Frontiers in Geofluids

FRONTIERS IN GEOFLUIDS Edited by

Bruce Yardley, Craig Manning and Grant Garven

A John Wiley & Sons, Ltd., Publication

Frontiers in Geofluids

FRONTIERS IN GEOFLUIDS Edited by

Bruce Yardley, Craig Manning and Grant Garven

A John Wiley & Sons, Ltd., Publication

This edition first published 2011 © 2011 by Blackwell Publishing Ltd Originally published as Volume 10, Numbers 1–2 of Geofluids Blackwell Publishing was acquired by John Wiley & Sons in February 2007. Blackwell’s publishing program has been merged with Wiley’s global Scientific, Technical and Medical business to form Wiley-Blackwell. Registered Office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Offices 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 111 River Street, Hoboken, NJ 07030-5774, USA 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/wiley-blackwell. The right of the author to be identified as the author of this work has been asserted in accordance with the UK 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. 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 professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloguing-in-Publication Data has been applied for. ISBN 978-1-4443-3330-5 A catalogue record for this book is available from the British Library. This book is published in the following electronic formats: ePDF 978-1-4443-9488-7; Wiley Online Library 978-1-4443-9490-0; ePub 978-1-4443-9489-4 Set in 9/12pt ITC Galliard by SPi Publisher Services, Pondicherry, India

1

2011

CONTENTS

List of Contributors

vii

Frontiers in geofluids: introduction G. Garven, C. E. Manning and B. W. D. Yardley

1

Aqueous fluids at elevated pressure and temperature A. Liebscher

3

Thermodynamic model for mineral solubility in aqueous fluids: theory, calibration and application to model fluid-flow systems D. Dolejš and C. E. Manning

20

Metal complexation and ion association in hydrothermal fluids: insights from quantum chemistry and molecular dynamics D. M. Sherman

41

Role of saline fluids in deep-crustal and upper-mantle metasomatism: insights from experimental studies R. C. Newton and C. E. Manning

58

Potential of palaeofluid analysis for understanding oil charge history J. Parnell Spatial variations in the salinity of pore waters in northern deep water Gulf of Mexico sediments: implications for pathways and mechanisms of solute transport J. S. Hanor and J. A. Mercer Faults and fault properties in hydrocarbon flow models T. Manzocchi, C. Childs and J. J. Walsh

73

83

94

Hydrostratigraphy as a control on subduction zone mechanics through its effects on drainage: an example from the Nankai Margin, SW Japan D. M. Saffer

114

The interplay of permeability and fluid properties as a first order control of heat transport, venting temperatures and venting salinities at mid-ocean ridge hydrothermal systems T. Driesner

132

Using seafloor heat flow as a tracer to map subseafloor fluid flow in the ocean crust A. T. Fisher and R. N. Harris

142

The potential for abiotic organic synthesis and biosynthesis at seafloor hydrothermal systems E. Shock and P. Canovas

161

vi

Contents

Permeability of the continental crust: dynamic variations inferred from seismicity and metamorphism S. E. Ingebritsen and C. E. Manning

193

Hydrologic responses to earthquakes and a general metric Chi-Yuen Wang and Michael Manga

206

The application of failure mode diagrams for exploring the roles of fluid pressure and stress states in controlling styles of fracture-controlled permeability enhancement in faults and shear zones S. F. Cox

217

Rates of retrograde metamorphism and their implications for crustal rheology B. W. D. Yardley, D. E. Harlov and W. Heinrich

234

Fluids in the upper continental crust Kurt Bucher and Ingrid Stober

241

Fluid-induced processes: metasomatism and metamorphism A. Putnis and H. Austrheim

254

Fluid flows and metal deposition near basement ⁄cover unconformity: lessons and analogies from Pb–Zn–F–Ba systems for the understanding of Proterozoic U deposits M.-C. Boiron, M. Cathelineau and A. Richard

270

Magmatic fluids immiscible with silicate melts: examples from inclusions in phenocrysts and glasses, and implications for magma evolution and metal transport Vadim S. Kamenetsky and Maya B. Kamenetsky

293

Index

312

CONTRIBUTORS

H. Austrheim Physics of Geological Processes, University of Oslo, Oslo, Norway

J. S. Hanor Department of Geology and Geophysics, Louisiana State University, Baton Rouge, LA, USA

M.-C. Boiron G2R, Nancy Université, CNRS, CREGU, Vandoeuvre lés Nancy, France

D. E. Harlov Section 3.3, Chemistry and Physics of Earth Materials, Deutsches GeoForschungsZentrum, Telegrafenberg, Potsdam, Germany

Kurt Bucher Institute of Geosciences, Geochemistry, University of Freiburg, Freiburg, Germany P. Canovas GEOPIG, School of Earth & Space Exploration Arizona State University, Tempe, AZ, USA M. Cathelineau G2R, Nancy Université, CNRS, CREGU, Vandoeuvre lés Nancy, France C. Childs Fault Analysis Group, UCD School of Geological Sciences, University College Dublin, Dublin, Ireland S. F. Cox Research School of Earth Sciences, The Australian National University, Canberra, ACT, Australia D. Dolejš Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany and Institute of Petrology and Structural Geology, Charles University, Praha, Czech Republic

R. N. Harris College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA W. Heinrich Section 3.3, Chemistry and Physics of Earth Materials, Deutsches GeoForschungsZentrum, Telegrafenberg, Potsdam, Germany S. E. Ingebritsen US Geological Survey, Menlo Park, CA, USA Maya B. Kamenetsky ARC Centre of Excellence on Ore Deposits and School of Earth Sciences, University of Tasmania, Hobart, Tas., Australia Vadim S. Kamenetsky ARC Centre of Excellence on Ore Deposits and School of Earth Sciences, University of Tasmania, Hobart, Tas., Australia

T. Driesner Department of Earth Sciences, ETH Zurich, Switzerland

A. Liebscher Centre for CO2 Storage, Helmholtz Centre Potsdam, German Research Centre for Geosciences GFZ, Telegrafenberg, Potsdam,Germany

A. T. Fisher Earth and Planetary Sciences Department and Institute for Geophysics and Planetary Physics, University of California, Santa Cruz, CA, USA

Michael Manga Department of Earth and Planetary Science, University of California, Berkeley, CA, USA

G. Garven Department of Geology, Tufts University, Medford, MA, USA

C. E. Manning Department of Earth and Space Sciences, University of California, Los Angeles, CA, USA

viii Contributors T. Manzocchi Fault Analysis Group, UCD School of Geological Sciences, University College Dublin, Dublin, Ireland J. A. Mercer Department of Geology and Geophysics, Louisiana State University, Baton Rouge, LA, USA R. C. Newton Department of Earth and Space Sciences, University of California, Los Angeles, CA, USA J. Parnell Department of Geology and Petroleum Geology, University of Aberdeen, Aberdeen, UK A. Putnis Institut für Mineralogie, University of Münster, Münster, Germany A. Richard G2R, Nancy Université, CNRS, CREGU, Vandoeuvre lés Nancy, France D. M. Saffer Department of Geosciences, The Pennsylvania State University, University Park, PA, USA

D. M. Sherman Department of Earth Sciences, University of Bristol, Bristol UK. E. Shock GEOPIG, School of Earth & Space Exploration and Department of Chemistry & Biochemistry, Arizona State University, Tempe, AZ, USA Ingrid Stober Institute of Geosciences, Geochemistry, University of Freiburg, Freiburg, Germany J. J. Walsh Fault Analysis Group, UCD School of Geological Sciences, University College Dublin, Dublin, Ireland Chi-Yuen Wang Department of Earth and Planetary Science, University of California, Berkeley, CA, USA B. W. D. Yardley School of Earth and Environment, University of Leeds, Leeds, UK

INTRODU CTION Frontiers in geofluids: introduc tion This set of papers was originally published electronically as a special double issue of Geofluids to mark the tenth anniversary of the launch of the journal. For this volume, we sought to bring together a collection of papers spanning a range of topics to which the role of fluids in the Earth is central. Geofluids was founded to help emphasise the common ground between fluid processes that take place in different geological settings, and to provide an outlet for research that considers the interactions of chemical and physical processes. While we cannot pretend to provide a comprehensive coverage of all the important recent advances, we are delighted to have been able to bring together some excellent and wide-ranging new science that continues in this tradition. The first four articles all concern our fundamental theoretical and experimental understanding of essentially aqueous fluids. Liebscher provides an overview of the properties of water-rich fluid systems and how these are affected by solutes, while noting the remaining limitations in the experimental database. Dolejs and Manning present the first comprehensive study to produce a more flexible alternative to the HKF model for aqueous electrolytes, better suited to the range of compositions and conditions encountered in nature, while Sherman shows how modern computational power means that some fundamental problems in natural fluid chemistry can be addressed from first principles using quantum chemistry and molecular dynamics. In the final article in this section, Newton and Manning review recent experimental results for lower crustal conditions and present new data to quantify the importance of dissolved salts for the solubility of the major rock –forming elements, Si and Al, and for a range of important Ca-minerals. The second group of articles relate to a specific geological setting where fluid processes are of the highest importance: sedimentary basins. Parnell provides a concise review of the use of hydrocarbon fluid inclusions to understand the evolution of reservoirs through time and the relationships between fluid stages and mineral cements. He shows in particular how this approach has contributed to understanding the oil charge history of the North Sea and UK Atlantic margin. Hanor and Mercer describe the behaviour of saline waters and their distribution in the Gulf of Mexico, and show how salinity differences arising through salt dissolution can dictate flow patterns. They

also explore the likely impacts of salt on the potential of the region as a source of methane hydrates. The article by Manzocchi, Childs and Walsh reviews how faults affect the flow of fluids, in particular hydrocarbons, in siliciclastic basins, and also comment on the extent to which current industry practice for evaluating the effects of faults is actually grounded in science. A third group of article deals with fluid processes in oceanic settings. Saffer has modelled the lateral variations along the Nankai margin of Japan and shown that large scale variations along strike in the taper angle of the accretionary wedge can be linked back to lithological variations from more turbidite-rich sequences to mudrocks. The lithology affects the development of fluid overpressure and the draining of the subduction zone fault, which in turn influences the overall geometry of the wedge. The interplay between permeability, heat flow and discharge characteristics at mid-ocean ridges is explored by Driesner. His results support some findings from terrestrial geothermal systems: high temperature discharges, and the highest fluid salinities, may be associated with low fluid fluxes, while large discharges at relatively low temperatures may in fact dominate the removal of heat. Fisher and Harris take three specific examples of mid-ocean ridge settings to explore the controls on heat loss. The relative importance of conductive heat loss is variable, and specific features of the basement geology can serve to target fluid flow and hence heat loss. Hydrothermal vents are also of likely significance for both abiotic and metabolic organosynthesis and this is explored by Shock and Canovas. Different patterns of mixing of seawater with different hydrothermal fluids can lead to different evolutionary paths, but in general, the mixing favours formation of organic compounds from inorganic reactants. Hence, microbes could produce components of biomolecules simply by catalysis of reactions that are already energetically favoured. A fourth group of articles deals with the continental crust. Ingebritsen and Manning present a crustal-scale overview of permeability and argue that while there is a power–law relation between permeability and depth in tectonically active continental crust, some regions exhibit markedly higher permeabilities, probably as transients, while stable crust may decay to lower permeability. The specific issue of the relationship of hydrologic response to earthquake activity is discussed by Wang and Manga. They

Frontiers in Geofluids, 1st edition. Edited by Bruce Yardley, Craig Manning and Grant Garven. © 2011 by Blackwell Publishing Ltd.

2 C. Garven et al. demonstrate that, in the intermediate and far-field, changes in groundwater flow are linked to changes in permeability which arise in response to cyclic deformation and oscillatory flow. The relationships between faulting and flow at depth is explored by Cox, who shows how fluid pressure and stress influence failure modes and hence the styles of permeability enhancement and vein development, in both mineralized and unmineralized systems. Fluid flow coupled to deformation often introduces water into high grade crystalline basement rocks which undergo retrogression. Yardley, Harlov and Heinrich present the results of experiments designed to measure the rate at which high grade rocks undergo retrogression under mid- to lower-crustal conditions, and conclude that water infiltrated along fine cracks is likely to be rapidly consumed. The article by Bucher and Stober addresses deep groundwaters found in crystalline basement rocks today by tunnelling and drilling. They argue that in areas of high relief such as the Alps, such waters are of relatively low TDS because of flushing by meteoric water, whereas much more saline brines may evolve where the hydraulic gradients are less. Migration of fluids can lead to mineralogical and chemical changes (metasomatism) in a wide variety of crustal settings, and Putnis and Austreheim explore some diverse examples of metasomatism on a range of scales. They are able to demonstrate that, while aqueous fluids partly act as a catalyst to permit minerals to react, they can also influence the course of the reaction through a thermodynamic role. The final section comprises two interdisciplinary articles that deal with ore deposits and draw on a range of aspects of fluids. Boiron, Cathelineau and Richard review the fluid systems that give rise to ore deposits near the unconformity between sedimentary basins and their underlying crystalline basement. They contrast the Proterozoic uncon-

formity uranium deposits with younger base metal deposits that develop in similar settings, and conclude that there are many similarities in both the nature of the fluids and the flow patterns that give rise to mineralization. Kamenetsky and Kamenetsky evaluate fluid processes at the other temperature extreme of ore formation, associated with magmatism. They present evidence from inclusions to document the development of immiscibility as magmas cool, and evaluate the importance of immiscibility for magma chamber processes, including degassing and the partitioning of metals. Although we have grouped the articles for convenience, we believe that the true value of the collection arises from the basic new data presented, from the insight into the interactions between physical and chemical processes, and from the opportunity they provide to take ideas developed in a field where particular types of observation or measurement may be possible to understand processes in different settings or at different times, where different types of data may be available. G. GARVEN1, C. E. MANNING 2 and B. W. D. YARDLEY3 1 Department of Geology, Tufts University, Medford, MA, USA; 2Department of Earth and Space Sciences, University of California, Los Angeles, CA, USA; 3 School of Earth and Environment, University of Leeds, Leeds, UK Corresponding author: B. W. D. Yardley School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK. Email: B. W. D. [email protected]. Tel: +44 113 343 5227. Fax: +44 113 343 5259.

REVIEW Aqueous fluids at elevated pressure and temperature A. LIEBSCHER Centre for CO2 Storage, Helmholtz Centre Potsdam, German Research Centre for Geosciences GFZ, Telegrafenberg, Potsdam, Germany

ABSTRACT The general major component composition of aqueous fluids at elevated pressure and temperature conditions can be represented by H2O, different non-polar gases like CO2 and different dissolved metal halides like NaCl or CaCl2. At high pressure, the mutual solubility of H2O and silicate melts increases and also silicates may form essential components of aqueous fluids. Given the huge range of P–T–x regimes in crust and mantle, aqueous fluids at elevated pressure and temperature are highly variable in composition and exhibit specific physicochemical properties. This paper reviews principal phase relations in one- and two-component fluid systems, phase relations and properties of binary and ternary fluid systems, properties of pure H2O at elevated P–T conditions, and aqueous fluids in H2O–silicate systems at high pressure and temperature. At metamorphic conditions, even the physicochemical properties of pure water substantially differ from those at ambient conditions. Under typical mid- to lower-crustal metamorphic conditions, the density of pure H2O is qH2 O ¼ 0:61:0 g cm3 , the ion product Kw = 10)7.5 to approximately 10)12.5, the dielectric constant e = 8–25, and the viscosity g = 0.0001– 0.0002 Pa sec compared to qH2 O ¼ 1:0 g cm3 , Kw = 10)14, e = 78 and g = 0.001 Pa sec at ambient conditions. Adding dissolved metal halides and non-polar gases to H2O significantly enlarges the pressure–temperature range, where different aqueous fluids may co-exist and leads to potential two-phase fluid conditions under must mid- to lower-crustal P–T conditions. As a result of the increased mutual solubility between aqueous fluids and silicate melts at high pressure, the differences between fluid and melt vanishes and the distinction between fluid and melt becomes obsolete. Both are completely miscible at pressures above the respective critical curve giving rise to so-called supercritical fluids. These supercritical fluids combine comparably low viscosity with high solute contents and are very effective metasomatising agents within the mantle wedge above subduction zones. Key words: fluid–fluid interactions, fluid phase relations, fluid properties, fluid systems, metamorphic fluids, supercritical melts ⁄ fluids Received 23 July 2009; accepted 14 March 2010 Corresponding author: Axel Liebscher, Centre for CO2 Storage, Helmholtz Centre Potsdam, German Research Centre for Geosciences GFZ, Telegrafenberg, D-14473 Potsdam, Germany. Email: [email protected]. Tel: +49 (0)331 288 1553. Fax: +49 (0)331 288 1502. Geofluids (2010) 10, 3–19

INTRODUCTION Aqueous fluids play a fundamental role in the geochemical evolution of the Earth. By transport and recycling of volatile components and different solutes from the atmosphere and hydrosphere through the solid interior of the Earth and back to the surface they chemically link the different spheres of the Earth on the local, regional and also global scale. As a mobile phase, they can transport heat very effi-

ciently by convection and contribute to the local and regional heat budget and heat distribution. The highly variable P–T–x regimes at the surface, in the crust and in the mantle generate equally variable, characteristic fluids with specific compositions and specific physical properties like density and viscosity. Aqueous fluids at elevated pressure and temperature conditions may form by infiltration of meteoric waters in geothermal and basinal systems (e.g., Hanor 1994; Arno´rsson et al. 2007), by diagenetic reac-

Frontiers in Geofluids, 1st edition. Edited by Bruce Yardley, Craig Manning and Grant Garven. © 2011 by Blackwell Publishing Ltd.

4 A. LIEBSCHER tions with connate fluids (Hanor 1994), by infiltration of seawater in oceanic hydrothermal systems (e.g., German & Von Damm 2003; Foustoukos & Seyfried 2007), by prograde metamorphic dehydration and decarbonation reactions as response to changes in P–T–x conditions (e.g., Yardley & Graham 2002; W. Heinrich 2007), and by liberation from crystallizing magmas (e.g., Cline & Bodnar 1994; C.A. Heinrich 2007). Due to the different fluid sources and different geologic environments with notably different P–T–x regimes, the composition of these aqueous fluids is highly variable. Meteoric fluids are almost pure water, which may gain considerable amounts of dissolved salts during diagenetic reactions. The salinity of aqueous basinal fluids ranges over five orders of magnitude from a few ppm in shallow meteoric regimes to more than approximately 40 wt% in evaporite-rich basins (Hanor 1994). In oceanic hydrothermal systems, the dominant fluid source is seawater, which can be modelled as a 3.3 wt% aqueous NaCl equivalent solution (NaCleq; Bischoff & Rosenbauer 1984). However, by interaction with the oceanic crust, the salinity of the generated hydrothermal fluids may range from only approximately 0.2 up to approximately 7.3 wt% NaCl (e.g., Oosting & Von Damm 1996; Lu¨ders et al. 2002). Prograde metamorphic dehydration reactions form highly variable saline fluids that may even reach salt saturation (Fig. 1B; Yardley & Graham 2002). However, the salinity of metamorphic fluids depends only little on metamorphic grade but is strongly linked to the protolith’s original setting. Metamorphism of oceanic or accretionary prism protoliths generally forms fluids with salinity below approximately 6 wt% NaCleq, whereas metamorphism of rocks from shallow marine or continental margin origin forms fluids that span the complete range from almost salt free up to approximately 60 wt% NaCleq (Fig. 1B; most (A)

salinity data for metamorphic fluids come from fluid inclusions and are estimated from the melting temperature of ice. They are usually given as ‘equivalent’ concentration of NaCl or NaCleq, referring to the salinity of a NaCl solution that would yield the same melting temperature of ice as the measured fluid inclusion). Metamorphic decarbonation reactions, triggerd by changes in pressure and temperature or by an infiltrating fluid itself, potentially supply CO2 to the system, force the fluids to un-mix and generate aquocarbonic fluids co-existing with variable saline H2O–salt fluids (e.g., Trommsdorff et al. 1985; Skippen & Trommsdorff 1986; Trommsdorff & Skippen 1986; W. Heinrich 1993, 2007). H2O–salt fluids are also reported from fluid inclusions in diamonds from the upper mantle (Navon et al. 1988; Izraeli et al. 2001). But at high pressure, also the solubility of silicates in aqueous fluids notably increases and silicates may form important solutes at these conditions. This may even lead to complete miscibility between aqueous fluids and silicate melts (e.g., Shen & Keppler 1997; Hack et al. 2007) and individual components continuously change their character from low, typical solute-like concentrations to high, typical solvent-like concentrations; finally, any major element may become an essential phase component of the fluid. This review aims at presenting some of the fundamental topics of aqueous fluids at elevated pressure and temperature. Given the vast number of different geological environments in which fluids evolve, each of which is unique in space, time and physicochemical properties, such a review is necessarily incomplete and the reader is kindly referred to the references given for more and detailed information on specific aspects of aqueous fluids. The review first describes the principal phase relations in one- and two-component fluid systems. Then, phase (B) 700

Geothermal systems

Magmatic

600

Magmatic hydrothermal systems Metamorphic

Basinal systems systems

on

Hydrated oceanic crust Mid ocean C ridge

m

is ph or am et m of n -P io gh at Hi b dr hy sla de ng us cti uo du tin sub

Mantle

ting

500 400 300 Oceanic

200

erpla

Und

Mantle melting

Basinal

100 Mantle

0 0

sa Ap lt sa pro tu x. ra tio n

Meteoric systems

Oceanic systems

Temperature (°C)

Volcanic systems

Metamorphic

10

20 30 40 50 Salinity (eq. wt% NaCl)

60

Fig. 1. (A) Schematic drawing showing the different geological fluid systems in crust and mantle. Modified from Liebscher & Heinrich (2007). (B) Compilation of salinity data for metamorphic fluids. Dark grey fields represent protoliths of shallow marine or continental margin origin, white boxes those from oceanic or accretionary prism origin. Hatched boxes indicate high-pressure metamorphic rocks. Redrawn and modified from Yardley & Graham (2002). Lighter grey fields indicate compositional ranges for fluids from magmatic, metamorphic, oceanic and basinal systems as compiled by Kesler (2005).

Aqueous fluids at elevated pressure and temperature 5 relations and properties of binary and ternary fluid systems, mostly based on experimental studies, are summarized followed by a review of the properties of pure H2O at elevated P–T conditions. Finally, aqueous fluids in H2O–silicate systems at high pressure and temperature are discussed.

PRINCIPAL PHASE RELATIONS IN ONE- AND TWO-COMPONENT FLUID SYSTEMS Aqueous geological fluids are rarely pure water at elevated P–T conditions and represent mixtures with several additional major components like salts (here used in the restricted sense of dissolved metal halides), non-polar gases and rock components like silica. In these multicomponent systems, phase relations become more complicated, fluid miscibility and immiscibility play an important role and concentrations of individual components may continuously change from solute-like to solvent-like or vice versa. In the following, the principal phase relations in two-component model fluid systems are described starting from the onecomponent case as exemplified for H2O (Fig. 2A). In any one-component system, the three phase states solid (in case of H2O ‘ice’), liquid and vapour (in case of H2O ‘steam’) have identical and fixed composition. All three co-exist at the invariant triple point from which the three univariant solid–liquid, solid–vapour and liquid– vapour equilibria emanate (Fig. 2A). In case of H2O, the triple point is at 0.00061 MPa ⁄ 0.01C. In one-component systems, co-existence of different fluid phases is exclusively restricted to the liquid–vapour equilibrium. However, although identical in composition, liquid and vapour differ in their physical properties like density, viscosity and electric permittivity. These properties show abrupt, discontinuous changes at the first-order liquid–vapour phase transition along the liquid–vapour equilibrium. The differences in physical properties, however, diminish along the Critical isochore (0.322 g cm–3)

(B)

100

H2O–

22.1 Liquid

Critical point

0.00061 s+

Pressure (MPa)

CO2

s+l

Pressure (MPa)

(A)

liquid–vapour equilibrium towards higher temperature and pressure and finally disappear at the critical point. The critical point of H2O is at 373.95C ⁄ 22.06 MPa (Wagner & Pruß 2002). Above critical temperature and pressure, neither changes in temperature nor pressure induce any phase transition and the physical properties of the homogeneous single phase fluid continuously change in response to changes in P and T. Addition of a second component to a one-component system adds composition as an additional degree of freedom and co-existing fluids not only differ in their physical properties but also in composition. Consequently, the invariant triple point, the univariant liquid–vapour equilibrium and the critical point of the one-component system turn into a univariant solid–liquid–vapour equilibrium, a divariant liquid–vapour field and a critical curve in the twocomponent system. The P–T range in which two fluids coexist may thereby greatly expand (Fig. 2B). The principal phase relations of two-component fluid systems and how they apply to different H2O–salt systems are shown in Fig. 3. For an in-depth presentation and discussion of the different phase topologies the reader is referred to Ravich (1974) and Valyashko (1990, 2004) and references given therein. A discussion of the principal phase topologies in the context of liquid–liquid immiscibility and the magmatic-hydrothermal transition is given by Veksler (2004). The overall phase topology of H2O–salt systems is determined by the pressure and temperature conditions of the univariant salt–liquid–vapour equilibrium, which emanates from the triple point of the salt endmember systems, relative to the pressure–temperature conditions of the critical curve. In so-called Type 1-systems, with a high and prograde solubility of the salt in H2O, the univariant salt– liquid–vapour equilibrium does not intersect the critical curve, which is continuous over the entire P–T–x space and connects the critical points of the pure systems (Fig. 3A, B). Between the univariant salt–liquid–vapour

H2O– CaCl2

50

NaCl Critical point H2O

v

Triple point

0.01 374 Temperature (°C)

CH4

apo Liquid-v

0 200

2O ur H

300 400 Temperature (°C)

500

Fig. 2. (A) Phase diagram for pure H2O showing the stability fields of the different phase states of H2O. Co-existing fluid phases are restricted to the liquid–vapour (‘l + v’) curve. Above the critical point, only one homogeneous single phase fluid exists. (B) P–T projection of the critical curves for the systems H2O–CO2, H2O–CH4, H2O–CaCl2 and H2O–NaCl. Hatched sides for of the critical curves mark direction of fluid un-mixing. Based on data by Takenouchi & Kennedy (1964) for H2O–CO2, Welsch (1973) for H2O–CH4, Shmulovich et al. (1995), Bischoff et al. (1996) and Zhang & Frantz (1989) for H2O–CaCl2, and Driesner & Heinrich (2007) for H2O–NaCl. Liquid–vapour curve for H2O from Wagner & Pruß (2002).

6 A. LIEBSCHER

(A)

Type 1a

Liquid c.p. (H2O)

t.p. (H2O)

v+l Water Steam

Ice + v+l

Steam

I

t.p. (salt)

lt

Temperature

Salt

T1

T3

T2

Tem

salt = NaCl, KCl, LiCl, MgCl2, CaCl2, MnCl2, NaOH, K2CO3

TI < T1 < Tt.p. (H2O)

Tt.p. (H2O) < T2 < Tc.p. (H2O)

Tc.p. (H2O) < T3 < Tt.p. (salt)

Water Ice

Pressure

Pressure

Ice + l l + Salt

Ice Steam

Pressure

Single phase fluid

l

Ice +v

t.p. Vapour

ture pera

Compo

sition

c.p. Liquid

Sa l t + l + v

Solid salt

l + Salt

v + Sa

H2O

t.p.

Ice

salt + v+l

v+l

Ice Steam v

c.p. (salt)

v+l

urve v = l lc

c.p. C

Pressure

Pressure

Water Ice

rit ic a

Critical cur ve

l

water steam

l + Salt v+l

v

l + Salt

l v+l

v

v+l

v + Salt

v

v + Salt

v + Salt

H2O

Salt

H2O

Salt

(B)

H2O

Salt

Type 1d Critical cur ve

c.p. (H2O)

Ice

R

l1 + l 2

c.p. (salt)

t.p. (H2O)

Steam v

H2O

N Steam

v + Sa

lt

Compo

l + Salt

sition

p Tem

t.p. Vapour

Temperature

N

v+l

Liquid

Solid salt

ure erat Salt = KH2PO4, Na2B4O7, Na2HPO4, UO2SO4

Salt

(C)

Type 2a Upper critical endpoint

Critical

Upper

C

Lower c.p.

t.p.

v

Ice Steam

c.p. Liquid

+

Salt + v+l

Liquid

=l

c.p. (salt)

l+

v+l

v ve

Lower critical endpoint

v

t.p. (H2O)

c.p. (H2O)

Critical endpoints

ur

Ice

Critical cur ve

salt + l +

Water

Pressure

Ice

t.p. (salt)

vv ++ l l

Ice

c.p.

l2 l1 + v+ Sa l t + l + v

t.p.

v + l1

Steam

cur ve l1 = l2

c.p. v = l1 R

Liquid

l1 + l2

Water

Pressure

Pressure

Water

Pressure

al itic Cr

lt Sa

Water

Solid salt

t.p.

Vapour

Steam t.p. (salt)

Temperature

Ice

v+l Steam v

H2O

v + Sa

lt

sition

ure

erat

l + Salt

p Tem

Compo

Salt = Al2O3, SiO2, BaCl2, BaSO4, K2SO4, Na2SO4, Na2CO3

Salt

Fig. 3. Schematic drawings of phase relations in water–salt systems of (A) Type 1a, (B) Type 1d and (C) Type 2a as P–T–x presentation and projections onto the P–T and P–x planes. Assignment of different salts to the different systems after Valyashko (2004). Drawn and modified according to Valyashko (1990, 2004).

Aqueous fluids at elevated pressure and temperature 7 equilibrium and the critical curve a two-phase fluid volume forms in P–T–x space. The univariant salt–liquid– vapour equilibrium may intersect the univariant ice–liquid– vapour equilibrium, which emanates from the triple point of pure H2O, forming an invariant point where liquid, vapour, ice, and salt co-exist (Fig. 3A). In so-called Type 2-systems, with a low solubility of the salt in H2O, the univariant salt–liquid–vapour equilibrium intersects the critical curve at the lower and upper critical endpoints (Fig. 3C). These general Type 1 and 2 phase topologies may get more complicated due to liquid–liquid immiscibility. Such liquid–liquid immiscibility gives rise to a number of principal phase topologies, which are presented and discussed in detail by Valyashko (1990, 2004). Not all of these principal phase topologies, however, have yet been found or are relevant for geological fluid systems. The most simple Type 1a system represents the binaries between H2O and the highly soluble salts like NaCl (e.g., Sourirajan & Kennedy 1962), KCl (Tkachenko & Shmulovich 1992; Dubois et al. 1994), CaCl2 (Tkachenko & Shmulovich 1992; Bischoff et al. 1996) but also NaOH (Urusova 1974) (Fig. 3A). Here, the critical curve is continuous over the entire P–T–x space and no liquid–liquid immiscibility occurs. The effects of liquid–liquid immiscibility are exemplified by Type 1d (Fig. 3B). Here, two separate critical curves form. One critical curve emanates from the critical point of the more volatile component (H2O in Fig. 3B) and shows critical behaviour between vapour and liquid 1, the other critical curve emanates from the critical point of the less volatile component (‘salt’ in Fig. 3B) and shows critical behaviour between liquid 1 and 2. H2O–salt systems of Type 1d include exotic salts like KH2PO4 (Marshall et al. 1981) and are not relevant for geological fluids. The simple Type 2a topology without liquid–liquid immiscibility is representative for binaries between H2O and sparingly soluble second components like SiO2, Al2O3 and other silicates, different sulphates and carbonates (Fig. 3C). Owing to the intersection of the univariant liquid–vapour– salt equilibrium with the critical curve at the lower and upper critical endpoints, lower and upper segments of the two-phase fluid volume form. In systems in which silicates are the additional second component, the high temperature part of the liquid–vapour–salt equilibrium is identical to the wet solidus and describes the silicate’s water saturated melting behaviour. As the upper liquid–vapour–salt equilibrium or wet solidus terminates at the upper critical endpoint, no discrete melting reaction is possible at pressure above the upper critical endpoint (see below).

BINARY AND TERNARY FLUID SYSTEMS The phase relations in binary and ternary fluid systems are simplified representations of natural fluids but form the framework for the more realistic higher component sys-

tems. The most important binary systems for aqueous fluids are the H2O–non-polar gas systems H2O–CO2 and H2O–CH4 and the H2O–salt systems H2O–NaCl, H2O–CaCl2 and H2O–KCl. Other components like the non-polar gas N2 and salts like LiCl, SrCl2 or MgCl2 are normally present only at the minor or even trace element level. Combining these binary systems yields the important ternary fluid systems H2O–NaCl–CO2, H2O–CaCl2–CO2 and H2O–NaCl–CH4. The principal phase relations in the systems H2O–CO2 and H2O–CH4 resemble each other and can be taken as proxies for other H2O–non-polar gas systems (Fig. 4A, B). Starting from the critical point of pure water, their critical curves initially extend towards lower temperature with only minor pressure dependence, then pass through temperature minima and extend to high pressure with only minor temperature increase. The temperature minima occur at 155–190 MPa and approximately 265C in the H2O–CO2 system (Takenouchi & Kennedy 1964) and approximately 100 MPa and 353C in the H2O–CH4 system (Welsch 1973). At temperatures below the critical curves, both systems show pronounced opening of the two-phase fluid region towards lower temperature, reflecting the very low solubility of non-polar solutes in water at low temperatures. A detailed and thorough discussion of phase relations within the H2O–CO2 system that also treats the important formation of clathrates at low temperatures is given by Diamond (2001). Most aqueous fluids contain important amounts of dissolved salts (see above), and water–salt systems therefore have attracted much interest. The H2O–NaCl system has been studied among others by Keevil (1942), Sourirajan & Kennedy (1962), Khaibullin & Borisov (1966), Urusova (1975), Bischoff & Rosenbauer (1984), Bodnar et al. (1985), Chou (1987), Bischoff et al. (1986), Rosenbauer & Bischoff (1987), Bischoff & Rosenbauer (1988), Bischoff & Pitzer (1989), Bischoff (1991) and Shmulovich et al. (1995). Based on the available experimental data, Driesner & Heinrich (2007) derived the most recent representation of the phase topology in the H2O–NaCl system up to 1000C ⁄ 220 MPa, and xNaCl = 0–1.0, where x is mole fraction. Their data form the basis for the H2O–NaCl phase relations shown in Fig. 4C. The critical curve in the H2O–NaCl system monotonously extends from the critical point of pure H2O towards higher pressure and salinity with increasing temperature, at least within reasonable crustal P–T conditions. Beside salinity also the density increases along the critical curve with increasing pressure and temperature (Fig. 4D; Urusova 1975; Chou 1987; Bischoff 1991). The data show that at elevated P–T conditions even the vapour in H2O–salt systems is considerably dense and notably differ from vapour at ambient conditions. For the role of dense vapour as an ore-forming fluid of its own the reader is referred to C.A. Heinrich (2007;

8 A. LIEBSCHER

50 c.p. H2O 0

50

0

0.4 0.6 XCO2 H2O–NaCl

140

0.8

0

1

0

Pressure (MPa)

450

40 c.p. H O 2 20

400 350

55

60

500

50

475

40

0

430 400

30 20

350 310

c.p. H2O

10 0

0.0001 0.01 XNaCl

1

0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Density (g cm–3)

(E)

(F)

H2O–CaCl2

CaCl2

200

90

500°C

CaCl2

0 200

NaCl KCl

300 400 500 600 700 Temperature (°C)

800

ur po Va

Onset of hydrolysis

40 30

a 2+

50

C

Pressure (MPa)

c.p. H2O

60

Cl–

Pressure (MPa)

100

70

id

NaCl KCl

150

Liqu

80

50

1

70

550 500

60

0.8

Critical curve

80

600

80

0.4 0.6 XCH4 H2O–NaCl

90

650

100

0.2

(D) Critical curve 70

120

0 0.000001

330

0

0.2

(C)

0

36

c.p. H2O

300

325

0

100

30

250 200

0

270 275

150

28

100 200

36

0

265

250

200

35 35 0 3

150

264

3

Pressure (MPa)

265 264

350 330

Pressure (MPa)

250 280

200

H2O–CH4 Critical curve

300

Critical curve

250

Pressure (MPa)

(B)

H2O–CO2

300

35

(A)

20 10

CaCl2 Ion imbalance 0 0.000001 0.0001 0.01 1 100 CaCl2, Ca2+, Cl– (eq per kg)

and references given therein). The system H2O–KCl has been studied by Keevil (1942), Hovey et al. (1990), Dubois et al. (1994) and Shmulovich et al. (1995). The critical curve in the H2O–KCl system as well as the corresponding phase relations closely resemble those of the H2O–NaCl system and the phase relations of natural KCl dominated fluids may be approximated by the H2O–NaCl system (Fig. 4E). However, the liquid–vapour–salt equilibrium is at slightly lower pressure in the H2O–KCl than in the H2O–NaCl system. H2O–alkaline earth salt systems were studied among others by Zhang & Frantz (1989), Tkachenko & Shmulovich (1992), Shmulovich et al. (1995), and Bischoff et al. (1996) for H2O–CaCl2 and Urusova & Valyashko (1983, 1984) and Shmulovich et al. (1995) for H2O–MgCl2. The data indicate that the critical curves in H2O-alkaline earth salt systems are at higher pressure than in the H2O-alkaline salt systems, whereas the

Fig. 4. Phase relations in the binary systems (A) H2O–CO2, (B) H2O–CH4, and (C) H2O– NaCl; (D) densities in the system H2O–NaCl; (E) P–T projections of the critical curves and liquid + vapour + salt equilibria in the systems H2O–NaCl, H2O–CaCl2 and H2O–KCl showing the limits for co-existing fluids; and (F) hydrolysis reaction in the system H2O–CaCl2. Thin lines in (A), (B), (C), and (E) are isotherms with temperature given in C. Based on data in (A) from Takenouchi & Kennedy (1964), in (B) from Welsch (1973), in (C) from Shmulovich et al. (1995) and Driesner & Heinrich (2007), in (D) from Urusova (1975), Chou (1987) and Bischoff (1991), in (E) from Keevil (1942), Sourirajan & Kennedy (1962), Ketsko et al. (1984), Chou (1987), Zhang & Frantz (1989), Hovey et al. (1990), Shmulovich et al. (1995), Bischoff et al. (1996), and in (F) from Bischoff et al. (1996).

liquid–vapour–salt equilibrium is at lower pressure. In H2O-alkaline earth salt systems the P–T range where a low salinity vapour co-exists with high salinity liquid therefore expands compared to H2O-alkaline salt systems. Fluid un-mixing into low salinity vapour and high salinity liquid in water–salt systems not only influences salinity and density of the co-existing fluid phases but may also change the availability of ligands and the acid or basic character of the co-existing fluids. In H2O–salt systems hydrolysis occurs according to the equilibrium  xþ xH2 O þ Mxþ Cl x ¼ xHCl þ M ðOHÞx :

At ambient conditions, the equilibrium constant is such that reactant activities are significantly greater than those of the products and the amounts of HCl and Mxþ ðOHÞ x in the fluid are negligible. At elevated P–T conditions, however, the equilibrium constant may change in such a

Aqueous fluids at elevated pressure and temperature 9

(A)

160

Increasing salt

140 Pressure (MPa)

120 100 80 60 nNaCl/(nNaCl + nH O) 2 = 0.0 = 0.0715 250°C 150°C

40 20 0 0

0.04

(B)

0.08 XCO2

0.12

0.16

500°C/50 MPa XNaCl 0.6 Na C +N l aC l l+v

l

0.2

Single-phase Liquid or vapour

l+

0.4

0.2

v + NaCl l+v v

0

H2 O

0

0.2

0.4

0.6

0 1.0

0.8

XCO2

(C)

CO2

500°C/100 MPa NaCl, CaCl2

v + Salt

id lim

xC l;

0.2

Liqu

aC

l + v + Salt

b

aC

l2

l+

sal

t

Salt saturation in H2O–NaCl–CO2

xN

Two-phase fluid

Vapour limb

0 H2 O 0

0.2 xCO2

CO2

0.4

Single-phase fluid H2O–NaCl–CO2

(D)

H2O–CaCl2–CO2

50 MPa

550°C

l+v 500°C Critical point H2O-NaCl

450°C

400°C

Temperature

way that product activities are significantly greater than those of the reactants leading to notable amounts of HCl and Mxþ ðOHÞ x . In case of co-existing fluids, HCl preferentially fractionates into the vapour whereas Mxþ ðOHÞ x fractionates into the liquid. This gives rise to an HCl-enriched, potentially acidic vapour and a co-existing Mxþ ðOHÞ x -enriched, potentially basic liquid. This effect of fluid un-mixing has been experimentally studied by Bischoff et al. (1996), Vakulenko et al. (1989) and Shmulovich et al. (2002). Bischoff et al. (1996) analysed experimentally phase separated fluids in the system H2O– CaCl2 for Ca and Cl. Below 25.0 MPa at 400C and 58.0 MPa at 500C they observed an increasing ion imbalance between Ca2+ and Cl) in the vapour with Cl) concentrations being notably higher than Ca2+ concentrations (Fig. 4F). This observation reflects formation and preferential fractionation of HCl into the vapour. The amount of HCl produced by this reaction is remarkable and may reach 0.1 mol kg)1 in the vapour. The phase relations of the two binary H2O–non-polar gas and H2O–salt subsystems form the framework for the phase relations within the ternary H2O–salt–non-polar gas systems. The third binary subsystem salt–non-polar gas can safely be assumed as immiscible at all geologic relevant P–T conditions. All ternary H2O–salt–non-polar gas systems share some common features. Increasing salt concentrations decrease the solubility of the non-polar gas in H2O–salt mixtures (‘salting out’; Fig. 5A) and salt concentrations in H2O–non-polar gas mixtures are generally low. The P–T–x range of fluid immiscibility therefore greatly expands and extends to conditions where the binary subsystems may already be completely miscible. Fluid immiscibility may therefore prevail over the entire crustal P–T range (Heinrich et al. 2004). The H2O–NaCl–CO2 system is the most relevant ternary system and has been studied, among others, by Takenouchi & Kennedy (1965), Gehrig et al. (1986), Kotel’nikov & Kotel’nikova (1991), Joyce & Holloway (1993), Shmulovich & Plyasunova (1993), Gibert et al. (1998), Shmulovich & Graham (1999, 2004), Schmidt & Bodnar (2000) and Anovitz et al. (2004). The H2O–CaCl2–CO2 ternary has been experimentally determined by Zhang & Frantz (1989), Plyasunova & Shmulovich (1991), Shmulovich & Plyasunova (1993), and Shmulovich & Graham (2004) and the H2O–NaCl–CH4 ternary by Krader (1985) and Lamb et al. (1996, 2002).

Critical point H2O-CH4

Fig. 5. (A) Salting-out effect in the system H2O–NaCl–CO2 at 150 and 250C, and phase relations in the ternary systems (B) H2O–NaCl–CO2, (C) H2O–NaCl–CO2 and H2O–CaCl2–CO2 and (D) H2O–NaCl–CH4. Thin lines in (B) and dashed lines in (C) are only schematic to indicate principal phase relations. Data in (A) from Takenouchi & Kennedy (1964, 1965), in (B) from Anovitz et al. (2004), and in (C) from Kotel’nikov & Kotel’nikova (1991) and Zhang & Frantz (1989). (D) Redrawn and modified after Krader (1985).

350°C

NaCl l+v

CH4

X

Na

Cl

H2O

X CH

4

Liquid + vapour Single-phase fluid

10 A. LIEBSCHER The principal phase relations that occur in the H2O–NaCl– CO2 but also in the other H2O–salt–non-polar gas systems are exemplified in Fig. 5B based on the data by Anovitz et al. (2004) for 500C ⁄ 50 MPa. At these conditions, the H2O–NaCl binary shows liquid–vapour immiscibility and six principal stability fields can be distinguished: (i) At low NaCl concentrations, single phase H2O–CO2 vapour is stable; (ii) at H2O rich compositions, the NaCl poor H2O– CO2 vapour co-exists with a CO2 poor H2O–NaCl liquid, defining a vapour + liquid two-phase field; (iii) at higher NaCl concentrations, a single phase field of H2O–NaCl liquid with only minor amounts of CO2 forms; (iv)–(vi) at high NaCl concentrations the fluids are salt saturated and, depending on the H2O ⁄ CO2 ratio, liquid + salt, liquid + vapour + salt or vapour + salt co-exist. With increasing pressure, the miscibility gap within the H2O–NaCl binary closes and the single phase fluid field extend from salt-saturated CO2–poor H2O–NaCl fluids through ternary fluids at H2O-dominated conditions to NaCl poor H2O–CO2 fluids (Fig. 5C). The available data clearly show that the solubility of NaCl in H2O–CO2 vapour is very low and substantially decreases with increasing pressure and temperature. For instance, at 500C, e.g., xNaCl in H2O–CO2 vapour decreases from about 0.074 at 50 MPa to 150C. Metamorphic conditions are limited towards low temperature and high pressure by the lowest possible geotherm, which was assumed to 5 MPa ⁄ C. The shown boundaries of the different metamorphic facies are from Spear (1993). Some of the reviewed studies report the respective properties as a function of temperature and density while others use temperature and pressure. In Fig. 6, all properties are plotted as a function of temperature with isobars showing the pressure dependence. For data that were presented as function of temperature and density in the original papers density was converted to pressure by applying the IAPWS formulation for H2O by Wagner & Pruß (2002). For near-critical behaviour of H2O and aqueous systems, see Anisimov et al. (2004). Density At ambient conditions, liquid water has a density of approximately 1 g cm)3. With increasing pressure and temperature along the liquid–vapour equilibrium, the density contrast between liquid water and steam diminishes and at the critical point both approach the critical density of 0.322 g cm)3. Numerous EOS and molecular dynamics simulations describe the PVT properties of pure H2O.

Aqueous fluids at elevated pressure and temperature 11

(A)

(B)

1100

Isobars (MPa) 100

1000

250

900

500

1000

2000

Temperature (°C)

th

700 600

Not realiz ed on Ear

Temperature (°C)

800 A EA

500 Gr

400 10

Critical point

300 200

B

0.4 0.6 0.8 1.0 Density (g cm–3)

Temperature (°C)

800 700

Fernández et al. (1997)

E

400

B

A

600

Franck et al. (1990a,b) 255 MPa ~ 500 MPa 1.55 GPa

EA E

50 10

Gr

B

229 MPa 885 MPa

SGr Liquid + Vapour

100 0 0

10 20

tr ea

5

30 40 50 60 70 80 Static dielectric constant

50

10

Quist (1970) 100 200 MPa

Tanger & Pitzer (1989) Marshall & Franck (1981)

15 20 25 -log ion product KW

30

1100 Isobars (MPa) 100

900 800

200 300

700

Sengers & Kamgar-Parsi (1984)

G

600 A

500

Abramson (2007)

350

10 50

400

500 1000 1500

300

Critical point

200 liz ed on Ea r th

Liquid + Vapour

SGr

Gr B SGr

100

ze ali

No

200

Franck (1956) 350 670 970 MPa

t re No

Critical point

300

Pitzer (1983)

Critical point

Gr

1000

Shock et al. (1992) Heger (1969) Deul (1984) 50 MPa 100 MPa 250 MPa 500 MPa

G

400

A

500

0

1.4

(D) Isobars (MPa) 100 250 500 1000

900

500

1.2

Temperature (°C)

1000

EA

600

200

SGr

0

1100

700

100 0.2

25

G

300

100 0

50

ed liz ea rth t r Ea No on

Liquid + Vapour

100

900

E

800

(C)

Isobars (MPa) 200

1000 500

1000

G

50

1100

d

on E

Liquid + Vapour

ar th

0 90

0

0.0001 0.0002 0.0003 0.0004 0.0005 Dynamic viscosity (Pa s)

Fig. 6. Density (A), ion product (B), static dielectric constant (C) and dynamic viscosity (D) of pure water as function of temperature. Thin lines are isobars with pressure given in MPa. Shadowed fields represent range of metamorphic conditions with 100 MPa arbitrarily chosen as lower P-limit. Thick grey lines define the different metamorphic facies where SGr = sub-greenschist, Gr = greenschist, B = blueschist, EA = epidote-amphibolite, A = amphibolites, G = granulite and E = eclogite facies (after Spear 1993). Data in (A) from Wagner & Pruß (2002), other data sources given in the Figure. Stippled lines in (D) are eye-drawn through the data points of Abramson (2007).

Among others, these include those by Kerrick & Jacobs (1981), Halbach & Chatterjee (1982), Saul & Wagner (1989), Belonoshko & Saxena (1991) and Wagner & Pruß (2002). At elevated P–T conditions, the density of H2O ranges from approximately 0.3 g cm)3 up to >1.2 g cm)3 (Fig. 6A; calculated with the IAPWS formulation by Wagner & Pruß 2002). Only at low pressure the density may be < 0.3 g cm)3. Increasing temperature generally decreases density whereas increasing pressure has the opposite effect. In low-P ⁄ high-T settings as they occur in oceanic hydrothermal systems, volcanic systems and meta-

morphic systems with very high geothermal gradients H2O densities are below approximately 0.6 g cm)3. Under typical crustal metamorphic conditions, however, the density of H2O ranges between approximately 0.6 and 1.0 g cm)3. Only at rather high pressures, as in subduction zones or within the upper mantle, are conditions such that H2O densities exceed 1.2 g cm)3. Self-dissociation The dissociation equilibrium of water

12 A. LIEBSCHER H2 O ¼ Hþ þOH

Dielectric constant

is described by the equilibrium constant

The dielectric constant is of primary importance for the evaluation of the solvent properties of water. The attractive or repulsive force between any point charges q1 and q2 in a medium, e.g., ions in aqueous solution, that are separated by distance r is given by

K¼

aHþ  aOH aH2 O

or by the ion product Kw ¼ aHþ  aOH : At ambient conditions, the dissociation equilibrium of liquid water is strongly shifted to the left hand side, concentrations and activities of H+ and OH) are low and Kw = 1 · 10)14. With pH ¼  log aHþ this turns into the well known value of pH = 7 for neutral water. At elevated P–T conditions, however, Kw notably changes. The ion product along the liquid–vapour equilibrium has been experimentally determined among others by Bignold et al. (1971), Fischer & Barnes (1972), MacDonald et al. (1973) and Sweeton et al. (1974). Measurements at elevated pressure and temperature conditions above the critical point of water were performed by Franck (1956) at 350–970 MPa ⁄ 500–1000C and by Quist (1970) up to 555 MPa and 800C. Extreme conditions have been studied by Holzapfel & Franck (1966) at 4.5– 10.0 GPa ⁄ 600–1000C. Formulations for the change of Kw with pressure and temperature are given by Marshall & Franck (1981) up to 1000C ⁄ 1000 MPa, Pitzer (1983) for low densities up to approximately 0.1 g cm)3, Tanger & Pitzer (1989) up to 500 MPa ⁄ 2000C, and Bandura & Lvov (2006) up to 1.0 GPa ⁄ 1000C. Kw as function of pressure and temperature calculated by the formulations of Marshall & Franck (1981) and Tanger & Pitzer (1989) together with selected data by Franck (1956) and Quist (1970) are shown in Fig. 6B. The Marshall & Franck (1981) and Tanger & Pitzer (1989) data agree well for the pressure range between 100 and 500 MPa and reproduce the available experimental data by Quist (1970). However, at pressures below approximately 100 MPa, both formulations diverge and the formulation by Marshall & Franck (1981) predicts notably higher values for Kw than the Pitzer (1983) and Tanger & Pitzer (1989) formulations. In this low pressure, low density region the formulations of Pitzer (1983) and Tanger & Pitzer (1989) are probably more reliable (see discussion in Tanger & Pitzer 1989). Within the pressure range 200–1000 MPa, temperature has only a minor effect on Kw, whereas Kw generally increases with increasing pressure. Under normal mid- to lower-crustal P–T conditions, Kw ranges between approximately 10)7.5 and approximately 10)12.5. However, at very high pressures of the eclogite facies, Kw may even be substantially higher than 10)7.5. In line with this, Holzapfel & Franck (1966) determined Kw = 10)2.8 to 10)1.2 at approximately 7–9 GPa ⁄ 500–1000C.

F¼

q1 q2 4p"r 2

with e being the electric permittivity of the medium. The electric permittivity of the vacuum is typically designated e0 and the dimensionless ratio e ⁄ e0 then yields the static relative permittivity or static dielectric constant for any medium. A high dielectric constant corresponds to a high resistance of the medium to the transmission of an electric field. At ambient pressure and 25C liquid water has a notably high static dielectric constant of 78.4 (Ferna´ndez et al. 1995). This high static dielectric constant makes liquid water a good solvent for charged species at ambient conditions as it minimizes the electrostatic forces between the dissolved ions and prevents them to combine to crystals. However, with increasing pressure and temperature, the static dielectric constant of liquid water substantially decreases. Ferna´ndez et al. (1995) presented a database for the static dielectric constant of water and steam. It extends up to a temperature of 873 K and a pressure of 1189 MPa and covers the data available at that time. The static dielectric constant along the liquid–vapour equilibrium has been studied by Oshry (1949), Svistunov (1975), Lukashov (1981), Muchailov (1988) and Mulev et al. (1994). Along the liquid–vapour equilibrium, e of liquid water continuously decreases from approximately 55 at 100C to only approximately 9.7 at 370C, whereas e of co-existing steam only slightly increases from approximately 1.03 at 150C to approximately 3.02 at 370C. Above the critical point, e has been measured by Heger (1969) and Heger et al. (1980) at 25–500 MPa ⁄ 400–550C, Lukashov et al. (1975) at 23–58 MPa ⁄ 400–600C, Golubev (1978) at 23–39 MPa ⁄ 420–510C, Lukashov (1981) at 24–580 MPa ⁄ 400–600C, and Deul (1984) at 30–300 MPa ⁄ 400C. Based on the available experimental data, formulations and calculated values for e up to high P–T conditions are given by Quist & Marshall (1965) up to 1.55 GPa ⁄ 800C, Bradley & Pitzer (1979) up to 100 MPa ⁄ 350C, Pitzer (1983) up to 880 MPa ⁄ 927C, Franck et al. (1990a,b) up to 1.55 GPa ⁄ 1000C, Shock et al. (1992) up to 500 MPa ⁄ 1000C, Wasserman et al. (1995), and Ferna´ndez et al. (1997) up to 1.2 GPa ⁄ 600C. Fig. 6C reviews the experimental data by Heger (1969) and Deul (1984) together with isobars calculated by formulations of Shock et al. (1992) and Ferna´ndez et al. (1997). Also shown are values for the static dielectric constant for selected P–T conditions as calculated by formulations of Pitzer (1983) and

Aqueous fluids at elevated pressure and temperature 13 Franck et al. (1990a,b). For temperatures up to 1000C and pressures up to 500 MPa, i.e. the P-range largely covered by experimental data, the different formulations agree quite well. However, at pressures above 500 MPa, the different formulations diverge. At 800C, e.g., Ferna´ndez et al. (1997) predict a static dielectric constant of approximately 14 at 1.0 GPa, whereas Franck et al. (1990b) predict e  14 only at notably higher pressure of 1.55 GPa. At slightly higher temperature of 930C, Pitzer (1983) predicts e  11 at 885 MPa, roughly 120 MPa below the prediction of Ferna´ndez et al. (1997). This indicates a higher pressure dependence of e in Pitzer (1983) compared to Ferna´ndez et al. (1997) and Franck et al. (1990a,b). Despite these differences at high P conditions, the static dielectric constant of H2O generally decreases with increasing temperature but increases only slightly with increasing pressure. Because the effect of temperature is more pronounced than that of pressure, e decreases with increasing P–T conditions and range between approximately 8 and 25 at normal crustal P–T conditions. Only at low temperature of greenschist to sub-greenschist facies conditions or notably high pressure of blueschist to eclogite facies conditions e may exceed 25. But given the restricted P–T range covered by experimental data, any calculation of the static dielectric constant at pressures notably in excess of 500 MPa has to be done with great caution. Viscosity The transport properties of water strongly depend on its dynamic viscosity g, which also plays an important role for diffusion. Several studies have addressed the dynamic viscosity of water at low to moderate temperature and pressure (see Watson et al. (1980) for a review of available experiments at that time). The dynamic viscosity of water at elevated P–T conditions has been studied by Dudziak & Franck (1966) up to 350 MPa and 560C and by Abramson (2007) up to 6 GPa and 300C. Based on the available data, Watson et al. (1980) and Sengers & Kamgar-Parsi (1984) derived representative equations for g (Fig. 6D). At ambient conditions, liquid water has a dynamic viscosity of g = 0.001 Pa sec (Sengers & Kamgar-Parsi 1984). Along the liquid–vapour equilibrium, the viscosity of liquid water substantially decreases whereas that of steam only slightly increases, so that the critical dynamic viscosity of H2O is approximately 3.9 · 10)5 Pa sec. At temperature conditions above approximately 400C, the data suggest that at isobaric conditions the temperature effect on the dynamic viscosity is only minor whereas increasing pressure increases g. Except for low temperatures of sub-greenschist facies conditions, H2O has dynamic viscosities at normal crustal P–T conditions between 0.0001 and 0.0002 Pa sec. Although no data are available for upper blueschist and

eclogite facies, the data suggest that at these high pressure conditions the dynamic viscosity of H2O may range up to 0.0003 Pa sec (Fig. 6D).

H 2 O–SILICATE SYSTEMS AT HIGH P–T CONDITIONS Aqueous fluids and silicate melts are the two most important mobile phases in the Earth crust and mantle. H2O– silicate systems typically belong to Type 2 systems (see above), which are characterized by a discontinuous critical curve and lower and upper segments of the two-phase fluid volume that terminate at the lower and upper critical endpoints (see Fig. 7C). Up to moderate pressure and temperature conditions the solubility of silicates in aqueous fluids and of H2O in silicate melts is typically low and both phases fundamentally differ in their physicochemical properties. With increasing pressure, however, the solubility of H2O in silicate melts and of silicates in aqueous fluids increases and the differences between both phases finally vanish at the critical curve above which aqueous fluids and silicate melts are completely miscible giving rise to socalled ‘supercritical’ fluids. Here, only some key aspects of H2O–silicate systems at high pressure and temperature conditions are reviewed. A thorough review of this topic is given by Hack et al. (2007). Kennedy et al. (1962) provided the first experimental evidence for complete miscibility between aqueous fluids and silicate melts at high pressure and temperature within the system H2O–SiO2 and proposed an upper critical endpoint at 970 MPa ⁄ 1080C with a composition of approximately 25 wt% H2O ⁄ 75 wt% SiO2. This has been confirmed by Newton & Manning (2008). Shen & Keppler (1997) directly observed complete miscibility between aqueous fluids and silicate melts in the system H2O–albite and determined the location of the critical curve (Fig. 7A). Further experiments by Stalder et al. (2000) at near wet solidus conditions then located the upper critical endpoint in the system H2O– albite at approximately 1.5 GPa ⁄ 700C (Fig. 7A). The resulting phase relations within the system H2O–albite up to 1.7 GPa and T > 500C based on the data by Paillat et al. (1992), Shen & Keppler (1997) and Stalder et al. (2000) are shown in Fig. 7B. At pressure below approximately 1.5 GPa, the critical curve is at higher temperature than the wet solidus, which is defined as onset of melting by the reaction albite + vapour = liquid. However, with increasing pressure, the critical curve shifts to lower temperature, the liquid + vapour two-phase field narrows and at approximately 1.5 GPa the critical curve intersects the wet solidus at about 700C. Above approximately 1.5 GPa no discrete melting occurs but albite continuously dissolves in the fluid with increasing temperature giving rise to a continuous range from solute poor, almost pure H2O at low temperature to H2O poor silicate dominated liquids at

14 A. LIEBSCHER

(A)

(B) T (°C)

Upper critical endpoint

1.5

2500

2500

2000

2000 C

rit ur lc ica

Albite Liquid

1000

1000

5

0.

75

P

0.

) Pa

(G

900 Temperature (°C)

1300

us lid us so lid so

id us

ol

0 500

ab + l

y

1 0. 5 2 0.

Dr

ts We

Dr y s olidus

500

et W

ur vapo

Liquid

0.5

1500

ve

1.0

Albite +

Pressure (GPa)

1500

ab + v

Upper critical endpoint

1500 1000

0

1.

25

1.

500

ab + scf

5

1.

.7

25 1 NaAlSi3O8

(C)

l+v

50 75 mol % H2O

H2O

(D)

T (°C) 1600 1400

Critical curve

4.0

2

1200 l+v

t us We solid

800

1400

33 mol % H2O

Rock + l

us solid

1000

3

1000 800

Rock +v

Upper critical endpoint

Rock + scf

Pa)

P (G

1000

5.0

6.0 Eclogite

Log viscosity (Pa s)

Dr y

1200

1600

1 0

57 mol % H2O

–1

72 mol % H2O

–2

81 mol % H2O

–3 –4 6

20

40 60 mol % H2O

93 mol % H2O

800

80

H2O

8

10

12

14

Temperature (10 000/K)

Fig. 7. Water–silicate systems at high pressure and temperature. (A) P–T diagram showing location of the wet and dry solidus, critical curve and upper critical endpoint in the system H2O–albite. Wet solidus, filled and empty circles from Stalder et al. (2000), critical curve and diamonds from Shen & Keppler (1997) and dry solidus from Boyd & England (1963). (B) Phase relations within the system albite–H2O up to 1.7 GPa and T > 500C showing the termination of the water saturated solidus and the critical curve at the upper critical endpoint. Drawn and modified after Paillat et al. (1992), Shen & Keppler (1997) and Stalder et al. (2000) (ab = albite, v = vapour, l = liquid, scf = supercritical fluid). (C) Phase relations within the system eclogite–H2O at 4–6 GPa and T > 600C based on the data of Kessel et al. (2005a). Critical curve, dashed and stippled lines are hypothetical additions to the data given in Kessel et al. (2005a) to clarify phase relations (v = vapour, l = liquid, scf = supercritical fluid). (D) Arrhenius plot showing the viscosity of H2O–albite solutions as function of temperature and water content at high pressures >1.0 GPa. Data from Aude´tat & Keppler (2004), stippled lines calculated according to their Eqn (1).

high temperature. Addition of fluorine, boron and sodium to the H2O–albite system shifts the location of the critical curve to even lower pressure and temperature (Sowerby & Keppler 2002). Critical curves for the systems H2O–nepheline and H2O–jadeite have then been determined by Bureau & Keppler (1999). Termination of the wet solidus at the upper critical endpoint, however, not only occurs in simple H2O–mineral systems but is also observed in H2O–rock systems. Kessel et al. (2005a,b) studied the system H2O– potassium-free basalt at 4–6 GPa ⁄ 700–1400C. They observed eutectic and peritectic melting at pressures of 4 and 5 GPa, respectively, but no discrete melting at

6 GPa (Fig. 7C). At 6 GPa, the aqueous fluid continuously increases its solute content with increasing temperature suggesting a critical endpoint in this system between 5 and 6 GPa ⁄ 1050C. Complete miscibility between aqueous fluids and silicate melts in the systems H2O–Ca-bearing granite and H2O–haplogranite was observed by Bureau & Keppler (1999). The corresponding critical curves are located at 1.34 GPa ⁄ 1003C to 2.04 GPa ⁄ 735C in the H2O–haplogranite system and at slightly higher pressure and temperature conditions of 1.61 GPa ⁄ 898C to 2.08 GPa ⁄ 820C in the H2O–Ca-bearing granite system. However, no critical endpoints, which determine the ter-

Aqueous fluids at elevated pressure and temperature 15 mination of the wet solidus, are given for the systems H2O–Ca-bearing granite and H2O–haplogranite in Bureau & Keppler (1999). One important aspect of H2O–silicate systems at pressure conditions above the critical endpoint is the combination of high solute contents in the fluids with comparably low viscosities. Aude´tat & Keppler (2004) performed a seminal experimental study on the viscosity of high-pressure silicate rich aqueous fluids in the systems H2O–albite, H2O–nepheline and H2O–pectolite. In the H2O–albite system, fluid viscosity linearly increases with increasing solute content from approximately 3.5 · 10)4 Pa sec for 7 mol% solutes to approximately 4 · 100 Pa sec for 67 mol% solutes (Fig. 7D). The viscosity of dry and hydrous albite melts with up to 3 wt% H2O is notably higher and ranges between approximately 109 and 1011.5 Pa sec (Romano et al. 2001). The data therefore indicate an exponentially decrease of viscosity with increasing H2O content for 0.322 g cm)3 to 1000C and 5 kbar; (ii) it cannot accurately reproduce the derivative properties in the vicinity of the critical point of H2O; (iii) it becomes particularly inaccurate for gaseous non-electrolytes at their low-density limit (Plyasunov et al. 2000; Akinfiev & Diamond 2003); (iv) the static permittivity of water, which is required for the Helgeson–Kirkham–Flowers equation of state, has not been determined experimentally at T > 600C or P > 20 kbar, and current models strongly diverge in these regions (Franck et al. 1990; Shock et al. 1992; Wasserman et al. 1995, Fernande´z et al. 1997; Marshall 2008a). In contrast to the static permittivity, the volumetric properties of H2O are known with reasonable accuracy at nearly all conditions of terrestrial water–rock interaction. Simple extrapolation schemes and more advanced models based on H2O volumetric properties have been successful in representing association–dissociation equilibria (Franck 1956a; Marshall & Quist 1967; Mesmer et al. 1988; Anderson et al. 1991; Plyasunov 1993), element partitioning in vapor–liquid systems (Pokrovski et al. 2005a, 2008), dissolution of gaseous species in aqueous fluids (Plyasunov et al. 2000; Akinfiev & Diamond 2003), mineral solubilities over a wide range of temperatures and pressures in aqueous solvents (Fournier & Potter 1982; Manning 1994; Pokrovski et al. 2005b), extrapolation to mixed solvents (Marshall 2008b; Akinfiev & Diamond 2009) and describing near-critical thermodynamic properties of inorganic and organic solutes (Clarke et al. 2000; Sedlbauer & Wood 2004; Majer et al. 2008). In this paper, we investigate the thermodynamic relationships between mineral solubility, solvent density and other intensive variables, with the main focus on metamorphic and magmatic temperatures and pressures. The ‘density model’ will be derived from the thermodynamics of solute hydration, emphasizing consistency with conventional caloric properties and thermodynamic parameters resulting from statistical mechanics of solute–solvent interactions. This optimized functional form is shown to serve for interpolation and extrapolation of mineral solubilities in aqueous fluids at high temperatures and pressures, as well as for retrieving the thermodynamic properties of dissolution that are necessary for mass transfer and transport modeling.

THERMODYNAMIC MODEL Thermodynamic properties of hydration, which result from electrostatic interactions between solute species and aqueous solvent, have traditionally been described by the Born theory (Born 1920; Helgeson & Kirkham 1974; Wood

22 D. DOLEJSˇ & C. E. MANNING et al. 1981, 1994; Atkins & MacDermott 1982; Pitzer 1983b; Tanger & Helgeson 1988; Tremaine et al. 1997), which states that 1 DB G ¼ ! ; "

ð1Þ

where DBG is the Born energy, x is the species-specific Born parameter and e is static permittivity (dielectric constant) of the aqueous solvent. However, the reciprocal dielectric constant varies nearly linearly with temperature at constant water density at 200–1100C and up to 10 kbar (Fig. 2). The linear trend corresponds to 1 ¼ 4:928  104 T log w þ 3:497  102 "

ð2Þ

where T is absolute temperature (K) and qw is water density (g cm)3). Consequently, the electrostatic contribution can be, to a high degree of accuracy, implicitly accounted for via correlations with solvent density. Such an approach would alleviate a number of drawbacks due to: (i) lack of calibration of the static permittivity at high temperatures and pressures (cf. Pitzer 1983b; McKenzie & Helgeson 1984; Franck et al. 1990; Shock et al. 1992; Wasserman et al. 1995; Fernande´z et al. 1997) and (ii) inadequate representation by Born theory of near-critical and low-pressure thermodynamic properties (Tanger & Pitzer 1989a; Shock et al. 1992; Plyasunov et al. 2000; Sue et al. 2002; Akinfiev & Diamond 2003, 2004), where formulations based on solvent density are more accurate (Fournier 1983, Manning 1994; Plyasunov et al. 2000; Sedlbauer et al. 2001; Sedlbauer & Wood 2004; Majer et al. 2008).

An alternative thermodynamic model can be formulated by accounting for three thermodynamic contributions to mineral dissolution into an aqueous fluid. At a given temperature and pressure, these are: (i) disruption of local structure of the crystal lattice, (ii) hydration of the solute species and (iii) volumetric solute–solvent interactions resulting from electrostriction. These contributions are added in a Born–Haber thermodynamic cycle to derive the standard thermodynamic properties of dissolution. Lattice breakdown and hydration The first two steps in the dissolution process – disruption of solid phase MX and formation of hydrated aqueous species – are represented by a series of chemical equilibria (cf. Kebarle 1977; Pitzer 1983a; Borg & Dienes 1992, pp. 126–137), e.g. for ion MðH2 O)zþ n : MXðsÞ ! Mzþ þ Xz zþ

M

ð3Þ zþ

þ H2 O ! MðH2 OÞ ; . . . ;

zþ MðH2 OÞzþ n1 þ H2 O ! MðH2 OÞn

0.5 0.4

1/

2 0.3 0.2 5

Dcl G ¼ a þ bT þ cT ln T þ dT 2

10

0.1

–800

Tref

where T and Tref represent the temperature of interest and reference temperature (e.g. 298.15 K) respectively. An explicit PV term is not required here because the standard state is chosen to be that at the pressure of interest and the volumetric contribution will be included in a density term, as shown below. When the heat capacity, cP, is a polynomial linear in temperature, which appears to be sufficient to represent the properties of aqueous species up to high temperatures (Pitzer 1982; Tanger & Pitzer 1989a,b; Holland & Powell 1998), Eq. 6 leads upon substitution and integration to the following Gibbs function:

1

0 –1200

ð5Þ

where n represents hydration number. Equations similar to 3–5 also apply to negatively charged species, ion pairs and neutral complexes. The standard Gibbs energy change of the two combined steps is described at the pressure of interest by a caloric (cl) equation of state: 1 0 ZT ZT cP C B ð6Þ dTA cP dT  T @DS þ Dcl G ¼ DH þ T Tref

0.6

ð4Þ

–400

T log

w

0

200

(K)

Fig. 2. Correlation between the reciprocal dielectric constant of H2O, 1 ⁄ e, and the T log q term illustrated for isobars of 1, 2, 5 and 10 kbar (labels of dotted curves) at a temperature range of 200–1100C (point symbols in 100C steps). Dashed line is a linear fit of the set (Eq. 2).

ð7Þ

where the coefficients a to d are related to enthalpy, entropy and the heat capacity polynomial (Hillert 2008, pp. 407–408). Volumetric solute–solvent interactions Additional thermochemical contributions arise from volumetric collapse (electrostriction) of the hydration shell. The contribution to the Gibbs energy corresponds to the

Thermodynamic model for mineral solubility in aqueous fluids 23 PV work required to compress H2O molecules from the bulk solvent (w) density to that in the hydration shell (hs) (Pierotti 1963, 1976; Ben-Naim 2006, pp. 12), Dco G ¼ Dw!hs G ¼ RT ln

Vw  ¼ RT ln hs Vhs w

ð8Þ

where bw is the compressibility of H2O (cf. Mesmer et al. 1988; Anderson et al. 1991; Ben-Amotz et al. 2005). This form has an independent origin in fluctuation solution theory, which defines linear scaling between the standard partial molar volume of aqueous species, Vaq, and the solvent compressibility as the generalized Krichevskii parameter, A (Levelt Sengers 1991; O’Connell et al. 1996; Plyasunov et al. 2000): Vaq : bRT

Dds G ¼ Dcl G þ Dco G

ð11Þ

leading to

where the subscript ‘co’ stands for compression, and V and q are the molar volume and density at each state respectively. Assuming negligible compressibility of the hydration shell, that is, qhs is constant (Mesmer et al. 1988; Tanger & Pitzer 1989a), Eq. 8 introduces two terms to the overall Gibbs energy of dissolution – an RT ln qhs term, where R ln qhs has dimension of entropy, and an RT ln qw term, which varies with temperature and pressure. Note that the T ln qw product has the same form as the term in the proposed correlation for the reciprocal dielectric constant (Eq. 2). Differentiation of DcoG (Eq. 8) with respect to pressure provides the standard molar volume change during the formation of the hydration shell,   oDco G Dco V ¼ ¼ bw RT ; ð9Þ oP T

A¼

solvent compression (DcoG, Eq. 8) including solute–solvent interactions, are summed to give the standard Gibbs energy of dissolution, DdsG:

ð10Þ

The function 1 ) A is complementary to the generalized Krichevskii parameter and represents the dimensionless spatial integral of the infinite-dilution solute–solvent direct-correlation function (Kirkwood & Buff 1951; O’Connell 1971, 1990). It has the advantage of behaving as a finite smooth function in the vicinity of the critical point and it is nearly independent of temperature when applied to both electrolyte and non-electrolyte systems (Cooney & O’Connell 1987; Crovetto et al. 1991). The constant relationship between the solute partial molar volume and the solvent compressibility has, in addition, been confirmed experimentally up to elevated temperatures for inorganic solutes in aqueous and organic solvents (Hamann & Lim 1954; Ellis 1966).

MODEL FOR MINERAL DISSOLUTION The energetic terms associated with lattice breakdown (dissociation) and solute hydration (DclG, Eq. 7), and with

Dds G ¼ a þ bT þ cT ln T þ dT 2 þ eT ln ;

ð12Þ

which represents the standard reaction Gibbs energy of equilibria such as SiO2 (quartz) = SiO2 (aq) or CaF2 (fluorite) = Ca2+ (aq) + 2F) (aq). In Eq. 12, a to e are parameters of the model. Parameters c and d represent the constant and the linear terms in the heat capacity of dissolution respectively; where experimental data are sparse, these terms may be set to zero. As discussed below, the reduced three-parameter form (a, b and e) is sufficient to represent data that extend over at least 400C. An explicit term representing the intrinsic volume of species is not required for the properties of dissolution when the hardcore volumes of ions in the lattice and in the hydration sphere are assumed to be comparable. Using the relationship between the standard reaction Gibbs energy and equilibrium constant, K, 0 ¼ Dds G þ RT ln K ;

ð13Þ

Eq. 12 leads to ln K ¼ 

o 1 na þ b þ c ln T þ dT þ e ln w : R T

ð14Þ

Equation 14 indicates that there is an isothermal linear dependence of the logarithm of the equilibrium constant on the logarithm of solvent density, and that this linear slope is independent of temperature. Dissolution and association–dissociation equilibria at elevated pressures indeed appear to conform to a simple linear relationship including a logarithmic term of the solvent density, log K ¼ m þ n log w ;

ð15Þ

where m and n are fit parameters, which are often empirical polynomial expansions in temperature (Mosebach 1955; Franck 1956a; Marshall & Quist 1967; Mesmer et al. 1988; Anderson et al. 1991). Such a behavior is characteristic of the dissociation of water up to 1000C and 10 kbar (Sweeton et al. 1974, Marshall & Franck 1981; Fig. 3A), the dissociation of alkali halides up to 800C and 4 kbar (Franck 1956b; Quist & Marshall 1968; Frantz & Marshall 1982; Fig. 3B), the dissociation of acids and bases (Eugster & Baumgartner 1987; Mesmer et al. 1988, 1991; Tremaine et al. 2004) and the dissolution of quartz, calcite, apatite, halite and other minerals up to 900C and 20 kbar (Mosebach 1955; Franck 1956b; Martynova 1964; Fournier & Potter 1982; Manning 1994;

24 D. DOLEJSˇ & C. E. MANNING

–7

(A) H2O dissociation

800 600 400

–8

Log Kw

–9 –10 –11 –12 –13 –0.4

–0.3

–0.2

–0.1

0

0

0.1

400 600 800

(B) NaCl dissociation –1

Log K

–2 –3 –4 –5

–6 –0.6

–0.5

–0.4 –0.3

–0.2

–0.1

0

–1

(C) NaCl solubility

550 450 350

Log molality NaCl

–2

Caciagli & Manning 2003; Antignano & Manning 2008a; Fig. 3C). The solubility model represented by Eqs 12 and 14 differs from previous empirical density models. The first part (a–d terms) has frequently been used with inverse temperature factors (e.g. Fournier & Potter 1982; Mesmer et al. 1988, 1991; Anderson et al. 1991). Such a Gibbs energy function is, however, inconsistent with a constant heat capacity term (cf. Hillert 2008, pp. 407–408) and we prefer a rigorous combination of enthalpy, entropy and heat capacity contributions. Similarly, the ln q term was used with either no or inverse temperature dependence (e.g. Fournier & Potter 1982; Mesmer et al. 1988, 1991; Holland & Powell 1998), which may, in part, simplify the macroscopic relationship between the solute volume and heat capacity (Anderson et al. 1991; Anderson 2005, pp. 260–263). However, these forms prevent extrapolation of thermodynamic properties above approximately 300C (Anderson et al. 1991). Therefore, Anderson et al. (1991) and Holland & Powell (1998) proposed a modification, essentially a scaled T ln qw term, in order to improve and extend the applicability to 800C. This modification is fortuitously identical in form to the model that we derived using the compression of H2O in the hydration sphere. Thermodynamic identities lead to the standard thermodynamic properties of dissolution, as follows:   oDds G Dds S ¼  ¼ b  cð1 þ ln T Þ  2dT oT P  e ln w þ eT w ; Dds H ¼ Dds G þ T Dds S ¼ a  cT  dT 2 þ eT 2 w ;

–3



–4

Dds cP ¼ T

–5



–6

o2 Dds G oT 2

oDds G Dds V ¼  oP

–7 –8 –3.0

ð16Þ

–2.5

–2.0

–1.5

–1.0

–0.5

Log H2O density (g cm–3) Fig. 3. Linear relationships between logarithmic density of aqueous solvent and logarithmic equilibrium constants for homogeneous solvent and salt dissociation, and salt solubility: (A) Self-dissociation of H2O with experimental data at liquidlike densities. Solid lines represent the fit of Marshall & Franck (1981), dotted curves are the model of Bandura & Lvov (2006), and point symbols are experimental data from Quist (1970), at 400, 600 and 800C. (B) Dissociation of NaCl (aq). Experimental data by Quist & Marshall (1968) are shown by point symbols at 400, 500, 600, 700 and 800C, with isotherms fitted to the data set. (C) Halite solubility in aqueous vapor. Experimental measurements are indicated by the following symbols – circles: Galobardes et al. (1981); diamonds: Armellini & Tester (1993); triangles: Higashi et al. (2005). Dashed lines are isotherms at 350, 450 and 550C fitted to the data set.

Dds b ¼ 



¼ c 2dT þ2eT w þeT 2

P

ð17Þ

  ow ; oT P ð18Þ

 ¼ eT bw ;

ð19Þ

    1 oDds V obw ¼ eT ; oP T Dds V oP T

ð20Þ

T

where qw, aw and bw represent the density, isobaric expansivity and isothermal compressibility of the solvent respectively. These thermodynamic relationships can also be used for deriving model parameters for a solubility equilibrium of interest by using the DdsH, DdsS and DdsV or DdscP at reference temperature and pressure (e.g. 25C and 1 bar) from existing thermodynamic databases (e.g. Wagman et al. 1982; Johnson et al. 1992; Oelkers et al. 1995; Parkhurst & Appelo 1999; Hummel et al. 2002). The calculation procedure for a three-parameter version of the model is given in Appendix A.

Thermodynamic model for mineral solubility in aqueous fluids 25 The new thermodynamic model (Eq. 12) suggests a functional form for a stand-alone equation of state for aqueous species. Any arbitrary standard thermodynamic property, Y, of bulk aqueous solute (aq) is a combination of corresponding property of dissolving solid phase (s) and its change during dissolution: ð21Þ

Y ðaqÞ ¼ Y ðsÞ þ Dds Y :

An equation of state for a solid phase and the standard thermodynamic properties of dissolution (Eq. 12, 16–18 or 19) can thus be added to obtain an equation of state for aqueous solutes applicable at high temperatures and pressures, which will consist of a caloric term (enthalpy, entropy and a heat capacity polynomial), a volumetric term (intrinsic volume of the species) and a density term.

CALIBRATION OF THE MODEL Solubilities of seven simple minerals – three oxides (quartz, corundum and rutile) and four calcium-bearing phases (anhydrite, apatite, calcite and fluorite) – have been determined experimentally at high temperatures and pressures and were used to explore the model and evaluate its performance. These minerals dissolve both as neutral or charged aqueous species, and their solubilities differ by seven orders of magnitude. For the solvent properties, we

have employed the equation of state of H2O for scientific use (Harvey 1998; Wagner & Prub 2002), which is calibrated by experiments to 1 GPa but extrapolates reasonably to very high pressures. Experimental solubility data at elevated pressure and temperature were first converted to molal concentration of the solute, temperature and density of H2O; multiple experiments at the same pressure and temperature were averaged to a single value in order to avoid artificial weighting of the fit. The reduced data sets were fitted by linear least squares to the equation of state for dissolution (Eq. 14). The resulting model parameters are listed in Table 1, standard thermodynamic properties at 25C and 1 bar are presented in Table 2 and the results plotted in Figs 4 and 5. The solubility of quartz in aqueous fluids and fluid mixtures has been extensively studied from ambient conditions up to 1100C and 20 kbar (e.g. Manning 1994 and references therein, Newton & Manning 2008a) and evaluated by Walther & Helgeson (1977), Fournier & Potter (1982), Manning (1994), Akinfiev (2001) and Gerya et al. (2005). We have calibrated our thermodynamic model using a subset of direct-sampling or rapid-quench experimental data (Hemley et al. 1980; Walther & Orville 1983; Manning 1994) augmented by calculated values from Fournier & Marshall (1983). The five-parameter fit (Table 1) reproduces experimental data set from 25 to 900C and from saturation vapor pressure up to 20 kbar

Table 1 Parameters of the thermodynamic model (Eqs 12, 14 and 16–20).

Apatite-F Calcite Corundum Fluorite Portlandite Quartz Rutile

a (kJ mol)1)

b (J K)1 mol)1)

63.4 57.4 80.3 56.4 13.1 23.6 104.0

3.90 )35.71 )29.31 )24.89 10.05 )52.92 )33.72

(11.6) (7.6) (5.9) (5.0) (2.8) (1.5) (5.1)

(10.83) (8.55) (5.72) (4.92) (4.99) (34.9) (4.88)

c (J K)1 mol)1)

10.93 (5.46)

d (J K)2 mol)1)

)0.0463 (0.0044)

e (J K)1 mol)1)

Data sources

)89.32 )72.98 )37.01 )59.73 )94.74 )18.52 )13.32

1 2, 3 4, 5 6 7 8–11 12

(8.95) (6.83) (2.82) (3.89) (3.47) (0.27) (3.77)

The model parameters are consistent with equilibrium constant defined on the molal concentration scale (Eq. 14). Values in parentheses are 1 standard error. Sources of experimental data – 1: Antignano & Manning (2008a); 2: Fein & Walther (1989); 3: Caciagli & Manning (2003); 4: Becker et al. (1983); 5: Tropper & Manning (2007a); 6: Tropper & Manning (2007b); 7: Walther (1986); 8: Hemley et al. (1980); 9: Fournier & Marshall (1983); 10: Walther & Orville (1983); 11: Manning (1994); 12: Antignano & Manning (2008b).

Table 2 Standard thermodynamic properties of dissolution at T = 25C and P = 1 bar. log K Apatite-F Calcite Corundum* Fluorite Portlandite Quartz Rutile

)11.31 )8.20 )12.54 )8.59 )2.82 )3.91 )16.45

(0.09) (0.22) (0.15) (0.11) (0.09) (0.02) (0.05)

DdsG (kJ mol)1)

DdsH (kJ mol)1)

DdsS (J K)1 mol)1)

DdscP (J K)1 mol)1)

DdsV (cm3 mol)1)

64.53 46.78 71.60 49.01 16.08 22.32 93.93

61.24 55.69 79.46 55.01 10.84 24.05 103.98

)11.02 29.90 26.37 20.13 )17.60 5.80 33.72

)90.13 )73.65 )37.35 )60.27 )95.60 )2.04 )13.43

)12.08 )9.87 )5.00 )8.07 )12.81 )2.50 )1.80

(0.49) (1.27) (0.83) (0.60) (0.53) (0.13) (0.27)

*Properties metastable with respect to gibbsite. Thermodynamic properties are referred to the molality concentration scale. Values in parentheses represent 1 standard error on the fit over the whole range of temperature and pressure. Comparison with experimental solubilities not used in regression reveals errors of 1 kJ for DdsG and 3 kJ for DdsH, respectively, at 25C and 1 bar for quartz (Rimstidt 1997).

26 D. DOLEJSˇ & C. E. MANNING

–1

2

(A) Quartz 1

1000

0 –1

400 300

–2

200

200

–3

100

Log molality AIO1.5

800

Log molality SiO2

(B) Corundum

1000

V+L

–2

800

–3

600

–4 400

–4 –5 –0.4

–0.3

–0.2

0

–0.1

–5 –0.4

0.1

–0.2

–0.3

–2

0 1000

(C) Calcite

800

0.1

0

–0.1

1000

(D) Apatite

Log molality CaCO3

400

–2

–3 200

–4

–5 –0.3

Log molality Ca5 (PO4)3F

800 600

–1

V+L

–0.2

–0.1

0

–3

600

–4 400

–5 –0.2

0.1

–1

–0.1

0

0.1

0

(E) Rutile

(F) Fluorite 1000

–2 –3

800

–4 600

–5 –6

Log molality CaF2

Log molality TiO2

1000

800

–1

600

–2 400

–3

400

–7 –0.4

–0.3

–0.2

–0.1

0

0.1

–4 –0.4

–0.3

–0.2

–0.1

0

Log H2O density (g cm–3) –1

Log molality Ca(OH)2

(G) Portlandite

1000 400

–2 200

–3

V+L

–4

–5 –0.4

–0.3

–0.2

–0.1

0

Log H2O density (g cm–3)

0.1

0.1

Fig. 4. Solubilities of rock-forming minerals in pure H2O, expressed on the molality scale, and their changes with the H2O density. Isotherms of solubility are calculated using the thermodynamic model (Eq. 14, Table 1), fitted to experimental data shown by filled symbols at selected temperatures and the liquid–vapor coexistence curve (experimental studies illustrated in open symbols were not used in fitting). Sources of experimental data – (A) solid upright triangles: Anderson & Burnham (1965); solid inverted triangles: Hemley et al. (1980); solid diamonds: Walther & Orville (1983); solid circles: Manning (1994); open circles: Kennedy (1950), Morey & Hesselgesser (1951), Wyart & Sabatier (1955), Kitahara (1960), Morey et al. (1962), Weill & Fyfe (1964), Crerar & Anderson (1971), at isotherms of 25, 100–900C; (B) solid diamonds: Becker et al. (1983) at 666–700C; solid circles: Tropper & Manning (2007a) at 700, 800, 900, 1000 and 1100C; open circles: Walther (1997) at 400, 500 and 600C; (C) solid diamonds: Fein & Walther (1989) at 400, 500 and 600C; solid circles: Caciagli & Manning (2003) at 500, 600 and 700C; (D) solid circles: Antignano & Manning (2008a) at 700, 800 and 900C; (E) solid circles: Antignano & Manning (2008b) at 800, 900 and 1000C; open circles: Tropper & Manning (2005) at 1000 and 1100C; open diamonds: Aude´tat & Keppler (2005) at 821–1025C; open triangle: Ryzhenko et al. (2006) at 500C; (F) solid circles: Tropper & Manning (2007b) at 600, 700, 800, 900 and 1000C; open diamonds: Stru¨bel (1965) at 200, 300, 400, 500 and 600C; (G) solid circles: Walther (1986) at 300, 400, 500 and 600C. The V + L represents subcritical coexistence of aqueous liquid and vapor. Calculated solubilities in this and subsequent figures are extended into metastable regions where some phases may either transform (e.g. portlandite to portlandite II), hydrate (e.g. corundum to boehmite or gibbsite) or melt (e.g. calcite at T > 750C).

Thermodynamic model for mineral solubility in aqueous fluids 27

0

2

(A) Quartz

(B) Corundum –1 1.2

Log molality AIO1.5

Log molality SiO2

1.2 1 20 5

0

0.4 2 1

–1 0.7 0.5 0.4

–2

20

0.6 5

–3 0.4

–5

–3 0.6

1.0

1.8

1.4

0.7

–1

(C) Calcite 1.0

20

0.8

1.5

1.2

1.8

(D) Apatite 1.2

1.2

Log molality Ca5(PO4)3F

Log molality CaCO3

1

–6 0.6

2.2

–1 10 0.8

–2 5 0.6

–3 –4

2

–4

V+L

0

10

–2

0.4 2

–5

–2 1.0 20

–3 0.8 10

–4

0.6

–5

5 0.7

1

–6 0.8

Log molality TiO2

–3 –4

1.6

–1

(E) Rutile 1.2 20 5 0.4 2

–2

1 0.7 0.4

–5

0.8

1.0

1.2

(F) Fluorite 1.0 20

1.2

0.8 10

–3 0.6 5

–4 0.4

–5

–6

2

–7 0.6

0.8

1.0

1.2

1.4

–6 0.6

1

0.8

1.0

1.2

0.7

1.4

0.4

1.6

1.8

2.0

Inverse temperature (10–3 K–1) –1

(G) Portlandite Log molality Ca(OH)2

Fig. 5. Solubilities of rock-forming minerals in pure H2O as a function of inverse absolute temperature. Isobars of solubility are indicated by solid and dotted curves, respectively, and labeled in upright numerals (pressure in kbar), whereas isochores are drawn by dashed and dot-dashed curves, respectively, and labeled in italic numerals (H2O density in g cm)3). Experimental solubility measurements are plotted along selected isobars and the liquid–vapor coexistence curve – (A) open circles: liquid–vapor coexistence curve; solid circles: 0.5 kbar; upright triangles: 1 kbar; inverted triangles: 2 kbar; diamonds: 5 kbar; squares: 10 kbar; hexagons: 20 kbar (Kennedy 1950; Morey & Hesselgesser 1951; Kitahara 1960; Morey et al. 1962; Weill & Fyfe 1964; Anderson & Burnham 1965; Crerar & Anderson 1971; Hemley et al. 1980; Walther & Orville 1983; Manning 1994); (B) diamonds: Becker et al. (1983) at 5, 10 and 20 kbar; circles: Tropper & Manning (2007a) at 10 and 20 kbar; (C) diamonds: Fein & Walther (1989) at 2 kbar; circles: Caciagli & Manning (2003) at 10 kbar; (D) circles: Antignano & Manning (2008a) at 10, 15 and 20 kbar; (E) diamond: Ryzhenko et al. (2006) at 1 kbar; circles: Antignano & Manning (2008b) at 10 and 20 kbar.

–2

1.4

–6 0.6

Log molality CaF2

–1

1.2

1.0

0.4

1.0

–2 0.8 10

–3 0.6

–4

–5 0.6

5

V+L

1 0.7

2

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Inverse temperature (10–3 K–1)

with remarkable accuracy (Figs 4A and 5A). In most cases, the scatter of multiple experiments exceeds the deviation between the experimental and calculated solubilities.

Despite the small data subset (n = 84) used in fitting the model, other experimental data are reproduced remarkably well (Fig. 5), with average deviation r = 0.017, 5.23%.

28 D. DOLEJSˇ & C. E. MANNING Corundum solubilities in pure H2O were experimentally determined by Becker et al. (1983), Ragnarsdo´ttir & Walther (1985), Walther (1997) and Tropper & Manning (2007a). The measurements of Becker et al. (1983) and Tropper & Manning (2007a) at 660–1100C and 2.5– 20 kbar are very consistent mutually and in their temperature and pressure dependencies (Figs 4B and 5B). The two studies of Walther and coworkers differ by log molality unit at H2 O > 0.5 g cm)3. Careful examination of the data reveals that isothermal solubilities of Walther (1997) have a very similar dependence on the solvent density as those of Becker et al. (1983) and Tropper & Manning (2007a), but his reported solubilities are systematically greater by 1.2–1.5 log molality units. This suggests formation of additional Al-bearing complexes in Walther’s (1997) experiments. Consequently, our thermodynamic model was fitted with experimental solubilities of Becker et al. (1983) and Tropper & Manning (2007a). The set of experiments (n = 24) is satisfactorily reproduced (r = 0.092, 3.12%) with the reduced, three-parameter form of the model, ln K ¼ 1=Rða=T þ b þ e ln Þ; of the model (Table 1). Rutile dissolves in pure H2O to form neutral hydroxyspecies but is characterized by extremely low solubility. Neglecting an early study of Ayers & Watson (1993), which reported anomalously high solubilities due to mass transport in experiments, the rutile solubility has been experimentally determined by Tropper & Manning (2005), Aude´tat & Keppler (2005), Ryzhenko et al. (2006) and Antignano & Manning (2008b). These studies cover a temperature range of 500–1100C at pressures of 1–20 kbar, and are complemented by low-temperature investigations of Vasilev et al. (1974), Zemniak et al. (1993) and Knauss et al. (2001) between 100 and 300C and up to 200 bar. Earlier measurements of Tropper & Manning (2005) are associated with high analytical uncertainties and limited to temperatures of 1000–1100C. By contrast, the diamond-anvil cell determinations by Aude´tat & Keppler (2005) gave consistently lower titanium concentrations and much lower dependence on temperature. A three-parameter fit to the data at 700–1000C and 7–20 kbar of Antignano & Manning (2008b) (n = 8, r = 0.028, 0.85%) reproduces rutile solubilities determined by fluid extraction at 500C and 1 kbar (Ryzhenko et al. 2006) and 300C and 200 bar (Knauss et al. 2001), respectively, to 0.2 log molality units (Fig. 4E). Calcite dissolves congruently in pure water, and its solubility has been experimentally determined at high temperatures and pressures by Walther & Long (1986), Fein & Walther (1989) and Caciagli & Manning (2003), in addition to exploratory studies of Schloemer (1952) and Morey (1962). The solubilities reported by Walther & Long (1986) are 0.3–0.5 log molality units lower than subsequent measurements of Fein & Walther (1989) and were, therefore, discarded. The experimental results of Fein & Walther (1989) and Caciagli & Manning (2003) show

consistent and continuous behavior from 400 to 750C and from 2 to 16 kbar, and were satisfactorily described by a three-parameter model (n = 21, r = 0.159, 9.28%) to the thermodynamic model (Figs 4C and 5C). Apatite solubility, using nearly pure fluorapatite (Durango, Mexico) comes from a single study of Antignano & Manning (2008a) at 700–900C and 10–20 kbar (n = 6). Individual experimental measurements show consistent isothermal linearity in the log q versus log m space (Fig. 4D) and were fitted to a three-parameter model with r = 0.050, 1.34%. Fluorite solubility in pure water has been investigated by Stru¨bel (1965) at 150–620C up to 2.1 kbar and by Tropper & Manning (2007b) at 600–1000C and 5–20 kbar. The earlier experiments are associated with very large analytical uncertainties and show no clear temperature dependence. By contrast, the recent measurements of Tropper & Manning (2007b) have high precision and display systematic variations with temperature and solvent density. This data set (n = 12) has been used for calibrating a three-parameter model fit (r = 0.086, 3.84%). Walther (1986) determined the solubility of portlandite in pure H2O. Although the pressure–temperature range was smaller than for the other minerals considered here, the data were included in this study for several comparative purposes: (i) portlandite produces basic solution with high ionic strength, (ii) the data set covers a temperature range of 300–600C, where significant changes in speciation are expected to occur and (iii) solubilities show a strong negative temperature dependence. As shown in Figs 4G and 5G, the experimental data (n = 34) are very well reproduced by a three-parameter fit to the thermodynamic model (r = 0.087, 1.82%), which extends and confirms its application to systems with substantial changes in dissociation and variable ionic strength.

DISCUSSION We fitted the experimental solubilities of seven minerals in pure water to a thermodynamic model (Eq. 14). The fitted experimental data cover a temperature range of 100– 1100C at pressures up to 20 kbar. The solubilities vary by up to six orders of magnitude on the molality concentration scale and are reproduced by the model to better than 5%, or 0.1 log molality units. Larger deviations, such as for calcite, are related not to the functional form of the thermodynamic model but rather to the scatter of repeated experiments at the same temperature and pressure or to poor consistency of different experimental or analytical methods. The solubilities of six minerals were reproduced satisfactorily by a three-parameter function only, whereas quartz solubility required two additional terms to describe the heat capacity of the dissolution reaction and its linear dependence on temperature. It is noteworthy that quartz is

Thermodynamic model for mineral solubility in aqueous fluids 29 the most soluble mineral in our data set and that solute silica is known to polymerize (Zotov & Keppler 2000, 2002; Newton & Manning 2002, 2003, 2008a). In our model, aqueous silica reflects total dissolved silica in an unspecified but implicit mixture of monomeric and polymerized species. As the equilibrium constant for the homogeneous polymerization equilibrium is temperature dependent (Newton & Manning 2003; Manning et al. 2010), the heat capacity term – required to fit experimental data over an extended temperature range – presumably incorporates differences in enthalpies and entropies of the monomer and dimer, respectively, as their proportions in the bulk solute change with increasing temperature and pressure. The isothermal, isobaric, isochoric and vapor-saturation solubilities presented in Figs 4 and 5 provide insights into interpolation and predictive capabilities of the new thermodynamic model, and illustrate the controls of aqueous speciation on these trends. In all cases, the mineral solubilities increase with the H2O density at constant temperature (Fig. 4). The magnitude of this increase, (¶ log m ⁄ ¶ log q)S, depends on parameter e only, i.e. it is dictated by the combination of the generalized Krichevskii and Born parameter of the solute species. Quartz, corundum and rutile, which congruently dissolve as neutral hydroxyspecies at neutral conditions, e.g. Si(OH)4, Al(OH)3 and Ti(OH)4 (Walther & Helgeson 1977; Bourcier et al. 1993; Knauss et al. 2001), show a relatively small increase in solubility with increasing water density at constant temperature, (¶ log m ⁄ ¶ log q)S = 1.6–4.5. By contrast, the solubilities of Ca-bearing minerals – calcite, apatite, fluorite and portlandite – exhibit much stronger dependence on the water density, (¶ log m ⁄ ¶ log q)S = 7.2–11.4. These phases involve congruent dissolution to a variety of charged species, ion pairs and neutral complexes (e.g. Ca2+, CO2 3 , ) ) +  HCO 3 , OH , F , CaF , H2 PO4 , etc.; Walther 1986; Shock & Helgeson 1988; Fein & Walther 1989). The charged species cause much stronger electrostriction effects in the hydration shell as illustrated by the dependence of the species Helgeson–Kirkham–Flowers Born parameter on species charge (Shock & Helgeson 1988; Sverjensky et al. 1997). This translates to partial molar volumes of dissolution that grow more negative with increasing charge of the solute species. Using Eq. 19 at 25C and 1 bar, the partial molar volumes of dissolution for quartz, corundum and rutile are )1.8 to )5.0 cm)3 mol)1, whereas those for Ca-bearing phases are )8.1 to )12.8 cm)3 mol)1. Consequently, electrostriction in the vicinity of the charged species promotes the solubility increase with pressure by a factor of three to four. The spacing of isotherms in Fig. 4, (¶ log m ⁄ ¶T)q, varies between 7.7 · 10)3 and 6.1 · 10)2 and 5.9 · 10)4 and 4.7 · 10)3 K)1 at 25 and 800C, respectively, and q = 1 g cm)3. These variations are related to caloric properties in our model (Eq. 14) as follows:

  o o ln K 1na c ¼   d : oT  R T 2 T

ð22Þ

Equation 22 demonstrates that an increase in mineral solubility with temperature at constant density is free of hydration–compression effects. The caloric terms of all minerals broadly overlap at 25C, but quartz, corundum and rutile are more endothermic at 800C. Consequently, solubilities of these three minerals increase by a greater degree with temperature than that of the Ca-bearing minerals along isochores (cf. Fig. 1). This behavior is related either to distinct lattice enthalpies of oxides versus other minerals considered in this study, or to variably endothermic nature of chemical hydration of neutral versus charged aqueous species. The changes in mineral solubilities with temperature at constant pressure are depicted in Fig. 5. The solubility isobars are highly nonlinear and often show retrograde solubility effects. The slope 

o ln K oð1=T Þ

 ¼ P

Dds H R

ð23Þ

corresponds to the standard enthalpy of dissolution, which consists of caloric and volumetric contributions (Eq. 17). The caloric term is quasilinear or, more often, constant (when c = d = 0). By contrast, the volumetric term scales by parameter e in the model and is responsible for the reversals of solubility isobars as temperature changes. The solvent contribution to the enthalpy (Eq. 17) depends on the isobaric expansivity of H2O, a, which is low, 0.5– 2.0 · 10)3 K)1 at low and high temperatures, respectively, but it diverges to infinity at the critical point of H2O. This feature is inherited as a maximum in the expansivity versus temperature at supercritical pressures until it disappears at approximately 8 kbar (Helgeson & Kirkham 1974; Fletcher 1993, p. 221). As a consequence, the eawT2 term in Eq. 17 becomes very negative as the expansivity approaches its maximum. Depending on the magnitude of e, the expansivity term may counteract the positive caloric contribution (a – cT – dT2), leading to negative enthalpy of dissolution and hence mineral solubility that decreases with temperature at the highest values of a. The magnitude of this effect increases towards the critical point of H2O. The onset and extent of the isobaric retrograde solubility is directly related to the parameter e of the density term, i.e. it depends on the generalized Krichevskii and Born parameters of aqueous solute (Fig. 6A). For Ca-bearing minerals, the isobaric retrograde solubility appears from low- to medium-grade metamorphic temperatures and covers the high-temperature space through the granulite facies (Figs 6 and 7). The remarkable offset of the

30 D. DOLEJSˇ & C. E. MANNING

(A) 5

Mineral solubilities along geothermal gradients

Po (–94.7) Ap (–89.3)

retrograde solubility of portlandite is due to its unusually low-standard enthalpy of dissolution (Table 2). By contrast, retrograde solubility behavior is suppressed where mineral dissolution produces neutral solutes, due to their very low electrostriction volumes (Table 2). Thus, for oxide minerals, retrograde solubility is more restricted in the pressure–temperature space (Fig. 7), and for the oxides considered in this study is limited to low pressures (rutile: 403 bar, quartz: 972 bar, corundum: 1231 bar).

The calibrated thermodynamic model (Table 1, Eq. 14) allows the calculation of mineral solubilities at geothermal gradients of interest, chosen here as 20C km)1 approximating the Barrovian continental gradient and 7C km)1, which corresponds to a representative subducting slab geotherm (cf. Fig. 1). In order to express the results in comparable quantities (ppm, wt% solute or vol% mineral), mass amounts of minerals have been recalculated to volumes using volumetric properties summarized in Table 3. The density of water has been calculated using the equation of state of Wagner & Pruß (2002), consistent with the model. Figure 8 shows that mineral solubilities in aqueous fluids vary by 10 orders of magnitude, from sub-ppb to greater than 10 wt%. For all minerals except portlandite, the solubilities regularly increase with increasing depth along both gradients. The solubility increases by three to seven orders of magnitude between 200 and 1100C. Although the portrayal using temperature as the independent variable (Fig. 8) shows little difference between the continental and the slab gradients, respectively, the limits of the diagram correspond to different pressures and depths. The observed trends are in agreement with general rule that mineral solubilities are mainly dependent on temperature. The calculations also imply that substantial changes in the solubilities are expected around thermal disturbances, e.g. magma chambers, emplaced at a given depth. The sequence of minerals in Fig. 8 starts with quartz and calcite, followed by portlandite, fluorite, and apatite, whereas corundum and rutile are the least soluble and mobile phases in pure H2O. These predictions are in good agreement with observed or inferred element mobilities during crustal fluid flow (e.g. Ague 2003). Titanium and aluminum solubilities are quite low in pure H2O at all conditions. While this nominally supports their use as immobile elements in mass transfer, hydrothermal alteration and ore deposit studies (Maclean 1990; Maclean & Barrett 1993; Ague 1994; Dolejsˇ & Wagner 2008), it is important to note that both elements may form soluble complexes with other elements (alkalies, halogens, silica, etc.) which can cause them to be mobilized in certain metasomatic environments (e.g. Tagirov & Schott 2001; Manning 2007; Manning et al. 2008; Newton & Manning 2008b).

GEOLOGICAL APPLICATIONS

Mineral solubilities at constant pressure

We illustrate the performance and application of the thermodynamic model by evaluating the mineral solubilities in aqueous fluids along representative geotherms and by applying transport theory to assess mass transfer and fluid flux associated with model metasomatic scenarios.

Mineral solubilities at constant pressure allow investigation of the potential for element mobility along flow paths associated with thermally induced gradients at a fixed crustal level, such as out- and inflow accompanying cooling of intrusions (Norton & Knight 1977; Hanson 1992;

4

Cc (–73.0)

Pressure (kbar)

Fr (–59.7)

3

2 Co (–37.0) Qz (–18.5)

1

Ru (–13.3)

0

0

200

400

600

800

1000

Temperature (°C) 0

(B)

Ru Qz

(cm3 mol–1)

–6

dsV

–3

–9

Co Fr Cc

–12

–15

Ap

Po

100

200

300

400

Temperature (°C) Fig. 6. Correlations between the isobaric retrograde solubility and its onset, and (A) model parameter e (numerical labels), which scales the solvent density, and (B) partial volume of dissolution (per mole of solute at T = 25C and P = 1 bar) versus the onset of isobaric retrograde solubility (at P = 300 bar).

Thermodynamic model for mineral solubility in aqueous fluids 31

Quartz

(A) 105

20

Corundum

(B) 103

5

20

10

104

1 0.7 0.5 0.4

103

102 200

500

800

Solubility (ppm Al2O3)

Solubility (ppm SiO2)

2

101

1

10–1

Calcite

Apatite-F Calcite Corundum Fluorite Portlandite Quartz Rutile

800

1100

Rutile 20 5

102 5

102 101 2

100

2 1 0.7

101

0.4

100

10–1

10–1 0.4

10–2 200

500

0.7

1

800

Temperature (°C)

6

500

10

103

Table 3 Volumetric properties of minerals. 5

0.4

(D) 103

20

Solubility (ppm TiO2)

Solubility (ppm CaCO3)

Fig. 7. Retrograde solubility behavior illustrated for (A) quartz, (B) corundum, (C) calcite and (D) rutile. Gray shading indicates regions where the isobaric mineral solubility decreases with increasing temperature. Experimental data and symbols are as in Fig. 5.

0.7

Temperature (°C)

Temperature (°C)

(C) 104

2

100

10–2 200

1100

5

102

V (cm3 mol)1)

¶V ⁄ ¶T · 10 (cm3 K)1 mol)1)

¶V ⁄ ¶P · 10 (cm3 bar)1 mol)1)

Data sources

157.14 36.59 25.37 23.30 32.25 22.55 18.65

12.24* 12.24 6.70 41.97 19.14* 11.03 5.33

)5.38* )5.38 )1.21 )10.15 )5.11* )5.21 )1.00

1 2 2 3 4 2 2

*Estimate obtained by correlation with similar substance. Molar volume of mineral at temperature and pressure of interest is defined by: VP,T = V + (¶V ⁄ ¶T)T + (¶V ⁄ ¶P)P where temperature, T, is in kelvin and pressure, P, in bar. Sources of data – 1: Mackie & Young (1974); 2: Holland & Powell (1998), updated in 2004 and available from the Thermocalc website (Richard White, University of Mainz); 3: Speziale & Duffy (2002); 4: Megaw (1933).

Norton & Dutrow 2001). Figure 9 compares predicted isobaric temperature dependence of mineral solubilities at 1 and 10 kbar respectively. With the exception of portlandite, the 10 kbar mineral solubilities and their temperature dependencies are very similar to those along geothermal gradients (Fig. 8); however, in detail, the magnitude of solubility increase above approximately 700C is lower. Portlandite solubility declines with rising temperature. These features are a consequence of the larger decrease in H2O density with temperature than along the geotherms.

1100

10–2 200

500

800

1100

Temperature (°C)

The solubility behavior changes dramatically at low pressures, e.g. 1 kbar (Fig. 9B), as is expected from the variations in isobaric expansivity of H2O. Rutile, which has the smallest parameter e is above its retrograde maximum, and its solubility increases monotonously with temperature. Quartz and corundum show a solubility plateau above 500C; hence, mass transfer will be minimized at these conditions. The solubilities of Ca-bearing phases substantially decrease above 350–450C; that of portlandite shows a steady decline over the whole temperature range. These results imply that temperature gradients in isobaric aquifers may alone be responsible for substantial decoupling of mineral precipitation and dissolution. The Ca-bearing minerals all dissolve as the fluid cools down to approximately 400C, and the precipitation of, for instance, calcite or fluorite will be suppressed until temperature declines to below 350C. This may explain a generally late nature of carbonate precipitation in hydrothermal ore veins (Mangas & Arribas 1987) or low temperatures of fluorite–barite mineralization (Baatartsogt et al. 2007). By contrast, quartz and aluminosilicate alteration reactions are predicted to experience a reversal (cf. Fournier & Potter 1982; Fournier 1999), i.e. mineral precipitation at magmatic and low temperatures, separated by a dissolution gap at near-critical conditions (cf. Fig. 7A, B). This mechanism has been postulated for the formation of quartz veins and desilicification in plutonic environments (Nichols & Wiebe 1998).

32 D. DOLEJSˇ & C. E. MANNING

(A)

6

(B) dT/dz = 20°C km–1

6

dT/dz = 7°C km–1

Qz

Qz

4

Cc Po

Fr

Log solubility (ppm)

Log solubility (ppm)

4

1 wt.%

Co Ap

2 Ru

0

–2

Ap

500

800

Ru

0

–4 200

1100

500

800

(B)

Fig. 8. Solubilities of rock-forming minerals in pure H2O along geothermal gradients of (A) 20 and (B) 7C km)1. Solubilities of oxides are shown by solid curves whereas Ca-bearing phases are in dashed style.

6

P = 10 kbar

P = 1 kbar Qz

1 wt.%

4

Log solubility (ppm)

Cc

Po Fr

Co

2 Ap

Ru

0

–2

1 wt.% Qz

2

0 Co Ru Cc

–2

500

800

–4 200

1100

Temperature (°C)

Fr

Po

Ap

–4 200

1100

Temperature (°C)

(A) 6

500

800

1100

Temperature (°C)

(A)

Fig. 9. Solubilities of rock-forming minerals in pure H2O at constant pressure of (A) 10 and (B) 1 kbar. Line styles are as in Fig. 8.

(B)

14

14

dT/dz = 20°C km–1

Log integrated fluid flux (m3 m–2)

Log integrated fluid flux (m3 m–2)

Co

2

Temperature (°C)

Log solubility (ppm)

Fr

Cc

–2

–4 200

4

Po

1 wt.%

12 Ru

10

Ap Po

8

Fr 1%

Co

Cc

6 Shear zone veins 100%

Qz

4 Pervasive metamorphic flow

2 200

500

8 00

Temperature (°C)

1100

dT/dz = 7°C km–1

12 10 Ru Co

8

Fr

Ap 1%

Po

6 Shear zone veins 100%

Cc Qz

4 Pervasive metamorphic flow

2 200

500

800

Temperature (°C)

Mass transfer and mineral mobility in the Earth’s interior The present thermodynamic model provides a self-consistent formulation of all thermodynamic properties of mineral dissolution equilibria and their pressure and temperature dependence. We illustrate its utility by calculating the intensity of mass transfer and metasomatism and the related integrated fluid fluxes in several representative settings. Transport theory (see Appendix B) was applied to the calculation of the time-integrated fluid fluxes necessary to precipitate a unit volume of vein material (1 m3). The integrated fluid fluxes for mineral precipitation along the

1100

Fig. 10. The time-integrated fluid flux necessary to precipitate mineral vein filling (1 m3) as a function of temperature along geothermal gradients of (A) 20 and (B) 7C km)1. Typical integrated fluid fluxes for diffuse metamorphic fluid flow and focused shear zone flow (Ague 2003) are shown by dotted lines. The range of partial vein filling (100 to 1 vol% of precipitating phase) is indicated by gray areas. Line styles are as in Fig. 8.

geothermal gradients of 20 and 7C km)1 are very similar, but vary significantly with temperature. They range from 107–1015 m3 m)2 at 200C to 104–108 m3 m)2 at 1100C (Fig. 10). When compared with characteristic integrated fluid fluxes during diffusive metamorphic flow and in crustal shear zones (Ferry 1994; Ague 2003), medium- to high-grade metamorphic temperatures are sufficient to cause substantial mobility of quartz, calcite and fluorite (in decreasing order; Fig. 10). Conversely, a predefined integrated fluid flux may be used to calculate and compare the magnitudes of mass transfer (in volume fraction precipitated or dissolved; Fig. 11). Along the geotherms and at a

Thermodynamic model for mineral solubility in aqueous fluids 33

(B)

Log amount of mineral precipitated (vol. fraction)

0

dT/dz = 20°C

km–1

Log amount of mineral precipitated (vol. fraction)

(A) Qz Cc

–2

Fr Po

–4

Co

Ap

Ru

–6

–8

–10 200

500

800

0

–2

Fr Ap Co

–4

Ru

–6

–8

500

Temperature (°C)

1100

(D) 0

Log amount of mineral precipitated or dissolved (vol. fraction)

0

Log amount of mineral precipitated or dissolved (vol. fraction)

800

Temperature (°C)

(C)

Fig. 11. Amount of precipitated or dissolved minerals produced by the integrated fluid flux, q = 105 m3 m)2 (Ague 2003) at geothermal gradients of (A) 20 and (B) 7C km)1, and at constant pressure of (C) 10 and (D) 1 kbar. Mineral precipitation (as temperature decreases) is indicated by black curves, whereas dissolution is shown by gray dashed and dotted patterns. Gray area indicates a range between 1 and 100 vol% in the rock. Line styles are as in Fig. 8.

Cc Po

–10 200

1100

Qz

dT/dz = 7°C km–1

Qz Cc

Po Fr

–2

Co Ap

–4

Ru

–6

–8

P = 10 kbar & dT/dz = 200°C km–1 –10 200

500

800

Temperature (°C)

constant pressure of 10 kbar, the integrated fluid flux characteristic for metamorphic shear zones (105 m3 m)2; Ague 2003) leads to mobilities of SiO2 from 1 vol% at 300–350C to 10 vol% at 600–620C and a complete silicification above 900C. This is in good agreement with macroscopic observation of quartz segregations and veining from greenschist facies conditions. The fluid-mediated mobilities of calcite are one-half to one order of magnitude lower, but metasomatism of fluorite and apatite components may reach vol% levels at the highest subduction temperatures (Fig. 11b). Amounts of precipitation of rutile and corundum are low, from sub-ppm (at 200C) to a few tenths of vol% (at 1100C) but, importantly, these values are probably still significant for trace element redistribution during metamorphic events, focused fluid flow, or hydrothermal alteration. During lateral fluid flow at constant pressure the extent of the mineral precipitation is expected to vary along the cooling path, or precipitation will alternate with mineral dissolution and loss in certain temperature segments (Fig. 11C, D). At 10 kbar, retrograde solubility occurs for portlandite above 290C and above 1000C for apatite. Other Ca-bearing phases such as calcite or fluorite variably precipitate during cooling (2–7 vol%), whereas the capability of oxide precipitation (quartz, corundum and rutile) strongly decreases with decreasing temperature. At 1 kbar, all minerals except rutile exhibit rapid changes in

1100

Qz

–2 Po

–4

Cc Fr Ru Co

–6

Ap

–8

P = 1 kbar & dT/dz = 200°C km–1 –10 200

500

800

1100

Temperature (°C)

precipitation and ⁄ or dissolution as a function of temperature (Fig. 11D). The intensity of silicification drops to below 1 vol% between 700 and 400C, whereas corundum will dissolve between 720 and 530C bracketed by precipitation at high or low temperatures. No Ca-bearing minerals precipitate above 390C. These results are applicable to spatial hydrothermal zoning in the vicinity of upper crustal intrusions. The intensity of silicification varies by nearly two orders of magnitude and quartz veining is expected to be most intense at 300– 400C. The behavior of aluminum, as judged from the corundum solubility, reverses from precipitation and dissolution, and back, which will probably enhance its local redistribution and hence mobility. Carbonates will not precipitate in high-temperature contact aureoles even if the fluids are CO2 bearing, which promotes, by extrapolation, the formation of skarns replacing carbonate host rocks. Limitations and extensions of the modeling Our mass transport calculations illustrate the applicability and versatility of a density-based model to investigate fluid-mediated mass transfer in the Earth’s crust and upper mantle. The results also highlight some limitations that stem from focusing only on congruent dissolution equilibria in pure water in the modeling. For example, for phases where the fluid–mineral interaction is controlled by the

34 D. DOLEJSˇ & C. E. MANNING formation of additional species or complexing, our calculations provide a minimum estimate of the mass transfer (that is, the amount of mineral precipitated or dissolved) or a maximum estimate for the integrated fluid flux. These observations indicate that, if formed under local equilibrium, metamorphic veins containing sparingly soluble minerals such as kyanite or rutile require either enormously large fluid fluxes or the presence of complexing agents, such as, halide, carbonate or aluminosilicate ligands and their polymeric successors (Tagirov & Schott 2001; Manning 2007; Antignano & Manning 2008b). The magnitude of this effect can be quantified by considering that ¶ log m ⁄ ¶z is approximately independent of the nature of the mineral (Fig. 8); hence, the integrated fluid flux scales in direct proportion to the solubility increase in the presence of other aqueous complexes. The presence of 10 wt% dissolved silicates lowers the necessary fluid flux for rutile crystallization by a factor of 13 at 900C and 10 kbar, or the quartz saturation enhance the kyanite precipitation by a factor of 6 at 700C and 10 kbar. This brings the mobility of Ti and Al to wt% level at the highest temperatures modeled in this study (Fig. 11). Increasing self-dissociation of H2O at high pressures and the presence of other complexing ions also play important roles.

CONCLUSIONS (1) We have developed a new thermodynamic model for dissolution of minerals in aqueous fluids at high temperatures and pressures. The model incorporates thermodynamic contributions from lattice breakdown, ionization and hydration, which depend on temperature, and the effects associated with the compression in the hydration sphere and electrostatic solute–solvent interactions, which are formulated as a function of solvent volumetric properties. The solvent density term has the form of the generalized Krichevskii parameter, which is a finite and smooth function near the critical point of water, and has a simple linear scaling with the reciprocal dielectric constant. (2) Experimental solubilities of seven rock-forming minerals were used to calibrate the model and demonstrate its performance. With the exception of quartz, solubilities in aqueous fluids at metamorphic and magmatic conditions can be described by three parameters to within the experimental scatter or accuracy. The solubility of quartz required a five-parameter formulation, which includes heat capacity and its temperature dependence. We propose that these terms probably assimilate the distinct enthalpy and entropy of the silica monomer and dimer, respectively, and ⁄ or deviations from the infinite-dilution limiting behavior as fluids become solute rich. (3) Solubilities of all seven rock-forming minerals increase smoothly with temperature along metamorphic geotherms or water isochores. Temperature dependence is

fairly similar for all solid phases but portlandite. The solubility of a given phase increases for a given phase by three to seven orders of magnitudes as temperature rises from 200 to 1100C along typical geotherms. At constant pressure, however, mineral solubilities initially increase with rising temperature but subsequently drop. This effect is caused by a reversal in isobaric expansivity of the aqueous solvent, which propagates into the enthalpy of dissolution. The onset of retrograde solubility typically occurs at 300– 400C and it is a characteristic of all minerals. (4) Solute speciation, volume of dissolution and the prograde–retrograde solubility behavior are inter-related. Oxide minerals such as quartz, corundum and rutile, which dissolve as predominantly neutral species, exhibit very small dependence on the solvent properties. Consequently, their isobaric retrograde solubility is limited to pressures below 1.3 kbar. The Ca-bearing phases, by contrast, produce variably charged species upon dissolution, where the electrostriction effects are more significant. Calcite, fluorite, apatite and portlandite show a decrease in mineral solubility at medium to high metamorphic grades over a wide range of pressures. (5) Application of solute transport theory to our thermodynamic model permits calculation of time-integrated fluid fluxes, which are necessary to precipitate mineral veins during metamorphic events. The integrated fluid fluxes along geotherms of 20 and 7C km)1 vary from 104 to 1015 m3 m)2 in the following sequence: quartz, calcite, fluorite, corundum and apatite, and rutile. This is in broad agreement with observations of high mobility and veining of quartz and calcite as the most mobile-predicted phases in many metamorphic environments. Conversely, typical integrated fluid fluxes in crustal shear zones produce a transfer of quartz and calcite in quantities of several tens of vol%, whereas the solubility of apatite or rutile lies below 1000 ppm, which may still be important for the trace element budget in metasomatized rocks. (6) The small number of parameters in the thermodynamic model allows correlation with the standard thermodynamic properties at arbitrary reference conditions (e.g. 25C and 1 bar), which are readily available. In the appendix A we provide relationships for transformation of standard enthalpies, entropies, volumes and heat capacities into the model parameters. This approach enables utilization of existing thermodynamic data (e.g. the Helgeson– Kirkham–Flowers equation of state) in the framework of our model and allows extrapolation of standard thermodynamic properties over a wide range of metamorphic and magmatic temperatures and pressures.

ACKNOWLEDGEMENTS This study was supported by a postdoctoral fellowship from the Elite Network of Bavaria, the Ministry of Education of the Czech Republic research project MSM002162085, by

Thermodynamic model for mineral solubility in aqueous fluids 35 the Czech Science Foundation project 205 ⁄ 09 ⁄ P135 (to D.D.) and by a research award from the Alexander von Humboldt Foundation (to C.E.M.). We appreciate stimulating discussions with T. Wagner (ETH Zu¨rich) as well as critical comments by the journal reviewers: G. M. Anderson and G. Pokrovski that helped us to improve the manuscript.

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APPENDIX. A Thermodynamic equivalences The new thermodynamic model in reduced form with three independent parameters can be calibrated using the standard thermodynamic properties of minerals and aqueous species at reference temperature and pressure, e.g. 25C and 1 bar (e.g. Johnson et al. 1992; Oelkers et al. 1995). The three-parameter form, Dds G ¼ a þ bT þ eT ln ; o 1 na ln K ¼  þ b þ e ln  ; R T

(A1) (A2)

requires that three independent thermodynamic properties must be known – DdsG or DdsH, DdsS, and DdsV or DdscP; note that volume and heat capacity are not independent (cf. Anderson et al. 1991). Using Eq. A1 and rearranging Eqs 16–19, the model parameters are obtained as follows: e¼

Dds V Dds cP ; ¼ 2T w þ T 2 ðow =oT ÞP T

(A3)

b ¼ Dds S þ eðT w  ln w Þ; 2

(A4) 2

a ¼ Dds H  eT w ¼ Dds G þ T Dds S  eT w :

(A5)

The above relationships can be used with the standard thermodynamic properties at any temperature and pressure by employing T and q, b, a and (da ⁄ dT)P of water at the preferred reference conditions (e.g. 25C and 1 bar). The calibration provides means of predicting mineral solubilities (Eq. 14) at any temperature and pressure of interest.

APPENDIX. B Transport theory The transport theory is used to calculate amounts of solids precipitating from ascending aqueous fluids (Baumgartner & Ferry 1991; Ferry & Dipple 1991). In advectionreaction equation the mass conservation during porous isotropic flow is expressed as follows (e.g. Bear 1972, pp. 77–78; Ague 1998): oci oci ¼ v þ Ri ot ox

(B1)

where c is the molar concentration of solute i, t is time, x and v are the distance and flow velocity, respectively, and

40 D. DOLEJSˇ & C. E. MANNING R denotes the reaction rate. At steady state, which is closely approached during mineral-fluid buffering (Ferry & Burt 1982), the solute concentration is invariant with time, ¶ci ⁄ ¶t = 0; hence, Ri ¼

oci v: ox

(B2)

As mineralogical record in rocks reflects the time-integrated result of fluid–rock interaction, integrating Eq. B2 over time, Z t Z t oci v dt; (B3) Ri dt ¼ 0 0 ox

¶mi ⁄ ¶z, is recast into temperature and pressure dependence: omi omi oT omi oP ¼ þ oz oT oz oP oz

(B5)

where ¶T ⁄ ¶z and ¶T ⁄ ¶P represent the geothermal and pressure gradient of interest, whereas the molality changes with temperature and pressure are obtained from the standard thermodynamic properties of dissolution (cf. Eqs 17 and 19) as follows: omi o ln K Dds H ¼K ; ¼K oT oT RT 2

(B6)

omi o ln K Dds V ¼K ¼ K : oP oP RT

(B7)

leads to qV omi ; ni ¼ V oz

(B4)

where n is the number of moles of i precipitated per rock volume, qV is the time-integrated fluid, and V is the molar volume of aqueous fluid. The gradient of molality with vertical distance during one-dimensional flow,

These relationships illustrate that the amount of substance precipitated from 1 kg of aqueous fluid per temperature or pressure increment depends on both the solute concentration (expressed by K = m) and its gradient.

Metal complexation and ion association in hydrothermal fluids: insights from quantum chemistry and molecular dynamics D. M. SHERMAN Department of Earth Sciences, University of Bristol, Bristol, UK

ABSTRACT Complexation by ligands in hydrothermal brines is a fundamental step in the transport of metals in the Earth’s crust and the formation of ore deposits. Thermodynamic models of mineral solubility require an understanding of metal complexation as a function of pressure, temperature and composition. Over the past 40 years, mineral solubilities and complexation equilibria under hydrothermal conditions have been predicted by extrapolating thermodynamic quantities using equations of state based on the Born model of solvation. However, advances in theoretical algorithms and computational facilities mean that we can now explore hydrothermal fluids at the molecular level. Molecular or atomistic models of hydrothermal fluids avoid the approximations of the Born model and are necessary for any reliable prediction of metal complexation. First principles (quantum mechanical) calculations based on density functional theory can be easily used to predict the structures and relative energies of metal complexes in the ideal gas phase. However, calculations of metal complexation in condensed fluids as a function of temperature and pressure require sampling the configuration degrees of freedom using molecular dynamics (MD). Simulations of dilute solutions require very large systems (thousands of atoms) and very long simulation times; such calculations are only practical by treating the interatomic interactions using classical two- or threebody interatomic potentials. Although such calculations provide some fundamental insights into the nature of crustal fluids, simple two- or three-body classical potentials appear to be inadequate for reliably predicting metal complexation, especially in covalent systems such as Sn2+, Au3+ and Cu+. Ab initio MD (i.e. where the bonding is treated quantum mechanically, but the molecular motions are treated classically) avoids the use of interatomic potentials. These calculations are practical for systems with hundreds of atoms over short times (