generation and disappaerance o f phases can be followed by t h e model w i t h o u t d i f f i c u l t i e s . The computer model was used t o simulate p a r t i a l l y m i s c i b l e carbonated n a t u r a l gas f l o o d i n g i n t h e western area o f t h e Budafa o i l f i e l d . The production h i s t o r y match and p r e d i c t i o n agreed w e l l w i t h t h e f i e l d data.

INTRODUCTION The o i l resources o f Hungarian r e s e r v o i r s cover o n l y a small p a r t o f t h e country’s demand, and t h e import of crude o i l imposes a considerable economic burden on a c o u n t r y developing i t s i n d u s t r y . Apart from t h e n e e d - t o search f o r new o i l f i e l d s , it became e v i d e n t as long ago as t h e f i f t i e s t h a t it was important t o consider secondary and l a t e r t h e t e r t i a r y recovery methods. Among t h e o t h e r p o s s i b i l i t i e s t h e e f f e c t o f carbon d i o x i d e was a l s o studied, and

300 very soon most a t t e n t i o n focused on t h e questions o f C02 f l o o d i n g because i n Hungary t h e occurrence o f n a t u r a l carbon d i o x i d e i n h i g h carbon d i o x i d e content n a t u r a l gases i s more o f t e n found and t o a g r e a t e r e x t e n t than t h e world average. Some r e s u l t s o f C02 f l o o d i n g i n Hungary can be found i n Ref. 1 .

PVT AND PHASE BEHAVIOUR MEASUREMENTS F e a s i b i l i t y s t u d i e s o f t h e a p p l i c a t i o n p o s s i b i l i t i e s o f carbon d i o x i d e and carbonated n a t u r a l gases s t a r t e d i n 1955 w i t h a s e r i e s o f PVT measurements. The very f i r s t PVT s t u d i e s proved t h a t carbonated n a t u r a l gas a l t e r s t h e v i s c o s i t i e s and v o l u m e t r i c p r o p e r t i e s o f crudes w i t h very d i f f e r e n t d e n s i t i e s i n a favourable way compared w i t h t h e e f f e c t o f lean o r wet n a t u r a l gases under t h e same c o n d i t i o n s , mainly i f t h e carbon d i o x i d e c o n t e n t o f t h e d i s s o l v e d gas i s above 60 mole 5 . Based upon t h e r e s u l t s o f more d e t a i l e d PVT measurement, s e t s o f curves have been developed t o p r e d i c t t h e s o l u b i l i t y , s w e l l i n g and v i s c o s i t y o f monophase r e s e r v o i r oil--carbonated n a t u r a l gas systems. The a c t u a l PVT p r o p e r t i e s o f t h e o r i g i n a l gas saturated o i l were chosen as a reference s t a t e t o e l i m i n a t e t h e p o s s i b l e l a r g e e r r o r s coming from t h e unknown parameters o f such very complex systems, and o n l y t h e change o f t h e given p r o p e r t i e s was c o r r e l a t e d w i t h t h e d i s s o l v e d carbon d i o x i d e cont e n t . I n t h i s way simple, easy t o use equations w i t h good accuracy have been developed. For example, t h e p r e d i c t i o n o f v i s c o s i t i e s o f saturated and undersaturated crudes under d i f f e r e n t c o n d i t i o n s i s p o s s i b l e w i t h t h e use o f o n l y one measured v i s c o s i t y value.

I t has been proved t h a t i n t h e case o f Hungarian crude o i l s , bearing i n mind t h e a c t u a l r e s e r v o i r conditions, t h a t no complete m i s c i b i l i t y occurs even i f . t h e d i s s o l v e d gas i s pure carbon d i o x i d e . I n t h e course o f t h e thorough examination o f t h e PVT data "unusual" behaviour was observed. Repeated measurements i n a windowed PVT c e l l revealed t h e presence o f a carbon d i o x i d e r i c h second l i q u i d phase which e x i s t s w i t h i n a d e f i n i t e pressure-temperature range above a c e r t a i n gas--oil r a t i o . T h i s r e g i o n depends upon t h e t o t a l composition o f t h e system and t h e phenomenon i s connected w i t h t h e r e s t r i c t e d s o l u b i l i t y o f carbon d i o x i d e i n r e s e r v o i r o i l s . P a r t i t i o n o f l i g h t and intermediate hydrocarbons between t h e r e s e r v o i r o i l and t h e second l i q u i d phase has been proven i n agreement w i t h o t h e r experience. I n t h e case o f c e r t a i n Hungarian crude o i l s r e v e r s i b l e p r e c i p i t a t i o n o f semi-solid p a r t i c l e s has a l s o been observed b u t mostly under such circumstances which cannot be r e a l i z e d i n a c t u a l r e s e r v o i r s . I t i s i n t e r e s t i n g t h a t these phenomena occur i n t h e presence o f carbonated n a t u r a l gases, too, even i f they a r e r e l a t i v e l y r i c h I n l i g h t hydrocarbon f r a c t i o n . The existence o f t h e mentioned multiphase systems had t o be considered i n planning vapour--liquid e q u i l i b r i u m studies.

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The aim o f these s t u d i e s i s t o determine exact K values according t o t h e need o f compositional mathematical s i m u l a t i o n . E q u i l i b r i u m r a t i o s had been d e t e r mined f o r c h a r a c t e r i s t i c r e s e r v o i r oil--carbonated n a t u r a l gas as w e l l as r e s e r v o i r oil--water--carbonated n a t u r a l gas systems and a method f o r e s t i mation was developed. As a r e s u l t o f a d d i t i o n a l measurements and comparison of experimental w i t h computed data u s i n g d i f f e r e n t equations o f s t a t e i t i s concluded t h a t f u r t h e r improvements a r e necessary both f o r t h e development o f generalized K f u n c t i o n s and equations o f s t a t e t o g e t h e r w i t h t h e improvement o f interaction coefficients.

30 1 Judging by t h e r e s u l t s o f o t h e r studies, t h e i n t e r f a c i a l t e n s i o n decreases w i t h i n c r e a s i n g carbon d i o x i d e c o n t e n t i n gas--oil--water systems. Volumetric and phase behaviour as well as water c o n t e n t and hydrate forming c o n d i t i o n s o f carbonated n a t u r a l gases i n Hungary were a l s o s t u d i e d and t h e r e s u l t i n g data used t o formulate generalized r e l a t i o n s h i p s . Experimental data on s o l u b i l i t y , s w e l l i n g and v i s c o s i t y o f t y p i c a l r e s e r v o i r waters - s a t u r a t e d w i t h carbonated n a t u r a l gases having d i f f e r e n t composition, even i n t h e presence o f calcium carbonate and r e s e r v o i r rocks c o n t a i n i n g c l a y minerals t o g e t h e r w i t h vapour--liquid e q u i l i b r i u m r a t i o s supplied f u r t h e r i n f o r m a t i o n e n a b l i n g a b e t t e r understanding o f t h e mechanism o f carbonated n a t u r a l gas f l o o d i n g . I t has been pointed o u t t h a t because o f t h e i n t e r a c t i o n o f carbonated water and r e s e r v o i r rocks c e r t a i n c l a y m i n e r a l s c o n t r a c t and t h i s may improve t h e e f f i c i e n c y o f t h e process i n p r a c t i c e .

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A PVT model was used t o f o l l o w t h e change o f t h e v o l u m e t r i c and phase behaviour and t h e e q u i l i b r i u m composition o f phases i n t h e course o f f l o o d i n g . T h i s model contained water-, o i l - and gas-phases under r e s e r v o i r c o n d i t i o n s w i t h a r a t i o corresponding t o t h e a c t u a l s a t u r a t i o n a t a given, depleted f i e l d . The pressure was increased t o t h e o r i g i n a l r e s e r v o i r pressure d i r e c t l y by t h e i n j e c t i o n gas. I n another s e t o f experiments t h e f i n a l pressure was reached step by step, t h e vapour phase g r a d u a l l y being changed by t h e i n j e c t i o n gas a t each i n t e r mediate pressure u n t i l e q u i l i b r i u m composition was approached. These experiments were repeated f o r d i f f e r e n t f i e l d c o n d i t i o n s u s i n g i n j e c t i o n gases w i t h d i f f e r e n t carbon d i o x i d e content. I n t e r p r e t a t i o n o f t h e r e s u l t s revealed t h e Importance o f t h e dynamic pressure-increase process being a p p l i e d f o r carbonated n a t u r a l gas f l o o d i n g , t h e r o l e o f t h e l i g h t hydrocarbon f r a c t i o n present and supported t h e conclusion p r e v i o u s l y drawn on t h e b a s i s o f PVT s t u d i e s o f mono-and two-phase systems.

Taking i n t o c o n s i d e r a t i o n t h e composition o f t h e g r a d u a l l y displaced gas, i t has been concluded t h a t it i s n o t p o s s i b l e i n p r a c t i c e t o replace a l l t h e f r e e and d i s s o l v e d gas by a carbon d i o x i d e s l u g o f reasonable s i z e . I t has a l s o been found t h a t d e s p i t e t h e d i l u t i o n o f t h e s l u g by hydrocarbon gas i n t h e pores, r e l a t i v e l y s i g n i f i c a n t v a p o r i z a t i o n o f t h e o i l takes place i f t h e carbon d i o x i d e c o n t e n t o f t h e f r e e gas phase i s above a c e r t a i n c r i t i c a l concentration. T h i s c r i t i c a l value, which depends upon t h e pressure, temperature and t h e c h a r a c t e r i s t i c s o f t h e o i l , can a l s o be exceeded by using carbonated n a t u r a l gases f o r t h e i n j e c t i o n . These observations confirmed i n d i r e c t l y t h e idea about t h e probable formation o f a m i s c i b l e f r o n t i n t h e r e s e r v o i r under dynamic c o n d i t i o n s d u r i n g carbonated n a t u r a l gas f l o o d i n g . As t o t h e v o l u m e t r i c p r o p e r t i e s and v i s c o s i t i e s o f t h e e q u i l i b r i u m l i q u i d phases no s u b s t a n t i a l d i f f e r e n c e c o u l d be found on comparing t h e e f f e c t o f a carbon d i o x i d e s l u g and a l a r g e r volume o f carbonated n a t u r a l gas w i t h higher carbon d i o x i d e content.

LABORATORY DISPLACEMENT STUDIES F o l l o w i n g encouraging PVT r e s u l t s dynamical l a b o r a t o r y s t u d i e s were c a r r i e d o u t displacement processes. The l i n e a r model t o examine t h e e f f i c i e n c y o f C02 used f o r t h e measurements was 1 m long and 25 mm i n diameter. Nonconsolidated r e s e r v o i r sandstone cores and r e s e r v o i r f l u i d were used f o r these displacement t e s t s . T h i s technique i s s u i t a b l e f o r s t u d y i n g p r o d u c t i o n h i s t o r i e s , as well as f l o o d i n g and t h e a c t u a l mechanism o f t h e process. v a r i o u s forms o f C02

302 As a f i r s t s t e p t h e e f f e c t o f carbonated w a t e r was examined. Carbonated water s a t u r a t e d a t r e s e r v o i r p r e s s u r e and t e m p e r a t u r e was i n j e c t e d i n t o t h e p r e v i o u s l y water f l o o d e d c o r e . Carbon d i o x i d e appeared i n t h e e f f l u e n t a f t e r i n j e c t i n g one p o r e volume o f s a t u r a t e d w a t e r . To reach t h e i n j e c t e d e q u i l i b r i u m c o n c e n t r a t i o n o f t h e carbonated water i n t h e e f f l u e n t 4-8 p o r e volumes o f s a t u r a t e d water were necessary. Consequently, t h e a d d i t i o n a l o i l was produced w i t h a r a t h e r h i g h water c u t . The a d d i t i o n a l o i l was 5-7 % o f t h e o r i g i n a l o i l an p l a c e . Because o f t h e i n j e c t i o n o f a l a r g e volume o f w a t e r and t h e modest a d d i t i o n a l o i l recovery, t h i s method i s uneconomic. To i n c r e a s e t h e amount o f i n j e c t e d carbon d i o x i d e , o v e r s a t u r a t e d water was used i n t h e n e x t s e r i e s o f experiments. The a d d i t i o n a l o i l reached 10 % o f 0 . i . p . and f a v o u r a b l e e f f e c t s o f f r e e gas s a t u r a t i o n were observed, t o o . However even i n t h i s case, 3-5 p o r e volumes o f carbonated w a t e r were used t o obtain t h i s result. Gaseous carbon d i o x i d e was i n j e c t e d i n t o t h e model when s t u d y i n g t e r t i a r y r e c o v e r y methods f o r d e p l e t e d r e s e r v o i r s . Two d i f f e r e n t i n i t i a l s a t u r a t i o n c o n d i t i o n s were used as average r e s e r v o i r c o n d i t i o n s f o r m o d e l l i n g p r o d u c t i o n his t o r i e s : - t h e d e p l e t e d r e s e r v o i r has a h i g h gas s a t u r a t i o n , -25-35 %; - t h e d e p l e t e d r e s e r v o i r has a low gas s a t u r a t i o n and h i g h w a t e r s a t u r a t i o n , -50-60 $. The p r e s s u r e was increased t o t h e o r i g i n a l r e s e r v o i r p r e s s u r e by i n j e c t i n g carbon d i o x i d e gas. A f t e r t h e p r e s s u r e b u i l d - u p , d i f f e r e n t s i z e s o f C02 s l u g s were i n j e c t e d and f o l l o w e d by r e s e r v o i r w a t e r f l o o d i n g . The a d d i t i o n a l o i l r e c o v e r y a s a f u n c t i o n o f s l u g s i z e was s t u d i e d . The p r o b a b l e o p t i m a l s l u g s i z e was about 0.2 PV. Using t h i s , t h e a d d i t i o n a l o i l r e c o v e r y was 12-16 % o f t h e o r i g i n a l o i l i n p l a c e f o r systems h a v i n g a h i g h i n i t i a l gas s a t u r a t i o n and 8-12 % f o r t h e case o f h i g h i n i t i a l w a t e r s a t u r a t i o n . The a d d i t i o n a l o i l r e c o v e r y was always r e l a t e d t o t h e r e s i d u a l o i l s a t u r a t i o n o f t r a d i t i o n a l water f l o o d i n g . A l l o f t h e dynamic displacement t e s t s , mentioned above were performed w i t h p r a c t i c a l l y p u r e carbon d i o x i d e . T e s t s were conducted u s i n g carbonated n a t u r a l gases, t o o . The r e s u l t s showed t h a t t h e use o f c a r b o r a t e d n a t u r a l gases h a v i n g a CO c o n t e n t above 80 mole $, g i v e n o t worse, b u t b e t t e r r e s u l t s i n most 2 cases i f t h e p r o p e r d i s p l a c e m e n t t e c h n o l o g y i s used. Complex f l o w c o n d i t i o n s and physico-chemical processes e x i s t i n r e s e r v o i r o i l - - r e s e r v o i r water--carbon d i o x i d e - - r e s e r v o i r r o c k systems. The parameters i n f l u e n c i n g t h e e f f e c t i v e n e s s o f C02 f l o o d i n g must be i n d i v i d u a l l y determined f o r each p r o j e c t . I f t h e w e t t a b i l i t y o f r e s e r v o i r r o c k changes f r o m water-wet t o o i l - w e t t h e f a v o u r a b l e e f f e c t s o f f r e e gas s a t u r a t i o n and t h e l a t e r w a t e r f l o o d i n g a r e reduced. T h i s change of w e t t a b i l i t y depends upon many f a c t o r s among o t h e r s , on t h e q u a n t i t y o f i n j e c t e d C02 ( 2 ) . I f carbon d i o x i d e i s i n j e c t e d i n t o t h e d e p l e t e d o i l r e s e r v o i r i t i n t e r a c t s w i t h t h e r e s e r v o i r f l u i d and component mass t r a n s f e r s t a r t s among t h e phases. As a r e s u l t o f t h i s process t h e o i l phase w i l l be r i c h e r i n components h a v i n g h i g h e r m o l e c u l a r w e i g h t s . I n extreme cases some o f t h e components w i t h i n t e r f a c i a l a c t i v e c h a r a c t e r i s t i c s may adsorb on t h e r o c k s u r f a c e , t h e r e b y changing t h e w e t t a b i l i t y p r o p e r t i e s o f t h e system and l e a d i n g t o t h e r o c k becoming more o i l - w e t . A l t h o u g h t h e carbon d i o x i d e c o n t e n t o f t h e o i l phase decreases t h e v i s c o s i t y o f c r u d e r i c h i n h i g h m o l e c u l a r components and s w e l l s t h e o i l - p h a s e a possible increase i n the o i l - w e t character counteracts these favourable e f f e c t .

303 R e l a t i v e p e r m e a b i l i t y curves f o r saturated carbonated water systems were a l s o measured. The c h a r a c t e r o f r e l a t i v e p e r m e a b i l i t y curves j u s t i f i e d t h e e f f e c t mentioned above. Under some circumstances t h e porous medium became more o i l - w e t . Decreasing o i l and i n c r e a s i n g water p e r m e a b i l i t i e s c o u l d be observed i n c e r t a i n s a t u r a t i o n ranges, depending upon t h e CO content o f t h e gas used. The increase 2 i n r e s i d u a l o i l s a t u r a t i o n was a l s o observed w i t h i n c r e a s i n g C02 content. The bases o f comparison were t h e r e l a t i v e curves o f hydrocarbon gas saturated s y s terns.

COMPUTER MODEL A three-phase, ten-component mathematical model has been developed t o study carbon d i o x i d e displacement experiments and t o p r e d i c t performances (3, P a r t I . ) . The governing d i f f e r e n t i a l equations o f t h e compositional model w r i t t e n i n a usual form a r e as f o l l o w s :

=

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[5 2 j

kjfj

Aj

C. (grad p j Jti

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i = l,Z,

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j = gas, o i l ,

water

The b a s i s o f t h e c a l c u l a t i o n s i s t h e assumption t h a t local thermodynamic e q u i l i b r i u m e x i s t s d u r i n g displacement. I n t h i s way, t h e r e l a t i o n s h i p s c o r r e l a t e d w i t h l a b o r a t o r y PVT and e q u i l i b r i u m measurements can d i r e c t l y be employed. I n accordance w i t h t h e l a b o r a t o r y measurements, t h e formation f l u i d o f Budafa o i l f i e l d was considered as a ten-component system. The components a r e : seven hydrocarbon components /C,, C2, C3, C4, C5, C6, C /, nitrogen, carbon d i x i d e 7+ and water. As t h e water phase e x i s t s everywhere i n t h e formation, and d u r i n g t h e water

i n j e c t i o n a g r e a t amount of carbon d i o x i d e i s t o be transported by water, t h e s o l u t i o n o f t h e carbon d i o x i d e component i n t h e water phase cannot be neglected. Besides three-phase regions, two-, moreover one-phase regions occur d u r i n g t h e processes, thus a method has been developed t h a t a l l o w s one t o e a s i l y c a l c u l a t e a change i n t h e number o f phases. The three-phase e q u i l i b r i u m was i n t e r p r e t e d as t h e simultaneous existence o f two two-phase e q u i l i b r i u m s . To s i m p l i f y t h e e q u i l i b r i u m c a l c u l a t i o n s t h e f o l l o w i n g assumptions were made: - t h e gas and o i l phases do n o t c o n t a i n a water component, - t h e d i s s o l v e d gas i n t h e water phase c o n s i s t s o f carbon d i o x i d e o n l y . /When checking t h e c a l c u l a t i o n s t h e d i s s o l v e d gas i n t h e water phase contained methane, as well, b u t t h e l i t t l e i n f l u e n c e o f t h i s on t h e phase e q u i l i b r i u m made i t reasonable t o n e g l e c t it./

304 When c a l c u l a t i n g t h e phase e q u i l i b r i u m , f l a s h c a l c u l a t i . o n s a r e used t o d e t e r mine t h e mole f r a c t i o n s o f t h e phases; however, t h e c a l c u l a t i o n o f three-phase e q u i l i b r i u m make i t necessary t o s o l v e a coupled system o f two n o n l i n e a r a l gebraic equations. Occasionally, mainly when t h e number o f phases changes, convergence problems o f i t e r a t i v e techniques occur. The system was transformed i n t o one n o n l i n e a r a l g e b r a i c equation, and a numerical procedure combining t h e Newton-method and t h e method o f halving, ensure f a s t convergence i n every case. The d e n s i t y o f t h e gas phase i s c a l c u l a t e d using t h e Redlich-Kwong equation o f s t a t e . When determining d e n s i t i e s o f t h e f l u i d phases t h e labor a t o r y c o r r e l a t i o n s a r e applied. I n accordance w i t h these c o r r e l a t i o n s t h e formation volume f a c t o r i s c a l c u l a t e d as a f u n c t i o n o f t h e d i s s o l v e d g a s / f l u i d r a t i o f o r both f l u i d phases. Thus t h e q u a n t i t y o f t h e dissolved gas has t o be known. Because t h e composition o f t h e phases i s known, t h e d i s s o l v e d g a s / o i I r a t i o can be determined from t h e composition o f t h e o i l phase by normal f l a s h c a l c u l a t i o n . As f o r t h e dissolved gas/water r a t i o , i t was assumed t h a t water i n i t s normal s t a t e i s f r e e o f gas. I n order t o check t h e PVT and e q u i l i b r i u m c a l c u l a t i o n s l a b o r a t o r y pressure-build-up measurements were simulated by a one-volume element model. Very good matches could be achieved by modifying t h e molecular weight o f t h e C7+ component by 5 $.

FIELD EXPERIMENT A f t e r some p i l o t t e s t s t h e f i r s t large-scale process was s t a r t e d i n t h e western area o f t h e Budafa o i l f i e l d i n 1972. The area i s a s e c t i o n o f t h e Lower-Pannonian /Lower-Pliocene/ Budafa r e s e r v o i r which c o n s i s t s o f f o u r separable sequences o f s t r a t a o f t h e same hydrodynamic system. The formations a r e heterogeneous v e r t i c a l l y and h o r i z o n t a l l y . The e f f e c t i v e formation t h i c k n e s s v a r i e s from 1-2 m t 30 m. The average p o r o s i t y i s 21 $, t h e average h o r i z o n t a l 9 p e r m e a b i l i t y 0.1 pm

.

The sandstone formations o c c u r r i n g a t an average depth o f 850 m have a temp e r a t u r e o f 64 OC. The i n i t i a l pressure level j u d g i n g by t h e h y d r o s t a t i c c o n d i t i o n a t t h e beginning o f p r o d u c t i o n was 9800 kPa. The producgd crude i s o f an i n ermed a t e - p a r a f f i n character, i t s average d e n s i t y a t 20 C being 0.817.10' kg/mf. The r e s e r v o i r o i I was i n i t i a l l y saturated, t h e two upper sequences o r i g i n a l l y had an e x t e n s i v e gas cap. T h i s accumulation was unfavourable from t h e p o i n t o f view o f t e r t i a r y recovery because t h e o i l zones o f t h e two lower l a y e r s were s i t u a t e d under t h e gas caps o f t h e two upper I ayers. Production was begun i n J u l y o f 1937. F o l l o w i n g t h e r a i d increase i n t h e !? number o f wells, crude p r o d u c t i o n amounted t o 89,800 m /year i n t941 which was t h e peak p r o d u c t i o n o f t h i s area. The energy o f the formation decreased because o f t h e h i g h p r o d u c t i o n l e v e l and r e s t r i c t e d egge water d r i v e . I n o r d e r t o overcome t h e energy reduction, 139 m i l l i o n m hydrocarbon gas was i n j e c t e d i n t o t h e r e s e r v o i r from 1942 t o 1958. During t h e primary and secondary displacements t h e s o l u t i o n gas d r i v e , t h e energy o f gas caps and, t o a s l i g h t extent, edge water d r i v e worked w h i l e t h e formation pressure decreased t o an average level o f 2900 kP3, which was considered as an 3 abandon pressure. A t o t a l o f 1 m i l l i o n m o i l and 600 m i l l i o n m gas was produced. The average recovery e f f i c i e n c y was 22.6 $.

305

I

306 A t t h e b e g i n n i n g o f t e r t i a r y r e c o v e r y t h e o i l zones o f t h e a r e a had a h i g h gas s a t u r a t i o n . T e r t i a r y r e c o v e r y by carbonated n a t u r a l gas was r e a l i z e d by u s i n g 41 i n j e c t i o n , 71 p r o d u c t i o n and 9 o b s e r v a t i o n w e l l s . When d e s i g n i n g t h e technology, t h e e x i s t i n g w e l l s i n t h e a r e a were t a k e n i n t o account, and t h e system c o u l d be c h a r a c t e r i z e d by an i r r e g u l a r m u l t i - s p o t p a t t e r n . The w e l l p a t t e r n used i s shown i n F i g . 1. I n t h e f i r s t phase o f t h e t e r t i a r y recovery, carbonated n a t u r a l gas was i n j e c t e d i n t o t h e f o r m a t i o n d u r i n g which c o n t r o l l e d p r o d u c t i o n was r e a l i z e d . The carbonated n a t u r a l gas used was produced f r o m a h i g h p r e s s u r e r e s e r v o i r d i s c o v e r e d i n t h e a c t u a l area o f Budafa. T h i s gas - h a v i n g a carbon d i o x i d e c o n t e n t o f 81 m l e % and l i g h t hydrocarbons - was i n j e c t e d i n t o t h e low p r e s s u r e o i l r e s e r v o i r by means o f n a t u r a l energy. The carbon d i o x i d e appeared i n t h e p r o d u c t i o n w e l l s 1-2 months a f t e r t h e b e g i n n i n g o f i n j e c t i o n . Data r e l a t i n g t o i n j e c t i o n and p r o d u c t f o n 3 r a t e s / F i g . 2/ show t h a t t h e GOR amounted t o a v e r y h i g h l e v e l /3000-5000 m /m / d u r i n g t h e i n j e c t i o n . T h i s disadvantageous e f f e c t was caused by t h e h i g h gas s a t u r a t i o n d a t i n g back t o t h e p r i m a r y and secondary r e c o v e r y . No o i l bank f o r m a t i o n c o u l d be observed i n any o f t h e p r o d u c t i o n w e l l s . Gas and l i q u i d f l o w always o c c u r r e d s i m u l t a n e o u s l y i n t h e l a y e r s . I n o r d e r t o d i m i n i s h t h e h i g h GOR v a l u e o f t h e p r o duced f l u i d , w a t e r i n j e c t i o n was s t a r t e d a t t h e g a s - o i l c o n t a c t o f t h e two upper l a y e r s i n t h e autumn o f 1974, and t h e whole a r e a was w a t e r f l o o d e d f r o m t h e summer o f 1975. A t t h a t t i m e t h e averag? p r e s s u r e o f t h e r e s e r v o i r was 10,900 kPa, t h e water i n j e c t i o n r a t e f 5 0 0 m /day. GOR response t o w a t e r f l o o d i n g was observed f r o m t h e end o f 1974 when t h e c h a r a c t e r o f p r o d u c t i o n changed remarkably. Along w i t h i n c r e a s i n g o i l p r o d u c t i o 3 r y t e , t h e g a s / o i I r a i o decreased f r o m t h e p r e v i o u s y e a r s ’ l e v e l o f 5000 m /m t o a b o u t 600 m3/$. The changed c o n d i t i o n s can be seen i n F i g . 2. The carbon d i o x i d e c o n t e n t o f t h e produced gas remained above 65 mole % d u r i n g t h e w a t e r i n j e c t i o n , which made i t e v i d e n t t h a t i n j e c t i o n o f a d d i t i o n a l c rbonated n a t u r a l gas was n o t necessary. U n t f I 1 s t January 1981, 694 m i l l i o n m carbonated n a t u r a l gas and 3.013 m i l l i o n m w a t e r had been i n j e c t e d i n t o t h e f o r m a t i o n . I t should be mentioned t h a t t h e g r e a t e r p a r t o f t 9 e i n j e c t e d gas was used t o f i l l up t h e gas caps. By January 1981, 173,000 m o i l and 3 1.072 m i l l i o n m w a t e r had been produced and t h e average r e c o v e r y e f f i c i e n c y had been 27.5 %, t h u s t e r t i a r y r e c o v e r y r e s u l t e d i n a d d i t i o n a l o i l o f 3.9 T h i s amount o f a d d i t i o n a l o i l i s , however, an average v a l u e . For example, t h e a d d i t i o n a l o i l from Section I I . q u i t e considerable i n t h a t t h e e a r l i e r value was ‘12.7 % 0 . i . p . The method has proved t o be s u c c e s s f u l f o r one-layer, r e l a t i v e l y homogeneous s e c t i o n s h a v i n g low w a t e r s a t u r a t i o n , and t h e e f f e c t i v e n e s s was poor, a b o u t 1-2 % f o r t h e m u l t i - l a y e r s f o r m a t i o n under t h e gas caps. The d i s p l a c e m e n t i s s t i l l c o n t i n u i n g . The f i n a l amount o f a d d i t i o n a l The p r o d u c t i o n o f a d d i t i o n a l o i l proved t o be economo i l expected i s 5.7 I. i c a l l y worth w h i l e .

3

%.

HISTORY MATCH AND PREDICTION The f i e l d e x p e r i m e n t was analysed by s i m u l a t i o n o f performance h i s t o r y (3, P a r t I I.). The r e s e r v o i r i s t h i n , heterogeneous, laminated and n e a r l y h o r i z o n t a l , t h u s an a r e a l model was used and t h e e f f e c t s o f c a p i l l a r i t y and g r a v i t a t i o n were n e g l e c t e d . Because of t h e complex p e t r o g r a p h i c and h e t e r ogeneous s a t u r a t i o n c o n d i t i o n s , t h e Budafa-West m u l t i - l a y e r r e s e r v o i r

L---n I

Grp Butlofa-West

Unit

performcnce

history

307

FIGURE 2

308 c o n s t i t u t e s a c o m p l i c a t e d system. For t h i s reason an e a s i l y separable, one- l a y e r s e c t i o n o f t h e r e s e r v o i r was examined b e l o n g i n g t o t h a t a r e a where t h e h i g h e s t amount o f o i l o r i g i n a t e d from. /Primary and secondary displacement r e s u l t e d i n 45.2 % f o r t h i s s e c t i o n . / The s e c t i o n i s shown i s F i g . ‘I as Section 1 1 . Because o f computer r e s t r i c t i o n /an ICT 1905 computer w i t h a memory o f 32 Kwords was used/, we c o u l d n o t d e s c r i b e a l l t h e i n j e c t i o n and p r o d u c t i o n w e l l s o f t h e s e c t i o n ; o u r i n t e n t i o n was t o o b t a i n an o v e r a l l p i c t u r e o f t h e process. / I t i s t o be noted t h a t d e t a i l e d d a t a on f o r m a t i o n parameters were a l s o i n a c c e s s i b l e . / The s e c t i o n was c o n s i d e r e d t o be o f c o n s t a n t t h i c k n e s s , h o r i z o n t a l , and t h e average r o c k parameters and i n i t i a l s a t u r a t i o n r e f e r r i n g t o t h e b e g i n n i n g o f t h e t e r t a r y r e c o v e r y were used. We wished t o make use o f a l l t h e measured data, t h e r e f o r e on t h e bases o f a v e r a g i n g t h e d i s t a n c e s o f t h e i n j e c t i o n and p r o d u c t i o n w e l l s o f t h e s e c t i o n an e i g h t h o f a f i v e - s p o t element was cons t r u c t e d . The i n j e c t i o n and t h e p r o d u c t i o n d a t a o f t h e model were c a l c u l a t e d from t h e c u m u l a t i v e d a t a o f t h e s e c t i o n u s i n g t h e p o r e volume r a t i o o f t h e s e c t i o n and t h o s e o f t h e e i g h t h o f t h e f i v e - s p o t element. R e l a t i v e p e r m e a b i l i t y c u r v e s f o r three-phase carbonated systems were n o t a v a i l a b l e . Based upon l a b o r a t o r y measurements and p u b l i s h e d d a t a a s i m p l e f o r m o f p a r a m e t r i c r e l a t i v e p e r m e a b i l i t y c u r v e s were c o n s t r u c t e d , and parameters o f t h e c u r v e s were determined by h i s t o r y matching. P r e s s u r e and p r o d u c t i o n d a t a o f 5.5 y e a r s /2.5 y e a r s o f gas i n j e c t i o n , 3 y e a r s o f water i n j e c t i o n / were used. I t seemed t h a t no parameter group can be chosen t o s i m u l a t e e a r l y breakthrough o f carbon d i o x i d e . A n a l y s i s o f h o r i z o n t a l p e r m e a b i l i t y d i s t r i b u t i o n i n t o v e r t i c a l d i r e c t i o n u s i n g c o n t i n u o u s c o r e samples o f t h e r p s e r v o i r examined showed t h a t 20 % o f t h e p e r m e a b i l i t y d a t a were above 0.31 pm which d i f f e r e d remarkably f r o m t h e average v a l u e . The f l o o d i n g process i s v e r y s t r o n g l y i n f l u e n c e d by t h e presence o f h i g h p e r m e a b i l i t y zones. The h e t e r o g e n e i t y was t a k e n i n t o a c c o u n t i n a s i m p l e way, t h e t h i c k n e s s was d i v i d e d i n t o a good and a poor p e r m e a b i l i t y l a y e r . The r e s u l t s o f t h e h i s t o r y match can be seen i n F i g . 3 . The computed average p r e s s u r e s d i f f e r e d f r o m t h e measured ones by o n l y a b o u t 5

%.

A f t e r h a v i n g good r e s u l t s on t h e h i s t o r y match f o r S e c t i o n I I , t h e model was a p p l i e d t o t h e o t h e r 5 s e c t i o n s o f t h e area. 15-25 s i m u l a t i o n s were used t o reach t h e f i n a l r e s u l t s f o r each case. We had t o assume i n t h e m o d e l l i n g , t h a t no f l o w b o u n d a r i e s e x i s t e d between t h e s e c t i o n s though, as i s t o be expected, t h i s i s n o t t h e case. T h i s f a c t was proved by t h e c a l c u l a t i o n s . To some e x t e n t we had t o m o d i f y t h e i n j e c t e d gas t o g e t t h e good p r e s s u r e h i s t o r y match. However, t h e s e m o d i f i c a t i o n s were e q u a l i z e d f r o m t h e v i e w p o i n t o f t h e whole area, and a c a l c u l a t e d gas l o s s o f o n l y 6 % r e s u l t e d . The r e s u l t s o f h i s t o r y matching a r e summarized i n F i g . 4 . The c a l c u l a t i o n s were performed i n 1978. The f i g u r e shows p r e d i c t i o n s u n t i l 1983 t o g e t h e r w i t h t h e a c t u a l p r o d u c t i o n parameters o f t h e l a s t t h r e e y e a r s .

CONCLUSIONS A f t e r t h o r o u g h and e x t e n s i v e s t u d i e s economic f i e l d - w i d e t e r t i a r y displacement by carbon d i o x i d e c a r r i e d o u t i n Hungary. V o l u m e t r i c and phase behaviour o f t h e three-phase system can be modelled w i t h good a c c u r a r c y u s i n g t h e l a b o r a t o r y c o r r e l a t i o n s . The CO d i s p l a c e m e n t has proved t o be s u c c e s s f u l f o r 2 one-layer, r e l a t i v e l y homogeneous s e c t i o n s h a v i n g low w a t e r s a t u r a t i o n .

Budofo-West

unit

Sert;on

II.

309

FIGURE 3. Comparison of measured and cornouted data

b

c

/ /'

/

/

,

r01.r

-.mom\ .-

FIGURE L.

Comparison of measured a n d computed data Budafa-West unit

311 U t i l i z a t i o n o f t h e l o c a l p o t e n t i a l proved, i n t h i s case, t o be a s u b s t a n t i a l f a c t o r i n a c h i e v i n g economic a d d i t i o n a l o i l p r o d u c t i o n t h e r e b y overcoming t h e e f f e c t s o f unfavourable r e s e r v o i r conditions.

NOMENCLATURE

C

mass c o n c e n t r a t i o n

D

di f f usi v i t y

9

gravitational acceleration

-K

permeability tensor

k

r e l a t i v e permeability

P

pressure

9

mass s i n k p e r u n i t volume p e r u n i t t i m e

S

sa t u r a t i on

t

time depth viscosity density porosity

Subscripts

i

r e f e r s t o i t h component

j

r e f e r s t o j t h phase

REFERENCES

1. Ba'n, A.,

B a ' l i n t , V., D o l e s c h a l l , S., Zabrodin, P. I., Torok, J.: " P r i m e n e n i j e u g l e k i s l o v o gaza v d o b i c h e n e f t i " / " A p p l i c a t i o n o f carbon d i o x i d e i n o i l p r o d u c t i o n " / , Nedra Publ. Co., Moscow, 1977

2. B a ' l i n t , V., Paa'l, T.: "A n e d v e s i t 6 s i a ' l l a p o t 6s a z a'ramla'si jellemzo'k va'ltoza'sa CO d a l t e l i t e t t f l u i d u m - r e n d s z e r e k por6zus kozegben V a l 6 a'ramoltata'sakor~-/"Changes o f w e t t a b i I i t y c o n d i t i o n s and f l o w c h a r a c t e r i s t i c s f o r f l o w i n g c a r b o n d i o x i d e s a t u r a t e d f l u i d system i n porous media"/, KColaj 6s Foldga'z, Nov. 1979 3. Acs, G., D o I e s c h a I I , S., B i r 6 , Z., Farkas c . : "HBromfa'zisu, kompozici6s modell 6s alkalmaza'sa a Budafa-nyugat t e l e p sz6n-dioxidos muvel6s6nek l e ira'sa'ra" /"A three-phase, c o m p o s i t i o n a l model and i t s a p p l i c a t i o n f o r d e s c r i b i n g CO d i s p l a c e m e n t o f t h e Budafa-West r e s e r v o i r " / , P a r t I, Ko'olaj 6 s Folzga'z, Jan. i981; P a r t I I, Ko'olaj 6 s Foldga'z, Feb. 1981

This Page Intentionally Left Blank

MISCIBLE GAS DISPLACEMENT

313

AN ITERATIVE METHOD FOR PHASE EQUILIBRIA CALCULATIONS WITH PARTICULAR APPLICATION TO MULTICOMPONENTMISCIBLE SYSTEMS NIKOS VAROTSIS, ADRIAN C. TODD, GEORGE STEWART Petroleum Engineering Department, Heriot- Watt University

ABSTRACT equation of state based method is used to establish phase behaviour and properties for mixtures of injection gases and reservoir fluids with specific application to multicomponent miscible systems including CO2' An

The modified Soave-Redlich-Kwong or the Peng-Robinson or a version of the The Redlich-Kwong equation of state can be selected to be used in the model. iteration method used requires a minimum number of variables for which simultaneous iteration is required and an algorithm based on the Broyden's modification of the full Newton step gives consistent phase properties and rapid convergence even near the very sensitive for a miscible displacement critical point area. The model has been tested against published data including simple binaries, ternaries and multicomponent mixtures of reservoir oil and C02 injection gases. Good agreement between the predicted and the experimental values has been found together with a minimum number of iterations required to solve each problem. The paper discusses briefly the specific use of the model in an experimental phase behaviour study for UK oil-C02 systems and as an integral part of a compositional reservoir simulator.

INTRODUCTION One of today's more promising oil recovery techniques is miscible C02 flooding. The use of CO to improve oil recovery is not a new idea since C02 has been investigated $or miscible displacement, for immiscible displacement of reservoir oil, for producing well stimulation and for carbonated water flooding. The current industry interest in co flooding is mainly concentrated on the mass transfer effect that takes place begween the injected CO2 phase and the reservoir oil inside the reservoir. The co extracts hydrocarbons from the oil phase and 2 at the same time co2 is absorbed into the liquid phase up to the moment that The study and prediction of oil recovery involving miscibility is achieved. injection of CO requires a knowledge of the vapour-liquid equilibria especially 2 . at the very sensitive critical point. A method is needed, first to calculate the saturation conditions for the mixtures of the injected gases and reservoir oils from which a prediction of the miscible pressure can be made and second to carry out the isothermal flash calculations for different pressures so that the phase behaviour of the system can be studied in detail. Such a model will be described which using any of the Peng-Robinson, modified Soave-Redlich-Kwong and

314 a version of the Redlich-Kwong equations of state can give predictions of the vapour-liquid equilibria of multicomponent mixtures and especially good and rapid convergence in the critical point region where most of the methods according to the literature fail to converge. extrapolation technique is used to improve the initial estimates for the consequative calculations of the saturation pressure of a reservoir oil-CO2 mixture across the phase envelope and up to the crLtica1 point. Although the model has been specifically applied to CO -oil systems is obviously applicable to 2 any injected gas or flowing system. An

MISCIBILITY MECHANISMS

-

DIFFERENT MODELLING APPROACHES

Two of the most important and promising gas injection enhanced oil recovery practices are C02 flooding and lean gas injection.

The major mechanisms to improve the oil recovery in a carbon dioxide flooding are vaporization and condensation. Mass transfer takes place between the C02 rich phase and the oil rich phase and the initially immiscible phases gradually become miscible as they are enriched in intermediate and even heavy hydrocarbons and C02 respectively. The extraction of hydrocarbons by CO and its condensation into 2 the reservoir fluid results finally in an one phase miscible fluid. The development of miscibility can be visualised conceptually with a ternary diagram (Figure 1 ) . This representation although not quantitative demonstrates how

F I G U R ~ 1. SCHEMATIC

TERNARY

DlAGRAM

315 important it is to be able to predict the critical point of a mixture for a The miscibility path passes throush the multiple contact miscible process. critical point and it is its relative position in respect of the point that represents the reservoir fluid composition that defines whether under certain conditions the mixture of the injected qas and the reservoir fluid can obtain miscibility (Figure 2). The requirement for the generation of a miscible displacement is that the reservoir fluid composition must lie either to the right of the extension of the tangent to the phase boundary curve at the critical point or above the critical point in the single phase region. The same remarks apply more or less for a lean gas injection flooding where the vaporization of the light hydrocarbons from the reservoir fluid to the gas phase controls the whole process. There are also some minor mechanisms to improve the enhanced oil recovery by injection of CO These are: oil swelling, reduction of oil viscosity, increase in oil density,2high solubility of CO in water which reduces the water density and therefore the overriding of the ca2-water mixture and the acidic effect on the rock which increases the permeability of the reservoir.

.

The theoretical studv of a miscible displacement experiment or of a miscible reservoir flooding requires accurate and reliable phase behaviour data. The phase envelope of the mixture at different conditions is required to determine the minimum miscibility pressure and the equilibrium lines (tie-lines) in order to study in detail the distribution of the different components in the two-phases.

CRITICAL POINT

TWO PHASE REGION

FIGURE 2. MISCIBILITY

CONDITIONS

A

3 16 Either an equation of state based method is used to establish phase behaviour and properties or equations are used which have been obtained by curve fitting experimentally derived data. Due to inconsistent phase properties near the critical point and the requirement for comprehensive experimental data for each oil composition of the latter, the equation of state based method is now widely preferred. Most of the current published equation of state based methods appear to suffer from requiring a great number of iterations or do not converge at all in the critical point area, the key area for any miscible displacement.

PHASE EQUILIBRIA MODEL FOR A MISCIBLE OIL RECOVERY PROJECT The technique being presented here for calculating vapour-liquid equilibria using an equation of state includes a system of non-linear equations and an iterative sequence to solve the equations. The system of equations consists of: (i) An overall material balance equation L + V = 1 (ii) Component material balance equations Lxi + vy = zi i = l,n i (iii) Restrictive equations on the phase compositions n c x i = l , i = l

n c y i = l i = l

(iv) Thermodynamic phase equilibria equations i = l,n

fiL = fiv

Three different equations of state can be used to provide values for the These are: compressibility factor of the vapour and liquid phase.

(1) The Peng-Robinson equation of state p=-RT v-b

v(v+b)

a (TI + b(v-b)

(P-Rl

or in terms of the compressibility factor: Z3

-

(1-B)Z

2

+

2 (A-3B -2B)Z

-

2 3 (AB-B -B )

= 0

where:

a(T) = 0.45724

J

R2Tc2 pC

RT

,A

b = 0.0778 pC

=

i+m(l-T:)

r2

-, B R T

,m = 0.37464

=

bP RT

+

1.542261

-

(for pure components)

2 026992W

317 (2) The modified Soave-Redlich-Kwong equation of state: p

-

RT v-b

(M-S-R-K)

v(v+b)

or in terms of the compressibility factor 3

Z -Z

2 2 +(A-B-B )Z-AB =

0

where: a(T) = 0.42727

J

RT b = 0.0867 2,A =

-,ap 2 2

B =

R T

pC

m = 0.48508

l+m(l-.,'),

R2T pC

-

bP RT

+

1.551711

-

0.15613W

(for pure components)

(3) Modified Redlich-Kwong Equation of State aT-4 v(v+~)

RT p=--v-b

(M-R-K)

or in terms of the compressibility factor

where: 2

a = R A

2.5

Tc t b

=

pc

S

RTC

&

~

h

bP

=

s

A

aP

bP RT

= 2- 2, B = -

R T

C

(pure components).

RA,nB are supposed to be functions of temperature and of the nature of each component. The values of these parameters are calculated from generalised correlations applicable over a wide range of temperature. In Table Ivalues of the parameters RA, RB calculated by our model are compared against those obtained bg Coats and Fussell for a ternary mixture of C - nC4 - nC at 160 F (344.3K). 10

RB

Ci nC4 nCIO

RA COATS

% COATS

A '

FUSS

% FUSS

0.4265

0.0862

0.42617

0.086173

0.4251

0.0859

0.4198

0.0794

0.419367

0.0794

0.4154

0.0759

0.4638

0.0734

0.451875

0,070452

0.46512

0.07259

2

318 For the same mixture and for composition (mole fraction) CH4

:

0.253

n-Butane

:

0.661

n-Decane

:

0.086

:

the K-values and the saturation pressure estimated using the Modified Redli' Kwonq Equation of State compared to the values predicted by Coats and to th, experimental ones are given in Table 11.

K-Val OUR MODEL

K-Val. COATS

K-Val. EXPER.

3.173

3.174

3 -174

nC 4

0.297

0.2969

0.297

nC

0.008

0.00806

0.013

972.7 psia

975.1 psia

1000 psia

10

Satur. Press.

For multicomponent mixtures the following mixing rules proposed by Soave are used: n a =

b =

n

C x x ai,. , aij

C

i=l

j=1

n C xibi i=l

,

0.5 a 0.5 (1-ki j

= ai

)

Kij = interaction parameter

The fugacity coefficients of component i in a mixture are calculated using the following equations For the liquid phase: (2 - 1 ) )

Px.exp{b fiL

-

(2 -B )

L

L

iL L B~ i' {1+ -} zL

1

z-

0.11

P = 6.980 MPa

Figure 7 Residual norm plots for a 11% I-Cq

-

P - 6 . 9 8 1 MPa

89% COP mixture at 311 K.

342 0

I

I

OSS X SSwithur.

10-5

z

10-1(

P

I

K

::

I

5

I

I 10-l!

i

,

x

I

I

- __ __ __ 10-n

-

p 6.94 MPa p 8.98

1

1

I

l

l

l

,

,

50

l

,

loo

,

,

mh

,

0

NO. OF ITERATIONS

Figure 8

Iteration performance for a 11% I-CL

-

89% CO mixture at 311 K. 2

Another aspect of the refined successive substitution method presented here is illustrated in Fig. 9. It depicts the iteration performance for a step in a series of flash calculations where resulting K-values from one point is used as initial estimates for the next. A 89.3% CO mixture is considered and the pressure step in question is from 6.82 to 6.6% m a , corresponding to a decrease in liquid mole fraction from 9.01 to 0.46%. The solution escapes the two-phase region after 3 iterations, but with Eq. (14) defining a hypothetical liquid phase, the iteration is continued and brings the solution back into the twophase region before the tolerance level is met. The figure also shows the favourable effect of the multiplication factor y defined by Eq. (23). The solution is much more quickly returned to the two-phase region, and the no. of iterations required to achieve convergence is significantly reduced.

343 0.12

B

B

10-

1.10

10-

1.08

10-

10-

I

10-

\ Y

LO2

\

\ \ \


~ + ~ ~ - w ~ c where 8 and W are t h e t i m e and d i s t a n c e weighting f a c t o r s , w i t h values between 0 and 1. W o c o n d i t i o n s must be s a t i s f i e d f o r l i n e a r i n t e r p o l a t i o n t o b e valid. (1) A continuous l i n e a r ( o r near l i n e a r ) curve between t h e p i v o t a l points. (2) The p i v o t a l p o i n t s must be "mobile". By t h i s we mean t h a t C should be For i n t h e mobile range bounded by t h e maximum and minimum p o s s i b l e v a l u e s . example, t h e mobile range of water s a t u r a t i o n i s between Swc and (1-Sor),but does not include t h e s e a c t u a l values. Our a i m i s t o u s e e q u a t i o n ( 3 ) t o p r e d i c t t h e v a l u e of an i n t e r b l o c k c o n v e c t i v e p a r a m e t e r such t h a t i t l i e s c l o g e t o t h e t r u e t i m e - i n t e g r a l a v e r a g e v a l u e of C on t h e h i s t o r y curve a t L*. Before doing t h i s , i t i s necessary t o examine t h e r e p r e s e n t a t i v e curves which a r e t o be i n t e r p o l a t e d . 2.2 Curve Anal sis C o n s i d e r 4 arYbitrary p r o f i l e s a t a f i x e d t i m e l e v e l ( F i g . 2 ) . following d e s c r i p t i o n , equal g r i d spacing is assumed.

-c

Figure2a

PROFILE

1

I

In the

1FigureZb

r

igure 2d

I

I

I I

1

Figure (2a) Curve (2b) Curve ( 2 c ) Curve (2d) Curve

1 2 3

4

: increasing : increasing : decreasing : decreasing

J

I

gradient, gradient, gradient, gradient,

concave convex convex concave

We a r e i n t e r e s t e d i n a p p r o x i m a t i n g t h e value of C at I*. Both upstream e x t r a p o l a t i o n from 1-1 and 1, and i n t e r p o l a t i o n b e t w e e n i a n d i + l , a r e possible. On Curves 1 and 2 , t h e e x t r a p o l a t e d values can be found on t h e upstream p o r t i o n of t h e c u r v e s , w h i l e t h e i n t e r p o l a t e d v a l u e s l i e o n t h e downstream p a r t of t h e curves with r e f e r e n c e t o I+$. This implies that t h e use of upstream e x t r a p o l a t i o n i s e f f e c t i v e l y upstream weighted ( f c w < l ) , a n d

428 hence s t a b l e . The use of i n t e r p o l a t i o n i s e f f e c t i v e l y downstream weighted (o< W < i ) , and h e n c e u n s t a b l e . T h i s s i t u a t i o n occurs j u s t behind an immiscible Thus Curve 1 c a n displacement,where a shock i s p r e s e n t , o r i s b u i l d i n g up. r e p r e s e n t t h e o i l s a t u r a t i o n , and Curve 2 can r e p r e s e n t t h e water S a t u r a t i o n . It i s w e l l known that t h e u s e of mid-point weighting c r e a t e s o v e r s h o o t u n d e r such circumstances,while full upstream weighting r e s u l t s i n a n undershoot o f t h e d i s p l a c i n g phase ( s a t u r a t i o n d i s p e r s i o n ) . The u s e of u p s t r e a m On C u r v e s 3 a n d 4, t h e r e v e r s e c o n d i t i o n s o c c u r . e x t r a p o l a t i o n is e f f e c t i v e l y downstream weighted. Thus on Curve 3 , u p s t r e a m e x t r a p o l a t i o n c r e a t e s u n d e r s h o o t , a n d on C u r v e 4, i t c r e a t e s o v e r s h o o t . F u r t h e r a n a l y s i s of upstream e x t r a p o l a t i o n and m i d - p o i n t I n t e r p o l a t i o n i s given i n t h e Appendix A2. S u f f i c e i t t o s a y h e r e t h a t both e x t r a p o l a t i o n and i n t e r p o l a t i o n have t h e i r advantages and l i m i t a t i o n s . They are camplementary i n t h e i r f u n c t i o n s . When e x t r a p o l a t i o n i s u n s t a b l e , i n t e r p o l a t i o n i s s t a b l e , and v i c e v e r s a . Under c e r t a i n c o n d i t i o n s t h e y a r e b o t h m i s t a b l e . This o c c u r s when t h e p i o v o t ( s ) become "immobile". In s u c h s i t u a t i o n s upstream weighting i s t h e b e s t s t a b l e approximation. e The same a n a l y s i s can be extended t o t h e h i s t o r y c u r v e s a t a f i x e d point. W are i n t e r e s t e d i n t h e h i s t o r y curve a t 1% o v e r t h e time s t e p . Due t o t h e c o n v e c t i v e n a t u r e of C, a h i s t o r y curve a t a f i x e d p o i n t over a t i m e s t e p i s r e l a t e d t o t h e p o r t i o n of t h e d i s t a n c e p r o f i l e i m m e d i a t e l y u p s t r e a m of t h e f i x e d p o i n t a t t h e beginning of t h e t i m e s t e p . 2.3 A Dynamic Weighting Scheme The p u r p o s e o f t h i s d e v e l o p m e n t i s t o f i n d a method of e v a l u a t i n g e x p l i c i t l o c a l weighting f a c t o r s , such t h a t t h e l i n e a r i n t e r p o l a t i o n formula, e q u a t i o n ( 3 ) . c a n be incorporated i n t o an i m p l i c i t simulator t o s u b s t i t u t e f o r i n t e r b l o c k convective parameters o r t h e i r dependent f u n c t i o n s . The 4 b a s i c c u r v e t y p e s ( F i g 2.) can be subdivided i n t o 2 groups. Group 1 (curves 1 and 2 ) h a s i n c r e a s i n g g r a d i e n t s i n t h e flow d i r e c t i o n , a n d Group 2 ( c u r v e s 3 a n d 4 ) h a s d e c r e a s i n g g r a d i e n t s . E i t h e r Group 1 or Group 2 are p r e s e n t l o c a l l y a t a f i x e d t i m e . I d e n t i f i c a t i o n is p o s s i b l e through g r a d i e n t testing.

[\Gi\-~GIL-,\]

> < =

0

.=$

crouP

'

0 4 Group 2},

0

S)

&-car

[

G i = q+l-c;

- xi - ci xi - xiXk,

(4)

ci-l

I The b,ssic assumptions are:Group 1 curves do n o t evolve i n t o Group 2 c u r v e s over a time s t e p . The (1) same d i s t a n c e weighting f a c t o r s can be used a t two f i x e d t i m e l e v e l s , n and n+l, i n t h e l i n e a r i n t e r p o l a t i o n equation. (2) The h i s t o r y curve a t t h e block i n t e r f a c e over t h e t i m e s t e p i s i n t h e same c u r v e g r o u p as t h e immediate upstream p r o f i l e a t t i m e l e v e l n (see next s e c t i o n ) . Therefore, t h e i n t e r p o l a t i o n f a c t o r on t h e h i s t o r y p r o f i l e , 8 , i s assumed t o be e q u a l t o t h e d i s t a n c e i n t e r p o l a t i o n f a c t o r , W. Based on t h e previous curve a n a l y s i s , t h e following s t r a t e g y i s adopted. When a Group 1 c u r v e i s d e t e c t e d , a n upstream e x t r a p o l a t i o n i s r e q u i r e d t o provide low numerical d i s p e r s i o n , w h i l e maintaining numerical s t a b i l i t y . T h i s c a n b e i n v o k e d on t h e l i n e a r i n t e r p o l a t i o n f o r m u l a by choosing weighting Simple g e o m e t r i c a l f a c t o r s between 0 . 5 and 1.0 ( e q u a l g r i d s p a c i n g ) . c o n s t r u c t i o n s show how t h i s can b e done. (Pigs. 3a, b).

ie

F i q r e 3.3

2 - p i n t upstream extraplation. D can be foundon t h e chord BF.

Firmre 3b

/lE

t

429 BF is a downstream chord. It is required t o f i n d t h e e x t r a p o l a t e d p o i n t D on BF. This point is D’. The necessary weighting f a c t o r f o r t h e i n t e r p o l a t i o n formula, W, is derived below.

A B is an upstream chord.

= ai + (I- a L ) ( x - x , ) / x .

(54)

s u b s t i t u t i n g equation (5c) i n t o equation (5b) g i v e s (54 w b = I (ai-i)/Q The w e i g h t i n g When a Group 2 curve is d e t e c t e d , i n t e r p o l a t i o n is s u p e r i o r . I f t h e g r i d spacing is miform, t h i s f a c t o r s are c a l c u l a t e d by s e t t i n g R i l l . g i v e s Wi-ai-0.5.

+

S c r e e n i n g must be a p p l i e d t o e x c l u d e t h e use of t h e i n t e r p o l a t i o n formula under 2 i n v a l i d conditions:(1) Gradient r e v e r s a l (R i is n e g a t i v e ) (2) E i t h e r , o r both,of t h e p i v o t s (%, c ) are ”immobile” Once t h e s e c o n d i t i o n s are d e t e c t e d , f u l f upstream weighting a f f o r d s t h e best s t a b l e a l t e r n a t i v e available. The i n t e r p o l a t i o n scheme proposed is t h e r e f o r e dynamic i n nature. E f f e c t i v e f u l l upstream, 2-point upstream e x t r a p o l a t i o n , o r mid-stream i n t e r p o l a t i o n w i t h v a r y i n g d e g r e e of i m p l i c i t n e s s c a n be invoked l o c a l l y via t h e same l i n e a r i n t e r p o l a t i o n formula. 2.4

R e l a t i o n s h i p Between Time Weighting and Distance Weighting

Figure 4a

Figure 4b

Figure 4c

F i g u r e 4a shows t h e p r o f i l e of a t y p i c a l parameter C a t t i m c t“ , CI being i t s value a t t h e i n t e r f a c e between b l o c k s i and i+l. F i g u r e 4 b shows t h e same p r o f i l e w i t h r e s p e c t t o X , t h e d i s t a n c e measured upstream from t h e i n t e r f a c e . Assuming that t h e p r o f i l e X(C) and t h e v e l o c i t y of p r o p a g a t i o n V ( C ) a r e known, i t is required t o determine t h e shape of t h e h i s t o r y curve, t ( c ) (Figure 4 c ) , a t t h e i n t e r f a c e , which is given by:-

-

-

Case 1 V(C) constant v T h i s assumption is approximately v a l i d i f t h e t i m e s t e p is smal1,so that t h e band of v a l u e s ( c l , c2),which c r o s s e s t h e i n t e r f a c e o v e r t h e t i m e - s t e p , i s narrow. For such a case, t(c)

-,

= x(4 V

-

and hence t ”(C) X “(C)/V. S i n c e V is p o s i t i v e , t ” has t h e same sign a s X”, and hence t (C) belongs t o t h e same group of curves as X (C).

4 30 Case 2 V(C) i s v a r i a b l e . D i f f e r e n t i a t i n g ( 6 ) w.r.t.

t J= (vx'-

C, we o b t a i n :

xv')/v2,

a n d , d i f f e r e n t i a t i n g y e t a g a i n , we have

tJ'= [v(vx"-

xv'/) - ~ V / ( V X ' - X V ' ) ] / V 3

Now, s i n c e X ' and V' have o p p o s i t e s i g n s , i t follows t h a t t h e second term of X V ' ) ] i s always p o s i t i v e . Furthermore, i f t h e above e x p r e s s i o n [ - 2 v - (VX' X '*70, t h e n V Y 0, and t h e e n t i r e e x p r e s s i o n w i l l be p o s i t i v e , and so X" and t " w i l l have t h e same s i g n , and t h e c u r v e s w i l l b e l o n g t o t h e same g r o u p ( 1 . e . Group 1). I f , however, X Z O (1.e. Group 2 ) , t h e n , due t o t h e second be c e r t a i n w h e t h e r or n o t t " w i l l c h a n g e term being p o s i t i v e , we cannot sign. N e v e r t h e l e s s , f o r p r a c t i c a l purposes, we s h a l l assume that, f o r a l l c a s e s , X and t belong t o t h e same group.

-

3.0

OVERALL APPLICATION TO AN IMPLICIT COMPOSITIONAL SIMULATOR

There is a unique dependence of t h e o v e r a l l component f r a c t i o n a l flows on t h e o v e r a l l composition. For p r o p a g a t i o n a l s t a b i l i t y , c o n c e n t r a t i o n v e l o c i t i e s a t a f i x e d p o i n t i n s p a c e and t i m e a r e e q u a l ( H e l f f e r i c h (13)). It i s t h e r e f o r e a p p r o p r i a t e t o f i n d t h e dynamic w e i g h t i n g f a c t o r s b a s e d o n t h e l o c a l overal concentration profiles. W e f u r t h e r assume t h e l o c a l e x i s t e n c e of e i t h e r t h e Group 1 c u r v e s , o r t h e Group 2 c u r v e s . The c o n c e n t r a t i o n p r o f i l e o f t h e most " s e n s i t i v e " component i s u t i l i s e d t o e v a l u a t e t h e weighting f a c t o r s . They a r e used f o r a l l components i n b o t h h y d r o c a r b o n p h a s e s , i f 2 phases e x i s t . S e l e c t i o n of t h e most " s e n s i t i v e " component i s important t o a v o i d t h e need t o c h o o s e t h e most s t a b l e w e i g h t i n g f a c t o r s evaluated f r a n a l l t h e c o n c e n t r a t i o n p r o f i l e s . The "immobile" c o n d i t i o n s f o r t h e s e l e c t e d canponents must a l s o be d e f i n e d . These i d e a s are i l l u s t r a t e d i n t h e n u m e r i c a l examples. To account f o r phase d i s c o n t i n u i t y , f u l l upstream weighting i s used i f t h e upstream and downstream blocks do not have t h e same number of hydrocarbon phases. C o n s t r u c t i o n of t h e Model The c o m p o s i t i o n a l model used i n t h i s s t u d y i s based on a n e q u a t i o n of s t a t e , a n d f o l l o w s t h e i m p l i c i t f o r m u l a t i o n p r e s e n t e d by C o a t s (14). We w i l l , t h e r e f o r e , o n l y d i s c u s s t h e model where i t h a s b e e n modified t o take i n t o account t h e preceding d i s c u s s i o n .

3.1

3.1.1

Temporal and S p a t i a l Weightin

Figure 5

A t any p o i n t i n t h e system, t h e v a l u e of a v a r i a b l e u, a t t i m e t*(where tnS t% tn+' 1, can be r e l a t e d t o i t s v a l u e s a t tn and tn+' by:-

*

u =

n+I

eK

+(I-e)Z =

kn+

eSu""

(10%)

Of,

2'-

U"

= SU*

= e Sun+'-

00 4)

431 so, f o r each i t e r a t i o n , t h i s implies:-

st$ - 8 sLn+l 4

(4

U

C+l

c+:

-

%

u. ) denote t h e change i n u over t h e The symbols %AI' (=cC K ) and SK (=V i t e r a t i o n 1, and t h e cumulative change, r e s p e c t i v e l y . I f , however, i n a d d i t i o n t o t h i s intermediate time-level, u i s also evaluated a t a p o i n t o t h e r than t h e b l o c k - c e n t r e s , t h e n i t h a s t o be r e l a t e d t o t h e block-centre values by means of t h e d i s t a n c e weighting formula. Thus:-

* u" = wu;* +(l-w)uL+l

;

s u b s t i t u t i o n then l e a d s to: 4 n+l

?'S

-!n+( = ewsKL; + e(i-w)Sai+,.

3.1.2 Expansion of t h e "Flow" term The f l o w between two n e i g h b o u r i n g b l o c k s i a n d i + i can be expressed i n t h e form:-

T+(C,-) : P .

I n c r e m e n t s i n t h e t r a n s m i s s i b i l i t y term T are c a l c u l a t e d by means of partial derivatives w.r.t. t h e complete set of v a r i a b l e s (U, , Un).

.....

and, f i n a l l y , using equations ( ~ O C ) ,( l l b ) and (12a), we o b t a i n t h e expansion of t h e flaw term, as follows:-

4.0

DISCUSSION OF RESULTS

T h r e e d i f f e r e n t d i s p l a c e m e n t p r o b l e m were chosen, i n o r d e r t o demonstrate t h e a p p l i c a t i o n of t h e above theory i n a v a r i e t y of s i t u a t i o n s . The d a t a f o r t h e s e r u n s were t a k e n from Coats (14). Leach and Y e l l i g ( 1 5 ) , and Smith and Yarborough ( 1 6 ) , r e s p e c t i v e l y . 4.1 Displacement 1 (Coats (14)). T h i s i s a n MCM problem, involving components: C1,n-C4 and n-C 10. The system e x i s t s i n i t i a l l y as a n undersaturated l i q u i d , and i s displaced by a r i c h gas. I n t h e s i m u l a t i o n , t h r e e zones can be i d e n t i f i e d : a downstream zone containing undersaturated o i l , a middle zone comprising two p h a s e s whose c o a p o s i t i o n s c o n v e r g e i n t h e u p s t r e a m d i r e c t i o n , and f i n a l l y an upstream miscible zone containing a s i n g l e dense f l u i d whose composition changes from t h e c r i t i c a l composition t o t h a t of t h e i n j e c t i o n gas. The boundary between t h e f i r s t two zones w i l l be r e f e r r e d t o a s t h e g a s f r o n t , while t h a t between t h e latter two w i l l be c a l l e d t h e miscible f r o n t . In MCM problems, t h e use of s i n g l e p o i n t upstream weighting l e a d s t o s e v e r e c o m p o s i t i o n a l d i s p e r s i o n which causes s u b s t a n t i a l delay i n t h e attainment of miscibility. T h i s r e t a r d a t i o n of t h e m i s c i b l e f r o n t i s c o n s p i c u o u s in C o a t s ' r e s u l t s , where t h e u s e of 20, 4 O m d 80 b l o c k s show a p r o g r e s s i v e

432 8.2-

,

,

,

,

,

,

,

.

COAT S I - D M C M P R O B L E M 1.0'

TIME=210 DAYS

20 BLKS

COAT S I - D M C M P R O B L E M

D l M A X = 7 . 5 DAYS

z

0 L 200

-NO c o u r m

DINAMC WEICIIIWC

TIME.DAYS

0

0.5

COAT S I - D M C M PROBLEM TlMEn2lO D A Y S 20 BLKS OlMAX=T.S DAYS

U

.

+

-"0 CO"TI10L

a

COAT S I - D M C M PROBLEM 6 1 . 0 U

4

W U

I-

m 3 0.1

.

@z

0.2.

_I

0

-

Figure 6 D i s p l a c e m e n t 1 (MCH) : 1-D c o m p a r i s o n o f d y n a m i c weighting with f u l l upstream weighting. (a) Sg p r o f i l e . ( b ) Advance of m i s c i b l e f r o n t . c o n c e n t r a t i o n p r o f i l e ( d ) o i l recovery and GOR vs time.

(c)

C4

i n c r e a s e i n i t s speed of p r o p a g a t i o n . I n t h e a b s e n c e of a n a n a l y t i c ' a l s o l u t i o n , i t is j u s t i f i a b l e t o assume t h a t t h e 80-block s o l u t i o n is t h e nearest t o real i t y. The i n t r o d u c t i o n of t h e dynamic w e i g h t i n g scheme described i n t h i s paper produces a marked improvement, and has enabled u s t o o b t a i n , w i t h 2 0 b l o c k s , a n s w e r s w h i c h a r e of c o m p a r a b l e a c c u r a c y t o C o a t s ' 40-block s o l u t i o n . Figures 6a, b, c , d show a comparison between t h e use of t h i s t e c h n i q u e and s i n g l e - p o i n t u p s t r e a m weighting. The use of t h e proposed technique c l e a r l y results In a f a s t e r advance of t h e m i s c i b l e f r o n t , which is confirmed by t h e e a r l y and s t e e p rise i n GOR, following i t s breakthrough t o t h e producer. The scheme has a l s o been t e s t e d i n 2D, using a C a r t e s i a n g r i d of 9x9 b l o c k s , w i t h t h e i n j e c t i o n and p r o d u c t i o n w e l l s l o c a t e d i n two diagonally-opposite Once a g a i n , a n improvement i n t h e c o r n e r blocks. ( F i g u r e s 7a, b, c, d ) . s i z e of t h e miscible zone can be observed, using our technique. 4.2 Displacement 2 (Smith and Yarborough (16)). The system used i n t h i s displacement was a binary mixture of C 1 and nC5,being displaced by d r y g a s (Cl). I n t h i s case, e v a l u a t i o n of weighting f a c t o r s can be c a r r i e d out on e i t h e r component. Thus C 1 was a r b i t r a r i l y chosen f o r t h i s purpose. Tbo runs were perfomed on t h i s system, t h e f d r s t of t h e s e b e i n g d e s i g n e d t o s i m u l a t e FCN d i s p l a c e m e n t . T h i s was achieved by assuming a n i n i t i a l composition of 50% C 1 and 50% n-CS,and simulating t h e displacement i n t h e s u p e r c r i t i c a l region ( a t 3000 psi). Since t h i s is a p e r f e c t piston-type displacement, t h e a n a l y t i c a l s o l u t i o n c o n s i s t s of a s t e p change i n c o m p o s i t i o n from t h e i n j e c t i o n c o m p o s i t i o n t o t h e i n i t i a l c o m p o s i t i o n .

-

433

''''

T I VF I 0 1.240 PV INJ ~0.637

0

OIL R E C ~ 0 . 5 6 4

\

v.

?\

c 7 d)

A

Figure 7

- Displacement 1 (MCM)

: 2-D

o 1-240 INJ -0.637 = O .564

T IVEI PV

\

\

I

0

\

comparisons.

( a ) Gas s a t u r a t i o n map, dynamic weighting. ( b ) C4 c o n c e n t r a t i o n map, dynamic weighting. ( c ) Gas s a t u r a t i o n map, f u l l u p s t r e a m weighting. ( d ) C4 c o n c e n t r a t i o n map, f u l l upstream weighting. F i g u r e s 8a and 8 b show t h e C 1 p r o f i l e a t 210 days, and the n-C5 concentration i n t h e e f f l u e n t a s a f u n c t i o n of time. The weighting technique shove better r e s u l t s than t h e "full u p s t r e a m " case, a l t h o u g h b o t h show a n a p p r e c i a b l e compositional d i s p e r s i o n r e l a t i v e t o t h e a n a l y t i c a l s o l u t i o n . I n t h e second run, a n i n i t i a l c o m p o s i t i o n of 87.5% C 1 and 12.5% n-C5 was c h o s e n , so a s t o y i e l d an i n i t i a l condensate l i q u i d of 7% s a t u r a t i o n a t 1525 p s i , which was a l s o t h e p r e s s u r e a t which t h e s i m u l a t i o n was c o n d u c t e d . Agein, C 1 was i n j e c t e d , and t h e problem was run i n t h e 2-phase mode, with t h e l i q u i d assumed t o be immobile. The purpose of t h i s r u n was t o d e m o n s t r a t e t h a t , f o r some problems ( s u c h a s of t h i s type) t h e amount of compositional dispersion i s negligible. T h i s p o s t u l a t e d a b s e n c e of c o m p o s i t i o n a l d i s p e r s i o n i s v e r i f i e d by t h e numerical results shown i n Figures 8 c and Ed, i n both of which t h e results of u s i n g s i n g l e p o i n t upstream weighting are v i r t u a l l y i d e n t i c a l t o t h o s e obtained with t h e p r e s e n t technique.

434

':

DRY GAS DISPLACING RICH GAS ' ' ' ' ' ' ''' ' '''' 1.1

=

0

i4

'

'

'

'

'

'

.385 PV INJECTED

DRY GAS DISPLACING RlCH G A S

210 D A Y S ( 3 4 S T E P S ) .

l=W=DYN

50

100

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200

,

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DISTANCE ,FEET CONOENSATE REVAPORIZATION

PV CH4 INJECTED CONDENSATE REVAPORIZATION I

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0.06--

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DISTANCE ,FEET PV METHANE INJECTED Figure 8 Displacement 2 : 1-D c o m p a r i s o n of dynamic w e i g h t i n g with f u l l upstream weighting. ( a ) C1 c o n c e n t r a t i o n p r o f i l e (FCN). ( b ) C5 c o n c e n t r a t i o n i n e f f l u e n t v s t i m e (FCN). ( c ) C1 and o i l s a t u r a t i o n p r o f i l e s (re-vaporieation). (d) C5 c o n c e n t r a t i o n i n e f f l u e n t , and advance of "dry f r o n t " v s t i m e (re-vaporization).

-

4.3 Displacement 3 (Leach and Y e l l i g ( 1 5 ) ) . This m e a study of t h e mechanisms involved i n t h e displacement, by CO2, of a s y n t h e t i c crude o i l . Leach e t a1 (15) presented l a b o r a t o r y results c o v e r i n g t h e various displacement t y p e s (PCM, MCM and NM), and aleo simulated t h e s e on t h e i r compositional model, using 100 blocks. To t e s t our technique, two rune were chosen: an MCM d r i v e (Run 61, and a n NM d r i v e (Run 7). The component which we s e l e c t e d f o r " g r a d i e n t t e s t i n g " was namely C6. The rJeighting t h e one which had t h e least i n i t i a l c o n c e n t r a t i o n technique h a s enabled u s t o match t h e l a b o r a t o r y results t o a good a c c u r a c y , with merely 20 blocks. C o n s i d e r i n g t h e MCM r e s u l t s f i r s t , F i g u r e 9 a demonstrates t h e f a s t e r advance of t h e m i s c i b l e f r o n t , and t h e s t e e p e r C02 p r o f i l e r e s u l t i n g f r a n t h e use of t h i s technique. Figures 9b and 9c f u r t h e r support our d i s p e r s i o n c o n t r o l method, by showing t h e delayed breakthrough of C02, and t h e s t e e p change i n t h e GOR and t h e e f f l u e n t composition. The above f e a t u r e s have a l s o been v e r i f i e d i n t h e NM r u n , p e r h a p s t o a g r e a t e r e x t e n t , a s c a n be s e e n , f o r example, i n t h e s i g n i f i c a n t sharpening

-

435 LEACH ETAL DATA 20 BLK DT=.I

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Figure 9 Dirplacement 3 : 1-D comparison of dynamic VOightlng vlth full uprtrerm Wlghting. (a) Sg and COZ concentration (b) Normalized concentration of 032, rod CZ-C6 in profller (MCM). ( c ) COR and o i l recovery vs HCPV effluent vr HCPV injected (MCW). injected (ncn). (d) Sg and COZ concentration profilea (Nn). (e) Norullred concentrrtlon of CO2 and C 1 i n effluent v. HCPV injected (f) COR and 011 recovery va HCPV injected (NH). (Nn).

which o c c u r s i n t h e Sg and C02 p r o f i l e s , due t o t h e weighting scheme ( F i g u r e 9d). The p r o d u c t i o n h i s t o r y ( F i g u r e 9 e ) and t h e e f f l u e n t C 1 and C02 c o n c e n t r a t i o n s ( F i g u r e 9 f ) confirm t h e delayed a r r i v a l of t h e 2-phase z o n e , and t h e consequent h i g h e r recovery r e s u l t i n g from t h e u s e of t h i s technique. It needs t o be mentioned, however, t h a t a c r i t i c a l g a s s a t u r a t i o n o f 1 5 % had t o be i n t r o d u c e d t o t h e r e l a t i v e p e r m e a b i l i t y t a b l e , b e f o r e t h e r e s u l t s o f Leach e t a1 ( 1 5 ) could be s u c c e s s f u l l y reproduced.

-

5.0

-

CONCLUSIONS

The work d e s c r i b e d i n t h i s p a p e r l e a d s u s t o t h e f o l l o w i n g main conclusions : (1) The u s e of single-point upstream weighting c a u s e s s e v e r e c o m p o s i t i o n a l d i s p e r s i o n , p a r t i c u l a r l y when s i m u l a t i n g FCM, MCM and NM displacements. (2) A dynamic w e i g h t i n g scheme h a s b e e n d e v e l o p e d , which u t i l i s e s t h e p r o f i l e of t h e v a r i a b l e concerned, t o determine t h e optimum weighting f a c t o r s i n t i m e and space. I t e x p l o i t s t h e c l a s s i c a l f e a t u r e s of mid-stream, t w o - p o i n t u p s t r e a m , and s i n g l e - p o i n t u p s t r e a m s c h e m e s , b a s e d o n t h e p r o p e r t i e s of t h e p r o f i l e . (3) The t e c h n i q u e h a s been s u c c e s s f u l l y t e s t e d o n M C M , FCM a n d NM d i s p l a c e m e n t s , a n d y i e l d s r e s u l t s which, i f t h e i r a c c u r a c y i s t o be reproduced on a " f u l l y upstream" model, would r e q u i r e s e v e r a l times a s many g r i d blocks. (4) The method i s supported by g e o m e t r i c a l arguments, and can beimplemented e a s i l y i n multi-dimensional s i m u l a t o r s .

-

437 ACKNOWLEDGEMENTS The a u t h o r s would l i k e t o t h a n k t h e UK D e p a r t m e n t of Energy and Imperial College of S c i e n c e and Technology f o r s u p p o r t i n g t h i s r e s e a r c h , P r o f e s s o r C.G. Wall, D r . R.A. Dam f o r t h e i r c o n t i n u i n g i n t e r e s t , a n d Hiss M. Green o f ERC f o r h e r p a t i e n c e i n typing t h e v a r i o u s d r a f t s of t h i s paper.

REFERENCES

1. MCFARWE, R.C., MUELLER, T.D., MILLER, F.G.; " U n s t e a d y - S t a t e D i s t r i b u t i o n s o f F l u i d C o m p o s i t i o n s i n Two-Phase O i l R e s e r v o i r s U n d e r g o i n g Gas I n j e c t i o n " , S o c i e t y o f Petroleum Engineers J. (March, 1967), 1, 61-74. 2. PRICJ3,H.S. and DONOHUE, D.A.T., "Isothermal Displacement P r o c e s s e s w i t h I n t e r p h a s e Mass Transfer", Society of J. (June 1967) 1, 115-130. PetroleumEngineers 3. P E A C W , D.W. "Fundamentals of Numerical R e s e r v o i r Simulation", E l s e v i e t , Amsterdam, ( 1 9 7 7 ) 65-82 4. LANTZ, R.B. " Q u a n t i t a t i v e Evaluation of Numerical D i f f u s i o n (Truncation Error)", s o c i e t y of PetroleumEngineers J. (1971), 11, 315-320; Trans. AIME, 251 5 . CHAUDHARI, N.M. "An Improved N u m e r i c a l T e c h n i q u e f o r S o l v i n g M u l t i - D i m e n s i o n a l M i s c i b l e D i s p l a c e m e n t E q u a t i o n s " , S o c i e t y o f P e t r o l e u m E n g i n e e r s J. ( 1 9 7 7 ) , 2, 277-284; Trans., AIME, 251 6. VAN QUY, N., SIMANWUX, P. and CORTEVILLE, J . ; "A Numerical Study of Diphasic Multicomponent Flow", S o c i e t y o f P e t r o l e u m Engineers J. ( A p r i l 1972), 12, 171-184; Trans., AIME 253 7. LAUMBACH, D.D.; "A H i g h A c c u r a c y , F i n i t e D i f f e r e n c e T e c h n i q u e f o r T r e a t i n g t h e Convection-Diffusion Equation", S o c i e t y o f P e t r o l e u m E n g i n e e r s J . , ( 1 9 7 5 ) -1,5 517-531 8. GARDNER, A.O. and P E A C W , D.W. and POZZI, A.I.; "Numerical C a l c u l a t i o n o f M u l t i d i m e n s i o n a l M i s c i b l e D i s p l a c e m e n t by t h e Method of C h a r a c t e r i s t i c s " , S o c i e t y o f P e t r o l e u m E n g i n e e r s J . (19641, 26-36 9. TODD, M.R., ODELL, P.M., and HIRASAKI, G.J.; "Methods f o r I n c r e a s e d Accuracy i n Numerical R e s e r v o i r Simulators", S o c i e t y of Petroleum Engineers J. (1972), l.2, 515-530 10. BANKS, D., 'CHESHIRE, I.M., and POLLARD, R.K.; "A Technique f o r C o n t r o l l i n g Numerical D i s p e r s i o n i n F i n i t e - D i f f e r e n c e O i l R e s e r v o i r S i m u l a t i o n " , P r o c e e d i n g s of BAIL Conference, Dublin (June 1980). 99-203 11. WHEATLEY, M.J.; "A Version of Tvo P o i n t U p s t r e a m W e i g h t i n g For Use i n I m p l i c i t N u m e r i c a l R e s e r v o i r Simulators", paper presented a t S o c i e t y of Petroleum Engineers 5 t h Symp. On R e s e r v o i r Simulation, Denver, 1979; SPE Paper No. 7677 12. NGHIEM, L.X., FONG, D.K., and AZIZ, K.; "Compositional Modelling w i t h An E q u a t i o n o f S t a t e " , SPE P a p e r 9306, SPE Annual F a l l Meeting, Dallas, Texas (September 1980) 13. HELFFERICH, F.G.; " G e n e r a l Theory of Multicomponent, Multiphase Displacement I n Porous Media", Trans., AIME, 261 S o c i e t y of Petroleum Engineers J. (February 1981), 14. COATS, K.H.; "An Equation of S t a t e Compositional Model", S o c i e t y of Petroleum Engineere J. (October 1980). 20, 363-377

A,

z,

438 LEACH, M.P. and YELLIG, W.F.; "Compositional Model S t u d i e s : Co2 O i l Displacement Mechanisms", SPE P a p e r 8368, SPE Annual F a l l Meeting, Las Vagas, Nevada (September 1979) 16. SMITH, L.R. and YARBOROUGH, L.; " E q u i l i b r i u m R e v a p o r i z a t i o n of Retrograde Condensate by Dry Gas I n j e c t i o n , " 87-94 Trans. AIM, (1968), 17. P E A C W , D.W.; "A Nonlinear S t a b i l i t y A n a l y s i s f o r D i f f e r e n c e Equations Using S e m i - I m p l i c i t Mobility", S o c i e t y of P e t r o l e u m E n g i n e e r s J. ( F e b r u a r y 1 9 7 7 ) . 79-91; Trans., AIME 259 15.

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243

17,

APPENDICES Al.

S t a b i l i t y , T r u n c a t i o n Errors and Numerical D i s p e r s i o n

The n o n l i n e a r c o n v e c t i o n e q u a t i o n is:

ax

2.

(A\.\)

T r u n c a t i o n e r r o r a n a l y s i s o n t h e f i n i t e d i f f e r e n c e a p p r o x i m a t i o n of t h e l i n e a r i s e d equation

(A I . 2 ) shows a l e a d i n g t r u n c a t i o n e r r o r term of t h e form:

ank*a+ 2% DalLm =

1

(A I .3) V / A ~ [w-+) vd+g(e--:)]. W and 8 a r e t h e d i s t a n c e and time weightinn f a c t o r s f o r C i n t h e d i f f e r e n c e equation. By s o l v i n g t h e d i f f e r e n c e e q u a t i o n of e q u a t i o n A1.2, w e are, i n convection e q u a t i o n of t h e form: e f f e c t , solving a d i f f u s i o n

+

-

-

a%"f';: ac. %&* ax+ at

(A 1 . 4 ) .

This c r e a t e s a r t i f i c i a l d i f f u s i o n of C,and is terned numerical d i s p e r s i o n . L i n e a r i s e d s t a b i l i t y a n a l y s i s shove that t h e numerical s o l u t i o n s a r e s t a b l e i f t h e w e i g h t i n g f a c t o r s l i e i n t h e r a n g e 0.5 t o 1 (Equal g r i d s p a c i n g ) . Peaceman ( 1 7 ) showed t h a t a n o n l i n e a r s t a b i l i t y a n a l y s i s g a v e t h e same p r a c t i c a l c r i t e r i a for a f u l l upstream d i f f e r e n c e scheme (W-1). The r e s u l t s of t h e l i n e a r i z e d s t a b i l i t y a n a l y s i s a r e summarised i n t h e diagram shown below. The a p p r o x i m a t e s t a b i l i t y subdomain i n which t h e dynamic weighting scheme is o p e r a t i n g is more r e s t r i c t i v e t h a n t h a t permitted by t h e l i n e a r i z e d S t a b i l i t y analysis.

A Schematic I l l u s t r a t i o n of The Numerical S t a b i l i t y Domains

S t a b i l i t y Domain Domain i n whichdynamic weighting schemeoperates

0

w-

I

Conditional S t a b i l i t y Domain

la

I n c r e a s i n g Numerical S t a b i l i t y and Truncation Errors

0

439

A.2 A d d i t i o n a l Notes on 2-Point Upstream Weighting and Mid-Point Schemes

Weighting

The p r e v i o u s c u r v e a n a l y s i s shows t h a t 2-point upstream weighting cannot be a p p l i e d on Group 2 curves. Todd e t a 1 ( 9 ) showed 2 c a s e s which,according t o our p r e s e n t a n a l y s i s , b e l o n g t o t h e Group 2 curves category. Case 1: Todd e t a 1 showed a n example of u n i t m o b i l i t y , m i s c i b l e d i s p l a c e m e n t It i s p o s s i b l e t o c a l c u l a t e o i l r e l a t i v e permeability o f o i l by s o l v e n t . which is g r e a t e r t h a n 1 by 2-point upstream eXtraFQlatiOn,aS shown. T o d d e t a1 recommended s e t t i n g t h e s p u r i o u s e x t r a p o l a t e d value t o t h e maximum of t h e 2 bounding v a l u e s . Our c u r v e a n a l y s i s i n d i c a t e s t h a t t h i s i s e f f e c t i v e l y downstream weighting and could create a n undershoot of t h e o i l phase i f i t i s approaching zero s a t u r a t i o n . A m i d s t r e a m i n t e r p o l a t i o n is t h e b e s t alternative. I t i s e f f e c t i v e l y upstream,but not f u l l y upstream weighted on t h e a c t u a l curve p r o f i l e . Case 2: Todd showed t h a t a s p u r i o u s e x t r a p o l a t i o n e r r o r would o c c u r n e a r a s h a r p WOC or GOC. T h i s i s a Group 2 curve s i t u a t i o n c r e a t e d by t h e use o f r e l a t i v e p e r m e a b i l i t y (Kr) e x t r a p o l a t i o n , w h i c h i s l e s s c o n s i s t e n t t h a n s a t u r a t i o n e x t r a p o l a t i o n on t h e following grounds:(1) S a t u r a t i o n s a t t h e block interface d i c t a t e t h e i n t e r b l o c k flow. However, t h e e x t r a p o l a t e d r e l a t i v e p e r m e a b i l i t i e s w i l l not correspond t o a t o t a l s a t u r a t i o n of 1. (2) I t c r e a t e s , o r a c c e n t u a t e s t h e c r e a t i o n o f , a Group 2 p r o f i l e (which i s n o t amenable t o l i n e a r e x t r a p o l a t i o n ) . I n t h i s example, a Group 1 s a t u r a t i o n p r o f i l e exists. Had s a t u r a t i o n e x t r a p o l a t i o n been used, Krw a t 1124 would be 0.7 i n s t e a d of t h e s p u r i o u s n e g a t i v e value. (3) T y p i c a l l y , f o r a water f l o o d i n g problem, Group 2 s a t u r a t i o n p r o f i l e s e x i s t above t h e shock f r o n t s a t u r a t i o n value. The corresponding K r w p r o f i l e s

1.1

.

.

.

,

.

.

.

LANGSRUD DA TA

-

F i g u r e LO Comparison of w a t e r s a t u r a t i o n p r o f i l e s f o r v a r i o u s m o b i l i t y e v a l u a t i o n schemes ( b l a c k o i l model). (a) Spivak d a t a (SPEJ, February 1977). ( b ) Langsrud d a t a (Nolen and Berry, SPEJ June 1972).

.

.

44 0

have s t r o n g e r Group 2 c h a r a c t e r i s t i c s . The f a c t that e x p l i c i t 2-point Kr e x t r a p o l a t i o n d o e s n o t c a u s e i n s t a b i l i t y is p r o b a b l y d u e t o t h e non-sharpening n a t u r e of t h i s s a t u r a t i o n range. On t h e o t h e r hand, Group 1 curves (which are not amenable t o i n t e r p o l a t i o n ) a r e p r e s e n t around t h e flood front. The s a t u r a t i o n r a n g e b e l o w t h e s h o c k f r o n t s a t u r a t i o n i s self-sharpening, thereby a g g r a v a t i n g t h e weakness of i n t e r p o l a t i o n . This supports t h e evidence that mid-point weighting i s unstable. Figure 1Oa i l l u s t r a t e s some ueaknesees of u s i n g Kr e x t r a p o l a t i o n , n o r m a l l y n o t o b s e r v a b l e without imposing f r o n t a l c o n t r o l . An e x p l i c i t v e r s i o n of t h e dynamic weighting scheme, using 2 - p o i n t s a t u r a t i o n e x t r a p o l a t i o n a t t h e c o n t r o l l e d f r o n t and m i d s t r e a m weighting everywhere else, i s i l l u s t r a t e d i n Figure lob.

441

NUMERICAL METHODS

INTERPHASE MASS TRANSFER EFFECTS IN IMPLICIT BLACK OIL SIMULATORS D.BANKS and D.K.PONTING Atomic Energy Research Establishment, Hanuell, Oxfordshire,Enghnd

ABSTRACT

Mass t r a n s f e r may be described i n black o i l s i m u l a t o r s by allowing o i l and gas t o e x i s t i n both l i q u i d and vapour phases. A n q f f i c i e n t f u l l y implicit method of simultaneously modelling bubble and dew p o i n t is described. A s u b t r a c t e d t o t a l gaa formulation is found t o combine t h e advantages of t h e free and total gas approaches. A partial re-solution algorithm o p t i o n is d e s c r i b e d which I n t e r p o l a t e s bettween total- and no- re-solution logic. The d l s p r e i o n o f di88olved gaa and vapourlsed o i l is discussed.

B l a c k o i l s i m u l a t o r s , c h a r a c t e r i s e d by the treatment of j u s t two hydrocarbon

components, have t r a d i t i o n a l l y been more concerned w i t h d i 8 p l a c e m n t mechanisms t h a t the PVT dominated processes of EOR 8 t u d i e s . C-sltional effects are modelled simply by mass t r a n a f e r between l i q u i d and vapour phases. I n t h i s paper we d i s c u s s a n u m b e r o f v p e c t s ofma8stransferinblackoilsimulator8, mainly f r o m t h e s t a n d p o i n t of a f u l l y implicit formulation. Black o i l models g e n e r a l l y d e s c r i b e the c o n c e n t r a t i o n o f d i s s o l v e d gaa i n the reservoir l i q u i d by t h e bubble p o i n t p r e s s u r e , Pb, or the rrolution g a a - o i l ratio, R The q u a n t i t y o f o i l i n t h e vapour is described by t h e dew p o i n t p r e s s u r e , Pa, or t t e vapour oil-gaa ratio r or R ,[1,23. The vapour oil-gru ratio is g e n e r a l l y preferable, aa it enabfes thx vapour t o be described i n r e g l o n s o f low p r e s s u r e and re, for which no dew p o i n t exists. The ‘ o i l ’ and ‘gaa’ M y be any two groups of

.

hydrocarbon components, or t r u e stock tank o i l and gaa. I n a g e n e r a l b l a c k o i l model t h e r e are therefore f i v e independent v a r i a b l e s per cell: , Pb or Re, Pd or re, Sw, S The equation6 determining P and r8 would involve d f f f u s i o n , convection and &EI transfer rates. A t p r e s e n t , t h e extra c a p l t a t i o n a l effort r e q u i r e d t o s o l v e the f o u r t h and f i f t h e q u a t i o n s is p r o h i b i t i v e . The three equation p i c t u r e may be r e s t o r e d by employing bubble and dew p o i n t models, d i n g two o f t h e v a r i a b l e s dependent on t h e primary ones. A v a r i a b l e s u b s t i t u t i o n method for simultaneouslymodellingofp and rs v a r i a t i o n s i n an implicit b l a c k s i m u l a t o r is d e s c r i b e d i n S e c t i o n 2. mil%thi8 cannot y i e l d the d e t a i l e d d a c r i p t l o n obtrined from a t r u e multi-coaponent compositional s i m u l a t o r , the greater computational

P

.

442

e f f i c i e n c y enables detailed f u l l f i e l d s t u d i e s t o be performed. F a c i l i t i e s such as f a u l t connections and d i r e c t i o n a l r e l a t i v e permeabilities are t h e n a v a i l a b l e for s t u d i e s involving m i l d l y v o l a t i l e o i l s or dew p o i n t t r a n s i t i o n s , and numerical d i s p e r s i o n may be limited by the use of amall g r i d blocks. I n o u r experience v a r i a b l e s u b s t i t u t i o n is t h e o n l y method of modelling mass t r a n s f e r which does not l i m i t the a b i l i t y of the s i m u l a t o r t o t a k e l a r g e time steps, although other methodg are possible i f t h e time step l e n g t h is restricted. The q u a n t i t y o f g a s e x i s t i n g i n s o l u t i o n may be t y p i c a l l y 50-1000 times g r e a t e r t h a n t h a t e x i s t i n g i n t h e vapour phaae. The q u e s t i o n arises aa t o whether t h e maas conservation equation for g a s should involve a l l t h e g a s , or j u s t the f r e e component. O r i g i n a l l y a free g a s formulation w a a used i n PORES [lo]. I n s o l v i n g t h e material

c o n a e r v a t i o n e q u a t i o n s , however, a c o l u m n s u m c o n d i t i o n i s i m p o s e d w h i c h a t t e m p t s t o z e r o the sum of errors on d i a g o n a l p l a n e s of cells w i t h i n the reservoir model. T h i s is p a r t i c u l a r l y important i n the s e q u e n t i a l method of s o l v i n g t h e l i n e a r matrix equations. For a free g a s formulation, t h e column sum c o n d i t i o n r e p r e s e n t s an attempt t o c o n s e n e free gas, a conservation c o n d i t i o n v i o l a t e d when i n t e r p h a s e maas t r a n s f e r occurs. A t o t a l gaa formulation avoids t h i s , b u t , due t o the l a r g e d i s s o l v e d g a s c o n t r i b u t i o n , leaas t o p o o r l y conditioned e q u a t i o n s which t h e s e q u e n t i a l method f r e q u e n t l y fails t o s o l v e . A subtracted t o t a l gaa method which overcomes t h i s is described i n S e c t i o n 3. Such methods may be important f o r compositional s i m u l a t o r s aa the i n c r e a s i n g number of e q u a t i o n s r e n d e r s f u l l y simultaneous s o l u t i o n methods i m p r a c t i c a l l y expensive. Gas must come o u t o f s o l u t i o n when the o i l p r e s s u r e crosses the bubble p o i n t , b u t the re-solutionof gasdepends on t h e p r e s e n c e o f g a s i n c o n t a c t w i t h l i q u i d o i l , and the rate at which s o l u t i o n o c c u r s . Experiment [7] i n d i c a t e s that, where an i n t i m a t e gas-oil c o n t a c t e x i s t s , e q u i l i b r i u m is established on a timescale short compared t o those t y p i c a l l y involved i n reservoir engineering. The determining factor i n g a s s o l u t i o n is the rate a t which g a s d i f f u s e s through l i q u i d o i l . I n PORES, and other black o i l s i m u l a t o r s , t w o a l t e r n a t i v e s are a v a i l a b l e f o r the t r e a t m e n t o f g a s s o l u t i o n . Those are the no- r e - s o l u t i o n and total- r e - s o l u t i o n o p t i o n s . No- res o l u t i o n assumes that d i s s o l v e d gaa does not d i f f u s e through o i l , so that a layer of s a t u r a t e d o i l w i l l immediately b u i l d up at a gas-oil i n t e r f a c e and p r e v e n t f u r t h e r solution. While t h i s o p t i o n is l o g i c a l l y c o n s i s t e n t , it is u n r e a l i s t i c f o r r e s i d u a l o i l droplets, and w i l l o v e r e s t i m a t e g a s cap sizes. Using typical d i f f u s i o n c o e f f i c i e n t s , it can e a s i l y be shown t h a t a Inm d r o p l e t w i l l reach 991 of its u l t i m a t e d i s s o l v e d g a s c o n c e n t r a t i o n i n less than 24 hours. Total re-solution l o g i c assumes that i n t e r p h a s e e q u i l i b r i u m always exists i n each cell, so that free g a s may o n l y exist w i t h s a t u r a t e d o i l . T h i s aSSumptiOn of instantaneous e q u i l i b r i u m is u s u a l l y also made i n compositional s i m u l a t o r s . and e s s e n t i a l l y implies i n s t a n t a n e o u s flow of d i s s o l v e d gaa through o i l . I n practice, however, vapour invading o i l is l i k e l y t o f i n g e r or channel, r e s u l t i n g i n the gas bypassing some of the o i l . Free g a s may t h e n pass through a cell without Coqpletely s a t u r a t i n g the o i l . I n S e c t i o n 4 we d e s c r i b e a partial re-solution o p t i o n which enables the engineer t o set a r e - s o l u t i o n or e q u i l i b r i u m f r a c t i o n for each cell, the f r a c t i o n o f the l i q u i d hydrocarbon i n a cell i n c o n t a c t w i t h the vapour. This can s t i l l be f u l l y expanded i n a three v a r i a b l e formulation, and is similar t o the

t r a p p i n g f r a c t i o n approach. Simulators which permit g a s s o l u t i o n have d i f f i c u l t i e s w i t h the d i s p e r s i o n of d i s s o l v e d g a s and cell size dependence. These problem8 are, i f anything, more s e v e r e for vapourised o i l . This is due t o the non-specification of the d e t e d n i n g d i f f u s i o n rates, so that changes i n R and r are M i a t e l y p r o m a t e d across cells. I n a sense, t h e artificial'cell k u n d a r i e s introduced by t h e s i m u l a t o r prevent d i s p e r s i o n f r o m b e i n g t o t a l , rather than c a u s i n g it. NO r e - s o l u t i o n logic has an e q u i v a l e n t problem i n t h a t g a s is evolved from undersaturated o i l when flow

443

o c c u r s across an R g r a d i e n t . It is possible t o c o n t r o l t h i s d i s p e r s i o n for t h e simple case of fret g a s invading o i l by o n l y allowing R t o rise due t o c o n t a c t w i t h f r e e vapour. However, such methods run i n t o t r o u b l e &en a d r y vapour or d i s s o l v e d g a s s l u g is propogated, as t h e y modify the s l u g shape by sharpening t h e l e a d i n g edge.

MODELLING BUBBLE AND DEW POINT VARIATIONS

Two main approaches e x i s t t o modelling mass t r a n s f e r i n black o i l s i m u l a t o r s : the v a r i a b l e s u b s t i t u t i o n method [ 4 , 5 ] , and one cell methods i n which cell properties are modified t o be c o n s i s t e n t w i t h t h e s o l u t i o n i n terms of a f i x e d set of v a r i a b l e s [3]. These correspond t o s a t u r a t i o n p r e s s u r e and flash technique8 i n compositional s i m u l a t i o n [ 5 , 6 ] . Both methods have been used i n PORES, and v a r i a b l e s u b s t i t u t i o n has proved s u p e r i o r , although it i n v o l v e s o r g a n i s a t i o n a l d i f f i c u l t i e s i n keeping trackof whether t h e t h i r d s o l u t i o n v a r i a b l e is S P o r r The cell by cell b 8' technique r e t a i n s Po, Sw and S as s o l u t i o n varia%;es, and a d j u s t s R (Pb) t o s a t i s f y phase e q u i l i b r i u m . If g a s i a e c t i o n o c c u r s i n t o u n d e r s a t u r a t e d 011.for example, R;I is i n c r e a s e d , as i n the pseudo s o l u t i o n gas method. Unless t h i s is done e x a c t l y , a n e g a t i v e gas s a t u r a t i o n is o b t a i n e d on t h e subsequent i t e r a t i o n and g e n e r a l l y c a u s e s m a t e r i a l b a l a n c e errors. This can be overcome by u s i n g a one cell Newtonian i t e r a t i o n toexact m a t e r i a l b a l a n c e t o f i x t h e Rs change p r e c i s e l y . This y i e l d s a working scheme, b u t r u n s i n t o convergence problem on l o n g t i m e steps, as t h e p r e s s u r e changes which occur when free gas goes i n t o s o l u t i o n d i s t u r b the i n t e r b l o c k flows i n a manner n o t i n c o r p o r a t e d i n t o the Jacobian of the newtonian i t e r a t i o n . I n t h e u n d e r s a t u r a t e d o i l case t h e gas e q u a t i o n is b e i n g converged t o a known s o l u t i o n , S 0 ; more p r e c i s e l y , the bubble p o i n t is implicit, b u t n o t f u l l y expanded. 9

-

V a r i a b l e s u b s t i t u t i o n does n o t attempt t o r e t a i n gas S a t u r a t i o n as the t h i r d

v a r i a b l e a t a l l times.

Depending on the c o n d i t i o n s i n a cell, gas 8 a t u r a t i o n ,

bubble p o i n t or vapour oil-gas ratio, r , may be the primary s o l u t i o n v a r i a b l e . I n each case it is c r u c i a l that the f u n c t f o n a l dependence o f the secondary variables, ( s u c h as Pb and r i n a cell i n which S is the primary v a r i a b l e ) , and of f u n c t i o n s of t h e s e secondary bariables, is knoun 8nd included i n the Jacobian. The omission of a p p a r e n t l y minor terme from the Jacobian can l i m i t convergence of t h e non l i n e a r e q u a t i o n s unacceptably. However, t h e exact c a l c u l a t i o n of i n t e r b l o c k and w e l l flows a t the advanced time level, which is o b t a i n e d w i t h i n c r e a s i n g accuracy as the Newtonian i t e r a t i o n converges, p r e v e n t s i n s t a b i l i t i e s which can occur using first order approximations t o the implicit flows [ll].

Assuminginterphase e q u i l i b r i u m , there areonlythreepossibilities f o r t h e state of a cell:-

(i) Vapouronly. Po, Swandr a r e s o l u t i o n v a r i a b l e s , w i t h S -1-S andPb-Po s o w S and S are Solution ( ii ) Liquid and vapour hydrocarbon A t e s e n t . P g variables, w i t h Pb-Po, rs-rs ( Po+Pcq?kg fi (iii) Liquid only. S -0

g

Po,

s and

and rS-r

sat

s

P are s o l u t i o n v a r i a b l e s , w i t h b

(Po+Pcog( 0 ) )

.........................

(1)

r sat( P ) is t h e curve d e s c r i b i n g the oil-gas ratio for vagour in e q u i l i b r i u m w i t h

lfquid

811.

444

The maas conservation equations take the form

Rj

j-l,..,N

-

1 TAT -[m. AT J

-

mT] j

-

TAT

qJ

-

T+AT

& fnj n

I

............

(2)

, N the number of c e l l s .

Elements of the residual, R, mass terms, w e l l term and flows have a three vector formr-

-

Rj

qj W + R s

qO j w1

............... where fo Law

fw

i n t%' us&

(3)

and fg are the free o i l , water and free gaa flows given by Darcy's way, "Ad g,w are the corresponding w e l l terms.

The equatioagiven by R ( X w A T a are solved by Newtonian iteration, derivatives being taken w i t h respect t o the primary solution variables for each c e l l . Transitions may occur between t h e three states of (l), on the -is of the c u r r e n t approximation t o

the advanced time step solution, as follows:-

From s t a t e

(i), if rs)rss a t (Po+P (1-5 ) ) . S e t rs-r s a t , S -6, cog w 0 9 . c h a n g e t o (ii) sat

Prom s t a t e

(ii), i f So

P r o p e r t i e s of the o i l s s t u d i e d .

474 r e s e r v o i r and was s t u d i e d i n t h e e a r l y p a r t of BP's East Midlands Additional O i l P r o j e c t where a number of s m a l l , h i g h l y d e p l e t e d r e s e r v o i r s were e v a l u a t e d a s EOR candidates (5). This r e s e r v o i r was over-pressured by w a t e r i n j e c t i o n and i t was of i n t e r e s t t o know the e x t e n t t o which i t could be depressured while allowing t h e process t o o p e r a t e . The only source of gas a v a i l a b l e was pure COq formed as a b i p r o d u c t of annnonia production. O i l B i s from a p a r t i a l l y depleted r e s e r v o i r c l o s e t o a source of a s s o c i a t e d gas c o n t a i n i n g a s u b s t a n t i a l q u a n t i t y of C02. I t was t h e r e f o r e of i n t e r e s t t o determine what enrichment of the C02 by t h e i n t e r m e d i a t e hydrocarbons might be required f o r a dynamic m i s c i b l e displacement process t o o p e r a t e . For o i l A a s e r i e s o f displacement experiments were c a r r i e d o u t a t d i f f e r e n t displacement p r e s s u r e s . Two sets of experiments were performed with and without formation water being p r e s e n t a t connate s a t u r a t i o n w i t h i n t h e s l i m tube. The r e s u l t s f o r these a r e shown i n Figs. 6 and 7 where curve ( a ) i s t h e r e s u l t obtained when connate water was p r e s e n t i n each case. In Figure 6 t h e u l t i m a t e recovery, approximated by t h e recovery when 1.2 pure volumes had been i n j e c t e d i s p l o t t e d , whereas i n Figure 7 the recovery i s t h a t obtained a t gas breakthrough. Ihe curves a r e

100

A T = ! =

--. ~5

6

Figure 6.

b

-0-

---7

--7

8

--

1 -

0

10

P M P4

11

12

Ultimate recovery a s a f u n c t i o n of p r e s s u r e f o r o i l A.

0

S

6

7

Figure 7.

8

B

lo

-

P UP0

II

Recovery a t breakthrough f o r o i l A

'I2

475 t y p i c a l l y sigmoid and t h e r e i s seen t o be a s l i g h t l y b e t t e r recovery when connate w a t e r i s p r e s e n t than i n i t s absence. This i s thought to be due t o the o i l b e i n g a non-wetting phase when w a t e r i s p r e s e n t b u t t h e w e t t i n g phase when i t i s absent. 'Ihe p r e s s u r e a t which the sudden i n c r e a s e i n recovery i s observed i s independent o f the p o i n t on t h e recovery curve a t which measurements a r e made. However, i t i s g e n e r a l l y more convenient t o use t h e value a t ca V i = 1.2 s i n c e dVr : 0 dVi

The p o i n t of gas breakthrough was determined i n these experiments by o b s e r v i n g t h e change i n t h e GOR and by monitoring the pH of a small f l a s k c o n t a i n i n g d i s t i l l e d water through which t h e e f f l u e n t gas was passed. As t h e a s s o c i a t e d gas c o n t a i n s no GO2 o r H2S a sudden decrease i n pH i s observed as Cog f i r s t emerges from t h e tube as shown i n Fig. 8.

0.50.

0

02

O&

0.6

1.0

0.8

11

V.

Figure 8.

Recovery and pH v a r i a t i o n d u r i n g a s l i m tube displacement o f o i l A.

The sequence of events observed i n t h e v i s u a l c e l l was s i m i l a r t o t h a t described by Henry and Metcalf ( 6 ) with t h e exception t h a t a heavy phase was never observed. A t p r e s s u r e s below 8MPa breakthrough was accompanied by t h e appearance of a c o l o u r l e s s CO2 r i c h phase a s bubbles w i t h i n t h e o i l r i c h phase. A t 8.5 MPa a p r o g r e s s i v e sequence of l i g h t e n i n g i n t h e colour of t h e o i l r i c h phase w a s observed b u t w i t h t h e presence of a c o l o u r l e s s C02 r i c h phase. Bubbles o f t h i s c o l o u r l e s s phase were s e e n t o accompany t h e o i l up t o c a 10.5 ma. I n o r d e r t o determine t h e e f f e c t of the o p e r a t i o n a l v a r i a b l e s on t h e r e c o v e r i e s observed a series of measurements were perfonned a t 12MPa, where dVr is small, i n which t h e displacement rate was varied. dP No d i f f e r e n c e w a s observed w i t h i n experimental e r r o r as shown i n Fig. 9. Recently, we have been a b l e t o compare the r e c o v e r i e s with those o b t a i n e d using a v e r t i c a l 2m longcolumn 2.5cm i n diameter used by IFP who are now p a r t i c i p a t i n g i n t h e Egmanton CO2 p r o j e c t . A t p r e s s u r e s above ca 9MPa very good agreement e x i s t s between t h e r e s u l t s o b t a i n e d from t h e two p i e c e s of apparatus. The break i n s l o p e and minimum dynamic m i s c i b i l i t y p r e s s u r e s are l i k e w i s e i n good agreement. However, a t p r e s s u r e s below 8MPa where an immiscible gas displacement i s t a k i n g p l a c e t h e v e r t i c a l column c o n s i s t a n t l y gives h i g h e r

476 lQ0 0

Q

0

'c 0.50

P; 12 cpo

0

50

100

oco

2

Figure 9 .

Dependance of Recovery on Flow Rate a t 12MPa.

r e c o v e r i e s than thoseobtained from t h e h o r i z o n t a l l y c o i l e d tube. As t h e displacement i n t h e v e r t i c a l column i s g r a v i t y s t a b i l i s e d t h i s i s taken t o i n d i c a t e t h a t hydrodynamic i n s t a b i l i t i e s may be p r e s e n t i n the flow i n the s l i m tube even though i t i s of small diameter. For o i l B, t h e e f f e c t of p r o g r e s s i v e l y i n c r e a s i n g the mole f r a c t i o n of propane i n t h e displacement gas (mixtures of CO2 w i t h propane) i s shown i n Fig. 10.

1.2

0

Figure 10.

0 25

0.5

Recovery a s a f u n c t i o n of g a s composition f o r O i l B

0 . 2 t h e displacements show a l l of t h e c h a r a c t e r i s t i c s With Xc3 r e f e r r e d t o previously which are observed when a dynamic m i s c i b l e process i s t a k i n g place. With Xc3 < 0 . 2 t h e displacements are t y p i c a l l y i n m i s c i b l e i n c h a r a c t e r . The diagram shows a break i n s l o p e a t 0 . 2 which is similar t o t h a t seen on t h e Vr(p) diagrams. This Xc3 p o i n t i s r e f e r r e d t o as t h e minimum dynamic m i s c i b i l i t y composition by analogy with t h e minimum dynamic m i s c i b i l i t y pressure.

477 I t h a s been observed t h a t when t h e dynamic m i s c i b l e process i s o p e r a t i n g u l t i m a t e recovery i s reached by V i = 1 . 2 . To i l l u s t r a t e this is p l o t t e d as a f u n c t i o n of X3 i n Figure 11. dVi

dVr

XC

Figure 11.

3

The v a r i a t i o n of % w i t h dVi

composition

Since O i l B contains an a p p r e c i a b l e amount of C02, gas breakthrough could not be d e t e c t e d by monitoring the pH as with O i l A. Figures 12 and 13 show t h e v a r i a t i o n observed i n t h e t o t a l stream d e n s i t y and t h e gas-oil r a t i o during an experiment. I t w a s found t h a t t h e d e n s i t y measurement gave a much more s e n s i t i v e i n d i c a t i o n of t h e f i r s t change i n compq8ition than d i d t h e COR. Furthermore i f gas bubbles of low d e n s i t y a r e e n t r a i n e d w i t h i n t h e o i l t h e recorded d e n s i t y becomes very erratic. When a dynamic m i s c i b l e process is o p e r a t i n g t h e d e n s i t y v a r i e s f a i r l y smoothly a s shown i n Figure 12 This a l s o s e r v e s t o show t h a t t h e composition of t h e t r a n s i t i o n zone may b e more complex than i s u s u a l l y depicted.

.

-

1.0

"I-

0.5'

0 0

0'5

I

.o

V.

Figure 12.

Recovery and d e n s i t y as f u n c t i o n s of V i a t Xc3

12

-

0.5

478 1.0

vr

0'5

0

0

05

Figure 13.

V.

PO

k2

Recovery and GOR as f u n c t i o n s of V i a t Xc3 = 0 . 5

DISCUSSION The break i n s l o p e of t h e Vr(p) and Vr(x) f u n c t i o n s i s now known t o be a f u n c t i o n of t h e composition of t h e d i s p l a c i n g f l u i d , the composition of t h e o i l and t h e displacement temperature ( 7 ) . Recently, Johnson and P o l l i n (8) have shown t h a t t h e minimum dynamic m i s c i b i l i t y p r e s s u r e f o r C02 d i s p l a c i n g a s e r i e s of pure n-alkanes i s almost e x a c t l y given by the c r i t i c a l p r e s s u r e of t h e b i n a r y mixture a t t h e temperature a t which the displacement i s c a r r i e d out. I f e q u i l i b r i u m e x i s t s w i t h i n t h e displacement tube t h e sudden i n c r e a s e i n recovery which i s observed m u s t b e l a r g e l y a r e s u l t df t h e increased s o l v e n t powers of t h e displacement gas w i t h i n t h e c r i t i c a l region. The increased s o l u b i l i t y i s a r e s u l t of t h e l a r g e d e v i a t i o n s from i d e a l i t y which occur w i t h i n t h e c r i t i c a l region. A s c r i t i c a l i t y i s reached l a r g e changes a r e observed t o occur i n many p h y s i c a l p r o p e r t i e s as shown i n Figure 14 f o r pure C02. The Vr(p) curve f o r O i l A has been superimposed upon t h i s . A t t h e same t i m e as t h e s o l u b i l i t y i n c r e a s e s

- 4.0

1000

P

,

L lo

*

*

1.00

D"P

vI-

&Om-' 5 00

0

Figure 14.

-2.0

10

The v a r i a t i o n i n t h e p h y s i c a l p r o p e r t i e s of C02 i n t h e c r i t i c a l region.

0 50

0

479 w i t h i n t h e c r i t i c a l region o t h e r physical p r o p e r t i e s change i n such a way a s t o favour the displacement. Thus the d e n s i t y and v i s c o s i t y both i n c r e a s e while t h e product of t h e d e n s i t y and s e l f - d i f f u s i o n c o e f f i c i e n t decreases i n agreement with k i n e t i c theory. Although t h e s e l f d i f f u s i o n c o e f f i c i e n t decreases i t s value s t i l l remains considerably h i g h e r than t h a t found i n normal l i q u i d s enabling trapped o i l t o be more r e a d i l y contacted. I t i s not known a t t h e p r e s e n t time whether these changes i n p h y s i c a l p r o p e r t i e s w i l l e f f e c t convective d i s p e r s i o n o t h e r than through the mutual d i f f u s i o n c o e f f i c i e n t which appears t o follow t h e behaviour of t h e s e l f d i f f u s i o n c o e f f i c i e n t i n t h e c r i t i c a l region. The s o l u b i l i t y of a given compound depends upon t h e n a t u r e of t h e i n t e r m o l e c u l a r i n t e r a c t i o n s between i t and the s o l v e n t a s i s r e f l e c t e d i n the phase diagram. A t the p r e s e n t time phase diagrams have been determined f o r mixtures of C02 with a range of n-alkanes and a few simple cycloalkane and aromatic hydrocarbons ( 9 ) . p(T) s e c t i o n s f o r t h e n-alkanes are shown i n Figure 15. I t can be seen from t h i s diagram t h a t f o r t h e lower homologues the c r i t i c a l l i n e i s s e p a r a t e d i n t o two branches, one of V-L c r i t i c a l p o i n t connecting t h e c r i t i c a l p o i n t s of t h e pure end members and t h e o t h e r of L-L c r i t i c a l p o i n t s which terminates a t a c r i t i c a l end p o i n t . For t h e

LO

J

vapov' p-csrure c u r v e of

Figure 15.

co2

t

/'c

C r i t i c a l Lines f o r CO2 + n-alkane mixtures.

h i g h e r homologues the c r i t i c a l l i n e i s continuous b u t may f o l d back upon i t s e l f r e s u l t i n g i n gas-gas i m m i s c i b i l i t y of the f i r s t kind. The c r i t i c a l p r e s s u r e i n c r e a s e s with t h e carbon number a t a given temperature. Thus f o r e x t r a c t i o n a t a given temperature and p r e s s u r e some of t h e homologues w i l l have t h e i r c r i t i c a l regions w i t h i n t h e range of p r e s s u r e s considered, while o t h e r s w i l l r e q u i r e a much h i g h e r p r e s s u r e and y e t o t h e r s , i f t h e temperature i s s u f f i c i e n t l y low,can never be brought i n t o t h e c r i t i c a l r e g i o n by i n c r e a s e i n p r e s s u r e alone. This w i l l account a t l e a s t i n p a r t f o r a r e s i d u a l 'heavy" o i l b e i n g l e f t behind a f t e r t h e displacement and f o r t h e small b u t p e r s i s t a n t i n c r e a s e i n recovery t h a t i s observed a f t e r t h e minimum dynamic m i s c i b i l i t y p r e s s u r e h a s been reached. A

4 80 s i m i l a r s u i t e of curves e x i s t f o r t h e aromatic and naphthenic compounds. "he displacement of t h e s e curves from one another suggests a degree of s e l e c t i v i t y i n t h e e x t r a c t i o n process and i t is i n t e r e s t i n g t o s p e c u l a t e t h a t t h e p a r a f f i n , naphthene, aromatic d i s t r i b u t i o n w i t h i n t h e o i l s recovered may change a s t h e p r e s s u r e changes. Although t h e minimum dynamic m i s c i b i l i t y p r e s s u r e appears t o be l a r g e l y governed by t h e . e q u i l i b r i u m thermodynamic p r o p e r t i e s of t h e f l u i d s the a b s o l u t e recovery w i l l depend both on t h e proportion of u n e x t r a c t a b l e components i n t h e o i l and on t h e hydrodynamics of t h e displacement. I t does not seem reasonable t h e r e f o r e t o quote a f i x e d recovery which m u s t be reached b e f o r e i t can be coficluded t h a t t h e m u l t i p l e c o n t a c t mass t r a n s f e r mechanism is o p e r a t i n g . Deduction of t h e process mechanism m u s t thus b e made on t h e b a s i s of many d i f f e r e n t observations r a t h e r than a s i n g l e one. An attempt t o summarise t h e more g e n e r a l characteristics of t h e d i f f e r e n t process types i s given i n t a b l e 3.

TABLE 3

KEY

TO

PROCESS

IDENTIFICATION

Process 5 p e PROPERTY [miscible Recovery a t V i = 1.2

dVf a t dVi

vi

= 1.2

lOW

Low IFT

intermediate

large

Breakthrough

early

First Contact

high

high

zero

zero

none

none

intermediate

late

late

high

Rate Dependance

Mu1 t i p l e Contact

small

Density Change a t breakthrough

Becomes very erratic

erratic a t times

smooth

smooth

S i g h t Glass Observations a t breakthrough

colooties! bubbles i n dark o i1

Colourless bubbles i n lighter coloured o i l

Dark t o light colour change i n o i l with occasional colourless bubbles

Progressive lightening i n colour of the o i l w i t h o u t gas bubbles

I f a series of displacements are c a r r i e d o u t a t d i f f e r i n g compositions o r p r e s s u r e s a s i n t h e example given above s e v e r a l o f t h e s e mechanisms w i l l be observed t o o p e r a t e . Considerable refinement of t h i s scheme i s r e q u i r e d p a r t i c u l a r l y i n r e l a t i o n t o t h e d i f f e r e n t types of displacement which may take p l a c e i n t h e L-L and L-V r e g i o n s .

481 CONCLUSIONS

I t has been s h a m above t h a t s l i m tube displacement experiments may be used t o optimise i n d i v i d u a l p r o j e c t s with r e s p e c t t o both p r e s s u r e and composition. A considerable amount of information may be gathered i n the course of t h e s t u d i e s upon which t h e dominent mechanism which o p e r a t e s i n a given p r e s s u r e o r composition may be deduced.

ACKNOlrTLEDGEMENT The author wishes t o thank G . J . J . Williams. A . G . Steven, A. Booth, C.G. Osborne, D . J . Thomas, S . Takhar. S . Bahal and C. Liang from whose work t h e contents of t h i s paper have been drawn. NOMENCLATURE

Bo

Flash formation volume f a c t o r of o i l

Fg

Volume f r a c t i o n of gas phase

COR

Gas o i l r a t i o

i , j, k

I n d i c e s i n equation of s t a t e

ml

Mass of evacuated s l i m tube

m2

Mass of water f i l l e d s l i m tube