Hydrothermal Properties of Materials: Experimental Data on Aqueous Phase Equilibria and Solution Properties at Elevated Temperatures and Pressures

Hydrothermal Experimental Data Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. I...

Author: Vladimir Valyashko

87 downloads 1066 Views 5MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Hydrothermal Experimental Data

Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-09465-5


Edited by Vladimir M. Valyashko

A John Wiley & Sons, Ltd., Publication

This edition first published 2008 © 2008 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. 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, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If rofessional advice or other expert assistance is required, the services of a competent professional should be sought. The Publisher and the Author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the Author or the Publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the Publisher nor the Author shall be liable for any damages arising herefrom. Library of Congress Cataloging-in-Publication Data Valyashko, V. M. (Vladimir Mikhailovich) Hydrothermal properties of materials : experimental data on aqueous phase equilibria and solution properties at elevated temperatures and pressures / Vladimir Valyashko. p. cm. Includes bibliographical references and index. ISBN 978-0-470-09465-5 (cloth) 1. High temperature chemistry. 2. Solution (Chemistry) 3. Phase rule and equilibrium. 4. Materials–Thermal properties. I. Title. QD515.V35 2008 541′.34 – dc22 2008027453 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-09465-5 Typeset in 10/12 pt Times New Roman PS by SNP Best-set Typesetter Ltd., Hong Kong Printed and bound in Singapore by Markono Print Media Pte Ltd, Singapore

Dedication

This book is dedicated to the memory of Professor Dr E. U. Franck (Ulrich Franck) (1920–2004) who made fundamental contributions in the field of solution chemistry and phase equilibria in aqueous systems at high temperatures and pressures, and whose idea to create an ‘Atlas on Hydrothermal Chemistry’ was realised with the publication of Aqueous Systems at Elevated Temperatures and Pressures in 2004 and this book.

Contents CD Table of Contents Foreword Preface Acknowledgements 1 Phase Equilibria in Binary and Ternary Hydrothermal Systems Vladimir M. Valyashko 1.1 Introduction 1.2 Experimental methods for studying hydrothermal phase equilibria 1.2.1 Methods of visual observation 1.2.2 Methods of sampling 1.2.3 Methods of quenching 1.2.4 Indirect methods 1.3 Phase equilibria in binary systems 1.3.1 Main types of fluid phase behavior 1.3.2 Classification of complete phase diagrams 1.3.3 Graphical representation and experimental examples of binary phase diagrams 1.4 Phase equilibria in ternary systems 1.4.1 Graphical representation of ternary phase diagrams 1.4.2 Derivation and classification of ternary phase diagrams References 2 pVTx Properties of Hydrothermal Systems Horacio R. Corti and Ilmutdin M. Abdulagatov 2.1 Basic principles and definitions 2.2 Experimental methods 2.2.1 Constant volume piezometers (CVP) 2.2.2 Variable volume piezometers (VVP) 2.2.3 Hydrostatic weighing technique (HWT) 2.2.4 Vibrating tube densimeter (VTD) 2.2.5 Synthetic fluid inclusion technique 2.3 Theoretical treatment of pVTx data 2.3.1 Excess volume 2.3.2 Models for the standard partial molar volume 2.4 pVTx data for hydrothermal systems 2.4.1 Laboratory activities 2.4.2 Summary table References 3 High Temperature Potentiometry Donald A. Palmer and Serguei N. Lvov 3.1 Introduction 3.1.1 Reference electrodes 3.1.2 Indicator electrodes 3.1.3 Diffusion, thermal diffusion, thermoelectric, and streaming potentials 3.1.4 Reference and buffer solutions 3.2 Experimental methods 3.2.1 Hydrogen-electrode concentration cell 3.2.2 Flow-through conventional potentiometric cells

ix xi xiii xv 1 1 3 73 74 80 82 86 86 87 91 103 103 105 119 135 135 136 136 137 138 139 140 140 140 153 159 159 185 186 195 195 198 198 199 200 200 200 202

viii Contents

3.3

Data treatment References

4 Electrical Conductivity in Hydrothermal Binary and Ternary Systems Horacio R. Corti 4.1 Introduction 4.2 Basic principles and definitions 4.3 Experimental methods 4.3.1 Static high temperature and pressure conductivity cells 4.3.2 Flow-through conductivity cell 4.3.3 Measurement procedure 4.4 Data treatment 4.4.1 Dissociated electrolytes 4.4.2 Associated electrolytes 4.4.3 Getting information from electrical conductivity data 4.5 General trends 4.5.1 Specific conductivity as a function of temperature, concentration and density 4.5.2 The limiting molar conductivity 4.5.3 Concentration dependence of the molar conductivity and association constants 4.5.4 Molar conductivity as a function of temperature and density 4.5.5 Conductivity in ternary systems References

203 205 207 207 207 215 215 217 218 219 219 219 221 221 221 222 223 224 224 224

5 Thermal Conductivity Ilmutdin M. Abdulagatov and Marc J. Assael 5.1 Introduction 5.2 Experimental techniques 5.2.1 Parallel-plate technique 5.2.2 Coaxial-cylinder technique 5.2.3 Transient hot-wire technique 5.2.4 Conclusion 5.3 Available experimental data 5.3.1 Temperature dependence 5.3.2 Pressure dependence 5.3.3 Concentration dependence 5.4 Discussion of experimental data References

227

6 Viscosity Ilmutdin M. Abdulagatov and Marc J. Assael 6.1 Introduction 6.2 Experimental techniques 6.2.1 Capillary-flow technique 6.2.2 Oscillating-disk technique 6.2.3 Falling-body viscometer 6.2.4 Conclusion 6.3 Available experimental data 6.3.1 Temperature dependence 6.3.2 Pressure dependence 6.3.3 Concentration dependence 6.4 Discussion of experimental viscosity data References

249

7 Calorimetric Properties of Hydrothermal Solutions Vladimir M. Valyashko and Miroslav S. Gruszkiewicz 7.1 Batch techniques 7.2 Flow techniques 7.3 Summary table References

271

Index

227 228 228 235 239 241 242 242 244 245 245 246

249 252 253 255 257 259 260 261 261 264 265 267

272 272 274 284 289

CD Table of Contents

Appendix to Chapter 1

pTX


pVTX


Potentiometry


Electrical Conductivity


Thermal Conductivity


Viscosity


Calorimetric

Foreword Dr. Vladimir Valyashko invited me to write the foreword to this substantial book that contains all existing evaluated experimental data on thermodynamic, electrochemical, and transport properties of two- and three-component aqueous systems in the hydrothermal region. This invitation is unquestionably quite an honor. However, accepting it did make me feel somewhat of an impostor. The person who should have written this foreword is our revered predecessor, colleague and friend Ulrich Franck, but unfortunately, he did not live to see the completion of an endeavor that he had most arduously advocated. It is therefore with trepidation that I, who consider myself at best as one of his many disciples, act here as his substitute. An immense amount of experimental material on water/ steam and aqueous systems has been obtained during the past century, and even before, in laboratories around the world, much of it not readily accessible. Especially during the cold-war years, the International Association for Properties of Water and Steam (IAPS, later IAPWS) was among the few international organizations in which experts in the former Soviet Union actively participated. Franck, impressed by the access IAPWS had to experimental data obtained worldwide, repeatedly urged the organization to collect and evaluate these data, bundling them in what he used to call an Atlas. This book presents evaluated experimental data acquired, as well as some of the theoretical models developed, for two-and three-component hydrothermal systems. These are aqueous solutions containing both molecular and/or electrolytic solutes at high temperature and pressure, approaching and exceeding water’s critical temperature. Hydrothermal systems are ubiquitous, in the deep ocean and in the earth’s crust, and of major importance in geology, geochemistry, mining, and in industrial practices such as metallurgy and the synthesis and growth of crystals. The theoretical understanding of the phase behavior of fluid mixtures was developed in the second half of the 19th century, starting with the work of Gibbs (1873–1878) and culminating in Van der Waals’s theory of mixtures (1890), which was a generalization of his 1873 equation of state. The first phase separation experiments by Kuenen (early 1890s) involved binary mixtures of simple organics both below and above the critical point of the more volatile component. Gradually, between the early 1890s and 1903, the various types of binary fluid phase separation became known. Van Laar actually was able to derive them from a version of Van der Waals’s mixture equation. Nature’s most unusual fluid: “associating” water, however, with its very high critical point, and its high dielectric constant yielding

electrolytic properties in the liquid phase, was not expected to behave as air constituents and organics. The question of how the solvent water would behave around and above its critical point was first addressed by the Dutch chemist Bakhuis Roozeboom and his school, who were experts at measuring and classifying the phase separation of binary and ternary mixtures, including solid phases. By 1904, Bakhuis Roozeboom had explored the case of the liquid-vapor-solid curve intersecting the critical line of a binary mixture in two critical endpoints and predicted that this would also happen in aqueous solutions of poorly soluble salts, as his successors indeed confirmed in 1910. His experiments and classification scheme pertain to a multitude of both non-aqueous and aqueous binary and ternary systems. Somewhat fortuitously, Göttingen became the nexus from which “phase theory” would spread to Russia. The Russian organic chemist Vittorf (1869–1929) met Bakhuis Roozeboom in Göttingen in 1904. Vittorf then used Bakhuis Roozeboom’s phase theory and classification as the basis for his own 1909 book “Theory of Alloys in Application to Metallic Systems”. From the late 1930s through the 1980s, physical chemist Krichevskii and his many collaborators, thoroughly familiar with the work of the Dutch School, studied fluid phase behavior and critical phenomena experimentally, and discovered several predicted effects, such as tricriticality, as well as gas-gas phase separation in both nonaqueous and aqueous mixtures. Starting just after WWII, thermal physicist Stirikovich, physical chemists Mashovetz and Ravich, and geochemist Khitarov, began to explore phase behavior and solution properties of aqueous systems up to high temperatures and pressures. Göttingen professors Nernst, Tammann, and Eucken had built a physical chemistry laboratory for electrochemistry, as well as for high-pressure phase equilibria studies and calorimetry. It was there that Franck, a pupil of Eucken, began his life’s work on the experimental exploration of the properties of high-temperature, high-pressure aqueous solutions of air constituents, acids, bases, and salts, studying phase behavior as well as dielectric and electrochemical properties. He and his disciples explored this field throughout the second half of the 20th century. In the USA, just after WWI, geochemist Morey began the first phase equilibria studies in hydrothermal systems. By the middle of the 20th century, there was a flourishing discipline in geochemistry in the USA, culminating the work of Kennedy and collaborators on phase separation in aqueous salt solutions at high pressures and temperatures. Time and again, it was rediscovered that the phase

xii Foreword

separation characteristics of fluid mixtures first classified by Bakhuis Roozeboom do apply to aqueous systems as well. Valyashko, the chief editor of the present book, has, throughout the years, exhaustively classified the experimental phase diagrams of binary and ternary aqueous solutions including solid phases in the hydrothermal range. He frequently consulted with Franck, and assembled the work in collaboration with Lentz, from the Franck school. This work forms a substantial part of the present book. Independently, however, in the 20th century, physical chemists studying aqueous electrolyte solutions set up a framework of description unlike that used for fluid mixtures. It is founded on increasingly more detailed and accurate measurement and modeling of electrolyte solution properties in the solvent water, usually below the boiling temperature. Here the pure solvent at the same pressure and temperature, and the infinite-dilution properties of the solute, serve as an asymmetric reference state. Kenneth Pitzer was a pioneer in this field, systematically pushing the modeling of solution behavior to higher concentrations and temperatures. Geochemist Helgeson and his school introduced practical models for use in the field. On approaching the critical point, however, water’s unusual dielectric and electrolytic properties diminish, its compressibility increases hugely, and its behavior becomes more like that of other, simpler near-critical fluids. The asymmetric solution model then becomes increasingly strained. This message was brought home forcefully in the early 1980s by the elegant experimental data of Wood and coworkers on partial molar properties of the solute in dilute electrolyte solutions near the water critical point. These usually well-behaved properties exhibited divergences at that critical point, while higher derivatives, such as the partial molar heat capacity, displayed wild swings in water’s critical region. When Wood et al. repeated the experiments in the argon-water system, however, similar anomalies were found, be it of the opposite sign and of smaller amplitude – a sure sign that the effects they had seen were not electrolytic

in origin, but a general thermodynamic property of a dilute near-critical mixture. In fact, in the early 1970s, Krichevskii and coworkers had discovered the divergence of the infinite-dilution partial molar volume of the solute experimentally, and explained it correctly. Aqueous mixtures near and above the water critical point can then be modeled by Van der Waals-like descriptions of fluid mixtures that treat the solvent and solutes equivalently but ignore the charges. Franck and coworkers, for instance, produced the phase separations observed in several binary and ternary aqueous systems in the hydrothermal range from simple Van-der-Waals type models. A theory that combines in a unified way the electrolytic behavior with Van-der Waals-like classical critical behavior (let alone the actual non-classical critical behavior known to characterize water as well as all other fluids) remains a formidable challenge. Recent fundamental work by M.E. Fisher and coworkers is making this increasingly clear. The various chapters of the present book, instead, offer a practical and useful overview of modeling approaches, focused on the current needs, methods and understanding of a wide range of hydrothermal systems. They show a discipline still in development, one of the last enduring challenges in the field of thermodynamics and electrochemistry of solutions. The book may transcend Franck’s original concept of an “Atlas,” but he certainly would have been most pleased with the authors’ efforts of understanding and representing data, an effort that he himself amply exemplified in his scientific output of half a century. It is my hope and expectation that the book will be received by a diverse class of users as a highly useful compendium of knowledge about hydrothermal systems, accumulated globally over more than a century. Johanna (Anneke) Levelt Sengers Scientist Emeritus National Institute of Standards and Technology Gaithersburg, MD, USA

Preface Knowledge of equilibria in aqueous systems as well as understanding the processes occurring in hydrothermal mixtures are based to a large extent on experimental data on phase equilibria and solution properties for aqueous systems at temperatures above 150–200 °C. These data have been extensively applied in a variety of fields of science and technology, ranging from development of the chemistry of solutions and heterogeneous mixtures, thermophysics, crystallography, geochemistry and oceanography to industrial and environmental applications, such as electric power generation, hydrothermal technologies of crystal growth and nanoparticle syntheses, hydrometallurgy and the treatment of sewage and the destruction of hazardous waste. The available experimental data for binary and ternary systems can be used as primary reference data, or as the initial values for further refinement, in order to obtain recommended values, particularly, the internally consistent values that are used for thermodynamic calculations and modelling of multicomponent equilibria and reactions. However, the recommended values are derivatives and largely depend on the method of treatment based on more or less rigorous and varying models. Thus, a collection of experimental data not only incorporates original information from widely scattered scientific publications, it is fundamental and provides the foundation for modern and future databases, and recommended values. The main goals of this book are to collect, collate and compile the available original experimental data on phase equilibria and solution properties for binary and ternary hydrothermal systems, to review these data, and to consider the employed experimental methods and the ways these data were refined/processed and presented. The work on collecting hydrothermal experimental data was started in the mid-1990s by Dr V. M. Valyashko (Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences (KIGIC RAS), Moscow, Russia) and Dr H. Lentz (University of Siegen, Germany) and was supported by the Russian Fund for Basic Research and the Deutsche Forschungsgemeinschaft. After the retirement of Dr Lentz in 1999, collection of data at temperatures above 200 °C was continued by Dr Valyashko and Mrs Ivanova (KIGIC RAS). The development of the project was supported by the International Association for the Properties of Water and Steam (IAPWS), the organization which is renowned for setting international standards for properties of pure water and high-temperature aqueous systems. According to the IAPWS project accepted in 2004, this book should have had seven chapters – Phase equilibria

data, pVTX data, Calorimetric data, Electrochemical data, Electrical conductivity data, Thermal conductivity data and Viscosity data. However, the planned chapter on calorimetry was not forthcoming due to personal commitments of the author. Only a summary table of calorimetric data with a short introduction about the experimental methods used for hydrothermal measurements are provided in Chapter 7 of this book but a collection of the experimental calorimetric data is available on the CD. In the final version of this book each chapter consists of two parts: the descriptive text part that appears in the pages of this book and the data part which appears as appendices organized on the CD. The descriptive part contains the basic principles and definitions, description of experimental methods, discussion of available data and reviews of theoretical or empirical approaches used for treatment of the original experimental values. The accompanying summary tables, arranged in alphabetic order of the nonaqueous components, list the temperatures, pressures and concentrations, types of data and experimental methods employed in their measurements, the uncertainty claimed by the authors as well as the references (the first author and the year of publication). The table code refers the reader to the original data set in the appendices on the CD. The tables of experimental data (with brief comments on each set of experimental measurements) in the appendices are also arranged in alphabetic order of nonaqueous components. However, the order of the systems in the appendices is usually not exactly the same as in the summary tables. There are no subdivisions in appendices, whereas in the summary tables the binary and ternary systems are often placed in separate divisions or subdivisions such as inorganic and organic compounds or electrolytes, nonelectrolytes, acids, etc. The text parts of the chapters, besides the general characteristics of the available experimental data mentioned above, usually contain several special topics and aspects of material presentation. Chapter 1 (Phase Equilibria in Binary and Ternary Hydrothermal Systems, V. M. Valyashko, Russia) contains a description of the general trends of sub- and supercritical phase behaviour in binary and ternary systems taking into account both stable and metastable equilibria. A presentation of the various types of phase diagrams aims to show the possible versions of phase transitions under hydrothermal conditions and to help the reader with the determination of where the phase equilibrium occurs in p–T–X space, and what happens to this equilibrium if the parameters of state are changed. Special attention is paid to continuous phase transformations taking place with variations of temperature,

xiv

Preface

pressure and composition of the mixtures, and to a systematic classification and theoretical derivation of binary and ternary phase diagrams. Chapter 2 (pVTx Properties of Hydrothermal Systems, H. R. Corti (Argentina) and I. M. Abdulagatov (Russia/ USA)) describes many theories and models developed to accurately reproduce the excess volumetric properties and to assess the standard partial molar volumes of the solute in aqueous electrolyte and nonelectrolyte solutions under suband supercritical conditions. Most of these models and equations, particularly the equations of state, are used to compute both the thermodynamic properties of solutions and the phase equilibria. This chapter is concerned with theoretical approaches in modern chemical thermodynamics of hydrothermal systems. Chapter 3 (High Temperature Potentiometry, D. A. Palmer and S. N. Lvov (USA)) focuses on ionization equilibria that are an important part of acid–base, metal–ion hydrolysis, metal complexation and metal–oxide solubility studies under hydrothermal conditions. Most of the hydrothermal investigations used potentiometric measurements with various types of electrochemical cells, mainly covering ranges of temperature below 200 °C, the minimum limit generally adhered to in this book. Therefore, the experimental data discussed in the text part, collected in the appendix and in the summary tables include both high-temperature (up to 400–450 °C) and low-temperature results available in the literature.

Special attention in Chapter 4 (Electrical Conductivity in Hydrothermal Binary and Ternary Systems, H. R. Corti (Argentina)) is paid to the procedures for obtaining information on the thermodynamic properties of electrolytes (including a determination of the limiting conductivity and association constants) from the measured electrical conductivity of diluted solutions above 200 °C. However, the behaviour of specific and molar conductivity in concentrated electrolyte solutions is also carefully discussed in the chapter. Chapters 5 and 6 (Thermal Conductivity and Viscosity, I. M. Abdulagatov (Russia/USA) and M. J. Assael (Greece)) show not only the typical temperature, pressure and concentration dependencies of properties in hydrothermal solutions, but also make a preliminary comparison of various datasets for several systems to help the reader choose which values to use. The empirical and semiempirical correlations which are necessary because of the lack of theoretical background, employed in the reviewed literature are also discussed. Chapter 7 (Calorimetric Properties of Hydrothermal Solutions, V. M. Valyashko (Russia) and M. S. Gruszkiewicz (USA)), indicates the experimentally determined calorimetric quantities of considerable current use, gives a brief description of experimental methods for hydrothermal measurements and contains a summary table with information about the systems studied and the corresponding calorimetric measurements.

Acknowledgements

Preparing this book required the talents and cooperation of many individuals. It was a long and sometimes painful process. However, it was very interesting and fulfilling project for me to accumulate and finally see the results. I would like to thank my colleagues and co-authors Dr Ilmutdin M. Abdulagatov, Dr Marc J. Assael, Dr Horacio R. Corti, Dr Miroslav S. Gruszkiewicz, Mrs Nataliya N. Ivanova, Dr Serguey N. Lvov and Dr Donald A. Palmer for their tremendous work, initiative and their patience during the long and difficult gestation of this book. We are all grateful to Dr Johanna M. H. Levelt Sengers (Anneke Sengers), who played a significant role in the development of this project within IAPWS and agreed to write a Foreword for us, and to Dr Peter G. T. Fogg for his assistance in searching for a publisher. I would like to acknowledge our colleagues from different countries for their help. Since we started this project these people donated their time, assisted with references, files, publications, useful information, recommendations and comments. My sincere gratitude goes to R. J.

Fernandez-Prini (Argentina), T. A. Akhundov, N. D. Azizov, N. V. Lobkova, D. T. Safarov (Azerbaijan), P. Tremaine (Canada), I. Cibulka (Czech Republic), K. Ballerat-Busserolles, R. Cohen-Adad, (France), J. Barthel, E. U. Franck, H. Lentz, K. Todheide, G. M. Schneider, H. Voigt, W. Voigt, G. Wiegand (Germany), Th. W. de Loos, C. J. Peters (Netherlands), A. M. Aksyuk, A. A. Aleksandrov, I. L. Khodakovsky, S. V. Makaev, S. D. Malinin, O. I. Martinova, A. A. Migdisov, A.Yu Namiot, T. I. Petrova, L. V. Puchkov, K. I. Schmulovich, A. A. Slobodov, N. A. Smirnova, N. G. Sretenskaya, M. A. Urusova, A. S. Viktorov, I. V. Zakirov, V. I. Zarembo, A. V. Zotov (Russia), L. Z. Boshkov (Ukraine), R. B. Dooley, A. H. Harvey, P. C. Ho, W. L. Marshall, R. E. Mesmer, A. V. Plyasunov, J. M. Simonson, R. H. Wood (USA). Finally, I also would like to express my thanks to my wife Luba and daughters Aliona and Katya for their constant support and understanding. Vladimir M.Valyashko Moscow

1

Phase Equilibria in Binary and Ternary Hydrothermal Systems Vladimir M. Valyashko Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow, Russia

1.1 INTRODUCTION Defining the phase composition of the mixture at a certain pressure and temperature is the first step in any scientific investigation and obligatory information for any practical application of that mixture. If the physical state of aqueous or any other systems at ambient conditions can easily be determined, the phase composition of the systems at high temperatures and pressures should be specially studied using fairly complex equipment. Systematic scientific studies of influence of temperature and pressure on a phase state of individual compounds and mixtures were begun in the eighteenth century (D. Fahrenheit, R. Reaumur, A. Celsius, M.V. Lomonosov, A. Lavoisier, D. Dalton, W. Henry). However, the variety and complexity of phase behavior at superambient conditions in early experiments, even in two-component systems, seemed, at first, chaotic. The discovery of the phase rule by Gibbs in 1875 and the investigations of van der Waals and his school on the equation of state and the thermodynamics of mixture, lasting until about 1915, brought a measure of order by providing a framework for the interpretation and classification of phase diagrams and led to a period of intense experimental studies. These pioneer publications at the end of the nineteenth and beginning of the twentieth centuries laid a foundation for the modern theory of heterogeneous equilibria and phase diagrams. During the first half of the last century interest in high-temperature highpressure equilibria was quite limited and concentrated mainly around certain aspects of power engineering and geological problems. As a result progress was not comparable with the previous fifty years; moreover knowledge accumulated earlier gradually disappeared from the literature of physics and chemistry. The most famous discovery of that time was the experimental observation of gas–gas equilibria by I.R. Krichevskii in N2 – NH3, CH4 – NH3, He2 – CO2, He2 – NH3 and in Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-09465-5

Ar – NH3 mixtures (Krichevskii and Bol’shakov, 1941; Krichevskii, 1952; Tsiklis, 1969), that confirmed theoretical prediction of Van der Waals (Van der Waals and Kohnstamm, 1927). It was shown that a separation of supercritical fluids can exist in the temperature range above the highest critical temperature of the less volatile component. Another important result obtained in the last century was also connected with the critical phenomena. In 1926 Kohnstamm (Kohnstamm, 1926) pointed out the theoretical possibility of finding a critical point ‘of second order’ in a ternary liquid mixture – a point at which three coexisting fluid phases simultaneously become identical. In 1962–70 this point was confirmed experimentally in two Russian aboratories (of Prof. I.R. Krichevskii and Prof. R.V. Mertslin) (Radyshevskaya et al., 1962; Krichevskii et al., 1963; Myasnikova et al., 1969; Efremova and Shvarts, 1966, 1969, 1972; Shvarts and Efremova, 1970; Nikurashina et al., 1971). In the 1970s such a type of phase transition, called ‘a tricritical point’, was theoretically interpreted within a framework of ‘classical’ and ‘non-classical’ phenomenological models (Griffiths, 1970; Widom, 1973; Griffiths and Widom, 1973; Griffiths, 1974; Kaufman and Griffiths, 1982; Anisimov, 1987/1991). At the same time, it was thought that the sets of phase equilibria in water-salt (electrolyte) systems were different from those in water-organic, water-gas and organic systems due to a special nature of ion-molecular interactions in aqueous electrolyte solutions. In particular, the phase diagram with the two critical endpoints in solid saturated solutions was known for a long time only for systems with the molecular species (without ions) such as ether (C4H10O) – anthraquinone (C14H8O2), CO2 – diphenylamine ((C6H5)2NH) and ethylene (C2H4)) – p-chloroaniline (oxylidin (C8H11N), o-nitrophenol (C6H5NO3), m-chloronitrobenzene (C6H4ClNO2)) (Smits, 1905, 1911; Buechner, 1906, 1918; Scheffer and Smittenberg, 1933). However, the first experimental studies of H2O – SiO2, H2O – Na2SO4, H2O – Li2SO3 and H2O – Na2CO3 systems

2


(Kennedy et al., 1961, 1962; Ravich and Borovaya, 1964a,b,c) proved that the same phase equilibria can be observed also in water–electrolyte mixtures. A revival of interest in hydrothermal phase behavior occurred in the middle and second half of the last century, sparked by the growth of chemical engineering technology (hydrothermal crystal growth, hydrometallurgy, natural gas and petroleum industry, supercritical fluid extraction and material synthesis, supercritical water oxidation for hazardous waste destruction) and of fossil and nuclear power engineering. The main volume of experimental data for aqueous systems at high temperatures and pressures now available was obtained during the past 50–60 years, whereas the most precise measurements of hydrothermal solution properties became possible only from the 1980s onwards (Wood, 1989). Van der Waals and his school developed the ‘classical approach’ to phase diagram derivation, in which phase behavior of mixtures was established by investigation of the behavior of thermodynamic functions (free energy) in p-VT-x space, calculated with the equation of state. Originally, theoretical derivations of phase diagrams were done by a topological method. After the main features of a geometry of thermodynamic surfaces (p-V-T-x dependences of Helmholtz or Gibbs free energy) were obtained from limited calculations available at that time using the equation of state. The following continuous transformations and combinations of the geometrical features of the surfaces were determined topologically as well as a derivation of topological schemes of phase diagrams from the interplay of the thermodynamic surfaces. As a result of such investigations it was established that there is a limited number of various types of fluid phase diagram for binary systems. A topological approach and knowledge of the regularities of phase behavior and intersections of thermodynamic surfaces for various phases (included the solid phase) permitted derivation of not only several types of fluid phase diagrams but also of the schemes of phase diagrams with solid phase (Roozeboom, 1899, 1904; Tammann, 1924; Van der Waals and Kohnstamm, 1927). In contrast to the term ‘fluid phase diagrams’, which means the phase diagrams, which describe the phase behavior of mixture without solid phase, the term ‘complete phase diagrams’ is for the diagrams which display any equilibria between liquid, gas and/or solid phases in a wide range of temperature and pressure. Since the first publication of Scott and van Konynenburg in 1970 on global phase behavior of binary fluid mixtures based on the Van der Waals equation of state, the classical approach to the derivation of phase diagrams has changed from topological method to analytical method. The analytical method of derivation for various liquid-gas equations of state shows the same main types of fluid phase behavior for different kind of molecular interactions and the same sequences of transformation of one type of binary phase diagram into another due to continuous alteration of molecular parameters in the equations of state (Scott and van Konynenburg, 1970; Boshkov, 1987; Deiters and Pegg 1989; van Pelt et al., 1991; Harvey, 1991; Kraska and Deiters, 1992; Yelash and Kraska, 1998, 1999a,b; Thiery et al., 1998;

Yelash et al., 1999; Kolafa et al., 1999). Most of the types of fluid phase behavior described by Van der Waals and his school as well as by recent experimentalists can be recognized in analytically derived global phase diagrams. Those diagrams describe (in the coordinates of molecular parameters of each model) the regions of different types of fluid phase diagrams generated from the equations of state. Due to the absence of a general liquid-gas-solid equation of state such analytical method would not work for derivation of phase equilibria with solid phases. To do so either simultaneous investigation of two equations of state (for liquid-gas and for solid phases) should be considered or the usage of the topological method at the level of topological schemes of phase diagram rather than at the level of thermodynamic surfaces. Modern knowledge of phase diagrams construction allows us to classify the main types of diagrams and to define a few regularities of transformation of one type of phase diagram into another. This chapter reviews general characteristics of phase behavior in sub- and supercritical binary and ternary aqueous systems obtained in theoretical and experimental studies. It starts with a brief presentation of the main experimental methods employed to study the hydrothermal phase equilibria. The major body of the chapter provides an overview of recent developments in our understanding of binary and ternary phase diagram construction based on modern theoretical approaches to phase diagram derivation and on the available experimental data. In case of binary system special attention is drawn to the method of continuous topological transformation of phase diagrams and to a demonstration of systematic classification of complete phase diagrams, which describe all possible types of phase behavior in a wide range of parameters. The main types of binary phase diagrams are represented by topological schemes illustrated by experimental results. Methods of topological schemes for fluid and complete phase diagrams derivation and main features of phase behavior at sub- and supercritical conditions for ternary systems are discussed later in the chapter. The available experimental data are used to demonstrate some regularity of solid solubility, liquid immiscibility and critical behavior in ternary mixtures. The original experimental data on phase equilibria (solubility of solid in fluid phases, heterogeneous fluids, liquidgas (vapor) equilibria, immiscibility of liquids and critical phenomena) at elevated temperatures (mainly above 200 °C) and pressures are presented in Appendix 1.1. The values were extracted from the papers in national and international journals, monographs and collected articles, as well as from the deposited materials, reports and dissertations. For literature search, besides the Chemical Abstracts Data Base, the database system ELDAR (Prof. J. Barthel, Institute for Physical and Theoretical Chemistry, the Regensburg University, Germany) (Barthel and Popp, 1991) and the databank for water-organic systems (Prof. N.I. Smirnova, Prof. A.I. Viktorov, Department of Physical Chemistry, the St Petersburg University, Russia), the following reference books were used (Seidell, 1940, 1941; Seidell and Linke,

Phase Equilibria in Binary and Ternary Hydrothermal Systems 3

1952; Pel’sh et al., 1953–2004; Linke and Seidell, 1958; Timmermans, 1960; Kogan et al., 1961–63, 1969, 1970; Kirgintsev et al., 1972; Valyashko et al., 1984; Buksha and Shestakov, 1997; Harvey and Bellows, 1997). However, the main volume of bibliography were obtained from references in ordinary papers and reviews. This information, arranged in alphabetical order of nonaqueous components is presented in the Summary table (Table 1.1). Each line of the Summary table contains brief information (types of studied phase equilibria, experimental methods, ranges of studied temperature, pressure and composition) about the experimental data obtained for one system or several relevant systems from the publication(s) and collected in Appendix 1.1. 1.2 EXPERIMENTAL METHODS FOR STUDYING HYDROTHERMAL PHASE EQUILIBRIA Over the years different experimental techniques at high parameters of state were implied to study phase behaviors (Tsiklis, 1968, 1976; Laudise, 1970; Ulmer, 1971; Jones and Staehle, 1976; Styrikovich and Reznikov, 1977; Isaacs, 1981; Garmenitskiy and Kotelnikov, 1984; Zharikov et al., 1985; Sherman and Tadtmuller, 1987; Ulmer and Barnes, 1987; Byrappa and Yoshimura, 2001; Hefter and Tomkins, 2003). The purpose of this review is to summarize existing experimental methods for studing phase equilibria in aqueous systems over a wide range of p-T-x parameters, to describe briefly major features of experimental procedures, and to provide examples of the method related apparatus along with their advantages and limitations. Experimental methods could be considered as either ‘synthetic’ and ‘analytic’ or static and dynamic (flow) methods. In the ‘synthetic’ methods the phase transitions are studied and the p-T parameters of phase transformations are recorded, whereas the compositions of the coexistent phases are determined from the composition of initial mixture charged into the cell. The ‘analytic’ methods determine compositions of equilibrium phases directly at given temperature and pressure, ignoring the study of phase transitions. The dynamic (flow) methods are distinguished from the static ones by the fact that at least one of the phases in the system is subjected to a flow with respect to the other phase. In our attempt to classify the available experimental methods for studying the hydrothermal equilibria there are five groups that differ in the technique of obtaining information on phase equilibria and on coexisting phase compositions at high temperatures and pressures. These groups comprise: 1. methods of visual observation of phase equilibria (‘Vis. obs.’ in Table 1.1); 2. methods of solution sampling under experimental conditions (‘Sampl’, ‘Flw.Sampl’ and ‘Isopiest’ in Table 1.1); 3. methods of quenching of high temperature phase equilibria (‘Quench’ in Table 1.1) and of weight loss of crystal (‘Wt-loss’ in Table 1.1); 4. method using potentiometric determination (‘Potentio’ in Table 1.1) for salt solubility measurements;

5. indirect methods – determination of discontinuities (‘break points’) in the property-parameter curves; description of the behavior of interdependent parameters and/or properties of the system during the phase transformation (methods of p-T, p-V, p-x, T-V, T-Cv, p-∆H curves, ‘Therm.anal.’ and VTFD in Table 1.1). The sixth group ‘Methods using radioactive tracers’ (‘Rad. tr’ in Table 1.1) could be added to the list. However, those methods are used rarely in hydrothermal investigations due to the environmental risk, technical problems and moderate accuracy of solubility measurements. Only in the publication of Alekhin and Vakulenko (1987) there is a description of an apparatus for continuous determination of the hydrothermal fluid composition and salt solubility in vapor by measuring the intensity of radiation of aqueous solution without sampling or quenching. There are several cases of tentative experiments on solubility measurements of sulfides (Ag2S, SnS and ZnS) at elevated temperatures (below 200 °C) (Olshanski et al., 1959; Nekrasov et al., 1982) and in temperature gradient conditions (Relly, 1959). In some cases the radioactive tracers are used only to determine the concentration of samples obtained by the method of sampling or quenching (Ampelogova et al., 1989). The experimental studies of isotope partitioning in hydrothermal systems (e.g. Shmulovich et al., 1999; Driesner and Seward, 2000; Chacko et al., 2001; Horita and Cole, 2004 etc.) are relevant to isotope chemistry in aqueous reactions but do not pursue the goal of phase equilibria determination and will be not discussed in this chapter. Certainly, this classification is largely arbitrary and not exhaustive because in reality experimental methods are highly diversified and often contain the combinations of various techniques in one run. For instance, the measurements using the visual cell with a movable piston (for changing the inner volume of the vessel and for separation of the studied mixture from the pressure medium) (see Figure 1.1) permit us to observe the phase transformation, to determine the break points (corresponding to the phase transition) on the pressure versus temperature isochore or on the pressure versus volume isotherm for the known composition and to sample the equilibrium phases at predetermined temperatures and pressures (Lentz, 1969 etc.). The apparatus, described by Khaibullin and Borisov (1965, 1966), permits us to determine both the density and composition of coexisting liquid and vapor solutions (at temperatures up to 450 °C and pressures up to 40 MPa) by measuring intensity of the g-ray beams (pass through the bomb on different levels from the outside radioactive sources) (‘g-ray’ in Table 1.1) and by sampling the equilibrium phases. Besides methods which involve determination of phase compositions of equilibrium associations, other approaches to phase equilibria studies are possible. An example is the special method for determining the vapor pressure of solutions with a given composition (‘Vap.pr.’ and ‘Vap.pr.diff’ in Table 1.1). In such apparatus the composition is not measured but taken from the initial charge, whereas the vapor pressure is measured directly with a pressure gage (Mashovets et al., 1973; Bhatnagar and Campbell, 1982;

Summary of experimental data on phase equilibria in hydrothermal systems

H-Fl

CH4 (Methane) Sampl

Methods 298/473; 518 K

Temperature 1.3/3.2; 6.5 MPa

Pressure −4

2.1 * 10 /4.1 * 10 –0.49/0.998 (CH4) mol.fr.

−4

Composition

ptx-CH4-7.1

Tables

Crovetto et al., 1982

REFERENCE

Methods: Sampl – the method of fluid phase sampling is used for determination of solution composition (static apparatus); Flw.Sampl – the method of flow-sampling is used for determination of solution composition (Flow-apparatus); Fl.inclus – the method of fluid inclusions is used for phase equilibria studies in hydrothermal conditions, sometimes for determination not only the types of phase equilibria, but the composition of phases at high temperatures also; Isopiest – the method of isopiestic measurements is used for determination of the isopiestic molality (molality at a known activity of water in aqueous solutions); Quench – the method of quenching is used to fix the high-temperature equilibria by a fast cooling and to determine both the hydrothermal equilibria and the composition of high-temperature phases; Wt-loss – the method of weight-loss of crystalls is used for measurements of solid solubility; Vis.obs. – the method of visual observations is used for determination of phase equilibria at elevated temperatures and pressures, sometimes – for determination the composition of phases; p-T, p-V, p-x, T-V, T-Cv, p-DH curves – the methods of p-V-T-x-Cv-∆H curves are used for determination the parameters of phase transformations in hydrothermal conditions; Vap.pr. – the method of direct measurements of equilibrium vapor pressure; Vap.pr.diff. – the measurements of vapor pressure difference between the vapor pressures of pure water and solutions; Therm.anal. – the method of high-pressure thermal analysis (Diff. thermal analysis); VTFD – the method for determination of hydrothermal phase transition (an appearance/disapprearance of liquid-gas equilibrium) using the vibration tube flow densimeter masurments; Potentio – the potentiometric measurements for studies of solubility equilibria; Calcul. – the methods of calculation/estimation; g-ray – determination of concentration and density of hydrothermal solution by the method of g-ray adsorption measurements; Rad.tr – method using radioactive tracers for phase equilibria studies.

Types of phase equilibria: Soly – solid solubility equilibria, heterogeneous equilibria with solid phase(s). LGE – in the most cases it is liquid-gas equilibrium, but could be another heterogeneous equilibria with gas phase, where the vapour pressure is measured (for example, in the case of equilibrium L-G-S) or used for measurements (such as in the isopiestic molality measurements (LGE; isop-m)). H-Fl – indiscernible heterogeneous sub- and supercritical fluid equilibria. In the most cases it is two-phase fluid equilibria such as LGE, L1-L2 and G1-G2, which continuously transform one into another with a small variation of pTx- parameters. Sometimes it is the more complex fluid equilibria (especially, in ternary system). Immisc – immiscibility equilibria such as L1-L2; L1-L2-G; L1-L2-S etc. Cr.ph-critical phenomena

For example, the line means – the publication [Crovetto et al., 1982] contains the experimental data for H2O – CH4 system on heterogeneous fluids (H-Fl ) obtained by the method of fluid phase sampling (Sampl) at temperatures from 298 up to 518 K and pressures from 1.3 up to 6.5 MPa. However, the table ptx-CH4-7.1 (in the Appendix) contains only data at 473 and 518 K, 3.3 and 6.5 MPa. The composition of studied phases is varied from 0.00021 to 0.998 mol.fr. of CH4, whereas the variation of CH4 concentration in high-temperature phases shown in the Appendix’s table are 0.00041–0.49 mol.fr. Sometimes the box ‘Composition’ shows a composition of equilibrium phases (as in the example), in other cases it could be the chemical compositions of initial mixtures used for phase equilibria studies or the phase composition of studied equilibria. The contractions for types of phase equilibria and the experimental methods are shown below. SVP is a saturation vapor pressure. ‘??’ indicates that the information is absent or the symbol accompanied by ‘??’ is questionable.

Phase equilibria

Non-aqueous components

COMMENTS: Each line contains a breaf information about the experimental data obtained for one system or several relevant systems from the publication(s) and in the table(s) collected in the Appendix. This information includes the name of aqueous system (only the non-aqueous component(s) is(are) shown in the 1st column), the studied types of phase equilibria – Phase equilibria (2nd column), the experimental methods employed for studies – Methods (3rd column), the ranges of studied temperature – Temperature (4th column), pressure – Pressure (5th column), and composition – Composition (6th column). The numbers of tables with hydrothermal experimental data, located in the Appendix (Tables), and the literature sources of that data (Reference) are indicated in the 7th and 8th columns, respectively. Although the tables in the Appendix contain only high-temperature data (usually starting from 200 °C and above), an information about the low-temperature data available from the publications is indicated in the Summary table. The oblique (/) indicates and separates the low-temperature and high-temperature values of properties or parameters represented in Table 1.1.

Table 1.1

4 Hydrothermal Experimental Data

Wt-loss; Quench Quench

Wt-loss; Sampl

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Ag + buff.

Ag in CH2O (formaldehyde)

Ag in (HCl + H2)

Ag in (HCl + KCl + H2)

Ag in (HCl + NaCl + H2)

Ag in (HCl + NaCl)

(Ag + AgCl) in (HCl + buff) (Ag/Au + AgCl) in (HCl + NaCl)

Soly

Soly

AgBr; AgBr in NaBr

Wt-loss; Sampl

Wt-loss

Soly

(Ag + Cu) in (HCl + NaCl) (Ag/Pd + AgCl) in (HCl + NaCl) AgBr

Soly

Wt-loss; Sampl Wt-loss; Sampl Wt-loss

Soly

(Ag + Cu) in HCl

Sampl

Soly

AgxAuySz


Quench

Quench

Quench

3

2

1

Methods

Phase equil


200; 300 C

20/269–349 C

300 C

40/200–300 C

40/200–300 C

91/150; 250 C

300 C

450–800 C

350–500 C

200 C

450 C

200; 280 C

200 C

300; 450 C

4

Temperature

SVP

SVP

SVP

SVP

SVP

SVP

SVP

1; 2 kbar

500–2500 bar

SVP

500; 1000 bar

SVP

SVP

SVP; 500 atm

5

Pressure

−6

3.9–1.5 (AgBr) (−log m); 0–1 m NaBr

ptx-AgBr + NaBr-1.1

ptx-Ag + Cu + HCl-1.1 ptx-Ag + Cu + HCl + NaCl-1.1 ptx-Ag/Pd + AgCl-1.1 ptx-AgBr-1.1

ptx- AgxAuySz-1.1

(2–6)*10−5 (Au); (2–6)*10−7(Ag); 0.5 (S); 0.002 (NaOH) m 5.8–3.54 (Ag); 2.8–0.72 (Cu) (−log m); 0.004–1.0 (HCl) m 5.92–4.12 (Ag); 2.56–1.01 (Cu) (−log m)]; 0.001–0.1 (HCl); 0.01–0.9 (NaCl) m 1.58–0.4 (Ag); 5.7–3.4 (Pd) (−log m); 0.1; 1 (HCl); 0.1–3 (NaCl) m 44.7 * 10−7/0.007–0.013 (AgBr) m

1.92–0.4 (Ag); 5.8–1.8 (Au) (−log m); 0.01–3 (HCl); 0–3 (NaCl) m

ptx-Ag + HCl + NaCl-2.1 ptx-Ag + AgCl + HCl-1.1 ptx-Ag/Au + AgCl-1.1

ptx-Ag + HCl + KCl-1.1 ptx-Ag + HCl + NaCl-1.1

Gammons et al., 1993 Gavrish and Galinker, 1955 Gammons and Yu, 1997

Xiao et al., 1998

Xiao et al., 1998

Chou and Frantz, 1977 Gammons and Williams-Jones, 1995 Tagirov et al., 2006

Kozlov and Khodakovskiy, 1983 Tagirov et al., 1997

Kozlov and Khodakovskiy, 1983 Kozlov and Khodakovskiy, 1983 Tagirov et al., 1997

ptx-Ag + CH2O-1.1 ptx-Ag + HCl-1.1

Zotov et al., 1985a

8

7 ptx-Ag-1.1

REFERENCE

Table

0.0013–0.0246 (Ag); 0.02–0.25 (HCl); 0.2–1 (NaCl) m 0; 3 (HCl) mol/L; Buff: Fe2O3/Fe3O4; Ni/NiO

(5.6–50) * 10−5 (Ag) 0.016–0.056 (HCl); 0.064–0.09 (NaCl) m

0.004–0.019 (Ag); 0.1 (HCl); 0.2 (KCl) m

(1.2–52) * 10−5 (Ag); 0.0001–0.1 (HCl) m

(0.5–2) * 10 (Ag) m; Buff: Fe2O3/Fe3O4; Ni/NiO; Al. (2.7–4.1) * 10−5 (Ag); 0.34–0.5 (CH2O) m

6

Composition

Units: Temperature: C – grad. Celsium (°C); K – Kelvin Pressure: MPa – mega-pascales (106 * Pa); GPa – giga-pascales (109 * Pa); Kbar – kilo-bars (103 bar); bar; kg/cm2; atm; mm of Hg; 1 MPa = 10 bar = 10.197 kg/cm2 = 9.87 atm = 7502.4 mm Hg Concentration: Basic quantities used in definitions of concentration in aqueous solution are based on mass, chemical amount of substance and/or volume and are designed by the traditional symbols such as m - molality (moles of solute per kilogram of solvent (H2O); 1 m = 103 mm = 106 mm; (- log m) is a negative decimal logarithm of molality, mol/L - molarity (moles of solute per a liter of solution usually at room temperature), mass.% or mol.% - mass or mole per cent, mol.fr., mass.fr. or vol.fr. - mole, mass or volume fraction, ppm or ppb - parts per million or parts per billion, or by the complex symbols, such as g/100g H2O; mmol/kg; mg/mL; cm3/100cm3H2O etc, which are the proper fractions where the numerator indicates the number of units of solute and the denominator shows the number of units (usually one unit) of solution (or of solvent, if it is indicated). A designation of the units - g (gram), mol (mole), L (liter), cm (centimeter) and the decimal prefix - m (micro, 10−6), m (milli, 10−3), c (centi, 10−2), k (kilo, 103), M (mega, 106), G (giga, 109)


Sampl

Sampl

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

AgCl

AgCl AgCl

AgCl

AgCl in HCl

AgCl in (HCl + NaCl + NdCl3) AgCl in (HCl + Nd2O3)

AgCl in (HCl + ZnCl2)

AgCl in KCl

AgCl in KCl

AgCl in NaCl

AgCl in NaCl

AgCl in NaCl

AgCl in NaCl

AgCl in NaCl

Quench

Soly

Soly

Soly

Soly

Ag2CrO4

AgF

Sampl

Sampl


Soly

AgCl in (NaCl + NaClO4) AgCl in (NaCl + NaClO4) AgCl in (NaCl + NaClO4 + NaOH) AgCl in NaClO4

Wt-loss; Quench Wt-loss; Quench Wt-loss; Quench Quench

Quench

Wt-loss; Quench Wt-loss; Quench Sampl

Sampl

Sampl

Quench Wt-loss; Quench Sampl

Wt-loss

3

2

1

Methods

Phase equil

Continued


Table 1.1

22/200; 250 C

25/195–260 C

250; 300 C

200–300 C

250 C

200; 250 C

400; 425 C

450 C

300 C

300 C

100/197–353 C

450 C

300 C

100/200–350 C

40/200–300 C

200; 300 C

100/200–350 C

300–360 C

250; 300 C 450 C

20/220–359 C

4

Temperature

SVP

SVP

SVP

SVP

SVP

SVP

500–1500 bar

500–1750 bar

SVP

SVP

SVP

500; 1000 bar

SVP

SVP

SVP

SVP

SVP

41–183 bar

SVP 500–1500 bar

SVP

5

Pressure

176/143; 97.4 (AgF) g/100 g H2O

0.0036/0.08–0.12 (Ag2CrO4) g/100 g H2O

0.0038–0.028 (AgCl); 0.2; 0.5 (NaCl); 0–1 (NaClO4) m 0.01–0.03 (Ag); 0.2; 0.5 (NaCl); 0–1 (NaClO4) m 0.0038–0.093 (AgCl); 0.2; 0.5 (NaCl); 0–0.3 (NaClO4); 0–0.3 (NaOH) m 0.0026–0.0054 (AgCl); 0.01–1 (NaClO4) m

0.08–0.17 (AgCl); 0.2; 0.5 (NaCl) m

0.04–1.05 (Ag); 0.09–2.56 (NaCl) m

0.005–0.86 (Ag); 0.025–7 (NaCl) m

2.2 * 10−5/5.3 * 10−4–0.256 (AgCl); 5 * 10−5–3 (NaCl) m 0.0021–0.334 (AgCl); 0.0001–3 (NaCl) m

ptx-AgF-1.1

ptx-AgCl + HCl-1.1 ptx-AgCl + H,Na,Nd/Cl-1.1 ptx-AgCl + HCl + Nd2O3-1.1 ptx-AgCl + HCl + ZnCl2-1.1 ptx-AgCl + KCl-1.1 ptx-AgCl + KCl-2.1 ptx-AgCl + NaCl-1.1 ptx-AgCl + NaCl-2.1 ptx-AgCl + NaCl-3.1 ptx-AgCl + NaCl-4.1 ptx-AgCl + NaCl-5.1 ptx-AgCl + NaCl + NaClO4-1.1 ptx-AgCl + NaCl + NaClO4-2.1 ptx-AgCl + Na/Cl,ClO4,OH-1.1 ptx-AgCl + NaClO4-1.1 ptx-Ag2CrO4-1.1

0.03 * 10−4/0.0007–0.125 (AgCl); 6.4 * 10−5–3.5 (HCl) m 2.69–0.86 (Ag) (−log m); 0.03–1 (HCl + NaCl); 0–0.24 (NdCl3) m 4.63/3.68–1 (Ag) (−log m); 0.03–5 (HCl); 0–1.16 (NdO1.5) m 2.4 * 10−4/0.00263–0.099 (AgCl); 0.29–3.54 (HCl); 0.1 (ZnCl2) m 0.0051–1.35 (Ag); 0.025–6 (KCl) m 0.041–0.22 (Ag); 0.46; 0.9 (KCl) m

ptx-AgCl-4.1; 4.2

9.82–7.9 (AgCl) (−log mol.fr.)

ptx-AgCl-2.1 ptx-AgCl-3.1

ptx-AgCl-1.1

10.8 * 10−5/0.013–0.059 (AgCl) m 0.0025–0.0029 (AgCl) m 0.008–0.05 (Ag) m

8

7

6

Gavrish and Galinker, 1970 Gavrish and Galinker, 1970

Zotov et al., 1985

Zotov et al., 1982

Levin, 1991

Zotov et al., 1986

Tagirov 1997

Levin, 1993

Levin, 1991

Zotov et al., 1986

Seward, 1976

Levin, 1993

Migdisov et al., 1999 Ruaya and Seward, 1987 Gammons et al., 1995 Gammons et al., 1995 Ruaya and Seward, 1986 Levin, 1991

Gavrish and Galinker, 1955 Zotov et al., 1985c Levin, 1993

REFERENCE

Table

Composition


Sampl

Sampl

Soly

Soly

Soly LGE

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

AgI

AgI in NaI

AgNO3 AgNO3

Ag2O

Ag2S in (NaOH + H2S)

Ag2S in (NaOH + H2S)

Ag2S in (NaOH + S)

Ag2SO4 in D2SO4

Ag2SO4 in H2SO4

Ag2SO4 in UO2SO4

Ag2SO4 in UO2SO4

AlOOH (boehmite) + Buff AlOOH (boehmite) in (C2H4O2 + C2H3O2Na)

Sampl

Sampl

Quench

Sampl

Sampl

Sampl

Soly

Soly

Soly

Soly

Soly

Soly

AlOOH (boehmite) in (HCl + NaCl)

AlOOH (boehmite) in (HCl + SiO2) AlOOH (boehmite) in HClO4 AlOOH (boehmite) in (NH3/NH4Cl + SiO2)

AlOOH (boehmite) in (NH4OH + NH4Cl)

AlOOH (boehmite) in (NH4OH + NH4Cl)

Vis.obs.

Vis.obs.

Vis.obs.

Vis.obs.

Flw.Sampl

Sampl

Sampl

Sampl

Sampl; Wt-loss Vis.obs. Vap.pr.

Wt-loss

3

2

1

Methods

Phase equil


150/200–350 C

70/200 C

150/200; 250 C 300 C

300 C

90/200–350 C

25/175; 200 C 150/200; 250 C 170; 200 C

25/200; 250 C 36/197–259 C

25/195–234 C

25/200–400 C

25/200; 250 C 18/199–302 C

25/200–260 C

150/200; 250 C 112/173–198 C 152/219 C

20/300–365 C

4

Temperature

SVP

SVP??

SVP (86 bar)

SVP

SVP (86 bar)

SVP

SVP

100 bar

SVP

SVP

SVP

SVP

1/40–500 bar

1.3/18.7–121 bar

SVP

SVP SVP (2.53/3.3–21.2 bar) SVP

SVP

SVP

5

Pressure

3.02/2.98–2.13 (AlOOH) (−log m); 0.0034–0.28 (NH4OH); 0.01 (NH4Cl) m

5.25–4.60 (AlOOH) (−log m); (pH21 = 9.44–10.14)

6.8/6.54–4.96/3.56 (AlOOH) (−log m); (1.05/1.35–105) * 10−4 (HCl); 0–0.01/0.025 (NaCl) m 6.65–4.26 (Al); 3.19–2.33 (Si) (−log m); 0.00074–0.038 (HCl) m (0.01–6/183) * 10−4 (AlOOH); 3.1 * 10−6–0.1 (HClO4) m 5.9–4.26 (Al); 3.37–1.97 (Si) (−log m); 0.005–16.5 (NH3) m

0.018/0.023–470/933 (AlOOH) mg/kg; Buffer soln. (pH25 = 1.17–9.44) 6.37–6.09 (AlOOH) (−log m); 0.01–0.02 (C2H4O2); 0.01 (C2H3O2Na) m

1.04/12.8–17.3 (Ag2SO4) mass.%; 0.13/1.35 (UO2SO4) m 0.22–0.73 (Ag2SO4); 0.1/0.41–1.35 UO2SO4 m

0.1/0.2–2140 (Ag) ppm; 0–4.1 (NaOH) m; 0.8–54.3 atm PH2S 0.28/2.6–331.5 (Ag) ppm; 0.05–1.64 (NaOH); 0.46–5.39 (H2S) mol.% (0.01/0.02–8.5) * 10−5 (Ag); 0–0.4 (NaOH); 0.014–0.12/0.18 (S) m 0.02/0.029–0.67 (AgSO4); 0–1 D2SO4 mol/kg D2O 0.02/0.12–0.68 (AgSO4); 0.1–1 H2SO4 m

0.0022/0.063–0.022 (Ag2O) g/100 g H2O

91.6/98–99.4 (AgNO3) mass.% 8.4–89.6 (AgNO3) mol.%

ptx-Ag2S + NaOH + H2S-1.1 ptx-Ag2S + NaOH + H2S-2.1 ptx-Ag2S + NaOH + S-1.1 ptx-Ag2SO4 + D2SO4-1.1 ptx-Ag2SO4 + H2SO4-1.1 ptx-Ag2SO4 + UO2SO4-1.1 ptx-Ag2SO4 + UO2SO4-2.1 ptx-AlOOH + Buff-1.1; 1.2 ptx-AlOOH + C2H4O2 + C2H3O2Na-1.1 ptx-AlOOH + HCl + NaCl-1.1 ptx-AlOOH + HCl + SiO2-1.1 ptx-AlOOH + HClO4-1.1 ptx-AlOOH + NH3/NH4Cl + SiO2-1.1 ptx-AlOOH + NH4OH + NH4Cl-1.1 ptx-AlOOH + NH4OH + NH4Cl-2.1

ptx-Ag2O-1.1

ptx-AgNO3-1.1 ptx-AgNO3-2.1

ptx-AgI + NaI-1.1

ptx-AgI-1.1

1.4 * 10−6/0.0008–0.0029 (AgI) m 5.6/4.2–1.2 (AgI) (−log m); 0.001–0.89 (NaI) m

8

7

6

Castet et al., 1993

Verdes et al., 1992

Kuyunko et al., 1983 Salvi et al., 1998

Salvi et al., 1998

Castetet al., 1993

Lietzke and Stoughton, 1960 Bourcier et al., 1993 Castet et al., 1993

Gammons and Barnes, 1989 Stefansson and Seward, 2003a Lietzke and Stoughton, 1963 Lietzke and Stoughton, 1956 Jones et al., 1957

Gavrish and Galinker, 1955 Gammons and Yu, 1997 Benrath et al., 1937 Geerlings and Richter, 1997 Gavrish and Galinker, 1970 Sugaki et al., 1987

REFERENCE

Table

Composition


Potentio; Sampl

Sampl

Sampl

Sampl

Soly

Soly

Soly

Soly

Soly

AlOOH (boehmite) in (NaCl + HCl/NaOH)

AlOOH (boehmite) in (NaCl + HCl/NaOH)

AlOOH (boehmite) in NaOH AlOOH (boehmite) in NaOH AlOOH (boehmite) in (NaOH + NaCl)

Sampl

Wt-loss; Quench Sampl

Soly

Soly

AlO2H (diaspore) in NaOH AlO2H (diaspore) in NaOH AlO2H (diaspore) in (NaOH + NaCl)

Soly Soly

Soly

Soly

Soly Soly

Soly

Soly Soly

Al2O3 (corundum) Al2O3 (corundum)

Al2O3 (corundum)

Al2O3 (corundum)

Al2O3 (corundum) Al2O3 (corundum)

Al2O3(corundum)

Al2O3 (corundum) Al2O3 (corundum) in AlCl3

Sampl Quench

Wt-loss

Wt-loss Sampl

Wt-loss

Wt-loss

Quench Wt-loss

Sampl

Soly

AlOOH (boehmite) in (NaOH + SiO2)

Soly

Sampl

Soly

AlOOH (boehmite) in (NaOH + NaCl)

Potentio; Sampl

3

2

1

Methods

Phase equil


Table 1.1 Continued

272–600 C 600 C

700–1100 C

666–700 C 400–720 C

350–500 C

500–800 C

380–420 C 700–900 C

135/200–300 C

523–598 K

250; 300 C

300 C

170/200–350 C

135/200–300 C

200; 250 C

250; 300 C

101.5/203–290 C

100/203–290 C

4

Temperature

500–2480 bar 2 kbar

500–2000 MPa

3.005–4.994 (Al) (−log m) 2.4 (Al2O3) (−log mol/L); 0.1; 1 (AlCl3) mol/L

(−3.4)-(−1.56) (Al) (log m)

2.7–139.4 (Al2O3) ppm 1.0–4.2 (Al) ppm

0.008–0.19 (Al2O3) g/L

200–2000 kg/cm2 2.5–20 kbar 730–3120 kbar

0.0008–0.0059 (Al2O3) mass.%

0.00006–0.0009 (Al2O3) m 0.043–0.105 (Al2O3) mass.%

0.08–4.34 (AlO2) equiv/L; 4.9–150.7 (Na2O) g/L 3.28/2.89–2.22 (AlO2H) (−log m); 0.005; 0.01 (NaOH); 0/0.01–0.02 (NaCl) m

8.3–33.7 (Al2O3); 6.4–22.9 (Na2O) mass.%

2.44 (Al); 3.24 (Si) (−log m); 0.004 (NaOH) m

3.02/2.98–2.13 (AlOOH) (−log m); 0.0025–0.009 (NaOH); 0.001–0.0075 (NaCl) m

3.71/3.45–2.08 (AlOOH) (−log m); 0.001–0.01 (NaOH); 0.002–0.05 (NaCl) m

0.016–3.78 (AlOOH); 0.0088/2.04 (NaOH) m

6.8–37.6 (Al2O3); 5.9–24.3 (Na2O) mass.%

7.2/6.9–2.4 (Al) (−log m); pH = 2.2–8.3 (HCl/NaOH)

7.3/6.5–2.0 (Al) (−log m); pH = 1.7–8.5 (HCl/NaOH)

6

Composition

6 kbar

25–49 MPa 6–6.75 kbar

SVP??

SVP??

SVP

SVP (86 bar)

SVP

SVP??

SVP

SVP

SVP

SVP-68 bar

5

Pressure

ptx-Al2O3-7.1 ptx-Al2O3 + AlCl3-1.1

ptx-Al2O3–8.1

ptx-Al2O3-5.1 ptx-Al2O3-6.1

ptx-Al2O3-4.1

ptx-Al2O3-3.1

Yalman et al., 1960 Anderson and Burnham, 1967 Burnham et al., 1973 Ganeev and Rumyancev, 1974 Becker et al., 1983 Ragnarsdottir and Walther, 1985 Tropper and Manning, 2007 Walther, 1997 Korzhinskiy, 1987

Verdes et al., 1992

Bernshtein and Matsenok, 1965 Chang et al., 1979

Salvi et al., 1998

Castet et al., 1993

Bernshtein and Matsenok, 1961 Kuyunko et al., 1983 Verdes et al., 1992

Benezeth et al., 2001

Palmer et al., 2001

8

7 ptx-AlOOH-NaCl + HCl/NaOH1.1; 1.2; 1.3; 1.4 ptx-AlOOH-NaCl + HCl/NaOH-2.1 ptx-AlOOH + NaOH-1.1; 1.2 ptx-AlOOH + NaOH-2.1 ptx-AlOOH + NaOH + NaCl-1.1 ptx-AlOOH + NaOH + NaCl-2.1 ptx-AlOOH + NaOH + SiO2-1.1 ptx-AlO2H + NaOH-1.1 ptx-AlO2H + NaOH-2.1 ptx-AlOOH + NaOH + NaCl-1.1 ptx-Al2O3-1.1 ptx-Al2O3-2.1

REFERENCE

Table


Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

in KF

Al2O3 (corundum) in KF

in

in

in

in

in

in

in

in

Al2O3 (corundum) KOH Al2O3 (corundum) KOH Al2O3 (corundum) KOH Al2O3 (corundum) KOH Al2O3 (corundum) LiOH Al2O3 (corundum) MgCl2 Al2O3 (corundum) NH4OH Al2O3 (corundum) Na2CO3

Soly

in HF

Soly

Soly

in

in

Soly

in

Soly

Soly

in

in

Soly

in

Soly

Soly

in

in

Soly

in

Soly

Soly

in

Al2O3 (corundum) Ba(OH)2 Al2O3 (corundum) CaCl2 Al2O3 (corundum) CaCl2 Al2O3 (corundum) Cs2CO3 Al2O3 (corundum) CsOH Al2O3 (corundum) HCl Al2O3 (corundum) HCl Al2O3 (corundum)

in

2

1

Al2O3 (corundum) K2CO3 Al2O3 (corundum) KCl Al2O3 (corundum) KCl Al2O3 (corundum) KCl Al2O3 (corundum)

Phase equil


Quench

Wt-loss

Quench

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Quench

Quench

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Quench

Wt-loss

Wt-loss

Wt-loss

Sampl

Quench

Wt-loss

3

Methods

450 C

430–600 C

600 C

430 C

400 C

500–700 C

600–900 C

430; 600 C

430; 600 C

400 C

600 C

800 C

430

430; 600 C

430 C

450–700 C

430

430; 600 C

430; 600 C

198–600 C

600 C

430; 600 C

4

Temperature

1000 atm

1450–2760 bar

2 kbar

1450 bar

0.5–2 kbar

1.86–2.65 kbar

2–6 kbar

1450 bar

1380; 1450 bar

??50 MPa

2 kbar

6; 6.17 kbar

1450 bar

1450 bar

1450 bar

1; 2 kbar

1450 bar

1450 bar

1450 bar

625–2100 bar

2 kbar

1450 bar

5

Pressure

1.12–3.46 (Al2O3); 14 (Na2CO3) mass.%

SVP

SVP

6/27–1304/1410 bar SVP

>SVP

0.0005–0.015/0.06 (CaSO4); 0/0.0005–3.2/5.4 (NaCl) m 0.00003–0.019 (CaSO4); 0.00024–5.8 (NaCl) m

0.002–0.006 (CaSO4); 0.03–0.3 (Mg(NO3)2) m

>SVP SVP

0.001–0.0057 (CaSO4); 0–0.16 (MgCl2); 0–0.5 (NaCl) m

0.00001–0.028/0.034 (CaSO4); 0.0001–5.5 (LiNO3) m 0.0013–0.009 (CaSO4) 0.03–0.3 (MgCl2) m

0.00002–0.04/0.085 (CaSO4); 0–1.2/4.7 (H2SO4) m 0.049–0.11 (CaSO4); 13.2–32.8 (K2SO4) g/100 g H2O 0.001–0.009 (CaSO4); 0.27–2.07 (K2SO4) m

6

Composition

>SVP

>SVP

SVP

SVP

SVP

SVP

5

Pressure 8

Marshall and Jones, 1966 Clarke and Partridge, 1934 Freyer and Voigt, 2004 Marshall and Slusher1973 Templeton and Rodgers, 1967 Templeton and Rodgers, 1967

7 ptx-CaSO4 + H2SO4-1.1 ptx-CaSO4 + K2SO4-1.1 ptx-CaSO4 + K2SO4-2.1 ptx-CaSO4 + LiNO3-1.1 ptx-CaSO4 + MgCl2-1.1 ptx-CaSO4 + MgCl2 + NaCl-1.1 ptx-CaSO4 + Mg(NO3)2-1.1 ptx-CaSO4 + NaCl-1.1 ptx-CaSO4 + NaCl-2.1 ptx-CaSO4 + NaCl-3.1; 3.2 ptx-CaSO4 + NaCl-4.1 ptx-CaSO4 + NaClO4-1.1 ptx-CaSO4 + NaNO3-1.1 ptx-CaSO4 + NaNO3-2.1 ptx-CaSO4 + Na2SO4-1.1 ptx-CaSO4 + Na2SO4-2.1 ptx-CaSO4 + Na2SO4-3.1 ptx-CaSO4 + Na2SO4 + NaCl-1.1

Templeton and Rodgers, 1967 Freyer and Voigt, 2004 Templeton and Rodgers, 1967

Templeton and Rodgers, 1967 Marshall et al., 1964 Templeton and Rodgers, 1967 Blount and Dickson, 1969 Freyer and Voigt, 2004 Kalyanaraman et al., 1973a Templeton and Rodgers, 1967 Marshall and Slusher, 1973 Straub, 1932

REFERENCE

Table


Quench Wt-loss; Quench

Wt-loss Quench

Vis.obs. Vis.obs. Vis.obs. Vis.obs. Vis.obs. Vis.obs. Vis.obs. Vis.obs.

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly Soly Soly Soly Soly Soly Soly Soly; Immisc Soly

Soly

CaSO4 in (Na2SO4 + NaClO4)

CaSO4 in (Na2SO4 + NaNO3)

CaSiO3(wollastonite) in NaCl CaWO4 CaWO4 in CaCl2

CaWO4 in KCl

CaWO4 in KCl

CaWO4 in (KCl + NaCl)

CaWO4 in K2SO4

CaWO4 in LiCl

CaWO4 in NaCl

CaWO4 in NaCl

CaWO4 in (NaCl + CaCl2)

CdBr2 CdBr2 CdCl2 CdCl2 CdI2 CdSO4 CdSO4 CdSO4 in UO2SO4

CdWO4 in (KCl + NaCl)

CdWO4 in KCl

Wt-loss

2

1

Sampl

Sampl

Wt-loss; Quench

Wt-loss; Quench

Sampl

Wt-loss

Sampl

Wt-loss; Quench

Quench

Sampl

Sampl

3

Methods

Phase equil


350 C

200–400 C

153/237–419 C 185–350 C 141/207–481 C 124/174–342 C 128/211–318 C 119/159–187 C 124–190 C 21/200–251 C

600; 800 C

600 C

600; 800 C

300–500 C

397–500 C

300–500 C

800 C

252–561 C

110/265–555 C 800 C

800 C

0.05/250; 350 C

273.5/523; 623 K

4

Temperature

SVP

SVP

SVP SVP SVP SVP SVP SVP SVP SVP

2 kbar

0.5–2 kbar

2 kbar

SVP

400–2300 kg/cm2

SVP

2 kbar

1; 2 kbar

SVP/1–2 kbar 2 kbar

10 kbar

SVP

SVP

5

Pressure

3.9–11.1 (CdWO4); 36–66 (NaCl + KCl) mass.%; [KCl/NaCl = 2.2 : 1 mass.ratio]

64.6/72–89.6 (CdBr2) mass.% 67.2–82.9 (CdBr2) mass.% 62.6/72.7–94.6 (CdCl2) mass.% 61/69–85.5 (CdCl2) mass.% 59.1/73.3–94.8 (CdI2) mass.% 32.3/15.6–4.9 (CdSO4) mass.% 29.6–3 (CdSO4) mass.% 31.6/29.4–2.8 (CdSO4) mass.%; 0.13; 1.35 (UO2SO4) m 0.1–7.6 (CdWO4); 4.7–51 (KCl) mass.%

0.00015–0.0107 (CaWO4); 0–4.8 (NaCl); 0.03–2.5 (CaCl2) m

0.0004–0.01 (CaWO4); 2 (NaCl) m

0.000089–0.269 (CaWO4); 0.2–10 (NaCl) m

0.04–3.8 (CaWO4); 31–78 (LiCl) mass.%

0.007–0.26 (CaWO4); 30.4–81.2 (KCl + NaCl) mass.% 0.003–1.68 (CaWO4); 5–50 (K2SO4) mass.%

0.00088–0.053 (CaWO4); 1–10 (KCl) m

31–1075 (CaWO4) ppm.; 0.5; 1 (KCl) mol/L

1–6.6 (CaWO4) ppm 0.000076–0.033 (CaWO4); 0.2–2.5 (CaCl2) m

0.02–0.5 (CaSiO3) (m); 0–0.6 (NaCl) mol.fr.

0.00015–0.0046/0.035 (CaSO4); 0–0.064//0.32 (Na2SO4); 0 0.5–5.9 (NaClO4) m 0.000014–0.02/0.086 (CaSO4); 0.23/0.25–6.1 (Na2SO4 + NaNO3) m

6

Composition

ptx-CaWO4 + NaCl + CaCl2-1.1 ptx-CdBr2-1.1 ptx-CdBr2-2.1 ptx-CdCl2-1.1 ptx-CdCl2-2.1 ptx-CdI2-1.1 ptx-CdSO4-1.1 ptx-CdSO4-2.1 ptx-CdSO4 + UO2SO4-1.1 ptx-CdWO4 + KCl-1.1 ptx-CdWO4 + K,Na/Cl-1.1

ptx-CaWO4 + NaCl-2.1

ptx-CaWO4 + KCl + NaCl-1.1 ptx-CaWO4 + K2SO4-1.1 ptx-CaWO4 + LiCl-1.1 ptx-CaWO4 + NaCl-1.1

ptx-CaWO4 + KCl-1.1 ptx-CaWO4 + KCl-2.1

ptx-CaWO4-1.1 ptx-CaWO4 + CaCl2-1.1

Dem’yanets and Ravich, 1972 Dem’yanets and Ravich, 1972

Malinin and Kurovskaya, 1992a Yastrebova et al., 1963 Ravich and Borovaya, 1970 Ravich and Yastrebova, 1961 Malinin and Kurovskaya, 1992a Malinin and Kurovskaya, 1996a Malinin and Kurovskaya, 1992a Benrath et al., 1937 Benrath, 1941 Benrath et al., 1937 Benrath, 1941 Benrath, et al., 1937 Benrath et al., 1937 Jones et al., 1957 Jones et al., 1957

Newton and Manning, 2006 Foster, 1977 Malinin and Kurovskaya, 1992a Foster, 1977

Yeatts and Marshall, 1969

Kalyanaraman et al., 1973b

8

7 ptx-CaSO4 + Na2SO4 + NaClO4-1.1 ptx-CaSO4 + Na2SO4 + NaNO3-1.1 ptx-CaSiO3-1.1

REFERENCE

Table


2

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly Soly Soly

LGE; Isop-m Soly; LGE

LGE

LGE, Isop-m LGE, Isop-m LGE

LGE; Cr.ph

1

CdWO4 in NaCl

(Ce,La)PO4 (monazite)

CoCO3 in CsCl

CoCO3 in LiCl

CoCO3 in NH4Cl

CoCO3 in NaCl

CoO

CoO

CoO in NH4OH; in NaOH

Co3O4

CoSO4 Cr2O3 Cr2O3 in NH4OH; in NaOH; Na(2.1–2.8)PO4

CsBr

CsCl

CsCl

CsCl

CsCl

CsCl

CsCl

Phase equil

Continued


Table 1.1

Fl.inclus; Calcul

p-V curves

Isopiest

Isopiest

Vap.pr.diff.

Vap.pr.

Isopiest

Quench; Rad.tr Vis.obs. Sampl Flw.Sampl

Flw.Sampl

Quench; Rad.tr Sampl

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Sampl

3

Methods

500; 600 C

250; 300 C

225; 250 C

383/474

125/200–300 C

383/473; 498 K 400–638 C

115/185–205 C 200 C 21/190–288 C

20/150–300 C

373/473; 523 K 25/200–295 C

20/150–300 C

250–400 C

200–350 C

251–451 C

400 C

1000; 1100 C

250–400 C

4

Temperature

SVP (29.2–62.3 kg/cm2) 400–900 bar

SVP

SVP

SVP

SVP

SVP

SVP SVP ?? 8–9 MPa

SVP

8–9 MPa

SVP

SVP

SVP??

SVP??

SVP??

SVP??

1–2 GPa

SVP

5

Pressure

ptx-CoO + NH4,Na/OH1.1; 1.2 ptx-Co3O4-1.1

(0.04/0.07–3.33/6.14) * 10−3 (CoO); 0.06–6.2 (NH4OH); 0.18–2 (NaOH) mm

ptx-CsCl-6.1; 6.2

ptx-CsCl-5.1

14.3 (CsCl) mol.% 4.4–68.7 (CsCl) mass.%

ptx-CsCl-4.1

ptx-CsCl-3.1

ptx-CsCl-2.1

ptx-CsCl-1.1;

ptx-CsBr-1.1

0.73–8.48 (CsCl) m

0.68/0.8–7.31 7.66 (CsCl) m

1.01/1.02–1.07 (CsCl) m

L-G-S

47//30–5 (CoSO4) mass.% 2.24 * 10−8 (Cr) m (0.05–38.5/159) * 10−9 (Cr) m; 0.07; 0.68 (NH4OH); 1 (NaOH); 0.5–106 (PO4) mm; 2.14–2.82 (Na/P) mol.ratio 0.73–8.01/8.28 (CsBr) m

(13/7–4) * 10−8 (Co) mol/L

ptx-CoSO4-1.1 ptx-Cr2O3-1.1 ptx-Cr2O3-2.1; 2.2; 2.3; 2.4

ptx-CoO-2.1

(52/1.5–0.4) * 10−6 (Co) mol/L

0.2–2.67 (CoCO3) g/L; 2–6 (NaCl) m

0.4–25.7 (CoCO3) g/L; 2–9 (LiCl) m

0.5–4.1 (CoCO3) g/L; 2–9 (CsCl) m

1.9–264 (Co) µm

Dem’yanets and Ravich, 1972 Ayers and Watson, 1991 Ikornikova, 1975

ptx-CdWO4 + NaCl-1.1 ptx-(Ce,La)PO4-1.1

0.5–26 (CoCO3) g/L; 0.5–2 (NH4Cl) m

8

7

Holmes and Mesmer, 1998 Morey and Chen, 1956 Lindsay and Liu, 1971 Holmes and Mesmer, 1981b Holmes and Mesmer, 1983 Urusova and Valyashko, 1987 Dubois et al., 1994

Ampelogova et al., 1989 Benrath, 1941 Hiroishi et al., 1998 Ziemniak and Jones, 1998

Ziemniak et al., 1999

Ampelogova et al., 1989 Dinov et al., 1993

Ikornikova, 1975

Ikornikova, 1975

Ikornikova, 1975

REFERENCE

Table

ptx-CoCO3 + CsCl-1.1 ptx-CoCO3 + LiCl-1.1 ptx-CoCO3 + NH4Cl-1.1 ptx-CoCO3 + NaCl-1.1 ptx-CoO-1.1

0.09–0.2 (Ce,La)PO4 mass.%; 0; 1 (NaCl) m

0.1–7.7 (CdWO4); 5.3–40.2 (NaCl); mass.%

6

Composition


Isopiest

Vis.obs.

Vap.pr.

LGE Isop-m

LGE

LGE

LGE; Isop-m crit ph

LGE

LGE

Soly

LGE

LGE

Soly LGE Isop-m

Soly; immisc Soly

Soly Soly

Soly

Soly

Soly

Soly

CsCl + BaCl2

CsCl + CaCl2

CsCl + MgCl2

CsHSO4

CsNO3

CsNO3 + AgNO3

CsOH

CsOH

Cs2SO4

Cs2SO4 Cs2SO4

Cs2SO4 in UO2SO4

Cu; Cu in HCl CuBr

CuCl

CuCl; CuCl in HCl

CuI

CuO

Cu

CsNO3

p-V curves

LGE; Soly; Cr.ph

CsCl

151/218 C

151/218 C

383.5/473; 498 K 384–415 C

250; 300 C

250; 300 C

383/473–524 K

300–500 C

4

Temperature

Flw.Sampl

Wt-loss

Sampl

Wt-loss

Quench Wt-loss

Flw.Sampl

Vis.obs.

Vis.obs. Isopiest

Vap.pr.

749–896 K

180/200–340 C

280–320 C

160/200–360 C

300–450 C 200–330 C

873–896 K

23/211–292 C 383/473; 498 K 54/215–289 C

400–700 C

Sampl; −73.5/154.5– Therm.anal. 346 C Flw.Sampl 598–645 K

Vap.pr.

p-V curves

Vis.obs.; pV, p-x curves Isopiest

3

2

1

Methods

Phase equil


13–31 MPa

SVP

58–103 bar

SVP

500; 1000 bar SVP

17.3–31 MPa

SVP

SVP SVP

SVP

120–215 bar

SVP (3/9.3–21.2 bar) SVP (2.08/8.45– 21.6 bar) SVP

SVP

SVP (24.2–62.2 kg/cm2) SVP (18.7–59.1 kg/cm2) SVP

SVP

SVP

5

Pressure

ptx-CuCl-2.1; ptx-CuCl + HCl-1.1 ptx-CuI-1.1 ptx-CuO-1.1; 1.2

7.1–7.9 (CuCl) (−log mol.fr).; pH = 1.7–3.7 (HCl)

(0.14–15.7) * 10−9 (CuO) mol.fr.; pH = 7.3–9.6

0.0036/0.0065–0.089 (CuI) m

ptx-CuCl-1.1

ptx-Cu + HCl-1.1 ptx-CuBr-1.1

1.4 * 10−7–1.3 * 10−4 (Cu); 0–0.001 (HCl) m 0.15–1 (CuBr) m 0.43/0.96–6.9 (CuCl) m

ptx-Cs2SO4 + UO2SO4-1.1 ptx-Cu-1.1; 1.2

ptx-CsSO4-2.1 ptx-Cs2SO4-3.1

0.3//0.44–78 (Cs2SO4) mass.%; 0.13; 1.35 (UO2SO4) m 1.4–9.0 (Cu) ppb; pH = 7.7; 9.6 (NH4OH)

63.5/73.5–75.5 (Cs2SO4) mass.% 0.53/0.56–5.77 (Cs2SO4) m

L-G-S

ptx-CsSO4-1.1

ptx-CsOH-2.1

0.003 * 10−4–0.16 (CsOH) m

57.6/84.2–100 (CsOH) mass.%

ptx-CsNO3 + AgNO3-1.1 ptx-CsOH-1.1

ptx-CsNO3-2.1

ptx-CsNO3-1.1

2–41 (CsNO3); 3–42 (AgNO3) mol.%

5.1–61.3 (CsNO3) mol.%

0.1–0.8 (CsNO3) m

ptx-CsHSO4-1.1

ptx-CsCl + BaCl2-1.1 ptx-CsCl + CaCl2-1.1 ptx-CsCl-MgCl2-1.1

0.64–7.38 (CsCl + BaCl2); [CsCl/BaCl2 = 0.7 : 0.3; 0.5 : 0.5; 0.3 : 0.7)] m 0.24–0.75 [CsCl in (CsCl + CaCl2)] mol.fr.; (CsCl + CaCl2)/H2O = 1 : 6 (mol.ratio) 0.25–0.75 [CsCl in (CsCl + MgCl2)] mol.fr.; (CsCl + MgCl2)/H2O = 1 : 6 (mol.ratio) 0.56/0.60–9.54/9.67 (CsHSO4) m

Gavrish and Galinker, 1955 Pocock and Stewart, 1963, Harvey and Bellows, 1997

Pocock and Stewart, 1997 Var’yash, 1989 Gavrish and Galinker, 1955 Gavrish and Galinker, 1955 Archibald et al., 2002

Holmes and Mesmer, 1992b Urusova and Valyashko, 1987 Urusova and Valyashko, 1987 Holmes and Mesmer, 1996a Marshall and Jones, 1974a Geerlings and Richter, 1997 Geerlings and Richter, 1997 Rollet and CohenAdad, 1964 Stephan and Kuske, 1983 Morey and Chen, 1956 Jones et al., 1957 Holmes and Mesmer, 1986 Jones et al., 1957

Urusova et al., 1994

8

7 ptx-CsCl-7.1; 7.2

REFERENCE

Table

0.23–97.7 (CsCl) mass.%

6

Composition


Flw.Sampl; Sampl

Quench

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly; Immisc; Cr.ph Immisc

CuO

CuO CuO in HNO3

CuO + NH4OH

CuO; CuO in NaOH, CuO in NH4OH, CuO in HNO3, CuO in HCF3SO3 CuO in NaOH

CuO in Na(2.5–2.8)PO4

CuO in SO3 + D2O

Soly

Cu2O in NaCl

Quench

Immisc

Quench

Quench Flw.Sampl

Quench

Immisc

Soly Soly

Quench

Quench

Vis.obs.

Flw.Sampl

Flw.Sampl Quench

Quench

Flw.Sampl

Immisc

Cu2O Cu2O in NH4OH

CuO in (UO3 + SO3 + D2O) (CuO + NiO) in (UO3 + SO3) (CuO + NiO) in (UO3 + SO3 + D2O)

CuO in (UO3 + SO3)

Flw.Sampl

Soly

CuO

3

2

1

Methods

Phase equil

Continued


Table 1.1

50/250

200–450 C 892–896 K

300; 325; 350 C 300; 325; 350 C 300; 325; 350 C 300; 325; 350 C

325–428 C

292/478–535 K

473–623 K

100/200–400 C

754–895 K

300–450 C 473–573 K

200–450 K

57/207–550 K

4

Temperature

SVP

SVP; 500 bar 19–31 MPa

SVP

SVP

SVP

SVP

8.59/ 9.28 MPa SVP

SVP

SVP-200 bar

19–31 MPa

28 MPa SVP

SVP

8.3/13–42 MPa

5

Pressure

ptx-CuO-2.1

ptx-CuO-3.1

ptx-CuO-4.1 ptx-CuO + HNO3-1.1 ptx-CuO + NH4OH-1.1; 1.2 ptx-CuO-5.1; 5.2; 5.3; 5.4; 5.5

(12.4/46–610) * 10−6 (Cu) g/kg H2O (5–31) * 10−7 (CuO) m

1.3–7.8 (CuO) µmol/kg H2O 8.9 * 10−7–4.1 * 10−3 (CuO); 0.00003–0.01 (HNO3) m 1–23 (CuO) ppb.; pH = 9.5 (NH4OH)

18–9206/9740 (Cu) ppm; 0.001–2 (NaCl) m

ptx-Cu2O + NaCl-1.1

ptx-CuO + UO3 + SO3-1.1 ptx-CuO + UO3 + SO3 + D2O-1.1 ptx-CuNiO + UO3 + SO3-1.1 ptx-CuNiO + UO3 + SO3 + D2O-1.1 ptx-Cu2O-1.1 ptx-Cu2O + NH4OH-1.1

ptx-CuO + NanPO4−1.1 ptx-CuO + SO3 + D2O-1.1

(0.2/7.8–1208) * 10−6 (Cu); (3.2–209) * 10−3 (Na/PO4) m 1–0.1 (mCuO/mSO3); 0.02–1 (SO3) m

0.2–6.6 (SO3); 0.3–0.9 (UO3/SO3); 0.01–0.4 (CuO/SO3) m 0.3–6.7 (SO3); 0.4–0.9 (UO3/SO3); 0.04–0.15 (CuO/SO3) m 0.2–6.4 (SO3); 0.3–0.85 (UO3/SO3); 0.05–0.15 (CuO/SO3); 0.05–0.15 (NiO/SO3) m 0.3–7.2 (SO3); 0.3–0.82 (UO3/SO3); 0.05–0.18 (CuO/SO3); 0.025–0.16 (NiO/SO3) m 7.5 * 10−7–0.0013 (Cu2O) m 0.3–11.5 (Cu) ppb; pH = 7.5–9.6 (NH4OH)

ptx-CuO + NaOH-1.1

1.3 * 10−7–2.9 * 10−4 (CuO); 0.00001–1 (NaOH) m

0.02–8880 (CuO) ppb; 0.001–0.1 (NH3); 0.0001–0.16 (NaOH); 0.0001 (HNO3); 0.0001; 0.0002 (HCF3SO3) m

8

7

6

Marshall,

Marshall,

Marshall,

Marshall,

Var’yash, 1989 Pocock and Stewart, 1963; Harvey and Bellows, 1997 Liu et al., 2001

Jones and 1961b Jones and 1961b Jones and 1961b Jones and 1961b

Var’yash, 1985; Harvey and Bellows, 1997 Ziemniak et al., 1992a Marshall et al., 1962b

Hearn et al., 1969; Harvey and Bellows, 1997 Var’yash, 1985; Harvey and Bellows, 1997 Sue et al., 1999 Var’yash, 1986; Harvey and Bellows, 1997 Pocock and Stewart, 1963; Harvey and Bellows, 1997 Palmer et al., 2000

REFERENCE

Table

Composition


285–361 163/260; 302 C 643.9–647.1 K

Sampl

Vis.obs.

Sampl; Vap.pr. Vis.obs.

Sampl Sampl Quench

Sampl

Quench

Flw.Sampl

Flw.Sampl

Flw.Sampl

Quench

Sampl

Soly

Soly

Soly

Immisc; Soly LGE; H-Fl

Cr.ph

Soly Soly

Soly

Soly Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

CuS (covellite) in NaHS

Cu9S5 (duigenite) in NaHS (CuSO4 + UO2SO4) in H2SO4 D2 in D2O

D 2O

FeCl3 FeCr2O4 in NH4OH

Fe2O3; Fe2O3 + SiO2 (Glass)

Fe2O3 in HClO4 Fe2O3 in KOH Fe2O3 in HClO4, NaClO4, NaOH Fe2O3 in NaOH; Fe2O3 in (NaOH + NaCl) Fe2O3 – SO3

Fe3O4 (magnetite) in HCl

Fe3O4; Fe3O4 in HCl; Fe3O4 in KOH; Fe3O4 in NaOH Fe3O4 in HCl; Fe3O4 in NaOH Fe3O4 in NH4OH; Fe3O4 in Na(2.1–2.8)PO4 FeS2 + S; (FeS2 + S) in NaCl FeS2 + Fe1-XS + Fe3O4

Fe10S11 in HCl

Fe10S11 in MgCl2

Wt-loss

Wt-loss

Quench

Flw.Sampl

Sampl Flw.Sampl

Sampl

Quench

400 C

150–540 C

300–500 C

250–350 C

295/477–562 K

373/473–573 K

50/200–303 C

499–649 C

50/200 C

60/200–300 C

300 C 300 C 200 C

500 C

80/140–305 C 293/461–561 C

26.3/198 C

18.5/196.6–208.5 C

150/200–350 C

4

Cu2O in NaOH

3

2

Temperature

1

Methods

Phase equil


300–1200 atm

800 atm

100–1000 bar

SVP

9.28 MPa?

G) takes place again with a drop in heat capacity. Such phenomena were observed in aqueous solutions of KNO3, CH4O, KCl, NaCl, NaOH (Abdulagatov et al., 1997, 1998, 2000). A method of T-Cv curve was also used to determine the parameters of phase transformations in fluid systems complicated with immiscibility phenomena (aqueous n-heptane, n-hexane, n-hexane+1-propanol mixtures) (Mirskaya, 1998; Stepanov et al., 1999; Kamilov et al., 2001). For binary systems where a solubility of solid in liquid phase decreases with temperature, heating of the liquid solution in the equilibrium with vapor can lead to other phase transitions besides those mentioned above. Heating at intermediate average densities and before thermal expansion causes the liquid to fill the entire volume, the initially unsaturated liquid solution becomes saturated with solid due to the negative temperature coefficient of solubility. In this case, the first phase transition is the crystallization of solid from the liquid solution in equilibrium with its vapor (L-G = >L-G-S) with an increase in heat capacity. With further heating of the mixture the concentration of the saturated with solid liquid solution decreases along the three-phase solubility curve. Finally, the expanding liquid or vapor solution fills the cell except for the volume occupied by the solid. A transition (L-G-S = >L-S or L-G-S = >G-S) takes place, with a decrease in heat capacity. Such phase behavior was observed in experimental studies of aqueous Na2SO4 solutions. However, the experimental

curves show two peaks rather than two steps. The appearance of the first peak, corresponding to the crystallization of solid salt, is the result of superheating (about 1 K beyond the three-phase temperature) of saturated solution and sudden release of heat as the system relaxed to the threephase state. The second peak arose due to vapor or liquid disappearance from the cell because the fluid was close to (though not at) the critical point of steam and close to the critical endpoint. The system was close enough to a criticalpoint phase transition to display the lambda-shaped heat capacity anomaly typical of the weakly diverging CV of pure fluids (Valyashko et al., 2000). High pressure DTA measurements. Differential Thermal Analysis (DTA) is a version of the method of ‘parameter – property’ curves in which the thermal effect is a measured property of a system and temperature or time are the parameters (‘Therm.anal.’ in Table 1.1). High pressure thermal analysis is performed in pressure vessels. The first cells for thermal analysis of hydrothermal systems (Antropoff and Sommer, 1926; Bouaziz, 1961; Kessis, 1967; Cohen-Adad et al., 1968) were constructed of stainless steel (sometimes with chemically resistant materials such as a silver for studies of alkaline solutions), or made of a sealed glass tube, placed in the pressure vessel where the vapor pressure in the glass cell was balanced by a nitrogen counter pressure. During thermal analysis of liquid-vapor system the composition of the condensed phase were corrected for the amount of solvent contained in the vapor. However those corrections were not accurate and the samples became compressed to the pressures much higher than its vapor pressure. For isobaric high pressure DTA experiments, the samples are enclosed in welded gold or platinum capsules to ensure that the composition of the sample will not change during the experiment (Koster van Groos, A.F., 1979; 1982; 1990; Gunter et al., 1983; Chou, 1987; Chou et al., 1992). The DTA assembly containing the thermocouples and welded capsules with samples and references is placed in an externally or internally heated high-pressure vessel. Usually argon is used as the pressure medium. All the difficulties that are common to DTA measurements (Wendlandt, 1986) occur in the high pressure DTA experiments. Therefore, interpretation of the DTA signals is the main topic of discussion. Basic factors that affect the results are: thermal contact between the sample or reference and the tip of the thermocouple; thermal gradients (in the DTA assembly as a whole and inside the capsules); and the mass of the sample (a larger sample produces a larger signal, but the interpretation is less certain). For each investigation, one must make special efforts to find the best design of equipment and, by testing some known phase transitions, to find reasons to use heating or cooling experiments, to take onset or peak temperatures as real information, and so on. It is difficult, if not impossible, to apply this technique to investigate phase transitions in which vapor phase is involved, especially at moderately high and low pressures. In this case the sample undergoes a large volume change at the phase transition, which causes the capsule to blow up or

86


collapse. This may be the reason that for most binary water – salt systems the p–T position of the high-temperature part of the three-phase equilibrium vapor – liquid – solid salt (G–L–S) is unknown. The DTA assembly which can accommodate large volume changes and which enables measurements of G–L-S equilibria up to the triple point temperature of the pure salt (Figure 1.11) is described in Kravchuk and Toedheide (1996). The salt sample and the reference are placed in open crucibles inside a high-pressure vessel. Preheated water vapor is pumped through the bore of the upper Bridgman closure. After reaching the desired pressure (the higher pressure, the more water was added), the vessel is removed from the pressure generating system, and the pressure is monitored as the temperature is varied. Interaction between the fluid and other phases must be reflected on the pressure curve. Temperature (T), temperature difference (∆T) and pressure (p) are measured as functions of time (t) and the experimental curves T-t, ∆T-t and p-t of each run are compared and processed according to standard DTA procedures. If water-salt mixture is heated the phase transformations from G-S to L-S take place, the T-t and p-t curves have the inflections at the same time. At the same time the ∆T-t curve has main peak with a shoulder at its high-temperature side, which can be interpreted as an indication of crossing from three-phase (G-L-S) state to two-phase (L-S) one. This main peak on the DTA curve and the pressure ‘plateau’ on the p-t curve, corresponding to three-phase equilibrium of the system, permitted to determine the p-T position of this

Figure 1.11 Pressure vessel and DTA cell (enlarged scale) (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins, Kravchuk, K.G. and Todheide, K. (1996) Z. Phys. Chem., 193, pp. 139–150.). (1) metallic cell, (2) lid, (3) bottom-side Bridgman closure, (4) quartz glass disk, (5) crucibles for sample and reference.

equilibrium for the studied mixture. There is a good agreement of DTA experimental data for positioning three-phase equilibrium on p-T diagram with other experimental techniques for those binary systems: H2O – NaCl, H2O – NaBr and H2O – Na2WO4 (Kravchuk and Toedheide, 1996). Thus DTA measurements with an ‘open’ cell enable the determination of such phase transitions. 1.3 PHASE EQUILIBRIA IN BINARY SYSTEMS 1.3.1 Main types of fluid phase behavior Scott and van Konynenburg in 1970 introduced classification of six types (I-VI) of binary fluid phase behavior (I-VI) based on analytical and experimental studies. Type VII, although there is no experimental examples for binary systems up to now, was added to the classification since works of Boshkov, 1987, and others (van Pelt et al., 1991; Boshkov and Yelash, 1995a; Yelash and Kraska, 1998, Yelash and Kraska, 1999a,b, Yelash et al., 1999) using various equations of state (Figure 1.12). It is necessary to note that there are several types of binary phase diagrams generated from the equations of state but not included in the above-mentioned classifications of binary fluid phase behavior. Among those theoretical diagrams there are two groups of fluid phase diagrams with the equilibria of three liquid phases (F-types, Q-types) (Scott and van Konynenburg, 1970; Furman and Griffiths, 1978; van Konynenburg and Scott, 1980; Deiters and Pegg 1989; Kraska and Deiters, 1992; Boshkov and Yelash, 1995b; Deiters et al., 1998b) and the diagrams with two or more separated immiscibility regions of the same nature (Boshkov, 1987; Deiters et al., 1998a). The traditional classification of fluid phase behavior can easily be discussed with the aid of the p-T projections of fluid phase diagrams (Figure 1.12) because it is mainly based on the characteristic behavior of the various monovariant critical loci present in the binary mixture, and on the occurrence of monovariant three-phase equilibria liquidliquid-vapor (L1-L2-G). It is clear from the Figure 1.12 that there are two kinds of phase diagrams. Phase diagrams of types I, V, VI and VII are characterized by the binary monovariant curves that are started and ended in nonvariant points with equilibria where the solid phase is absent. These types show the main types of fluid phase behavior. In the case of types II, III and IV, some binary monovariant curves, starting in high-temperature nonvariant points, are not ended by the nonvariant points from the lower temperature side, where the solid phase should exist. A solid phase is absent in calculations of fluid phase diagrams using liquid-gas equations of state and the nonvariant equilibria with solid could not be obtained even at 0 K. Therefore the monovariant curves remain incomplete on the theoretical p–T projections, although it is clear that in the case of real systems the fluid equilibria are terminated by a crystallization of solid phases at low temperatures and high pressures. As a result these diagrams can be considered as the ‘derivative’ versions that show the same main types of fluid phase behavior where a part of fluid equilibria was hidden by the occurrence of a solid phase.


Figure 1.12 Main types of binary fluid phase diagrams (p-T projections) (Scott, R.L. van Konynenburg, P.N. (1970) Faraday Discuss. Chem. Soc. 49, 87–97; Boshkov, L.Z. (1987) Dokl. Akad. Nauk SSSR, 294, pp. 901–905.). Solid circles are the critical points of pure components A and B; open triangles are the critical endpoints N (L1 = L2-G) and R (L1 = G-L2). Solid lines are the monovariant curves L-G of pure components A and B; dashed lines are three-phase equilibrium L1-L2-G; dot-dashed lines are the critical curves L = G, originated in the critical points of pure components; two-dots-dashed lines are the critical curves L1 = L2 originated in critical endpoint N.

It is obvious from the classification (Figure 1.12), that types of immiscibility phenomena control the diversity of fluid phase behavior in binary systems. Only type I systems do not have the immiscibility region and are characterized by one heterogeneous fluid equilibrium – liquid-gas (L-G) and one continuous critical curve (L = G) between the critical points of pure components. All other types of phase diagrams in Figure 1.12 are complicated by three-phase of immiscibility region and, as was discussed above, each type of immiscibility region has two versions of phase diagram (types II and VI, III and V, IV and VII), where the types II, III and VI show the results of solid-fluid interactions for each of three main types (IV, V and VII) of immiscibility regions.

The classification shown in Figure 1.12 is popular and is convenient to use because it demonstrates not only the main types of fluid phase behavior but also the fluid phase diagrams which appear when the heterogeneous fluid equilibria are bounded not only by another fluid equilibria but also by the equilibria with solid phase that is usually observed in the most real systems. However, the available experimental data show that the above-mentioned seven types of phase diagrams do not describe some versions of fluid phase behavior in the highly asymmetric binary systems where the melting temperature of nonvolatile component is significantly greater than the vapor-liquid critical point of the volatile one. To give an exhaustive description of phase behavior in binary systems, the systematic classification of the main types of complete phase diagrams that considers any equilibria between liquid, gas and/or solid phases in a wide range of temperatures and pressures should be suggested. However, the above reasons for subdividing fluid phase diagrams onto the main types (I (1P), V (2P), VI (1PnM), VII (2PnM)) and the ‘derivative’ ones (II (1Pl), III (1ClZ), IV (2Pl)) as well as the mentioned imperfection of the traditional classification for highly asymmetric systems do not permit us to use an arbitrary nomenclature (Roman numbers) introduced by Scott and van Konynenburg (1970) or a systematic (but rather complex) nomenclature suggested by Bolz et al. (1998) (this nomenclature is shown in square brackets) for a designation of complete phase diagrams. In the new nomenclature, suggested by Valyashko (1990a,b; 2002b) for systematic classification of binary complete phase diagrams, four main types of fluid phase behavior are designated in order of their continuous topological transformation as a, b, c and d types. Type a corresponds to type I (1P) (Figure 1.1), type b = > type VI (1PnM), type c = > type VII (2PnM), type d = > Type V (2P). The designations of ‘derivative’ and of complete phase diagrams would reflect the modifications of corresponding main types of fluid phase diagrams due to interference of solid phase in immiscibility regions and critical equilibria. 1.3.2 Classification of complete phase diagrams In order to simplify the construction of phase diagrams the following limitations for the main types of binary complete phase diagrams are accepted: 1. The melting temperature of the pure nonvolatile component is higher than the critical temperature of the volatile component. 2. There are no solid-phase transformations such as polymorphism, formation of solid solutions and compounds, and azeotropy in liquid-gas equilibria in the systems under consideration. 3. Liquid immiscibility is terminated by the critical region (L1 = L2) at high pressures and cannot be represented by more than two separated immiscibility regions of different types.

88


4. All geometric elements of phase diagrams, their reactions and shapes (but not the combinations of these elements) can be illustrated by existing experimental examples. To obtain the systematic classification of complete phase diagrams for binary systems the method of continuous topological transformation was used (Valyashko, 1990a,b; 2002a,b). This method is based on the following two main principles: • Topological scheme of phase diagram can be transformed continuously from one type to another through the special boundary versions of phase diagrams. Each boundary version of phase diagram has the properties of both neighboring types and contains equilibrium possible as nonvariant equilibria only in the systems with a number of components greater than in the systems under consideration. The boundary versions for binary phase diagrams contain the nonvariant equilibria of ternary mixture. In general case for multicomponent systems it means that the phase diagram of n-component system is a result of continuous topological transformation of the phase diagrams of (n–1)-component subsystems. • When fluid phase equilibria (immiscibility phenomena, for instance) are hidden by occurrence of a solid, the modifications of fluid equilibria in presence of solid phase do not change the type and topological scheme of fluid phase behavior. As a result of such modification a part of immiscibility regions is suppressed by solidification of the nonvolatile component and transforms into the metastable equilibria. Such metastable equilibria have an effect on a form of adjacent stable phase equilibria, and may emerge in stable equilibria with increasing the number of degrees of freedom (for instance, with increasing the number of components) or could be observed in nonequilibrium conditions of superheated or supersaturated solutions. The fundamental idea of continuous transitions between the various forms of heterogeneous fluid equilibria was formulated by G.M. Schneider in the 1960s and confirmed by systematic investigations of so-called ‘families’ of binary systems in which one component is the same while the other is altered in size, shape and/or polarity (Schneider, 1966, 1968, 1978, 2002). It has been also proved by the studies of ternary systems where the quasi-binary cross-sections show a continuous transformation of phase behavior while passing from one binary subsystem to another. Theoretical calculation of binary fluid phase diagrams also shows that each diagram transforms continuously into another if the model parameters are changed and the boundary versions of phase diagrams arise in the process of transformation. The curves in the global phase diagrams divide the diagram field into regions of different phase behavior and correspond to the boundary versions of the fluid phase diagram (Scott and van Konynenburg, 1970; Boshkov and Mazur, 1985; Deiters and Pegg, 1989 etc.). Due to existence of special equilibria such as tricritical points, double critical endpoints etc., which are possible only in ternary or more

complicated systems, these boundary versions are only theoretical, and, according to Phase rule, could not be found among the real systems. Figure 1.13 shows a systematic classification that includes both known and new types of complete phase diagrams (p-T projections) arranged in the order corresponding to their continuous topological transformation. The new types appear to fill the empty places in the process of continuous transformation. Each diagram is labeled with number (1, 2) followed by a type (a, b, c, d) of fluid phase behavior. Titles of boundary versions of the complete phase diagram contain two letters (ab, CD, 1bb¢, 1dd¢ etc.) or numbers (12a, 12c¢, 12d≤ etc.) according to the neighboring types, which transform one into another. The number (1, 2) reflects both features of solubility and critical equilibria as well as the traditional division of the complete phase diagrams into two types. The first type (type 1) has no intersection of solubility (L-G-S) and critical (L = G) curves. Type 2 (or type p-Q), the second type, presents intersections of solubility and critical curves at two critical endpoints ‘p’ (L = G-S) and ‘Q’ (L = G-S; L1 = L2-S) (Van der Waals and Kohnstamm, 1927; Ricci, 1951; Morey and Chen, 1956; Ravich, 1974; Valyashko, 1990a,b). The systems of type 1 have a positive temperature coefficient of solubility (t.c.s.) in the three-phase equilibrium (L–G–S) and an uninterrupted solubility curve at supercritical temperatures. Type 2 is characterized by a negative t.c.s. in the subcritical equilibrium region (L–G–S), critical phenomena in solid saturated solutions (L = G-S), and supercritical fluid equilibria (the equilibria where a homogeneous fluid phase does not have phase separation (heterogenization) at any variation of pressure) in the temperature range between the critical endpoints ‘p’ and Q. It is important to note that in the case of the type 2 systems, the melting temperature of low-volatile component should be above the critical temperature of volatile one, whereas the melting temperature of low-volatile components in the systems of type 1 can be both above and below the critical temperature of the volatile components. Phase equilibria in types 1 and 2 can be complicated by the immiscibility of liquid phases taking place both in solid saturated or unsaturated solutions and in stable or metastable conditions. The systematic classification in Figure 1.13 consists of four rows (a, b, c, and d) of the diagrams corresponding to the described four main types of fluid phase behavior. Complete phase diagrams in the row a are characterized by a fluid phase behavior without liquid–liquid immiscibility phenomena. A limited immiscibility region terminated by two critical endpoints N (L1 = L2-G) (so called a ‘closed loop’ immiscibility region) is a permanent element of complete phase diagrams of the row b. Two three-phase immiscibility regions L1-L2-G of different nature are the constituents of complete phase diagrams in the row c. Fluid phase behavior of type d (three-phase immiscibility region L1-L2-G is terminated by two critical endpoints N and R (L1 = L2-G and L1 = G-L2) of different nature) can be found in any complete phase diagrams of the row d.


P

KA NR

KB T

ad P

KA pQ

KA

TA

KB TB

E

T

P

KA

T

ab P

KA NL

TA

KB

N’ TB

N

P

M

KB

N

1b’ KA N’

N

KB

KB T

12b’

TB

12b”

N’

L TB

E

L

T

T

2b” KA Q p

M

pQ

L

T

M Q p

T P

M

N TB

2b’ KA

N’

R

P

1b” KA

L

T

KA pQ

T

M

KB

N’L 1bb”

Q p

P

M

P

L P

P

T

T

T

1bb’

KA

KB

KB

NL ab’

KB

N’

1b KA

KA

KB

2a

T

12a P

NN’

P

P

P

1a

T

P KA NR

KB

N’

N

T

bc

P

P R

P

N

1c NL

R N’ N

N

KB

P

P

T

KB

E P

MQ

2c”

p TB

L

KB T

Q

M p

p

12c”

T

L

T

TA

KB

T

P R N

N’N

CD

KA KB T

N

P KA R

1d KA R

NL

TA

KB

1dd’

T

KB T

L

1dd” KA NR da

T

12d’ P

N

L

N T

TB P

MQ

L 12d”

Q

TA T

p KB

2d’ p

pR

p T

P

M

KA

1d”

KA pR N

P

1d’ M KA R TA E

P

P

T

R

N’N cd

P

P

T

KA L

P

TB

12c’ P

1c”

T

Q

p pR

KB T

pR

1cc”

N

R

L

2c’

KA

N T

1cc’

N

P

KA

P

M

P

1c’ M

T

2d” M N L

KB T

Q p TB KB

T

KB T

Figure 1.13 Systematic classification of binary complete phase diagrams (p-T projections). Boundary versions of phase diagram are shown in frames (Reproduced by permission of the PCCP Owner Societies). Solid circles are nonvariant points in one- and two-component systems (TA, TB and KA, KB – triple (L-G-S) and critical (L = G) points of pure components A and B, euthectic point E (L-G-SA-SB), L (L1-L2-G-SB); critical endpoints: N (N′) (L1 = L2-G), R (L1 = G-L2), p (L = G-S), Q (L = G-S or L1 = L2-S), M (L1 = L2-S)); open dots are the nonvariant equilibria of ternary systems: NL and N′L (L1 = L2G-S), pR (L1 = G-L2-S), double critical endpoints (DCEPs): N′N (L1 = L2-G), pQ (L = G-S), MQ (L1 = L2-S); tricritical point NR (L1 = L2 = G)) in the boundary versions of phase diagram (in frames). Thin lines are the monovariant equilibria L-G and L-S of pure components A and B; dashed lines are the critical curves L = G and L1 = L2; heavy lines are the monovariant curves (non-critical) of binary system; dotted lines are the metastable parts of monovariant curves in binary systems.

There are two reasons why the horizontal rows b, c and d consist of two lines of phase diagrams: 1. The existence of experimental evidences of two versions of immiscibility region of type d in the systems PbBr2 –

H2O (Benrath et al., 1937), PbI2 – H2O (Benrath et al., 1937; Valyashko and Urusova, 1996) and UO2F2 – H2O (Marshall et al., 1954a), BaCl2 – H2O (Valyashko et al., 1983). In the PbBr2 – H2O, PbI2 – H2O phase diagrams the stable immiscibility regions originate in solid

90


saturated solutions L1-L2-G-S (point L), transform into three-phase equilibrium L1-L2-G and terminate in the critical endpoints R (L1 = G-L2) with increasing temperature. The salt solubility increases dramatically in this immiscibility region. The opposite sequence of phase equilibria is observed in the UO2F2 – H2O and BaCl2 – H2O systems. Three-phase immiscibility region (L1-L2G) arises in unsaturated solutions in the lower critical endpoint N (L1 = L2-G) and terminates in solid saturated solutions L1-L2-G-S (point L) at higher temperatures. Salt solubility decreases sharply in the immiscibility region. 2. In a process of topological transformation the initial intersection (tangency) of solubility (L-G-S) and immiscibility (L1-L2-G) curves can be at either the lowtemperature high-order critical point NL (L1 = L2-G-S) or the high-temperature high-order critical points pR (L1 = G-L2-S) (or N ′L (L1 = L2-G-S) in row b) depending on dp/dT slopes of these three-phase monovariant curves. If (dp/dT) soly < (dp/dT) immisc (as in PbBr2 – H2O, PbI2 – H2O systems) the solubility curve touches the immiscibility curve in the low-temperature high-order critical point NL (Figure 1.2, diagram 1dd¢) and the type 1d¢ arises. The opposite relation of the slope leads to an intersection of the monovariant curves in the high-temperature high-order critical point pR (Figure 1.2, diagram 1dd≤), that produces the phase diagrams of type d≤ such as in the systems UO2F2 – H2O and BaCl2 – H2O. There is no reason to exclude various possibilities of the interference of the solubility curve with three-phase immiscibility regions of type b and c. Therefore rows b and c also have two lines of phase diagrams which could exist, although there are no experimental data of such phase behavior. In Figure 1.13 there are three columns (right, central and left) of complete phase diagrams (p-T diagrams without frames) separated by two vertical columns of boundary versions (p-T diagrams in frames). The complete phase diagrams, which correspond to the four main types of fluid phase behavior and lack critical phenomena in solidsaturated solutions, are found in left column. Central and right columns contain complete phase diagrams with nonvariant points where critical phenomena occur in equilibrium with a solid phase. So-called supercritical fluid equilibria are absent in the diagrams from central column (types 1b¢, 1b≤, 1c¢, 1c≤, 1d¢, 1d≤) but they appear in the systems of type 2 described by the diagrams in the right column. Equilibria are defined here as ‘supercritical fluid equilibria’ if they occur in a temperature range between the critical point of the volatile component and the melting curve of the non-volatile component. They include only one fluid phase (with or without equilibrium solid phase), despite of pressure variations. A transition from the gas-like state of fluid at low pressures (densities) to the liquid-like fluid at high pressures (densities) occurs upon compression and takes place continuously without the two-phase fluid equilibrium and density jump. As mentioned above, supercritical fluid equilibria are distributed in the highly asymmetric binary mixtures where the

triple point temperature of the low-volatile (nonvolatile) component is significantly greater than the critical point of the more volatile (volatile) one. Such phase behavior (type 2) was established in gaseous systems (He – H2, He – N2, He – CH4, He – CO2, He – C2H4, Ne – Ar, Ne – CH4, H2 – CO2, H2 – CH4, H2 – C2H4, H2 – C2H6 etc. (Streett, 1983; Gubbins et al., 1983)), organic and CO2 – organic systems (ether – anthraquinone (Smiths, 1905, 1911)), CO2 – diphenylamine (C6H5)2NH)) (Buechner, 1906), methane (CH4) – cyclohexane, CH4 – n-octane, ethylene – naphthalene, ethylene – anthracene (C14H10), etc. (Paulaitis et al., 1983), CO2 – naphthalene (C10H8), CO2 – biphenyl (C12H10), CO2 – m-terphenyl (C18H14), CO2 – phenanthrene (C14H10) (Lu and Zhang, 1989), ethylene (C2H4) – eicosane (C20H42) (Gregorowicz et al., 1993), ethane (C2H6) – adamantane (C10H16) (Poot and de Loos, 2004) and water-salt systems (H2O – SiO2, H2O – Na2CO3, H2O – Li2SO4, H2O – K2SO4, H2O – BaCl2, etc.). It is important to note that most of the type 2 systems in which high-temperature supercritical equilibria were studied in detail are complicated by metastable immiscibility regions and they belong to type 2d¢ or 2d≤. Only ether (C4H10O) – anthraquinone (C14H8O2) (Smits, 1905, 1911) and ethane (C2H6) – adamantane (C10H16) (Poot and de Loos, 2004) systems show type 2a phase behavior without immiscibility phenomena. Diagrams from Figure 1.13 included in boxes (frames) are the boundary versions of a binary phase diagram. They contain special points representing nonvariant equilibria in ternary systems and demonstrate continuity of topological transformation of one binary type of a complete phase diagram into another. The boundary versions of a binary phase diagram between the rows show the phase equilibria taking place at transition of phase diagrams (both types 1 and 2) from one row to another. There are two boundary versions of a binary phase diagram between rows a and b and between rows c and d. In the first case the boundary version ab appears at transition of type 1a into type 1b (1a⇔ab⇔1b). The boundary version ab¢ takes place in the transformation 1b¢⇔ab¢⇔1a, 1b≤ab¢⇔1a, 2b¢⇔ab¢⇔2a, 2b≤⇔ab¢⇔2a. In the second case the boundary version cd may take part in a continuous topological transformation of any phase diagrams in the rows c and d (1c⇔cd⇔1d; 1c¢⇔cd⇔1d¢; 1c≤⇔cd⇔1d≤; 2c¢⇔cd⇔2d¢; 2c≤⇔cd⇔2d≤). However, the global phase diagrams of binary fluid mixtures (Yelash and Kraska, 1998; 1999) show also another way of continuous transformation for phase diagrams of types c and d through the boundary version CD (1c⇔CD⇔1d; 1c¢⇔CD⇔1d; 1c≤⇔CD⇔ 1d≤; 2c¢⇔CD⇔2d¢; 2c≤⇔CD⇔2d≤). All seven types of fluid phase diagrams introduced by Scott and Konynenburg (1970) (six types) and Boshkov (1987) (the seventh type) can be easily found as a part of the following complete phase diagrams of type 1 (placed in the left and central columns): type I (fluid phase diagram) = type 1a (complete phase diagram), type II = type 1b¢, type III = type 1db¢, type IV = type 1a¢, type V = type 1d, type VI = type 1b, type VII = type 1c. Seven out of ten types of complete phase diagram from left and central columns (type 1) have experimental data.


Here are a few examples of each type: type 1a (CH4 – propane, CO2 – cyclohexane, NH3 – H2O, ethanol – H2O, methanol – H2O, acetone – H2O, H2O – NaCl etc. (Schneider, 1978)); type 1b (2-butanol – H2O, 2-methylpyridine – D2O, 2-butanone – H2O (Schneider, 1978)); type 1b¢ (CO2 – octane (Schneider, 1978), H2O – HgI2 (Benrath et al., 1937; Valyashko and Urusova, 1996); type 1c¢ (CH4 – 1hexene, CH4 – 2-methyl-1-pentene, CH4 – 3.3-dimethylpentane, CH4 – 2.3-dimethyl-1-buten (Schneider, 1978)); type 1d (CO2 – nitrobenzene, CH4 – hexane (Schneider, 1978), H2O – UO2SO4 (Marshall and Gill, 1963; 1974), H2O – Na2B4O7 (Urusova and Valyashko, 1990)); type 1d¢ (CH4 – methylcyclopentane, CO2 – hexadecane, CO2 – H2O (Schneider, 1978), H2O – PbBr2, H2O – PbI2 (Benrath et al., 1937; Valyashko and Urusova, 1996); type 1d≤ H2O – UO2F2 (Marshall et al., 1954a)). Some types of complete phase diagrams, shown in Figure 1.13, were derived theoretically (1b≤, 2b¢, 2b≤, 1c, 1c≤, 2c¢, 2c≤) and have not been experimentally documented up to now. 1.3.3 Graphical representation and experimental examples of binary phase diagrams The three-dimensional p-T-x phase diagrams represent the most complete and exhaustive information on phase behavior in binary system. In these diagrams a homogeneous single phase occupies a volume in p-T-x space, and the conditions of two-, three- and four-phase equilibrium give rise to pairs of surfaces, triplets of lines and quadruplets of points, respectively. However, it is difficult to see the shapes of these surfaces even if they are shaded, due to overlapping. Therefore the p-T, T-x and p-x projections of p-T-x diagram are often used to obtain the two-dimensional representation of binary phase equilibria which could better demonstrate some aspects of phase behavior. For instance, the classification of binary phase diagrams is based on the characteristic behavior of critical and non-critical monovariant phase equilibria, and therefore the p-T projections of these phase diagrams with well-defined monovariant curves were used. To display a temperature behavior of phase transformations and/or phase compositions the T-x projection should be selected. The p-x projections are used to show the variations of phase equilibria due to the pressure change. To obtain the detailed graphical information on phase equilibria, the cross-sections of that p-T-x diagram at constant temperature (isotherms), pressure (isobars) and composition (isoplets) are employed. To show graphical representations of various types of complete phase diagrams and to pay attention on some important features of phase behavior, several topological schemes will be discussed in greater details. In particularly, the metastable phase equilibria that are hidden by the crystallization surface but may emerge when additional degrees of freedom (e.g. the third component) are of great importance for further derivations. A topological scheme of phase diagrams, plotted in dimensionless coordinates, describes the combination and sequence of phase equilibria for a given type of systems in p-T-x space or on p-T, T-x and p-x projections. To make the

schemes easy to read and to indicate some equilibria, the tie-lines between phases in equilibrium are shown on those schemes. In most cases the tie-lines show the monovariant equilibria, such as L-G-S. However, they connect not all of the equilibrium phase but only the compositions of fluid phases and never the solid ones, which are the pure components A or B. Only in the cases of nonvariant equilibria, such as L-G-SA-SB, L1-L2-G-SB, L = G-SB or L1 = L2-SB, the solid phases are also indicated by rhombs on the schemes. All the limitations for the classification of binary complete phase diagrams, mentioned above, are kept constant for the following discussion and topological schemes of phase diagrams. However, the topological p-T-x, p-T, T-x and p-x schemes of complete phase diagram for binary systems of type 1a with solid phase transformations (polymorphism) and binary compounds formation are available (Valyashko, 1995; Valyashko and Churagulov, 2003). 1.3.3.1 Binary systems without liquid-liquid immiscibility Systems of type 1a (without critical phenomena in solid saturated solutions) (Figure 1.14). This is the simplest type of binary system. Most of the divariant (L-G, L-SA, L-SB, G-SA, G-SB) and monovariant equilibria (L-G-SA, L-G-SB, L = G) in the binary system (A-B) are the monovariant and nonvariant, respectively, with equilibria of one-component subsystems (A and B), spreading into two-component region of composition. Only the phase equilibria with two solid phases (invariant eutectic equilibrium E (L-G-SA-SB); monovariant equilibria (L-SA-SB, G-SA-SB) and divariant equilibrium (SA-SB)) appear in the binary mixture as a result of an interaction of phase equilibria that extend from onecomponent subsystems. Since some characteristic features and geometric view of type 1a equilibria remain the same in all other types of binary systems they are considered in detail only in this section. Furthermore, only the distinctive properties of these equilibria will be discussed if they are encountered in the phase diagrams of another types. The solubility of a solid phase in a solvent under the pressure of saturated vapor corresponds to monovariant three-phase equilibria (L-G-S), which are depicted in the p-T-x, T-x and p-x diagrams as the solid and dashed curves (ETA, ETB) of compositions of coexisting liquid and gas (vapor) phases, respectively, or their projection on the coordinate plane p-T. Only curves of liquid and vapor compositions for this equilibrium are given in the figures, since the compositions of equilibrium solid phases correspond to pure components and do not change with temperature and pressure. Monovariant equilibria (L-G-SA) and (L-G-SB) originate at the eutectic point E (L-G-SA-SB) and extend to the triple points (L-G-S) of the corresponding components (TA and TB). Solubility curves of nonvolatile component (ETB) extend over a wide range of parameters and are characterized by maximum vapor pressure and positive temperature coefficient of solubility (t.c.s.). Two other monovariant curves extend from the invariant eutectic point E in the direction of higher (L-SA-SB equilibrium) and lower (G-SA-SB) pressures are the curves of liquid

92


a

KB

b T KB

TB

p KA TB KA

T TA TB E A

x

B

A

x

c

B

d

p

p

KA

KA KB

TA E

KB TA

TB

E T

A

TB x

B

Figure 1.14 Complete phase diagram (three-dimensional p-T-x scheme (a), T-x (b), p-T (c), p-X (d) projections) for binary system A-B of type 1 without liquid-liquid immiscibility (type 1a) (Reproduced by permission of MAIK / Nauka Interperiodica). T and K – triple and critical points of component A and B; E – eutectic equilibrium (L-G-SA-SB). Open circles – nonvariant points in one-component systems. Solid circles – nonvariant points in binary systems (p-T projection) and compositions of fluid (liquid, gas and critical) phases in binary nonvariant equilibria (p-T-x, T-x and p-x schemes). Diamonds – compositions of solid phases in binary nonvariant equilibria. Heavy lines – monovariant curves in one-component systems (A, B); solid lines – compositions of liquid phases in monovariant equilibria of binary systems; dashed lines – compositions of vapor (gas) phases in monovariant equilibria of binary systems; dash-dotted lines – critical curves; thin lines – isothermal cross-sections of the p-T-x diagram and tie-lines in T-x and p-x projections. For clarity, only tie-lines between fluid phases are shown in monovariant equilibria.

or gas compositions, respectively, or are its projections on the p-T plane. The critical points of the pure components, KA and KB, are connected by the critical curve (KAKB) corresponding to the monovariant critical equilibrium (G = L). Between the critical curve KAKB and the curves of threephase equilibria (ETB and ETA) there is the area of two-phase equilibria (L-G). The composition of coexisting liquid and vapor phases generate two surfaces starting from the curves ETB and ETA of three-phase equilibrium (L-G-S) and ending at the monovariant curves (TAKA) and (TBKB) of the onecomponent systems and the critical curve KAKB. The surfaces of the liquid phase in equilibrium (L-S) also extend from the curves corresponding to the composition of the saturated liquid phases in equilibrium (L-G-S). Such surfaces are limited from the high-temperature side by the monovariant melting curves (L-S) of the pure components A and B. At low temperatures those surfaces meet along the curve of liquid solutions, which saturated with A and B phases (L-SA-SB) that extends from the composition of the eutectic liquid solution (points E; equilibrium L-G-SA-SB). At pressures lower than the three-phase equilibrium (LG-S) only vapor solutions and solid phases of components exist. The surfaces of vapor (gas) phase compositions of divariant equilibria (G-SA) and (G-SB) extend in the direc-

tion of lower pressures from the curves of vapor compositions in equilibrium (L-G-S). As for equilibrium (L-S), the surfaces of solid saturated vapor solutions (G-S) are limited by monovariant sublimation curves (S-G) of one-component systems and meet at the minimum temperatures along the curve of vapor saturated with two solid phases (G-SA-SB), which starts at the eutectic point E (L-G-SA- SB). Before considering experimental examples of the main types of complete phase diagrams it is necessary to make some general remarks on volatility of components. The relative volatility of the components in a mixture is determined by the ratio of their critical parameters. The critical temperature of the more volatile (volatile) component is lower and its critical pressure is usually higher than the corresponding parameters of the less volatile (nonvolatile) component. Water in binary mixtures can play the role of both: it could be more volatile component as in water-salt systems and mixtures with the heavy hydrocarbons or less volatile constituent as in mixtures with high-volatility gases, such as Ar, CO2, NH3, and in most of the aqueous-organic systems. Most of water-salt systems are in near full accord with accepted limitations for the main types of complete phase diagrams (see above). Sometimes the melting temperatures of salts are below the critical temperature of water (but it is


not important in the case of type 1 systems) and the formation of crystal-hydrates are common phenomenon in watersalt systems but usually it is observed at temperatures below 200 °C. In most cases of water-organic systems critical temperature of volatile component (KA) is above the melting temperature of the nonvolatile one (TB), however the sets of phase equilibria observed in such systems of type 1 are exactly the same as shown by the topological schemes of type 1, where TB > KA. Figure 1.15 shows T-x projection of NaCl – H2O system – one of the well-studied systems of type 1a, where the solubility curve (the curve of liquid phase composition in equilibrium L-G-S) has positive temperature coefficient of salt solubility at sub- and super critical temperatures. The isobaric cross-sections of two-phase equilibrium L-G at temperatures below the critical temperature of water originate on the L-G curve of pure water and end on the solubility curve. At temperatures above KH2O the compositions of equilibrium liquid and vapor (gas) phases at constant pressures are brought to a point of the critical curve L = G, which starts from KH2O and runs in the direction of the critical point of NaCl. Similar phase behavior was established in a lot of hydrothermal systems with such nonvolatile components as AgNO3, Ba(NO3)2, CaCl2, CsCl, KBr, KCl, KF, KNO3, KOH, LiOH, MgCl2, NaBr, NaI, SrCl2, ZnCl2 etc.). The most detail experimental data on L-G and L = G equilibria have been obtained for aqueous systems of type 1a with NH3, ethanol, methanol and acetone, where water is a nonvolatile component.

T, ºC 800

106 MPa

TNaCl

600 50 400

KH2O

10 MPa

200 0.1

Systems of type 2a (with critical phenomena in solid saturated solutions) (Figure 1.16). The phase diagram of this type is a result of the intersection of critical (L = G) and three-phase (L-G-SB) monovariant curves. The compositions of solid saturated vapor and liquid solutions coincide in the low-temperature critical endpoint ‘p’ (L = G-SB) due to the decrease in solubility of B in the liquid phase as temperature increases approaching critical temperature of A component. The second critical endpoints ‘Q’ (L = G-SB) is placed at higher temperature but below the melting temperature of B. Curves and surfaces of gas and liquid phases in equilibria (L-G-SB) and (L-G) coincide at these points. The surfaces of solutions in equilibria (L-SB) and (G-SB) generate a single surface of supercritical fluid in two-phase equilibrium (Fl-SB). This supercritical fluid equilibrium exists in the temperature range between the critical endpoints p and Q. As mentioned above, any change in pressure in presence or absence of a solid phase do not causes boiling of the solution or phase separation, which is a characteristic for this equilibrium. For a long time this type of phase diagram (type 2a), described by Smiths and confirmed by the experimental data for the system ether (C4H10O) – anthraquinone (C14H8O2) (Smiths, 1911), was mentioned in a lot of reviews and monographs as the only type for binary systems with critical phenomena in solid saturated solutions (points p and Q) and supercritical fluid region between them (type 2). However, Buechner (1906, 1918) has described (and confirmed by experimental study of CO2 – diphenylamine (C6H5)2NH) another version of phase diagram for binary systems with very similar stable critical and supercritical phase equilibria but complicated by metastable immiscibility phenomena (type 2d¢). Unfortunately, most reviewers have not pay attention to Buechner’s version in their publications, although due to available now experimental data it became clear, that this version is more common for the real systems, especially, for water-salt systems of type 2. Although there are no studied examples of aqueous systems of type 2a up to now, the recent experimental investigations (Poot and de Loos, 2004) on binary system ethane (C2H6) – adamantane(C10H16) which is type 2a proved it to be the system with two critical end-points with critical phenomena in solid saturated solutions (L = G-S) and without any evidences of immiscibility in the system. 1.3.3.2 Binary systems with liquid-liquid immiscibility

TH2O H2O 20 40

60

NaCl

x, mass.% Figure 1.15 T-x projections of phase diagrams for NaCl – H2O system (type 1a) (Reproduced by permission of MAIK / Nauka Interperiodica). T and K are the triple (L-G-S) and critical (L = G) points of pure components. Heavy lines are the composition of liquid phases in monovariant equilibria L-G-S; dot-dashed line is the critical curves L = G (originated in KH2O); solid lines are the composition of liquid phases in isobaric cross-sections of two-phase equilibrium L-G; thin lines are the tie-lines.

The complete form of the liquid-liquid immiscibility region can be achieved only if there is no interference of immiscibility region and crystallization surface, and this region does not ‘touch’ the crystallization surfaces but exists only in solid unsaturated solutions (the main types of fluid phase behavior). Types 1b, 1c and 1d are the versions of complete phase diagrams with three different types of immiscibility region in their complete form. Systems of type 1b with limited (closed-loop) immiscibility region and without critical phenomena in solid saturated solutions (Figure 1.17). In systems of this type, the

94


a

b

T

Q KB

p

KB

p KA TB

p

Q

KA T

TA TA

E

E A

x

B

A

c

p

x

B

d

p

Q

Q

p

p KA

KA TA

KB

KB TA

E

TB

E T

TB

A

x

B

Figure 1.16 Complete phase diagram (three-dimensional p-T-x scheme (a), T-x (b), p-T (c), p-X (d) projections) for binary system A-B of the type 2 without liquid-liquid immiscibility (type 2a) (Reproduced by permission of MAIK / Nauka Interperiodica). p, Q – critical endpoints (L = G-SB); Line values and points as for Figure 1.15.

a

b

KB

T p KB

KA N'

TB KA

TB TA

N'

T N

N

E

E

TA

A

x

B

A

x

c

B

d

p

p KA N'

KA KB

N'

KB

TA N E

TA

N

TB

E T

A

TB x

B

Figure 1.17 Complete phase diagram (three-dimensional p-T-x scheme (a), T-x (b), p-T (c), p-X (d) projections) for binary system A-B of the type 1 with limited immiscibility region (type 1b) (Reproduced by permission of MAIK / Nauka Interperiodica). N, N′ – critical end-points (L = L-G); Line values and points as for Figure 1.15.

monovariant equilibrium (L1-L2-G) is limited by two critical endpoints N and N′ of the same nature (L1 = L2-G). In the p-T-x, p-x and T-x diagrams, the three-phase equilibrium (L1-L2-G) is shown by three curves, two of which (corresponding to the compositions of coexisting liquid phases) coincide in critical points N and N′ (L1 = L2-G). Two

surfaces of coexisting liquid phases in p-T-x space extend from the curves of liquid phases in three-phase equilibrium (L1-L2-G), rise in the direction of higher pressures and interfere along the monovariant critical curve L1 = L2 which connects the critical endpoints N and N′, passing through a pressure maximum – so-called hypercritical solution point.


The isobaric sections of the two-phase immiscibility region produce closed loops that become smaller with increasing pressure therefore such immiscibility regions are sometimes called the ‘closed-loop’ type. Figure 1.18 represents the experimental examples of such phase behavior with limited immiscibility region bounded by the critical curve (L1 = L2) with the hypercritical solution point. However, there are several types of pressure dependence of those closed loops, as it was established by Schneider (1970, 1973, 1976). With increasing pressure the loops may become smaller and finally disappeared completely as shown in Figures 1.17 and 1.18. The loops may first shrinks but do not disappear completely and even become wider again with pressure, as in the systems 4-methylpiperidine (C6H13N) – H2O and 3-methylpyridine (3-C6H7N)- D2O (Figure 1.19). Similar type of phase behavior was found in the system tetraisopentylammonium bromide (C20H44NBr) – H2O (Weingartner and Steinle, 1992), where the upper critical solution temperature (UCST), observed at 369.2 K and atmospheric pressure, displays a minimum in the pressure dependence at about 60 MPa. The low-temperature parts of the closed loops are suppressed by crystallization at around 303 K. The LCST was estimated by symmetrical extrapolation of the upper part of the gap to be about 273 K and shows a maximum in the pressure dependence. In the system 2-methylpyridine (2-C6H7N) – D2O the closed loops shrink and disappear completely with increasing pressures and reappear at higher pressure (Figure 1.19). This high-pressure part of the immiscibility region is called ‘high-pressure immiscibility’ and sometimes it is observed alone without the low-pressure part, as in case of systems 2-methylpyridine – H2O, 3-methylpyridine – H2O, 4methylpyridine (4-C6H7N) – H2O and 4-methylpyridine – D2O (Figure 1.19).

Figure 1.18 p-T projection of limited immiscibility regions (‘closed-loop’ or b type) with the hypercritical solution points in the systems methylketone (C4H8O) – H2O (1), 2-butanol (C4H10O) – H2O (2), 2-butoxyethanol (C6H14O2) – H2O (3) and 2-methylpyridine (C6H7N) – H2O (4) (Schneider, G.M. (1973) In “Water – A Comprehensive Treatise”, edt. F. Franks, Plenum Press, v.2, ch.6, pp. 381–404.).

The available experimental data show a wide diversity of lower and upper critical solution temperature variation with increasing pressure. If the critical curves L1 = L2 do not have the hypercritical solution point, they should intersect a crystallization surface at high pressures and end in the nonvariant critical point L1 = L2-S (Valyashko, 1990a), as it was found for acetonitrile (C2H3N) – H2O and other binary mixtures (Schneider, 1964, 1970). Systems of type 1d (with continuous transition of liquidliquid immiscibility into liquid-gas equilibrium, without critical phenomena in solid saturated solutions) (Figure 1.20). The three-phase equilibrium (L1-L2-G), starting at critical endpoint N (L1 = L2-G), exists in these systems as well as in the systems with an isolated region of immiscibility (Figure 1.17). However, as one can see from Figure 1.20, an increase in temperature results in a three-phase equilibrium (L1-L2-G) ending not at point N1 (L1 = L2-G) but at point R (L1 = G-L2) where the compositions of gas (G) and dilute liquid solutions (L1) coincide. Point R terminates the low temperature branch of the critical curve (L = G) that extends from the critical point KA. In this type of system, immiscibility of liquids does not disappear with the completion of the three-phase equilibrium, but spreads in the direction of higher temperatures in the form of a two-phase equilibrium (L1-L2) or (Fl-L) which passes continuously into equilibrium (G-L) with decrease in pressure. Critical curve NKB, extending from point N, corresponds to the equilibrium (L1 = L2) but it gradually merges into the critical curve (L = G) as it approaches critical point KB.

Figure 1.19 Influence of high pressure on liquid-liquid immiscibility regions of ‘closed-loop’ or b type in the systems 2-methylpyridine (C6H7N) – H2O (1), 4-methylpyridine (C6H7N) – H2O (2), 4-methylpyridine (C6H7N) – D2O (3), 2-methylpyridine (C6H7N) – D2O (4), 3-methylpyridine (C6H7N) – H2O (5), 3-methylpyridine (C6H7N) – D2O (6) and 4-methylpiperdine (C6H13N) – H2O (7) (Schneider, G.M. (1973) In “Water – A Comprehensive Treatise”, edt. F. Franks, Plenum Press, v.2, ch.6, pp. 381–404.).

96


a

b KB

T KB

TB R

p KA

R

R

TB

N

R

KA

TA

T N E

TA E

A

x

B

A

c

p

x

B

d

p

KA

R

R

KA

R TA

KB

KB

N

N TA

E

E

TA T

A

TB x

B

Figure 1.20 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 1 with continuous transition of liquid-liquid immiscibility into liquid-gas equilibrium (type 1d) (Reproduced by permission of MAIK / Nauka Interperiodica). R-critical end-point (L1 = G-L2); Line values and points as for Figures 1.15 and 1.17.

The experimental and theoretical studies of fluid phase equilibria in this type of binary systems demonstrate that the critical curve NKB may have several extremes in temperature and pressure, and not only one pressure maximum as in the version, shown in Figure 1.20. Some of these extremes are due to continuous phase transition from L1 = L2 to L = G; other ones are due to the hypercritical solution points. Two types of phase equilibria gas = gas (with temperature maximum (type 1) and with temperature minimum (type 2) on the critical curve originated in the critical point of nonvolatile component) could be considered as the versions of binary phase diagram of type 1d (Krichevsky, 1940, 1952; Tsiklis, 1969, 1977; Schneider, 1966, 1970, 1978; Rowlinson and Swinton,1982). However, it should be mentioned that the temperature maximum on the critical curve in the case of gas = gas equilibrium, as it was predicted by van der Waals (1894), has not been found experimentally up to now, only the rise of critical temperature with pressure (up to 100 kbar (Van den Bergh et al., 1987; Van den Bergh and Shouten, 1988)) was observed in number of binary mixtures. Aqueous systems with non-polar volatile components, such as Ar (Tsiklis and Prokhorov, 1966; Tsiklis, 1969; Wu et al., 1990), methane (CH4) (Brunner, 1990; Shmonov et al., 1993), ethane (C2H6) (Danneil et al., 1967; Brunner, 1990), CO2 (Todheide and Franck, 1963; Takenouchi, S. and Kennedy, G.C., 1964); Kr (Mather et al., 1993); H2 (Seward and Franck, 1981); N2 (Japas and Franck, 1985a); O2 (Japas and Franck, 1985b); Xe (Franck et al., 1974), where water is less volatile component, are characterized by the high-temperature critical curves (starting in the critical point of water) with temperature minimum

(type 2 of gas = gas equilibrium). Same type of phase behavior was observed in hydrocarbon – water systems (Figure 1.21), such as alkanes – H2O, benzene – H2O (D2O), toluene – H2O, o-xylene – H2O, 1,3,5-trimethylbezene – H2O, carbon tetrafluoride (CF4) – H2O etc. (Schneider, 1970, 1978; Brunner, 1990; Smits et al., 1998). As for binary mixtures with water, such as HCl – H2O (Bach and Friedrichs, 1977), He – H2O (Sretenskaja et al., 1995) or Ne – H2O (Mather et al., 1993), the critical curve commencing from the critical point of water extends to higher temperatures (type 1 of gas = gas equilibrium). When the phase equilibria around the critical point of more volatile component were studied, such as in the cases of aqueous solutions of benzene, cyclohexane, HCl, CO2 etc., an existence of three-phase immiscibility region was established, which gives an additional proof that it is the immiscibility phenomena of type d. Some critical curves in Figure 1.21 pass through a pressure minimum that can be interpreted as a continuous transition of L1 = L2 into L = G. This behavior of critical curve is much more pronounced in the case of carbon dioxide and methane solutions where a transformation of immiscibility region of type d into type c is observed in a set (‘family’) of binary systems with one constant and second variable component (Schneider, 1966, 1970, 1978). In Figures 1.22a,b the T-x projections of binary phase diagrams of type 1d with the low-temperature parts of critical curves L1 = L2 are shown for the water-salt systems H2O – Na2B4O7, H2O – NaHPO4, H2O – UO2SO4 and H2O – K2CO3. However, the studied range of temperatures is far apart from critical temperatures of nonvolatile components


(salts) where the extreme of critical curves L1 = L2 could be observed.

3000 2 p, bar

7 1

2000

5 2 phase

3 4 6

1000 8 1 phase

Systems of type 1c (with two immiscibility regions of different nature, without critical phenomena in solid saturated solutions) (Figure 1.23). As one can see from Figure 1.23, this version of the complete phase diagram includes all the phase equilibria discussed above for two versions of phase diagrams with immiscibility phenomena. The closed-loop immiscibility region (as in Figure 1.17) occurs at lower temperatures, whereas the second immiscibility region with continuous transition of liquid-liquid into liquid-gas equilibrium (as in Figure 1.20) occurs at higher temperatures. As it was mentioned above, there is no experimental examples for binary systems of exactly type 1c. However, in binary mixtures of methane (CH4) with 1-hexane (C6H12) and 3.4dimethylpentane (Schneider, 1970, 1976, 1978) the phase behavior of type 1c’ (see Figure 1.13) was observed.

0 300

320

340

360

380

400

420 T, ºC

Figure 1.21 High temperature branches of binary critical curves starting from critical point of water pass temperature minimum showing gas = gas equilibria of type 2 (Schneider, G.M. (1973) In “Water – A Comprehensive Treatise”, edt. F. Franks, Plenum Press, v.2, ch.6, pp. 381–404.). Binary systems with the immiscibility region of type d: 1benzene (C6H6) – H2O; 2 – benzene (C6H6) – D2O; 3- toluene(C7H8) – H2O; 4 – o-xylene (C8H10) – H2O; 5 – 1,3,5-trimethylbenzene(C9H12) – H2O; 6 – cyclohexane (C6H12) – H2O; 7 – ethane (C2H6) – H2O; 8 – n-butane (C4H10) – H2O.

When the region of immiscibility overlaps with the surfaces of crystallization, new equilibria (L1-L2-S), (L1-L2-GS), (L1 = L2-S) appear, thus giving another types of complete phase diagram presented in the central column of systematic classification (Figure 1.13). Systems of type 1b¢ (with limited immiscibility region in solid saturated and unsaturated solutions, without critical phenomena L = G in solid saturated solutions) (Figure 1.24). The intersection of two three-phase equilibria (L-GSB) and (L1-L2-G) results in the nonvariant equilibrium L (L1-L2-G-SB). There is a jump in composition on the curve of solid saturated liquid solution ETB in the equilibrium (LG-SB). The low-temperature critical endpoint N (L1 = L2-G)

T, ºC TNa2B4O7 700

500 RK2CO3

RNa2B4O7

KH2O NK2CO3 300 NNa2B4O7 0 (a)

(b)

40

80

x, mass.%

Figure 1.22 T-x projections of three-phase immiscibility region, salt solubility and critical (G = L and L1 = L2) curves for binary water-salt systems of type 1d: a) H2O – K2HPO4 and H2O – UO2SO4, b) H2O – K2CO3 and H2O – Na2B4O7. Dashed lines show the composition of critical phase G = L (critical curve KH2OR); dash-dotted lines show the composition of critical phase L1 = L2 (critical curve starting from critical endpoint N (L1 = L2-G)); solid lines show the composition of liquid phases in equilibrium L1-L2-G and liquid solutions saturated with solid salt in equilibrium L-G-S. Circles show the composition of critical phase in nonvariant equilibria KH2O (L = G for pure water) and R (L1 = G-L2), N (L1 = L2-G) for binary systems. Triangles show the composition of liquid phase in nonvariant equilibria for one-component (L-G-SNa2B4O7) and binary (L1 = G-L2; L-G-S1-S2) systems.

98


a

b

KB

T R

p

R

KB

TB

KA R

N'' N'

TB

TA

KA N'' N'

T N

N

E

TA

A

x

E

B

A

x

c

B

d

p

p KA

R

R

R

KA KB

N'' TA

N'

N''

KB

x

TB B

N' N

N E

TA

TB

E T

A

Figure 1.23 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 1 with two three-phase immiscibility regions of different types (type 1c) (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins). Line values and points as for Figures 1.15, 1.17 and 1.20. KB

T

a

b KB

p

TB KA

M N

TB KA

T L

L L

TA

N L

TA

E

M

E A

x

B

A

c

x

B

d

p

p

KA M

KA

N

M

KB

KB

TA L

N L L. E

TA

E TB

TB T

A

x

B

Figure 1.24 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 1 with limited immiscibility region in saturated and unsaturated solutions (type 1b¢) (Reproduced by permission of MAIK / Nauka Interperiodica). L – nonvariant equilibrium (L1-L2-SB-G); M – critical equilibrium (L1 = L2-SB); Line values and points as for Figures 1.15 and 1.17.

is in the metastable region of supersaturated solutions (MLN′). The monovariant curve LM representing the immiscible liquids saturated with crystals B (equilibrium L1-L2SB) starts from the points of coexisting liquid phase

compositions of equilibrium L (L1-L2-G-SB) in the direction of higher pressures. This equilibrium ends at the critical endpoint M (L1 = L2-SB), where the stable critical curve of immiscibility MN (L1 = L2) starts.


T-x projection of phase diagram for the system HgI2 – H2O is in Figure 1.25. Salt solubility (L-G-S, L1-L2-G-S), liquidliquid immiscibility (L1-L2-G, L1-L2-G-S) and critical phenomena (L = G) are displayed as the curves corresponding

to the compositions of liquid phases at equilibrium. Similar phase behavior was found in water-hydrocarbon systems (H2O – acetonitrile (C2H3N), H2O – o-xylene (C8H10), H2O – naphthalene (C10H8), H2O – biphenyl (C12H10) etc. (Schneider, 1966, 1970; Alwani and Schneider, 1969)) which were studied not only at saturation vapor pressure, as the water-salt system, but also in a wide range of pressures. It is evident that exactly the same phase behavior should be found in the complete phase diagram of type 1c¢ when the low-temperature region of closed-loop immiscibility overlaps with the surface of crystallization for a system with two types of immiscibility region. The second high-temperature immiscibility region with continuous transition of liquidliquid into liquid-gas equilibrium is the same as in type 1c. Such phase behaviour was established in the systems methane (CH4) – 1-hexene (C6H12) and methane (CH4) – 3.3-dimethylpentane (C7H16) (Schneider, 1970, 1976, 1978). Threedimensional P-T-X scheme for type 1c¢ is not shown.

Figure 1.25 T-X projection of phase diagram for the system HgI2 – H2O (type 1b¢) (Valyashko, V.M. and Urusova, M.A. (1996) Zh. Neorgan. Khimii, 41, n.8, pp. 1355–1369(russ); Russ. J. Inorgan. Chem., 41, pp. 1297–1310(eng). From Elsevier). KH2O and THgI2 are the critical and triple points of pure H2O and HgI2 (open circle and square); solid circle and square are the composition of liquid phases in critical nonvariant equilibrium N (L1 = L2-G) and in nonvariant equilibrium L (L1-L2-G-S); dots are the experimental points (Valyashko and Urusova, 1996). Heavy lines are the composition of liquid phases in monovariant equilibria LG-S and L1-L2-S; dot-dashed line is the critical curves L = G originated in KH2O; thin lines are the tie-lines in nonvariant equilibria.

Systems of type 1d¢ (with immiscible saturated and unsaturated solutions, and continuous transition of liquid-liquid into liquid-gas equilibrium; without critical phenomena L = G in solid saturated solutions) (Figure 1.26). The immiscibility region of solid saturated solutions (LM) in systems of this type is the similar to that considered above (Figure 1.24). Comparing schemes of phase diagrams in Figures 1.17 and 1.24, and in Figures 1.20 and 26 one can see that the overlap of fluid equilibria (L1-L2-G) with the crystallization surfaces (L1-L2-G) cuts the low-temperature part of the immiscibility regions of types b and d, and

a

b

KB

T KB TB

p R

R

KA

TB

R

M L

M

KA

T

L

R

L

L

TA TA

E

E A

x

B

A

x

c

B

d

p

p M

M KA R

R

R

KA TA

KB

L

L

KB L

TA E

TB

E T

A

TB x

B

Figure 1.26 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 1 with immiscible saturated and unsaturated solutions and continuous transition of liquid-liquid equilibrium into liquidgas one (type 1d¢) (Reproduced by permission of MAIK / Nauka Interperiodica). Line values and points as for Figures 1.15 and 1.20.

100


transforms it into a state of metastable supersaturated solutions (see field MLN). Solubility curve in equilibrium L-G-S, broken by the immiscibility region, as well as compositions of coexisting liquid solutions at saturation vapor pressure near the critical point of water KH2O (the volatile component in water-salt system) and end-point R (L1 = G-L2), corresponding to the topological scheme of type 1d¢ (Figure 1.26), are shown in Figure 1.27 for the system PbI2 – H2O. The same type of phase behavior was found for the water-organic systems, shown in Figure 1.21, with water being the nonvolatile component. The dp/dT slope of the monovariant curves L1-L2-G and L-G-S can be different in various systems and the overlap of fluid equilibria (L1-L2-G) with the crystallization surface (L-G-S) could make high-temperature part of the threephase immiscibility region (L1-L2-G) metastable and lowtemperature part stable (see schemes for types 1b≤, 1c≤ and 1d≤ in Figure 1.13). There are several experimental examples of phase behavior of type 1d¢ (see above). The system UO2F2 – H2O [Marshall et al, 1954a] with some reservations can be related to type 1d≤, since the experimental studies are limited by temperature of the critical point “p” (L = G-SB) and it is not clear whether or not there is the supercritical fluid region at higher temperatures as in the case of type 2d≤ or this region is absent as in type 1d≤.

Figure 1.27 T-X projection of phase diagram for the system PbI2 – H2O (type 1d¢) (Valyashko, V.M. and Urusova, M.A. (1996) Zh. Neorgan. Khimii, 41, n.8, pp. 1355–1369(russ); Russ. J. Inorgan. Chem., 41, pp. 1297–1310(eng). From Elsevier). KH2 O and TPbI2 are the critical and triple points of pure H2O and PbI2 (open circle and square); solid circle and square are the composition of fluid phases in critical nonvariant equilibrium R (L1 = G-L2) and in nonvariant equilibrium L (L1-L2-G-S); dots are the experimental points (Valyashko and Urusova, 1996). Heavy lines are the composition of liquid phases in monovariant equilibria LG-S and L1-L2-S; KH2 OR is the critical curve L = G; thin lines are the tie-lines in nonvariant equilibria.

Systems of type 2d≤ (with stable and metastable three-phase (L1-L2-G) immiscibility and critical phenomena L = G in solid saturated solutions) (Figure 1.28). Immiscibility of the a

b

KB

T KB TB

Q TB

p

Q M

M p

p

T

KB

L N

L

L

KB

TA

N TA E

A

x

B

A

c

x

d

p Q

p

Q M

M p

KA

p KB

TA E

N

B

L

KA TA

L

B

E

TB T

KB N

A

TB x

B

Figure 1.28 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 2 with immiscibility arising at vapor pressures (type 2d≤) (Reproduced by permission of MAIK / Nauka Interperiodica). Q – critical end-point (L1 = L2-SB); Line values and points as for Figures 1.15, 1.17, 1.20.


liquid phases arises in the region of unsaturated solutions, similar to that in type 1d (see Figure 1.20). However, in Figure 1.28 (in contrast to Figure 1.20) there is no high-temperature part of the three-phase equilibrium (L1-L2-G) with critical endpoint R (L1 = G-L2) because they are metastable due to the overlap of equilibria (L-G-SB) and (L1-L2-G). As a result, there is an invariant equilibrium L (L1-L2-GSB) where the composition of the liquid phase decreases stepwise towards the composition of dilute liquid solution and vapor. Further increase in temperature leads to the threephase equilibrium (L-G-SB) (curve Lp) and to critical phenomena between liquid and vapor in the presence of crystals B (critical endpoint ‘p’, L = G-SB). The low-temperature part of the critical curve (L = G), extending from the critical point of component A (KA) to the critical endpoint ‘p’, is the stable curve KAp, whereas the high-temperature part (pKB) is absent. Immiscibility region of solid saturated solutions (curves LM, L1-L2-SB) ends at critical point M (L1 = L2-SB), which is the critical endpoint for the critical curve NM (L1 = L2), originated in another critical endpoint N (L1 = L2G). At higher temperatures, as in all systems of type 2 (p-Q), there is a region of supercritical fluid equilibria that exists up to the temperature of the second critical endpoint Q (L1 = L2-SB) where the fluid acquires the ability to become heterogeneous with changing pressure. Further increase in temperature and decrease in pressure results in a continuous transition of liquid-liquid immiscibility to gas-liquid equilibrium: equilibrium (L1-L2-SB) becomes (G-L-SB) with decreasing pressure along curve QTB, equilibrium (L1 = L2) becomes (L = G) along curve QKB and equilibrium (L1-L2) becomes (G-L) as they approach the liquid-gas curve TBKB. This type of complete phase diagram was discovered as a result of experimental study the binary system H2O – BaCl2 (Valyashko et al., 1983). As one can see from Figure 1.29, the low-temperature part of immiscibility region NLML is in a very narrow region of temperatures (380–385 °C) and pressures (24–28 MPa) and bounded by the stable critical curve NM (L1 = L2). High-temperature part of immiscibility region appears in the critical endpoint Q (485 °C; 95–100 MPa; 30–40 mass.%). Dotted line shows the metastable part of critical curve (L1 = L2), which occurs under the surface of salt solubility in supercritical fluid solution. Systems of type 2d¢ (with metastable three-phase (L1-L2-G) immiscibility and critical phenomena L = G in solid saturated solutions) (Figure 1.30). In systems of this type, the entire three-phase equilibrium (L1-L2-G) is in the metastable region of supersaturated solutions. The metastable immiscibility equilibria (L1 = L2, L1-L2) become stable only for temperatures at and above the second critical endpoint Q (L1 = L2-SB). The metastable equilibria in systems of type 2d¢ and 2d≤, shown in Figures 1.28 and 1.30, cannot be observed experimentally. In the case of type 2d≤ there are stable equilibria L1-L2-G and L1-L2-G-S indicating an existence of immiscibility phenomena hidden in part by the occurrence of a solid phase. Such indicators are absent in the systems of type 2d¢, moreover the stable equilibria in the types 2d¢ and 2a are very similar and therefore difficult to tell these phase behavior apart. However, the presence of

p, MPa 140

L1=L2 524 oC

120 500 oC 100 480 oC 450 oC

Q 80 Fl-S 60 40

KH2O

o p M 385

L N

H2O 20

382 oC 375 o

L

40

60

80

BaCl2

x, mass.%

Figure 1.29 p-X projection of phase diagram for the system BaCl2 – H2O (type 2d≤) (Valyashko, V.M., Urusova, M.A. and Kravchuk, K.G. (1983) Dokl. Akad. Nauk SSSR, 272, pp. 390–394. Reproduced by permission of MAIK / Nauka Interperiodica). Open circle and square are the critical (KH2O) and triple points (TBaCl2) of pure components; solid circles are the composition of liquid phases in critical equilibria N (L1 = L2-G), M (L1 = L2-S), p (L = G-S) and Q (L1 = L2-S); solid triangles are the composition of liquid phases in nonvariant equilibrium L (L1-L2-G-S); solid squares are the composition of liquid and solid (hydrate) phases in the lowtemperature part of equilibrium L-G-S, which ends in critical endpoint ‘p’. Heavy lines are the composition of liquid phases in monovariant equilibria L-G-S, L1-L2-G, L1-L2-S; dashed lines show the composition of liquid phases in the extension of the studied high-temperature part of three-phase curves L1 = L2-S to the triple point of BaCl2 (L-G-S); dot-dashed lines are the critical curves L = G (KH2Op) and L1 = L2 (NM and the curve originated in point Q ); dotted line is the metastable part of the critical curve L1 = L2; solid lines show the composition of liquid (fluid) phases in two-phase equilibria Fl(L)-S and L1-L2; thin lines are the tie-lines.

metastable regions of immiscibility reflects the features of stable equilibria, thus making it possible to determine which type of phase diagram the system under study belongs to. In the case of type 2a, the low- and high-temperature branches of the three-phase (L-G-S) solubility and critical (L = G) curves are the same, whereas in the case of type 2d¢ the high-temperature part (in the vicinity of critical endpoint Q) of solubility and critical curves correspond to another equilibria L1-L2-S and L1 = L2, respectively. The distinctions between the p-T projections of ether – anthraquinone (type 2a) and CO2 – diphenylamine (type 2d¢) are evident from Figure 1.31. It is clear that the stable parts of binary monovariant curves in Figure 1.31a belong to the same interrupted solubility and critical curves, whereas the nature of low- and high-temperature branches of solubility curves in the system CO2 – diphenylamine (Figure 1.31b) are different. Moreover, as it was mentioned by Buechner (1906, 1918), the bend of high-temperature branch of a solubility curve indicates a continuous phase transition from G-L-S to L1-L2-S with increasing pressure. Such inflexion and sometimes even a temperature

102


a

b

KB

T

Q

KB TB

p KA

Q

p

TB

p KA

T TA E

TA E

A

x

B

A

x

c

B

d Q

Q

p

p p

p KA

KA KB

KB

TA TA E

TB

E T

A

TB x

B

Figure 1.30 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 2 with metastable three-phase immiscibility region (type 2d¢) (Reproduced by permission of MAIK / Nauka Interperiodica). Line values and points as for Figures 1.15 and 1.26.

(a)

(b)

Figure 1.31 p-T projections of phase diagrams for (a) ether (C4H10O) – anthraquinone (C14H8O2) (type 2a) (Smits, 1905, 1911) and (b) CO2 – diphenylamine ((C6H5)2NH) (type 2d¢) (Buechner, E.H. (1906) Z. Phys. Chem., 56, pp. 257–318.). Open circles are the critical points of volatile components (KC7H16O and KCO2) and triple points of nonvolatile components (TC14H18O2 and TDH). Solid circles are the critical endpoints p (G = L-S) and Q (G = L-S). Dots are the experimental points. Thin lines are the monovariant curves for one component systems. Heavy lines are the monovariant curves for binary systems.


p, MPa

T, ºC

250 600

8

a

b

9

200 7

7

1

500

3

.

5 2

2

100

4

400 KH2O

3 14

4 5 13

6 12,11

9 10

6 11 12

300 13

KH2O 14

200

1

8

16

15

300

400

500

600

H2O

T, ºC

5

10

x, mol.%

T, ºC TNa2SO4

800

600 150 Q 400

KH2O p

130 MPa 120 MPa 100 80 20 40 60 MPa

200

TH2O H2O

50

15

Figure 1.32 Monovariant curves and nonvariant critical points of the binary aqueous systems of types 1a (9, 10), 1d (11–13, 15, 16), 2d¢ (1, 3–8) and 2d≤(2) with Na2CO3 (1), Na2SO4 (2), BaCl2 (3), Li2SO4 (4), K2SO4 (5), KLiSO4 (6), Na2SiO3 (7), Na2Si2O5 (8), NaCl (9, 10), Na2WO4 (11), Na2MoO4 (12), UO2SO4 (13), Na2B4O7(15) and Na2HPO4 (16) on p-T (a) and T-x (b) projections of phase diagrams (Reproduced by permission of MAIK / Nauka Interperiodica). Dot-dashed lines 1–8, 11–13,15, 16 are the critical curve L1 = L2 in binary systems of types 2d¢, 2d≤ and 1d. Twodots-dashed line (9) and solid line (10) are the critical curve L = G and monovariant curve L-G-S in the system of type 1a. Solid lines (1–8) are the parts of high-temperature monovariant curves L1-L2-S in binary systems of types 2d¢ and 2d≤. Heavy and dashed lines (14) are the curve L-G of pure H2O and the supercritical extrapolation of this curve. KH2O – critical point of pure H2O. Open circles are the critical endpoints Q (L1 = L2-S) in binary systems of types 2d¢(1, 3–8) and 2d≤(2). Solid circles are the critical endpoints N (L1 = L2-G) in binary systems of type 1d (11–13, 15, 16).

1. The parameters of the second critical endpoint Q (L1 = L2-S) and neighboring portions of curves QTB (L1-L2-S) and QKB (L1 = L2-S) are characterized by pressure values that are considerably higher than those of the supercritical transition of water from a gas-like to a liquid-like state (critical isochore or supercritical extrapolation of liquid-gas curve for pure water or those which correspond to the critical curves L = G in water-salt systems of type 1a (two-dots-dashed line in Figure 1.32) at the same temperature). 2. The extrapolation of critical curve QKB to the region of lower temperatures (in the vicinity of critical point of pure water (KA) and the first critical endpoint p) on the p-x projection of the phase diagram leads to a region of compositions of supersaturated concentrated solutions rather than to the critical point of pure water.

Na2SO4

x, mass.% Figure 1.33 T-x projection of phase diagram for the system Na2SO4 – H2O (type 2d¢) (From Elsevier). T and K are the triple (L-G-S) and critical (L = G) points of pure components; Q and p are the critical endpoints L1 = L2-S and L = G-S. Heavy lines are the composition of liquid phases in monovariant equilibria L-G-S and L1-L2-S; dashed lines show an extension of the studied part of three-phase curves L1 = L2-S up to the triple point TNa2SO4; dot-dashed lines are the critical curve L1 = L2 (originated in Q); solid lines are the composition of liquid phases in isobaric cross-sections of two-phase equilibria; thin lines are the tie-lines.

minimum were observed in several non-aqueous systems. In some non-aqueous systems with gases the p-T projection of solubility curve starting in the triple point of the nonvolatile component has a positive slope (Streett, 1983; Paulaitis et al., 1983; Lu and Zhang, 1989). Solubility curves in watersalt systems, extending from the melting point of salts, usually have the negative slope (Kravchuk and Todheide, 1996), and can have a pressure maximum (Figure 1.32a). Other features listed below for type 2d¢ with a metastable three-phase immiscibility region are shown in Figure 1.32.

Figure 1.33 shows a T-x projection of phase diagram for H2O – Na2SO4 that is typical for binary water-salt systems of type 2d¢. It has two three-phase solubility regions terminated by the critical endpoint p and Q, which are separated by a field of supercritical fluid-solid (Fl-S) equilibrium, shown as the isobars of solubility at 20–120 MPa. Lowtemperature solubility region, shown by the curve of liquid phase composition, has a negative temperature coefficient of salt solubility and ends in the critical point p (L = G-S). High-temperature three-phase region in the vicinity of the second critical endpoint Q (L1 = L2-S) is described as L1-L2-S (by two curves running to the triple point of pure Na2SO4 (TNa2SO4). 1.4 PHASE EQUILIBRIA IN TERNARY SYSTEMS 1.4.1 Graphical representation of ternary phase diagrams The most correct and complete representations of fourdimensional ternary phase diagrams would be the isothermal or isobaric triangle prisms with vertical axis as either pressure or temperature and triangle base as the ternary

104


concentrations. All types of phase behavior can be described by sets of such prisms. However, these phase diagrams would be very difficult to interpret due to numerous points, curves and surfaces. And there is not enough experimental data on ternary equilibria in a wide range of temperature, pressure and composition to draw those sets of prisms. The two-dimensional p-T projection or triangle prism of T-x and p-x projections can be used for correct representations of mono- and nonvariant equilibria over the wide ranges of temperature and pressure. Sometimes the threedimensional T-x or p-x projection can be drawn as a triangle of ternary concentrations with a set of isotherms or isobars, which describe the phase behavior in a range of temperature or pressure. Usually such triangles are used to show only one surface. For instance, a critical surface or a surface of liquid phase composition in equilibrium with other phases in a wide range of ternary composition, or the borders between several adjacent surfaces – the eutonic curves (LG-SB-SC) between the two solubility surfaces of several nonvolatile components. Figure 1.34 is an example of three-dimensional T-x projection for ternary system A-B-C, where the nonvolatile

components (B, C) form continuous solid solutions, the binary subsystems A-B and A-C (with the volatile component A) are characterized by the eutectic equilibria (L-GS1-S2). Binary subsystems A-C and C-B belong to the type 1a, whereas the subsystem A-B belongs to the type 1b¢. The ternary phase diagram shows only the surfaces of liquid phase compositions in equilibria L1-L2-G (N-L-LN-L-N) and L-G-S (shady surface (TA-EAC-TC-TB-L-LN-L-EAB-TA), and the critical surfaces KAKBKC (L = G) (shady surface) and N-M-LN (L1 = L2) (dark shady surface). The T-x projections of binary phase diagrams are simplified since the points and curves of vapor (gas) phase compositions in non- and monovariant equilibria L-G-S1-S2, L1-L2G-S, L-G-S and L1-L2-G are not shown in Figure 1.34a. Thin lines on the surfaces show the ternary cross-sections at constant ratios of nonvolatile components (B/C). These sections depict the continuously transforming T-x diagrams of quasi-binary subsystems with permanent volatile component A and nonvolatile component represented by a continuously changed mixture (solid solution) of B and C. The stable (N-L-LN-L-N) and metastable (Nms-L-LN-L-Nms) parts of ternary immiscibility region shrink with increase of C

KB

KC

T N

T KA

T

TB

N

M L

N

M L L

EAB Nms NL LN

M L LN

X*

TA EAC

A

B

TB

N Nms

EAB

(a)

LN

EAC

X

EAB Nms

EAC

B

C

X*

C

(b)

Figure 1.34 Prismatic representation of T-x projection for complete phase diagram of ternary system A-B-C (A is volatile component (solvent), B and C are nonvolatile components) (a) and T-X* projection of ternary monovariant curves on the plane T-B-C (b) (Reproduced by permission of IUPAC). Points TA, TB, TC and KA, KB, KC are the triple and critical points of pure components; points EAB, EAC, L, M, N are the compositions of liquid and critical phases in binary nonvariant equilibria L-G-SA-SB, L-G-SA-SC, L1-L2-G-SB and L1-L2-G-SB. Solid lines are the compositions of liquid and critical phases in binary monovariant equilibria L-G-S, L1-L2-G and L1-L2-S. Thin lines are the composition of liquid and critical phases at constant B/C ratio in ternary equilibria L-G-S, L1-L2-G, L1-L2-S and L = G. Dashed lines are the composition of critical phase in binary (L1 = L2) and ternary (L1 = L2-G) monovariant equilibria. Dot-dashed line is the composition of critical phase in ternary monovariant equilibrium L1 = L2-S. Dotted lines are the metastable parts of binary (L1-L2-G and L1 = L2) and ternary (L1 = L2-G) monovariant curves. Heavy lines are the compositions of liquid and critical phases in ternary monovariant equilibria L1-L2-G-S, L-G-SA-SBC, L1 = L2-G and ternary L1 = L2-S. Shaded surfaces are the compositions of liquid phase in ternary equilibrium L-G-S (in Figure 1.34(a)) and the compositions of critical phases in ternary equilibrium L = G (in Figure 1.34(a)) and L1 = L2 (in Figures 1.34(a) and (b)). X* is the relative amounts of the nonvolatile component B in ternary solutions [X* = xB/(xB+xC)] (solvent-free concentration).


concentration in the mixture, and end in the nonvariant critical point LN (L1 = L2-G-S), which coincides with double critical endpoint NN′ (L1 = L2-G) on this figure. The p-T projections do not carry information on composition of the equilibrium phases. An attempt has been made to use a four-angle prism with p, T, and X* as axes for a representation of divariant critical surfaces and monovariant critical curves in the ternary systems as a continuous set of quasi-binary p-T sections at constant X* (Schneider, 1993; Bluma and Deiters, 1999). The X* axis denotes relative amounts of the non-volatile components X* = x2/(x2 + x3) in ternary solutions. However, in such diagrams the representations of the critical point of a volatile component and equilibria in the vicinity of composition enriched with volatile component are not visually correct, because the critical point of volatile component is displayed as a straight line. To avoid this uncertainty and to circumvent an application of three-dimensional figures which are usually complicated for perception, the two-dimensional T-X* projections can be used for presentation the ternary equilibria between phases enriched with nonvolatile components. As one can see from Figure 1.34, the T-X* diagram (Figure 1.34b) is obtained by a projection of the three-dimensional ternary T-x diagram into the T-X* plane (C-B-TB-KB-KC-TC-C) and contains only binary (EAB, EAC, N, L, M, Nms) and ternary (LN) nonvariant points and ternary monovariant curves (EAB-EAC, N-LN, LLN, M-LN, Nms-LN). Nonvariant points of pure components can be omitted on the T-X* projection because they do not take part in a formation of ternary monovariant curves. Various points on the ordinates of T-X* diagram show temperature of all nonvariant equilibria (stable and metastable) in binary subsystems A-B and A-C, and are the starting points for ternary monovariant curves, corresponding to the equilibria spreading from the binary subsystems into three-component region of composition. The type of binary subsystems is uniquely determined by a combination of these binary nonvariant points on the ordinate of T-X* diagram. For instance, the set of nonvariant points Nms; L; M; N′ corresponds to type 1b¢, N; N′ – type 1b, N; L; M; Nms – type 1b≤, N; N′; N; R – type 1c, Nms; L; M; N′; N; R – type 1c¢, N; R – type 1d, Nms; L; M; R – type 1d¢, N; L; p; Rms – type 1d≤, Nms; p; Rms; Q – type 2d¢, N; L; M; p; Rms; Q – type 2d¢ (where Nms and Rms are the metastable nonvariant points N and R, respectively) etc. It is assumed that the vapor (gas) phase of the equilibria (L1 = L2-G) and (L1-L2-G-S) as well as the critical phase of the equilibrium (L1 = G-L2) are almost pure volatile component and not plotted on the T-X* projection. Therefore, the position of the monovariant equilibria on the T-X* diagrams (Figures 1.34–1.37) are shown by the composition of liquid or critical phases enriched with non-volatile components. The critical curves L1 = L2 (see curves N-LN (dashed line) and M-LN (dot-dashed line) in Figure 1.34b) indicate the equilibria (L1 = L2-G) and (L1 = L2-S); the curves of the liquid phase composition (one or both equilibrium liquids if they have the same B/C ratio) – the equilibria (L1-L2-G-S) and (L-G-S1-S2) (see solid lines L-LN and EAB-EAC in Figure 1.34b), the curve of non-critical phase (L2) composition

(absent in Figure 1.34, see dashed lines in Figures 1.35– 1.37) – the critical equilibrium L1 = G-L2, the curve of critical phase (L = G) composition (absent in Figure 1.34, see dot-dashed lines in Figures 1.35–1.37) – the critical equilibrium (L = G-S). As it was mentioned above, the quasi-binary sections AB/C (where the ratio of nonvolatile components is constant) there is the vertical cross-section traversing the divariant surfaces and monovariant curves in the three-dimensional T-x projection (Figure 1.34a). In the case of T-X* diagram (Figures 1.34b, 1.35, 1.36), it is the vertical line that intersects the monovariant curves at points corresponding to the nonvariant equilibria in a quasi-binary section.

1.4.2 Derivation and classification of ternary phase diagrams The experimental investigations were and are the main sources of information about phase behavior in ternary systems. In the beginning of the twentieth century Smiths (1910, 1913, 1915) using the topological method and available experimental information has considered 12 versions of complete phase diagrams with various types of fluid phase behavior and solid phase transformations. But it was not a systematic classification. A great amount of experimental data on solubility, immiscibility and critical phenomena in various ternary mixtures was collected during the twentieth century. These data were summarized in many reviews and monographs (Tamman, 1924; Anosov and Pogodin, 1947; Ricci, 1951; Ravich, 1974; Rowlinson and Swinton, 1982; McHugh and Krukonis, 1994; Valyashko, 1990; Sadus, 1992; Prausnitz et al., 1998, etc.). The main principles of phase behavior in ternary systems were considered in these books and several classifications of ternary mixtures based on chemical compositions of components or on various features of solid or fluid phase behavior were suggested. However, all these classifications based on the experimental results did not take into account global phase behavior of fluid mixtures which is especially important for derivation of systematic classification for ternary systems at sub- and supercritical conditions. The first systematic approach to a derivation the global phase diagram of ternary fluid mixture using an analytical investigation of the Van der Waals equation of state with standard one-fluid mixing rules was developed by Bluma and Deiters (1999). Eight major classes of ternary fluid phase diagrams were outlined and their relationship to the main types of binary subsystems were established. As mentioned above, the method of continuous topological transformation (Valyashko, 1990a,b; 2002a,b) can be used to study not only the fluid phase diagrams but also the complete phase diagrams where the equilibria with solid phase occur. This advantage of the topological approach permits to obtain more general, complete and systematic information about the main features of phase behavior in ternary mixtures. Therefore, additional information concerning the topological approach to the derivation of ternary phase diagrams as well as some conclusions obtained as a

106


- binary critical point N (L1=L2-G) - binary critical point R (L1=G-L2) - ternary critical point N'N (L1=L2-S) - tricritical point NR (L1=L2=G) - ternary monovariant critical curves

1b

α

β

1c 1b

γ

1c 1b

1c 1b

B

X*

C B

X*

C B

X* C B

1c

α

1d 1c

β

1d 1c

ε

B

X*

C B

X*

C B

X* C B

1d 1c

δ

ε

1c 1b

X* C B γ

1d 1c

X* C B

1c

X* C δ

1d

X* C

Figure 1.35 Main types of fluid phase diagrams (T-X* projections) for ternary mixtures with one volatile component (A) and immiscibility phenomena of types b, c and d in binary subsystems A-B and A-C (Reproduced by permission of the PCCP Owner Societies). Row I contains the fluid phase diagrams of ternary class (1a-1b-1b), row II – ternary class (1a-1c-1c), row III – ternary class (1a-1d-1d), row IV – ternary class (1a-1b-1d), row V – ternary class (1a-1b-1c), row VI – ternary class (1a-1c-1d).

result of systematic investigation of ternary phase behavior for the systems with one volatile and two non-volatile will be discussed further in details. To simplify ternary phase diagrams the following limitations are accepted in a process of phase diagrams derivation: 1. Ternary system consists of one volatile and two nonvolatile components, such phenomena as an azeotropy in liquid-gas equilibria and a formation of binary or ternary compounds are absent. Solid phases of volatile and each non-volatile components are completely immiscible and have the eutectic relations in equilibrium with fluid phases, whereas the solid phases of non-volatile components form a continuous solid solution. 2. Binary subsystems with volatile component are complicated with the immiscibility phenomena. However, the immiscibility regions spreading from the binary subsystems are not necessarily joined to form a unified immiscibility region, they can be separated in ternary solutions by the miscibility region. 3. Binary subsystem, consisted of two non-volatile components, does not have immiscibility phenomena and characterized by complete miscibility of components in solid state and by fluid phase behavior of type 1a (no immis-

cibility and critical phenomena in solid saturated solutions). 1.4.2.1 Derivation of ternary phase diagrams using the systematic classification of binary phase diagrams In case the phase behavior of the constituent binary subsystems is known, the task of constructing a topological scheme for a ternary system translates into finding a new nonvariant equilibria. These equilibria are represented as the points on the phase diagram. Those points are the intersections of monovariant curves originated at nonvariant points of the constituent binary subsystems. While changing from one subsystem to another, the phase diagrams of the binary subsystems must undergo continuous topological transformations in the three-component region of composition. Generally this process can be seen as a continuous phase diagram transformation of quasi-binary sections of the ternary system with one constant component and another continuously changing one. In this discussion we will only consider the case with one constant component being a volatile component and a second nonvolatile component being continuously changing one. It would be a mixture of second and third nonvolatile components of that ternary


system. This approach is called ‘quasi-binary approach’ to the ternary phase equilibria and is used often in modern literature (Schneider, 1978, 2005; Smiths et al., 1998; Peters and Gauter, 1999, etc.). Representation of three-component systems as a set of quasi-binary cross-sections is not quite rigorous for the most real ternary mixtures because a ratio of second and third components in equilibrium phases is not usually constant. However, if we intend to study the phase behavior from the point of view of topological schemes, the sequence of binary phase diagrams of quasi-binary sections (including the sections through the ternary nonvariant points) give an exhaustive description of possible phase equilibria and phase transformations in ternary systems. If the phase diagrams of the binary subsystems are present in Figure 1.13, then all the steps of the topological transformation between these diagrams are also shown on the same figure as a set of complete phase diagrams corresponding to the quasi-binary sections. Such sets include the boundary versions of phase diagrams, which show ternary nonvariant points that should appear in the studied three-component systems. For example, the sequence of quasi-binary sections of ternary phase diagram for the systems with binary subsystems of types 1a and 1b¢ should be the following: 1a⇔ 1ab¢⇔1b¢ or 1a⇔1ab⇔1b⇔1bb¢⇔1b¢, according to Figure 1.13. The first version of phase behavior one can see in Figure 1.34 where the cross-section through the ternary critical point LN corresponds to the boundary phase diagram 1ab¢ in Figure 1.13. Usually this approach for ternary phase diagram derivation gives several versions of ternary diagrams for each combination of binary subsystems because there are several ways for continuous transformation of a set of binary phase equilibria into another one. For instance, the immiscibility regions spreading from two binary subsystems of type 1 can either merge or be separated by a miscibility region. Hence, if two binary subsystems belong to types 1b and 1d, the set of quasi-binary sections should be 1b⇔1bc⇔1c⇔1cd⇔ 1d or 1b⇔1bc⇔1c⇔1CD⇔1d when spreading immiscibility regions are joined, or 1b⇔1ab⇔1a⇔1ad⇔1d when a miscibility region separates the immiscibility regions. When two binary subsystems belong to types 1b¢ and 1d¢ even in the case of two immiscibility regions separated by a miscibility one, the following sequences of phase transformations are possible in the ternary systems: 1b¢⇔1ab¢⇔ 1a⇔1ad⇔1d⇔1dd¢⇔1d¢ or 1b¢⇔1b¢b⇔1b⇔1ab⇔1a ⇔1ad⇔1d⇔ 1dd¢⇔1d. A selection of phase diagram type for given system from the possible versions obtained by the theoretical derivation (based only on the information about phase behavior in binary subsystems) can be made using an additional experimental data on the ternary phase equilibria. It is clear that the number of experimental measurements needed for a selection of the right phase diagram type is significantly lower than in the case of experimental way without any theoretical derivations beforehand. Harnessing the contents of Figure 1.13 opens up an ample opportunity for derivation of possible versions of complete phase diagram for ternary systems when the phase diagrams

of binary subsystems are known. At the same time, it is necessary to consider the abundance of possible types of ternary phase diagrams. Simple combination of 17 types of binary complete phase diagrams shown in Figure 1.13 as the subsystems for ternary systems with one volatile component gives near a thousand (969) combinations. There are many more possible types of ternary phase diagrams because each combination of binary subsystems may have several types of ternary phase behavior. Therefore, there is no sense to create a comprehensive classification of ternary phase behavior or even a list of all types of ternary phase diagrams. However, it is possible to define the major classes of ternary systems in a frame of predetermined limitations and to name general features of phase transformations in the process of continuous transition from one type into another. 1.4.2.2 Fluid phase behavior in ternary systems with one volatile component and immiscibility phenomena in binary mixtures with components of different volatility Similarly to the phase diagrams for binary systems, the main types for fluid phase diagrams of ternary mixtures should not have an intersection of critical curves and immiscibility regions with a crystallization surface in them. Combination of four main types of binary fluid phase behavior 1a, 1b, 1c and 1d (Figure 1.2) for constituting binary subsystems gives six major classes of ternary fluid mixtures with one volatile component, two binary subsystems (with volatile component) complicated by the immiscibility phenomena and the third binary subsystem (consisted from two nonvolatile components) of type 1a with a continuous solid solutions. These six classes of ternary fluid mixtures can be referred as ternary class I (with binary subsystems 1b-1b1a), ternary class II (with binary subsystems 1c-1c-1a), ternary class III (with binary subsystems 1d-1d-1a), or ternary class IV (with binary subsystems 1b-1d-1a), ternary class V (with binary subsystems 1b-1c-1a) and ternary class VI (with binary subsystems 1c-1d-1a). T-X* diagrams were used for an investigation of ternary fluid phase behavior by the method of continuous topological transformation of ternary monovariant curves originated in the nonvariant points of binary subsystems with volatile component. In the case of fluid phase diagrams all these nonvariant points are the binary critical points and the ternary monovariant curves are the critical curves, which join the binary critical points of the same nature or intersect at ternary nonvariant critical point if they start in the binary critical points of different nature. T-X* projections of possible fluid phase behavior diagrams in ternary systems with one volatile component and immiscibility phenomena in both binary subsystems consisting of the volatile and nonvolatile components are shown in Figure 1.35. Each ternary class has several types of fluid phase behavior, described by various versions of fluid phase diagrams, where the monovariant critical curves, originating in the same binary critical endpoints, show the different ways of intersection. A designation of each version of ternary fluid phase diagram contains a Roman number (I-VI), corresponding

108


to a definite combination of binary subsystems or to one of the ternary classes mentioned above, and a Greek letter (a, b, g, d, e) without and with superscripts (¢, ‘, °), which indicate the version of interaction of the monovariant curves and the position of the T-X* diagram in the row (Figure 1.35). As mentioned above, the immiscibility regions spreading from two binary subsystems can either merge or be separated by a field of liquid phases miscibility. The second case is especially important since it illustrates the phase transformations where only one of the binary subsystems with volatile component is complicated by liquid-liquid immiscibility. Each scheme of ternary phase diagram (even a half of this scheme) where the immiscibility regions are separated by a field of liquid phase miscibility show the set and sequence of phase equilibria taking place in ternary mixtures where a homogeneous liquid phase of one binary subsystems transforms into two liquids in approaching to the second binary subsystems with the immiscibility phenomena. Therefore the schemes Ia, IIa, IIa≤, IIao, IIIa, IVa, Va, VIa and VIa¢ (Figure 1.35), in fact, show the phase diagrams for the following new classes 1a-1b-1a, 1a-1c-1a and 1a-1d-1a of ternary systems. In derivation of ternary fluid phase diagrams (Figure 1.35) the experimental observations of an occurrence of two-phase hole L-G (completely bounded by a closed-loop critical curve L1 = L2-G) in the three-phase immiscibility region bounded by a critical curve L1 = G-L2 from the hightemperature side (quasi-binary cross-sections of type 1d) (Peters and Gauter, 1999) are taken into account. In our derivations it was assumed that this two-phase hole L-G may appear in ternary three-phase immiscibility regions that spread from the binary subsystems of types 1b and 1c. The following are general regularities for fluid phase behavior in ternary mixtures summarized after the analysis of all main types of fluid phase diagrams: 1. The immiscibility regions of type b and d spreading from the binary subsystems are terminated by one nonvariant point in ternary systems (the double critical endpoint N′N (L1 = L2-G) and the tricritical point RN (L1 = L2 = G), respectively). Disappearance of the immiscibility region of type c takes place only after transformation (through the tricritical or double critical points) into immiscibility region of type b or d. 2. Quasi-binary cross-sections of ternary systems with binary subsystems of type c (in the case of two-phase hole in particular) can contain two separated immiscibility regions of type b or two immiscibility regions of type b and the third immiscibility region of type d. These types of binary fluid phase diagrams cannot be found in Figure 1.13 due to the accepted limitations. However, they were obtained by calculations (Boshkov, 1987; Yelash and Kraska, 1999a,b) and can be derived by the method of topological transformation if the mentioned limitations are omitted. 3. Ternary critical curves L1 = L2-G, joining the binary nonvariant critical endpoints N of the same nature, pass through the double critical endpoint (DCEP) N′N (L1 = L2-G) if the critical endpoints N belong to one binary

subsystem. In fact, two critical curves L1 = L2-G starting in binary critical endpoints N meets in DCEP. Ternary critical curve L1 = L2-G joining the critical endpoints N of various binary subsystems does not have DCEP. The critical curve L1 = G-L2 connected the critical endpoints R of various binary subsystems also does not have any nonvariant points. DCEP N′N appears on the critical curve L1 = L2-G which intersects with another critical curve L1 = G-L2 in the tricritical point (TCP) NR (L1 = L2 = G) when these critical curves originate in different binary subsystems. If both critical curves of different nature start from the same binary subsystem and are intersected in TCP, the critical curve L1 = L2-G does not have DCEP. Two DCEP are located on the closed-loop critical curve L1 = L2-G bounded a two-phase hole L-G in three-phase immiscibility region at extreme contents of nonvolatile components. 1.4.4.3 Complete phase diagrams for ternary systems with one volatile component and immiscibility phenomena in binary subsystems with components of different volatility Presence of solid phases in phase equilibria described by the complete phase diagrams increases the number of stable equilibria in comparison with that shown in the fluid phase diagrams. Besides there are the metastable equilibria, which influence on adjacent stable equilibria and can themselves transform into the stable equilibria under certain conditions. As a result, the topological T-X* schemes of ternary fluid phase diagrams (Figure 1.35) contain only two nonvariant critical points and two monovariant critical curves of different natures, the examples of ternary complete T-X* phase diagrams, shown in Figure 1.36, have already eight nonvariant stable and metastable critical points and more than four stable and metastable monovariant critical curves. The symbols used in Figure 1.34–1.36, are the filled symbols (circle, square, triangle etc.) signify the binary stable nonvariant points, the empty symbols – the ternary stable nonvariant points, the shaded symbols – the metastable binary and ternary nonvariant points. The monovariant eutonic curve EAC-EAB (L-G-SA-SBC) situated at the lowest temperatures are shown in Figure 1.34, but is omitted in the T-X* schemes in Figure 1.36 to simplify the schemes. For the same reason two ternary monovariant curves L-LN (L1-L2G-S) and M-LN (L1 = L2-S), shown in Figure 1.34, are indicated as one double line in Figure 1.36 because the temperatures of binary nonvariant points L and M can coincide, and both monovariant curves end in the ternary nonvariant point LN. The fluid phase diagram could be represented as the high temperature part of complete phase diagram where the equilibria with solid phase occur in a much lower temperature range, far below the temperatures of critical phenomena shown in the fluid phase diagram. A continuous transition from fluid to complete phase diagram could be imagined as an appearance (from the low temperature side) of the crystallization border rising up to an intersection with monovariant critical curves seen in the fluid phase diagrams. If the immiscibility of liquids occurs, the boundary version of


1b

Ia-1

B

X*

1b' 1b' Ia-2 1b' 1b'' Ia-3 1b'' 1b' Ib-4 1b' 1b' Ib-5

1b''

C

C

T

B

X*

C B

X* C B

X*

C B

X*

1c' IIa-1 1c' 1c' IIa'-2 1c' 1c'' IIb'-3 1c' 1c' IIb''-4 1c' 1c' IId-5 1c''

T

B

X*

C

B

X*

C B

X* C B

X*

C B

X*

C

1d' IIIg-1 1d' 1d' IIId-2 1d' 1d IIIb-3 2d' 2d' IIIb-4 2d' 2d'' IIIb-5 2d''

T

B

X*

C

B

X*

C B

X* C B

X*

C B

X*

C

1b' IVa-1 1d' 1b IVa-2 2d' 1b' IVb-3 2d' 1b' IVb-4 1d' 1b'' IVb-5 2d''

T

B 1b'

X*

C

B

X*

C B

X* C B

X*

C B

X*

C

Va-1 1c 1b' Vb-2 1c' 1b'' Vg-3 1c'' 1b'' Vd-4 1c 1b'' Ve-5 1c''

T

B

X*

C

B

X*

C B

X* C B

X*

C B

X*

C

1c' VIb-1 1d' 1c' VIb-2 2d'' 1c VIe-3 2d' 2c' VIb'-4 2d' 1c' VId'-5 1d'

T

B

X*

C

B

X*

C B

X* C B

- Q ((L1=L2-S) - R m/s (L1=G-L2) - N m/s (L1=L2-G) - R (L1=G-L2) - N (L1=L2-G) - N’N m/s (L1=L2-G) - p (L=G-S) - NR m/s (L1=G=L2) - L (L1-L2-G-S)+M (L1=L2-S) - L (L1-L2-G-S)

X*

- pQ (L=G-S) - N’N (L1=L2-G) - LN (L1=L2-G-S) - pR (L1=G-L2-S) - MQ (L1=L2-S) - NR (L1=L2=G)

C B

X* C

- (L1-L2-G-S) + (L1=L2-S) - (L1-L2-G-S) - (L1=L2-G) or (L1=G-L2) - (L1=L2-S) or (L=G-S) - m/s (L1=L2-G) or (L1=G-L2)

Figure 1.36 T-X* projections (schemes) of some complete phase diagrams for ternary systems with one volatile component (A) and immiscibility phenomena of types b, c and d in binary subsystems A-B and A-C (Reproduced by permission of IUPAC). Solid triangles, circles, diamonds, eight-pointed stars and squares are the binary nonvariant points (L and Q, N, p, L+M and R) in the subsystems A-B and A-C. It is accepted that temperatures of nonvariant binary points M and L are coincided. Open triangles, circles, diamonds, five-pointed stars, eight-pointed stars and squares are the ternary nonvariant points MQ, N′N, pR, NR, LN and pQ. Shaded circles and squares in binary systems are the metastable points N and R. Shaded circles and five-pointed stars are the metastable points N′N and NR. Dashed line is the monovariant curve L1 = L2-G or L1 = G-L2. Dash-dotted line is the monovariant curve L1 = L2-S or L = G-S. Solid line is the monovariant curve L1-L2-G-S. Double line is the coincided monovariant curves L1-L2-G-S and L1 = L2-S. Dotted line is the metastable part of critical curve L1 = L2-G or L1 = G-L2. X* is the relative amounts of the nonvolatile component in ternary solutions [X* = xB/(xB+xC)] (solvent-free concentration).

such continuous topological transformation is an appearance of ternary nonvariant equilibrium LN (L1 = L2-G-S) when the solubility surface L-G-S touches the three-phase immiscibility region L1-L2-G in the low-temperature critical point N (L1 = L2-G). Then the solubility surface intersects

the immiscibility region generating an equilibrium L1-L2-GS. This L1-L2-G-S equilibrium (the nonvariant point L in binary and quasi-binary systems or the monovariant curve in ternary mixture) leads to a transition of a part of immiscibility region into metastable conditions.

110


Various steps of phase transformation taking place as a result of intersection the solubility surface with the threephase immiscibility region could be considered using the example of a completed phase diagram for ternary system A-B-C with one volatile component (A) where one binary subsystems A-B belongs to type 1d, and the second one A-C – to types 2d¢. Scheme IIIb-3 (Figure 1.36) shows the T-X* projection where the immiscibility regions from binary subsystems are joined to form a single immiscibility region of ternary system, and the binary phase diagram of type 1d continuously transforms into the phase diagram of type 2d¢. According to Figure 1.13, the sequence of binary phase diagrams for quasi-binary sections in this process should be the following: 1d⇔1dd¢⇔1d¢⇔12d¢⇔2d¢. The same sequence of phase transition is shown in the T-X* scheme IIIb-3 (Figure 1.36). Binary system A-B and each quasibinary sections A-B/C (up to the section through ternary nonvariant point LN (L1 = L2-G-S) has two binary critical endpoints N (L1 = L2-G) and R (G = L1-L2) that indicates the phase behavior of type 1d. The quasi-binary section through the point LN, besides the equilibrium L1 = L2-G-S (point LN) also has the binary critical endpoint R (L1 = G-L2), such a combination is possible only in the boundary version 1dd¢. The quasi-binary sections A-B/C at B/C ratio between points LN and pR intersect three stable ternary monovariant curves LN-Q (L1 = L2-S), LN-pR (L1 = L2-G-S), R-pR (G = L1-L2) and one ternary metastable curve LN-N (L1 = L2-G)ms shown in the T-X* scheme IIIb-3 (Figure 1.36), and are characterized by the listed set of binary nonvariant points which corresponds to the phase behavior of type 1d¢. The set of nonvariant points (G = L1-L2-S; L1 = L2-S; (L1 = L2-G)ms) for the section through point pR indicates the boundary version of phase diagram 12d¢. The subsequent quasi-binary sections A-B/C up to the binary system A-C intersect two stable (pR-p; LN-Q) and two metastable (LN-N; pR-R) ternary monovariant curves and contains two stable (G = L-S; L1 = L2-S) and two metastable ((L1 = L2-G)ms; (L1 = L2-S)ms) binary nonvariant points, respectively, that is typical for binary phase behavior of type 2d¢. 1d

The T-X* scheme IIIb-3 (Figure 1.36) clearly shows that the metastable immiscibility region spreading from the binary subsystem A-C of type 2¢ can transform into the stable equilibria, and how the stable immiscibility region, spreading from the binary subsystem A-B of type 1d, transforms into the metastable equilibria as a result of intersection with a crystallization surface. The schemes IIIa-1, IIIa-2 and IIIa-3 (Figure 1.37) demonstrate other cases where the immiscibility regions spreading from binary subsystems into the three-component region are terminated by ternary critical endpoints (pQ, NR) and are separated by a field of liquid phases miscibility. In fact, these schemes show the phase behavior for ternary systems with one of the binary subsystems having a volatile component with type d immiscibility region. And another binary subsystem with a volatile component does not have immiscibility phenomena and belong to type 1a. The metastable immiscibility region can disappear in metastable conditions (see scheme IIIa-1), or after a transition into the stable one at temperature range around the first critical endpoint p (see scheme IIIa-2) or at higher temperatures above the second critical endpoint Q (see scheme IIIa-3). The scheme IIIb-6 shows the case where the immiscibility regions spreading from the binary subsystems A-B and A-C are joined, as well as in the cases of IIIb-3, IIIb-4 and IIIb5, but not transformed into the stable equilibria in ternary mixtures. The following features of global phase behavior in ternary systems can be formulated from the analysis of the derived complete phase diagrams (Figures 1.36 and 1.37): 1. (a) If the immiscibility region originates in the binary subsystem of type 1b¢, 1c¢ or 1d¢ (the subsystems with immiscibility phenomena in solid saturated solutions), the monovariant curve L-LN (L1-L2-G-S), starting in binary nonvariant point L, is located at temperature range below the temperature of point L and terminated by ternary nonvariant point LN (L1 = L2-G-S) (see Fig.36, diagrams Ia-1, Ia-2, Ib-5, IIa-

IIIa-1 2d' 1d IIIa-2 2d' 1d IIIa-3 2d' 2d' IIIb-6 2d'

T

B

X* C B

X* C B

X* C B

X* C

Binary critical points Ternary critical points - L1=L2-G-S (LN); - L1=L2=G (NR) - L1=L2-G (N); - L=G-S (p) - L=G-S (pQ) - L1=L2-S (Q); - L1=G-L2 (R) - L1=G-L2-S (pR); - (NRms) L1=L2=G+S - (Nms) L1=L2-G+S; - (Rms) L1=G-L2+S Ternary monovariant curves - L1-L2-G-S - L1=L2-G or L1=G-L2 - (ms) L1=L2-G+S or L1=G-L2+S - L1=L2-S or L=G-S

Figure 1.37 T-X* projections (schemes) of some complete phase diagrams for ternary systems with one volatile component (A) and immiscibility phenomena of type d in binary subsystems A-B and A-C of types 1d and 2d¢. Line values and points as for Figure 1.36.


(b)

(c)

2. (a)

(b)

1, IIb¢-3, IId-5, IVa-1, IVb-3, IVb-4,Va-1, VIb-2). The low-temperature part of immiscibility region located on the T-X* projections below the monovariant curve L-LN (L1-L2-G-S) is metastable. The monovariant curve L1-L2-G-S originated in binary subsystem of type 1b≤, 1c≤ or 1d≤ in binary nonvariant point L is terminated by ternary critical point LN (in the case of type 1b≤) (see diagrams Ia3, Ib-5, IVb-5, Vg-3, Vd-4, Ve-5) or by ternary critical point pR (L1 = G-L2-S) (in the cases of types 1c≤ or 1d≤) (see diagrams IIb¢-3, IId-5, Vg-3, Ve-5). In this case the temperature of points LN or pR is higher than that of binary point L and the high-temperature part of immiscibility region is metastable in the range of composition (X*) from binary subsystem to ternary critical point LN or pR. Another important property of ternary phase diagrams with binary subsystems of type 1c≤ and 1d≤ is the existence of binary critical endpoint ‘p’ (L = G-S), as well as in the case of binary subsystems of type 2d≤, and the ternary monovariant curve p-pR (which ends in ternary critical point pR (L1 = G-L2-S)) (see diagrams IIb¢-3, IId-5, IVb-5, Vg-3, Ve-5, VIb-2). Theoretical analysis of ternary complete phase diagrams shows that the stable immiscibility region originated in the binary subsystem of types 1b¢, 1c¢ or 1b≤, 1c≤ can disappear not only in ternary solid saturated solutions (in nonvariant point LN) such as in schemes Ia-2 or IVa-1, but also in unsaturated solution in DCEP N′N (L1 = L2-G) (see diagrams Ia-1, Ia-3, IIa-1, Va-1, Vd-4). In ternary systems, where a binary subsystem belongs to type 2 complicated by a metastable immiscibility region, the immiscibility region can either end in metastable conditions (diagrams IVa-2, IVb-3, VIb¢-4) or transform into the stable equilibria (diagrams IIIb-4, IIIb-5, IVb-5, VIb-2, VIe-3). If the immiscibility region ends in metastable conditions of ternary system, the following transformation of quasi-binary sections from type 2a into type 1a takes place through the boundary version 12a with the double critical endpoint pQ (L = G-S) (diagrams IIIg-1; IVa-2, IVb-3). Transition of three-phase immiscibility region of types 2d¢ or 2c¢ from metastable into stable equilibria takes place through the immiscibility of solid saturated solutions (L1-L2-G-S) in a range of concentration of the second nonvolatile component that is added to the binary mixture of type 2d¢ or 2c¢ (diagrams IIIb-3, IIIb-4, IIIb-5, VIe-3). That transition starts from high-temperature equilibria (point pR (L1 = G-L2-S)) at lowest concentration of the second nonvolatile component and terminates in the lowtemperature point LN (L1 = L2-G-S) at the higher contents of the second salt. The latest experimental data (Urusova et al., 2007) show that a transition of metastable immiscibility region of type 2d¢ most likely can occur not only in a range of the critical

temperature of volatile component and the first critical endpoint p (L = G-S) but also above the temperature of the second critical endpoint Q (L1 = L2-S) of binary system of type 2 (see scheme IIIb-5). In this case the four-phase equilibrium L1-L2-G-S within two nonvariant critical points pR (L1 = G-L2-S) and LN (may be better QL in this case) (L1 = L2-G-S) can exist at rather high temperature and pressure. (c) In binary subsystems of types 2d≤ or 2c≤ (with stable three-phase immiscibility region at temperatures below the first critical endpoint p) an increase in concentration of the second nonvolatile component could possibly lead to a transition of a high-temperature part of immiscibility region into stable equilibria and an appearance of the ternary nonvariant points pR (L1 = G-L2-S) (diagrams IVb-5, VIb-2). Simultaneously the high-pressure critical curves L1 = L2-S, originated in the binary critical endpoints Q and M come close together and meet in a DCEP MQ (L1 = L2-S). It can be shown that a DCEP MQ appears at lower contents of the second nonvolatile component in ternary mixture than the nonvariant critical point pR. 1.4.4.4 Experimental observations of phase behavior in ternary mixtures with water As in binary aqueous systems, water can be volatile or nonvolatile component in ternary mixtures. It is the volatile component in ternary water-salt systems, such as H2O – NaCl – KCl, H2O – NaCl – Na2SO4, H2O – SiO2 – Na2O etc. In the case of ternary mixtures with such volatile components as N2, CO2, C2H6, C6H4, C6H6, CH4O etc., water is the nonvolatile component, whereas in such systems as CO2 – H2O – NaCl, C3H8O – H2O – KCl or CF3 – H2O – NaCl, water is the more volatile component than the salts, but the less volatile one than CO2, C3H8O and CF3. However, as was shown for binary systems, the major features of phase behavior depend on the types of equilibria (solid solubility, liquid immiscibility or critical phenomena) but not on a chemical composition of components. The same phase behavior is observed both in organic and inorganic mixtures. The type of immiscibility region as well as the phase diagram construction could be the same for various systems where water is volatile component in one case, but nonvolatile component in another system. The major features of phase behavior in ternary systems are determined by the types of phase diagrams of the constituting binary subsystems, since all binary equilibria spread into the three-component region of composition and take part in the generation of ternary phase diagrams. As in the binary systems discussed above, the ternary have two types of phase equilibria: fluid (including liquidgas, liquid-liquid, liquid-liquid-gas and etc.) equilibria and equilibria with participation of solid phase(s). Those types of phase equilibria starting in binary boundary subsystems and exposing different behavior may interact with the formation of new phase equilibria or may not.

112


(a) Fluid phase equilibria In most cases, the fluid equilibria of the similar nature, spreading from binary subsystems, are joined to form the same ternary fluid equilibria, where the compositions of equilibrium phases can be described by smooth curves and/ or surfaces between binary subsystems, plotted in coordinates T-x and p-x or on a triangle of composition. However, the heterogeneous fluid equilibria can be terminated by critical phenomena or by intersection with another heterogeneous equilibria. The composition of vapor (gas) phase in liquid-vapor equilibrium at 250 °C is in Figure 1.38 (Griswold and Wong, 1952). This equilibrium ends in the critical locus where the surfaces of composition of liquid and vapor phases are intersected. As one can see from Figure 1.38, the ternary critical locus L = G connects the critical points (L = G) of binary subsystems acetone (C3H6O) – water and methanol (CH4O) – water. All binary subsystems of the ternary system C3H6O – CH4O -H2O belong to 1a type (the one without immiscibility phenomena) and has only one critical surface (L = G) which joins the monovariant critical curves of binary subsystems. The critical locus, shown in Figure 1.38, is the isothermal section of this critical surface. An existence of immiscibility region in any binary subsystem leads to an appearance of immiscibility phenomena in ternary mixtures and the second critical surfaces with the equilibrium L1 = L2. The available experimental data on ternary aqueous systems with volatile (inorganic gas or organic compound) and salt component show the influence of added salts on the mutual miscibility of water and the volatile component.

in aqueous solutions of KCl and 1-propanol (C2H8O), is shrinking with increasing pressure and decreasing salt content. Similar behavior is obsewed in 2-butanol – H2O – NaClO4. (Schneider and Russo, 1966). In Figure 1.40 influence of adding salt (Na2SO4) to the the system 3-methylpyridine – H2O – Na2SO4 is shown. A continuous transformation of the single tube-like shape (with a waist) immiscibility region of type b (at sulphate concentrations 0.0084 mol/L and above) into another version of type b with two separated low- and high-pressure parts of immiscibility region (in the salt-free mixture and at salt contents up to 0.007 mol/L) can be observed (Schneider, 1966; 1973). Similar behavior was established in pyridine – H2O – KCl. (Schneider and Russo, 1966). An influence of salt addition on the immiscibility region of type d was studied in ternary systems CO2 – H2O – NaCl (Gehrig et al., 1986), CH4 – H2O – NaCl, CH4 – H2O – CaCl2 (Krader and Franck, 1987), C2H6 – H2O – NaCl, C6H14 – H2O – NaCl (Michelberger and Franck, 1990), CF4 – H2O – NaCl, CHF3 – H2O – NaCl (Smits et al., 1997a,b,c). The upper temperature boundary of immiscibility region of type d in binary subsystems volatile component (CO2, CH4, C2H6, C6H14, CF4, CHF3) – water is the critical curve originated in the critical point of water. It extends to high pressures and passes through a local temperature minimum, corresponding to an appearance of gas = gas equilibria of type 2. An addition of salt component to the binary aqueous mixture shifts the immiscibility region towards higher tem-

Influence of salts on ternary immiscibility regions. Figures 1.39a,b show how the closed-loop immiscibility region (type b) with the hypercritical solution point, observed

Figure 1.38 Vapor-liquid equilibrium of acetone (C3H6O) – methanol (CH4O) – water at 250 °C. The isopleths of acetone and water show a composition of equilibrium vapor phase are terminated by the critical locus where the compositions of liquid and vapor phases become equal (Griswold, J. and Wong, S.Y. (1952) Chem. Eng. Prog., Symp. Ser., n.3, 48, pp. 18–34.).

Figure 1.39 Liquid-liquid immiscibility of type b in the system 1-propanol (C2H8O) – H2O – KCl at constant mass ratio H2O/ C2H8O = 1.5. (a)Salt influence at normal pressure (1 bar). (b) Pressure influence for constant concentration of KCl (12.5 g KCl per 100 g H2O) (Schneider, G.M. and Russo, C. (1966) Ber. Bunsenges. Phys. Chem., v.70, pp. 1008–1014.).


Figure 1.40 Salt and pressure effects on liquid-liquid immiscibility of type b in the system 3-methylpyridine (C6H7N) – H2O – Na2SO4 (Schneider, G. (1966) Ber. Bunsenges. Phys. Chem., 70, pp. 10–16, 497–519.).

Figure 1.41 p-T projection of binary critical curves CH4 – H2O and H2O – NaCl and phase boundary curves in binary system CH4 – H2O at constant content of CH4 (17 mol.%) and in ternary system methane (CH4) – H2O – NaCl with the same CH4 content and increasing concentration of NaCl (0.53, 2.61 mol.%) (Krader, N. and Franck, E.U. (1987) Ber. Bunsenges. Phys. Chem., 91, pp. 627–634.). A repositioning of the phase boundary curves in high-temperature direction indicates that two-phase heterogeneous region, terminated by critical curve CH4 – H2O in the binary system, is spreading into higher temperature region with the addition of NaCl.

peratures. Figure 1.41 shows the isopleths (phase boundary curves at constant concentration (17 mol.%) of CH4) of two-phase region in binary CH4 – H2O mixture (dashed line) and in the ternary system CH4 – H2O – NaCl (solid lines) at various contents of NaCl (0.53 and 2.61 mol.%). The

advance of the isopleths towards higher temperatures with addition of NaCl observed in Figure 1.41 is proof of an extension of the immiscibility region in a ternary system CH4 – H2O- NaCl. It is clear that the two-phase region in a ternary mixture with constant content of salt should end at higher temperatures by the critical phenomena taking place along the critical curve started at the critical curve of binary water-salt subsystem (H2O – NaCl). Although the critical curves with constant concentration of salt were not established in the experimental studies, these curves belong to the ternary critical surface. This critical surface originates in the critical point of pure water and extends in the ternary phase diagram between the binary critical curves of binary subsystems CH4 – H2O and H2O – NaCl, shown in Figure 1.41. Critical curves in water-salt system are extended usually toward temperatures higher than the critical temperature of water; hence a high-temperature shift of immiscibility region upon addition of salt is a common phenomenon. It was mentioned in (Krader and Franck, 1987; Smits et al., 1997b,c) that this phenomenon is similar to the salting-out effect of ions observed in water-nonpolar gases mixtures at ambient conditions, and the electrolytes could be regarded as an anti-solvent for the volatile reactants and reaction products in supercritical water oxidation processes. Extrema on ternary critical curves and surfaces. As discussed above, the immiscibility region may advance into the higher temperature region with an addition of salt, however, it may not be possible if water in the system considered as a nonvolatile component and the critical temperatures of volatile components are lower than one of water. Experimental studies of phase equilibria in the systems nitrogen (N2) – hexane (C6H14) – H2O (Heilig and Franck, 1990) and CO2 – benzene (C6H6) – H2O (Brandt et al., 2000) (the binary subsystems with water are complicated with the immiscibility phenomena of type c) show that the hightemperature critical surface, originated in the critical point of pure water, extends to high pressure and passes through a temperature minimum. This critical surface exists between the two high-temperature branches of critical curves with temperature minimum in the binary subsystems volatile component – water (the systems CO2 – H2O and C6H6 – H2O in Figure 1.42). As mentioned above, the temperature minimum on the high-temperature branches of critical curves corresponds to a continuous transition of critical equilibrium L = G into G1 = G2 (‘double homogeneous critical point’ according to the terminology of Tsiklis (1969/1972)) and indicates an appearance of gas = gas critical equilibria of type 2 at temperatures above the minimum and at elevated pressures. The low-pressure part of this critical curve started in the critical point of nonvolatile component (H2O in given examples) corresponds to liquid = gas critical equilibrium. In the case of gas = gas equilibria of type 1, the critical curve begins at the critical point of nonvolatile component and extends to high temperatures and pressures. In ternary systems where one binary subsystem has gas = gas equilibria of type 2 and another one – of type 1, the curve of temperature minima

114


Figure 1.42 p-T projection of two critical surfaces in the system CO2-benzene (C6H6)-H2O (ternary class 1a-1d-1d¢). High-pressure critical surface (L = G, G1 = G2 (L1 = L2)) extends between the high-temperature high-pressure branches of binary critical curves CO2 – H2O and C6H6 -H2O. Low-pressure critical surface (L = G) extends between the low-temperature low-pressure branches of critical curves in binary aqueous systems and binary critical curve CO2 – C6H6, and ends in the ternary critical curve RCO2RC6H6 (L1 = G-L2) (Brandt, E., Franck, E.U., Wei, Ya S. and Sadus, R.J. (2000) Phys. Chem. Chem. Phys., 2, pp. 4157–4164. Reproduced by permission of the PCCP Owner Societies). Dash-dotted and heavy lines show the monovariant critical curves in binary aqueous and ternary systems, respectively. Thin lines show the cross-sections of critical surfaces at constant contents (mol.%) of benzene.

starts form the binary subsystem of type 2 towards critical point of nonvolatile component in the second binary subsystem of type 1. It was established for the system He – N2 – NH3 (Tsiklis et al., 1970), with binary subsystem He – NH3 belonging to type 1 and N2 – NH3 – to type 2, that the phase transition from L = G to G1 = G2 (corresponding to the double homogeneous critical point) in the binary systems of type 1 takes place in the vicinity of the critical point of the more volatile component. Several interesting phenomena that are important for supercritical fluid were found in recent systematic experimental investigations of fluid multiphase behavior mainly in non-aqueous ternary mixtures (Kordikowski and Schneider, 1993, 1995; Peters and Gauter, 1999; Gauter et al., 2000; Schneider et al., 2000; Scheidgen and Schneider, 2002). The cosolvency effect consists of an increase in mutual miscibility in ternary mixture in comparison with those in the binaries. A substance is more soluble in a supercritical mixture of two solvents than in each of the solvents separately. Or the solubility of a mixture of two substances in a given solvent is higher than that of each of the pure substances alone in the same solvent. As a rule, the binary subsystems with components of different volatility (solvent-solute mixture) are complicated with the immiscibility region of type d with the temperature and (sometimes) pressure minima on the high-temperature

Figure 1.43 Three-dimensional p-T-X* scheme of ternary critical surface extends between the critical curves (solid lines) of binary subsystems and exhibiting cosolvency effect (critical curve of quasibinary isopleth (dash-dotted line) has lower temperatures and pressures than the binary ones) and isothermal/isobaric miscibility windows (shown by thin lines). X* is the solvent-free concentration of less-volatile components.

branches of critical curves. For ternary systems with cosolvency effects, the critical surface, joining these binary critical curves can run through the minima pressure and temperature, that are lower than ones on the both critical curves. As shown in the scheme (Figure 1.43), for some isobaric and isothermal sections through such ternary critical surface, the closed isobaric and isothermal miscibility windows result. The homogeneous range of such section is inside and the heterogeneous state – outside the windows. If the ternary critical surface is displaced to very low pressures, it might intersect the three-phase immiscibility region (L1-L2-G) and a two-phase hole in this three-phase surface results. Such two-phase holes in ternary three-phase equilibria are discussed in details in (Peters and Gauter, 1999) and used in our approach to derive ternary fluid phase diagrams (see above). Transformation of immiscibility equilibria in ternary mixtures. In the above examples both binary subsystems with components of different volatility are complicated by immiscibility regions of the same nature (belong to the same type). However, the immiscibility region spreading from binary subsystems can end in ternary solutions or meet with another immiscibility region of a different nature. Since it was previously discussed in details, only a few experimental examples will be given. Figure 1.44 shows T-X* projections of immiscibility regions in the systems H2O – NaCl – Na2B4O7, H2O – HgI2PbI2 and CO2 – tetradecane (C13H28) – pentanol (C5H12O), where the immiscibility equilibria are transformed in ternary mixtures while passing from one binary subsystem with volatile component (H2O or CO2) to another. There is only one binary subsystem (H2O – Na2B4O7) with the immiscibility region of type d in the first ternary system. The phase diagram demonstrates disappearance of immiscibility phenomena in ternary solution as a result of nonvariant tricritical equilibria (L1 = L2 = G) (point NR in Figure 1.44a).


Figure 1.44 T-X* projections of ternary immiscibility regions bounded by the critical curves L1 = L2-G and L1 = G-L2 in the systems (a) H2O – Na2B4O7 – NaCl (ternary class 1a-1a-1d) [Urusova and Valyashko, 1998], (b) H2O – HgI2 – PbI2 (ternary class 1a-1b¢-1d¢) [Valyashko and Urusova, 1996] and (c) CO2 – tetradecane (C13H28) – pentanol (C5H12O) (ternary class 1a-1c¢-1d¢) (Peters and Gauter, 1999). N (L1 = L2-G) and R (L1 = G-L2) are the critical endpoints in binary subsystems; LN (L1 = L2-G-S), NN′ (L1 = L2-G) and NR (L1 = L2 = G) are the nonvariant critical points in ternary systems. One-dotted-dashed line is the ternary monovariant critical curve L1 = L2-G, two-dotted-dashed line is the ternary monovariant critical curve L1 = G-L2; dashed line is the approximate compositions of liquid phase in equilibria L1-L2-G-S and L-G-S.

Similar phase behavior with the tricritical point was established in ternary aqueous systems butan(C4H10)-H2O-acetic acid(C2H4O2),CO2-methanol(CH4O)-H2O,CO2-ethanol(C2H6O)H2O and cyclohexane (C6H12)-NH3-H2O (Krichevskii et al., 1963; Efremova and Shvarz, 1966; Shvarz and Efremova, 1970; Efremova et al., 1973) where one of binary subsystem belongs to type d. These systems were the first aqueous mixtures where the tricritical phenomena were discovered. As one can see the experimental phase diagram in Figure 44a is the same as the left-hand parts of topological schemes IIIa-1, IIIa-2 or IIIa-3 (see Figure 37). The right-hand parts of these schemes are complicated with the another immiscibility regions which spread from binary subsystems A-C. The immiscibility phenomenon is absent in the binary subsystem H2O – NaCl as well as in intermediate quasibinary cross-sections of ternary systems A – B – C in IIIa1, IIIa-2 or IIIa-3 topological schemes. Binary subsystems with volatile components and immiscibility regions of different natures – 1b¢ and 1d¢ in H2O – HgI2 – PbI2, and 1c¢ and 1d¢ in CO2 – tetradecane (C14H30) – pentanol (C5H12O) are presented in Figure 1.44(b,c). It is clear from Figure 1.44c, that the immiscibility regions spreading from the binary subsystems are joining in ternary solutions and a continuous transformation of immiscibility region of type c into type d is accompanied by an appearance of two tricritical points NR (L1 = L2 = G). Similar phase behavior was observed in several ternary mixtures of CO2 – tetradecane (C13H28) – 1-alkanols, CO2 – tridecane (C13H28) – 1-alkanols and CO2 – o-nitrophenol (C6H5NO3) – 1alkanols (Peters and Gauter,1999). In the system H2O – HgI2 – PbI2 the immiscibility regions of types b and d interfere with the solubility surfaces of solid salts leading to the occurrence of monovariant equilibria (L1-L2-G-S) and nonvariant critical point LN (L1 = L2-G-S). As a result the low-temperature parts of immiscibility regions becomes metastable and it is impossible to establish whether these immiscibility regions are joined in ternary mixtures or not. However, in any case the stable part of the ternary phase diagram does not change and is characterized by an appearance of tricritical point NR.

(b) Solid solubility phenomena Eutonic equilibria. In case of solubility phenomena in ternary mixtures, the appearance of eutonic equilibria, when two solid phases of components coexist with liquid and vapor solutions is the general feature of the most ternary systems. Although a mutual miscibility of solids is usual phenomena in multicomponent systems, the special property of solubility of solid solutions in fluids is out of frame of this part. The monovariant eutonic equilibria can be considered as the result of spreading of the binary eutectic equilibria (L-G-S1-S2) into the three-component region or an intersection of two three-phase (L-G-S) solubility surfaces. The monovariant eutonic curves in the p-T diagram are characterized by local extreme parameters and join the eutectic point of ternary system (L-G-SA-SB-SC) with the eutectic points of binary subsystems. Figure 1.45a is a projection of three-phase solubility surfaces in the system NaCl – KCl – H2O on the triangle of composition as a set of isothermal cross-sections with concentration maxima on the polythermal eutonic curve. The eutonic curve joining the eutectic point of ternary system and binary anhydrous subsystem usually passes through a maximum of vapor pressure, which is at lower pressure than similar maxima on the three-phase solubility curves in binary water-salt subsystems (see Figure 1.46). Vapor pressure behavior in the ternary water-salt system is shown in Figure 1.45b as a set of isobaric cross-sections of the solid saturated solution surfaces (with the extreme temperatures at eutonic compositions) projected on the T-X* diagram (where X* is the relative amount of NaCl in NaCl + KCl mixture for ternary aqueous solution). Ternary systems with binary subsystems of types 1 and 2. If the binary subsystems with a volatile component belong to type 1a and have a single (uninterrupted) three-phase solubility curves for each solid phase, as in the case of H2O – NaCl – KCl system, the three-phase solubility surfaces of ternary system are also smooth and uninterrupted. However, if one of the binary subsystems belongs to type 2 with the

116


Figure 1.45 Solubility surface L-G-S in the system H2O – KCl – NaCl (ternary class 1a-1a-1a) presented as the solubility isotherms on the triangular diagram (a) and T-X* projection of isobaric cross-sections (b) (Reproduced by permission of MAIK / Nauka Interperiodica). X*KCl = 100*WKCl/(WKCl + WNaCl), where WKCl and WNaCl are the weight amounts of KCl and NaCl in aqueous solution (solvent-free concentration); temperature near isotherms (a) shown in °C; pressure near isobars (b) shown in MPa. Heavy lines are the composition of eutonic solutions saturated with two solid phases at vapor pressure; solid lines show (a) the isothermal composition of solid saturated liquid solutions at vapor pressure and (b) the composition of solid saturated liquid solution at constant vapor pressure. p, MPa Na2WO4

40

NaCl 30 Na2SO4+NaCl KH2O

KCl

20

K2SO4+KCl KF H2O KCl+NaCl LiF+KF LiCl

10

300

400

500

600

700

800

T, ºC

Figure 1.46 p-T projections of the three-phase solubility curves (L-G-S) in binary systems of type 1 (solid lines), and eutonic curves (L-G-S1-S2) (dashed lines) in ternary systems of types 1a1a-1a (H2O – KCl – NaCl) and 1a-1a-2d¢ (H2O – KCl – K2SO4, H2O – NaCl – Na2SO4, H2O – KF – LiF) and liquid-gas curve for pure H2O (heavy line) (From Elsevier).

intersections of solubility and critical curves in the critical endpoints p and Q, the supercritical fluid equilibria are spreading into the three-component region and cut a part of the three-phase solubility surface of ternary system. As it was mentioned above, in the cases of binary subsystem of type 2 being complicated by a metastable immiscibility region, situated under a stable surface of supercritical fluid saturated with solid phase, there are two possibility of ternary phase behavior. The metastable immiscibility region, spreading into ternary system, can retain metastable or can transform into the stable equilibria. There are several experi-

mental examples of ternary water – salt systems (H2O – Na2CO3 – NaCl, H2O – Na2CO3 – NaOH, H2O – Na2SO4 – NaCl, H2O – Na2SO4 – NaOH, H2O – K2SO4 – KCl, H2O – K2SO4 – KNO3 etc.) where aqueous binary subsystems belong to types 2d¢ and 1a, and salt solubility was studied at sub- and supercritical conditions. The general feature of such ternary systems is the change of the t.c.s sign from negative to positive in ternary solutions. As a result the three-phase solubility surface (L-G-S) attains a new configuration near the type 2d¢ binary subsystem – the isotherms of Na2SO4 and K2SO4 solubility in NaCl and KCl solutions, respectively, are intersected (see Figure 1.47). However, plausible transition of metastable immiscibility region into the stable equilibria was not observed in the ternary mixtures. Only the last experiments in the system H2O – K2SO4 – KCl permit to make a suggestion that such transition may take place but at unusually high temperatures and pressures (Urusova et al., 2007). However, shape of a tie-line of 350, 360 and 370 °C solubility isotherms, such as (Figure 1.47b) clearly shows that the metastable immiscibility region spreads from the binary subsystem of type 2d¢ into ternary mixtures and it takes place very close to the stable solubility surface. A transition of metastable immiscibility region into a stable equilibria was established in the system ethylene (C2H4) – propane (C3H8) – eicosane (C20H42) (Gregorowicz et al., 1993), where the binary subsystem ethylene (C2H4) – eicosane (C20H42) belongs to type 2d¢ and the other subsystem – to type 1a. An observation of critical phenomena (G = L1-L2 and L1 = L2-G) bounded a stable part of threephase immiscibility region L1-L2-G permitted to conclude that these monovariant critical curves intersect in a tricritical point L1 = L2 = G. Rough estimate of the coordinates of the


NaCl

50 mass %

Na2SO4

b

700 C 600 500

a

Figure 1.47 Solubility isotherms at vapor pressure in the systems NaCl – Na2SO4 –H2O (a) and KCl – K2SO4 – H2O (b) (ternary class 1a-1a-2d¢) (From Elsevier). Solid lines show the composition of solid saturated liquid solutions at vapor pressure; heavy line is the composition of liquid solutions saturated with two solid phases at vapor pressure.

H 2O

o

10

10 370

400

30 350 300 200

o

350

350 C 200 oC 300

360 oC 300

30 350

370

50

50 360 oC

350 oC

H2O K2SO4

x, mass %

tricritical points (316.4 K and 6.15 MPa) shows that it takes place not far from the critical endpoint p (283.84 K and 5.17 MPa) in binary subsystem ethylene – eicosane. Experimental studies of ternary water-salt systems of type 2d¢-1d-1a, with both binary water-salt subsystems being complicated by three-phase immiscibility regions in stable (type 1d) and metastable (type 2d¢) conditions, show that a transition of metastable immiscibility into stable one occurs through the immiscibility phenomena in solid saturated solutions. At first it was shown for the system H2O – Na3PO4 – Na2HPO4 (Urusova and Valyashko, 2001a,b), then – for H2O – Na2CO3 – K2CO3 (Urusova and Valyashko, 2005), H2O – K2SO4 – K2CO3 and H2O – K2SO4 – K2HPO4 (Urusova and Valyashko, 2007, 2008), where the binary subsystems H2O – Na3PO4, H2O – Na2CO3 and H2O – K2SO4 belong to type 2d¢, and H2O – Na2HPO4, H2O – K2CO3, H2O – K2HPO4 – to type 1d. Besides the change of the t.c.s sign, another general feature of phase behavior in ternary mixtures, where binary subsystems with volatile component belong to types 1 and 2, is a heterogenization of supercritical fluid spreading into three-component mixtures from the binary subsystems of type 2. In the case of binary subsystem of type 2d¢ and transition of metastable immiscibility into stable equilibria, separation of the three-component homogeneous fluid saturated with a salt into two solutions occurs as a result of critical phenomena L = G-S and L1 = L2-S taking place along the critical curves, which originate at the binary critical endpoints p (L = G-S) and Q (L1 = L2-S) and end in the ternary critical points pR (L1 = G-L2-S) and NQ (L1 = L2G-S), respectively. These ternary nonvariant points are the high- and low-temperature limits of the equilibrium L1-L2G-S that appears when three-phase immiscibility region (L1-L2-G) transforms from metastable into stable conditions. Figure 1.48 displaces the p-T projection of phase diagram for ternary system H2O – K2SO4 – K2CO3 with the monovariant critical curves p-pR (L = G-S) and Q-NQ (L1 = L2-S), which show the borders of homogeneous supercritical fluid in ternary mixtures. However, as was shown in Figure 1.37 especially in the case when the immiscibility phenomena exist in the binary water-salt subsystem of type 2d¢ but absent in the second water-salt subsystem (type 1a), there is a chance of continuous transition of one ternary critical curve L = G-S (originated in the binary critical endpoints p) into another ternary

KCl

p, MPa L1=L2

(K2SO4)

100

p, MPa

L1-L2-SK2SO4

(K2CO3)

80

40

L1=L2-SK2SO4

Q

60

R

L1=L2-SK2SO4 L1=L2

(K2CO3)

R

40

30

KH2O; p

20

20

N

pR G-L1-L2-SK2SO4

N QN

370 KH2O;p

L1=L2

390

pR QN

o

410 T, C

L-G-SK2CO3 TK2CO3

300

400 500 600

700 T,oC

Figure 1.48 p-T projection of phase diagram for the system H2O – K2CO3 – K2SO4 (ternary class 1a-1d-2d¢). Heterogenization of homogeneous supercritical fluid (existing in temperature range between the critical endpoint p and Q in the binary H2O – K2SO4 system) takes place as a result of critical phenomena L = G-SK2SO4 or L1 = L2-SK2SO4 when K2CO3 is added. Corresponding ternary critical curves are originated in the binary critical points p (L = G-SK2SO4) and Q (L1 = L2-SK2SO4). Thin line is the L-G curve for pure water. Dashed lines are the monovariant curves L-G-S, L1-L2-S and L1 = L2 for the system H2O – K2SO4. Dash-dotted lines are the monovariant curves L-G-S, L1-L2-G, L = G and L1 = L2 for the system H2O – K2CO3. Solid lines are the monovariant curves L1-L2 -G-SK2SO4, L1 = G-L2, L1 = L2-G, L = G-SK2SO4 and L1 = L2-SK2SO4 for ternary system. Dotted lines are the unexplored parts of the monovariant curve L-GSK2CO3. Nonvariant points in one-component systems: KH2O – critical point of pure water, TK2CO3 – triple point of K2CO3; nonvariant points in binary systems – p(L = G-SK2SO4), Q (L1 = L2-SK2SO4), N (L1 = L2-G) and R (L1 = G-L2); nonvariant points in ternary system – pR (L1 = G-L2-SK2SO4), QN ((L1 = L2-G-SK2SO4).

critical curve L1 = L2-S) (started in the binary critical endpoint Q) if a three-phase immiscibility region ends in the metastable conditions (Figure 1.37, scheme IIIa-1). Obviously such ternary critical curve pQ should pass a double critical endpoint (DCEP), where the critical phenomena of the same nature coincide under extreme parameters. The available experimental data for the system H2O – K2SO4 – KCl (Urusova et al., 2007) do not permit us to establish

118


unambiguously whether the metastable immiscibility region transforms into the stable equilibria or disappears in metastable conditions and there is a single ternary critical curve pQ with a DCEP. Therefore two versions of p-T phase diagram for this ternary system could be suggested. The version in Figure 1.49a corresponds to the scheme IIIa-1 in Figure 1.37, and the version in Figure 1.49b is similar to the scheme IIIa-3 in Figure 1.37. A comparison of phase diagrams for ternary systems H2O – K2SO4 – KCl and H2O – K2SO4 – K2CO3 (Figures 1.48, 1.49) shows their distinctions in spite of a general similarity in phase behavior of the both. Both systems are characterized by a disappearance of critical phenomena in solid saturated solutions and supercritical fluid equilibria with increasing of KCl or K2CO3 concentration, have the similar features of salt solubility behavior and the critical equilibria of two different natures. However, in the case of the system H2O – K2SO4 – KCl where the binary subsystem H2O – KCl belongs to type 1a, the ternary critical curve (L1 = L2-S), originated in the binary critical endpoint Q, is rather short and runs in the high-temperature direction as well as the second critical curve (L = G-S), started in the binary critical endpoint p. The second critical curve extends (from the point p) for a much longer distance than the critical curves of the same nature (L = G-S) in the ternary system H2O – K2SO4 – K2CO3 (Figure 1.48). The critical curve (L1 = L2-S) in the system H2O – K2SO4 – K2CO3 runs from the binary critical endpoint Q to lower temperature and extends for a long distance up to the ternary critical point NQ (L1 = L2G-S). The same phase behavior observed in several studied

ternary mixtures, where the binary water-salt subsystem belongs to type 1d. This shows that the mentioned peculiarities depend on the existence or absence of the immiscibility region in the binary water-salt subsystem of type 1. If the added salt forms with water a binary system of type 1d, the metastable immiscibility region usually transforms into the stable equilibria and the homogeneous supercritical fluid separates mainly into two liquids. It happens because the critical equilibria L1 = L2-S and L1 = L2 occur in a wider range of temperatures and pressures. When the added salt forms with water a binary system of type 1a (without liquid immiscibility) the metastable immiscibility region probably would end in the metastable conditions, but in any case the heterogenization of supercritical fluid in ternary mixtures occurs mainly through the critical equilibrium L = G-S. Ternary systems with two binary subsystems of types 2. The experimental data on phase equilibria in the systems H2O – K2SO4 – KLiSO4 (Ravich and Valyashko, 1969; Valyashko, 1975) and H2O – SiO2 – Na2Si2O5 (Valyashko and Kravchuk, 1977, 1978; etc.) provided the most direct evidence of a transition of metastable immiscibility region, extending from the binary subsystems of type 2d¢, into stable equilibria in ternary solutions. All binary subsystems with water belong to type 2d¢ and there is no three-phase equilibrium L1-L2-G in stable equilibria. However, this three-phase equilibrium L1-L2-G was found in ternary mixtures. It was especially clear in case of H2O – K2SO4 – KLiSO4 system, where the liquid immiscibility in a presence of vapor phase (with and without equilibrium

p, MPa

p, MPa

L1=L2

L1=L2

100

100

p, MPa L1-L2-SK2SO4

L1-L2-SK2SO4 L1=L2-SK2SO4

60

60

Q G=L-SK2SO4 KH2O

20

G=L

(a)

KH2O

G-L-SKCl

20

G-L-SK2SO4-SKCl

500

pR RN

E

1

2

L1=L2-G

G=L

QN

490 T,oC

450 G-L-SKCl

L-G-SK2SO4-SKCl

700 T, C

L1=L2-SK2SO4 RN pR L =G-L

p

TKCl o

Q

60

G=L-SK2SO4

p

300

Q QN

70

300

500

E

700

TKCl

T,oC

(b)

Figure 1.49 Two versions of p-T projection of phase diagram for the system H2O – KCl – K2SO4 (ternary class 1a-1a-2d¢). Version (a) shows a continuous transition of the ternary critical curve L = G-S into the critical curve L1 = L2-S through a temperature maximum. Version (b) shows an appearance of metastable immiscibility region in stable equilibrium L1-L2-G-S (curve pR-QN) and a termination of critical curves L = G-S and L1 = L2-S in the nonvariant critical points pR (L1 = G-L2-S) and QN (L1 = L2-G-S), respectively (Urusova, M.A., Valyashko, V.M. and Grigoriev, I.M. (2007) Zh. Neorgan. Khimii, 52, pp. 456–470; Russ. J. Inorg. Chem. 52, with permission from Academizdatcenter “Nauka”, Russian Academy of Sciences). Thin line is the L-G curve for pure water. Dashed lines are the monovariant curves L-G-S, L1-L2-S and L1 = L2 for the system H2O – K2SO4. Dash-dotted lines are the monovariant curves L-G-S and L = G for the system H2O – KCl. Solid lines are the monovariant curves G-L-SK2SO4-SKCl, L = G-SK2SO4 and L1 = L2-SK2SO4 for ternary system. Dotted lines are the probable monovariant curves pR-QN (L1-L2-G-S), pR-RN (L1 = G-L2), QN-RN (L1 = L2-G) and the unexplored parts of critical curves L-G-S and L1 = L2-S for the ternary system. Nonvariant points in one-component systems: KH2O – critical point of pure water, TKCl – triple point of KCl; nonvariant points in binary systems – p (L = G-SK2SO4), Q ((L1 = L2-SK2SO4), E (L-G-SKCl-SK2SO4); nonvariant points in ternary system – pR (L1 = G-L2SK2SO4), QN ((L1 = L2-G-SK2SO4), RN ((L1 = L2 = G).


p, MPa 500 QDs QMs QDsMs NDs 40 60

300

QDs Q DsMs 100 NQz NDs NQz 80 200 400

X*, mol.%

80 60

Figure 1.50 Solubility isotherms at 350, 370 and 380 °C and saturation vapor pressure in the system H2O – KLiSO4 – K2SO4 (ternary class 1a-2d¢-2d¢) exhibiting transition of metastable immiscibility region (at 350 °C) into the stable equilibria (at 370 and 380 °C) (Valyashko, V.M. (1975) Zh. Neorgan. Khimii, 20, n.4, pp. 1129–1131. Reproduced by permission of MAIK / Nauka Interperiodica).

solid phase) was visually observed in the sealed thick-walled glass capsules at temperatures above 350 °C. An appearance of immiscibility phenomena drastically influences the salt solubility behavior. As shown in Figure 1.50, the joint solubility of two salts strongly increases, because the eutonic curve (compositions of liquid solution in the equilibrium L-G-S1-S2) is separated from the solubility curves in the binary water-salt subsystems by the immiscibility region. The temperature coefficient of salt solubility (t.c.s.) in eutonic solutions becomes positive and there are no critical phenomena in the solutions saturated with two solid phases. Figure 1.51 displays the T-x, p-T and p-x projections of critical surface, and monovariant critical and solubility curves of H2O – SiO2 – Na2O system. The critical surface expanding between the critical curves of binary subsystems is rather smooth and simple because it joins the binary critical curves of the same nature (L1 = L2). An intersection of the critical surface with the surfaces of composition of liquid phase in divariant noncritical equilibria of salt solubility and liquid immiscibility produce the monovariant critical curves. As one can see from Figure 1.51, the immiscibility region in the system H2O – SiO2 – Na2Si2O5 becomes stable when the SiO2 + Na2Si2O5 mixture contains 65– 80 mol.% SiO2 as indicated by a decrease of temperature and pressure of the critical surface up to vapor pressures at 200 °C. It is necessary to point out that this figure does not show a concentration of water in the critical solution when homogeneous fluid is separated into two liquid phases. Such experimental data are not available, however, from some hydrothermal measurements (see, for instance, Valyashko and Kravchuk (1977)); these critical solutions should not contain high concentrations of sodium silicate, whereas the eutonic liquid phase (not shown in Figure 1.51) of the system H2O – SiO2 – Na2Si2O5 is a very strong aqueous solution of sodium silicate. Figure 1.51 also depicts another type of phase behavior in ternary system H2O – Na2Si2O5 – Na2SiO3, where the immiscibility region is retained in metastable conditions and

40

QMs o 600 T, C

NQz NDs QDs QDsMs QMs

X*, mol.% Figure 1.51 p-X*, p-T and T-X* projections of the critical surface L1 = L2 and monovariant curves of the system SiO2 – Na2O – H2O. Ternary systems SiO2 – Na2Si2O5 – H2O and – Na2Si2O5 – Na2SiO3 – H2O belong to one ternary class 1a-2d¢-2d¢ but have different types of phase behavior (Valyashko, V.M. and Kravchuk, K.G. (1978) Dokl. Akad. Nauk SSSR, 242, pp. 1104–1107.Reproduced by permission of MAIK / Nauka Interperiodica). X*SiO2 = 100*xSiO2/(xSiO2 + xNa2O), where xSiO2 and xNa2O are the molar amounts of SiO2 and Na2O in aqueous solution (solvent-free concentration). Qz is a quartz (SiO2); Ds is a disilicate (Na2Si2O5); Ms is a metasilicate (Na2SiO3) (Valyashko and Kravchuk, 1978). Dots in circles are the critical endpoints QMs and QDs (L1 = L2-S) in binary Na2SiO3 – H2O and Na2Si2O5 – H2O subsystems and the ternary critical endpoints NQz and NDs (L1 = L2-G-S), QDsMs (L1 = L2-SDs-SMs). Open circles are the experimental points. Dashed lines are the monovariant critical curves L1 = L2-S and L1 = L2-G; solid lines are the isothermal (p-X* projection) or isobaric (T-X* projection) cross-sections of the critical surface L1 = L2; solid lines on the p-T projection are the cross-sections of the critical and solubility surfaces at constant ratio SiO2/Na2O in the mixtures.

eutonic curve between the ternary eutectic point and the eutectic of anhydrous binary systems consists of two separated branches as the solubility curves in the type 2d¢ binary subsystems H2O – Na2Si2O5 and H2O – Na2SiO3. The topological T-X* scheme IIIb-6 (Figure 1.37) shows such phase behavior for ternary system of type 1a-2d¢-2d¢. This type of phase behavior is widely present in most aqueous systems with high melting point oxides and alumosilicates, such as H2O – NaAlSi3O8 – KAlSi3O8, H2O – SiO2 – NaAlSi3O8, H2O – SiO2 – KAlSi3O8, H2O – SiO2 – CaAl2Si2O8, H2O – CaO – SiO2, etc. (Kennedy et al., 1962; Stewart, 1967; Boettcher and Wyllie, 1969; Merrill et al., 1970; Huang and Wyllie, 1974). The same type of ternary phase diagram was found for the organic systems, such as ethylene(C2H4) – naphthalene(C10H8) – hexachloroethane (C2Cl6) (Van Gunst et al., 1953). REFERENCES Abdulagatov, I.M. and Azizov, N.D. (2004a) J. Soln. Chem. 33: 1501–20. Abdulagatov, I.M. and Azizov, N.D. (2004b) Fluid Phase Equil. 216: 189–99. Abdulagatov, I.M. and Azizov, N.D. (2004c) J. Soln. Chem. 33: 1501–20.

120


Abdulagatov, I.M. and Magomedov, U.B. (1992) High Temp.-High Press. 24: 465–8. Abdulagatov, I.M., Dvoryanchikov, V.I. and Kamalov, A.N. (1997) J. Chem. Thermodyn. 29: 1387–1407. Abdulagatov, I.M., Dvoryanchikov, V.I., Mursalov, B.A. and Kamalov, A.N. (1998) Fluid Phase Equil. 143: 213–39. Abdulagatov, I.M., Dvoryanchikov, V.I., Aliev, M.M. and Kamalov, A.N. (2000) in P.R. Tremaine et al. (eds), Steam, Water and Hydrothermal Systems: Physics and Chemistry Needs of Industry. NRC Research Press, pp. 157–63. Aftienjew, J. and Zawisza, A. (1977) J.Chem. Thermod. 9: 153–65. Aim, K. and Fermeglia, M. (2003) in G.T. Hefter and R.P.T. Tomkins (eds), The Experimental Determination of Solubilities, Chapter 5.1, John Wiley & Sons, Ltd, pp. 493–556. Akhumov, E.I. and Vasil’ev, B.B. (1932) Zh.Obschey Khimii 2(3): 282–9. Akhumov, E.I. and Vasil’ev, B.B. (1935) in Solikamskie Karnalliti. ONTI Publ., pp. 102–5. Akhumov, E.I. and Vasil’ev, B.B. (1936) Izv. Sekt. Fiz.Khim.Analiza 9: 295–315. Akhumov, E.I. and Pilkova, E.V. (1958) Zh. Neorgan. Khimii 3(9): 2178–83. Akolzin P.A. and Mostovenko, L.N. (1969) Zavodsk.Lab. (Russ) (4): 459–60. Aleinikov, G.I., Kostrikin, Yu.M., Novi, Y.O. and Taratuta, V.A. (1956) Teploenergetika 3(12): 10–14. Alekhin, Yu.V. and Vakulenko, A.G. (1987) Geokhimiya (10): 1468–1481; (1988) Geochem. Intern. 25(5): 97–110. Allmon, W.E. et al. (1983) Deposition of Corrosive Salts from Steam. Electric Power Research Institute, Research Project 1068-1(NP-3002), USA. Alvarez, J., Crovetto. R. and Fernandez-Prini, R. (1988) Ber. Bunsenges. Phys. Chem. 92: 935–40. Alwani, Z. and Schneider, G.M. (1967) Ber. Bunsenges. Phys. Chem. 71(6): 633–8. Alwani, Z. and Schneider, G.M. (1969) Ber. Bunsenges. Phys. Chem. 73(3): 294–301. Ampelogova, N.I., Bashilov, S.M. and Pentin, V.I. (1989) Radiokhimiya 31(4): 160–5. Anderson G.K. (1995) in H.J.White, Jr. et al. (eds), Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry, pp. 573–80. Anderson, C.J., Keeler, R.A. and Klach, S.J. (1962) J.Chem.Eng. Data. 7(2): 290–4. Anderson, F.E. and Prausnitz, J.M. (1986) Fluid Phase Equil. 32: 63–76. Anderson, G.M. and Burnham, C.W. (1965) Amer.J.Sci. 263: 494–511. Anderson, G.M. and Burnham, W.G. (1967) Amer. J. Sci. 265: 12–27. Andersson, T.A., Hartonen, K.M and Riekkola, M.-L. (2005) J. Chem. Eng. Data 50: 1177–1183. Anikin, I.N. and Shushkanov, A.D. (1963) Kristallografiya 8(1): 128–30. Anisimov, M.A. (1987) Critical Phenomena in Liquids and Liquid Crystals, Nauka, Moscow; Gordon & Breach, Philadelphia (1991). Anosov, V.Y. and Pogodin, S.A. (1947) Main Bases of Physicochemical Analysis, Acad.Sci. USSR, Moscow-Leningrad. Antropoff, A. and Sommer, W. (1926) Z. Phys. Chem. 123: 161–98. Apps, J.A. (1970) Dissert., Harvard Univ., Cambridge, Massachusetts, USA, pp. 122–5, 280–5.

Archibald, S.M., Migdisov, A.A. and Williams-Jones, A.E. (2002) Geochim. Cosmochim. Acta 66(9): 1611–1919. Armellini, F.J. and Tester, J.W. (1991) J. Supercrit. Fluids 4: 254–64. Armellini, F.J. and Tester, J.W. (1993) Fluid Phase Equil. 84: 123–42. Arutyunyan, L.A., Malinin, S.D. and Petrenko, G.V. (1984) Geokhimiya (7): 1029–39. Ashmyan, K.D., Skripka, V.G. and Namiot, A.Y. (1984) Geokhimiya (4): 580–1. Ataev, K., Valyashko, VM., Kravchuk, K.G. et al. (1994) Zh. Neorgan. Khimii 39: 523–8. Ayers, J.C. and Watson, E.B. (1991) Phil. Trans. R. Soc. London 335: 365–75. Azaroual, M., Pascal, M.-L. and Roux, J. (1996) Geochim. Cosmochim. Acta 60: 4601–14. Azizov, N.D. (1994) Izv. Visch. Ucheb. Zaved., Neft’ i Gaz (3): 47–9. Azizov, N.D. and Akhundov, T.S. (1998) Zh. Neorgan. Khimii 43: 1723–7. Azizov, N.D. and Akhundov, T.S. (1995) Izv. Vish. Ucheb. Zaved., Neft’ i Gaz (2): 37–9. Bach, R.W., Friedrichs, H.A. and Rau, H. (1977) High Temp. – High Press. 9: 305–12. Bai, T.B. and Koster van Groos, A.F. (1998) Amer. Mineralogist 83: 205–12. Baierlein, H. (1983) Dissert., Univer. Erlangen- Nurenberg, FRG. Bakhuis Roozeboom, H.W. (1889) Z. Phys. Chem. 4: 31–65. Balitskiy, V.S., Orlova, V.P., Ostapenko, G.T. and Khetchikov, L.N. (1971) in Trudi VIII Soveschiya po Eksper. i Tekhnich. Mineralogii i Petrografii. Nauka, Moskva, pp. 220–4. Baranova, N.N. and Barsukov, V.L. (1965) Geochimiya (9): 1093–1100. Baranova, N.N., Barsukov, V.L., Dar’ina, T.G. and Bannikh, L.N. (1977) Geokhimiya (6): 877–84. Barnes, H.L. (1971) In G.G. Ulmer (ed.), Research Techniques for High Pressure and High Temperature. Springer-Verlag: Berlin, pp. 317–35. Barnes, H.L., Romberger, S.B. and Stemprok, M. (1967) Econ. Geology 62: 957–82. Barns, R.L., Laudise, R.A. and Shields, R.M. (1963) J. Phys. Chem. 67: 835–9. Barr-David, F. and Dodge, B.F. (1959) J. Chem. Eng. Data 4(2): 107–21. Barry, J.C., Richter, J. and Stich, E. (1988) Ber. Bunsenges. Phys. Chem. 92: 1118–22. Barsukov, V.L., Kuznetsov, B.A., Dorofeeva, V.A. and Khodakovsky, I.L. (1979) Geokhimia (7): 1017–27. Barthel, J. and Popp, H. (1991) J. Chem. Inform. Computer Sci. 31: 107–15. Barton, C.J., Hebert, G.M. and Marshall, W.L. (1961) J. Inorg. Nucl. Chem. 21: 141–51. Bassett, W.A., Shen, A.N., Bucknum, M. and Chou, I.-M. (1993) Rev. Sci. Istrum. 64: 2340–5. Bassett, W.A., Anderson, A.J., Mayanovic, R.A. and Chou, I.-M. (2000) Chem. Geology 167: 3–10. Bazaev, A.R., Abdulagatov, I.M., Bazaev, E.A. and Abdurashidova, A. (2007) J. Chem. Thermod. 39: 385–411. Becker, K.H., Cemic, L. and Langer, K.E. (1983) Geochim. Cosmochim. Acta 47: 1573–8. Becker, P.J. and Schneider, G.M. (1993) J. Chem. Thermod. 25: 795–800.


Bell, M.J., Mravich, N.J., Pocock, F.J. and Rubright, M.M. (1977) Proceedings of the American Power Conference 39: 849–67. Benedict, M. (1939) J. Geology 47: 252–76. Benezeth, P., Diakonov, I.I., Pokrovski, G.S., Dandurand, J.L.Schott, J. et al. (1997) Geochim. Cosmochim. Acta 61(7): 1345–7. Benezeth, P., Palmer, D.A. and Wesolowski, D.J. (1999) Geochim. Cosmochim. Acta 63(10): 1571–86. Benezeth, P., Palmer, D.A. and Wesolowski, D.J. (2001) Geochim. Cosmochim. Acta 65: 2097–2111. Benezeth, P., Palmer, D.A., Wesolowski, D.J. and Xiao, C. (2002) J. Soln. Chem. 31(12): 947–73. Benning, L.G. and Seward, T.M. (1996) Geochim. Cosmochim. Acta 60(11): 1849–71. Benrath, A. (1941) Z. Anorg. Allg. Chem. 247: 147–60. Benrath, A. (1942) Z. Anorg. Allg. Chem. 249: 245–50. Benrath, A. and Braun, A. (1940). Z. Anorg. Allgem. Chem. 244: 348–57. Benrath, A. and Lechner, K. (1940) Z. Anorg. Allgem. Chem. 244: 359–76. Benrath, A., Gjedebo, F., Schiffers, B. and Wunderlich, H. (1937) Z. Anorg. Allg. Chem. 231: 285–97. Bergman, A.G. and Kuznetsova, A.I. (1959) Zh. Neorgan. Khimii 4(1): 194–204. Bernshtein, V.A. and Matsenok, E.A. (1961) Zh. Prikl. Khimii 34: 982–6; Russ. J. Appl. Chem. 34: 948–51. Bernshtein, V.A. and Matsenok, E.A. (1965) Zh. Prikl. Khimii 38: 1935–8; Russ. J. Appl. Chem. 38: 1898–1901. Bhatnagar, O.N. and Campbell, A.N. (1982) Can. J. Chem. 60: 1754–8. Bischoff, J.L. and Rosenbauer, R.J. (1988) Geochim. Cosmochim. Acta 52: 2121–6. Bischoff, J.L., Rosenbauer, R J. and Fournier, R.O. (1996) Geochim. Cosmochim. Acta 60: 7–16. Bischoff, J.L., Rosenbauer, R.J. and Pitzer, K.S. (1986) Geochim. Cosmochim. Acta 50: 1437–44. Blasdale, W.C. and Robson, H.L. (1928) J. Amer. Chem. Soc. 50: 35–46. Blount, C.W. (1977) Amer. Mineralogist 62: 942–57. Blount, C.W. and Dickson, F.W. (1967). Trans. Amer. Geophys. Union 48: 249–50. Blount, C.W. and Dickson, F.W. (1969) Geochim. Cosmochim. Acta 33: 227–45. Bluma, M. and Deiters, U.K. (1999) Phys.Chem.Chem.Phys. 1: 4307–13. Bodnar, R.J. and Sterner, S.M. (1985) Geochim. Cosmochim. Acta 49: 1855–9. Bodnar, R.J., Burnham, C.W. and Sterner, S.M. (1985) Geochim. Cosmochim. Acta 49: 1861–73. Boettcher, A.L. and Wyllie, P.J. (1969) Geochim. Cosmochim. Acta 33: 611–32. Bolz, A., Deiters, U.K., Peters, C.J. and de Loos, T.W. (1998) Pure Appl. Chem. 70(11): 2233–40. Booth, H.S. and Bidwell, R.M. (1950) J. Amer. Chem. Soc. 72: 2567–75. Borina, A.F. (1963) Geokhimiya (7): 658–66. Borina, A.F. and Ravich, M.I. (1964) Zh. Neorgan. Khimii 9(4): 975–81. Borovaya, F.E. and Ravich, M.I. (1968) Zh. Neorgan. Khimii 13: 3337–41. Boshkov, L.Z. (1987) Dokl. Akad. Nauk SSSR 294: 901–5. Boshkov, L.Z. and Mazur, V.A. (1985) Phase Behaviour of Binary Lennard-Jones Liquids, Deposit. VINITI, № 6844-В85, Moscow.

Boshkov, L.Z. and Yelash, L.V. (1995a) Dokl. Akad. Nauk (Russ.) 340: 622–5. Boshkov, L.Z. and Yelash, L.V. (1995b) Dokl. Akad. Nauk (Russ.) 341: 61–5. Boettcher, A.L. and Wyllie, P.J. (1969) Geochim. Cosmochim. Acta 33: 611–32. Bouaziz, R. (1961) Ann. Chimie 6: 345–93. Bourcier, W.L., Knauss, K.G. and Jackson, K.J. (1993) Geochim. Cosmochim. Acta 57: 747–62. Bowers, W.J., Jr. Bean, V.E. and Hurst, W.S. (1995) Rev. Sci. Instrum. 66(2): 1128–30. Bowman L.E. and Fulton, J.L. (1995) in H.J. White, Jr and J.V. Sengers et al. (eds), Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry. Begell House, pp. 625–31. Brandt, E., Franck, E.U., Wei, Y.S. and Sadus, R.J. (2000) Phys. Chem. Chem. Phys. 2: 4157–64. Breman, B.B., Beenackers, A.A.C.M., Rietjens, E.W.J. and Stege, R.J.H. (1994) J. Chem. Eng. Data 39: 647–66. Brill, T.B., Kieke, M.J and Schoppelrei, J.W. (1995) in H.J. White, Jr and J.V. Sengers et al. (eds), Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry. Begell House, pp. 610–16. Broadbent, D., Levis G.G. and Wetton, E.A.M. (1977) J. Chem. Soc., Dalton Trans. 464–8. Bröllos, K., Peter, K. and Schneider, G.M. (1970) Ber. Bunsenges. Phys. Chem. 74(7): 682–6. Brown, E.H. and Whitt, C.D. (1952) Ind. Eng. Chem. 44(3): 615–18. Brown, J.S., Hallett, J.P., Bush, D. and Eckert, C.A. (2000) J. Chem. Eng. Data 45: 846–50. Brunner, E. (1990) J.Chem.Thermod. 22: 335–53. Brunner, G., Steffen, A. and Dohrn, R. (1993) Fluid Phase Equil. 82: 165–72. Brunner, G., Teich, J. and Dohrn, R. (1994) Fluid Phase Equil. 100: 253–68. Bryzgalin, O.V. (1976) Geokhimiya (6): 864–70. Buechner, E.H. (1906) Z. Phys. Chem. 56: 257–318. Buechner, E.H. (1918) Die Heterogenen Gleichgewichte vom St andpunkte der Phasenlehre von H.W.Bakhuis Roozeboom, Systeme Mit Zwei Flussigen Phasen; Systeme Aus Zwei Komponenten. T.2, H.2, Braunschweig. Buksha, Y.V. and Shestakov, N.E. (eds) (1997) Properties of Aqueous Solutions and Systems with Chlorides of Sodium, Potassium and Magnesium (Russ.), Handbook. Khimiya, St Petersburg. Burnham, S.W., Ryzhenko, B.N. and Schitel, D. (1973) Geokhimia (12): 1880; Geochem. Intern. 10(12): 1374. Bussey, R.H., Holmes, H.F. and Mesmer, R.E. (1984) J. Chem. Thermod. 16: 343–72. Byers, W.A., Lindsay, W.T., Jr. and Kunig, R.H. (2000) J. Soln. Chem. 29(6): 541–59. Byrappa, K. and Yoshimura, M. (2001) Handbook of Hydrothermal Technology: A Technology for Crystal Growth and Material Processing. Noyes Publications, Park Ridge, NJ. Campbell, A.N. (1943) J. Amer. Chem. Soc. 65: 2268–71. Campbell, A.N. and Bhatnagar, O.N. (1979) Canad. J. Chem. 57: 2542–45. Campbell, A.N. and Bhatnagar, O.N. (1984) J. Chem. Eng. Data 29: 166–8. Carlson, E.T., Peppler, R.B. and Wells, L.S. (1953) J. Research National Bureau Standards 51(4): 179–84. Castet, S., Dandurand, J.-J., Schott, J. and Gout, R. (1993) Geochim. Cosmochim. Acta 57: 4869–84.

122


Chacko, T., Cole, D.R. and Horita, J. (2001) In: Stable Isotope Geochemistry. Mineral. Soc. of Amer., Washington, pp. 1–81. Chandler, K., Eason, B., Liotta, C.L. and Eckert, C.A. (1998) Ind. Eng. Chem. Res. 36: 3515–18. Chang, B.-T., Pak, L.-H. and Li, Yu-S. (1979) Bull. Chem. Soc. Japan 52(5): 1321–6. Chen, C.A. and Marshall, W.L. (1982) Geochim. Cosmochim. Acta 46: 279–87. Chou, I.-M. (1987) Geochim. Cosmochim. Acta 51: 1965–75. Chou, I.-M. and Eugster, H.P. (1977) Amer. J. Sci. 277: 1296–1314. Chou, I.-M. and Frantz, J.D. (1977) Amer. J. Sci, 277: 1067–72. Chou, I-M., Sterner, S.M. and Pitzer, K.S. (1992) Geochim. Cosmochim. Acta 56: 2281–93. Christensen, S.P. and Paulaitis, M.E. (1992) Fluid Phase. Equil. 71: 63–83. Chufarov, G.I., Zhuravleva, M.G., Tatievskaya, E.P., Averbukh, B.D. and Antonov, V.K. (1953) Zh. Prikl. Khimii 26(6): 652–5. Clancy, P. Gubbins, K.E. and Grey, C.G. (1979) Faraday Disc. Chem. Soc. 66: 116–29. Clark F.E., Gill, J.S., Slusher, R. and Secoy, C.H. (1959) J. Chem. Eng. Data 4: 12–15. Clarke, L. and Partridge, E.P. (1934) Ind. Eng. Chem. 26(8): 897–903. Cohen-Adad, R., Tranquard, A. and Marchand, A. (1968) Bull. Soc. Chim. France (1): 65–71. Connolly, J.F. (1966) J. Chem. Eng. Data 11(1): 13–16. Copeland, C.S., Silverman, J. and Benson S.W. (1953) J. Chem. Phys. 21: 12–17. Cramer, S.D. (1980) Ind. Eng. Chem. Process Des. Dev. 19: 300–5. Cramer, S.D. (1982) Report No. 8706, Bureau of Mines, US Depart. of the Interior, USA. Cramer, S.D. (1984) Ind. Eng. Chem. Process Des. Dev. 23: 618–20. Crerar, D.A. and Anderson, G.M. (1971) Chem. Geology 8: 107–22. Crovetto, R. and Wood, R.H. (1991) Fluid Phase Equil. 65: 253–61. Crovetto, R. and Wood, R.H. (1992) Fluid Phase Equil., 74, pp. 271–88. Crovetto, R. and Wood, R.H. (1996) Fluid Phase Equil. 121: 293. Crovetto, R., Fernandez-Prini, R. and Japas, M.L. (1982) J. Chem. Phys. 76(2): 1077–86. Crovetto, R., Fernandez-Prini, R. and Japas, M.L. (1984) Ber. Bunsenges. Phys. Chem. 88: 484–8. Crovetto, R., Lvov, S.N. and Wood, R.H. (1993) J.Chem.Thermod. 25: 127–38. Currie, K.L. (1968) Amer. J. Sci. 266: 321–41. Dandge, D.K., Heller, J.P and Wilson, K.V. (1985) Ind. Eng. Chem. Prod. Res. Dev. 24: 162–6. D′Ans, J. and Sypiena, G. (1942) Kali, Z.Kali-, Steinsalz- Erdolind. Sowie Salin. 6: 88–95. Dadze, T.P., Sorokin, V.I. and Nekrasov, I.Y. (1981) Geokhimiya (10): 1482–92. Danneil, A., Tödheide, K. and Franck, E.U. (1967) Chemie-Ing.Techn. 39(13): 816–22. De Loos, T.W., Wijen, A.J.M. and Diepen, G.A.M. (1980) J. Chem. Thermod. 12: 193–204. De Loos, T.W., Penders, W.G. and Lichtenthaler, R.N. (1982) J. Chem. Thermod. 14: 83–91. De Loos, T.W., Van Dorp, J.H. and Lichtenthaler, R.N. (1983) Fluid Phase Equil. 10: 279–87.

Deiters, U.K. and Pegg, I.L. (1989) J. Chem. Phys. 90: 6632–41. Deiters, U.K., Boshkov, L.Z.,Yelash, L.V. and Mazur, V.A. (1998a) Doklad. Akad. Nauk 358(4): 497–501. Deiters, U.K., Boshkov, L.Z., Yelash, L.V. and Mazur, V.A. (1998b) Doklad. Akad. Nauk 359(3): 343–7. Dell’Orco, P., Eaton, H., Reynold, T. and Buelow, S. (1995) J. Supercrit. Fluids 8(3): 217–27. Dem´yanets, L.N., Lobachev, A.N. and Usov, L.V. (1976) Izv. Akad. Nauk SSSR, Neorgan. Mater. 12(3): 498–501. Dem’yanets, L.P. and Ravich, M.I. (1972) Zh. Neorgan. Khimii 17: 2816–20. Dernov-Pegarev, V.F. and Malinin, S.D. (1976) Geokhimiya (5): 643–58. Dernov-Pegarev, V.F. and Malinin, S.D. (1985) Geokhimiya (8): 1196–1205. Dernov-Pegarev, V.F., Bogomolova, V.I. and Malinin, S.D. (1988) Geokhimiya (11): 1612–17. Diakonov, I.I., Schott, J., Martin, F., Harrichourry, J.-C. and Escalier, J. (1999) Geochim. Cosmochim. Acta 63(15): 2247–61. Dibrov, I.A., Mal’tsev, G.Z. and Mashovets, V.P. (1964) Zh. Prikl. Khimii 37(9): 1920–9. Dickson, F.W. (1964) Econ. Geology 59: 625–35. Dickson, F.W., Blount, C.W. and Tunell, G. (1963) Amer. J. Sci. 261: 61–78. Dingemans, P. (1939) Rec. Trav. Chim. 58: 559–81. Dingemans, P. (1945) Rec. Trav. Chim. 64: 194–204. Dinh, C.M., Kim, H., Lin, H.-M., and Chao, K.-C. (1985) J. Chem. Eng. Data 30: 326–327. Dinov, K. Matsuura, Ch. Hiroishi, D. and Ishigure, K. (1993) Nucl. Sci. Eng., 113: 207–16. DiPippo, M.M., Sako, K. and Tester, J.W. (1999) Fluid Phase Equil., 157: 229–55. Distanov, G.K. (1937) Zh. Obschey Khimii 7(3–4): 677–80. Dohrn, R. and Brunner, G. (1986) Fluid Phase Equil. 29: 535–44. Driesner, T. and Seward, T.M. (2000) Geochim. Cosmochim. Acta 64: 1773–84. Dubois, M., Weisbrod, A. and Shtuka, A. (1994) Chem. Geology 115: 227–38. Economou, I.G., Heidman, J.L., Tsonopoulos, C. and Wilson, G.M. (1997) AIChE Journ., 43(2): 535–46. Economou, I.G., Peters, C.J. and de Swaan Arons, J. (1995) J. Phys. Chem. 99: 6182–93. Efremova, E.P., Kuznetsov, V.A. and Shikina, N.D. (1982) Geokhimiya (1): 56–63. Efremova, G.D. and Shvarts, A.V. (1966) Zh. Fizich. Khimii 40: 907–11; Russ. J. Phys. Chem. 40: 486–9. Efremova, G.D. and Shvarts, A.V. (1969) Zh. Fizich. Khimii 43: 1732–6; Russ. J. Phys. Chem. 43: 968–70. Efremova, G.D. and Shvarts, A.V. (1970) Zh. Fizich. Khimii 44(3): 837. Efremova, G.D. and Shvarts, A.V. (1972) Zh. Fizich. Khimii 46(2): 408–12; Russ. J. Phys. Chem. 46: 237. Efremova, G.D., Pryanikova, R.O and Plenkina, R.M. (1973) Zh. Fizich. Khimii 47(3): 609–12. Elenevskaya, V.M. and Ravich, M.I. (1961) Zh. Neorgan. Khimii 6(10): 2380–6. Ellis, A.J. (1959a) Amer. J. Sci. 257: 354–65. Ellis, A.J. (1959b) Amer. J. Sci. 257(3): 217–34. Ellis, A.J. (1963) Amer. J. Sci. 261: 259–67. Ellis, A.J. and Giggenbach, W. (1971) Geochim. Cosmochim. Acta 35: 247–60.


Ellis, A.J. and Golding, R.M. (1963) Amer. J. Sci. 261: 47–60. Emons, H.H., Dittrich, A. and Voigt, W. (1987) In: Proc. of the Joint Intern. Symp. on Molten Salts, Honolulu, Hawaii, 18– 23.10.1987, pp. 111–29. Emons, H.-H., Voigt, W. and Wollny, F.-W. (1986) Z. phys. Chem., Leipzig, 267(1): 1–8. Etard, A. (1894) Ann. Chim. Phys. 7(2): 503–74; (1997) from Databook: Fiz.-Khim. Svoystva Galurg. Rastvorov i Soley (Russ.), Buksha, Y.V. and Shestakov, N.E. (eds), Khimiya, St Petersburg, Russia, p. 326. Eubank, P.T., Wu, C.H., Alvarado, J.F.J., Forero, A. and Beladi, M.K. (1994) Fluid Phase Equilibra 102: 181–203. Eugster, H.P. (1957) J. Chem. Phys., 26: 1760–1. Fanghanel, T., Kravchuk, K.G., Voigt, W. and Emons, H.H. (1987) Z. Anorg. Allg. Chem. 547: 21–6. Fein, J.B. and Walther, J.V. (1989) Amer. J. Sci. 289(10): 975–93. Fein, J.B. and Walther, J.V. (1987) Geochim. Cosmochim. Acta 51: 1665–73. Fenghour, A., Wakeham, W.A., Ferguson, D., Scott, A.C. and Watson, J.T.R. (1993) J. Chem. Thermod. 25: 1151–9. Fenghour, A., Wakeham, W.A. and Watson, J.T.R. (1996a) J. Chem. Thermod. 28: 433–6. Fenghour, A., Wakeham, W.A. and Watson, J.T.R. (1996b) J. Chem. Thermod. 28: 447–458. Feodorov, M.K. (1982). Dissert., Technol Institute, Leningrad, USSR, 420 p. Feodorov, M.K., Antonov, N.A. and Lvov, S.N. (1976) Zh. Prikl. Khimii 49(6): 1226–32. Feodotiev, K.M. and Tereshina, I.A. (1963) In Trudi Inst. Geol. Rudnikh Mestorozhdeniy, Petrogr., Mineral. i Geokhimii (IGEM) Izd.ANSSSR, Moscow, 99: 40–50. Fleet, M.E. and Knipe, S.W. (2000) J. Soln. Chem. 29(11): 1143–57. Foster, R.P. (1977) Chem. Geology 20: 27–43. Fournier, R.O. and Thompson, J.M. (1993) Geochim. Cosmochim. Acta 57: 4365–75. Fournier, R.O., Rosenbauer, R.J. and Bischoff J.L. (1982) Geochim. Cosmochim. Acta 46: 1975–8. Fournier, R.O. and Rowe, J.J. (1962) Amer. Mineral. 47: 897–902. Franck, E.U., Lentz, H. and Welsch, H. (1974) Z. Phys. Chemie, N.F. 93: 95–108. Freyer, D. and Voigt, W. (2004) Geochim. Cosmochim. Acta, 68(2): 307–18. Friedman, I. (1950) J. Amer. Chem. Soc. 72: 4570–4. Froehlich, W. (1929) Mitt. Kali - Forsch. - Amst. 68: 37–66. Fulton, J.L., Darab, J.G. and Hoffmann, M.M. (2000) in P.R. Tremaine, P.G. Hill, D.E. Irish and P.V. Balakrishnan (eds), Steam, Water and Hydrothermal Systems, NRC Research Press, Ottawa, pp. 593–8. Furman, D. and Griffiths, R.B. (1978) Phys. Rev.A 17: 1139–49. Galinker, I.S. and Korobkov, V.I. (1951) Dokl. Akad. Nauk SSSR 81(3): 407–10. Galobardes, J.F., Oweimreen, G.A. and Rogers, L.B. (1981a) Anal. Chem. 53: 1043–7. Galobardes, J.F., Van Hare, D.R. and Rogers, L.B. (1981b) J. Chem. Eng. Data 26: 363–6. Gammons, C.H. and Barnes, H.L. (1989) Geochim. Cosmochim. Acta 57: 279–90. Gammons, C.H. and Bloom, M.S. (1993) Geochim. Cosmochim. Acta 57: 2451–67. Gammons, C.H. and Williams-Jones, A.E. (1995) Geochim. Cosmochim. Acta 59: 3453–68.

Gammons, C.H. and Yu, Y. (1997) Chem. Geology 137: 155–73. Gammons, C.H., Wood, S.A .and Williams-Jones, A.E. (1996) Geochim. Cosmochim. Acta 60: 4615–30. Gammons, C.H., Yu.Y. and Bloom, M.S. (1993) Geochim. Cosmochim. Acta 57: 2469–79. Gammons, C.H., Yu, Y. and Williams-Jones, A.E. (1997) Geochim. Cosmochim. Acta 61: 1971–83. Ganeev, I.G. and Rumyantsev, V.N. (1974) Geokhimiya (9): 1402–3. Gardner, E.R., Jones, P.J. and de Nordwall, H.J. (1963) J. Chem. Soc., Faraday Trans. 59(9): 1994–2000. Garmenitskiy, T.N. and Kotel’nikov, A.R. (1984) Experimental Petrography (Russ.). Moscow Univ. Gauter, K., Florusse, L.J., Smits, J.C. and Peters, C.J. (1998) J. Chem. Thermodyn. 30: 1617–31. Gauter, K. Peters, C.J. Scheidgen, A.L. and Schneider, G.M. (2000) Fluid Phase Equil. 171: 127–33. Gavrish, M.L. and Galinker, I.S. (1955) Dokl. Akad. Nauk SSSR 102:(1): 89–91. Gavrish, M.L. and Galinker, I.S. (1970) Zh. Neorgan. Khimii 15(7): 1979–81. Gavrish, M.L. and Galinker, I.S. (1957) Zapiski Khar’kovskogo Sel.-Khoz. Inst. 14(51): 30; (2003) Citated from Databook: Eksper. Dannie po Rastvor-ti Mnogokomp. Vodno-Solevikh Sistem. V.I-1 Khimizdat, St Petersburg, p. 478. Gavrish, M.L. and Galinker, I.S. (1955) Dokl. Akad. Nauk SSSR 102: 89–91. Geerlings, J., Richter, J., Rormark, L. and Oye, H.A. (1997) Ber. Bunsenges. Phys. Chem. 101(8): 1129–35. Gehrig, M., Lentz, H. and Franck, E.U. (1986) Ber. Bunsenges. Phys. Chem. 90: 525–33. Gibert, F, Pascal, M.L. and Pichavant, M. (1998) Geochim. Cosmochim. Acta 62(17): 2931–47. Gibert, R., Guillaume, D. and Laporte, D. (1998) Europ. J. Mineral. 10: 1109–23. Gill, J.S. and Marshall, W.L. (1961) Rev. Sci. Inst. 32: 1060–2. Gillespie, P.C. and Wilson, G.M. (1980) Gas Processors Association, Research Report (RR-41), USA. Gillespie, P.C. and Wilson, G.M. (1982) Gas Procession Association, Research Report (RR-48), USA. Gillingham, T.E. (1948) Econ. Geology 43(4,): 241–72. Giordano, T.H. and Barnes, H.I. (1979) Econ. Geology 74: 1637–46. Golubev, B.P., Smirnov, S.N., Lukashov, Yu.M. and Svistunov, E.P. (1985) Electro-Physical Methods for Studying the Properties of Heat Transfer Media (Russ.), Energoatomizdat, Moscow, pp. 58–9. Gorbachev, S.V., Kondrat’ev, V.P., Belousov, A.I. and Kopylov, V.V. (1972) Trudy Mosk. Khim.-Tekhnol. Inst. im. D.I.Mendeleeva 71: 62–5. Gregorowicz, J., de Loos, Th.W. and de Swan Arons, J. (1993) J. Chem. Eng. Data 38: 417–21. Gregory, N.W. and Mohr, R. H. (1955) J. Amer. Chem. Soc. 77:. 2142–4. Griffiths, R.B. (1970) Phys. Rev. Lett. 24: 715–17. Griffiths, R.B. (1974) J. Chem. Phys. 60: 195–206. Griffiths, R.B. and Widom, B. (1973) Phys. Rev. A 8: 2173–5. Grigoriev, A.P. and Nikolaev, A.V. (1967) Dokl. Akad. Nauk SSSR 174(1): 93–5. Griswold, J. and Wong, S.Y. (1952) Chem. Eng. Prog., Symp. Ser. 48(3): 18–34. Griswold, J., Haney, J.D. and Klein, V.A. (1943) Ind. Eng. Chem. 35: 701–4.

124


Groitheim, K., Voigt, W., Haugsdal, B. and Dittrich, D. (1978) Acta Chem. Scand. 42A: 470–6. Gruszkiewicz, M.S. and Simonson. J.M. (2005) J. Chem. Thermodyn. 37: 906–930. Gubbins, K.E., Shing, K.S. and Streett, W.B. (1983) J. Phys. Chem. 87: 4573–4585. Guillaume, D., Tkachenko, S., Dubessy, J. and Pironon, J. (2001) Geochim. Cosmochim. Acta 65: 3319–24. Guillevic, J.-L., Richon, D. and Renon, H. (1985) J. Chem. Eng. Data 30: 332–5. Gundlach, H., Stoppel, D., Strubel, G. and Germany, F.R. (1972) In Proceedings of the 24th Intern. Geol. Congress, 1972, sec.10, pp. 219–29. Gunter, W.D., Chou, I.-M. and Girsperger S. (1983) Geochim. Cosmochim. Acta 47: 863–73. Guseva, A.N. and Parnov, E.I. (1963) Radiokhimiya 5(4): 507–9. Guseynov, A.G., Iskanderov, A.I., Akhundov, R.T., Agaeva, D.A. and Akhundov, T.S. (1989). In: Termodyn. i Perenosn Svoystva Veschestv , Sbornik Azerb. Polytechn. Instit., Baku, pp. 14–20. Harvey A.H. (1991) J. Chem. Phys. 95: pp. 479–484. Harvey, A.H. and Bellows, J.C. (1997) Evaluation and Correlation of Steam Solubility Data for Salts and Minerals of Interest in the Power Industry, NIST Technical Note 1387, USA. Hearn, B., Hunt, M.R. and Hayward, A. (1969) J. Chem. Eng. Data 14(4): 442–7. Hefter, G.T. and Tomkins, R.P.T. (eds) (2003) The Experimental Determination of Solubilities. John Wiley & Sons, Ltd.. Heidman, J.L., Tsonopoulos, C., Brady, C.J. and Wilson, G.M. (1985) AIChE Journ. 31(3): 376–84. Heilig, M. and Franck, E.U. (1990) Ber. Bunsenges. Phys. Chem. 94: 27–35. Heitmann, H.G. (1964) Chemisker-Ztg. Chem. Apparatur 88(22): 891–3. Heitmann, H.G. (1965) Glastechn. Ber. 38(2): 41–54. Helz, G.R. and Holland, H.D. (1965) Geochim. Cosmochim. Acta 29: 1303–15. Hemley, J.J., Montoya, J.W, Marinenko, J.W. and Luce, R.W. (1980) Econ. Geology 75: 210–28. Henley, R.W. (1973) Chem. Geology 11: 73–87. Higgins, S.R., Eggleston, C.M., Jordan, G., Knauss, K.G. and Boro, C.O. (1998) Min. Mag. 62A: 618–19; Rev. Sci. Instr. 69: 2994–8. Hiroishi, D., Matsuura, C. and Ishigure, K. (1998) Mineralog. Magazine 62A: 626–7. Hitchen, C. (1935) Bull. Inst. Mining. Metal. 364: 1–26. Hodes M.S., Smith, K.A., Hurst, W.S., Bowers,nd W.J., Jr. and Griffith, P. (1997) Proc. Am. Soc. Mech. Eng. 32 National Heat Transfer 12, HTD-350(ASME, NY), pp. 107–9. Hoffmann, F.P. and Voigt, W. (1996) ELDATA: Intern. Electron. J. Phys.-Chem. Data 2: 31–6. Hölemann, H. and Kleese, W. (1938) Z. anorg. allgem. Chem. 237: 172—6. Holmes, H.F. and Mesmer, R.E. (1981a) J. Chem. Thermod. 13: 1025–33. Holmes, H.F. and Mesmer, R.E. (1981b) J. Chem. Thermod. 13: 1035–46. Holmes, H.F. and Mesmer, R.E. (1983) J. Phys. Chem. 87: 1242–55. Holmes, H.F. and Mesmer, R.E. (1986) J. Chem. Thermod. 18: 263–75. Holmes, H.F. and Mesmer, R.E. (1988) J. Chem. Thermod. 20: 1049–60. Holmes, H.F. and Mesmer, R.E. (1990) J. Phys. Chem. 94(20): 7800–5.

Holmes, H.F. and Mesmer, R.E. (1992a) J. Chem. Thermod. 24: 317–28. Holmes, H.F. and Mesmer, R.E. (1992b) J. Chem. Thermod. 24: 829–41. Holmes, H.F. and Mesmer, R.E. (1993) J. Chem. Thermod. 25: 99–110. Holmes, H.F. and Mesmer, R.E. (1994) J. Chem. Thermod. 26: 581–94. Holmes, H.F. and Mesmer, R.E. (1996a) J. Chem. Thermod. 28: 67–81. Holmes, H.F. and Mesmer, R.E. (1996b) J. Chem. Thermod. 28: 1325–58. Holmes, H.F. and Mesmer, R.E. (1998) J. Chem. Thermod 30: 723–41. Holmes, H.F. and Mesmer, R.E. (1999) J. Soln. Chem. 28: 327–40. Holmes H.F., Baes, C.F. and Mesmer, R.E. (1978) J. Chem. Thermod. 10: 983–96. Holmes, H.F., Baes, C.F. and Mesmer, R.E. (1979) J. Chem. Thermod. 11: 1035–50. Holmes, H.F., Baes, C.F. and Mesmer, R.E. (1981) J. Chem. Thermod. 13: 101–13. Holmes, H.F., Busey, R.H., Simonson, J.M. and Mesmer, R.E. (1994) J. Chem. Thermod. 26(3): 271–98. Holmes, H.F., Simonson, J.M. and Mesmer, R.E. (2000) J. Chem. Thermod. 32: 77–96. Hooper, H.H., Michel, S. and Prausnitz, J.M. (1988) J. Chem. Eng. Data 33: 502–5. Horita, J. and Cole, D.R. (2004) in D.A. Palmer et al. (eds), Aqueous Systems at Elevated Temperatures and Pressures, Elsevier, Chap. 9, pp. 277–320. Hovey, J.K., Pitzer, K.S., Tanger, J.C., Bischoff, J.L. and Rosenbauer, R.J. (1990) J. Phys. Chem. 94: 1175–9. Howell, R.D., Raju, K. and Atkinson, G. (1992) J. Chem. Eng. Data 37: 464–9. Hoyt, E.B. (1967) J. Chem. Eng. Data 12(4): 461–4. Huang, S.S., Leu, A.D., Ng, H.-J. and Robinson, D.B. (1985) Fluid Phase Equil. 19: 21–32. Huang, W.I. and Wyllie, P.J. (1974) Amer. J. Sci. 274: 378–95. Ikornikova N.Y. (1975) Hydrothermal Crystal Growth in Chloride Systems (Russ.), Nauka, Moscow, USSR. Il’in, K.K. and Cherkasov, D.G. (2005) Izv. Vissh. Ucheb. Zaved., Khimiya i Khim. Tekhnol. 48(3): 3–15; (2006) 49(1): 3–11. Ipatiev, V. and Teodorovich, V.P. (1934) Zh. Obschey Khimii 4(3): 395–9. Irani, C.A. and McHugh, D.J. (1979) High Press. Sci. Tech. 6th AIRAPT Conf. 1: 600–8. Isaacs, N.S. (1981) Liquid Phase High Pressure Chemistry. John Wiley & Sons, Ltd, Chichester. Itkina, L.S. (1973) Lithium, Rubidium and Cesium Hydroxides (Russ). Nauka, Moscow. Jaeger, A. (1923) Brennstoff-Chemie 4(17): 259–61. Japas, M.L. and Franck, E.U. (1985a) Ber. Bunsenges. Phys. Chem. 89: 793–800. Japas, M.L. and Franck, E.U. (1985b) Ber. Bunsenges. Phys. Chem. 89: 1268–75. Jasmund, K. (1952/1953) Heidelberg. Beitr. Min. Petr. 3: 380–405. Jensen, J.P. and Daucik, K. (2002) Power Plant Chem. 4(11): 653–9. Jockers, R. and Schneider, G.M. (1978) Ber. Bunsenges. Phys. Chem. 82: 576–82.


Jockers, R., Paas, R. and Schneider, G.M. (1977) Ber. Bunsenges. Phys. Chem. 81(10): 1093–6. Jones, D.G. and Staehle, R.W. (eds.) (1976) High Temperature High Pressure Electrochemistry in Aqueous Solutions, Nat. Assoc. Corros. Eng., Houston, USA. Jones, E.V. and Marshall, W.L. (1961a) J. Inorg. Nucl. Chem. 23: 287–93. Jones, E.V. and Marshall, W.L. (1961b) J. Inorg. Nucl. Chem. 23: 295–303. Jones, E.V., Lietzke, M.H. and Marshall, W.L. (1957) J. Amer. Chem. Soc. 79: 267–71. Jones, M.E. (1963) J. Phys. Chem. 67: 1113–15. Joyce, D.B. and Holloway, J.R. (1993) Geochim. Cosmochim. Acta 57: 733–46. Kalyanaraman, R. Yeatts, L.B. and Marshall, W.L. (1973a) J. Chem. Thermod. 5: 891–8. Kalyanaraman, R., Yeatts, L.B. and Marshall, W.L. (1973b) J. Chem. Thermod. 5: 899–909. Kamilov, I.K., Stepanov, G.V., Abdulagatov, I.M., Rasulov, A.R. and Milikhina, E.I. (2001) J. Chem. Eng. Data, 46: 1556–67. Kaufman, M. and Griffiths, R.B. (1982) J. Chem. Phys. 76: 1508–24. Keevil, N.B. (1942) J. Amer. Chem. Soc. 64: 841–50. Kennedy, G.C. (1950) Econ. Geology 45(7): 629–53. Kennedy, G.C., Wasserburg, G.J., Heard, H.C. and Newton, R.C. (1961) In Bundy, Hibbard and Strong (eds), Progress in Very High Pressure Research, JohnWiley & Sons, Inc., pp. 28–45. Kennedy, G.C., Wasserburg, G.J., Heard, H.C. and Newton, R.C. (1962) Amer. J. Sci. 260: 501–21. Kessis, J.J. (1967) Comp. rend. Acad. Sc. Paris, ser. C, 264: 973–5. Ketsko, V.A., Urusova, M.A. and Valyashko, V.M. (1984) Zh. Neorgan. Khimii 29(9): 2443–6. Khaibullin, I.Kh. and Borisov, N.M. (1965) Zh. Fizich. Khimii 39(3): 688–92. Khaibullin, I.Kh. and Borisov, N.M. (1966) Teplofiz. Visok. Temp. 4: 518–23; High Temp. 4: 489–94. Khaibulin, I.Kh. and Novikov, B.E. (1973) In Mater. Vses. NauchnoTekhn. Soveshch. po Teploobmen. Teplofiz. Svoistvam Morsk. Solonovatykh Vod i ikh Ispol’z., pp. 339–50. Khaibullin, I.Kh. and Novikov, B.E. (1972) Teplofiz. Visok. Temp. 10: 895–7. Khaibullin, I.Kh. and Novikov, B.E. (1973) Teplofiz. Visok. Temp. 11: 320–7; High Temp. 11(2): 276–82. Khitarov, N.I. (1956) Geokhimiya (1): 62–6; (1956) Geochim. Intern. 1: 55–61. Khodakovsky, I.L. and Elkin, A.E. (1975) Geokhimiya (10): 1490–8. Kiran, E., Debenedetti, P.G. and Peters, C.J. (eds) (2000) Supercritical Fluids: Fundamental and Applications, Kluwer Acad. Publishers, Dordrecht, Netherlands. Kirgintsev, A.N., Trushnikova, L.N. and Lavrentieva, V.G. (1972) Solubility of Inorganic Substances in Water (Russ.), Handbook, Khimiya, Leningrad, USSR. Kishima, N. (1989) Geochim. Cosmochim. Acta 53: 2143–55. Kitahara, S. (1960) Rev. Phys. Chem. Japan 30(2): 109–14. Klement’ev, V. (1997) In Trudi VAMI 14: 5–12 (1937); from Y.V. Buksha and N.E. Shestakov (eds), Databook Fiz.-Khim. Svoystva Galug. Rastvorov i Soley, St Petersburg, Khimiya. Klintsova, A.P. and Barsukov, V.L. (1973) Geokhimiya (5): 701–9. Klintsova, A.P., Barsukov, V.L., Shemarykina, T.P. and Khodakovsky, I.L. (1975) Geokhimiya (4): 556–65. Knauss, K.G. Dibley, M. J. Bourcier, W.L. and Shaw, H.F. (2001) Applied Geochemistry 16: 1115–28.

Knight, C.L. and Bodnar, R.J. (1989) Geochim. Cosmochim. Acta 53: 3–8. Kogan, V.B., Fridman, V.M., Ogorodnikov, S.K and Kafarov, V.V. (1961–63, 1969, 1970) Databook on Solubility (Russ), v. I(1, 2), II(1, 2), III (1, 2, 3), Binary, ternary and multicomponent systems, ed. V.V.Kafarov, Publ.Acad.of Sci./Nauka, MoscowLeningrad. Kohnstamm, Ph. (1926) in H.Geiger and K.Scheel (eds), Handbuch der Physik, Springer, Berlin, 10, p. 223. Kolafa, J., Nezbeda, I., Pavlicek, J. and Smith, W.R. (1999) Phys. Chem.Chem. Phys. 1: 4233. Kolonin, G.R. and Laptev, Yu.V. (1982) Geokhimiya (11): 1621–31. Kordikowski, A. and Schneider, G.M. (1993) Fluid Phase Equil. 90: 149. Kordikowski, A. and Schneider, G.M. (1995) Fluid Phase Equil. 105: 129. Korobkov, V.I. and Galinker, I.S. (1956) Zh. Prikl. Khimii 23(10): 1479–83. Korzhinskiy, M.A. (1987) Geokhimiya (4): 580–5; Geochem. Intern., 24(11): 105–10. Kosova, T.B., Dem’yanets, L.N. and Uvarova, T.G. (1987) Zh. Neorgan. Khimii 32(3): 768–72. Koster van Groos, A.F. (1979) J. Phys. Chem. 83: 2976–8. Koster van Groos A.F. (1982) Amer. Mineralogist 67: 234–7. Koster van Groos A.F. (1990) Amer. Mineralogist 75:. 667–75. Koster van Groos, A.F. (1991) Geochim. Cosmochim. Acta 55: 2811–17. Kotel’nikov, A.R. and Kotel’nikova, Z.A. (1990) Geokhimiya (4): 526–37. Kotel’nikova, Z.A. and Kotel’nikov, A.R. (2002) Geokhimiya (6): 657–63 (2002); Geochem. Intern. 42: 594–600. Kovalenko, N.I., Ryzhenko, B.N., Dorofeyeva, V.A. and Bannykh, L.N. (1992) Geokhimiya (1): 88–98 (1992); Geochem. Intern. 29(8): 84–94. Kovalenko, N.I., Ryzhenko, B.N., Dorofeyeva, V.A., Volosov, A.G. and Bannykh, L.N. (1991) Geokhimiya (2): 238–49. Koz’menko, O.A., Peshchevitskiy, B.I. and Belevantsev, V.I. (1985) Geokhimia (11): 1614–20; (1986) Geochem. Intern. 23(4): 162–9. Kozintseva, T.N. (1964) Geokhimiya (8): 758–65. Kozintseva, T.N. (1965) In N.I.Khitarov (ed.), Geochemical Investigation in the Field of Elevated Pressures and Temperatures (Russ.), Nauka, Moscow, pp. 121–34. Kozlov, Vl.K. and Khodakovskiy, I.L. (1983) Geokhimiya (5): 836–48; Geochem. Intern. 20(3): 118–31. Kracek, F.C. (1931a) J. Phys. Chem. 35: 417–22. Kracek, F.C. (1931b) J. Phys. Chem. 35: 947–9. Kracek, F.C. (1931c) Amer. Chem. Soc. 53: 2609–24. Kracek, F.C., Morey, G.W. and Merwin, H.E. (1938) Amer. J. Sci. 35A: 143–71. Krader, N. and Franck, E.U. (1987) Ber. Bunsenges. Phys. Chem. 91: 627–34. Kraska, T. and Deiters, U.K. (1992) J. Chem. Phys. 96: 539–47. Kravchuk, K.G. and Todheide, K. (1996) Z. Phys. Chem. 193: 139–50. Krey, J. (1970) Dissertation; Braunschweig, FRG. Krey, J. (1972) Z. Phys. Chem. 81: 252–73. Krichevskii, I.R. (1940) Acta Phys. Chim. URSS 12: 480. Krichevskii, I.R. (1952) Phase Equilibria in Solutions at High Pressures (Russ), Goskhimizdat, Moscow. Krichevskii, I.R. and Bol’shakov, P.E. (1941) Zh. Fizich. Khimii 15: 184.

126


Krichevskii, I.R. and Tsiklis, D.S. (1941) Zh. Fizich. Khimii 15: 1059. Krichevskii, I.R., Efremova, G.D., Pranikova, R.O. and Serebryakova, A.V. (1963) Zh. Fizich. Khim. 37: 1924–7; Russ. J. Phys. Chem. 37: 1046. Krumgalz, B.S. and Mashovets, V.P. (1964) Zh. Prikl. Khimii 37(12): 2750–2. Krumgalz, B.S. and Mashovets, V.P. (1965) Zh. Neorgan. Khimii 10(11): 2564–5. Krupp. R.E. (1988) Geochim. Cosmochim. Acta 52: 3005–15. Kudrin, A.V., Rekharsky, V.I. and Khodakovsky, I.L. (1980) Geokhimiya (12): 1825–34. Kukuljan, J.A., Alvarez, J.L. and Fernandez-Prini, R. (1999) J. Chem. Thermod. 31: 1511–21. Kuyunko, N.S., Malinin, S.D. and Khodakovsky, I.L. (1983) Geokhimiya (3): 419–28. Lamb, W.M.L., McShane, C.J. and Popp, R.K. (2002) Geochim. Cosmochim. Acta 66(22): 3971–86. Lamb, W.M.L., Popp, R.K. and Boockoff, L.A. (1996). Geochim. Cosmochim. Acta 60(11): 1885–97. Lambert, I., Lefevre, A. and Montel, J. (1982) Commun. 8th Intern. CODATA Conf., Jachranka Zegrzynek, Pologne. Laudise, R.A. (1970) The Growth of Single Crystals. PrenticeHall, Englewood Cliffs, NJ. Laudise, R.A., Kolb, E.D. and De Neufville, J.P. (1965) Amer. Mineralogist 50: 382–91. Lentz, H. (1969) Rev. Sci. Instr. 40: 371–2. Lentz, H. and Franck, E.U. (1969) Ber. Bunsenges. Phys. Chem. 73: 28–35. Levin, K.A. (1991) Geokhimiya (10): 1463–8; (1992) Geochem. Intern. 29(5): 103–8. Levin, K.A. (1993) Geokhimiya (12): 1724–30. Liebscher, A., Meixner, A., Romer, R.L. and Heinrich, W. (2005) Geochim. Cosmochim. Acta 69(24): 5693–5704. Lietzke, M.H. and Marshall, W.L. (1986) J. Soln. Chem. 15(11): 903–17. Lietzke, M.H. and Stoughton, R.W. (1956) J. Amer. Chem. Soc. 78: 3023–5. Lietzke, M.H. and Stoughton, R.W. (1960) J. Phys. Chem. 64: 816–20. Lietzke, M.H. and Stoughton, R.W. (1963) J. Phys. Chem. 67: 652–4. Lin, H.-M., Leet, W.A., Kim, H. and Chao, K.C. (1985) J. Chem. Eng. Data 30: 324–5. Lindsay, W.T. and Liu, C.T. (1971) J. Phys. Chem. 75(24): 3723–7. Linke, F. and Seidell, A. (1958) Solubilities of Inorganic and Metal-organic Compounds, 4th edn., D.Van Nostrand Co. Inc., New York. Liu, C.T. and Lindsay, W.T. (1970) J. Phys. Chem. 74(2): 341–6. Liu, C.T. and Lindsay, W.T. (1972) J. Soln. Chem. 1(1): 45–9. Liu, W., McPhail, D.C. and Brugger, J. (2001) Geochim. Cosmochim. Acta 65: 2937–48. Lobachev, A.N., Dem’yanets, L.N., Kuzmina, I.P. and Emelianova, E.N. (1972) J. Crystal Growth 13/14: 540–4. Lu, B.C.-Y. and Zhang, D. (1989) Pure and Appl. Chem. 61: 1065–74. Luchinskiy, G.P. (1956) Zh. Fizich. Khimii 30(6): 1207–22. Lux, H. and Brändl, F. (1963) Z. anorg. allg. Chem. 326(1–2): 25–30. Lvov, S.N., Antonov, N.A. and Feodorov, M.K. (1976) Zh. Prikl. Khimii 49(5): 1048–51. Malinin, S.D. (1959) Geokhimiya (3): 235–45.

Malinin, S.D. (1962) In: Trudy 6 Sovesch. po Eksper. i Tekhnich. Mineral. i Petrogr, Izd. AN SSSR, 103–7. Malinin, S.D. (1976) Geokhimiya (2): 223–8. Malinin, S.D. and Dernov-Pegarev, V.F. (1974) Geokhimiya (3): 454–62. Malinin, S.D. and Kurovskaya, N.A. (1992a) Geokhimiya (7): 993–1006. Malinin, S.D. and Kurovskaya, N.A. (1992b) Geokhimiya (11): 1473–82. Malinin, S.D. and Kurovskaya, N.A. (1996a) Geokhimiya (1): 51–8. Malinin, S.D. and Kurovskaya, N.A. (1996b) Geokhimiya (12): 1183–7. Malinin, S.D. and Kurovskaya, N.A. (1998) Geokhimiya (3): 324–8. Malinin, S.D. and Kurovskaya, N.A. (1999) Geokhimiya (7): 696– 704; Geochem.Intern. 37(7): 616–23. Manning, G.E. (1994) Geochim. Cosmochim. Acta 58(22): 4831–9. Marshall, W.L. (1955) Analytical Chem. 27(12): 1923–7. Marshall, W.L. (1975) J. Inorg. Nucl. Chem. 37: 2155–63. Marshall, W.L. (1980) Geochim. Cosmochim. Acta 44: 907–13. Marshall, W.L. (1982) J. Chem. Eng. Data 27: 175–80. Marshall, W.L. (1990) J. Chem. Soc., Faraday Trans., 86(10): 1807–14. Marshall, W.L. and Chen, C.-T.A. (1982) Geochim. Cosmochim. Acta 46: 289–91. Marshall, W.L. and Gill, J.S. (1963) J. Inorg.Nucl.Chem. 25: 1033–41. Marshall, W.L. and Gill, J.S. (1974) J. Inorg.Nucl.Chem. 36: 2303–12. Marshall, W.L. and Jones, E.V. (1966) J. Phys. Chem. 70: 4028–40. Marshall, W.L. and Jones, E.V. (1974a) J. Inorg. Nucl. Chem. 36: 2313–18. Marshall, W.L. and Jones, E.V. (1974b) J. Inorg. Nucl. Chem. 36: 2319–23. Marshall, W.L. and Simonson, J.M. (1991) J. Chem. Thermod. 23: 613–16. Marshall, W.L. and Slusher, R. (1965) J. Chem. Eng. Data 10(4): 353–8. Marshall, W.L. and Slusher, R. (1973) J. Chem. Thermod. 5: 189–97. Marshall, W.L. and Slusher, R. (1975a) J. Inorg. Nucl. Chem. 37: 1191–1202. Marshall, W.L. and Slusher, R. (1975b) J. Inorg. Nucl. Chem. 37: 2165–70. Marshall, W.L. and Slusher, R. (1975c) J. Inorg. Nucl. Chem. 37: 2171–6. Marshall, W.L., Gill, J.S. and Secoy, C.H. (1951) J. Amer. Chem. Soc. 73: 4991–2. Marshall, W.L., Gill, J.S. and Secoy, C.H. (1954a) J. Amer. Chem. Soc. 76: 4279–81. Marshall, W.L., Wright, H.W. and Secoy, C.H. (1954b) J. Chem. Educ. 31: 34–6. Marshall, W.L., Loprest, F.J. and Secoy, C.H. (1958) J. Amer. Chem. Soc. 80: 5646–8. Marshall, W.L., Gill, J.S. and Slusher, R. (1962a) J. Inorg. Nucl. Chem. 24: 889–97. Marshall, W.L., Jones, E.V., Hebert, G.M. and Smith, F.J. (1962b) J. Inorg. Nucl. Chem. 24: 995–1000. Marshall, W.L., Slusher, R. and Smith, F.J. (1963) J. Inorg. Nucl. Chem. 25: pp. 559–566.


Marshall, W.L., Slusher, R. and Jones, E.V. (1964) J. Chem. Eng. Data., 9, n.2, pp. 187–191. Marshall, W.L., Hall, C.E. and Mesmer, R.E. (1981) J. Inorg. Nucl. Chem. 43: 449–55. Martinova, O.I. and Samoylov, Y.F. (1962) Zh. Neorgan. Khimii 7(4): 722–8. Mashovets, V.P., Krumgalz, B.S., Dibrov, I.A. and Matveeva, R.P. (1965) Zh. Prikl. Khimii 38(10): 2342–4. Mashovets, V.P., Penkina, N.V., Puchkov, L.V. and Kurochkina, V.V. (1971) Zh. Prikl. Khimii 44: 339–43. Mashovets, V.P., Puchkov, L.V., Sidorova, S.N. and Feodorov, M. K. (1974) Zh. Prikl. Khimii 47(3): 546–9. Mashovets, V.P., Zarembo, V.I. and Feodorov, M.K. (1973) Zh. Prikl. Khimii 46(3): 650–2. Maslennikova, V.Y., Vdovina, N.A. and Tsiklis, D.S. (1971) Zh. Fizich. Khimii 45(9): 2384. Mather, A.E. and Franck, E.U. (1992) J. Phys. Chem. 96(1): 6–8. Mather, A.E., Sadus, R.J. and Franck, E.U. (1993) J. Chem. Thermod. 25: 771–9. Mathis, J., Gizir, A.M. and Yang, Y. (2004) J. Chem. Eng. Data 49: 1269–1272. Matuzenko, M.Y., Zarembo, V.I. and Puchkov, L.V. (1984) Zh. Obschey Khimii 54(11): 2414–19. Mayanovic, R.A., Jayanetti, S., Anderson, A.J., Bassett, W.A. and Chou, I.-M. J. (2003) Chem. Phys. 118: 719–27. McHugh, M.A. and Krukonis, V.J. (1994) Supercritical Fluid Extraction (Principles and Practice), 2nd edn, Butterworths, Stoneham, MA, USA. Menzies, W.C. (1936) J. Amer. Chem. Soc. 58: 934–7. Merrill, R.B., Robertson, J.K. and Wyllie, P.J. (1970) J. Geol. 78: 558–69. Michelberger, T. and Franck, E.U. (1990) Ber. Bunsenges. Phys. Chem. 94: 1134–43. Migdisov, A.A., Williams-Jones, A.E. and Suleimenov, O.M. (1999) Geochim. Cosmochim. Acta 63(22): 3817–27. Migdisov, A.A. and Williams-Jones, A.E.(2005) Chem. Geology 217: 29–40. Migdisov, A.A. and Williams-Jones, A.E.(2007) Geochim. Cosmochim. Acta 71: 3056–3069. Miller, D.J. and Hawthorne, S.B. (1998) Analytical Chem. 70:1618–1621. Miller, D.J. and Hawthorne, S.B. (2000a) J. Chem. Eng. Data 45: 78–81. Miller, D.J. and Hawthorne, S.B. (2000b) J. Chem. Eng. Data 45: 315–18. Miller, D.J., Hawthorne, S.B., Gizir, A.M. and Clifford, A.A. (1998) J. Chem. Eng. Data 43: 1043–7. Mirskaya, V. (1998) High Temp.-High Press. 30: 555–8. Moore, R.C., Mesmer, R.E. and Simonson, J.M. (1997) J. Chem. Eng. Data 42: 1078–81. Morey, G.W. (1953) J. Amer. Chem. Soc. 75: 5794–7. Morey, G.W. and Burlew, J.S. (1964) J. Phys. Chem. 68: 1706–12. Morey, G.W. and Chen, W.T. (1956) J. Amer. Chem. Soc. 78: 4249–52. Morey, G.W. and Hesselgesser, J.M. (1951a) Trans. ASME (Am. Soc.Engrs.Trans.) 73(7): 865–75. Morey, G.W. and Hesselgesser, J.M. (1951b) Econ. Geology 46: 821–35. Morey, G.W. and Hesselgesser, J.M. (1952) Amer. J. Sci., Bowen volume, 343–57. Morey, G.W. and Ingerson, E. (1938) Amer. J. Sci. 35A: 217–25. Morey, G.W., Fournier, R.O. and Rowe, J.J. (1962) Geochim. Cosmochim. Acta 26: 1029–43.

Mroczek, E.K. (1997) J. Chem. Eng. Data 42: 116–19. Muller, G., Bender, E. and Maurer, G. (1992) Ber. Bunsenges. Phys. Chem. 92: 148–60. Myasnikova, K.R., Nikurashina, N.I. and Mertslin, R.V. (1969) Zh. Fizich. Khimii 43: 416–19; Russ. J. Phys. Chem. 43: 223–5. Namiot, A.Yu. (1976) In: Fazovie ravnovesiya v dobiche nefti (Russ.), Nedra Publ., Moscow, USSR. Nekrasov, I.Y., Ryabchikov, I.D. and Zuev, A.P. (1982) in Physicochemical Petrology Sketches (Ocherki fiziko-khimich.petrologii) (Russ.), Nauka, Moscow, 10: 161–70. Newton, R.C. and Manning, C.E. (2000) Geochim. Cosmochim. Acta 64: 2993–3005. Newton, R.C. and Manning, C.E. (2006) Geochim. Cosmochim. Acta 70: 5571–5582. Ng, H.-J., Robinson, D.B. and Leu, A.D. (1985) Fl. Phase Equil. 19: 273–82. Niesen, V., Palavra, A., Kindnay, A.J. and Yesavage, V.F. (1986) Fluid Phase Equilibria 31: 283–98. Nighswander, J.A., Kalogerakis, N. and Mehrotra, A.K. (1989) J. Chem. Eng. Data 34: 355–60. Nikitin, A.A., Sergeeva, Z.I., Khodakovsky, I.L. and Naumov, G.B. (1982) Geokhimiya (3): 297–307. Nikolaev, V.I. (1929) Zh. Ross. Fiz.-Khim. Obschestva 61(6): 939–45. Nikurashina, N.I., Kharitonova, G.I and Pichugina, L.M. (1971) Zh. Fizich. Khimii 45: 797–801; Russ J. Phys. Chem. 45: 444–6. Novgorodov, P.G. (1975) Geokhimiya (10): 1484–9. Novikov, B.E. (1973) Dissertation: Moscow Power Instit., USSR. Novikov, B.E. and Khaibullin, I.K. (1973) Zh. Fizich. Khimii 47(7): 1688–90. O´Grady, T.M. (1967) J. Chem. Eng. Data 12(1): 9–12. Oakes, C.S., Bodnar, R.J., Simonson, J.M. and Pitzer, K.S. (1994) Geochim. Cosmochim. Acta 58(11): 2421–31. Oakes, C.S., Bodnar, R.J., Simonson, J.M. and Pitzer, K.S. (1995) Intern. J. Thermophys. 16(2): 483–92. Ogryzlo, S.P. (1935) Econ. Geology 30: 400–24. Ohmoto, H., Hayashi, K.Y. and Kajisa, Y. (1994) Geochim. Cosmochim. Acta 58(10): 2169–85. Olander, A. and Liander, H. (1950) Acta Chemica Scand. 4: 1437–45. Olds, R.H., Sage, B.H. and Lacey, W.N. (1942) Ind. Engin. Chem. 34(10): 1223–7. Olshanski, Y.I., Ivanenko, V.V. and Khromov, A.V. (1959) Dokl. Akad. Nauk SSSR 124: 410–13. Palmer, D., Benezeth, P.and Wesolowski, D.J. (2001) Geochim. Cosmochim. Acta 65: 2081–95. Palmer, D.A. and Simonson, J.M. (1993) J. Chem. Eng. Data 38: 465–74. Palmer, D.A., Benezeth, P., Petrov, A.Y., Anovitz, L.M. and Simonson, J.M. (2000) Behavior of Aqueous Electrolytes in Stream Cycles: The Solubility and Volatility of Cupric Oxide, EPRI Report: 2000.1000455, Palo Alto, CA, USA. Palmer, D.A., Fernandez-Prini, R. and Harvey, A.H. (eds) (2004) Aqueous Systems at Elevated Temperatures and Pressures (Physical Chemistry in Water, Steam and Hydrothermal Solutions, Elsevier. Panson, A.J., Economy, G., Liu, Chia-tsun, Bulischeck, T.S. and Lindsay, W.T. (1975) J. Electrochem. Soc. 122(7): 915–18. Parks, G.A. and Pohl, D.C. (1988) Geochim.Cosmochim. Acta 52: 863–75. Parlsod, Ch.J. and Plattner, E. (1981) J. Chem. Eng. Data 26(1): 16–20.

128


Partridge, E.P. and White, A.H. (1929) J. Amer. Chem. Soc. 51: 360–70. Pascal, M.L. and Anderson, G.M. (1989) Geochim. Cosmochim. Acta 53: 1843–55. Patel, M.R., Holste, J.C., Hall, K.R. and Eubank, P.T. (1987) Fluid Phase Equil. 36: 279–99. Patton, C.L., Kisler, S.H. and Luks, K.D. (1993) In E. Kiran and J.F. Brennecke (eds), Supercritical Fluid Engineering Science, Fundamental and Applications. ACS Symp.Series 514; Amer. Chem.Soc.: Washington, pp. 55–70. Paulaitis, M.E., McHugh, M.A. and Chai, C.P (1983) In M.E. Paulaitis, J.M.L. Penninger et al. (eds), Chem. Eng. at Supercrit. Fluid Conds. Ann Arboe Science Publrs, pp. 139–58. Pel’sh, A.D. et al. (eds) (1953–2004) Hand book of experimental data on solubility in water-salt systems (Russ.), v.I (Ternary systems) (1953), v.II (Four and more components systems) (1954), v.III (Binary systems) (1961), v.IV (Binary systems), 1st edn, Goskhimizdat, Leningrad; v.I-1, I-2 (Ternary systems) (1973), v.II-1, II-2 (Four and more components systems) (1975), 2nd edn, Khimiya, Leningrad; N.E.Shestakov et al. (eds), v.I-1, I-2 (Ternary systems) (2003), v.II-1, II-2 (Four and more components systems) (2003, 2004), 3rd edn, Khimizdat, St Petersburg. Peppler, R.B. and Wells, L.S. (1954) J. Research National Bureau Standards 52(2): 75–92. Peters, C.J. (1993) In E.Kiran and J.M.H. Levelt Sengers (eds), Supercritical Fluids. Fundamentals for Application. Kluwer Acad.Publ., Dordrecht. pp. 117–45. Peters, C.J. and Gauter, K. (1999) Chem. Rev. 99: 419–31. Pitzer, K.S., Bishoff, J.L. and Rosenbauer R.J. (1987) Chem. Physics Letters 134(1): 60–3. Plyasunov, A.V., Belonozhko, A.B., Ivanov, I.P. and Khodakovsky, I.L. (1988) Geokhimiya (3): 409–17. Plyasunova, N.V. and Shmulovich, K.I. (1991) Dokl. Akad. Nauk SSSR 319(3): 738–42. Pocock, F.J. and Stewart, J.F. (1963) J. Engineering for Power 85(ser.A, 1): 33–45. Pokrovski, G.S., Gout, R., Schott, J., Zotov, A. and Harrichoury, J.C. (1996) Geochim. Cosmochim. Acta 60: 737–49. Pokrovski, G.S. and Schott, J. (1998) Geochim. Cosmochim. Acta 62(9): 1631–42. Pokrovski, G.S., Zakirov, I.V., Roux, J., Testemale, D., Hazemann, J.-L. et al. (2002) Geochim. Cosmochim. Acta 66: 3453–80. Pokrovski, G.S., Borisova, A.Yu., Roux, J., Hazemann, J.-L., Petdang, A. and Testemale, D. (2006) Geochim. Cosmochim. Acta 70: 4196–4214. Poot, W. and de Loos, T.W. (2004) Fluid Phase Equil. 221: 165–74. Poot, W., Kruger, K.-M. and de Loos, T.W. (2003) J. Chem. Thermod. 35: 591–604. Popova, M.Y., Khodakovsky, I.L. and Ozerova, N.A. (1975) Geokhimiya (6): 835–43. Posnjak, E. and Merwin, H.E. (1922) J. Amer. Chem. Soc. 44: 1965–95. Potter, R.W. and Clynne, M.A. (1978) J. Soln. Chem. 7: 837–44. Potter, R.W., Babcock, R.S. and Czamanske, G.K. (1976) J. Soln. Chem. 5(3): 223–30. Potter, R.W., Babcock, R.S. and Brown, D.L. (1977) J. Research U.S. Geol. Survey 5(3): 389–95. Poty, B., Holland, H.D. and Borcsik, M. (1972) Geochim Cosmochim. Acta 36(15): 1101–13. Prausnitz, J.M., Lichtenthaler, R.N. and de Azevedo, E.G. (1998) Molecular Thermodynamics of Fluid Phase Equilibria. Prentice-Hall, Englewood Cliffs.

Pray, H.A., Schweickert, C.E. and Minnich, B.H. (1952) Ind. Eng. Chem. 44(5): 1146–52. Price, L.C. (1979) Amer. Ass. Petrol. Geol. Bull. 63(9): 1527–33. Prokhorov, V.M. (1966) Zh. Fizich. Khimii 40: 2335–7. Prokhorov, V.M. and Tsiklis, D.S. (1970) Zh. Fizich. Khimii 44(8): 2069–70; Russ. J. Phys. Chem. 44: 1173. Pryor, W.A. and Jentoft, R.E. (1961) J. Chem. Eng. Data 6: 36–7. Puchkov, L.V. and Kurochkina, V.V. (1972). in Issledovaniya v oblasti neorganich. tekhnologii. Soli. Okisli. Kisloti. (Russ), Nauka, Leninigrad, pp. 263–7. Puchkov, L.V. and Matashkin, V.G. (1970) Zh. Prikl. Khimii 43(9):1963–1966. Puchkov, L.V., Matveeva, R.P. and Matashkin, V.G. (1989) Deposit. VINITI USSR, n.1100-B-89 Dep.. Rabenau A. (1981) in D.T. Rickard and F.E. Wickman (eds), Chemistry and Geochemistry of Solutions at High Temperatures and Pressures. Pergamon Press, London, pp. 361–72. Radyshevskaya, G.S., Nikurashina, N.I. and Mertslin, R.V. (1962) Zh. Obschey Khim. USSR 32: 673–6. Ragnarsdottir, K.V. and Walther, J.V. (1983) Geochim. Cosmochim. Acta 47: 941–6. Ragnarsdottir, K.V. and Walther, J.V. (1985) Geochim. Cosmochim. Acta 49: 2109–15. Rasulov, S.V. and Isaev, I.A. (2002) Teplofiz. Visok. Temp. 40: 344–7. Ravich, M.I. (1974) Water-Salt Systems at Elevated Temperatures and Pressures (Russ.), Nauka, Moscow. Ravich, M.I. and Borovaya, F.E. (1949) Izv. Sektora Fiz.-Khim. Analyza 19: 69–81. Ravich, M.I. and Borovaya, F.E. (1950) Izv. Sektora Fiz.-Khim. Analyza 20: 165–83. Ravich, M.I. and Borovaya, F.E. (1955) Izv. Sektora Fiz.-Khim. Analyza 26: 229–41. Ravich, M.I. and Borovaya, F.E. (1959) Zh. Neorgan. Khimii 4: 2100–15. Ravich, M.I. and Borovaya, F.E. (1964a) Zh. Neorgan. Khimii 9: 952–74. Ravich, M.I. and Borovaya, F.E. (1964b) Zh. Neorgan. Khimii 9: 1960–73. Ravich, M.I. and Borovaya, F.E. (1964c) Dokl. Akad. Nauk SSSR 155(6): 1375–9. Ravich, M.I. and Borovaya, F.E. (1964d) Dokl. Akad. Nauk SSSR 156: 894–7. Ravich, M.I. and Borina, A.F. (1965) Zh. Neorgan. Khimii 10(3): 724–7. Ravich, M.I. and Borovaya, F.E. (1968a) Dokl. Akad. Nauk SSSR 180: 1372–5. Ravich, M.I. and Borovaya, F.E. (1968b) Zh. Neorgan. Khimii 13: 1418–25. Ravich, M.I. and Borovaya, F.E. (1969) Zh. Neorgan. Khimii 14: 1644–9. Ravich, M.I. and Borovaya, F.E. (1970) Zh. Neorgan. Khimii 15(1): 231–5. Ravich, M.I. and Elenevskaya, V.M. (1955) Izv.Sektora Fiz.-Khim. Analyza 26: 290–7. Ravich, M.I. and Ginzburg, F.B. (1947) Izv. Akad. Nauk SSSR, Otd. Khim. Nauk (2):141–51. Ravich, M.I. and Scherbakova, L.G. (1955) Izv. Sektora Fiz.-Khim. Analyza 26: 248–58. Ravich, M.I. and Urusova, M.A. (1967) Zh. Neorgan. Khimii 12(5): 1335–42. Ravich, M.I. and Valyashko, V.M. (1965) Zh. Neorgan. Khimii 10(1): 204–8.


Ravich, M.I. and Valyashko, V.M. (1969) Zh. Neorgan. Khimii 14(6): 1650–4. Ravich, M.I. and Yastrebova, L.F. (1958) Zh. Neorgan. Khimii 3(12): 2771–80. Ravich, M.I. and Yastrebova, L.F. (1959) Zh. Neorgan. Khimii 4(1): 169–81. Ravich, M.I. and Yastrebova, L.F. (1961) Zh. Neorgan. Khimii 6(2): 431–7. Ravich, M.I. and Yastrebova, L.F. (1963) Zh. Neorgan. Khimii 8(1): 202–7. Ravich, M.I., Borovaya, F.E. and Ketkovich, V.Ya, (1953a) Izv. Sektora Fiz.-Khim. Analyza 22: 225–39. Ravich, M.I., Borovaya, F.E. and Ketkovich, V.Ya. (1953b) Izv. Sektora Fiz.-Khim. Analyza 22: 240–54. Ravich, M.I., Borovaya, F.E., Luk’yanova, E.I. and Elenevskaya, V.M. (1954) Izv. Sektora Fiz.-Khim. Analyza 24: 280–98. Ravich, M.I., Borovaya, F.E. and Smirnova, E.G. (1968) Zh. Neorgan. Khim. 13(7): 1922–7. Reamer, H.H., Olds, R.H., Sage, B.H. and Lacey, W.N. (1943) Ind. Eng. Chem. 35(7): 790–3. Reamer, H.H., Sage, B.H. and Lacey, W.N. (1952) Ind. Eng. Chem. 44(3): 609–15. Rebert, C.J. and Hayworth, K.E. (1967) AIChE Journ. 13(1): 118–21. Rebert, C.J. and Kay, W.B. (1959) AIChE Journ. 5(3): 285–9. Redkin, A.F., Stoyanovskaya, F.M. and Kotova, N.P. (2005) Dokl. Akad. Nauk 401(3): 679–82 (2005); Dokl. Earth Sci., 401A(3): 465–8. Relly, B.H. (1959) Econ. Geol. 54: 1496–1505. Ricci, E.J. (1951) The Phase Rule and Heterogeneous Equilibria. Van Nostrand, Toronto, NY, London. Ridded, M., Dreier, T., Schiff, G. and Suvernev, A.A. (1995) in H.J. White, Jr. et al. (eds), Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry, pp. 617–24. Rizvi, S.S.H. and Heidemann, R.A. (1987) J. Chem. Eng. Data 32: 183–91. Robson, H.L. (1927) J. Amer. Chem. Soc. 49: 2772–83. Rollet, A.P. and Cohen-Adad, R. (1964) Rev. Chimie Minerale 1: 451–78. Romberger, S.B. and Barnes, H.L. (1970) Econ. Geology 65(8): 901–19. Roof, J.G. (1970) J. Chem. Eng. Data 15(2): 301–3. Roozeboom, B.H.W. (1899) Z. Phys. Chem. 30: 385–412. Roozeboom, B.H.W. (1904) Die Heterogenen Gleichgewichte vom St andpunkte der Phasenlehre, Systeme Aus Zwei Komponenten. T.2, H.1, Braunschweig. Rosenbauer, R.J. and Bischoff, J.L. (1987) Geochim. Cosmochim. Acta 51: 2349–54. Rossling, G.L. and Franck, E.U. (1983) Ber. Bunsenges. Phys. Chem. 87: 882–90. Rowe, J.J.; Fournier, R.O. and Morey, G.W. (1967) Inorg. Chem. 6(6): 1183–8. Rowlinson, J.S. and Swinton, F.L. (1982) Liquids and Liquid Mixtures, 3rd edn, Butterworth, London. Ruaya, J.R. and Seward, T.M. (1986) Geochim. Cosmochim. Acta 50: 651–61. Ruaya, J.R. and Seward, T.M. (1987) Geochim. Cosmochim. Acta 51: 121–30. Rumyantsev, V.N. (1995) Zh. Neorgan. Khimii 40(1): 42–8. Saddington, A.W. and Krase, N.W. (1934) J. Amer. Chem. Soc. 56: 353–61. Sadus, R.J. (1992) High Pressure Phase Behaviour of Multicomponent Fluid Mixtures. Elsevier, Amsterdam.

Salvi, S., Pokrovski, G.S. and Schott, J. (1998) Chem.Geology 151: 51–67. Sanchez, M. and Lentz, H. (1973) High Temp.-High Press. 5: 689–99. Sassen, C.L., van Kwartel, R.A.C.; van der Kool, H.J. and de Swaan Arons, J. (1990) J.Chem.Eng.Data 35: 140–4. Sastry, V. (1957) Dissertation: Technische Hochschule Karlsruhe, Germany. Schäfer, H. (1949) Z. Anorg. Allg. Chem. 260: 127–40. Scheffer, F.E.C. and Smittenberg, J. (1933) Rec. Trav. Chim. 51: 607–14. Scheidgen, A.L. and Schneider, G.M. (2002) Phys. Chem. Chem. Phys. 4: 963–7. Schloemer, H. (1952) Neues Jahrb. Mineral. Msh. 129–35. Schmidt, C. and Bondar, R.J. (2000) Geochim. Cosmochim. Acta 64: 3853–69. Schmidt, C. and Rickers, K. (2003) Amer. Mineral. 88: 288–92 Schmidt, C., Chou, I.-Ch., Bondar, R.J. and Basset, W.A. (1998) Amer. Mineralogist 83: 995–1007. Schneider, G. (1964) Z. Phys. Chem., N.F. 41: 327–38. Schneider, G. (1966) Ber.Bunsenges. Phys. Chem. 70: 10–16, 497–519. Schneider, G. (1968) Chem. Eng. Prog. Symp. Series 64(88): 9–15. Schneider, G.M. (1970) Advan. Chem. Physics 17: 1–42. Schneider, G.M. (1973) In F. Franks (ed.), Water – A Comprehensive Treatise, Plenum Press, vol. .2, ch. 6, pp. 381–404. Schneider, G.M. (1976) Pure and Appl. Chem. 47: 277–91. Schneider, G.M. (1978) In Chemical Thermodynamics 2: 105–46. Spec. Periodical Repts. The Chem. Society, London. Schneider, G.M. (1993) Pure and Appl. Chem. 65: 173–82. Schneider, G.M. (2002) Phys.Chem.Chem.Phys. 4: 845–51. Schneider, G.M. and Russo, C. (1966) Ber. Bunsenges. Phys. Chem. 70: 1008–14. Schneider, G.M., Scheidgen, A.L. and Klante, D. (2000) Ind. Eng. Chem. Research 39: 4476–82. Schroeder, W.C., Gabriel, A. and Partridge, E.P. (1935) J. Amer. Chem. Soc. 57: 1539–46. Schroeder, W.C., Berk, A.A. and Gabriel, A. (1936) J. Amer. Chem. Soc. 58: 843–9. Schroeder, W.C., Berk, A.A. and Gabriel, A. (1937a) J. Amer. Chem. Soc. 59: 1783–90. Schroeder, W.C., Berk, A.A. and Partridge, E.P. (1937b) J. Amer. Chem. Soc. 59: 1790–5. Schröer, E. (1927) Z. phys. Chem. 129: 79–110. Schuiling, R.D. and Vink, B.W. (1967) Geochim. Cosmochim. Acta 31: 2399–2411. Scott, R.L. and van Konynenburg, P.N. (1970) Faraday Discuss. Chem. Soc. 49: 87–97. Secoy, C.H. (1948) J. Amer. Chem. Soc. 70: 3450–2. Secoy, C.H. (1950) J. Phys. Chem. 54: 1337–46. Seewald, J.S. (1974) Geochim. Cosmochim. Acta 38: 1651–64. Seewald, J.S. (1976) Geochim. Cosmochim. Acta 40: 1329–41. Seewald, J.S. and Seyfried, J.W.E. (1991) Geochim. Cosmochim. Acta 55: 659–69. Segnit, E.R., Holland, H.D. and Biscardi, C.J. (1962) Geochim. Cosmochim. Acta 26: 1301–31. Seidell, A. (1940, 1941) Solubilities of Inorganic, Metal Organic and Organic Compounds. v.I, II, D.Van Nostrand Co. Inc., New York. Seidell, A. and Linke, W.F. (1952) Solubilities of Inorganic and Organic Compounds, Suppl. to 3rd edn, D.Van Nostrand Co. Inc., New York.

130


Semenova, A.I. and Tsiklis, D.S. (1970) Zh.Fizich.Khimii 44(10): 2505–8; Russ.J.Phys.Chem. 44(10): 1420–2. Sergeeva, E.I., Suleymenov, O.M., Evstigneev, A.V. and Khodakovskiy, I.L. (1999) Geokhimiya 11: 1218–29. Seward, T.M. (1974) Geochim. Cosmochim. Acta 38: 1651–64. Seward, T.M. (1976) Geochim. Cosmochim. Acta 40: 1329–41. Seward, T.M. and Franck, E.U. (1981) Ber. Bunsenges. Phys. Chem. 85: 2–7. Sharp, W.E. and Kennedy, G.C. (1965) J. Geology 73(2): 391–403. Shen, A.H. and Keppler, H. (1997) Nature 385: 710–12. Shenberger, D.M. and Barnes, H.L. (1989) Geochim. Cosmochim. Acta 53: 269–78. Sherman, W.F. and Tadtmuller, A.A. (1987) Experimental Techniques in High-Pressure Research, John Wiley & Sons, Ltd, Chichester. Shikina, N.D. and Zotov, A.V. (1999) Geokhimiya (1): 90–4. Shimoyama, Y., Iwai, Y., Yamakita, M., Shinkai, I. and Arai, Y. (2004) J. Chem. Eng. Data 49: 301–305. Shmonov, V.M., Sadus, R.J. and Franck, E.U. (1993) J. Phys. Chem. 97: 9054–9. Shmulovich, K.I., Landwehr, D., Simon, K. and Heinrich, W. (1999) Chem.Geol. 157: 343–54. Shmulovich, K.I. and Plyasunova, N.V. (1993) Geokhimiya (5): 666–84. Shmulovich, K.I., Tkachenko, S.I. and Plyasunova, N.V. (1994) in K.I. Shmulovich, B.W.D. Yardley and G.G. Gonchar (eds), Fluids in the Crust. Equilibrium and Transport Properties. Chapman & Hall, London, pp. 193–214. Shvarts, A.V. and Efremova, G.D. (1970) Zh. Fizich. Khimii 44(4): 1105–7; Russ. J. Phys. Chem. 44: 614. Shvedov, D. and Tremaine, P.R. (2000) J. Soln. Chem. 29: 889–904. Simonson, J.M. and Palmer, D.A. (1993) Geochim. Cosmochim. Acta 57: 1–7. Sinke, G.C., Mossner, E.H. and Curnutt, J.L. (1985) J. Chem. Thermod. 17: 893–9. Smits, A. (1905) Z. Phys. Chem. 51: 193–221, 587–601. Smits, A. (1910) Proc. Roy. Acad. Amsterdam 13: 330–42. Smits, A. (1911) Z. Phys. Chem. 76: 445–9. Smits, A. (1913) Proc. Roy. Acad. Amsterdam 15: 184–92. Smits, A. (1915) Proc. Roy. Acad. Amsterdam 18: 795–9. Smits, A. and Mazee, W.M. (1928) Z. Phys. Chem. 135: 73–8. Smits, A. and Mazee, W.M. (1928) Z. Phys. Chem. 135: 73–6. Smits, A. and Wuite, J.P. (1909) Proc. Roy. Acad. Amsterdam 12: 244–57. Smits, A., Rinse, J. and Louwe Kooymans, L.H. (1928) Z. Phys. Chem. 135(1–2): 78–84. Smits, P.J., Peters, C.J. and de Swaan Arons, J. (1997a) J. Chem. Thermod. 29: 1517–27. Smits, P.J., Smits, R.J.A. Peters, C.J. and de Swaan Arons, J. (1997b) J. Chem. Thermod. 29: 23–30. Smits, P.J., Smits, R.J.A. Peters, C.J. and de Swaan Arons, J. (1997c) J. Chem. Thermod. 29: 385–93. Smits, P.J., Peters, C.J. and de Swaan Arons, J. (1998) Fluid Phase Equil., 150–151, pp. 745–751. Sourirajan, S. and Kennedy, G. (1962) Amer. J. Sci. 260: 115–41. Soweby, J.R. and Keppler, H. (2002) Contrib. Mineral. Petrol. 143: 32–7. Spillner, F. (1940) Die Chemische Fabrik 13(22): 405–16. Sretenskaja, N.G., Sadus, R.J. and Franck, E.U. (1995) J. Phys. Chem. 99(12): 4273–7.

Stefansson, A. and Seward, T.W. (2003a) Geochim. Cosmochim. Acta 67(7): 1395–1413. Stefansson, A. and Seward, T.W. (2003b) Geochim. Cosmochim. Acta 67(9): 1677–88. Stefansson, A. and Seward, T.W. (2003c) Geochim. Cosmochim. Acta 67(23): 4559–76. Stepanov, G.V., Rasulov, A.R., Malysheva, L.V. and Shakhbanov, K.A. (1999) Fluid Phase Equil. 157: 309–16. Stepanov, G.V., Shakhbanov, K.A. and Abdurakhmanov, I.M. (1996) Zh. Fizich. Khimii 70(1): 90–3. Stephan, E.F. and Miller, P.D. (1962) J. Chem. Eng. Data 7(4): 501–4. Stephan, E.F., Hatfield, N.S., Peoples, R.S. and Pray, H.A.H. (1956) Report No.BMI-1067, Battelle Memorial Institute, Columbus, Ohio, USA. Stephan, K. and Kuske, E. (1983) Chem. Eng. Fundamental 2(2): 50–65. Sterner, S.M. and Bodnar, R.J. (1991) Amer. J. Sci. 291: 1–54. Sterner, S.M., Hall, D.L. and Bodnar, R.J. (1988) Geochim. Cosmochim. Acta 52: 989–1005. Stevenson, R.L., La Bracio, D.S., Beaton, T.A. and Thies, M.C. (1994) Fluid Phase Equil. 93: 317–36. Stewart, D.B. (1967) Schweiz. Miner. Petrogr. Mitt. 47: 35–61. Straub, F.G. (1932) Ind. Eng. Chem. 24(8): 914–17. Street, W.B. (1983) In M.E. Paulaitis, J.M.L. Penninger et al., (eds.) Chem. Eng. at Supercrit.Fluid Conds. Ann Arboe Science Publrs, pp. 3–30. Strübel, B. (1965) Neues Jahrbuch.Min.Mh. 3: 83–95. Strübel, B. (1966) Neues Jahrbuch. Min. Mh. 4: 99–108. Strübel, B. (1967) Neues Jahrbuch. Min. Mh. 7/8: 223–333. Stuckey, J.E.and Secoy, C.H. (1963) J. Chem. Eng. Data 8(3): 386–9. Styrikovich, M.A. and Khokhlov, L.K. (1957) Teploenergetika 4(2): 3–7. Styrikovich, M.A. and Reznikov, M.I. (1977) Methods of Experimental Study of Steam Generation Processes (Russ.), Energia, Moscow. Styrikovich, M.A., Khaibullin, I.Kh. and Tschvireshvili, D.G. (1955) Dokl. Akad. Nauk SSSR 100: 1123–6. Sue, K., Hakuta, Y., Smits, R.L., Adschiri, T. and Arai, K. (1999) J. Chem. Eng. Data 44: 1422–6. Sugaki, A., Scott, S.D., Hayashi, K. and Kitakaze, A. (1987) Geochemical J. 21: 291–305. Suleimenov, O.M. and Krupp, R.E. (1994) Geochim. Cosmochim. Acta 58(11): 2433–44. Sultanov, R.G., Skripka, V.G. and Namiot, A.Yu. (1971) Gazov. Promishlen. (4): 6–8. Sultanov, R.G., Skripka, V.G. and Namiot, A.Yu. (1972a) Gazov. Promishlen. (5): 6–7. Sultanov, R.G., Skripka, V.G. and Namiot, A.Yu. (1972b) Neftyanoe Khozyaystvo (2): 57–9. Susarla, V.R., Eber, A. and Franck, E.U. (1987) Proc. Indian Acad. Sci.(Chem. Sci.) 99(3): 195–202. Sweeton, F.A. and Baes, C.F. (1970) J. Chem. Thermod. 2: 479–500. Tagirov, B.R., Zotov, A.V. and Akinfiev, N.N. (1997) Geochim. Cosmochim. Acta 61: 4267–80. Tagirov, B.R., Salvi, S., Schott, J. and Baranova, N.N. (2005) Geochim. Cosmochim. Acta 69: 2119–2132. Tagirov, B.R., Baranova, N.N., Zotov, A.V., Schott, J. and Bannykh, L.N. (2006) Geochim. Cosmochim. Acta 70: 3689–3701. Takenouchi, S. and Kennedy, G.C. (1964) Amer.J.Sci. 262(9): 1055–74; (1968) Russ. transl. in L.V. Tauson (ed.), Termodynamika Postmagmatich. Protsessov, Mir, Moscow, pp. 110–36.


Takenouchi, S. and Kennedy, G.G. (1965) Amer. J. Sci. 263(5): 445–54; (1968) Russ. transl. in L.V. Tauson (ed.), Termodynamika Postmagmatich. Protsessov, Mir, Moscow, pp. 137–49. Tamman, G. (1924) Lehrbuch der Heterogenen Gleichgewichte, Braunschweig. Templeton, C.C. and Rodgers, J.C. (1967) J. Chem. Eng. Data 12(4): 536–47. Thiery R. and Dubessy J. (1998) Eur. J. Mineral. 10: 1151–65. Thiery R., Lvov S.N. and Dubessy J. (1998) J. Chem. Phys. 109: 214–22. Thomas, J.S. and Barker, W.F. (1925) J. Chem. Soc. 127: 2820–31. Thompson, W.H. and Snyder, J.R. (1964) J. Chem. Eng. Data 9(4): 516–20. Tilden, W.A. and Shenstone, W.A. (1883) Proc. Royal Soc. London 35A: 345–6. Timmermans, J. (1960) The Physico-chemical Constants of Binary Systems in Concentrated Solutions, vol. 3, 4. Intersci. Publ. Inc., New York. Tkachenko, S.I. (1996) Dissert., Moscow State Univ., Russia. Tkachenko, S.I. and Shmulovich, K.I. (1992) Dokl. Akad. Nauk Russ. 326(6): 1055–9. Tödheide, K. and Franck, E.U. (1963) Z. phys. Chem. 37(5–6): 387–401. Toledano, P. (1964) Rev. Chimie Minerale 1: 353–413. Tremaine, P.R. and LeBlanc J.C. (1980a) J. Soln. Chem. 9: 415–42. Tremaine, P.R. and LeBlanc, J.C. (1980b) J. Chem. Thermod. 12: 521–38. Tropper, P. and Manning, C.E. (2007) Chem. Geology 240: 54–60. Tsiklis, D.S. (1965) Dokl. Akad. Nauk SSSR 161: 645–7. Tsiklis, D.S. (1968) Handbook of Techniques in High Pressure Research and Engineering, Plenum Press, NY; (1976) Techniques for physical chemistry studies at high and super high pressures (Russ), 4th edn, Khimia, Moscow, USSR. Tsiklis, D.S. (1969) Immiscibility of Gas Mixtures (Russ), Khimiya, Moscow, USSR; (1972) Phasentrennung in Gasgemischen, VEB Deut. Verl. Fur Grundstoffindustrie, Leipzig. Tsiklis, D.C. (1977) Compressed Gases (Russ.), Khimia, Moscow. Tsiklis, D.S. and Maslennikova, V.Y. (1965) Dokl.Akad.Nauk SSSR 161: 645–7. Tsiklis, D.S. and Prokhorov, V.M. (1966) Zh. Fizich. Khimii 40: 2335–7. Tsiklis, D.C., Maslenikova, V.Y. and Orlova, A.A. (1970) Dokl. Akad. Nauk SSSR 195: 1381–4. Tsonopoulos, C. and Wilson, G.M. (1983) AIChE Journ. 29(6): 990–9. Tudorovckaya, G.L., Shtol’ts, N.V., Konovalova, T.P. and Simonova, T.A. (1990) Zh. Prikl. Khimii 63(1): 212–14. Tugarunov, I.A., Ganeev, I.G. and Khodakovsky, I.L. (1975) Geokhimiya (9): 1345–54. Tuttle, O.F. (1949) Bull. Geol. Soc. Am. 60: 1727–9. Tuttle, O.F. and Friedman, I.I. (1948) J. Amer. Chem. Soc. 70: 919–26. Uchameishvili, N.E., Malinin, S.D. and Khitarov, N.I. (1966) Geokhimiya (10): 1193–1205. Udovenko, A.G., Zarembo, V.I. and Puchkov, L.V. (1986a) Depozit VINITI USSR 1708-B-86 Dep., Redkoll. Zh. Prikl. Khim. Udovenko, A.G., Zarembo, V.I. and Puchkov, L.V. (1986b) Depozit. VINITI USSR 1706-B-86 Dep., Redkoll. Zh. Prikl. Khim.

Ulmer G.C. (ed.) (1971) Research Techniques for High Pressure and High Temperature. Springer-Verlag. Ulmer G.C. and Barnes, H.L. (eds) (1987) Hydrothermal Experimental Techniques. J. Wiley & Sons Inc., New York. Urusova, M.A. (1974) Zh. Neorgan. Khimii 19: 828–33. Urusova, M.A. and Ravich, M.I. (1966) Zh. Neorgan. Khimii 11(3): 652–60. Urusova, M.A. and Ravich, M.I. (1969) Zh. Neorgan. Khimii 14(9): 2500–2. Urusova, M.A. and Ravich, M.I. (1971) Zh. Neorgan. Khimii. 16(10): 2881–3. Urusova, M.A. and Valyashko, V.M. (1976) Zh. Neorgan. Khimii 21(10): 2805–10. Urusova, M.A. and Valyashko, V.M. (1983a) Zh. Neorgan. Khimii 28(7): 1834–40. Urusova, M.A. and Valyashko, V.M. (1983b) Zh. Neorgan. Khimii 28(7): 1845–50. Urusova, M.A. and Valyashko, V.M. (1984) Zh. Neorgan. Khimii 29(9): 2437–40. Urusova, M.A. and Valyashko, V.M. (1987) Zh. Neorgan. Khimii 32(1): 44–8. Urusova, M.A. and Valyashko. V.M. (1990) Zh. Neorgan. Khimii 35(5): 1273–80 (Russ); pp. 719–23(Eng). Urusova, M.A. and Valyashko, V.M. (1993a) Zh. Neorgan. Khimii 38(4): 714–16. Urusova, M.A. and Valyashko, V.M. (1993b) Zh. Neorgan. Khimii 38(6): 1074–6. Urusova, M.A. and Valyashko, V.M. (1998) Zh. Neorgan. Khimii 43(6): 1034–41; Russ. J. Inorg. Chem. 43: 948–55. Urusova, M.A. and Valyashko, V.M. (2001a) Zh. Neorgan. Khimii 46(5): 866–72; Russ J. Inorg. Chem. 46: 770–6. Urusova, M.A. and Valyashko, V.M. (2001b) Zh. Neorgan. Khimii 46(5): 873–9; Russ J. Inorg. Chem. 46: 777–83. Urusova, M.A. and Valyashko, V.M. (2002) Zh. Neorgan. Khimii 47(10): 1723–7; Russ J. Inorg. Chem. 47: 1581–5. Urusova, M.A. and Valyashko, V.M. (2005) Zh. Neorgan. Khimii 50(11): 1873–87; Russ. J. Inorg. Chem. 50: 1754–67. Urusova, M.A. and Valyashko, V.M. (2008) Zh. Neorgan. Khimii, 53: 660–672; Russ. J. Inorg. Chem. 53: 604–16. Urusova, M.A., Rakova, N.N., Valyashko, V.M. and Zelikman, A.N. (1975a) Zh. Neorgan. Khimii. 20(8): 2239–43. Urusova, M.A., Valyashko, V.M., Rakova, N.N., Zelikman, A.N. and Evdokimova, G.V. (1975b) Zh. Neorgan. Khimii 20(9): 2585–7. Urusova, M.A., Rakova, N.N., Valyashko, V.M. and Zelikman, A.N. (1978) Zh. Neorgan. Khimii 23(2): 553–5. Urusova, M.A., Rakova, N.N., Valyashko, V.M., Zelikman, A.N. and Belous, E.D. (1982) Zh. Neorgan. Khimii 27(5): 1331–3. Urusova, M.A., Valyashko, V.M., Petrenko, S.V. and Bichkov, D.A. (1994) Zh. Neorgan. Khimii 39(12): 2068–78. Urusova, M.A., Valyashko, V.M. and Grigoriev, I.M. (2007) Zh. Neorgan. Khimii 52: 456–70; Russ. J. Inorg. Chem. 52: 405–18. Valyashko, V.M. (1973) Zh. Neorgan. Khimii 18(4): 1114–18. Valyashko, V.M. (1975) Zh. Neorgan. Khimii 20(4): 1129–31. Valyashko, V.M. (1990a) Phase Equilibria and Properties of Hydrothermal Systems (Russ.), Nauka, Moscow. Valyashko, V.M. (1990b) Pure and Appl. Chem. 62: 2129–38. Valyashko, V.M. (1995) Pure and Appl.Chem. 67: 569–78. Valyashko, V.M. (1997) Pure and Appl. Chem. 69: 2271–80. Valyashko, V.M. (2002a) Phys. Chem.Chem.Phys. 4: 1178–89. Valyashko, V.M. (2002b) Pure and Appl. Chem. 74: 1871–84. Valyashko, V.M. (2004) in D.A. Palmer et al. (eds), Aqueous Systems at Elevated Temperatures and Pressures, Elsevier, Chap. 15, pp. 597–642.

132


Valyashko, V.M. and Churagulov, B.R. (2003) in G.T. Hefter and R.P.T. Tomkins (eds), The Experimental Determination of Solubilities, John Wiley & Sons, Ltd, pp. 359–426. Valyashko, V.M. and Kravchuk, K.G. (1977) Zh. Neorgan. Khimii 22(1): 278–82. Valyashko, V.M. and Kravchuk, K.G. (1978) Dokl. Akad. Nauk SSSR 242:1104–7. Valyashko, V.M. and Ravich, M.I. (1968) Zh. Neorgan. Khimii 13(5): 1426–31. Valyashko, V.M. and Urusova, M.A. (1996) Zh. Neorgan. Khimii 41(8): 1355–69 (Russ); Russ. J. Inorgan. Chem. 41: 1297–1310 (Eng.). Valyashko, V.M. and Urusova, M.A. (2005) in Book of Abstracts, th 29 Intern. Conf. on Solution Chemistry, Portoroz, Slovenia, p. 257. Valyashko, V.M., Urusova, M.A. and Kravchuk, K.G. (1982) Deposit. VINITI, IONKh AN SSSR 3286–82 Dep. Valyashko, V.M., Urusova, M.A. and Kravchuk, K.G. (1983) Dokl. Akad. Nauk SSSR 272: 390–4. Valyashko, V.M., Kravchuk, K.G. and Korotaev, M.Y. (1984) Review of Thermophysical Properties of Substances, (Russ.) Moscow, IVTAN, Inst. of High Temp., Acad. Scs.USSR, 5(49): 57–126. Valyashko, V.M., Ataev, Kh. and Aleshko-Ozhevskiy, P.Y. (1996) Deposit. VINITI 2610-B96. Valyashko, V.M., Abdulagatov, I.M. and Levelt Sengers, M.H. (2000) J. Chem. End, Data 45: 1139–46. Van den Bergh, L.C. and Schouten, J.A. (1988) Chem. Phys. Lett. 145: 471. Van den Bergh, L.C., Schouten, J.A. and Trappeniers, N.J. (1987) Physica 141A: 524. Van der Waals, J.D. (1894) Zittingsversl. Kon. Acad. V. Wetensch. Amst. Nov., p.133. Van der Waals, J.D. and Kohnstamm, Ph. (1927) Lehrbuch der Thermostatik, Vol. I, Allgemeine Thermostatik; Vol. II, Binäre Gemische, Verlag J. Am. Barth, Leipzig. Van Gunst, C.A., Scheffer, F.E.C and Diepen, G.A.M. (1953) J. Phys. Chem. 57: 581–5. Van Konynenburg, P.N. and Scott, R.L. (1980) Philos. Trans. R. Soc. London, Ser.A, 298: 495–540. Van Pelt, A., Peters, C.A. and de Swaan Arons, J. (1991) J. Chem. Phys. 95: 7569–75. Van Valkenburg, A., Bell, P.H. and Ho-Kwang, M. (1987) In G.C. Ulmer and H.L. Barnes (eds), Hydrothermal Experimental Techniques. J. Wiley & Sons Inc., New York, pp. 458–68. Vandana, V. and Teja, A.S. (1995) Fluid Phase Equil. 103: 113–18. Var’yash, L.N. (1985) Geokhimiya (7): 1003–13; Geochem.Intern. 23(1): 82–92. Var’yash, L.N. (1989) Geokhimiya (3): 412–22. Verdes, G., Gout, R. and Castet, S. (1992) Eur. J. Mineral. 4: 767–92. Voigt, W., Fanghanel, T. and Emons, H.H. (1985) Z. Phys. Chem. 266: 522–8. Waldeck, W.F., Lynn, G. and Hill, A.E. (1932) J. Amer. Chem. Soc. 54: 929–36. Waldeck, W.F., Lynn, G. and Hill, A.E. (1934) J. Amer. Chem. Soc. 56: 43–7. Walther, J.V. (1986) Geochim. Cosmochim. Acta 50: 733–9. Walther, J.V. (1997) Geochim. Cosmochim. Acta 61: 4955–64. Walther, J.V. (2001) Geochim. Cosmochim. Acta 65: 2843–51. Walther, J.V. (2002) Geochim. Cosmochim. Acta 66(9): 1621–6. Walther, J.V. and Orville, P.M. (1983) Amer. Mineralogist 68: 731–4.

Wang, Q. and Chao, K.C. (1990) Fluid Phase Equil. 59: 207–15. Weill, D.F. and Fyfe, W.S. (1964) Geochim. Cosmochim. Acta 28: 1243–55. Weingartner, H. and Steinle, E. (1992) J. Phys. Chem. 96: 2407–2509. Weissberg, B.G., Dickson F.W. and Tunell G. (1966) Geochim. Cosmochim. Acta 30: 815–27. Welsch, H. (1973) Dissert.; Fakultat fur Chemie; University Karlsruhe, Karlsruhe. Wendlandt, W.W. (1986) Thermal Methods of Analysis, 3rd edn. J.Wiley & Sons, Inc., New York. Wendlandt, H.G. (1963) Dissertation: University of Gottingen, Germany. Wesolowski, D.J., Benezeth, P. and Palmer, D.A. (1998) Geochim. Cosmochim. Acta 62(6): 971–84. Wesolowski, D.J., Ziemniak, S.E., Anovitz, L.M., Machesky, M.L., Benezeth, P. et al. (2004) in D.A. Palmer et al. (eds), Aqueous Systems at Elevated Temperatures and Pressures. Elsevier, Chap. 14, pp. 493–596. Wetton, E.A.M. (1981) Power Indust. Res. 1: 151–8. Widom, B. (1973) J. Phys. Chem. 77: 2196–2200. Wofford, W.T., Dell’Orco, P.C. and Gloyna, E.F. (1995) J. Chem. Eng. Data 40(4): 968–73. Wormald, C.J. and Vine, M.D. (2000) J. Chem. Thermod. 32: 439–49. Wormald, C.J. and Yerlett, T.K. (2000) J. Chem. Thermod. 32: 97–105. Wormald, C.J. and Yerlett, T.K. (2002) J. Chem. Thermod. 34: 1659–69. Wood, R.H. (1989) Thermochim. Acta 154: 1–11. Wood, S.A. (1992) Geochim. Cosmochim. Acta 56: 1827–36. Wood, S.A. and Vlassopoulos, D. (1989) Geochim. Cosmochim. Acta 53: 303–12. Wood, S.A., Crerar, D.A., Brantley, S.L. and Borcsik, M. (1984) Amer. J. Sci. 284: 668–705. Wu, G., Heilig, M., Lentz, H. and Franck, E.U. (1990) Ber. Bunsenges. Phys. Chem. 94: 24–7. Wuster, G., Wozny, G. and Giazitzoglou, Z. (1981) Fluid Phase Equil. 6: 93–111. Wyart, J. and Sabatier, G. (1955) Acad. Sci. Paris Comptes Rendus 240: 1905–7. Xiao, Z., Gammons, C.H. and Williams-Jones, A.E. (1998) Geochim. Cosmochim. Acta 62: 2949–64. Xie, Zh. and Walther, J.V. (1993) Geochim. Cosmochim. Acta 57: 1947–55. Yalman, R.G., Shaw, E.R. and Corwin, J.F. (1960) J. Phys. Chem. 64: 300–3. Yamaguchi, G., Yanagida, H. and Soejima, S. (1962) Bull. Chem. Soc. Japan, 35(11): 1789–94. Yang, Y., Miller, D.J. and Hawthorne, B. (1997) J. Chem. Eng. Data 42: 908–13. Yarrison, M., Cox, K.R. and Chapman, W.G. (2006) Ind. Eng. Chem. Res. 45: 6770–6777. Yastrebova, L.F., Borina, A.F. and Ravich, M.I. (1963) Zh. Neorgan. Khimii 8(1): 208–17. Yeatts, L.B. and Marshall, W.L. (1967) J. Phys. Chem. 71: 2641–50. Yeatts, L.B. and Marshall, W.L. (1969) J. Phys. Chem. 73(1): 81–90. Yelash, L.V. and Kraska T. (1998) Ber. Bunsenges. Phys. Chem. 102: 213–23. Yelash, L.V. and Kraska, T. (1999a) Phys.Chem.Chem.Phys. 1: 307–11.


Yelash, L.V. and Kraska, T. (1999b) Z. Phys. Chem. 211: 159–79. Yelash, L.V., Kraska, T. and Deiters, U.K. (1999) J. Phys. Chem. 111: 3079–84. Yiling, T., Michelberger, T. and Franck, E.U. (1991) J. Chem. Thermod. 23: 105–12. Yishan, Z., Ruiying, A.and Yuetuan, C. (1986) Scientia Sinica, ser. B, 29(11): 1221–32. Yokogama, C., Iwabuchi, A., Takahashi, S. and Takeuchi, K. (1993) Fluid Phase Equil. 82: 323–31. Young C.L. (1978) in Specialist Periodical Reports, Chemical Thermodynamics. The Chemical Society, London Vol. 2, Chap. 4, pp. 71–104. Zagvozdkin, K.I., Rabinovich, Y.M. and Barilko, N.A. (1940) Zh. Prikl. Khimii 13(1): 29–36. Zakirov, I.V. and Sretenskaya, N.G. (1994) In Experimental Problems of Geology, Nauka, Moscow, pp. 664–7. Zarembo, V.I. (1985) Dissert., Tekhnolog. Institut, Leningrad, USSR. Zarembo, V.I., Antonov, N.A., Gilyarov, V.N. and Feodorov, M.K. (1976) Zh. Prikl. Khimii 49(6): 1221–5. Zarembo, V.I., Lvov, S.N. and Matuzenko, M.U. (1980) Geokhimiya (4): 610–14. Zawisza, A. and Malesinska, B. (1981) J. Chem. Eng. Data 26: 388–91. Zhang, Y.G. and Frantz, J.D. (1989) Chem. Geology 74: 289–308. Zharikov, V.A., Ivanov, I.P. and Laptev, Y.A. (eds) (1985) Modern Techniques and Methods of Experimental Mineralogy (Russ), Nauka, Moscow. Zhidikova, A.P. and Malinin, S.D. (1972) Geokhimiya (1): 28–34. Zhidikova, A.P., Khodakovsky, I.L., Urusova, M.A. and Valyashko, V.M. (1973) Zh. Neorgan. Khimii 18(5): 1160–5.

Ziemniak, S.E. and Goyette, M.A. (2004) J. Soln. Chem. 33(9): 1135–1159. Ziemniak, S.E., Goyette, M.A. and Combs, K.E.S. (1999) J. Soln. Chem. 28(7): 809–36. Ziemniak, S.E., Jones, M.E. and Combs, K.E.S. (1989) J. Soln. Chem. 18(12): 1133–52. Ziemniak, S.E., Jones, M.E. and Combs, K.E.S. (1992a) J. Soln. Chem. 21(2): 179–200. Ziemniak, S.E., Jones, M.E. and Combs, K.E.S. (1992b) J. Soln. Chem. 21(11): 1153–76. Ziemniak, S.E., Jones, M.E. and Combs, K.E.S. (1993) J. Soln. Chem. 22(7): 601–23. Ziemniak, S.E., Jones, M.E. and Combs, K.E.S. (1995) J. Soln. Chem. 24(9): 837–77. Ziemniak, S.E., Jones, M.E .and Combs, K.E.S. (1998) J. Soln. Chem. 27(1): 33–66. Zotov, A.V., Levin, K.A., Kotova, Z.Y. and Volchenkova, V.A. (1982) Geokhimiya (8): 1124–36; Geochem. Intern. 19: 151–64. Zotov, A.V., Levin, K.A. and Kotova, Z.Y. (1985a) Geokhimiya (6): 903–6; Geochem. Intern. 22(9): 156–8. Zotov, A.V., Baranova, T.F., Dar’yina, T.G., Bannykh, L.N. and Kolotov, V.P. (1985b) Geokhimiya (1): 105–10; Geochem. Intern. 22(5): 156–61. Zotov, A.V., Levin, K.A., Khodakovskyi, I.L. and Kozlov, V.K. (1985c) Geokhimiya (9): 1300–1310; (1986) Geochem. Intern. 23(3): 23–33. Zotov, A.V., Levin, K.A., Khodakovsky, I.L. and Kozlov, V.K. (1986) Geokhimiya (5): 690–701; Geochem. Intern. 23(9): 103–16. Zotov, A.V., Shikina. N.D. and Akinfiev. N.N. (2003) Geochim. et Cosmochim. Acta 67(10): 1821–36. Zotov, N. and Keppler, H. (2000) Am. Mineral. 85: 600–2.

2

pVTx Properties of Hydrothermal Systems Horacio R. Corti Department of Physics of Condensed Matter, Atomic Energy Commission (CNEA), and Institute of Physical Chemistry of Materials, Environment and Energy (INQUIMAE), University of Buenos Aires, Buenos Aires, Argentina

Ilmutdin M. Abdulagatov Geothermal Research Institute of the Dagestan Scientific Center of the Russian Academy of Sciences, Thermophysical Division, Makhachkala 367030, Dagestan Russia

2.1 BASIC PRINCIPLES AND DEFINITIONS The thermodynamic properties of binary or multi-component systems are better described in terms of the partial molar quantities of their components (Pitzer, 1995). The partial molar property of a given component of the mixture physically represent the change in the property by addition to a large multi-component system of a small amount of one of the components at constant p, T and mole number of the other components. N

Vm = x1V1 + ∑ xiVi

(2.1)

i=2

j ≠i

o

j ≠i

 ∂µ  = lim mi → 0  i   ∂p  T , n

= lim mi → 0 Vi

j ≠i

(2.4)

In this unsymmetrical convention, the limit value of the partial molar volume of the solvent is: (2.5)

where V1o is the molar volume of pure water. Most of the hydrothermal systems in this chapter are binary solutions containing water (1) and a single electrolyte or non-electrolyte solute (2). In that case, Equation (2.1) becomes:

(2.2) Vm = x1V1 + x2V2

j ≠i

Since the volume is related to the pressure derivative of the Gibbs energy, it follows the relationship 2  ∂G    ∂p∂ni  T , n

 ∂µ  Vi o =  i   ∂p  T , n

lim mi → 0 V1 = V1o

Thus, the molar volume Vm of a multi-component aqueous solution can be written in terms of the partial molar volume, Vi, of its components (1-water, 2, . . . , I, . . . N -solutes) defined by  ∂V  Vi =  m   ∂ni  T , p, n

infinite dilution. If we select the solute molality as concentration scale, which is the more convenient when dealing with high temperature and high pressure systems, the definition of the solute partial molar volume is:

 ∂V  = m  ∂ni  T , p , n

j ≠i

 ∂µ  = i  ∂p  T , n

= Vi

(2.3)

j ≠i

between the partial molar volume and the pressure derivative of the chemical potential. In the unsymmetric standard state convention, where the solvent is referenced to its pure state (Raoult’s law reference state) and the solutes to the infinite dilution state (Henry’s law reference state), the standard partial molar volume is equal to the pressure derivative of the chemical potential at Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-09465-5

(2.6)

One can assume that the change of the molar volume upon mixing is only due to change in the partial molar volume of the solute, that is equivalent to consider the partial molar volume of water, V1, equal to the molar volume of pure water, V1o all over the range of concentration. In that case the partial molar volume of the solute in Equation (2.6) is, by definition, the apparent molar volume of the solute: Vm = (1 − x )V1o + xφv

(2.7)

where x = x2 represents the molar fraction of the solute. The apparent molar volume, fv, of the solute at molality m at a given temperature is calculated from the measured densities

136


of the solution (d) and pure water (do) by resorting to Equation (2.7),

φv =

1000 ( do − d ) M 2 + ddo m d

(2.8)

where M2 is the molar mass of the solute. The relation between the partial molar and apparent molar volumes is given by ∂φ V2 = φv + m  v   ∂m  T , p , x

(2.9)

As any partial molar property, V2 can be split into a standard state term plus an excess term, which depends on the solute concentration. V2 ( m, T ) = V2o (T ) + V2ex (T .m)

(2.10)

The standard state partial molar volume is the value of V2 at infinite dilution, V2o , and it is obtained by extrapolation of fv at infinite dilution. V2o represents the solute-solvent interaction and is related to the salt-solvent direct correlation function, c12(r), through the relationship (Brelvi and O’Connell, 1971):

(

V2o = kT κ 1o 1 − 4π d ∫ c12 ( r ) r 2 dr

)

(2.11)

k 1o being the isothermal compressibility of the pure solvent. This equation will be used later to explain the observed behavior of the standard partial molar volume of solutes near the solvent critical point. V2ex or f vex accounts for the non-ideality of the mixture. It is a measure of the solute-solute interaction, and the concentration dependence is different for electrolyte and nonelectrolyte solutes. In the case of aqueous electrolytes the classical DebyeHückel theory (Debye and Hückel, 1923) predicts that the excess apparent molar volume of the solute is given by

φvex (T .m) = ν z+ z−

Av 1/2 I 2

(2.12)

where v = v+ + v− is the number of ions resulting from the electrolyte dissociation, z+ and z− are the charges of the ions (in electron charge units), I is the ionic strength (–12 Σmiz2i ), and Av is the Debye-Hückel limiting slope for the partial molar volume, given by 2  12 e Av = 2 RT ( 2π N A do )   ε kT 

32

κ 1o   ∂ ln ε  −  ∂p  3   T

values of Av are sensitive to the choice of the equation of state for pure water and the equation describing the pressure and temperature dependence of the dielectric constant. 2.2 EXPERIMENTAL METHODS Several methods were developed to measure the volumetric properties of hydrothermal systems. This section summarizes the basic principle and the typical accuracy of those most widely used to determine the densities of the systems listed in Table 2.5. A detailed description of different densimeter types, included those used in high temperature, high pressure aqueous systems, can be found in a recent IUPAC publication (Wagner et al., 2003). 2.2.1 Constant volume piezometers (CVP) There are several types of piezometer (Wagner et al., 2003) for the determination of fluid densities but here we will describe those more commonly used in hydrothermal systems. One of these instruments, widely used for nonelectrolyte density measurements in the Abdulagatov’s group (Abdulagatov et al., 1994), consists of a constant volume piezometer (CVP) of cylindrical form, constructed in a corrosion resistance alloy (stainless steel, titanium alloy, hastelloy, etc.) with a volume of 30–200 cm3 (see Figure 2.1). At one end of the piezometer is mounted a diaphragmtype null detector (2, 6, 8–10, 11, 12), connected to a pressure measuring system, usually a deadweight gauge. The stainless steel diaphragm (6) separates the sample from the pressure-transmitting liquid in the pressure sensor. The sample inside the piezometer is commonly stirred with a ball-bearing (4) for achieving homogenization. The other end of the piezometer is connected through a charge line (14) and high-pressure valve (3) to a high-pressure pump used to fill the piezometer with the sample. In the complete setup, shown in Figure 2.2, the piezometer (1) is placed horizontally in an air thermostat (2, 5) having external (3) and internal (4) electrical heaters. The temperature is monitored with platinum resistance thermometers (6) with a typical uncertainty of ±0.01 K and thermocouples (11–14).

7 mA

8 9 10 2

11 6 12 13 15 5

1 14 3

4

(2.13)

where e is the electron charge, k the Boltzmann’s constant, NA the Avogadro’s number and e the static dielectric constant of the solvent. The values of Av as a function of temperature and pressure have been tabulated by Rogers and Pitzer (1982) up to 300 °C and 100 MPa and by Helgeson and Kirkham (1974) in the range 0–650 °C and from saturation to 500 MPa. The

Figure 2.1 Scheme of the constant volume piezometer (Abdulagatov, I.M., Bazaev, A.R. and Ramazanova, A.E. (1994). Ber. Bunsenges Phys. Chem. 98, 1596–1600. Reproduced by permission of Deutsche Bunsen-Gesellschaft); 1: piezometer block; 2: diaphragm separator block; 3: needle valve stem; 4: stirrer ball; 5: heating wire; 6: diaphragm; 7: enclosure bolt; 8: microammeter; 9: leadcontact; 10: ceramic tube; 11: mica isolator; 12: cylindrical plug with holes; 13: thermocouple well; 14: charge line connection; 15: heater jacket.

pVTx Properties of Hydrothermal Systems 137

The sample pressure is determined with a deadweight gauge (7) and diaphragm-type null detector (9, 10) with an accuracy of around ±0.002 MPa. Figure 2.2 also shows the high pressure pumps (17, 18) used for filling the piezometer with pure water and the liquid solute (19, 20). Before that the capillary tubes (8, 16, 27–29) and valves (15, 22–26) are washed with acetone and evacuated. When the sample is heated to the desired temperature value, the sample is withdrawn through the valve in order to maintain the pressure at a fixed value. The volume of the piezometer is calibrated with water with accuracy better than 0.03 cm3. Abdulagatov reported density measurement uncertainty around 0.1% in the temperature range 523–673 K and pressures up to 100 MPa (Abdulagatov et al., 1996a) using this type of piezometer. Errors ranging between ±0.2% and ±0.7% were reported by some authors (Shmulovich et al., 1979) at 450–500 MPa using similar apparatuses. Another type of fixed volume piezometer was used by the Russian groups (Abdulagatov, Azizov and Akhundov) for the measurements of density in electrolyte solutions. The apparatus, shown schematically in Figure 2.3, consists of a stainless steel piezometer (11) of volume around 95 cm3 having two capillaries (2 and 7) soldered to its ends. The lower capillary (7) is connected to a viewing window (8), which permits us to fix the volume of the solution by observing the border between the solution and mercury in a Ushaped tube (9); the mercury was connected through an oil-separator with the pressure-gauges (10). The upper capillary (2) is connected to a valve (5) used to extract the sample (4). The piezometer (11) is located vertically in a liquid thermostat (12) having a pump stirrer (1), bottom heater (3), side heater (13), temperature regulator with thermocouple (15) and microheater (16). The temperature is measured with a platinum resistance thermometer (14). The reported uncertainty in density determination using this piezometer was ±0.06% up to 573 K and 40 MPa.

Akhundov reported uncertainties of ±0.1% using a piezometer having a volume of 13.6 cm3 on the same temperature and pressure range (Akhundov and Imanova, 1983). A similar piezometer having a larger volume (177 cm3) was used by Zarembo’s group (Lvov et al., 1981) and the estimated uncertainty up to 573 K and 80 MPa was ±0.03%. 2.2.2 Variable volume piezometers (VVP) 2.2.2.1 Dilatometer A dilatometer can also be considered as a piezometer of variable volume, where the change in volume can be achieved using pistons. Older devices often used mercury as a liquid piston with the consequent environmental risk and moderate accuracy (±0.5–1%) of density measurements (Ravich and Borovaya, 1971a–b; Urusova, 1975). Accuracy density data were obtained with high temperature dilatometers, where the solution is contained in a stainless-steel autoclave connected through a capillary tube to a mercury reservoir thermostatized at 25 °C. When the sample autoclave is heated, the solution expands and the excess mercury is discharged into a weighing bottle, to keep the pressure constant. The volume of mercury displaced is equal to the volume change of the solution due to the temperature change. The scheme of a dilatometer, which was used extensively by Ellis during the 1960s (Ellis and Golding, 1963; Ellis, 1966, 1967, 1968; Ellis and McFadden, 1968) for determining the

8 4

14

5 13

9

13

26

12

11

16

16 27 28 29

11

22

6 24

19

6

17 10

20 25

14

12

21

15 1

10 mA

2

1 2

7 3

15

Precision Temperature Regulator

23

18

Figure 2.2 Scheme of the complete setup used for pVTx measurements using a CVP (Abdulagatov, I.M., Bazaev, A.R. and Ramazanova, A.E. (1994). Ber. Bunsenges Phys. Chem. 98, 1596–1600. Reproduced by permission of Deutsche BunsenGesellschaft); 1: piezometer; 2: air thermostat; 3: electrical heater; 4: regulating heater; 5: circulation fan; 6: PRT; 7: dead-weight gauge; 8: capillary tube; 9: instrument adapter and diaphragm-type null detector; 10: microammeter; 11, 13: thermocouples; 12, 14: differential thermocouples; 15: needle valve handle; 16: fillingdischarging capillary line; 17, 18: hand-operated screw press; 19– 21: samples; 22–26: valves; 27–29: capillary tube.

PM-60

5

7 8

3 4

PM-600 9 Hg filled

Figure 2.3 Scheme of the CVP used by (Abdulagatov, I.M. and Azizov, N.D. (2004a). J. Chem. Thermod., 36, 17–27, reproduced by permission of Elsevier) for pVTx measurements in electrolytes; 1: mixer; 2: upper capillary; 3: bottom heater; 4: sample weighing container; 5: discharge valve; 6: capillary pass-through; 7: lower capillary; 8: viewing window; 9: separating U-tube; 10: deadweight gauges (60 and 600 bar); 11: piezometer; 12: liquid-filled thermostat; 13: side heater; 14: PRT; 15: thermocouple; 16: microheater.

138


density of aqueous electrolytes is shown in Figure 2.4. The error in density estimated by Ellis is ±0.00005 g·cm−3 or ±0.005% at the higher temperature (200 °C) and 2 MPa. The Pitzer’s group in Berkeley used a similar dilatometer for aqueous electrolytes, except that the expansion of the solution volume on heating was determined by measuring the height of mercury in a column using a cathetometer. The estimated density uncertainty at 200 °C is ±0.0005 g·cm−3 or ±0.05% (Rogers et al., 1982). The dilatometer described by Pepinov et al. (1982) where the height of the mercury level in the separator is also measured has an estimated accuracy of density of ±0.15% in the range 150–350 °C. 2.2.2.2 Piston densimeter A variable volume piezometer for fluid density measurements at high-temperature high-pressure was used by Franck’s group in Karlsruhe for more than two decades. The original high-pressure cell design (Lentz, 1969) is shown in Figure 2.5 and it allows pVT measurements up to 500 °C and 300 MPa.

The high pressure cylindrical cell (Figure 2.5) made in a nickel–steel alloy contains the sample, which extends from a synthetic sapphire window at the extreme of the cell to the front side of a movable piston. A platinum mirror is attached to the piston to allow the direct visual observation of the sample. The position of a movable piston, and hence the sample volume, can be determined with a magnetic device with an uncertainty close to ±0.4–1% (Gehrig et al., 1986). 2.2.2.3 Metal bellows densimeter For pVTx measurements in highly concentrated electrolyte solutions, Franck’s group used a variable volume piezometer designed by Hilbert (1979) and shown schematically in Figure 2.6. The sample is filled in a pure nickel bellows to prevent corrosion and to permit elastic volume changes. This cell is located inside a stainlesssteel autoclave immersed in an internally heated, argonfilled vessel. The water-filled autoclave containing the closed inner nickel cell is always in pressure equilibrium with an outside, room temperature, high-pressure vessel partially filled with mercury. Variation of the volume of the bellows is recorded by a float on the mercury contained in the room temperature vessel. The position of the float is determined magnetically (inductively) from outside. The uncertainty in the volume measurement varied from ±0.013% at 373 K and 100 MPa to ±0.42% at 673 K and 400 MPa. 2.2.3 Hydrostatic weighing technique (HWT)

Figure 2.4 Scheme of the dilatometer used by Ellis and coworkers (Ellis, A.J. (1966). J. Chem. Soc. Section A: Inorganic, Physical, Theoretical, no 11, 1579–1584. Reproduced by permission of The Royal Society of Chemistry). sapphire window

sample space

This kind of technique was used by Russian groups, as those of Mashovets, Puchkov, Zarembo and others since the 1960s. For instance, Dibrov et al. (1963) reported a hydrostatic weighing apparatus as shown in Figure 2.7. The high pressure cell (1) located in an electric furnace (2) contains a hollow cylindrical float made in steel. This float is suspended of a nichrone wire which passes through coils fixed to the upper cylindrical cap. The cylinder is connected to two intermediate vessels (3) which avoids direct contact of the sample with the oil of the press (9) and receive the solution displaced from the cell upon heating. The vessels are half-filled with mercury, above which the sample is present in the left-hand vessel and the oil in the right-hand one. The later contains a movable contact (4) to check that mercury has not been ejected into the oil system. The system mirror piston

o-rings

wire to inductive position indicator

Figure 2.5 Scheme of the piston peizometer used by Franck and co-workers (Gehrig, M., Lentz, H. and Franck, E.U. (1986). Ber. Bunsenges. Phys. Chem., 90, 525–533. Reproduced by permisson of Deutsche Bunsen-Gesellschaft).


cooling water

To = 20°C

Figure 2.6 Metal bellows variable volume piezometer (Hilbert, R. (1979). Ph.D. Dissertation, Universitat Fridericiana Karlsruhe).

N S

Inductive sensor

magnet

pVT cell water solution calefactor mobile rod magnet thermoelement

Float Hg

Argon

8 5 1

4

2 3

6

7

9

Figure 2.7 Scheme of the hydrostatic weighing apparatus (Dibrov, I.A., Mashovets, V.P. and Federov, M.K. (1963). Zh. Prikl. Khimii, 36, 1250–1253.).

is completed with pressure gauge (5), valves (6 and 7) and reference gauges (8). The operating principle consists in measuring the strength of the current passing through the solenoid to keep the float suspended. The relation between this current produced by the magnetic field in the solenoid and its supporting power is used for determining the weight of the float. The system is calibrated by replacing the float with known weights. The typical accuracy in density measurements using this technique is between 0.3% and 0.5%. 2.2.4 Vibrating tube densimeter (VTD) Kratky et al. (1969) and Picker et al. (1974) used a highprecision flow densimeter based on the vibrating tube principle to measure the density of fluids up to 150 °C. These authors use a configuration as shown in Figure 2.8a, where one or two small permanent magnets mounted on the tube move along the axes of drive and pick-up coils. Albert and Wood (1984) built a VTD for density measurements with a precision of 30 ppm up to 325 °C and 40 MPa, with a configuration shown in Figure 2.8b, where the arrangement is inverse, avoiding the loss of sensitivity because the mass of the magnet is attached to the tube.

As shown in Figure 2.8b, the VTD design by Albert and Wood consists in a Hastelloy U-tube (2) silver soldered to a brass block (4). Two constantan wires (1) are attached across the U-tube with ceramic cement, perpendicular to the magnetic field generated by a permanent magnet (5). The electrical current flowing through one of the wires (drive) induces oscillation of the U-tube in the direction perpendicular to both, the field and the wires. Thus, an electrical current is induced in the other wire (pickup) which is amplified by an electronic feedback circuit that sustains the oscillation of the vibrating tube at the resonance frequency. The setup is completed with transporting tube (3), extension pole piece (6), cover (7) and densitometer block (8). The resonance frequency is related to the mass, m, of the vibrating tube by

ω2 =

Kf C2 − m 2m 2

(2.14)

where Kf is the force constant and C the damping constant of the vibrating tube. To determine the relationship between the period (t = w−1) of the vibration and the mass of the fluid within the tube of volume V, it is assumed that the damping constant is small and the second term in Equation (2.14) can be neglected. Thus, the difference between the density, d, of the fluid under study and the density, do, some reference fluid is given by d − do = K (τ 2 − τ o2 )

(2.15)

where K = Kf /V is the VTD constant, which is determined from measurements of the resonance period of two fluids of known density. A VTD, improved with a phase-locked loop for driving the oscillation (Majer et al., 1991b) was used by Wood and co-workers for measuring the pVTx properties of several metal halides aqueous solutions. Later, this group modified the VTD to improve its accuracy and reliability at higher temperatures. The Hastelloy U-tube was replaced by a platinum-rhodium alloy, more resistant to corrosion, and the new VTD assembly included two permanent magnets and softsteel pole pieces to increases the magnetic field. The new VTD version was used in supercritical aqueous solutions up to 450 °C and 38 MPa.

140


Figure 2.8

Schemes of the different configurations of a VTD (Wagner et al., (2003)).

Simonson et al. (1994) constructed a VTD based on the same principle, except that they exchanged the position of the permanent magnet and the drive/pickup wires. In this VTD the permanent magnet was mounted on the vibrating tube close to the U-bend, while two wire-coil electromagnets were fixed to the block. Blencoe et al. (1996) developed a VTD for determine the densities of fluids in the range 10–200 MPa and 150–500 °C. Hynek et al. (1997a) describe a modified version of the flow vibrating-tube densimeter with a photoelectric pick-up system and a new concept of an electromagnetic drive system was designed for density difference measurements in the temperature and pressure ranges from 25 to 300 °C and up to 35 MPa. Similar equipment was used by Hakin et al. (2000). Typical accuracy in density measurements with a VTD ranges from 0.002% to 0.04%. 2.2.5 Synthetic fluid inclusion technique This technique, in which small amounts of fluid are trapped by healing fractures in quartz, has been used by Sterner and Bodnar (1984) for studying pVTx properties of aqueous electrolytes (CaCl2, KCl, NaCl) and aqueous CO2 at supercritical temperatures up to 820 °C (Knight and Bodnar,1989), and extended by Frost and Wood (1997) up to 1400 °C. The experimental procedure to produce synthetic fluid inclusions uses quartz cores approximately 4 mm in diameter and 1–2 cm in length, which are fractured by thermalshock technique at 350 °C. The cleaned and dried cores are placed into platinum capsules along with the fluid sample, sealed with and arc-welder and placed into cold-sealed pressure vessels and taken rapidly to the desired temperature. After quenching the quartz cores were cut into ∼1 mm thick disks, polished, and homogenization temperatures of the inclusions were determined (±2 °C) on a microscope heating stage. It is assumed that fluid inclusions represent isochoric systems, and consequently the specific volume of the fluid

inclusion at the homogenization temperature is the same as the specific volume of the fluid at formation conditions. The obtained densities could be corrected taking into account the thermal expansion of quartz (the magnitude of this correction ranged from ∼0.4 to 3.1% of the uncorrected specific volume). 2.3 THEORETICAL TREATMENT OF pVTx DATA Many of the theories and models described in this section were developed for the excess thermodynamic properties of solutions, including not only the excess partial molar volume, but also other excess properties. In the following subsections we have restricted the discussion to the volumetric properties of aqueous systems. 2.3.1 Excess volume As mentioned in Section 2.1, V2ex accounts for the non-ideality of the mixture (Equation (2.10) and reflects the solute– solute interaction. For this reason its nature and T, p dependence is different for electrolyte and non-electrolyte solutes and will be analyzed separately. 2.3.1.1 Ionic solutes The Debye-Hückel (DH) theory (Debye and Hückel, 1923) gives a simple expression for the excess volume in the framework of the primitive model, which consider the systems as ions immersed in a continuum, structureless solvent of dielectric constant, e, The excess apparent molar volume of electrolytes solutes in the DH model is given by Equation (2.12), referred to as the Debye-Hückel limiting law (DHLL), which becomes exact in the infinite dilution limit. Beyond the dilute region the short-range interactions among ions, neglected in the DH model, are responsible for the deviation to the DHLL. Kumar (1986a,b), Connaughton et al. (1986), Lo Surdo et al. (1982), Novotný and Söhnel (1988), Isono (1980,


1984), Apelblat and Manzurola (1999, 2001), and Laliberte and Cooper (2004) used various types (polynomial, exponential, power, and their various combinations) of empirical equations to describe the concentration and temperature dependences of the densities of aqueous salt (NaCl, MgCl2, MgSO4, Na2SO4, SrCl2). For example, Kumar (1986a,b), proposed the equation at temperatures from 50 to 200 °C and at pressure of 20.27 MPa.

ρ − ρ0 = Am1 2 + Bm + Cm3 2 + Dm 2 ,

(2.17)

Connaughton et al. (1986) use another form of polynomial Equation (2.16)

ρ − ρ0 = Am + Bm3 2 + Cm 2 + Dm5 2 ,

(2.18)

where A,B,C, and D are polynomial functions like Equation (2.17). The values of density for aqueous NaCl, MgCl2, Na2SO4, MgSO4 solutions calculated with Equation (2.18) were used to calculate the apparent molar volumes, fV, and the derived values were fitted to the Pitzer’s relation (see below, Equation 2.23). Gates and Wood (1989) used a cubic spline surface in three dimensions (p,T, and m) to represent their experimental pVTm data for CaCl2 in the temperature range from 323 to 600 K and at pressure up to 40 MPa. The accuracy of the representation is about 0.33 kg·m−3 above 500 K and 0.16 kg·m−3 below 500 K. Most of these equations were developed to calculate the density at atmospheric pressure and at concentrations up to saturation. Several empirical extensions of Equation (2.12) has been proposed (Millero, 1971) to account for the short-range contribution to fVex. One of the commonly used for hydrothermal electrolyte systems, is the Redlich-Mayer equation (Redlich and Mayer, 1964),

φ = Av m ex V

12

+ bm + dm

32

1000G E 4I = − Aφ   ln (1 + bI 1 2 ) + 2m 2ν M ν X  n1 MW RT b 2β 1MX  0 12 β MX + 2 [1 − (1 + α I ) α I 

}

exp ( −α I 1 2 )] + m3 (ν M ν X )

(2.16)

where m is the molality, A, B, C, and D are the temperature dependent parameters Y ( A, B, C , D ) = y0 + y1T + y2T 2 +

assumes that the excess Gibbs free energy of a binary solution containing 1 kg of solvent, GE, can be represented as

(2.19)

This equation was used by Abdulagatov, Azizov and coworkers to extrapolate the partial molar volume of aqueous electrolytes such as LiI (Abdulagatov and Azizov, 2004b), Li2SO4 (Abdulagatov and Azizov, 2003a), NaNO3 (Abdulagatov and Azizov, 2005), MgCl2 (Azizov and Akhundov, 1998), Na2SO4 (Azizov and Akhundov, 2000), at infinite dilution. Pitzer’s ion-interaction model Pitzer (1973) developed a semi-empirical equation (ioninteraction model) to reproduce accurately the volumetric properties of aqueous electrolyte solutions. This model has been used to calculate accurately other thermodynamic properties such as expansivity, compressibility, free energy, enthalpy, and heat capacity. The ion-interaction model

32

φ C Mx ,

(2.20)

where MW is the molecular weight of water; m is the molality; v = vM + vX is the total number of ions formed from the dissociation of the salt; R is the gas constant; I = 0.5∑ mi zi2 i

is the ionic strength; zi is the ions charge. The excess molar Gibbs energy Gex is defined as G = x1G10 + x2G20 + G ex + x2ν RT ( ln m − 1) .

(2.21)

Therefore, the pressure derivative of Gibbs energy is defined as the total volume of the solution V(p,T )  ∂G  0 0 V = nV . 1 1 + n2V2 +   ∂p  T ex

(2.22)

By substitution of Equation (2.22) into Equation (2.7) we obtain,

φV = V20 +

1  ∂G ex    . n2  ∂p  T

(2.23)

Therefore, by using the pressure derivative of Equation (2.20)

φV = V20 + ν z M z X AV h ( I ) + 2ν M ν X RT [ mBVMX + m 2 ( ν M ν X ) C VMX ],

(2.24)

where h ( I ) = ln (1 + bI 1 2 ) 2b ,

 ∂Aφ  AV = −4 RT  ,  ∂p  T

0 BMX = β MX + 2β 1MX [1 − (1 + α I 1 2 ) exp ( −α I 1 2 )] α 2 I ,

 ∂B  BVMX ( I ) =  MX  ,  ∂p  T , I φ C MX = C MX 2 zM z X

12

 ∂C  , C VMX =  MX  ,  ∂p  T

AΦ is the Debye-Hückel slope for the osmotic coefficient (Bradley and Pitzer, 1979), b = 1.2(kg/mol)1/2, BMX and CMX are the second and third virial coefficients. Equation (2.24) combines the long-range coulombic potential with the hard sphere (short-range) potential. Pitzer’s model takes into account the size of the ions in the coulombic part of the ion-ion potential and, as a consequence, the electrostatic part of f Vex (second term in

142


Equation 2.24) differs from the DH Equation (2.12), but the DHLL is recovered in the infinite dilution limit. Rogers and Pitzer (1982) applied the described model to the volumetric properties of H2O + NaCl solutions at temperatures from 0 to 300 °C and at pressures up to 100 MPa. This model was used by several authors (Pabalan and Pitzer, 1987; Holmes and Mesmer, 1994, 1996; Holmes et al., 1994; Oakes et al., 1995b; Ob il et al., 1997a,b; Sharygin and Wood, 1997; Petrenko and Pitzer, 1997; Phutela et al., 1987; Monnin, 1987; and Wang et al., 1998) to represent accurately volumetric data for various aqueous salt (NaOH, HCl, CaCl2, MgCl2, SrCl2, BaCl2, K2SO4 and Na2SO4) solutions in the range of temperature and pressure (density) where the electrolyte could be considered as fully dissociated. The Pitzer Equation (2.24) describes quite well the experimental data over a wide range of temperature, pressure and concentration provided that the coefficients b (0)v, b (1)v and Cv are fitted as a function of pressure and temperature. Usually the precision of the high temperature volumetric data does not justify the use of a second virial parameter dependent of the concentration and b (1)v is taken as zero. For instance, to describe the volumetric properties of NaCl up to 250 °C and 40 MPa (Simonson et al., 1994), 14 parameters are needed for fitting V o2 , b (0)v and Cv. This behavior is also observed for HCl (Sharygin and Wood, 1997) up to 350 °C and 28 MPa and for CaCl2 (Oakes et al., 1995b) up to 250 °C and 40 MPa, which requires 20 and 24 parameters, respectively. Thus, the extrapolation of the volumetric properties beyond the temperature and pressure range where these parameters were adjusted is not reliable. It is possible to take into account the short range ion–ion interaction effect on the volumetric properties of electrolytes by resorting to integral equation theories, as the mean spherical approximation (MSA). The MSA model renders an analytical solution (Blum, 1975) for the unrestricted primitive model of electrolytes (ions of different sizes immersed in a continuous solvent). Thus, the excess volume can be described in terms of an electrostatic contribution given by the MSA expression (Corti, 1997) and a hard sphere contribution obtained form the excess pressure of a hard sphere mixture (Mansoori et al., 1971). The only parameters of the model are the ionic diameters and numerical densities. Even when the MSA model has not been extensively used for fitting volumetric properties of electrolyte aqueous solutions it is an interesting alternative to the ion-interaction model for predictive purpose because it renders reasonable values of the excess volume using the crystallographic values of ionic diameters (Corti, 1997). Sedlbauer and Wood (2004) used the MSA model to describe the thermodynamics properties of NaCl near the critical point. In this case the crystallographic diameters of the ions were used along with a model (Sedlbauer et al., 2000) for the standard state term. The MSA model without adjustable parameters provides a better fit of the partial molar volume than the Pitzer model. It should be noted that MSA is a theory cast in the McMillan-Mayer reference state framework, while the

experimental data are referenced to the Lewis-Randall framework. The conversion from the MM to the LR reference state can be performed by resorting to the approximated expression derived by Friedman (1972) as described previously (Fernandez-Prini et al., 1992). The conversion term can be neglected below 573 K at moderate pressure but becomes quite important in the critical region. 2.3.1.2 Ion association effects on excess volumes Positive deviations to the DHLL are observed for strongly associated electrolytes as MgSO4 at moderate temperatures or NaCl close to the water critical temperature. The reason of the deviation is the reduction of the electrostrictive effect when ion-pairs are formed, which leads to an expansion of the solution. The degree of association, 1 − a, of a symmetrical electrolyte is related to the association equilibrium constant for the ion-pair formation, KA, by, KA =

(1 − α ) γ ip α 2 mγ ±2

,

(2.25)

where m is the electrolyte molality and g± is the electrolyte mean activity coefficient and gip is the activity coefficient of the ion-pair. The relative population of ion-pairs depends of the inverse reduced temperature, b, defined by (FernándezPrini et al., 1992), b=

z+ z− e 2 , σε kT

(2.26)

where s is the distance of closest approach between ions (usually taken as the sum of ionic radii), e the relative dielectric constant of water and zie the ion charge. For aqueous electrolytes the ionic association become important when b is higher than 5, a value typical of a 2 : 2 electrolyte at room temperature or a 1 : 1 electrolyte above 300 °C. Thus, the extrapolation of the apparent partial volume of these electrolytes at infinite dilution to obtain the standard partial molar volume is uncertain, because the free ions concentration depends on the stoichiometric electrolyte concentration. For a 2 : 2 electrolyte, as MgSO4, at 25 °C the apparent partial molar volume approach the DHLL value at concentrations bellow 0.01 mol·kg−1 (Franks and Smith, 1967) and, at least the density could be measured with a precision of ±1 ppm, V o for MgSO4 can not be obtained by extrapolation. In this case one can calculate the standard partial molar volume from the known values of standard partial volume of 1 : 2 and 1 : 1 electrolytes by using the additivity rule (Lo Surdo et al., 1982): o o o o VMgSO = VMgCl + VNa − 2VNaCl 4 2 2 SO4

(2.27)

This is not possible for aqueous electrolytes at high temperature because even the 1 : 1 electrolytes are extensively associated under these conditions. The Pitzer model, which successfully describes the volumetric properties of fully dissociated electrolytes over an


impressive range of temperature and pressure at concentrations up to 5–8 mol/kg, could lead to unrealistic values of the partial molar volume at infinite dilution if ion association is important. For associated electrolytes, the correct extrapolation of the partial molar volume to zero concentration requires the inclusion of an extra term, b (2)v, in Bv (Equation (2.24)). Thus, Phutela and Pitzer (1986) could fit the volumetric properties of MgSO4 up to 200 °C and 10 MPa using BV = β (0)V + β (1)V g (α1 I 1 2 ) + β (2)V g (α 2 I 1 2 ) ,

(2.28)

where g(x) = 2[1 − (1 + x)exp(−x)]/x2 and for 2 : 2 electrolytes a1 = 1.4 kg1/2·mol−1/2 and a2 = 12.0 kg1/2·mol−1/2. In spite of the fact that this equation allows the description of the volumetric properties of associated electrolytes without resorting to the association constant, its predictive power is quite poor and its use is not recommended out of the concentration and temperature range where the model parameters were fitted. In order to deal with the volumetric properties of associated electrolytes, Millero and Masterton (1974), proposed the additivity of the apparent molar volume of the free ions (i) and ion pair (ip):

φV = αφV (i ) + (1 − α ) φV (ip) = φV (i ) + (1 − α ) ∆φV (ip)

(2.29)

where ∆fV(ip) = fV(ip) − fV(i), the apparent molar volume change for the association equilibrium, can be obtained at infinite dilution by knowing the pressure dependence of KA, ∆φV (ip)  ∂ ln K A   = −  ∂p T RT o

(2.30)

Majer and Wood (1994) used this procedure to extrapolate the apparent molar volume of NaCl solution between 548 and 710 K and pressures up to 38 MPa, by assuming that in Equation (2.27) the ion-pairs do not contribute to the excess volume, while the free ions contributions is given by the Pitzer model. Thus,

φVex = φVo (i ) + (1 − α )∆φVo (ip) + να z+ z− Av ln (1 + bI 1 2 ) + 2ν + ν − RT α mBv 2b

(2.31)

The dissociation degree, a, is obtained from Equation (2.24) assuming that the activity coefficient of the ion pair to be equal to unity and resorting to an extended DHLL equation for the activity coefficient for the free ions, as the expression given by the Pitzer ion interaction model (Pitzer, 1995). The calculation of g± is iterative because the activity coefficient of the electrolyte depends on the degree of dissociation. The same procedure is used to obtain the apparent partial molar volume of weak electrolyte, such as the organic acids studied by Wood and co-workers (Majer et al., 2000).

Near the critical point, where the association constant KA (determined by electrical conductivity) is large, the correction for ion-pairing is very important and the extrapolation to infinite dilution is quite sensitive to the magnitude of the association. Thus, for NaCl solutions at 670 K and 28 MPa (KA ≈ 7000), the extrapolated value of fVo is − 16300 cm3 mol−1, while the value without ion-pairing is −8065 cm3 mol−1. Unfortunately, the association constant of aqueous electrolytes at high temperature and pressure are only known with accuracy for a few systems where electrical conductivity has been measured in low concentration solutions. 2.3.1.3 Non-ionic solutes For neutral solutes the concentration dependence of the excess apparent molar volume is fitted to the experimental results using relationships derived from Equation (2.23),

φV ex = bm + dm n

(2.32)

where n could be 3/2 or 2 depending on the semiempirical model used to describe the apparent molar volume. Usually, for moderate concentrations the linear relationship (d = 0) is enough to represent the concentration dependence of the volumetric properties. Franck equations of state for water + hydrocarbon mixtures An equation of state of the perturbation type with repulsive and attractive terms with square-well potential for intermolecular interaction has been developed by Neichel and Franck (1996) for water + n-alkane (C1 to C6 and C12H26) mixtures, having the form: Vm3 + Vm2 β x + Vm β x2 − β x3 + 3 Vm (Vm − β x ) Bx , RT V 2 − V C x  m  m  Bx

p = RT

(2.33)

The molar Helmholtz energy derived from Equation (2.33) is  RT  Am = ∑ xi µio − RT + RT ∑ xi ln xi + RT ln  o  +  p Vm    Bx2  Vm  β x2  4β x  + RT  + RT ln 2  C  C x   Vm − β x (Vm − β x )  Vm − x   Bx  (2.34) where Vm is the molar volume,

β x = ∑ ∑ xi x j βij,

T π 3 σ ij N A , βii (T ) = βii  Ci  , Tci is the critical tem T  6 perature, m is a temperature dependence exponent. The attractive virial terms Bx and Cx are 3m

βij =

144


Bx = ∑ ∑ xi x j Bij , C x = ∑ ∑ ∑ xi x j xk Cijk ,

Cubic equation of state for binary aqueous solutions

Bij = −4βij ( wij3 − 1) ∆ ij ,

The representation of pVTx properties of mixtures by using the cubic EOS is still a subject of active research. Kiselev (1998), Kiselev and Friend (1999), and Kiselev and Ely (2003) developed a cubic crossover equation of state for fluids and fluid mixtures, which incorporates the scaling laws asymptotically close to the critical point and is transformed into the original classical cubic equation of state far away from the critical point. Anderko (2000) and Wei and Sadus (2000) reported comprehensive review of the cubic and generalized van der Waals equations of state and their applicability for modeling of the properties of multicomponent mixtures. In this section a wide range of EOS from cubic equations of state for simple molecules to theoretically based equations of state for molecular chains are considered, which are capable of providing reliable calculations of the thermodynamic and phase equilibrium properties of fluids and fluid mixtures. The various mixing rules that are used to apply equation of state to mixtures are also given. The EOS of Peng and Robinson (Peng and Robinson, 1976a, 1976b) and the modification of the Redlich–Kwong EOS (Redlich and Kwong, 1949) by Soave (1972) have been applied successfully for water + hydrocarbon systems (Kabadi and Danner, 1985). The parameter a of the Soave– Redlich–Kwong (SRK) equation is defined as a(T) = aCa, where ac is the value of the parameter a at the critical point, and a is a function of the reduced temperature and acentric factor of the compound. A new a function was regressed for water from the vapor-pressure data. The functional form used for the a function was the same as the original SRK equation a1/2 = 1 + C1(1 − T rC’2 ), where C1 = 0.662 and C2 = 0.8. The new a function predicted the vapor-pressure data within 0.5%. The original SRK used geometric mixing rule for the parameter a

1 1 ( I 33∆ ij ∆ ik ∆ jk ) − ( I11∆ ij + I12 ∆ ik + I13∆ jk ) 3 3 1 + ( I 21∆ ij ∆ ik + I 22 ∆ ij ∆ jk + I 23 ∆ ik ∆ jk ) 3

Cijk = −

 ε ij  ∆ ij = exp   − 1, T where s is the spherical particles diameter (or the potential core diameter), wij is the width and eij is the depth of the potential well relative to s. The auxiliary functions for third virial coefficients I11 to I33 are given by Heilig and Franck (1989, 1990), Christoforakos and Franck (1986), Hirschfelder et al. (1964). The three adjustable parameters wij, ke and ks for the square-well molecular interaction potential are wij = wii = wjj, and the Lorentz–Berthelot mixing rules are k ε ij = kε ε ii ε jj and σ ij = σ (σ ii + σ jj ). The values of the 2 wij, ke and ks parameters for H2O + n-alkane mixtures were calculated using the critical curve data. This model can be used to calculate the isothermal twophase boundary curves (p − x diagrams) for aqueous hydrocarbon mixtures. Heilig and Franck (1989, 1990) and Christoforakos and Franck (1986) applied the model for H2O + gas (CO2 and N2) mixtures and ternary aqueous mixtures. This model has also been used by Mather et al. (1993) for the H2O + Kr and H2O + Ne binary mixtures at temperatures from 610 to 700 K and at pressures between 45 and 255 MPa. Good agreement was found between the calculated and experimental critical locus and phase equilibrium data. Sretenskaya et al. (1995) used this EOS to describe the phase-equilibria, critical locus and pVTx properties of H2O + He mixtures at temperatures from 683 to 723 K and at pressures between 60 and 200 MPa. High-pressure phase equilibrium and supercritical pVTx data of the binary H2O + CH4 mixture at temperatures up to 723 K and pressures up to 200 MPa were represented by Shmonov et al. (1993) with the Franck model with only two physically meaning adjustable parameters (depth of the intermolecular potential, e/RTC, and the relative width of the well, l). Reasonable agreement between the experiment and prediction values of the phase equilibrium (pTx), volumetric (pVTx) properties and critical lines data were found. The high-pressure (up to 300 MPa) and high-temperature (up to 800 K) phase behavior (pTx) of three ternary aqueous solutions (H2O + n-alkane + NaCl; H2O + CH4 + CaCl2; and H2O + CO2 + C6H6) were experimentally and theoretically studied by Krader and Franck (1987), Michelberger and Franck (1990), and Brandt et al. (2000). A square-well potential with a slightly temperature dependent inner diameter was used to describe the measured values of pVT, phase equilibrium (pTx) and critical lines data.

n

n

amix = ∑ ∑ aij xi x j (1 − kij ),

(2.35)

i =1 j =1

where aij = (aiaj)1/2 and kij = 0 if i = j. Kabadi and Danner (1985) used the following mixing rule for water + hydrocarbon mixtures n

n

n

amix = ∑ ∑ aij xi x j + ∑ awi ′′ xw2 xi i =1 j =1

(2.36)

i =1

awi ′ = 2 ( aw ai ) (1 − kwi ) , 12

  T  1 awi ′′ = Gi 1 −   ,   Tcw   C

(2.37)

where aij = aji, aij = (aiaj)1/2 if i and j are both hydrocarbons, and aij = 0.5a′wj if i is water j is a hydrocarbon, Gi is the sum of the contributions of different groups which make up a n

molecule of hydrocarbon i Gi = ∑ gi , c1 is the regression j =1

constant, Tcw is the critical temperature of pure water. The


values of parameters a′wi and a″wi were calculated by Kabadi and Danner (1985) for 32 water + hydrocarbon mixtures at 91 constant temperatures. The term a′wi was assumed to represent the interactions between water and hydrocarbons molecules. The group contribution parameters gj for each group and the regression constant c1 were obtained by regressing the a″ wi values with the groups constituting different hydrocarbon molecules and with temperature. The best-fit value of c1 is 0.812. A modified- Soave–Redlich–Kwong (MSRK) EOS with an exponent-type mixing rule (Higashi et al., 1994) for the energy parameter and a conventional mixing rule for the size parameter is applied to correlate the phase equilibria for four binary mixtures of water + hydrocarbon (benzene, n-hexane, n-decane, and dodecane) systems at high temperatures and pressures by Haruki et al. (1999, 2000). The MSRK EOS is given as follows (Sandarusi et al., 1986): p=

RT a (T ) − , V − b V (V + b)

(2.38)

with 0.42747α (T ) R 2TC2 0.08664 RTC ,b= , and pC pC n α (T ) = 1 + (1 − Tr )  m +  .  Tr  a (T ) =

49 for the water + benzene mixtures, though T l12 and b12 are constants. The optimal values of the interaction parameters for water + n-decane and water + toluene at two temperatures have been determined by Haruki et al. (2000) using VLE and LLE data. Polishuk et al. (2000) studied van der Waals-type and Carnahan-Starling-type (Carnahan and Starling, 1969) equations of state to predict the critical locus in water + nalkanes binary mixtures. A temperature dependent combining rule for the binary attraction parameter yields quite accurate results from both equations. k12 = −0.30 +

Quasilattice equation of state for mixtures The basic features of the lattice theory and structure of a quasilattice EOS and its application to fluids and fluid mixtures was reviewed by Smirnova and Victorov (2000). Victorov et al. (1991) used the hole quasi-chemical groupcontribution model of Victorov and Smirnova (1985) and Smirnova and Victorov (1987) to calculate the phase equilibria in water + n-alkane binary mixtures. This model is essentially a generalization of the Barker lattice theory in its group-contribution formulation, the main difference being the presence of vacant lattice sites (holes). The model becomes volume-dependent, and thus the derived EOS adopted the following form (Smirnova and Victorov, 1987). p = prep + pres ,

The parameter a is given by

(2.42) n

a = ∑ ∑ xi ij x j ji aij β

i

β

(2.39)

j

∑ prepVm* = − ln (1 − ρ ) + ρ i =n1 RT

∑xr

b = ∑ ∑ xi x j bij and bij = (1 − lij ) i

j

i =1

   xi qi   ∑  Z  ln 1 − ρ 1 − i =n1  , 2   ∑ xi ri     i =1 n

(2.40)

where kij is the interaction energy parameter between unlike molecules. Haruki et al. (1999) used the following mixing and combining rules for the size parameter b bi + b j , 2

(2.41)

where lij is the interaction size parameter between unlike molecules. Equation (2.38) with mixing rules (2.39) to (2.41) has been used by Haruki et al. (1999, 2000) to correlate the phase equilibria for water + hydrocarbon binary systems. For water + n-decane system the values of k12, l12, and b12 have been evaluated from vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE) data. In the VLE region, the parameter k12 was expressed by the following 700 equation: k12 = −0.78 + for the water + n-decane and T

+

i i

The empirical exponents b represent a deviation from random mixing, and it was assumed that b11 = b22 = b21 = 1 (Haruki et al., 1999, 2000). Furthermore, the following combining rule is adopted aij = (1 − kij ) ai a j ,

xi li

presVm* = − Z ln X 0 , RT

(2.43)

(2.44)

where V* m is the molar volume per lattice site, xi is the mole fraction of component i in the n-component mixture, li = Z(ri − qi)/2 − ri + 1 is the molecular bulkiness factor, Z is the coordination number, ri and qi are the geometrical parameters characterizing molecular size and surface area, n

ρ = V *∑ xi ri Vm is the reduced density, and X0 is the solui =1

tion of the following set of ‘quasi-chemical’ equations: ∆ε X S ∑ α t X t exp  − st  = 1,  RT  t =0

(2.45)

where the indices s and t denote parts of the molecular surface (groups of kind s and t), whose interaction is described in terms of interchange energies ∆est (s = 0 imply

146


holes), at is the surface fraction of groups of kind t in the system. The temperature dependence of ∆est is (Kehiaian, 1983): ∆ε st T T −T  = ω st + hst (T0 − T ) T + cst  ln 0 − 0 , (2.46)  T RT T  where wst, hst, and cst are the interchange free energy, enthalpy, and heat capacity, respectively, and T0 is an arbitrary reference temperature. This model is very similar to those by Panayiotou and Vera (1982), Panayiotou (2003), and by Kumar et al. (1986). Victorov et al. (1991) calculated all the parameters of the model for pure components (nalkanes and water). The mixtures parameters were calculated using experimental pTx liquid-vapor equilibrium data. Panayiotou (2003) and Panayiotou et al. (2007) developed quasi-chemical hydrogen bonding EOS for two supercritical binary aqueous methane and n-pentane mixtures. Excellent agreement was found between the predictions and measured by Abdulagatov et al. (1996a) pVTx properties for H2O + CH4 and H2O + n-C5H12 (see Figure 2.9). 2.3.1.4 Classical Pitzer’s equation of state for aqueous salt solutions in the critical and supercritical regions The basic concept of the Pitzer’s EOS for aqueous salt solutions is an expansion of solution pressure p(T,r,x) around the critical point of pure water. The effect of salt is expressed by a very small number of temperature-dependent terms in increasing powers of the amount of salt added and of density differences from that of water at the critical point. For the pressure the expansion can be write as (Pitzer, 1986, 1989,

1990, 1998; Pitzer and Tanger, 1988; Tanger and Pitzer, 1989; Hovey et al., 1990; Pabalan and Pitzer, 1988) p (T , ρ, x ) = pH 2O (T , ρ ) + y [b10 + b11 ( d − 1) + ] + y 2 [b20 + ] + , (2.47) where pH2O(T,r) represents the pressure of pure water at T and d as derived from Wagner and Pruß (2002) fundamental EOS, y = x/(1 − x), x is the mole fraction, d is the density ratio r(H2O)/rC(H2O). The temperature dependent terms b10, b11, and b20 are given in the form b10 = c1 + c2T + c3T 2 + c4 T , b11 = c5 + c6T + c7 T 4 , b20 = c8 + c9T + c10 T 6 . The physical significance of each of these parameters was discussed by Pitzer (1986, 1989, 1990, 1998) and Tanger and Pitzer (1989). Hovey et al. (1990) have correlated the measurements of isothermal vapor-liquid compositions for H2O + KCl and H2O + NaCl using the equation of state (2.47). An equation of state (2.47), which was originally proposed by Pitzer (1986) was improved and used by Tanger and Pitzer (1989) to describe the pTx properties of NaCl(aq) and KCl(aq) solutions. The Pitzer-Tanger-Hovey (PTH) EOS (Hovey et al., 1990) for H2O + NaCl solutions is based on an expansion of pressure around the critical point of pure water (see Equation (2.47)). Only a few simple terms of the expansion were used for the H2O + NaCl solution, and the equation of Haar et al. (1984) was used to calculate the properties of pure water. The theoretical basis for the PTH EOS Hovey et al. (1990) is given in the work by Pitzer (1986) and Pitzer et al. (1987). Hovey et al. (1990) pre600

Water+n-Methane

Water+n-Pentane

750 500 600

T=647.05 K

T=653.15 K

Vm, cm3·mol-1

400 0.1576 0.6291 0.2100 0.5087

450

mol mol mol mol

fraction fraction fraction fraction

0.6938 0.2830 0.0880 0.0184

300

mol mol mol mol

fraction fraction fraction fraction

300 200

150

100

0

0 2

12

22

32 p, MPa

42

52

62

8

16

24

32

40

p, MPa

Figure 2.9 Experimental molar volumes of supercritical mixtures (Abdulagatov et al., 1996a) as a function of pressure, at different mol fraction of the hydrocarbon, together with values calculated from quasi-chemical hydrogen-bonding model (solid lines) by Panayiotou (2003).


Figure 2.10 Compositions of equilibrium vapor and liquid phases in the H2O + NaCl system at constant temperature of 673.15 K and various pressures reported by various authors and calculated with Tanger and Pitzer (1989) EOS.

T=673.15 K

H2O + NaCl 29

27

ps, MPa

25

23 Bischoff and Rosenbauer, (1988) Tanger and Pitzer, (1989) Bischoff and Pitzer, (1989) Gehrig et al., (1983) Shmulovich et al., (1994) Sourirajan and Kennedy, (1962) Olander and Liander, (1950) Urusova, (1975) Khaibullin and Borisov, (1966)

21

19

17

15 2

6

10

14 x, wt %

18

sented improved parameters for solutions of H2O + NaCl from 473 K to 773 K recalculated by using the newer more precise measurements. Figure 2.10 shows the comparison pS − x data calculated with the EOS by Tanger and Pitzer (1989) and reported data for H2O + NaCl solutions at temperature of 673.15 K. Anderko and Pitzer (1991, 1993a,b), Jiang and Pitzer (1996), Pitzer (1998), and Anderko et al. (2002) developed an EOS for geologically and industrially important aqueous electrolyte solutions H2O + NaCl, H2O + KCl, and H2O + CaCl2. These equations are based on a theoretical model for mixtures of hard spheres with appropriate diameters and dipole moments for H2O, NaCl, and KCl and with a quadrupole moment for CaCl2. Residual Helmholtz energy have been defined as (Pitzer, 1998) a res. (T , Vm , x ) = a (T , Vm , x ) − aid . (T , Vm , x )

(2.48)

The Helmholtz energy is convenient as a generating thermodynamic function because its derivatives, with respect to volume and each of the components moles numbers, yield the pressure and the chemical potentials, respectively. The residual Helmholtz energy is then a

res .

(T , Vm , x ) = a

ref .

(T , Vm , x ) − a

per .

(T , Vm , x ) ,

(2.49)

where aref is the reference Helmholtz energy, and aper. is the perturbation contribution. The reference Helmholtz energy is a sum of a repulsive contribution, ahs, due to hard -core effects, and an electrostatic contribution, aes, from dipoles or quadrupoles a ref . (T , Vm , x ) = a hs (Vm , x ) + aes (T , Vm , x )

(2.50)

The molar Helmholtz energy of a hard sphere mixture is (Boublik, 1970 and Mansoori et al., (1971)

22

26

30

a hs [(3DE F ) η − ( E 3 F 2 )] ( E 3 F 2 ) + = + RT 1− η (1 − η)2 3 E   2 − 1 ln (1 − η) , F

(2.51)

where n

n

n

i =1

i =1

i =1

D = ∑ xiσ i , E = ∑ xiσ i2 , and F = ∑ xiσ i3 , with xi and si the mole fraction and hard sphere diameter, respectively, of species i, h = b/4V is the reduced density, and b = (2/3)pNAF is the van der Waals co-volume parameter. According to the perturbation theory for dipolar hard sphere (Stell et al., 1972, 1974; Rushbrooke et al., 1973) the expression for the dipolar contribution to the Helmholtz energy is aes = RT

A2 , A3 1− A2

(2.52)

where A2 and A3 are the second- and third-order perturbation terms involving the dipole or quadrupole moments and the hard-core diameter of the pair or triplet interactions (Gubbins and Twu, 1978; Larsen et al., 1977). The electric moments appear in reduced form as follows (Pitzer, 1998)

( µ*)2 =

Q2 µ2 2 ( ) Q , and * = σ 3 kT σ 5 kT

(2.53)

where µ is the dipole moment and Q is the quadrupole moment. Dohrn and Prausnitz (1990) and Anderko and Pitzer (1991) generalized the van der Waals attractive term

148


using a truncated virial expansion for the perturbation contribution per

1 a =− RT RT

acbρ adb ρ aeb ρ   + + ,  aρ + 4 16 64  2

2

3

3

4

(2.54)

where the perturbation term parameters a, c, d, e are needed to represent the properties of pure water. According to the statistical mechanics formalism, the second virial coefficient of a mixture is a quadratic function of composition, the third virial coefficient a cubic, and so on. Therefore, the mixing rules becomes (Pitzer, 1998): n

n

n

n

n

n

i

i

n

2 adb 2 = ∑ ∑ ∑ ∑ xi x j xk xl ( ad )ijkl bijkl , n

n

n

i =1 j =1 k =1 l =1 m =1

The cross terms were expressed using pure fluid parameters as bij = [( bi1 3 + b1j 3 ) 2] and aij = ( ai a j ) α ij . 12

j

k

i

j

k

l

where VCi is the critical volume for component i. For the effective critical volume of the (ij),(ijk), and (ijkl) pairs the following combining rule are defined: 3

res .

(2.55)

For water, the experimental value of the dipole moment was used and other parameters were adjusted to fit its properties. The model described above has been used to represent experimental vapor-liquid equilibria for H2O + NaCl, H2O + KCl, and H2O + CaCl2 solutions. The full sets of parameters for these systems were given by Anderko and Pitzer (1991) and by Jiang and Pitzer (1996). An equation of state has been developed by Kosinski and Anderko (2001) for the representation of the phase behavior of high-temperature and supercritical aqueous systems containing salts. They improved the EOS by Anderko and Pitzer (1993a) to enhance the predictive capability of the EOS using the three-parameter corresponding-states principle. The model was successfully applied to the H2O + NaCl solutions up to 573 K, and correctly predicts the pVTx properties of H2O + KCl solution up to 773 K. This EOS also considerably extended the validity range. The EOS is also applicable to water + nonelectrolyte solutions such as water + methane and water + n-decane systems. Pitzer et al. (1992) developed virial type EOS for H2O + CH4 mixtures 1 + cVC ρ + αVC ρ + βVC2 ρ 2 + γ VC3 ρ 3 1 + bVC ρ

i

VCij = [(VCi1 3 + VCj1 3 ) 2] , VCijk = [(VCi1 3 + VCj1 3 + VCk1 3 ) 3] ,

Equations for the other thermodynamic properties can be readily obtained by applying usual thermodynamic relations to the Helmholtz energy. For example, the compressibility factor is given by

Z=

j

3 γ VC3 = ∑ ∑ ∑ ∑ xi x j xk xl γ ijklVCijkl

3 aeb3 = ∑ ∑ ∑ ∑ ∑ xi x j xk xl xm ( ae )ijklm bijklm .

 ∂ ( a RT )  Z = ρ  + 1. ∂ρ  T , ni

j

2 βV = ∑ ∑ ∑ xi x j xk βijkVCijk ,

n

3

i

2 C

i =1 j =1 k =1 l =1 n

(2.57)

The coefficient b should be linear, c and a-quadratic, bcubic, and g-quartic functions of composition. Therefore, the mixing rules for the parameters are

αVC = ∑ ∑ xi x j α ijVCij ,

i =1 j =1 k =1

n

Z = 1 + Bρ + C ρ 2 + D ρ 3 + E ρ 4 + B = bVC + cVC + αVC , 2 C = ( bVC ) + ( bVC )( cVC ) + βVC2 , 3 2 D = ( bVC ) + ( bVC ) ( cVC ) + γ VC3 , 4 3 E = ( bVC ) + ( bVC ) ( cVC ) .

bVC = ∑ xi bV i Ci , cVC = ∑ ∑ xi x j cijVCij ,

n

a = ∑ ∑ xi x j aij , acb = ∑ ∑ ∑ xi x j xk ( ac )ijk bijk , i =1 j =1

The virial expansion of equation (2.56) is

(2.56)

3

VCijkl = [(VCi1 3 + VCj1 3 + VCk1 3 + VCl1 3 ) 4 ] . 3

The combining rules for the aij,bijk, and gijkl are

α ij = (α iα j ) k1ij , βijk = (βij β jk βik ) , and 12

13

γ ijkl = ( γ ij γ jk γ kl γ ik γ il γ jl ) . 16

These combined rules include only four binary parameters (ki, i = 1,4). EOS (2.56) was applied to the H2O + CH4 mixture where the two pure fluids are very different. For the H2O + CH4 mixture k2 = k4 = 1.0. In the temperature range from 523 to 633 K the parameters k1 and k3 are linear function of temperature (k1 = −0.5399 + 0.00339T and k3 = 2.9968 − 0.002892T). This model represents the reported pVTx data for H2O + CH4 mixture within their experimental uncertainty. 2.3.1.5 Parametric crossover equations of state for aqueous solutions in the critical and supercritical regions Belyakov et al. (1997) developed a parametric crossover model for the phase behavior of H2O + NaCl solutions that corresponds to the Leung-Criffiths model in the critical region and is transformed into the regular classical expansion far away from the critical point. The model was optimized, and leads to excellent agreement with vapor-liquid equilibrium data for dilute aqueous solutions of NaCl near the critical points. This crossover model is capable of representing the thermodynamic surface of H2O + NaCl solutions in the critical and supercritical regions. The system-dependent constant of the model are: the critical parameters TC(x),pC(x), and rC(x); the asymptotic


critical amplitudes Ci (i = 1 − 5), where C4 is the heat capacity background amplitude; the Ginzburg number g; and the coefficients Ai(i = 1 − 3) in the analytical part of the thermodynamic potential. These constants were determined using the experimental critical parameter data and reported p-T and p-r equilibrium data from the literature. The structure of the crossover free-energy for binary mixtures was developed by Kiselev (1997). The isomorphic free-energy density of a binary mixture is given by

ρ A (T , ρ, x ) = ρ A (T , ρ, x ) − ρµ (T , ρ, x ) ,

(2.58)

where µ = m2 − m1 is the difference in the chemical potentials µ1 and µ2 of the mixture components, x = N2/(N1 + N2) is the mole fraction of the second component in the mixture, rA(T,r,x) is the Helmholtz free-energy density of the mixture, and the isomorphic variabl x is related to the field variable z by the relation x = 1− ζ =

eµ RT . 1 + e µ RT

(2.59)

The relation between the concentration x and the isomorphic variable x is 1  ∂A  , x = − x (1 − x )    ∂x  T , ρ RT

(2.60)

where R is the universal gas constant. At fixed x the isomorphic free-energy density r A(T,r,x) is same function of T and r as the Helmholtz free-energy density of a onecomponent fluid. Therefore, the isomorphic free-energy density of binary mixtures is

ρ A (T , ρ, x ) = kr 2−α Rα ( q) RρCOTCO ∆i − ∆i   ( q) Ψi (ϑ )  +  a Ψ0 (ϑ ) ∑ ci r R  i =1 

ρ

∑  Ai + ρ i =1

CO

 ∂∆A    − ∆A − A0 , ∂∆ρ  τ , x

∆A(τ , ∆ρ, x ) = kr 2−α Rα ( q) 4   a Ψ ( ϑ ) + ci r ∆i R − ∆i ( q)Ψi (ϑ )  , 0 ∑   i =1 4 pC ( x ) i A0 (T , x ) = ∑ Aiτ ( x ) − , RTC 0 ρC 0 i =1 1 dpC dm0 = + dx RTC ρC dx ρ T dT ( A1 + m1 ) C 0 C20 C , ρC TC dx

(2.63)

(2.64)

with  ∂x  = −  ∂x   ∂x  ,  ∂T  ρ , x  ∂ T  ρ , x  ∂ x  ρ ,T  ∂x   ∂x   ∂x    = −     , ∂ρ T , x ∂ρ T , x ∂x ρ ,T

ρC 0TC 0 ρT  ∂∆A  ρ  ∂∆M 0    ∂A0     ,  +  +  ∂ ∂ ∂x  T  ρ x x C0  T ρ ,T  ∆M 0 = ∑ M 0( i ) xi , x = x − x (1 − x )

where M 0(i) are the system-dependent coefficients. The critical curves were expressed as

p (x)  mi  τ i ( x ) − CO +  RρCOTCO

ρT [ ln (1 − x ) + mO ], ρCOTCO

p ( ρ, T , x ) ρ = RTC 0 ρC 0 ρC

i

4

4

cients (functions of the isomorphic variable x), while R(q) and Ψi(J) are universal functions. The scaled functions Ψi(J) are the universal analytical functions of the parametric variable J. The exact expressions for these functions and the values of all the universal constants have been given by Abdulagatov et al. (2005). The expression of pressure p as a function of T,r, and concentration using the crossover model is

(2.61)

TC ( x ) = TCO (1 − x ) + TC1 x + 2

x (1 − x ) ∑ Ti (1 − 2 x ) , i

(2.65)

i =1

where

τ=

ρC ( x ) = ρCO (1 − x ) + ρC1 x + T

2

x (1 − x ) ∑ ρi (1 − 2 x ) ,

− 1 = r (1 − b 2ϑ 2 ) and

Tc ( x ) ρ ∆ρ = − 1 = kr β R − β +1 2 ( q) ϑ + d1τ . ρC ( x )

i

(2.66)

i=0

(2.62)

All non-universal parameters of the model are analytic functions of the isomorphic variable x. In equations (2.61) and (2.62) a,b, and ∆i are the universal critical exponents, b2 = (g − 2b)/g (1 − 2b) is the universal linear-model parameter, k , d 1, a, mi, m0, Ai and c-i are the system-dependent coeffi-

pC ( x ) = pCO (1 − x ) + pC1 x + 2

x (1 − x ) ∑ pi (1 − 2 x ) , i

(2.67)

i =0

where subscript 0 and 1 correspond to the first and second components of the mixture, respectively. Along the critical line x = x and

150


TC ( x ) = TC ( x ) , ρC ( x ) = ρC ( x ) , and pC ( x ) = pC ( x ) . To represent all of the system-dependent parameters d 1(x), k (x), a(x), c i(x), g(x), mi(x) and Ai(x) the isomorphic generalization of the law of corresponding states (LCS) developed by Kiselev and Povodyrev (1992) has been used, and the dimensionless coefficients d 1(x), k (x), g(x) can be written in the form ki ( x ) = kio + ( ki1 − kio ) x + ki(1) ∆ZC ( x ) , and all others coefficients are given by ki ( x ) =

pC ( x ) [kio + ( ki1 − kio ) x + ki(1) ∆ZC ( x )], RρCOTCO

where ∆ZC(x) = ZC(x) − ZCID(x) is the difference between the actual compressibility factor of a mixture pC ( x ) and its ideal part ZCID(x) = ZCO(1 − x) ZC ( x ) = Rρc ( x )Tc ( x ) + ZC1 x. In the context of the LCS, the mixing coefficients k (1) i are universal constants for all binary mixtures of simple fluids (Kiselev, 1997; Kiselev and Rainwater, 1997). For mixtures with ∆ZC > 0.06, one needs to use an extended version of the law of corresponding states, with additional terms quadratic in ∆ZC(x).

This crossover equation of state (CREOS) (2.61)–(2.64) has been applied for dilute aqueous NaCl solutions (Belyakov et al., 1997), aqueous toluene (Kiselev et al., 2002) and nhexane (Abdulagatov et al., 2005) mixtures, and H2O + NH3 (Kiselev and Rainwater, 1997) solution near the critical point of pure water and supercritical conditions. The values of the parameters Ti,pi,ri were found from fit of equation (2.61) to the reported experimental TC − x,pC − x,rC − x data. Figures 2.11 and 2.12 compare the pVTx data reported by Abdulagatov et al. (2001, 2005) for H2O + n-hexane and H2O + toluene (Rabezkii et al., 2001 and Degrange, 1998) mixtures with the values calculated from the crossover model described above (Kiselev et al., 2002 and Abdulagatov et al., 2005). According to the classification of Scott and Konynenburg (1970, the binary systems of Type I, have only one critical locus between both critical points of the pure components and do not have the immiscibility phenomena. For this type binary aqueous solutions, the functions TC(x),rC(x), and pC(x) were represented as simple polynomial forms (see Equations (2.65)–(2.67) of x and (1 − x) (Kiselev and Rainwater, 1997, 1998; Kiselev et al., 1998). Water + toluene system corresponds to a Type III mixture (Scott and Konynenburg, 1970), in which there is a three-phase immiscibility region L1-L2-V with two critical endpoints (L1 = VL2 and L1 = L2-V) where the VLE critical locus, originated in the critical point of pure more-volatile component (toluene) and the LLE critical locus, started in the critical point of less-volatile component (water), are terminated.

H2O + n-Hexane

35

35

p, MPa

x=0.005 mol fraction

T=647.10 K

30

30

25

25

20

20 643.15 K 645.15 K 647.15 K CREOS (Abdulagatov et al., 2005) 649.15 K x=0.0 (pure water CREOS) Critical curve (CREOS) 651.15 K coexistence curve (CREOS)

15

10 40

0.0201 mol fraction 0.0021 mol fraction 0.0085 mol fraction CREOS (Abdulagatov et al., 2005) 0.0138 mol fraction Critical curve (CREOS) x=0.0 (pure water, CREOS)

15

10 140

240

340 ρ, kg·m–3

440

540

40

140

240

340

440

540

ρ, kg·m–3

Figure 2.11 Pressures as a function of density along the different supercritical isotherms at a fixed composition (left) and different molar fraction of n-hexane at fixed critical isotherm (right) (Ind. Eng. Chem. Res., 44, 1967–1984. Copyright 2005 American Chemical Society).


Water + Toluene x=0.0287 mol frac. 43

38

x=0.0166 mol frac. 52

647.10 K 673.15 K 623.15 K 629.15 K 643.15 K 651.15 K CREOS (one-phase) 633.15 K CREOS (Coexistance curve) Critical point (CP) CREOS (two-phase)

47

643.15 K 658.52 K 667.93 K 675.15 K 685.15 K CREOS (Kiselev et al., 2002)

42

p, MPa

33 37

32

28

27 23 CP 22 18 17

13 60

180

300

420

540

ρ, kg·m–3

12 100

200

300

400

500

ρ, kg·m–3

Figure 2.12 Pressures of mixtures as a function of density along the different supercritical isotherms at two fixed mol fractions of toluene together with values calculated with a crossover model by Kiselev et al. (2002). The symbols represent the experimental data by Rabezkii et al. (2001) (left) and by Degrange (1998) (right). (Ind. Eng. Chem. Res., 41, 1000–1016. Copyright 2002 American Chemical Society).

Therefore, for TC(x) and rC(x) in dilute water + toluene solutions (x ≤ 0.15), Kiselev et al. (2002) used the same expressions as in the works (Kiselev et al., 1999; Kiselev and Rainwater, 1997, 1998; Kiselev et al., 1998) (2.65) and (2.66), while the critical pressure pC(x) is expressed as a function of TC(x) c  pc 0 + ∑ pi (Tc ( x ) − Tc 0 )i , Tmin < Tc ( x ) ≤ Tc 0 (2.68) pc ( x ) =  i =1  pc1 , x = 1 c where T min is the lowest critical temperature at the pC − TC critical locus, and the subscripts c0 and c1 correspond to the pure solvent (water) and solute (toluene or n-hexane), respectively. The range of validity of the parametric crossover model is

τ + 1.2∆ρ 2 ≤ 0.5, T ≥ 0.98Tc . In Figure 2.13, the partial molar volumes of n-hexane and toluene derived from the pVTx measurements (Abdulagatov et al., 2001, 2005; Rabezkii et al., 2001; Degrange, 1998) and the values calculated with semiempirical equation developed by Majer et al. (1999) and crossover model (Kiselev et al., 2002 and Abdulagatov et al., 2005) are shown as a function of pure solvent (water) density along the various near-critical and supercritical isotherms.

The semiempirical model by Majer et al. (1999) is valid only up to 623 K. Therefore, in Figure 2.13 the values of V2 were obtained by extrapolation of this model to high temperatures. As one can see from Figure 2.13a, the agreement between the crossover model and the semiempirical equation is good in the region far from the critical point. However, in the critical region the discrepancy between both models is large due to differences in the critical density of pure water adopted by Kiselev et al. (2002) and Majer et al. (1999). In reduced coordinates V2/VC and r/rC the agreement between both models is fairly good. Figure 2.14 show the density dependencies of the partial molar volumes at infinite dilution for H2O + NaCl solutions along the supercritical isotherms calculated with the crossover model (Belyakov et al., 1997 and Kiselev and Rainwater, 1997) and the semiempirical equation developed by Sedlbauer et al. (1998). Povodyrev et al. (1997) have developed a six-term Landau expansion crossover scaling model to describe the thermodynamic properties of near-critical binary mixtures, based on the same model for pure fluids and the isomorphism principle of the critical phenomena. The model describes densities and concentrations at vapor-liquid equilibrium and isochoric heat capacities in the one-phase region. The description shows crossover from asymptotic Ising-like critical behavior to classical (mean-field) behavior. This model was applied to aqueous solutions of sodium chloride.

Figure 2.13 Comparison of the experimental partial molar volumes at infinite dilution from (Abdulagatov et al., 2001, 2005; Rabezkii et al., 2001) with the crossover model by Kiselev et al. (2002), Abdulagatov et al. (2005) and semiempirical equation by Majer et al. (1999) along the near critical and supercritical isotherms. (a): symbols are reported data (Abdulagatov et al., 2001, 2005); dashed lines are calculated with CREOS (Abdulagatov, I.M., Bazaev, A.R., Magee, J.W., Kiselev, S.B. and Ely, J.F. (2005). Ind. Eng. Chem. Res., 44, 1967–1984); 䊉-651.05 K; 䊊649.05 K; 䉱-647.05 K; (——), Majer et al. (1999). (b): 1-647.5 K; 2648.0 K; 3-649.0 K; Solid lines are calculated from CREOS (Kiselev, S. B., Ely, J.F., Abdulagatov, I.M., Bazaev, E.A. and Magee, J.W. (2002). Ind. Eng. Chem. Res., 41, 1000– 1016.), and dashed lines are calculated with semiempirical model by Majer et al. (1999). 䊉, Kiselev et al. (2002); 䊊, Degrange (1998).

30000

25000

Water+n-Hexane

651.05 K 649.05 K 647.05 K Majer et al. (1999)

V2 cm3·mol-1

20000

o

15000

10000

5000

0

-5000 90

170

250

330

490

410

ρw, kg·m-3

(a) 22

1 19 Water+Toluene 16

10

2

o

V2 I·mol-1

13

7 4 1 -2 -5 150

200

250

300

(b)

350

400

450

500

550

ρ, kg·m-3

H2O+ NaCl

-20

-20 4 3

-100

o

V2 I·mol-1

-100

-180

-180

2

-340

Tc=647.05 K

-260

-260

1 2 3 4

-

647.5 648.0 649.0 650.0

K K K K

-340 CREOS (Belyakov et al., 1997 ) Sedlbauer et al. (1998)

-420

-420 1

-500 150

250

350 ρ, kg·m–3

450

-500 150

250

350 ρ, kg·m–3

450

Figure 2.14 Partial molar volume as a function of density along the near-critical and supercritical isotherms. Solid lines are from crossover model (Belyakov et al., 1997), and dashed lines are from the semiempirical equation by Sedlbauer et al. (1998) (Belyakov, M.Yu., Kiselev, S. B. and Rainwater, J.C. (1997) J. Chem. Phys., 107, 3085–3097).


2.3.1.6 Multi-component systems There are a few studies of the volumetric properties of multi-component systems. As shown in Table 2.5, nine ternary ionic systems have been reported along with six electrolytes-nonelectrolytes mixtures and only one ternary nonelectrolytes system. On the other hand, the volumetric properties of only two quaternary ionic systems have been reported at high temperature. Also, a complex system containing non-dissociated boric acid and sodium borate, sodium diborate and higher species were reported (Ganopolsky et al., 1996a, 1996b). Tremaine and co-workers (Tremaine et al., 1997, Shvedov and Tremaine, 1997) have studied the volumetric properties of mixtures of dimethylammonium chloride and morpholine chloride (2) with hydrochloric acid (3). They described the volumetric properties of the mixture by Young’s rule m2   m3  +φ +δ φV = φV , 2   m2 + m3  V , 3  m2 + m3 

(2.69)

Since the amount of HCl is small as compared with the organic component, its apparent molar volume is approximated by the standard partial molar volume. The excess mixing term, d, is ignored in the calculation of the apparent partial molar volume of the major component having a common anion. An alternative way to describe the apparent molar volume of mixtures of strong electrolytes is by means of the multicomponent form of the Pitzer equation (2.24). For a mixture of two 1 : 1 electrolytes with one common ion the expression reduces to (Corti and Svarc, 1995) Av ln (1 + bI 1 2 ) + b 2 RTm { yBv, 2 + (1 − y ) Bv ,3 + m [ yCv , 2 + (1 − y ) Cv, 3 ]} + 2 RTy (1 − y ) mθ 2,3 + RTy (1 − y ) m 2ψ 2,3

φV = V o +

(2.70)

where V o = yV1o + (1 − y)V2o , y is the molar fraction of the electrolyte 2 in the mixture, BV and CV are the usual virial coefficients for the pure electrolytes and q2,3 and y2,3 are the binary and ternary mixture parameters. For instance for the LiCl + KCl mixture, q2,3 is the parameter related with the Li+-K+ interaction, while y2,3 accounts for the Li+-K+-Cl− interaction. The lack of information on the volumetric properties of mixing electrolytes prevents us from making any generalization on the values of the mixing parameters. The situation is even worse in the case of mixtures of nonelectrolytes, for which the experimental information is almost inexistent. 2.3.2 Models for the standard partial molar volume In this section we will briefly summarize the models proposed to assess the standard partial molar volume of solute at high temperature and pressure. The standard state partial molar volume or partial molar at infinite dilution of electrolytes, V2o , reflects the solute-

solvent interaction; consequently the behavior of electrolytes and non-electrolytes is expected to be qualitatively different, particularly close to the water critical region where the compressibility diverges. 2.3.2.1 Ionic solutes The standard state partial molar volume or partial molar at infinite dilution of electrolytes, V2o , reflects the solutesolvent interaction and it is additive that is, it is the sum of the anion and cation contributions: V2o = ν +V+o + ν −V−o

(2.71)

Zana and Yeager (1966) measured the individual or absolute ionic partial molar volumes of ions at room temperature using the ultrasonic vibration potentials and they could assign values for the Vio of some ions with an error of ±2 cm3·mol−1, while the uncertainty was higher for others. o Thus, for H+ at 22 °C they found V H+ = −5.4 cm3·mol−1. The assigning of absolute ionic volumes at infinite dilution with uncertainties close to the experimental error commonly achieved for V2o can only be made by using a non-thermodynamic assumption. For instance, Conway et al. (1965) proposed to obtain absolute Vio of anions by using the expression V−o = lim M R N + →0 (VRo4 NX − bM R4 N + ) 4

(2.72)

where MR4N+ is the molar mass of the tetraalkylammonium o cation. This assumption leads to VH+ = −6.2 ± 0.8 cm3·mol−1 at 25 °C. Alternatively, one could assume (Marcus, 1985) that the ratio of the limiting partial molar volume of cation and anion in a reference electrolyte, tetraphenylarsonium tetraphenyl- borate (Ph4AsBPh4), equals the ratio of the corresponding van der Waals volumes: VPho

4 As

vdW

+

o BPh4 −

V

=

VPh

+ 4 As vdW BPh4 −

V

= 1.0337 ± 0.0034

(2.73)

By using this extra-thermodynamic assumption we get o V H+ = −6.7 ± 0.7 cm3·mol−1 at 25 °C. Other reference electrolytes could be chosen, but the partial molar volume of the H+ ion results close to the above-cited values. In order to avoid these non-thermodynamic assumptions in the assigning of ionic partial molar volume at infinite dilution, it is useful to define a conventional V i′o for ions based on the value V H+ ′o = 0 at all temperatures and pressures. The absolute value of the partial molar volumes at infinite dilution of an ion of charge zi at 25 °C can be calculated from the conventional one by means of, Vi o = Vi ′ o + ziVHo +

(2.74)

The calculation of Vio from first principles is not straightforward because this property is related to the ion-water

154


interaction and the volume change of the hydration water around the ion must be taking into account in the model. It is common to consider two main contributions to V oi Vi o = Vi oint + Vi oelec

(2.75)

where V ioint represents the intrinsic partial molar volume and V ioelec the electrostriction partial molar volume. The intrinsic term is related to the non-hydrated part of Vio and it is common (Millero, 1971) to express it as the sum of the crystal volume, (4pNA/3)r3, obtained from the Pauling crystal radii, r, plus a term which accounts for the disorded or void-space volume which is characteristic of ‘structure breaking’ ions. Thus, the following expression is derived Vi oint

4π N A 3 2.52 ( r + a) = 3

(2.76)

where a is a constant related to the disorder in the water hydration layer. Glueckauf (1965) postuled that the void space is a hollow sphere of radius r + a with a = 0.055 nm if one assumes that the void space of an ion with r = rH2O = 0.138 nm is equal to that for pure water. The electrostiction part of V io is calculated from the Born equation (Born, 1920) for the standard partial molar Gibbs free energy of solvation, that is the work to bring an ion from vacuum and introduce it in the bulk of a solvent with dielectric constant e. ∆ hGeo = −

( zi e)2 N A  8πε o



1 1−  ε

(2.77)

where, e is the dielectric constant of the solvent, zi and ri are the ion charge and radius, respectively. The standard partial molar volume can be obtained from Equation (2.77) by calculating the pressure dependence of ∆G eo: Vi ,oe = −

ωi ε2

 ∂ε    ∂p T

(2.78)

where wi = NA(zie)2/(8peori). Helgeson and co-workers (Helgeson and Kirkham, 1974, 1976; Helgeson et al., 1981) developed an equation of state for aqueous electrolytes based on this continuum model. The model, known as HKF, has two contributions to the standard partial volume: an electrostatic part given by Equation (2.78) and the nonelectrostatic part having an intrinsic term, temperature and pressure independent, and a shortrange term related to the electrostriction of water around the ion, equivalent to a change of density and dielectric constant of the continuum near the ion. This last contribution was considered to be dependent on temperature and pressure. The HKF model was modified later (Tanger and Helgeson, 1988; Shock and Helgeson, 1988) in order to extend its range of validity although, as in the original equation of state, the nonelectrostatic parts are treated empirically. The revised electrostatic part is given by equation (2.78) with

ri = ri c + zi ( ki + g (T , p)

(2.79)

where r ic is the crystallographic radius of the ion, and ki is a constant (zero for anions and 0.094 nm for cations). The g(T,p) function, which describes the temperature and pressure dependence of the effective radius, is negative and make an important contribution above 473 K and pressures below 200 MPa. The revised HKF equation for the nonelectrostatic part of the ionic standard partial molar volume is: Vi ,one = a1i +

1  a2i a4 i  +  a3iT +  Φ+ p T −Θ  Φ + p

(2.80)

where Θ = 228 K, Φ = 260 MPa, a1i is the intrinsic volume of the ion, while a2i, a3i and a4i are adjustable parameters. The values of the parameters for several aqueous ions (Shock and Helgeson, 1988) are summarized in Table 2.1 and according to the authors allow calculating partial molar volume of ions up to 723 K and 500 MPa. For ionic species linear correlations were found between a1 and the nonelectrostatic part, V on , of the standard partial molar volume, and between a2 and the nonelectrostatic part, k no, of the compressibility. On the other hand, a linear correlation was observed between a4 and a2, namely a4 = −4.134 a2 − 27790, and a3 could be calculated from the measured standard partial molar volume using Equation (2.80). In case V o were not available, even at ambient temperature and pressure, a correspondence principle was proposed by Shock and Helgeson (Shock and Helgeson, 1988), which correlates the standard ionic partial molar volume with the conventional standard ionic entropy, Vi o = c + dSio

(2.81)

where the parameters c and d are tabulated in Table 2.2 for several ion groups. The standard partial molar volume of any complex ion can be estimated by using the corresponding parameters according to the nature of the species. The revised HFK model is the basis of the SUPCRT92 software (Johnson et al., 1992) widely used by chemists and geochemists. It has proved to be successful for electrolyte, except near the critical point of water. The temperature and pressure dependence of Vo is usually expressed by means of empirical equations such as those used for NaCl and NaOH (Simonson et al., 1994; Corti and Simonson, 2006)

{

T  1 V2o = c1 + κ T p* c2 + c3   + c4    T *  Tx 

}

(2.82)

where Tx = (T/T*) −227, T* = 1 K, p* = 1 MPa, and kT is the isothermal compressibility factor coefficient of water. A similar empirical equation has been proposed to account for the temperature dependence of V o2 with temperature (Pabalan and Pitzer, 1987). In Figures 2.15a and 2.15b we can see the experimental values of V2o for NaOH and HCl as compared to the predictions of the HFK model.


Table 2.1 Revised HKF parameters, entropy and effective radii of aqueous ions (Reproduced from Geochimica et Cosmochimica Acta, Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures with permission from Elsevier) Ion H+ Li+ Na+ K+ Rb+ Cs+ Ag+ NH+4 Mg2+ Ca2+ Sr2+ Ba2+ Pb2+ Ni2+ Co2+ Cu2+ Zn2+ Cd2+ Mn2+ Al3+ F− Cl− Br− I− HO− HS− HSO4− H2PO4− BrO3− ClO3− IO3− ClO4− NO−2 NO3− HCO3− MnO4− CO2− 3 SO2− 4 CrO2− 4 HPO2− 4 PO3− 4

a1 (J·mol−1·bar−1)

a2·10−2 (J·mol−1·K−1)

a3 (J.K.mol−1bar−1)

a4·10−4 (J.K.mol−1)

So (J.K−1.mol−1)

re (nm)

0 −0.0099 0.7694 1.4891 1.7954 2.5720 0.7232 1.6218 −0.3438 −0.0815 0.2958 1.1457 −0.0021 −0.7088 −0.4497 −0.4611 −0.4467 0.0225 0.0425 −1.3976 0.2874 1.6870 2.2045 3.2477 0.5241 2.0969 2.9199 2.7143 2.9127 2.9984 2.3910 3.4062 2.3373 3.0610 3.1639 3.2755 1.1934 3.4732 2.3350 1.5194 −0.2200

0 −0.2887 −9.5603 −6.1629 3.7827 −0.5477 −14.8980 9.8105 −35.9776 −30.3419 −42.4702 −42.0757 −32.6091 −49.8645 −54.3689 −43.8166 −43.4643 −44.8012 −33.5946 −71.5904 5.6851 20.0870 27.5888 34.6270 0.3088 20.8354 38.7387 33.7197 38.5642 40.6558 25.8251 72.4062 24.5135 28.3771 4.8136 47.4228 −16.6703 −8.3034 24.4566 4.5425 −37.9287

0 48.4499 13.6229 22.7396 30.9901 17.6118 29.9132 35.8165 35.1032 22.1606 29.2988 −0.1966 36.8746 43.6568 68.6628 41.2795 41.1410 69.1080 37.2618 62.7242 31.8117 23.2752 19.8527 6.1123 7.7080 14.5453 8.8314 10.8041 8.9004 8.0779 13.9073 −51.1499 14.4227 13.6229 13.6229 5.4182 26.8364 48.4499 14.4449 22.2721 38.9651

0 −11.615 −11.405 −11.347 −11.471 −11.604 −11.011 −12.034 −10.000 −10.373 −9.8726 −9.8879 −10.279 −9.5657 −9.3795 −9.8159 −9.8301 −9.7748 −10.238 −8.6674 −11.862 −11.912 −13.150 −13.058 −11.640 −12.488 −13.229 −13.021 −13.221 −13.308 −12.695 −14.620 −12.640 −12.800 −11.826 −13.588 −10.938 −11.284 −12.638 −11.815 −10.059

0 11.3 58.41 101.0 120 132.8 73.4 111.2 −138 −56.5 −31.5 9.6 17.6 −128.9 −113 −97.1 −109.6 −72.8 −73.6 −316.3 −13.2 56.73 82.8 106.7 −10.71 68.2 125 90.4 161.7 162.3 118.4 182.0 146.9 123.1 98.45 191.2 −50.00 18.8 50 −33 −222

0.308 0.162 0.097 0.227 0.241 0.261 0.220 0.241 0.254 0.287 0.300 0.322 0.308 0.257 0.260 0.260 0.262 0.285 0.268 0.333 0.133 0.181 0.196 0.220 0.140 0.184 0.254 0.218 0.451 0.330 0.251 0.385 0.257 0.297 0.226 0.417 0.287 0.321 0.340 0.293 0.374

Table 2.2 Correspondence principle parameters for the standard ionic partial molar volume (Reproduced from Geochimica et Cosmochimica Acta, Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures with permission from Elsevier) Species Monovalent cations Divalent transition metal Alkaline earth and Pb2+ Rare earth cations and Al3+ Halides Monovalent oxy-anions Divalent oxy-anions

c (cm3·mol−1)

d (cm3·K·J−1)

−20.5 0.0 −14.8 −31.5 1.8 0.0 13.4

0.308 0.220 0.045 0.041 0.308 0.239 0.239

It should be pointed out that the ionic association in NaOH aqueous solutions is important at temperatures above 523 K and the extrapolation of the apparent molar volume in this case was performed using Equation (2.29) for associated electrolytes. The agreement between the experimental V o2 values for NaOH and HCl and those calculated by using the revised HFK model is surprisingly good. As expected, the correlation by Pabalan and Pitzer (1987) does not work so well as the HFK model because it was based on the previous experimental volumetric properties of NaOH which are not as precise as those determined with VTD. The range of temperature and pressure experimentally covered for pVTx properties of aqueous electrolytes usually


vf° (cm 3 ·mol−1)

(a)

25

500

0

0 V2° (cm3 mol-1)

156

–25 –50

-500

-1000

–75 -1500

–100 273 (b)

373

T (K)

473

573

0.2

–100 vf° ( cm3 ·mol−1)

0.4

0.5 0.6 density (gcm-3)

0.7

0.8

0.9

Figure 2.16 Partial molar volume at infinite dilution of: (ⵧ) ionized NaCl; (䊊) NaCl ion pair. (-----) estimation using the revised HFK model.

0 –200 –300 –400 –500 –600 –700 350

0.3

400

450

500 T (K)

550

600

650

Figure 2.15 Standard partial molar volume as a function of temperature at saturation pressure. (a) HCl (–––) experimental (Shargyn and Wood, 1997); (.........) Hershey et al. (1984); (-----) HFK model (Reproduced from The Journal of Chemical Thermodynamics, Volumes and heat capacities of aqueous solutions of hydochloric acid at temperatures from 298.15K to 623K and pressures to 28MPa with permission from Elsevier). (b) NaOH (䊊) experimental (Corti and Simonson, 2006); (.........) Pabalan and Pitzer (1987); (-----) HFK model.

where q = 228 K, and f = 250 MPa., Vi, n1, n2 and a are adjustable coefficients. The range of validity of this equation is for densities above 0.4 g·cm−3. Based on the fluctuation theory of solutions (Kirkwood and Buff, 1951), Brelvi and O’Connell (1971) derived Equation (2.11), where the ratio V2o /koRT, also known as the generalized Krichevskii parameter, Ao, is related to the spatial integral of the infinite dilution solute-solvent direct correlation function C12o , (see Equation 2.11): Ao =

V2o = 1 − C12o κ 1o RT

Cooney and O’Connell (1987) found a correlation between Ao and the reduced density for electrolytes which allow them to estimate the standard partial molar volumes of aqueous salts, Ao = b + a [1 − 7.10 −9 exp ( χ T ) exp (ξρo )]

correspond to densities from 1 g·cm−3 down to 0.57 g·cm−3 (623 K at saturation pressure). Only few accuracy measurements have been performed in the supercritical regime, for NaCl (Majer et al., 1991a; Hynek et al., 1997a), LiCl and NaBr (Majer et al., 1991c) and CsBr (Majer and Wood, 1994). The values of V2o for NaCl in the density range 0.23–0.50 g·cm−3 for both, the ionized salt and the ion pair deviates from the estimations from the SUPCRT92 package (Johnson et al., 1992), as shown in Figure 2.16. The problem with the equations based on the continuum electrostatic Born model is that it predicts an unphysical first coordination shell near the critical point of water (Wood et al., 1994). Indeed, the experimental evidence shows that the behavior of V2o near the critical point of the solvent is determined by the solvent compressibility rather than its dielectric constant (Levelt Sengers, 1991). Plyasunov developed an equation for V o (Plyasunov, 1993) based on the concept of total equilibrium constant (Marshall, 1970) and a nonelectrostatic term similar to that of the HFK model: V2 o = Vi − κ 1o RT ( n1 + n2T ) −

aR (T − θ ) ( p + φ )

(2.83)

(2.84)

(2.85)

where ro is the specific density of pure water, a and b are adjustable parameters, c = 4500 K and x = 0.00588 m3·kg−1. Later, O’Connell et al. (1996) proposed a new correlation, applicable mainly to nonelectrolytes, leading to a revised version of Equation (2.85): Ao =

1 + ρo ( a + b ( exp [0.005ρo ] − 1)) κ 1 ρo RT o

(2.86)

Sedlbauer et al. (2000) observed that Equation (2.86) fails for NaCl at low and high densities. They modified Equation (2.86) introducing a term involving temperature with an additional adjustable parameter, c, and a universal coefficient, q, is able to describe the high-density regime. The lowdensity region could be correlated by using an extra adjustable parameter, d, and another universal parameter, l. To improve the description of the infinite dilution partial molar compressibility the reference volume term was adjusted with a single parameter, d. The final equation for a single ion is, V2o = κ 1o RT + d (Vo − κ 1o RT ) +

κ 1o RT ρo {( a + c(exp [θ T ] + b ( exp [ϑρo ] − 1) + δ ( exp [λρo ] − 1)}

(2.87)


Table 2.3 Test of the different equations for the standard partial molar volume of aqueous ions (Reproduced from Chemical Geology, A new equation of state for correlation and prediction of standard molal thermodynamic properties of aqueous species at high temperatures and pressures with permission from Elsevier) HFK (Eqs. 2.78–2.80)

Simonson (Eq. 2.82)

Plyasunov (Eq. 2.83)

0.44

0.62 397

0.45 254

su (cm3 mol−1)

where d is 0 for aqueous cations and −0.645 m3·kg−1 for aqueous anions, l = −0.01 m3·kg−1, and q = 1500 K, and a, b, c and d are adjustable parameters for each ion. Sedlbauer et al. (2000) tested this equation using newly established database of experimental V2o for 1-1 electrolytes and compare the average value of the ratio ∆/s, where ∆ is the absolute value of the difference between experimental and calculated V o2 and s is the estimated uncertainty of the experimental data, with others equations. The results of such a comparison is shown in Table 2.3, where the unweighted standard deviation of the fit, su, is also shown. This last quantity mainly reflects deviations in the high temperature region where the absolute values of V2o and their uncertainties are very high. 2.3.2.2 Non ionic solutes A classical theory of partial molar volume, the Scaled Particle Theory (SPT) was developed (Pierotti, 1976) to explain the partial molar volume of gases in solvents. The expression for V2o includes the volume of the solute, Vca, a term which accounts for the solute-solvent interaction, Vin, and the term related to the pressure derivative of the hydration free energy: V2o = Vca + Vin + κ o1 RT

(2.88)

Criss and Wood (1996) used the following expression for V2o inspired by the SPT V2o = a1 + a2T + a3κ o1 RT

(2.89)

The HFK correlation was extended to cover inorganic neutral species (Shock et al., 1989), organic species (Shock and Helgeson, 1990; Amend and Helgeson, 1997), and metal complexes (Shock et al., 1997; Sverjensky et al., 1997), which allowed assessing the standard partial molar volume of over 200 species up to 723 K and 500 MPa. In most of the cases the predicted values of V2o up to 500 K agree reasonably well with experimental values performed after the HFK correlations were formulated. However, the revised HFK model does not represent correctly the behavior of nonelectrolytes in the nearcritical and supercritical regions. Wood and co-workers (Hn dkovský and Wood, 1997; O’Connell et al., 1996) discussed the behavior of aqueous CH4, CO2, H2S, NH3 for conditions from ambient up to 704 K and 28 MPa, and H3BO3 up to 725 K and 40 MPa. They observed that the predictions of the revised HFK model are reliable at densities above 0.6 g·cm−3 for H3BO3 and above 0.75 g·cm−3 for H2S, but important deviations are observed near the

Cooney (Eq. 2.85) 1.20 144

Sedlbauer (Eq. 2.87) 0.44 118

Figure 2.17 The temperature dependence of V o2 for some aqueous solutes at 28 MPa (Plyasunov, A.V. and Shock, E.L. (2001). Geochim. Cosmochim. Acta, 65, 3879–3900. With permission from Elsevier).

critical region. We will discuss this regime in detail in the next section. 2.3.2.3 Partial molar volumes near critical conditions The failure of the revised HFK model to predict the standard partial molar volume of electrolytes and nonelectrolytes in the near critical conditions is not unexpected taking into account the effect of the solvent compressibility on V2o near the critical point, as mentioned before, and the limited data set of high temperature data considered in the fit for aqueous nonelectrolytes (Shock et al., 1989). Because the compressibility of pure water has a singularity at the critical point, Equation (2.11) predicts that the standard partial molar volume should diverge in the critical point. The sign of the critical divergence, determined by the o spatial integral of the direct correlation function, C 12 , depends on the nature of the solute-solvent interaction. Figure 2.17 shows that the standard partial molar volume is negative for nonvolatile strong electrolytes and becomes increasingly positive for volatile nonelectrolytes with decreasing polarity. Wheeler (1972) resorted for the first time to the relationship ∂p ∂p  ∂V  V2o = V1 −    m  = V1 1 + κ 1o     ∂x  TV  ∂p  T  ∂x  TV  

(2.90)

to analyze the critical behavior of V2o . He pointed out that when there is a repulsion between solute and solvent, the addition of solute at constant volume will cause an increase of pressure, and due to the critical divergence of the compressibility, the volume must increase dramatically to bring the pressure back to the initial value. On the other hand the

158


opposite is valid in the case that solute and solvent attract each other. According to Krichevskii (1967) this derivative is well behaved at the critical point of the solvent, and its value can be calculated from the derivatives (∂p/∂T)ccrl and (∂T/∂x)ccrl taken along the critical line of the mixture and (∂p/∂T)cs along the coexistence curve of the pure solvent. Thus, both the fluctuation theory (Equation 2.11) and the classical thermodynamics (Equation 2.90) predict that the divergence of V o2 is determined by the solvent’s compressibility, while their sign and amplitude depends on the solute–solvent o interactions described by the integral C 12 or the Krichevskii o parameter (∂p/∂x)T,V . Fernandez-Prini and Japas (1994) analyzed the effect of the intermolecular parameters upon V o2 . They showed that the sign of V o2 changes with solvent density, and at low density becomes more negative for bigger solutes. On the other hand, the limiting expression of the Krichevskii parameter for low density is Japas et al. (1998). ∂p lim ρo → 0   = ρo2 2 RT ( B12 − B11 )  ∂x  TV

(2.91)

The generalized Krichevskii parameter or its equivalent, the o direct correlation function integral, C 12 , is well behaved in the critical region, as shown in Figure 2.18, and on this is based Equation (2.85) (O’Connell et al., 1996), which was used to fit the standard partial molar volume of nonelectrolytes all over the density range. The results are shown in Figure 2.19a–b for H2S and H3BO3 in comparison with the predictions of the revised HFK model. For H2S, as well as for CH4, CO2, and NH3, the five parameters HFK model renders to values of ∆/s more than three times that of Equation (2.85) with only two parameters. The fit for H3BO3 has almost identical deviations for both models. Plyasunov et al. (2000) have proposed a semitheoretical expression for V o2 based on the fluctuation theory of solution which included the second virial coefficient, B12, to give a rigorous expression in the low density region. The equation, limited to solutes for which B12 is known or can be estimated, has the form:

V2o = NV1o + κ o1 RT (1 − N ) + ρ ( 2Ω { B (T ) − NB (T )} o 12 11  a exp ( −c1ρo ) +  5 + b ( exp [c2 ρo ] − 1)  T  

(2.92)

where Ω = 55.51.10−6 mol·kg−1, N, a, and b are adjustable parameters, c1 = 0.0033 m3·kg−1, and c2 = 0.002 m3 kg−1. The expression for B12 includes the collision diameter s12 and the depth of the potential well, e12/kB. At the limit of low densities Equation (2.92) becomes, V2o = NV1o + κ o1 RT [(1 − N ) + ρo ( 2Ω { B12 (T ) − NB11 (T )}] (2.93) About 300 experimental points for V o2 were used in the correlation over the temperature and pressure range 283 K < T < 705 K and 0.1 MPa < p < 35 MPa. The three adjustable parameters, N, a and b were tabulated for organic and inorganic nonelectrolytes, although a linear correlation was found between a and (B12-NB11). Equation (2.92) has been found to describe V o2 of aqueous nonelectrolytes much better than the revised HFK model and Equation (2.86), except for

Figure 2.18 Direct correlation function integral as a function of density for: (䊊) CH4; (䊉) CO2; (ⵧ) H2S: (䊏) NH3. (Hn dkovský, L. and Wood, R.H. (1997). J. Chem. Thermod., 29, 731–747 with permission of Elsevier).

Figure 2.19 V o2 of: (a) H2S at p = 20 MPa; (b) H3BO3 at p = 28 MPa (Reprinted with permission from O’Connell, J.P., Sharygin, A.V. and Wood, R.H. Ind. Eng. Chem. Res., 35, 2808–2812. Copyright 1996 American Chemical Society).


a few solutes (propanoic acid, 1,4-butanediamine, 1,6hexanediamine, 1,4-butanediol and 1,6-hexanediol). In Figure 2.20 the comparison of the model results and experimental V o2 values (Biggerstaff and Wood, 1988) are shown for Xe at temperatures from 300 to 716 K and pressures between 20 and 35 MPa. The correlation equations for V o2 are based on the revised HFK model, the semiempirical equations using the compressibility of water, as Equation (2.89), and the model proposed by Harvey et al. (1991): V2o = a + aT T − ωκ o1

(2.94)

and Equations (2.86) and (2.87) based on the fluctuation theory were tested by Majer et al. (1999) using data of aqueous hydrocarbons (benzene, toluene, cyclohexane and hexane) at infinite dilution up to 623 K and 30 MPa. As an example, Table 2.4 shows the results for benzene and cyclohexane, mp being the total number of adjustable parameters. The number in parenthesis in the third and fourth columns indicates the number of ill-conditioned parameters, that is, the number of parameters whose uncertainties are larger than their absolute values. The results indicates that the HKF model gives the worst results, being the pressure dependent terms in Equation (2.80) redundant (the correlation is better taking a2 = a4 = 0). Equations based on water compressibility improve the correlation and yield to similar

standard deviation, the performance of the two parameters Equation (2.86) by O’Connell et al. (1996), being remarkable where the parameter a is always ill-conditioned. Equation (2.87) proposed by Sedlbauer et al. (2000) was used in a simplified 3-parameter form, namely V2o = Vo + κ o1 RT ρo {a + b ( exp [ϑρo ] − 1) + c exp [θ T ]} (2.95) As occurred with electrolytes (see Table 2.3), the simplified version of Equation (2.87) lead to excellent correlation with the available experimental data of aqueous hydrocarbons. The correlation strategy of the revised HKF model for aqueous nonelectrolytes was reanalyzed by Plyasunov and Shock (Plyasunov and Shock, 2001) to incorporate a large body of experimental values of V2o published during the 1990s. The new set of experimental data include now nonpolar compounds (CH4, Ar, Xe, cyclohexane), polar compounds (NH3, alcohols, monocarboxilic acids, amides, boric acid and glycine). The authors concluded that the new formulation can be used along the saturation vapor-liquid curve in the density region sufficiently remote from the critical point, around 630 K. at densities above 0.5–0.6 g·cm−3 the range of applicability for nonelectrolytes may extend up to higher temperatures. At temperatures up to 500 K at pressures up to 50 MPa, the revised HFK model gives an excellent description of V2o , except in the narrow temperature range below 280–290 K. 2.4 pVTx DATA FOR HYDROTHERMAL SYSTEMS This section summarizes all the experimental information available on the volumetric properties of hydrothermal systems, mainly above 200 °C, although some results for reported on aqueous systems above 100 °C are also included in Table 2.5. 2.4.1 Laboratory activities

Figure 2.20 Predicted (solid line) and experimental (䊉) values of V 2o for Xe at 35 MPa. (Plyasunov, A.V., O’Connell, J.P. and Wood, R.H. (2000). Geochim. Cosmochim. Acta,64, 495–512. With permission from Elsevier). Table 2.4 Test of equations for correlating V o2 of aqueous hydrocarbons (Reproduced from Fluid Phase Equilibria, temperature correlation of partial molar volumes of aquaeous hydrocarbons at infinite dilution: test of equations with permission from Elsevier). Model

mp

Benzenea

Cyclohexanea

HFK HFKb Eq. (2.88) Eq. (2.93) Eq. (2.85) Eq. (2.94)

5 3 3 3 2 3

13.4 (4) 14.0 (0) 4.9 (1) 4.0 (0) 3.1 (1) 1.5 (0)

19.4 (4) 16.4 (0) 7.4 (0) 6.4 (0) 6.5 (1) 2.7 (1)

(a)

Standard deviation in cm3·mol−1;

(b)

a2 = a4 = 0 in Equation (2.80).

Observing Table 2.5 one can conclude that most of the volumetric properties of hydrothermal systems were determined by a reduced number of research groups. It follows a brief description of the main contributions of these groups to the pVTx data of hydrothermal systems. At the end of the 1960s the only reported data for hydrothermal systems were those of Ellis for electrolytes and Franck for non-electrolytes. Ellis, in New Zealand, used a piezometer to determine the partial molar volume of several 1 : 1 and 1 : 2 electrolytes up to 200 °Cand 2 MPa, most of the cases in the concentration range 0.1 to 1.0 mol·kg−1 (errors in the densities are considered ±0.005%). Therefore, the extrapolation to infinite dilution was not very precise but the data were the first on ionic species above 100 °C after the pioneering density measurements of aqueous electrolytes by Noyes and co-workers at the beginning of the twentieth century. Noyes also performed the first measurements of electrical conductivity at high temperature and the specific volume determinations (with an accuracy ±0.2– 0.5%) were done with the conductivity cell.

w m m m m

m

m m w m w m x

m m w m m m m

silver nitrate

arsenious acid

arsenic acid

barium chloride barium chloride

barium chloride

barium chloride barium nitrate

barium nitrate

calcium chloride

calcium chloride calcium chloride calcium chloride

calcium chloride calcium chloride

calcium chloride

calcium chloride

calcium chloride

calcium chloride

calcium chloride

AgNO3

As(OH)3

AsO(OH)3

BaCl2 BaCl2

BaCl2

BaCl2 Ba(NO3)2

Ba(NO3)2

CaCl2

CaCl2 CaCl2 CaCl2

CaCl2 CaCl2

CaCl2

CaCl2

CaCl2

CaCl2

CaCl2

3 c

2

1

Binary systems – electrolytes silver nitrate AgNO3

Chemical names

Formula

unit

pVTx properties of hydrothermal systems

Nonaqueous components

Table 2.5

0.3

0.24

0.225

0.015

0.010

0.50 0.022

0.10 0.050 0.014

0.25

0.005

0.097 0.05

0.0093

0.10 0.097

0.1

0.1

0.02

0.025

4

min

2.0

6.15

3.23

6.4

0.20

6.4 0.19

1.0 0.33

3.0

0.08

0.90 0.1

1.60

1.0 0.90

0.6

0.3

0.92

0.10

5

max

Concentration (c, m, v, w, x)

388

25

350

50

25

50 25

20 50 238

25

25

17 218

15

50 75

298

298

222

218

6

min

465

250

370

324

350

200 301

300 200 388

340

325

300 306

140

200 300

624

624

306

7

max

Temp-re (°C)

Crit.

7.1

15

0.10

2

2 9.9

10 2 10

Sat

0.003

2.00 Sat

0.10

2 0.30

0.1

0.1

Sat

Sat

8

min

42

22

40

30

79

60

150

50

40

20

40

30

30

9

max

Pressure (MPa)

d

Vs

d

dd.Vf.Vo

dd.Vf

dd

d

d Vs.Vf

d d.Vf.Vo Vs.Vf

d

d

d Vs

dd.Vf.Vo

d.Vf.Vo d.Vf

dd.Vf.Vo

dd.Vf.Vo

10

Exper’tal data

SFIT

VTD

VTD

VTD

VVP

VVP CVP

VVP VVP PYC

VVP

CVP

CVP PYC

VTD

VVP CVP

VTD

VTD

PYC

PYC

11

Technique

Noyes et al. (1910) Campbell et al. (1954) Perfetti et al. (2008) Perfetti et al. (2008) Ellis (1967) Azizov & Akhundov (1994) Puchalska & Atkinson (1994) Azizov (2003) Noyes et al. (1910) Akhundov et al. (1988a) Rodnianski et al. (1962) Polyakov (1965) Ellis (1967) Ketsko & Valyashko (1986) Kumar (1986b) Tsay et al. (1988) Pepinov et al. (1988) Gates & Wood (1989) Crovetto et al. (1993) Oakes et al. (1995b) Oakes et al. (1995a)

12

Reference

r-CaCl2-11.1

r-CaCl2-10.1

r-CaCl2-9.1

r-CaCl2-8.1

r-CaCl2-7.1

r-CaCl2-5.1 r-CaCl2-6.1

r-CaCl2-2.1 r-CaCl2-3.1 r-CaCl2-4.1

r-CaCl2-1.1

r-Ba(NO3)2-2.1

r-BaCl2-3.1 r-Ba(NO3)2-1.1

r-BaCl2-1.1 r-BaCl2-2.1

r-AsO(OH)3-1.1

r-As(OH)3-1.1

r-AgNO3-2.1

r-AgNO3-1.1

13

Table code for Appendix


calcium nitrate

calcium nitrate

calcium nitrate

decyltrimethylammonium bromide dodecyltrimethylammonium bromide cesium bromide

cesium chloride cesium chloride

gadolinium triflate

potassium bromide potassium bromide

potassium bromide

potassium bromide

potassium bromide

potassium bromide

potassium carbonate

potassium carbonate

potassium chloride

potassium chloride

Ca(NO3)2

Ca(NO3)2

Ca(NO3)2

C13H30NBr

CsCl CsCl

Gd(CF3SO3)3

KBr KBr

KBr

KBr

KBr

KBr

K2CO3

K2CO3

KCl

KCl

CsBr

C15H34NBr

m

calcium chloride

CaCl2

c

c

w

m

m

w

w

w

m m

m

m m

m

m

m

w

w

m

3

2

1

unit

Chemical names

Formula


0.01

0.01

0.025

0.25

0.24

0.020

0.093

0.019

0.10 0.10

0.029

0.1 1.0

0.0024

0.011

0.0078

0.042

0.30

0.25

0.18

4

min

0.1

0.1

0.50

3.0

2.24

0.048

0.37

0.36

1.0 1.5

0.72

0.4 9.0

0.50

1.02

0.97

0.20

0.41

3.0

6.0

5

max


218

305

25

25

25

25

25

25

50 40

100

25 204

331

74

74

25

25

25

25

6

min

306

306

300

340

355

325

325

350

200 280

200

200 874

452

176

176

325

325

340

125

7

max

Temp-re (°C)

Sat?

Sat?

Sat.

Sat

2

0.1

0.1

10

2 10

7.1

2 50

18

0.9

1

4.2

1.3

Sat

0.1

8

min

30

40

40

150

26

150

33

33.4

33.4

20

49

60

9

max

Pressure (MPa)

dd

dd

d

d

d

d.Vf.Vo

Vs

Vs

d

d

d

d

d

d

d.Vf.Vo Vs

d.Vf.Vo

d.Vf.Vo Vf

dd.Vf.Vo

10

Exper’tal data

PYC

PYC

HWT

VVP

CVP

CVP

CVP

HWT

VVP PYC

VTD

VVP CVP

VTD

VTD

VTD

CVP

CVP

VVP

CVP

11

Technique

Safarov et al. (2005b) Rodnianski et al. (1962) Akhundov et al. (1989a) Akhundov et al. (1989b) Archer et al. (1988) Archer et al. (1988) Majer & Wood (1994) Ellis (1966) Egorov & Ikornikova (1973) Xiao et al. (1999) Ellis (1968) Gorbachev et al. (1974a) Feodorov & Zarembo (1983) Akhundov et al. (1984b) Akhundov et al. (1986b) Abdulagatov & Azizov (2006a) Rodnianski et al. (1962) Kurochkina (1972) Noyes & Coolidge (1903) Noyes et al. (1910)

12

Reference

r-KCl-2.1

r-KCl-1.1

r-K2CO3-2.1

r-K2CO3-1.1

r-KBr-6.1

r-KBr-5.1

r-KBr-4.1

r-KBr-3.1

r-Gd(CF3SO3)3-1.1; 1.2 r-KBr-1.1 r-KBr-2.1

r-CsCl-1.1 r-CsCl-2.1

r-CsBr-1.1

r-Ca(NO3)2-3.1

r-Ca(NO3)2-2.1

r-Ca(NO3)2-1.1

13



Continued

Chemical names

2

potassium chloride

potassium chloride potassium chloride

potassium chloride

potassium chloride potassium chloride potassium chloride


potassium chloride

potassium chloride

potassium chloride

potassium chloride

potassium chloride


potassium chloride

potassium chloride

potassium chloride

potassium chloride

Formula

1

KCl

KCl KCl

KCl

KCl KCl KCl

KCl KCl

KCl

KCl

KCl

KCl

KCl

KCl KCl

KCl

KCl

KCl

KCl


Table 2.5

x

m

m

w

w w

w

w

m

w

m

c m

w m w

m

w c

w

3

unit

3.0

1.02

0.049

0.23

0.20

0.57

0.21

1.5

1.0

1.0 0.20

3.0

0.78 3.0

0.45

5

max

Concentration

0.0024

0.25

0.099

0.020

0.095 0.18

0.20

0.050

0.006

0.012

0.0010

0.058 0.25

0.10 0.1 0.01

0.25

0.49 1.0

0.36

4

min


388

350

25

25

22 25

300

25

187

25

40

25 40

20 25 100

25

250 25

100

6

min

300

325

325 325

700

350

411

350

280

370 280

300 200 440

340

550 340

200

7

max

Temp-re (°C)

17

79

40

40 40

300

30

150

39

150

22

9

max

Pressure

Crit.

15

9.9

0.1

0.1 0.1

100

2

Sat.

10

10

Sat. 7.5

10 2 0.1

Sat

2.4 Sat.

Sat.

8

min

Pressure (MPa)

10

d

dd.Vf

d.Vf

d

d d

d

d

d

d

Vs

d Vs

d d.Vf.Vo d

d.Vf

Vs d

d

Exper’tal data

CVP

VTD

CVP

CVP

CVP CVP

SFIT

VVP

PYC

HWT

PYC

XRD PYC

VVP VVP γRD

VVP

VVP VVP

PYC

11

Technique

Akhumov & Vasil’ev (1932) Benedict (1939) Rodnianski & Galinker (1955) Rodnianski et al. (1962) Polyakov (1965) Ellis (1966) Khaibullin & Borisov (1966) Bell et al. (1970) Gorbachev et al. (1971) Gorbachev et al. (1974b) Egorov et al. (1976) Potter et al. (1976) Pepinov et al. (1984) Bodnar & Sterner (1985) Imanova (1985) Imanova et al. (1985) Akhundov et al. (1986b) Tsay et al. (1986a) Crovetto et al. (1993) Abdulagatov et al. (1998a)

12

Reference

r-KCl-22.1

r-KCl-21.1

r-KCl-20.1

r-KCl-19.1

r-KCl-17.1 r-KCl-18.1

r-KCl-16.1

r-KCl-15.1; 15.2

r-KCl-14.1; 14.2

r-KCl-13.1

r-KCl-12.1

r-KCl-10.1 r-KCl-11.1

r-KCl-7.1 r-KCl-8.1 r-KCl-9.1

r-KCl-6.1

r-KCl-4.1 r-KCl-5.1

r-KCl-3.1

13



w m m m w w m

potassium chromate

potassium fluoride potassium fluoride

potassium fluoride

potassium iodide potassium iodide

potassium iodide

potassium iodide

potassium iodide

potassium nitrate

potassium nitrate potassium nitrate

potassium nitrate

potassium nitrate

potassium nitrate

potassium hydroxide

potassium hydroxide

potassium hydroxide

potassium hydroxide

potassium sulphate

potassium sulphate potassium sulphate

K2CrO4

KF KF

KF

KI KI

KI

KI

KI

KNO3

KNO3 KNO3

KNO3

KNO3

KNO3

KOH

KOH

KOH

KOH

K2SO4

K2SO4 K2SO4

m w

c

w

w

m

w

w

w

m m

m

m w

m

3

2

1

unit

Chemical names

Formula


0.050 0.050

0.025

0.024

0.054

0.087

0.045

0.096

0.050

0.050

0.10 0.10

0.25

0.020

0.18

0.014

0.10 0.10

0.01

0.10 0.050

0.25

4

min

0.50 0.35

0.050

0.50

0.6

2.7

0.99

0.94

0.20

0.90

1.0 1.5

3.0

0.49

0.42

0.57

1.0 1.5

3.0

1.0 0.20

3.0

5

max

(c, m, v, w, x)

50 397

200

306

300

−20

218

300

250

400

300

350

350

200 280

340

325

325

350

200 280

354

200 325

340

7

max

0

55

0

18

20

25

50 40

25

25

25

25

50 40

25

50 25

25

6

min

Temp-re (°C)

2 60

Sat.

5.0

5.0

0.1

Sat.

2.1

1.5

Sat.

2 10

Sat

0.1

0.1

10

2 10

10

2 0.1

Sat

8

min

150

59

59

4.8

40

30

40

40

150

31

40

9

max

(MPa)

d.Vf.Vo d

d

d.Vf.Vo Vs

Vs

sv

sv

d.Vf.Vo

d

d.Vo

d

d

d.Vf.Vo Vs

d

d

d

d

d.Vf.Vo Vs

dd.Vf.Vo

10

Exper’tal data

VVP PYC

PYC

EP

EP

VTD

HWT

HWT

CVP

HWT

VVP PYC

VVP

CVP

CVP

HWT

VVP PYC

VTD

VVP CVP

VVP

11

Technique

Rodnianski et al. (1962) Ellis (1968) Guseynov et al. (1990) Majer et al. (1997) Ellis (1968) Gorvachev et al. (1974a) Feodorov & Zarembo (1983) Akhundov et al. (1985b) Akhundov et al. (1986b) Rodnianski et al. (1962) Ellis (1968) Gorvachev et al. (1974a) Puchkov et al. (1979a) Traktuev & Ptitzina (1989) Domanin et al. (1998) Mashovets et al. (1965) Corti et al. (1990) Tsatsuryan et al. (1992) Alexsandrov & Tsatsuryan (1995) Noyes et al. (1910) Ellis (1968) Ravich & Borovaya (1971a)

12

Reference

r-K2SO4-2.1 r-K2SO4-3.1

r-K2SO4-1.1

r-KOH-4.1

r-KOH-3.1

r-KOH-2.1

r-KOH-1.1

r-KNO3-6.1

r-KNO3-5.1

r-KNO3-4.1

r-KNO3-2.1 r-KNO3-3.1

r-KNO3-1.1

r-KI-5.1

r-KI-4.1

r-KI-3.1

r-KI-1.1 r-KI-2.1

r-KF-3.1

r-KF-1.1 r-KF-2.1

r-K2CrO4-1.1

13



Continued

Chemical names

2

potassium sulphate

potassium sulphate

potassium sulphate

potassium sulphate lithium bromide

lithium bromide

lithium bromide lithium bromide lithium chloride

lithium chloride lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

Formula

1

K2SO4

K2SO4

K2SO4

K2SO4 LiBr

LiBr

LiBr LiBr LiCl

LiCl LiCl

LiCl

LiCl

LiCl

LiCl

LiCl

LiCl

LiCl


Table 2.5

m

m

w

w

m

w

m

m m

w w c

w

m w

m

w

w

3

unit

15.5

3.0

0.20

0.20

3.0

0.43

9.0

1.0 1.5

0.4 0.6 3.0

0.20

0.41 0.55

0.50

0.10

0.50

5

max

Concentration

0.13

0.0025

0.047

0.010

0.051

0.017

1.0

0.1 0.0010

0.3 0.45 1.0

0.060

0.066 0.016

0.0048

0.011

0.050

4

min


17

331

25

25

48

25

212

25 40

25 25 25

25

20 25

25

25

300

6

min

335

452

325

350

277

350

720

200 280

325 202 340

325

300 350

400

300

500

7

max

Temp-re (°C)

31

38

40

30

33

150

150

40

40

38 150

31

150

9

max

Pressure

0.1

18.5

0.1

2

0.76

10

50

2 10

0.1 1.0 Sat.

0.1

2.2 10

9.9

Sat

30

8

min

Pressure (MPa)

d

Vs

d.Vf

dd.Vf

d

d

dd.Vf.Vo

d

Vf

d.Vf.Vo Vs

d d d

d

d d

dd.Vf.Vo

10

Exper’tal data

CVP

VTD

CVP

VVP

VTD

HWT

CVP

VVP PYC

CVP Pyc VVP

CVP

CVP HWT

VTD

HWT

PYC

11

Technique

Ravich & Borovaya (1971b) Puchkov et al. (1976) Obsil et al. (1997; 1997a) Azizov (1998) Feodorov & Zarembo (1983) Akhundov et al. (1990) Abdullaev (1990) Lee et al. (1990) Rodnianski & Galinker (1955) Ellis (1966) Gorvachev et al. (1974b) Egorov & Ikornikova (1973) Egorov et al. (1975) Majer et al. (1989a) Pepinov et al. (1989) Abdullaev et al. (1990) Majer et al. (1991c) Abdulagatov & Azizov (2006b)

12

Reference

r-LiCl-10.1

r-LiCl-9.1

r-LiCl-8.1

r-LiCl-7.1

r-LiCl-6.1

r-LiCl-5.1

r-LiCl-4.1

r-LiCl-2.1 r-LiCl-3.1

r-LiBr-3.1 r-LiBr-4.1 r-LiCl-1.1

r-LiBr-2.1

r-K2SO4-7.1; 7.2; 7.3 r-LiBr-1.1

r-K2SO4-6.1

r-K2SO4-5.1

r-K2SO4-4.1; 4.2

13



m w w

w m

m

m

w

m w m m

w c w

lithium iodide

lithium iodide

lithium iodide

lithium iodide lithium nitrate

lithium nitrate

lithium nitrate

lithium nitrate

lithium nitrate

lithium hydroxide

lithium sulphate

lithium sulphate

magnesium chloride

magnesium chloride magnesium chloride

magnesium chloride

magnesium chloride

magnesium nitrate

magnesium sulphate

magnesium sulphate

LiI

LiI

LiI

LiI LiNO3

LiNO3

LiNO3

LiNO3

LiNO3

LiOH

Li2SO4

Li2SO4

MgCl2

MgCl2 MgCl2

MgCl2

MgCl2

Mg(NO3)2

MgSO4

MgSO4

w

m

m

w

w

3

2

1

unit

Chemical names

Formula


0.10

0.050

0.050

0.11

0.0050

0.10 0.050

0.42

0.094

0.0062

0.38

0.30

0.18

0.40

0.052

0.11 0.007

0.091

0.050

0.013

4

min

0.40

1.04

3.0

1.0 0.15

0.57

0.89

0.21

3.1

7.8

1.7

0.90

0.41

4.88 0.67

3.1

0.59

5

max

(c, m, v, w, x)

20

218

25

18

96

50 25

100

25

25

55

25

19

25

25

25 25

25

25

25

6

min

300

325

300

354

200 300

200

300

300

250

125

300

350

300

125 110

327

325

350

7

max

Temp-re ( C)

10

Sat.

0.1

0.94

10

2 2

Sat.

5

Sat.

0.1

0.1

2.0

Sat.

Sat.

0.1 Sat.

2.0

0.1

10

8

min

150

49

40

31

30

4.0

4.8

60

40

60

31

40

150

9

max

(MPa)

d,Vf,Vo d

d

d.Vf.Vo

d

d.Vf.Vo

d.Vf

d

d

d

d.Vf.Vo d

d.Vf

d

d

d

Vs

d

d,Vo

dd,Vf,Vo

10

Exper’tal data

VVP

PYC

CVP

CVP

VTD

VVP VVP

PYC

CVP

HWT

VTD

CVP

CVP

HWT

HWT

CVP PYC

CVP

CVP

HWT

11

Technique

Feodorov & Zarembo (1983) Abdullaev et al. (1991) Abdulagatov & Azizov (2004b) Safarov (2006) Campbell et al. (1955) Puchkov & Matashkin (1970) Puchkov et al. (1979b) Abdulagatov & Azizov (2004a) Safarov et al. (2005a) Corti et al. (1990) Puchkov et al. (1976) Abdulagatov & Azizov (2003a) Akhumov & Vasil’ev (1932, 1936) Ellis (1967) Pepinov et al. (1992) Obsil et al. (1997b) Azizov & Akhundov (1998) Akhundov et al. (1989c) Noyes et al. (1910) Polyakov (1965)

12

Reference

r-MgSO4-2.1

r-MgSO4-1.1

r-Mg(NO3)2-1.1

r-MgCl2-5.1

r-MgCl2-4.1

r-MgCl2-2.1 r-MgCl2-3.1

r-MgCl2-1.1

r-Li2SO4-2.1; 2.2

r-Li2SO4-1.1

r-LiOH-1.1

r-LiNO3-3.1; 3.2

r-LiNO3-2.1

r-LiNO3-1.1

r-LiI-3.1; 3.2

r-LiI-2.1

r-LiI-1.1

13



Continued

m w m

m w w m

magnesium sulphate

magnesium sulphate

magnesium sulphate

ammonium chloride ammonium chloride

ammonium chloride

ammonium perchlorate ammonium nitrate

sodium borate

sodium borate

sodium bromide

sodium bromide

sodium bromide

sodium bromide

sodium triflate

sodium carbonate

sodium carbonate

MgSO4

MgSO4

MgSO4

NH4Cl NH4Cl

NH4Cl

NH4ClO4 NH4NO3

NaB(OH)4

NaB(OH)4

NaBr

NaBr

NaBr

NaBr

NaCF3SO3

Na2CO3

Na2CO3

m

w

m

m

m

m

w

m

m m

3

2

1

unit

Chemical names

Formula


Table 2.5

0.99

0.20

1.68

4.9

3.0

3.0

0.44

1

0.19

1.0 0.89

6.0

1.0 5.0

0.84

0.10

0.25

5

max

Concentration

0.10

0.051

0.045

0.21

0.0025

0.050

0.022

0.12

0.051

0.010 0.0080

0.10

0.010 0.50

0.084

0.010

0.072

4

min


25

25

10

100

331

49

25

25

25

50 180

25

50 143

18

25

21

6

min

350

300

327

249

452

277

350

302

300

200 180

350

200 581

175

175

203

7

max

Temp-re (°C)

28

20

30

38

32

150

79

28

150

40

30

10

9

max

Pressure

10

Sat.

0.1

10

18

8.4

10

9.9

Sat.

2 Sat

9.9

2 50

2.1

2

2.1

8

min

Pressure (MPa)

d,Vf,Vo Vf

d,Vo

d

d,Vf,Vo

dd,Vf

d

dd,Vf,Vo

dd,Vf

dd,Vf

dd,Vf,Vo

d

Vs,Vo

d

d,Vf,Vo d

dd,Vf,Vo

10

Exper’tal data

VTD

HWT

VTD

VTD

VTD

VTD

HWT

CVP

HWT

VVP PYC

VTD

VVP CVP

CVP

VVP

VVP

11

Technique

Phutela & Pitzer (1986) Pepinov et al. (1992) Azizov & Akhundov (1997) Ellis (1968) Egorov & Ikornikova (1973) Sharygin & Wood (1996) Ellis (1968) Campbell et al. (1954) Mashovets et al. (1974) Alekhin et al. (1993b) Feodorov & Zarembo (1983) Majer et al. (1989b) Majer et al. (1991c) Hakin et al. (2000) Xiao & Tremaine (1997) Puchkov & Kurochkina (1972) Sharygin & Wood (1998)

12

Reference

r-Na2CO3-2.1

r-Na2CO3-1.1

r-NaCF3SO3-1.1

r-NaBr-4.1

r-NaBr-3.1

r-NaBr-2.1

r-NaBr-1.1

r-NaB(OH)4-2.1

r-NaB(OH)4-1.1

r-NH4ClO4-1.1

r-NH4Cl-3.1

r-NH4Cl-1.1 r-NH4Cl-2.1

r-MgSO4-5.1

r-MgSO4-4.1

r-MgSO4-3.1

13



Chemical names

2

sodium carbonate

sodium acetate

sodium propionate

disodium tartrate sodium benzenesulfonate

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride sodium chloride sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride sodium chloride

Formula

1

Na2CO3

NaC2O2H3

NaC3O2H5

Na2C4O6H4 NaC6H5O3S

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl NaCl NaCl

NaCl

NaCl

NaCl

NaCl

NaCl NaCl


w w

m

w

m

w

w m w

m

c

w

w

w

c

c

m m

m

m

w

3

unit

0.10 0.010

1.0

0.020

0.0010

0.010

0.010 0.1 0.010

0.5

1.0

0.002

0.0012

0.28

0.002

0.002

0.043 0.12

0.12

0.12

Hydrothermal Properties of Materials: Experimental Data on Aqueous Phase Equilibria and Solution Properties at Elevated Temperatures and Pressures

Electronic properties of materials

Concrete: Microstructure, Properties, and Materials

Electronic properties of materials

Electronic properties of materials

Thermophysical Properties of Materials

Thermophysical Properties of Materials

Thermophysical Properties of Materials

Electrical properties of materials

Thermophysical Properties of Materials

Gear Materials, Properties, and Manufacture

Phase equilibria, phase diagrams and phase transformations

Electroceramics: Materials, Properties, Applications

Fundamentals of Semiconductors: Physics and Materials Properties

Colour and The Optical Properties of Materials

The Structure and Properties of Ferromagnetic Materials

Water-Soluble Polymers : Solution Properties and Applications

Water Soluble Polymers - Solution Properties and Applications

Materials with Rheological Properties

Electroceramics: Materials, Properties, Applications

Electroceramics: Materials, Properties, Applications

Mechanical Properties of Engineered Materials

Mechanical Properties Of Engineered Materials

Photovoltaic Materials (Series on Properties of Semiconductor Materials Vol 1)

Ceramic Materials: Processes, Properties and Applications

NANOSTRUCTURED MATERIALS Processing Properties and Potential Applications

Nanoporous Materials: Types, Properties and Uses

Ion Exchange Materials: Properties and Applications

Multifunctional Polycrystalline Ferroelectric Materials: Processing and Properties

Monolithic Materials: Preparation, Properties and Applications

Concrete Materials: Properties, Specifications and Testing

Hydrothermal Properties of Materials: Experimental Data on Aqueous Phase Equilibria and Solution Properties at Elevated Temperatures and Pressures

Electronic properties of materials

Concrete: Microstructure, Properties, and Materials

Electronic properties of materials

Electronic properties of materials

Thermophysical Properties of Materials

Thermophysical Properties of Materials

Thermophysical Properties of Materials

Electrical properties of materials

Thermophysical Properties of Materials

Gear Materials, Properties, and Manufacture

Phase equilibria, phase diagrams and phase transformations

Electroceramics: Materials, Properties, Applications

Fundamentals of Semiconductors: Physics and Materials Properties

Colour and The Optical Properties of Materials

The Structure and Properties of Ferromagnetic Materials

Water-Soluble Polymers : Solution Properties and Applications

Water Soluble Polymers - Solution Properties and Applications

Materials with Rheological Properties

Electroceramics: Materials, Properties, Applications

Electroceramics: Materials, Properties, Applications

Mechanical Properties of Engineered Materials

Mechanical Properties Of Engineered Materials

Photovoltaic Materials (Series on Properties of Semiconductor Materials Vol 1)

Ceramic Materials: Processes, Properties and Applications

NANOSTRUCTURED MATERIALS Processing Properties and Potential Applications

Nanoporous Materials: Types, Properties and Uses

Ion Exchange Materials: Properties and Applications

Multifunctional Polycrystalline Ferroelectric Materials: Processing and Properties

Monolithic Materials: Preparation, Properties and Applications

Concrete Materials: Properties, Specifications and Testing

Recommend Documents