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

Hydrothermal Experimental Data

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

Hydrothermal Experimental Data

Edited by Vladimir M. Valyashko

A John Wiley & Sons, Ltd., Publication

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

Dedication

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

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

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

viii Contents

3.3

Data treatment References

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

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

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

227

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

249

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

271

Index

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

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

272 272 274 284 289

CD Table of Contents

Appendix to Chapter 1

pTX

Appendix to Chapter 2

pVTX

Appendix to Chapter 3

Potentiometry

Appendix to Chapter 4

Electrical Conductivity

Appendix to Chapter 5

Thermal Conductivity

Appendix to Chapter 6

Viscosity

Appendix to Chapter 7

Calorimetric

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

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

xii Foreword

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

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

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

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

xiv

Preface

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

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

Acknowledgements

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

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

1

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

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

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

2

Hydrothermal Experimental Data

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 3

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

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

Summary of experimental data on phase equilibria in hydrothermal systems

H-Fl

CH4 (Methane) Sampl

Methods 298/473; 518 K

Temperature 1.3/3.2; 6.5 MPa

Pressure −4

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

−4

Composition

ptx-CH4-7.1

Tables

Crovetto et al., 1982

REFERENCE

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

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

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

Phase equilibria

Non-aqueous components

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

Table 1.1

4 Hydrothermal Experimental Data

Wt-loss; Quench Quench

Wt-loss; Sampl

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Ag + buff.

Ag in CH2O (formaldehyde)

Ag in (HCl + H2)

Ag in (HCl + KCl + H2)

Ag in (HCl + NaCl + H2)

Ag in (HCl + NaCl)

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

Soly

Soly

AgBr; AgBr in NaBr

Wt-loss; Sampl

Wt-loss

Soly

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

Soly

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

Soly

(Ag + Cu) in HCl

Sampl

Soly

AgxAuySz

Wt-loss; Quench Quench

Quench

Quench

Quench

3

2

1

Methods

Phase equil

Non-aqueous components

200; 300 C

20/269–349 C

300 C

40/200–300 C

40/200–300 C

91/150; 250 C

300 C

450–800 C

350–500 C

200 C

450 C

200; 280 C

200 C

300; 450 C

4

Temperature

SVP

SVP

SVP

SVP

SVP

SVP

SVP

1; 2 kbar

500–2500 bar

SVP

500; 1000 bar

SVP

SVP

SVP; 500 atm

5

Pressure

−6

3.9–1.5 (AgBr) (−log m); 0–1 m NaBr

ptx-AgBr + NaBr-1.1

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

ptx- AgxAuySz-1.1

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

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

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

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

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

Xiao et al., 1998

Xiao et al., 1998

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

Kozlov and Khodakovskiy, 1983 Tagirov et al., 1997

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

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

Zotov et al., 1985a

8

7 ptx-Ag-1.1

REFERENCE

Table

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

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

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

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

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

6

Composition

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 5

Sampl

Sampl

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

AgCl

AgCl AgCl

AgCl

AgCl in HCl

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

AgCl in (HCl + ZnCl2)

AgCl in KCl

AgCl in KCl

AgCl in NaCl

AgCl in NaCl

AgCl in NaCl

AgCl in NaCl

AgCl in NaCl

Quench

Soly

Soly

Soly

Soly

Ag2CrO4

AgF

Sampl

Sampl

Wt-loss; Quench Quench

Soly

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

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

Quench

Wt-loss; Quench Wt-loss; Quench Sampl

Sampl

Sampl

Quench Wt-loss; Quench Sampl

Wt-loss

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

22/200; 250 C

25/195–260 C

250; 300 C

200–300 C

250 C

200; 250 C

400; 425 C

450 C

300 C

300 C

100/197–353 C

450 C

300 C

100/200–350 C

40/200–300 C

200; 300 C

100/200–350 C

300–360 C

250; 300 C 450 C

20/220–359 C

4

Temperature

SVP

SVP

SVP

SVP

SVP

SVP

500–1500 bar

500–1750 bar

SVP

SVP

SVP

500; 1000 bar

SVP

SVP

SVP

SVP

SVP

41–183 bar

SVP 500–1500 bar

SVP

5

Pressure

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

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

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

0.08–0.17 (AgCl); 0.2; 0.5 (NaCl) m

0.04–1.05 (Ag); 0.09–2.56 (NaCl) m

0.005–0.86 (Ag); 0.025–7 (NaCl) m

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

ptx-AgF-1.1

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

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

ptx-AgCl-4.1; 4.2

9.82–7.9 (AgCl) (−log mol.fr.)

ptx-AgCl-2.1 ptx-AgCl-3.1

ptx-AgCl-1.1

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

8

7

6

Gavrish and Galinker, 1970 Gavrish and Galinker, 1970

Zotov et al., 1985

Zotov et al., 1982

Levin, 1991

Zotov et al., 1986

Tagirov 1997

Levin, 1993

Levin, 1991

Zotov et al., 1986

Seward, 1976

Levin, 1993

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

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

REFERENCE

Table

Composition

6 Hydrothermal Experimental Data

Sampl

Sampl

Soly

Soly

Soly LGE

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

AgI

AgI in NaI

AgNO3 AgNO3

Ag2O

Ag2S in (NaOH + H2S)

Ag2S in (NaOH + H2S)

Ag2S in (NaOH + S)

Ag2SO4 in D2SO4

Ag2SO4 in H2SO4

Ag2SO4 in UO2SO4

Ag2SO4 in UO2SO4

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

Sampl

Sampl

Quench

Sampl

Sampl

Sampl

Soly

Soly

Soly

Soly

Soly

Soly

AlOOH (boehmite) in (HCl + NaCl)

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

AlOOH (boehmite) in (NH4OH + NH4Cl)

AlOOH (boehmite) in (NH4OH + NH4Cl)

Vis.obs.

Vis.obs.

Vis.obs.

Vis.obs.

Flw.Sampl

Sampl

Sampl

Sampl

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

Wt-loss

3

2

1

Methods

Phase equil

Non-aqueous components

150/200–350 C

70/200 C

150/200; 250 C 300 C

300 C

90/200–350 C

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

25/200; 250 C 36/197–259 C

25/195–234 C

25/200–400 C

25/200; 250 C 18/199–302 C

25/200–260 C

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

20/300–365 C

4

Temperature

SVP

SVP??

SVP (86 bar)

SVP

SVP (86 bar)

SVP

SVP

100 bar

SVP

SVP

SVP

SVP

1/40–500 bar

1.3/18.7–121 bar

SVP

SVP SVP (2.53/3.3–21.2 bar) SVP

SVP

SVP

5

Pressure

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

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

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

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

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

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

0.0022/0.063–0.022 (Ag2O) g/100 g H2O

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

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

ptx-Ag2O-1.1

ptx-AgNO3-1.1 ptx-AgNO3-2.1

ptx-AgI + NaI-1.1

ptx-AgI-1.1

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

8

7

6

Castet et al., 1993

Verdes et al., 1992

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

Salvi et al., 1998

Castetet al., 1993

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

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

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

REFERENCE

Table

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 7

Potentio; Sampl

Sampl

Sampl

Sampl

Soly

Soly

Soly

Soly

Soly

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

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

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

Sampl

Wt-loss; Quench Sampl

Soly

Soly

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

Soly Soly

Soly

Soly

Soly Soly

Soly

Soly Soly

Al2O3 (corundum) Al2O3 (corundum)

Al2O3 (corundum)

Al2O3 (corundum)

Al2O3 (corundum) Al2O3 (corundum)

Al2O3(corundum)

Al2O3 (corundum) Al2O3 (corundum) in AlCl3

Sampl Quench

Wt-loss

Wt-loss Sampl

Wt-loss

Wt-loss

Quench Wt-loss

Sampl

Soly

AlOOH (boehmite) in (NaOH + SiO2)

Soly

Sampl

Soly

AlOOH (boehmite) in (NaOH + NaCl)

Potentio; Sampl

3

2

1

Methods

Phase equil

Non-aqueous components

Table 1.1 Continued

272–600 C 600 C

700–1100 C

666–700 C 400–720 C

350–500 C

500–800 C

380–420 C 700–900 C

135/200–300 C

523–598 K

250; 300 C

300 C

170/200–350 C

135/200–300 C

200; 250 C

250; 300 C

101.5/203–290 C

100/203–290 C

4

Temperature

500–2480 bar 2 kbar

500–2000 MPa

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

(−3.4)-(−1.56) (Al) (log m)

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

0.008–0.19 (Al2O3) g/L

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

0.0008–0.0059 (Al2O3) mass.%

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

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

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

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

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

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

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

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

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

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

6

Composition

6 kbar

25–49 MPa 6–6.75 kbar

SVP??

SVP??

SVP

SVP (86 bar)

SVP

SVP??

SVP

SVP

SVP

SVP-68 bar

5

Pressure

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

ptx-Al2O3–8.1

ptx-Al2O3-5.1 ptx-Al2O3-6.1

ptx-Al2O3-4.1

ptx-Al2O3-3.1

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

Verdes et al., 1992

Bernshtein and Matsenok, 1965 Chang et al., 1979

Salvi et al., 1998

Castet et al., 1993

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

Benezeth et al., 2001

Palmer et al., 2001

8

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

REFERENCE

Table

8 Hydrothermal Experimental Data

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

in KF

Al2O3 (corundum) in KF

in

in

in

in

in

in

in

in

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

Soly

in HF

Soly

Soly

in

in

Soly

in

Soly

Soly

in

in

Soly

in

Soly

Soly

in

in

Soly

in

Soly

Soly

in

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

in

2

1

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

Phase equil

Non-aqueous components

Quench

Wt-loss

Quench

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Quench

Quench

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Quench

Wt-loss

Wt-loss

Wt-loss

Sampl

Quench

Wt-loss

3

Methods

450 C

430–600 C

600 C

430 C

400 C

500–700 C

600–900 C

430; 600 C

430; 600 C

400 C

600 C

800 C

430

430; 600 C

430 C

450–700 C

430

430; 600 C

430; 600 C

198–600 C

600 C

430; 600 C

4

Temperature

1000 atm

1450–2760 bar

2 kbar

1450 bar

0.5–2 kbar

1.86–2.65 kbar

2–6 kbar

1450 bar

1380; 1450 bar

??50 MPa

2 kbar

6; 6.17 kbar

1450 bar

1450 bar

1450 bar

1; 2 kbar

1450 bar

1450 bar

1450 bar

625–2100 bar

2 kbar

1450 bar

5

Pressure

1.12–3.46 (Al2O3); 14 (Na2CO3) mass.%

<2 (Al2O3) mass.%

4 (LiOH) m; Solid-[LiAlO2] 2.3 (Al2O3) (−log mol/L); 1 (MgCl2) mol/L

(0.064–7.1) * 10−2 (Al2O3); 0.001–0.1 (KOH) m

0.09–0.89 (Al); 0.1–1.0 (KOH) m

1.3–7.2 (Al2O3) mass.%; 0.35–1.5 (KOH) m

0.0032; 0.0066 (Al2O3) m; 0.01; 0.2 (KF) mol/L 2; 10 (KF) m; Solid ph.-[K3AlF6] 6.6; 6.9 (Al2O3) mass.%; 2 (KOH) m

2.3 (Al2O3) (−log mol/L); 1 (KCl) mol/L

0.13; 0.15 (Al2O3) mass.%; 4.6 (KCl) m

<2 (Al2O3) mass.%; 2–20 (KCl) m

2.23; 2.37 (Al2O3) (−log mol/L); 1 CaCl2 mol/L 2.83–3.99 (Al2O3) (−log m); 0.1 (CaCl2) m 3.4; 4.8 (Al2O3) mass.%; 2 (Cs2CO3) m 5.2; 5.7 (Al2O3) mass.%; 2 (CsOH) m <0.2 (Al2O3) mass.%; 3.3 (HCl) m 4.42–1.72 (Al2O3) (−log mol/L); 0.07–1.9 HCl mol/L 7.8 (HF) m; Solid ph.-[Al(OHF)3] 4.3; 5.8 (Al2O3) mass.%; 2 (K2CO3) m

2 (Ba(OH)2) m; Solid ph.-not Al2O3

6

Composition 8 Barns et al., 1963

7 ptx-Al2O3 + Ba(OH)2-1.1 ptx-Al2O3 + CaCl2-1.1 ptx-Al2O3 + CaCl2-2.1 ptx- Al2O3 + Cs2CO3-1.1 ptx-Al2O3 + CsOH-1.1 ptx-Al2O3 + HCl-1.1 ptx-Al2O3 + HCl-2.1 ptx-Al2O3 + HF-1.1 ptx-Al2O3 + K2CO3-1.1 ptx-Al2O3 + KCl-1.1 ptx-Al2O3 + KCl-2.1 ptx-Al2O3 + KCl-3.1 ptx-Al2O3 + KF-1.1 ptx-Al2O3 + KF-2.1 ptx-Al2O3 + KOH-1.1 ptx-Al2O3 + KOH-2.1 ptx-Al2O3 + KOH-3.1 ptx-Al2O3 + KOH-4.1 ptx-Al2O3 + LiOH-1.1 ptx-Al2O3 + MgCl2-1.1 ptx-Al2O3 + NH4OH-1.1 ptx-Al2O3 + Na2CO3-1.1 Yamaguchi et al., 1962

Barns et al., 1963

Korzhinskiy, 1987

Anderson and Burnham, 1967 Pascal and Anderson, 1989 Azaroual et al., 1996 Barns et al., 1963

Barns et al., 1963

Barns et al., 1963

Yalman et al., 1960

Anderson and Burnham, 1967 Korzhinskiy, 1987

Barns et al., 1963

Barns et al., 1963

Barns et al., 1963

Korzhinskiy, 1987

Barns et al., 1963

Barns et al., 1963

Barns et al., 1963

Walther, 2002

Korzhinskiy, 1987

REFERENCE

Table

Phase Equilibria in Binary and Ternary Hydrothermal Systems 9

Wt-loss

Wt-loss

Quench

Sampl

Wt-loss

Quench

Quench

Wt-loss

Wt-loss

Wt-loss

Sampl

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

H-Fl; Cr.ph

Cr.ph; H-Fl

H-Fl

H-Fl; Cr.ph

LGE

H-Fl Soly

LGE; Soly

Soly

Ar

Ar

Ar

Ar

Ar in D2O As2O3 (claudetite)

As2O3; As2O3 + NaCl, in HCl, H2S As2O5

As2S3 (orpiment) in (As2O3 + HCl)

Non-aqueous

Wt-loss

Soly

Al2O3 (corundum) in Na2CO3 Al2O3 (corundum) in NaCl Al2O3 (corundum) in NaCl Al2O3 (corundum) in NaCl Al2O3 (corundum) in NaCl Al2O3(corundum) in NaCl Al2O3 (corundum) in NaOH Al2O3 (corundum) in NaOH Al2O3 (corundum) in NaOH Al2O3 (corundum) in NaOH Al2O3 (corundum) in NaOH Ar

Sampl; Quench; Potentio Wt-loss; Sampl

Sampl Wt-loss

Vis.obs.; p-T curves Sampl

Vis.obs.; p-T curves p-x curves

3

2

1

Methods

Phase equil

Non-aqueous components

Table 1.1 Continued

200–300 C

130/250–450 C

307/454; 568 K 297/461–584 K 22/150–250 C

477–663

298/496–561 K

375–400 C

350–400 C

500; 700 C

800; 900 C

400–600 C

400; 450 C

380–420 C

800 C

400–600 C

600 C

800 C

430 C

430; 600 C

4

Temperature

SVP

SVP (0–356 bar)

1.32/2.7–13.28 MPa SVP

1.67/2.2; 9.7 MPa

10.4–337.2 MPa

SVP

230–3100 bar

221–4000 bar

2–2.62 kbar

6–6.13 kbar

140–2760 bar

100–1500 atm

25–49 MPa

10 kbar

491–2010 bar

2 kbar

6.0 kbar

1450 bar

1450 bar

5

Pressure

2.33–0.49 (As) (−log m); 0–740 (As2O3) mg; 0; 0.01 (HCl) mol/L

0–9 (NaCl); 0–0.09 (HCl); 0–0.2 (H2S) m

0.04–53.8 (Ar) mol.% 0.21–1.2 (As) (log m)

0.027–52.12 (Ar) mol.%

0.05–0.8 (Ar) mol.fr.

0.009–0.021/0.074 (Ar) mol.%

1–28 (Ar) mol.%

0–87 (Ar) mol.%

0.1–0.81 (Al); 0.11–0.94 (NaOH) m

0.64; 0.65 (Al2O3) mass.%; 0.113 (NaOH) m

2.74–26.5 (Al2O3) mass.%; 31.25–400 (NaOH) g/L 2–31.5 (Al2O3) mass.%; 0.5–10 (NaOH) m

0.00021–0.1975 (Al2O3); 0–0.5 (NaOH) m

0.001–0.02 (Al2O3) (m); 0–0.6 (NaCl) mol.fr.

1.44–3.37 (Al2O3) (−log m); 0.1; 0.5 (NaCl) m

2.3 (Al2O3) (−log mol/L); 1 (NaCl) mol/L

0.092 (Al2O3) mass.%; 0.90 (NaCl) m

<0.02 (Al2O3) mass.%; 20 (NaCl) m

4.9; 7.0 (Al2O3) mass.%; 2 (Na2CO3) m

6

Composition

Barns et al., 1963

ptx-Al2O3 + Na2CO3-2.1 ptx-Al2O3 + NaCl-1.1 ptx-Al2O3 + NaCl-2.1 ptx-Al2O3 + NaCl+-3.1 ptx-Al2O3 + NaCl-4.1 ptx-Al2O3+ NaCl-5.1 ptx-Al2O3 + NaOH-1.1; 1.2 ptx-Al2O3 + NaOH-2.1 ptx-Al2O3 + NaOH-3.1 ptx-Al2O3 + NaOH-4.1 ptx-Al2O3 + NaOH-5.1 ptx-Ar-1.1; 1.2

Pokrovski et al., 1996

Crovetto et al., 1982 Pokrovski et al., 1996 Pokrovski et al., 2002

ptx-Ar + D2O-1.1 ptx-As2O3-1.1 ptx-As2O3-2.1– 2.5; ptx-As2O5-1.1 ptx-As2S3 + HCl-1.1

Crovetto et al., 1982

Anderson and Burnham, 1967 Pascal and Anderson, 1989 Tsiklis and Prokhorov, 1966 Lentz and Franck, 1969 Potter II and Clynne, 1978 Wu et al., 1990

Yamaguchi et al., 1962 Barns et al., 1963

Newton and Manning, 2006 Yalman et al., 1960

Walther, 2001

Anderson and Burnham, 1967 Korzhinskiy, 1987

ptx-Ar-5.1

ptx-Ar-4.1; 4.2

ptx-Ar-3.1

ptx-Ar-2.1

8

7

Barns et al., 1963

REFERENCE

Table

10 Hydrothermal Experimental Data

Quench

Wt-loss

Flw.Sampl

Flw.Sampl

Sampl

Sampl

Sampl

Soly

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

As2S3 (orpiment) in Na2S

Au + buff.

Au in Cl2

Au in H2

Au in HCl Au in HCl

Au in (HCl + H2)

Au in (HCl + NaCl + H2) Au in H2S

Au in (H2S + H2)

Au in (H2S + H3PO4 + H2) Au in (H2S + H3PO4 + KH2PO4)

Sampl

Quench Sampl Sampl

Flw.Sampl

Quench

Soly

Soly Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Au in (H2S + NaOH + Na2SO4) Au in (KCl + buffer) Au in (KCl + buffer) Au in (KCl+ buffer)

Au in MgS

Au in NaHS

Au in NaCl + NaOH + H2 Au in (NaOH + buffer)

Au in (NaOH + H2)

Au in Na2S

Quench

Flw.Sampl

Quench

Quench

Sampl

Soly

Au in (H2S + NaOH + H2)

Sampl

Soly

Au in (H2S + NaOH)

Sampl

Quench Quench; Sampl Flw.Sampl

Sampl

3

2

1

Methods

Phase equil

components

590 C

300–600 C

25/250 C

300–450 C

200; 300 C

117/200–399 C

293–556 C 350–450 C 350–500 C

296.2–351 C

150/200–400 C

133/196–356 C

150/199.4–300.8 C

150/200–400 C

150/200–300 C

143/197–352 C

300–500 C

300–600 C

200; 300 C 100/200 C

300–600 C

125/200–500 C

25/200; 253 C 300–500 C

4

Temperature

0.15 GPa

500–1500 bar

SVP

500 bar

SVP

0.14–0.17 GPa

1; 2 kbar 500 bar 500–1000 bar

96.4–234 atm

500–1500 bar

22/37–210.8 atm

27/38–132 atm

500–1500 bar

500 bar

18.4/31–214 atm

500–1800 bar

500–1800 bar

SVP SVP

500–1500 bar

1 atm

500–1500 atm

100–1500 bar

5

Pressure

648–2113 (Au) ppm; 5–13 (Na2S); 10.0; 10.7 (NaOH) mass.% (2.8–55.6) * 10−8 (Au); 0.51; 0.52 (NaCl); 0.11; 0.3 (NaOH); (3.56–3.78) * 10−5 (H2) m 0.4 * 10−9/(0.3–9.1) * 10−7 (Au) mol/L; pH = 7.7/9.2–14 (NaOH); Buff. (Fe2O3/Fe3O4) (0.012–2) * 10−6 (Au); 0.05–0.5 (NaOH); (3.58–3.98) * 10−5 (H2) m 0.1 (Au) g/kg; (Na2S)

0.029–1.21 (Au) ppm; 0.011–0.11 (S) m; 0.036 (H2) bar 0.001–0.365 (Au) ppm; 0.007–0.095 (S); 0.0007–0.144 (H3PO4) m; 0.036 (H2) bar 7.8/7.24–6.13 (Au) (−log m); 0.73; 1.56 (H2S); 0.044; 0.17 (H3PO4); 7.8/0.015; 0.033 (KH2PO4) m 4.53/4.08–2.36 (Au) (−log m); 1.24; 2.13 (H2S); 0.05; 1.67 (NaOH) m 2.075–108.4 (Au) ppm; 0.0176–0.114 (S); 0.0023–0.037 (NaOH) m; 0.036–0.37 (H2) bar 1.9–1.44 (Au) (−log m); 0.9–1.5 (H2S); 0.16–0.98 (NaOH); 0.07–0.12 (Na2SO4) m 2.9–2987 (Au) ppm; 0.5–2 (KCl) mol/L + buff. 6.64–5.45 (Au) (−log m); 0.5 (KCl) m + buff. 5.8–7.5 (Au) (−log m); 0.001–0.1 (KCl) m + buff. 0.1–29.4 (Au) g/kg; 66 (MgS) mass.%

92–1.396 (Au) ppm; 0.05–0.5 (HCl) mol/L 3.67/3.05–2.0/1.79 (Au) (−log m); 0.02–1 (HCl) m (0.01–3.26) * 10−5 (Au); 0.47–1.72 (HCl); (3.76–5.73) * 10−5 (H2) m (0.049–6.65) 10−6 (Au); 0.104–0.975 (NaCl); 1 * 10−9–0.586 (HCl); (0.04–7.9) * 10−4 (H2) m 7.04–5.69 (Au) (−log m); 0.8–1.93 (H2S) m

0.01/1.8–12.1 (As2S3); 0/0.55–3.43 (Na2S) mass.% 8.13–6.46 (Au) (−log m); Buff. (Ni-NiO; Fe2O4-Fe2O3; Cu-Cu2O) 0.08–9.54 (Au) mass. % (Wt-loss); (Cl2 + H2O − gaseous stream) (0.17–17.9) * 10−7 (Au); 4 * 10−5 (H2) m

6

Composition

Weissberg et al., 1966 Zotov et al., 1985b Ogryzlo, 1935 Stefansson and Seward, 2003b Ogryzlo, 1935 Gammons et al., 1997 Stefansson and Seward, 2003c Stefansson and Seward, 2003c Shenberger and Barnes, 1989 Benning and Seward, 1996 Benning and Seward, 1996 Shenberger and Barnes, 1989

ptx-As2S3 + Na2S-1.1 ptx-Au-1.1; 1.2 ptx-Au + Cl2-1.1 ptx-Au + H2-1.1

ptx-Au + MgS-1.1 ptx-Au + NaHS-1.1 ptx-Au + Na/ Cl,OH + H2-1.1 ptx-Au + NaOH-1.1 ptx-Au + NaOH + H2-1.1 ptx-Au + Na2S-1.1

ptx-Au + H2S + Na/OH,SO4-1.1 ptx-Au + KCl-1.1 ptx-Au + KCl-2.1 ptx-Au+KCl-3.1

ptx-Au + H2S + NaOH-1.1 ptx-Au + H2S + NaOH + H2-1.1

ptx-Au + H2S + H3PO4 + H2-1.1 ptx-Au + H2S + H,K/PO4-1.1

ptx-Au + H2S-2.1

ptx-Au + HCl + H2-1.1 ptx-Au + HCl + NaCl + H2-1.1 ptx-Au + H2S-1.1

Stefansson and Seward, 2003c Baranova et al., 1977 Stefansson and Seward, 2003b Fleet and Knipe, 2000

Shenberger and Barnes, 1989 Henley, 1973 Gibert et al., 1998 Tagirov et al, 2005 Fleet and Knipe, 2000 Ogryzlo, 1935

Shenberger and Barnes, 1989 Benning and Seward, 1996

8

7

ptx-Au + HCl-1.1 ptx-Au + HCl-2.1

REFERENCE

Table

Phase Equilibria in Binary and Ternary Hydrothermal Systems 11

383/474–524 K 200–395 C

Vis.obs.

Vis.obs. Vis.obs.

Quench Therm. anal Isopiestc.

Vis.obs.; Sampl; p-V; p-x; p-T curves Vap.pr.

Vap.pr.

Isopiestc.

Sampl

Vis.obs. Flw.Sampl

Sampl Wt-loss; Quench Sampl

Sampl Wt-loss; quench Wt-loss; quench

Soly H-Fl

Soly

Soly Soly

Soly Soly LGE; Isop-m Soly; H-Fl; Immisc; Cr.ph

LGE

LGE

LGE; Isop-m Soly

Soly

Soly Soly

Soly Soly

soly

soly soly

soly

B2O3; HBO2 B2O3+ NaCl

BaBr2

BaBr2 BaCl2

BaCl2 BaCl2 BaCl2

BaCl2

BaCl2

BaCl2

BaF2 in KF

Ba(NO3)2 BaSO4

BaSO4 BaSO4

BaSO4

BaSO4 BaSO4 in CaCl2

BaSO4 in KCl

BaF2

BaCl2

Vis.obs. Sampl

LGE

Sampl

Sampl

110/210–300 C

23/189–279 C 100/210–255 C

100/200–359 C

250 C 100/200–600 C

112/209–417 C 500 C

350–500 C

150/200–350 C

SVP

36/92–1010 bar SVP

1/16–169 atm

SVP 1/15–2100 bar

SVP 1000 bar

SVP

SVP

SVP

4.45/24–165 bar

0.02/0.01–0.005 (BaSO4) mmol/kg H2O 0.002–0.5 (CaCl2); (0.3–22) * 10−4 (BaSO4) mol/L 0.025 (KCl); (0.34–0.8/1.1) * 10−4 (BaSO4) mol/L

4.4/4.5–5 (BaSO4) ppm

ptx-BaSO4-5.1 ptx-BaSO4 + CaCl2-1.1 ptx-BaSO4 + KCl-1.1

ptx-BaSO4-2.1 ptx-BaSO4-3.1; 3.2 ptx-BaSO4-4.1

0.5 * 10−5 (BaSO4) m 3.0–10 (BaSO4) mg/kg H2O

28.4/45.5–82.3 (Ba(NO3)2) mass.% 0.004 (BaSO4) mass.%

ptx-BaF2 + KF-1.1 ptx-Ba(NO3)2-1.1 ptx-BaSO4-1.1

ptx-BaF2-1.1

ptx-BaCl2-8.1

ptx-BaCl2-7.1

ptx-BaCl2-6.1

ptx-BaCl2-5.1; 5.2; 5.3; 5.4

ptx-BaCl2-2.1 ptx-BaCl2-3.1 ptx-BaCl2-4.1

ptx-BaBr2-2.1 ptx-BaCl2-1.1

ptx-BaBr2-1.1

ptx-B2O3-1.1 ptx-B2O3+NaCl-1.1

Gundlach, et al., 1972 Blount, 1977 Uchameishvili et al., 1966 Uchameishvili et al., 1966

Matuzenko et al., 1984 Azizov and Akhundov, 1995 Holmes and Mesmer, 1996b Booth and Bidwell, 1950 Urusova and Ravich, 1969 Benrath et al., 1937 Morey and Hesselgesser, 1951b Jones et al., 1957 Strübel, 1967

Kukuljan et al., 1999 Kracek et al., 1938 Liebscher et al., 2005 Benrath and Lechner, 1940 Benrath, 1941 Benrath and Lechner, 1940 Gillingham, 1948 Kessis, 1967 Holmes and Mesmer, 1981a Valyashko et al., 1983

8

7 ptx-B(OH)3-1.1

REFERENCE

Table

0.09–3.3 (BaF2); 40–69 (KF) mass.%

0.03–0.002 (BaF2) g/100 g H2O

0.42–4.1 (BaCl2) m

0.1–1.45 (BaCl2) m

0.25–1.55 (BaCl2) m

3–67 (BaCl2) mass.%

6/9.5–1405 kg/cm2

175/190–637

0.3/0.9–17.5 MPa

0.04 (BaCl2) mass.% BaCl2 * H2O ⇒ BaCl2 * 0.5H2O ⇒ BaCl2 0.49/0.64–3.62 (BaCl2) m

273 kg/cm2 SVP SVP

426 C 209; 272 C 383/473.6

412/452.5–630 K

83–85 (BaBr2) mass.% 37/50–0 (BaCl2) mass.%

50/65–81.5 (BaBr2) mass.%

0.33–100 (B2O3) mol.% 173–410 (B) ppm; 0.1–26(NaCl) mass.%

0.0007–0.11 (B(OH)3) m

6

Composition

SVP SVP

350–415 C 25/200–370 C

SVP

SVP SVP

−0.76/169–450 C 400; 450 C 25/195–342 C

SVP

5

Pressure

452–645 K

4

B(OH)3

3

2

Temperature

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

12 Hydrothermal Experimental Data

Sampl

Sampl

Quench; Wt-loss Quench; Wt-loss Quench; Wt-loss Quench; Wt-loss Quench; Wt-loss Vis.obs.

soly

soly

Soly

soly

soly

soly

soly

soly

Soly

Soly

Soly

Soly

Soly

H-Fl; Immisc H-Fl; Immisc H-Fl; Immisc H-Fl; Immisc H-Fl

H-Fl

H-Fl

H-Fl H-Fl H-Fl; Immisc

BaSO4 in MgCl2

BaSO4 in NaCl

BaSO4 in NaCl

BaSO4 in NaCl

BaSO4 in NaCl

BaSO4 + UO2SO4

BaSrSO4

BaSrSO4 in NaCl

BeO in HClO4

BeO in HF

Bi2O3

Bi2O3 in HClO4

Bi2O3 in NaOH

CF4

CH4 (methane)

CH4 (methane)

CH4 (methane)

CH4 (methane) CH4 (methane) CH4 (methane)

CHF3 + NaCl

CHF3

CF4 + NaCl

Sampl

2

1

Sampl Sampl Sampl

Sampl

Sampl

Sampl

154/221–354 C 4.5/200–300 C 323/478–589 K

150/200–360 C

38/204.4; 237.8 C 150/200–360 C

492–625 K

471–606 K

Vis.obs.

Vis.obs.

586–663 K

587–669 K

75/200; 300 C 75/200; 300 C 300 C

300 C

300 C

24/200–350 C

25/195–350 C

250 C

94/200–253 C

20/200–450 C

20/200–600 C

95/200–370 C

110/200–310 C

4

Temperature

Vis.obs.

Sampl

Wt-loss; Quench Wt-loss; quench Wt-loss; Quench Sampl

3

Methods

Phase equil

Non-aqueous components

1/1.24–193 (CH4) cm3/g H2O

50–1100 kg/cm2

0.07/0.12–10.9 (CH4) mol.% 1.13–3.1/7 MPa (Henry’s const) 0.02/0.13–84/99.9 (CH4) mol.%

0.985/0.96–0.074 (CH4) mol.fr.

50–1100 kg/cm2

3.5/4–197 MPa 1.1/6.9–13.3 MPa 1.4/6–17 MPa

0.04/19.2–94.6 (CH4) mol.%

3–11 (CHF3); 0.5; 1 (NaCl) mol.%

3–14 (CHF3) mol.%

0.76–3.35 (CF4); 0.3–1 (NaCl) mol.%

1.2–5.8 (CF4) mol.%

ptx-CH4-4.1 ptx-CH4-5.1 ptx-CH4-6.1

ptx-CH4-3.1

ptx-CH4-2.1; 2.2

ptx-CHF3 + NaCl-1.1 ptx-CH4-1.1

ptx-CF4 + NaCl-1.1 ptx-CHF3-1.1

ptx-Bi2O3 + HClO4-1.1 ptx-Bi2O3 + NaOH-1.1 ptx-CF4-1.1

(0.2/3.03–25.9/68.5) * 10−4 (Bi); (0.32/0.79–34) * 10−4 (HClO4) m (16–73) * 10−4 (Bi); 0.0001–5.1 (NaOH) m

Uchameishvili et al., 1966 Uchameishvili et al., 1966 Strübel, 1967

ptx-BaSO4 + MgCl2-1.1 ptx-BaSO4 + NaCl-1.1 ptx-BaSO4 + NaCl-2.1 ptx-BaSO4 + NaCl-3.1 ptx-BaSO4 + NaCl-4.1 ptx-BaSO4 + UO2SO4-1.1 ptx-BaSrSO4-1.1 ptx-BaSrSO4 + NaCl-1.1 ptx-BeO + HClO4-1.1 ptx-BeO + HF-1.1 ptx-Bi2O3-1.1

8

7

Sultanov et al., 1971 Sultanov et al., 1972a Price, 1979 Cramer, S.D., 1982 Gillespie, P.C.; Wilson, G.M., 1982

Olds et al., 1942

Smits et al., 1997a

Smits et al., 1997a

Smits et al., 1997c

Gundlach et al., 1972 Gundlach et al., 1972 Koz’menko et al., 1986 Koz’menko et al., 1985 Kolonin and Laptev, 1982 Kolonin and Laptev, 1982 Kolonin and Laptev, 1982 Smits et al., 1997b

Jones et al., 1957

Gundlach et al., 1972 Blount, 1977

REFERENCE

Table

1.7/5–3 (Ba); 48//91–40 (Sr) ppm; 1 (NaCl) mol/L 5.1 * 10−6–5.5 * 10−3 (BeO); 0–0.026 (HClO4) mol/L (7 * 10−6–2 * 10−3) (BeO); 0.00027–0.013 (HF) mol/L (0.03 1.96–23.6) * 10−4 (Bi) m

1.7/1.2–3.4 (Ba); 3.4/5.0–0.5 (Sr) ppm

0.02–1.0 (MgCl2); (0.8–18.6) * 10−4 (BaSO4) mol/L 0.25–2.0 (NaCl); (0.2–8.4) * 10−4 (BaSO4) mol/L 0.1/2.0 (NaCl) m; 10/145–970 (BaSO4) mg/kg H2O 23/77–426–142 (BaSO4) ppm; 1; 2 (NaCl) mol/L 0.1/0.7–0.06 (BaSO4) mmol/kg; 0.2, 4 (NaCl) m 0.13–1.3 (UO2SO4); (1.5–40) * 10−5 (BaSO4) m

6

Composition

1.4/2.76–69 MPa

32–200 MPa

33–200 MPa

35–200 MPa

26–200 MPa

SVP

SVP

SVP

SVP

SVP

1/15–915 atm

0.03/14–169 atm

SVP

5/103–507 bar

D= 0.3–0.9/1.0 (g/cm3) 1/15–915 atm

SVP

SVP

5

Pressure

Phase Equilibria in Binary and Ternary Hydrothermal Systems 13

Flw.Sampl

Sampl

H-Fl

Cr.ph H-Fl; Cr.ph

H-Fl

H-Fl

H-Fl; Immisc H-Fl; Immisc H-Fl

H-Fl

H-Fl

H-Fl; Immisc H-Fl; Immisc H-Fl; Immisc LGE; Cr.ph

LGE

Cr.ph

L-V

H-Fl

H-Fl

crit ph

CH4 (methane)

CH4 (methane) CH4 (Methane)

CH4 (methane)

CH4 (methane)

CH4 + C5H12 (methane + n-pentane) CH4 (methane) + CaCl2

CH4 (methane) + NaCl

CH4 (methane) + NaCl

CH4 (methane) + NaCl

CH4O (methanol)

CH4O (methanol)

CH4O (methanol)

C2Cl4 (tetrachloroethylene) C2H4 (ethylene)

C2H4O2 (acetic acid)

Non-aqueous

CH4O (methanol)

CH4 (methane) + NaCl

CH4 (methane) + NaCl

CH4 (methane) + D2O

H-Fl

CH4 (methane)

Vis.obs.

p-∆H curves

Vis.obs.

p-T curves

Sampl

Fl.inclus

Vis.obs.; p-T curves Fl.inclus

Sampl

Sampl

652–723 K

Vis.obs.; p-T curves Sampl

166/250, 350 C 376–369 C

298/473 K

373/473–548 K

242–374 C

100/200; 250 C 150/200–300 C

300–600 C

400–600 C

638–799 K

0.5/204–301 C

50/200–350 C

298/474–517.5 K

411/422–589 K

311/467–478 K

427/494–596 C

632–647 K 627–649

298/473; 518 K 350 C

4

Temperature

Sampl

Flw. sampl

Vis.obs. Vis.obs., p-T curves p-T curves

Sampl

Sampl

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

SVP

100/190–730 bar

65 bar

0.2/2.7–11.3 MPa

SVP

4.7/15.4–115 atm

0.1/1.63–8.5 MPa

2 kbar

1 kbar

40–263 MPa

1.1/5.77–12.4 MPa

29.5 MPa

1.8/4.1–7.2 MPa

67–265 MPa

3.1–20.7 MPa

3.4–110 MPa

7.4/10.5–22.5

22–50 MPa 22–298 MPa

98 MPa

1.3/3.2; 6.5 MPa

5

Pressure

0.1–2.5 (C2H4O2) m

0.4/1.4–81/91 (C2H4) mol.%

0.0023/0.059 (C2Cl4) mol.%

0.5 (CH4O) mol.fr.

0–1 (CH4O) mol.fr.

0–1 (CH4O) mol.fr

0.2/0.5–97 (CH4O) mol.%

1.2–63 (CH4); 0–18.3 (NaCl) mass.%

1.7–59 (CH4); 0.4–6.4 (NaCl) mol.%

2–15.4/28.2 MPa Henry’s const.; 0.81–4.70 (NaCl) mol/L 5.8–71.3 (CH4); 0.05–2.37 (NaCl) mol.%

1–32 (CH4) cm3/g; 0–16.7 (NaCl) m

0.00025/0.0007–0.6/0.998 (CH4) mol.fr.

0.03–51/83 (CH4); 0.001/0.0023–65 87 (C5H12) mol.% 23.5 (CH4); 0.65–0.78 (CaCl2) mol.%

0.0005/0.03–0.5 (H2O) mol.fr.

ptx-C2H4O2-1.1

ptx-C2H4-1.1

ptx-C2Cl4-1.1

ptx-CH4O-4.1

ptx-CH4O-3.1

ptx-CH4O-2.1

ptx-CH4 + C5H12-1.1 ptx-CH4 + CaCl2-1.1 ptx-CH4 + D2O-1.1 ptx-CH4 + NaCl-1.1 ptx-CH4 + NaCl-2.1 ptx-CH4 + NaCl-3.1 ptx-CH4 + NaCl-4.1 ptx-CH4 + NaCl-5.1 ptx-CH4O-1.1

ptx- CH4–12.1

ptx-CH4-9.1 ptx-CH4-10.1; 10.2 ptx-CH4-11.1

L=G 0–0.46 (CH4) mol.fr. 0.92/0.74–0.32 (CH4) mol.fr.

ptx-CH4-8.1

Griswold and Wong, 1952 Pryanikova and Efremova, 1972 Marshall and Jones, 1974b Wormald and Yerlett, 2000 Miller and Hawthorne, 2000 Sanchez and Lentz, 1973 Marshall and Jones, 1974a

Lamb et al., 2002

Krader and Franck, 1987 Lamb et al., 1996

Cramer, 1982

Namiot et al., 1979

Ashmyan et al., 1984 Brunner, 1990 Shmonov et al., 1993 Fenghour et al., 1996 Yarrison et al., 2006 Gillespie and Wilson, 1982 Krader and Franck, 1987 Crovetto et al., 1982

Crovetto et al., 1982

8

7

180 (CH4) cm3/g H2O

−4

ptx-CH4-7.1

−4

REFERENCE

Table

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

6

Composition

14 Hydrothermal Experimental Data

Sampl

Vis.obs.; p-x curves Vis.obs. Sampl

H-Fl

H-Fl; Immisc; Cr.ph H-Fl

Cr.ph H-Fl

H-Fl

LGE; Cr.ph

LGE; Cr.ph

Cr.ph

LGE L-V

LGE; Cr.ph

H-Fl; Immisc; Cr.ph LGE

Cr.ph

LGE

LGE

H-Fl; Cr.ph

Cr.ph LGE; Cr.ph

Immisc

Cr.ph

Cr.ph

C2H6 (ethane)

C2H6 (ethane)

C2H6 (ethane) C2H6 (ethane)

C2H6 (ethane + NaCl)

C2H6O (ethanol)

C2H6O (ethanol)

C2H6O (ethanol)

C2H6O (ethanol) C2H6O (ethanol)

C2H6O (ethanol)

C3H6 (propene)

C3H6O (acetone)

C3H6O (acetone)

C3H6O (acetone)

C3H6O + CH4O (acetone + methanol) C3H8 (propane)

C3H8 (propane) C3H8O (2-propanol)

C4H4S (thiophene)

C4H8O (tetrahydrofuran)

C4H8O2 (dioxane)

C2H6 (ethane)

Cr.ph

C2H4O2 (acetic acid)

Vis.obs.

Vis.obs.

Sampl

p-∆H curves

Vis.obs.

p-T, p-V curves Sampl; Vis. obs.; p-T curve Sampl

Flw.Sampl p-∆H curves

Vis.obs.

Sampl

p-T curves; Vis.obs. Sampl

Sampl; Vis. obs. Vis.obs. Flw. sampl

Sampl

Sampl

Vis.obs.

3

2

1

Methods

Phase equil

components

312–374 C

267.5–374 C

125/200 C

312/622–647 K 150/200–300 C

587–663 C

250 C

373/473–538 K

100/200; 250 C 238–374

128/246–368 C

457–598 K

150–250 C ∆H-p-curves

243–374 C

150/200–350 C

150/200–345 C

631–789 K

621–647 K 314/467 K

295–474 K

38/204.4; 238 C 200–400 C

596–604 K

4

Temperature

SVP

SVP

5.5/29.2 bar

1.4/22–49 MPa 0.5/1.85–12.3 MPa

SVP (4.75–8.20 MPa) 17.37–187.17 MPa

SVP

SVP (0.1/1.6–6.8 MPa) SVP

100–3000 bar

2.1–15.5 MPa

743–7123 kPa 423/473–548 K

SVP

0.6/1.8–19 MPa

0.7/2.1–19.5 MPa

48.6–251.8 MPa

22–50 MPa 3.4–110 MPa

SVP

SVP (2.76–69 MPa) 200–3700 bar

SVP

5

Pressure

ptx-C2H6-4.1 ptx- C2H6–5.1

L=G 0.0004/0.043–0.4 (H2O) mol.fr.

0–1 (C4H8O2) mol.fr.

0–1 (C4H8O) mol.fr.

0.26/0.99–80.27/95.7 (C4H4S) mol.%

ptx-C4H8O2-1.1

ptx-C4H8O-1.1

ptx-C4H4S-1.1

ptx-C3H8-2.1 ptx-C3H8O-1.1

L=G 0.003–0.93 (C3H8O) mol.fr.

0.03–0.26 (C3H8) mol.fr.

ptx-C3H6O + CH4O-1.1 ptx-C3H8-1.1; 1.2

ptx-C3H6O-3.1

ptx-C3H6O-2.1

ptx-C3H6O-1.1

ptx-C2H6O-6.1; 6.2 ptx-C3H6-1.1; 1.2; 1.3

ptx-C2H6O-4.1 ptx-C2H6O-5.1

ptx-C2H6O-3.1

1.5–47 (C3H6O); 2.2–73 (CH4O) mol.%

0.5 C3H6O mol.fr.

0.1–1 (C3H6O) mor.fr.

0.1–98 (C3H6O) mol.%

0.27–90 (C3H6) mol.%

0.2–0.8 (C2H6O) mol.fr.

0.1–0.73 (C2H6O) mol.fr. 0.5 (C2H6O) mol.fr.

0–1 (C2H6O) mol.fr.

0.006–0.93/0.97 (C2H6O) mol.fr.

6–100 (C2H6O) mol.%

ptx-C2H6 + NaCl-1.1 ptx-C2H6O-1.1; 1.2 ptx-C2H6O-2.1

ptx-C2H6-3.1

1.035–1.905 ln(kOH ) (GPa) (Henry’s const)

5.07–50 (C2H6); 0.015–2.5 (NaCl) mol.%

ptx-C2H6-2.1

ptx-C2H6-1.1

Brunner, 1990 Barr-David and Dodge, 1959 Anderson and Prausnitz, 1986 Marshall and Jones, 1974b Marshall and Jones, 1974b

Griswold and Wong, 1952 Marshall and Jones, 1974b Wormald and Yerlett, 2002 Griswold and Wong, 1952 de Loos et al., 1980

Sanchez and Lentz, 1973

Brunner, 1990 Yarrison et al., 2006 Michelberger and Franck, 1990 Griswold et al., 1943 Barr-David and Dodge, 1959 Marshall and Jones, 1974b Niesen et al., 1986 Wormald and Vine, 2000 Bazaev et al., 2007

Crovetto et al., 1984

Danneil et al., 1967

Vandana and Teja, 1995 Reamer et al., 1943

8

7 ptx-C2H4O2-2.1

REFERENCE

Table

0.5–93 (C2H6) mol.%

20.6–94.4/99.94 (C2H6) mol.%

0.54–0.94 (C2H4O2) mol.fr.

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 15

Flw.Sampl

Vis.obs.

Sampl

H-Fl; Immisc Cr.ph H-Fl; Cr.ph

Cr.ph; Immisc H-Fl; Cr.ph Cr.ph

LGE; Immisc Cr.ph; H-Fl Cr.ph

H-Fl

Cr.ph

Immisc

Cr.ph

H-Fl

H-Fl; Cr.ph; Immisc H-Fl; Immisc H-Fl; Cr.ph H-Fl; Immisc Cr.ph

Cr.ph H-Fl; Immisc Immisc

C4H10 (n-butane)

C5H8 (cyclopetane)

C5H12 (n-pentane)

C6H4Cl2 (dichlorobenzene) C6H4F2 (1,4-difluorobenzene) C6H5Cl (chlorbenzene)

C6H5F (fluorobenzene)

C6H6 (benzene)

C6H6 (benzene)

C6H6 (benzene) C6H6 (benzene)

Non-aqueous

C6H6 (benzene)

C6H6 (benzene)

C6H6 (benzene) C6H6 (benzene)

C6H6 (benzene)

C5H12 (n-pentane) C5H12 (pentane)

C5H12 (n-pentane) C5H12 (n-pentane)

C4H10 (n-butane) C4H10 (n-butane)

Immisc

C4H10 (n-butane)

??

Vis.obs. Sampl

Vis.obs.

Vis.obs. Vis.obs.

Sampl

Vis.obs.

Sampl

Vis.obs.

Vis.obs. Vis.obs.

Sampl

Vis.obs. Vis.obs.

Vis.obs. Vis.obs.; p-T curves Vis.obs.

Sampl

Sampl

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

269.44 C 110/204– 303.5 C 313/473.15 K

294–363 C

38/202.4– 237.8 C 260–300 C 250–368 C

374.2– 294–360 C 99.8/175– 200 C 374.2– 294–360 C 100/200– 300 C 180–365 C

626–647 K 378/625– 647 K 298/473 K

300–352 C 190.5; 301.1 C 311/469–589 K

226.1 C

326/623–647 K 496–700 K

38/204.4; 237.8 C 355, 364 C

4

Temperature

0.3/3 MPa

9.46 MPa ??

154–2000 bar

100–800 atm 100–3700 bar

6.9; 34.48 MPa

2–21 MPa

??

22.1–14–342 MPa

1.6/12.2; 21.4 bar

22.1–14–297 MPa

65 bar

24–77 MPa 0.8/22–47 MPa

0.12/4.1–21 MPa

150–700 atm 4.5; 11.2 MPa

6.80 MPa

0.5/22–50 MPa 9–310 MPa

225–1125 bar

0.14/2–69 MPa

5

Pressure

ptx-C6H6-1.1

0.2/2.1–14.6 (C6H6) cm3/100 cm3 H2O

L1-L2-G

cr.point 0.2/1.50–93 (C6H6) mass.%

p-T crit.curve

6.6–56 (C6H6) mass.% 11–86 (C6H6) mass.%

0.04/0.73–84.3/99.6 (C6H6) mol.%

ptx-C6H6-9.1

ptx-C6H6-7.1 ptx-C6H6-8.1; 8.2

ptx-C6H6-6.1

ptx-C6H6-4.1 ptx-C6H6-5.1

ptx-C6H6-3.1

ptx-C6H6-2.1; 2.2

ptx-C6H5F-1.1

L = G; Fl1 = Fl2

6–94.5 (C6H6) mass.%

ptx-C6H5Cl-1.1

ptx-C6H4F2-1.1

L=V 0.04/0.13–90/97.5 (C6H5Cl) mol.%

ptx-C6H4Cl2-1.1

ptx-C5H12-4.1 ptx-C5H12-5.1

ptx-C5H12-3.1

ptx-C5H12-1.1 ptx-C5H12-2.1

0.0017/0.057 (C6H4Cl2) mol.%

0.02–0.11 (C5H12) mol.fr L=G

0.01/0.025–90.9/99.95 (C5H12) mol.%

1.3–40.7 (C5H12) mass.% cr.point

ptx-C5H8-1.1

ptx-C4H10-3.1 ptx-C4H10-4.1; 4.2

L=G 0.015–0.9 (C4H10) mol.fr. cr.point

ptx-C4H10-2.1

Rebert and Kay, 1959 Thompson and Snyder, 1964 Connolly, 1966 Alwani and Schneider, 1967 Alwani and Schneider, 1969 Roof, 1970 Gorbachev et al., 1972 Tsonopoulos and Wilson, 1983

Jockers and Schneider, 1978 Jaeger, 1923

Miller and Hawthorne, 2000 Jockers and Schneider, 1978 Hooper et al., 1988

Gillespie and Wilson, 1982 de Loos et al., 1983 Brunner, 1990

Connolly, 1966 Roof, 1970

Roof, 1970

Brunner, 1990 Yiling et al., 1991

Danneil et al., 1967

Reamer et al., 1952

8

7 ptx-C4H10-1.1

REFERENCE

Table

2.5–41.7 (C4H10) mol.%

0–95/99.95 (C4H10) mol.%

6

Composition

16 Hydrothermal Experimental Data

288–332 C 299 C

573 K 275–355 C

Sampl

Flw.Sampl

Sampl

Sampl

Sampl

Vis.obs.

Immisc

H-Fl

H-Fl; Immisc H-Fl

H-Fl

H-Fl; Immisc H-Fl

H-Fl

H-Fl; Immisc H-Fl; Immisc H-Fl; Immisc soly

C6H6 (benzene)

C6H6 (benzene)

C6H6 (benzene)

Vis.obs.

H-Fl; Cr.ph; Immisc H-Fl; Immisc Cr.ph; Immisc Immisc

Vis.obs.

H-Fl; Cr.ph

H-Fl; Cr.ph

Cr.ph

C6H14 (2-methylpentane)

C6H14 (2,2-dimethylbutane)

Vis.obs.

Vis.obs.

Vis.obs.

Cr.ph

??

Vis.obs.

Vis.obs.

Vis.obs.

H-Fl; Immisc

Vis.obs.

Sampl

Flw.Sampl

Sampl

Sampl

C6H12 (methylcyclopentane) C6H12 (1-hexene)

C6H12 (cyclohexane)

C6H12 (cyclohexane)

C6H12 (cyclohexane)

C6H6O2 (trimellitic acid) in C2H4O2 (acetic acid) C6H12 (cyclohexane); C6H12 (cyclohexane) in D2O C6H12 (cyclohexane)

C6H6 (benzene) + H2

C6H6 + C6H12 (benzene + 1-hexene) C6H6 + C7H14 (benzene + 1-heptene) C6H6 + C7H16 (benzene + n-heptane) (C6H6 + C7H16 ) (benzene + n-heptane) + CO2 C6H6 + C8H18 (benzene + 3-methyl hexane C6H6 + C16H34 (benzene + n-hexadecane C6H6 (benzene) + D2O

Flw. Sampl Sampl

Immisc

210 C

300–355 C

311/475–496 K

313/473; 482 K 245 C

256.7 C

275–421.5 C

130–370 C

56/162– 220.5 C

293/473 K

300 C

298.8 C

293.3 C

298/423; 473 K 293.3 C

298/473 K

101/200; 204 C 200–275 C

4

C6H6 (benzene)

3

2

Temperature

1

Methods

Phase equil

components

4.77 MPa

140–700 atm

0.2/3.9–5.4 MPa

7.09 MPa

0.03/3 MPa

8.04 MPa

195–1742 bar

0.7–23.5 MPa

SVP

SVP?

100–300 bar

158–2855 bar

20 MPa

24.83 MPa

24.83 MPa

25; 33 MPa

25 MPa

25 MPa

50 bar

1/65; 400 bar

27–172 bar

2.9/30.5; 32.2 bar

5

Pressure

ptx-C6H12chn-1.1

0.003/0.03–0.38 (C6H12) mol.% in H2O; D2O

cr.point

1.1–37.4 (C6H14) mass.%

0.001/0.15–0.43 (H2O) mol.fr.

cr.point

L1-L2-G

cr.point

10–80 (C6H12) mass.%

2.7–94.8 (C6H12) mass.%; L1-L2-G

ptx-C6H14 mep-1.1 ptx-C6H14 dmb-1.1

ptx-C6H12 mcp-1.1 ptx-C6H12 hxn-1.1

ptx-C6H12 chn-5.1

ptx-C6H12chn-4.1

ptx-C6H12chn-3.1

ptx-C6H12chn-2.1

ptx-C6H6O6 + C2H4O2-1.1

0–100% [C2H4O2 in (H2O + C2H4O2)]; 0.3/51–76 (C6H6O2) mass.%

25–75.5 (C6H6) mass.%

0–29 (C6H6); 0.01–54 (C16H34) mol.%

0–56 (C6H6); 0.55–87 (C8H18) mass.%

3.4–70 (C6H6); 0–41.4 (C7H16) mass.%

0.5–69 (C6H6); 0.3–85.6 (C7H16) mass.%

0–62 (C6H6); 0.7–71 (C7H14) mass.%

0.002–0.24 (C6H6); 0.0008–0.62 (H2) mol.fr

ptx-C6H6–13.1

ptx-C6H6-12.1

ptx-C6H6-11.1

Roof, 1970

Economou et al., 1997 Connolly, 1966

Tsonopoulos and Wilson, 1983 Roof, 1970

Roof, 1970

Rebert and Hayworth, 1967 Brollos et al., 1970

Guseva and Parnov, 1963

Dohrn and Brunner, 1986 Tudorovckaya et al., 1990

Brollos et al., 1970

Irani and McHugh, 1979 Irani and McHugh, 1979 Brunner et al., 1993

Anderson and Prausnitz, 1986 Chandler et al., 1998 Miller and Hawthorne, 2000 Mathis et al., 2004 Irani and McHugh, 1979 Irani and McHugh, 1979 O’Grady, 1967

8

7 ptx-C6H6-10.1

REFERENCE

Table

ptx-C6H6 + C6H12 (hex)-1.1 ptx-C6H6 + C7H14 (hen)-1.1 ptx-C6H6 + C7H16 (hpn)-1.1 ptx-C6H6 + C7H16 (hpn)-2.1 ptx-C6H6 + C8H18 (mhn)-1.1 ptx-C6H6 + C16H34-1.1 ptx C6H6 + D2O-1.1 ptx-C6H6 + H2-1.1

0–64 (C6H6); 0.9–71 (C6H12) mass.%

0.04/0.17; 0.46 (C6H6) mol.%

0.04/0.41; 0.50 (C6H6) mol.%

0.6–81.2 (C6H6) mol.%

0.1/0.6–82 98 (C6H6) mol.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 17

H-Fl; Cr.ph; Immisc Cr.ph H-Fl; Cr.ph

Immisc

Immisc; Cr.ph Immisc; Cr.ph Immisc

H-Fl; Cr.ph

Immisc, Cr.ph LGE; Cr.ph; Immisc H-Fl; Immisc H-Fl; Immisc Immisc

C6H14 n-hexane

C6H14 (n-hexane) C6H14 (n-hexane)

C6H14 (n-hexane)

C6H14 (n-hexane)

C6H14 (n-hexane)

C6H14 (n-hexane)

Cr.ph

C7H8 (toluene)

C7H8 (toluene)

C7H8 (toluene) C7H8 (toluene); C7H8 (toluene) in D2O C7H8 (toluene)

C6H14O (1-hexanol)

H-Fl; Immisc Immisc; Cr.ph H-Fl H-Fl; immisc Immisc; Cr.ph Cr.ph

C6H14 n-hexane + NaCl

C6H14 + C3H8O (nhexane + 1-propanol) C6H14 + C3H8O (nhexane+ 2-propanol) C6H14 + C16H34 (n-hexane + n-hexadecane) C6H14 (hexane) + N2

C6H14 (n-hexane)

C6H14 (n-hexane)

Immisc

2

1

C6H14 (n-hexane)

Phase equil

Continued

Non-aqueous components

Table 1.1

Vis.obs.

285 C

314–366 C

280–310 C

Vis.obs.

Vis.obs.

150/200–300 C 87/169–207

499–506 K

651–701 K

10.1 MPa

163–2005 bar

150–600 atm

?? SVP

10–90 MPa

41.7–154.3 MPa

25–270 MPa

20 MPa

573 K 563–679 K

20 MPa

0.71–15 MPa

1/1.5–5.3 MPa

0.6/3.5–5.3 MPa (SVP) 0.67/3.76–5.25 MPa

0.73/2.61–6.73 MPa

19.8–246.7 MPa

1.1/3.7–47 MPa

0.05/3.5 MPa

5.3 MPa 17–136 MPa

4.6–22.6 MPa

5

Pressure

573 K

420/450– 495 K 397/467–577 K

396–644 K

390/473–495 K

381/451.2– 505.2 K

555–699 K

419/477–647 K

313/473 K

223; 225 C 610–674 K

220–372 C

4

Temperature

Sampl Vis.obs.

T-p curves; Vis.obs. p-T curves; Vis.obs. Vis.obs.

Sampl; Vis. obs. Sampl

T-CV curves

p-T curves

T-CV curves

Vap.pr.

p-T curves; Vis.obs. Vis.obs.

Vis.obs.

??

Vis.obs. Vis.obs.

Vis.obs.

3

Methods

cr.point

p-T crit.curve

5.8–50.5 (C6H14) mass.%

0.2/0.7–13 (C6H6) cm3/100 cm3 H2O 0.06/0.45–0.80 (C7H8) in H2O; D2O mol.%

30 (C6H14O) mass.%.[L1 = L2]

9.9–30 (C6H14); 0.025–0.48 (NaCl) mol.%

0.05–0.4 (C6H14); 0.09–0.39 (N2) mol.fr.

0–46 (C6H14); 0.01–54 (C16H34) mol.%

0.003–0.4(C6H14); 0.01–0.13 (2-C3H8O) mol.fr.

0.11 (C6H14); + 0.18 (C3H8O) mol.fr.

90–96 (C6H14) mass.%

0.13-.0.994 (C6H14) mol.fr.

93.27 (C6H14) mass.%

15/50; 75 (C6H14) mass.%

0.2–0.6 (C6H14) mol.fr.

ptx-C7H8-5.1

ptx-C7H8-4.1

ptx-C7H8-3.1

ptx-C7H8-1.1 ptx-C7H8-2.1

ptx-C6H14 hxn9.1; 9.2 ptx-C6H14 hxn-10.1 ptx-C6H14 hxn + C3H8O-1.1 ptx-C6H14 hxn+2-C3H8O–1.1 ptx-C6H14 hxn + C16H34-1.1 ptx-C6H14 hxn + N2-1.1 ptx-C6H14 hxn + NaCl-1.1 ptx-C6H14O-1.1

ptx-C6H14hxn-8.1

ptx-C6H14 hxn6.1; 6.2 ptx-C6H14 hxn-7.1

ptx-C6H14 hxn-5.1

L1-L2-G; L = G

L1-L2-G

ptx-C6H14 hxn-2.1 ptx-C6H14 hxn3.1; 3.2 ptx-C6H14 hxn-4.1

Alwani and Schneider, 1969 Roof, 1970

Heilig and Franck, 1990 Michelberger and Franck, 1990 Becker and Schneider, 1993 Jaeger, 1923 Guseva and Parnov, 1963 Connolly, 1966

Abdulagatov and Magomedov, 1992 Stepanov et al., 1996 Kamilov et al., 2001 Rasulov and Isaev, 2002 Stepanov et al., 1999 Shimoyama et al., 2004 Brunner et al., 1993

Yiling et al., 1991

Tsonopoulos and Wilson, 1983 Brunner, 1990

Rebert and Hayworth, 1967 Roof, 1970 de Loos et al., 1982

8

7 ptx-C6H14hxn-1.1

REFERENCE

Table

cr.point 0.005–0.135 (C6H14) mol.fr.

2–85.34 (C6H14) mass.%

6

Composition

18 Hydrothermal Experimental Data

Sampl

Vis.obs. Flw.Sampl

Immisc Immisc

Immisc H-Fl

Immisc

Immisc

Immisc H-Fl; LGE

C7H8 (toluene) C7H8 (toluene)

C7H8 (toluene) C7H8 (toluene)

C7H8 + C6H6O (toluene + phenol) C7H8 + C16H34 (toluene + n-hexadecane ) C7H8O (anisole) C7H8O (m-cresol) + H2

Flw. Sampl Sampl

Sampl

Immisc Cr.ph

Cr.phen Immisc; Cr.ph H-Fl

H-Fl

H-Fl

H-Fl

C8H8O (acetophenone) C8H10 (ethylbenzene)

C8H10 (ethylbenzene) C8H10 (eethylbenzene)

C8H10 (ethylbenzene)

C8H10 + C2H4O2 (ethylbenzene + acetic acid) C8H10 (xylene)

C8H10 ethylbenzene

Sampl

Vis.obs. Vis.obs.

150/200; 250 C

298/423; 472 K 150/200 C

100/200 C

301 C 311/480–568 K

25/150; 200 C 340/471–502 K 319.5–386.7 C

Flw.Sampl

Vis.obs. Vis.obs.

380–528 K

Sampl

442–535 C

C7H16 + C12H26 (nheptane + n-dodecane) C8Cl4N2 (chlorothalonil)

T-CV curves

295–355 C 246; 301 C 628.5 415/474–647 K

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

C7H16 (n-heptane)

68/158–193

Vis.obs.

H-Fl; immisc H-Fl; Cr.ph Cr.ph H-Fl; Cr.ph Immisc; Cr.ph LGE; Immisc H-Fl; Immisc Soly

345/478–552 K 463/544; 620 K 271.1 C

573 K

150/200 C

341/471–524 K 298/473 K

20/200 C 200–275 C

99.4/200 C

Vis.obs.

Vis.obs. Flw.Sampl

Sampl Sampl

Sampl

4

Temperature

Cr.ph

C7H14 (methylcyclo-hexane) C7H16 (n-heptane); C7H16 (n-heptane) in D2O C7H16 (n-heptane) C7H16 (n-heptane) C7H16 (n-heptane) C7H16 (heptane)

Sampl

Immisc

C7H8 (toluene)

3

2

1

Methods

Phase equil

Non-aqueous components

??

541–1012.5 bar

50 bar

457–1006 bar

11.2 MPa 0.1/2.32–10.7 MPa

6.8 MPa 174–2000 bar

60–70 bar

(dens) 162–335 kg/m3 2–58 bar

170–700 atm 6.3–11.2 MPa 28.7 MPa 0.7/2.7–50 MPa

SVP

8.33 MPa

6.80–8.2 MPa 5–20.4 MPa

20 MPa

6.5/21.4–22.1 bar

6.8 MPa 50 MPa

1/50 bar 25–172 bar

1.5/23.6 bar

5

Pressure

hpn-2.1 hpn-3.1 hpn-4.1 hpn-5.1

ptx-C8H10 etb + C2H4O2-1.1 ptx-C8H10 xyl-1.1

0.1/0.35; 1.1 (C8H10) cm3/100 cm3 H2O

ptx-C8H10 etb-5.1

ptx-C8H10 etb-4.1

ptx-C8H10 etb-2.1 ptx-C8H10 etb-3.1

ptx-C8H8O-1.1 ptx-C8H10 etb-1.1

ptx-C7H16 hpn + C12H26-1.1 ptx-C8Cl4N2-1.1

ptx-C7H16 hpn-6.1

ptx-C7H16 ptx-C7H16 ptx-C7H16 ptx-C7H16

ptx-C7H8 + C6H6O-1.1 ptx-C7H8 + C16H34-1.1 ptx-C7H8O ani-1.1 ptx-C7H8O cre + H2-1.1 ptx-C7H14 mch-1.1 ptx-C7H16 hpn-1.1

ptx-C7H8-9.1 ptx-C7H8-10.1

0.73/1.52–1.79 (H2O); 0.08/0.11–0.15 (C2H4O2) m

0.003/0.024; 0.081 mol.%

0.19/1.07–1.25 m

cr.point 0.003/0.06–83.7 (C8H10) mol.%.

0.15/1.8–42.5 84 (C8H8O) mol.% p-T crit.curve

0.18/950–23400 (C8Cl4N2) µg/g

17.5–65 (C7H16); 1.1–7 (C12H26) mol.%

L1-L2-G; LGE

1.1–41.7 (C7H16) mass.% cr.point 0.05 (C7H16) mol.fr. L1-L2-G; L = G

0.002 0.001–0.01 (C7H16) mol.% in H2O; D2O

0.08/0.62–69/97 (C7H8O) mol.% 0.005/0.04–0.95 (C7H8O); 0.02–0.93 0.98 (H2) mol.fr cr.point

0.009/0.33–77 85 (C7H8); 0.62–23/32 (C6H5OH) mol.% 0–38 (C7H8); 0.01–54 (C16H34) mol.%

0.02/0.27–86 (C7H8) mol.% 0.3/8.8 * 10−4 * mol.fr (C7H8)

ptx-C7H8-7.1 ptx-C7H8-8.1

92/12600 (C6H5CH3) µg/mL 0.24–76.8 (C7H8) mol.%

Jaeger, 1923

Miller and Hawthorne, 1998 Brown et al., 2000 Alwani and Schneider, 1969 Roof, 1970 Heidman et al., 1985 Guillaume et al., 2001 Mathis et al., 2004 Guillaume et al., 2001

Eubank et al., 1994

Mirskaya, 1998

Guseva and Parnov, 1963 Connolly, 1966 Roof, 1970 de Loos et al., 1983 Brunner, 1990

Roof, 1970

Brown et al., 2000 Dinh et al., 1985

Brunner et al., 1993

Anderson and Prausnitz, 1986 Yang et al., 1997 Chandler et al., 1998 Brown et al., 2000 Miller and Hawthorne, 2000 Hooper et al., 1988

8

7 ptx-C7H8-6.1

REFERENCE

Table

0.03/0.26–84.1/98 (C7H8) mol.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 19

Vis.obs.

Vis.obs.

Immisc

H-Fl

H-Fl

Cr.ph

H-Fl

H-Fl

H-Fl

Immisc; Cr.ph H-Fl; Cr.ph

C8H10 (m-xylene)

C8H10 (m-xylene)

C8H10 (m-xylene)

C8H10 (o-xylene)

C8H10 (p-xylene)

C8H10 (m-xylene) + NH4OH C8H10 (p-xylene) + NH4OH C8H16 (ethylcyclohexane)

Vis.obs.

Vis.obs. Vap.pr.

Flw.Sampl

Flw.Sampl

Immisc; Cr.ph Immisc LGE

Soly

H-Fl; LGE

Non-aqueous

C9H12 (1,3,5-trimethylbenzene)

C8H18O (1-octanol) C8H18O5 (tetraethylene glycol) C9H6Cl6O3S (endosulfan II) C9H7N (quinoline) + H2

Cr.ph

Flw.Sampl

H-Fl

Vis.obs.

Flw.Sampl

Vis.obs.

Vis.obs.

C8H18 (2,2,4-trimethylpentane) C8H18O (1-octanol)

C8H18 (octane)

C8H18 (octane)

C8H18 (n-octane)

Vis.obs.

H-Fl; Immisc Immisc; Cr.ph Immisc; Cr.ph H-Fl

Vis.obs.

Vis.obs.

Flw. Sampl Vis.obs.

Flw.Sampl

Sampl

Vis.obs.

C8H18 (n-octane)

C8H16 (1-octene)

Vis.obs.

H-Fl

C8H10 (m-xylene)

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

25/150; 200 C 463/544; 622 K 327–404.8 C

354/478–543 K 450/474–538 K

542–559 K

298/473 K

298/473 K

418/484–647 K

311/478–553 K

267.2 C

311/478–550 K

311/480–561.4 K

12/177–237 C

0.83/196–240 C

43/188–295 C

298/423; 473 K 317–386 C

298/473 K

100/200 C

68/186–271 C

4

Temperature

171–2000 bar

5–20 MPa

30–40 bar

6.8 MPa 1.4/2.4–7.4 bar

15–90 MPa

65 bar

65 bar

0.6/2.7–45.6 MPa

0.1/2.51–8.86

7.4 MPa

0.1/2.4–9.3 MPa

0.1/2.36–9.93 MPa

SVP

SVP

SVP

154–2000 bar

50 bar

60 bar

2.7/20 bar

SVP

5

Pressure

−3

ptx-C8H10 xyl + NH4OH-1.1 ptx-C8H10 xyl + NH4OH-1.2 ptx-C8H16 etc-1.1

(0.09/7.5–17.9) * 10−3 (C8H10) mol.fr.; 14.6 (NH4OH) mol/L (0.11/4.4–13.7) * 10−3 (C8H10) mol.fr.; 14.6 (NH4OH) mol/L 0.0001/0.01–89 (C8H16) mol.%

ptx-C8H18 oct-3.1

L1-L2-G; L = G

ptx-C9H7N + H2-1.1 ptx-C9H12 tmb-1.1

ptx-C9H6Cl6O3S-1.1

0.27/720–4500 (C9H6Cl6O3S) µg/g 0.002–0.94 (C9H7N); 0.01/0.02–0.94 0.97 (H2) mol.fr. p-T crit.curve

ptx-C8H18O-2.1 ptx-C8H18O5-1.1

ptx-C8H18O-1.1

ptx-C8H18 tmp-1.1

0.01/0.18–42/69 (C8H18O) mol.% 0.79 (C8H18O5) mol.fr.

30 (C8H18O) mass.%

0.000044/0.0061 (C8H18) mol.fr

ptx-C8H18 oct-4.1

ptx-C8H18 oct-2.1

1.2 * 10−5/4 * 10−3–87 (C8H18) mol.%

0.000014/0.0029 (C8H18) mol.fr

ptx-C8H18 oct-1.1

cr.point

ptx-C8H16-1.1

ptx-C8H10 xyl-7.1

(0.04/0.77–7.60 * 10−3 (C8H10) mol.fr.

0.002/0.16–0.7 (H2O) mol.fr.

ptx-C8H10 xyl-6.1

ptx-C8H10 xyl-5.1

ptx-C8H10 xyl-4.1

ptx-C8H10 xyl-3.1

Alwani and Schneider, 1969

Miller and Hawthorne, 1998 Lin et al., 1985

Miller and Hawthorne, 2000 Miller and Hawthorne, 2000 Becker and Schneider, 1993 Brown et al., 2000 Breman et al., 1994

Heidman et al., 1985 Brunner, 1990

Pryor and Jentoft, 1961 Anderson and Prausnitz, 1986 Miller and Hawthorne, 2000 Mathis et al., 2004 Alwani and Schneider, 1969 Pryor and Jentoft, 1961 Pryor and Jentoft, 1961 Pryor and Jentoft, 1961 Heidman et al., 1985 Economou et al., 1997 Roof, 1970

8

7 ptx-C8H10 xyl-2.1

REFERENCE

Table

p-T crit.curve

0.0037/0.027; 0.102 mol.%

0.0029/0.088 (C8H10(CH3)2) mol.%.

0.01/0.09–85/98 (C8H10) mol.%.

(0.06/0.78–5.0) * 10 mol.fr.

6

Composition

20 Hydrothermal Experimental Data

Vis.obs.

Vap.pr. Flw.Sampl

Vis.obs.

Vis.obs.

Flw.Sampl

Vis.obs.

Vis.obs.

H-Fl

H-Fl; Cr.ph

LGE H-Fl

H-Fl

Cr.ph

H-Fl; Cr.ph

H-Fl

H-Fl

H-Fl; Cr.ph

H-Fl; Cr.ph

C10H14 (p-cymene)

C10H14 (m-diethylbenzene) C10H14 (phenanthrene) C10H14O (carvone)

C10H16 (d-limonene)

C10H18 (cisdecahydronaphthalene) C10H18 (cisdecahydronaphthalene) C10H18O (1,8-cineole)

C10H18O (nerol)

C10H20 (n-butylcyclohexane) C10H20 (1-decene)

C10H22 (n-decane) C10H22 (n-decane)

Cr.ph H-Fl; Immisc; Cr.ph

Vis.obs.

H-Fl

Vis.obs. Flw.Sampl; Vis.obs.

Flw.Sampl

Flw.Sampl

Flw.Sampl

Flw.Sampl

Vis.obs.

C10H12O2 (eugenol)

C10H12 (tetralin)

Flw.Sampl

H-Fl; Cr.ph; Immisc H-Fl; Cr.ph

C10H12 (tetralin)

C10H12 (1,2,3,4tetrahydronaphthalene) C10H12 (tetralin)

C10H8 (naphthalene)

Vis.obs.

Vis.obs. Vis.obs.

Sampl

Cr.ph Immisc; Cr.ph Immisc; Cr.ph Cr.ph

C9H20 (n-nonane) C9H20 (nonane)

Flw.Sampl

H-Fl

Soly

C9H16ClN2 (propazine)

Vis.obs.

Vis.obs.

Cr.ph

C9H12 (n-propylbenzene)

3

Methods

Cr.ph

2

1

C9H20O (nonan-1-ol)

Phase equil

components

296.11 C 573.2–613.2 K

374/475–569 K

298/423; 473 K 311/478–584 K

298/473 K

374/475–599 K

340–400 C

298/473 K

420/474–542 K 298/473 K

311/478–583 K

298/473 K

298/473 K

150/200; 250 C 300; 350; 400 C 374/475–596 K

390–324 C

307–382.8 C

557–573 K

25/150; 200 C 282.2 C 448/479–654 K

327.5–405 C

4

Temperature

9.63 MPa 13–231 bar

0.1/1.8–11.4 MPa

0.5/1.9–11.8 MPa

68/69; 70 bar

66/64 bar

0.1/1.7–14.4 MPa

180–710 bar

70/69 bar

3.6/6.8–10.55 bar 64/64 bar

0.5/1.9–11.7 MPa

60 bar

65/69 bar

0.1/1.7–13.2 MPa

5.8–179 atm

SVP??

125–1320 bar

101–2000 bar

20–90 MPa

8.55 MPa 1.1/2.2–51 MPa

60–70 bar

160–2000 bar

5

Pressure

ptx-C10H12 ttl-1.1

0.02/0.04; 0.4 (C10H12) cm3/100 cm3 H2O

cr.point 0–0.993 (C10H22) mol.fr.

0.01/0.13–0.7 (H2O) mol.fr.

0.001//0.1–0.9 (H2O) mol.fr.

0.006/0.051; ND (C10H18O) mol.%

0.03/0.05 (C10H18O) mol.%

ptx-C10H20 bch-1.1 ptx-C10H20 dec-1.1 ptx-C10H22-1.1 ptx-C10H22-2.1

ptx-C10H18O-1.2

ptx-C10H18O-1.1

ptx-C10H18-2.1

ptx-C10H18-1.1

L1 = L2 0.01/0.05–0.8 (H2O) mol.fr.

ptx-C10H16-1.1

ptx-C10H14 cym-1.1 ptx-C10H14 deb-1.1 ptx-C10H14 pht-1.1 ptx-C10H14O-1.1

ptx-C10H12O2-1.1

ptx-C10H12 ttl-3.1

0.0001/0.0057 (C10H16) mol.%

0.92 (C10H14) mol.fr. 0.01 025 (C10H14O) mol.%

0.003/0.15–0.9 (H2O) mol.fr.

0.0003/0.02 (C10H14) mol.%

0.02/0.49 (C10H12O2) mol.%

0.02 0.12–0.9 (H2O) mol.fr.

ptx-C10H12 ttl-2.1

ptx-C10H12 thn-1.1

L1 = L2

0.003–0.973 (C10H12) mol.fr.

ptx-C10H8-1.1

ptx-C9H20O-1.1

ptx-C9H20-1.1 ptx-C9H20-2.1

p-T crit.curve

30 (C9H20O) mass.%

cr.point L1-L2-G; L = G

ptx-C9H16ClN2-1.1

6.3/2560–26800 (C9H16ClN2) µg/g

Economou et al., 1997 Miller and Hawthorne, 2000 Miller and Hawthorne, 2000 Economou et al., 1997 Economou et al., 1997 Roof, 1970 Wang and Chao, 1990

Christensen and Paulaitis, 1992 Economou et al., 1997 Miller and Hawthorne, 2000 Miller and Hawthorne, 2000 Economou et al., 1997 Breman et al., 1994 Miller and Hawthorne, 2000 Miller and Hawthorne, 2000 Jockers et al., 1977

Jaeger, 1923

Becker and Schneider, 1993 Alwani and Schneider, 1969 Jockers et al., 1977

Alwani and Schneider, 1969 Miller and Hawthorne, 1998 Roof, 1970 Brunner, 1990

8

7 ptx-C9H12 ppb-1.1

REFERENCE

Table

p-T crit.curve

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 21

Immisc; Cr.ph H-Fl; Cr.ph

H-Fl; Immisc H-Fl; Immisc H-Fl; Immisc Immisc; Cr.ph H-Fl; Cr.ph; Immisc H-Fl; crph

C10H22 (decane)

C10H22 (decane)

Non-aqueous

C14H10 (anthracene); C14D10 (anthracene-D10)

C14H10 (anthracene)

C12H26O (dodecan-1-ol)

C12H26 (n-dodecane)

C12H12 (1-ethylnaphthalene) C12H18 (p-diisopropylbenzene) C12H26 (dodecane)

C12H10 (acenaphthene)

C12H9N (carbazole) C12H10 (biphenyl)

C11H10 (1-methylnaphthalen) C11H10 (1-methylnaphthalen) C11H24 (undecane)

C10H22 + C3H8O(decane + 2-propanol) C10H22 + C4H10O(decane +2-butanol) C10H22O (1-decanol)

Soly

603.6, 633 K

Flw.Sampl

Flw.Sampl

UV-spectr.

Vis.obs.

519–659 K

Vis.obs.

Immisc; Cr.ph H-Fl; Immisc; Cr.ph Immisc; Cr.ph Soly; H-Fl 298/473 C

323/473–553 C

553–610 K

311/478–590 K

Vis.obs.

H-Fl; Cr.ph

311/478–594 K

250 C

298/473 K 298–403 C

476–647 K

Vis.obs.

Sampl.

Flw.Sampl Vis.obs.

Vis.obs.

311/478–589 K

Vis.obs.

20–90 MPa

570–590 C

20/800–1955/2850 bar 45/48/50 bar

7.3–80 MPa

8.8–249.2 bar

4–34 MPa

0.5/1.8–12.4 MPa

0.5/1.8–12.4 MPa

5 MPa

54/52 bar 100–2000 bar

1.8–33 MPa

4.9–11.3 MPa

2.9–174.5 atm

20 MPa

573 K

300–400 C

15; 20 MPa

15; 20 MPa

0.1/1.8–11.2 MPa

1.5–42 MPa

5

Pressure

573; 593 K

573; 593 K

374/475–576 K

466–649 K

4

Temperature

Flw.Sampl

Sampl; Vis. obs. Sampl; Vis. obs. Sampl; Vis. obs. Vis.obs.

Vis.obs.

Vis.obs.

3

Methods

H-Fl; Cr.ph

Immisc; Cr.ph PTX, Soly Immisc; H-Fl Immisc

2

1

C10H22 (decane)

Phase equil

Continued

Non-aqueous components

Table 1.1

ptx-C12H9N-1.1 ptx-C12H10-1.1

1.1 * 10−9/1.9 * 10−3 (C12H9N) mol.fr. 10–80 (C12H10) mass.%

ptx-C12H26-2.1

ptx-C12H26O-1.1; 1.2 ptx-C14H8O2-1.1 ptx-C14H10-2.1

0.20–0.60 (C12H26O) mass.fr.; [L1 = L2, L1-L2-G] 1.4 * 10−6/(1.5–10.9) * 10−3 (C14H10) mol/L 8 * 10−9/21 * 10−5 (C14H10; C14D10) mol.fr.

ptx-C12H26-1.1

L1-L2-G; L = G 0–1.0 (C12H26) mol.fr.

ptx-C12H18-1.1

0.003/0.2–0.9 (H2O) mol.fr.

0.005/0.15–0.93 (H2O) mol.fr.

ptxC12H10(aph)-1.1 ptx-C12H12-1.1

ptx-C11H24-1.1

L1-L2-G; L = G

0.0012 mol.fr.

ptx-C11H10-2.1

ptx-C11H10-1.1

ptx-(C10H22+ 2-C3H8O)-1.1 ptx-(C10H22+ 2-C4H10O)-1.1 ptx-C10H22O-1.1

ptx-C10H22-5.1

0.005/0.15–0.98 (H2O) mol.fr.

0.01–1 (C11H10) mol.fr.

0.001–0.45(C10H22) + 0.01–0.16 (2-C3H8O) mol. fr. 0.001–0.43(C10H22) + 0.01–0.16 (2-C4H10O) mol.fr. 30 (C10H22O): mass.%; [L1 = L2]

0.5–1.0(H2O)

ptx-C10H22-4.1

ptx-C10H22-3.1

L1-L2-G; L = G 0.008//0.12–0.7 (H2O) mol.fr.

8

7

6

Becker and Schneider, 1993 Rossling and Franck, 1983 Miller et al., 1998

Stevenson et al., 1994

Andersson et al., 2005 Economou et al., 1997 Economou et al., 1997 Brunner, 1990

Miller et al., 1998 Bröllos et al., 1970

Economou et al., 1997 Shimoyama et al., 2004 Shimoyama et al., 2004 Shimoyama et al., 2004 Becker and Schneider, 1993 Christensen and Paulaitis, 1992 Economou et al., 1997 Brunner, 1990

Brunner, 1990

REFERENCE

Table

Composition

22 Hydrothermal Experimental Data

2

Soly; Immisc Soly

1

C14H10 (anthracene)

Immisc; H-Fl H-Fl; immisc LGE Soly

Immisc; Cr.ph Immisc; Cr.ph Soly Soly

C16H34 (n-hexadecane) + CO2 C16H34 (hexadecane) + H2 C16H34O (1-hexadecanol) C18H12 (chrysene)

C18H38 (octadecane)

C30H62 (tricontane)

C28H58 (octacosane) C30H50 (squalene)

C28H58 (octacosane)

C26H54 (hexacosane)

C25H52 (pentacosane)

C24H50 (tetracosane)

C20H42 (eicosane)

C20H12 (perylene) C20H12 (benzo[a]pyrene)

C18H38O (1-octadecanol)

C16H34 (hexadecane)

Immisc; Cr.ph Immisc; Cr.ph Immisc; Cr.ph Immisc; Cr.ph Immisc; Cr.ph LGE H-Fl; Cr.ph; Immisc Immisc; Cr.ph

Immisc; Cr.ph LGE

C16H34 (hexadecane)

373/471–516 K 298/473, 498 K 439/499–749 K

Vap.pr. Flw.Sampl

Vis.obs.

Vap.pr. Flw.Sampl

Vis.obs.

Vis.obs.

Vis.obs.

Vis.obs.

Vis.obs.

Flw.Sampl Flw.Sampl

Vis.obs.

Vis.obs.

503–857 K

429/474–519 K 637.2–659 K

534–843 K

488–827 K

451/481–818 K

456/484–809 K

422/479–771 K

323/473 K 100/150–250 C

573–622 K

200–350 C

Sampl

Sampl

414/472.4– 525.5 K 473; 573 K

456/487–722 K

200–338 C

50/140–300 C

563–610 K

447/478–693 K

298/473 C

100/150–300 C

4

Temperature

Vap.pr.

Vis.obs.

Sampl

H-Fl; Cr.ph

C16H34 (hexadecane)

C16H10 (pyrene)

C14H30O (1-tetradecanol)

Flw.Sampl

Sampl.

3

Methods

Immisc; Sampl Cr.ph Immisc; Vis.obs. Cr.ph Soly; Immisc Sampl.

C14H10 (antracene) + C12H9N (carbazole) + C18H12 (chrysene) C14H30 (tetradecane)

Phase equil

components

−7

−3

ptx-C14H30O-1.1; 1.2 ptx-C16H10-1.1

30 (C14H30O) mass.%; [L1 = L2, L1-L2-G]

0.8–30 MPa

1.5/2.06–2.53 bar 1.8–312 bar

0.9–27 MPa

1–30 MPa

1–32 MPa

1.0–29 MPa

0.5/1.2–30 MPa

45/48/50 bar 60–70 bar

11–40 MPa

0.7/1.3–30 MPa

0.34/2.22–3.34 bar 32/45, 62 bar

100–300 bar

10–30 MPa

2.7/4.5–6.39 bar

ptx-C18H38O-1.1; 1.2 ptx-C20H12-1.1 ptx-C20H12-2.1 ptx-C20H42-1.1 ptx-C24H50-1.1 ptx-C25H52-1.1 ptx-C26H54-1.1 ptx-C28H58-1.1

30 (C18H38O) mass.%; [L1 = L2, L1-L2-G]

L1-L2-G; L = G L1-L2-G; L = G L1-L2-G; L = G L1-L2-G; L = G L1-L2-G; L = G

ptx-C28H58-2.1 ptx-C30H50-1.1 ptx-C30H62-1.1

0.85 (C28H58) mol.fr 0–1.0 (C30H50) mol.fr L1-L2-G; L = G

(0.003/50) * 10−7 (C20H12) mol.fr 5.4–1142 (C20H12) µg/g

ptx-C18H38-1.1

ptx-C16H34 + CO2-1.1 ptx-C16H34 + H2-1.1 ptx-C16H34O-1.1 ptx-C18H12-1.1

L1-L2-G; L = G

0.94 (C16H34O mol.fr. (0.006/158; 758) * 10−7 (C18H12) mol.fr

0.0005–0.8 (C16H34); 0.0006–0.998 (H2) mol.fr

0–1 (C16H34); 0.1–0.9 (CO2) mol.fr.

ptx-C16H34-3.1

L1-L2-G; L = G 0.93 (C16H34) mol.fr.

ptx-C16H34-2.1

9.2–99.3 (n-C16H34) mass.%

17.3–160 kg/cm2 1.1/1.4–31 MPa

ptx-C16H34-1.1

7*10−8 – 1.4*10−3 mol.fr.

L1-L2-G; L = G

ptx-C14H10 + C12H9N + C18H12-1.1 ptx-C14H30-1.1

Breman et al., 1994 Stevenson et al., 1994 Brunner, 1990

Brunner, 1990

Brunner, 1990

Brunner, 1990

Brunner, 1990

Becker and Schneider, 1993 Miller et al., 1998 Miller and Hawthorne, 1998 Brunner, 1990

Brunner, 1990

Dohrn and Brunner, 1986 Breman et al., 1994 Miller et al., 1998

Brunner et al., 1994

Breman et al., 1994

Becker and Schneider, 1993 Andersson et al., 2005 Sultanov et al., 1972b Brunner, 1990

Brunner, 1990

Andersson et al., 2005 Miller et al., 1998

8

7 ptx-C14H10-3.1

REFERENCE

Table

[0.09/1200 (C14H10) + 1.4/2500 (C12H8) + 0.005/17 (C18H12)] 10−7 mol.fr.

3*10 – 4*10 mol.fr.

6

Composition

5; 10 MPa

9.6–50 MPa

0.9/1.7–36 MPa

50–60 bar

5; 10 MPa

5

Pressure

Phase Equilibria in Binary and Ternary Hydrothermal Systems 23

2

Immisc; Cr.ph Immisc; Cr.ph H-Fl; Immisc H-Fl; Immisc H-Fl

1

C32H66 (dotriacontane)

CO2

Sampl

Sampl

Sampl p-T curves; Vap.pr. Sampl Sampl

H-Fl

H-Fl

H-Fl H-Fl

H-Fl; LGE H-Fl; LGE

CO2

CO2

CO2 CO2

CO2 CO2

CO2

Non-aqueous

p-T curves; Vis.obs.; Sampl

LGE; Immisc

340–605.5 K

2.9–304 MPa

5.7/8.83–24 MPa

405/486–613 K

CO2 + C6H6

CO2

17.6–22.5 MPa

1–6 kbar

0.3/2–8.1 2/2.5–10.2 MPa

0.8/5.8 MPa 0.09/0.3–9.6 MPa

0.7/2.5–20 MPa

0.15/0.93–4.6 MPa

100–1400 bars

100–3000 bars

SVP

200–3500 bar

0.11–0.88 (CO2); 0.05–0.379 (C6H6) mol.fr.

0.21–0.71/0.94 (CO2) mol.fr.

0.53–0.79 (CO2) mol.fr

0.48–0.87 (CO2) mol.%

0.12–0.87 (CO2) mol.fr

0.04/0.07–76/95.5 (CO2) mol.% 0.22–1.4/1.7 (CO2) mol.%

484 MPa (Henry’s const.) 50–98 (CO2) mol.%

0.05/0.14–85.3 95 (CO2) mol.%

0.0005–0.5/0.88 (CO2) mol.fr

1–29 (CO2) mass.%

8–99 (CO2) mol.%

0.0022/0.0028–0.0217 (CO2) mol/mole H2O

0.8–87.5/99 (CO2) mol.%

1.2–85 (CO2) mol.%

100–600 kg/cm2

0.00002/0.0002–0.4 (CO, H2) mol.fr. 2.7–4.5 (CO2) mass.%

114.4–311 MPa

p-T curves; Vis.obs. p-T curves

H-Fl; Immisc H-Fl; LGE

CO2

ptx-C36H74-1.1

L1-L2-G; L = G

ptx-CO2 + C6H61.1; 1.2

ptx-CO2-16.1

ptx-CO2-15.1

ptx-CO2-14.1

ptx-CO2-13.1

ptx-CO2-11.1 ptx-CO2-12.1

ptx-CO2-9.1 ptx-CO2-10.1

ptx-CO2-8.1

ptx-CO2-7.1; 7.2

ptx-CO2-6.1

ptx-CO2-5.1; 5.2

ptx-CO2-4.1

ptx-CO2-3.1; 3.2

ptx-CO2-2.1; 2.2

ptx-CO2-1.1

ptx-CO + H2-1.1

ptx-CO-1.1

ptx-C32H66-1.1

L1-L2-G; L = G

0.00005/0.00036–0.78 (CO) mol.fr.

8

7

6

Muller et al., 1988 Nighswander et al., 1989 Sterner and Bodnar, 1991 Crovetto and Wood, 1992, 1996 Mather and Franck, 1992 Fenghour et al., 1996 Brandt et al., 2000

Todheide and Franck, 1963 Ellis and Golding, 1963 Takenouchi and Kennedy, 1964 Takenouchi and Kennedy, 1965 Zawisza and Malesinska, 1981 Gillespie and Wilson, 1982 Cramer, 1982 Patel et al., 1987

Gillespie and Wilson, 1980 Gillespie and Wilson, 1980 Marshall et al., 1958 Malinin, 1959

Brunner, 1990

Brunner, 1990

REFERENCE

Table

Composition

65–123 atm CO2

0.34/3–14 MPa

0.34/3–14 MPa

0.7–38 MPa

0.8–32.5 MPa

5

Pressure

225–273.3 C

623–643 K

Flw.densmtr.

CO2

400–700 C

Fl.inclus

H-Fl; Immisc LGE

373/473 K 80/197.6–198.1 C

323/448; 470 K 15/478; 533 K 33/213 C 312.5/382–482 K

150/200–450 C

CO2

Sampl

177/202–334 C

Samp. 110/200–350 C

50/200–350 C

Sampl

Sampl

200–330 C

38/204; 316 C 38/204; 316 C 250 C

549–895 K

429/499–871 K

4

Temperature

Sampl

Vap.pr.

Sampl

Sampl

Vis.obs.

Vis.obs.

3

Methods

H-Fl; Cr.ph; Immisc H-Fl

CO2

CO2

H-Fl; immisc H-Fl; Cr.ph; immisc H-Fl

CO2

CO2

CO + H2

CO

C36H74 (hexatriacontane)

Phase equil

Continued

Non-aqueous components

Table 1.1

24 Hydrothermal Experimental Data

Sampl

Isopiest

Sampl Quench Wt-loss; Quench Wt-loss

LGE

LGE

LGE

H-Fl

H-Fl

H-Fl; LGE

LGE; H-Fl; Cr.ph LGE

H-Fl; LGE

LGE; Isop-m

Soly Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

CO2 + CaCl2

CO2 + CaCl2

CO2 + HCl + NaHCO3

CO2 in Li2CO3

CO2 in NH3

CO2 in NaCl

CO2 in NaCl

CO2 in NaCl

CaBr2

CaCO3 CaCO3 (calcite) CaCO3 in CO2

CaCO3 in CO2

CaCO3 in CO2

CaCO3 in CO2

CaCO3 in CO2

CaCO3 in CO2

CaCO3 in (CaCl2 + CO2)

CaCO3 + Ca(OH)2

CaCO3 in CsCl

CaCO3 in K2CO3

CO2 in NaCl

H-Fl

CO2 + CaCl2

Wt-loss; Quench Wt-loss

Therm. anal.

Wt-loss

Sampl

Sampl

Wt-loss

Sampl

Sampl

Sampl

Samp.

Sampl

Sampl

Sampl

Fl.inclus

Fl.inclus

Sampl

3

2

1

Methods

Phase equil

components

200–350 C

400 C

574–647 C

223 C

238–622 C

197–599 C

100/200–300 C

75/200 C

223 C

182/207–316 C 370 C 98/201–300 C

380/473–523 K

80/200 C

239 C

150/200–450 C

172/195–330 C

373/473 K

250 C

114/199–348 C

500; 700 C

500 C

200–350 C

4

Temperature

2

3

0.7–0.22 (CaCO3) g/L; 14.4–60.2 (CsCl) mass.% 0.4–23.3 (CaCO3); 0.92–29 (K2CO3) m

1000 kg/cm2 SVP

37–44 (CaCO3); 47–56 (Ca(OH)2) mass.%

0.14–732 (CaCO3) mg/kg; 0.26–10.2 (CO2) mass.% 5.19–2.23 (Ca) (−log(m)); 0.02–0.15 (CO2) mol.fr. 61–498 (CaCO3) mg/cm3; (PCO2) 18–384 kg/ cm2; 10 (CaCl2) mass.%

(0.08–0.14/0.25) * 10−3 (Ca) mol/dm3 0.01–0.04 (CaCO3) g/100 g H2O (0.084–1.6/5.3) * 10−3 (CaCO3); 0.012/0.015–0.11 (CO2) m 26.3–142 (CaCO3) mg/mL; (PCO2)34–374 kg/cm2 0.05–0.18/1 (CaCO3) g/1000 g; 4–49 (PCO2) atm 0.06–0.152/5.55 (CaCO3) mm

2.15/2.45–13.1 (CaBr2); 4.22/4.75–9.14 (NaCl) m

0.3 0.5–1.32 1.5 (CO2) mol.%; 1 NaCl mass.%

928 MPa Henry’s const.; 1.95 NaCl m

0.003/0.0045–0.018 (CO2) mol/mole H2O; 0.5–2 (NaCl) m 0.9–34 (CO2); 6; 20 mass.% (NaCl)

0–73/92 (CO2); 4–57/93 (NH3) mol.%

0.04–0.19 (CO2); 0.06–0.19 (HCl); 0.13–0.48 (NaHCO3) mol/L 2.1–3.37 (CO2) mass.%

4.6–50.9 (CO2); 4–27.1 (CaCl2) mass.%

9.9–47.8 (CO2); 6.6–31.1 (CaCl2) mass.%

15.0–76.5 (CO2) mg/cm ; 10.1 (CaCl2) mass.%

6

Composition

0.21–10 kbar

24–408 kg/cm2

1; 2 kbar

1–62 atm part.pr CO2 20–1433 bar

5/20–65 atm

SVP 200 atm 0.97/1.15–63 atm (part.pr) CO2 25–409 kg/cm2

SVP

2.1/4–9.9/10 MPa

6.2 MPa

100–1400 bars

SVP

0.2/1.9–8.8 MPa

22.9–53 atm

5/16–162 atm

3; 5 kbar

3; 5 Kbar

100–400 kg/cm

5

Pressure

Malinin, 1959

ptx-CO2 + CaCl2-1.1 ptx-CO2 + CaCl2-2.1 ptx-CO2 + CaCl2-3.1 ptx-CO2 + HCl + NaHCO3-1.1 ptx-CO2 + Li2CO3-1.1 ptx-CO2 + NH3-1.1 ptx-CO2 + NaCl-1.1 ptx-CO2 + NaCl2.1; 2.2 ptx-CO2 + NaCl-3.1 ptx-CO2 + NaCl-4.1 ptx-CaBr2-1.1; 1.2

ptx-CaCO3-1.1 ptx-CaCO3-2.1 ptx-CaCO3 + CO2-1.1 ptx-CaCO3 + CO2-2.1 ptx-CaCO3 + CO2-3.1 ptx-CaCO3 + CO2-4.1 ptx-CaCO3 + CO2-5.1 ptx-CaCO3 + CO2-6.1 ptx-CaCO3 + CaCl2 + CO2-1.1 ptx-CaCO3 + Ca(OH)2-1.1 ptx-CaCO3 + CsCl-1.1 ptx-CaCO3 + K2CO3-1.1

8

7

Malinin and Dernov-Pegarev, 1974

Koster van Groos, 1982 Ikornikova, 1975

Sharp and Kennedy, 1965 Fein and Walther, 1987 Malinin, 1962

Ellis, 1963

Segnit et al., 1962

Malinin, 1962

Nighswander et al., 1989 Gruszkiewicz and Simonson, 2005 Straub, 1932 Schloemer, 1952 Ellis, 1959a

Ellis and Golding, 1963 Takenouchi and Kennedy, 1965 Cramer, 1982

Marshall et al., 1958 Muller et al., 1988

Plyasunova and Shmulovich, 1991 Shmulovich and Plyasunova, 1993 Ellis, 1959b

REFERENCE

Table

Phase Equilibria in Binary and Ternary Hydrothermal Systems 25

473–623 K

Vap.pr.; Vis. obs.

Vis.obs.

Isopiest

Vap.pr.

Vap.pr.diff. p-V curves Vis.obs. p-V curves

Fl.inclus

Sampl

VTFD

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly; LGE

Cr.ph

LGE; Isop-m LGE

LGE LGE Soly LGE

H-Fl; LGE

LGE

LGE

CaCO3 in (K2CO3 + KCl)

CaCO3 in KCl

CaCO3 in LiCl

CaCO3 in NaCO3

CaCO3 in (NaCO3 + K2CO3)

CaCO3 in NaCl

CaCO3 in NaCl

CaCO3 in Na2SO4

CaCl2

CaCl2

CaCl2

CaCl2 CaCl2 CaCl2 CaCl2

CaCl2

CaCl2

CaCl2

Non-aqueous

CaCl2

382/474

Wt-loss; Quench Wt-loss; Quench Sampl

Soly

Wt-loss

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

Wt-loss

Wt-loss

2

0.15–2.18 (CaCO3) g/L; 4.1–27.3 (LiCl) mass.%; 0.035; 0.04 (CaCO3); 0.88; 1.69 (Na2CO3) m

400; 1000 kg/cm2

623, 643 K

400–600 C

600–700 C

200–350 C 250–490 C 329/470–559 K 250, 300 C

382–403 C

17; 22 MPa

41.6–1324 bar

1000–1900 bar

SVP 4.6–230 kg/cm2 SVP SVP

SVP

SVP

SVP

SVP (0/842– 1491 mm.Hg)

−55/175–260 C

0.23–3.2 (CaCl2) m

0.35–85.0 (CaCl2) mass.%

5.3–21 (CaCl2) mass.%

0.5–6.8 (CaCl2) m 25.3–94.6 (CaCl2) mass.% 57/75–78 (CaCl2) mass.% 14.3 (CaCl2) mol.%

0–5.5 (CaCl2) m

0.79–3.96 (CaCl2); 1.04–6.87/7.23 (NaCl) m

0.1–1.8 (CaCl2) m

9.5/75–77.6 (CaCl2) mass.%

0.02–0.32/0.47 (Ca); 0–19.4 (SO4) [103 * mol/L]

0.1–0.93 (CaCO3) g/L; 5.5–25.9 (NaCl) mass.%

400; 1000 kg/cm2 SVP

(0.67–3.94/7.8) * 10−3 (CaCO3); 0.2–1 (NaCl) m

12 atm part.pr CO2

SVP

0.42–3.55 (CaCO3); 0.43–3.92 (Na2CO3); 2.0–4.27 (K2CO3) m

0.11–0.55 (CaCO3) g/L; 7–27.2 (KCl) mass.%

400; 1000 kg/cm2

SVP

0.02–0.6 (CaCO3); 0.7–2.7 (K2CO3); 2.8–5.6 (KCl) m

0.0001–1.014 (CaCO3); 0.3–21.7 (K2CO3) m

6

Composition

SVP

55–1200 kg/cm

5

Pressure

182/207–316 C

400 C

119/201–322 C

300 C

200; 300 C

400 C

400 C

200–350 C

350–500 C

4

CaCO3 in K2CO3

3

2

Temperature

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

Dernov-Pegarev and Malinin, 1976 Malinin and Dernov-Pegarev, 1974 Ikornikova, 1975

ptx-CaCO3 + K2CO3-2.1 ptx-CaCO3 + K2CO3 + KCl-1.1 ptx-CaCO3 + KCl-1.1 ptx-CaCO3 + LiCl-1.1; 1.2 ptx-CaCO3 + Na2CO3-1.1

ptx-CaCl2-11.1

ptx-CaCl2-10.1

ptx-CaCl2-9.1

ptx-CaCl2-5.1 ptx-CaCl2-6.1 ptx-CaCl2-7.1 ptx-CaCl2-8.1

ptx-CaCl2-4.1

ptx-CaCl2-3.1

ptx-CaCl2-2.1

ptx-CaCO3 + Na2CO3 + K2CO3-1.1 ptx-CaCO3 + NaCl-1.1 ptx-CaCO3 + NaCl-2.1 ptx-CaCO3 + Na2SO4-1.1 ptx-CaCl2-1.1

8

7

Zarembo et al., 1980 Wood et al., 1984 Ketsko et al., 1984 Sinke et al., 1985 Urusova and Valyashko, 1987 Zhang and Frantz, 1989 Tkachenko and Shmulovich, 1992 Crovetto et al., 1993, 1996

Bakhuis Roozeboom, 1889 Marshall, W.L.; Jones, E.V. 1974a Holmes et al., 1978

Straub, 1932

Ikornikova, 1975

Malinin and Dernov-Pegarev, 1974 Malinin and Dernov-Pegarev, 1974 Ellis, 1963

Ikornikova, 1975

REFERENCE

Table

26 Hydrothermal Experimental Data

Sampl

Isopiest

Fl.inclus

Sampl

Wt-loss; Quench Wt-loss

Cr.ph

LGE

LGE; Cr.ph

LGE; Isop-m

LGE

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

CaCl2

CaCl2

CaCl2

CaCl2

CaCl2 + CO2

CaF2

CaF2

CaF2 in CaCl2

CaF2 in CaCl2

CaF2 in CaCl2

CaF2 in CaCl2

CaF2 in (HCl + NaCl)

CaF2 in LiCl

CaF2 in NaCl

CaF2 in NaCl

CaF2 in NaCl

CaF2 in NaCl

CaF2 in NaCl

CaCl2

LGE; Isop-m Cr.ph

CaCl2

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

388–662 C

Vis.obs.; Fl.inclus Vis.obs.; Fl.inclus Vap.pr.

800 C

600; 800 C

600 C

400–600 C

600–800 C

105–530 C.

260 C

600 C

400–600 C

600–800 C

150–300 C.

150/200–620 C

179/199–421 C

500–700 C

380/473–523 K

380–500 C

373/472–526 K

661–935 K

444/474–524 K

4

Temperature

Isopiest

3

2

1

Methods

Phase equil

components

1–2 kbar

0.5; 1; 1.3 kbar

0.5–2 kbar

2 kbar

2 kbar

<250–300 atm

SVP

0.5–2 kbar

2 kbar

0.0037–0.705 (CaF2); 1–34.7 (NaCl) m

0.0037–0.705 (CaF2); 1–34.7 (NaCl) m

0.003–0.04 (CaF2); 2 (NaCl) m

0.00067–0.194 (CaF2); 1–34.7 (NaCl) m

(90–696) * 10−3 (CaF2); 0.2–34.7 (NaCl) m

0.0008–0.44 (CaF2); 0–2.08 (HCl); 0–2.13 (NaCl) m 0.03–13 (CaF2) g/L; 12; 21; 44 (LiCl) mass.%

0.08–0.35 (CaF2); 2 (CaCl2) m

0.0007–0.16 (CaF2); 0.5–34.7 (CaCl2) m

0.004–0.27 (CaF2); 0.05–2.5 (CaCl2) m

0.04–2.3 (CaF2) g/L; 25; 42 (CaCl2) mass.%

<250–300 atm 2 kbar

4.7–63.8 (CaF2) mg/kg H2O

0.0007–0.0062 (CaF2) g/100 g H2O

0–20.8 (CaCl2); 1–86 (CO2) mass.%

2.4/2.9–21.9 (CaCl2); 4.22/4.75–9.14 (NaCl) m

0.003–11.0 (CaCl2) equiv/kg H2O

3.8/11.15–25.56 (CaCl2) m

0.3–4.0 (CaCl2) m

0.3–4.0 (CaCl2) m

0.41–4.81 (CaCl2) m

6

Composition

4.8/15.6–3020 bar

SVP

1–3 kbar

SVP

60–804 bar

0.1/0.23–0.69 MPa

SVP

SVP

SVP

5

Pressure

ptx-CaF2 + NaCl-4.1 ptx-CaF2 + NaCl-5.1

ptx-CaF2 + NaCl-3.1

ptx-CaF2 + NaCl-2.1

ptx-CaF2 + CaCl2-4.1 ptx-CaF2 + HCl + NaCl-1.1 ptx-CaF2 + LiCl-1.1 ptx-CaF2 + NaCl-1.1

ptx-CaF2 + CaCl2-3.1

ptx-CaF2 + CaCl2-1.1 ptx-CaF2 + CaCl2-2.1

ptx-CaF2-2.1; 2.2

ptx-CaCl2 + CO21.1; 1.2 ptx-CaF2-1.1

ptx-CaCl2-16.1; 16.2 ptx-CaCl2-17.1; 17.2

ptx-CaCl2-15.1

ptx-CaCl2-13.1; 13.2 ptx-CaCl2-14.1

Anikin and Shushkanov, 1963 Malinin and Kurovskaya, 1992b Malinin and Kurovskaya, 1996b Malinin and Kurovskaya, 1996a Malinin and Kurovskaya, 1998 Malinin and Kurovskaya, 1999

Anikin and Shushkanov, 1963 Malinin and Kurovskaya, 1992b Malinin and Kurovskaya, 1996b Malinin and Kurovskaya, 1999 Malinin, 1976

Gruszkiewicz and Simonson, 2005 Zhang and Frantz, 1989 Booth and Bidwell 1950 Strubel, 1965

Hoffmann and Voigt, 1996 Bischoff et al., 1996

Oakes et al., 1995

Oakes et al., 1994

Holmes et al., 1994

8

7 ptx-CaCl2-12.1

REFERENCE

Table

Phase Equilibria in Binary and Ternary Hydrothermal Systems 27

Sampl

p-V curves Sampl

Sampl

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly; LGE Soly

Soly

CaF2 in (NaCl + CaCl2)

CaF2 in (NaCl + CaCl2)

CaF2 in (NaCl + CaCl2)

CaMg(CO3)2 (dolomite) CaMoO4

CaMoO4 in KCl

CaMoO4 in (KCl + NaCl)

CaMoO4 in (KCl + NaCl)

CaMoO4 in KNO3

CaMoO4 in (KNO3 + NaCl)

CaMoO4 in NaCl

CaMoO4 in NaCl

CaMoO4 in NaCl

CaMoO4 + CaWO4 in (KCl + NaCl)

CaMoO4 + CaWO4 in LiCl Ca(NO3)2 CaO + Al2O3

Ca(OH)2

Sampl; Quench Sampl

Sampl

Sampl

Sampl; Quench Sampl; Quench

Sampl

Sampl

Sampl

Quench Sampl

Wt-loss

Wt-loss

Wt-loss

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

329–500 C 50/200; 250 C 30/200; 250 C

320 C

520; 550 C

200–300 C

25/100–250 C

350 C

200 C

200 C

300–500 C

300–400 C

350 C

370 C 25/100–250 C

600 C

500 C

600–800 C

4

Temperature

SVP

SVP (19–35 atm) SVP

SVP

SVP

SVP

SVP

SVP

SVP

SVP

SVP

SVP

SVP

200 atm SVP

0.5–2 kbar

2 kbar

2 kbar

5

Pressure

0.04; 0.5/1.03 (CaO) g/L

(0.31–6.05) * 10−4 (CaMoO4); 0.001–2.0 NaCl m 0–4.8 (CaMoO4); 0–4.7 (CaWO4); 79 (KCl + NaCl) mass.%; (mass. ratio KCl/NaCl = 2.2 : 1) 0–2 (CaMoO4); 0.07–3.5 (CaWO4); 63.5 (LiCl) mass.% 0.4–0.8 (Ca(NO3)2) mol.fr. 0.003–0.11 (CaO); 0.001–0.15 (Al2O3) g/L

0.007–0.0098 (CaMoO4); 15 (NaCl) mass.%

(2.5–3.3) * 10−4 (CaMoO4); 0.2–1 (KNO3 + NaCl) m; (KNO3:NaCl = 1 : 1 mol.ratio) 0.007–0.017 (CaMoO4); 20–39 (NaCl) mass.%

(1.5–4.6) * 10−4 (CaMoO4); 0.2–1 (KNO3) m

0.007–0.036 (CaMoO4); 20.2–50.4 (KCl) mass.% 0.0003–0.015 (CaMoO4); 1.02–30.9 (NaCl + KCl) mass.%; (mass ratio NaCl/KCl = 1 : 2.2) 0.01–0.34 (CaMoO4); 31–76.4 (NaCl + KCl) mass.% (mass.ratio NaCl/KCl = 1 : 2.2)

0.0011–0.024 (CaMg(CO3)2) g/100 g H2O 0.0095 0.0046–0.0016 (CaMoO4) mass.%

0.032–0.106 (CaF2); 1 (NaCl); 1 (CaCl2) m

0.01–0.06 (CaF2); 5.0–9.6 (NaCl); 0.2–2.5 (CaCl2) m

0.0083–0.511 (CaF2); 0.6–4.8 (NaCl); 0.025–2.5 (CaCl2) m

6

Composition

ptx-CaMoO4 + CaWO4-2.1 ptx-Ca(NO3)2-1.1 ptx-CaO + Al2O3-1.1 ptx-Ca(OH)2-1.1

ptx-CaMoO4 + KCl-1.1 ptx-CaMoO4 + KCl + NaCl-1.1 ptx-CaMoO4 + KCl + NaCl-2.1 ptx-CaMoO4 + KNO3-1.1 ptx-CaMoO4 + KNO3 + NaCl-1.1 ptx-CaMoO4 + NaCl-1.1 ptx-CaMoO4 + NaCl-2.1 ptx-CaMoO4 + NaCl-3.1; 3.2 ptx-CaMoO4 + CaWO4-1.1; 1.2

ptx-CaF2 + NaCl + CaCl2-3.1 ptx-CaMg(CO3)2-1.1 ptx-CaMoO4-1.1

ptx-CaF2 + NaCl + CaCl2-2.1

Borina and Ravich, 1964 Keevil, 1942 Peppler and Wells, 1954 Peppler and Wells, 1954

Yastrebova et al., 1963 Feodotiev and Tereshina, 1963 Zhidikova and Malinin, 1972 Ravich and Borina, 1965

Zhidikova asnd Malinin, 1972 Zhidikova and Malinin, 1972

Yastrebova et al., 1963

Malinin and Kurovskaya, 1992b Malinin and Kurovskaya, 1996b Malinin and Kurovskaya, 1999 Schloemer, 1952 Feodotiev and Tereshina, 1963 Yastrebova et al., 1963 Borina, 1963

8

7 ptx-CaF2 + NaCl + CaCl2-1.1

REFERENCE

Table

28 Hydrothermal Experimental Data

Sampl

Sampl

Sampl Sampl

Sampl

Sampl

Soly

Soly

Soly Soly

Soly

Soly

Ca(OH)2 (portlandite)

Ca(OH)2

Ca(OH)2 (portlandite) Ca(OH)2 (portlandite) in Ar Ca(OH)2 (portlandite) in C2H4O2 (acetic acid) Ca(OH)2 + CaCO3

Wt-loss

Wt-loss

Sampl Sampl

Sampl

Sampl

Flw.Sampl

Sampl

Flw.Sampl

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Ca5(PO4)3F (F-apatite); Ca5(PO4)3F + CO2; Ca5(PO4)3F + HCl; Ca5(PO4)3F + NaCl Ca5(PO4)3OH (OHapatite) in K2CO3; in (K2CO3 + Na2CO3) CaSO4 CaSO4

CaSO4

CaSO4

CaSO4

CaSO4

CaSO4

CaSO4 in CaCl2

CaSO4 in (CaCl2 + NaCl)

CaSO4 in HNO3

Sampl

Flw.Sampl

Flw.Sampl

Sampl

Soly

Ca(OH)2 + NaNO3

Sampl

Soly

Ca(OH)2 + CaCO3 in NaNO3

3

2

1

Methods

Phase equil

Non-aqueous components

100/200–350 C

250; 300 C

250–300 C

200–325 C

96/221–263 C

500 C

141/198–408 C

182/207–316 C

100/182–207 C 98.5/194–220 C

300–500 C

800–1200 C

0.5/200–350 C

0.5/200–350 C

0.5/200–350 C

100/199–350 C

302–604 C 388–620 C

0.5/200–350 C

100; 257 C

4

Temperature

SVP

0.00005–0.15/0.25 (CaSO4); 0.00016–9.7 (HNO3) m

0.0001–0.003 (CaSO4); 0–0.3 (CaCl2); 0–0.9 (NaCl) m

0.00004–0.00036 (CaSO4); 0.03–0.3 (CaCl2) m

>SVP >SVP

0.02–0.5 (Ca); 0.01–0.5 (SO4) mm

0.004–0.015/0.19 (CaSO4) mass.%

0.002 (CaSO4) mass.%

ptx-CaSO4 + CaCl2-1.1 ptx-CaSO4 + CaCl2 + NaCl-1.1 ptx-CaSO4 + HNO3-1.1

ptx-CaSO4-7.1

ptx-CaSO4-6.1

ptx-CaSO4-5.1

ptx-CaSO4-4.1

ptx-CaSO4-3.1

ptx-CaSO4-1.1 ptx-CaSO4-2.1

ptx-Ca5(PO4)3OH1.1; 1.2

0.0002–35.3 (Ca5(PO4)3OH) g/kg H2O; 0.48–16 (K2CO3) mass.%; (2.2–3.6) (K2CO3) + (0.2–1.3) (Na2CO3) m 810/120–65 (CaSO4) ppm. 677/92–55 (CaSO4); 1645/205–165 (CaSO4 * 0.5H2O) ppm. 0.9/0.52–0.23 (Ca); 0.8/0.44–0.08 (SO4) mmol/L 22.3/7.5–0.5 (CaSO4) mg/100 g H2O

0.0009–0.014/0.04 (Ca(OH)2); 0.02–6.3 (NaNO3) m 0.06–3 (Ca5(PO4)3F) mass.%; 0.5 (CO2) mol.fr.; 1 (NaCl; HCl) m

0.0002–0.014/0.4 [Ca(OH)2 + CaCO3]; 0.004–6.26 (NaNO3) m

0.00014–0.003/0.2 [Ca(OH)2 + CaCO3] m

0.5–17.7 (Ca); 0–9.7 (CH3O2) mm

ptx-Ca(OH)2-4.1 ptx-Ca(OH)2 + Ar-1.1 ptx-Ca(OH)2 + C2H4O2-1.1 ptx-Ca(OH)2 + CaCO3-1.1 ptx-Ca(OH)2 + CaCO3 + NaNO3-1.1 ptx-Ca(OH)2 + NaNO3-1.1 ptx-Ca5(PO4)3F-1.1

ptx-Ca(OH)2-3.1

Marshall and Slusher, 1975a

Templeton and Rodgers, 1967 Templeton and Rodgers, 1967 Templeton and Rodgers, 1967

Booth and Bidwell, 1950 Morey and Hesselgesser, 1951b Dickson et al., 1963

Hall et al., 1926 Partridge and White, 1929 Straub, 1932

Dernov-Pegarev and Malinin, 1985

Yeatts and Marshall, 1967 Ayers and Watson, 1991

Blount and Dickson, 1967 Yeatts and Marshall, 1967 Walther, 1986 Fein and Walther, 1989 Seewald and Seyfried, 1991 Yeatts and Marshall, 1967 Yeatts and Marshall, 1967

8

7 ptx-Ca(OH)2-2.1

REFERENCE

Table

4.6–2.34 (Ca) (−log m) 4.9–2.34 (Ca) (−log m); 0.03–0.33 (Ar) mol.fr.

0.0002–0.003/0.23 Ca(OH)2) m

0.00097–0.023 (Ca(OH)2) m

6

Composition

2/74–1004/1010 bar >SVP

1000 bar

SVP

SVP

SVP SVP

0.2–0.95 Degree. of filling

1; 2 GPa

SVP

SVP

SVP

393–514 bar

990–3020 bar 2 kbar

SVP

1–1500 bar

5

Pressure

Phase Equilibria in Binary and Ternary Hydrothermal Systems 29

Phase equil

2

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

1

CaSO4 in H2SO4

CaSO4 + K2SO4

CaSO4 in K2SO4

CaSO4 in LiNO3

CaSO4 in MgCl2

CaSO4 in (MgCl2 + NaCl)

CaSO4 in Mg(NO3)2

CaSO4 in NaCl

CaSO4 in NaCl

CaSO4 in NaCl

CaSO4 in NaCl

CaSO4 in NaClO4

CaSO4 in NaNO3

CaSO4 in NaNO3

CaSO4 in Na2SO4

CaSO4 in Na2SO4

CaSO4 in Na2SO4

CaSO4 in (Na2SO4 + NaCl)

Continued

Non-aqueous components

Table 1.1

Flw.Sampl

Sampl

Flw.Sampl

Sampl

Sampl

Flw.Sampl

Sampl

Sampl

Sampl

Flw.Sampl

Sampl

Flw.Sampl

Flw.Sampl

Flw.Sampl

Sampl

Sampl

Sampl

Sampl

3

Methods

250; 300 C

100/200 C

250; 300 C

182/207–316 C

398/473–623 K

300 C

268/523 K

100/200 C

72.5/198–451 C

250–325 C

20/200 C

250 C

250; 300 C

250; 300 C

398/473–623 K

137.5/200; 250 C 150/200 C

25/200–350 C

4

Temperature

>SVP

0.001/0.002–0.004 (CaSO4); 0.3/0.5–3.1 (Na2SO4) m 0.00014–0.0033 (CaSO4); 0–0.3 (Na2SO4); 0–0.89 (NaCl) m

>SVP SVP

0.00008–0.0008 (CaSO4); 0.03–0.3 (NaSO4) m

SVP

0.085–0.28/0.52 (CaSO4); 0/8.3–26.6 (NaCl) mass.% 0.029/0.022–0.0093 (CaSO4); 1.7/1.9–8.2 (NaCl) m 0.00026–0.0046/0.035 (CaSO4); 0–5.9 (NaClO4) m 0.000075–0.016 (CaSO4); 0.02–5 (NaNO3) m 0.00001–0.029/0.035 (CaSO4); 0.0001–8 (NaNO3) m 0.02–0.41/78 (Ca); 0.27–20.4 (SO4) mmol/L

SVP

>SVP

SVP

6/27–1304/1410 bar SVP

>SVP

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

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

>SVP SVP

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

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

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

6

Composition

>SVP

>SVP

SVP

SVP

SVP

SVP

5

Pressure 8

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

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

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

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

REFERENCE

Table

30 Hydrothermal Experimental Data

Quench Wt-loss; Quench

Wt-loss Quench

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

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly Soly Soly Soly Soly Soly Soly Soly; Immisc Soly

Soly

CaSO4 in (Na2SO4 + NaClO4)

CaSO4 in (Na2SO4 + NaNO3)

CaSiO3(wollastonite) in NaCl CaWO4 CaWO4 in CaCl2

CaWO4 in KCl

CaWO4 in KCl

CaWO4 in (KCl + NaCl)

CaWO4 in K2SO4

CaWO4 in LiCl

CaWO4 in NaCl

CaWO4 in NaCl

CaWO4 in (NaCl + CaCl2)

CdBr2 CdBr2 CdCl2 CdCl2 CdI2 CdSO4 CdSO4 CdSO4 in UO2SO4

CdWO4 in (KCl + NaCl)

CdWO4 in KCl

Wt-loss

2

1

Sampl

Sampl

Wt-loss; Quench

Wt-loss; Quench

Sampl

Wt-loss

Sampl

Wt-loss; Quench

Quench

Sampl

Sampl

3

Methods

Phase equil

Non-aqueous components

350 C

200–400 C

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

600; 800 C

600 C

600; 800 C

300–500 C

397–500 C

300–500 C

800 C

252–561 C

110/265–555 C 800 C

800 C

0.05/250; 350 C

273.5/523; 623 K

4

Temperature

SVP

SVP

SVP SVP SVP SVP SVP SVP SVP SVP

2 kbar

0.5–2 kbar

2 kbar

SVP

400–2300 kg/cm2

SVP

2 kbar

1; 2 kbar

SVP/1–2 kbar 2 kbar

10 kbar

SVP

SVP

5

Pressure

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

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

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

0.0004–0.01 (CaWO4); 2 (NaCl) m

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

0.04–3.8 (CaWO4); 31–78 (LiCl) mass.%

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

0.00088–0.053 (CaWO4); 1–10 (KCl) m

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

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

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

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

6

Composition

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

ptx-CaWO4 + NaCl-2.1

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

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

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

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

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

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

Yeatts and Marshall, 1969

Kalyanaraman et al., 1973b

8

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

REFERENCE

Table

Phase Equilibria in Binary and Ternary Hydrothermal Systems 31

2

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly Soly Soly

LGE; Isop-m Soly; LGE

LGE

LGE, Isop-m LGE, Isop-m LGE

LGE; Cr.ph

1

CdWO4 in NaCl

(Ce,La)PO4 (monazite)

CoCO3 in CsCl

CoCO3 in LiCl

CoCO3 in NH4Cl

CoCO3 in NaCl

CoO

CoO

CoO in NH4OH; in NaOH

Co3O4

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

CsBr

CsCl

CsCl

CsCl

CsCl

CsCl

CsCl

Phase equil

Continued

Non-aqueous components

Table 1.1

Fl.inclus; Calcul

p-V curves

Isopiest

Isopiest

Vap.pr.diff.

Vap.pr.

Isopiest

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

Flw.Sampl

Quench; Rad.tr Sampl

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Sampl

3

Methods

500; 600 C

250; 300 C

225; 250 C

383/474

125/200–300 C

383/473; 498 K 400–638 C

115/185–205 C 200 C 21/190–288 C

20/150–300 C

373/473; 523 K 25/200–295 C

20/150–300 C

250–400 C

200–350 C

251–451 C

400 C

1000; 1100 C

250–400 C

4

Temperature

SVP (29.2–62.3 kg/cm2) 400–900 bar

SVP

SVP

SVP

SVP

SVP

SVP SVP ?? 8–9 MPa

SVP

8–9 MPa

SVP

SVP

SVP??

SVP??

SVP??

SVP??

1–2 GPa

SVP

5

Pressure

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

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

ptx-CsCl-6.1; 6.2

ptx-CsCl-5.1

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

ptx-CsCl-4.1

ptx-CsCl-3.1

ptx-CsCl-2.1

ptx-CsCl-1.1;

ptx-CsBr-1.1

0.73–8.48 (CsCl) m

0.68/0.8–7.31 7.66 (CsCl) m

1.01/1.02–1.07 (CsCl) m

L-G-S

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

(13/7–4) * 10−8 (Co) mol/L

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

ptx-CoO-2.1

(52/1.5–0.4) * 10−6 (Co) mol/L

0.2–2.67 (CoCO3) g/L; 2–6 (NaCl) m

0.4–25.7 (CoCO3) g/L; 2–9 (LiCl) m

0.5–4.1 (CoCO3) g/L; 2–9 (CsCl) m

1.9–264 (Co) µm

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

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

0.5–26 (CoCO3) g/L; 0.5–2 (NH4Cl) m

8

7

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

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

Ziemniak et al., 1999

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

Ikornikova, 1975

Ikornikova, 1975

Ikornikova, 1975

REFERENCE

Table

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

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

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

6

Composition

32 Hydrothermal Experimental Data

Isopiest

Vis.obs.

Vap.pr.

LGE Isop-m

LGE

LGE

LGE; Isop-m crit ph

LGE

LGE

Soly

LGE

LGE

Soly LGE Isop-m

Soly; immisc Soly

Soly Soly

Soly

Soly

Soly

Soly

CsCl + BaCl2

CsCl + CaCl2

CsCl + MgCl2

CsHSO4

CsNO3

CsNO3 + AgNO3

CsOH

CsOH

Cs2SO4

Cs2SO4 Cs2SO4

Cs2SO4 in UO2SO4

Cu; Cu in HCl CuBr

CuCl

CuCl; CuCl in HCl

CuI

CuO

Cu

CsNO3

p-V curves

LGE; Soly; Cr.ph

CsCl

151/218 C

151/218 C

383.5/473; 498 K 384–415 C

250; 300 C

250; 300 C

383/473–524 K

300–500 C

4

Temperature

Flw.Sampl

Wt-loss

Sampl

Wt-loss

Quench Wt-loss

Flw.Sampl

Vis.obs.

Vis.obs. Isopiest

Vap.pr.

749–896 K

180/200–340 C

280–320 C

160/200–360 C

300–450 C 200–330 C

873–896 K

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

400–700 C

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

Vap.pr.

p-V curves

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

3

2

1

Methods

Phase equil

Non-aqueous components

13–31 MPa

SVP

58–103 bar

SVP

500; 1000 bar SVP

17.3–31 MPa

SVP

SVP SVP

SVP

120–215 bar

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

SVP

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

SVP

SVP

5

Pressure

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

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

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

0.0036/0.0065–0.089 (CuI) m

ptx-CuCl-1.1

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

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

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

ptx-CsSO4-2.1 ptx-Cs2SO4-3.1

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

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

L-G-S

ptx-CsSO4-1.1

ptx-CsOH-2.1

0.003 * 10−4–0.16 (CsOH) m

57.6/84.2–100 (CsOH) mass.%

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

ptx-CsNO3-2.1

ptx-CsNO3-1.1

2–41 (CsNO3); 3–42 (AgNO3) mol.%

5.1–61.3 (CsNO3) mol.%

0.1–0.8 (CsNO3) m

ptx-CsHSO4-1.1

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

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

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

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

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

Urusova et al., 1994

8

7 ptx-CsCl-7.1; 7.2

REFERENCE

Table

0.23–97.7 (CsCl) mass.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 33

Flw.Sampl; Sampl

Quench

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly; Immisc; Cr.ph Immisc

CuO

CuO CuO in HNO3

CuO + NH4OH

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

CuO in Na(2.5–2.8)PO4

CuO in SO3 + D2O

Soly

Cu2O in NaCl

Quench

Immisc

Quench

Quench Flw.Sampl

Quench

Immisc

Soly Soly

Quench

Quench

Vis.obs.

Flw.Sampl

Flw.Sampl Quench

Quench

Flw.Sampl

Immisc

Cu2O Cu2O in NH4OH

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

CuO in (UO3 + SO3)

Flw.Sampl

Soly

CuO

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

50/250

200–450 C 892–896 K

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

325–428 C

292/478–535 K

473–623 K

100/200–400 C

754–895 K

300–450 C 473–573 K

200–450 K

57/207–550 K

4

Temperature

SVP

SVP; 500 bar 19–31 MPa

SVP

SVP

SVP

SVP

8.59/ 9.28 MPa SVP

SVP

SVP-200 bar

19–31 MPa

28 MPa SVP

SVP

8.3/13–42 MPa

5

Pressure

ptx-CuO-2.1

ptx-CuO-3.1

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

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

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

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

ptx-Cu2O + NaCl-1.1

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

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

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

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

ptx-CuO + NaOH-1.1

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

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

8

7

6

Marshall,

Marshall,

Marshall,

Marshall,

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

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

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

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

REFERENCE

Table

Composition

34 Hydrothermal Experimental Data

285–361 163/260; 302 C 643.9–647.1 K

Sampl

Vis.obs.

Sampl; Vap.pr. Vis.obs.

Sampl Sampl Quench

Sampl

Quench

Flw.Sampl

Flw.Sampl

Flw.Sampl

Quench

Sampl

Soly

Soly

Soly

Immisc; Soly LGE; H-Fl

Cr.ph

Soly Soly

Soly

Soly Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

CuS (covellite) in NaHS

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

D 2O

FeCl3 FeCr2O4 in NH4OH

Fe2O3; Fe2O3 + SiO2 (Glass)

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

Fe3O4 (magnetite) in HCl

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

Fe10S11 in HCl

Fe10S11 in MgCl2

Wt-loss

Wt-loss

Quench

Flw.Sampl

Sampl Flw.Sampl

Sampl

Quench

400 C

150–540 C

300–500 C

250–350 C

295/477–562 K

373/473–573 K

50/200–303 C

499–649 C

50/200 C

60/200–300 C

300 C 300 C 200 C

500 C

80/140–305 C 293/461–561 C

26.3/198 C

18.5/196.6–208.5 C

150/200–350 C

4

Cu2O in NaOH

3

2

Temperature

1

Methods

Phase equil

Non-aqueous components

300–1200 atm

800 atm

100–1000 bar

SVP

9.28 MPa?

<12 MPa

55–125 bar

2 kbar

SVP

SVP

10 MPa 10 MPa SVP

1000 bar

SVP 8–9 MPa

0.4–2.85 MPa (Part.pr. D2) SVP

SVP

2.0 MPa

2–5.7 MPa

SVP

5

Pressure

−6

7–12 (Fe10S11) (g S/kg H2O); 2 (MgCl2) m

0.2–4.6 (H2); 1.6–188 (H2S); 0–0.047 (SO42−) 103 * m; [buff.-PPM] 13–15 (Fe10S11) (g S/kg H2O) 0.35 (HCl) m

1.2 * 10−5 – 1 * 10−3 (HCl); 4 * 10−6 – 4 * 10−2 (NaOH) m 0.00/0.026–27.3 (Fe); 0.08–0.75 (NH4OH); 0.5–107 (Phosphate) mm 4.71–1.63 (Fe) (−log m); 0–4 (NaCl) m

(0.4–3.7) * 10−6 (Fe) m; pH = 5.5–6.9 (HClO4) (0.5–108) * 10−6 (Fe) m; pH = 7.5–11.9 (KOH) 3 * 10−7–9 * 10−5 (Fe); 0–0.32 (HClO4); 0–0.3 (NaClO4); 0–0.3 (NaOH) m 7.55–5.14 (Fe) (−log m); 0.003–0.1 (NaOH); 0.01–0.02 (NaCl) m 0.01/0.03–3.5 21 (Fe2O3); 0.4/4.9–76 (SO3) mass.% 0.18–2.6 (Fe2+); 0.33–5.4 (Cl−) m; [buff.-Ag/AgCl; Fe2O3/Fe3O4] 0.043–43.2 (Fe); 0–114.4 (HCl); 0–386 (KOH); 0–99.4 NaOH [106 * m]

ptx-FeCl3-1.1 ptx-FeCr2O4-1.1

H2O/FeCl3 = 0–1.11 (mol.ratio) (6/18–95) * 10−9 (Fe); (0.05/0.063–0.22) * 10−9 (Cr); (0.07–6) * 10−3 (NH4OH) m 0.009 (Fe2O3); [0.001 (Fe2O3) + 0.3 (SiO2)] mass.%

ptx-FeXSY + Fe3O4-1.1 ptx-Fe10S11-1.1; 1.2 ptx-Fe10S11-1.2

ptx-FeS2 + S-1.1

Ptx-Fe3O4-4.1; 4.2

ptx-Fe3O4-3.1-3.4

ptx-Fe3O4-2.1

ptx-Fe3O4-1.1

ptx-Fe2O3-5.1

ptx-Fe2O3-1.1; ptx-Fe2O3 + SiO2-1.1 ptx-Fe2O3-2.1 ptx-Fe2O3-2.2 ptx-Fe2O3-3.1; 3.2; 3.3 ptx-Fe2O3-4.1; 4.2

ptx-D2O-1.1

Arutyunyan et al., 1984 Arutyunyan et al., 1984

Kishima, 1989

Tremaine and LeBlanc, 1980a Ziemniak et al., 1995 Ohmoto et al., 1994

Marshall and Simonson, 1991 Schäfer, 1949 Ziemniak et al., 1998 Morey and Hesselgesser, 1951b Yishan et al., 1986 Yishan et al., 1986 Sergeeva et al., 1999 Diakonov et al., 1999 Posnjak and Merwin, 1922 Chou, I-Ming and Eugster, 1977 Sweeton and Baes, 1970

Stephan et al., 1956

Romberger and Barnes, 1970 Romberger and Barnes, 1970 Clark et al., 1959

Var’yash, 1989

8

7 ptx-Cu2O + NaOH-1.1 ptx-CuS + NaHS1.1; 1.2 ptx-Cu9S5 + NaHS-1.1 ptx-Cu,UO2,H2/ SO4-1.1 ptx-D2-1.1

REFERENCE

Table

0.0–100.0 (D2O) mol.%

16.5–17.2 (CuSO4); 45.4–47.6 (UO2SO4); 0–38.75 (H2SO4) mol.% 0.35–2.1 (D2mL/D2O g )

9.62/1493; 1623 (CuS) mg/L; 3.81 (NaHS) m

1.7/29–9108 (CuS) mg/L; 0–9.87 (NaHS) m

7.4 * 10 –0.0003 (Cu2O); 0.00001–1 (NaOH) m

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 35

Sampl

Sampl

Quench

Sampl; Quench

Sampl

Sampl p-T curves; Vis.obs. Sampl

Sampl Vis.obs.

Sampl

Vis.obs.

Vis.obs.

Soly

Soly

Soly

Soly

Soly

Soly

LGE; H-Fl

LGE Cr.ph; H-Fl

LGE

LGE Cr.ph

LGE Cr.ph

LGE

Cr.ph

Cr.ph

Cr.ph

LGE, Isop-m

Fe10S11 in NH4Cl

Fe10S11 in NaCl

GaOOH in (NaOH + NaCl); in (NH3 + NH4Cl); in (C2H4O2 + C2H3O2Na) GaOOH in (HCl + NaCl)

GeO2

GeO2; GeO2 in HClO4; in NaCl; in (HCl + NaCl); in (C2H4O2 + NaC2H3O2) H2

H2 H2

H2

H2 H3BO2

HBr HCl

HCl

HClO4

HNO3

H3PO4

H3PO4

Isopiest

Vis.obs.

Vap.pr.diff. Vis.obs.

Wt-loss

Wt-loss

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

383/473–523 K

378–442 C

371–375; 379–381 C 375–369 C

50/200–350 C

40–240 C 375–370 C

38/204; 315.6 C 319/471–636 K 376–381 C

52/260–343 C 374.3–383.3 C

100/200–225

25/200–350 C

150/200; 250 C 25/190–300 C

25/200–250 C

400 C

400 C

4

Temperature

SVP

SVP

SVP

SVP

1/14–166 bar

SVP (0.2–40 bar) SVP

0.7/2.1–28.5 MPa SVP

0.3/3–14 MPa

0.69–2.07 MPa 229–3000 bar

31/41–116 atm

0.75–90 (coef. of fil.) SVP

SVP

SVP

300–1200 atm

300–1200 atm

5

Pressure

1.08–11.06 (H3PO4) m

0.1–2.5 (H3PO4) m

ptx-H3PO4-2.1

ptx-H3PO4-1.1

ptx-HNO3-1.1

ptx-HClO4-1.1

0.1–1.4 (HClO4) ⇒ (HCl + 2O2) m 0.1–2.5 (HNO3) m

ptx-HCl-2.1

ptx-HBr-1.1 ptx-HCl-1.1 0.004/0.01–2.8 (HCl) m

8–65 (HBr) mass.% 0.1–2.5 (HCl) m

ptx-H2-5.1 ptx-H3BO3-1.1

ptx-H2-2.1 ptx-H2-3.1

0.33/0.39–2.01 (H2) [cm3/g H2O] 0–40 (H2) mol.fr.

(0.6/1.5–164) * 10−4 (H2) mol.fr. 0.1–1.8 (H3BO3) m

ptx-H2-1.1

54/68.8–202.1 (H2) [cm3/100 g H2O]

ptx-H2-4.1

ptx-GeO2-2.1

125–1600 (Ge) mg/L; pH = 1.7–5.8

0.0004–0.8 (H2) mol.fr.

ptx-GeO2-1.1

ptx-GaOOH-2.1

ptx-GaOOH-1.1

7.12/6.32–4.7 (Ga) (−log m); 1–251/316 (HCl); 9–250 (NaCl) [104 * m] 1.2 * 10−5/0.045–0.20 (GeO2) mass.%

6–1.7 (Ga) (−log m); pH(4–9/12.4)

ptx-Fe10S11-1.2

ptx-Fe10S11-1.2

13–25 (Fe10S11) (g S/kg H2O); 1.9 (NH4Cl) m 1.1–3.3 (Fe10S11) (g S/kg H2O); 2 (NaCl) m

8

7

6

Ipatiev and Teodorovich, 1934 Pray et al., 1952 Seward and Franck, 1981 Gillespie and Wilson, 1980 Alvarez et al., 1988 Marshall and Jones, 1974a Wunster et al., 1981 Marshall and Jones, 1974a Simonson and Palmer, 1993 Marshall and Jones, 1974a Marshall and Jones, 1974a Marshall and Jones, 1974a Holmes and Mesmer, 1999

Pokrovski and Schott, 1998

Benezeth et al., 1997 Kosova et al., 1987

Arutyunyan et al., 1984 Arutyunyan et al., 1984 Diakonov et al., 1997

REFERENCE

Table

Composition

36 Hydrothermal Experimental Data

Vis.obs. Vis.obs. Vis.obs. Immisc; Vis. obs. Vis.obs.

LGE

H-Fl; LGE

LGE; H-Fl

LGE

LGE

LGE

LGE

LGE

Cr.ph

LGE Isop-m

Soly; Quench Soly

LGE

LGE

H-Fl; Cr.ph

LGE; H-Fl

Soly Soly Soly Soly

Soly; Cr.ph; Immisc Soly; Cr.ph; Immisc Soly

H2S

H2S

H2S

H2S in CaCl2

H2S in NaCl

H2S in NaCl

H2S in Na2SO4

H2SO4

H3SO4

H2SO4

H2WO4 in KCl

H2WO4 in NaCl

He

He

He

He in UO2SO4

HgBr2 Hg(CN)2 HgCl2 HgI2

HgI2

HgS in H2S

HgI2 + PbI2

p-T curves; Vis.obs.; Sampl Sampl

2

1

Sampl

Vis.obs.

p-x curves

Sampl

Quench

Vap.pr.

Isopiest

Vap.pr.; Sampl Vis.obs.

Vap.pr.; Calcul. Sampl

Sampl

Vap.pr.; Calcul. Sampl

Sampl

Sampl

3

Methods

Phase equil

Non aqueous components

49/198 C

225–402 C

241–415 C

160/260; 301.7 C 142/193–237 C 108/209 C 105/206–235 C 196–334 C

162/260– 315.6 C 377/423– 548 K 523–696 K

300–400 C

325 C

383.5/473 K

380–448 C

180/200–295 C

155/216; 320 C 202 C

202; 262 C

202 C

20.8/200–321 C

311/478–589 K

160/202–330 C

4

Temperature

1.1/4.45 MPa

SVP

SVP

1.03–3.5 MPa (Part.pr. He) SVP SVP SVP SVP

16–223 MPa

SVP

0.69–3.45 MPa

SVP

SVP

SVP

SVP (5.9–462 mm Hg) SVP

SVP

12/28; 138 bar

SVP

SVP

3/22–139 bar

0.84–2.07 atm (Part.pr. H2S) 0.35/3.1–20.7 MPa

5

Pressure

−3

54–80 (HgI2 + PbI2) mass.%; 4.7–70.8 (PbI2) mass.% in (HgI2 + PbI2) 0.050/0.187–0.214 (HgS) g/L; 0.94 (H2S) m

52–80 (HgI2) mass.%

12/92.8–100 (HgBr2) mass.% 35.8/72.8 (Hg(CN)2) mass.% 38.9/69–96 (HgCl2) mass.% 35–100 (HgI2) mass.%

0.6–1.13 (He) mL/g; 40–243 (U) g/L

0.03–0.8 (He) mol%

ptx-HgI2 + PbI2-1.1 ptx-HgS + H2S-1.1

ptx-HgI2-2.1

ptx-He + UO2SO4-1.1 ptx-HgBr2-1.1 ptx-Hg(CN)2-1.1 ptx-HgCl2-1.1 ptx-HgI2-1.1; 1.2

ptx-He-3.1; 3.2; 3.3; 3.4; 3.5

ptx-He-2.1

(10/12–19) * 10−5 (He) mol.fr.

0.2 0.4–2.99 (He) cm3/g H2O

0.026–5.4 (W) g/L; 0.02–2.00 NaCl mol/L

ptx-H2SO4-3.1

ptx-H2SO4-2.1

ptx-H2S + CaCl2-1.1 ptx-H2S + NaCl-1.1 ptx-H2S + NaCl-2.1 ptx-H2S + Na2SO4-1.1 ptx-H2SO4-1.1

ptx-H2S-3.1

ptx-H2S-2.1

et et et et

al., al., al., al.,

1937 1937 1937 1937 Valyashko and Urusova, 1996 Valyashko and Urusova, 1996 Barnes et al., 1967

Benrath Benrath Benrath Benrath

Stephan et al., 1956

Potter II and Clynne, 1978 Sretenskaja et al., 1995

Pray et al., 1952

Bryzgalin, 1976

Thomas and Barker, 1925 Marshall and Jones, 1974a Holmes and Mesmer, 1992a Bryzgalin, 1976

Suleimenov and Krupp, 1994 Kozintseva, 1965

Kozintseva, 1965

Gillespie and Wilson, 1980, 1982 Suleimenov and Krupp, 1994 Kozintseva, 1965

Kozintseva, 1964

8

7 ptx-H2S-1.1

REFERENCE

Table

ptx-H2WO4 + KCl-1.1 ptx-H2WO4 + NaCl-1.1 ptx-He-1.1

0.5/0.55–5.11/5.61 (H2SO4); 0.52/0.56–6.17/7.10 (NaCl) m 0.033–1 (W) g/L; 0.02–2.00 (KCl) mol/L

0.1–2.5 (H2SO4) m

89.25–99.23 (H2SO4) mass.%

0.0023–0.27/0.63 (H2S); 0.42–3.54/4.36 (NaCl) mol.fr. 2050–2355 Henry’s const.

2155–2110 Henry’s const.

2130–2530 Henry’s const.

0.0025–0.34/0.99 (H2S) mol.fr.

0.4–76/99.6 (H2S) mol.%

(4–88) * 10 (H2S) mol/L

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 37

Sampl

Wt-loss; Quench Sampl

Vis.obs. Flw.Sampl

Sampl Vis.obs.; Sampl Sampl

Soly

Soly

Soly

Soly

Immisc Soly

LGE; ?Soly Soly; Immisc LGE

LGE

Soly; Immisc Soly

Soly

LGE; ?soly Soly; Immisc Soly

Soly

Cr.ph Soly Cr.ph

HgS in NaHS

HgS in (NaHS + NH4Cl + H2S) HgS in NaHS

HgS (cinnabar) in Na2S

I2 KAlSi3O8

KBO2 KBO2

KBO2 in NaBO2

KBO2 in NaOH

KB5O8

K2B2O4

K2B4O7

K2B4O7 K2B4O7

K2B10O16

K4B10O17

KBr KBr KBr

Vis.obs.; Sampl Sampl; Therm. anal. Sampl; Therm. anal. Sampl Vis.obs.; Sampl Sampl; Therm. anal. Sampl; Therm. anal. Vis.obs. Vis.obs. Vis.obs.

Sampl

Sampl

3

2

1

Methods

Phase equil

Non-aqueous components

Table 1.1 Continued

379.5–399.35 C 103/208–421 C 652.7–705 K

330 C

0/165–300

460–663 C 350–400 C

SVP SVP SVP

SVP

SVP

240–482 bar. SVP

SVP

SVP

−20/180–300 C

145–300 C

SVP

226–495 bar.

220–491 bar.

174–496 bar. SVP

SVP 1; 2 kbar

1/750 bar

SVP

2/14.2 MPa

0.4/2.8–8.8 MPa

5

Pressure

140–410 C

455; 656 C

455; 656 C

377–657 C 200–413 C

77/143–225 C 500 C

50/199–250 C

180–270 C

24/198 C

21/200 C

4

Temperature

Barnes et al., 1967

ptx-HgS + NaHS-1.1 ptx-HgS + NaHS-1.2 ptx-HgS + NaHS + H2S-2.1 ptx-HgS + Na2S-1.1 ptx-I2-1.1 ptx-KAlSi3O8-1.1

ptx-K4B10O17-1.1

ptx-KBr-1.1 ptx-KBr-2.1 ptx-KBr-3.1

0.04–0.34 (KBr) mol/dm3 51.5/61.1–73.3 (KBr) mass.% 0.08–2.1 (KBr) mol.%

ptx-K2B10O16-1.1, 1.2

ptx-K2B4O7-2.1 ptx-K2B4O7-3.1

ptx-K2B4O7-1.1

ptx-K2B2O4-1.1; 1.2

ptx-KBO2 + NaBO2-1.1 ptx-KBO2 + NaOH-1.1 ptx-KB5O8-1.1

ptx-KBO2-1.1 ptx-KBO2-2.1

8

7

Schr er, 1927 Benrath et al., 1937 Secoy, 1950

Toledano, 1964

Baierlein, 1983 Urusova and Valyashko, 1993a Toledano, 1964

Toledano, 1964

Urusova and Valyashko, 1993a Toledano, 1964

Baierlein, 1983

Kracek, 1931a Morey and Hesselgesser, 1951b Baierlein, 1983 Urusova and Valyashko, 1993a Baierlein, 1983

Efremova et al., 1982 Dickson, 1964

Barnes et al., 1967

REFERENCE

Table

80 (K4B10O17) mass.%

1.6/40–66 (K2B10O16) mass.%

0.003–16.9 (K) mass.% 31–76 (K2B4O7) mass.%

63–75 (K2B4O7) mass.%

13/68.8–73 (K2B2O4) mass.%

30–55 (KB5O8) mass.%

0.0017–10.0 (K); 0.0009–15.2 (Na) mass.%

0.0034–16 (K); 0.0002–8.1 (Na) mass.%

0.0021–24.3 (K) mass.% 30.3–75.1 (KBO2) mass.%

0.09–0.99/3.3 (HgS); 0.7; 2.2/3.8 (Na2S) mass.% 0.2/1.4–99.7 (I2) mass.% 0.076; 0.248 (KAlSi3O8) mass.%

0.076/0.732–4.027 (HgS) g/L; 0.4; 3.7 (NaHS) m 0.526/3.5; 3.7 (HgS) g/L; 3.72 (NaHS); 1.85 (H2S); 2.79 (NH4Cl) m 0.003–0.02 (HgS) m; 0.54–2.11 (HS−) m

6

Composition

38 Hydrothermal Experimental Data

Cr.ph

LGE

LGE LGE; Isop-m Soly Soly Soly; LGE

KBr

KBr

KBr KBr

LGE; Soly; Immisc; Cr.ph

LGE

Soly Soly Cr.ph Soly

Soly LGE; Soly

Soly

Soly; LGE

Cr.ph Soly Soly; LGE

K2CO3 + Na2CO3

K2CO3 + NaOH

K2C2O4 KCl KCl KCl

KCl KCl

KCl

KCl

KCl KCl KCl

K2CO3 + KOH

K2CO3 K2CO3 K2CO3

K2CO3

Soly; LGE; H-Fl LGE; ?Soly Soly LGE; Soly; Immisc; Cr.ph LGE

2

1

KBrO3 K2CO3 K2CO3

Phase equil

Non-aqueous components

Vap.pr.; p-V curves p-x; p-T curves Vis.obs. Sampl Vap.pr.

Vis.obs. p-V curves

Vis.obs. Vis.obs. Vis.obs. Vis.obs.; Sampl

Sampl

p-V curves

Sampl

p-V; p-T curves Sampl Vis.obs. p-V curves

Vis.obs. Sampl Vap.pr.

Sampl Isopiest

Vap.pr.

Vis.obs.

3

Methods

SVP (11–223.5 kg/cm2) SVP 20–309 atm 112–218 bar

200–637 C 652–700 C 400–500 C 374–700 C

190–645 C

SVP SVP (24.4–224 atm) SVP (8.6–224 atm)

SVP SVP SVP SVP

202–500 bar

9.3–90.2 MPa

208–500 bar

SVP (12.8–317 kg/cm2) 162–554 bar SVP 10–53 MPa

SVP 170–272 kg/cm2 31–203 bar

SVP (1.3–16.1 MPa) 218–337 bar SVP

SVP

5

Pressure

110/199–454 C 250–600 C

130/219–330 C 142/190–232 C 379–412 C 100/200–300 C

457 C

425 C

457 C

391–500 C 384/468–529 K 368–450 C

250–600 C

458 C 383/473; 498 K 134/204–312 C 350–425 C 374–600 C

423/473–623 K

384–480 C

4

Temperature

ptx-KCl-8.1 ptx-KCl-9.1 ptx-KCl-10.1

ptx-KCl-7.1

44.5–87.5 (KCl) mass.% 0.08–2.6 (KCl) mol.% 0.025–1042 (KCl) mg/L L-G-S

ptx-KCl-6.1

ptx-KCl-4.1 ptx-KCl-5.1

ptx-K2CO3 + KOH-1.1 ptx-K2CO3 + Na2CO3-1.1; 1.2; 1.3; 1.4; 1.5; 1.6 ptx-K2CO3 + NaOH-1.1 ptx-K2C2O4-1.1 ptx-KCl-1.1 ptx-KCl-2.1 ptx-KCl-3.1

ptx-K2CO3-3.1; 3.2 ptx-K2CO3-4.1 ptx-K2CO3-5.1 ptx-K2CO3-6.1

ptx-KBrO3-1.1 ptx-K2CO3-1.1 ptx-K2CO3-2.1

ptx-KBr-6.1 ptx-KBr-7.1

ptx-KBr-5.1

Ravich and Borovaya, 1950 Secoy, 1950 Jasmund, 1952/1953 Morey and Chen, 1956

Keevil, 1942

Benrath, 1942 Etard, 1894 Schroer, 1927 Akhumov and Vasil’ev, 1932, 1936 Benrath et al., 1937 Benedict, 1939

Baierlein, 1983

Urusova and Valyashko, 2005

Baierlein, 1983

Baierlein, 1983 Moore et al., 1997 Urusova and Valyashko, 2005

Baierlein, 1983 Holmes and Mesmer, 1998 Benrath et al., 1937 Gilligham, 1948 Morey and Chen, 1956 Ravich et al., 1968

Marshall and Jones, 1974a Lvov et al., 1976

8

7 ptx-KBr-4.1

REFERENCE

Table

0.16–0.624 (KCl) mol.fr.

36.4/44.7–69.0 (KCl) mass.% 49–82.9 (KCl) mass.%

50/65–80 (K2C2O4) mass.% 38.6/43–48 (KCl) mass.% 0.043–0.684 (KCl) mol/L 35.9/44.9–52.2 (KCl) mass.%

0.0047–0.56 (K); 0.0003–0.08 (Na) mass.%

0.005–0.85 (K) mass.%; K2CO3/KOH = 2.5 (mass.ratio) 5.4–73 (K2CO3); 7.2–54 (Na2CO3) mass.%

0.00036–28 (K2CO3) mass.% 11.8/18–19 (K2CO3) m 5–45 (K2CO3) mass.%

25.2–88.5 (K2CO3) mass.%

43.6/64.2–86.4 (KBrO3) mass.% 0.23–0.69 (K2CO3) mass.% L-G-S

0.008–0.09 (KBr) mass.% 0.67/0.70–7.30/7.43 (KBr) m

0.53–4.56 (KBr) m

0.1–1.8 (KBr) m

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 39

2

LGE; Cr.ph

Cr.ph

Cr.ph

Soly LGE

LGE, Isop-m LGE; ?Soly LGE Isop-m

LGE LGE

Soly LGE; Soly

LGE

Soly

LGE

LGE; Cr.ph

Cr.ph

LGE; Cr.ph

Soly

LGE

LGE

1

KCl

KCl

KCl

KCl KCl

KCl

KCl KCl

KCl KCl

KCl

KCl

KCl

KCl

KCl

KCl

KCl + CaCl2

KCl + CaCl2

KCl + CsCl

KCl KCl

Phase equil

Continued

Non-aqueous components

Table 1.1

p-V curves

p-V curves 250, 300 C

250, 300 C

SVP (24–61.5 kg/sm2) SVP (29.2; 63 kg/sm2)

SVP

−50/200–300 C

0.2–0.75 (KCl) [mol.fr. in (KCl + CaCl2)]; (salts/water = 1/6 mol.ratio) 0.3; 06 (KCl) [mol.fr] in (KCl + CsCl); (salts/water = 1/6 mol.ratio)

0–80.0 (CaCl2); 0–52.5 (KCl) mass.%

7.1–25 mass.%

0.244 (KCl) mol.%

dens 368.3 kg/m3 42–50 MPa

0.4–52.5 (KCl) mass.%

0.25–3 (KCl) m

70–100 (KCl) mass.%

0.0014–82.7 (KCl) mass.%

26.3/40–44 mass.% 0.0013–12.23 (KCl) mass.%

0.5–5 (KCl) m 14.3 (KCl) mol.%

0.0075–2.8 (KCl) mass.% 0.72–8.52 (KCl) m

1.06–7.51/8.08 (KCl) m

ptx-KCl + CaCl2-1.1 ptx-KCl + CaCl2-2.1 ptx-KCl + CsCl-1.2

ptx-KCl-28.1

ptx-KCl-26.1; 26.2 ptx-KCl-27.1

ptx-KCl-24.1; 24.2 ptx-KCl-25.1

ptx-KCl-21.1 ptx-KCl-22.1; 22.2; 22.3 ptx-KCl-23.1

ptx-KCl-19.1 ptx-KCl-20.1

ptx-KCl-17.1 ptx-KCl-18.1

ptx-KCl-16.1

ptx-KCl-13.1; 13.2 ptx-KCl-14.1 ptx-KCl-15.1

0.006–0.568 (KCl) m 40.2/44–51 (KCl) mass.% 0.55–4.53 (KCl) m

ptx-KCl-12.1

ptx-KCl-11.1

1–20 mass.% 0.1–1.4 (KCl) m

8

7

6

Bergman and Kuznetsova, 1959 Urusova and Valyashko, 1987 Urusova and Valyashko, 1987

Abdulagatov et al., 1998 Urusova et al., 2007

Crovetto et al., 1993, 1996 Dubois et al., 1994

Tkachenko and Shmulovich, 1992, 1996 Chou et al., 1992

Susarla et al., 1987 Hovey et al., 1990

Baierlein, 1983 Holmes and Mesmer, 1983 Wood et al., 1984 Urusova and Valyashko, 1987

Potter II et al., 1977 Zarembo et al., 1976 Holmes et al., 1978

Khaibullin and Borisov, 1966 Marshall and Jones, 1974a Potter II et al., 1976

REFERENCE

Table

Composition

400–963 bar

14.7–16.2 MPa

201–2015 bar

SVP (127–1204 bar)

SVP SVP (29.7; 63.5 kg/cm2) 16 bar SVP (82–309 bar)

203; 439 bar SVP

dens (0.52–0.9) g/cm3 SVP SVP (0.4/1.33–16.1 MPa) SVP

SVP (1/15–398 kg/cm2) SVP

5

Pressure

460; 480 C

661 K

T-Cv curves

p-V, p-X curves Vis.obs.

500; 600 C

623 K

439–821 C

400–700 °C

30/153.4–195.2 C 347–499 C

200–350 C 250, 300 C

420; 470 C 225; 250 C

382/474 K

148.6/192–371 C 423/473–623 K

187–411 C

383–447 C

100/200–440 C

4

Temperature

Fl.inclus

VTFD

Therm.anal.

Sampl

Sampl Sampl

Vap.pr.diff. p-V curves

Sampl Isopiest

Isopiest

p-T curves Vap.pr.

p-T curves

Vap.pr.; g-ray Vis.obs.

3

Methods

40 Hydrothermal Experimental Data

Vis.obs.; Sampl

Vis.obs.

Vis.obs.; Sampl

Vis.obs. Vis.obs. Vis.obs. Vap.pr.

Soly

Soly

Soly

Soly

Soly

LGE

LGE; Soly

Soly

Soly; LGE

Soly

Soly

Soly Soly Soly Soly; LGE

Soly; LGE

PTX, Soly

LGE; ?Soly LGE; ?Soly

LGE; ?Soly

LGE, Isop-m

KCl + KClO3

KCl + KClO4

KCl + KNO3

KCl + MgCl2

KCl in MgCl2

KCl + MgCl2

KCl + NaBr

KCl + NaCl

KCl + NaCl

KCl + NaCl

(KCl + NaCl) in MgCl2

KClO3 KClO4 K2CrO4 KF

KF

K2HB5O9

KHCO3 KHCO3 + CO2

KHCO3 + KNO3

KH2PO4

Isopiest

Sampl

p-x; p-V curves; Sampl Sampl; Therm. anal Sampl Sampl

p-x; p-T curves Therm.anal.

Vis.obs.; Sampl

p-V curves

p-V curves

Vis.obs.

Vis.obs.

Vis.obs.

3

2

1

Methods

Phase equil

Non-aqueous components

383/473–523 K

429–583 C

408–448 C 402–450 C

40/180–330

200–632 C

177/203–305 C 117/198–265 C 133/198–327 C 374–600 C

125/200; 265 C

411–784 C

225–598 C

100/200–300 C

439–540 C

250; 300 C

121/202–227 C

150/200, 250 C 125/200 C

150/200–250 C

150/200 C

4

Temperature

SVP

202–493 bar

168–461 bar 180–484 bar

SVP

SVP (4–302 kg/cm2)

SVP SVP SVP 60–116 bar

SVP

SVP (16.5–199 kg/cm2) 500–2000 bar

SVP

SVP (16–58 kg/cm2) SVP (76–105.6)

SVP

SVP

SVP

SVP

SVP

5

Pressure

0.79–15.15 (KH2PO4) m

0.0007–26 (K) mass.%

0.0041–58 (KHCO3) mass.% 0.0029–63 (KHCO3) mass.%

24/50–82.7 (K2HB5O9) mass.%

9.6–75.1 (KF) mass.%

65.1/73.1–95.7 (KClO3) mass.% 23.1/52.5–69.9 (KClO4) mass.% 46.1/49.4–55.7 (K2CrO4) mass.% L-G-S

1.8/21.5–32.5 (KCl); 0.35/3.1–12.8 (NaCl); 8.4/11–36.7 (MgCl2) mass.%

70–100 (KCl) mass.%

L-G-SKCl; L-G-SNaBr; L-G-SKCl-SNaBr

52–0 (KCl); 0–35 (NaCl) mass.%

0.2–0.8 (KCl) [mol.fr] in (KCl + MgCl2); (salts/water = 1/6 mol.ratio) L-G-SKCl-SNaBr

2.3/15–24 (KCl); 52/39.4–20.5 (MgCl2) mass.%

0–44.9 (KCl); 56.8–0 (MgCl2) mass.%

0.6–45 (KCl); 6–94 (KNO3) mass.%

11–43 (KCl); 3.5 6–56 (KClO4) mass.%

3–39 (KCl); 10/12–69 (KClO3) mass.%

6

Composition

ptx-KHCO3-1.1 ptx-KHCO3 + CO2-1.1 ptx-KHCO3 + KNO3-1.1 ptx-KH2PO4-1.1

ptx-K2HB5O9-1.1

ptx-KF-2.1; 2.2

ptx-KClO3-1.1 ptx-KClO4-1.1 ptx-K2CrO4-1.1 ptx-KF-1.2

ptx-KCl + NaCl2.1; 2.2 ptx-KCl + NaCl-3.1 ptx-K,Na,Mg/Cl-1.1

ptx-KCl + MgCl2-2.1 ptx-KCl + MgCl2-3.1 ptx-KCl + NaBr-1.1 ptx-KCl + NaCl-1.1

Holmes et al., 2000

Baierlein, 1983

Baierlein, 1983 Baierlein, 1983

Toledano, 1964

Akhumov and Vasil’ev, 1932, 1935, 1936 Benrath et al., 1937 Benrath et al., 1937 Benrath et al., 1937 Morey and Chen, 1956 Urusova and Ravich, 1966

Akhumov and Vasil’ev, 1932, 1935, 1936 Ravich and Borovaya, 1950 Chou et al., 1992

Benrath and Braun, 1940 Benrath and Braun, 1940 Benrath and Braun, 1940 Akhumov and Vasil’ev, 1932, 1936 D’Ans and Sypiena, 1942 Urusova and Valyashko, 1987 Keevil, 1942

8

7 ptx-KCl + KClO3-1.1 ptx-KCl + KClO4-1.1 ptx-KCl + KNO3-1.1 ptx-KCl + MgCl2-1.1

REFERENCE

Table

Phase Equilibria in Binary and Ternary Hydrothermal Systems 41

2

Soly; Immisc; Cr.ph Soly LGE; Isop-m Immisc; Cr.ph Cr.ph

1

K2HPO4

Vap.pr.

Vis.obs. Sampl; p-x; p-V; p-T; T-V curves Vis.obs. Sampl Vap.pr.

Vap.pr. Vap.pr.

Flw.Sampl

Vap.pr.

LGE

Soly Soly; LGE; Immisc; Cr.ph

Soly LGE LGE

LGE LGE

Soly

LGE

Soly

KIO3 KLiSO4

KNO3 KNO3 KNO3

KNO3 KNO3

KNO3

KNO3

KNO3 + NaNO3

Vis.obs.; Sampl

Vis.obs. Vis.obs. Vis.obs. p-V curves Vis.obs. Vis.obs.

KI

KI KI KI KI KI KI

Isopiest

SVP (0.3/1.0–16.1 MPa) SVP 16–1180 kg/cm2

SVP SVP SVP SVP (40–78 atm) SVP SVP

SVP

SVP

SVP

24.9–30.4 MPa SVP

SVP

5

Pressure

−19/179–279 C

423/448–623 K

SVP (0.4/0.8–163 MPa) SVP

100/212–307 C SVP 407–465 C 188–488 bar 425.5/492.3 K 2.29/9.35–22.74 bar 423/473–623 K SVP (2/7–169 bar) 150/200–350 C SVP (4.3/14–163 bar) 475 K SVP (247–302 bar)

117/201–300 C 148–450 C

423/473–623 K

383.5/473; 498 K 379.45–400 C 0/199–236.4 C 108/198–450 C 306–602 C 652.6–717.8 C 385–455 C

384–449 C

Vis.obs.

LGE; Isop-m Cr.ph Soly Soly Soly; LGE Cr.ph Cr.ph

360–389 C

400–450 C 383/473–523 K

100/200–400 C

4

Temperature

Vis.obs.

Flw.Sampl Isopiest

Quench; Vis. obs.

3

Methods

KHSO4

KHSO4

KxHyPO4

K2HPO4 K2HPO4

Phase equil

Continued

Non-aqueous components

Table 1.1

0–11 (H2O) mass.%; 20–80 (KNO3) mass.% in (KNO3 + NaNO3)

0.31–3.03 (KNO3) m

275–746 (KNO3) mg/kg

5–90 (KNO3) mass.% 0.31–3.03 (KNO3) m

70.8/89.9–98.1 (KNO3) mass.% 0.028–6.1 (KNO3) mass.% 0–51.2 (KNO3) m

26.1/41.6–58 (KIO3) mass.% 1–62 (K2SO4*Li2SO4) mass.%

7.4–59.6 (KI) mass.%

0.4–0.34 (KI) mol/L 56.3/74.5–76.9 (KI) mass.% 68/74.3–88.9 (KI) mass.% 0.3–0.8 (KI) mol.% 0.08–2.4 (KI) mol.% 0.1–1.4 (KI) m

0.55/0.58–9.57/9.78 (KHSO4) m

ptx-KNO3 + NaNO3-1.1; 1.2

ptx-KNO3-7.1

ptx-KNO3-6.1

ptx-KNO3-4.1 ptx-KNO3-5.1

ptx-KNO3-1.1 ptx-KNO3-2.1 ptx-KNO3-3.1

ptx-KIO3-1.1 ptx-KLiSO4-1.1; 1.2; 1.3; 1.4

ptx-KI-7.1

ptx-KI-1.1 ptx-KI-2.1 ptx-KI-3.1 ptx-KI-4.1 ptx-KI-5.1 ptx-KI-6.1

ptx-KHSO4-2.1

ptx-KHSO4-1.1

ptx-KXHyPO4-1.1

K/PO4 = 1; 1.2; 1.5; 2; 2.12 (mol.ratio) 0.1–1.4 (KHSO4) m

ptx-K2HPO4-2.1 ptx-K2HPO4-3.1

(0.1–23.9) * 10−4 (K2HPO4) m 0.59/0.63–7.40 (K2HPO4) m

Dell’Orco et al., 1995 Azizov and Akhundov, 1998 Ravich and Ginzburg, 1947

Puchkov et al., 1989 Azizov, 1994

Benrath et al., 1937 Baierlein, 1983 Barry et al., 1988

Benrath et al., 1937 Valyashko and Ravich, 1968

Marshall and Jones, 1974a Holmes and Mesmer, 1996a Schroer, 1927 Kracek, 1931b Benrath et al., 1937 Keevil, 1942 Secoy, 1950 Marshall and Jones, 1974a Lvov et al., 1976

Marshall, 1982

Wofford et al., 1995 Holmes et al., 2000

Marshall et al., 1981

8

7 ptx-K2HPO4-1.1; 1.2; 1.3

REFERENCE

Table

4.6–83 (K2HPO4) mass.%

6

Composition

42 Hydrothermal Experimental Data

Vis.obs.

LGE

Soly; LGE

Soly

LGE

LGE

LGE LGE

Soly LGE

LGE

Soly; LGE

Soly

Soly Soly; LGE

Soly; H-Fl

Soly; Immisc; Cr.ph Soly LGE; Isop-m Solty Soly; Immisc; Cr.ph Soly; LGE

Soly

KOH

KOH

KOH

KOH

KOH

KOH KOH

KOH KOH + NaOH

K2O/Al2O3

K4P2O7

KReO4

K2SO4 K2SO4

K2SO4

K2SO4

K2SO4 + KCl

K2SO4 in KCl

K2SO4 K2SO4

K2SO4 K2SO4

Vap.pr.

LGE

KOH

Vis.obs.; px; p-T curves Sampl

Vis.obs. p-V; p-X curves

p-x; p-V; pT; T-V curves Sampl Isopiest

Vis.obs. p-x; p-T curves Vap.pr.

Vap.pr.

Flw.Sampl Sampl

Sampl Flw.Sampl

Vap.pr.

Vap.pr.

Vis.obs.; Vap.pr. Therm.anal.

Vap.pr.

Vap.pr.

3

2

1

Methods

Phase equil

Non-aqueous components

350–370 C

145/197–616 C

457 C 383/473; 498 K 76–367 C 440–480 C

200–506 C

374–500 C

179/208–357 C 200–350 C

10.5/220–498 C

374–700 C

150/200–350 C

423–525 C 456 C

455 C 598–645 K

150/200–350 C

150/200–400 C

(−8)/206–401 C

112/262–416 C

300–420 C

300–460 C

4

Temperature

ptx-KOH-6.1

5.1–38.5 (K2O) mass.%

SVP

SVP (10–208 kg/cm2)

SVP 65–100 MPa

3.8–22 (K2SO4); 1.1–13.7 (KCl) mass.%

7–80 (H2O); 0–97.5 [(KCl) in (KCl + K2SO4)] mass.%

1.5–3.3 (K2SO4) mol.% 25–35 (K2SO4) mass.%

0009–0.049 (K2SO4) mass.% 0.55/0.62–2.71 (K2SO4) m

Ravich et al., 1953a

Valyashko, 1973

ptx-K2SO4 + KCl-2.1

Baierlein, 1983 Holmes and Mesmer, 1986 Ataev et al., 1994 Urusova et al., 2007

Morey and Chen, 1956 Ravich and Borovaya, 1968b

Mashovets et al., 1971 Morey and Chen, 1956 Holemann and Kleese, 1938 Benrath et al., 1937 Ravich et al., 1953

Galinker and Korobkov, 1951 Korobkov and Galinker, 1956 Lux and Brandl, 1963 Rollet and CohenAdad, 1964 Mashovets et al., 1965 Mashovets et al., 1971 Baierlein, 1983 Stephan and Kuske, 1983 Wofford et al., 1995 Baierlein, 1983

ptx-K2SO4 + KCl1.1; 1.2; 1.3

ptx-K2SO4-7.1 ptx-K2SO4-8.1

ptx-K2SO4-5.1 ptx-K2SO4-6.1

ptx-K2SO4-4.1; 4.2; 4.3

<1–60 (K2SO4) mass.%

170–1762 kg/cm2

218–481 bar SVP

ptx-K2SO4-3.1

ptx-K2SO4-1.1 ptx-K2SO4-2.1

ptx-KReO4-1.1

[ L-G-S]

25–3.9 (K2SO4) mass.% 26–20 (K2SO4) mass.%; [ L-G-S]

0.6/50.7–97.4 (KReO4) mass.%

ptx-K4P2O7-1.1

ptx-KOH-9.1 ptx-KOH + NaOH-1.1 ptx-K2O/Al2O3-1.1

(1.1–10.6) * 10−3 (KOH) m 0.005–12.2 (K); 0.002–11.5 (Na) mass.% 5–38.5 (K2O) mass.%; K2O/Al2O3 = 2–15 (mol.ratio) L-G-S

ptx-KOH-7.1 ptx-KOH-8.1

0.01–24.5 (K) mass.% 0.33 * 10−6–0.256 (KCl) m

SVP SVP (15–165 kg/cm2) 250–850 bar

SVP

220–230 bar

SVP (2/8–16 atm)

22–30 MPa 208–470 bar

SVP (1.68/6–167 atm) 222–381 bar 120–215 bar

ptx-KOH-5.1

8.8–82.4 (KOH) mass.%

ptx-KOH-4.1

ptx-KOH-3.1

0.25–208.4 kg/cm2

L-G-S 9.5/90–100 (KOH) mass

ptx-KOH-2.1

0.45–0.97 (KOH) mol.fr.

SVP (5–239 kg/cm2) SVP (0–64.8 mm Hg) SVP

ptx-KOH-1.1

43–99 (KOH) mol.%

8

7

5–220 kg/cm2

REFERENCE

Table

6

Composition

5

Pressure

Phase Equilibria in Binary and Ternary Hydrothermal Systems 43

2

LGE; Soly; Immisc; Cr.ph Soly; LGE

1

K2SO4 in KCl

Soly

Soly; LGE

LiCNS Li2CO3; Li2CO3 in CO2

Li2CO3

LiCl

Non-aqueous

LGE; Isop-m Soly Soly

LiBr

p-x; p-T curves

Sampl

Vis.obs. Sampl

Isopiest

250–556 C

150–370 C

383/473; 498 K −33/144–260 C 40/200–290 C

423/473–623 K

250–360 C 23.5/200–275 C 37.5/200–300 C 130–400 C

Sampl Sampl Sampl Sampl; Therm. anal. Vap.pr.

LGE

78/199–291 C

100/200–300 C

293/425–523 K

Vis.obs.

Sampl

Soly; Immisc Soly Soly Soly Soly

LiBr

LiBO2 Li2B2O4 Li2B10O16 xLi2O * yB2O3

Kr + O2 (Kr + O2) in (UO2SO4 + CuSO4 + H2SO4) La2(SO4)3 in UO2SO4

Kr; Kr in D2O

p-T curves; Vis.obs.

343.5/448– 525.6 K 610–661 K

75–531 C

350–380 C

148/200–600 C

420–500 C

4

Temperature

Sampl

H-Fl; Immisc; Cr.ph LGE

Kr

Vis.obs.; Sampl p-x curves

p-V; p-X curves; Wt-loss Sampl; p-x; p-V curves Sampl

3

Methods

LGE

H-Fl

Kr

K2SO4 + KNO3

Soly; Immisc Soly

K2SO4 + KLiSO4

K2SO4 + KLiSO4

Phase equil

Continued

Non-aqueous components

Table 1.1

SVP (6.1–45.5 kg/cm2)

SVP

SVP SVP

SVP (0.12/0.44– 15.7 MPa) SVP

208 bar SVP SVP SVP

SVP

1.9/3–13.9 MPa

1.7/2.1–7 MPa

31–273 MPa

SVP (4.3–5.7 atm)

SVP

SVP

SVP (5/15–409 kg/cm2)

30–81 MPa

5

Pressure

Urusova et al., 2007

ptx-K2SO4 + KCl3.1, 3.2

ptx-Li2CO3-2.1 ptx-LiCl-1.1; 1.2

15.5–93.5 (LiCl) mass.%

ptx-LiCNS-1.1 ptx-Li2CO3-1.1

ptx-LiBr-2.1

ptx-LiBr-1.1

ptx-LiBO2-1.1 ptx-Li2B2O4-1.1 ptx-Li2B10O16-1.1 ptx-xLi2O * yB2O3-1.1

ptx-La2(SO4)3-1.1

ptx-Kr-3.1; ptxKr + D2O-1.1 ptx-Kr + O2-1.1; 1.2

ptx-Kr-2.1

ptx-K2SO4 + KLiSO4-2.1 ptx-K2SO4 + KNO3-1.1; 1.2 ptx-Kr-1.1

Feodorov et al., 1976 Holmes and Mesmer, 1998 Nikolaev, 1929 Marshall et al., 1958 Elenevskaya and Ravich, 1961 Ravich and Yastrebova, 1963

Byers et al., 2000 Bouaziz, 1961 Bouaziz, 1961 Bouaziz, 1961

Jones et al., 1957

Anderson et al., 1962

Crovetto et al., 1982

Potter II and Clynne, 1978 Mather et al., 1993

Ataev et al., 1994

Valyashko, 1975

Ravich and Valyashko, 1969

8

7

ptx-K2SO4 + KLiSO4-1.1

REFERENCE

Table

0.42–0.039 (Li2CO2) mass.%

53–83 (LiCNS) mol.% 2.06/0.8–0.06 (Li) m; 0–189 (CO2) atm

0.63/0.69–5.39 (LiBr) m

8.3–56.3 (LiBr) mass.%

0.056–0.38 (Li) m 3.12/7.90–2.60 (Li2B2O4) mass.% 17.9/50.8–48 (Li2B10O16) mass.% 3; 8.75 (Li2O * B2O3); 10 (Li2O * 2B2O3); 52 (Li2O * 5B2O3) mass.%

4.39/1.22–0.042 (La2(SO4)3) mass.%

(1.01–38.4) * 10−6 (Kr) (part.pr, MPa); (0–23.5) * 10−4 (O2) mol.fr.

0.016/0.04–99 (Kr) mol.%

0.19–0.62 (Kr) mol.fr.

(11.5–24.0) * 10−5 (Kr) mol.fr

0.2–41 (K2SO4); 2–98 (KNO3) mol.%

2.2–31.5 (K2SO4); 0.6–22.6 (KLiSO4) mass.%

24/30–38 (K2SO4); 4–50 (KLiSO4) mass.%

4–50 (K2SO4); 0–20 (KCl) mass.%

6

Composition

44 Hydrothermal Experimental Data

Vap.pr.

Vap.pr.

Vap.pr.

Flw.Sampl

Vap.pr.

Cr.ph

LGE

LGE; Isop-m LGE; Isop-m LGE

LGE; Cr.ph

LGE

LGE

LGE

Soly

Soly; LGE

LGE Isop-m

LGE

LGE

LGE

Soly

LGE

LGE

Soly; LGE

Soly

LGE

LiCl

LiCl

LiCl

LiCl

LiCl + CaCl2

LiCl + KCl

LiCl + MgCl2

LiF

LiF + KF

LiHSO4

LiI

LiNO3

LiNO3

LiNO3

LiNO3

LiOH

LiOH

LiOH

LiOH

LiCl

LiCl

LGE

LiCl

Vap.pr.

Themal.anal

Sampl

Vap.pr.

p-V curves; Sampl Isopiest

Sampl

p-V curves

p-V curves

Fl.inclus; Calcul. p-V curves

p-V curves

Isopiest

Isopiest

Vap.pr.

Vis.obs.

Vap.pr.diff.

3

2

1

Methods

Phase equil

components

300, 350 C

(−18)/186–442 C

60/206–365 C

300–420 C

423/473–623 K

475 C

150/200–350 C

423/473–623 K

383.5/473; 498 K 423/473–623 K

250–470 C

198–448 C

250, 300 C

250, 300 C

250, 300 C

500; 600 C

250; 300 C

225; 250 C

383/474 K

423/473–623 K

383–482 C

125/200–275 C

4

Temperature

SVP (81–162 kg/cm2)

SVP

SVP (0.4/1.25–16.5 MPa) SVP (66–300 kg/cm2) SVP (1.6–8.7 MPa)

SVP (3.8/12.5– 164.6 bar) SVP (246–302 bar)

SVP (0.15/0.6–16.1 MPa) SVP (1/1.5–90.2 kg/cm2)

SVP (21.3–52.5 kg/cm2) SVP (26.7–61.2 kg/cm2) SVP (15.7–48 kg/cm2) SVP; d = 0.28–0.49 g/cm3 SVP (11.4–59 kg/cm2) SVP

SVP (25.6–156 kg/cm2) 400–900 bar

SVP

SVP (0.14–16.5 kg/cm2) SVP

SVP

SVP

5

Pressure

ptx-LiOH-4.1

3–9 (LiOH) mol.%

ptx-LiOH-2.1; 2.2

5–15 (LiOH) g/100 g H2O

ptx-LiOH-3.1

ptx-LiOH-1.1

0.03–0.46 (LiOH) mol.fr.

10.5/12–100 (LiOH) mass.%

ptx-LiNO3-4.1

ptx-LiNO3-3.1

ptx-LiNO3-2.1

ptx-LiNO3-1.1; 1.2

ptx-LiI-1.1

ptx-LiF + KF-1.1; 1.2 ptx-LiHSO4-1.1

0–5.25 (LiNO3) m

0.433–2.167 (LiNO3) g/kg H2O

0.18–5.25 (LiNO3) m

50–90 (LiNO3) mass.%

5.9–58.7 (LiI) mass.%

0.50/0.56–7.20 (LiHSO4) m

0.05–18.7 (LiF); 9.7–74.3 (KF) mass.%

tx-LiCl + CaCl2-1.1 tx-LiCl + KCl-1.1

0.25–0.92 (LiCl) in (LiCl + CaCl2) mol.fr; (LiCl + CaCl2)/H2O = 1/6 mol.ratio 0.3–0.74 (LiCl in LiCl + KCl) mol.fr.; (LiCl + KCl)/H2O = 1/6 mol.ratio 0.25–0.87 (LiCl in LiCl + MgCl2) mol.fr.; (LiCl + MgCl2)/H2O = 1/6 mol.ratio 0.0026–0.11 (LiF) g/100 g H2O

ptx-LiCl + MgCl2-1.1 ptx-LiF-1.1; 1.2

ptx-LiCl-8.1; 8.2

ptx-LiCl-7.1

14.3 (LiCl) mol.% 4.1–23.2 (LiCl) mass.%

ptx-LiCl-6.1

0.68–6.34 (LiCl) m

ptx-LiCl-5.1

ptx-LiCl-4.1

3.4–41.6 (LiCl) mass.% 0.6/0.74–5.54 5.57 (LiCl) m

ptx-LiCl-3.1

Dell’Orco et al., 1995 Abdulagatov and Azizov, 2004 Korobkov and Galinker, 1956 Stephan and Miller, 1962 Rollet and CohenAdad, 1964 Krumgalz and Mashovets, 1965

Urusova and Valyashko, 1987 Urusova and Valyashko, 1987 Urusova and Valyashko, 1987 Booth and Bidwell, 1950 Ravich and Urusova, 1967 Holmes and Mesmer, 1996a Feodorov et al., 1976 Puchkov and Matashkin, 1970; Puchkov et al., 1989 Azizov, 1994

Lindsay and Liu, 1971 Marshall and Jones, 1974a Feodorov et al., 1976 Holmes and Mesmer, 1981b Holmes and Mesmer, 1983 Urusova and Valyashko, 1987 Dubois et al., 1994

8

7 ptx-LiCl-2.1

REFERENCE

Table

0.1–2.2 (LiCl) m

0.99/1.00–1.4 (LiCl) m

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 45

2

LGE

S-G

Soly; Cr.ph

LGE; Soly

Soly; H-Fl

Soly

Soly

Soly; Immisc; Cr.ph LGE Isop-m

LGE

Soly

Soly

Soly Soly

1

LiOH

LiOH + Li2O

Li2O – SO3 – D2O

Li2SO4

Li2SO4

Li2SO4

Li2SO4

Li2SO4

Li2SO4

Li2SO4 in D2SO4

Li2SO4 in H2SO4

MgCO3 (magnesite) MgCl2

MgCl2

Vap.pr.

p-V curves

Vap.pr.diff.

Sampl

LGE

LGE

LGE

Soly

MgCl2

MgCl2

MgCl2

MgCl2

130/200–250 C

402/473–507 K

250 C

410/469–617 K

300; 350 C

p-V curves

MgCl2

382–474

370 C 100/200–300 C

200–350 C

200–350 C

383/473; 498 K 423–573 K

248–507 C

248–388 C

225–370 C

374–860 C

114/142.5–232 C

204–466 C

537–621 K

598–645 K

4

Temperature

LGE; Isop-m LGE; soly

Sampl

Sampl

Vap.pr.

p-x; p-V; T-V; p-T curves Isopiest

p-x curves

Sampl

Vap.pr.; Sampl Vap.pr.

Vis.obs.

Effusion

Flw.Sampl

3

Methods

Quench Vis.obs.; Sampl Isopiest

Li2SO4

Phase equil

Continued

Non-aqueous components

Table 1.1

(<1)–60 (Li2SO4) mass.%

290–2100 kg/cm2

SVP (37/180–612 kPa) SVP

SVP (0.24/0.9– 15.22 MPa) SVP

SVP

170/250.2–301 mol MgCl2/1000 mol H2O

6.9–12 (MgCl2) m

10.3–63.0 (MgCl2) mass.%

0.29–4.6 (MgCl2) m

9.6–80.0 (MgCl2) mass.%

0.79–3.5 (MgCl2) m

0.08–0.29 (MgCO3) g/100 g H2O 42/57–68 (MgCl2) mass.%

∼200 atm SVP SVP

0.12–2.8 (Li2SO4); 0–1.5 (H2SO4) m

0.069–2.7 (Li2SO4); 0–1.6 (D2SO4) m

0–1.6 (Li2SO4) m

SVP

SVP (0.44–8.59 MPa) SVP

0.54/0.64–3.18 (Li2SO4) m

3–42.5 (Li2SO4) mass.%

293–1070 kg/cm2

SVP

23–0.5 (Li2SO4) mass.%

L-G-S

22.7–23 (Li2SO4) mass.%; [L-G-S; G-S]

SVP

SVP (1.4/10–24.5 atm) 4.22 > 1000 bar

SVP

1–0 mLi2O/mSO3; 0.02–2.5 (SO3) m

LiOH[S] + Li2O[S] + H2O[G]

(6.25–648) * 10−7 atm

ptx-MgCl2-7.1

ptx-MgCl2-6.1

ptx-MgCl2-5.1

ptx-MgCl2-4.1

ptx-MgCl2-3.1

ptx-MgCl2-2.1

ptx-Li2SO4 + D2SO4-1.1 ptx-Li2SO4 + H2SO4-1.1 ptx-MgCO3-1.1 ptx-MgCl2-1.1

ptx-Li2SO4-7.1

ptx-Li2SO4-6.1

ptx-Li2SO4-5.1; 5.2; 5.3; 5.4

ptx-Li2SO4-4.1

ptx-Li2SO4-3.1

ptx-Li2SO4-2.1

ptx-LiOH + Li2O-1.1 ptx-LiO2 + SO3-1.1 ptx-Li2SO4-1.1

ptx-LiOH-5.1

0.12 * 10−6–035 (LiOH) m

120–215 bar

Fanghangel et al., 1987

Urusova and Valyashko, 1983b Matuzenko et al., 1984 Urusova and Valyashko, 1984 Emons et al., 1986

Holmes and Mesmer, 1986 Abduiagatov and Azizov, 2004 Marshall et al., 1963 Marshall et al., 1963 Schloemer, 1952 Akhumov and Vasil’ev, 1932 Holmes et al., 1978

Morey and Chen, 1956 Elenevskaya and Ravich, 1961 Ravich and Borovaya, 1964c Ravich and Borovaya, 1964b

Stephan and Kuske, 1983 Gregory and Mohr, 1955 Marshall et al., 1963 Campbell, 1943

8

7

6

5

REFERENCE

Composition

Table

Pressure

46 Hydrothermal Experimental Data

Soly

MgSO4*H2O in H2SO4

Soly

Soly

Soly

Mg(OH)2 (brucite) in K2CO3 Mg(OH)2 (brucite) in (K2CO3 + Na2CO3) Mg(OH)2 in NaCl

MgSO4*H2O in HNO3; in NaNO3 + HNO3

Soly

Mg(OH)2 (brucite) Mg(OH)2 (brucite) Mg(OH)2 in HCl

Soly Soly Soly

Soly Soly Soly

Mg(OH)2

MgSO4*H2O MgSO4*H2O MgSO4*H2O

Sampl

Soly

MgO-B2O3

Soly

Wt-loss

Soly

MgCl2 + KCl

MgSO4*D2O in D2SO4

Wt-loss

LGE

MgCl2 + CaCl2

Soly

Isopiest

LGE, Isop-m LGE

MgCl2

Mg(OH)2 in NaNO3

Vap.pr.

LGE

MgCl2

Soly

Sampl

LGE

MgCl2

Mg(OH)2 (brucite) + NaCl

p-V curves

LGE

MgCl2

Sapml.

Sampl

Sampl Vis.obs. Vis.obs.

Sampl

Sampl

Therm.anal.

Quench Sampl Sampl

Wt-loss; Quench Sampl

Vap.pr.diff.

p-V curves

3

2

1

Methods

Phase equil

Non-aqueous components

200–350 C

75/195–238 C 75/203–238 C 125/210; 212 C 200–350 C

200, 370 C

22/180–300 C

400–708 C

21/183–300 C

300, 400 C

300, 400 C

30/200; 245 C 500 C 350–629 C 21/175–300 C

402/472– 524 K 400 C

150/200– 350 C 383/474– 524.12 K 250, 300 C

400–600 C

250, 300 C

4

Temperature

SVP

SVP

SVP SVP SVP

SVP

SVP

1–2455 bar

SVP

SVP

SVP

1 kbar 985–3000 bars SVP

SVP

SVP (34/178–1105 kPa) SVP

SVP

SVP (3.2/18.6–163 bar) SVP

SVP (11.3–28.5 kg/cm2) 276–1037 bar

5

Pressure

0.0048–1.48 (MgSO4); 0.0017–1.8 (H2SO4) m

0.01–1.14 (MgSO4); 0.03–0.93 (HNO3); 0.15–2.11 (NaNO3) m

0.0052–1.237 (MgSO4); 0.0086–1.418 (D2SO4) mol/kg D2O 1.9–0.56 (MgSO4) g/100 g H2O 7.9/0.3–0.1 (MgSO4) mol.% 30–5 (MgSO4) mass.%

(0.88–1.69) * 10−3 (Mg); 0.5 (NaNO3) m

0–38 (NaCl) mol.%

0.97–26.85 (Mg(OH)2) g/kg H2O; 7.08 (K2CO3 + Na2CO3) m (0.62–1.65) * 10−4 (Mg); 0.5 (NaCl) m

(1.34–304) * 10−3 (Mg(OH)2); 0.5–7 (K2CO3) m

0–1.25 (Mg) ppm 4–5.43 (−log(mol Mg/kg H2O)) (0.08–3.78) * 10−3 (Mg); 0.01 (HCl) m

ptx-MgSO4 + HNO3-1.1; ptxMgSO4 + H,Na/NO3-1.1 ptx-MgSO4 + H2SO4-1.1

ptx-MgSO4*H2O-1.1 ptx-MgSO4*H2O-2.1 ptx-MgSO4*H2O-3.1

ptx-Mg(OH)2-2.1 ptx-Mg(OH)2-3.1 ptx-Mg(OH)2 + HCl-1.1 ptx-Mg(OH)2 + K2CO3-1.1 ptx-Mg(OH)2 + K,Na/CO3-1.1 ptx-Mg(OH)2 + NaCl-1.1 ptx-Mg(OH)2-4.1; ptx-Mg(OH)2 + NaCl-2.1; 2.2 ptx-Mg(OH)2 + NaNO3-1.1 ptx-MgSO4*D2O-1.1

ptx-Mg(OH)2-1.1

0.2/0.04; 0.01 (Mg(OH)2) mmol/dm3

22.5–50 (B2O3) mass.%

ptx-MgCl2 + CaCl2-1.1 ptx-MgCl2 + KCl-1.1 ptx-MgO-B2O3-1.1

ptx-MgCl2-11.1

ptx-MgCl2-10.1

ptx-MgCl2-9.1

Marshall and Slusher, 1965

Marshall and Slusher, 1975b

Marshall and Slusher, 1965 Robson, 1927 Smits et al., 1928 Benrath, 1941

Lambert et al., 1982

Bai et al., 1998

Dernov-Pegarev et al., 1988 Dernov-Pegarev et al., 1988 Lambert et al., 1982

Poty et al., 1972 Walther, 1986 Lambert et al., 1982

Grigoriev and Nikolaev, 1967 Carlson et al., 1953

Urusova and Valyashko, 1987 Tkachenko and Shmulovich, 1992, 1994 Azizov and Akhundov, 1995 Holmes and Mesmer, 1996 Urusova and Valyashko, 1987 Emons et al., 1987

8

7 ptx-MgCl2-8.1

REFERENCE

Table

0.34–0.75 (MgCl2) [mol.fr. in (MgCl2 + CaCl2)]; salts/H2O = 1/6 (mol.ratio) 9.3–12.18 (MgCl2); 0–5.2 (KCl) m

0.42–3.95 (MgCl2) m

0.32–4.1 (MgCl2) m

0.33–43 (MgCl2) mass.%

14.3 (MgCl2) mol.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 47

Sampl

Vis.obs. Quench; Rad.tr Quench

Sampl

Sampl

Sampl

Sampl Sampl

Sampl

Sampl

Sampl

Sampl

Sampl; Vis. obs. Sampl p-T curves

Sampl Sampl

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

LGE

LGE LGE; Cr.ph

Cr.ph; H-Fl

LGE; H-Fl

H-Fl

H-Fl

H-Fl; Cr.ph

Soly H-Fl; LGE

H-FL; LGE LGE

Mg2SiO4 in K2CO3

Mg2Si2O6

MnCl2 Mn2O3

MoO2 (+Buff)

MoS2

MoS2 in H2S

MoS in (NaCl + H2S)

N2

N2 N2

N2

N2

N2

N2

N2

N2 N2

NH3 NH3

Sampl

Wt-loss

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

147/201–326 C 403/503 C

336/476–637 K 410/474–595 K

480–659 K

350 C

37.8/204; 315 C

25/200–350 C

364–385 C

25/260–315.6 C 330–385 C

65/190–240 C

100–250 C

100–250 C

100–250 C

450 C

113/198–430 C 100/150–300 C

600 C

400 C

4

Temperature

SVP 0.78/3.55–7.17 MPa

0.53/2.1–25.6 MPa 7.8/10.4–23.5 MPa

15.5–270 MPa

98 MPa

0.34/3.1–13.8 MPa

50–500 atm

225.65–2200 atm

1.03–3.45 MPa 220–3700 bar

100–300 atm

SVP

SVP

SVP

500 bar

SVP SVP

1000 bar

SVP

5

Pressure

ptx-Mg2SiO4 + K2CO3-1.1 ptx-Mg2Si2O6-1.1

(2.7–69.3) * 10−3 (Mg2SiO4); 0.5–3.2 (K2CO3) m

ptx-NH3-1.1 ptx-NH3-2.1

ptx-N2-9.1 ptx-N2-10.1

(0.25/0.8–109) * 10−4 (N2) mol.fr. 0.95/0.82–0.36 (N2) mol.fr. 1.7–1750 (NH3) ppm 7.6–59.0 (NH3) mol.%

ptx-N2-8.1; 8.2

ptx-N2-7.1

102 (N2) cm3/g H2O 0.1–0.866 (N2) mol.fr.

ptx-N2-6.1

ptx-N2-5.1

ptx-N2-4.1

ptx-N2-2.1 ptx-N2-3.1; 3.2

ptx-MoS2 + H2S-1.1 ptx-MoS2-NaCl + H2S-1.1 ptx-N2-1.1; 1.2

0.0003–0.80 (N2) mol.fr.

3.4–94.1 (N2) mol.%

0–48 (N2) mol.%

(0.0007–0.031) (MoS2); 0.043–0.218 (H2S) mass.% 0.01–0.037 (MoS2); 15 (NaCl); 0.04–0.1 (H2S) mass.% 0.98/1.8–6.06 (N2) [cm3/g H2O] (L); 0.8–0.94 [g(N2)/g(N2 + H2O)] (G) 0.44–2.32 (N2) cm3/g H2O 2–84 (N2) mol.%

ptx-MoO2-1.1

(0.1–100) * 10−5 (Mo) m; (Buffers with Cu, Fe, Ni oxides) (0.33–1.87) * 10−3 (MoS2) mass.%

ptx-MoS2-1.1

ptx-MnCl2-1.1 ptx-Mn2O3-1.1

55/63.7–86.5 (MnCl2) mass.% (33.9–5) * 10−9 (Mn) mol/L

0.007; 0.009 (MgO); 0.06; 0.07 (SiO2) mass.%

8

7

6

Feodotiev and Tereshina, 1963 Feodotiev and Tereshina, 1963 Feodotiev and Tereshina, 1963 Saddington and Krase, 1934 Pray et al., 1952 Tsiklis et al., 1965, 1969 Prokhorov and Tsiklis, 1970 Maslennikova et al., 1971 Gillespie and Wilson, 1980, 1982 Ashmyan et al., 1984 Japas and Franck, 1985 Alvarez et al., 1988 Fenghour et al., 1993 Jones, 1963 Guillevic et al., 1985

Dernov-Pegarev et al., 1988 Morey and Hesselgesser, 1951b Benrath, 1941 Ampelogova et al., 1989 Kudrin et al., 1980

REFERENCE

Table

Composition

48 Hydrothermal Experimental Data

Vis.obs.

Vis.obs.

Sampl

LGE

LGE; Cr.ph

Soly Cr.ph

Soly Cr.ph

LGE

Cr.ph

Soly Cr.ph

Soly

Soly

Soly

LGE

LGE Soly; Immisc Soly; immisc Soly

NH3

NH3

NH4Br (NH4)2CO3

NH4Cl NH4Cl

NH4Cl

NH4HCO3

(NH4)2SO4 (NH4)2SO4

N2H4*H2SO4 (hydrazinsulfate) NaAlSi3O8 (albite)

NaAlSi3O8 (albite)

NaBO2 [NaB(OH)4]

NaBO2 [NaB(OH)4] NaBO2 [NaB(OH)4]

LGE; Soly Soly; LGE; Immisc; Cr.ph

Soly; LGE

Na2B4O7 Na2B4O7

Na2B8O13

Na2B2O4 [Na2O*5B2O3]

NaB5O8

Sampl; Vap. pr.; Vis. obs. Sampl

LGE; Cr.ph

NH3

Sampl Vis.obs.; Sampl Vis.obs.; Sampl Sampl; Therm. anal. Sampl Sampl; p-x; p-V; T-V curves; Vis.obs. Vap.pr.

Vap.pr.

Flw.Sampl

Vis.obs. Vis.obs.

Vis.obs.

Sampl

Vis.obs. Vis.obs.

Vis.obs. Vis.obs.

3

2

1

Methods

Phase equil

Non-aqueous components

374–600 C

456 C 199–425 C

125/200–275 C

100–416 C

461 C 270–408 C

150/200–300 C

400–600 C

500 C

94/198–216 C

138/199–410 C 384–429 C

374–358 C

120/200–300 C

129/211–417 C 382–420

116/203–462 C 374–361 C

373/405–614 K

373/473 K

305.6/405–618 K

4

Temperature

SVP

269–409 bar 12–476 kg/cm2

SVP

SVP

SVP (4/14–88 kg/cm2) 238–395 bar SVP

0.75–3.50 kbar

400–2000 bar

SVP

SVP SVP

SVP

SVP

SVP SVP

SVP (0.19/1.9– 3.12 MPa) SVP (0.93–21.5 MPa) SVP SVP

SVP (0.005/1.9– 22.5 MPa)

5

Pressure

ptx-NaAlSi3O8-2.1

272–3201 (SiO2); 11–738 (Al2O3); 15–545 (Na) ppm 0–20 (NaBO2) mass%

L-G-S

0.0008–0.058 mass.% 5.9–81 (Na2B4O7) mass.%

56.6/58.5–59.5 mass.%

30–69.5 (NaB5O8) mass.%

0.008–46 (Na) mass.% 18–69.5 (NaBO2) mass.%

ptx-NaAlSi3O8-1.1

0.006–0.27 (NaAlSi3O8) mass.%

ptx-Na2B8O13-1.1

ptx-Na2B4O7-1.1 ptx-Na2B4O7-2.1; 2.2; 2.3

ptx-Na2B2O4-1.1; 1.2

ptx-NaB5O8-1.1

ptx-NaB(OH)4-2.1 ptx-NaB(OH)4-3.1

ptx-NaB(OH)4-1.1

ptx-N2H4*H2SO4-1.1

14/60–70 (N2H4*H2SO4) mass.%

54.5/59.5–79.6 ((NH4)2SO4) mass.% 0.1–1.4 ((NH4)2SO4) m

ptx-(NH4)2SO4-1.1 ptx-(NH4)2SO4-2.1

ptx-NH4Cl-3.1; 3.2 ptx-NH4HCO3-1.1

2 * 10−11/1.6 * 10−5–1.9 (NH4Cl) m 0.1–1.4 (NH4HCO3) m

ptx-NH4Cl-1.1 ptx-NH4Cl-2.1

ptx-NH4Br-1.1 ptx-(NH4)2CO3-1.1

ptx-NH3-5.1; 5.2

ptx-NH3-4.1

Morey and Chen, 1956

Baierlein, 1983 Urusova and Valyashko, 1990

Mashovets et al., 1974 Baierlein, 1983 Urusova and Valyashko, 1993a Urusova and Valyashko, 1993a Bouaziz, 1961

Morey and Hesselgesser, 1951b Currie, 1968

Benrath et al., 1937 Marshall and Jones, 1974a Benrath et al., 1937 Marshall and Jones, 1974a Palmer and Simonson, 1993 Marshall and Jones, 1974a Benrath et al., 1937 Marshall and Jones, 1974a Benrath, 1942

Sassen et al., 1990

Muller et al., 1992

Rizvi and Heidemann, 1987

8

7 ptx-NH3-3.1; 3.2

REFERENCE

Table

48.9/62.4–90.8 (NH4Cl) mass.% 0.1–1.0 (NH4Cl) m

60.6/72.1–90.4 (NH4Br) mass.% 0.1–1.4 ((NH4)2CO3) m

0.19–0.8 (NH3) mol.fr.

4.18–57/93 (NH3) mol.%

0–1 (NH3) mol.fr.

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 49

2

Soly Soly; LGE LGE

LGE

Soly; LGE

LGE; Isop-m Soly; LGE

Soly

Soly; LGE

Soly

Soly

Soly; Immisc; Cr.ph LGE

Soly; Immisc Soly; LGE; Cr.ph LGE; Soly

Soly; LGE

Soly

Soly

1

NaBr NaBr NaBr

NaBr

NaBr

NaBr

Na2CO3

Na2CO3

Na2CO3

Na2CO3

Na2CO3

Na2CO3

Na2CO3

Na2CO3 in K2CO3

Na2CO3 + NaCl

Na2CO3 + NaF

Na2CO3 in NaOH

Na2CO3

Na2CO3

Phase equil

Continued

Non-aqueous components

Table 1.1

Sampl

Sampl; p-x, p-V curves; Wt-loss Sampl

p-x curves

T-CV curves

Therm.anal

Vap.pr.

p-x, p-V curves p-x, p-V curves p-V, p-T; T-V curves

p-V curves

Sampl; Vap. pr. Sampl

Isopiest

Therm.anal

Vap.pr.

Vis.obs. p-V curves Vap.pr.

3

Methods

150/250; 350 C

225 C

294–520 C

425 C

647.1–649 K

490–924 C

150/200–300 C

SVP

SVP

v.pr-49 MPa

(Dens) 245.5–412.1 kg/m3 58–70 MPa

4.9–14 (Na2CO3); 7.2–21.4 (NaOH) g/100 g H2O

0–20.7 (Na2CO3); 0–3.2 (NaF) mass.%

9–33 (NaCl); 2.8–13 (Na2CO3) mass.%

2.3–7 (Na2CO3); 0–4 (K2CO3) mass.%

L-G-S

8–100 (Na2CO3) mass.%

4–22 (Na2CO3) mass.%

3–50 (Na2CO3) mass.%

1510–1600 kg/cm2

480–540 C

SVP (4.54– 86 kg/cm2) 0.4–3.7 kbar

58–1 (Na2CO3) mass.%

900–1955 kg/cm2

475–540 C

200–500 C

0.53–0.0002 (Na2CO3) mol.fr.

37.5/20–2 (Na2CO3) g/100 g H2O

32/23–0 (Na2CO3) mass.%; G-L-S

0.65/0.68–6.19 (NaBr) m

L-G-S

10–42.7 (NaBr) mass.%

54/58–61 (NaBr) mass.% 0.25–0.78 (NaBr) mol.fr 6.8–47.2 (NaBr) mass.%

6

Composition

41.5–1 (Na2CO3) mass.%

SVP

1/26.6–199 atm

SVP

SVP SVP (35–110 atm) SVP (3/10– 165 kg/cm2) SVP (0.4/1.3– 16.1 MPa) 3–180 bar

5

Pressure

SVP (9.72–202.7 atm) 200–2385 kg/cm2

183.6–368.5 C

150/252–350 C

383/473; 498 K 50/200–365 C

603–746 C

150/200–350 C

107/199–248 C 293–678 C 150/200–350 C

4

Temperature

ptx-Na2CO3 + NaF-1.1 ptx-Na2CO3 + NaOH-1.1

ptx-Na2CO3 + K2CO3-1.1 ptx-Na2CO3 + NaCl-1.1–1.3

ptx-Na2CO3-9.1

ptx-Na2CO3-8.1

ptx-Na2CO3-7.1

ptx-Na2CO3-5.1; 5.2 ptx-Na2CO3-6.1

ptx-Na2CO3-4.1

ptx-Na2CO3-3.1

ptx-Na2CO3-1.1; 1.2 ptx-Na2CO3-2.1

ptx-NaBr-6.1

ptx-NaBr-5.1

ptx-NaBr-4.1

Schroeder et al., 1936

Urusova et al., 1982

Puchkov and Kurochkina, 1972 Koster van Groos, 1990 Valyashko et al., 2000 Urusova and Valyashko, 2005 Urusova and Valyashko, 2002

Ravich and Borovaya, 1964d Ravich and Borovaya, 1968a Ravich and Borovaya, 1969

Kravchuk and Todheide, 1996 Holmes and Mesmer, 1998 Waldeck et al., 1932 Schroeder et al., 1936 Keevil, 1942

Distanov, 1937 Keevil, 1942 Mashovets et al., 1973 Feodorov, 1982

8

7 ptx-NaBr-1.1 ptx-NaBr-2.1 ptx-NaBr-3.1

REFERENCE

Table

50 Hydrothermal Experimental Data

2

Soly

Cr.ph Soly Soly

Soly

Soly Soly

Soly; LGE

LGE; Cr.ph

Soly; LGE

Cr.ph LGE

Soly

Soly; LGE

Soly

Soly

Soly

Soly; LGE; Cr.ph LGE

LGE; Cr.ph

1

Na2CO3 in Na2WO4

NaCl NaCl NaCl

NaCl

NaCl NaCl

NaCl

NaCl

NaCl

NaCl NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

Phase equil

Non-aqueous components

Vap.pr.; g-ray

Vap.pr.; Sampl Vap.pr.diff.

Flw.Sampl

??

Flw.Sampl

Vap.pr.

Flw.Sampl

p-T, p-x curves Vis.obs. Sampl

Sampl

p-V curves

Vis.obs. Flw.Sampl

Sampl

Vis.obs. Sampl Vis.obs.; Sampl

Sampl

3

Methods

100/200–440 C

122.4/180.6–270 C

219.5–750 C

661–852 K

637–867 K

633–695 K

374–700 C

673–826 K

651.3–693.8 K 385–396 C

300–456 C

350–475 C

183/205–646 C

285–455 C 130/365–408 C

150/200–350 C

374–410.7 C 142/205 C 100/200–300 C

225 C

4

Temperature

SVP (1.1/9–47.4-atm) SVP (1/13– 398 kg/cm2)

20–1237 bar

18–29 MPa

8–26 MPa

10.8 MPa

SVP

3–18 MPa

SVP (7.3–68.5 atm) SVP (113– 436 kg/cm2) SVP (59–261 kg/cm2) SVP 210–265 atm

SVP 7.4–27 MPa

SVP

SVP 2.1/12 atm SVP

SVP

5

Pressure

Urusova et al., 1978

ptx-Na2CO3 + Na2WO4-1 ptx-NaCl-1.1 ptx-NaCl-2.1 ptx-NaCl-3.1

ptx-NaCl-4.1

0–20.7 (Na2CO3); 0–46.4 (Na2WO4) mass.%

42/46.2–72.4 (NaCl) g/100 g H2O

ptx-NaCl-8.1; 8.2; 8.3 ptx-NaCl-9.1

0–27 (NaCl) mass.%

ptx-NaCl-15.1

ptx-NaCl-16.1

(0.2–56.6) * 10−6 (NaCl) mol.fr. (0.7–17) * 10−5 (NaCl) mol.fr.

1–25 (NaCl) mass.%

1; 2; 3 (NaCl) m

ptx-NaCl-19.1

ptx-NaCl-17.1; 17.2; 17.3; 17.4 ptx-NaCl-18.1

ptx-NaCl-14.1

(0.86–2.56) * 10−6 (NaCl) mol.fr.

0–27.5 (NaCl) mass.%

ptx-NaCl-13.1

L-G-S

(0.13–15) * 10−6 (NaCl) mol.fr.

0.08–2.43 (NaCl) mol.% 0.03–20.5 (NaCl) mass.%

ptx-NaCl-10.1 ptx-NaCl-11.1; 11.2 ptx-NaCl-12.1

ptx-NaCl-7.1

0.12–0.51 (NaCl) mol.fr.

LGE+Solid

ptx-NaCl-5.1 ptx-NaCl-6.1; 6.2

36–51 (NaCl) mass.% (7–16) * 104 (NaCl) mg/kg H2O

0–0.85 (NaCl) mol/L 29.7/31.8 (NaCl) mass.% 28.4/31.6–35 (NaCl) mass.%

Khaibullin and Borisov, 1966

Olander and Liander, 1950 Ravich and Borovaya, 1950 Secoy, 1950 Copeland et al., 1953 Styrikovich et al., 1955; Harvey and Bellows, 1997 Morey and Chen, 1956 Aleinikov et al., 1956; Harvey and Bellows, 1997 Sastry, 1957; Harvey and Bellows, 1997 Styrikovich and Khokhlov, 1957; Harvey and Bellows, 1997 Sourirajan and Kennedy, 1962 Gardner et al., 1963

Schroer, 1927 Froehlich, 1929 Akhumov and Vasil’ev, 1932, 1936 Schroeder et al., 1935 Benrath et al., 1937 Spillner, 1940; Harvey and Bellows, 1997 Keevil, 1942

8

7

6

REFERENCE

Table

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 51

2

LGE

LGE; Soly

LGE

LGE

PTX, LGE; Cr.ph

Cr.ph

LGE; Cr.ph; Soly Soly

Soly Soly

LGE

LGE

LGE; ?Soly LGE

Soly; LGE Soly

LGE LGE LGE; Soly

LGE; Cr.ph Soly

1

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl NaCl

NaCl

NaCl

NaCl NaCl

NaCl NaCl

NaCl NaCl NaCl

NaCl NaCl

NaCl

Phase equil

Continued

Non-aqueous components

Table 1.1

Sampl Rad.tr

Vap.pr.diff. Fl.inclus Sampl

Therm.anal. ??

Sampl Flw.Sampl

Vap.pr.

Sampl

p-T curves Flw.Sampl

Flw.Sampl

p-V curves

Vap.pr.; g-ray; T-V, p-V curves Vis.obs.

Vap.pr.

Vap.pr.diff

p-V curves

Vap.pr.diff

3

Methods

380.0 C 310–500 C

200–350 C 550–1000 C 300–503.4 C

450–825 C 499–544 K

370–448 C 598–645 K

150/473–623 K

300–440 C

148/202–425 C 400–550 C

573–600 K

450–550 C

384–462 C

100/220–416 C

150/200–350 C

75/200–300 C

350, 400 C

125/200–300 C

4

Temperature

215–235 bar 2.6–32.4 MPa

SVP 500–1300 bar 57.6–328.0 bar

0.3–4 kbar 2.4–4.6 MPa

SVP (60– 396 kg/cm2) SVP (0.38/1.27– 16.1 MPa) 175–409 bar 120–215 bar

SVP 1.4–10.3 MPa

SVP (251–770 kg/cm2) 5.3–8.1 MPa

SVP

SVP (3.8/12.7– 168.6 kg/cm2) 1/23–338 kg/cm2

SVP (107.5– 290.5 kg/cm2) SVP

SVP

5

Pressure

0.05–2.4 (NaCl) mass.% (0.11–104.5) * 10−5 (NaCl) mol.fr.

0.5–6 (NaCl) m 0.4–77 (NaCl) mass.% 0.0014–9.2 (NaCl) mass.%

53.5–100 (NaCl) mass.% (2.2–18.8) * 10−9 (NaCl) mol.fr.

0.0024–20.1 (NaCl) mass.% 0.02 * 10−5–0.285 (NaCl) m

4.0–24 (NaCl) mass.%

1 * 10−3–48.8 (NaCl) mass.%

29.62/32–48.4 (NaCl) mass.% 1.1–1114 (Na+) ppb

(0.3–5.3) * 10−7 (NaCl) mol.fr.

ptx-NaCl-36.1 ptx-NaCl-37.1 ptx-NaCl-38.1; 38.2 ptx-NaCl-39.1 ptx-NaCl-40.1

ptx-NaCl-32.1 ptx-NaCl-33.1; 33.2 ptx-NaCl-34.1 ptx-NaCl-35.1

ptx-NaCl-31.1

ptx-NaCl-28.1 ptx-NaCl-29.1; 29.2 ptx-NaCl-30.1

ptx-NaCl-26.1; 26.2 ptx-NaCl-27.1

3–72 (NaCl) mass.%

ptx-NaCl-24.1

1; 3; 5 (NaCl) mass.%

ptx-NaCl-25.1

ptx-NaCl-23.1

0–24.5 (NaCl) mass.%

0.1–1.8 (NaCl) m

ptx-NaCl-22.1

3.8/3.9–10.4 (NaCl) m

ptx-NaCl-21.1

3.0–49.5 (NaCl) mass.%

Pitzer et al., 1987 Alekhin and Vakulenko, 1988

Baierlein, 1983 Stephan and Kuske, 1983 Gunter et al., 1983 Allmon, 1983; Harvey and Bellows, 1997 Wood et al., 1984 Bodnar et al., 1985 Bischoff et al., 1986

Bell et al., 1977; Harvey and Bellows, 1997 Potter II et al., 1977 Galobardes et al., 1981 Parlsod and Plattner, 1981 Feodorov, 1982

Marshall and Jones, 1974 Urusova, 1974

Liu and Lindsay, 1970 Urusova and Ravich, 1971 Liu and Lindsay, 1972 Mashovets et al., 1973 Khaibullin and Novikov, 1973

8

7 ptx-NaCl-20.1

REFERENCE

Table

0.1–1.07 (NaCl) m

6

Composition

52 Hydrothermal Experimental Data

Phase equil

2

Soly; LGE LGE; Cr.ph

Soly

LGE; Cr.ph

Cr.ph

Cr.ph LGE

Soly

LGE

Soly

LGE; Soly

LGE

Soly Soly; LGE

Cr.ph

PTX, Soly

Soly; LGE

H-Fl

H-Fl

H-Fl

LGE; H-Fl

LGE; Soly

Non-aqueous components

1

NaCl NaCl

NaCl

NaCl

NaCl

NaCl NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl NaCl

NaCl

NaCl

NaCl + CH4

NaCl + CH4

NaCl + CO2

NaCl + CO2

NaCl + CO2

NaCl + CO2

Fl.inclus

Fl.inclus

Vis.obs.; p-T curves Fl.inclus

Fl.inclus

Fl.inclus

311–659 C

500 C

400–800 C

408–793 C

300–600 C

400–600 C

350–475 C

652.4–661.1 K

T-CV curves

Flw.Sampl

450; 470 C 625–801 C

623 K

600 C

450–550 C

400–700 C

442–899 C

374–396 C 350 C

374–842 C

30/150; 200 C 374–415 C

621–788 C 450–500 C

4

Temperature

Flw.Sampl Therm.anal.

VTFD

Sampl

Flw.Sampl

Sampl

Therm.anal.

Vis.obs. VTFD

Fl.inclus

Sampl

Therm.anal. Sampl; Vap.pr. Sampl

3

Methods

2.5–4.5.0 kbar

5 kbar

1; 2 kbar

3–281 MPa

2 kbar

1 kbar

dens 341.7–367.4 kg/m3 1.75–20 MPa

25 MPa 2–397 bar

15–16 MPa

0.5–77.6 MPa

100–250 bar

172–1254 bars

502–5960 bar

SVP 15 MPa

220–1574 bar

SVP

16 bar

320–803 bars 250–580 bar

5

Pressure

ptx-NaCl-53.1 ptx-KCl-54.1

195; 233 (NaCl) mg/kg H2O L-G-S

20; 40 (NaCl) mass.%; 0–20 (CO2) mol.%

10–25 (NaCl); 10.9–42.8 (CO2) mass.%

0–50 (NaCl); 0–48 (CO2) mol.%

0.3–7 (NaCl); 0.2–85 (CO2) mol.%

0–17.7 (NaCl); 1.23–66.5 (CH4) mass.%

1.3–18.4 (NaCl); 1.5–55.8 (CH4) mass.%

0.006–183 (NaCl) m

ptx-NaCl2 + CO2-3.1 ptx-NaCl + CO24.1; 4.2

ptx-NaCl + CH4-1.1 ptx-NaCl + CH4-2.1 ptx-NaCl2 + CO2-1.1 ptx-NaCl2 + CO2-2.1

ptx-NaCl-56.1

ptx-NaCl-55.1

ptx-NaCl-52.1

0.25–3.0 (CaCl2) m

0.092–0.31 (NaCl) mol.%

ptx-NaCl-51.1

ptx-NaCl-50.1

ptx-NaCl-49.1

ptx-NaCl-48.1

ptx-NaCl-46.1 ptx-NaCl-47.1

ptx-NaCl-44.1; 44.2 ptx-NaCl-45.1

ptx-NaCl-43.1

Kotel’nikov and Kotel’nikova, 1990 Shmulovich and Plyasunova, 1993 Schmidt et al., 1998

Gehrig et al., 1986

Lamb et al., 2002

Bischoff and Rosenbauer, 1988 Knight and Bodnar, 1989 Marshall, 1990 Crovetto and Wood, 1991 Koster van Groos, 1991 Tkachenko and Shmulovich, 1992, 1994 Armellini and Tester, 1993 Fournier and Thompson, 1993 Crovetto et al., 1993, 1996 Wofford et al., 1995 Kravchuk and Todheide, 1996 Abdulagatov et al., 1998 Jensen and Daucik, 2002 Lamb et al., 1996

Chou, 1987 Rosenbauer and Bischoff, 1987 Susarla et al., 1987

8

7 ptx-NaCl-41.1 ptx-NaCl-42.1

REFERENCE

Table

0.0004–0.157 (Na); 0.001–0.160 (Cl) m

0.9–101 (NaCl) ppm

0.0064–76 (NaCl) mass.%

27.6–100 (NaCl) mol.%

0–0.3 (NaCl) m 1; 3 (NaCl) m

0–30 (NaCl) mass.%

0.03–15.9 (NaCl) mass.%

26.4/30; 34.2 (NaCl) mass.%

78.3; 86.5 (NaCl) mass.% 0.03–25 (NaCl) mass.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 53

??

Vis.obs.

LGE; Soly

LGE; Isop-m LGE; Isop-m Soly

LGE; Isop-m LGE

Soly

Soly

Soly

LGE; Soly

LGE; Soly

Soly

LGE; Isop-m Soly

Soly

Soly

LGE; Immisc; Cr.ph

NaCl + CO2

NaCl + CaCl2

NaCl + KCl

NaCl + KCl

NaCl + KCl

NaCl + KCl

NaCl + KCl

NaCl + KCl + SiO2

NaCl in LiCl

NaCl + LiCl

NaCl + MgCl2

NaCl in MgCl2

NaCl in MgCl2

NaCl + Na2B4O7

NaCl + KCl

NaCl + KCl

NaCl + CsCl

LGE; Soly

NaCl + CO2

p-V, p-x curves

Vis.obs.; Sampl

Isopiest

Flw.Sampl

Sampl

Sampl

Therm.anal.

Fl.inclus

Fl.inclus

Vap.pr.

Isopiest

Sampl

Isopiest

Isopiest

Fl.inclus

Fl.inclus

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

388–410 C

114/195–225 C

230; 300 C

125/150–200 C

383.2/473.2–523.2

499–502 C

600 C

600 C

411–772 °C

−2/200–490 C

−22/58.7–714 C

426/473–625 C

382.8/474

66/194–213 C

383/473–523 K

383.5/474.17

275–650 C

900 C

4

Temperature

228–325 kg/cm2

SVP

SVP

SVP

SVP

73; 140 atm

0–79.2 MPa

0–98.6 MPa

500–2000 bar

SVP

??

SVP

SVP

1/11.5 atm

SVP

SVP

44–370 MPa

5; 7 kbar

5

Pressure

5–60 mol% (NaCl in NaCl + Na2B4O7)

0.3 2–8 (NaCl); 28; 46 (MgCl2) mass.%

0–35 (NaCl); 0–68 (MgCl2) mass.%

1.36–7.77 (NaCl + LiCl) m; [NaCl/LiCl = 0.3 : 0.7–0.7 : 0.3] mol.ratio 0–32 (NaCl); 56.8–0 (MgCl2) mass.%

1.2–54 (NaCl + KCl) m; [NaCl/KCl = 3.83; 6.38 mol.ratio] 3.08 (NaCl + KCl + SiO2) m; [NaCl/KCl = 3.83 mol.ratio] 2–10 (NaCl); 0–4.2 (LiCl) mg/kg H2O

37.8–90 (NaCl + KCl) m; [NaCl/KCl = 0–1 mass.ratio] 49–85 (NaCl + KCl) mass.%; [NaCl/KCl = 32–38] 9.7–82.3 (KCl) mass.%

0.57/0.61–7.3/7.65 (NaCl + KCl) m; [NaCl/KCl = 0.9 : 01–0.3 : 0.7] mol.ratio 0.13–5.04 (NaCl); 0.1–3.9 (KCl) m

0.55/0.59–6.40 (NaCl + CaCl2) m; [NaCl/CaCl2 = 0.92 : 0.08–0.39 : 0.61] mol.ratio 1.41/1.43–8.27 (NaCl + CsCl) m; [NaCl/CsCl = 0.7 : 03–0.3 : 0.7] mol.ratio 15–17 (NaCl); 35/47–50 (KCl) mass.%

6–40 (NaCl) mass.%; 5–20 (CO2) mol.%

6–38 (NaCl); 10–54 (CO2) mass.%

6

Composition

ptx-NaCl + MgCl2-2.1 ptx-NaCl + MgCl2-3.1 ptx-NaCl + Na2B4O7-1.1

D’Ans and Sypiena, 1942 Urusova and Valyashko, 1998

Fournier and Thompson, 1993 Fournier and Thompson, 1993 Martinova and Samoylov, 1962 Holmes and Mesmer, 1988 Akhumov and Vasil’ev, 1932, 1936 Klement’ev, 1937

Chou et al., 1992

Sterner et al., 1988

Udovenko et al., 1986b Sterner et al., 1988

Holmes et al., 1979

Holmes and Mesmer, 1990 Froehlich, 1929

Schmidt and Bondar, 2000 Holmes et al., 1981

Gibert et al., 1998

8

7 ptx-NaCl + CO2-5.1 ptx-NaCl + CO26.1; 6.2 ptx-NaCl + CaCl2-1.1 ptx-NaCl + CsCl-1.1 ptx-NaCl + KCl-1.1 ptx-NaCl + KCl-2.1 ptx-NaCl + KCl-3.1 ptx-NaCl + KCl-4.1 ptx-NaCl + KCl-4.2 ptx-NaCl + KCl-5.1 ptx-NaCl + KCl-6.1 ptx-NaCl + KCl + SiO2-1.1 ptx-NaCl + LiCl-1.1 ptx-NaCl + LiCl-2.1 ptx-NaCl + MgCl2-1.1

REFERENCE

Table

54 Hydrothermal Experimental Data

Sampl

Soly

Soly; LGE

Soly Soly

LGE

PTX, H-Fl

PTX, Soly PTX, Soly

PTX, Soly

Soly

PTX, Soly

Soly

Soly

LGE; Isop-m Soly

LGE; Isop-m LGE; Immisc

Soly

Immisc; Cr.ph LGE; Isop-m

NaCl in NaOH

NaCl in Na2SO4

Na2CrO4 NaF

NaF

NaF

NaF NaF in HCl

NaF in (KCl + HCl)

NaF in (KCl + NaCl)

NaF in (NaCl + HCl)

NaHCO3

NaHCO3 + Na2CO3

NaH2PO4

Na2HPO4

Na2HPO4 + NaOH

NaxHyPO4

NaHSO4

Na2HPO4

Na2HPO4

Wt-loss

Soly; LGE

NaCl in NaOH

279–384 C 383.5/473; 498 K

Isopiest

250–365 C

250–400 C

383/473–523 K

38/204–359 C

100/190; 200 C 383/473–523 K

100/170–200 C

400; 500 C

250–500 C

400; 500 C

500 C 500 C

450–800 C

298/473–598 K

140/210–372 C 125/200–370

156/193–609 C

337–557 C

150/200–650 C

4

Temperature

Vis.obs.

p-V curves; Sampl; Vis.obs. Sampl

Isopiest

Sampl

Isopiest

Sampl

Sampl

Wt-loss

Wt-loss Wt-loss

Fl.inclus

Vap.pr.

Vis.obs.; px, p-T curves Vis.obs. Sampl

p-x, p-T curves; Sampl Flw.Sampl

3

2

1

Methods

Phase equil

Non-aqueous components

SVP

SVP

0.52/0.56–8.99 (NaHSO4) m

Na/PO4 = 1.0; 1.2; 1.5; 2.0; 2.16 (mol.ratio)

ptx-NaHSO4-1.1

ptx-Na2HPO4 + NaOH-1.1; 1.2; 1.3 ptx-NaxHyPO4-1.1

0.1–0.3 (Na+); 0.05–0.1 (PO42− ) mass.%

SVP

ptx-Na2HPO4-3.1; 3.2

3–95 (Na2HPO4) mass.%

40–1400 kg/cm2

ptx-Na2HPO4-1.1; 1.2; 1.3 ptx-Na2HPO4-2.1

ptx-NaHCO3 + Na2CO3-1.1 ptx-NaH2PO4-1.1

ptx-NaF-4.1 ptx-NaF + HCl-1.1 ptx-NaF + KCl + HCl-1.1 ptx-NaF + KCl + NaCl-1.1 ptx-NaF + NaCl + HCl-1.1 ptx-NaHCO3-1.1

ptx-NaF-3.1

ptx-NaF-2.1

Ravich et al., 1954

ptx-NaCl + NaOH-1.1; 1.2; 1.3 ptx-NaCl + NaOH-2.1 ptx-NaCl + Na2SO4-1.1; 1.2; 1.3 ptx-Na2CrO4-1.1 ptx-NaF-1.1

0.64/0.74–14.3 (Na2HPO4) m

0.06–6.95 (PO4) m

2/7.5–38.6 (NaHCO3); 1.2/1.7–24 (Na2CO3) mass.% 0.78–15.5 (NaH2PO4) m

0.06–0.75 (NaF); 0.01 (HCl); 0.85–4.6; (NaCl) m 19–43 mass.% (NaHCO3)

0.07–5.3 (NaF); 4.8–72.3 (KCl + NaCl) mass.%

0.13–2.53 (NaF); 0.01 (HCl); 0.85; 4.6 (KCl) m

1.27–2.66 (NaF) mass.% 0.27; 0.32 (NaF); 0.01 (HCl) m

2.1–10 (NaF) mass.%

2.5; 0.75; 1.5 (NaF) mass.%

8

7

Holmes and Mesmer, 1993

Ravich and Scherbakova, 1955 Marshall, 1982

Urusova and Valyashko, 2001a

Holmes et al., 2000

Panson et al., 1975

Waldeck et al., 1934 Waldeck et al., 1934 Holmes et al., 2000

Ravich and Valyashko, 1965 Redkin et al., 2005

Redkin et al., 2005

Benrath, 1942 Ravich and Valyashko, 1965 Guseynov et al., 1989 Kotel’nikova and Kotel’nikov, 2002 Redkin et al., 2005 Redkin et al., 2005

Martinova and Samoylov, 1962 Ravich et al., 1953b

REFERENCE

Table

SVP

SVP

SVP

SVP

SVP

200–1000 bar

SVP

200–1000 bar

1000 bar 1000 bar

500–2000 bar

SVP

56/59–76 (Na2CrO4) mass.% 0.3–3.6/4.36 (NaF) mass.%

9–90 (H2O); 0–91.5 (NaCl) mass.%; 8.5–100 (Na2SO4) [mass.% in NaCl + Na2SO4]

10–307 kg/cm2

SVP SVP

2.42–28 (NaCl); 0–20 (NaOH) mg/kg H2O

7–69.5 (NaCl); 12–87 (NaOH) mass.%

6

Composition

100–180 atm

SVP

5

Pressure

Phase Equilibria in Binary and Ternary Hydrothermal Systems 55

Flw.Sampl

Vap.pr.

LGE LGE

LGE

Soly

LGE; Soly

LGE; Soly; Immisc Soly Soly LGE

Soly

LGE

Soly

LGE

LGE

Soly

Soly; LGE

Soly

LGE

NaI NaI

NaI

Na2MoO4

Na2MoO4

Na2MoO4

NaNO3

NaNO3

NaOH

NaOH

NaOH

NaOH

NaOH

NaOH

NaOH

NaNO3 NaNO3 NaNO3

LGE; Isop-m

NaHSO4 + Na2SO4

Vap.pr.

Vis.obs.; Vap.pr. Therm. anal

??

Vap.pr.

Vap.pr.

Quench

p-V; p-x curve; Sampl p-V; p-x curves Vis.obs. Vis.obs. Vap.pr.

Sampl

Vap.pr.

p-V curves Vap.pr.

Isopiest

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

−5.6/62; 164–321 C 25/200–350 C

126/204–323 C

675 K

300–420 C

300–460 C

205–322 C

448–598 K

450–525 C

SVP (5.9–160 kg/cm2)

SVP (0/546 mm Hg) SVP

SVP (5–235 kg/cm3) SVP (3–222 kg/cm2) 6–17 MPa

SVP (0.8–11.9 MPa) 1 atm

248–306 bar

SVP SVP SVP

94/202–310 C 102/198–308 C 423/473–623 K

ptx-NaOH-3.1 ptx-NaOH-4.1

0.04–0.85 (NaOH) mol.fr (0.32–8.7) * 10−6 (NaOH) mol.fr.

ptx-NaOH-6.1 ptx-NaOH-7.1

20.55/74–100 (NaOH) mass.% 5–35 (Na2O) mass.%

ptx-NaOH-5.1

ptx-NaOH-2.1

18–99 (NaOH) mol.%

L-G-S

ptx-NaOH-1.1

ptx-NaNO3-5.1

ptx-NaNO3-4.1

ptx-Na2MoO4-3.1; 3.2 ptx-NaNO3-1.1 ptx-NaNO3-2.1 ptx-NaNO3-3.1; 3.2

ptx-Na2MoO4-2.1

ptx-Na2MoO4-1.1

ptx-NaI-3.1

ptx-NaI-1.1 ptx-NaI-2.1

Urusova and Valyashko, 1983a Kracek, 1931c Benrath et al., 1937 Puchkov and Matashkin, 1970; Puchkov et al., 1989 Dell’Orco et al., 1995 Azizov and Akhundov, 1998 Antropoff and Sommer, 1926 Galinker and Korobkov, 1951 Korobkov and Galinker, 1956 Sastry, 1957; Harvey and Bellows, 1997 Lux and Brandl, 1963 Rollet and CohenAdad, 1964 Dibrov et al., 1964

Feodotiev and Tereshina, 1963 Zhidikova et al., 1973

Keevil, 1942 Mashovets et al., 1973 Feodorov, 1982

Holmes and Mesmer, 1994

8

7 ptx-NaHSO4 + Na2SO4-1.1

REFERENCE

Table

85.5–100 (NaOH) mass.%

0.3–4 (NaNO3) m

0.293–1.963 (NaNO3) g/kg

62/84–100.0 (NaNO3) mass.% 64/83–100.0 (NaNO3) mass.% 0/50–90 (NaNO3) mass.%

8.9–69.5 (Na2MoO4) mass.%

60–514 kg/cm2

294.5–567 C

45–52 (Na2MoO4) mass.%

10–56.8 (NaI) mass.%

0.48/056–7.4 (NaHSO4 + Na2SO4) m; [NaHSO4/ Na2SO4 = 0.65 : 0.35; 0.5 : 0.5; 0.35 : 0.65 mol. ratio] 0.34–0.89 (NaI) mol.fr. 10–61 (NaI) mass.%

6

Composition

0–9.34 (Na2MoO4) m

2.4–189 atm SVP (2.42– 164.6 kg/cm2) SVP (0.27/0.9– 15.9 MPa) SVP

SVP

5

Pressure

SVP (81–59.5 kg/cm2)

294; 300 C

100–250 C

423/473–623 K

185–600 C 150–350 C

383.5/473; 498 K

4

Temperature

56 Hydrothermal Experimental Data

2

LGE

LGE

LGE

LGE; Cr.ph

Soly

LGE LGE

Soly

LGE

Cr.ph

Soly

Soly

LGE

Soly; Immisc

Immisc; Soly; Cr.ph Soly Soly

Soly; LGE

Soly; LGE; Immisc

Soly

1

NaOH

NaOH

NaOH

NaOH

NaOH

NaOH NaOH

NaOH

NaOH

NaOH

NaOH + Na2CO3

NaOH + NaCl

NaOH + Na2O*nAl2O3

Na2O*n P2O5

Na2O*n P2O5

Na3PO4

Na3PO4 + Na2HPO4

Na3PO4 in NaOH

NaPO3 Na3PO4

Phase equil

Non-aqueous components

Sampl

Sampl; p-x, p-V curves p-V curves; Sampl

147/169–517 C 83/204–350 C

Vis.obs. Sampl

150/250; 350 C

350 C

250–450 C

251; 300 C

350 C

25/200–350 C

180/213–644 C

62.5/210–300 C

660.6–823.2 K

150/200–250 C

403/473– 575 K

456 C 598–645 K

535.4–602.6 K

350–550 C

0/200–350 C

367–415 C

150/200–400 C

4

Temperature

Vis.obs.; Vap.pr. Sampl; Quench; Vis.obs. Sampl

Therm.anal.

Sampl

T-Cv curves

Vap.pr.

??

Sampl Flw.Sampl

??

p-V curves

Vap.pr.

Sampl

Vap.pr.

3

Methods

SVP

SVP; 45–1560 kg/cm2 145–300 kg/cm2

SVP SVP

SVP

SVP (5.9–165 kg/cm2) SVP

SVP

Diff.pr. (40/134– 3894 mm Hg) dens 379.9– 501.2 kg/m3 SVP

0.16/1–5.5 MPa

202–469 bar 120–215 bar

1.2–7.4 MPa

SVP (0.3–215 kg/cm2) SVP (7.6–447 mm Hg) SVP (0.004/0.67– 80 bar) SVP

5

Pressure

82/8.6–0.15 (Na3PO4); 0–29 (NaOH) g/100 g H2O

0–100 (Na2PO4) [mass.% in (Na2PO4 + NaHPO4)]

1.4–74.5 (Na3PO4) mass.%

70/77–96 (NaPO3) mass.% 61/62–0.15 (Na3PO4) g/100 g H2O

(Mol.ratio) Na2O/P2O5 = 1.8–10 (liq)

0–35 (Na2O); 0–23.6 (Al2O3) mass.%

30–95 (NaOH); 4.5–70 (NaCl) mass.%

ptx-Na3PO4-2.1; 2.2 ptx-Na3PO4 + Na2HPO4-1.1; 1.2 ptx-Na3PO4 + NaOH-1.1

ptx-NaPO3-1.1 ptx-Na3PO4-1.1

ptx-Na2O*nP2O5-2.1

ptx-NaOH-17.1

0.452–0.101 (NaOH) mol.%

(Mol.ratio) Na2O/P2O5 = 1–70 (liq); 1–2.8 (solid)

ptx-NaOH-16.1

0.3–3.7 (NaOH) m

ptx-NaOH + Na2CO3-1.1; 1.2 ptx-NaOH + NaCl-1.1 ptx-NaOH + Na2O*nAl2O3-1.1 ptx-Na2O*nP2O5-1.1

ptx-NaOH-15.1

(0.45/0.63–79.72) * 10−9 (NaOH) mol.fr.

67/66–76 (Na2O); 0.11/0.24–7.7 (CO2) mass.%

ptx-NaOH-13.1 ptx-NaOH-14.1

ptx-NaOH-10.1; 10.2 ptx-NaOH-11.1; 11.2 ptx-NaOH-12.1

ptx-NaOH-9.1

Schroeder et al., 1937a

Morey, 1953 Schroeder et al., 1937a Urusova and Valyashko, 2001a Urusova and Valyashko, 2001b

Wetton, 1981

Broadbent et al., 1977

Antropoff and Sommer, 1926 Dibrov et al., 1964

Bell et al., 1977; Harvey and Bellows, 1997 Baierlein, 1983 Stephan and Kuske, 1983 Allmon, 1983; Harvey and Bellows, 1997 Campbell and Bhatnagar, 1984 Abdulagatov et al., 1998 Morey and Burlew, 1964

Urusova, 1974

Krey, 1970, 1972

Krumgalz and Mashovets, 1964 Hoyt, 1967

8

7 ptx-NaOH-8.1

REFERENCE

Table

0.003–25.8 (Na) mass.% 0.16 * 10−6–0.24 (NaOH) m

(0.47–58.8) * 10−8 (NaOH) mol.fr.

2.5–49.4 (NaOH) mass.%

0.1–0.84 (NaOH) mass fr.

99.2–99.98 (NaOH) mass.%

30–90 (NaOH) mass.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 57

Soly

Soly

Soly Soly Soly; LGE Soly

Soly

Soly

Soly

Na2SO4

Na2SO4

Na2SO4 Na2SO4 Na2SO4 Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na4P2O7

Soly; LGE

Soly

Na2SO4

Soly

(Na3PO4 + Na2SO4) in NaOH Na3PO4 + Na2WO4

Soly

Soly

Na3PO4 + Na2SO4

Na2SO4

Soly

Na3PO4 + Na2SO4

GLE; immisc Soly; H-Fl

Sampl

Soly

Na3PO4 + Na2SO4

Na3PO4 + SiO2

Sampl

Soly; LGE

Na3PO4 + Na2SO4

Flw.Sampl

Vis.obs.

Sampl

Vap.pr. Sampl Vis.obs. Vis.obs. p-V curves Sampl

Vis.obs.; Vap.pr. Sampl

Sampl

Vap.pr.

p-V curves

Sampl

Sampl

Sampl; Vap.pr. Sampl

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

601/643–817 K

266–354 C

500 C

249–325 C 262–319 C 158.8/210–367 C 330–382 C

196–347 C

140/204–350 C

142/201–365 C

0/180; 230 C

374–985 C

350 C

150/250; 350 C 230 C

200–350 C

250 C

150/200–350 C

150/200–350 C

4

Temperature

3–20 MPa

SVP

67–1000 bar

SVP SVP SVP (17–201 atm) SVP

1.38–16.03 MPa

SVP (3.5/14.2– 45 atm) SVP

SVP??

SVP (219–467 bar)

165; 168 kg/cm2

SVP

SVP

SVP

SVP

SVP

1.34–16.3 MPa

5

Pressure

ptx-Na2SO4-10.1 ptx-Na2SO4-11.1

(1.7–18.3) * 10−9 (Na2SO4) mol.fr.

ptx-Na2SO4-9.1

ptx-Na2SO4-5.1 ptx-Na2SO4-6.1 ptx-Na2SO4-7.1 ptx-Na2SO4-8.1

ptx-Na2SO4-4.1

ptx-Na2SO4-2.1; 2.2 ptx-Na2SO4-3.1

ptx-Na2SO4-1.1

Urusova and Valyashko, 2001a Morey and Chen, 1956 Tilden and Shenstone, 1883, 1884 Smits and Wuite, 1909 Schroeder et al., 1935 Schroeder et al., 1937b Benrath et al., 1937 Benrath, 1941 Keevil, 1942 Booth and Bidwell, 1950 Morey and Hesselgesser, 1951b Marshall et al., 1954b Styrikovich et al., 1955; Harvey and Bellows, 1997

Schroeder et al., 1937a Urusova et al., 1975

Schroeder et al., 1937b Schroeder et al., 1937a Ravich and Yastrebova, 1958 Ravich and Yastrebova, 1959

8

7 ptx-Na3PO4 + Na2SO4-1.1 ptx-Na3PO4 + Na2SO4-2.1 ptx-Na3PO4 + Na2SO4-3.1; 3.2 ptx-Na3PO4 + Na2SO4-4.1; 4.2; 4.3; 4.4 ptx-Na/PO4,SO4, OH-1.1 ptx-Na3PO4 + Na2WO4-1.1 ptx-Na3PO4 + SiO2-1.1 ptx-Na4P2O7-1.1

REFERENCE

Table

27.6–1.75 (Na2SO4) mass.%

0.0009–0.43 (Na2SO4) mass.%

30–7.8 (Na2SO4) mass.% 28–5 (Na2SO4) mass.% 0.051–0.001 (Na2SO4) mol.fr.; [L-G-S] 0.4–5.7 (Na2SO4) g/100 g H2O

44–3 (Na2SO4) g/100 g H2O

42/46–2.4 (Na2SO4) g/100 g H2O

L-G-S

5/30.7; 31.7 (Na2SO4) mass.%

L-G-S

43.0; 56.0 (Na3PO4); 11.1; 11.9 (SiO2) mass.%

0.3–4.9 (Na3PO4); 0.7–56.6 (Na2SO4) g/100 g H2O 3.6–19.3 (Na3PO4); 0–47 (Na2WO4) mass%

0.15–28.5 (Na3PO4); 2.5–48 (Na2SO4) g/100 g H2O 0.1–49 (Na2SO4); 0.11–56 (Na3PO4) g/100 g H2O 4.6–38 (Na2SO4); 1.5–33.4 (Na3PO4); (NaOH) mass.% 0–40.5 (Na2SO4); 0.26–46.1 (Na3PO4) mass.%

6

Composition

58 Hydrothermal Experimental Data

2

Soly

Soly

Soly

Soly; metast

Soly; Immisc; Cr.ph LGE; Soly

Soly

Soly

LGE

LGE; Isop-m Soly; Soly; Cr.ph; LGE Soly

Soly

Soly

Soly

Soly

Soly

1

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4 in H2SO4

Na2SO4 in (H2SO4 + NaCl)

Na2SO4 in K2SO4

Na2SO4 + MgSO4

Na2SO4 + MgSO4

Na2SO4

Na2SO4 Na2SO4

Na2SO4

Phase equil

Non-aqueous components

Sampl

Sampl

Sampl

Vis.obs.

Sampl

Flw.Sampl

Vis.obs. T-CV curves

Isopiest

Vap.pr.diff.

Vis.obs.; Sampl p-X; p-V; TV; p-T curves p-V, T-V curves Vap.pr.; p-V, T-V curves Vap.pr.; d-p, d-T curves

Flw.Sampl

??

Vap.pr.

3

Methods

175–295 C

0/180; 210 C

150/200 C

250–400 C

300–350 C

353–375 C

383/473; 498 K 321–365 C 354–647 K

150/200–250 C

583–633 K

487–641 K

100/220–367 C

320–600 C

77/200–290 C

668–973 K

675 K

374–884 C

4

Temperature

ptx-Na2SO4-14.1

(2–501) * 10−9 (Na2SO4) mol.fr.

3.1 * 10−18–2.0 * 10−7 (Na2SO4) mol.fr. (1.3–23.9) * 10−5 (Na2SO4) mol.fr.

SVP

SVP

SVP

SVP

SVP

200; 250 bar 250–1073 (dens) kg/m3 191–306 bar

SVP

SVP

10–18.7 MPa

4–15 (Na2SO4); 1–16 (MgSO4) mass.%

14–17 (Na2SO4); 6.64–11.35 (MgSO4) mass.%

0–3.9 (Na2SO4); 0–2.4 (K2SO4) m

1.0–2.75 (Na2SO4); 0.25–0.75 (H2SO4); 0.8–2.25 (NaCl) m

0.16–2.8 (Na2SO4); 0–0.8 (H2SO4) m

0.065–0.21 (Na2SO4) m

5–20 (Na2SO4) mass.% <0.3–10.47 (Na2SO4) mass.%

0.56/0.65–3.43 (Na2SO4) m

ptx-Na2SO4 + H2SO4-1.1 ptx-Na2SO4 + H2SO4 + NaCl-1.1 ptx-Na2SO4 + K2SO4-1.1 ptx-Na2SO4 + MgSO4-1.1 ptx-Na2SO4 + MgSO4-2.1

ptx-Na2SO4-22.1 ptx-Na2SO4-23.1; 23.2; 23.3 ptx-Na2SO4-24.1

ptx-Na2SO4-21.1

ptx-Na2SO4-20.1

ptx-Na2SO4-19.1

0.5–30 (Na2SO4) mass.%

0.6/22–208 kg/cm2

0.3–3.2 (Na2SO4) m

ptx-Na2SO4-18.1

0.5–70 (Na2SO4) mass.%

113–1500 kg/cm2

2–20 MPa

ptx-Na2SO4-16.1; 16.2; 16.3; 16.4; 16.5 ptx-Na2SO4-17.1

20–32 (Na2SO4) mass.%

ptx-Na2SO4-15.1

ptx-Na2SO4-13.1

(2.5–11) * 10−8 (Na2SO4) mol.fr.

Freyer and Voigt, 2004 Blasdale and Robson, 1928 Gavrish and Galinker, 1957

Lietzke and Marshall, 1986

Khaibullin and Novikov, 1973 Novikov, 1973; Harvey and Bellows, 1997 Khaibullin and Novikov, 1973; Harvey and Bellows, 1997 Bhatnagar and Campbell, 1982 Holmes and Mesmer, 1986 DiPippo et al., 1999 Valyashko et al., 2000 Shvedov and Tremaine, 2000 Marshall, 1975

Morey and Chen, 1956 Sastry, 1957; Harvey and Bellows, 1997 Styrikovich and Khokhlov, 1957; Harvey and Bellows, 1997 Akhumov and Pilkova, 1958 Ravich and Borovaya, 1964a

8

7 ptx-Na2SO4-12.1

REFERENCE

Table

L-G-S

6

Composition

SVP

3–29 MPa

8–17 MPa

(>250)–(>1000) bar

5

Pressure

Phase Equilibria in Binary and Ternary Hydrothermal Systems 59

Sampl

Soly

Soly

Soly

Soly; LGE

LGE

Soly

Soly

Soly

Soly; LGE

Soly

Soly

Soly

Soly; H-Fl

Soly; immisc Soly; Immisc Soly

(Na2SO4 + Na2CO3) in NaOH Na2SO4 in NaCl

Na2SO4 in NaCl

Na2SO4 + NaCl

Na2SO4 in NaCl

Na2SO4 + NaCl

Na2SO4 in NaCl

Na2SO4 in NaOH

Na2SO4 in NaOH

Na2SO4 + NaOH

Na2SO4 in NaOH

Na2SO4 in (NaOH + NaCl)

Na2SeO4

NanSiO2

NanSiO2

Non-aqueous

NanSiO2

NanSiO2

Vap.pr.; Sampl Sampl

Soly

Soly

Sampl

Soly

(Na2SO4 + Na2CO3) in NaOH Na2SO4 + Na2CO3

Quench; Sampl Sampl; Vap.pr.

Quench

Quench

Vis.obs.

Sampl

Vap.pr.; Sampl Sampl; p-x, p-T curves Sampl

Sampl

Vis.obs.

d-T; d-p curves Vap.pr.

Vap.pr.; Sampl Flw.Sampl

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

350 C

200–300 C

350–450 C

718–843 C

76/232–372 C

150/200–350 C

70/200 C

200–600 C

150/200–350 C

150/200–350 C

319–400 C

426/473–624 K

310–360 C

500 C

200–351 C

150/200–350 C

150/250–350 C

200–354 C

150/200–350 C

4

Temperature

SVP

SVP

SVP

1.4–13.8 MPa

SVP

SVP

SVP

SVP (4.5–322 kg/cm2)

1.34–16.3 MPa

SVP

200; 250 bar

SVP (85–190 kg/cm2) 4.1/13–162 bar

180 atm

1.39–16.1 MPa

SVP

SVP

1.45–17.4 MPa

SVP

5

Pressure

5.2–44.7 (SiO2); 5.6–28 (Na2O) mass.%

1–10(Na2O); 2.5–27.5(SiO2) mass.%

15–23.6 (SiO2); 5–7.4 (Na2O) mass.%

L-G-S

6.7/6.4–8.3 mol.%

12.2–54.2 (Na2SO4); 0–30.6 (NaCl); 3.0–25.8 (NaOH) g/100 g H2O

0.2/3.2–12.0 (Na2SO4); 22.9–80.3 (NaOH) mass.%

5–20 (NaCl + Na2SO4); 0–100 (NaCl in Na2SO4) mass.% 4.1–69.4 (Na2SO4); 0.8–43 (NaOH) g/100 g H2O 3.7–34.8 (Na2SO4); 1.2–17.8 (NaOH) g/100 g H2O 7.7–73.2 (Na2SO4); 7.4–72 (NaOH) mass.%

0.05–1.05 (Na2SO4); 0.17–4.9 (NaCl) m

0.04–0.9 (Na2SO4); 0–0.78 (NaCl) mol/L

0.4–44 (Na2SO4); 0.5–28.7/37 (Na2CO3) g/100 g H2O 1.7–34.5 (Na2SO4); 0.63–5.7 (Na2CO3) g/100 g H2O 1.5–46 (Na2SO4); 0.3–16/26 (Na2CO3); 8–21 (NaOH) g/100 g H2O 3.1–36.0 (Na2SO4); 1.4–35.2 (NaCl) g/100 g H2O 5.4–34.5 (Na2SO4); 5.4–14.6 (NaCl) g/100 g H2O 0–0.25 (Na2SO4); 0–23 (NaCl) mg/kg H2O

6

Composition

ptx-NanSiO2-4.1

ptx-NanSiO2-2.1; 2.2 ptx-NanSiO2-3.1

ptx-NanSiO2-1.1

ptx-Na2SO4 + NaOH + NaCl-1.1 ptx-Na2SeO4-1.1

ptx-Na2SO4 + NaOH-4.1

Valyashko and Kravchuk, 1977

Rowe et al., 1967

Smits and Mazee, 1928 Morey and Ingerson, 1938 Friedman, 1950

Ravich and Elenevskaya, 1955 Schroeder et al., 1935

Schroeder et al., 1935 Schroeder et al., 1937b Ravich and Borovaya, 1955

Schroeder et al., 1936 Schroeder et al., 1937b Schroeder et al., 1936 Schroeder et al., 1935 Schroeder et al., 1937b Martinova and Samoylov, 1962 Novikov and Khaibullin, 1973 Udovenko et al., 1986a DiPippo et al., 1999

8

7 ptx-Na2SO4 + Na2CO3-1.1 ptx-Na2SO4 + Na2CO3-2.1 ptx-Na/SO4,CO3, OH-1.1 ptx-Na2SO4 + NaCl-1.1 ptx-Na2SO4 + NaCl-2.1 ptx-Na2SO4 + NaCl-3.1 ptx-Na2SO4 + NaCl-4.1 ptx-Na2SO4 + NaCl-5.1 ptx-Na2SO4 + NaCl-6.1 ptx-Na2SO4 + NaOH-1.1 ptx-Na2SO4 + NaOH-2.1 ptx-Na2SO4 + NaOH-3.1; 3.2

REFERENCE

Table

60 Hydrothermal Experimental Data

Sampl

Sampl; Quench

Quench

Vis.obs. Sampl

Sampl; Vap.pr. Sampl Sampl

Soly

Soly

Soly

Soly

H-Fl; LGE

Soly; L-V H-Fl; Cr.ph; Immisc LGE Soly

Soly

Soly

Soly

Soly

Immisc

Immisc

Soly Soly

LGE

LGE; Soly LGE

Na2WO4 in Na2CO3

Na2WO4 + NaF

Na2WO4 + Na3PO4

NdF3

Ne

Ne Ne

Ne in D2O NiO

NiO in HCl

NiO in NaOH

NiO in NaOH/NH4OH

NiO in NanPO4

NiO in (UO3 + SO3)

Ni in (UO3 + SO3 + D2O) NiSO4 NiSO4 in H2SO4; NiSO4 in D2SO4

O2

O2 O2; O2 in NaCl

Na2WO4

Soly LGE; Soly; immisc Soly; LGE

Na2WO4 Na2WO4

Quench

Flw.Sampl

Flw.Sampl

Flw.Sampl

Flw.Sampl

Sampl Vis.obs.; p-T curves Sampl Sampl

p-x curves

Sampl

Sampl

Sampl p-V, p-x curves Therm.anal.

3

2

1

Methods

Phase equil

components

100/204–288 C 0/200–300 C

0/204–343 C

300; 325; 350 C 300; 325; 350 C 150/195–205 C 200–350 C

291/463–562 K

295/450–589 K

423/473–573 K

293/428–550 K 373/473; 523 K 423/473–573 K

343/447.6– 556.9 K 295/428–543 K 651–705 K

150–250 C

230 C

225 C

225 C

557–695 C

100/200–400 C 198–550 C

4

Temperature

1.7–19 MPa 0.1/5.7–12.9 MPa

0.69–2.76 MPa

SVP SVP

SVP

SVP

8–9 MPa

13–14 MPa.

up to 12 MPa

up to 12 MPa

2.186–8.9 MPa SVP

2.4/2.2–8.2 MPa 54.3–254.8 MPa

11.7/12.4–8.3 atm

SVP

SVP

SVP

SVP

2–338 bar

SVP 13–707 kg/cm2

5

Pressure

ptx-Ne + D2O-1.1 ptx-NiO-1.1 ptx-NiO + HCl-1.1 ptx-NiO + NaOH-1.1 ptx-NiO/ Ni(OH)2+ NH4OH-1.1; ptx-NiO+ NaOH/ NH4OH-1.1;1.2 ptx-NiO + NanPO4-1.1; 1.2 ptx-NiO + UO3 + SO3-1.1 ptx-NiO + UO3 + SO3 + D2O-1.1 ptx-NiSO4-1.1 ptx-NiSO4-2.1 ptx-NiSO4 + D2SO4-1.1 ptx-O2-1.1

(2–8.8) * 10−4 (Ne) mol.fr. 2.8 2–0.8 (Ni) µmol/kg H2O (0.001–165) * 10−6 (NiO); (0.12–5) * 10−4 (HCl) m (0.001–165) * 10−6 (NiO); (0.012–373) * 10−4 (NaOH) m (0.05–436)*10−9 (NiO); (0.07–5.7)*10−3 (NaOH/NH4OH) m

0.61–7.75 (O2) mL/g H2O) 2620/4190–1190 MPa (Henry’s law const)

0.15/0.18–3.0 (O2) cm3/g H2O

ptx-O2-2.1 ptx-O2-3.1; 3.2

ptx-Ne-2.1 ptx-Ne-3.1

(2–8.4) * 10−4 (Ne) mol.fr. 0.14–0.45 (Ne) mol.fr.

(0.01–0.74) * 10−6 (NiO); (0.54–213) * 10−3 (Na(2.1–2.9)PO4) m 0.3–8.7 (SO3); 0.35–0.98 (UO3/SO3); 0.03–0.19 (NiO/SO3) m 0.3–6.6 (SO3); 0.3–0.84 (UO3/SO3); 0.01–0.15 (NiO/SO3) m 55/44–1 (NiSO4) mass.% 0.002–1.3 (NiSO4); 0.001–1.8 (H2SO4) m; 0.001–0.6 (NiSO4); 0.001–1.05 (D2SO4) m

ptx-Ne-1.1

ptx-Na2WO4 + Na2CO3-1.1 ptx-Na2WO4 + NaF-1.1 ptx-Na2WO4 + Na3PO4-1.1 ptx-NdF3-1.1

Stephan et al., 1956 Cramer, 1980, 1982, 1984

Pray et al., 1952

Ziemniak et al., 1989 Jones and Marshall, 1961 Jones and Marshall, 1961 Benrath, 1941 Marshall et al., 1962a

Tremaine and LeBlanc, 1980b Tremaine and LeBlanc, 1980b Ziemniak et al., 2004

Crovetto et al., 1982 Dinov et al., 1993

Urusova et al., 1975a Urusova et al., 1975b Migdisov and Williams-Jones, 2007 Potter II and Clynne, 1978 Crovetto et al., 1982 Mather et al., 1993

Urusova et al., 1975 Urusova and Valyashko, 1976 Kravchuk and Todheide, 1996 Urusova et al., 1978

8

7 ptx-Na2WO4-1.1 ptx-Na2WO4-2.1; 2.2 ptx-Na2WO4-3.1

REFERENCE

Table

(9/12.6–20) * 10−5 (Ne) mol.fr.

0.13–19050*10–7(Nd); 0.06–0.2(ClO4); 0.002– 0.23(HF+F) mol/L

0–47 (Na2WO4); 0–19 (Na3PO4) mass.%

11–47.5 (Na2WO4); 0.4–2.3 (NaF) mass.%

12–44 (Na2WO4); 2.7–15.8 (Na2CO3) mass.%

L-G-S

44–64 (Na2WO4) mass.% 7.5–70 (Na2WO4) mass.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 61

Quench

Queuch

Soly

Soly

Flw.Sampl

Soly

PbTiO3 + TiO2 (rutile) in NaOH PdS (vysotskite) in (H2S + Buff)

Sampl

Soly

PbS (galena) in (NaHS + H2S) PbSO4

Flw.Sampl Quench

Soly Soly

Flw.Sampl

150/200–300 C

150/200–300 C

500 C

27/200–305 C

250–500 C 100/200 C

673–773 K

256–377

300 C

250 C

Vis.obs.

PbO PbO in NaOH

PbO

PbI2

PbI2

PbCO3 in (NaCl + KHCO3 + CO2) PbCl2

Sampl

143/217–373 C

175/234–412 C

Soly; Immisc Soly

PbBr2

86/154–866

150/200–300 C

Vis.obs.

LGE

P4O10

Vap.pr.; Sampl Vap.pr.; Sampl Vis.obs.

100/204.4–287 C

141/195–499 C

LGE

P2O5

Sampl

Vis.obs.

LGE; Soly

O2 in UO2SO4

204.4 C 0/200–300 C

472–663 K

Soly; Immisc Soly; Immisc Soly; Cr.ph; Immisc Soly

LGE LGE

O2 + H2 O2 in NaCl

p-T curves; Sampl Sampl Sampl

4

Temperature

Sampl

H-Fl; Cr.ph

O2

3

Methods

Soly

2

1

PbCO3 in (KCl + K2CO3)

Phase equil

Continued

Non-aqueous components

Table 1.1

SVP

SVP

1000 bar

2–75 atm. (PH2S)

26–34 MPa SVP

22–32 MPa

SVP

SVP

SVP

SVP

SVP

SVP

SVP

SVP

0.6–16.6 MPa

3.7–8.3 MPa 0.1/5.7–12.9 MPa

22.2–260 MPa

5

Pressure

ptx-PbO-1.1 ptx-PbO-2.1 ptx-PbO + NaOH-1.1 ptx-PbS-1.1

(2.8–15) * 10−5 (PbO) mol.fr. 351–8246 (PbO) µm 0–0.04 (NaOH); 0.001–0.005 (Pb) m

ptx-PbTiO3 + NaOH-1.1 ptx-PdS + HCl + NaHS-1.1; 1.2; ptx-PdS + H3PO4 + NaHS-1.1; ptxPdS + H2S + KnHPO4-1.1

0–0.6 (NaOH); 0.3–16 * 10−5 (Pb) m <1–11140 (Pd) ppb; 0.01–1.0 (Σ S2− aq ) m; [Buff. (HCl/Cl−), (H3PO4/H2PO−4 ); (H2S/HS−)]

ptx-PbSO4-1.1

0.01 (PbSO4) mass.%

0.06/0.16–41.3 (Pb) ppm; 0–2.85 (NaHS) m

ptx-PbI2-2.1

ptx-PbI2-1.1

ptx-PbCO3 + K/Cl,CO3-1.1 PbCO3 + Na,K/Cl,HCO3-1.1 ptx-PbCl2-1.1

ptx-PbBr2-1.1; 1.2

ptx-P4O10-1.1; 1.2

Valyashko and Urusova, 1996 Yokogama et al., 1993 Sue et al., 1999 Tugarunov et al., 1975 Giordano and Barnes, 1979 Morey and Hesselgesser, 1951b Tugarunov et al., 1975 Gammons and Bloom, 1993

Benrath et al., 1937

Baranova and Barsukov, 1965 Baranova and Barsukov, 1965 Benrath et al., 1937

Zagvozdkin et al., 1940 Brown and Whitt, 1952 Benrath et al., 1937

Stephan et al., 1956

Japas and Franck, 1985 Stephan et al., 1956 Cramer, 1980, 1984

8

7 ptx-O2-4.1; 4.2; 4.3 ptx-O2 + H2-1.1 ptx-O2 + NaCl1.1; 1.2 ptx-O2 + UO2SO4-1.1 ptx-P2O5-1.1

REFERENCE

Table

4.14–49.5 (PbI2) mass.%

1.4/3.65–100.0 (PbI2) mass.%

0.5–1.4 (Pb) g/L; 0.1 (KCl); 0.06–0.48 (K2CO3) m 0.07–2.3 (Pb) g/L; 0.1 (NaCl); 0.06–0.48 (KHCO3) m; 5; 15; 45 (CO2) atm 4.74/8.5–100 (PbCl2) mass.%

7.3 17–100 (PbBr2) mass.%

0.009–93 (P4O10) mass.%

63.4/68.6–88.7 (P2O5) mass.%

0.29–3.3 (O2) mL/g; 40–243 (U) g/L

0.32–0.92 (O2); 0.91–2.3 (H2) mL/gH2O 0.87–5.7 NaCl m

1–94 (O2) mol.%

6

Composition

62 Hydrothermal Experimental Data

Wt-loss

Sampl

2

Soly

Cr.ph Soly; LGE

PTX, Soly

Soly

Immisc; hydrolysis

H-Fl LGE

Cr.ph

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

1

PtS (cooperite) in (H2S + Buff)

RbCl RbCl

Rb2O*nB2O3

RbOH

S

SF6 (sulfur hexafluoride) SO3

SO3

Sb2O3 Sb2O3 in HF; Sb2O3 in NaOH

Sb2O3

Sb2O3 (senarmontite) in NaCl+HCl

Sb2S3 (stibnite)

Sb2S3 (stibnite) in HCl

Sb2S3 (stibnite) in (HCl + C2H4O2 + NH4OH)

Sb2S3 (stibnite) in H2S

Sb2S3(stibnite) in NaCl+HCl SiO2 (silica)

SiO2 (silica glass)

Sampl

Sampl

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

XAFS; Wt-loss

Quench

Quench

Sampl Vap.pr.; Sampl Vis.obs.

Quench; Sampl

Therm.anal.; Sampl Therm.anal.

Vis.obs. Vap.pr.

Queuch

3

Methods

Phase equil

Non-aqueous components

350–450 C

128/195–336 C

300–403 C

25/200–350 C

198–306 C

198–306 C

198–306 C

200–400 C 300–400 C

80/350; 400 C

90/200 C

218−666

74/206–232 C 20/180–339 C

100/200–300 C

(−77)/104–380 C

20/166–327 C

374–383 C 400–715 C

200–300

4

Temperature

SVP; 2.51/14–137 atm 171–304 kg/cm2

130–600 bar

SVP

SVP; 500 bar

SVP; 500 bar

SVP; 500 bar

304–610 bar 300–600 bar

SVP; 500 bar

SVP

SVP

0.2/1.9–3 MPa SVP

SVP; 100–1000 bar

SVP

SVP

SVP SVP

SVP

5

Pressure

ptx-SF6-1.1 ptx-SO3-1.1; 1.2; 1.3; 1.4 ptx-SO3-2.1 ptx-Sb2O3-1.1; ptx-Sb2O3 + HF-1.1; ptxSb2O3 + NaOH-1.1 ptx-Sb2O3-2.1; ptx-Sb2O3 + N2-1.1 ptx-Sb2O3+ Na,H/ Cl-1.1 ptx-Sb2O3+ Na,H/Cl-1.2 ptx-Sb2S3-1.1

3.86 * 10−6–0.046 (SF6) mol.fr 0–100 (SO3) mass.%

(0.31/3.7–14.9) * 10−3 (Sb); 0–0.03 (HF); 0–0.1 (NaOH) m

80–240 (SiO2) ppm

0.05/0.09–0.22 (SiO2) g/100 g H2O

0.003–0.1(Sb); 0–0.24(HCl); 0–2.3(NaCl) m

(0.26–37) * 10−4 (Sb); (0.03–10) * 10−2 (H2S); 0.001 (HC1) m (0.26–37) * 10−4 (Sb); (0.03–10) * 10−2 (H2S); 0; 0.001 (HC1); 0–1.7 (C2H4O2); 0–1.6 (NH4OH) m 1.98–5.53 (Sb); 0.89–3.58 (S) [−log m]

(0.26–37) * 10−4 (Sb); (0.03–10) * 10−2 (H2S) m

0.01–0.4(Sb); 0–0.1(HCl); 0–2.3(NaCl) m 0.02–0.28 (Sb); 0–0.1(HCl); 0–5(NaCl ) m

0.01–0.078 (Sb) m; 0–0.33 (N2) mol.fr.

ptx-SiO2-2.1

ptx-Sb2S3 + HCl-1.1 ptx-Sb2S3 + H/Cl, C2H3O2 + NH5O-1.1 ptx-Sb2S3 + H2S-1.1 ptx-Sb2S3+ Na,H/Cl-1.1 ptx-SiO2-1.1

ptx-S-1.1; 1.2; 1.3

S + H2O ⇒ H2S + H2SO4; L1-L2-G; L1-L2

1.93–100.00 (SO3) mol.%

ptx-RbOH-1.1

ptx-Rb2O*nB2O3-1.1

10.35/91.4–100 (RbOH) mass.%

Invariant equilibria

0–0.855 (RbCl) mol/L L-G-S

ptx-PtS + HCl + NaHS-1.1; ptxPtS + HCl + NaHS-1.2 ptx-RbCl-1.1 ptx-RbCl-2.1

<1–2400 (Pt) ppb; 0.01–1.0 (Σ S ) m; Buff. (HCl/H+), (H2S/HS−)

Gilligham, 1948

Pokrovski et al., 2006 Hitchen, 1935

Krupp, 1988

Shikina and Zotov, 1999 Shikina and Zotov, 1999 Shikina and Zotov, 1999

Pokrovski et al., 2006

Zotov et al., 2003

Stuckey and Secoy, 1963 Popova et al., 1975

Rollet and CohenAdad, 1964 Ellis and Giggenbach, 1971 Mroczek, 1997 Luchinskiy, 1956

Schroer, 1927 Morey and Chen, 1956 Toledano, 1964

Gammons and Bloom, 1993

8

7

6 2− aq

REFERENCE

Table

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 63

2

Soly

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly; Cr.ph; Immisc

Soly

Soly

Soly

Soly

Soly

Soly

1

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz; Silica Glass)

SiO2 (quartz; Silica Glass)

SiO2 (quartz) SiO2 (quartz; cristobalite; tridimite)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (cristobalite)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz; silica)

SiO2 (quartz)

Non-aqueous

Phase equil

Continued

Non-aqueous components

Table 1.1

Wt-loss

Flw.Sampl

Wt-loss

??

Flw.Sampl

Quench; Wtloss; Vap. pr. Quench

Wt-loss, Quench

Sampl

Quench Wt-loss

Sampl

Sampl

Sampl

Wt-loss

3

Methods

500–900 C

26/473–913 K

400–625 C

673, 773 K

45/200–300 C

84/198–255 C

995–1420

140/200–500 C

623, 673, 723 K

370 C 400 C

300–500 C

300–600 C

633–773 K

160/200–610 C

4

Temperature

1–9.85 kbar

0.03–29.4 MPa

1000–4000 bars

1–50 MPa

22.5; 33; 1000 atm

SVP

450–9500 bar

SVP; 4/208 atm; 1.5–4 cm3/g

0.24–9.1 (SiO2) mass.%

0.034–2264 (SiO2) mg/kg

0.14–0.88 (SiO2) mass.%

(0.18–246.3) * 10−6 (SiO2) mol.fr.

21 328–924 (SiO2) ppm

0.00768–0.0123 (SiO2) m

5.7–95.6 (SiO2) mass.%

0.018–0.185 (SiO2) mass.%

0.0003–0.0013 (SiO2) mol.fr.

0.033–0.046 (SiO2) g/100 g H2O 1.10–2.62 (SiO2) g/kg H2O

∼200 atm 500–2000; 450, 1000; 1500 bar 59–392 MPa

3.1–4179 (SiO2) ppm

0.036–0.765 (SiO2) mass.%

ptx-SiO2-17.1

ptx-SiO2-16.1; 16.2

ptx-SiO2-15.1

ptx-SiO2-13.1; 13.2 ptx-SiO2-14.1

ptx-SiO2-12.1

ptx-SiO2-11.1; 11.2; 11.3

ptx-SiO2-10.1 ptx-SiO2-10.2

ptx-SiO2-9.1

ptx-SiO2-7.1 ptx-SiO2-8.1; 8.2

ptx-SiO2-6.1; 6.2

ptx-SiO2-5.1; 5.2; 5.3

ptx-SiO2-4.1

(0.03–78) * 10−5 (SiO2) mol.fr.

Wendlandt, 1963; Harvey and Bellows, 1997 Weill and Fyfe, 1964 Heitmann, 1964, 1965; Harvey and Bellows, 1997 Anderson and Burnham, 1965

Fournier and Rowe, 1962 Morey et al., 1962

Kennedy, 1950; Harvey and Bellows, 1997 Morey and Hesselgesser, 1950; Harvey and Bellows, 1997 Morey and Hesselgesser, 1951b Morey and Hesselgesser, 1951a Schloemer, 1952 Wyart and Sabatier, 1955; Harvey and Bellows, 1997 Khitarov, 1956; Harvey and Bellows, 1997 Kitahara, 1960; Harvey and Bellows, 1997 Kennedy et al., 1961, 1962

8

7 ptx-SiO2-3.1

REFERENCE

Table

0.007/0.023–0.456 (SiO2) mass.%

6

Composition

14–103 MPa

33–2000 bar

3.4–103 MPa

6.2/15–1740 bar

5

Pressure

64 Hydrothermal Experimental Data

Sampl

Wt-loss

Soly

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

SiO2 (quartz)

SiO2 (silica)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz) SiO2 (amorph)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz)

SiO2 (quartz) SiO2 (quartz) in Ar

SiO2 (quartz) in (B(OH)3 + KOH) SiO2 (quartz) in CO2

SiO2 (quartz) in CO2

SiO2 (quartz) in CO2

SiO2 (quartz) in HCl

SiO2 (quartz) in KCl

SiO2 (quartz) in KCl

SiO2 (quartz) in KF

SiO2 (quartz) in KOH

SiO2 (quartz) in KOH

SiO2 (amorph) in MgCl2

Sampl

Wt-loss

Wt-loss; Quench Wt-loss

Quench

Wt-loss

Wt-loss

Wt-loss

Sampl

Wt-loss Sampl

Sampl

Sampl

Sampl

Sampl

Quench Sampl

Sampl

Wt-loss

Sampl

Wt-loss

3

2

1

Methods

Phase equil

components

100/200–300 C

600; 700 C

500–700 C

280 C

200–400 C

600–800 C

600 C

800 C

600 C

700 C

181; 242 C

500–900 C 400–618 C

412–573 C

673, 773 K

350–525 C and 250 C

200–500 C 100/200–350 C

179/229–330 C

365/476.64; 521.95 K 873–1173 K

700 C

4

Temperature

SVP

2 kbar

3; 4 kbar

SVP

1 kbar (?)

3; 4 kbar

3 kbar

10 kbar

2 kbar

10–15 bar above SVP 3; 5 kbars

5–20 MPa 1; 2 kbar

2000 bar

20–39 MPa

250–1000 bar

1; 2 kbar

SVP-2 kbar SVP

SVP

97–305 MPa

SVP

4 kbar

5

Pressure

0.0004/0.002–0.026 (SiO2); 0.50–6.0 (MgCl2) m

0.17–0.4 (Si); 0.05–0.25 (KOH) m

1.04–2.32 (SiO2) mass.%; 0.01; 0.067 (KOH) m

1.5–2.34 (SiO2) (−log mol/L); 0.5; 4 (KCl) mol/L 0.65; 0.78 (SiO2) g/L; 1 (KF) mass.%

0.99–3.13 (SiO2) mass.%; 0.7–11.25 (KCl) m

0.62–1.0 (SiO2) mass.%; 0.12; 6.95 (HCl) m

0.0078–2.35 (SiO2) mass.%; 0–0.96 (CO2) mol. fr. 0.964–1.51 (SiO2) (−log m); 0.023–0.32 (CO2) mol.fr. 0.7–0.86 * 10−3 (SiO2); 0.2–0.7 (CO2) m

515–1012 (SiO2) mg/kg H2O; 0.1–0.6 (B) m

0.78–12.56 (SiO2) mass.% 1.54–2.29 (SiO2) (−log m); 0–0.42 (Ar) m

ptx-SiO2 + KOH-2.1 ptx-SiO2 + MgCl2-1.1

ptx-SiO2-28.1 ptx-SiO2 + Ar-1.1; 1.2 ptx-SiO2 + B,K/OH-1.1 ptx-SiO2 + CO2-1.1 ptx-SiO2 + CO2-2.1 ptx-SiO2 + CO2-3.1 ptx-SiO2 + HCl-1.1 ptx-SiO2 + KCl-1.1 ptx-SiO2 + KCl-2.1 ptx-SiO2 + KF-1.1 ptx-SiO2KOH-1.1

ptx-SiO2-27.1

Ptx-SiO2-26.1

1.36–23.1 * 10−5 (SiO2) mol. Fr. 1.27–1.05 (SiO2) (−log m)

ptx-SiO2-25.1

ptx-SiO2-24.1

ptx-SiO2-22.1 ptx-SiO2-23.1

2.03–2.13 (Si(OH)4 * 2H2O) (−log m)

1.06–1.66 (SiO2) (−log m)

1.12–2.33 (SiO2) (−log mol/L) 0.0063/0.016–0.029 (SiO2) m

ptx-SiO2-21.1

ptx-SiO2-20.1

0.06–0.57 * 10−4 (SiO2) mol.fr.

163/406–676 (SiO2) ppm

ptx-SiO2-19.1

Balitskiy et al., 1971 Anderson and Burnham, 1967 Pascal and Anderson, 1989 Chen and Marshall, 1982

Walter and Orville, 1983 Newton and Manning, 2000 Anderson and Burnham, 1967 Anderson and Burnham, 1967 Hemley et al., 1980

Novgorodov, 1975

Semenova and Tsiklis, 1970; Harvey and Bellows, 1997 Crerar and Anderson, 1971 Hemley et al., 1980 Chen and Marshall, 1982 Walther and Orville, 1983 Ragnarsdottir and Walther, 1983 Yokogama et al., 1993 Xie and Walther, 1993 Manning, 1994 Walter and Orville, 1983 Seward, 1974

Anderson and Burnham, 1967 Apps, 1970

8

7 ptx-SiO2-18.1

REFERENCE

Table

0.006/0.0157; 0.0197 (SiO2) mol/L

1.95; 1.97 (SiO2) mass.%

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 65

Sampl

Sampl

Sampl

Sampl

Wt-loss; Quench Sampl

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly; Immisc Soly; Immisc Soly

Soly

SiO2 (quartz) in Na2B4O7

SiO2 (Quartz) in NaCl

SiO2 (quartz) in NaCl

SiO2 (amorph) in NaCl

SiO2 (quartz) in NaCl

SiO2 (quartz) in NaCl

SiO2 (quartz) in NaCl

SiO2(quartz) in NaCl

SiO2 (amorph) in (NaCl + MgCl2) SiO2 (amorph) in (NaCl + MgSO4) SiO2 (amorph) in (NaCl + Na2SO4) SiO2 (quartz) in NaF

SiO2 (amorph) in NaNO3

SiO2 (amorph) in NaNO3

SiO2 (quartz) in NaOH

SiO2 (amorph) in NaOH

Non-aqueous

SiO2 (quartz) in NaOH

SiO2 (quartz) in NaOH

Sampl

Soly

SiO2 (amorph) in (MgCl2 + MgSO4) SiO2 (amorph) in MgSO4

Sampl

Wt-loss

Quench

Quench

Sampl

Wt-loss

Wt-loss

Sampl

Sampl

Sampl

Quench

Wt-loss

Sampl

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

372/473–534 K

600; 700 C

350–450 C

250–357 C

100/150–350 C

25/200–300 C

280 C

100/150–300 C

100/150–300 C

100/150–300 C

800 C

500–900 C

402–595 C

350 C

100/200–350 C

200–400 C

600 C

100/200; 250 C 133/175–345 C

100/150–250 C

4

Temperature

SVP

3; 4 kbar

SVP

SVP

SVP

SVP

SVP

SVP

SVP

SVP

10 kbar

2–15 kbar

1725–1800 bar

165–525 bar

SVP

1 kbar(?)

10–15 bar above SVP 3 kbar

SVP

SVP

5

Pressure

0.36–0.43 mol/L (SiO2); 1.26–1.45 (NaOH) (−log m/L)

1.69–2.76 (SiO2) mass.%; 0.113 (NaOH) m

14–24 (SiO2); 5–7.4 (Na2O) mass.%

1.4–55.4 (SiO2); 0.98–24.8 (Na2O) mass.%

0.0026/0.005–0.022 (SiO2); 2.1–6.3 (NaNO3) m

0.00086/0.01–0.27 (SiO2); 0–6 (NaNO3) m

0.004–0.02 (SiO2); 0.8, 1.2 (NaCl); 1.2; 0.7 (MgCl2) m 0.005–0.03 (SiO2); 0.8–1.5 (NaCl); 1.0–0.1 (MgSO4) m 0.005–0.03 (SiO2); 0.2–1.4 (NaCl); 1.5–0.3 (Na2SO4) m 0.7; 0.73 (SiO2) g/L; 1 (NaF) mass.%

0.76 (SiO2) (m); 0.17 (NaCl) mol.fr.

0.6–29.5 * 10−3 (SiO2); 0.00–0.76 (NaCl) mol.fr.

1.36–1.05 (SiO2) (−log m); 0.1 (NaCl) m

1.5–2.5 (SiO2) (−log mol/L); 0.5; 4 (NaCl) mol/L 0.0034/0.0077–0.027 (SiO2); 0.19–6.4 (NaCl) m 734–1074 (SiO2) mg/kg; 0–4 (NaCl) m

0.004–0.02 (SiO2); 1.1 (MgCl2); 1.0–0.4 (MgSO4) m 0.0035/0.015–0.021 (SiO2); 0.013–0.11 (MgSO4) m 203/473–3723 (SiO2) mg/kg H2O; 0.1–0.6 (B) m 0.98 (SiO2) mass.%; 0.91 (NaCl) m

6

Composition

Marshall and Chen, 1982 Chen and Marshall, 1982 Seward, 1974

ptx-SiO2 + Mg/Cl,SO4-1.1 ptx-SiO2 + MgSO4-1.1 ptx-SiO2 + Na2B4O7-1.1 ptx-SiO2 + NaCl-1.1 ptx-SiO2 + NaCl-2.1 ptx-SiO2 + NaCl-3.1 ptx-SiO2 + NaCl-4.1 ptx-SiO2 + NaCl-5.1 ptx-SiO2 + NaCl-6.1 ptx- SiO2+NaCl-7.1 ptx-SiO2 + Na,Mg/Cl-1.1 ptx-SiO2 + Na,Mg/Cl,SO4-1.1 ptx-SiO2 + Na/Cl,SO4-1.1 ptx-SiO2 + NaF-1.1 ptx-SiO2 + NaNO3-1.1 ptx-SiO2 + NaNO3-2.1 ptx-SiO2 + NaOH-1.1; 1.2 ptx-SiO2 + NaOH-2.1; 2.2 ptx-SiO2 + NaOH-3.1 ptx-SiO2 + NaOH-4.1

8

7

Anderson and Burnham, 1967 Apps, 1970

Chen and Marshall, 1982 Tuttle and Friedman, 1948 Friedman, 1950

Xie and Walther, 1993 Newton and Manning, 2000 Newton and Manning, 2006 Marshall and Chen, 1982 Marshall and Chen, 1982 Marshall and Chen, 1982 Balitskiy et al., 1971 Marshall, 1980

Chen and Marshall, 1982 Fournier et al., 1982

Anderson and Burnham, 1967 Hemley et al., 1980

REFERENCE

Table

66 Hydrothermal Experimental Data

Wt-loss; Quench Sampl

Sampl

Sampl

Sampl

Sampl

Sampl

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

H-Fl

Soly

Soly

Soly

Soly

Soly

Soly

Soly

SiO2 (quartz) in NaOH

SiO2 (quartz) in NaOH

SiO2 (quartz) in NaOH

SiO2 (quartz) in Na2S

SiO2 (amorph) in Na2SO4 SiO2 (amorph) in (Na2SO4 + MgCl2) SiO2 (amorph) in (Na2SO4 + MgSO4) SiO2 (amorph) in Na2SiO4 (SiO2 (quartz) + CaSiO3 (wollastonite)) in NaCl Sm2(SO4)3 + H2SO4

Sn(C2H5)4 (tetraethyltin)

SnO2

SnO2; SnO2 in HCl; SnO2 in (HCl + KCl)

SnO2 in HCl

SnO2 in HF

SnO2 in HNO3

SnO2 in HNO3

SnO2 in NaF; SnO2 in HNO3; SnO2 in (NaF + NaOH)

Quench

Quench

Sampl

Quench

Sampl-Quench

Quench

Sampl

Flw.Sampl

Wt-loss

Sampl

Sampl

3

2

1

Methods

Phase equil

components

25/200

300

100/200

50/200

300–350 C

200–500

25/200; 300

298/473 K

25/200–350

299–512 C

127/195–280 C

100/150–250 C

100/150–300 C

100/200–350 C

280 C

150/200–450 C

125/175; 225 C 350 C

4

Temperature

SVP (?)

101.3 MPa

SVP

SVP (?)

Up to 180 bar

101.3 MPa

SVP

65 bar

SVP

465–580 bar

SVP

SVP

SVP

SVP

SVP

500–2200 bar

SVP

SVP

5

Pressure

ptx-SnO2 + HF-1.1 ptx-SnO2 + HNO3-1.1 ptx-SnO2 + HNO3-2.1 ptx-SnO2 + NaF1.1; ptx-SnO2 + NaF + HNO31.1; ptx-SnO2 + NaF + NaOH-1.1

(4.6–84.0) * 10−6 (SnO2); 0.05–0.5 (HF) mol/L

(0.5/3.8–49) * 10−6 (Sn); 0.05–0.50 (NaF); 0.001–0.01 (NaOH) mol/L

(0.24–7.8) * 10−5 (SnO2); 0.01–0.5 (HNO3) m

1.1/30.3 * 10−7 (SnO2); 0.1 (HNO3) mol/L

(−11) – (−8.3) (Sn) log(mol.fr.)

ptx-SnO2-2.1; ptx-SnO2 + HCl-1.1; ptxSnO2 + HCl + KCl-1.1 ptx-SnO2+HCl-2.1

5.76 * 10−7–0.006 (SnO2); 0–0.2 (HCl); 0–0.5 (KCl) m

Crerar and Anderson, 1971 Valyashko and Kravchuk, 1977 Rumyantsev, 1995

ptx-SiO2 + NaOH-5.1 ptx-SiO2 + NaOH-6.1 ptx-SiO2 + NaOH-7.1; 7.2 ptx-SiO2 + Na2S-1.1 ptx-SiO2 + Na2SO4-1.1 ptx-SiO2 + Na,Mg/SO4,Cl-1.1 ptx-SiO2 + Na,Mg/SO4-1.1 ptx-SiO2 + Na2SiO4-1.1 ptx-SiO2 + CaSiO3 + NaCl-5.1 ptx-Sm2(SO4)31.1; ptxSm2(SO4)3 + H2SO4-1.1 ptx-Sn(C2H5)4-1.1 ptx-SnO2-1.1

8

7

Klintsova et al., 1975

Migdisov and WilliamsJones, 2005 Klintsova et al., 1975 Klintsova and Barsukov, 1973 Dadze et al., 1981

Miller and Hawthorne, 2000 Klintsova and Barsukov, 1973 Dadze et al., 1981

Marshall and Slusher, 1975c

Xie and Walther, 1993

Balitskiy et al., 1971 Chen and Marshall, 1982 Marshall and Chen, 1982 Marshall and Chen, 1982 Hitchen, 1935

REFERENCE

Table

3.63/(32.0–56.7) * 10−6 (Sn) mol/L

0.034 * 10−5/8.08 * 10−5 (Sn(C2H5)4) mol.%

0.02/0.0074–0.000008 (Sm2(SO4)3); 0–0.3 (H2SO4) m

1.87–1.54 (SiO2), 2.9–5.0 (Ca2+) (−log m); 0.8, 1.9 (NaCl) m

0.0055/0.016–0.04 (SiO2); 0.07–3.11 (Na2SO4) m 0.003–0.03 (SiO2); 1.4, 0.4 (MgCl2); 1.3–0.7 (Na2SO4) m 0.006–0.03 (SiO2); 0.4, 0.8 (MgSO4); 0.9, 0.8 (Na2SO4) m 0.8–1.2 (SiO2); 0.58–0.65 (Na2O) [g/100 g H2O]

17.4–37 (SiO2) g/L; 3; 5 (Na2S) mass.%

4.08–33.6 (SiO2) g/L; 0.10–0.50 (NaOH) mol/L

1.7–63.7 (SiO2); 0.4–20.3 (Na2O) mass.%

523/617–689 (SiO2) ppm; 0.01 (NaOH) m

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 67

Quench

Vis.obs. Sampl

Soly

Soly

Soly Soly

(SnO2 + buff.) in H3BO3; in (H3BO3 + HF); in (HF + H3BO3 + NaOH); in (Na2B4O7); in (NaOH) (SnO2 + buff.) in NaF; in NaOH; in (NaOH + NaCl) SrBr2 SrCO3 in CO2

Sampl

Wt-loss

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

Soly

SrSO4

SrSO4

SrSO4 in NaCl

SrSO4 in NaCl

SrSO4 in NaCl

Th(NO3)4

TiO2 (rutile)

TiO2 (rutile) in NaNO3 (buff.solns.) TiO2 in KF

Wt-loss

Vis.obs.

Sampl

Wt-loss; Quench Sampl

Wt-loss; Quench Sampl

Vis.obs. Sampl

Isopiest

Sr(NO3)2 SrSO4

SrCl2

Vis.obs. Vis.obs. Isopiest

Sampl

Soly Soly LGE; Isop-m LGE; Isop-m Soly Soly

SrCl2 SrCl2 SrCl2

Quench

Soly

SnO2 in NaOH

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

400; 450 C

99/197–326 C

37/159; 211 C 1100 C

25/200–254 C

20/200–450 C

20/200–600 C

25/200–350 C

22/200–600

179/225–475 C 194–426 C

383/474–524 K

22.9/183–200 C 124/200–412 C 383/473.6

104/212–383 C 50/200 C

500 C

500 C

200

4

Temperature

ptx-SnO2 + buff2.1; 2.2; 2.3

(4.25 * 10−6–6.7 * 10−3) (SnO2); 0.0001–0.5 (NaF); 0.001–0.5 (NaOH); 0.5–4 (NaCl) m

1000; 1400 atm

200 bar

2.0; 2.8 GPa

SVP

1/15–600 bar

0.00014–0.00513 (Ti(OH)4 F2− 2 ); 0.34–2.13 (F−) m

3.89–7.05 (TiO2) [−log m]; buff.solns.

1.0–5.9 (TiO2) mass.%

67/87.41; 92 (Th(NO3)4) mass.%

0.06–3.95 (SrSO4) mm; 0–4 (NaCl) m

963/235–529 (SrSO4) ppm; 1; 2 (NaCl) mol/L

0.386–20.46 (SrSO4) g/kg H2O; 2 (NaCl) mol/L

1/0.865–0.4 g/cm3 1/15–915 atm

114/23.8–2.6 (SrSO4) ppm

114/23.8–1.0 (SrSO4) (mg/kg H2O)

55/60–85 (Sr(NO3)2) mass.% 0.0003–0.0032 (SrSO4) g/100 g H2O

0.41–5.54 (SrCl2) m

ptx-TiO2 + buff.-1.1 ptx-TiO2 + KF-1.1

ptx-TiO2-1.1

ptx-SrSO4 + NaCl-1.1 ptx-SrSO4 + NaCl-2.1 ptx-SrSO4 + NaCl-3.1; 3.2 ptx-Th(NO3)4-1.1

ptx-SrSO4-2.1; 2.2 ptx-SrSO4-3.1

ptx-Sr(NO3)2-1.1 ptx-SrSO4-1.1

ptx-SrCl2-4.1

ptx-SrBr2-1.1 ptx-SrCO3 + CO2-1.1 ptx-SrCl2-1.1 ptx-SrCl2-2.1 ptx-SrCl2-3.1

ptx-SnO2 + NaOH-1.1 ptx-SnO2 + buff1.1; 1.2; 1.3; 1.4; 1.5

(54.6–110) * 10−5 * (Sn) mol/L); 0.05–0.5 (NaOH) m (0.5 * 10−6–7.2 * 10−3) (SnO2); (0.0025–7) (H3BO3); 0.01–0.075 (HF); 0.0025–0.5 (NaOH); 0.0005–0.25 (Na2B4O7) m

69/75–94 (SrBr2) mass.% 0.012–0.026 (SrCO3) mass.%; 5.6–47 (CO2) atm 3.4/9.49–10.29 (SrCl2) m 54/62–81 (SrCl2) mass.% 0.47/0.61–4.22 (SrCl2) m

8

7

6

Barsukova et al., 1979

Marshall et al., 1951 Ayers and Watson, 1991 Knauss et al., 2001

Gundlach et al., 1972 Howell et al., 1992

Gundlach et al., 1972 Strubel, 1966

Benrath, 1941 Helz and Holland, 1965 Menzies, 1936 Benrath, 1941 Holmes and Mesmer, 1981a Holmes and Mesmer, 1996b Benrath, 1942 Booth and Bidwell, 1950 Strubel, 1966

Kovalenko et al., 1992

Klintsova and Barsukov, 1973 Kovalenko et al., 1991

REFERENCE

Table

Composition

0.02/16–169 atm

v.pr-1990 bar

SVP SVP

SVP

SVP SVP SVP

SVP 20–63 atm

1000 bar

1000 bar

SVP

5

Pressure

68 Hydrothermal Experimental Data

Soly

Soly

TiO2 (anatase; rutile) in NaCl TiO2 in NH4OH; NaOH; Na(2.2–2.8)PO4

Quench

Quench

Immisc

Soly; Immisc; Cr.ph Soly

Soly

Soly

(UO3 + SO3) in D2O

(UO3 + SO3) in D2O

WO3

WO3 in HCl

WO2

Soly

UO3 in H2SO4

Quench

Quench; Sampl; Vis.obs. Vis.obs.

Sampl

Vis.obs.

Immisc

UO2SO4 in H2SO4

Vis.obs.

Vis.obs.; Quench Quench Vis.obs. Vis.obs.

Soly; Cr.ph; Immisc Soly soly Immisc

Immisc

Sampl

Soly

Vap.pr.

Vis.obs.

Vis.obs.

Vis.obs.

Wt-loss

3

UO2SO4

UO2(OH)2 UO2SO4 UO2SO4

UO2; UO2 in HCl, NaCl, NaOH, LiOH UO2F2

Tl2SO4

Tl2SO4

TlCl

Soly; Immisc Soly; Immisc Soly; Immisc Soly; LGE

Flw.Sampl

Soly

TiO2 in NH4F

TlBr

Sampl

2

1

Methods

Phase equil

Non-aqueous components

Barsukova et al., 1979 Schuiling and Vink, 1967 Ziemniak et al., 1993

ptx-TiO2 + NH4F-1.1 ptx-TiO2 + NaCl-1.1 ptx-TiO2 + Na/ PO4,OH + NH4OH-1.1; 1.2 ptx-TlBr-1.1

494–512 C

495–517 C

496–507 C

278–408 C

280–350 C

150/200–290 C

286–468 C

286–413 C

973–1082 bars

1000–1320 bars

1007–1034 bars

SVP

SVP

SVP

SVP; 92–1429 bar

70–1768 bar

0.001–0.006 (W); 0.5–5.37 (HCl) m

0.001–0.005 (W) m

0.011–0.015 (WO2) m

0.02–0.2 (SO3) m; m(UO3)/m(SO3) = 0–1

0.07–4.5 (UO2SO3); 0.6–4 (SO3) m; m(UO3)/m(SO3) = 0.2–1 0.00015–1.28/1.32 (UO3); 0.0002–1 (H2SO4) mol/L 0.01–10 (SO3) m; m(UO3)/m(SO3) = 0.5–1.1

0.071–4.53 (UO2SO4) m

ptx-UO2(OH)2-1.1 ptx-UO2SO4-1.1 ptx-UO2SO4-2.1

1/15.9; 500 atm SVP 70–324 bar

(0.89/9.2) * 10−6 (U) m 6.9–9 (UO2SO4) m 0.14–4.53 (UO2SO4) m

25/200 C −38.5/150–287 C 286–318 C

ptx-UO2F2-1.1

SVP

−13/150–376 C

ptx-WO3 + HCl-1.1

ptx-WO3-1.1

ptx-WO2-1.1

ptx-UO2SO4 + H2SO4-1.1; 1.2 ptx-UO3 + H2SO4-1.1 ptx-UO3 + SO31.1; 1.2; 1.3; 1.4 ptx-UO3 + SO32.1; 2.2

ptx-UO2SO4-3.1

ptx-UO2-1.1

6.1–9.8 (UO2) (−log m); 0–0.11 (HCl); 0–0.016 (NaOH; LiOH); 0–0.099 (NaCl) m 5–83 (UO2F2) mass.%

∼50 MPa

ptx-Tl2SO4-2.1

ptx-Tl2SO4-1.1

ptx-TlCl-1.1

8

7

Wood and Vlassopoulos, 1989 Wood and Vlassopoulos, 1989 Wood and Vlassopoulos, 1989

Marshall et al., 1962b

Jones and Marshall, 1961a

Morey and Chen, 1956 Parks and Pohl, 1988 Marshall et al., 1954a Nikitin et al., 1972 Secoy, 1948 Marshall and Gill, 1963 Marshall and Gill, 1974 Marshall and Gill, 1974 Marshall, 1955

Benrath et al., 1937

Benrath et al., 1937

Benrath et al., 1937

REFERENCE

Table

100/200–300 C

18/29–100 (Tl2SO4) mass.%

4/9–100 (TlCl) mass.%

1.7/3.1–100.0 (TlBr) mass.%

0.001–11.0 (TiO2) µm; 0.58–110.6 (Phosphate); 7.75 (NaOH); 0.070; 0.752 (NH4OH) mm; Na/P = 2.2–2.8 (mol.ratio)

1.11–2.13 (Ti) ppm; 1 (NaCl) m

0.0004–0.13 (Ti(IV)); 0.55–2.35 (NH4F) m

6

Composition

L-G-S

SVP

SVP

SVP

8–9 MPa

SVP

400; 600 atm

5

Pressure

230; 272

400; 500 C

116/208–632 C

144/205–430 C

162/215–457 C

293/462–561.5 K

200; 300 C

225–400 C

4

Temperature

Phase Equilibria in Binary and Ternary Hydrothermal Systems 69

Sampl Sampl

p-V curves; Vis.obs. Wt-loss

Soly

Soly

Soly

Soly

LGE; Soly

H-Fl; LGE; Cr.ph H-Fl; LGE

Soly

LGE; Soly

Soly LGE; Soly

Soly; LGE

Soly

Soly; Immisc LGE

LGE

WO3 in KCl

WO3 in NaCl

WO3 in NaOH

WO3 + WO2

Xe

Xe

Xe

Xe in D2O

Xe in D2O Xe in UO2SO4

YCl3

YFeO3 in KOH

Y2(SO4)3; Y2(SO4)3 in UO2SO4 ZnCl2

ZnCl2 + SnCl2

Xe

Soly

WO3 in HCl

160/170–300 C

120/170–230 C

Sampl

Sampl

108/186–277 C

350–450 C

152/185–380 C

334/473; 476 K 100/260; 302 C 295/466 K 100/260 C

343/449–557 K

216–500 C

100/260; 302 C

499–502 C

487–522 C

490–505 C

499–506 C

300–600 C

4

Temperature

Vis.obs.

Sampl

Sampl

Vis.obs.; p-T curves p-X curves

Sampl

Quench

Quench

Quench

Quench

Quench

3

2

1

Methods

Phase equil

Continued

Non-aqueous components

Table 1.1

SVP

SVP

SVP

(partial pr.Xe) 0.6–1.2 MPa 2/3 MPa (partial pr.Xe) 1.2/1.75–1.9 MPa SVP (13–38 kg/cm2) 500–1500 atm

2/2.4–5.4 MPa

SVP

150–4100 bar

(partial pr.Xe) 0.6–1.5 MPa

1014–1027 bars

912–1068 bars

1007–1109 bars

1034–1054 bars

1 kbar

5

Pressure

0.0–14.0 (H2O) mass.%; ZnCl2/SnCl2 = 4 : 1 (mass. ratio)

61/83–97.2 (ZnCl2) mass.%

0.12–4.32 (Y2(SO4)3; 0–1.35 (UO2SO4) mass.%

0.016–0.49 (YFeO3)); 19–46 (KOH) mass.%

27.6–77 (YCl3) mass.%

0.00067; 0.54 mol.fr. 1.51–1.66 (Xe) mL/g; 40 (U) g/L

0.64–1.33 (Xe) mL/g D2O

0.0003–0.68 (Xe) mol.fr.

(19.5–30.0) * 10−5 (Xe) mol.fr.

3–77 (Xe) mol.%

1.12–1.54 (Xe) mL/g soln

0.004–0.007 (WO3/WO2) m

0.005–0.69 (W); 0.01–1 (NaOH) m

0.007–0.019 (W); 1; 6 (NaCl) m

0.009–0.012 (W); 1.0 (KCl) m

13–758 (W) mg/kg H2O; 0.001–05 (HCl) m

6

Composition

Wood, 1992

ptx-WO3 + HCl-2.1 ptx-WO3 + KCl-1.1

ptx-ZnCl2 + SnCl2-1.1

ptx-ZnCl2-1.1

ptx-YFeO3 + KOH-1.1 ptx-Y(SO4)3-1.1

Crovetto et al., 1982 Stephan et al., 1956

ptx-Xe + D2O-2.1 ptx-Xe + UO2SO4-1.1 ptx-YCl3-1.1; 1.2

Chufarov et al., 1953 Chufarov et al., 1953

Urusova and Valyashko, 1993a Dem’yanets et al., 1976 Jones et al., 1957

Stephan et al., 1956

Potter II and Clynne, 1978 Crovetto et al., 1982 ptx-Xe + D2O-1.1

ptx-Xe-4.1

ptx-Xe-2.1; 2.2; 2.3 ptx-Xe-3.1

ptx-Xe-1.1

ptx-WO3 + WO2-1.1

ptx-WO3 + NaOH-1.1

ptx-WO3 + NaCl-1.1

8

7

Wood and Vlassopoulos, 1989 Wood and Vlassopoulos, 1989 Wood and Vlassopoulos, 1989 Wood and Vlassopoulos, 1989 Stephan,E.F; Hatfield et al., 1956 Franck et al., 1974

REFERENCE

Table

70 Hydrothermal Experimental Data

Sampl; Potentio Sampl; Potentio

Soly

Wt-loss

Wt-loss

Wt-loss

Wt-loss

Vis.obs. Vis.obs. Wt-loss

Soly

Soly

Soly

Soly

Soly Soly

Soly

Soly

Soly

Soly

Soly Soly Soly

ZnO in NaOH

ZnO in Na(2.3–2.8)PO4

ZnS

ZnS in K2CO3

ZnS in KF ZnS in LiCl

ZnS in LiOH

ZnS in NaBO2

ZnS in NaCl

ZnS in ZnCl2

ZnSO4 ZnSO4 ZrSiO4 (Zircon)

Wt-loss Wt-loss

Wt-loss

Sampl

Quench; Wt-loss Sampl; Potentio Flw.Sampl

Soly

ZnO in NaOH

Quench

Soly

ZnO in NaOH

Soly

Sampl; Potentio

Soly

ZnO in (NaCF3SO3 + NaCl); ZnO in (NaCF3SO3 + Na2SO4) ZnO in NaCF3SO3 (Na trifluoro-methanesulfate) ZnO in NaCF3SO3 (Na trifluoro-methanesulfate)

3

2

1

Methods

Phase equil

Non-aqueous components

90/205–255 C 178/203–257 C 1000; 1100 C

360; 450 C

360; 450 C

360; 450 C

360; 450 C

360; 450 C 360; 450 C

360; 450 C

500 C

65/200–287 C

25/200–290 C

200–350 C

100/200 C

150/200–350 C

100/200 C

50/200, 250, 290 C

4

Temperature

SVP SVP 1; 2 GPa

550 bar

550 bar

550 bar

550 bar

550 bar 550 bar

550 bar

1000 bars

8–9 MPa

SVP

SVP

SVP

15/34–268 MPa

SVP

SVP

5

Pressure 8

7

50/25–5 (ZnSO4) mass.% 34/25.5–2.1 (ZnSO4) mass.% 0.12–6.9 (ZrSiO4) mass.%

0.175; 0.375 (ZnS) mass.%; [solution saturated with solid NaBO2 at 25 °C] 0.05; 0.08 mass.% (ZnS); [solution saturated with solid NaCl at 25 °C] 0.04; 0.08 (ZnS) mass.%; 3 (ZnCl2) m

0.10; 0.20 (ZnS) mass.%; 6 (KF) m 0.11; 0.28 (ZnS) mass.%; [solution saturated with solid LiCl at 25 °C] 0.40; 0.59 (ZnS) mass.%; 4.65 (LiOH) m

0.20; 0.64 (ZnS) mass.%; 3 (K2CO3) m

5.34/4.25–4.13 (Zn) (−log m); 5.35/0.03 (NaOH) m (2.11–11.32) * 10−6 (Zn) m; 0.55–53.0 (Phosphate) mm; Na/P = 2.2–2.8 (molar ratio) 0.17 (ZnS) mass.%

0.6 * 10−5–0.2 (ZnO); 0–0.96 (NaOH) m

ptx-ZnS + K2CO3-1.1 ptx-ZnS + KF-1.1 ptx-ZnS + LiCl-1.1 ptx-ZnS + LiOH-1.1 ptx-ZnS + NaBO2-1.1 ptx-ZnS + NaCl-1.1 ptx-ZnS + ZnCl2-1.1 ptx-ZnSO4-1.1 ptx-ZnSO4-2.1 ptx-ZrSiO4-1.1

Benrath, 1941 Jones et al., 1957 Ayers and Watson, 1991

Laudise et al., 1965

Laudise et al., 1965

Laudise et al., 1965

Laudise et al., 1965

Laudise et al., 1965 Laudise et al., 1965

Morey and Hesselgesser, 1951b Laudise et al., 1965

ptx-ZnO + NaOH-1.1 ptx-ZnO + NaOH-2.1 ptx-ZnO + NaOH-3.1 ptx-ZnO + NanPO4-1.1; 1.2 ptx-ZnS-1.1

Khodakovsky and Elkin, 1975 Plyasunov et al., 1988 Benezeth et al., 1999 Ziemniak et al., 1992b

ptx-ZnO + NaCF3SO3-2.1 ptx-ZnO + NaF3CSO3-3.1; 3.2

6.4–4.1 (Zn) (−log m); pH = 4.95–8.18/9.4 {ptx-3.1} 6.98–3.75 (Zn) [−log m]; pH = 4.65–9.12 {ptx-3.2} 7.96–3.07 (Zn) (−log m); pH = 3.13–10.76 0.0049–0.192 (ZnO) mm; 0–8.7 (NaOH) m

Benezeth et al., 1999 Benezeth et al., 2002

ptx-ZnO + NaCF3SO3-1.1 Wesolowski et al., 1998

REFERENCE

Table

3.32–2.17 (Zn) (−log m); pH = 3.65–6.76

6

Composition

Phase Equilibria in Binary and Ternary Hydrothermal Systems 71

72

Hydrothermal Experimental Data

Figure 1.1 High-pressure optical cell with a piston for static method of investigation (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins, Lentz, H. (1969) Rev. Sci. Instr., 40, pp. 371–372.). (a) schematic diagram of equipment including high-pressure optical cell with a piston (1), heater (2), pressure-temperature recorder (3), screw press (4), pressure gauges (5); piston position controller (6); valves (7); (b) high pressure optical cell – sapphire window (1), pressure vessel (2), thermocouple (3), piston (4) with platinum mirror (5), clod magnetic stirrer (6), cooling jacket (7). Arrows show inlets/ outlets for solution and cooling water.

Campbell and Bhatnagar, 1984; Barry et al., 1988; Abdulagatov and Azizov, 2004a,b, etc.). There are the arrangements (Morey and Chen, 1956; Liu and Lindsay, 1970; Campbell and Bhatnagar, 1979; Wood et al., 1984; Emons et al., 1986; Stepanov et al., 1996, etc.) that are designed exclusively to study the vapor pressure of solutions by comparing it with the known or measured vapor pressure of pure water. In fact, it is the vapor pressure lowering measurements for osmotic coefficient determination that is an alternative method to the isopiestic measurements. Phase equilibria data are extremely important not only because this is information about the state of the phases in the system under study, but also these data themselves provide the experimental basis of several physicochemical methods. It is a source of thermodynamic information that permits us to calculate the thermodynamic functions both for chemical equilibria and reactions, and for individual substances and aqueous species. Although methods of thermodynamic characteristic are not the subject of our review, some experimental methods to study phase equilibria and later determination of thermodynamic functions are so deeply intertwined that they should be mentioned in it. For example, even though the main objective of the isopiestic method is to determine the osmotic and activity coefficient of a solvent, the isopiestic technique is a precise measurement of the composition of liquid phase in liquidgas equilibrium. Some details of isopiestic apparatus used for hydrothermal measurements will be discussed later in ‘Methods of sampling’. Phase equilibria, particularly the solubility of sparingly soluble ionic solids can be calculated if the standard thermodynamic functions for aqueous species, the constants of

solubility (as well as any other equilibria where these species take part) and the activity coefficients are available. However, The thermodynamic view on solubility phenomenon requires different approach to its experimental investigations. Determination of solubility values is not the only task. Other aspects include understanding the solubility phenomena from the thermodynamic point of view. The experimental studies are accompanied with an estimation of the equilibrium constants and thermodynamic characteristics that permit us to consolidate and correlate all available thermodynamic data for those systems under study and to use those data for further thermodynamic calculations of solubility behavior and chemical reactions in multicomponent systems. Chapters 3–6, 8, 11–14 in the book Aqueous Systems at Elevated Temperatures and Pressures (Palmer et al., 2004) provide detailed analysis of interdependence and complementation of those thermodynamic calculations in hydrothermal solution and experimental measurements of phase equilibria in superambient conditions. When an ion of the added electrolyte interacts with one of the ions of the saturating salt, the activity of the latter is reduced, so that quantities of the saturating salt dissolve to satisfy the solubility constant expression. The correlation of quantities of the added electrolyte and the dissolved salt (or the concentration of solution obtained as a result of solubility measurements) permits us to study complex formation, identify the major species contributing to solubility and estimate the equilibrium constants. In aqueous systems the solubility of most inorganic compounds always depend on the pH, because if there is no H+ or OH− ions in saturating solid, they usually take part in complex formation.

Phase Equilibria in Binary and Ternary Hydrothermal Systems 73

Therefore the setup where the dissolution reaction is followed by potentiometric measurements of the pertinent H+concentration within the galvanic cell (glass electrode solution salt bridge reference electrode) is an optimal system for solubility measurements. This method is called ‘potentiometric method of solubility measurements’ (‘Potentio’ in Table 1.1). An example of such measurements could be that of solubility of metal oxides at temperatures up to 300 °C performed in ORNL using simultaneously sampling method and the hydrogen-electrode concentration cell (HECC). The details of such measurements and experimental setup can be found in Chapter 3 in this Book. 1.2.1 Methods of visual observation Methods of visual observation permit us to determine the phase constitution of a system and parameters of phase transformations, and to record an appearance (or disappearance) of phases and critical phenomena with changing temperature and pressure (‘Vis.obs.’ in Table 1.1). These are the typical synthetic method. The composition of equilibrium phases can also sometimes be determined from the known composition of the initial charge. Two types of apparatus are used for visual observations: those using a container with transparent walls (heavy, thickwalled glass capsule (sealed from both sides thick-walled tube) or cylinder (thick-walled tube) mounted between two headers with the necessary lead lines or sealed from one side and closed by the pressurizing liquid from another one) and those with special windows in stainless steel cells. For pressures up to 15–25 MPa, thick-walled capsules (6–3 mm o.d., 2-0.8 mm i.d., 2.5–5 cm length) or transparent tubes placed in the heating device may be used. The capsules are made of fused silica (Marshall et al., 1954a,b; Barton et al., 1961; Valyashko, 1990a, etc.) or Pyrex glass (Etard, 1894; Schroer, 1927; Kracek, 1931a,b,c; Akhumov and Vasil’ev, 1932; Benrath et al., 1937; Secoy, 1948; Marshall et al., 1954a,b; Bergman and Kuznetsova,1959, Sinke et al., 1985 etc.) capillary tubes. Known quantities of solid and liquid phases are introduced into the transparent container. The capsule is then frozen (in liquid nitrogen), evacuated and sealed. A setup with the transparent cylinder (quartz or sapphire tube) (Rebert and Kay, 1959; Roof, 1970; Aftienjew and Zawisza, 1977; De Loos et al., 1980; Huang et al., 1985; Dandge et al., 1985; Ng et al., 1985, etc.) is loaded in the same manner as the metallic autoclaves. Sometimes such apparatus is equipped with the assay chamber for sampling. Heating devices comprise thermostated metal blocks with a viewing slit and a resistance furnace (Etard, 1894; Schroer, 1927; Benrath et al., 1937; Marshall et al., 1954a,b; Abdulagatov and Magomedov, 1992, etc.) or transparentwalled thermostats. Such thermostat can be a stirred air bath (Kracek, 1931a,b,c; Akhumov and Vasil’ev, 1936; Bergman and Kuznetsova, 1959; Huang et al., 1985; Wang and Chao, 1990; Brown et al., 2000, etc.) or liquid thermostat with low-melting salt mixtures (LiNO3 (30 mass %), NaNO3 (14 mass %), KNO3 (56 mass %) (Tmelt = 113 °C) or NaNO3 (46 mass %), KNO3 (54 mass %) (Tmelt = 222 °C) (Clark et al.,

1959; Barton et al., 1961; Connolly, 1966, etc.) or with silicone oil (Pryor and Jentoft, 1961; Sinke et al., 1985). All the apparatus are equipped with special devices for stirring the contents of the capsules by rocking the furnace or shaking the capsule in the furnace or a Teflon-covered magnetic stirring bar in the case of a transparent cylinder. The error in the determination of phase transition temperatures in a capsule apparatus depends on the rates of phase reaction and variations in temperature as well as on thermal gradients along the capsule and between the capsule and the wall of furnace. The reproducibility of the temperature of such phase transitions as liquid immiscibility or critical phenomena is in the range of several tenths of a Kelvin for the best measurements. However, an error can reach ±1–2 K in most available publications on salt solubility measurements. Studies of aqueous systems using the sealed thick-walled capsules do not provide any information about the pressure. The influence of dissolution of the capsule wall on the composition and properties of the system under study is another complicated problem. At pressures above 15–25 MPa, stainless steel vessels with quartz (Ikornikova, 1975; Rabenau, 1981, etc.) or sapphire (Lentz, 1969; Alwani and Schneider, 1969; Marshall and Gill, 1974; Japas and Franck; 1985a,b; Gehrig et al., 1986; Young, 1978; Brunner, 1990; Armelini and Tester, 1991; Abdulagatov and Magomedov, 1992; Brill et al., 1995; Ridder et al., 1995; Bowman and Fulton, 1995; Bowers et al., 1995; Hodes et al., 1997; Moore et al., 1997; Brown et al., 2000, etc.) windows are used for visual observation. Diamond window cells are also used for studying solubility phenomena at low temperatures and very high pressures (Van Valkenburg et al., 1987) and under hydrothermal conditions (Bassett et al., 1993; Anderson, 1995; Shen and Keppler, 1997; Schmidt et al., 1998; Soweby and Keppler, 2002; Schmidt and Rickers, 2003). Solubility of sapphire and, especially, diamond in hydrothermal apparatus is considerably lower than that of quartz or fused silica. In many cases, these materials solve the problem of window corrosion; however, sapphire is unstable in alkaline hydrothermal solutions. This apparatus permit observation of the phase relations in a system with the registration of both temperature (precision ±0.2–1 K) and pressure (with ±0.1– 1%) on heating up to 500 °C and at pressures up to 350 MPa. One of the best multi-purpose visual cell was developed in the Institute of Prof. E.U. Franck in Karlsruhe (Figure 1.1) and used for a long time (Lentz, 1969; Japas and Franck, 1985a,b; Gehrig et al., 1986; Krader and Franck, 1987; Michelberger and Franck, 1990; Heilig and Franck, 1990; Shmonov et al., 1993; Sretenskaja et al., 1995; Brandt et al., 2000, etc.). It permitted us not only to observe the phase transformation and to record the temperature and pressure, but also to change and measure the reaction volume during an experiment by a displacement of the piston. The sample temperature inside the autoclave could be obtained to ±0.25–0.5 K. After considering a certain friction loss at the piston O-ring, the pressure could be determined up to 40 MPa to ±0.3 MPa and from 400– 350 MPa to ±0.5 MPa. The sample volume was determined

74

Hydrothermal Experimental Data

with an uncertainty ±0.4–0.7%. However, at pressures of a few tens of MPa and also at the highest pressures applied, the probable error could reach ±1.5% (Krader and Franck, 1987). Similar experimental set up (variable-volume windowed vessel) was described in McHugh and Krukonis (1994) and Brown et al. (2000). Various visual cells used to study phase equilibria in non-aqueous systems at elevated temperatures and pressures have been described in Young (1978) and Aim and Fermeglia (2003). The flow methods to study sub- and supercritical equilibria became very popular in the 1990s, and the optical cells have been widely used for investigation of phase behavior and hydrothermal reactions in connection with the problems of SCWO in flow systems (Wang and Chao, 1990; DiPippo et al., 1999; Brill et al., 1995; Ridder et al., 1995; Bowman and Fulton, 1995; Bowers et al., 1995; Hodes et al., 1997; McHugh and Krukonis, 1994; Kiran et al., 2000). The impetus for the design of the flow technique was the intention to reduce the time required to attain the desired state conditions and, sometimes, to reduce the residence time of the studied mixture in the high-temperature reactor that is especially important for systems with thermally unstable compounds and for reacting systems. Besides, the flow stream sweeps the contaminants dissolving from the inner part of the cell. However, it is necessary to consider that the flow methods have some limitations. First of all there is a limitation in pressure due to a pressure limit of the pumps that usually (for high-pressure liquidchromatography and differential proportioning pumps) does not exceed 30–50 MPa. Although the flow apparatus with sapphire windows equipped with a ‘hot finger’ (internally heated cylinder with the surface temperature approximately 15 K above the bulk temperature of flowing solution) was used for solubility measurements of Na2SO4 (the salt with a negative temperature coefficient of solubility in water) (Hodes et al., 1997; DiPippo et al., 1999), usually the high-temperature solubility of such salts should not be measured by the flow technique due to precipitation at high temperatures and plugging the flow in the system. In the static apparatus, the phase transitions in any system (either with a negative or positive temperature coefficient of solubility) can be studied, since the charge is placed only in the high-temperature part of the cell. When using the methods of visual observation, especially with capsule apparatus, particular attention should be paid not only to the composition of the charge but to the fill coefficient of the capsules. This latter condition (the ratio of volume of the charge to the volume of the vessel at room temperature) controls both the resulting pressure in the vessel and the mass relation between equilibrium phases at high temperatures. In sub- and supercritical equilibria, one should not neglect the considerable increase of vapor phase density with pressure. The larger the vapor volume, the more water evaporates and the more concentrated the liquid solution becomes. An approximate evaluation of the process can be made using mass and volume balance, data on the density of steam, the composition of the charge and the coexisting phase volumes at the experimental temperature.

The most exhaustive and accurate information about phase equilibria can be obtained by visual observation of the transformation from a two-phase system into a homogeneous one. If a critical phenomenon is involved or a homogenization takes place as a result of disappearance of the second phase, the parameters of phase transition correspond to the phase equilibrium, where the composition of the main solution is equal to the known composition of the initial charge and the second phase (the last crystal or the last drop of vapor or of second liquid) exists in a vanishingly small quantity. If the solid phase appears at high temperature and liquidgas (vapor) equilibrium, it can be separated from liquid solution (replaced into a gas (vapor) phase), cooled and used for determining the composition of solid phase (Etard, 1894; Akhumov and Vasil’ev, 1936; Ravich and Ginzburg, 1947). Sometimes such an approach can be used, as in the case of transformation of a three-phase into a two-phase equilibrium, where the quantity of the third phase is very small or can be taken into account in an estimate of the solution composition at the observed temperature from the composition of the initial solution. An example is a vapor phase at 200–300 °C if the transition takes place at the vapor pressure of the system. When the parameters of two-phase equilibria L-G and L1-L2 come close to their critical values, a considerable change of coexisting phase compositions takes place with changing temperature and pressure that makes it extremely complicated to use the composition of the initial solution to get an idea about the compositions of the subcritical phases. The method of direct visual observation can be used in conjunction with in-situ Raman spectra, X-ray absorption fine structure (XAFS) and X-ray diffraction measurements (Zotov and Keppler, 2000; Fulton et al., 2000; Schmidt and Rickers, 2003; Bassett et al., 2000; Mayanovic et al., 2003) to study salt solubility, metal ion hydration, complexation and oxidation state in aqueous solution in a wide range of temperatures and pressures, and with the hydrothermal scanning force microscopy technique (Higgins et al., 1998) for observation of the advance or retreat of atomic layers (steps) on a crystal surface during the processes of dissolution or crystal growth. 1.2.2 Methods of sampling To sample a hydrothermal solution means to take an aliquot from the bulk mixture without disturbing the equilibrium conditions in such a way that the composition of that sample could not be changed by interaction with the remains of mixture during cooling. Samples of hydrothermal solutions can be withdrawn during a high p-T experiment either by flow methods (‘Flw.Sampl’ in Table 1.1) or by static withdrawal of an aliquot of fluid (‘Sampl’ in Table 1.1). In the 1940s–1970s flow apparatus was used mainly in thermal power engineering laboratories for studying dissolution/precipitation processes (Spillner, 1940; Styrikovich et al., 1955; Styrikovich and Khokhlov, 1957; Aleinikov

Phase Equilibria in Binary and Ternary Hydrothermal Systems 75

et al., 1956; Martinova and Samoylova, 1962; Styrikovich and Reznikov, 1977, etc.). Steam generated in a boiler was pumped continuously into the reactor vessel, where the grains of the solid of interest were placed. It was a so-called one-pass flow system that could be used both for thermodynamic and kinetic studies. Similar one-pass flow apparatus was used for investigation of processes of liquid or fluid filtration through rocks at high temperatures and pressures (Zarikov et al., 1985; Ulmer and Barnes, 1987). A pressure generating system in such apparatus was a screw press. Flow method and liquid phase sampling at high pressures (up to 350 MPa) were used for solubility measurements in the geochemical experi-ments with an air operated hydraulic pump (Morey and Hesselgesser, 1951a,b; Currie, 1968). Modern designs of flow systems involve the pumps (usually, HPLC pump) for mechanically driven flow of the experimental solution through the reactor, either in a one-pass, or re-circulating configuration (Byrappa and Yoshimura, 2001; Aim and Fermeglia, 2003). Several pumps are used sometimes for a circulation of each phase (for instance, vapor and liquid) through external thermostated loops, where a portion of such a phase can be trapped (after equilibration) in a sampling cell for analysis. An external circulation of phase(s) makes the stirring more intensive (than in the case of one-pass flow) and decreases the equilibration time. Besides, the phase circulated through an external loop already represents a separated equilibrium phase that facilitates taking samples for an off-line analysis or to carry out an on-line analysis without disturbing the phase stream in the circulation loop, if a suitable detection method (such as continuous spectrometry, densitometry, refractometry) is available. A typical plug-flow solubility apparatus consists of a set of compartments and devices, connected in sequence: a reservoir for feed solution, an HPLC pump to deliver the feed solution to a heat exchanger (preheater) and through a reactor, and a pressure gauge for pressure measurements. Then there is a high-temperature compartment, which consists of a preheater and reactor (saturator) with the species of solute and a filter for separation of solid particles from the flow solution; followed by a low-temperature compartment – a sampler(s), a backpressure regulator to maintain a constant pressure in the system and an outlet solution reservoir. Figure 1.2 shows a schematic diagram of such flow apparatus for measurements of equilibrium phase composition in a heterogeneous mixture (Christensen and Paulaitis, 1992). The high-pressure view cell has an internal volume of approximately 60 mL and is contained in a constant temperature nitrogen bath. The liquid solute and solvent are compressed and delivered to the view cell by two reciprocating, positive displacement pumps through 24 m of 0.76 mm i.d. stainless steel tubing (a preheater) positioned in a thermostat. Sample lines of the same tubing exit the top and the bottom of the cell. A back-pressure regulator controls flow of the top phase out of the cell, and a micrometering valve sets the flow rate of the bottom phase and thereby controls the height of the meniscus in the cell. Samples are collected in loops made of approximately 12 m of coiled 0.76 mm i.d. stainless-steel tubing.

Solute container

Solvent container

Pump

Pump

Mixing tee Preheater THERMOSTAT

Pressure gauges HPLC Back-pressure regulator valve Waste

Sample loop Sample loop Equilibrium view cell

Micrometering valve HPLC valve Waste

Figure 1.2 Schematic diagram of the flow apparatus for phase composition measurements and critical point observations with a thermostated view cell (equipped with sapphire windows) and two sample loops for collections the samples of both the lighter (gas) and heavier (liquid) phases (Christensen, S.P. and Paulaitis, M.E. (1992) Fluid Phase. Equil., 71, pp. 63–83. Copyright Elsevier).

In the case of the recirculation method the thermostated high-temperature compartments include the circulation loop(s) with a pump (usually, it is a magnetically operated high-pressure pump) and the facilities for sampling (sometimes from the different levels of reactor) and for switching the regimes of flow. If the feed solution is an aggressive, to avoid a contact with the pump, the feed solution is contained in collapsible (polyethylene) bag, inside a stainless-steel high-pressure displacement cell. A HPLC pump is used to pump pure water into the displacement cell and the solution is pressed out into the line and pumped through the reactor (Bussey et al., 1984; Shvedov and Tremaine, 2000). The recirculation method makes the stirring and contacting of the phases more effective and reduce the period of equilibration. Sample withdrawal of each phase from the heterogeneous fluid mixture can be dangerous in a general case due to entrainment of droplets (or bubbles) of the second phase. To avoid this the special geometry of the feed inlet port or of cell itself is designed. For liquid-gas mixture a suitable porous filter is locked in the top part of the cell. The sampling of the equilibrium phases in the recirculation method is substantially facilitated because the phase circulated through an external loop already represents a separated equilibrium phase. A portion of such a phase can be easy trapped in a compartment and taken for analysis. In Wesolowski et al. (2004) the following major advantages of such flow systems are indicated: high solid/liquid ratios shorten equilibration times and the flow rate can be varied to verify equilibrium; the system can be flushed at temperature and pressure with large volumes of solution to

76

Hydrothermal Experimental Data

remove contaminants and ultra fine particles; large samples can be accumulated for subsequent concentration; two-fluid phase or single-fluid phase p-T conditions can be maintained and p, T and flow rate can be varied independently during a single experiment; and online analysis methods can be configured into the flow path. Although most measurements using flow methods resulted in characterization of reaction kinetics or stationary processes, a number of high-quality solubility data in aqueous mixtures at high temperatures and pressures were also produced (Tremaine and LeBlanc, 1980a,b; Galobardes et al., 1981a,b; Christensen and Paulaitis, 1992; Stefansson and Seward, 2003a,b,c, etc.). Nevertheless, the most of data on hydrothermal solubility of solid phases have been obtained by static sampling methods, which can be used for determination of both liquid and vapor phase compositions. Data on the composition of high-temperature solid saturated solutions in ternary and more complex water-salt systems have also been obtained, using mainly apparatus that allow sampling the liquid phase under static conditions. The designs of static equipment for sampling described further can be grouped into three types according to how temperature and pressure in the reaction volume and in the sampler (or in the equilibrium mixture and the sample) are compared.

Figure 1.3 Schematic diagram of apparatus for solubility determination by method of sampling with temperature and pressure drops (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins). (1) pressure vessel, (2) rocking furnace, (3) thermocouple well, (4) sample tubing for liquid and vapor solutions, (5) sample line heater, (6) condenser, (7) valve, (8) sample collector, (9) pressure gauge.

1.2.2.1 Sampling with temperature and pressure drops Figure 1.3 is a schematic diagram of the simplest version of apparatus to study composition of phases in heterogeneous hydrothermal equilibria (Olander and Liander, 1950; Stephan and Miller, 1952; Gill and Marshall, 1961; Sourirajan and Kennedy, 1962; Anderson et al., 1962; Barnes, 1971; Cramer, 1980; Chen and Marshall, 1982; Crovetto et al., 1984; Sugaki et al., 1987; Giordano and Barnes, 1979; Castet et al., 1993; Palmer and Simonson, 1993; Simonson and Palmer, 1993; Brunner et al., 1994, Chandler et al., 1998; Byers et al., 2000, etc.). For that apparatus, the experimental procedure includes charging the autoclave (1), attaining the operating conditions and equilibrium in the system and, finally, sampling the high-temperature solutions through the capillaries (4) and valves (7) into the sample collectors (8). Separate runs are performed to determine the time of for equilibrium to be established. The evidence of the achieved equilibrium in the system is consistency in the composition of collected samples. Stirring, required during the experiment, is discontinued before sampling to allow suspended particles to settle. Sometimes the sampling tube is equipped with a filter, the sample line heaters (5) and condensers (6). At the moment of sampling and pressure drop, the temperature decreases since some water evaporates to compensate that drop. These changes are small in smaller volumes and bigger in larger volumes. Presence of a vapor phase, which exhibits small variations of properties during the volume change, is a required condition for employing this apparatus (Figure 1.3) to obtain reliable data on the composition of high-temperature solutions.

However, this drop of both pressure and temperature is the main problem in using such simple apparatus. The resulting crystallization and boiling processes may lead to considerable changes in the sample composition. To decrease these changes as well as to prevent spattering and evaporation the portions of fluid removed should be cooled rapidly during sampling. Therefore, strong limitations are imposed on the use of this equipment in relation to temperatures, compositions of solutions being sampled and volume of samples. The apparatus is most appropriate for studying solubility of slightly soluble compounds, dilute solutions of which tend to supersaturate, and for compounds with a negative temperature coefficient of solubility. 1.2.2.2 Sampling with pressure drop In the following group of apparatus, so called ‘hydrothermal bombs with sampler devices’, some of the above-mentioned problems were solved by using a hermetic sampler, a component of the hydrothermal bomb that is placed in a hot part of the apparatus (Waldeck et al., 1932; Schroeder et al., 1935; Ravich and Borovaya, 1959; Ravich and Yastrebova, 1961; Bernshtain and Matsenok, 1961, 1965; Itkina, 1973; Ravich, 1974; Broadbent et al., 1977). The pressure drop takes place at the moment of opening the empty sampler after equilibration of the hydrothermal mixture. The presence of a vapor phase to compensate for the increase in volume of the system when the sampler opens is a necessary condition for using hydrothermal bombs. Evaporation of the first portion of solution equalizes the pressure in the sampler

Phase Equilibria in Binary and Ternary Hydrothermal Systems 77

Figure 1.4 Two-chamber pressure vessel for solubility determination by method of sampling with pressure drop: (a) hydrothermal bomb for sampling noncrystallizing saturated solutions (Ravich and Borovaya, 1959); (b) hydrothermal bomb for sampling crystallizing saturated solutions (Ravich, M.I. and Yastrebova, L.F. (1961) Zh. Neorgan. Khimii, 6, n.2, pp. 431–437. Reproduced by permisson of MAIK / Nauka Interperiodica): (1) pressure vessel where the charge is placed (reactor), (2) thermocouple well, (3) filter from pressed fine silver wire, (4) channel between two chambers, (5) sampler, (6) valve needle, (7) valve packing (Teflon, asbestos with graphite), (8) screw, (9) extension tube; (10) separable stainless steel cup for a sample of crystallizing solution, (11) screw stopper.

and in the reaction space of the bomb. The pressure of the vapor is not measured in most apparatus. Figure 1.4 shows the examples of hydrothermal bombs with sampler devices. The first two-chamber pressure vessel (Figure 1.4a) is an apparatus designed for sampling of noncrystallizing saturated solutions occurring in the systems, where the solid phase has negative temperature coefficient of solubility. The second hydrothermal bomb (Figure 1.4b) is an apparatus for sampling of saturated solutions of any kind of solid phases. The apparatus contains an empty sampler isolated from the main vessel of the bomb by a valve needle until equilibrium is established. Before the liquid phase is sampled, the bomb is set in a vertical position with the sampler at the bottom. The sampler channel is opened for a few minutes and the liquid phase, after flowing through a dense filter, is injected into the empty sampler. Stainless steel mesh or frit (Schroeder et al., 1935; Stephan and Miller, 1962; Ulmer, 1971; Susarla et al., 1987), sintered Teflon (Dickson et al., 1963), porous ceramics (Voigt et al., 1985) or a fine silver wire (Bernshtain and Matsenok, 1961, 1965; Itkina, 1973; Ravich, 1974; Valyashko, 1990) pressed into the sampler channel have all been used as filtering materials. Extension

tubes (9) in Figure 1.4(a) are clamped to the sampler to allow sampling of solutions from a certain level of liquid, and are important for studying compositions of immiscible liquids. The presence of vapor makes this technique efficient for an accurate determination of salt solubility in water at temperatures and pressures where salt solubility in the vapor can be neglected and where an estimate can be made of the amount of water transforming into vapor. The pressure of the vapor is not measured in most of the apparatus. Sampling of highly concentrated liquid phases causes some experimental problems. When the sampler opens, a rapid evaporation of the first drops of filtered solution occurs. Salt crystals can plug the filter and sampling is stopped. In some cases, this could be overcome by either preliminary pumping of inert gas at high pressure into the main vessel of the bomb to force liquid through the filter or by an adding of a small quantity of water into the sampler to create a vapor pressure to prevent rapid evaporation of those first drops of the solution on the filter. However, this water has to be marked with an alternative salt to be further easily detected by chemical analyses as an addition to the real sample.

78

Hydrothermal Experimental Data

1.2.2.3 Sampling without temperature and pressure drops It is evident that an optimum method of sampling is sample withdrawal without any change in temperature and pressure. This can be achieved either by placing an open sampler inside main reaction vessel or by maintaining it at the same temperature and pressure during a separation the part of equilibrium phase. In such design only one of the equilibrium phases try to be sampled and be closed without changing either temperature or pressure. One of the first versions of such set up was a hydrothermal reactor with two chambers connected by a narrow aperture that can be closed by a valve at equilibrium temperature and pressure (Copeland et al., 1953). This apparatus was used to study the compositions of liquid and vapor in twophase equilibrium. In a vertical position of autoclave the sampling chamber, separated by a valve, could be filled by either liquid phase or vapor phase only, whereas main chamber contains both phases. A separation of the contents of these chambers by a valve permitted to keep the sample of liquid or vapor for analysis after cooling. A recent example of a similar apparatus is in Figure 1.5. It is designed to study salt solubility in homogeneous vapor phase or supercritical fluid at temperatures up to 500 °C and pressures up to 1000 bars (Zakirov and Sretenskaya, 1994; Pokrovski et al., 2002). The inner volume of the highpressure vessel – a reactor (made of titanium alloy) is about 120 cm3, whereas the inner volume of the sampler (10) can be varied from 1 to 20 cm3 depending on the task imposed. The sampler can be opened at any time during the experiment with the so-called ‘hot’ valve. Sealing of the valve in the high temperature zone is provided by graphite washers (Graflex seals) (8), attached to the valve rod (7) by sleeve (5) with a packing nut (9). The lock needle (4) is a square in external cross-section and is connected with the valve needle (7) by means of a thread. Thus, the lock needle (4) only moves (without rotation) when the valve rod (7) rotates, providing a constant inner volume of the reactor. A solid phase can be placed on the bottom of the reactor and equilibrium aqueous solution can be sampled at any stage of the experiment. To obtain a larger volume of sample, the solid

Figure 1.5 Scheme of apparatus for sampling without pressure and temperature drops (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins, Zakirov, I.V. and Sretenskaya, N.G. (1994) In “Experimental Problems of Geology”, Nauka, Moscow, pp. 664–667.). (1) high pressure vessel, (2) coupling nut, (3) seal ring, (4) lock needle, (5) sleeve gate, (6) sealing cap, (7) valve needle, (8) washer, (9) nut, (10) sampler.

phase can be placed in the sampler (10) and locked. At high temperatures, the sampler can be open and the salt comes in contact with steam. After equilibration the sampler, with the remains of the solid, is locked up again and all the solution in the reactor can be used for determination of solution composition. Similar kind of sampling method was utilized by Migdisov et al. (1999) for solubility measurements of salts in undersaturated water vapor at temperatures 300–360 °C with the only difference being that the solid was placed not in the sampler, which could be locked and open, but in open-ended platinum or quartz ampoules positioned near the top of the autoclave. After each run, the autoclave was quenched rapidly by air-cooling or placing it in a cold-water bath. The condensates from the autoclave interior of the autoclave were washed for chemical analysis. An instrumental method described in (Booth and Bidwell, 1950; Malinin, 1962; Akolzin and Mostovenko, 1969), also used to determine salt solubility in water and hydrothermal solutions without pressure and temperature drops. In this method the solid is transferred from liquid to vapor and back by rotating the reactor or by moving solid phase. After reaching the experimental parameters a solid phase was brought into contact with liquid and then transferred to the vapor phase when equilibrium is established. After that, the reactor is cooled down rapidly. Solubility is determined both by a weight loss in solids and by chemistry of the solution, taking into account the fact that some water has vaporized at high temperatures. The evident disadvantage of this instrumental method is the combination of sampling and quenching, which may lead to a significant dissolution of salt in vapor at high parameters. However, it is known from experience (Booth and Bidwell, 1950; Akolzin and Mostovenko, 1969; Malinin, 1962) that the use of this instrumental method for the solubility determination of slightly soluble compounds, even in a homogeneous supercritical fluid (below 450 °C), gives quite reasonable results with the estimated error of the order of ±3%. Apparently, this is due to the fact that the abrupt cooling makes the fluid pass into the two-phase state so rapidly that the crystal ended up instantly in the vapor space, so there is no precipitation happens on them. A simpler version of an apparatus for solubility determination of slightly soluble substances in heterogeneous water and aqueous solutions was developed by Seward (1976) and slightly modified by Gammons et al. (1993). Solid phase of solute in the form of a pressed pellets and aqueous solution were sealed in a silica glass tube, having a slight constriction near one end or at the midpoint of its 20 cm length. The sealed tubes were placed inside a stainless steel pressure vessel, containing 5–10 mL of water in order to minimize any pressure difference between the inside and outside of the tubes. The pressure vessel was heated in a thermostated oven to reach equilibrium in the system. After that the autoclave was removed from the oven, inverted and quenched. A narrow constriction of each tube allowed for the conventional separation of liquid solution and solid phase after inverting the tubes. There are two limitations in application of this method: the solvent should be heterogeneous (liquidvapor) and the solid solubility in one of the equilibrium

Phase Equilibria in Binary and Ternary Hydrothermal Systems 79

phases should be negligible to measure a solubility of the solid in the second one. The next instrumental method within the discussed group is the one developed by Morey and Hesselgesser (1952) (Rowe et al., 1967) and used for studying solubility in the system Na2O-SiO2-H2O where solid Na silicates were in equilibrium with a heterogeneous fluid. A reactor contains a support for cylindrical platinum loosely covered crucible with known quantity and composition of sodium silicate glass. The reactor was then put into a furnace and connected to the pressure water line, but water was not pumped in until the reactor was at the required temperature. At the end of the experiment, the furnace was dropped down from the reactor for it to cool quickly. During cooling, most of the gaslike fluid condensed on the walls and ran down to the bottom of the reactor. A small amount of this fluid also condensed inside the crucible on the top of a gel-like concentrated liquid. This low-density condensate was further removed with a pipette. In this way separation of the heterogeneous fluid was obtained. Another version of the apparatus (Rowe et al., 1967) was equipped with a small cup placed on a top part of the reactor in a vapor space, so that the liquid phase can enter the cup only when the bomb was tilted to pour liquid into the cup. The bomb was then returned to an upright position and quenched in ice water. The apparatus for solubility measurements in multicomponent water-salt systems at saturation vapor pressures and temperatures below 250 °C was described by Voigt et al. (1985) and Freyer and Voigt (2004). The main advantage of this setup is the possibility of forcing the liquid phase through a filter into the second chamber, leaving the solid and vapor phases in the main volume of the autoclave. The separation of solid and liquid phases is achieved by centrifugation of a two-chamber autoclave with solid-liquid mixtures. A valve closes the aperture between those chambers immediately after discontinuing the rotation. Thus, this apparatus makes it possible to obtain reliable information about composition of the high-temperature liquid and the solid phase at equilibrium. To obtain samples of saturated solutions at constant pressure, especially, at pressures exceeding the vapor pressure of saturation, it is necessary to produce special devices for maintaining the pressure in the system during sampling (Dikson et al.,1963; Blount and Dickson, 1969; Seward, 1974; Blount, 1977; Anderson and Prausnitz, 1986; Ulmer and Barnes, 1987; Bourcier et al., 1993). Figure 1.6 is a schematic diagram of this flexible cell system. An important element of its design is a bellows or bag made of Teflon or gold (3), i.e. a device capable of changing its volume and transferring the pressure. In the case of solid solubility studies, liquid and solid phases come to equilibrium in the deformable sample cell (bag) (3) held in a stainless steel pressure vessel (1). The bellows or bag isolates the aqueous mixture inside from the water outside. An internally filtered liquid sample can be withdrawn without significant disturbance at the equilibrium temperature and pressure, by pumping water into the steel vessel at the same rate that saturated solution is removed from the cell. Another complex design apparatus for sampling without any change of temperature and pressure by isolating a part

Figure 1.6 Schematic diagram of flexible cell system for solubility determination at elevated pressure by method of sampling (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins. Dickson, F.W., Blount, C.W. and Tunell, G. (1963) Amer. J. Sci., 261, pp. 61–78; Blount, C.W. and Dickson, F.W. (1969) Geochim. Cosmochim. Acta, 33, pp. 227–245.). (1) pressure vessel, (2) rocking furnace, (3) flexible sample cell (Teflon, gold), (4) thermocouple well, (5) sample tubing, (6) capillary pressure line, (7) separator, (8) pressure gauge, (9) valve, (10) electromagnet, (11) clad magnetic stirrer.

of the volume in the high-pressure vessel at temperatures up to 400 °C and pressures up to 100 MPa was described in (Zharikov et al., 1985). The device for sealing the capsules is placed in a high-pressure vessel where dissolution of the solid occurs in homogeneous fluid under specified conditions. Hermetic sealing of the capsules (of silver, gold or other thermostable plastic materials) is carried out in the experiment by the special clamps, which are actuated by moving the rod. The same clamps may be used for constricting the sealed capsules in the high-pressure vessel and for separation of the liquid phase from crystals. Method of synthetic fluid inclusions. This method also belongs to those of sampling without temperature and pressure drops (‘Fl.inclus.’ in Table 1.1). In the method the equilibrium fluids are sampled at high temperatures (up to 1500 °C) and pressures (up to several hundred MPa) using the ‘healing and trapping’ ability of fractures in quartz pieces placed with the experimental solution into a capsule (Bodnar et al., 1985; Ulmer and Barnes, 1987; Zhang and Frantz, 1989). The inclusion-free cores of natural or artificial quartz are placed into 5 mm diameter platinum capsules. A small

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amount (up to 20 mg) of crushed quartz or silica gel is added to the capsule to promote fracture healing. Approximately 10–50 microliter of the under study salt solution is injected into the capsule which is then welded to seal it. The loaded capsule is placed in a cold-seal or internally heated pressure vessel and taken to the experimental conditions. The p-T path followed during heating of the samples from ambient conditions to the final conditions is found to have an important effect on the type of inclusions formed. The pressure at any given temperature is recommended to be well above the region of heterogeneous fluid. As the desired temperature is reached, the pressure is then decreased rapidly to the desired value. Samples are run for 2–10 days with longer durations corresponding to lower temperature experiments. At the final stage of the experiment, the system is quenched. Then the capsules are weighed to check for leakage and the quartz removed from the capsules to be cleaned and dried to prepare for petrographic and microthermometric analyses of the synthetic inclusions of those trapped fluids. The method of synthetic inclusions permits us not only to determine the phase equilibrium in studied system at high temperatures and pressures, and phase transition if the experimental conditions are changed, but also to estimate the composition of high-temperature phases. Salinities of the two coexisting fluids at room temperature can be obtained by microthermometric (heating and freezing) experiments on those inclusions, since they have trapped a homogeneous fluid phase at the high temperatures. Isopiestic measurements. High-temperature isopiestic method could be considered as an instrumental method among other methods of sampling without temperature and pressure drops to study liquid-gas equilibrium (‘Isopiest’ in Table 1.1). One of the electrolyte solutions present in the isopiestic vessel is a reference since its vapor pressure is known under the conditions of the experiment. The compositions of the solutions placed in the same vessel change during equilibration due to a redistribution of water between liquid solutions to reach the common vapor pressure at the constant temperature. The equilibrium composition of the isopiestic solutions could be measured at the experimental or at the room temperature if the samples of isopiestic solutions carefully preserved and analyzed in order to determine the concentration (isopiestic molality) at the equilibrium, isopiestic vapor pressures and activity coefficients for the electrolytes. In the ORNL’s isopiestic system (Holmes et al., 1978; Holmes and Mesmer, 1986), operating at temperatures and pressures up to 250 °C and 3.5 MPa, a number of electrolyte solutions, placed in different metallic cups, attain an equilibrium with a common vapor phase at a well-controlled temperature. The equilibrium compositions are determined by weighing the cups in place (inside of the pressure vessel) with an electromagnetic balance calibrated frequently using a set of standard masses interspersed with the solution cups (Figure 1.7). The design of a much simpler isopiestic vessel that can operate at temperatures up to 150 °C is described in (Groitheim et al., 1978). This apparatus is really a sampling

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Figure 1.7 Isopiestic system with in situ electrobalance and a number of sample cups in well-thermostated vessel (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins. Holmes H.F., Baes, C.F. and Mesmer, R.E. (1978) J. Chem. Thermod., 10, pp. 983–996; Holmes, H.F. and Mesmer, R.E. (1986) J. Chem. Thermod., 18, pp. 263–275.). (1) light source, (2) sapphire window, (3) platinum mirror, (4) electromagnet, (5) isopiestic vessel, (6) thermostat block, (7) cups with solutions, (8) calibrating weights, (9) dual photocell, (10) current controller, (11) standard resistor, (12) voltmeter.

system, because each cup placed in the thermostated isopiestic vessel is closed with a special lid under high temperature conditions and the samples of solutions are cooled for chemical analysis. The lid-lowering mechanism closes all caps at the same time even if there are small differences in the height of the cups. 1.2.3 Methods of quenching Methods of quenching are based on the possibility of fixing and keeping unchanged the phase assemblage present during an experiment at high temperatures and pressures by fast cooling and subsequent study of quenched phases under normal conditions. Such methods are acceptable for studying systems with low rates of phase reactions. Systems with high-temperature liquid phases quenched in glass are the most favorable. Therefore, methods of quenching are widely used in mineralogy and petrography for studying hightemperature equilibria in aqueous systems with silicates and aluminosilicates. Common water-salt systems of readily soluble compounds, such as NaCl, K2SO4, KOH, cannot usually be quenched and change their phase state and solution composition even at the highest rates of cooling. It was observed that some saturated solutions of slightly soluble compounds can maintain a state of supersaturation during an abrupt cooling of the system. This phenomenon is used in quenching versions of the weight-loss methods in which a dissolving crystal is not isolated from the solvent. It is assumed that the solubility of the solid phase is reached at equilibrium rather than in the process of heating or cooling, and there is no precipitation on the surface of the weighed crystal even when a solid phase forms from supersaturated solution. Those assumptions make the solubility data less reliable. Special work, such as a study of the interactions among solutions, crystals and quenched phases, is needed. Such solubility determinations are carried out in high-pressure vessels (Morey type bombs) with volume of 50–500 cm3 (Gavrish and Galinker, 1955; Laudise, 1970; Ikornikova, 1975; Rabenau, 1981; Sergeeva et al., 1999,

Phase Equilibria in Binary and Ternary Hydrothermal Systems 81

etc.) or in small-sized platinum or gold capsules placed in the cold-seal pressure vessel with an external heater or in the internally heated pressure vessel (Barns et al., 1963; Anderson and Burnham, 1967; Ayers and Watson, 1991; Fleet and Knipe, 2000, etc.). The weight-loss method (‘Wt-loss’ in Table 1.1) is also widely used for solid solubility measurements in liquid-gas mixtures as it was for the sampling technique. The advantage of weight-loss procedure in the case of sampling technique consists in the possibility of replacing the solid phase from liquid into vapor phase during cooling. In experiments with a quenching version of the weight-loss method the solid phase is in direct contact with a saturated (supersaturated) liquid solution. The purpose of the majority of quenching experiments (particularly, with aqueous silicate and aluminosilicate systems) in capsules is not the solubility measurements, but a determination of phase relations in the multi-component systems at high parameters. Only in some cases, methods of microanalysis make it possible to determine compositions of quenched liquid and fluid phases. Defining a phase boundary on a diagram is usually done by drawing a line between the points corresponding to various phase associations. The uncertainty of those phase boundaries depends not only on the experimental errors, but also on the density of the points on the diagram.

A very important feature of capsule techniques in quenching experiments is the possibility of using the buffers. Buffers are the additional phases placed in a charge capsule or in the second capsule in the experiments with hydrothermal systems to control the activity of some components. Most often it is the acidity of aqueous fluid. This approach to the study of natural hydrothermal systems, where the activity of one (or several) of the system’s component(s) (for example pH or fugacity of O2, H2, S2, CO2) is under control of special reactions, was developed by Eugster (1957) and is widely used in experimental geochemistry. Details of the buffer technique have been reviewed by Huebner (Ulmer, 1971) and by Eugster et al. (Ulmer and Barnes, 1987). Figure 1.8 shows the construction of a cold-seal vessel originally developed by Tuttle (1949). Most hydrothermal research in experimental petrology at pressures up to 300 MPa and at temperatures below 900 °C has been conducted in such relatively simple autoclaves where the sealed capsules with charges are placed. Specially modified equipment of this type permits the attainment of pressures up to 1000 MPa at temperatures below 750 °C. The most important change in the traditional design of cold-seal vessels is the possibility of conducting the internal isobaric quenching of samples by displacing the capsules from a hot to a cold region under experimental conditions

Figure 1.8 Schematic diagram of cold-seal pressure vessel for high temperature/high pressure phase equilibria studies with quenching method (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins). (1) pump, (2) pressure intensifier, (3) valve, (4) pressure gauge, (5) furnace, (6) thermocouple, (7) device for quenching, (8) high pressure cold-seal vessel, (9) stainless steel filler rod, (10) sealed capsule with a charge, (11) cold seal vessel for internal isobaric quench, (12) electromagnet supported filler rod and capsule in a hot region of vessel during experiment.

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(Ulmer, 1971; Ulmer and Barnes, 1987). To achieve this, the internal channel in the room temperature part of the high-pressure vessel is extended (see Figure 1.8). During the experiment the sealed capsules and a stainless-steel filler rod that damps water convection in the vessel are maintained in the thermostated hot region by an external electromagnet or by turning the autoclave. Upon switching off the electromagnet or turning the autoclave, the ampoule and filler rod fall down and enter the cold region of the channel where isobaric quenching takes place. One may note some other technical parts such as an electromagnetic device for shaking the capsule (Zharikov et al., 1985) to accelerate the reaction and to decrease the time for the equilibrium to be established. Detailed description of the device and experimental techniques for cold-seal vessels can be found in reviews by Kerrick (Ulmer, 1971; Ulmer and Barnes, 1987) and in the book (Zharikov et al., 1985). The other widely used equipment for studying equilibria in aqueous systems by the method of quenching at temperatures up to 1000–1200 °C and pressures up to 1000– 1500 MPa consists of internally heated pressure vessels of the gas media type. The experimental conditions in the equipment lie between and overlap those of the pistoncylinder systems for higher pressure (the low-pressure limit is 500–1000 MPa) and externally heated pressure vessels, such as cold-seal types, for lower temperatures and pressures. The vessel is a metallic cylinder with outside diameter 15–30 cm and inside diameter 2.5–5 cm. The length is about twice the outside diameter. The actual pressure seals are attached to the heads. Electrical leads to provide power to the furnace and to measure the temperature pass through the heads as well as inlets for the pressurizing medium (usually argon gas). A resistance furnace is placed inside. Those vessels are capable of holding samples of up to 30 cm3 volume at very high temperature and pressure for long periods of time. These are the main advantages of the equipment, although the system is one of the most difficult p, Tsystems to operate and maintain. In spite of these difficulties, geochemical laboratories use internally heated pressure vessel systems because the desired experimental conditions cannot be achieved with other types of equipment. The most

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comprehensive reviews of the design and operation of these systems are provided by Holloway (Ulmer, 1971), Lofgren (Ulmer and Barnes, 1987) and Chapter II.1 in Zharikov et al. (1985). 1.2.4 Indirect methods The type of correlation between experimentally measured variable parameters in the system is changing as a result of phase transformations within that system. The indirect methods are used to identify the changes in those correlations. For example, the p-V-T-x curves (pressure as a function of temperature (p-T curves); pressure or temperature as a function of volume (p-V or T-V curves); pressure drop during salt dissolution as a function of solution composition (p-x curves)) show a break at the location of the phase transformation. Not only pressure or temperature or composition could be considered as variables. The properties of the solution or the whole system itself as well as heating or cooling period in thermal analysis can be used as variables to find the phase transitions. 1.2.4.1 Methods of p-V-T-x curves The first apparatus with mercury as a pressure medium (liquid piston) for phase equilibria measurements at high temperatures and pressures was developed by Benedict (1939), who has studied the vapor pressure of solid saturated and unsaturated water-salt solutions at temperatures up to 600 °C using the method of p-V curves. The systematic investigation of vapor pressures of a series of aqueous salt solutions at high temperatures with the same apparatus was continued by Keevil (1942). Ravich and Borovaya (1964a), by carrying out experiments in newly designed autoclave with mercury for studying water-salt equilibria at temperatures up to 600 °C and pressures up to 200 MPa (Figure 1.9), showed various applications of the p-V-T-x curve methods. This autoclave consists of a rocking furnace with a highpressure vessel (1, 2 in Figure 1.9) connected to a manometer (6) by means of a capillary tube (4). The capillary and a part of the autoclave are filled with mercury, which is inert

Figure 1.9 Schematic diagram of autoclave for p-V-T-x measurements (Ravich, M.I. and Borovaya, F.E. (1964a) Zh. Neorgan. Khimii, 9, pp. 952–974. With permission from MAIL / Nauka Interperiodica). (1) high pressure vessel, (2) rocking furnace, (3) thermocouple well, (4) capillary filled by mercury, (5) valve for admission and release of mercury, (6) pressure gauge, (7) capsule with holes (for crystals).

Phase Equilibria in Binary and Ternary Hydrothermal Systems 83

to aqueous salt solutions at high temperatures and used as pressure media and solution agitator. The vapor pressure of Hg is not high but it increases rapidly with temperature (0.1 MPa at 350 °C, 0.9 MPa at 500 °C, 2.4 MPa at 600 °C without pressure of inert gas) and increases with the pressure of inert media, reaching 0.2 MPa at 350 °C, 1.4 MPa at 500 °C and 3.7 MPa at 600 °C for total pressure 200 MPa (Ravich, 1974). The release and admission of mercury through valve (5) permits changing the reaction volume of the autoclave during the experiment, i.e. to vary the volume of the system with simultaneous registration of temperature and pressure. The precision of temperature measurement is ±0.5–1 K; the error in pressure determination depends on the type of manometer. We shall consider in detail some versions of p-V-T-x curve methods using schemes of typical isothermal and isobaric sections (Figure 1.10) of phase diagrams for binary systems. Method of p-x curves. Ravich’s design of the autoclave makes it possible to isolate salt placed under a layer of mercury in a capsule with holes ((7) in Figure 1.9) from water or solution above mercury until the specified temperature at the starting pressure is reached. In the isothermal experiments with either change of composition of initial solution (case 1) with a constant amount of solid phase, or an amount of solid phase (case 2) with a constant amount and composition of initial solution, the resulting p-x curves reveal phase transformation. In the first case, the starting pressure does not change on contact of the solution with salt until the starting composition of the solution is higher than the solubility at a specified temperature and pressure. When the composition of the initial solution becomes lower than saturated at specified parameters, the salt in the capsule begins to dissolve and the pressure drops in the system. The intersection of horizontal and inclined curves in coordinates p-x (where x is a composition of initial solution) corresponds to the composition of the saturated solution (see Figure 1.10(a), curves (P-X)1) at given temperature and pressure. In the second case, the initial solution has a composition lower than the solubility at specified parameters. Therefore, in all experiments the final pressure is lower than the initial pressure, and this pressure drop becomes greater as salt is added, until saturation of the solution is achieved. New additions of salt do not change the value of the final pressure. Again, the solubility is determined from the intersection of inclined and horizontal curves in coordinate p-x (where x is the composition of the resulting solution) at a specified temperature and final pressure (see Figure 1.10(a), curves (P-X)2). This method was also developed for determination of the composition of solutions saturated simultaneously with two solid phases in ternary systems (Valyashko, 1990a; Urusova and Valyashko, 2005). In the case of the water – salt equilibrium L-G, one can concentrate a solution until a saturated solution (L-G-S) is reached by releasing steam at a constant temperature until the vapor pressure remains constant, notwithstanding the removal of steam.

Figure 1.10 Behavior of p-V-T-x curves at phase transformations during experiments. Fl – fluid phase; S – solid phase (The Experimental Determination of Solubilities, Vol 6, Hefter & Tomkins). (a) p-x and p-V curves: Isothermal sections of binary phase diagram and p-x paths followed during runs with isothermal volume increasing (lines with arrows 1,2,3,4,5) and change of solution composition (P-X)1 or quantity of salt (P-X)2. Corresponding experimental p-x ((P-X)1, (P-X)2) and p-V (1, 2, 3, 4, 5) curves are also shown. (b) p-T curves (1, 2) plotted on a p-T projection of three-phase solubility curve with pressure maximum and another experimental curves (3, 4) corresponding to transition of cooling system from homogeneous to heterogeneous state. The intersection of the p-x path followed during cooling with solubility isotherm is shown in the p-x diagram. (c) T-V curves: Isobaric sections of phase diagram and T-x path followed during the runs with isobaric volume increasing and heating (lines with arrows 1, 2, 3) and corresponding experimental T-V curves (1, 2, 3).

The method of p-x curves was used for solubility measurements of noble gases in water at elevated temperatures (Potter and Clynne, 1978). The known amounts of water were injected in increments into the thermostated bomb with the known quantity of gas and pressure measured after thermal equilibration. As long as gas phase remains in the bomb along with liquid, those water injections alter pressure moderately. Only after the last bubble of gas dissolves in the water, further addition of water cause a relatively large increase in pressure.

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Method of p-V curves. An increase of the volume of a system in a homogeneous state (by release of mercury from the autoclave at constant temperature) results in a pressure drop and may result in an appearance of a new phase. The change of the phase state is determined as the break in the p-V curve. The change in volume of the system is measured by weighing the mercury vented from the autoclave through the valve; p-V curves are in fact ‘pressure – weight of mercury’ curves, while T-V curves are ‘temperature – weight of mercury’ curves. If a new heterogeneous equilibrium is a two-phase equilibrium in a binary system (G-L, L-S, G-S, Fl-S in Figure 1.10(a)), the change in the system volume is accompanied by a decrease in pressure (at constant T) but the slope of the p-V curve becomes flatter than that for a homogeneous liquid. However, for monovariant phase equilibrium (threephase equilibrium in a binary system (L-G-S in Figure 1.10(a)) the change of the system volume under isothermal conditions will keep the pressure constant. This method is widely used for the determination of solubility in the twophase fluid region and for the measurement of the vapor pressure of unsaturated and solid saturated solutions. Examples of p-V curves (1–5) at constant T for various phase transformations are given in Figure 1.10(a). Method of p-T curves. At parameters higher than those defining the three-phase equilibrium L-G-S or L1-L2-S, a two-component system may be either in a two-phase state (L-S, L-G or L1-L2) or in a single-phase state (L(Fl)). Cooling of an autoclave will result in a decrease of pressure in a system. If that system was initially in the single-phase state, the first break point of the p-T curve (discontinuity in the slope) is observed when the conditions for two-phase equilibrium are reached. The break point allows determination of the temperature and pressure of the beginning of salt crystallization in the fluid region (equilibrium (L(Fl) – S) (3, 4 in Figure 1.10(b)), or parameters of the immiscibility region L1-L2 or of equilibrium L-G. Additional measurements and knowledge of the complete phase diagram are required to recognize what kind of equilibrium has been detected by the experiment. Further cooling of the system, in the case of equilibria L-G or L1-L2, may result in the crystallization of the solid phase and appearance of the monovariant equilibrium L-G-S or L1-L2-S, and this will be accompanied by the second break point in the p-T curve. After that, the system will remain in the three-phase state during cooling until one of the phases disappears, i.e. the low-temperature part of the experimental curve (after the last break point) gives the pressures and temperatures of the monovariant three-phase equilibrium curve. Figure 1.10(b) shows examples of experimental p-T curves (1, 2 in Figure 1.10(b)) as p-T projections of the three-phase solubility curve of a binary system with a pressure maximum. The other apparatus used to obtain the p-T curves for solubility determinations (i.e. phase transition from a single phase to a two-phase equilibrium L-S) is described in Potter et al. (1976, 1977). The method of p-T curves in a set-up with visual cell and a piston (Figure 1.1) was employed for the determination of phase transitions in Gehrig et al. (1986)

and in Prof. Franck’s other experimental works. In Fenghour et al. (1993, 1996a,b) measurements of p-T relation of the water-N2, water-CO2 and water-methane (CH4) mixtures, placed in a isochoric apparatus, were used to determine a dew point temperatures and pressures for various concentrations of water. The slopes of experimental p-T curves were changed in a process of sample heating/cooling as soon as the phase transition (Fl = >L-G; Fl = >L1-L2) happens in the system. Method of T-V curves. The release of mercury to maintain constant pressure during heating of the autoclave results in an increase of the system’s volume. If that system is initially in a homogeneous state and a new phase appears during isobaric increase of temperature and volume, the discontinuity in the slope of the T-V curve will indicate the temperature of this phase transformation at a given pressure and known composition of the system. Further increase of temperature and volume may result in an appearance of a third phase and will lead to another break in the T-V curve at the temperature of the new phase transformation at the same pressure. Figure 1.10(c) shows the behavior of the isobaric boundary lines of a binary system and the paths of T-V experiments followed during heating in T-x coordinates as well as examples of the corresponding T-V curves. 1.2.4.2 Methods of property-parameter curves Studies of temperature, pressure and composition dependencies of various properties of systems or of individual phases show that the coordinates of a phase transformation will become apparent as a change in the slope of the property curve against one of the variables. A method of determining salt solubility using density measurements was developed to study high-temperature binary and ternary water-salt systems (Khaibullin and Novikov, 1972; Novikov and Khaibullin, 1973; Basaev et al., 2007). It was shown that the curves of solution density as a function of temperature or pressure (methods of T-V or p-V curves in Table 1.1) exhibit a change in slope at the temperature or pressure of formation of a solid phase. A method of sharp drop in the amplitude of vibration of the tube in a vibrating tube densimeter (VTFD in Table 1.1) was suggested by Crovetto and Wood (1991) for experimental determination of phase boundary and phase transition from homogeneous fluid to liquid-gas equilibrium. Electrical conductivity of solutions may also be used as a property. Measurements of the conductivity of solutions have to be performed at of variable composition, temperatures and pressures in the vicinity of the heterogeneous region. The composition of coexisting phases may then be determined by a short extrapolation of the conductivity of the homogeneous solutions to the temperature and pressure of the heterogeneous equilibrium. The compositions of vapor solutions in equilibrium L-G under subcritical conditions were determined by this method (Golubev et al., 1985). Method p-∆H curves was used to study the property of two-phase equilibrium for aqueous mixtures with ethanol

Phase Equilibria in Binary and Ternary Hydrothermal Systems 85

(C2H6O), methanol (CH4O) and acetone (C3H6O) at a constant content of water (0.5 mol.fr.) (Wormald and Vine, 2000; Wormald and Yerlett, 2000, 2002). The enthalpy increments (∆H), measured with a counter-current watercooled flow calorimeter, were plotted as a function of pressure and represented as a set of isothermal p-∆H curves. If these curves cross a two-phase region, they have two breaks at the dew and bubble point pressures, and the straight lines between them. In this way the values of the molar enthalpy of the saturated vapor and the molar enthalpy of the saturated liquid were obtained, as well as the molar enthalpy of flash vaporization of the mixtures. Isochoric heat capacities (Cv) for aqueous solutions as a function of temperature (method of T-Cv curves in Table 1.1) were used for determination of phase transformations taking place in the mixtures (Abdulagatov et al., 1997; Valyashko et al., 2000). Knowledge of the phase diagrams permits to predict behavior of a binary mixture when heated or cooled in a closed volume and to explain the drastic changes in measurable properties expected when a phase transition occurs. For binary systems with a positive temperature coefficient of solid solubility or for noncrystallizing mixtures, a heating of the solution in equilibrium with vapor can lead to the following phase transitions. At the highest average density of the system, the liquid phase expands with heating and fills the entire vessel, while the vapor phase disappears. A transition from (L-G) to L occurs, with a drop in heat capacity as the number of phases decreases. At low average density of the system and at very low salt content of the initial mixture, the heating increases the vapor density and salt concentration in it. Liquid phase is disappearing. This transition (L-G = >G) takes place again with a drop in heat capacity. Such phenomena were observed in aqueous solutions of KNO3, CH4O, KCl, NaCl, NaOH (Abdulagatov et al., 1997, 1998, 2000). A method of T-Cv curve was also used to determine the parameters of phase transformations in fluid systems complicated with immiscibility phenomena (aqueous n-heptane, n-hexane, n-hexane+1-propanol mixtures) (Mirskaya, 1998; Stepanov et al., 1999; Kamilov et al., 2001). For binary systems where a solubility of solid in liquid phase decreases with temperature, heating of the liquid solution in the equilibrium with vapor can lead to other phase transitions besides those mentioned above. Heating at intermediate average densities and before thermal expansion causes the liquid to fill the entire volume, the initially unsaturated liquid solution becomes saturated with solid due to the negative temperature coefficient of solubility. In this case, the first phase transition is the crystallization of solid from the liquid solution in equilibrium with its vapor (L-G = >L-G-S) with an increase in heat capacity. With further heating of the mixture the concentration of the saturated with solid liquid solution decreases along the three-phase solubility curve. Finally, the expanding liquid or vapor solution fills the cell except for the volume occupied by the solid. A transition (L-G-S = >L-S or L-G-S = >G-S) takes place, with a decrease in heat capacity. Such phase behavior was observed in experimental studies of aqueous Na2SO4 solutions. However, the experimental

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

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 87

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

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

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 89

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

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

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

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Hydrothermal Experimental Data

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 91

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

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

92

Hydrothermal Experimental Data

a

KB

b T KB

TB

p KA TB KA

T TA TB E A

x

B

A

x

c

B

d

p

p

KA

KA KB

TA E

KB TA

TB

E T

A

TB x

B

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 93

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

T, ºC 800

106 MPa

TNaCl

600 50 400

KH2O

10 MPa

200 0.1

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

TH2O H2O 20 40

60

NaCl

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

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

94

Hydrothermal Experimental Data

a

b

T

Q KB

p

KB

p KA TB

p

Q

KA T

TA TA

E

E A

x

B

A

c

p

x

B

d

p

Q

Q

p

p KA

KA TA

KB

KB TA

E

TB

E T

TB

A

x

B

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

a

b

KB

T p KB

KA N'

TB KA

TB TA

N'

T N

N

E

E

TA

A

x

B

A

x

c

B

d

p

p KA N'

KA KB

N'

KB

TA N E

TA

N

TB

E T

A

TB x

B

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 95

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

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

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

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

96

Hydrothermal Experimental Data

a

b KB

T KB

TB R

p KA

R

R

TB

N

R

KA

TA

T N E

TA E

A

x

B

A

c

p

x

B

d

p

KA

R

R

KA

R TA

KB

KB

N

N TA

E

E

TA T

A

TB x

B

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 97

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

3000 2 p, bar

7 1

2000

5 2 phase

3 4 6

1000 8 1 phase

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

0 300

320

340

360

380

400

420 T, ºC

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

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

T, ºC TNa2B4O7 700

500 RK2CO3

RNa2B4O7

KH2O NK2CO3 300 NNa2B4O7 0 (a)

(b)

40

80

x, mass.%

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

98

Hydrothermal Experimental Data

a

b

KB

T R

p

R

KB

TB

KA R

N'' N'

TB

TA

KA N'' N'

T N

N

E

TA

A

x

E

B

A

x

c

B

d

p

p KA

R

R

R

KA KB

N'' TA

N'

N''

KB

x

TB B

N' N

N E

TA

TB

E T

A

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

T

a

b KB

p

TB KA

M N

TB KA

T L

L L

TA

N L

TA

E

M

E A

x

B

A

c

x

B

d

p

p

KA M

KA

N

M

KB

KB

TA L

N L L. E

TA

E TB

TB T

A

x

B

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 99

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

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

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

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

a

b

KB

T KB TB

p R

R

KA

TB

R

M L

M

KA

T

L

R

L

L

TA TA

E

E A

x

B

A

x

c

B

d

p

p M

M KA R

R

R

KA TA

KB

L

L

KB L

TA E

TB

E T

A

TB x

B

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

100

Hydrothermal Experimental Data

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

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

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

b

KB

T KB TB

Q TB

p

Q M

M p

p

T

KB

L N

L

L

KB

TA

N TA E

A

x

B

A

c

x

d

p Q

p

Q M

M p

KA

p KB

TA E

N

B

L

KA TA

L

B

E

TB T

KB N

A

TB x

B

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 101

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

p, MPa 140

L1=L2 524 oC

120 500 oC 100 480 oC 450 oC

Q 80 Fl-S 60 40

KH2O

o p M 385

L N

H2O 20

382 oC 375 o

L

40

60

80

BaCl2

x, mass.%

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

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

102

Hydrothermal Experimental Data

a

b

KB

T

Q

KB TB

p KA

Q

p

TB

p KA

T TA E

TA E

A

x

B

A

x

c

B

d Q

Q

p

p p

p KA

KA KB

KB

TA TA E

TB

E T

A

TB x

B

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

(a)

(b)

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 103

p, MPa

T, ºC

250 600

8

a

b

9

200 7

7

1

500

3

.

5 2

2

100

4

400 KH2O

3 14

4 5 13

6 12,11

9 10

6 11 12

300 13

KH2O 14

200

1

8

16

15

300

400

500

600

H2O

T, ºC

5

10

x, mol.%

T, ºC TNa2SO4

800

600 150 Q 400

KH2O p

130 MPa 120 MPa 100 80 20 40 60 MPa

200

TH2O H2O

50

15

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

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

Na2SO4

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

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

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

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

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

KB

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A

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(a)

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 105

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

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

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

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Hydrothermal Experimental Data

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

1b

α

β

1c 1b

γ

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1d 1c

δ

ε

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X* C B γ

1d 1c

X* C B

1c

X* C δ

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X* C

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 107

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

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 109

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

X*

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

C B

X* C

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

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

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

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

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

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

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

T

B

X* C B

X* C B

X* C B

X* C

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 111

(b)

(c)

2. (a)

(b)

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

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

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

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

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 113

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

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

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

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

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

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 115

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

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

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

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Hydrothermal Experimental Data

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

40

NaCl 30 Na2SO4+NaCl KH2O

KCl

20

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

10

300

400

500

600

700

800

T, ºC

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

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

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 117

NaCl

50 mass %

Na2SO4

b

700 C 600 500

a

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

H 2O

o

10

10 370

400

30 350 300 200

o

350

350 C 200 oC 300

360 oC 300

30 350

370

50

50 360 oC

350 oC

H2O K2SO4

x, mass %

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

KCl

p, MPa L1=L2

(K2SO4)

100

p, MPa

L1-L2-SK2SO4

(K2CO3)

80

40

L1=L2-SK2SO4

Q

60

R

L1=L2-SK2SO4 L1=L2

(K2CO3)

R

40

30

KH2O; p

20

20

N

pR G-L1-L2-SK2SO4

N QN

370 KH2O;p

L1=L2

390

pR QN

o

410 T, C

L-G-SK2CO3 TK2CO3

300

400 500 600

700 T,oC

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

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

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

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

p, MPa

p, MPa

L1=L2

L1=L2

100

100

p, MPa L1-L2-SK2SO4

L1-L2-SK2SO4 L1=L2-SK2SO4

60

60

Q G=L-SK2SO4 KH2O

20

G=L

(a)

KH2O

G-L-SKCl

20

G-L-SK2SO4-SKCl

500

pR RN

E

1

2

L1=L2-G

G=L

QN

490 T,oC

450 G-L-SKCl

L-G-SK2SO4-SKCl

700 T, C

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

p

TKCl o

Q

60

G=L-SK2SO4

p

300

Q QN

70

300

500

E

700

TKCl

T,oC

(b)

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

Phase Equilibria in Binary and Ternary Hydrothermal Systems 119

p, MPa 500 QDs QMs QDsMs NDs 40 60

300

QDs Q DsMs 100 NQz NDs NQz 80 200 400

X*, mol.%

80 60

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

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

40

QMs o 600 T, C

NQz NDs QDs QDsMs QMs

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

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

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2

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

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

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

Vm = x1V1 + ∑ xiVi

(2.1)

i=2

j ≠i

o

j ≠i

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

= lim mi → 0 Vi

j ≠i

(2.4)

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

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

(2.2) Vm = x1V1 + x2V2

j ≠i

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

 ∂µ  Vi o =  i   ∂p  T , n

lim mi → 0 V1 = V1o

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

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

 ∂V  = m  ∂ni  T , p , n

j ≠i

 ∂µ  = i  ∂p  T , n

= Vi

(2.3)

j ≠i

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

(2.6)

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

(2.7)

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

136

Hydrothermal Experimental Data

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

φv =

1000 ( do − d ) M 2 + ddo m d

(2.8)

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

(2.9)

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

(2.10)

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

(

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

)

(2.11)

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

φvex (T .m) = ν z+ z−

Av 1/2 I 2

(2.12)

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

32

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

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

7 mA

8 9 10 2

11 6 12 13 15 5

1 14 3

4

(2.13)

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

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

pVTx Properties of Hydrothermal Systems 137

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

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

8 4

14

5 13

9

13

26

12

11

16

16 27 28 29

11

22

6 24

19

6

17 10

20 25

14

12

21

15 1

10 mA

2

1 2

7 3

15

Precision Temperature Regulator

23

18

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

PM-60

5

7 8

3 4

PM-600 9 Hg filled

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

138

Hydrothermal Experimental Data

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

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

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

sample space

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

o-rings

wire to inductive position indicator

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

pVTx Properties of Hydrothermal Systems 139

cooling water

To = 20°C

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

N S

Inductive sensor

magnet

pVT cell water solution calefactor mobile rod magnet thermoelement

Float Hg

Argon

8 5 1

4

2 3

6

7

9

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

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

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

ω2 =

Kf C2 − m 2m 2

(2.14)

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

(2.15)

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

140

Hydrothermal Experimental Data

Figure 2.8

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

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

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

pVTx Properties of Hydrothermal Systems 141

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

ρ − ρ0 = Am1 2 + Bm + Cm3 2 + Dm 2 ,

(2.17)

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

ρ − ρ0 = Am + Bm3 2 + Cm 2 + Dm5 2 ,

(2.18)

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

φ = Av m ex V

12

+ bm + dm

32

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

}

exp ( −α I 1 2 )] + m3 (ν M ν X )

(2.16)

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


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

(2.19)

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

32

φ C Mx ,

(2.20)

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

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

(2.21)

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

(2.22)

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

φV = V20 +

1  ∂G ex    . n2  ∂p  T

(2.23)

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

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

(2.24)

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

 ∂Aφ  AV = −4 RT  ,  ∂p  T

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

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

12

 ∂C  , C VMX =  MX  ,  ∂p  T

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

142

Hydrothermal Experimental Data

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

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

(1 − α ) γ ip α 2 mγ ±2

,

(2.25)

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

z+ z− e 2 , σε kT

(2.26)

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

(2.27)

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

pVTx Properties of Hydrothermal Systems 143

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

(2.28)

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

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

(2.29)

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

(2.30)

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

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

(2.31)

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

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

φV ex = bm + dm n

(2.32)

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

p = RT

(2.33)

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

β x = ∑ ∑ xi x j βij,

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

βij =

144

Hydrothermal Experimental Data

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

Cubic equation of state for binary aqueous solutions

Bij = −4βij ( wij3 − 1) ∆ ij ,

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

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

Cijk = −

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

n

n

amix = ∑ ∑ aij xi x j (1 − kij ),

(2.35)

i =1 j =1

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

n

n

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

(2.36)

i =1

awi ′ = 2 ( aw ai ) (1 − kwi ) , 12

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

(2.37)

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

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

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

pVTx Properties of Hydrothermal Systems 145

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

RT a (T ) − , V − b V (V + b)

(2.38)

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

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

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

The parameter a is given by

(2.42) n

a = ∑ ∑ xi ij x j ji aij β

i

β

(2.39)

j

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

∑xr

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

j

i =1

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

(2.40)

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

(2.41)

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

+

i i

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

xi li

presVm* = − Z ln X 0 , RT

(2.43)

(2.44)

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

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

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

(2.45)

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

146

Hydrothermal Experimental Data

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

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

Water+n-Methane

Water+n-Pentane

750 500 600

T=647.05 K

T=653.15 K

Vm, cm3·mol-1

400 0.1576 0.6291 0.2100 0.5087

450

mol mol mol mol

fraction fraction fraction fraction

0.6938 0.2830 0.0880 0.0184

300

mol mol mol mol

fraction fraction fraction fraction

300 200

150

100

0

0 2

12

22

32 p, MPa

42

52

62

8

16

24

32

40

p, MPa

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

pVTx Properties of Hydrothermal Systems 147

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

T=673.15 K

H2O + NaCl 29

27

ps, MPa

25

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

21

19

17

15 2

6

10

14 x, wt %

18

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

(2.48)

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

res .

(T , Vm , x ) = a

ref .

(T , Vm , x ) − a

per .

(T , Vm , x ) ,

(2.49)

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

(2.50)

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

22

26

30

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

(2.51)

where n

n

n

i =1

i =1

i =1

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

A2 , A3 1− A2

(2.52)

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

( µ*)2 =

Q2 µ2 2 ( ) Q , and * = σ 3 kT σ 5 kT

(2.53)

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

148

Hydrothermal Experimental Data

using a truncated virial expansion for the perturbation contribution per

1 a =− RT RT

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

2

3

3

4

(2.54)

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

n

n

n

n

n

i

i

n

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

n

n

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

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

j

k

i

j

k

l

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

res .

(2.55)

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

i

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

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

Z=

j

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

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

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

j

2 βV = ∑ ∑ ∑ xi x j xk βijkVCijk ,

n

3

i

2 C

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

(2.57)

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

αVC = ∑ ∑ xi x j α ijVCij ,

i =1 j =1 k =1

n

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

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

n

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

The virial expansion of equation (2.56) is

(2.56)

3

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

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

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

13

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

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

pVTx Properties of Hydrothermal Systems 149

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

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

(2.58)

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

eµ RT . 1 + e µ RT

(2.59)

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

(2.60)

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

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

ρ

∑  Ai + ρ i =1

CO

 ∂∆A    − ∆A − A0 , ∂∆ρ  τ , x

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

(2.63)

(2.64)

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

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

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

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

ρT [ ln (1 − x ) + mO ], ρCOTCO

p ( ρ, T , x ) ρ = RTC 0 ρC 0 ρC

i

4

4

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

(2.61)

TC ( x ) = TCO (1 − x ) + TC1 x + 2

x (1 − x ) ∑ Ti (1 − 2 x ) , i

(2.65)

i =1

where

τ=

ρC ( x ) = ρCO (1 − x ) + ρC1 x + T

2

x (1 − x ) ∑ ρi (1 − 2 x ) ,

− 1 = r (1 − b 2ϑ 2 ) and

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

i

(2.66)

i=0

(2.62)

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

pC ( x ) = pCO (1 − x ) + pC1 x + 2

x (1 − x ) ∑ pi (1 − 2 x ) , i

(2.67)

i =0

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

150

Hydrothermal Experimental Data

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

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

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

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

H2O + n-Hexane

35

35

p, MPa

x=0.005 mol fraction

T=647.10 K

30

30

25

25

20

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

15

10 40

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

15

10 140

240

340 ρ, kg·m–3

440

540

40

140

240

340

440

540

ρ, kg·m–3

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

pVTx Properties of Hydrothermal Systems 151

Water + Toluene x=0.0287 mol frac. 43

38

x=0.0166 mol frac. 52

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

47

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

42

p, MPa

33 37

32

28

27 23 CP 22 18 17

13 60

180

300

420

540

ρ, kg·m–3

12 100

200

300

400

500

ρ, kg·m–3

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

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

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

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

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

30000

25000

Water+n-Hexane

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

V2 cm3·mol-1

20000

o

15000

10000

5000

0

-5000 90

170

250

330

490

410

ρw, kg·m-3

(a) 22

1 19 Water+Toluene 16

10

2

o

V2 I·mol-1

13

7 4 1 -2 -5 150

200

250

300

(b)

350

400

450

500

550

ρ, kg·m-3

H2O+ NaCl

-20

-20 4 3

-100

o

V2 I·mol-1

-100

-180

-180

2

-340

Tc=647.05 K

-260

-260

1 2 3 4

-

647.5 648.0 649.0 650.0

K K K K

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

-420

-420 1

-500 150

250

350 ρ, kg·m–3

450

-500 150

250

350 ρ, kg·m–3

450

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

pVTx Properties of Hydrothermal Systems 153

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

(2.69)

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

φV = V o +

(2.70)

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

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

(2.71)

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

(2.72)

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

4 As

vdW

+

o BPh4 −

V

=

VPh

+ 4 As vdW BPh4 −

V

= 1.0337 ± 0.0034

(2.73)

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

(2.74)

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

154

Hydrothermal Experimental Data

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

(2.75)

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

4π N A 3 2.52 ( r + a) = 3

(2.76)

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

( zi e)2 N A  8πε o



1 1−  ε

(2.77)

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

ωi ε2

 ∂ε    ∂p T

(2.78)

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

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

(2.79)

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

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

(2.80)

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

(2.81)

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

{

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

}

(2.82)

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

pVTx Properties of Hydrothermal Systems 155

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

a1 (J·mol−1·bar−1)

a2·10−2 (J·mol−1·K−1)

a3 (J.K.mol−1bar−1)

a4·10−4 (J.K.mol−1)

So (J.K−1.mol−1)

re (nm)

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

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

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

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

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

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

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

c (cm3·mol−1)

d (cm3·K·J−1)

−20.5 0.0 −14.8 −31.5 1.8 0.0 13.4

0.308 0.220 0.045 0.041 0.308 0.239 0.239

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

Hydrothermal Experimental Data

vf° (cm 3 ·mol−1)

(a)

25

500

0

0 V2° (cm3 mol-1)

156

–25 –50

-500

-1000

–75 -1500

–100 273 (b)

373

T (K)

473

573

0.2

–100 vf° ( cm3 ·mol−1)

0.4

0.5 0.6 density (gcm-3)

0.7

0.8

0.9

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

0 –200 –300 –400 –500 –600 –700 350

0.3

400

450

500 T (K)

550

600

650

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

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

V2o = 1 − C12o κ 1o RT

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

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

aR (T − θ ) ( p + φ )

(2.83)

(2.84)

(2.85)

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

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

(2.86)

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

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

(2.87)

pVTx Properties of Hydrothermal Systems 157

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

Simonson (Eq. 2.82)

Plyasunov (Eq. 2.83)

0.44

0.62 397

0.45 254

<∆/s> su (cm3 mol−1)

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

(2.88)

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

(2.89)

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

Cooney (Eq. 2.85) 1.20 144

Sedlbauer (Eq. 2.87) 0.44 118

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

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

(2.90)

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

158

Hydrothermal Experimental Data

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

(2.91)

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

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

(2.92)

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

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

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

pVTx Properties of Hydrothermal Systems 159

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

(2.94)

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

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

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

mp

Benzenea

Cyclohexanea

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

5 3 3 3 2 3

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

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

(a)

Standard deviation in cm3·mol−1;

(b)

a2 = a4 = 0 in Equation (2.80).

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

w m m m m

m

m m w m w m x

m m w m m m m

silver nitrate

arsenious acid

arsenic acid

barium chloride barium chloride

barium chloride

barium chloride barium nitrate

barium nitrate

calcium chloride

calcium chloride calcium chloride calcium chloride

calcium chloride calcium chloride

calcium chloride

calcium chloride

calcium chloride

calcium chloride

calcium chloride

AgNO3

As(OH)3

AsO(OH)3

BaCl2 BaCl2

BaCl2

BaCl2 Ba(NO3)2

Ba(NO3)2

CaCl2

CaCl2 CaCl2 CaCl2

CaCl2 CaCl2

CaCl2

CaCl2

CaCl2

CaCl2

CaCl2

3 c

2

1

Binary systems – electrolytes silver nitrate AgNO3

Chemical names

Formula

unit

pVTx properties of hydrothermal systems

Nonaqueous components

Table 2.5

0.3

0.24

0.225

0.015

0.010

0.50 0.022

0.10 0.050 0.014

0.25

0.005

0.097 0.05

0.0093

0.10 0.097

0.1

0.1

0.02

0.025

4

min

2.0

6.15

3.23

6.4

0.20

6.4 0.19

1.0 0.33

3.0

0.08

0.90 0.1

1.60

1.0 0.90

0.6

0.3

0.92

0.10

5

max

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

388

25

350

50

25

50 25

20 50 238

25

25

17 218

15

50 75

298

298

222

218

6

min

465

250

370

324

350

200 301

300 200 388

340

325

300 306

140

200 300

624

624

306

7

max

Temp-re (°C)

Crit.

7.1

15

0.10

2

2 9.9

10 2 10

Sat

0.003

2.00 Sat

0.10

2 0.30

0.1

0.1

Sat

Sat

8

min

42

22

40

30

79

60

150

50

40

20

40

30

30

9

max

Pressure (MPa)

d

Vs

d

dd.Vf.Vo

dd.Vf

dd

d

d Vs.Vf

d d.Vf.Vo Vs.Vf

d

d

d Vs

dd.Vf.Vo

d.Vf.Vo d.Vf

dd.Vf.Vo

dd.Vf.Vo

10

Exper’tal data

SFIT

VTD

VTD

VTD

VVP

VVP CVP

VVP VVP PYC

VVP

CVP

CVP PYC

VTD

VVP CVP

VTD

VTD

PYC

PYC

11

Technique

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

12

Reference

r-CaCl2-11.1

r-CaCl2-10.1

r-CaCl2-9.1

r-CaCl2-8.1

r-CaCl2-7.1

r-CaCl2-5.1 r-CaCl2-6.1

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

r-CaCl2-1.1

r-Ba(NO3)2-2.1

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

r-BaCl2-1.1 r-BaCl2-2.1

r-AsO(OH)3-1.1

r-As(OH)3-1.1

r-AgNO3-2.1

r-AgNO3-1.1

13

Table code for Appendix

160 Hydrothermal Experimental Data

calcium nitrate

calcium nitrate

calcium nitrate

decyltrimethylammonium bromide dodecyltrimethylammonium bromide cesium bromide

cesium chloride cesium chloride

gadolinium triflate

potassium bromide potassium bromide

potassium bromide

potassium bromide

potassium bromide

potassium bromide

potassium carbonate

potassium carbonate

potassium chloride

potassium chloride

Ca(NO3)2

Ca(NO3)2

Ca(NO3)2

C13H30NBr

CsCl CsCl

Gd(CF3SO3)3

KBr KBr

KBr

KBr

KBr

KBr

K2CO3

K2CO3

KCl

KCl

CsBr

C15H34NBr

m

calcium chloride

CaCl2

c

c

w

m

m

w

w

w

m m

m

m m

m

m

m

w

w

m

3

2

1

unit

Chemical names

Formula

Nonaqueous components

0.01

0.01

0.025

0.25

0.24

0.020

0.093

0.019

0.10 0.10

0.029

0.1 1.0

0.0024

0.011

0.0078

0.042

0.30

0.25

0.18

4

min

0.1

0.1

0.50

3.0

2.24

0.048

0.37

0.36

1.0 1.5

0.72

0.4 9.0

0.50

1.02

0.97

0.20

0.41

3.0

6.0

5

max

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

218

305

25

25

25

25

25

25

50 40

100

25 204

331

74

74

25

25

25

25

6

min

306

306

300

340

355

325

325

350

200 280

200

200 874

452

176

176

325

325

340

125

7

max

Temp-re (°C)

Sat?

Sat?

Sat.

Sat

2

0.1

0.1

10

2 10

7.1

2 50

18

0.9

1

4.2

1.3

Sat

0.1

8

min

30

40

40

150

26

150

33

33.4

33.4

20

49

60

9

max

Pressure (MPa)

dd

dd

d

d

d

d.Vf.Vo

Vs

Vs

d

d

d

d

d

d

d.Vf.Vo Vs

d.Vf.Vo

d.Vf.Vo Vf

dd.Vf.Vo

10

Exper’tal data

PYC

PYC

HWT

VVP

CVP

CVP

CVP

HWT

VVP PYC

VTD

VVP CVP

VTD

VTD

VTD

CVP

CVP

VVP

CVP

11

Technique

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

12

Reference

r-KCl-2.1

r-KCl-1.1

r-K2CO3-2.1

r-K2CO3-1.1

r-KBr-6.1

r-KBr-5.1

r-KBr-4.1

r-KBr-3.1

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

r-CsCl-1.1 r-CsCl-2.1

r-CsBr-1.1

r-Ca(NO3)2-3.1

r-Ca(NO3)2-2.1

r-Ca(NO3)2-1.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 161

Continued

Chemical names

2

potassium chloride

potassium chloride potassium chloride

potassium chloride

potassium chloride potassium chloride potassium chloride

potassium chloride potassium chloride

potassium chloride

potassium chloride

potassium chloride

potassium chloride

potassium chloride

potassium chloride potassium chloride

potassium chloride

potassium chloride

potassium chloride

potassium chloride

Formula

1

KCl

KCl KCl

KCl

KCl KCl KCl

KCl KCl

KCl

KCl

KCl

KCl

KCl

KCl KCl

KCl

KCl

KCl

KCl

Nonaqueous components

Table 2.5

x

m

m

w

w w

w

w

m

w

m

c m

w m w

m

w c

w

3

unit

3.0

1.02

0.049

0.23

0.20

0.57

0.21

1.5

1.0

1.0 0.20

3.0

0.78 3.0

0.45

5

max

Concentration

0.0024

0.25

0.099

0.020

0.095 0.18

0.20

0.050

0.006

0.012

0.0010

0.058 0.25

0.10 0.1 0.01

0.25

0.49 1.0

0.36

4

min

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

388

350

25

25

22 25

300

25

187

25

40

25 40

20 25 100

25

250 25

100

6

min

300

325

325 325

700

350

411

350

280

370 280

300 200 440

340

550 340

200

7

max

Temp-re (°C)

17

79

40

40 40

300

30

150

39

150

22

9

max

Pressure

Crit.

15

9.9

0.1

0.1 0.1

100

2

Sat.

10

10

Sat. 7.5

10 2 0.1

Sat

2.4 Sat.

Sat.

8

min

Pressure (MPa)

10

d

dd.Vf

d.Vf

d

d d

d

d

d

d

Vs

d Vs

d d.Vf.Vo d

d.Vf

Vs d

d

Exper’tal data

CVP

VTD

CVP

CVP

CVP CVP

SFIT

VVP

PYC

HWT

PYC

XRD PYC

VVP VVP γRD

VVP

VVP VVP

PYC

11

Technique

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

12

Reference

r-KCl-22.1

r-KCl-21.1

r-KCl-20.1

r-KCl-19.1

r-KCl-17.1 r-KCl-18.1

r-KCl-16.1

r-KCl-15.1; 15.2

r-KCl-14.1; 14.2

r-KCl-13.1

r-KCl-12.1

r-KCl-10.1 r-KCl-11.1

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

r-KCl-6.1

r-KCl-4.1 r-KCl-5.1

r-KCl-3.1

13

Table code for Appendix

162 Hydrothermal Experimental Data

w m m m w w m

potassium chromate

potassium fluoride potassium fluoride

potassium fluoride

potassium iodide potassium iodide

potassium iodide

potassium iodide

potassium iodide

potassium nitrate

potassium nitrate potassium nitrate

potassium nitrate

potassium nitrate

potassium nitrate

potassium hydroxide

potassium hydroxide

potassium hydroxide

potassium hydroxide

potassium sulphate

potassium sulphate potassium sulphate

K2CrO4

KF KF

KF

KI KI

KI

KI

KI

KNO3

KNO3 KNO3

KNO3

KNO3

KNO3

KOH

KOH

KOH

KOH

K2SO4

K2SO4 K2SO4

m w

c

w

w

m

w

w

w

m m

m

m w

m

3

2

1

unit

Chemical names

Formula

Nonaqueous components

0.050 0.050

0.025

0.024

0.054

0.087

0.045

0.096

0.050

0.050

0.10 0.10

0.25

0.020

0.18

0.014

0.10 0.10

0.01

0.10 0.050

0.25

4

min

0.50 0.35

0.050

0.50

0.6

2.7

0.99

0.94

0.20

0.90

1.0 1.5

3.0

0.49

0.42

0.57

1.0 1.5

3.0

1.0 0.20

3.0

5

max

(c, m, v, w, x)

50 397

200

306

300

−20

218

300

250

400

300

350

350

200 280

340

325

325

350

200 280

354

200 325

340

7

max

0

55

0

18

20

25

50 40

25

25

25

25

50 40

25

50 25

25

6

min

Temp-re (°C)

2 60

Sat.

5.0

5.0

0.1

Sat.

2.1

1.5

Sat.

2 10

Sat

0.1

0.1

10

2 10

10

2 0.1

Sat

8

min

150

59

59

4.8

40

30

40

40

150

31

40

9

max

(MPa)

d.Vf.Vo d

d

d.Vf.Vo Vs

Vs

sv

sv

d.Vf.Vo

d

d.Vo

d

d

d.Vf.Vo Vs

d

d

d

d

d.Vf.Vo Vs

dd.Vf.Vo

10

Exper’tal data

VVP PYC

PYC

EP

EP

VTD

HWT

HWT

CVP

HWT

VVP PYC

VVP

CVP

CVP

HWT

VVP PYC

VTD

VVP CVP

VVP

11

Technique

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

12

Reference

r-K2SO4-2.1 r-K2SO4-3.1

r-K2SO4-1.1

r-KOH-4.1

r-KOH-3.1

r-KOH-2.1

r-KOH-1.1

r-KNO3-6.1

r-KNO3-5.1

r-KNO3-4.1

r-KNO3-2.1 r-KNO3-3.1

r-KNO3-1.1

r-KI-5.1

r-KI-4.1

r-KI-3.1

r-KI-1.1 r-KI-2.1

r-KF-3.1

r-KF-1.1 r-KF-2.1

r-K2CrO4-1.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 163

Continued

Chemical names

2

potassium sulphate

potassium sulphate

potassium sulphate

potassium sulphate lithium bromide

lithium bromide

lithium bromide lithium bromide lithium chloride

lithium chloride lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

lithium chloride

Formula

1

K2SO4

K2SO4

K2SO4

K2SO4 LiBr

LiBr

LiBr LiBr LiCl

LiCl LiCl

LiCl

LiCl

LiCl

LiCl

LiCl

LiCl

LiCl

Nonaqueous components

Table 2.5

m

m

w

w

m

w

m

m m

w w c

w

m w

m

w

w

3

unit

15.5

3.0

0.20

0.20

3.0

0.43

9.0

1.0 1.5

0.4 0.6 3.0

0.20

0.41 0.55

0.50

0.10

0.50

5

max

Concentration

0.13

0.0025

0.047

0.010

0.051

0.017

1.0

0.1 0.0010

0.3 0.45 1.0

0.060

0.066 0.016

0.0048

0.011

0.050

4

min

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

17

331

25

25

48

25

212

25 40

25 25 25

25

20 25

25

25

300

6

min

335

452

325

350

277

350

720

200 280

325 202 340

325

300 350

400

300

500

7

max

Temp-re (°C)

31

38

40

30

33

150

150

40

40

38 150

31

150

9

max

Pressure

0.1

18.5

0.1

2

0.76

10

50

2 10

0.1 1.0 Sat.

0.1

2.2 10

9.9

Sat

30

8

min

Pressure (MPa)

d

Vs

d.Vf

dd.Vf

d

d

dd.Vf.Vo

d

Vf

d.Vf.Vo Vs

d d d

d

d d

dd.Vf.Vo

10

Exper’tal data

CVP

VTD

CVP

VVP

VTD

HWT

CVP

VVP PYC

CVP Pyc VVP

CVP

CVP HWT

VTD

HWT

PYC

11

Technique

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

12

Reference

r-LiCl-10.1

r-LiCl-9.1

r-LiCl-8.1

r-LiCl-7.1

r-LiCl-6.1

r-LiCl-5.1

r-LiCl-4.1

r-LiCl-2.1 r-LiCl-3.1

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

r-LiBr-2.1

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

r-K2SO4-6.1

r-K2SO4-5.1

r-K2SO4-4.1; 4.2

13

Table code for Appendix

164 Hydrothermal Experimental Data

m w w

w m

m

m

w

m w m m

w c w

lithium iodide

lithium iodide

lithium iodide

lithium iodide lithium nitrate

lithium nitrate

lithium nitrate

lithium nitrate

lithium nitrate

lithium hydroxide

lithium sulphate

lithium sulphate

magnesium chloride

magnesium chloride magnesium chloride

magnesium chloride

magnesium chloride

magnesium nitrate

magnesium sulphate

magnesium sulphate

LiI

LiI

LiI

LiI LiNO3

LiNO3

LiNO3

LiNO3

LiNO3

LiOH

Li2SO4

Li2SO4

MgCl2

MgCl2 MgCl2

MgCl2

MgCl2

Mg(NO3)2

MgSO4

MgSO4

w

m

m

w

w

3

2

1

unit

Chemical names

Formula

Nonaqueous components

0.10

0.050

0.050

0.11

0.0050

0.10 0.050

0.42

0.094

0.0062

0.38

0.30

0.18

0.40

0.052

0.11 0.007

0.091

0.050

0.013

4

min

0.40

1.04

3.0

1.0 0.15

0.57

0.89

0.21

3.1

7.8

1.7

0.90

0.41

4.88 0.67

3.1

0.59

5

max

(c, m, v, w, x)

20

218

25

18

96

50 25

100

25

25

55

25

19

25

25

25 25

25

25

25

6

min

300

325

300

354

200 300

200

300

300

250

125

300

350

300

125 110

327

325

350

7

max

Temp-re ( C)

10

Sat.

0.1

0.94

10

2 2

Sat.

5

Sat.

0.1

0.1

2.0

Sat.

Sat.

0.1 Sat.

2.0

0.1

10

8

min

150

49

40

31

30

4.0

4.8

60

40

60

31

40

150

9

max

(MPa)

d,Vf,Vo d

d

d.Vf.Vo

d

d.Vf.Vo

d.Vf

d

d

d

d.Vf.Vo d

d.Vf

d

d

d

Vs

d

d,Vo

dd,Vf,Vo

10

Exper’tal data

VVP

PYC

CVP

CVP

VTD

VVP VVP

PYC

CVP

HWT

VTD

CVP

CVP

HWT

HWT

CVP PYC

CVP

CVP

HWT

11

Technique

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

12

Reference

r-MgSO4-2.1

r-MgSO4-1.1

r-Mg(NO3)2-1.1

r-MgCl2-5.1

r-MgCl2-4.1

r-MgCl2-2.1 r-MgCl2-3.1

r-MgCl2-1.1

r-Li2SO4-2.1; 2.2

r-Li2SO4-1.1

r-LiOH-1.1

r-LiNO3-3.1; 3.2

r-LiNO3-2.1

r-LiNO3-1.1

r-LiI-3.1; 3.2

r-LiI-2.1

r-LiI-1.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 165

Continued

m w m

m w w m

magnesium sulphate

magnesium sulphate

magnesium sulphate

ammonium chloride ammonium chloride

ammonium chloride

ammonium perchlorate ammonium nitrate

sodium borate

sodium borate

sodium bromide

sodium bromide

sodium bromide

sodium bromide

sodium triflate

sodium carbonate

sodium carbonate

MgSO4

MgSO4

MgSO4

NH4Cl NH4Cl

NH4Cl

NH4ClO4 NH4NO3

NaB(OH)4

NaB(OH)4

NaBr

NaBr

NaBr

NaBr

NaCF3SO3

Na2CO3

Na2CO3

m

w

m

m

m

m

w

m

m m

3

2

1

unit

Chemical names

Formula

Nonaqueous components

Table 2.5

0.99

0.20

1.68

4.9

3.0

3.0

0.44

1

0.19

1.0 0.89

6.0

1.0 5.0

0.84

0.10

0.25

5

max

Concentration

0.10

0.051

0.045

0.21

0.0025

0.050

0.022

0.12

0.051

0.010 0.0080

0.10

0.010 0.50

0.084

0.010

0.072

4

min

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

25

25

10

100

331

49

25

25

25

50 180

25

50 143

18

25

21

6

min

350

300

327

249

452

277

350

302

300

200 180

350

200 581

175

175

203

7

max

Temp-re (°C)

28

20

30

38

32

150

79

28

150

40

30

10

9

max

Pressure

10

Sat.

0.1

10

18

8.4

10

9.9

Sat.

2 Sat

9.9

2 50

2.1

2

2.1

8

min

Pressure (MPa)

d,Vf,Vo Vf

d,Vo

d

d,Vf,Vo

dd,Vf

d

dd,Vf,Vo

dd,Vf

dd,Vf

dd,Vf,Vo

d

Vs,Vo

d

d,Vf,Vo d

dd,Vf,Vo

10

Exper’tal data

VTD

HWT

VTD

VTD

VTD

VTD

HWT

CVP

HWT

VVP PYC

VTD

VVP CVP

CVP

VVP

VVP

11

Technique

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

12

Reference

r-Na2CO3-2.1

r-Na2CO3-1.1

r-NaCF3SO3-1.1

r-NaBr-4.1

r-NaBr-3.1

r-NaBr-2.1

r-NaBr-1.1

r-NaB(OH)4-2.1

r-NaB(OH)4-1.1

r-NH4ClO4-1.1

r-NH4Cl-3.1

r-NH4Cl-1.1 r-NH4Cl-2.1

r-MgSO4-5.1

r-MgSO4-4.1

r-MgSO4-3.1

13

Table code for Appendix

166 Hydrothermal Experimental Data

Chemical names

2

sodium carbonate

sodium acetate

sodium propionate

disodium tartrate sodium benzenesulfonate

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride sodium chloride sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride sodium chloride

Formula

1

Na2CO3

NaC2O2H3

NaC3O2H5

Na2C4O6H4 NaC6H5O3S

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl NaCl NaCl

NaCl

NaCl

NaCl

NaCl

NaCl NaCl

Nonaqueous components

w w

m

w

m

w

w m w

m

c

w

w

w

c

c

m m

m

m

w

3

unit

0.10 0.010

1.0

0.020

0.0010

0.010

0.010 0.1 0.010

0.5

1.0

0.002

0.0012

0.28

0.002

0.002

0.043 0.12

0.12

0.12

<0.003

4

min

0.60 0.25

6.0

0.24

1.5

0.050

0.26 1.0 0.25

3

3

0.12

0.32

0.1

0.1

0.61

5

max

(c, m, v, w, x)

350 20

202

25

40

100

20 25 100

175

25

385

385

100

218

217

10 100

100

100

374

6

min

550 400

695

350

280

418

300 200 440

350

340

396

396

200

306

306

254 325

250

250

375

7

max

Temp-re (°C)

11 10

50

10

10

Sat.

10 2 0.1

Sat.

Sat.

23

21

Sat.

Sat.

Sat.

0.1 28

28

28

Sat.

8

min

100 400

150

100

40

150

29

30

10

9

max

(MPa)

Vf,Vo

Vf,Vo

d

d Vs

Vf

d

Vs

d

d d,Vf,Vo d

d

d

d

d

d

Vs

Vs

dd,Vf,Vo Vf,Vo

10

Exper’tal data

VVP MBVV

CVP

HWT

PYC

γRD

VVP VVP γRD

VVP

VVP

PYC

PYC

PYC

PYC

PYC

VTD VTD

VTD

VTD

PYC

11

Technique

Valyashko et al. (2000) Criss & Wood (1996) Criss & Wood (1996) Xie et al. (2004) Criss & Wood (1996) Noyes & Coolidge (1903) Noyes et al. (1910) Akhumov & Vasil’ev (1932) Copeland et al. (1953) Benson et al. (1953) Rodnianski & Galinker (1955) Ellis & Golding (1963) Polyakov (1965) Ellis (1966) Khaibullin & Borisov (1966) Khaibullin & Novikov (1973) Gorbachev et al. (1974b) Zarembo & Feodorov (1975) Egorov & Ikornikova (1973) Urusova (1975) Hilbert (1979)

12

Reference

r-NaCl-15.1 r-NaCl-16.1

r-NaCl-14.1

r-NaCl-13.1

r-NaCl-12.1

r-NaCl-11.1

r-NaCl-8.1 r-NaCl-9.1 r-NaCl-10.1

r-NaCl-7.1

r-NaCl-6.1

r-NaCl-5.1

r-NaCl-4.1; 4.2; 4.3

r-NaCl-3.1

r-NaCl-2.1

r-NaCl-1.1

r-C4H4O6Na2-1.1 r-C6H5O3SNa-1.1

r-C3H5O2Na-1.1

r-C2H3O2Na-1.1

r-Na2CO3-3.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 167

Continued

Chemical names

2

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

sodium chloride

Formula

1

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

NaCl

Nonaqueous components

Table 2.5

m

m

m

m

m

m

w

m

w

w

w

m

w

w

w

m

m

m

3

unit

0.50

0.0050

0.16

0.25

0.0025

0.051

0.032

0.0025

0.060

0.020

0.094

0.1

0.18

0.050

0.060

0.053

0.10

0.10

4

min

3.0

3.0

5.5

3.0

3.1

1.9

0.30

5.0

0.1

0.049

0.25

5.0

0.20

0.20

4.4

1.0

4.0

5

max

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

124

101

25

350

331

120

374

50

400

25

25

225

25

25

200

30

25

173

6

min

200

408

250

452

400

820

324

500

325

325

400

325

350

600

200

301

354

7

max

Temp-re (°C)

10

10

7

15

18

1

22

0.1

40

0.1

0.1

14

0.30

2

1.3

2

10

20

8

min

30

31

41

17

38

40

157

40

300

40

40

3

40

30

300

79

9

max

Pressure (MPa)

Vm

d

d

dd

d

d

Vs

d

d

d,Vo

dd,Vf

dd,Vf

Vf,Vo

dd,Vf

dd,Vf

dd

Vs

dd,Vs,Vf,Vo

10

Exper’tal data

VTD

VTD

VTD

VTD

VTD

VTD

SFIT

VTD

VVP

CVP

CVP

VTD

CVP

VVP

VVP

VVP

CVP

VVP

11

Technique

Grant-Taylor (1981) Lvov et al. (1981) Rogers et al. (1982) Gehrig et al. (1983) Pepinov et al. (1983; 1988) Akhundov & Imanova (1984) Albert & Wood (1984) Akhundov et al. (1985a) Akhundov et al. (1986a) Gehrig et al. (1986) Majer et al. (1988) Knight & Bodnar (1989) Majer et al. (1991b) Majer et al. (1991a) Crovetto et al. (1993) Simonson et al. (1994) Hynek et al. (1997a); Obsil (1997) Hakin et al. (1998)

12

Reference

r-NaCl-34.1

r-NaCl-33.1; 33.2

r-NaCl-32.1; 32.2

r-NaCl-31.1

r-NaCl-30.1

r-NaCl-29.1

r-NaCl-28.1

r-NaCl-27.1

r-NaCl-26.1

r-NaCl-25.1

r-NaCl-24.1

r-NaCl-23.1

r-NaCl-22.1

r-NaCl-21.1; 21.2

r-NaCl-20.1

r-NaCl-19.1

r-NaCl-18.1

r-NaCl-17.1

13

Table code for Appendix

168 Hydrothermal Experimental Data

m m m

m w m

m

w w

sodium chloride

sodium perchlorate

sodium perchlorate

sodium fluoride

sodium fluoride

sodium fluoride

sodium hydrogen carbonate sodium hydrogen carbonate

sodium hydrogen carbonate

sodium hydrogen sulfide

sodium iodide

sodium iodide

sodium iodide

sodium iodide

sodium iodide

sodium iodide

sodium molibdate

sodium nitrite

NaCl

NaClO4

NaClO4

NaF

NaF

NaF

NaHCO3 NaHCO3

NaHCO3

NaHS

NaI

NaI

NaI

NaI

NaI

NaI

Na2MoO4

NaNO2

w

w

w

w

w

w

m

w

w

x

sodium chloride

NaCl

3

2

1

unit

Chemical names

Formula

Nonaqueous components

0.050

0.10

0.0050

0.41

0.31

0.020

0.17

0.013

0.10

0.10

0.080 0.10

0.0097

0.0025

0.020

0.08

0.082

0.21

0.0009

4

min

0.20

0.39

0.048

0.62

1.0

1.0

0.70

0.90

0.015

0.030

0.97

0.96

2.50

0.0031

5

max

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

20

18

25

25

25

25

25

25

25

25

20 25

25

25

25

25

25

250

374

6

min

350

280

325

325

325

325

325

350

200

350

300 200

353

325

225

300

300

300

388

7

max

Temp-re (°C)

1.5

Sat.

0.1

0.1

0.1

0.1

0.1

10

2.0

9.8

10 2.0

10

Sat.

0.1

8

7.0

14

Sat

8

min

29

40

40

40

40

40

150

28

150

31

40

40

37

37

9

max

Pressure (MPa)

d

d

d

d

d

d

d

d

d

d,Va,Vo

dd,Vf

d d

dd,Vf,Vo

d

d

d,Vf,Vo

d

dd, Vf, Vo

10

Exper’tal data

CVP

HWT

CVP

CVP

CVP

CVP

CVP

HWT

VVP

VTD

VVP VVP

VTD

CVP

CVP

CVP

CVP

VTD

CVP

11

Technique

Abdulagatov et al. (1998a) Trevani et al. (2007) Akhundov et al. (1991b) Abdulagatov & Azizov (2004d) Akhundov et al. (1988b) Guseynov et al. (1989) Majer et al. (1997) Polyakov (1965) Ellis & McFadden (1972) Sharygin & Wood (1998) Ellis & McFadden (1972) Feodorov & Zarembo (1983) Akhundov & Imanova (1983) Akhundov et al. (1983a) Akhundov et al. (1983b) Akhundov et al. (1983c) Akhundov et al. (1984a) Maksimova et al. (1976) Traktuev & Ptitzina (1989)

12

Reference

r-NaNO2-1.1

r-Na2MoO4-1.1

r-NaI-6.1

r-NaI-5.1; 5.2

r-NaI-4.1

r-NaI-3.1

r-NaI-2.1

r-NaI-1.1

r-NaHS-1.1

r-NaHCO3-3.1

r-NaHCO3-1.1 r-NaHCO3-2.1

r-NaF-3.1

r-NaF-2.1

r-NaF-1.1

r-NaClO4-2.1; 2.2

r-NaClO4-1.1

r-NaCl-36.1; 36.2

r-NaCl-35.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 169

Continued

w

w w m m

m

m m

sodium nitrate

sodium nitrate

sodium nitrate

sodium nitrate

sodium nitrate

sodium nitrate

sodium hydroxide

sodium hydroxide

sodium hydroxide

sodium hydroxide

sodium hydroxide

sodium hydroxide

sodium hydroxide sodium hydroxide

sodium hydroxide

sodium hydroxide

sodium hydroxide

sodium perrhenate

sodium sulphate

NaNO3

NaNO3

NaNO3

NaNO3

NaNO3

NaNO3

NaOH

NaOH

NaOH

NaOH

NaOH

NaOH

NaOH NaOH

NaOH

NaOH

NaOH/NaOD

NaReO4

Na2SO4

w

m

m

m x

x

m

w

x

w

w

3

2

1

unit

Chemical names

Formula

Nonaqueous components

Table 2.5

0.65

2.52

8

6.0

1.1 0.10

0.93

3.1

0.75

0.80

0.91

0.49

6.3

0.89

0.88

0.20

0.90

0.47

5

max

Concentration

0.10

0.047

0.25

0.1

0.033

0.005 0.0045

0.024

0.29

0.002

0.048

0.45

0.030

2.1

0.10

0.10

0.050

0.40

0.050

4

min

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

20

15

250

323

100

25 374

25

100

30

20

150

0

16

19

50

20

25

25

6

min

300

125

300

573

350

412 550

400

250

350

400

400

350

334

300

300

350

350

300

7

max

Temp-re (°C)

150

0.55

10

30

30

300

4.8

50

400

30

30

30

30

9

max

Pressure

10

0.37

14

2

7.0

10 Sat

0.10

0.4

0.1

10

Sat.

Sat.

0.1

3.7

0.44

1.5

Sat.

Sat.

8

min

Pressure (MPa)

d, Vf

Vf,Vo

dd,Vf d

d

d,Vf,Vo

sv

Vs,Vm

d

d,Vo

d,Vf

d,Vf,Vo

d

d

d

d

d

dd,Vp

dd, Vf, Vo

10

Exper’tal data

VVP

VTD

VTD

VTD

VTD

VTD CVP

MBVV

VTD

EP

MBVV

HWT

HWT

VTD

CVP

CVP

CVP

HWT

HWT

11

Technique

Puchkov & Matashkin (1970) Puchkov et al. (1979a) Traktuev & Ptitzina (1989) Akhundov et al. (1991a) Abdulagatov & Azizov (2003b) Abdulagatov & Azizov (2005) Dibrov et al. (1964) Krumgalz & Mashovets (1964) Kerschbaum & Franck (1995) Alexandrov et al. (1989) Corti et al. (1990) Eberz & Franck (1995) Obsil (1997) Abdulagatov et al. (1998a) Corti & Simonson (2006) Hnedkovsky et al. (2007) Trevani et al. (2007) Lemire et al. (1992) Polyakov (1965)

12

Reference

r-Na2SO4-1.1

r-NaOH-10.1; 10.2

r-NaOH-10.1

r-NaOH-9.1

r-NaOH-7.1 r-NaOH-8.1

r-NaOH-6.1

r-NaOH-5.1

r-NaOH-4.1

r-NaOH-3.1;3.2

r-NaOH-2.1

r-NaOH-1.1

r-NaNO3-6.1

r-NaNO3-5.1; 5.2

r-NaNO3-4.1

r-NaNO3-3.1

r-NaNO3-2.1

r-NaNO3-1.1

13

Table code for Appendix

170 Hydrothermal Experimental Data

w m

m m m w

c m m m

sodium sulphate sodium sulphate

sodium sulphate

sodium sulphate

sodium sulphate

sodium sulphate

sodium sulphate

sodium sulphate

sodium sulphate

sodium pertechnetate

sodium wolframate

nickel nitrate

rubidium chloride

strontium chloride strontium chloride strontium nitrate

strontium nitrate

uranyl sulphate ytterbium perchlorate

zinc bromide

zinc chloride

zinc nitrate

Na2SO4 Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

Na2SO4

NaTcO4

Na2WO4

Ni(NO3)2

RbCl

SrCl2 SrCl2 Sr(NO3)2

Sr(NO3)2

UO2SO4 Yb(ClO4)3

ZnBr2

ZnCl2

Zn(NO3)2

m

w

m

w

m

m

m

m

w

w

m w

3

2

1

unit

Chemical names

Formula

Nonaqueous components

0.1

0.076

0.062

0.77 0.016

0.10

0.10 0.30 0.050

0.0010

0.29

0.098

0.01

0.0075

0.088

0.0049

0.058

0.058

0.050

0.0050

0.050 0.040

4

min

0.9

7.71

4.18

1.3 0.25

0.40

1.0 2.7

0.10

2.24

0.40

0.29

0.10

1.1

1.0

0.34

0.33

0.20

0.30

1.0 0.20

5

max

(c, m, v, w, x)

28

25

25

25 75

50

50 50 25

40

50

18

14

318

18

25

25

22

25

100

50 25

6

min

300

125

125

370 149

325

200 200 325

280

300

280

123

365

300

400

307

202

300

367

200 300

7

max

Temp-re (°C)

2.3

0.15

0.14

Sat 10

0.1

2 2.0 0.1

10

2

Sat.

0.6

Sat

2.4

9.9

9.9

2

2

Sat.

2 Sat.

8

min

40

60

60

30

50

50

35

40

31

79

10

30

9

max

(MPa)

Vs,Vf

d,Vf,Vo

d

d

d,Vf,Vo d

d

d,Vf,Vo

d,Vf,Vo

d dd,Vf,Vo

d

d,Vf,Vo d d

Vs

d,Vf

d

dd,Vp

d

d,Vo

dd,Vf,Vo

10

Exper’tal data

CVP

CVP

CVP

XRD VTD

CVP

VVP VVP CVP

PYC

CVP

HWT

VTD

PYC

CVP

VTD

CVP

VVP

VVP

g RD

VVP HWT

11

Technique

Ellis (1968) Puchkov et al. (1976) Khaibullin & Novikov (1973) Pepinov et al. (1985) Phutela & Pitzer (1986) Tsay et al. (1986b) Obsil et al. (1997; 1997a) Azizov & Akhundov (2000) Valyashko et al. (2000) Lemire et al. (1992) Maksimova et al. (1976) Azizov & Zeinalova (2004) Gorbachev et al. (1974b) Ellis (1967) Kumar (1986a) Akhmedova et al. (1991) Akhundov et al. (1992) Bell et al. (1970) Hakin et al. (2004) Safarov et al. (2006a) Safarov et al. (2006b) Azizov et al. (1996)

12

Reference

r-Zn(NO3)2-1.1

r-UO2SO4-1.1 r-Yb(ClO4)3-1.1

r-Sr(NO3)2-2.1

r-SrCl2-1.1 r-SrCl2-2.1 r-Sr(NO3)2-1.1

r-RbCl-1.1

r-Ni(NO3)2-1.1; 1.2

r-Na2WO4-1.1

r-Na2SO4-10.1

r-Na2SO4-9.1

r-Na2SO4-8.1

r-Na2SO4-7.1

r-Na2SO4-6.1

r-Na2SO4-5.1

r-Na2SO4-4.1

r-Na2SO4-2.1 r-Na2SO4-3.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 171

Continued

x x x w x x x m x x

argon methane methane

methane

methane

methane

methane

methane

methane

methane

methanol

methanol

methanol methanol

methanol

methanol

methanol

Ar CH4 CH4

CH4

CH4

CH4

CH4

CH4

CH4

CH4

CH4O

CH4O

CH4O CH4O

CH4O

CH4O

CH4O

x

x

x

m x

x

x

m

argon

Ar

3 x

2

1

unit

Binary systems – nonelectrolytes Ar argon

Chemical names

Formula

Nonaqueous components

Table 2.5

0.75

0.77

11.0 0.68

0.89

1.00

0.85

0.92

0.14

0.80

0.85

0.85

0.84

0.8 0.30 0.75

0.098

0.28

5

max

Concentration

0.36

0.25

0.23

0.15 0.10

0.099

0

0.05

0.32

0.110

0.06

0.06

0.16

0.05

0.05 0.062 0.11

0.076

0.01

4

min

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

60

25

10

150 200

50

150

250

157

25

353

250

250

250

204 353 375

50

374

6

min

148

250

120

250 250

300

300

380

426

432

450

380

380

380

390 376 450

443

400

7

max

Temp-re (°C)

18.4

60

21

30 13.5

13.7

11.5

63

30

35

250

63.2

63.2

62.4

337 250 200

34.6

310

9

max

Pressure

0.09

0.1

1.7

10 7

0.1

0.5

2.2

7.5

28

10

2.2

2.2

2.2

10 22 25

17.2

22.1

8

min

Pressure (MPa)

10

d.Ve

d

d

dd.Vf.V0 Vm

d.Ve

Vm

d

d

dd.Vf

Vm

Vm.B.C

d

d

Vm Vm Vm

dd.Vf

Vm

Exper’tal data

PYC

CVP

PYC

VTD VTD

VTD

PYC

CVP

CVP

VTD

VVP

CVP

CVP

CVP

VVP VVP VVP

VTD

VVP

11

Technique

Lentz & Franck (1969) Biggerstaff & Wood (1988) Wu et al. (1990) Welsh (1973) Sretenskaya et al. (1986) Abdulagatov et al. (1993a) Abdulagatov et al. (1993b) Abdulagatov et al. (1993c) Shmonov et al. (1993) Hnedkovsky et al. (1996) Fenghour et al. (1996b) Bazaev & Bazaev (2004) Pryanikova & Efremova (1972) Xiao et al. (1997) Degrange (1998) Hynek et al. (1999) Kuroki et al. (2001) Shahverdiyev & Safarov (2002) Aliev et al. (2003)

12

Reference

r-CH4O-4.1-4.3

r-CH4O-3.1

r-CH4O-2.1

r-CH4O-1.1-1.4

r-CH4-9.1

r-CH4-8.1;8.2

r-CH4-7.1

r-CH4-6.1; 6.2

r-CH4-5.1

r-CH4-4.1

r-CH4-3.1

r-Ar-3.1 r-CH4-1.1 r-CH4-2.1

r-Ar-2.1

r-Ar-1.1

13

Table code for Appendix

172 Hydrothermal Experimental Data

Chemical names

2

methanol

methanol

methanol

methanol

methanol

methanol

trifluoroethanol

trifluoroethanol

trifluoroethanol

trifluoroethanol

ethylene

glycine

ethanol

ethanol

ethanol

ethanol

ethanol

ethanol

ethanol

1,2-ethanediol

1,2-ethanediol

Formula

1

CH4O

CH4O

CH4O

CH4O

CH4O

CH4O

C2H3F3O2

C2H3F3O2

C2H3F3O2

C2H3F3O2

C2H4

C2H5NO2

C2H6O

C2H6O

C2H6O

C2H6O

C2H6O

C2H6O

C2H6O

C2H6O2

C2H6O2

Nonaqueous components

x

x

x

x

m

x

x

m

w

x

w

m

V%

m

m

x

x

x

x

x

m

3

unit

0.08

0.25

0.20

0.088

0.25

0.10

0.15

0.25

95

0.50

0.094

0.019

0.65

0.85

0.02

0.50

0.077

0.36

0.20

0.047

0.059

4

min

0.53

0.75

0.80

1.04

0.75

0.90

0.95

0.94

3.02

0.17

0.50

0.85

1.05

0.80

0.58

0.71

5

max

(c, m, v, w, x)

25

23

183

25

25

47

0

40

17

123

25

37

37

37

37

47

25

100

47

25

17

6

min

300

172.8

400

300

250

147

250

150

250

200

443

147

147

147

147

147

300

400

147

125

142

7

max

Temp-re (°C)

0.44

0.1

2.0

0.39

0.1

0.1

0.1

7.5

0.1

10

20

0.1

0.1

0.1

Sat.

0.1

0.4

0.04

0.1

0.1

5.6

8

min

30

2

51

30.3

60

200

78.4

30

12

30

34.3

200

200

200

200

30

91

200

60

28

9

max

(MPa)

d

d

d

dd,Vf,V0

d

d

dd

d

d

d

d

d

dd,Vf

dd,Vf

d

d,Ve

d,Ve

d

d

dd

d,B,C,D.E

10

Exper’tal data

VTD

PYC

CVP

VTD

CVP

MBVV

HWT

CVP

VVP

VTD

VTD

MBVV

MBVV

MBVV

MBVV

MBVV

VTD

CVP

MBVV

CVP

PYC

11

Technique

Kitajima et al. (2003) Safarov et al. (2003) Yokoyama & Uematsu (2003) Bazaev et al. (2004) Hyncica et al. (2004) Osada et al. (1999) Kabata et al. (1993a) Kabata et al. (1993b) Kabata et al. (1993c) Kabata et al. (1993d) Biggerstaff & Wood (1988) Hakin et al. (1998) Sheydlin & Sheyfer (1953) Popov & Malov (1972) Agaev et al. (1974) Takiguchi et al. (1996) Safarov & Shakhverdiev (2001) Hyncica et al. (2004) Bazaev et al. (2007) Sun & Teja (2003) Hyncˇ ica et al. (2006b)

12

Reference

r-1,2-C2H6O2-1.1

r-C2H6O-5.1; 5.2; 5.3

r-C2H6O-4.1

r-C2H6O-3.1

r-C2H6O-2.1

r-C2H6O-1.1

r-C2H5NO2-1.1

r-C2H4-1.1

r-CH4O-6.1

r-CH4O-5.1-5.4

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 173

Continued

m m

m

m x

dimethylamine

propene

acetone

propionamide

a-alanine

b-alanine

L-alanine

L-serine

1-propanol

1-propanol

1-propanol

1-propanol

2-propanol

2-propanol

propylene glycol

1,2-propanediol

1,3-propanediol

C2H7N

C3H6

C3H6O

C3H7NO

C3H7NO2

C3H7NO2

C3H7NO2

C3H7NO3

C3H8O

C3H8O

C3H8O

C3H8O

C3H8O

C3H8O

C3H8O2

C3H8O2

C3H8O2

m

m

m

m

x

x

m

m

m

m

x

m

3

2

1

unit

Chemical names

Formula

Nonaqueous components

Table 2.5

0.08

0.07

0.25

0.086

0.11

0.094

0.25

0.25

0.12

0.16

0.29

0.10

0.10

0.12

0.10

0.24

0.097

4

min

0.50

0.49

0.75

0.82

1.01

0.85

0.74

0.75

3.97

1.77

1.18

1.01

1.12

0.76

1.98

5

max

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

25

25

24

25

29

25

12

100

100

25

125

61

25

100

29

266

10

6

min

300

300

171

300

248

300

157

300

250

149

249

205

250

250

248

330

250

7

max

Temp-re (°C)

0.44

0.44

0.1

0.39

0.13

0.42

5.1

0.1

28

10

10

10.3

0.1

28

0.13

60

0.1

8

min

30

30

2.2

30.3

28

30.3

30

5.2

30

30

20.6

20

28

247

10

9

max

Pressure (MPa)

10

dd,Vf,V0

dd,Vf,V0

d

dd

dd,Vf

dd

d

d,B

Vf,V0

dd,Vf

dd,Vf

dd,Vf

dd,Vf

Vf,V0

dd,Vf

Vm

dd,Vf

Exper’tal data

VTD

VTD

PYC

VTD

VTD

VTD

PYC

CVP

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VVP

VTD

11

Technique

Shvedov & Tremaine (1997) Sanchez & Lentz (1973) Schulte et al. (1999) Criss & Wood (1996) Clarke & Tremaine (1999) Clarke & Tremaine (1999) Hakin et al. (2000) Marriott et al. (2001) Criss & Wood (1996) Shahverdiyev & Safarov (2002) Kitajima et al. (2003) Hyncica et al. (2004) Schulte et al. (1999) Hyncica et al. (2004) Sun & Teja (2004a) Hyncˇ ica et al. (2006b) Hyncˇ ica et al. (2006b)

12

Reference

r-1,3-C3H8O2-1.1

r-1,2-C3H8O2-1.1

r-C3H8O2-1.1

r-2-C3H8O-2.1

r-2-C3H8O-1.1

r-1-C3H8O-3.1

r-1-C3H8O-2.1;2.2

r-1-C3H8O-1.1

r-L-C3H7NO2-1.1

r-b-C3H7NO2-1.1

r-a-C3H7NO2-1.1

r-C3H7NO-1.1

r-C3H6O-1.1

r-C3H6-1.1

r-C2H7N-1.1

13

Table code for Appendix

174 Hydrothermal Experimental Data

Chemical names

2

1,2,3-propanetriol

propylamine

propylamine hydrochoride

glycylglycine

morpholine

n-butane

n-butane

diethyl ether

1-butanol

2-butanol

2-methyl-1-propanol

2-methyl-2-propanol

1,2-dimethoxyethane

1,2-dimethoxyethane

1,3-butanediol

1,4-butanediol

1,4-butanediol

2,3-butanediol

diethylene glycol

1,4-butanediamine

pyridine

Formula

1

C3H8O3

C3H9N

C3H10ClN

C4H8N2O3

C4H9NO

C4H10

C4H10

C4H10O

C4H10O

C4H10O

C4H10O

C4H10O

C4H10O2

C4H10O2

C4H10O2

C4H10O2

C4H10O2

C4H10O2

C4H10O3

C4H12N2

C5H5N

Nonaqueous components

m

m

x

m

m

m

m

m

m

m

m

m

m

m

x

x

m

m

m

m

m

3

unit

0.12

0.11

0.25

0.08

0.07

0.12

0.08

0.08

0.10

0.04

0.03

0.05

0.05

0.084

0.05

0.40

0.050

0.12

0.19

0.12

0.07

4

min

0.75

0.46

0.49

0.51

0.41

1.00

0.57

0.61

0.58

0.61

0.50

0.9

12.0

1.30

0.52

5

max

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

100

100

23

25

25

100

25

25

29

25

25

25

25

29

223

38

10

25

100

100

25

6

min

325

250

170

300

300

250

300

300

248

300

300

300

300

248

434

238

300

150

250

250

300

7

max

Temp-re (°C)

28

28

0.1

0.45

0.45

28

0.45

0.77

0.13

0.1

0.1

0.1

0.1

0.13

9

0.7

0.1

10

28

28

0.44

8

min

2

30

30

30

30

28

31

30

30

30

28

310

17

10

30

30

9

max

Pressure (MPa)

10

Vf,V0

Vf,V0

d

dd,Vf,V0

dd,Vf,V0

Vf,V0

dd,Vf,V0

dd,Vf,V0

dd,Vf

dd,Vf,V0

dd,Vf,V0

dd,Vf,V0

dd,Vf,V0

dd,Vf

Vm

Vm

dd,Vf

dd,Vf

Vf,V0

Vf,V0

dd,Vf,V0

Exper’tal data

VTD

VTD

PYC

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VVP

(*)

VTD

VTD

VTD

VTD

VTD

11

Technique

Hyncˇ ica et al. (2006b) Criss & Wood (1996) Criss & Wood (1996) Marriott et al. (2001) Tremaine et al. (1997) Reamer et al. (1952) Yiling et al. (1991) Schulte et al. (1999) Hyncˇ ica et al. (2006a) Hyncˇ ica et al. (2006a) Hyncˇ ica et al. (2006a) Hyncˇ ica et al. (2006a) Schulte et al. (1999) Cibulka et al. (2007b) Hyncˇ ica et al. (2006c) Criss & Wood (1996) Hyncˇ ica et al. (2006c) Hyncˇ ica et al. (2006c) Sun & Teja (2003) Criss & Wood (1996) Criss & Wood (1996)

12

Reference

r-C5H5N-1.1

r-1,4-C4H12N2-1.1

r-2,3-C4H10O2-1.1

r-1,4-C4H10O2-2.1

r-1,4-C4H10O2-1.1

r-1,3-C4H10O2-1.1

r-1,2-C4H10O2-2.1

r-1,2-C4H10O2-1.1

r-2-2-C4H10O-1.1

r-2-1-C4H10O-1.1

r-2-C4H10O-1.1

r-1-C4H10O-1.1

r-C4H10O-1.1

r-C4H10-2.1

r-C4H10 -1.1

r-C4H9NO-1.1

r-C3H10ClN-1.1

r-C3H9N-1.1

r-1,2,3-C3H8O3-1.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 175

Continued

2

2,4-pentanedione

proline

3-pentanone

n-pentane

n-pentane

n-pentane

1,5-pentanediol

2,2-dimethyl-1,3propanediol 3,5-dioxaheptane

3,6-dioxa-1-heptanol

2,2-bis(hydroximethyl)1,3-propanediol 1,2,3,4,5-pentanepentaol

1-pentanol

2-chlorophenol

4-chlorophenol

nitrobenzene

2-nitrophenol

1

C5H8O2

C5H9NO2

C5H10O

C5H12

C5H12

C5H12

C5H12O2

C5H12O2

C5H12O3

C5H12O4

C5H14

C6H5ClO

C6H5ClO

C6H5NO2

C6H5NO3

C5H12O5

C5H12O2

Chemical names

Formula

Nonaqueous components

Table 2.5

m

m

m

m

m

m

m

m

m

m

m

x

x

x

m

m

m

3

unit

0.020

0.0063

0.056

0.025

0.029

0.05

0.05

0.1

0.08

0.05

0.11

0.028

0.028

0.028

0.1

0.14

0.1

4

min

0.060

0.15

0.17

0.076

0.090

0.40

0.40

0.4

0.31

0.50

1.00

0.69

0.69

0.69

0.4

0.80

0.4

5

max

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

25

25

25

25

25

25

25

25

25

25

29

374.05 (crit) 374

374(crit)

25

61

25

6

min

300

300

300

300

140

300

300

300

170

300

248

300

251

225

7

max

Temp-re (°C)

0.1

0.1

0.1

0.1

0.1

0.33

0.47

0.8

0.24

0.33

0.13

4.3

5

4.3

0.8

10

0.8

8

min

30

30

30

30

19

30

30

30

30

30

28

41

37.5

dd

dd

dd

dd

dd,Vf

dd,Vf,V0

dd,Vf,V0

dd,Vf,V0

dd,Vf,V0

dd,Vf,V0

dd,Vf

d

Ve

d.VM.Ve.Vf

41

dd,Vf

dd,Vf,V0

dd,Vf,V0

10

Exper’tal data

30

20.2

30

9

max

Pressure (MPa)

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

CVP

CVP

CVP

VTD

VTD

VTD

11

Technique

Cibulka et al. (2007a) Clarke & Tremaine (1999) Cibulka et al. (2007a) Abdulagatov et al. (1998c) Abdulagatov et al. (1998b) Bazaev & Bazaev (2004) Schulte et al. (1999) Hnedkovsky & Cibulka (2007) Cibulka et al. (2007b) Cibulka et al. (2007b) Hnedkovsky & Cibulka (2007) Hnedkovsky & Cibulka (2007) Inglese et al. (1996) Hnedkovsky et al. (2001) Hnedkovsky et al. (2001) Hnedkovsky & Cibulka (2003) Hnedkovsky & Cibulka (2003)

12

Reference

r-2-C6H5NO3-1.1

r-C6H5NO2-1.1

r-4-C6H5ClO-1.1

r-2-C6H5ClO-1.1

r-C5H12O5-1.1

r-C5H12O4-1.1

r-3,6-C5H12O3-1.1

r-3,5-C5H12O2-1.1

r-2.2-C5H12O2-1.1

r-1,5-C5H12O2-1.1

r-C5H12-3.1

r-C5H12-2.1

r-C5H12-1.1

r-C5H10O-1.1

r-C5H9NO2-1.1

r-C5H8O2-1.1

13

Table code for Appendix

176 Hydrothermal Experimental Data

Chemical names

2

3-nitrophenol

4-nitrophenol

benzene

benzene

benzene benzene

benzene

benzene

phenol

phenol

pyrocatechol

resorcinol

hydroquinone

aniline

3-aminophenol

1,2-diaminobezene

2,5-hexanedione

cyclohexane cyclohexanol

n-hexane

n-hexane

Formula

1

C6H5NO3

C6H5NO3

C6H6

C6H6

C6H6 C6H6

C6H6

C6H6

C6H6O

C6H6O

C6H6O2

C6H6O2

C6H6O2

C6H7N

C6H7NO

C6H8N2

C6H10O2

C6H12 C6H12O

C6H14

C6H14

Nonaqueous components

w

x

m m

m

m

m

m

m

m

m

m

m

x

m

m x

x

x

m

m

3

unit

0.013

0.39

0.085 0.10

0.094

0.059

0.0048

0.11

0.13

0.20

0.20

0.16

0.11

0.028

0.022

0.054 0.028

0.93

0.0004

0.023

0.0026

4

min

0.46

0.80

1.31 0.30

1.01

0.25

0.24

0.29

0.53

3.45

3.0

0.82

0.93

2.50 0.44

0.28

1.0

0.092

0.0094

5

max

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

250

282

300 29

29

25

25

25

25

25

25

25

100

300

200 374.05 (crit) 25

350

38

25

25

6

min

350

426

402 248

248

300

300

300

200

200

200

300

325

375

300

412

238

275

300

7

max

Temp-re (°C)

2.1

19.8

10 0.13

0.13

0.1

0.1

0.1

0.1

0.1

0.1

0.1

28

2.3

0.47

10 3.5

2.6

6.9

0.1

0.1

8

min

15.1

247

33 28

28

30

32

30

30

30

30

31

40

30.3

33 38

15.2

34.5

30

30

9

max

Pressure (MPa)

10

d

Vm

dd,Vf,V0 dd,Vf

dd,Vf

dd

dd

dd

dd

dd

dd

dd

Vf,V0

d

dd

dd,Vf,V0 d.Vm

d

d

dd

dd

Exper’tal data

CVP

VVP

VTD VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

CVP

VTD

VTD CVP

CVP

VVP

VTD

VTD

11

Technique

Hnedkovsky & Cibulka (2003) Hnedkovsky & Cibulka (2003) Thompson & Snyder (1964) Abdulagatov et al. (1993b) Degrange (1998) Abdulagatov et al. (1998d) Hyncica et al. (2003) Bazaev & Bazaev (2004) Criss & Wood (1996) Hynek et al. (1997b) Jedelsky et al. (1999) Jedelsky et al. (1999) Jedelsky et al. (1999) Ruzicka et al. (2000) Striteska et al. (2003) Hyncica et al. (2002) Schulte et al. (1999) Degrange (1998) Schulte et al. (1999) Yiling et al. (1991) Abdulagatov et al. (1992)

12

Reference

r-C6H14-2.1

r-C6H14-1.1

r-C6H12O-1.1

r-2,5-C6H10O2-1.1

r-1,2-C6H8N2-1.1

r-3-C6H7NO-1.1

r-C6H7N-1.1

r-1,4-C6H6O2-1.1

r-1,3-C6H6O2-1.1

r-1,2-C6H6O2-1.1

r-C6H6O-2.1

r-C6H6O-1.1

r-C6H6-5.1

r-C6H6-4.1

r-C6H6-3.1

r-C6H6-2.1

r-C6H6-1.1

r-4-C6H5NO3-1.1

r-3-C6H5NO3-1.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 177

Continued

Chemical names

2

n-hexane

n-hexane

n-hexane

n-hexane n-hexane

n-hexane

n-hexane

n-hexane

n-hexane

1,6-hexanediol

1,6-hexanediol

3,6-dioxaoctane

Dipropylene glycol

2,5,8-trioxanonane

Triethylene glycol

1,6-hexanediamine

benzonitrile

2-cyanophenol

toluene

Formula

1

C6H14

C6H14

C6H14

C6H14 C6H14

C6H14

C6H14

C6H14

C6H14

C6H14O2

C6H14O2

C6H14O2

C6H14O3

C6H14O3

C6H14O4

C6H16N2

C7H5N

C7H5NO

C7H8

Nonaqueous components

Table 2.5

x

x

x

m

m

m

m

x

m

x

m

m

m

x

x

x

x

m x

3

unit

0.042

0.02

0.0094

0.120

0.25

0.1

0.25

0.04

0.05

0.061

0.020

0.002

0.129

0.0021

0.072 0.027

0.38

0.20

0.060

4

min

2.11

0.18

0.042

0.75

0.4

0.75

0.16

0.40

0.85

0.92

0.994

0.01

1.41 0.90

0.74

0.94

0.80

5

max

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

250

25

25

100

21

25

20

25

25

100

374.1(crit)

250

495

370

300 370

92

250

250

6

min

412

225

300

250

172

300

171

300

300

250

crit

378

644

378

402 375

349

350

350

7

max

Temp-re (°C)

10

0.1

0.1

28

0.1

0.8

0.1

0.24

0.33

28

8.5

2.1

8

20 5

0.29

2.1

2.1

8

min

33

30

30

2

30

2.2

30

30

33.5

40

dd,Vf,V0

dd

dd

Vf,V0

d

dd,Vf,V0

d

dd,Vf,V0

dd,Vf,V0

Vf,V0

d

d

d

<6

dd,Vf,V0 Ve

d

Vm,B,C

d

d,Vm,Z

10

Exper’tal data

34.7

33 37.5

24

15

15.1

9

max

Pressure (MPa)

VTD

VTD

VTD

VTD

PYC

VTD

PYC

VTD

VTD

VTD

CVP

CVP

CVP

CVP

VTD CVP

PYC

CVP

CVP

11

Technique

Abdulagatov et al. (1993b) Abdulagatov et al. (1994) Kamilov et al. (1996) Degrange (1998) Abdulagatov et al. (1998c) Abdulagatov et al. (2001) Kamilov et al. (2001) Bazaev & Bazaev (2004) Abdulagatov et al. (2005) Criss & Wood (1996) Hnedkovsky & Cibulka (2007) Cibulka et al. (2007b) Sun & Teja (2004a) Cibulka et al. (2007b) Sun & Teja (2003) Criss & Wood (1996) Striteska et al. (2003) Striteska et al. (2003) Degrange (1998)

12

Reference

r-2-C7H5NO-1.1

r-C7H5N-1.1

r-1,6-C6H16N2-1.1

r-2,5,8-C6H14O3-1.1

r-C6H14O3-1.1

r-3,6-C6H14O2-1.1

r-1,6-C6H14O2-2.1

r-1,6-C6H14O2-1.1

r-C6H14-10.1

r-C6H14-9.1

r-C6H14-8.1

r-C6H14-7.1

r-C6H14-6.1

r-C6H14-5.1

r-C6H14-4.1

r-C6H14-3.1

13

Table code for Appendix

178 Hydrothermal Experimental Data

Chemical names

2

toluene

toluene

toluene

toluene

m-cresol

o-cresol

p-cresol

benzyl alcohol

phenylmethanol

m-toluidine

o-toluidine

p-toluidine

n-heptane

n-heptane

n-heptane

n-heptane

n-heptane

n-heptane

2-phenylethanol

n-octane

Formula

1

C7H8

C7H8

C7H8

C7H8

C7H8O

C7H8O

C7H8O

C7H8O

C7H8O

C7H9N

C7H9N

C7H9N

C7H16

C7H16

C7H16

C7H16

C7H16

C7H16

C8H10O

C8H18

Nonaqueous components

x

x

x

m

x

x

x

x

x

w

m

m

m

m

m

m

m

m

x

m

3

unit

0.23

0.02922

0.028

0.028

0.028

0.042

0.0415

0.112

0.040

0.040

0.040

0.098

0.10

0.046

0.042

0.041

0.001

0.0062

0.029

0.0008

4

min

0.85

0.13

0.91

0.90

0.71

0.91

0.91

0.90

0.07

0.12

0.12

0.35

0.35

0.67

0.21

0.15

0.029

0.0085

5

max

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

350

25

300

374.05 (crit) 370

300

300

380

25

25

25

25

29

25

25

25

350

25

350

350

6

min

300

400

375

400

400

400

300

300

300

300

248

300

300

300

400

300

400

400

7

max

Temp-re (°C)

3.1

0.45

2.1

15.3

30.7

40

37.5

41

4.7 4

25

30

27

30

30

30

30.3

28

9.4

9.4

9.4

46

30.3

39.2

46

9

max

5

0.5

5

0.1

0.1

0.1

0.4

0.13

0.1

0.1

0.1

11.4

0.47

11.4

11

8

min

Pressure (MPa)

10

d

dd

d

Ve

d.Vm

Vm

Vm

Vm,Vf

dd

dd

dd

dd

dd,Vf

dd

dd

dd

d

dd

d

d

Exper’tal data

CVP

VTD

CVP

CVP

CVP

CVP

CVP

CVP

VTD

VTD

VTD

VTD

VTD

VTD

VTD

VTD

CVP

VTD

CVP

CVP

11

Technique

Rabezkii et al. (2001) Kiselev et al. (2002) Hyncica et al. (2003) Bazaev & Bazaev (2004) Hnedkovsky et al. (1998) Hnedkovsky et al. (1998) Hnedkovsky et al. (1998) Schulte et al. (1999) Striteska et al. (2004) Ruzicka et al. (2000) Ruzicka et al. (2000) Ruzicka et al. (2000) Abdulagatov et al. (1996b) Abdulagatov et al. (1997a) Abdulagatov et al. (1997b) Abdulagatov et al. (1998d) Abdulagatov et al. (1998c) Bazaev & Bazaev (2004) Striteska et al. (2004) Abdulagatov et al. (1993b)

12

Reference

r-C8H18-1.1

r-2-C8H10O-1.1

r-C7H16-6.1

r-C7H16-5.1

r-C7H16-4.1

r-C7H16-3.1

r-C7H16-2.1

r-C7H16-1.1

r-p-C7H9N-1.1

r-o-C7H9N-1.1

r-m-C7H9N-1.1

r-C7H8O-2.1

r-C7H8O-1.1

r-p-C7H8O-1.1

r-o-C7H8O-1.1

r-m-C7H8O-1.1

r-C7H8-4.1

r-C7H8-3.1

r-C7H8-2.1

r-C7H8-1.1;1.2

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 179

Continued

x w x

x x x x x w w m m x x

x

n-octane

n-octane

tripropylene glycol

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

C8H18

C8H18

C9H20O4

CO2

CO2

CO2

CO2

CO2

CO2

CO2 CO2

CO2

CO2

CO2

CO2

CO2

CO2

x

x

x

n-octane

C8H18

3

2

1

unit

Chemical names

Formula

Nonaqueous components

Table 2.5

0.60

0.0087

0.87

0.78

0.94

0.98

0.80 0.98

0.88

0.62

0.80

1.00

0.80

0.50

0.75

0.85

0.79

0.61

5

max

Concentration

0.20

0.0048

0.12

0.072

0.12

0.50

0.20 0.50

0.065

0.087

0.20

0

0.2

0.05

0.25

0.031

0.031

0.031

4

min

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

400

350

400

378

80

50

300 50

100

400

400

450

400

100

22

350

374.05 (crit) 374

6

min

370

700

452

198

225

400 225

200

500

500

800

750

500

174

374

7

max

Temp-re (°C)

40

28.1

600

38

102.1

10.3

180 10.3

3.3

500

570

50

200

184

2.2

43

Pressure

10

19.6

100

28

20.4

0.27

5 0.27

0.2

100

15

5

30

2

0.1

3.1

35

43

4.6 7.5

9

max

8

min

Pressure (MPa)

d

d

Vm,Ve B,C

Vm

Vm,Ve

Vm,Ve

Z

Z

?

d

d

Ve

d.Vm

Vm

dd,Vf,Vm

Vm,Ve,Vp

dd,Vf,Vm, Ve

10

Exper’tal data

CVP

VTD

SFIT

VTD

VVP

CVP

CVP CVP

VVP

CVP

CVP

PYC

VVP

CVP

PYC

CVP

CVP

CVP

11

Technique

Abdulagatov et al. (1998d) Abdulagatov et al. (1998c) Bazaev & Bazaev (2004) Sun & Teja (2004a) Khitarov & Malinin (1956) Franck & Todheide (1959) Greenwood (1969) Shmulovich et al. (1979) Shmulovich et al. (1980) Zawisza et al. (1981) Zakirov (1984) Patel et al. (1987) Patel & Eubank (1988) Nighswander et al. (1989) Crovetto et al. (1990; 1991) Sterner & Bodnar (1991) Crovetto & Wood (1992, 1996) Abdulagatov et al. (1995)

12

Reference

r-CO2-14.1

r-CO2-13.1

r-CO2-12.1

r-CO2-11.1

r-CO2-10.1

r-CO2-9.1

r-CO2-7.1 r-CO2-8.1

r-CO2-6.1

r-CO2-5.1

r-CO2-4.1

r-CO2-3.1

r-CO2-2.1

r-CO2-1.1-1.7

r-C9H20O4-1.1

r-C8H18-4.1

r-C8H18-3.1

r-C8H18-2.1

13

Table code for Appendix

180 Hydrothermal Experimental Data

x x x x x x x m w

x x x

carbon dioxide

carbon dioxide

carbon dioxide

carbon dioxide

hydrogen

helium

nitrogen

nitrogen

nitrogen

ammonia

ammonia

ammonia

ammonia

oxygen

xenon

xenon

CO2

CO2

CO2

CO2

H2

He

N2

N2

N2

NH3

NH3

NH3

NH3

O2

Xe

Xe

x

boric acid

boric acid boric acid

H3BO3

H3BO3 H3BO3

w m

w

Binary systems – acids boric acid H3BO3

m

x

m x

3

2

1

unit

Chemical names

Formula

Nonaqueous components

0.21 ?

?

0.91

0.60

0.072

0.77

0.94

0.84

0.70

0.90

3.11

0.95

0.94

0.87

0.80

0.38

0.90

0.79

0.94

0.18

5

max

0.04

0.10

0.20

0.060

0.030

0.1

0.30

0.10

0.70

0.19

0.36

0.07

0.1

0.20

0.005

0.10

0.108

0.21

0.150

4

min

(c, m, v, w, x)

18 25

210

200

26

216

199

37

37

28

25

156

250

207

410

374

400

1100

142

25

6

min

258 200

450

550

444

500

389

127

127

249

432

433

390

385

450

381

1400

427

432

7

max

Temp re ( C)

6

1

d Vo

d

dd,Vf

Vm

Vm

d

d

d

dd,Vf

d

d

Vm

Vm

Vm

d,Ve

Vm

d

dd,Vf

<20 Sat

10

Exper’tal data

d

35.8

410

280

17

17

20

37

31

69.3

270

200

252

100

1940

35

35

9

max

Sat

Sat

21

15

19.5

0.2

0.1

3

0.1

13

2.1

15.5

60

23

9.9

950

8

min

(MPa)

HWT VVP

PYC

PYC

VTD

VVP

VVP

MBVV

MBVV

PYC

VTD

CVP

CVP

VVP

VVP

VVP

VTD

SFIT

CVP

VTD

11

Technique

Grigoriev & Nikolaev (1967) Kodama & Yokokawa (1970) Popov (1970) Ellis & McFadden (1972)

Hnedkovsky et al. (1996) Fenghour et al. (1996a) Frost & Wood (1997) Seitz & Blencoe (1999) Seward & Franck (1981) Sretenskaja et al. (1995) Japas & Franck (1985a) Abdulagatov et al. (1993b) Fenghour et al. (1993) Hnedkovsky et al. (1996) Magee & Kagawa (1998) Munakata et al. (2002) Kondo et al. (2002) Japas & Franck (1985b) Franck et al. (1974) Biggerstaff & Wood (1988)

12

Reference

r-H3BO3-3.1

r-H3BO3-2.1

r-H3BO3-1.1

r-Xe-2.1

r-Xe-1.1;1.2

r-O2-1.1-1.3

r-NH3-2.1

r-NH3-1.1

r-N2-3.1

r-N2-2.1

r-N2-1.1-1,3

r-He-1.1

r-H2-1.1

r-CO2-18.1

r-CO2-17.1

r-CO2-16.1;16.2

r-CO2-15.1

13

Table code for Appendix

pVTx Properties of Hydrothermal Systems 181

Continued

m

boric acid

boric acid

boric acid

boric acid

boric acid

hydrochloric acid

hydrochloric acid

hydrochloric acid

hydrochloric acid

perchloric acid

hydrogen sulfide

sulphuric acid

acetic acid

acetic acid acetic acid

propionic acid

succinic acid

H3BO3

H3BO3

H3BO3

H3BO3

H3BO3

HCl

HCl

HCl

HCl

HClO4

H2S

H2SO4

C2H4O2

C2H4O2 C2H4O2

C3H6O2

C4H6O4

Nonaqueous components

m

boric acid

H3BO3

m

m

w m

x

w

m

m

w

c

m

m

m

m

m

w

3

2

1

unit

Chemical names

Formula

Nonaqueous components

Table 2.5

0.92 1.53

0.94

0.99

0.31

0.4

2.43

6.0

2.0

0.53

0.61

0.70

0.75

0.72

0.040

5

max

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

0.12

0.12

0.25 0.20

0.54

0.90

0.23

0.023

0.22

0.10

0.37

0.20

0.062

0.068

0.050

0.20

0.17

0.020

4

min

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

250

250

190 300

330

200

432

149

300

350

530

200

300

250

300

432

301

350

7

max

Temp-re (°C)

100

100

21 25

322

100

25

74

250

25

25

25

23

102

25

25

25

75

6

min

Temp-re (°C)

1.5 37

35

30

28

150

48

5.5

50

37

79

31

9

max

Pressure (MPa)

28

28

0.1 10

cr

Sat

1.0

10

14

10

2.5

2

0.82

0.6

10

0.1

9.9

1.4

8

min

Pressure (MPa)

Vs,Vf

d

Vf.Vo

Vf.Vo

d dd.Vf.Vo

d

d

dd.Vf

dd.Vf.Vo

d.Vf.Vo

d.Vf.Vo

d

Vo

d.Vf

d.Vf.Vo

d

dd,Vf,Vo

10

Exper’tal data

VTD

VTD

PYC VTD

SAM

PYC

VTD

VTD

VTD

VTD

CVP

VVP

CVP

VTD

CVP

VTD

CVP

CVP

11

Technique

Rivkin et al. (1986) Alekhin et al. (1993a) Hneˇ dkovsky et al. (1995) Azizov & Akhundov (1996) Ganopolsky et al. (1996a) Abdulagatov & Azizov (2004c) Ellis & McFadden (1968) Rau & Kutty (1972) Sharygin & Wood (1997) Trevani et al. (2007) Hakin et al. (2004) Hneˇ dkovsky et al. (1996) Zaitsev et al. (1996) Vandana & Teja (1995) Sun et al. (1995) Majer et al. (2000) Criss & Wood (1996) Criss & Wood (1996)

12

Reference

Table code for

r-C4H6O4-1.1

r-C3H6O2-1.1

r-C2H4O2-2.1 r-C2H4O2-3.1

r-C2H4O2-1.1

r-H2SO4-1.1

r-H2S-1.1

r-HClO4-1.1

r-HCl-3.1; 3.2

r-HCl-2.1

r-HCl-1.1

r-H3BO3-9.1

r-H3BO3-8.1

r-H3BO3-7.1

r-H3BO3-6.1

r-H3BO3-5.1

r-H3BO3-4.1

13

Table code for Appendix

182 Hydrothermal Experimental Data

NaCl + Na2SO4

NaCl + NaF

NaB(OH)4 + NaOH

MgCl2 + NaCl

MgCl2 + NaCl

magnesium chloride + sodium chloride sodium borate + sodium hydroxide sodium chloride + sodium fluoride sodium chloride + sodium sulphate w w w w w w w w

m m w w

0.05 0.05 0.006 0.003 0.05 0.005 0.01 0.01

0.12 0.12 0 0

0 0

potassium hydroxide + lithium hydroxide magnesium chloride + sodium chloride

0.012

KOH + LiOH

m

0.011

w w

4-aminobenzoic acid

C7H7NO2

m

0.0088

potassium chloride + magnesium chloride

2-aminobenzoic acid

C7H7NO2

m

0.015

KCl + MgCl2

4-hydroxybenzoic acid

C7H6O3

m

0.0037

0 0

3-hydroxybenzoic acid

C7H6O3

m

0.05

w w

2-hydroxybenzoic acid

C7H6O3

x

0.0062

0.007 0.06

benzoic acid

C7H6O2

m

0.090 0.12

m m

benzoic acid

C7H6O2

m m

4

0.018 0.1

tartaric acid adipic acid

C4H6O6 C6H10O4

3

min

m m

2

1

unit

Ternary systems – electrolytes hydrochloric acid + HCl + C2H8NCl dimethylammonium chloride hydrochloric HCl + C4H10ClNO acid + morpholinium chloride KCl + NaCl potassium chloride + sodium chloride

Chemical names

Formula

0.02 0.02

0.87 0.2 0.2

0.15

2.14 2.28 0.96 0.45

0.45 0.96

0.45 0.3

0.016 0.66

0.089 0.57

0.036

0.033

0.027

0.045

0.011

1.0

0.023

0.64

5

max

25

20

25

25

100

100

100

100

10

10

25

25

25

25

25

107

25

10 100

6

min

400

325

412

300

200

250

200

200

300

250

225

225

225

225

170

180

200

256 250

7

max

0.1

0.1

10

4.5

Sat

0.4

Sat

Sat

0.1

0.1

0.1

0.1

0.1

0.1

0.1

~20

0.1

0.1 28

8

min

58

40

30

40

4.8

10

10

30

30

30

30

30

30

10.4

9

max 10

d

d

dd.Vf

d

d

d.Vf.Vo

d

d

dd.Vf

dd.Vf

dd

dd

dd.Vo

dd.Vo

dd.Vo

d

dd.Vo

dd.Vf Vf.Vo

Exper’tal data

CVP

CVP

VTD

CVP

PYC

VTD

PYC

PYC

VTD

VTD

VTD

VTD

VTD

VTD

VTD

PYC

VTD

VTD VTD

11

Technique

Guseynov et al. (1991) Abdullaev et al. (1983)

Akhumov & Vasil’ev (1932, 1935, 1936) Akhumov & Vasil’ev (1932, 1935, 1936) Corti & Svarc (1995) Akhumov & Vasil’ev (1932, 1935, 1936) Melikov et al. (1995) Obsil (1997)

Shvedov & Tremaine (1997) Tremaine et al. (1997)

Xie et al. (2004) Criss & Wood (1996) Jedelsky´ et al. (2000) Sun and Teja (2004b) Jedelsky´ et al. (2000) Jedelsky´ et al. (2000) Jedelsky´ et al. (2000) Hyncica et al. (2002) Hyncica et al. (2002)

12

Reference

r-NaCl/SO4-1.1

r-NaF+NaCl-1.1

r-NaB(OH)4+NaOH-1.1

r-NaCl+MgCl2-2.1

r-NaCl+MgCl2-1.1

r-LiOH+KOH-1.1

r-KCl+ MgCl2-1.1

r-NaCl+ KCl-1.1

r- C4H10ClNO+HCl-1.1

r-C2H8ClN+HCl-1.1

r-4-C7H7NO2-1.1

r-2-C7H7NO2-1.1

r-4-C7H6O3-1.1

r-3-C7H6O3-1.1

r-C7H6O2-2.1

r-C7H6O2-1.1

r-C4H6O6-1.1 r-C6H10O4-1.1

13

Appendix

pVTx Properties of Hydrothermal Systems 183

Continued

2

1

25 25 25

0.20

0.036 0.10

w1 w1 0.15 w1 0.03 (1) – total concentration

NaCl – CaCl2 – MgCl2

KCl – CaCl2 – MgCl2 KCl – CaCl2 – MgCl2

200

25

102

300 300

350

250

200

200

80

102

520

428

135

378

516

526

450

406

350

7

max

2.0

100.3

281

154.3

251.8

263

265

270

57

9

max

0.4 0.35

1.2

0.60

0.60

21.1

3.0

41.7

48.6

40

67

25.2

0.1

8

min

Pressure (MPa)

10

d d

d

d.Vf.Vo

d.Vf.Vo

d

d

Vm

d

d

Vm

Vm

Vm

d

Exper’tal data

CVP CVP

CVP

VTD

VTD

VVP

VVP

VVP

VVP

VVP

VVP

VVP

VVP

CVP

11

Technique

Krader & Franck (1987) Krader & Franck (1987) Michelberger & Franck (1990) Michelberger & Franck (1990) Gehrig et al. (1986) Nighswander et al. (1989) Ellis & McFadden (1972) Ganopolsky et al. (1996a) Ganopolsky et al. (1996b) Abdullaev et al. (1992) Melikov (1999) Melikov (2000)

Heilig & Franck (1990)

Mamedov et al. (1984)

12

Reference

r-K,Ca,Mg/Cl-1.1 r-K,Ca,Mg/Cl-2.1

r-Na,Ca,Mg/Cl-1.1

r-H3BO3+ NaOH-1.2

r-H3BO3+ NaOH-1.1

r-NaHCO3-2.1

r-CO2+ NaCl-1.1

r-NaCl+ CO2-1.1;1.2

r-C6H14+ NaCl-1.1

r-C2H6+ NaCl-1.1

r- CH4+ NaCl-1.1

r-CH4+ CaCl2-1.1

r-C6H14+N2-1.1

r-NaCl/SO4-2.1

13

Table code for Appendix

(*) – The experimental method was described in the publication Reamer, H.H., Sage, B.H. and Lacey, W.N., American Documentation Institute, Washington, D.C., Document 3328 (1950), which was not available to the authors and which is cited in Reamer, H.H. Sage, B.H. and Lacey, W.N. (1952) Ind. Eng. Chemistry. 44(3): 609–15.

0.37

0.50

0.70

m1

n-hexane + sodium chloride

C6H14 + NaCl

358

365

H3BO3 – NaBx(OH)3x+1 – NaOH

ethane + sodium chloride

C2H6 + NaCl

CO2 + NaCl

methane + sodium chloride

CH4 + NaCl

0.017

379

290

M1

0.0078 0.71 0.024 0.50 0.025 0.30 0.0048 0.85 0.071 0.87

0.40 0.39

25

6

min

carbon dioxide + sodium chloride carbon dioxide + sodium CO2 + NaCl chloride carbon dioxide + sodium CO2 + NaHCO3 bicarbonate Quaternary systems – electrolytes H3BO3 – NaB(OH)4 – NaOH

0.05 0.094

x x

0.06 0.06

5

max

Temp-re (°C)

0.230 0.0007 0.058 0.0005 0.051 0.0002 0.099 0.0002 0.0018 0.0029 0.16 0.01 0.16 0.10

0.05 0.05

4

min

w w

3

unit

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

x x x x x x x x x x m w m m

Ternary systems – nonelectrolytes – electrolytes methane + calcium chloride CH4 + CaCl2

NaCl + Na2SO4

sodium chloride + sodium sulphate Ternary systems – nonelectrolytes n-hexane + nitrogen C6H14 + N2

Chemical names

Formula

Nonaqueous components

Table 2.5

184 Hydrothermal Experimental Data

pVTx Properties of Hydrothermal Systems 185

There are several groups from the former Soviet Union (Rodnyansky and Galinker in Kharkov; Mashovets, Puchkov, Feodorov and Zarembo in Leningrad and Gorbachov and Kondratiev; Khaibullin and Novikov; Ravich and Urusova in Moscow) that have contributed to the pVTx data summarized in Table 2.5. These groups performed, during the 1960s and 1970s, a systematic density measurements (at temperatures up 350 °C and pressures up to 150 MPa) of aqueous electrolyte solutions in a wide range of concentration for alkaline halides, hydroxides, nitrates, carbonates and sulfates. Most of them used piezometer and hydrostatic weighing techniques having an accuracy (±0.3–1%) lower than those obtained with the vibrating tube densimeters. Akhundov and co-workers in Azerbajian have measured the densities of several aqueous electrolytes during the period 1983–2000. The studied systems include alkaline halides, sodium nitrate, sodium perchlorate and earthalkaline chlorides and nitrates. This group used a fixed volume piezometer and the upper temperature and pressure are 325 °C and 40 MPa respectively and measurements were usually performed in moderate to very concentrated solutions with accuracy around ±0.1% and better. Currently the Azerbajian group, lead by Azizov, continues the study of electrolytes in collaboration with the group of I. Abdulagatov who initiated their studies in 1992 in Dagestan (Russia) and later moved to Boulder (USA). The Abdulagatov’s group have made a very important contribution to the pVTx properties in hydrothermal systems, not only in electrolytes (with an estimated uncertainty of density measurements ±0.06%), but also in nonelectrolytes (methane, benzene, pentane, hexane, heptane, octane, carbon dioxide) using a cylindrical constant-volume piezometer (with an accuracy better than ±0.5%). The group of Safarov, also from Azerbajian, has been active since 2000 and they have measured the pVTx properties of electrolytes (CaCl2, LiNO3, ZnBr2, ZnCl2) and nonelectrolytes (methanol, propanol) over a wide range of temperature and pressure using a constant-volume piezometer. The group of E.U. Franck in Karlsruhe (Germany) was a pioneer in the measurement of pVTx properties of hydrothermal systems over a wide range of pressures and temperatures. The first contribution of Franck’s group, dated from 1959, correspond to the density measurements of aqueous CO2 till 750 °C and 200 MPa. Franck’s group has contributed to the pVTx data in hydrothermal systems (electrolytes and non-electrolytes with accuracy better than ±1%) for decades, being the last contribution published in 1995. As we described in Section 2.2.2.2 Franck’s group developed very precise variable volume piezometer (with accuracy around ±0.01–0.42%) for fluid density up to very high pressure and temperature, including the supercritical water region. This group measured the density of several gases in water and also electrolytes, like NaOH, over all the achievable concentration range, that is from dilute solution to pure salt. The group of R. Wood in Delaware (USA) introduced the VTD for high temperature volumetric studies, leading to a dramatic improving in the quality of the data even under

extreme conditions (with accuracy up to ±0.002–0.02%). This group has made very important contributions to the study of electrolytes and nonelectrolytes over a wide range of temperature and pressure, including the near-critical and supercritical regions, not only experimentally but also theoretically. Pitzer and co-workers at the University of California at Berkeley have performed a reduced number of experimental studies on the pVTx properties of aqueous electrolytes (with an accuracy around ±0.01–0.05%), and the range of temperature was not very wide. However, K. Pitzer itself has performed a very important contribution to the theory of thermodynamic excess properties, including excess volume, as discussed in Sections 2.3.1.1 and 2.3.1.2. The contribution of the Oak Ridge National Laboratory to the pVTx properties of hydrothermal systems has not been so important as for other thermodynamic properties such as osmotic coefficients or electrical conductivity, but J. Simonson and co-workers in the 1990s have performed very precise measurements of densities (±0.002%) of electrolyte solutions using a modified VTD. The group of P. Tremaine in Canada used a VTD for accuracy measuring (±0.01–0.04%) the high temperature volumetric properties of a number of electrolytes (Gd(CF3SO3)3, NaCF3SO3, sodium tartrate dimethylammonium chloride, weak electrolytes (tartaric acid), non-electrolytes (methanol, morpholine, a-alanine, b-alanine, and proline and mixtures of non-electrolytes and electrolytes (morpholinium chloride + HCl, dimethylammonium chloride + HCl). The group of H. Corti in Buenos Aires (Argentina) studied mainly single and mixed strong electrolytes (KOH, LiOH, NaOH, LiOH +KOH), boric acid and its mixtures with NaOH to form complex H3BO3-NaBx(OH)3x+1-NaOH systems with an accuracy around ±0.005–0.02%. The temperature was limited to 250 °C, and pressure close to saturation, except for NaOH which was studied up to 325 °C and 30 MPa in collaboration with J. Simonson (ORNL). The Czech school started with V. Majer who integrated the Wood’s group in Delaware at the end of the 1980s and beginning of the 1990s. Later he moved to France and established collaboration with Hn dkovský and Cibulka at Prague. The Cibulka’s group is currently very active and in the last years they published several data on organic solutes in water up to 573 K and 30 MPa with accuracy around ±0.002–0.006%. 2.4.2 Summary table Table 2.5 summarizes all the available experimental pVTx data for aqueous electrolyte and nonelectrolyte solutions at high temperatures (usually above 200 °C). The systems are arranged in alphabetic order of nonaqueous components for each of seven groups of aqueous mixtures. Binary aqueous systems were divided into three groups – ‘Binary systems with electrolytes’, ‘Binary systems with nonelectrolytes’ and ‘Binary systems with acids’. There are also three groups of ternary aqueous systems – ‘Ternary systems – electrolytes’, ‘Ternary systems – nonelectrolytes’

186

Hydrothermal Experimental Data

and ‘Ternary systems – nonelectrolytes and electrolytes’. And five quaternary hydrothermal solutions with electrolytes form the 7th group – ‘Quaternary systems – electrolytes’. The first two columns in Table 2.5 show the chemical composition of each aqueous system and indicate general molecular formula (1st column) and the chemical names of nonaqueous components (2nd column). The concentration units, indicated in the 3rd column, are: molarity (c); molality (m); mass (w), volume (v) or mole (x) fractions; volume percent (V%). The columns from 4th to 9th contain the minimal and maximal values for solution concentration (4th and 5th columns), temperature (6th and 7th columns) and pressure (8th and 9th columns) to indicate the ranges of studied parameters of state. The experimental quantities reported in the study publication are indicated in the 10th column: density (d); differential density (solution density minus water density) (dd); solution molar volume (V); solution specific volume (Vs); apparent molar volume (Vf); solute infinite dilution partial molar volume (Vo), excess volume (Ve), volume of mixing (Vm), compressibility factor (Z), virial coefficients (B, C, D, E), and sound velocity (sv). The 11th column indicates the experimental technique employed in the study: constant volume piezometer (CVP); variable volume piezometer (VVP); hydrostatic weight technique (HWT), vibrating tube densimeter (VTD), and synthetic fluid inclusion technique (SFIT). The high-temperature pycnometer (PYC) as well as the metal bellows densimeter (MBVV), high-temperature dilatometer or piston densimeter can be considered as a piezometer of variable volume (VVP). Few studies have been carried out using special techniques, such as, echo pulse (EP) (Alexandrov et al., 1989; Tsatsuryan et al., 1992; Alexandrov and Tsatsuryan, 1995); sealed ampoule method (SAM) (Vandana and Teja, 1995); X-Ray dilatometer (XRD) (Bell et al., 1970) and g-ray densimeter (gRD) (Khaibullin and Borisov, 1966), Khaibullin and Novikov, 1973). We have not described them in detail in the experimental Section 2.2, but a brief description of these methods can be seen in the Appendices tables. References are listed in the 12th column. The 13th column indicates the tables where the experimental data on phase equilibria for hydrothermal systems are available in the Appendices. The empty boxes in this column mean that the measurements have been made at temperatures below 200 °C.

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3

High Temperature Potentiometry Donald A. Palmer Chemical Sciences Division, Oak Ridge National Laboratory, PO Box 2008, Building 4500S, Oak Ridge, TN 37831-6110, USA

Serguei N. Lvov Department of Energy and Geo-Environmental Engineering & The Energy Institute, The Pennsylvania State University, 207 Hosler Building, University Park, PA 16802, USA

3.1 INTRODUCTION The experimental data relevant to this chapter are to be found in the Appendices. Most of the studies cited in these Appendices mainly cover ranges of temperature below the 200 °C minimum limit generally adhered to in this book (see Table 3.1) and therefore whenever possible all of these lower-temperature results are also listed within each experimental summary. The use and application of electrochemical potentiometric cells have been described recently by Lvov (2005) and Lvov and Palmer (2004), and in the latter book there are chapters dealing specifically with measurements of hydrolysis constants for homogeneous systems (Tremaine et al., 2004) and solubility/hydrolysis constants for homogeneous systems (Wesolowski et al., 2004). A high-temperature potentiometric cell (system) consists of at least two electrodes at which the reversible electrochemical reactions take place. In such an equilibrium cell the electrode electric potential, Ei, can be related to the Gibbs energy, ∆rGi, of the corresponding electrochemical half-reaction as follows: ∆ rGi = − zi FEi

(3.1)

of E oi values estimated over a wide range of temperatures remains a major challenge in high temperature electrochemistry. The open-circuit potential measured between two reversible electrodes, also referred to as the electromotive force, E, is defined by the well-known Nernst equation. This equation relates the activities (and/or fugacities) of the substances or species, ai, involved in the electrochemical reactions within the cell and the standard open-circuit potential, Eo, of the cell as: E = E o − ( RT nF ) ∑ ν i ln ai

where vi is the stoichiometric number of the overall cell reaction and is positive for products and negative for reactants; n is the charge number of the cell reaction; R is the gas constant (8.3145 J·K−1·mol−1) and T is the temperature in K. Note that the current convention assumes that E is a difference between the right-hand side and the left-hand side terminals. The standard value of the open circuit potential is directly related to the standard Gibbs energy, ∆rGo, of the chemical reaction taking place in the electrochemical system: ∆ rG o = − nFE o.

where zi is the charge number of a half-cell electrochemical reaction and F is the Faraday’s constant (96485 C·mol−1). Conventionally, the standard values of both ∆rGi and Ei are zero at all temperatures (∆rG oi = 0, E oi = 0) for the hydrogen electrode reaction, 2H+ + 2e− ↔ H2(g), so that all other electrode potentials can be estimated with respect to the Standard Hydrogen Electrode (SHE) scale. The standard electrode potentials, E oi , of many electrodes have been measured at ambient conditions (25 °C and 0.1 MPa), but only a limited number of E oi values are available at high temperatures and pressures. Therefore, a comprehensive list Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-09465-5

(3.2)

(3.3)

The cell potential, E, can be measured directly and Eo is obtained using an appropriate extrapolation, so that in principle, ∆rGo can be derived using an appropriate hightemperature potentiometric cell. The electrochemical reactions occurring within this cell must be reversible and the cell potential should be measured with a high-impedance electrometer. Moreover, if ∆rGo can be calculated using the available thermodynamic data, the activities (and/or fugacities) of the chemical species can be measured. Therefore, high-temperature potentiometric measurements can be a

Ag2SO4(s) + H2(g) = 2Ag(s) + H2SO4(aq)

P-Ag/Ag2SO4-1.1

5–250 50–295 50–295 50–295 25–200 50–292.5

0.100–5.00 [NaCl] 1.0088 and 1.0200 [NaCl] 0.2008–4.998 [NaCl] 0.100–5.00 [NaCl] 0.100–5.00 [NaCl] 0.081 [KCl] 0.076–4.96 [NaCl] 0.081–0.032 [KCl] 0.100–5.00 [NaCl] 0.200–5.01 [NaCl] 0.218–5.074 [NaCl] 0.02–1.02 [KCl] 0.204 [KCl] 0.204 [KCl] 0–1 [NaCF3O3S] 1.000 [NaCF3O3S]

0.0080 and 0.0184 [KOH]D Test: 0.01 [HCl] Standard: 0.001 [HCl] E Sol.1: 0.001 [HCl] + 0.1 [NaCl] Sol. 2: 0.01 [HCl] + 0.1 [NaCl] E

CH2O2 = H+ + CHO2− H+ + C2H3O2− = C2H4O2(aq) C2H4O2(aq) = H+ + C2H3O2− C4H6O4 = H+ + C4H5O4− C4H5O4− = H+ + C4H4O2− 4 C4H10NO = H+ + C4H9NO− C4H11NO3 + H+ = C4H12NO3+ C6H13N = H+ + C6H12N− C7H6O2 = H+ + C7H5O−2 CO2(aq) + H2O = H+ + HCO−3 HCO−3 = H+ + CO2− 3 Co2+ + H2O = Co(OH)+ + H+ Co(OH)+ + H2O = Co(OH)20 + H+ D2O = H+ + DO− D2PO−4 = H+ + DPO4 (x=1−3) Fe2+ + xC2H3O−2 = Fe(C2H3O2)2−x x Fe2+ + Cl− = FeCl2− Ge(OH)40 = GeO(OH)−3 + H+ [pH difference between Test and Standard solutions] [Electric potential difference between Solutions 1 and 2]

P-C2H4O2-2.1; P-C2H4O2-2.2 (acetic acid) P-C4H6O4-1.1 (succinic acid) P-C4H6O4-1.2 (succinic acid) P-C4H9NO-1.1 (morpholine)

P-C4H11NO3-1.1 (tris(hydroxymethyl)aminomethane)

P- C6H13N-1.1 (cyclohexylamine)

P-C7H6O2-1.1 (benzoic acid) P-CO2-1.1; P-CO2-1.2 P-CO2-2.1 P-CoOH-1.1

P-D2PO4-1.1 P-FeC2H3O2-1.1

P-FeC2H3O2-2.1; P-FeC2H3O2/FeCl-2.1 P-FeCl-2.1 P-Ge(OH)4-1.1

P-HCl-2.1

P-HCl-1.1

P-D2O-1.1

SVP 2.8–14.0 SVP SVP 27.5–33.8 18.7–25.3

25–400 25–400

SVP SVP

SVP

SVP SVP SVP SVP SVP

SVP

SVP

SVP SVP SVP

SVP

SVP SVP SVP 10.8–100.5

SVP SVP 1.7–6.0 0.5–6.8 SVP

SVP

Pressure (MPa)

125–295 125–295 125–295 21–200

50–293.4 50–295

50–295

5–200

50–295 50–295 5–225 5–225 50–294

50–290 50–200 25–200 20–250

0.0300 [NaCl] 0.129–1.02 [KCl]

P-B(OH)3-1.1; P-B(OH)3-1.2 P-CH2O2-1.1 (formic acid) P-C2H4O2-1.1 (acetic acid)

P-AlOOH-1.1 P-AlOOH-1.2 P-AlOOH-1.3; P-AlOOH-1.4 P-AlOOH-2.1 −x AlOOH(cr) + xH+ = Al(OH)3x−3 + (2−x)H2O B(OH)3(aq) + OH− = B(OH)−4

25–200

Temp. Range (°C)

152; 203 100–290 100–253 100–254 100–290

0.05–1.00 [Na2SO4]

B

Ionic Strength [Electrolyte] (mol/kg H2O)

1.000–5.000 [NaCl]

−x AlOOH(cr) + xH+ = Al(OH)3x−3 + (2−x)H2O

Equilibrium [Measured Values]

Summary of potentiometric data obtained with the HECCA unless otherwise indicated

Appendix Table Nr.

Table 3.1

Lvov et al., 1999

Pokrovski and Schott, 1998 Lvov et al., 1998

Palmer and Drummond, 1988 Palmer and Hyde, 1993

Patterson et al., 1984 Giasson and Tewari, 1978 Mesmer and Herting, 1978

Kettler et al., 1995a Kettler et al., 1995a Mesmer and Hitch, 1977 Palmer and Wesolowski, 1987 Mesmer and Hitch, 1977 Kettler et al., 1995b Patterson et al., 1982

Bell et al., 1993 Becker and Bilal, 1987 Mesmer et al., 1989

Mesmer et al., 1972

Benezeth et al., 2001

Bilal and Müller, 1993 Palmer et al., 2001

Reference

196 Hydrothermal Experimental Data

B

HEEC: H2,Pt|NX,MY||NX,HX or NOH|Pt,H2 Pt,H2|H2SO4(aq)|Ag2SO4,Ag C Pt|I2,KI,HClO4||HClO4,KIO3,I2|Pt D Glass electrode|Ge(IV),KOH||AgCl,Ag(at 25 °C) E Thermocell: Cu|Ag|AgCl|reference NaCl(aq)||test H+(aq)|H2(Pt)|Pt . . . Pt|Cu, F Thermocell: Cu|Ag|AgCl|reference NaCl(aq)||test H+(aq)|YSZ|HgO|Hg|Pt . . . Pt|Cu G Isothermal cell: Hg|HgO| YSZ|NaOH(aq)|H2(Pt) SVP – saturation vapor pressure M – molarity (mol/L)

A

0.03 [NaCF3O3S]

ZnO(cr) + xH+ = Zn(OH)x2−x + (x−1)H2O (x=−1−2) ZnO(cr) + xH+ = Zn(OH)x2−x + (x−1)H2O (x=−1−2)

P-ZnO-2.1 P-ZnO-2.2 P-ZnO-3.1 P-ZnO-3.2

0.03 [NaCF3O3S]

0.03–1.0 [NaCF3O3S]

[pH difference between Test and Standard solutions]

P-NaOH-2.1

ZnO(cr) + 2H+ = Zn2+ + H2O

pH of NH3(aq) Na+ + B(OH)−4 = NaB(OH)4(aq) [Electrode calibration] [Henry’s constant of H2(aq)]

P-NH3-2.1; P-NH3-2.2 P-NaB(OH)4-1.1 P-NaCl-1.1 P-NaOH-1.1

P-ZnO-1.1

0.4–1.2 ppmE,F 0.15, 0.25, 0.5 M [NaCl] 0.01–0.5 M [NaCl] 0.001–0.1 [NaOH] Saturated at 25 °C with HG2 Test: 0.001 NaOH + 0.1 NaCl Standard: 0.01 NaOH + 0.1 NaClE 0.1, 0.25 M [NaCl]

NH3(aq) + H2O = NH4+ + OH−

P-NH3-1.1

0.0302–1.008 [NaCF3SO3]

0.0399–3.342 [KCl]

Mg2+ + 2H2O = Mg(OH)2(cr) + 2H+ Mg2+ + H2O = Mg(OH)+ + H+

P-Mg(OH)2-1.1 P-Mg(OH)2-2.1; P-Mg(OH)2-2.2

Zn2+ + xC2H3O2− = Zn(C2H3O2)2−x x (x=1−3)

0.02–0.10 [NaClO4, NaI, NaIO3]C 0.1–1.0 [NaCl] 0.11–5.0 [NaCl]

3I2(aq) + 3H2O = IO−3 + 5I− + 6H+

P-I2-1.1

P-ZnC2H3O2-1.1

400

0.104–5.12 [NaCl]

y−2x yH+ + xWO2− 4 = Hy(WO4)x

P-HY(WO4)X-1.2; P-Hy(WO4)X-1.1

− Na+ + SO2− 4 = NaSO4 (aq)

30.4

150–300 75–200 50–200 200–450

0.0512–1.008 [KCl] 0.100 and 5.00 [NaCl] 0.100–5.00 [NaCl]

H2PO−4 + OH− = HPO2− 4 + H2O HSO−4 = H+ + SO2− 4 xSi(OH)04 + yOH− = Si(OH)y− 4x−y

P-H3PO4-1.2 P-HSO4-1.1 P-H4SiO4-1.2 P-H4SiO4-1.1

P-NaSO4-1.1

11 SVP SVP 27.5

50–295

0.101–1.008 [KCl]

H3PO4(aq) + OH− = H2PO−4 + H2O

25–290 75–200 150–250 150–350

50–290

50–300

50–200

60–200 1–250

4-209

95–290

50–294 50–250 60–296

50–293

1.4–11.6 11.5–26.8

SVP

SVP

SVP

SVP

SVP

SVP SVP

SVP

SVP

SVP SVP SVP

SVP

3.1–108.2

P-H3PO4-1.1

35–250

H+ + F− = HF0

27.5; 33.8 23.0–28.1

P-HF-1.1

25–360 320–400

0.01 & 0.001 [HCl]E Sol.1: 0.015(0.01012)[HCl] Sol. 2: 0.0126(0.00109) [HCl]E 1.02 [NaCl]

[pH and Ka of H+ + Cl− = HCl°] [Electric potential difference between Solutions 1 and 2]

P-HCl-3.1 P-HCl-4.1

Benezeth et al., 2002

Pokrovsky et al., 1995 Giordano and Drummond, 1991 Wesolowski et al., 1998 Benezeth et al., 1999

Lvov et al., 1998

Eklund et al., 1997

Brown et al., 1996 Palmer and Wesolowski, 1997 Hitch and Mesmer, 1976 Lvov et al. 1995 Pokrovski et al., 1995

Dickson et al., 1990 Busey and Mesmer, 1977 Wesolowski et al., 1984 Palmer et al., 1984

Becker and Bilal, 1983 Mesmer and Baes, 1974

Lvov et al., 2000b Lvov et al., 2002; 2003

High Temperature Potentiometry 197

198

Hydrothermal Experimental Data

powerful tool in studying a number of thermodynamic phenomena if (i), the electrode electrochemical reactions are reversible, and (ii) the high-temperature potential measurements are stable and reproducible within a few mV or less. In addition, the electrodes should be resistant to chemical degradation and pressure (mechanical) stress in the hightemperature aqueous environment. It should be mentioned that, if the high-temperature thermodynamic properties (the standard Gibbs energies and the activity/fugacity coefficients) are available for all species of an electrochemical reaction, both Eo and E can be calculated theoretically and compared with observed potentiometric data. In this way the reliability of an experimental potentiometric system can be confirmed. 3.1.1 Reference electrodes Currently, two approaches have been employed for potentiometric measurements at elevated temperatures: (1) the use of an internal reference electrode operating within the hightemperature environment, and (2) the use of an external reference electrode working at room temperature, but connected to the high-temperature environment by a non-isothermal electrolyte bridge. The first approach requires solving the well-known problem of the diffusion potential whereas the latter approach involves the additional problem of estimating the thermal liquid-junction and thermoelectric potentials. A number of the electrochemical couples, such as Ag/ AgCl, Ag/AgBr, Hg/Hg2Cl2, Hg/Hg2SO4, Ag/Ag2SO4, Hg/ HgO, and Pb/PbSO4 have been tested as possible internal high-temperature reference electrodes. However, only the Ag/AgCl electrode has demonstrated the capability to be used at temperatures up to about 275 °C for a limited period of time. Note that the hydrogen-electrode concentration cell described below employs the second hydrogen electrode as the reference electrode and consequently no Eo is involved to treat the experimental data. The chemical stability of the reference electrode was improved significantly with the development of the external (pressure-balanced) reference electrode whereby the electrochemical couple (e.g. Ag/AgCl) was maintained at ambient temperature with connection to the high-temperature zone by a non-isothermal electrolyte bridge (Macdonald, 1978). Whereas this approach overcomes the stability and chemical degradation problems, it introduces the Soret effect originating from irreversible processes of heat and mass transport along the non-isothermal electrolyte bridge. This bridge introduces an additional thermal diffusion potential, which is a function of temperature, composition and time, and can be of a significant magnitude. A recent modification was to use a flow-through bridge (Lvov et al., 1998b) which minimizes interference from contaminates (e.g. corrosion products) and the magnitude of the Soret effect, providing a more stable and accurate reference potential. However, an additional streaming potential is generated because the electrolyte solution flows through a capillary channel. The stability the electrical potential of this flow-through external reference electrode is independent of the prevailing conditions

within the cell and this has been confirmed experimentally at temperatures from 25 to 400 °C at pressures up to 35 MPa. The reference solution flows through the electrode at a constant velocity so that the concentration of solution across the thermal junction remains constant so that the thermaljunction potential is constant over time. The latter can be either calculated or estimated experimentally, such that the electrode potential value can be evaluated with respect to the SHE scale. The flow-through external reference electrode has been used in a cell which had either a platinum (Lvov et al., 1999, 2000b) or a yttria-stabilized zirconia indicator electrode (Lvov et al., 2002, 2003) for potentiometric measurements up to 400 °C. The potential of this reference electrode was found to be stable within 1–3 mV while the reference solution was pumped through the electrode using a high-pressure chromatography pump. 3.1.2 Indicator electrodes The indicator electrode must have a stable and reproducible potential for the course of the measurement and should be able to respond in a Nernstian manner to varying conditions in the high-temperature aqueous environment. In other words, the activity of the dissolved species, ai, and the standard open-circuit potential, Eo, should be defined by measuring the open circuit potential between the indicator and reference electrodes and applying the Nernst equation (Equation (3.2)). Although a number of the indicator electrodes have been tested for operation over a wide range of temperatures, only the platinum/hydrogen, Pt(H2), and yttria-stabilized zirconia electrodes, with a mercury/mercury oxide electrochemical couple, YSZ(Hg/HgO), were found to be capable of operating in a Nernstian manner at temperatures up to 400 °C. The reversible reactions occurring at the Pt(H2) and YSZ(Hg/HgO) electrodes are 2H+ + 2e− H2(g) and 2H+ − + 2e + HgO(s) Hg(1) + H2O(1), respectively. The corresponding equations for the electrode potentials of the Pt(H2) and YSZ(Hg/HgO) electrodes can be written as follows:

W

W

EPt( H2 ) = ( RT 2 F ) ln ( aH2 + f H2 )

(3.4)

2 o EYSZ(Hg HgO) = EYSZ ( Hg HgO ) + ( RT 2 F ) ln ( aH+ aH2 O ) (3.5) o where E YSZ(Hg/HgO) is the standard YSZ(Hg/HgO) electrode potential and is independent of the solution composition, but depends on the standard Gibbs energies of formation, ∆fG oi , of reaction species, H+(aq), HgO(s), Hg(l), and H2O(l): o o o EYSZ ( Hg HgO ) = − ∆ r GYSZ ( Hg HgO ) 2 F = − ( ∆ f GH2 O + o o ∆ f GHg − ∆ f GHgO − 2∆ f GHo+ − 2∆ f GHo+ ) 2 F

(3.6)

The values of ∆fG Ho + and ∆fG Ho 2 are zero at any temperature. o Furthermore, E YSZ(Hg/HgO) is independent of the properties of the YSZ membrane so that for this electrode to operate effectively it only requires sufficient O2+ conductivity

High Temperature Potentiometry 199

through the membrane at the temperature of interest. This electrode must be coupled to a high-impedance (>1014 Ω) voltmeter; nevertheless, the membrane impedance is still too high to be used effectively at temperatures below 100 °C. The Pt(H2) indicator electrode has been widely used for measuring pHm in concentration cells housed in stirred Teflon-lined autoclaves (Palmer et al., 2001) and in a flowthrough design at temperatures below 300 °C (Sweeton et al., 1973). At temperatures above 300 °C the Pt(H2) indicator electrode was used in thermocells described in (Lvov et al., 1999, 2000b) and flow-through concentration cells (Sue et al., 2001). The YSZ(Hg/HgO) indicator electrode has also been used in both static (Eklund et al., 1997) and flow-through systems (Lvov et al., 2002, 2003) up to about 450 °C. These systems were found to behave in a Nernstian manner and are capable of measuring the electrode potential to a precision of ±5 mV or less. The main disadvantage of the Pt(H2) electrode is that they can be biased significantly by certain ‘poisons’ such as sulfides. The fugacity of H2 must be known in order to determine the activity of H+ using Equation (3.4). The main disadvantages of the YSZ(Hg/HgO) electrode are its complexity of design, its brittleness and the variability in both performance from batch to batch. In addition, the activity of H2O must be known to calculate the activity of H+ when using Equation (3.5). In addition, the chemical stability of commercially available membranes is still insufficient if the electrode is to be used in an aggressive, hightemperature, aqueous environment (Lvov et al., 2003). Other electrochemical couples (e.g. Cu/CuO, Ni/NiO) have been tested in the YSZ electrode, but have not reproduced the chemical stability of the Hg/HgO couple. Other metal/metal oxide (e.g. Ir/IrO2, Zr/ZrO2, W/WO2, etc.) electrodes have been tested over a wide range of temperatures, but their function with respect to the Nernst equation has not been established. Kriksunov et al. (1994) used a flow-through cell with tungsten/tungsten oxide and YSZ (Hg/HgO) pH-sensing electrodes and an external pressurebalanced Ag/AgCl electrode from 200 to 300 °C. The tungsten electrode exhibited a Nernstian response at 200 °C with a slope of (95 ± 5) mV·pH−1, (cf. calculated value: 93.9 mV·pH−1), but the deviation increased with temperature to (104 ± 3) mV·pH−1 at 300 °C (cf. calculated value: 113.7 mV·pH−1). Kriksunov and Macdonald (1994) used a thick-walled Pyrex glass tube with an Ag/Ag2SO4 in H2SO4(aq) inner electrode as an indicator electrode from 20 to 250 °C in acidic to mildly basic solutions. They gave an example of the response of this electrode as producing a mV/pH slope at 235 °C of 114 compared to the calculated Nernstian response of 100.8. Glass electrodes have been used in conjunction with an AgCl/Ag reference electrode kept at ambient temperature with a salt bridge providing electrical and thermal contact for potentiometric measurements from 70 to ca. 200 °C with a reported precision of ± 2 mV (Diakonov et al., 1996). This particular glass electrode utilizes a Li-Al-B-silicate glass bulb whose inner surface is coated with a thin layer of a Li-Sn alloy, which has direct electrical

contact with an internal Ni-Cu wire and hence requires no internal electrolyte solution. However, silica is soluble in alkaline solutions and the glass electrode is not stable over long periods of time. 3.1.3 Diffusion, thermal diffusion, thermoelectric, and streaming potentials The diffusion (ED), thermal diffusion (ETD), thermoelectric (ETE) and streaming (ESTR) potentials can contribute to the measured electrochemical potential to varying degrees. If these contributions are significant then they should be taken into account in order that the measured open-circuit potential can be related to thermodynamic properties of the electrochemical system using a generalized Nernst equation: E = E o − ( RT nF )

∑ ν ln a + ( E i

i

D

+ ETD + ETE + ESTR )

(3.7)

Note that the four potentials mentioned above are irreversible and must be treated using linear irreversible thermodynamics. The diffusion potential is common to all liquid junctions and results from the different mobilities of ions through a permeable membrane separating two solutions. Its magnitude can be estimated if the individual ionic conductivities and activities of the species are known (see the discussion below on the Henderson equation, Bates, 1964). At temperatures below 350 °C, if ED is not minimized, it could be 30 mV or greater. Mesmer and Holmes (1992) showed that for a given cell composition, the values of ED generally decrease with increasing temperature while the Nernst slope increases. Although there is concern that the Henderson equation could be difficult to apply at near critical conditions as the electrolytes become more associated, it is reasonable to assume that the contribution of the diffusion potential will also be smaller. The thermal diffusion potential arises when there is a temperature gradient within an electrolyte bridge and is due to heat transport by ionic species. The magnitude of ETD can be estimated from the entropy of transport, conductivity and activity coefficients of the individual ions. Therefore, the magnitude of ETD depends on the temperature, pressure and composition of the electrolyte liquid junction. The value of ETD can be as high as tens to hundreds of mV. The thermoelectric potential is created by the heat transport of electrons along an electron conductor (usually a wire) in a thermal gradient. Consequently, ETE is a function of the temperature and it is generally only a few mV. The magnitude of ETE can be calculated over a wide range of temperatures for most common wire materials, such as Pt, Ag, Cu, Fe, Ni, etc. The streaming potential, ESTR, is created in a capillary channel (or porous material) by a mass flow of solution under zero electric current conditions. The magnitude of ESTR depends on: (i) the capillary channel material; (ii) the composition of the flowing solution; (iii) the solution flow rate; and (iv) the temperature. Presently, there are no data to evaluate ESTR at high temperatures, but, if the flow rate is

200

Hydrothermal Experimental Data

sufficiently slow a linear dependence should exist between the streaming potential and flow rate. This simple dependence can be used to eliminate ESTR by extrapolating the measured potentials to zero flow rate. An example for estimating the values of ED, ETD, ETE, and ESTR is shown in Lvov et al. (1999). 3.1.4 Reference and buffer solutions For assessing the viability and accuracy of high-temperature potentiometric measurements, suitable reference systems should be used. It is highly desirable to establish a set of pH buffer solutions which can be used at temperatures above 100 °C. Thus far, little has been done to develop the necessary sets of the high-temperature buffer systems as primary standards. Only a 0.05 mol·kg−1 potassium hydrogen phthalate solution has been adopted by IUPAC as an appropriate primary buffer system to be used at temperatures up to about 225 °C. However, the acid dissociation constants of many organic and inorganic buffers have been measured with the hydrogen-electrode concentration cell (see discussion below) and these results are currently available for developing the secondary pH standards to 250 °C. In order to assess the viability and accuracy of hightemperature potentiometric measurements, reference systems should be used with a known activity of H+, aH+ One approach, which is applicable at temperatures below 300 °C, is to use dilute aqueous solutions of strong acids and bases, such as HCl(aq) (or F3CSO3H(aq) which is a strong organic acid used commonly in experimental studies as the large anion interacts only weakly with most cations) and NaOH(aq), respectively, to establish either aH+, or the molality of hydrogen or hydroxide ions, mH+ and mOH−, for comparison of the measured and calculated potentials. If these standard solutions are used at temperatures above 300 °C, then the ion-association constants of the electrolytes must be considered, i.e. the speciation of the solutions components must be known. Consequently, at these extreme temperatures the activity or concentration of H+ becomes more uncertain. Lvov et al. (2000a) proposed that even in the low-density, supercritical regime, several three-component aqueous reference solutions can be found to test the accuracy of the Pt(H2) or YSZ(Hg/HgO) electrodes within ≤ ± 3 mV. These three-component aqueous solutions may consist of NaCl and either HCl or NaOH with the concentration of NaCl being significantly greater than that of either HCl or NaOH. This approach was confirmed theoretically and experimentally at temperatures up to 400 °C and densities down to 0.17 g·cm−3 and does not require any knowledge of the association constants. These three-component reference solutions have been used as standard solutions in the hydrogen-electrode concentration cells, HECC, system at temperatures below 300 °C, where various other supporting strong electrolytes have also been employed. For a pH reference solution to be used at high temperatures, a rigorous speciated treatment of the hydrogen ion concentration or activity must be available (i.e. the concentration of free hydrogen ions must be calculable). Ion-association

data are becoming available from the recently developed flow-through conductivity cell measurements and recent advances in treating the conductance of mixed electrolytes. 3.2 EXPERIMENTAL METHODS The available experimental systems for potentiometric measurements, as well as for measurements of the electrochemical reaction rates as a function of temperature are represented here. 3.2.1 Hydrogen-electrode concentration cell The bulk of the currently available thermodynamic data on the hydrolysis of inorganic and organic solutes to 250 °C have been obtained potentiometrically using the hydrogenelectrode concentration cell (HECC) either as a stirred reactor (see Fig. 3.1, as described in for example, Mesmer et al., 1970, 1988; Bénézeth and Palmer, 2000; Wesolowski et al., 2000; Palmer et al., 2001) or for a limited number of systems as a flow-through cell. In both cases the cell consists of two compartments separated by a semi-porous membrane to maintain the zero-current electric circuit while restricting the mixing of the solutions on both sides of the membrane. The wetted walls of the cells were made from Teflon, the liquid junction was typically a porous Teflon plug pre-saturated with the reference solution, the magnetic stirring bars were Teflon coated, and the platinum electrodes were sheathed in commercially available heat-shrinkable Teflon. Note the no release of fluoride from the Teflon at high temperatures was ever reported. The electrochemical configuration of the HECC is as follows: H2 | Pt | Reference H+(aq)/H2(aq) Sol. 1 || Indicator H+(aq)/H2(aq) Sol. 2 | Pt | H2 where a single vertical bar is used to represent a phase boundary and double vertical bars represent the liquid junction between the two solutions. In the special case of solubility measurements, the prerequisite solid powder is added to the second compartment. In order to minimize the liquidjunction potential across the membrane and to equalize the activity coefficients of hydrogen ions in both compartments, the following restrictions must be placed on the composition of Sol. 1 in the reference compartment and Sol. 2 in the ‘test’ compartment, viz. (1) a supporting electrolyte composed of the same dominant ions must be present in each compartment of the cell; typically the lowest ionic strength that has been used routinely is 0.03 mol·kg−1; (2) the concentrations of hydrogen/hydroxide ions and those of the solute, molecular or ionic, must be maintained significantly less than the concentration of the supporting electrolyte, ideally ≤1%. Note also that in the case of the stirred reactor, both reference and test solutions are exposed to the same hydrogen gas pressure in the head space of the cell and therefore the activity of molecular hydrogen in solution is identical in both compartments. For the limited number of reports where a flow-cell was used, the two feed solutions

High Temperature Potentiometry 201

Figure 3.1 The stirred (static) hydrogen-electrode concentration cell for potentiometric measurements to 300 °C (Palmer, D.A., Bénézeth, P. and Wesolowski, D.J. (2001) Geochim. Cosmochim. Acta 65, 2081–2095 with permission from Elsevier.

were exposed initially to the same hydrogen pressure to equalize effectively their concentrations before they were pumped into the cell. Therefore, simply from the Nernst equation (Equation (3.4)), the open-circuit potential, EHECC, can be presented as follows: EHECC = ( RT ln (10) F ) log10 ( mH+ )2

( mH )1  ) + ED +

(3.8)

where mH+ is the hydrogen ion molality and ED is the diffusion liquid-junction potential, which is invariably computed from the Henderson equation (Bates, 1964). The subscripts 1 and 2 symbolize the molalities in the reference and test solutions, respectively. Typically, the supporting electrolyte was either NaCl or KCl, but in the cases where metal ion hydrolysis were investigated, NaF3CSO3 was used as the anion shows little tendency to complex metal ions compared to Cl−, for example, particularly at high temperatures. Moreover, sodium trifluoromethanesulfonate is a strong electrolyte and the anion is stable in a reducing atmosphere at moderately low and high pH for long periods of time, whereas nitrate and perchlorate anions are very unstable under these conditions. By maintaining a matching supporting electrolyte concentration in both compartments of the cell, ED values may be limited to only 1 to 2 mV. Mesmer and Homes (1992) estimated that the ED values calculated by the Henderson equation were accurate to within ±25%. Therefore, for an ED of 2 mV at 200 °C the uncertainty introduced in pHm according to the Henderson equation is 0.005.

It is immediately apparent from Equation (3.8) that knowledge of the desired quantity or dependent variable, (mH+)2, is based on the measured value of EHECC, the calculated value of ED, and the known molality, (mH+)1, in the reference compartment, where the latter is corrected for loss of water vapor to the head space when a static cell is used. Therefore, the pH obtained from these measurements is in fact defined on the molality rather than the commonly adopted activity scale according to Equation (3.9) pH m = − log mH+

(3.9)

The conventional pH defined on the activity scale is related to pHm by the relationship: pH = pHm − log g H+. The precision of these pHm measurements is generally ±0.01 for wellbehaved electrolyte solutions. This cell has also been utilized more recently for studying metal ion complexation reactions and the solubility of metal oxides/hydroxides to temperatures of 300 °C, which is the present working limit of this cell. Moreover, the surface charge characteristics of, and the adsorption of cations and anions onto, metal oxide surfaces in contact with aqueous solutions have been measured for the first time with this cell to temperatures in excess of 100 °C, in fact to 250 °C. The flow-through HECC, which does not contain a vapor phase, was constructed to allow the hydrolysis of volatile solutes, such as HF and CO2, to be studied. The internals of the original flow-through cell used at ORNL (Sweeton et al., 1973) were all made from Teflon which is malleable

202

Hydrothermal Experimental Data

and therefore there was a high failure rate as the channels were easily cut off as the temperature was raised. A recent flow-cell with the same HECC configuration was reported by Sue et al. (2001) to function to 400 °C and 35 MPa. The advantages of the HECC are: (1) no need to know standard electrode potentials; (2) high accuracy; (3) longterm stability (e.g. months as in solubility measurements, Palmer et al., 2001); (4) can operate to high ionic strengths; (5) the electrodes are rugged and simple to prepare. The disadvantages are: (1) the reducing atmosphere imposed by hydrogen, spontaneously reduces Fe3+, Cu2+, Cu+, UO 2+ 2 , etc.; (2) the static cell requires a vapor phase such that transfer of volatile acids limits their upper temperature to 300 °C; (3) the current stirred reactor designs utilize Teflon which is not thermally stable above 300 °C.

chemical diagram of the non-isothermal electrochemical system (thermocell), consisting of the flow-through external Ag/AgCl reference electrode and a flow-through YSZ(Hg/ HgO) electrode, can be presented as follows: | T2 | T1 | | T1 Cu|Ag|AgCl|Reference Electrode||Indicator Electrode| YSZ|HgO|Hg|Pt . . . Pt|CuCl− Sol. 1 H+ Sol. 2 where T1 is ambient temperature and T2 is any temperature higher than T1 Note that Cu in this diagram represents the wires connecting the terminals of the system to the a highimpedance voltmeter. The open-circuit potential of this thermocell, ETC, can be expressed as: o o ETC = [ EYSZ ( Hg HgO ) ]T2 − [ EAg AgCl ]T1 +

( RT2 F ) ln ( aH+ )T2 ( aH−02.O5 )T2  +

3.2.2 Flow-through conventional potentiometric cells A typical design of the conventional flow-through potentiometric cell (conventional refers to cells other than concentration cells) has a four-way configuration as shown in Figure 3.2 (Lvov et al., 2003). The once-through circulation system pumps fluids through the electrodes at rates faster than thermal diffusion so that no concentration gradients result from the Soret effect. Only the sensing portion of the system is maintained at a controlled temperature and pressure. The purity and concentration of the solutions are assured by maintaining a relatively rapid flow rate. In other words, as in most flow systems, contamination is minimized and corrosion of the system is significantly reduced. Because the low-temperature input flow comes only in contact with glass, Teflon, and PEEK tubes, and at high temperature the solutions only contact zirconia and platinum, the solution composition at the sensing portion of the system is well controlled. The precision of the potentiometric measurements using this design is typically ≤ ± 5 mV. An electro-

( RT1 F ) ln  ( aCl− )T1  + ED + ETD + ETE + ESTR

As an example of the utility of the system employed above, the association constants of HCl(aq) at temperatures from 300 to 400 °C were recently obtained (Lvov et al., 2000b, 2002, 2003). Also, using both the Pt(H2) and YSZ(Hg/HgO) electrodes in an isothermal flow-through system the Henry’s constant of H2(aq) was obtained at temperatures between 300 and 450 °C (Eklund et al., 1997; Ding and Seyfried, 1995). One of the disadvantages of any flow-through electrochemical system is the existence of a streaming potential, which must be taken into account or eliminated. To eliminate, ESTR, it is necessary to extrapolate the measured opencircuit potentials to zero flow rate so that at least four experimental points should be measured to provide a reliable linear extrapolation. Another possibility is to minimize

Test solution inlet (PEEK tube) Teflon Sealant B

Test solution inlet (PEEK tube)

Reference solution inlet (PEEK tube)

A C

High temperature zone

Thermocouple

Outlet (PEEK tube)

(3.10)

Figure 3.2 The flow-through electrochemical cell for potentiometric measurements at temperatures up to 400 °C: A, the flowthrough Pt(H2) electrode; B, the flow-through YSZ(Hg/HgO); C, the flow-through external Ag/AgCl reference electrode (Lvov, S.N., Zhou, X.Y., Ulmer, G.C., Barnes, H.L., Macdonald, D.D., Ulyanov, S.M., Benning, L.G., Grandstaff, D.E., Manna, M. and Vicenzi, E. (2003) Chem. Geol. 198/3–4, 141–162 with permission from Elsevier).

High Temperature Potentiometry 203

the flow rate so that the streaming potential will be negligible. Another disadvantage of the approach is the need for pumps and the higher risk of leaks and concomitant safety concerns. However, additional advantages are the ability to: (1) study the protolytic behavior of volatile solutes; (2) investigate the pressure dependence of protolytic reactions; (3) study thermally unstable solutes due to the small retention time at elevated temperature; and (4) the potential to apply this technology to industrial environments. 3.3 DATA TREATMENT According to the Bronsted definition of acids and bases, solutes release hydrogen ions and hydroxide ions, respectively. HA (aq ) ↔ H + + A −

(3.11)

and B (aq ) + H2 O (1) ↔ BH + + OH −

(3.12)

The ionization product A− is the conjugate base of HA(aq), because it acts as a base by reacting with water to form HA(aq). A − + H2 O (1) ↔ HA (aq ) + OH −

(3.13)

Conversely, BH+ is the conjugate acid of B(aq). Note that when fitting the experimental data, the hydrolysis equilibrium represented in Equation (3.13) is generally preferred over the ionization equilibrium, Equation (3.11), because it involves only anions with no net change in charge. This is commonly referred to as the isocoulombic approach. The equilibrium quotient of the acid ionization reaction, Equation (3.11), is defined as: Q1a = mA− mH+ mHA

(3.14)

where mA−, mH+ and mHA are molalities of the species A−, H+ and HA(aq), respectively. It is common practice to express concentration in molality units (mol·kg−1) rather than molarity units (mol·L−1) because the former are not affected by the thermal expansion or contraction of water with temperature and pressure. The equilibrium quotient Q1a is a function of temperature, pressure, and ionic strength. The equilibrium constant of reaction (3.11) refers to infinitely dilute solutions in the hypothetical 1 mol·kg−1 standard state: K1a = aA− aH+ aHA

(3.15)

where aA−, aHA, and aH+ are activities in molality units. The corresponding expressions may be written for the ionization of bases, which we define as Qb and Kb. The ratio between molality, mi, and activity, ai, of a solute species is defined as the activity coefficient, g i = ai/mi, so that log10 K1a = log10 Q1a − log10(γ A− γ H+ γ HA )

(3.16)

where g A −, g H +, and g HA are activity coefficients of A−, H+ and HA(aq), respectively. The value of log10 K1a is usually derived from experimental log10 Q1a values, which are commonly obtained from potentiometric measurements, by extrapolation to infinite dilution. Values for log10 K are related to the Gibbs energy change of the reaction by relationship: ∆ rG o = − RT ln K

(3.17)

where T is the temperature in Kelvin and R is the molar gas constant. The temperature dependence of log10 K is described by the following relationships. From the thermodynamic equations, ∆Go = ∆Ho − T∆So and ∆So = −(∂∆Go/∂T)p, it follows that:

∫ d ( ∆G

T ) = − ∆H o T 2 dT

o

(3.18)

Accurate estimations for log10 K require knowledge of the standard partial molar heat capacity and volume functions for the reaction, i.e., ∆Cp = −T(∂2∆G/∂T2)p and ∆V = (∂∆G/∂p)T, respectively. The exact differentiation equation yields the expression d∆G = {(∂∆G ∂T ) p + (∂∆G ∂p )T } dT

(3.19)

which can be integrated from the reference state (Tr, pr) to the state (T, p), yielding the expression ∆GTo, p = ∆GTor , pr +    o o o  ∫ ∆C p TdT + ∆STr , pr  dT + ∆V dp   path  path 

∫

(3.20)

where r is the reference state (Tr = 298.15 K and pr = 0.1 MPa). The above linear integral is independent of the path chosen. Integration along the saturation curve yields log10 KT , p = log KTr, pr + ∆H Tor, pr (1 T − 1 Tr ) (2.303R ) +

∫ ( ∆C

o p

T ) dT − (1 T )∫ ∆C op dT − ∫ ∆V o dp

(3.21)

Appropriate expressions for ∆C op and ∆V o can be used in Equation (3.21) to represent the temperature and pressure dependences of experimental values for log10 K. Conversely, if ∆C op and ∆Vo are known as functions of temperature, Equation (3.21) can be used to calculate log10 K versus T and p (Pitzer, 1995; Mesmer et al., 1988). In most cases in the potentiometric studies either the temperature range and/or the range of pressures were too limited to allow dVo to be evaluated from the experimental data and the contribution (Equation (3.21)) to log10 KT,p was either ignored or estimated based on values for an analogous equilibrium. On the other hand for equilibria studies over wide ranges of temperature and pressure, Franck (1956, 1961) observed that the ionization constants of many aqueous species at elevated temperatures and

204

Hydrothermal Experimental Data

pressures act as linear functions of the density of water, rw, when log10 K is plotted against log10 rw. Marshall and Franck (1981) developed this ‘density’ model to represent the ionization constant Kw of water at temperatures up to 1273 K and at pressures up to 1000 MPa. Equations of this form were used subsequently to represent K for the general ionization reactions by Mesmer et al. (1988): b c d log10 K =  a + + 2 + 3  +  T T T   e + f + g  log ρ 10 w  T T2 

(3.22)

where a, b, c, d, e, f, and g are adjustable parameters (any of these parameters may be set to zero); and rw is the density of pure water (in g·cm−3). Other thermodynamic quantities can be derived from the above equation. The Gibbs energy of ionization ∆Go is related to K by Equation (3.17): b c d ∆G = −2.303RT   a + + 2 + 3  + T T T    e + f + g  log ρ  10 w  T T2  

log10 Q = log10 K −

o

(3.23)

The enthalpy of ionization ∆Ho is then given by: o ∆H o  ∂ ∆G    = − 2 ∂T T p T

(3.24)

2c 3d  2g  ∆ H o = −2.303R  b + + 2+ f + log10 ρw  −    T T T  2 (3.25) RT kα w where aw = −(1/rw)(∂ rw /∂T)p is the thermal expansion coefficient of water and k is the second term in Equations (3.22) and (3.23). Similarly, the entropy of ionization, ∆So, the standard partial molar heat capacity of ionization, ∆rC op, and the standard partial molar volume of ionization, ∆Vo, can be derived from ∆Go using standard thermodynamic identities (Mesmer et al., 1988): c 2d g ∆S o = 2.303R  a − 2 − 3 +  e − 2  log10 ρw  −    T T T  (3.26) RTkα w

∆V o = − RTk βw

(

∆z 2 Aϕ I

(

2.303 1 + 1.2 I

)

)

+

1.667 ln 1 + 1.2 I + a1 I + a2 I 2 + a3 F ( I ) + 0.0157ΦI

(3.29)

1 ∑ mi zi2, where the 2 i summation extends to all ions in solution of molality mi and charge zi), ∆z2 = Σz2(products) − Σz2(reactants) is related to the coulombic asymmetry of the equilibrium, and Aϕ represents the Debye-Hückel limiting slope of the osmotic coefficient. The term Φ is the osmotic coefficient of the solution and is multiplied by the number water is involved in the equilibrium. The values of Φ are generally taken from those for NaCl reported by Archer (1992) as a function of temperature and ionic strength. The ion-interaction model (Pitzer, 1991) includes the function, F(I), which takes the form: Here I is the ionic strength ( I =

to yield:

2c 6d 2g ∆C op = −2.303R  − 2 − 3 −  2  log10 ρw  T  T  T  2 g ∂ α  − RT 2 k  w  − Rα w  2eT −   ∂Τ  p T 

where bw, = (1/rw)(∂rw/∂p)T, is the compressibility of water. Equation (3.21) can be further simplified over a restricted region, and the simplified form has fewer parameters (Anderson et al., 1991). More complex versions have been adopted to describe ∆Vo accurately at low temperatures (Clarke et al., 2000). In actual experiments, as indicated above, ionization quotients Q are usually measured in a solution at finite ionic strength made up by the addition of supporting electrolytes such as NaCl, KCl, or NaCF3SO3. Therefore, activity coefficient models are needed to extrapolate the Q values to infinite dilution for such equilibria. All of these models are based on some version of the Debye-Hückel equation, which determines the initial slope the log10 Q versus ionic strength dependence, with additional empirical ionic strength terms which are typically derived from those used in the Pitzer ion interaction model (Pitzer, 1991). An example of this empirical approach is given in Equation (3.29).

(3.27)

(3.28)

(

)

(

)

F ( I ) = 1 − 1 + 2 I − 2 I exp −2 I  (4 I )

(3.30)

For most of the high-temperature potentiometric studies of ionization equilibria carried in the past, a combination of temperature terms (Harned and Owen, 1950) to describe log10 K and versions the ionic strength terms in Equation (3.29), including combinations of temperature and ionic strength terms to account for the activity coefficient ratio, were tried, more or less in an empirical fashion, to provide the best fit of the log10 Q values with the minimum number of terms. In a limited number of cases, the complete Pitzer ion-interaction theory has been applied (e.g. the ionization of acetic acid, Mesmer and Holmes, 1992) to estimate activity coefficients utilizing literature values for the binary and ternary interaction parameters for the supporting ions. Many sophisticated software packages now exist that are readily available for the purpose of fitting potentiometric data using well documented ‘best fit’ criteria, although their use in fitting high-temperature data is still limited.

High Temperature Potentiometry 205

The above discussion in this section has focused on ionization equilibria, which are the most commonly available potentiometric data in the literature. However, the more limited data for solubility equilibria can be treated in a similar fashion. For example, for a divalent metal oxide, MO(s), the equilibria to be considered are MO (s ) + nH + ↔ M (OH )2 − n + (n − 1) H2 O (1) n

(3.30)

or these equilibria may be broken down into the dissolution equilibrium to form the unhydrolysed metal cation, MO (s ) + 2H + ↔ M 2 + + H2 O (1)

(3.31)

and the individual hydrolysis equilibria. When the isocoulombic approximation is not feasible, an approach suggested by Lindsay (1990a, b) can be useful in engineering calculations involving acid-base equilibria. Here, the activity coefficient of a single ion is estimated by using NaCl(aq) as a model system, through the expression: 2

γ z = γ ±z ( NaCl)

(3.32)

where z is the charge of the ion and g ±(NaCl) is the activity coefficient of NaCl(aq) at the same temperature and ionic strength. Acknowledgments DAP acknowledges the financial support by the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under contract DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC. SNL acknowledges financial support of the Department of Energy and Geo-Environmental Engineering and the Energy Institute of the College of Earth and Mineral Sciences at the Pennsylvania State University. REFERENCES Anderson, G.M., Castet, S., Schott, J. and Mesmer, R.E. (1991) Geochim. Cosmochim. Acta 55: 1769–79. Archer, D.G. (1992) J. Chem. Eng. Data 21: 793–829. Bates, R.G. (1964) Determination of pH, Theory and Practice. Wiley, New York. Becker, P. and Bilal, B.A. (1983) J. Solution Chem. 12: 573–580. Becker, P. and Bilal, B.A. (1987) Z. Naturforsch. 42a: 849–852. Bell, J.L.S., Wesolowski, D.J. and Palmer, D.A. (1993) J. Solution Chem. 22: 125–136. Bénézeth, P. and Palmer, D.A. (2000) Chem. Geol. 167: 11–24. Benezeth, P., Palmer, D.A. and Wesolowski, D.J. (1999) Geochim. Cosmochim. Acta 63(10): 1571–1586. Bénézeth, P., Palmer, D.A. and Wesolowski, D.J. (2001) Geochim. Cosmochim. Acta 65: 2097–2111. Benezeth, P., Palmer, D.A., Wesolowski, D.J. and Xiao, C. (2002) J. Solution Chem. 31(12): 947–973.

Bilal, B.A. and Müller, E. (1993) Z. Naturforsch. 48a: 743–747. Brown, P.L., Drummond, S.E. and Palmer, D.A. (1996) J. Chem. Soc. Dalton Trans. 3071–3075. Busey, R.H. and Mesmer, R.E. (1977) Inorg. Chem. 16: 2444–2450. Clarke, R.G., Hnêdkovský, L., Tremaine, P.R. and Majer V. (2000) J. Phys. Chem. B. 104: 11781–93. Diakonov, I., Pokrovski. G., Schott, J., Castet, S. and Gout, R. (1996) Geochim. Cosmochim. Acta 60: 197–211. Dickson, A.G., Wesolowski, D.J, Palmer, D.A. and Mesmer, R.E. (1990) J. Phys. Chem. 94: 7978–7985. Ding, K. and Seyfried, W.E., Jr. (1995) Geochim. Cosmochim. Acta 59: 4769–73. Eklund, K. E., Lvov, S. N. and Macdonald, D. D. (1997) J. Electroanal. Chem. 437: 99–110. Franck, E.U. (1956) Z. phys. Chem. N.F. 8: 92–126. Franck, E.U. (1961) Angew. Chem. 73: 309–322. Giasson, G., Tewari, P.H. (1978) Canadian J. Chem. 56: 435–440. Giordano, T.H., Drummond, S.E. (1991) Geochim. Cosmochim. Acta 55: 2401–2415. Harned, H.S. and Owen, B.B. (1950) The Physical Chemistry of Electrolyte Solutions, Reinhold Publishing Corp., New York, Chapter 15. Hitch, B.F. and Mesmer, R.E. (1976) J. Solution Chem. 5: 667–680. Kettler, R.M., Palmer, D.A. and Wesolowski, D.J. (1995a) J. Solution Chem. 24: 65–87. Kettler, R.M., Wesolowski, D.J. and Palmer, D.A. (1995b) J. Solution Chem. 24: 385–407. Kriksunov, L.B. and Macdonald, D.D. (1994) Sens. Actuators B 22: 201–4. Kriksunov, L.B., Macdonald, D.D. and Millett, P.J. (1994) J. Elctrochem. Soc. 141: 3002–5. Lindsay, W.T. Jr. (1990a) In M. Pichal and O. Sifner (eds), Properties of Water and Steam. Hemisphere, New York, pp. 29–38. Lindsay, W.T., Jr. (1990b) In Cohen, P. (ed.), The ASME Handbook on Water Technology for Thermal Power Systems, Amer. Soc. Mech. Engineers, New York, Chapter 7, pp. 341–544. Lvov S.N. (2005) In M. Stratmann and A. Bard (eds), Encyclopedia of Electrochemistry Vol. 6, Wiley-VCH. Lvov, S.N., Gao, H., Kouznetsov, D., Balachov, I. and Macdonald, D.D. (1998a) Fluid Phase Equil. 150–151: 515–523. Lvov, S.N., Gao, H. and Macdonald, D.D. (1998b) J. Electroanal. Chem. 443: 186–94. Lvov, S.N., Zhou, X.Y. and Macdonald, D.D. (1999) J. Electroanal. Chem. 463: 146–56. Lvov, S.N., Zhou, X.Y., Ulyanov, S.M. and Bandura, A.V. (2000a) Chem. Geol. 167: 105–15. Lvov, S.N., Zhou, X.Y., Ulyanov, S.M. and Macdonald, D.D. (2000b) Power Plant Chem. 2: 5–8. Lvov, S. N., Zhou, X.Y., Fedkin, M. V., Zhou, Z., Kathuria, A. and Barnes, H. L. (2002) Geochim. Cosmochim. Acta 66: A467. Lvov, S. N., Zhou, X.Y., Ulmer, G.C., Barnes, H.L., Macdonald, D.D., Ulyanov, S.M., Benning, L.G, Grandstaff, D. E., Manna, M. and Vicenzi, E. (2003) Chem. Geol. 198(3–4): 141–162. Lvov, S.N, Zhou, X.Y., Fedkin, M.V., Zhou, Z., Kathuria, A., and Barnes, H.L. (2002) Geochim. Cosmochim. Acta 66: A467. Lvov, S.N., Palmer, D.A. (2004) In D.A. Palmer, R. FernándezPrini, and A.H. Harvey (eds), The Physical and Chemical Properties of Aqueous Systems at Elevated Temperatures and

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Pressures: Water, Steam and Hydrothermal Solutions. Elsevier, Amsterdam, p. 377. Lvov, S.N., Perboni, G. and Broglia, M. (1995) In H.J.White, Jr., J.V.Sengers, D.B.Neumann, J.C.Bellows (eds), Physical Chemistry of Aqueous Systems. Meeting the Needs of Industry, (Proc. 12 Intern. Conf. on the Prop. of Water and Steam), Begell House, pp.441–448. Macdonald, D.D. (1978) Corrosion 34: 75–84. Marshall, W.L. and Franck, E.U. (1981) J. Phys. Chem. Ref. Data 10: 295–304. Mesmer, R.E. and Baes, C.F. (1974) J. Solution Chem. 3: 307–322. Mesmer, R.E. and Herting, D.L. (1978) J. Solution Chem. 7: 901–913. Mesmer, R.E. and Hitch, B.F. (1977) J. Solution Chem. 6: 251–161. Mesmer, R.E., Baes, C.F., Jr. and Sweeton, F.H. (1970) J. Phys. Chem. 74: 1937–42. Mesmer, R.E., Baes, C.F. and Sweeton, F.H.(1972) Inorg. Chem. 11(3): 537–543. Mesmer, R.E., Patterson, C.S., Busey, R.H. and Holmes, H.F. (1988) J. Phys. Chem. 93: 7483–90. Mesmer, R.E. and Holmes, H.F. (1992) J. Solution Chem. 21: 725–44. Palmer, D.A. and Drummond, S.E. (1988) J. Phys. Chem. 92: 6795–6800. Palmer, D.A. and Hyde, K.E. (1993) Geochim. Cosmochim. Acta 57: 1393–1408. Palmer, D.A. and Wesolowski, D.J. (1987) J. Solution Chem. 16: 571–581. Palmer, D.A. and Wesolowski, D.J. (1997) J. Solution Chem. 26: 217–232. Palmer, D.A., Ramette, R.W. and Mesmer, R.E. (1984) J. Solution Chem. 13: 685–697.

Palmer, D.A., Bénézeth, P. and Wesolowski, D.J. (2001) Geochim. Cosmochim. Acta 65: 2081–95. Patterson, C.S., Busey, R.H. and Mesmer, R.E. (1984) J. Solution Chem. 13: 647–661. Patterson, C.S., Slocum, G.H.: Busey, R.H. and Mesmer, R.E. (1982) Geochim. Cosmochim. Acta 46: 1653–1663. Pitzer, K.S. (1991) Activity Coefficients in Electrolyte Solutions. CRC Press: Boca Raton, FL. Pokrovski, G.S. and Schott, J. (1998) Geochim. Cosmochim. Acta 62: 1631–1642. Pokrovski, G.S., Schott, J. and Sergeev, A.S. (1995) Chem. Geology 124: 253–265. Sue, K., Murata, K., Matsuura, Y., Tsukagoshi, M., Adschiri, T. and Arai, K. (2001) Rev. Sci. Instr. 72: 4442–8. Sweeton, F.H., Mesmer, R.E. and Baes, Jr., C.F. (1973) J. Phys. E: Sci. Instr. 6: 165–8. Tremaine, P., Zhang, K., Benezeth, P. and Xiao, C. (2004) In D.A. Palmer, R. Fernández-Prini and A.H. Harvey (eds), The Physical and Chemical Properties of Aqueous Systems at Elevated Temperatures and Pressures: Water, Steam and Hydrothermal Solutions. Elsevier, Amsterdam, p. 441. Wesolowski, D.J., Drummond, S.E., Mesmer, R.E. and Ohmoto, H. (1984) Inorg. Chem. 23: 1120–1132. Wesolowski, D.J., Benezeth, P. and Palmer, D.A. (1998) Geochim. Cosmochim. Acts 62: 971–984. Wesolowski, D.J., Machesky, M.L., Palmer, D.A. and Anovitz, L.M. (2000) Chem. Geol. 167: 193–229. Wesolowski, D.J., Ziemniak, S.E., Anovitz, L.M., Machesky, M. L., Bénezéth, P. et al. (2004) In D.A. Palmer, R. FernándezPrini and A.H. Harvey (eds), The Physical and Chemical Properties of Aqueous Systems at Elevated Temperatures and Pressures: Water, Steam and Hydrothermal Solutions. Elsevier, Amsterdam, p. 493.

4

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

4.1 INTRODUCTION

4.2 BASIC PRINCIPLES AND DEFINITIONS

In this chapter the experimental data of electrical conductivity of hydrothermal systems reported at temperatures above 473.15 K are summarized. The summary tables (Table 4.1 and 4.2) also show the range of temperature covered in these studies and the number of data measured in the range 373.15 < T/K < 473.15. Since the limit for high temperature measurements is arbitrary we have also included in the summary tables the data for several aqueous electrolytes studied at temperatures above 373.15 K, with upper temperature limit below 473.15 K. The systems included in this chapter comprise binary aqueous electrolytes and ternary aqueous system containing two electrolytes or an electrolyte and a non-electrolyte. The electrical conductivity gives information on the ionion and ion-water interaction and also on the speciation in aqueous solutions. If the measurement of the electrical conductivity is precise enough it is possible to obtain not only information on the transport properties of the electrolyte but also on the thermodynamic of the ion association, which becomes very important as temperature increases and pressure or density decreases. On the other hand, the electrical conductivity information is essential for several practical applications of the hydrothermal systems. It is well known, for instance, the use of electrical conductivity measurements on line to prevent corrosion problems in steam generators and other applications of the steam/water cycle. Tracer diffusion coefficients of electrolytes can be calculated from limiting electrical conductivity and used to predict mass transfer in many geochemical processes and hydrothermal reactions. A recent review on the transport properties of hydrothermal systems (Corti et al., 2004) describes in detail the experimental and theoretical aspect of the electrical conductivity. A critical comparison of the classical and modern theories of electrical conductivity is also available (Bianchi et al., 2000).

We will assume that electrolytes of the type An−Cn+ dissociates in water according to

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

Aν −Cν + (aq ) → ν − A z − (aq ) + ν +C z + (aq ) If the molar concentration of electrolyte is c, the ionic concentration is ci = avic, where a is the degree of dissociation of the electrolyte, vi the stoichiometric number and zi the charges of ions. The electric neutrality condition holds, that is, z+v+ + z−v− = 0. The ions could form an ion pair, according to the equilibrium A z − (aq ) + C z + (aq ) ⇔ AC ( z ++ z − )(aq ) whose associated thermodynamic constant is given by Ka =

(1 − α ) cα 2γ ±2

(4.1)

being g ± the mean activity coefficient of the electrolyte. The electrical conductivity of this system involves fluxes of ionic solute species in the solvent due to the electrical potential gradient or electric field, E. In a system formed by solute particles (concentration ci) moving with velocity vi in a solvent which moves with a convective velocity vC , the molar flux Ji (the number of moles transported per unit area per time relative to fixed coordinates) is given by J i = ci ( v i − v C )

(4.2)

N

J q = ∑ zi FJ i

(4.3)

i =1

If the solute species contains N ions bearing charge zi the flow of charge is

HCH3CH2COO (propionic acid) HCH3(CH2)2COO (n-butyric acid)

CsI CsNO3 DyCl3 GdCl3 H3BO3 HBr HCHOO (formic acid) HCH3COO (acetic acid)

CsCl

Ca(NO3)2 CaSO4 CsBr

0.002–0.1* 0.002–0.1* 0.1–23* 0.05 0.001–0.01 0.001–0.05* 0.001–0.05* 0.0016–0.008 4 · 10−5–0.28 0.05–1 10# 0.001–0.005 1 · 10−4–0.09 0.0095 0.0007* 0.01 7 · 10−7–0.023 1.3 · 10−6–0.02 0.01 0.01 0.073–7.4* 0.01 0.0091 0.001* 0.001* 0.25–0.50 0.002–0.015 0.01–0.5* 0.01–0.1 0.01–0.3 0.01–0.1 0.02–1.5* 0.01 7 · 10−4–0.02 0.01–0.1 0.01–0.1

m (mol/kg)

a

18/218–306 18/218–306 222 25/200–300 46/255–760 18/218–306 18/218–306 50/253–760 75/200; 250 25/200–300 20/200–300 25/200–600 75/200; 250 25/200–454 18/218 0/220–813 332–400 330–401 0/201–796 300–1000 25/200–600 0/206–798 25/200–504 100/200–400 100/200–400 25/200–350 100/200–800 20/200–300 18/218; 306 18/218; 306 25/200; 225 25/200–300 25/200; 225 25/196; 275 25/200; 225 25/200; 225

T (°C)b

Variable range

Electrical conductivity of binary aqueous electrolytes

Ba(OH)2 Ca(CH3COO)2 (Ca-acetate) CaCl2

Ba(NO3)2

BaCl2

AgNO3

Electrolyte

Table 4.1

Sat. Sat. Sat. Sat. 0.5–1.05* Sat. Sat. 0.55–1.1* 8.4/9.4 Sat. 10/10; 150 0.3–1.0* 8.4/9.4 49 Sat. 0.1/2.3–400 22.5–28 15–28 0.1/2.3–400 0.65–1.1* 20–300 0.1/2.3–400 49 4.9/9.8–37.3 4.9/9.8–37.3 Sat. 0.3–1.0* Sat. Sat Sat. Sat. Sat. 0.1–300 0.1/20 Sat. Sat.

p (MPa)c Empirical (L°) Empirical (L°) – – FK (L°,K1,K2) Empirical (L°) Empirical (L°) FK (L°) TBBK (L°,K1) – – O (L°) TBBK (L°,K1) – – – FHFP (L°,K1) FHFP (L°,K1) – FK (L°) – – – – – – S (L°,K1) Empirical (L°, K1) Empirical (L°) Empirical (L°) Ost (L°,K1) Empirical (L°, K1) – FHFP/TBBK (L°,K1) Ost (L°,K1) Ost (L°,K1)

Fitting equationd 0.2–0.3 0.2–0.3 0.1 1.5 2 0.2–0.3 0.2–0.3 2 ≈0.2 1.5 3.5 1–2 ≈0.2 2–11 0.2–0.3 1–2 <0.1–1 <0.1–1 1–2 0.2–10 3–7 1–2 2–14 5–10 5–10 <0.1 1–2 1–10 0.2–0.3 0.2–0.3 ≈2 1–10 2 0.1–1 ≈2 ≈2

Error % Noyes et al (1908) Noyes et al (1910a) Campbell et al (1954) Kondrat’ev and Nikich (1963) Ritzert and Franck (1968) Noyes et al (1908) Noyes et al (1910a) Ritzert and Franck (1968) Mendez de Leo and Wood (2005) Kondrat’ev and Nikich (1963) Poliakov (1965) Frantz and Marshall (1982) Mendez de Leo and Wood (2005) Goemans et al (1997) Melcher (1910) Quist and Marshall (1969) Zimmerman et al (1995) Gruszkiewicz and Wood (1997) Quist and Marshall (1969) Mangold and Franck (1969) Hwang et al (1970) Quist and Marshall (1969) Goemans et al (1997) Ismail et al (2003) Ismail et al (2003) Ho and Palmer (1995b) Quist and Marshall (1968b) Maksimova and Yushkevich (1966) Noyes et al (1908) Noyes et al (1910b) Ellis (1963a) Maksimova and Yushkevich (1966) Lown et al (1970) Zimmerman and Wood (2002) Ellis (1963a) Ellis (1963a)

Reference

el-AgNO3–1.1 el-AgNO3–2.1 el-AgNO3–3.1 el-BaCl2–1.1 el-BaCl2–2.1 el-Ba(NO3)2–1.1 el-Ba(NO3)2–2.1 el-Ba(OH)2–1.1 el-Ca(C2H3O2)2–1.1 el-CaCl2–1.1 el-CaCl2–2.1 el-CaCl2–3.1 el-CaCl2–4.1 el-Ca(NO3)2–1.1 el-CaSO4–1.1 el-CsBr-1.1 el-CsBr-2.1 el-CsBr-3.1 el-CsCl-1.1 el-CsCl-2.1 el-CsCl-3.1 el-CsI-1.1 el-CsNO3–1.1 el-DyCl3–1.1 el-GdCl3–1.1 el-H3BO3–1.1 el-HBr-1.1 el-CH2O2–1.1 el-C2H4O2–1.1 el-C2H4O2–2.1 el-C2H4O2–3.1 el-C2H4O2–4.1 el-C2H4O2–5.1 el-C2H4O2–6.1 el-C3H6O2–1.1 el-C4H8O2–1.1

Table code

208 Hydrothermal Experimental Data

KCH3CH2COO (K-propionate) KCH3(CH2)2COO (K-butyrate) K(C6H5)COO (K-benzoate)

KCH3COO (K-acetate)

KBr

H2SO4

H3PO4

HNO3

HF

H2CO3 HCl

H(C6H5)COO (benzoic acid)

Electrolyte 25/200; 225 25/200; 251 100/200 18/218–306 18/218–306 200–700 25/200; 225 300–383 45/190; 220 373–804 25/200; 225 25/200; 250 100/200–700 100/200–410 25/175–200 100/218 18/218; 306 18/218; 306 25/200–300 25/200 18/218; 306 18/218; 306 45/190; 220 0/200–800 20/200–300 100/200–400 15/175–250 25/200–300 0/200–798 25/200; 225 25/200; 225 25/200; 225 25/200; 225 25/200; 225

T (°C)b

Variable range

0.01; 0.02 0.001 0.076–0.14* 0.002–0.1* 0.0004–0.1* 0.0002–0.001* 0.001–0.01 5 · 10−5–2.4 · 10−3 0.01* 0.033–0.1 0.01 0.01 0.002–0.01 1.5 · 10−5–2.2 · 10−3 0.012–0.093 0.0027–0.03* 0.002; 0.08* 0.002–0.1* 0.0007–0.7* 0.0078 0.002–0.1 0.00025–0.05 0.01* 0.002–0.01 0.002–0.5* 1.1 · 10−5–0.023 0.05–0.25 0.05–1 0.01 0.001–0.01 0.01 0.001; 0.002 0.001; 0.01 0.001; 0.002

m (mol/kg)

a

Sat. 0.1–200 Sat. Sat. Sat. 0.2–1.0* Sat. 0.4–0.53* Sat. (7–13) 103 0.1–300 0.1/20–200 0.4–1.05* 10–31 Sat. Sat. Sat. Sat. Sat. 0.1–200 Sat. Sat. Sat. 0.4–1.0* Sat. 12–28 Sat Sat. 0.1/2–400 Sat. 0.1–300 Sat. Sat. Sat.

p (MPa)c Ost (L°,K1) – – Empirical (L°) Empirical (L°) S (L°,K1) Empirical (L°) S (L°,K1) – – – – Ost (L°,K1) FHFP (L°,K1) Empirical (L°) – Empirical (L°) Empirical (L°) Empirical (L°, K1, K2) Ost (L°,K1) Empirical (L°) Empirical (L°) – S (L°,K1) Empirical (L°, K1) TBBK (L°,K1) – – – Empirical (L°) – Empirical (L°) Empirical (L°) Empirical (L°)

Fitting equationd Reference Ellis (1963a) Read (1981) Ryzhenko (1963) Noyes et al (1908) Noyes et al (1910a) Franck (1956c) Ellis (1963a) Pearson et al. (1963b) Franck et al (1965) Hamann and Linton (1969) Lown et al (1970) Read (1975) Frantz and Marshall (1984) Ho et al (2001) Ellis (1963b) Ryzhenko (1965) Noyes et al (1908) Noyes et al (1910a) Maksimova and Yushkevich (1966) Read (1988) Noyes et al (1908) Noyes et al (1910a) Franck et al (1965) Quist et al (1965) Maksimova and Yushkevich (1966) Hnedkovsky et al (2005) Huang and Papangelakis (2006) Kondrat’ev and Gorbachev (1965) Quist and Marshall (1969) Ellis (1963a) Lown et al (1970) Ellis (1963a) Ellis (1963a) Ellis (1963a)

Error % ≈2 0.2 1.5–5 0.2–0.3 0.2–0.3 10 ≈2 0.5–1 1.9 12–25 2 <0.1 1–2 0.2 ≈2 1.5–5 0.2–0.3 0.2–0.3 1–10 0.25 0.2–0.3 0.2–0.3 1.9 1–2 1–10 ≈0.2 0.5 <1.5 1–2 ≈2 2 ≈2 ≈2 ≈2

el-C7H6O2–1.1 el-C7H6O2–2.1 el-H2CO3–1.1 el-HCl-1.1 el-HCl-2.1 el-HCl-3.1 el-HCl-4.1 el-HCl-5.1 el-HCl-6.1 el-HCl-7.1 el-HCl-8.1 el-HCl-9.1 el-HCl-10.1 el-HCl-11.1 el-HF-1.1 el-HF-2.1 el-HNO3–1.1 el-HNO3–2.1 el-H3PO4–1.1 el-H3PO4–2.1 el-H2SO4–1.1 el-H2SO4–2.1 el-H2SO4–3.1 el-H2SO4–4.1; 4.2; 4.3 el-H2SO4–5.1 el-H2SO4–6.1 el-H2SO4–7.1 el-KBr-1.1 el-KBr-2.1 el-KC2H3O2–1.1 el-KC2H3O2–2.1 el-KC3H5O2–1.1 el-KC4H7O2–1.1 el-KC7H5O2–1.1

Table code

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 209

KNO3 KOH

KF KHCO3 KH2PO4 K2HPO4 KHSO4 KI

KCl

Electrolyte

Table 4.1

Continued

0.0005–0.1* 0.0005–0.1* 0.002–0.1* 0.01–0.1* 1–3* 0.0002–0.009* 0.05–1 0.01–0.05* 0.001–0.01 0.01* 10# 0.001–0.01 0.01 0.0001–0.007 0.01 0.1; 1 0.01 0.01 0.12–3.96* 0.01 0.002–0.01 0.001–0.01 0.00013–0.0043 0.001–4.5 0.002–0.01 0.01 0.0005–0.01* 0.0005–0.01* 0.0004–0.005 0.05–1 0.01 0.05–1 0.0002–0.001* 5–50# 0.1 0.1/2.85; 6.7 0.0009–0.01 0.0001–0.0026

m (mol/kg)

a

26/218–306 26/218–306 18/218–306 18/218–306 25/200–340 250–750 25/200–300 100/218 25/200; 225 45/190; 220 20/200–300 200–750 219–1000 440 0/202–799 240–670 25/200; 225 200–350 25/200–600 25/200; 250 25–150 300–600 25/200–410 200–600 25/175; 200 25/200; 250 25/200–325 25/200–325 0/200–700 25/200–300 0/210–803 25/200–300 200–700 25/200–260 373–804 25/201 100/200–600 100/200–405

T (°C)b

Variable range

Sat. Sat. Sat. Sat. Sat. 0.2–0.9* Sat. Sat. Sat. Sat. 10;150 0.5–1.0* 0.7–1.2* 0.4–0.7 0.1–400 (5–11) · 103 0.1–300 100–800 20–300 0.1/20–200 0.1–800 0.3–0.95* 5–31 20–300 Sat. 0.1–200 Sat. Sat. 0.4–1.0* Sat. 0.1/1.9–400 Sat. 0.2–1.0* Sat (7–13) · 103 0.1–300 0.3–1.0* 14/15–31

p (MPa)c Empirical (L°) Empirical (L°) Empirical (L°) Empirical (L°) – S (L°,K1) – – Empirical (L°) – – Ost (L°,K1) FK (L°) S (L°,K1) – – – – – – Empirical (L°) FHFP (L°,K1) FHFP (L°,K1) TBBK (L°,K1) Empirical (L°) – – – S (L°,K1) – – – S (L°,K1) – – – FHFP (L°,K1) FHFP (L°,K1)

Fitting equationd

<0.1 0.4 ≈0.2 ≈2 <0.1 1–2 1–2 2–3 <1.5 1–2 <1.5 10 2–5 17–37 <0.1 0.4

0.2–0.3 0.2–0.3 0.2–0.3 0.2–0.3 <10 10 1.5 >1 ≈2 1.9 3.5 2 0.2–10 3–7 1–2 14–25 2 3–7 3–7 <0.1

Error % Noyes and Coolidge (1903) Noyes and Coolidge (1904) Noyes et al (1908) Noyes et al (1910a) Rodnanskii and Galinker (1955) Franck (1956a, 1956b) Gorbachev and Kondrat’ev (1961) Khitarov et al (1963) Ellis (1963a) Franck et al (1965) Polyakov (1965) Ritzert and Franck (1968) Mangold and Franck (1969) Hartmann and Franck (1969) Quist and Marshall (1969) Hamann and Linton (1969) Lown et al (1970) Renkert and Franck (1970) Hwang et al (1970) Read (1975) Larionov and Kryukov (1976) Ho and Palmer (1997) Ho et al (2000a) Sharygin et al (2002) Ellis (1963b) Read (1975) Muccitelli and Diangelo (1994) Muccitelli and Diangelo (1994) Quist and Marshall (1966) Kondrat’ev and Gorbachev (1965) Quist and Marshall (1969) Kondrat’ev and Gorbachev (1965) Franck (1956c) Yushkevich et al (1967) Hamann and Linton (1969) Lown and Thirsk (1971) Ho and Palmer (1997) Ho et al (2000b)

Reference

el-KCl-21.1 el-KCl-22.1 el-KCl-23.1 el-KF-1.1 el-KHCO3–1.1 el-KH2PO4–1.1 el-K2HPO4–1.1 el-KHSO4–1.1 el-KI-1.1 el-KI-2.1 el-KNO3–1.1 el-KOH-1.1 el-KOH-2.1 el-KOH-3.1 el-KOH-4.1; 4.2 el-KOH-5.1 el-KOH-6.1

el-KCl-1.1 el-KCl-2.1 el-KCl-3.1 el-KCl-4.1 el-KCl-5.1 el-KCl-6.1 el-KCl-7.1 el-KCl-8.1 el-KCl-9.1 el-KCl-10.1 el-KCl-11.1 el-KCl-12.1 el-KCl-13.1 el-KCl-14.1 el-KCl-15.1 el-KCl-16.1 el-KCl-17.1 el-KCl-18.1 el-KCl-19.1 el-KCl-20.1

Table code

210 Hydrothermal Experimental Data

Na6Al4O9 NaBO2 NaBr

NH4NO3 NH4OH

NH4Br NH4C2H3O2 (NH4-acetate) NH4Cl

MgSO4

Li2SO4 MgCl2

LiOH

LiNO3

LiBr LiCl

K3PO4 K2SO4

Electrolyte 25/200–325 18/218–306 18/218–306 100/200–800 250–400 25/200–600 25/200–340 300–1000 0/207–795 25/200–600 332–400 330–375 100/200–600 50/200–405 25–110 25/203–504 49/204–271 25–150 100/200–600 50/200–410 250–400 25/200–300 200–600 18/218–306 18/218 20/200–300 23/220–350 15/175–250 0/200–800 18/218; 306 18/218; 306 18/218; 306 25/200; 250 180 18/218; 306 18/218; 306 27/204–293 0/200–700 25/200; 250 50/200–250 25/200–340 100/200–800 0/205–809 329–400 330–385

(0.004–26)*10−3

1.2–12* 1–3* 0.001–0.01 0.01 0.1–13.3* 7 · 10−7–0.026 2.1 · 10−6–0.013 0.0008–0.01 0.0002–0.0028 0.01–14.4* 0.0091 0.0006–0.0015* 1–5 0.001–0.01 4.7 · 10−5–0.0026 (0.009–23)*10−3 0.05–0.9 0.001–0.005 0.002–0.2* 0.002–0.2* 10# 0.002; 0.01 0.01–0.40 0.01 0.006–0.029* 0.002–0.030* 0.002–0.030* 0.001 0.09–18* 0.01–0.1* 0.01–0.5* 0.0034–0.093 0.01; 0.05 0.066 0.0006–0.026* 1–20# 0.002–0.015 0.01 1 · 10−6–0.0022 2.2 · 10−6–0.019

T (°C)b

Variable range

0.0005–0.01* 0.002–0.1 0.002–0.1 0.0005–0.005

m (mol/kg)

a

20–300 Sat. 0.6–1.1* 0.1/Sat-400 20–300 22–28 15–25 0.3–1.0* 1/5–32 Sat. 49 14 0.1–300 0.3–1.0* 4/10–32 20–29 Sat. 0.6–1.0* Sat. Sat. 10–150 0.8–1.15* Sat. 0.45–1.0* Sat. Sat. Sat. 0.1–200 Sat. Sat. Sat. 14 0.5–1.15* 0.1–200 Sat. Sat. 0.3–1.0* 0.1–400 28 15–25

20–29

Sat. Sat. Sat. 0.2–1.0*

p (MPa)c

– – FK (L°) – – FHFP (L°,K1) FHFP (L°,K1) S/FHFP (L°,K1) FHFP (L°,K1) Empirical (L°) – S (L°,K1) – S/FHFP (L°,K1) FHFP (L°,K1) TBBK (L°,K1) – O (L°) Empirical (L°) Empirical (L°) – Ost (L°,K1) – – Empirical (L°) Empirical (L°) Empirical (L°) – – Empirical (L°) Empirical (L°) S (L°,K1) S (L°,K1) – – – S (L°,K1) – FHFP (L°,K1) FHFP (L°,K1)

TBBK (L°,K1)

– Empirical (L°) Empirical (L°) FO (L°)

Fitting equationd

3–7 <10 0.2–10 1–2 3–7 <0.1–1 <0.1–1 1–12 0.4 0.1 2–10 1–12 0.4 ≈0.2 1.5 1–2 0.2–0.3 0.2–0.3 3.5 2 0.5 1–2 0.2–0.3 0.2–0.3 0.2–0.3 0.2 0.1 0.2–0.3 0.2–0.3 1–2 0.2 ≈2 1–10 1–2 1–2 <0.1–1 <0.1–1

≈0.2

1–2 0.2–0.3 0.2–0.3 1–2

Error %

Hwang et al (1970) Rodnanskii and Galinker (1955) Mangold and Franck (1969) Quist and Marshall (1969) Hwang et al (1970) Zimmerman et al (1995) Gruszkiewicz and Wood (1997) Ho and Palmer (1998) Ho et al (2000a) Campbell et al (1955) Goemans et al (1997) Wright et al (1961) Lown and Thirsk (1971) Ho and Palmer (1998) Ho et al (2000b) Sharygin et al (2006) Kondrat’ev and Nikich (1963) Frantz and Marshall (1982) Noyes et al (1908) Noyes et al (1910a) Polyakov (1965) Ritzert and Franck (1968) Huang and Papangelakis (2006) Quist (1970) Noyes et al (1910b) Noyes et al (1908) Noyes et al (1910b) Read (1982) Campbell et al (1954) Noyes et al (1908) Noyes et al (1910b) Wright et al (1961) Quist and Marshall (1968d) Read (1982) Ryzhenko (1967) Maksimova and Yushkevich (1963b) Quist and Marshall (1968c) Quist and Marshall (1969) Zimmerman et al (1995) Gruszkiewicz and Wood (1997)

Sharygin et al (2006)

Muccitelli and Diangelo (1994) Noyes et al (1908) Noyes et al (1910a) Quist et al (1963)

Reference

el-NH4OH-1.1 el-NH4OH-2.1 el-NH4OH-3.1 el-NH4OH-4.1 el-NH4OH-5.1 el-Na6Al4O9–1.1 el-NaBO2–1.1 el-NaBr-1.1 el-NaBr-2.1 el-NaBr.3.1 el-NaBr-4.1

el-LiOH-2.1 el-LiOH-3.1 el-Li2SO4–1.1 el-MgCl2–1.1 el-MgCl2–2.1 el-MgSO4–1.1 el-MgSO4–2.1 el-MgSO4–3.1 el-MgSO4–4.1 el-MgSO4–5.1 el-NH4Br-1.1 el-NH4C2H3O2–1.1; 1.2 el-NH4Cl-1.1 el-NH4Cl-2.1 el-NH4Cl-3.1

el-LiNO3–1.1 el-LiOH-1.1

el-LiBr-1.1 el-LiCl-1.1 el-LiCl-2.1 el-LiCl-3.1 el-LiCl-4.1 el-LiCl-5.1 el-LiCl-6.1 el-LiCl-7.1 el-LiCl-8.1

el-K2SO4–4.1

el-K3PO4–1.1 el-K2SO4–1.1 el-K2SO4–2.1 el-K2SO4–3.1

Table code

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 211

Na2HPO4 NaI

NaH2PO4

NaF NaHCO3

Na(C6H5)COO (Na-benzoate) NaCl

NaCF3SO3 (Na-trifluorome thanesulfonate) NaCH3COO (Na-acetate)

Electrolyte

Table 4.1 Continued

100/200–450 18/218; 306 18/218; 306 18/218; 306 25/196 25/200; 250 26/218–307 26/218–306 18/218–306 18/218–306 378–393 25/200–340 390 300–383 20/200–300 100/200–800 0/203–812 260–370 25/200; 250 100/200–600 306–404 330–401 250–405 351 378–397 308/429–458 100/218 100–218 20/200–300 25/200 25/200–325 25/200–325 100/200–800 0/207–796

0.002–0.08 0.002–0.08 0.0005–0.096 1 · 10−4–0.0057 0.001 0.0004–0.09* 0.0005–0.1* 0.002–0.1* 0.0005–0.1* 9 · 10−6–0.0025* 1–3* 0.0001–0.2* 0.00024–0.003 0.03#-sat. 0.001–0.1 0.01 0.01–5* 0.001 0.001–0.1

1.3 · 10−6–0.032 1.9 · 10−7–0.019 0.00016–0.002 0.0025–0.011 3 · 10−6–1.0 2 · 10−4–0.4 0.001–0.01* 0.001–0.04* 8# 0.0017–0.0032 0.0005–0.01* 0.0005–0.01* 0.001–0.1 0.01

T (°C)b

0.0009–0.09

m (mol/kg)a

Variable range

10–28 15–28 10–32 20 28 0.13/1.4 Sat. Sat. 10–150 0.1–200 Sat. Sat. 0.35–1.0* 0.1–400

Sat. Sat. Sat. 0.1/20 0.1–200 Sat. Sat Sat. Sat. 0.2–0.4* Sat. 0.2–0.5* 0.4–0.6* 10;150 0.3–1.0* 0.1–400 25–200 0.1–200 0.3–1.0*

0.1–350

p (MPa)c

FHFP (L°,K1) FHFP (L°,K1) FHFP (L°,K1) FHFP/TBBK (L°,K1) TBBK (L°,K1) FHFP (L°,K1) – – – Ost (L°,K1) – – S (L°,K1) –

Empirical (L°) Empirical (L°) Empirical (L°) FHFP/TBBK (L°,K1) – Empirical (L°) Empirical (L°) Empirical (L°) Empirical (L°) S (L°,K1) – – S (L°,K1) – S (L°,K1) – – – S (L°,K1)

S (L°,K1)

Fitting equationd

<0.1–1 <0.1–1 0.4 ≈0.2 ≈0.2 ≈0.15 ≈1 ≈1 3.5 <0.1 1–2 1–2 1–2 1–2

0.2–0.3 0.2–0.3 0.2–0.3 0.1–1 0.2 0.2–0.3 0.2–0.3 0.2–0.3 0.2–0.3 <10 >10 0.5–1 3.5 1–2 1–2 ≈1 0.2 <0.1

<0.1

Error %

Zimmerman et al (1995) Gruszkiewicz and Wood (1997) Ho et al (2000a) Sharygin et al (2001) Sharygin et al (2002) Zimmerman et al (2007) Ryzhenko (1965) Khitarov et al (1963) Polyakov (1965) Read (1988) Muccitelli and Diangelo (1994) Muccitelli and Diangelo (1994) Dunn and Marshall (1969) Quist and Marshall (1969)

Noyes et al (1908) Noyes et al (1910b) Noyes et al (1910a) Zimmerman and Wood (2002) Read (1981) Noyes and Coolidge (1903) Noyes and Coolidge (1904) Noyes et al (1908) Noyes et al (1910a) Fogo et al (1954) Rodnanskii and Galinker (1955) Corwin et al (1960) Pearson et al. (1963a) Polyakov (1965) Quist and Marshall (1968a) Quist and Marshall (1969) Bannard (1975) Read (1981) Ho et al (1994)

Ho and Palmer (1995a)

Reference

el-NaC2H3O2–1.1 el-NaC2H3O2–2.1 el-NaC2H3O2–3.1 el-NaC2H3O2–4.1 el-NaC7H5O2–1.1 el-NaCl-1.1 el-NaCl-2.1 el-NaCl-3.1 el-NaCl-4.1 el-NaCl-5.1 el-NaCl-6.1 el-NaCl-7.1;7.2 el-NaCl-8.1 el-NaCl-9.1 el-NaCl-10.1 el-NaCl-11.1 el-NaCl-12.1 el-NaCl-13.1 el-NaCl-14.1; 14.2;14.3 el-NaCl-15.1 el-NaCl-16.1 el-NaCl-17.1 el-NaCl-18.1 el-NaCl-19.1 el-NaCl-20.1 el-NaF-1.1 el-NaHCO3–1.1 el-NaHCO3–2.1 el-NaH2PO4–1.1 el-NaH2PO4–2.1 el-Na2HPO4–1.1 el-NaI-1.1 el-NaI-2.1

el-NaCF3SO3–1.1

Table code

212 Hydrothermal Experimental Data

1–40# 0.0039–0.038 0.002–0.05* 0.002–0.05* 0.5–49# 0.0098 0.001 0.0017–0.015 5–100# 0.0009–0.01 0.00013–0.0027 0.0005–0.01* 10# 0.00013–0.017 1.1 · 10−5–0.0087 0.0016–0.025* 0.0005–0.015* 1–40# 0.001* 0.01 0.01 0.01 0.01 0.001* 0.05–1 0.006–0.09* 1 · 10−4/0.001–2.5

Na2MoO4 NaNO3 NaOH

18/200–280 25/203–505 18/218 18/218 20/200–300 0/200–300 25/200–250 75/200 25/200–400 100/200–600 100/200–405 25/200–325 20/200–300 27/253–301 100/200–400 50/200; 250 100/200–250 18/200–280 100/200–400 0/102–809 0/102–793 0/100–801 0/100–802 100/200–400 25/200–300 100/200 0/200

T (°C)b

Variable range

Sat. 10–50 Sat. Sat. Sat. 0.7–1.15* 0.1–200 1.6 0.1–300 0.3–1.0* 10–31 Sat. 10–150 0.1–28 12–28 Sat. Sat. Sat. 4.9–37.3 0.1–400 0.1–400 0.1–400 0.1–400 4.9–37.3 Sat. Sat. Sat.

p (MPa)c – S (L°,K1) Empirical (L°) Empirical (L°) – – – FHFP/LW (L°,K1) – FHFP (L°,K1) FHFP (L°,K1) – – TBBK (L°,K1) TBBK (L°,K1) – – – – – – – – – – – S/FH (L°,K1)

Fitting equationd 1–10 1–15 0.2–0.3 0.2–0.3 1–10 1–2 0.2 ≈0.2 3–4.5 <0.1 0.4 1–2 3.5 ≈0.2 ≈0.2 ≈1 ≈1 1–10 5–10 1–2 1–2 1–2 1–2 5–10 1.5 ≈1 <0.1

Error % Maksimova et al (1976) Goemans et al (1997) Noyes et al (1908) Noyes et al (1910a) Maksimova and Yushkevich (1963a) Quist and Marshall (1968d) Read (1982) Bianchi (1990); Bianchi et al. (1994) Eberz and Franck (1995) Ho and Palmer (1996) Ho et al (2000b) Muccitelli and Diangelo (1994) Poliakov (1965) Sharygin et al (2001) Hnedkovsky et al (2005) Ryzhenko (1967) Ryzhenko (1967) Maksimova et al (1976) Ismail et al (2003) Quist and Marshall (1969) Quist and Marshall (1969) Quist and Marshall (1969) Quist and Marshall (1969) Ismail et al (2003) Kondrat’ev and Nikich (1963) Ryzhenko et al (1967) Brown et al. (1954)

Reference el-Na2MoO4–1.1 el-NaNO3–1.1 el-NaOH-1.1 el-NaOH-2.1 el-NaOH-3.1 el-NaOH-4.1 el-NaOH-5.1 el-NaOH-6.1 el-NaOH-7.1 el-NaOH-8.1 el-NaOH-9.1 el-Na3PO4–1.1 el-Na2SO4–1.1 el-Na2SO4–2.1 el-Na2SO4–3.1 el-Na2SiO3–1.1 el-Na2Si2O5–1.1 el-Na2WO4–1.1 el-NdCl3–1.1 el-RbBr-1.1 el-RbCl-1.1 el-RbF-1.1 el-RbI-1.1 el-SmCl3–1.1 el-SrCl2–1.1 el-UO2(NO3)2–1.1 el-UO2SO4–1.1

Table code

a) * symbol corresponds to concentration expressed as molarity (c) in mol·dm-3. # symbol corresponds to concentration expressed as % weight of solute. Number before (/)-slash shows the lowest concentration in conductivity measurements below 200 °C. It is absent in the Appendix but is given in the publication. b) Lowest experimental temperature, if lower than 200 °C, is indicated followed by the temperature range quoted in the Appendix c) * symbol corresponds to density range (in g·cm-3). Number before (/)-slash shows the lowest pressure in conductivity measurements below 200 °C. It is absent in the Appendix but is given in the publication. d) Ost: Otswald treatment; S: Shedlovsky; FH: Fuoss-Hsia; FHFP: Fuoss-Hsia-Fernández Prini; LW: Lee-Wheaton; TBBK: Turk-Blum-Bernard-Kunz.

Na2SiO3 Na2Si2O5 Na2WO4 NdCl3 RbBr RbCl RbF RbI SmCl3 SrCl2 UO2(NO3)2 UO2SO4

Na3PO4 Na2SO4

m (mol/kg)

Electrolyte

a

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 213

0.00014–0.0072 0.0005–0.01 0.1–2*

Electolyte + Non-electrolyte KCl+Ar NaCl+C4H8O2 NaI+CH3OH 440 300 25/200; 230

75/200; 250 196–275 15/200–250 15/175–250 100/200–400 100/150–350

T (°C)b

Variable range

0.02–0.04 Sat-400 Sat.

8.4–9.4 20 Sat. Sat. 12–28 Sat.

p (MPa)

S (L°,K1) S (L°,K1) –

TBBK (L°,K1) FHFP/TBBK (L°,K1) – – TBBK (L°,K1) –

Fitting equationc

3–7 1–2 >1

≈0.2 0.1–1 0.5 0.5 ≈0.2 3

Error %

a) * symbol corresponds to concentration expressed as molarity (c) in mol.dm-3. b) Lowest experimental temperature, if lower than 200 °C, is indicated followed by the temperature range quoted in the Appendix c) S: Shedlovsky; FHFP: Fuoss-Hsia-Fernández Prini; TBBK: Turk-Blum-Bernard-Kunz.

0.001–0.3 0.0005–0.023 0.40–0.65 0.45–0.75 1.7 · 10−5–0.0079 3 · 10−5–1 · 10−4

m (mol/kg)

a

Electrical conductivity of ternary aqueous electrolytes

Two electrolytes Ca(CH3COO)2+ HCH3COO HCH3COO+ NaCH3COO H2SO4+ Al2(SO4)3 H2SO4+MgSO4 H2SO4+Na2SO4 KOH+H3BO3

Electrolyte

Table 4.2

Hartmann and Franck (1969) Yeatts and Marshall (1972) Korobkov and Mikhilev (1970)

Mendez de Leo and Wood (2005) Zimmerman and Wood (2002) Baghalha and Papangelakis (2000) Huang and Papangelakis (2006) Hnedkovsky et al (2005) Sheynin (1980)

Reference

el-KCl+Ar-1.1 el-NaCl+C4H8O2–1.1 el-NaI+CH3OH-1.1

el-Ca(C2H3O2)2+ C2H4O2 -1.1 el-C2H4O2+ NaC2H4O2–1.1 el -H2SO4+Al2(SO4)3–1.1 el-H2SO4+MgSO4–1.1 el-Na2SO4+ H2SO4–1.1 el-KOH+H3BO3–1.1;1.2

Table code

214 Hydrothermal Experimental Data

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 215

where F is the Faraday constant, 96,498 coulombs/mole. This charge flow is called the current density, i, defined as the electric charge transported per unit of time and area. According to Ohm’s law J q = i = κ .E

(4.4)

where the specific conductivity, k, becomes a parameter depending on the ionic concentration and also on the electric mobility, ui, of the ions, defined as ui = (vi−vC)/E. The transport number, defined as ti = Ji /Jq, represents the fraction of the total current driven by ion i and, as ui , depend of the reference system adopted to measure the ionic velocities. For instance, the reference velocity could be the average velocity of the solvent molecules (Hittorf’s reference system) when measuring transport numbers. For a binary electrolyte solution, from Equations (4.3) and (4.4), we found that the specific conductivity is given by (Haase, 1969)

κ = F ( c+ z+ u+ + c− z− u− ) = ( v+ z+ λ + + v− z− λ − ) α c (4.5) where li = Fui is the ionic conductivity of the i ion. In order to eliminate the explicit concentration dependence, the equivalent conductivity, l, is defined in terms of the equivalent concentration, c* = v+z+c = v−/z−/c, Λ=

κ = α (λ+ + λ− ) c*

(4.6)

Following the recommendations of IUPAC, the equivalent conductivity has been substituted by the molar conductivity of the (1/v+z+)Av−Cv+ substance (Fernández-Prini and Justice, 1984), having the same numerical value as the former equivalent conductivity. At the infinite dilution limit (c→0) the dissociation is complete and the ion mobility only depends on the ionsolvent interactions and the ionic and the molar conductivities reach their infinite dilution values l oi and lo, respectively. In this limit the Kohlrausch’s law of independent ion migration (Kohlrausch, 1898) Λ o = λ +o + λ −o

(4.7)

holds and the ionic conductivity of a given ion is independent of the type of salts, that is, of the nature of the counterion. At infinite dilution the ionic conductivity is related to the tracer diffusion coefficient of the ion (D oi ) through the wellknown Nernst-Einstein relationship:

λio =

zi F 2 o Di RT

(4.8)

Thus, the electrical conductivity techniques at high temperature allow us to obtain information on the mass transport coefficient of electrolytes in water, which are rather difficult to measure directly under hydrothermal conditions.

The definition of Λ can be generalized to a multicomponent system with n electrolytes, but we must be careful with notation because some electrolytes could have common ions. Thus, a system with n electrolyte components will have N ionic components, with N ≤ 2n, and the following expression is valid n

Λ=

N

∑κ

k

k n

∑c

k

k

∑c

i

=

zi Λ i

i

(4.9)

N

∑c

i

i

where ck are the concentrations of the constituents electrolytes and ci are the ionic concentrations. It is important to note that due to the electroneutrality conditions, the total density current and therefore k and Λ are independent of the reference system. 4.3 EXPERIMENTAL METHODS In this section we present a summary of the experimental method used to obtain information on the electrical conductivity of high temperature, high pressure aqueous electrolyte solutions. An excellent review of the techniques used up to 1985 has been done by Marshall and Frantz (Marshall and Frantz, 1987). The reader could refer to classical books on electrolytes to learn about the common practice on calibration of cells and measurement procedures using impedance bridges (Robinson and Stokes, 1965; Spiro, 1984). 4.3.1 Static high temperature and pressure conductivity cells The first measurements of the electrical conductivity of aqueous electrolytes at high temperature were performed 100 years ago by Noyes and co-workers at MIT (Noyes et al., 1903, 1907, 1910a, 1910b) using a high-pressure platinum-lined steel vessel. The body of the cell is one of the electrodes, while two others platinum electrodes were located in the upper and lower part of the vessel and insulated from it by mica and quartz washers. The solution is filled into the cell and it remains static during the measurement performed near saturation with vapor phase. The platinum electrode on the vessel wall was in contact with the liquid and vapor phase and the conductivity of the solution was measured between this electrode and the electrode at the bottom vessel. The third electrode at the upper part of the cell was in contact with the vapor phase and it allowed determining the volume of the sample. Noyes and coworkers measured with this cell the conductivity of NaCl, KCl, HCl, NaOH, HNO3, AgNO3, Ba(NO3)2, H2SO4, K2SO4, MgSO4, and NaCH3COO at temperatures up to 306 °C. A number of static high temperature cells were developed later for electrical conductivity. Some of them have been used for measurements at temperatures below the critical temperature of water. Thus, Khitarov et al. (1963), Ellis

216

Hydrothermal Experimental Data

(1963a), Maksimova and Yushkevich (1963a) and Muccitelli and Diangelo (1994) used static cells at temperature up to 218 °C, 225 °C, 280 °C and 325 °C, respectively, and saturation vapor pressure. Read (1973) built a cell for measurements up to 250 °C and pressures up to 200 MPa. In many cases the presence of PTFE (Teflon), as an insulator or as a liner, limits the maximum temperature. Some authors have used conventional glass cell in sealed autoclave, but in this case the temperature was limited to 225 °C (Campbell et al., 1954), 230 °C (Korobkov et al., 1970), 250 °C (Baghalha and Papangelakis, 2000), 300 °C (Gorbachev and Kondrat’ev, 1961, 1965; Kondrat’ev and Nikich, 1963, Polyakov, 1965) or 340 °C (Rodnanskii and Galinker, 1955) and saturation vapor pressure. Other cell designs (Bannard, 1975; Goemans et al., 1997) used a furnace to heat the middle part of the cell while the end parts, where the pressure seals are located, remains cold. The first measurements of the conductivity of supercritical aqueous electrolyte solutions were performed by Fogo et al. (1954) using a small Pt-Ir static cell (Fogo et al., 1951) with sapphire insulators mounted inside a steel pressure vessel and an aneroid diaphragm allowed the counterbalance of the steam pressure with nitrogen. The conductivity of NaCl was studied at temperatures up to 400 °C and pressures to 30 MPa. The conductivity measurements at the highest pressure were performed in Australia by Hamann and Linton (Hamann and Linton, 1969) using an explosive, shock-wave technique at very short duration (Hamann and Linton, 1966) which allowed the use of polyethylene insulators. The authors performed electrical conductivity measurements of pure water and simple salts up to 10 GPa. In 1956 a cell developed by Franck (1956a) using ceramic insulators allowed the measurement of the electrical conductivity in the supercritical region of water, at temperatures up to 1000 °C (Mangold and Franck, 1969) and pressures up to 800 MPa (Renkert and Franck, 1970). Other cells with ceramic materials as insulators were used up to 600 °C and 300 MPa (Hartmann and Franck, 1969; Hwang et al., 1970).

NYLON CONE Pt–25% lr SCREW

A Pt–25% lr

Franck’s cell design, using ceramic insulators, has been used at ORNL by Marshall and coworkers (Franck et al., 1962; Quist and Marshall, 1968a–d, 1969, 1970; Frantz and Marshall, 1982; Frantz and Marshall, 1984), and later by Palmer and co-workers (Ho et al., 1994; Ho and Palmer, 1995a–b, 1996, 1997, 1998). A review of static high temperature cells by Marshall and Frantz is already available in the literature (Marshall and Frantz, 1987). They described in detail the static cell designed by Franck (1956a) in Germany and the modified version used during several years at the Oak Ridge National Laboratory (ORNL). The most recent version of the cell (Ho et al., 1994) consists of two coaxial 75% platinum-25% iridium electrodes coated with platinum black. As can be seen in Figure 4.1, one electrode is external platinum-iridium lined highpressure vessel (6.35 cm long and 1 cm3 volume) and the other, a thin platinum wire, insulated by a non-porous sintered Al2O3 or Al2O3/ZrO2 tube (for alkaline media), welded to a platinum-iridium cylinder located in the center. In this design, the major disadvantages are the high residence time of the solution in the cell, the possible presence of impurities that can concentrate or adsorb on the walls, and the temperature gradient developed along the cell. Due to these factors the accuracy of the cell is not good enough for low concentration (lower than 0.001 mol·kg−1) and low densities measurements. For concentrations ranging from 0.001 to 0.1 mol·kg−1, temperatures up to 600 °C, and pressures up to 300 MPa, Ho et al. have reported conductivity measurements of sodium (Ho et al., 1994; Ho and Palmer, 1996), lithium (Ho and Palmer, 1998) and potassium (Ho and Palmer, 1997) chlorides and hydroxides, with a precision better than 0.1%. Some static conductivity cells have been designed for measurements of concentrated solutions. The simpler design is a glass capillary cell (Campbell et al., 1954) in an autoclave, used to measure the density of AgNO3 up to 92 mass % at temperatures up to 225 °C. The electrical conductivity of very concentrated NaOH aqueous solutions and molten NaOH was measured (Eberz and Franck, 1995) up to 400 °C and 300 MPa using a cell with concentric nickel electrodes

B

D

TEFLON

Pt–25% lr

C Al2O3 INSULATING TUBE

A: HIGH–PRESSURE VESSEL B: INNER ELECTRODE C: Pt–Ir CYLINDER D: INNER ELECTRODE HOLDER

TEFLON PLUG STAINLESS STEEL CONE STAINLESS STEEL ELECTRODE HOLDER NEOPRENE PACKING RING

Figure 4.1 Alternating current static high temperature conductivity cell (Ho, P.C., Palmer, D.A. and Mesmer, R.E. (1994). J. Solution Chem. 23, 997 with permission from Elsevier).

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 217

(an external cylinder 5 mm internal diameter and a central nickel rod 1 mm diameter) insulated with pure alumina. The electrode arrangement, show in Figure 4.2, leads to sample resistances between 0.1 and 10 ohm, which could be measured with precision by using a four-pole lead method. This method requires pressure-proof insulating lead-ins and corrections have to be made for contact resistances. The contribution of the metal-electrolyte interphase is frequency dependent and the measurements should be extended up to 400 kHz. 4.3.2 Flow-through conductivity cell Due to the contribution of the corrosion products to the electrical conductivity the accuracy of the static cells is

Concentric electrodes Digital multimeter Thermocouples

Switch

Computer cbm 3032 Data storage and output

i Amperemeter

V

LCR Meter

IEEE-488-BUS

OSC Voltmeter

Figure 4.2 High pressure conductivity cell for concentrated solution with four pole lead arrangement (Eberz, A. and Franck, E.U. (1995). Ber. Bunsenges. Phys. Chem. 99, 1091. Reproduced by permission of Deutsche Bunsen-Gesellschaft).

MB

OH

TW

CP

SI

BW

IE IT

SR

PC

Flow

OT

Gold Pt/Rh S Steel Alumlnum Snpphir Quartz

LT

B

GW TT SH QT TW TW’ CP’

limited and it depends on the nature of the electrolyte and the materials chosen for the cell construction. In order to overcome the above-mentioned problems and to perform measurements on aqueous solutions near the critical point of water a flow-through conductance cell was developed by Wood and co-workers (Zimmerman et al., 1995; Gruszkiewicz and Wood, 1997; Sharygin et al., 2001). As described in Figure 4.3, the cell was constructed from a 80% platinum, 20% rhodium cup (outer electrode, PC), gold soldered to a platinum/rhodium tubing (IT) used as inlet tube. On the rim of the cup is located an annealed gold washer (GW) sitting on the top of a sapphire disc insulator (SI), through which is connected the inner-electrode (IE), a platinum/rhodium tubing extending about 9.5 mm into the cup. The inner electrode was previously gold-filled at one end, and two small holes on the other end act as the solution outlet. The inner electrode passed through another annealed gold washer located between the sapphire and a shorter thicker Pt/Rh tubing (TT) soldered on to the inner electrode. The Pt/Rh outflow tubing (OT) passed through a stainless steel tube (LT) and finally went out of the hot zone. Three sapphire rods (SR) were used to electrically insulate the inner and outer electrodes. The seals between the platinum cup and the inner electrode were made by compressing the gold washers with Belleville washer springs (BW), stainless steel washers (TW) and aluminum washers (TW′). Figure 4.3 also shows the compression plates (CP and CP′), the quartz tubing (QT) and the stainless steel shield (SH) and body (MB). The solution flowed into the cup, through the sapphire rod and finally through the holes at the back of the inner electrode. This flow stream sweeps the contaminants dissolving from the sapphire insulator out of the measuring zone and eliminates adsorption effects on the wall of the cell. A cell constant close to 0.2 cm−1 was determined from measurements on aqueous KCl at 25 °C and the cell constant change with temperature from the known coefficients of thermal expansion of sapphire and platinum was 0.4% over the entire temperature range (306 °C–400 °C).

Figure 4.3 Alternating current flow-through conductivity cell (Reprinted with permission from Zimmerman, G.H., Gruszkiewicz, M.S. and Wood, R.H. J. Phys. Chem. 99, 11612. Copyright 1995 American Chemical Society).

218

Hydrothermal Experimental Data

A significant improvement in the speed and accuracy of the conductance measurement was achieved by the use of this flow cell. Zimmerman et al. (1995) have reported conductivity measurements with a precision of about 1% for concentrations as low as 10−7 mol·kg−1 at a water density of 300 kg·m−3 and 0.1% or better for higher concentrations and water densities. The pressure upper limit of this cell is, however, restricted to 28 MPa. A modified cell is described (Sharygin et al., 2002) which avoids the cracking of the sapphire insulators by doing the pressure on them more uniform. This design used a CVD diamond washer was used to shield the surface of the sapphire in contact with the sample allowing the measurement of acids and bases. Oxidation of the steel caused by small leads made the cell unusable and a recent modification (Hnedkovsky et al., 2005) overcome this problem by replacing the stainless steel parts by titanium. Recently, the Oak Ridge’s static conductivity cell was modified (Ho et al., 2000a; 2000b; 2001) and converted into a flow-trough cell able to operate with high accuracy at densities lower than 0.4 g·cm−3. So far, the maximum temperature achieved was 410 °C and the maximum pressure was 33 MPa, but it is expected that the cell could operate up to 600 °C and 300 MPa. Other flow-through conductivity cell have been described recently (Goemans et al., 1997; Ismail et al., 2003) having accuracy lower than the cells described above and were used over a restricted range of electrolyte concentrations. 4.3.3 Measurement procedure In most of the studies reported in this book the conductivity measurements were carried out at variable frequencies (commonly from 0.5 to 10 kHz). The final resistance of the solution was obtained by extrapolation of the measured resistances to infinite frequency, as a function of the inverse of the square root of the frequency, to correct for polarization effects. The design and materials choice of the conductivity cells used at high temperature were suitable to guarantee very small and predictable changes in the cell constant with temperature. Formally the cell constant, a, is given by the ratio l/A, where l is the distance between electrodes and A the effective area, which is closer to the internal cross-sectional area of the tubing connecting the electrodes. A common practice for the determination of a is to determine resistance, R, of KCl aqueous solutions of known specific conductivity, k, at 25 °C or a moderate temperature. a =κR

(4.10)

Values of k for 0.01 and 0.1 demal standard KCl solutions are reported from 0 to 50 °C (Wu and Koch, 1991). To estimate the cell constant at higher temperatures the authors use temperature correction factors to correct for the thermal expansion of the materials used in its construction. Temperature correction factors within 0.1 to 0.4% are reported in the bibliography for different cells used in the temperature range from 298 to 673 K.

If this procedure is not found to be reliable one could perform a direct calibration at high temperature by resorting to the available high precision data for the conductivity of KCl solutions up to 410 °C and 33 MPa (Ho et al., 2000). This data are more precise than those reported in 1970 for aqueous 0.01 demal KCl solutions as reference solutions for electrical conductance measurements to 800 °C and 1200 MPa. (Quist el al., 1970). A criteria for assessing the quality of the conductivity measurement is to analyze the changes in the cell constant after a cycle of heating and cooling. Usually the change is larger in the first cycle due to annealing of the compression washers, but it becomes insignificant after the second cycle. When the values of the constant cell before and after the run are different an averaged value is used. The Soret effect, affecting the conductivity measurements in conventional cells due to concentration gradients produced by temperature gradients when the cell is immersed in the thermostat bath, is also present in static hightemperature conductivity cells. This effect is more pronounced at high temperature and its elimination by stirring is not so easy in high-temperature cells. The flow-through conductance cells have overcome this problem, as well as the ‘shaking effect’ which is present in static cells at very low electrolyte concentration as a consequence of ionexchange with the polar surfaces. The measured electrolyte specific conductivity has a contribution due to the solvent conductivity. In the case of aqueous systems, the self-dissociation of water contributes in 0.055 µS·cm−1 at 25 °C, but increases at higher temperatures and pressures due to the increase in Kw and the mobility of the H+ and HO− ions. The ion product of water up to 1000 °C and 1000 MPa can be obtained from the IAPWS Release on the Ion Product of Water Substance (IAPWS, 1980), reprinted in White et al. (1995). Besides the self-dissociation of water one should take into account the presence of traces of ionic impurities, such as the HCO3− ions coming from the dissolution of CO2 in the water used to prepare the solution. Because it is very difficult to make a precise estimation of the contribution of these impurities at high temperature and pressure, it is convenient to measure the conductivity of the water used to prepare the solution under the same conditions as the solution measurements. The solvent conductivity is discounted from the specific conductivity of the solution in order to obtain the real conductivity of the electrolyte. The conductivity of the solvent blank is the sum of the contributions due to the dissociation of pure water and to stray ions. In the case of electrolytes that produce acidic or basic solutions, which repress the ionization of water, only the contribution of the stray ions needs to be subtracted from the experimental conductivity. At room temperature the solvent correction for water distilled and passed through an ion exchange column is around 0.2–0.5 µS·cm−1. The magnitude of the solvent correction is a function of the concentration of the solution under study. It is obviously more important in very dilute solution, while it can be neglected in concentrated solutions. For instance the solvent correction for NaCl at 2.10−7 mol·dm−3 is close to

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 219

16% at high temperatures (Zimmerman et al., 1995), but decreases below 1% as the concentration increases twofold. The electrical conductivity of liquid and dense supercritical water (0–800 °C and up to 1000 MPa) are reported in an IAPWS Guideline (IAPWS, 1990), reprinted by White et al. (1995). 4.4 DATA TREATMENT 4.4.1 Dissociated electrolytes The effect of the concentration on the conductivity of an electrolyte in very dilute solution is represented by a simple empirical limiting law introduced by Kohlrausch (1898) and deduced theoretically by Onsager (1927): Λ = Λ 0 − Sc1 2

(4.11)

where Λ0 is the electrical conductivity of the electrolyte at infinite dilution and S is the limiting law slope, which in the case of symmetrical electrolytes can be expressed as S = al0 + b, where a and b are given by:

α= β=

820.46 × 104 z 2

(εT )3 2 8.2487 z

η (ε T )

12

(4.12a) (4.12b)

where z is the ionic charge, h, the water viscosity and e, the relative dielectric constant of the solvent. The units of S being S·cm2·mol−3/2·dm3/2 if h is expressed in Pa·s. The IAPWS recommended values for the viscosity and dielectric constant of water can be found in IAPWS Releases (IAPWS, 2003 and 1997 respectively). Equation (4.11) is a limiting law that in the case of fully dissociated electrolytes is used to obtain Λ0 by extrapolation at infinite dilution of the molar conductivity of very dilute solutions. This limiting law assumes that the electrophoretic and relaxational correction terms are separable and it ignores higher orders contributions to conductance due to shortrange interactions. The strategies for including these higher order contributions in the conductance equation have been analyzed in detail in the literature (Fernández-Prini, 1973). At the end of the 1970s there were several alternative equations to the original treatment by Fuoss and Onsager (1957) to account for the effect of concentration on electrolyte conductances: the Pitts (1953) equation (P), the Fuoss-Hsia (Fuoss and Hsia, 1967) equation (FH) later modified by FernándezPrini (1969) (FHFP) and valid only for dilute, binary, symmetrical electrolytes, and the Lee and Wheaton (1978) equation (LW) valid for unsymmetrical electrolytes. The FHFP equation, Λ = Λ 0 − SI 1 2 + EI ln I + J 1 I − J 2 I 3 2

(4.13)

where I is the ionic strength, defined by I = 1/2Σzici, has been widely used to describe the conductance of electrolyte

in hydrothermal systems. The coefficients S and E depend only on the charge type of the electrolyte, on the mobility of the ions, on the temperature and on the solvent properties (dielectric constant and viscosity). The J1 and J2 coefficients depend also on the minimum distance of approach of free ions, d, and whose expressions for symmetric electrolytes depend on the level of approximations used in their derivation (Fernández-Prini, 1973; Justice, 1983). The expressions for asymmetric electrolytes are also reported in the literature (Fernández-Prini and Justice, 1984; Lee and Wheaton, 1978). Turq et al. (1995) derived a conductivity equation (TBBK) based on the mean spherical approximation (MSA) that can also be applied to unsymmetrical electrolytes. The TBBK model is expressed in the form of the Fuoss-Onsager approach, that is, giving equations for the electrophoretic and relaxational correction terms, as in Equation (4.12). The resulting equation for the molar conductivity is algebraically complex and the reader could see it in the original article, taking into account some misprints quoted in the literature (Bianchi et al., 2000). When expanded, the exponential integrals of the TBBK model do not yield the logarithmic term (I ln I) which is present in the FHPP equation. Another difference of the TBBK equation from the classical equations is that it uses as parameters the ionic diameters instead of the distance of closest approach. A comparison of the performance of the FHFP and TBBK equations has been carried out recently by Fernández-Prini and co-workers (Bianchi et al., 2000) at 25 °C. They concluded that, for symmetrical electrolytes in dilute solutions the FHFP equation is superior to the TBBK equation. The TBBK equation is claimed to be precise even at high concentrations; however, the deviations from the experimental data are systematic. 4.4.2 Associated electrolytes The deviation from Onsager’s law is due to ion–ion interactions and is more pronounced for highly charged ions at high concentrations. The attractive interactions between opposite charged ions could yield to ion association, which is not explicitly taken into account in the Onsager theory of conductivity. The simplest way to express the conductivity of associated electrolyte is the Otswald approach Λ = aΛo, where a is the degree of dissociation of the electrolyte. Replacing a in equation (4.1) we obtain the following expression for Ka, Ka =

ΛO ( ΛO − Λ ) Λcγ ±2

(4.14)

This relationship can be rearranged to read (Harned and Owen, 1958), 1 1 AK a cγ ±2 = O− 2 Λ Λ ΛO

(4.15)

This equation was used by Frantz and Marshall to obtain the dissociation constant of HCl above 400 °C (Frantz and

220

Hydrothermal Experimental Data

Marshall, 1984) from data whose overall precision was estimated to be ±1%. Shedlovsky (Shedlovsky, 1938) proposed an improvement of this equation which takes into account the interionic effect on conductivity. 1 1 ΛT ( z ) K a cγ ±2 = O− ΛT ( z ) Λ ΛO 2

(4.16)

where z = S(Λc)1/2(Λo)−3/2, and T(z) = 1+z+z2/2+z3/8+ . . . is the series expanded form of the bracketed term. In general is not necessary to employ terms higher than z2 in evaluating T(z). According to equation (16), a plot of (ΛT(z))−1 against cg ±2∆T(z) should be a straight line with intercept (Λo)−1 and slope Ka.(Λo)−2. Fuoss and Kraus (1933) derived Equation (4.17) taking into account the effect of ion interactions T (z) 1 cγ 2 Λ K a = o+ ± T ( z ) ( Λ o )2 Λ Λ

(4.17)

where T(z) = 1 − z (1 − z (1 − . . .) −1/2)−1/2 ≈ (1 − z), being z = S(Λc)1/2 / (Λo)3/2 . When the conductivity measurements are extended down to very diluted solutions, a plot of T(z)/Λ as a function of cg ±2Λ/T(z) yields the values of KA/(Λo)2 and 1/Λo from the slope and the intercept, respectively. Equation (4.17) was used by Marshall and co-workers and Franck and co-workers to obtain Ka for several electrolytes 400 °C at densities below 0.75 g·cm−3 (Quist and Marshall, 1968a, 1968b, 1969; Franck, 1956b, 1956c). In fact this equation is used in modern literature to obtain Λo and Ka from conductivity measurements whose precision is not very high (Ho et al., 1994; Goemans et al., 1997) or to estimate initial Λo and Ka values for fitting conductivity data with modern equations which include the association effect. The most frequently used of these equations is that derived from the FHFP equation where the concentration dependence of the molar conductivity in electrolytes showing ionic association can be described by (FernándezPrini, 1973) Λ = Λ 0 − SI 1 2 + EI ln I + J 1 I − J 2 I 3 2 − K a Λγ ±2α c (4.18) where S is the limiting law slope, and E, J1 and J2 are parameters depending on the closest distance of approach of the ions, d. Ka is the ion pair formation constant. Equation (4.18) along with the extended Debye-Hückel equation for the mean activity coefficient A (α c ) 1 + dκ D

12

ln γ ± = −

(4.19)

(where kD = (8pe2NA / ekT)1/2I1/2 is the inverse Debye length) are used to calculate Λo and Ka from the conductivity data, by considering Λo, Ka and d as adjustable parameters. It should be noted that the fit using Equations (4.18) and

(4.19) requires very precise conductivity data, as those measured in hydrothermal systems with the flow-through cells (Zimmerman et al., 1995; Gruszkiewicz and Wood, 1997; Ho et al., 2000a; 2000b; 2001). Wood and co-workers (Sharygin et al., 2001) have compared the FHFP and TBBK equations for associated electrolytes using conductivity data for aqueous NaCl at high temperature and pressure (623.9 K, 19.79 MPa and r = 0.596 g·cm−3). The FHFP equation for associated electrolyte was used with the distance of closest approach fixed at the Bjerrum distance, d. The conductivity data were fitted with the FHFP equation using two (Λ0 and Ka) or three (Λ0, Ka and J2) parameters and the standard deviations were better than those obtained with the TBBK equation. When three parameters were used in the fit, the results became independent of the activity coefficient model used (Bjerrum or MSA). At lower densities (r = 0.200 g·cm−3) the performance of both conductivity equations is similarly independent of the activity coefficient model. This could be attributed to the poorer accuracy of the experimental data in the low-density region. The reduced temperature, T* = kTes / |z+z− |e2, where e is the dielectric constant of the solvent and s the sum of the crystallographic radii of anion and cation, is used as a parameter to determine the extension of ion association or clustering in ionic solutions (Fernández-Prini et al., 1992). It is predicted that ion pairs and higher clusters (ion triplets, quadruplets, etc.) are present in the solution at T* < 0.1, and this is the case for 2 : 2 electrolytes above 300 °C or 1 : 3 electrolytes at higher temperatures. If T* is very low the contribution of the charged triple ions to the conductivity becomes important. In that case the Fuoss-Kraus equation becomes: Λg (c ) c1 2 =

ΛO ΛTO KT  Λ − 1 2 1− O  c 12  Ka Ka Λ 

(4.20)

where: g (c ) =

γ ±2

(1 − z ) . (1 − Λ Λ o )

12

(4.21)

KT is the formation constant of triple ions and ΛoT the infinite dilution molar conductivity of the triple ions. Usually Ka and KT are obtained from Equation (4.20) by employing an estimated value of Λo calculated from Walden’s rule (Λoh = constant) and assuming that ΛoT = 2Λo/3. Franck and co-workers used this equation to calculate the association constant of BaCl2, Ba(OH)2 , MgSO4 (Ritzert and Franck, 1968), KCl and LiCl (Mangold and Franck, 1969). Wood and co-workers (Hnedkovsky et al., 2005) have analyzed the electrical conductances of Na2SO4, H2SO4 and their mixtures up to 673 K and densities as low as 0.23 g·cm−3. In this limit they observed that a simple association model including ion pairs and triple ions is not precise enough to fit the experimental data at the high

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 221

4.4.3 Getting information from electrical conductivity data It is convenient to summarize the recommended procedures to obtain information on the transport coefficients and thermodynamic properties of electrolyte from measured electrical conductivity above 200 °C. At high temperature the dielectric constant of water is low enough and even single 1 : 1 electrolytes which are fully dissociated at room temperature could associate in a degree that increases with increasing temperature and decreasing density (pressure). Therefore, the determination of Λo, which is a measure of the ionsolvent interaction and is related to the ion solvation, should be performed by using some of the equations valid for associated electrolytes (Equations (4.16), (4.17) or (4.18)). The FHFP equation (Equation (4.18)) can only be used for high accuracy molar conductivity data and provided that kDd < 0.1. The higher is the temperature the lower is the maximum concentration to fulfill this requirement. Consequently, the use of the FHFP equation is compatible with high accuracy results obtained in conductivity cells designed for very diluted solutions. When low accuracy data are fitted using the FHFP equation (even using two fitting parameters, Λ0 and Ka) a lack of convergence is observed. In this case the use of the simpler Equations (4.16) or (4.17) is preferable. The fitting of the experimental data beyond the limit imposed by the condition kDd < 0.1 could yield large overestimation of Λ0 in the low-density supercritical region, as discussed in the following section. In this region the contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower (Ibuki et al., 2000) and the difference among the equations for associated electrolytes becomes less important. For highly associated electrolytes, as those formed by high charge ions at high temperature and low density, the

description of ion-pairing in terms of a single association constant is incomplete. In that case, characterized by T* < 1, a minimum in the molar conductivity is observed at moderate or high concentration as a consequence of the formation of charged triple ions and the Fuoss-Kraus Equation (4.20) gives a reasonable description of the speciation and concentration dependence of the molar conductivity. 4.5 GENERAL TRENDS The summary tables summarize the results of electrical conductivity data for 76 binary aqueous electrolyte solution at temperatures above 100 °C, reported between 1903 and 2007. It should be noted that many of these studies (16 electrolytes) have been performed at a single electrolyte concentration, and almost 2/3 of them have reported or estimated uncertainties higher than 1%. Only a half of the studies have been performed at very low electrolyte concentration, allowing the limiting molar conductivity to be obtained by empirical equations or using theoretical equations for dissociated or associated electrolytes. Thus, Λ0 values are reported for 42 electrolytes above 200 °C, and a half of them above the critical point of water (374 °C). 4.5.1 Specific conductivity as a function of temperature, concentration and density All the electrolytes show a maximum in the specific conductivity as plotted as a function of temperature at constant concentration and pressure (see Figure 4.4). The initial increases of k with temperature is due to the increase in the mobility of the ions as the viscosity and dielectric constant of water decreases. At high temperature the ion association reduces the number of free ions and counterbalances the increasing mobility.

1e-2

log (κ/S.cm-1)

concentrations (m > 0.016 mol·kg−1). They include the species H9(SO4)5− in order to obtain a satisfactory fit, although there is no physical justification for the inclusion of such a cluster. A more detailed analysis of the multiple ion association has been given by Wood and co-workers (Sharygin et al., 2002) considering the high temperature electrical conductances of very concentrated NaCl and KCl solutions. Except for one experimental condition (NaCl at 670 K and 0.3 g·cm−3) the simple ion-pair association model fits the experimental results quite well up to 4.5 mol·kg−1. At the condition corresponding to the strongest interaction (T* = 0.056) the Oelkers and Helgeson (1993) model of multi-ion association fails to represent the experimental results without invoking physically unrealistic salting out coefficients. The redissociation of the ion pairs at high concentrations, as predicted by the cluster theory (Corti and Fernández-Prini, 1986) at very low T*, is consistent with the conductivity results and leads to a behavior of the system similar to that of a solvated molten salt, as previously proposed also by Hwang et al. (1970) and Valyashko (1977).

1e-3

1e-4

1e-5 0

100

200 300 400 Temperature (°C)

500

600

Figure 4.4 Isobaric specific conductivity as a function of temperature: (䊏) 0.05m CaCl2, psat.; (䊉) 0.01 m NaCl, p = 100 MPa; (䉲) 0.001 m GdCl3, p = 29.4 MPa; (䉱) H3BO3 0.50 m psat.

Hydrothermal Experimental Data

The maximum of the isobaric specific conductivity as a function of temperature at fixed concentration depends on the degree of dissociation of the salt. Thus, for strong electrolytes, like alkali metal halides, the maximum is at high temperatures (Quist and Marshall, 1969). For moderately associated electrolytes, like divalent alkali metal halides, the maximum shift to lower temperatures (Kondrat’ev and Nikich, 1963) and it appears at even lower temperatures for weak electrolytes, like NH4OH (Quist and Marshall, 1968b) or H3BO3 (Ho and Palmer, 1995b). For a given electrolyte, increasing the concentration and/or pressure shifts the maximum of the isobaric specific conductivity to higher temperatures. Valyashko and Ivanov (1979) noted that the maximum of the isothermal specific conductivity as a function of concentration is related to the charge, hydration, and degree of association of the electrolyte. Thus, electrolytes with the same charge-type have conductivity maximum in the same concentration range. Increasing hydration leads to a decrease in the concentration of the maximum. Frequently the maximum in conductivity is not observed because of the limited salt solubility. This is not the case of NaOH solutions at high temperature, whose specific conductivity as a function of concentration has been measured (Eberz and Franck, 1995) over the entire range of concentration, as shown in Figure 4.5. At low water content the specific conductance does not change significantly because the reduction in the number of ions is overcompensated by an increased mobility of the ions which is the dominant effect up to the maximum conductivity near 30 mol %. It is interesting to note that the conductivity in the maxima at 400 °C is almost one order of magnitude higher than at 25 °C and about twice as high as the conductivity of the molten hydroxide. The position of the conductivity maximum seems to shift slightly at higher concentration with increasing temperature, which could be related to a reduction in the ion hydration at high temperature. One should be cautious of using this argument near the solution critical point where enhanced compressibility could lead to increased solvent density around the ions.

5

4

When plotted as a function of pressure the specific conductivity of dilute electrolytes increases slightly with pressure at temperatures below the critical point. Above the critical point the specific conductivity decreases sharply with decreasing density. The behavior pattern is simpler as the specific conductivity is plotted as a function of density. In that case the specific conductivity goes through a maximum at temperatures above the critical point but the curves for different temperatures remain close together. 4.5.2 The limiting molar conductivity The value of Λ0 is a measure of the ion-solvent interaction and, within the scope of the continuum hydrodynamic model, is related to the bulk viscosity of the solvent, h, through the Nernst-Einstein equation or its empirical equivalent, Walden’s law (h.Λ0 = constant). However, it is well known that the simple continuum model is not valid in aqueous systems even at room temperature. Figure 4.6 shows the behavior of the limiting molar conductivity with temperature for NaCl, where it is clearly observed that the molar density is a function of the density. Marshall analyzed the limiting molar conductivity of simple electrolytes up to 800 °C and 400 MPa and proposed (Marshall, 1987) a reduced state relationship for the limiting conductivity of aqueous ions on the basis of the experimental information available at that time. He found that Λ0 was a linear function of density Λ 0(salt ) = Λ 00 − S ρ

(4.22)

1800 1600 1400

L° / S·cm2·mol-1

222

1200 1000 800 600

κ (S.cm-1)

400 3

200 0 200

2

400

500

600

700

800

900

T/K

1

0

300

0

20

60 40 mol % NaOH

80

100

Figure 4.5 Isotherms of the specific conductivity of NaOH solutions at 200 MPa as a function of the salt concentration. (¥) 25 °C; (䊊) 300 °C; (ⵧ) 350 °C; (䉭) 400 °C.

Figure 4.6 Limiting conductivities of NaCl as a function of temperature and density. Experimental data from: Smolyakov, 1969 (♦) and Quist et al., 1965 (䊏) at saturation; Ho et al., 1994, (丢) 1 g·cm−3, (䉮) 0.9 g·cm−3, (◊) 0.8 g·cm−3, (䉭) 0.6 g·cm−3, (ⵧ) 0.45 g·cm−3, (䊊) 0.3 g·cm−3; Gruszkiewicz and Wood, 1997 (䉱), 0.6 g·cm−3, (䊉) 0.25 g·cm−3. The dashed lines show the results calculated using the models of Marshall (1987).

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 223

4.5.3 Concentration dependence of the molar conductivity and association constants The dependence of the molar conductivity with concentration is primarily dominated by ion–ion interactions which, in the limit of low density, could lead to extensive clustering of the ions. The precision of the experimental data is a key issue in choosing a conductivity equation to fit the concentration dependence of the molar conductivity and, in the case of associated electrolytes, the association constant. Old measurements of conductivity, particularly those by Franck and co-workers in Germany and by Marshall and co-workers in ORNL (USA), having uncertainties around 1% were fitted using the Shedlovsky or the Fuoss-Kraus equations, which allows the simultaneous determination of Λo and Ka.

1500 1400 1300

L°/ S·cm2·mol–1

where Λ00 is the limiting conductivity extrapolated to zero density and S is the slope of the Λ vs. density linear plot. Interestingly, S is independent of temperature in the range 400 °C–800 °C for each salt and Λ00 reaches the same values for all the salts in that range of temperatures. For densities above ca. 0.5 g·cm−3, this reduced state equation reproduces the new experimental data with reasonable accuracy (see Figure 4.6). A linear increase of Λ0 with decreasing solvent density is suggested by the experimental data from the ORNL group (Ho et al., 1994, 1997, 1998) in good agreement with the Marshall model. However, from the precise measurements on very dilute solutions by Wood and co-workers (Zimmerman et al., 1995; Gruszkiewicz and Wood, 1997) it is observed that Λ0 reaches a plateau or even goes through a maximum and then decreases as the solvent density decreases. A very comprehensive analysis by Nakagara and coworkers (Ibuki et al., 2000) of the available data for the limiting conductivity of alkali chlorides in supercritical water concluded that the behavior of Λ0 is similar for all the salts. The ionic mobility reaches a plateau or decreases with decreasing solvent density, as experimentally shown by Wood and co-workers. The apparent linear increase of Λ0 with decreasing solvent density reported by the ORNL group was the result of fitting the conductivity data outside the concentration range where the conductivity equations are valid. By limiting the data analysis to concentrations within the correct range, they obtained extrapolated Λ0 values having the same density dependence reported by Wood and co-workers. This density dependence of Λ0 was also confirmed theoretically. Thus, the compressible continuum model (Xiao and Wood, 2000) predicts a decreasing limiting conductivity with decreasing solvent density for NaCl down to 0.2 g·cm−3. The molecular dynamics simulations of the limiting conductivity of NaCl (Lee et al., 1998) and LiCl, NaBr, CsBr (Lee and Cummings, 2000) in supercritical water at 400 °C and densities between 0.22 and 0.74 g·cm−3 show a maximum or a plateau at densities close to 0.3 g·cm−3, in good agreement with the experimental results (Zimmermann et al. 1995), as shown in Figure 4.7.

1200 1100 1000 900 800 0.2

0.3

0.4

0.5

0.6

0.7

0.8

r / g·cm–3

Figure 4.7 Limiting conductivities of several electrolytes at 673 K as a function of water density. Molecular dynamics simulation (Lee et al., 1998; Lee and Cummings, 2000): (䊊) NaCl; (䉮) NaBr; (䉭) CsBr; (ⵧ) LiCl. Experimental results for NaCl (䊉) at 656–677 K (Zimmerman et al., 1995).

During the last decade more precise conductivity data (<0.1%) could be obtained in the dilute region, especially in the low-density (supercritical) region. Thus, the more complete conductivity equations, like FHFP or TBBK, could been tested for a number of binary electrolytes. It is recognized that FHFP equation accounts for the concentration dependence of electrolyte solutions up to moderate concentrations and yields more reliable association constants than the Shedlovsky or Fuoss-Kraus equations. However, it was observed that the FHFP Equation (4.18), or the more simple Shedlovsky Equation (4.16), give similar fitting results, for some supercritical electrolyte solutions at low density (r < 0.3 g·cm−3). The contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower in supercritical water than in ambient water because of the much smaller viscosity and dielectric constant. Moreover, the higher-order terms in Equation (4.18) nearly cancel each other at moderate concentration in supercritical water (Ibuki et al., 2000). This could be the reason why differences among several conductivity equations vanish at supercritical conditions. For those electrolytes whose association constant was measured at high temperature it was observed that Ka increases with temperature at constant density, following the Arrhenius law. The density dependence of the association constant could be represented by the simple equation (Ho et al., 1994) log K a = a +

d b  + c +  log ρ  T T

(4.23)

a,b,c and d being constants. The equation is valid for r > 0.4 g·cm−3 and temperatures up to 600 °C,

224

Hydrothermal Experimental Data

4.5.4 Molar conductivity as a function of temperature and density The reported molar conductivity in very concentrated solutions over a wide range of temperature are restricted to aqueous CsCl, KCl, LiBr, LiCl (Hwang et al., 1970) and NaOH (Eberz and Franck, 1995). The results (see Figure 4.8) show the presence of a maximum for the molar conductivity in the diluted and moderate concentration region that, as expected, decrease with increasing concentration. Interestingly, the maximum evanesces at higher concentrations indicating the transition between the dilute and concentrated regime. Special analysis of experimental data for volume and spectroscopic properties of hydrothermal electrolyte solutions over a wide range of composition show the change of properties behavior from ‘water-like’ to ‘meltlike’ in the same concentration region (Valyashko, 1977, 1990). The sign of the temperature coefficient of solubility for various hydrothermal equilibria also changes in the transition region of concentration (Valyashko, 1977, 1990, 2000). Specific behavior of phase equilibria and solution properties in this region of composition permits us to conclude that the system of hydrogen bonds in dilute solutions transforms into the system of ionic bonds in strong electrolyte solutions at the concentration of transition region. The behavior of concentrated solutions can be explained in terms of the re-dissociation phenomena (Corti and Fernández-Prini, 1986) which take place at low reduced temperature, T*, and high packing fraction (rs 3). In this regime an ion is surrounded by ions of the same and opposite charge and the net result of the ion interactions is that the ions move essentially as free ions, as it occur in molten salts. The behavior of the molar conductivity of dilute electrolytes as a function of pressure at a fixed concentration is

similar to that already described for the specific conductivity, that is, the molar conductivity increases slightly with pressure at temperatures below the critical point, while above the critical point the molar conductivity decrease sharply with decreasing density. If plotted as a function of density the molar conductivity of dilute solutions goes through a maximum at temperatures above the critical point, and the curves for different temperatures tend to overlap each other. 4.5.5 Conductivity in ternary systems The information on the electrical conductivity of multicomponent aqueous systems was reviewed by Anderko and Lencka (1997). At that time only results at 25 °C had been reported for a few simple salt mixtures. Since then, a study of the electrical conductivity of H2SO4-Al2(SO4)3 mixtures was reported by Baghalha and Papangelakis (2000), while Wood and co-workers reported electrical conductivity of sodium acetate–acetic acid (Zimmerman and Wood, 2002), calcium acetate–acetic acid (Mendez de Leo and Wood, 2005) and H2SO4-Na2SO4 (Hnedkovsky et al., 2005). Recently, the ternary system H2SO4–MgSO4 and also the quaternary system H2SO4–MgSO4–Al2(SO4)3 up to 250 °C have been studied (Huang and Papangelakis, 2006, 2007). The electrical conductivity of mixtures of electrolytes and non-electrolytes are scarce. The only systems studied above 200 °C are KCl – Ar (Hartmann and Franck, 1969), NaCl – dioxane (Yeatts and Marshall, 1972) and NaI – methanol (Korobkov and Mikhilev, 1970). In these cases the system can be considered as a binary electrolyte solution in a mixed solvent. Therefore, the specific and molar conductivity decreases with the increase of the non-electrolyte in water due to the reduction of the dielectric constant of the mixed solvent.

700

REFERENCES 600

L (S.cm2/mol)

500

400

300

200

100

0

0

100

200

300

400

500

600

T (°C)

Figure 4.8 Molar conductivity as a function of temperature at several concentrations for LiCl (䊉) (from top to bottom: 0.18 mol %, 1.73 mol %, 6.58 mol % and 15.28 mol %) and NaOH (䊊) (from top to bottom: 2.37 mol %, 8.46 mol %, 30.43 mol % and 100 mol %).

Anderko, A. and Lencka, M.M. (1997) Ind. Eng. Chem. Res. 36: 1932. Baghalha, M and Papangelakis, V.G. (2000). Ind. Eng. Chem. Res. 39, 3646. Bannard, J.E. (1975) J. Appl.Electrochem. 5: 43. Bianchi, H. (1990) Conductivity of mixtures of symmetrialc and unsymmetrical electrolytes in aqueous solutions. Thesis, University of Buenos Aires. Bianchi, H. Corti, H.R. and Fernández-Prini, R. (1994) J. Solution Chem. 23: 1203. Bianchi, H. Dujovne, I. and Fernández-Prini, R. (2000) J. Solution Chem. 29: 237. Brown, R.D. Bunger, W.B. Marshall, W.L. and Secoy, C.H. (1954) J. Amer. Chem. Soc. 76: 1532. Campbell, A.N. Kartzmark, E.M. Bednas, M.E. and Herron. J.T (1954) Can. J. Chem. 32: 1051. Corti, H.R. and Fernández-Prini, R. (1986) J. Chem. Soc. Faraday Trans.II. 82: 921. Corti, H.R. Trevani, L.N. and Anderko, A. (2004) Transport properties in high temperature and pressure ionic solutions. In: D. Palmer, R. Fernández Prini and A. Harvey (eds), Steam, Water and Hydrothermal Solutions: Physical Chemistry of Aqueous

Electrical Conductivity in Hydrothermal Binary and Ternary Systems 225

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Ho, P.C., Palmer, D.A. and Wood, R.H. (2000b) J. Phys. Chem. B. 104: 12084. Ho, P.C. Palmer, D.A. and Gruszkiewicz, M.S. (2001) J. Phys. Chem. B. 105: 1260. “Huang, M. and Papangelakis, V.G. (2006) Ind. Eng. Chem. Reseach 45: 4757.” “Huang, M. and Papangelakis, V.G. (2007) Ind. Eng. Chem. Reseach 46: 1598.” Hwang, J.U., Luedemann, H.D. and Hartmann, D. (1970) High Temp.-High Press. 2: 651. IAPWS (1980), Release on the Ion Product of Water Substance. (1995) In Physical Chemistry of Aqueous Systems. Meeting the Needs of Industry. Edited by White et al. pp. A124–A131. IAPWS (1990), Guideline on Electrolytic Conductivity (Specific Conductance) of Liquid and Dense Supercritical Water from 0 °C to 800 °C and Pressures up to 1000 MPa. (1995) In Physical Chemistry of Aqueous Systems. Meeting the Needs of Industry. Edited by White et al. pp. A160–A165. IAPWS (1997) Release on the Static Dielectric Constant of Ordinary Water Substance for Temperatures from 238 K to 873 K and pressures up to 1000 MPa. IAPWS (2003) Revised Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance. Ibuki, K., Ueno, M. and Nakahara, M. (2000) J. Phys. Chem. B. 104: 5139. Ismail. I.M., Masuko, Y., Tomiyasu, H. and Fujii, Y. (2003) J. Supercritical Fluids. 25: 69. Justice, J-C. (1983) In B.E. Conway, J.O’M .Bockris, E. Yeager (eds), Comprehensive Treatise of Electrochemistry, Vol. 4, Chapter 3. Plenum Press, New York. Khitarov, N.I., Ryzhenko, B.N. and Lebedev, E.B. (1963) Geokhimiya. 1: 41. Kohlrausch, F. (1898) Ann. Phys. 66: 785. Kondrat’ev, V.P. and Nikich, V.I. (1963) Zh. Fizich. Khimii. 37: 100. Kondrat’ev, V.P. and Gorbachev, S.V. (1965). Zh. Fizich. Khimii. 39: 2993. Korobkov, V.I. and Mikhilev, A.D. (1970) Electrokhimiya. 6: 1002. Larionov, E.G. and Kryukov, P.A. (1976) International Corrosion Conference Series, NACE Proceedings, NACE-4 (High Temperature High Pressure Electrochemistry in Aqueous Solutions Conference), pp. 164–8. Lee, W. and Wheaton, R. (1978) J. Chem. Soc. Faraday Trans. II. 74: 743. Lee, S.H., Cummings, P.T., Simonson, J.M. and Mesmer, R.E. (1998) Chem. Phys. Lett. 293: 289. Lee, S.H. and Cummings, P.T. (2000) J. Chem. Phys. 112: 864. Lown, D.A. Thirsk, H.R. and Lord Wynne-Jones (1970) J. Chem. Soc. Faraday Trans. 66: 51. Lown, D.A. and Thirsk, H.R. (1971) J. Chem. Soc. Faraday Trans. 67: 132. Maksimova, I.N. and Yushkevich, V.F. (1963a) Zh. Fizich. Khim. 37: 903. Maksimova, I.N. and Yushkevich, V.F. (1963b) Zh Fizich. Khim. 37: 1859. Maksimova, I.N. and Yushkevich, V.F. (1966) Elektrokhimiay. 2: 577. Maksimova, I.N. Pravdin, N.N. Razuvaev, V.E. Sergeev, S.V. and Fedotov, N.V. (1976) Deposit VINITI USSR, 3366–76. Mangold, K and Franck, E.U. (1969) Ber. Bunsenges. Phys. Chem. 73: 21. Marshall, W.L. (1987) J. Chem. Phys. 87: 3639.

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5

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

Marc J. Assael Chemical Engineering Department, Aristotle University, Thessaloniki 54124, Greece

5.1 INTRODUCTION The thermal conductivity of a fluid measures its propensity to dissipate energy, when disturbed from equilibrium by the imposition of a temperature gradient. For isotropic fluids the thermal conductivity, l, is defined by Fourier’s law Q = − λ ∇T ,

(5.1)

where Q is the instantaneous flux of heat, which is the response of the medium to the instantaneous temperature gradient. Pure water is one of the primary standard thermal conductivity reference liquids. The thermal conductivity value proposed by the Subcommittee on Transport Properties of the International Union for Pure and Applied Chemistry (IUPAC) at 298.15 K and 0.101 325 MPa is (Nieto de Castro et al., 1986)

λ = 0.6067 ± 0.0061 W ⋅ m −1 ⋅ K −1.

(5.2)

The value of the thermal conductivity recommended by the International Association for the Properties of Water and Steam (IAPWS) is l = 0.6072 ± 0.009 W·m−1·K−1 (Kestin et al., 1984), which is in full agreement with the above IUPAC value. The temperature dependence of the thermal conductivity of water at atmospheric pressure in the temperature range 274 to 360 K, is given by the following recommended correlation (Nieto de Castro et al., 1986)

λ (T , 0.1 MPa ) T  = −1.26523 + 3.70483  −  λ (298.15 K ) 298.15  2

T  . 1.43955   298.15 

(5.3)

The maximum deviation of the experimental data employed, from this equation is 1.1%. In order to calculate of the Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-09465-5

thermal conductivity of pure water at high temperatures (from 251.17 to 1275.00 K) and at high pressures (up to 1000 MPa) the IAPWS formulation (Kestin et al., 1984) can be recommended. Tables (skeleton tables) based on the IAPWS formulation with only minor changes from a 1985 IAPWS document were published as the appendices ‘Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance’ to the Proceedings of the 12th and 13th International Conferences on the Properties of Water and Steam [0–800 °C and 0.1– 100 MPa] (White et al., 1995; Tremaine et al., 2000). Aqueous solutions at high temperatures (above 200 °C) and at high pressure play a major role in both natural and industrial processes. The thermal conductivity of aqueous electrolyte solutions is of fundamental importance to the understanding of the various physico-chemical processes occurring in the chemical industry and in the natural environment (Pitzer, 1993; Harvey and Bellows, 1997; Barthel et al., 1999; Gupta and Olson, 2003). The dominant solutes in such processes are often simple electrolytes such as NaCl, CaCl2, MgCl2, and Na2SO4 with lesser amounts of potassium salt, carbonates, borates, etc. Such aqueous solutions are usually present at high temperature and high pressure in deep geological formations (underground water). They also arise in steam-power generation, geothermal power plants (development and utilization of geothermal and ocean thermal energy), hydrothermal synthesis (hydrothermal formation of minerals, for example, growth of K2SO4 crystals from aqueous solutions (Mullin and Gaska, 1969; Ishii, 1973)), seawater desalination processes, and other industrial operations at high temperatures and high pressures. The H2O+NaCl system is very important in many geological and industrial processes. Theoretical modeling of the viscosity and thermal conductivity of this system serves as an example for other ionic systems of 1:1 charge-type electrolytes. The importance of CaCl2 in deep brines of

228

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the Earth’s crust, and its reactivity in fluid-rock interaction is becoming increasingly more recognized. Ca2+ is the second most important cation after Na+. At salinities in excess of about 30 mass. %, Ca2+ becomes the most abundant cation, and such brines are widespread in the deeper parts of many sedimentary basins. Ground-waters encountered in deep wells drilled in crystalline rocks are also commonly highly saline brines in which Ca2+ is the dominant cation, exceeding Na+ by a factor of 2 to 3 on a weight basis. In addition, CaCl2 is the premier example of an electrolyte of the 2 : 1 charge-type and its aqueous solution has been used considerably as an isopiestic standard. The knowledge of the transport properties of seawater brines (which contain primarily NaCl, Na2SO4, and MgSO4) is important in the development of an economic desalination process. MgSO4 is one of the major components of sea salt and many natural waters. The association and hydrolysis of the Na2SO4 in aqueous solutions are of great importance in many industrial processes such as material transport, solid deposition, corrosion in steam generators, and electrical power boilers (Sharygin et al., 2001; Gupta and Olson, 2003). Sodium sulfate is a common product of hydrothermal waste destruction by supercritical water oxidation. Aqueous Na2SO4 is also an important constituent of natural subsurface brines and sea floor vent fluids. LiCl is one of the dominant components of many aqueous fluids (natural fluids). LiCl concentration could equal NaCl in some Lirich pegmatites (London, 1985; Lagache and Sebastian, 1991; Wood and Williams-Jones, 1993) or in magmatic fluids associated with Li-rich leucogranites (Cuney et al., 1992). Although most saline ground waters are dominated by NaCl, Li+ one of the next most important cation after Na+, Ca2+, and Cl− is the dominant anion. LiCl-rich brines also may play a role in seafloor hydrothermal systems at mid-ocean ridges. The thermal conductivity and the viscosity of electrolyte solutions are also of research interest because of the longrange electrostatic interactions and the Coulombic forces between ions. A literature survey revealed that the number of measurements reported for the thermal conductivity of such aqueous systems under pressure and at high temperature (above 200 °C), is rather limited. Furthermore, the scatter of the reported data is quite large (up to 6%) and exceeds the quoted mutual uncertainties of the authors (about 1–2%). This chapter aims to provide the readers with a review of the available experimental data sets on the thermal conductivity of aqueous systems at high temperatures (above 200 °C) and high pressures, to present a critical analysis of the estimation, correlation, and prediction methods, to select the most reliable data sets and to propose preliminary recommendations. In Table 5.1, a summary of all thermal conductivity measurements at temperatures up to 200 °C and higher, to our knowledge, is presented. In the same table, for every composition of non-aqueous components, the first author and the year published, the concentration, the temperature and pressure ranges, the experimental method employed, and the uncertainty claimed by the authors is also shown. It is inter-

esting to note that the majority of the investigators quote uncertainty between 1–2%. A reference code assigned to each set refers the reader to the original data set in the Appendix. Tables of the original thermal conductivity measurements are given in the Appendix for easy access. The tables provide, to our knowledge, the largest and most useful collection of thermal conductivity data at high temperatures (t ≥ 200 °C) and high pressures at the present time. All tables are accompanied by additional information related to the experimental methods employed and their uncertainties. Correlation and prediction of these thermal conductivity measurements as a function of temperature, pressure, and concentration is also briefly considered, mostly as a means of interpreting and comparing the different data sets. 5.2 EXPERIMENTAL TECHNIQUES Most of the conventional techniques of thermal conductivity measurements are based on the steady-state solution of Equation (5.1), i.e. establishing a stationary temperature difference across a layer of liquid or gas confined between two cylinders or parallel plates (Kestin and Wakeham, 1987). In recent years, the transient hot-wire technique for the measurement of the thermal conductivity at high temperatures and high pressures has also widely been employed (Assael et al., 1981, 1988a,b, 1989, 1991, 1992, 1998; Nagasaka and Nagashima, 1981; Nagasaka et al., 1984, 1989; Mardolcar et al., 1985; Palavra et al., 1987; Roder and Perkins, 1989; Perkins et al., 1991, 1992; and Roder et al., 2000). In Table 5.1 all available experimental thermal conductivity data sources at high temperatures (above 200 °C) and high pressures are presented. As one can see from this table, all data were derived by the parallel-plate and the coaxialcylinder techniques, except only two datasets for LiBr by Bleazard et al. (1994) and DiGuilio and Teja (1992) which were obtained by the transient hot-wire technique. We further note that almost all investigators quote an uncertainty of better than 2%. In this section a brief analyses of these methods is presented. The theoretical bases of the methods, and the working equations employed is presented, together with a brief description of the experimental apparatus and the measurements procedure of each technique. For a more thorough discussion of the various techniques employed, the reader is referred to relevant literature (Kestin and Wakeham, 1987; Wakeham et al., 1991; Assael et al., 1991, and Wakeham and Assael, in press). 5.2.1 Parallel-plate technique In Table 5.1, it can be seen that 48 out of 103 data sets of thermal conductivity of aqueous solutions at high temperatures, were derived with the parallel-plate technique. This technique for the measurement of the thermal conductivity has been in use for almost a century (Todd, 1909), and it has in fact been considerably improved over the years (Sengers, 1962; Michels et al., 1962, 1963; Sirota et al., 1974; Amirkhanov and Adamov, 1963; Amirkhanov et al., 1974; Guseynov, 1987, 1989; Moster et al., 1989 and

K2CO3

KBr + NaBr

CoCl2 CsBr CsCl CsI KBr

CdCl2

CdBr2

CaI2 Ca(NO3)2

CaCl2

CH4O (methanol) C3H4F4O (tetrafluoropropanol) C2H4O2 (acetic acid) C3H8O2 (propylene glycol) C6H14O3 (dipropylene glycol) C7H6O2 (benzoic acid) C9H20O4 (tripropyleneglycol) CaBr2

2.5–25 mass % 2.5–25 mass % 5–40 mass % 0.7–4.1 mol·kg−1 0.7–4.1 mol·kg−1 0–50 mass % 2.5–20 mass % 0–50 mass % 2.5–20 mass % 2.5–25 mass % 0–50 mass % 0–50 mass % 0–40 mass % 0–50 mass % 2.5–25 mass % 4.4–17.5 mass % 2.5–25 mass % 2.5–25 mass % 10–30 mass % 5 : 10; 10 : 10; 20 : 10 mass % 2.5–25 mass %

tc-CaI2-1.1 tc-Ca(NO3)2-1.1 tc-Ca(NO3)2-2.1 tc-Ca(NO3)2-3.1 tc-Ca(NO3)2-4.1 tc-CdBr2-1.1 tc-CdBr2-2.1 tc-CdCl2-1.1 tc-CdCl2-2.1 tc-CoCl2-1.1 tc-CsBr-1.1 tc-CsCl-1.1 tc-CsI-1.1 tc-KBr-1.1 tc-KBr-2.1 tc-KBr-3.1 tc-KBr-4.1 tc-KBr-5.1 tc-KBr-6.1 tc-K,Na/Br-1.1 tc-K2CO3-1.1

Abdulagatov & Magomedov, 1995b

tc-C3H8O2-1.1 tc-C6H14O3-1.1 tc-C7H6O2-1.1 tc-C9H20O4-1.1 tc-CaBr2-1.1 tc-CaBr2-2.1 tc-CaCl2-1.1 tc-CaCl2-2.1 tc-CaCl2-3.1

10–50 mass % 2.5–25 mass % 2.5–20 mass % 0.08–0.33 mol·kg−1 0.16–0.33 mol·kg−1 25–100 mass % 15–100 mass % 25–100 mass % 0.25–0.75 mol.fr. 0.25–0.75 mol.fr. 0.05–1.0 mol.fr. 0.25–0.75 mol.fr. 0–50 mass % 2.5–25 mass % 2.5–20 mass % 1; 3 mass % 2.5–25 mass %

Concentration

tc-AgNO3-1.1 tc-BaBr2-1.1 tc-BaI2-1.1 tc-Ba(NO3)2-1.1 tc-Ba(NO3)2-2.1 tc-CH4O-1.1 tc-C3H4F4O-1.1

AgNO3 BaBr2 BaI2 Ba(NO3)2

Reference Code for Appendix*

Abdullaev & Eldarov, 1988 Magomedov, 1992 Abdulagatov & Magomedov, 2000b Akhmedova-Azizova, 2006a Akhmedova-Azizova, 2006b Yata et al., 1990 Yata et al., 1986 Bleazard, Sun and Teja, 1996 Sun and Teja, 2004a Sun and Teja, 2004a Sun and Teja, 2004b Sun and Teja, 2004a Eldarov, 1980 Magomedov, 1992; Magomedov, 1995 Magomedov, 1989a Pepinov & Guseynov, 1992 Magomedov, 1992; Magomedov, 1995; Abdulagatov & Magomedov, 1995a Abdulagatov & Magomedov, 2000a Magomedov, 1992 Akhundov et al., 1994 Akhmedova-Azizova, 2006a Akhmedova-Azizova, 2006b Eldarov, 1980 Abdulagatov & Magomedov, 1997a Eldarov, 1980 Abdulagatov & Magomedov, 1997a Abdulagatov & Magomedov, 1999b Eldarov, 1980 Eldarov, 1980 Eldarov, 1980 Eldarov, 1980 Magomedov, 1989a Safronov et al., 1990 Magomedov, 1992 Abdulagatov & Magomedov, 2001 Abdulagatov et al., 2004b Abdulagatov et al., 2004b

First author

Solute

293/473

293/473 293/473 298/498–590 295/446–589 298/473; 573 293/473 293/473 293/473 293/473 293/473 293/473 293/473 293/473 293/473 298/473 296/450–471 298/473 293/473 295/457–576 295/455–577

293/473 293/473 293/473 296/457–588 298/473; 573 302/448–473 300/473 298–412 299/420–442 298/424–449 379/418–465 297/423–449 293/473 293/473 293/473 293/473–613 293/473

Temperature* (K)

Table 5.1 Summary of experimental thermal conductivity data for aqueous solutions measured up to 473 K and higher temperatures

0.1/2–100

0.1/2–100 0.1/2–100 0.1/10–40 0.1/10–40 20 Sat. 0.1/2–100 Sat. 0.1/2–100 0.1/2–100 Sat. Sat. Sat. Sat. 0.1/2.0 0.1–100 0.1/2–100 0.1/2–100 0.1/2–40 0.1/2–40

0.1/2–30 0.1/2–100 0.1/2–100 0.1/10–40 20 0.1/10–50 0.1/2–50 1 0.1–2.2 0.1–2.2 ∼20 0.1–2.2 Sat. 0.1/2–100 0.1/2.0 Sat. 0.1/2–100

Pressure* (MPa)

PP

PP PP CC CC CC CC PP CC PP PP CC CC CC CC PP CC PP PP CC CC

CC PP PP CC CC CC CC CF CF CF CF CF CC PP PP PP PP

Method+

1.6

1.6 1.6 2.0 2.0 2.0 1.0 1.5 1.0 1.6 1.6 1.0 1.0 1.0 1.0 1.5 1.8–2.2 1.5 <2 1.6 <2

1.5 1.6 1.6 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.0 1.6 1.6 1.5–2.0 1.6

Uncertainty (%)

Thermal Conductivity 229

MgCl2 + MgSO4

LiNO3 Li2SO4 MgBr2 MgCl2

LiCl

LiBr

K2SO4 LaCl3 + La(NO3)3

KNO3

KF KI

tc-Mg/Cl,SO4-2.1

Vakhabov et al., 1992

tc-LiCl-2.1 tc-LiNO3-1.1 tc-Li2SO4-1.1 tc-MgBr2-1.1 tc-MgCl2-1.1 tc-MgCl2-2.1 tc-MgCl2-3.1 tc-MgCl2-4.1

tc-MgCl2-5.1 tc-Mg/Cl,SO4-1.1

3–20 mass % 2 : 1, 3 : 2; 5 : 5; 10 : 5; 10 : 10 mass % 2 : 1, 3 : 2; 5 : 5; 10 : 5; 10 : 10 mass %

2.5–25 mass % 1–20 mass % 1–3 mass % 2.5–20 mass % 1.0–3.9 mol·kg−1 0.61–2.27 mol·kg−1 2.5–25 mass % 2.5–20 mass % 2.5–25 mass % 5–25 mass % 2.5–25 mass %

tc-LiBr-2.1 tc-LiCl-1.1

tc-LiBr-1.1

3–20 mass % 3–15 mass % 4.7–19.7 mass % 0–50 mass % 6.9–17.5 mass % 2.5–25 mass % 5–40 mass % 2.5–25 mass % 0.24–0.78 mol·kg−1 10.85 : 4.6; 10.85 : 6.0; 10.85 : 11.6 10/20–65 mass.%

5.1; 10.0 mass % 1–3 mass % 1–3 mass % 1–20 mass % 5–20 mass % 0.7–13 mass % 2.5–25 mass %

Concentration

tc-K,Ca,Mg/Cl-1.1 tc-K,Ca,Mg/Cl-2.1 tc-KF-1.1 tc-KI-1.1 tc-KI-2.1 tc-KI-3.1 tc-KNO3-1.1 tc-KNO3-2.1 tc-K2SO4-1.1 tc-La/Cl,NO3-1.1

tc-KCl-1.1 tc-KCl-2.1 tc-KCl-2.2 tc-KCl-3.1 tc-KCl-3.2 tc-KCl-4.1 tc-KCl-5.1

Reference Code for Appendix*

Di Guilio & Teja, 1992; Bleazard et al., 1994 Abdulagatov & Magomedov, 1997b Pepinov & Guseynov, 1993 Pepinov & Guseynov, 1992 Abdulagatov & Magomedov, 1997b Abdulagatov et al., 2004a Azizov, 1999 Magomedov, 1992 Magomedov, 1989a Magomedov, 1990 Pepinov, 1992 Magomedov, 1992; Abdulagatov & Magomedov, 1995a Magomedov, 1995 Mamedov, 2000 Eldarov et al., 1992a

Safronov et al., 1990 Pepinov & Guseynov, 1991a Pepinov & Guseynov, 1992 Pepinov & Guseynov, 1991b Pepinov, 1992 Magomedov, 1989b; 1993 Abdulagatov & Magomedov, 1994 Magomedov, 1995 Mamedov et al., 1997 Mamedov et al., 1998 Safronov et al., 1990 Eldarov, 1980 Safronov et al., 1990 Abdulagatov & Magomedov, 2001 Abdullaev & Eldarov, 1988 Magomedov, 1992 Abdulagatov & Azizov, 2005 Grigoriev, 2003

KCl

KCl + CaCl2 + MgCl2

First author

Solute

Table 5.1 Continued

Sat. Sat.

5–50

293/473–573

0.1/2–100 Sat. Sat. 0.1/2–100 0.1/10–30 10–30 0.1/2–100 0.1/2.0 0.1/2–100 Sat. 0.1/2–100

Sat.

CC

CC CC

PP PP PP PP CC CC PP PP PP PP PP

THW

CC CC CC PP CC PP CC CC

CC

PP PP

0.1/2–100 0.1/2–100 1–10 5–50 0.1–100 Sat. 0.1–100 0.1/2–100 0.1/2–30 0.1/2–100 0.1/10; 30 0.1–100

CC PP PP PP

Method+

0.1–100 5–14 Sat. Sat.

Pressure* (MPa)

293/453–573 293/473–573

293/473 293/453–573 293/473–573 293/473 293/473 293/473 302/482–594 293/473

293/473 293/473–613

293/460–465

298/450; 471 293/473 300/450–471 293/473 293/473 293/473 298/448–574 299/420; 450

293/448–573

303/451–471 296/507–613 293/473–613 293/473–613 294/483–611 298/473 293/473

Temperature* (K)

2.2

1.8 2.2

1.6 1.5–2.0 1.3–1.6 1.6 1.6 <2.0 1.6 1.5 1.6 1.5–2.0 1.6

2

1.8–2.2 1.0 1.8–2.2 <2 1.5 1.6 1.6 1.3

1.8

1.6 1.6

1.8–2.2 1.5–2.0 1.3–1.6 1.3–1.6

Uncertainty (%)

230 Hydrothermal Experimental Data

tc-Na,Ca/Cl-2.1

tc-Na,Ca/Cl-3.1

tc-Na,Ca/Cl-4.1 tc-Na,Ca/Cl-5.1

Eldarov et al., 1996

Abdullaev et al., 1997

Abdullaev et al., 1998a Abdullaev et al., 1998b

NaCl + CaCl2 + KCl

NaCl + CaCl2

Eldarov, 2003

tc-NaCl-6.1 tc-NaCl-7.1 tc-Na,Ca/Cl-1.1

Magomedov, 1992; Abdulagatov & Magomedov, 1994; Magomedov, 1995 Abdullaev et al., 1998a Abdulagatov et al., 2004a Abdullaev et al., 1995

NaCl

NaCl

Na2CO3

MgSO4 NaBr

tc-Na,Ca,K/Cl-1.1

tc-Mg(NO3)2-1.1 tc-Mg(NO3)2-2.1 tc-Mg(NO3)2-3.1 tc-MgSO4-1.1 tc-NaBr-1.1 tc-NaBr-2.1 tc-NaBr-3.1 tc-Na2CO3-1.1 tc-Na2NO3-2.1 tc-NaCl-1.1 tc-NaCl-2.1 tc-NaCl-3.1 tc-NaCl-4.1 tc-NaCl-4.2 tc-NaCl-5.1

Akhmedova et al., 1995 Akhmedova-Azizova, 2006a Akhmedova-Azizova, 2006b Magomedov, 1992 Eldarov, 1986 Magomedov, 1992 Abdulagatov et al., 2004b Magomedov, 1995 Akhmedova-Azizova & Babaeva, 2008 Yusufova et al., 1975a; Pepinov, 1992 Eldarov, 1986 Magomedov, 1989b; 1993 Ganiev et al., 1990

Mg(NO3)2

Reference Code for Appendix*

First author

Solute

5–25 mass % 4.278 mol·kg−1 2 : 1; 3.33 : 1.67; 6.67 : 3.33; 10 : 5; 13.33 : 6.67 mass % 2 : 1; 3.33 : 1.67; 6.67 : 3.33; 10 : 5; 13.33 : 6.67 mass % 2 : 1; 3.33 : 1.67; 6.67 : 3.33; 10 : 5; 13.33 : 6.67 mass % 3 : 1 mass.% 2.25 : 0.75; 3.75 : 1.25; 6 : 2.5; 7.5 : 2.5; 11.25 : 3.75; 15 : 5; mass.% 1.8 : 0.6 : 0.6; 3 : 1 : 1; 6 : 2 : 2; 4 : 8 : 1; 6 : 1 : 6; 9 : 3 : 3; 12 : 4 : 4 mass %

2.5–25 mass %

20; 40 mass % 0.7–4.5 mol·kg−1 0.36–4.5 mol·kg−1 2.5–25 mass % 10–40 mass % 2.5–25 mass % 10–38 mass % 2.5–15 mass % 0.5–1.7 mol·kg−1 5–25 mass % 5–20 mass % 2.3–15 mass % 4 mol·kg−1

Concentration

0.1/5–50

293/473–573

293/473–573

5–50

Sat. 5–50

5–50

293/473–573

293/448–573 293/423–573

Sat. 20 Sat.

20; 40 0.1/10–40 20 0.1/2–100 0.1/2–30 0.1/2–100 0.1/2–40 0.1/2–100 0.1/10–30 Sat. 0.1/2–30 0.1/2–100 0.1/4–98 Sat. 0.1/2–100

Pressure* (MPa)

293/453; 473 293/473–573 293/473–573

293/473

295/473–591 295/454–590 298/473; 573 293/473 293/473 293/473 294/451–577 293/473 307/464–629 293/479–600 293/473 293/473 295/475–649

Temperature* (K)

CC

CC CC

CC

CC

CC CC CC

PP

CC CC CC PP CC PP CC PP CC PP CC PP CC

Method+

1.3–1.8

1.8 1.3

1.5–2.2

2.2

1.8 2.0 2.2

1.6

2.0 2.0 2.0 1.6 2.2 1.6 <2 1.6 2.0 1.5–2.0 2.2 1.6 1.8–2.2

Uncertainty (%)

Thermal Conductivity 231

tc-Na,Mg/Cl,SO4-2.1 tc-Na,Mg/Cl,SO4-2.2

Abdullaev et al., 1994b

Eldarov et al., 1992b,c

Abdullaev et al., 1992b

NaCl + MgCl2

NaCl + MgCl2 + Na2SO4

2.5–25 mass % 2.5–15 mass % 0.25–3.15 mol·kg−1 0.5–3.15 mol·kg−1 2.5–25 mass % 10–80 mass % 0.9–3.5 mol·kg−1

tc-ZnI2-1.1 tc-Zn(NO3)2-1.1

tc-Na2SO4-1.1 tc-SrBr2-1.1

Yusufova et al., 1975b; Pepinov, 1992 Abdulagatov & Magomedov, 2003/2004 Abdulagatov & Magomedov, 1999a Abdulagatov & Magomedov, 1999a Abdulagatov et al., 2004a Akhmedova-Azizova, 2006b Magomedov, 1992; Abdulagatov & Magomedov, 1998 Eldarov, 1980 Azizov, 1999

0.2117 : 0.1059; 0.3595 : 0.1798; 0.7547 : 0.3773; 1.1905 : 0.5953; 1.674 : 0.837 mol % 2 : 1 : 2; 5 : 2 : 3; 8 : 3 : 4; 10 : 5 : 5; 12 : 5 : 8; 15 : 10 : 5 mass % 2 : 1 : 2; 5 : 2 : 3; 8 : 3 : 4; 10 : 5 : 5; 12 : 5 : 8; 15 : 10 : 5 mass % 2 : 1 mass % 10–50 mass % 2.5–25 mass % 2.5–25 mass % 5–40 mass % 2.5–25 mass % 3 : 2; 5 : 5; 10 : 5; 10 : 10; 20 : 10 mass % 5–25 mass % 2.5–20 mass %

tc-SrCl2-1.1 tc-Sr(NO3)2-1.1 tc-Sr(NO3)2-2.1 tc-Sr(NO3)2-3.1 tc-ZnCl2-1.1

tc-Na/Cl,SO4-1.1 tc-NaI-1.1 tc-NaI-2.1 tc-NaI-3.1 tc-NaNO3-1.1 tc-NaNO3-2.1 tc-Na,K/NO3-1.1

Eldarov et al., 1992b,c Eldarov, 1986 Magomedov, 1994 Abdulagatov & Magomedov, 1995b Abdullaev & Eldarov, 1988 Magomedov, 1992 Abdullaev et al., 1994a

tc-Na,Mg/Cl-1.1

tc-Na,K/Cl-1.1

2 : 1 : 2; 4 : 2 : 4; 5 : 5 : 5; 10 : 5 : 5; 15 : 5 : 10; 15 : 10 : 15 mass % 2 : 1 mass %

Concentration

293/473 293/473–573

293/473 293/473 294/455–591 298/473; 573 293/473

293/473–586 293/453; 473

Sat. 10–30

0.1/2–100 0.1/2–100 0.1/10–40 20 0.1/2–100

Sat. 0.1/2–100

Sat. 0.1/2–30 0.1/2–100 0.1/2–100 0.1/2–30 0.1/2–100 Sat.

0.1/5–50

293/473–573

293/423; 473 293/473 293/473 293/473 293/473 293/473 293/473–573

Sat.

0.1/4–40

Sat.

5–40

Pressure* (MPa)

293/473–573

293/473–523

293/453–523

293/473–523

Temperature* (K)

CC CC

PP PP CC CC PP

PP PP

CC CC PP PP CC PP CC

CC

CC

CC

CC

CC

Method+

1.0 <2.0

1.6 1.6 1.6 2.0 1.6

2.0 1.6

2.2 2.2 1.6 1.6 1.5 1.6 2.2

2.2

2.2

2.2; 1.1–1.8 1.5–2.3

2.2

Uncertainty (%)

* The results of low-temperature measurements (below 473 K) are not given usually in the Appendix. Numbers separated by a slash show the minimal temperatures and pressures available in the publications (before a slash) and in the Appendix tables (after a slash). ‘Sat.’ means that equilibrium pressure is not shown in the publications but was near (above) the saturated vapor pressure at measured temperature. + CC – coaxial-cylinder; PP- parallel-plate; THW-transient hot-wire.

ZnI2 Zn(NO3)2

ZnCl2

SrCl2 Sr(NO3)2

Na2SO4 SrBr2

NaNO3 + KNO3

NaNO3

NaCl + Na2SO4 NaI

tc-Na,Mg/Cl,SO4-1.1

Eldarov et al., 1992b,c

NaCl + KCl

tc-Na,Ca,Mg/Cl-1.1 tc-Na,Ca,Mg/Cl-1.2

Abdullaev et al., 1992a

NaCl + CaCl2 + MgCl2

Reference Code for Appendix*

First author

Solute

Table 5.1 Continued

232 Hydrothermal Experimental Data

Thermal Conductivity

Abdulagatov and Magomedov, 1994, 1995a,b, 1997a,b, 1998, 1999a,b, 2000a,b, 2001, 2003/2004). 5.2.1.1 Theoretical According to the parallel-plate technique, the fluid under investigation is confined between two horizontal plates, heated from above, so that the upper plate is at a higher temperature than the lower one. Provided the two plates are maintained at constant uniform temperatures T1 and T2 respectively, the steady-state solution of Equation (5.1) is Q = λS

(T1 − T2 ) d

,

(5.4)

where d is the thickness of the fluid layer, S is the area across which the heat flows, l is the thermal conductivity and Q represents the total amount of heat generated in the emitter. In this solution it is assumed that the thermal conductivity of the fluid is constant over the temperature difference applied, that the plate dimensions are infinite and that the heat flux is in one dimension. In a real experiment, the measured heat flux Qexp and temperature difference ∆Texp, differ from the aforementioned Q and ∆T (= T1-T2), due to parasitic heat losses, Qp, heat losses due to radiation, Qr, and convective heat losses, Qc. Thus Q = Qexp − Qp − Qr − Qc.

Ra = GrPr = gαρ 2C P ∆Td 3 λη ,

(5.8)

where g is the gravitational acceleration, a is the thermal expansion coefficient of the fluid, r is the density, Cp the isobaric heat capacity, l the thermal conductivity, and h is the viscosity. For an infinite horizontal layer the critical value of the Rayleigh number, Ra, is 1708 (Gitterman, 1978). If the parallel plates that bind the liquid layer deviate from the horizontal plane by angle ϕ then convection of the fluid can occur. The values of the convective heat loss, Qc, can then be calculated from the de Groot theory (de Groot and Mazur, 1962; Michels et al., 1962) as Qc < Ral sin ϕ∆T 720 .

(5.6)

where ci are constants determined from cell design, and Qs is the heat relieved in the guard ring and plate. In most cases a correction is necessary for radiation. In order to reduce the radiation correction, the plate surfaces must have low emissivities, and thin layers of fluid (from 0.15 mm to 0.3 mm) should be employed. For this purposes the plate surfaces are polished and protected against oxidation, sometimes by coating with nickel, chrome, silver or silicon dioxide. Furthermore, the heat losses due to radiation, Qs, are rendered very small, as the temperature differences between plates are very small and the plate surfaces are gilded. From the Stefan-Boltzmann law for an upper and lower plate system, we can write Qr = 2σε ST 3∆T ,

radiation (partially transparent radiation), the problem is more complicated, as the radiative and conductive fluxes are then coupled. In this case the effect of the heat transferred by radiation can be derived from the solution of an integrodifferential equation describing the coupled radiative and conductive terms. This problem is amenable to exact study only numerically (Menashe and Wakeham, 1982; Nieto de Castro et al., 1984). The thermal conductivity cell design proposed by Moster et al. (1989) is a good example of a cell constructed in order to minimize the effects of convection. The Rayleigh number, Ra, for the laminar convection is

(5.9)

(5.5)

The parasitic heat losses, Qp, can be calculated (Moster et al., 1989) from Qp = (c1 + c2 λ ) Qexp − (c3 − c4 λ ) Qs,

233

(5.7)

where s is Boltzmann’s constant, T is the fluid’s temperature, S denotes the mean surface of the fluid layer, and e, the emissivity of the plates. This correction is valid when the optical density of the fluid layer is low. If the fluid is entirely transparent then the conductive and radiative heat fluxes are additive and independent and the simple correction given by Healy et al. (1976) is adequate and usually negligible. When the fluid absorbs and re-emits

This expression is valid at d / l << 1, where l denotes the diameter of the upper plate. It follows, from Equation (5.8) and (5.9), that the convective heat loss, Qc, is proportional to ∆T 2. Therefore, any deviation from the linearity of Qc vs. ∆T can be regarded as an indication of the presence of convection. In practice, the presence of convection can be checked by measuring the thermal conductivity at various temperature differences ∆T. The presence of convection will show as a dependence of the thermal conductivity on this temperature difference. The effects of convection can be made negligibly small by ensuring horizontality and employing a small distance d. The uncertainty in thermal conductivity measurement due to convection in a layer between two parallel plates is given by (Michels et al., 1962)

δλ = β

dRa sin ϕ , 180π D

(5.10)

where D is the diameter of the hot plate, and b is the constant (<1). A correction for the temperature difference can be expressed as ∆T = ∆Texp − ∆Ts − ∆Ta,

(5.11)

where ∆Ts is a correction connected with the temperature nonuniformity in the plates, and ∆Ta is the correction for the temperature drop at the surfaces of both upper and lower plates (the accommodation effect). The values of these corrections can be estimated as (Moster et al., 1989)

234

Hydrothermal Experimental Data

∆Ts = Cg λ∆Texp, ∆Ta = 2  

(5.12)

2 − 0.83α   α

∆Texp 2π kT λ , m CP + CV Pd

(5.13)

where Cg is a constant, a is the accommodation coefficient, P is the fluid’s pressure, and Cv is the isochoric heat capacity. It is apparent from Equation (5.13) that ∆Ta ≈ P−1, and therefore, the accommodation correction is important at low pressures only. The values of a depends on the nonideal behavior of thermal exchange between the plate surface and the fluid under study. For a detailed discussion of the parallel-plate technique, the reader is referred to the review by Sirota (1991). 5.2.1.2 Experimental In order to perform accurate measurements of the thermal conductivity of electrolyte solutions under high pressures (up to 100 MPa) and high temperatures (up to 650 K), a parallel-plate apparatus was originally developed by Amirkhanov and co-authors in 1963 (Amirkhanov and Adamov, 1963; Amirkhanov et al., 1974). This instrument was further improved by Magomedov (1995) and Abdulagatov and Magomedov (1994, 1995a,b, 1997a,b, 1998, 1999a,b, 2000a,b, 2001, 2003/2004). The thermal conductivity measurement system consists of a thermalconductivity cell, a high-pressure vessel, a liquid thermostat, dead-weight pressure gauge, a water-to-oil separator, containers for degassed water and solution, and backing pump. 16 P-136

5.2.1.3 Working equation and uncertainty The thermal conductivity l of the fluid was calculated from Equation (5.4), employing measurements of the heat Q transmitted across the solution layer, the temperature difference ∆T between the upper and lower plates, the thickness

17

Figure 5.1 Guarded parallel-plate thermal conductivity cell (Abdulagatov, I.M. and Magomedov U.B. (1999b) J. Chem. Eng. Japan, 32, 465–471. Reproduced by permission of The Society of Chemical Engineers, Japan). 1: guard plate; 2: upper (hot) plate; 3: inner heater; 4: guard heater; 5: lower (cool) plate; 6: differential thermocouple; 7: direct current potentiometer (R-348, a rated uncertainty of 0.002%); 8: Dewar vessel; 9: absolute thermocouple; 10: supports; 11: fluid layer; 12 and 14: arms of the Wheatstone bridge; 13: glass-fiber layer; 15 and 16: stabilized sources of direct current (P-136, a rated uncertainty of 0.02%); 17 and 18: digital potentiometer (III 300-1, a rated uncertainty of 0.07%); 19: Wheatstone bridge (a rated uncertainty of 0.001 K).

300-1 15

P-136

A schematic diagram of the experimental cell construction developed by Abdulagatov and Magomedov (1994, 1999b) for high temperature and high pressure thermal conductivity measurements of aqueous solutions is shown in Figure 5.1. The thermal-conductivity cell consists of three plates: guard plate-1, upper (hot) plate-2, and lower plate-5. The guard plate is surrounded by a guard heater-4. The thermalconductivity cell has a cylindrical form with a 21 mm height and 90 mm diameter. The thickness d of the gap between the upper and lower plates is fixed by supports-10. The upper plate has a diameter of 68.05 mm. The lower plate has a thickness of 9 mm. The cell is made from stainless steel. The fluid surrounds the cell and fills the gap between upper and lower plates. The gap between the guard and the upper plates is 1 mm and filled with glass fiber. Differential thermocouples-6 are used for the measurement of the temperature difference ∆T between the upper and lower plates. The temperature of the upper and the lower plates is measured with a chrome l – cope l thermocouple-9 with a precision of 0.02 K. The cell described above was used in conjunction with an automatic Wheatstone bridge-19. The thermal-conductivity cell is mounted inside a high-pressure vessel which is placed in the liquid thermostat.

18 300-1 19 Wheatstone bridge

12 13

14

1

2

3 4

11 10 9

5

7 6 R-348

8 Dewar vessel

Thermal Conductivity

of the solution layer d and the effective area of the upper plate S. The dimensions S and d of the thermal-conductivity cell entered in the working equation need some corrections in order to account for the effect of their changes due to the applied temperature and pressure. The cell constant (d/S) has also to be corrected for thermal expansion and compression. The effect of pressure is negligibly small in the pressure range of the experiments (up to 100 MPa) since the entire cell was under pressure. The uncertainty of the cell constant determination was 0.3%. The uncertainty of the power Qexp (amount of electrical energy released by the heater) measurements, was less than 0.08%. The uncertainty in the temperature difference ∆Texp was less than 0.14%. The correction for parasitic heat flow was of the order of 0.003%. Taking into account the uncertainties of temperature, pressure, and concentration measurements, the total experimental uncertainty in the thermal conductivity is estimated to be less than 1.6%. At low temperatures T = 313 K the values of Qr calculated from Equation (5.7) at ∆T = 0.5 K is 0.0617 W which is considerably less than values of heat Q = 7.5121 W, transmitted across the fluid layer. To reduce the values of Ra, a small gap distance d = 301.0 ± 0.1 µm was employed by Abdulagatov and Magomedov (1994, 1995a,b, 1997a,b, 1998, 1999a,b, 2000a,b, 2001, 2003/2004), while the temperature difference ∆T employed in the measurements was 1 K. In this way, it is possible to minimize the risk of convection. The guarded parallel-plate instrument, described above, has been used for the thermal conductivity measurements of light and heavy water and twenty one aqueous salt solutions, namely: H2O + NaCl, KCl, LiCl, MgCl2, CaCl2, CdCl2, ZnCl2, CoCl2, SrCl2, Sr(NO3)2, CdBr2, LiBr2, KBr, NaI, KI, CaI2, BaI2, ZnI2, K2CO3, MgSO4, and ZnSO4. Yusufova et al. (1975a,b), Pepinov and Guseynov (1991b, 1992, 1993), and Pepinov (1992) employed the same technique to measure the thermal conductivity of aqueous solutions of NaCl, KCl, LiCl, MgCl2, CaCl2, and Na2SO4 at temperatures up to 613 K. The parallel-plate thermal conductivity cell employed by Yusufova et al. (1975a,b), Pepinov and Guseynov (1991a,b, 1992, 1993), and Pepinov (1992)

1

2

3

4

5

is schematically shown in Figure 5.2. The construction of the cell is the same with that employed by Sirota et al. (1974) and Sirota (1991). The thermal conductivity cell consisted of (see Figure 5.2) a hot-2 and cold-17 plate made from stainless steel; guard plate-5 made from cooper; guard ring-21; guard heaters-6 and 7; main heater-1; thermocouples-15 and 16. The hot and cold plates are connected with a metallic ring-19. The working surface of the plates was machined flat within 0.2 mm and polished. The gap between the plates was adjusted with three packing washers-11 (diameter 4 mm). The temperature gradient between plates was within 0.5 to 1.5 K. The temperature difference between main and guard heaters were between 0.00 and 0.03 K. The plate distance was 0.85 mm. The uncertainty of the thermal conductivity measurements with this instrument is 1.5 to 2.0%. 5.2.2 Coaxial-cylinder technique The coaxial-cylinder technique was also employed for the measurement of the thermal conductivity of aqueous solutions at high temperatures. In Table 5.1, 53 out of 103 published data sets employed this technique. The coaxial-cylinder technique is a steady-state method which measures the heat exchange by conduction between two concentric cylindrical surfaces separated by a small gap filled with the fluid sample, each of these surfaces being maintained at constant temperature. This technique was successfully employed to measure the thermal conductivity of pure fluids (H2O, CO2, NH3, Ar, N2, C2H6, C3H8) at high temperatures (Vargaftik and Smirnova, 1956; Ziebland, 1958; Ziebland and Burton, 1960; Vines, 1960; Bailey and Kellner, 1967; and Yata et al., 1979b). The method was considerably improved by Le Neindre and co-authors (Le Neindre, 1969; Tufeu 1971; Le Neindre et al., 1984). 5.2.2.1 Theoretical In this technique, the fluid is placed in a ring-shaped gap between two coaxial cylinders with a common vertical axis. According to the ideal model, a thin layer of a homogeneous

6 7

20

8 9 10 11

19

12

21

13 18

17

16

15

22

14

235

Figure 5.2 Parallel-plate high temperature and high pressure thermal conductivity cell, developed by Yusufova et al. (1975a,b), Pepinov (1992), Pepinov and Guseynov (1991a,b, 1992, 1993) (Journal of Engineering Physics and Thermophysics). 1: main heater; 2: hot plate; 3: differential thermocouple; 4: plate; 5: guard plate; 6 and 7: guard heaters; 8: tumbler; 9: high pressure vessel; 10: spiral of the main and guard heaters; 11: washers; 12: contact with washer; 13: heater; 14: differential thermocouple; 15 and 16: thermocouples; 17: cold plate; 18: connecting piece; 19: jointing ring; 20: heater; 21: guard ring; 22: gap; 23: channel.

236

Hydrothermal Experimental Data

fluid with a uniform thermal conductivity, l, is enclosed between two coaxial cylinders of length l. If a heat flux is uniformly generated in the inner cylinder and propagates radially through the fluid under study, to the outer cylinder in steady state conditions, the temperatures of the inner and outer cylinders will be T1 and T2 respectively. The thermal conductivity is determined as a function of these two temperatures and the amount of heat, Q, released by the inner cylinder, as Q=

2π l λ (T1 − T2 ) . log ( d2 d1 )

(5.14)

In the above relation, d1 is the external radius of the inner cylinder; and d2 is the internal radius of the external cylinder. The ends of the cylinders can be made in different shapes: flat, conical or spherical. When measuring the thermal conductivity with this technique, some corrections should be made for: (1) radiationinduced heat transfer (radiative correction); (2) parasitic heat transfer from the inner to the outer cylinder through a central solid pintle, electric wires, and thermocouples; (3) convective heat transfer; and (4) effects of possible temperature jumps at the interface between the liquid layer and the cylinder surface. The correction for radiation is usually calculated by the Stefan-Boltzmann law – see Equation (5.7) – assuming the radiation absorption in the liquid is negligibly small. Le Neindre et al. (1976) employed silver cylinders with perfectly polished surfaces to reduce the heat transfer by radiation. The emissivity of these cylinders was small and Qr estimated from Equation (5.7) is negligible by comparison with the heat transfer by conduction. The convective heat transfer, Qc, can be calculated from the relation (Johannin, 1958)

Qc = Ra

π d1 λ ∆T , 720

(5.15)

where Ra is the Rayleigh number defined in Equation (5.8), d1 is the radius of the inner cylinder; and ∆T is the temperature difference between the cylinders. In most experimental cells, the radius of the inner cylinder is about 0.01 m and the gap between cylinders is between 0.2 and 0.4 mm. The corrections for heat losses through the solid parts of the cell are determined by calibrating with measurements on standard fluids, for which the thermal conductivity is well known. 5.2.2.2 Experimental The coaxial-cylinder apparatus and the thermal conductivity cell employed by Abdulagatov et al. (2004a,b), and Abdulagatov and Azizov (2005), to measure the thermal conductivity of aqueous LiNO3, Sr(NO3)2, K2SO4, NaBr, KBr, NaBr + KBr solutions at temperatures up to 591 K, is schematically shown in Figure 5.3. The main part of the apparatus consisted of a high-pressure autoclave-1, thermostat-2, and thermal conductivity cell. The thermal conductivity cell consisted of two coaxial cylinders: inner (emitting) cylinder-2 and outer (receiving) cylinder-3. The cylinders were made from stainless steel and located in a high pressure autoclave. The deviation from concentricity was 0.002 cm or 2% of the sample layer. The temperature in the thermostat was controlled with heater-3. The temperature differences between various sections (levels) of the copper block were within 0.02 K. The important dimensions of the thermal conductivity cell are: OD of the inner cylinder is d1 = (10.98 ± 0.01) × 10−3 m. ID of the outer cylinder is d2 = (12.92 ± 0.02) × 10−3 m. The length of the measuring section of the inner cylinder (emitter) is l = (150 ± 0.1) × 10−3 m. The gap Measuring Cell

Figure 5.3 Schematic diagram of the experimental apparatus and experimental cell for measuring the thermal conductivity of aqueous solutions at high temperatures and high pressures by the coaxial cylinders method (J. Chem. Eng. Data. 49, 688–704, Abdulagatov et al,. Copyright 2004 with permission from American Chemical Society). 1: high-pressure autoclave; 2: thermostat; 3: heater; 4: PRT; 5: thermocouple; 6: filling tank; 7: set of valves; 8: dead-weight pressure gauge (MP-600); 9: separating U-shape capillary tube; 10: electrical feedthrough. Measuring cell: 1: autoclave; 2: inner cylinder; 3: outer-cylinder; 4: microheater; 5: thermocouples; 6: axial alignment screws.

Thermal Conductivity

between cylinders (thickness of the liquid gap) was d = (0.97 ± 0.03) × 10−3 m. The choice of this gap represents a compromise between decreasing convection and accommodation effect. The acceptable value for the thickness of the liquid layer d is between 0.5 and 1 mm. The optimal value ratio of the length l to the diameter of the inner cylinder d1 should be l/d1 = 10 to 15. In the cell, the heat was generated in the micro-heater-4 which consists of an isolated constantan wire of 0.1 mm diameter. A micro-heater was mounted inside the inner cylinder (emitter) which was closely wound around a surface of a 2 mm diameter ceramic tube and isolated with high temperature lacquer. To reduce the values of the Rayleigh number, Ra, a small gap distance between cylinders d = (0.97 ± 0.03) × 10−3 m was used. This way the risk of convection was minimized. Convection could develop when the Ra exceeds a certain critical value Rac, which for vertical coaxial cylinders is about 1000 (Gershuni, 1952). The absence of convection can be verified experimentally by measuring the thermal conductivity with different temperature differences ∆T across the measuring gap and different power Q transferred from inner to outer cylinder. Since heat transfer by radiation is proportional to 4T 3∆T, we would expect radiation losses to substantially increase as a function of the cell temperature. This kind of correction is included in the calibration procedure. The emissivity of the walls was small and Qrad, estimated by Equation (5.7) is negligible (≈ 0.164 W) by comparison with the heat transfer (13.06 W) by conduction in the temperature range up to 600 K.

5.2.2.3 Working equation and uncertainty The thermal conductivity of the sample at a given temperature and pressure for this method is calculated from Equation (5.14), as

λ=

Q log ( d2 d1 ) , 2π l ∆T

(5.16)

where Q = Qmeas − Qlos is the amount of heat transferred by conduction alone across the sample layer between the cylinders. Qmeas is the amount of heat released by the calorimetric micro-heater, while Qlos is the amount of heat losses through the ends of the measuring cell (end effect). Equivalently, ∆T = ∆Tmeas − ∆Tcorr. The values of Q and ∆T are measured indirectly and some corrections are necessary. As however it is difficult to estimate the values of the Qlos and ∆Tcorr by calculation, they are estimated by measuring the thermal conductivity of standard liquids, such as water, whose thermal conductivity is very well known (IAPWS standard, Kestin et al., 1984). Typically, the amount of heat flow Q and the temperature difference ∆T were found to be 13.06 W and 3.5 K, respectively, while the estimated value of Qlos is about 0.05 W, which is negligible (0.38%). Taking into account all corrections, the final working equation for the thermal conductivity for this instrument can be rewritten as

λ=A

Qmeas − Qlos , ∆Tmeas − ∆Tcorr

237

(5.17)

where A = ln(d2 /d1) /2p l is the cell constant which can be determined either from its geometrical characteristics, or by means of a calibration technique using thermal conductivity data for a reference fluid (pure water, IAPWS, Kestin et al., 1984). The values of the cell constant determined in these two ways are 0.1727 m−1 and 0.1752 m−1, respectively. After a careful analysis of the uncertainties all of the quantities (Abdulagatov et al., 2004a) entering Equation (5.17), it is estimated that the combined relative uncertainty in the thermal conductivity measurements was 2%. This thermal conductivity apparatus has also been successfully employed by Akhundov et al. (1994), Akhmedova et al. (1995), and Azizov (1999), to study the thermal conductivity of aqueous Li2SO4, Zn(NO3)2, Ca(NO3)2, and Mg(NO3)2 solutions at temperatures up to 590 K and pressures up to 40 MPa. Another version of this technique was developed by Eldarov (1980, 1982, 1986, 2003), Eldarov et al. (1992a– c,1996), and Abdullaev et al. (1994a,b, 1995, 1997, 1998a,b) in order to measure the thermal conductivity of binary aqueous solutions of AgNO3, NaNO3, KNO3, CaBr2, CdBr2, NaCl, CdCl2, CsBr, CsCl, CsI, NaBr, KBr, KI, NaI, ZnI2, ternary aqueous solutions of MgCl2 + MgSO4, NaCl + CaCl2, NaCl + KCl, NaCl + MgCl2, NaCl + Na2SO4, NaNO3 + KNO3, and quaternary aqueous solutions of NaCl + CaCl2 + KCl, NaCl + Na2SO4 + MgCl2, NaCl + CaCl2 + MgCl2 at temperatures up to 573 K. Three versions of a coaxial cylinder instrument were employed by Eldarov (1980, 1982, 1986, 2003) and Eldarov et al. (1992a–c, 1996) to measure the thermal conductivity of aqueous salt solutions. In the first version, the instrument was composed of an 150 mm-stainless steel-inner cylinder and a 120 mm-length copper-outer cylinder with a 0.5 mm gap between cylinders. In the second version of the cell, the heater was inserted into melted tin in the inner cylinder. This arrangement reduced the heat loss generated in the inner cylinder and resulted in the accurate measurement of the temperature difference between the cylinders due to the excellent thermal contact between the heater and inner cylinder. Cylinders were made out of stainless steel, the length of the measuring part of the cylinder was 120 mm, and the gap between cylinders was 0.4 mm. In the third version the inner cylinder was filled with melted silver solder up to 125 mm from the bottom. The length and gap between the cylinders were 150 mm and 0.35 mm, respectively. All three versions of the measuring thermal conductivity cells were used to check how measured values of l depends on the ratio ∆T / d, where d is the distance between the cylinders. The apparatus and design of the coaxial-cylinder cell used by Eldarov (1980, 1982, 1986, 2003) and Eldarov et al. (1992a–c, 1996) is shown in Figure 5.4. Outer diameter of the internal cylinder was 8.301 ± 0.001 mm, and the inner diameter of the outer cylinder was 9.602 ± 0.001 mm. The length of the measuring part of the cell was 215 mm. The total uncertainty in thermal conductivity measurement in this instrument is estimated to be 1.33 to 2.2%.

238

Hydrothermal Experimental Data

Figure 5.4 Experimental apparatus (a) and experimental cell (b) for the high temperature and high pressure thermal conductivity measurements, developed by Eldarov (1980,1982, 1986, 2003) and Kerimov et al. (1969) (Izv. Akad. Nauk. Azer. SSR, 6, 112–116. Reproduced with permission from ELM Publishers). (a): 1: thermal conductivity cell; 2: autoclave; 3: liquid thermostat; 4: PRT; 5: U-shaped separated vessel; 6: lid; 7: hydraulic press; 8: high pressure valves; 9: sample; 10: mixer; 12: indicating tank; 13: separated flask; 14: vacuum pump. (b): 1: inner cylinder; 2: outer cylinder; 3: annular gap between the cylinders; 4: heater; 5: U-shaped quartz tube; 6: melted tin; 7: sprocket; 8: thin wall bushing; 9: filling tube; 10: differential thermocouples; 11: asbestos plug; 12: copper wires; 13: bushing.

9 8 11

10

6

8

8

7

12 5

4

13 2

1

3

(a)

12 13

11

1 2 3 4

10

5 6 7 8 9 (b)

A schematic diagram of the thermal conductivity instrument employed by Safronov et al. (1990) and Grigor’ev (1995, 2003) is shown in Figure 5.5. It consisted of a thermal conductivity cell-8 which was immersed in a high-pressure autoclave-9, a liquid (spindle oil) thermostat (0.09 m3) − 10, the system for create and measure pressure (hydrostatic press-4 and manometer-14, MP-2500), and four (3-main and 1 regulating) heaters and a thermo-regulator. The thermostat temperature was controlled with uncertainty of 0.02 °C. The thermal conductivity cell consisted of two coaxial chromium-plated cylinders (inner-1 and outer-3). The length of the inner cylinder was 199.890 ± 0.001 mm and its diameter was 19.989 ± 0.01 mm. The ID of the outer cylinder was 20.963 ± 0.005 mm. The cell constant A was calculated using a geometrical constant of the cell as d + ∆d 2   l + ∆l , A−1 = 2π  + 1 4δ T   ln ( d2 d1 )

(5.18)

where d1 is the diameter of the inner cylinder; d2 is the inner diameter of the outer cylinder; l is the length of the inner cylinder; ∆l the changes of the cylinder length; ∆d the changes of the cylinder diameter; d T the gap between end face of the inner cylinder and end covers. The value of A

calculated by Equation (5.18) was found to be equal to 0.0364166 m−1. The value of A was also calculated by using the dielectrical constants of vacuum (ev) and air (ea) and electrical capacity C of the gap between cylinders as A−1 =

εV ε a . C

(5.19)

The value of A calculated with Equation (5.19) is 0.0362582 m−1. The uncertainty in thermal conductivity measurements for this instrument is within 1.3 to 2.2%. Yata et al. (1979a, 1986, 1990) used a vertical coaxialcylinder instrument with guard cylinders to measure the thermal conductivity of pure water and aqueous CH3OH and C3H4F4O solutions at high temperatures. The details of the construction of the thermal conductivity cell are given by Yata et al. (1979a). Schematic representation of the apparatus and thermal conductivity cell is given in Fig. 5.6. The gap between the inner and outer cylinders is 0.9 mm. Increasing the width of the gap results in an increase in the accuracy of the measurements, but at the same time, convection in the fluid layer is apt to occur. The geometrical dimensions of the cell are: OD of inner cylinder is 19.170 ± 0.0015 mm; length of the inner cylinder is 120.000 ±

Thermal Conductivity

12

11

6

1

9 14

8

16

2

10

3 4 5 7 17

15

239

Figure 5.5 Experimental apparatus (a) and experimental cell (b) for the thermal conductivity measurements of aqueous solutions at high temperatures, developed by Safronov et al. (1990) and Grigor’ev (1995, 2003) (Reproduced from PhD thesis with permission from Institute of Geothermal Problems (IPG DSC RAS)). (a): 1: glass vessel with sample; 2: valve; 3: manometer; 4: hydraulic press; 5, 6, 7: valves; 8: thermal conductivity cell; 9: high pressure autoclave; 10: liquid thermostat; 11: vacuum-gauge; 12: glass vessel with sample; 13: vacuum pump; 14: deadweight pressure gauge (manometer MP-2500); 15: separating vessel; 16: manometer. (b): 1: inner cylinder; 2: heater; 3: outer cylinder; 4: centering body; 5: screws; 6: flat covers; 7: filling hole; 8: textolite standoff insulator; 9: autoclave; 10: scrolls; 11: jointing ring.

13 (a) 11

10

4 5

6

1 2 9

3

8 7

6

(b)

0.002 mm; ID of the outer cylinder is 21.002 ± 0.0015 mm; OD of the outer cylinder is 33.311 ± 0.002 mm; and the length of the outer cylinder is 199.780 ± 0.002 mm. In the cell heat is generated in the inner heater 5. The inner cylinder-1 and the guard cylinders −3 and −4 are separated by thin mica spacers-9, and connected by six alumina pieces10. The inner cylinder is connected to the outer cylinder-2 by six alumina pins-12 and brass screws-11. At the top and bottom of the cell the alumina insulators −7 and −8 are fitted to the outer cylinder with a brass screw −13. Eleven sheathed copper–constantan thermocouples −6 are employed for the temperature measurements. After correcting for radiation and minimizing convective heat loss, the uncertainty in the heat transferred was about 0.2%. Equivalently, the uncertainty in the experimental temperature rise was estimated to be less than 0.6%. The uncertainty in the geometrical constant A, was estimated to be

1.1% and thus the total uncertainty in thermal conductivity measurements was less than 2%. 5.2.3 Transient hot-wire technique Only two investigators (DiGuilio et al., 1990; Bleazard et al., 1994; and Bleazard and Teja, 1995) employed the transient hot-wire technique for the measurement of the thermal conductivity of aqueous solutions above 200 °C. Hence this technique will only be briefly described here. 5.2.3.1 Theoretical A transient thermal conductivity measurement is one in which a time-dependent perturbation, in the form of a heat flux, is applied to a fluid initially at equilibrium. The thermal conductivity is obtained from an appropriate working

240

Hydrothermal Experimental Data

7 9 8

case, it can easily be shown that for a cylindrical wire of radius ro, and for small values of the term (r2/4at), ∆T ( ro , t ) =

6 4 3 2 1

5

(a) 15 14 7 3 5 6

1 2 10

9 4

12 11 13

8 (b)

Figure 5.6 Thermal conductivity apparatus and coaxial-cylinder cell, developed by Yata et al. (1979a). (a): 1: high pressure vessel; 2: fluid separator; 3: heater; 4: heat insulator; 5: support table for bath; 6: heat transfer fluid (water or glycerin); 7: screw propeller; 8: standard resistance thermometer; 9: thermocouples and heaters. (b): 1: inner cylinder; 2: outer cylinder; 3: upper guard cylinder; 4: lower guard cylinder; 5: inner heater; 6: thermocouples; 7: upper alumina insulator; 8: lower alumina insulator; 9: mica spacer; 10: alumina piece; 11: brass screw; 12: alumina pin; 13: brass screw; 14: compensative heater; 15: top closure of high pressure vessel.

equation relating the observed response of the temperature of the fluid to the perturbation. In an actual instrument the perturbing heat flux is applied by means of electrical dissipation in a thin, cylindrical wire as a step function. In this case the wire is itself used as the thermometer to monitor the temperature rise of the fluid at its interface. In such a

q 4πλ

2   4 at   ro   + ln      r 2γ   4 at  +
 o

(5.20)

where ∆T(ro, t) is the transient temperature rise of the fluid at the wire surface, l and a the thermal conductivity and thermal diffusivity of the fluid, respectively, q the heat input power per unit length, and g = 0.577216 is the EulerMascheroni constant. In the ideal model, Equation (5.20) describes the temperature rise of the wire in contact with the fluid at its surface. In practice a real instrument departs from the ideal model in a number of respects and analytical corrections have been developed (Healy et al., 1976; Assael et al., 1991) for the departure of a practical instrument from the ideal one. The two major additive corrections to Equation (5.20) that need to be applied in practice are: (a) the heat capacity correction, significant only at short experimental times; and (b) the outer boundary correction, significant only at long experimental times. The application of this methodology to liquids and gases at moderate pressures has provided many reliable thermalconductivity data over the last two decades. Unfortunately, the analytical corrections proposed by Healy et al. (1976) proved to be inadequate (Assael et al., 1998) for the description of experiments in the gas phase at low densities, where fluids exhibit exceedingly high thermal-diffusivity values. To overcome these difficulties, a numerical finite element method was proposed by Assael et al. (1998), in order to solve the complete set of energy-conservation equations that describe the heat-transfer experimental processes. The choice of this particular numerical method was dictated by the high accuracy the method exhibits in computational heat transfer problems. Hence, two coupled partial differential energy-conservation equations, one for the wire and one for the fluid, with appropriate boundary conditions, were solved. In practice, experimental means are employed to yield a finite segment of a wire that behaves as if it were part of an infinite wire. This allows the numerical solution of the differential equations to be used iteratively to determine the thermal conductivity and diffusivity of the fluid that yields the best match between the experimental and calculated temperature rise of this finite segment of wire. 5.2.3.2 Experimental Since the technique was first employed in 1931 (Stahlane and Pyk, 1931) to measure the thermal conductivity of powders, there have been significant improvements in the practical realization of the technique. In modern instruments the wire sensor acts both as the heat source and as a thermometer. Rapid development of analogue and digital equipment as well as of computer-driven data-acquisition systems, have meant that precise measurements of transient electrical signals can be made quickly. Thus, it has become possible to measure the resistance change taking place in the hot wire as a consequence of its temperature rise with a

Thermal Conductivity

precision better than 0.1%. Furthermore, instead of a single wire, two wires identical in all respects except for length are employed (see Figure 5.7). This allows a practical and automatic means of compensating for the finite length of the wires. For electrically insulating fluids, platinum has usually been employed as the heating wire and sensing thermometer because of its chemical stability and resistance/temperature characteristics. In order to allow measurements of electrically conducting fluids, tantalum wires are often employed, because upon electrolytic oxidation, tantalum forms tantalum pentoxide on its surface, which is an electrical insulator. Together with a more systematic approach to the theory it has been possible to provide instruments with an uncertainty of 0.5%. 5.2.3.3 Working equation and uncertainty In the modern transient hot-wire instruments, operated for zero time to 5 s, with a resolution of 20 µs, the analytic working equation has been substituted by the FEM solution of the two coupled differential energy-conservation equations already discussed previously. As discussed above, in the modern instruments, composed of two-wires coupled to a fast bridge, the uncertainty attained is of the order of 0.5%. A transient hot-wire instrument was employed by DiGuilio et al. (1990), Bleazard et al. (1994), and Bleazard

241

and Teja (1995) to measure the thermal conductivity of aqueous solutions of LiBr at temperatures up to 493 K and up to the saturation pressure. The thermal conductivity cell constructed by Bleazard et al. (1994) is schematically shown in Figure 5.8. The thermal conductivity cell consisted of a fine pyrex (or borosilicate glass) capillary filled with liquid mercury (or gallium) to serve as the insulated hot-wire from the liquid. The hot-wire cell was made by forming a U shaped tube of Pyrex (2 mm ID by 4 mm OD). A tungsten wire, inserted into each end of the U tube, served as electrical leads. The other parts of the apparatus were a Wheatstone bridge, a data acquisition system, and a constant temperature bath. The mercury thread acted as the resistance in one arm of the Wheatstone bridge. Thermal conductivity measurements were made by placing the pyrex cell in a pressure vessel filled with the H2O+LiBr solution. The temperature rise was determined from the increased resistance of the wire. The uncertainty of the measurements estimated by the authors was 2%. Since however, only a one-wire arrangement, contained within a glass, was employed, it is most unlikely that this is a reasonable estimate. 5.2.4 Conclusion In this section the different techniques (parallel-plate, coaxial-cylinder, and transient hot-wire) employed to measure the thermal conductivity of aqueous solutions at high temperatures were discussed. In general, the uncertainty of all the available experimental thermal conductivity data derived with the first two methods should be within 1

Tungsten Wire Support for U Tube Mercury Filled Pyrex Capillary Glass Sleeve

Figure 5.7 Wires with weights arrangement, developed by Assael et al. (1998) for the measurement of electrically conducting liquids.

Glass Shielded Thermocouple

Figure 5.8 Liquid metal hot-wire thermal conductivity cell and accompanying pressure vessel, developed by Bleazard et al. (1994) (AICHE Symp. Ser. 298, 23–28. Reproduced by permission of the American Institute of Chemical Engineers AICHE).

242

Hydrothermal Experimental Data

to 2%. The data obtained with the transient hot-wire technique are expected to be of worse uncertainty.

and concentration dependency of thermal conductivity of aqueous solutions.

5.3 AVAILABLE EXPERIMENTAL DATA

5.3.1 Temperature dependence

The summary of the available thermal conductivity data sets of aqueous solutions at high temperatures (above 200 °C) are given in Table 5.1. In this table, the first author and the year published are given together with the method employed, the uncertainty claimed by the authors, and the temperature, pressure, and concentration ranges. Table 5.1 provides the most useful collection of all available thermal conductivity data at high temperatures (above 200 °C) at the present time. The Appendix includes only the data above 200 °C, although original sources also contain the data below 200 °C. A reference code assigned to each measurement set refers the reader to the original data set in the Appendix for easy access. To our knowledge this is the best and most comprehensive compilation of all available thermal conductivity data for aqueous solutions at high temperatures at the present time. All tables are accompanied by additional detailed information regarding experimental methods and their uncertainties. Table 5.1 does not include papers reporting aqueous solutions’ thermal conductivity values at temperatures below 200 °C. Some experimental thermal conductivity data for several selected aqueous electrolyte solutions are given in Figures 5.9 to 5.11. These figures show the typical temperature, pressure,

The thermal conductivity of aqueous solutions at constant pressure and concentration increases with temperature up to a maximum temperature, between 405 and 437 K (depending on pressure and concentration), and then decreases at higher temperatures like pure water (DiGuilio et al., 1990; Abdulagatov and Magomedov, 1994, 1995a,b, 1997a,b, 1998, 1999a,b, 2000a,b, 2001, 2003/2004; Bleazard et al., 1994; Bleazard and Teja, 1995; Abdulagatov et al., 2004a,b). For pure water this maximum occurs at temperatures between 409 and 421 K as pressure changes between 20 and 60 MPa. The maximum in the values of the thermal conductivity almost linearly increases with pressure, while monotonically decreases with concentration (see for example, Abdulagatov and Magomedov, 1994, 1995a,b, 1997a,b, 1998, 1999a,b, 2000a,b, 2001; Abdulagatov et al., 2004a,b). The observed temperature maximum in the values of the thermal conductivity indicates that the temperature coefficient aT = (∂ ln l / ∂T)PX has changed from positive to negative for all of the isobars and isopleths. The temperature coefficients of thermal conductivity aT for some selected aqueous salt solutions (BaI2 and CaI2) together with pure water values are presented in Figure 5.12. The values of temperature coefficient aT is monotonically decreased with

665

λ/mW·m–1·K–1

680 660

645

640

625

620

x = 5 wt %

600 580 280

605

H2O + NaCl

340

400 T/ K

x = 20 wt %

585

460

520

565 280

340

(a)

520

640

645

620

625 605

600

H2O + KCl

H2O + KCl x = 15 wt %

x = 10 wt % 580

585 565 280

460

400 T/ K

660

665

λ/mW·m–1·K–1

H2O + NaCl

340

400 T/ K

460

520

560 280 (b)

340

400 T/ K

460

520

Figure 5.9 Measured values of thermal conductivity l of aqueous electrolyte solutions as a function of temperature T at constant pressures and concentrations reported by various authors. (a) NaCl(aq): 䊉, Abdulagatov and Magomedov (1994); 䊊, Ozbek and Phillips (1980); ∆, Ramires and Nieto de Castro (1994); ×, Grigor’ev (1995); 䊏, Eldarov (1986); 䉱, Assael et al. (1989); ⵧ, Ganiev et al. (1990); +, Tufeu et al. (1966). (b) KCl(aq): 䊉, Abdulagatov and Magomedov (1994); 䊊, Pepinov and Guseynov (1991b); 䉱, Assael et al. (1989); ×, Safronov et al. (1990); ∆, Davis et al. (1971).

λ/W·m–1·K–1

0.692

H2O+NaBr T=373.15 K

H2O+KBr T=373.15 K

0.71

0.682 0.69 0.672 0.67 0.662

0.652 0

0.65 10

30 20 P/ MPa

40

0

20

40 60 P/ MPa

80

100

Figure 5.10 Measured values of thermal conductivity of aqueous electrolyte solutions as a function of pressure at constant temperatures and concentrations reported in the literature. (a) NaBr(aq): 䊉, Abdulagatov et al. (2004b); 䊊, Eldarov (1986); 䊏, Magomedov (1992); ⵧ, Rastorguev et al. (1986); ×, Aseyev (1998); pure water (IAPWS standard, Kestin et al., 1984). (b) KBr(aq): 䊉, Abdulagatov et al. (2004b); 䊊, Eldarov (1986); 䊏, Abdulagatov and Magomedov (2001); ⵧ, Safronov et al. (1990); ∆, Abdullaev et al. (1981); (–·–·–), pure water (IAPWS standard, Kestin et al., 1984).

0.67

H2O+NaBr

0.66

H2O+KBr T=453.15 K

T=453.15 K λ/W·m-1·K–1

0.64 0.64 0.61

0.62

0.58

0.60

0.55

0.58 0.56 0

10

20 30 x/ mass %

0.52 0

40

10

20 30 x/ mass %

40

50

Figure 5.11 Measured values of thermal conductivity of aqueous electrolyte solutions as a function of concentration along selected isotherms and isobars reported in the literature. NaBr(aq): 䊉, Abdulagatov et al. (2004b); 䊊, Eldarov (1986); 䊏, Magomedov (1992); ⵧ, Rastorguev et al. (1986); ×, Aseyev (1998). KBr(aq): 䊉, Abdulagatov et al. (2004b); 䊊, Eldarov (1986); 䊏, Abdulagatov and Magomedov (2001); ⵧ, Safronov et al. (1990); ×, Aseyev (1998). x=20 wt %

P=100 MPa 1.03

2.6

CaI2 H2O BaI2 αP/GPa–1

αT/K–1

1.6

0.6

0.83

0.73

-0.4

-1.4 280

BaI2 CaI2 ZnI2 H2O

0.93

0.63

330

380 T/ K

430

480

0.53 280

330

380 T/ K

430

480

Figure 5.12 The temperature, aT = (∂ ln l / ∂T)PX, and pressure, aP = (∂ ln l / ∂P)TX, coefficients of BaI2(aq), ZnI2(aq), and CaI2(aq) solutions and pure water as a function of temperature at pressure 100 MPa and concentration of 20 wt % calculated with Equation 5.25.

244

Hydrothermal Experimental Data

temperature and increased with pressure. At low temperatures (T ≈ 293 K), the temperature coefficient aT is almost independent of pressure and composition. Due to lack of theoretical background on the temperature dependency of the thermal conductivity of aqueous salt solutions, empirical and semi-empirical correlations and predictive schemes are usually employed in the literature. A number of such correlations and predictive schemes have been developed to calculate the thermal conductivity of aqueous salt solutions as a function of temperature (see for example, Riedel, 1951; McLaughlin, 1964; Chiquillo, 1967; Venart and Mani, 1971; Bibik et al., 1975; White et al., 1975; Yusufova et al., 1975a; Krönert and Schuberthy, 1977; Vargaftik et al., 1978; Ozbek and Pillips, 1980; Dietz et al., 1981; Alloush et al., 1982; Nagasaka et al., 1983; Matsunaga and Nagashima, 1983; Kawamata et al., 1988; Assael et al. 1989; Nagasaka et al., 1989; DiGuilio et al., 1990; DiGuilio and Teja, 1992; Ramires and Nieto de Castro, 1994, 2000). A review of the available correlations and predictive schemes for the thermal conductivity of aqueous salt solutions at low temperatures and concentrations has been reported by Horvath (1985). Hence, in this section, only some typical correlative schemes will be presented. For the calculation of thermal conductivity of an aqueous salt solution, l(t, x), Yusufova et al. (1975a) and Pepinov and Guseynov (1991b, 1993) proposed the following equation

 λ  = a + bm + ct   a + ct λw

where a = 0.561 Wm−1K−1 is the ‘absolute’ value of the thermal conductivity of pure water at 273.15 K, t is the temperature in °C, m is the concentration in molality, b = −0.051, and c = −0.00132. Kawamata et al. (1988) proposed the following equation

λ (T , P, x ) = λ0(T , x ) [1 + Φ (T , x ) P ],

(5.24)

where Φ(T, x) represents the pressure coefficient of the thermal conductivity, and l0(T, x) is the thermal conductivity extrapolated to zero pressure (P → 0). The temperature and concentration dependence of l0(T, x) and Φ(T, x) are expressed in polynomial form. This scheme reproduced their data with an uncertainty of 0.35%. Abdulagatov and Magomedov (1997a,b, 1998, 1999a,b, 2000a,b, 2001, 2003/2004) correlated the experimental thermal conductivity data of 40 aqueous electrolyte solutions as a function of the pressure, the temperature, and the concentration by a polynomial of the form

λ ( P , T , x ) = λ w ( P , T ) [1 − A( x + 2 × 10 −4 x 3 )] − 2 × 10 −8 PTx

(5.25)

λ w( P , T ) = 7 × 10 −8 T 3 − 1.511 × 10 −5 T 2 + 8.802 × 10 −3 T − 0.8624 + 1.6 × 10 −6 PT

λ (t , x) = λ w(t )[1− ( a0 + at 1 + a2t ) x −

(5.23)

(5.26)

2

( c0 + ct1 + c2t 2 ) x2 ]

(5.21)

where lw(t) is the thermal conductivity of water, x is the concentration in mass.%, and t is the temperature in °C. This equation reproduced the experimental data with an accuracy of 2%. Equation (5.21) has been used for the correlation of the thermal conductivity of aqueous NaCl, KCl, and LiCl solutions. In the restricted temperature range from 293 to 613 K and concentrations between 0 and 20 mass.%, and at pressures slightly above saturation, the above equation represented the experimental data with an uncertainty of 0.6%. To represent their thermal conductivity measurements of aqueous NaCl and KCl solutions with an uncertainty of 0.5%, Ramires and Nieto de Castro (1994, 2000) employed a polynomial form in T and m, as 2

2

λ (T , m) = ∑ ∑ aij ∆T j mi,

(5.22)

i =0 j =0

where ∆T = T − 273.15, m is the molality of the solution, and T is temperature in K. White et al. (1975) proposed a relation between the ratio of thermal conductivity, l, of the solution and the thermal conductivity of water, lw, as a function of the temperature T and the molality m for aqueous NaCl solutions at atmospheric pressure, as

where A is an adjustable parameter. The values of parameter A for 40 aqueous salt solutions are given in Magomedov (1992, 1995, 2001). The above scheme successfully correlated the experimental data in the temperature range from 273 to 473 K, pressures from 0.1 MPa to 100 MPa, and concentrations between 0 mass.% and 25 mass.%, with an uncertainty of up to 0.45%. 5.3.2 Pressure dependence The thermal conductivity of aqueous solutions increases almost linearly with pressure, at constant temperature and concentration, but not with the same slope as that of pure water – see Figure 5.10 – (DiGuilio et al., 1990; DiGuilio and Teja, 1992; Bleazard et al., 1994; Bleazard and Teja, 1995; Abdulagatov and Magomedov, 1994, 1995a,b, 1997a,b, 1998, 1999a,b, 2000a,b, 2001; Abdulagatov et al., 2004a,b). At high pressures, 40 MPa, and high concentrations, 20 mass.%, the absolute values of thermal conductivity of water are higher, by about 8–12%, than those of the aqueous salt solutions. At low pressures, 10 MPa, and low concentrations, 10 mass.%, the differences between pure water and aqueous salt solution thermal conductivities are about 5 to 8%. The pressure coefficient of the thermal conductivity, aP = (∂ ln l /∂P)Tx, as a function of the temperature at 100 MPa and a composition of 20 mass.%, for aqueous solutions of BaI2, CaI2, and ZnI2 and pure water is shown in Figure 5.12. The pressure coefficient is always positive and monotoni-

Thermal Conductivity

cally increasing with temperature and decreasing with pressure. The absolute values of the pressure coefficient aP for pure water are about 1.3 times higher than those of the aqueous solutions, while difference between various solutions is very small (within 1.5%). Based on the aforementioned discussion, DiGuilio et al. (1990), DiGuilio and Teja (1992), Bleazard et al. (1994), and Bleazard and Teja (1995), proposed a simple scheme for the prediction of the thermal conductivity of aqueous solutions at high pressures. According to this scheme, the thermal conductivity of the aqueous solution at a high pressure is obtained by the equivalent one at atmospheric pressure by multiplying it with the ratio of the thermal conductivity of water at that high pressure over its value at atmospheric pressure. This idea produced values that deviated by up to 2% from the experimental data. 5.3.3 Concentration dependence The concentration dependence of the experimental thermal conductivities for some selected aqueous solutions along various isotherms and isobars is shown in Figure 5.11. As the figures show, the thermal conductivity of most solutions monotonically decreases with composition. Furthermore, the composition dependence of the thermal conductivity exhibits a small curvature, especially at high concentrations (x > 20 mass.%). Some empirical equations employed for the correlation of the thermal conductivity with concentration will be briefly presented here. Alloush et al. (1982) represented, with an uncertainty of 0.8%, the concentration dependence of aqueous LiBr solutions by an equation of the form

245

stressed, however, that the conclusions derived here are only based on a preliminary comparison, and should be viewed accordingly. Below the discrepancies between different datasets were examined statistically in terms of the absolute 100 N average deviation, AAD = ∑ ( λ exp − λ cal ) λ exp . N i =1 i H2O + NaCl: Seven datasets were found, referring to five research groups (Yusufova et al., 1975a; El’darov, 1986; Ganiev et al., 1990; Pepinov, 1992; Magomedov, 1992, 1993, 1989b, 1995; Abdulagatov and Magomedov, 1994; Abdullaev et al., 1998a; Abdulagatov et al., 2004a). The differences between most of the reported data are lie between 0.4 and 1.7%. Hence, it seems that the deviations of these datasets are within the quoted mutual uncertainty of each investigator. H2O + KCl: Five datasets were found, referring to three research groups (Safronov et al., 1990; Pepinov and Guseynov, 1991a,b; 1992; 1993; Pepinov, 1992; Magomedov, 1993, 1989b, 1995; Abdulagatov and Magomedov, 1994). At low pressure, the deviations between the datasets are within 0.4 and 0.7%. Up to 60 MPa, excellent agreement, within 0.3%, is found between the data of Safronov et al. (1990) and Abdulagatov and Magomedov (1994). However, at pressures above 60 MPa the deviations increase up to 3%. H2O + Sr(NO3)2: Two datasets were found (Abdulagatov et al., 1999a and Abdulagatov et al., 2004a), but published from the same research group. Hence as expected the agreement is very good (deviations within 0.9%).

(5.27)

H2O + NaBr: Three datasets were found, referring to three research groups (Eldarov, 1986; Magomedov, 1992; Abdulagatov et al., 2004b). All data agree within 0.8%.

where x is the concentration in mass fraction. A polynomial function of temperature and concentration was also proposed by DiGuilio et al. (1990) for the same salt solution. Chiquillo (1967) proposed the following equation for the concentration dependence of the thermal conductivity of aqueous solutions

H2O + KBr: Six datasets were found, referring to four research groups (Eldarov, 1980; Magomedov, 1989a; Safronov et al., 1990; Magomedov, 1992; Abdulagatov and Magomedov, 2001; Abdulagatov et al., 2004b). In general, the data by all aforementioned authors agree within 2%.

λ (T , x ) = a0 + a1 x + a2 x + b1T , 2

λ = λ w (1 + A1 x + A2 x ) . 2

(5.28)

In this equation, Ai were adjustable parameters tabulated for several electrolyte solutions. A very similar relation was also proposed by Losenicky (1969) and Zaytsev and Aseyev (1992). 5.4 DISCUSSION OF EXPERIMENTAL DATA The comparison of the datasets given in Table 5.1 was difficult due to the temperature, pressure, and concentration differences between the measurements. Therefore, a regression analysis based on the schemes discussed in Section 5.3 was employed for the temperature and composition dependence for each isobar. In the analysis that follows, a preliminary comparison is given between the various datasets, aiming to help the reader choose which values to use. It should be

H2O + KI: Three datasets were found, referring to three research groups (Eldarov, 1980; Safronov et al., 1990; Abdulagatov and Magomedov, 2001). The measurements of Safronov et al. (1990) are in good agreement (within 1.0%) with the data reported by Abdulagatov and Magomedov (2001) in the overlapping range. In general, all of the available datasets are agreed within 2%. H2O + CdCl2 and H2O + CdBr2: Two datasets were found, referring to two research groups (Eldarov, 1980; Abdulagatov and Magomedov, 1997a). The maximum deviation between the datasets is 0.5%. H2O + LiCl: Two datasets were found, referring to two research groups (Pepinov and Guseynov, 1992, 1993; Abdulagatov and Magomedov, 1997b). Deviations up to 0.73% are observed between the datasets at low temperatures, rising up to 1.9% at temperatures above 473 K and concentrations at 20 mass.%.

246

Hydrothermal Experimental Data

H2O + LiBr: Two datasets were found, referring to two research groups (DiGuilio, 1992; Bleazard, 1994, Abdulagatov, 1997b). The deviations between these datasets are within 3%. Although at high concentrations (x > 25 mass. %) the agreement is very good, about 1%, at low compositions (x < 25 mass.%) the deviations rise up to 3%. H2O + CaCl2: Three datasets were found, referring to two research groups (Magomedov, 1989a; Pepinov, 1992; Abdulagatov and Magomedov, 1995a). The agreement between the datasets is excellent (about 0.2–0.5%). H2O + MgCl2: Five datasets were found, referring to three research groups (Magomedov, 1990, 1989a, 1995; Pepinov, 1992; Abdulagatov and Magomedov, 1995a; Mamedov, 2000). Deviation up to 1% is found between the data of Mamedov (2000) and the values reported by Abdulagatov and Magomedov (1995a) at low concentrations, while at high concentrations (20 mass.%) deviations rise up to 6%. H2O + NaI: Three datasets were found, referring to two research groups (Eldarov, 1986; Magomedov, 1994; Abdulagatov and Magomedov, 1995b). The data reported by these groups are agree within 0.5% at pressures up to 30 MPa and temperatures between 293 and 473 K. H2O + CaBr2: Two datasets were found, referring to two research groups (Eldarov, 1980; Magomedov, 1992, 1995). The agreement between the datasets is within 1.7–3.3% depending on temperature, pressure, and concentration ranges. H2O + KNO3 and H2O + NaNO3: Two datasets were found, referring to two research groups (Abdullaev, 1988; Magomedov, 1992). The deviations up to 1% are found between the datasets at low concentration and up to 2.5% at high concentrations (20 mass.%) at temperatures above 473 K, for aqueous solutions of KNO3, while for aqueous solutions of NaNO3, deviations are within 1–2% at low concentrations, rising to 4% at high concentrations (20 mass.%) and high temperatures (above 473 K).

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6

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

Marc J. Assael Chemical Engineering Department, Aristotle University, Thessaloniki 54124, Greece

6.1 INTRODUCTION For fluids that obey Newton’s Law, the dynamic viscosity, h, of a fluid is a measure of its tendency to dissipate energy when it is disturbed from equilibrium by a velocity field v. The dynamic viscosity is thus defined by the relationship  ∂v ∂v j 2 ∂vk  σ ij = − Pδ ij + η  i + − δ ij .  ∂x j ∂xi 3 ∂xk 

(6.1)

In this equation, sij are the instantaneous stresses, P, the pressure and dij is the Kronecker symbol. The viscosity depends on the thermodynamic state of the fluid and it is usually specified by the pairs of variables (T, P) or (T, r) for a pure fluid (where T is the temperature and r the density), to which must be added a composition dependence in the case of mixtures. The internationally agreed standard for viscosity, ISO/TR 3666 : 1998, is the viscosity of water at 20 °C and atmospheric pressure (0.101 325 MPa), and its approved value is

η = 1.0016 mPa⋅s.

(6.2)

This value has an estimated relative uncertainty of 0.17%. This is based on the value of 1.0019 mPa·s reported by Swindells in 1952 (Swindells et al., 1952), which was also the basis of ISO/TR 3666 : 1977. The small difference in value is due to the difference between the ITS-48 and ITS90 temperature scales. The temperature dependence of the viscosity of water at atmospheric pressure in the temperature range 0.01–100 °C, is given by the following recommended correlation (Kestin et al., 1978b) log

η (θ ) θ = {1.2378 − 1.303 ×10 −3θ + η ( 20°C ) 116 − θ

3.06 × 10 −6 θ 2 + 2.55 × 10 −8θ 3 } Hydrothermal Experimental Data Edited by V.M. Valyashko © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-09465-5

(6.3)

where q = 20 − t/ °C. The estimated uncertainty of Equation (6.3) is better than 0.1%. In order to calculate of the viscosity of pure water at high temperatures (from 251.17 to 1275 K) and at high pressures (up to 1000 MPa) the IAPWS formulation (Kestin et al., 1984a) can be recommended. Tables (skeleton tables) based on the IAPWS formulation with only minor changes from a 1985 IAPWS document were published as the appendices to the Proceedings of the 12th and 13th International Conferences on the Properties of Water and Steam (0–800 °C and 0.1–100 MPa) (White et al., 1995; Tremaine et al., 2000). Aqueous solutions at high temperatures (above 200 °C) and at high pressure, play a major role in both natural and industrial processes. The viscosity of aqueous electrolyte solutions is of fundamental importance to the understanding of the various physico-chemical processes occurring in the chemical industry and in the natural environment (Pitzer, 1993; Gupta and Olson, 2003; Harvey and Bellows, 1997; Barthel et al., 1999). The dominant solutes in such processes are often simple electrolytes such as NaCl, CaCl2, MgCl2, and Na2SO4 with lesser amounts of potassium salt, carbonates, borates, etc. Such aqueous solutions are usually present at high temperature and high pressure in deep geological formations (underground water). They also arise in steam-power generation, geothermal power plants (development and utilization of geothermal and ocean thermal energy), hydrothermal synthesis of single crystals and powders (Laudise, 1970; Balitsky and Lisitsina, 1981; Suchanek et al., 2004), seawater desalination processes, and other industrial hydrothermal operations at high temperatures and high pressures (Byrappa and Yoshimura, 2001; Feng et al., 2003). The H2O + NaCl system is very important in many geological and industrial processes. Theoretical modeling of the viscosity and thermal conductivity of this system serves as an example for other ionic systems of 1 : 1 charge-type

Azizov, 1996 Azizov & Akhundov, 1997 Azizov, 1999 Akhundov et al, 1991a Akhmedova-Azizova, 2006 Bleazard, Sun and Teja, 1996 Abaszade et al, 1971 Sun and Teja, 2004a Sun and Teja, 2004a Sun and Teja, 2004b Sun and Teja, 2004a Pepinov et al, 1988 Pepinov, 1992 Abdulagatov & Azizov, 2006b Zeynalova et al, 1991 Abdulagatov et al, 2004 Akhmedova-Azizova, 2006 Rivkin et al, 1986 Abdulagatov and Azizov, 2008 Semenyuk et al, 1977a Feodorov, 1982 Kestin et al, 1981a Pepinov et al, 1986 Pepinov, 1992 Melikov, 1999 Melikov, 2000 Guseynov et al, 1990 Mashovets et al, 1971 Puchkov & Sargaev, 1973 Azizov, 1999 Mashovets et al, 1971 Mashovets et al, 1973 Puchkov & Sargaev, 1974 Abdulagatov & Azizov, 2005b Abdullaev et al, 1990 Lee et al, 1990 Abdullaev et al, 1991a Semenyuk et al, 1977a Feodorov, 1982 Pepinov et al, 1989 Pepinov, 1992 Akhundov et al, 1990a Abdullaev, 1991 Abdullaev et al, 1991a Abdulagatov et al, 2006a Abdullaev et al, 1991a Abdullaev et al, 1991b Abdulagatov & Azizov, 2005d

BaCl2

LiI

LiCl

LiBr

K2SO4

KOH

KF KNO3

KCl+CaCl2+MgCl2

H3BO3 KBr KCl

Ca(NO3)2

C2H4O2 (acetic acid) C2H6O (ethanol) C3H8O2 (propylene glycol) C6H14O3 (dipropylene glycol) C7H6O2 (benzoic acid) C9H20O4 (tripropylene glycol) CaCl2

Ba(NO3)2

First authors, year

293/440–575 298/473–598 298/462–573 298/473; 573 323/498–623 298/446–577 373/473–623 298/473 298/473–623

0.1–2.0 mol·kg−1 5–40 mass % 0.32–6.1 mol·kg−1 0.68–4.06 mol·kg−1 0.5–4 mass % 0.12–2.23 mol·kg−1 5–25 mass % 1–4.6 mol·kg−1 0–20 mass %

vi-CaCl2-2.1 vi-Ca(NO3)2-1.1 vi-Ca(NO3)2-2.1; 2.2 vi-Ca(NO3)2-3.1 vi-H3BO3-1.1 vi-KBr-1.1 vi-KCl-1.1 vi-KCl-2.1 vi-KCl-3.1

298/473–598 298/448–598 298/447–574 298/448–598 293/444–525

1–20 mass% 5; 10; 20 mass % 5–41 mass % 0.05–16.4 mol·kg−1 5–40 mass % 0.08–3.09 mol·kg−1

vi-LiCl-2.1 vi-LiCl-3.1 vi-LiCl-4.1 vi-LiCl-5.1 vi-LiI-1.1; 1.2 vi-LiI-2.1

298/473–623

9:3:3 mass % 1.8 : 0.6 : 0.6 mass % 5–40 mass % 2.0 mol·kg−1 0.5–2.5 mol·kg−1 2–8 mass % 10 mol·kg−1 0–20 mol·kg−1 0.18; 0.37; 0.64 mol·kg−1 0.066–0.407 mol·kg−1 6–20 mass % 45–65 mass % 6–40 mass % 5–40 mass %

vi-K,Ca,Mg/Cl-1.1 vi-K,Ca,Mg/Cl-2.1 vi-KF-1.1 vi-KNO3-1.1 vi-KNO3-2.1 vi-KNO3-3.1 vi-KOH-1.1 vi-KOH-2.1 vi-K2SO4-1.1 vi-K2SO4-2.1 vi-LiBr-1.1 vi-LiBr-2.1 vi-LiBr-3.1 vi-LiCl-1.1

298/448–573 298/448–573 298/473–598 286/473 273/448; 473 298/473–573 299/475–548 273/473–548 298/448; 473 298/447–575 298/473–598 313/453–473 298/448–598 373/473–623

298/473–573 298/473–598 298/473; 573 294/425–460 323/473 299/410–450 298/421–458 381/427–456 298/428–450 298/473–623

2; 4; 6; 8 mass % 0.5–8.0 mass % 0.16–0.33 mol·kg−1 12–100 mass % 10–90 mass % 0.25–0.75 mol.fr. 0.25–0.75 mol.fr. 0.05–1.0 mol.fr. 0.25–0.75 mol.fr. 1–20 mass %

vi-BaCl2-2.1 vi-Ba(NO3)2-1.1 vi-Ba(NO3)2-2.1 vi-C2H4O2-1.1 vi-C2H6O-1.1 vi-C3H8O2-1.1 vi-C6H14O3-1.1 vi-C7H6O2-1.1 vi-C9H20O4-1.1 vi-CaCl2-1.1

293/473–573

Temperature (K)

0.097–0.895 mol·kg−1

Concentration

vi-BaCl2-1.1

Reference Code for Appendix*

Summary of experimental viscosity data for aqueous solutions

Solute

Table 6.1

0.1/10; 40

0.1–40 0.1–40

0.1/10–40 0.1/5–40

2–30

2–30 2–30 0.1/10–40 sat. sat. 10; 30 sat. sat. sat. 0.1/10–30 0.1/10–40 1.38 0.1/6–40 10–150

0.1/3–30 2–30

0.1/10–60 0.1/10–40 0.1/5–40 20 5–30 0.1/10; 30 10–150

10; 30 0.1/10–40 20 3 1/20–120 0.1–2.2 0.1–2.2 ~ 20 0.1–2.2 2–30

10, 20, 30

Pressure (MPa)

CF

CF CF

CF CF

CF

FB FB CF CF CF CF CF CF CF CF CF CF CF CF

OD CF

CF CF CF CF CF CF CF

CF CF CF CF QV CF CF CF CF CF

CF

Methoda

1.6

1.6 1.2

1.2 1.5

1.0

4.0 4.0 1.5 1.5 1.5 1.5–1.7 1.5 1.5 1.5 1.6 1.2 2.0 1.2 2.0

0.5–1.5 1.0

1.6 1.5 1.5 1.5 1.0 1.6 2.0

1.7 1.5 1.5 2.0 1.0 2.0 2.0 2.0 2.0 1.0

1.5

Uncertainty (%)

250 Hydrothermal Experimental Data

Abdulagatov et al, 2006c Maksimova et al, 1976 Puchkov & Sargaev, 1973 Abdulagatov & Azizov, 2005c Mashovets et al, 1973 Puchkov & Sargaev, 1974 Pepinov et al, 1978 Pepinov, 1992 Abdulagatov et al, 2005 Maksimova et al, 1976 Abdulagatov et al, 2006b Abdulagatov&Azizov, 2007 Akhundov et al, 1991c Akhmedova-Azizova, 2006

Puchkov & Sargaev, 1973 Azizov, 1999 Abdulagatov & Azizov, 2005a Mashovets et al, 1973 Puchkov & Sargaev, 1974 Azizov, 1999 Abdulagatov & Azizov, 2003 Pepinov et al, 1979b Pepinov et al, 1983 Pepinov, 1992 Azizov, 1996 Azizov & Akhundov, 1997 Azizov, 1999 Zeynalova et al, 1990 Akhmedova-Azizova, 2006 Lobkova & Pepinov, 1979 Pepinov, 1992 Abdulagatov et al, 2007 Iskenderov, 1996 Abdulagatov & Azizov, 2006a Semenyuk et al, 1977b Semenyuk et al, 1977a Feodorov, 1982 Pepinov et al, 1978 Pepinov et al, 1979a Pepinov et al, 1983 Pepinov, 1992 Kestin & Shankland, 1984b Akhundov et al, 1990b Guseynov et al, 1990 Akhundov et al, 1991b 0.1/10; 30 sat. sat. 0.1/10–30 sat. sat. 2/5–30

298/370–448 298/473–598 288/450–595 374/477–630 373/473–623 298/473–623

297/473 298/473–598 298/473–598 298/473–598 298/444–575 291/473 273/448; 473 298/440–576 273/473–548 298/448; 473 293/473–573

0.085–2.623 mol·kg−1 2–37 mass % 0.049–2.961 mol·kg−1 5; 19 mass % 2–24 mass % 1–20 mass %

1–6 mol·kg−1 2–20 mass % 1; 2; 3 mass % 0.5:5; 0.5:10; 0.5:20 mass % 0.062–4.7 mol·kg−1 8–40 mass % 0.5–10 mol·kg−1 0.27–6.27 mol·kg−1 0–20 mol·kg−1 0.5–1.8 mol·kg−1 1; 5; 10 mass % 1.5–26 mass % 8; 30; 39 mass % 0.05–2.25 mol·kg−1 0.27–2.63 mol·kg−1 5–40 mass % 0.53–3.15 mol·kg−1

vi-MgSO4-2.1 vi-NaBr-1.1 vi-NaBr-2.1 vi-NaCl-1.1 vi-NaCl-2.1 vi-NaCl-3.1

vi-NaCl-4.1 vi-NaCl-5.1 vi-NaF-1.1 vi-Na/F,Cl-1.1 vi-NaI-1.1 vi-Na2MoO4-1.1 vi-NaNO3-1.1 vi-NaNO3-2.1 vi-NaOH-1.1 vi-Na2SO4-1.1 vi-Na2SO4-2.1 vi-Na2SO4-3.1 vi-Na2WO4-1.1 vi-Ni(NO3)2-1.1 vi-SrCl2-1.1 vi-Sr(NO3)2-1.1 vi-Sr(NO3)2-2.1

298/470–573 291/473 298/448; 475 293/400–473 298/473–598 298/473; 573

0.1/2–30 2–40 0.1/10–40 0.1/10–40

298/473–573 298/473–598 298/473; 573 298/373–423

2–8 mass % 5–40 mass % 0.36–4.50 mol·kg−1 0.85–10 mass.%

vi-MgCl2-4.1 vi-Mg(NO3)2-1.1 vi-Mg(NO3)2-2.1 vi-MgSO4-1.1

2–40 sat. 0.1/10–30 0.1/10; 20 0.1/10–40 20

2/5–30

0.1–30 0.1/10–40 0.1/10–40 10–150 10–150

10; 30 0.1/10–40 20 2–30

10; 20; 30

293/473–573

0.11–1.04 mol·kg−1

vi-MgCl2-3.1

sat. 10; 30 0.1–30 sat. sat. 10; 30 10; 20; 30 2–30 2/10–30

298/473–548 298/473–573 298/459–573 273/473–548 298/448–548 298/473–573 298/467–575 298/473–623 298/473–623

0.57–9.64 mol·kg−1 2–8 mass % 0.265–1.540 mol·kg−1 0–4.5 mol·kg−1 0.49; 1.24; 2.27 mol·kg−1 2–8 mass % 0.1–0.9 mol·kg−1 1–20 mass % 1–17 mass %

vi-LiNO3-1.1 vi-LiNO3-2.1 vi-LiNO3-3.1 vi-LiOH-1.1 vi-Li2SO4-1.1 vi-Li2SO4-2.1 vi-Li2SO4-3.1; 3.2 vi-MgCl2-1.1 vi-MgCl2-2.1

CF CF CF CF CF CF

CF CF CF CF CF CF CF

OD CF CF CF

CF

CF CF CF CF CF

CF CF CF CF

CF

CF CF CF CF CF CF CF CF CF

1.5 1.5 1.5 1.6 1.5 1.5

1.6 1.5 1.5 1.6 1.5 1.5 1.0

0.5–1.5 1.5 1.2 1.5

1.0

1.7 1.6 2.0 2.0

1.5–1.7 1.5 1.5 1.5

1.5

1.5 1.5–1.7 1.5 1.5 1.5 1.5–1.7 1.5 1.0 1.0

*) – The results of low-temperature measurements (below 473 K) are not given usually in the Appendix. Numbers separated by a slash (/) show the minimal temperatures or pressures available in the publications (before a slash) and in the Appendix tables (after a slash). “Sat.” means that equilibrium pressure is not shown in the publications but was near (above) the saturation vapor pressure at measured temperature. a) – CF –capillary flow; OD- oscillating disk; QV-quartz viscometer; FB-falling-body

Na2WO4 Ni(NO3)2 SrCl2 Sr(NO3)2

NaOH Na2SO4

NaI Na2MoO4 NaNO3

NaF NaF+NaCl

NaCl

NaBr

MgSO4

Mg(NO3)2

MgCl2

LiOH Li2SO4

LiNO3

Viscosity 251

252

Hydrothermal Experimental Data

electrolytes. The importance of CaCl2 in deep brines of the Earth’s crust, and its reactivity in fluid-rock interaction is becoming increasingly more recognized. Ca2+ is the second most important cation after Na+. At salinities in excess of about 30 mass %, Ca2+ becomes the most abundant cation, and such brines are widespread in the deeper parts of many sedimentary basins. Ground-waters encountered in deep wells drilled in crystalline rocks are commonly highly saline brines, in which Ca2+ is the dominant cation, exceeding Na+ by factor of 2–3 on a weight basis. In addition, CaCl2 is the premier example of an electrolyte of the 2 : 1 charge-type, and its aqueous solution has been used extensively as an isopiestic standard. The knowledge of the transport properties of sea water brines, which contain primarily NaCl, Na2SO4, and MgSO4, is important in the development of an economic desalination process. MgSO4 is one of the major components of sea salt and many natural waters. Both the association and hydrolysis of the Na2SO4 in aqueous solutions are of great importance in many industrial processes such as material transport, solid deposition, corrosion in steam generators, and electrical power boilers (Sharygin et al., 2001; Gupta and Olson, 2003). Sodium sulfate is a common product of hydrothermal waste destruction by supercritical water oxidation. Aqueous Na2SO4 is also an important constituent of natural subsurface brines and sea floor vent fluids. LiCl is one of the dominant components of many aqueous fluids (natural fluids). LiCl concentration could equal NaCl in some Li-rich pegmatites (London, 1985; Lagache and Sebastian, 1991; Wood and Williams-Jones, 1993) or in magmatic fluids associated with Li-rich leucogranites (Cuney et al., 1992). Although most saline ground waters are dominated by NaCl, K+ is one of the next most important cations after Na+, Ca2+, and Cl− is the dominant anion. The viscosity of electrolyte solutions is also of research interest because of the long-range electrostatic interactions (Coulombic forces) between ions (Harrap and Heymann, 1951; Stokes and Mills, 1965; Horne, 1972; Horvath, 1985; Chandra and Bagchi, 2000a,b; Esteves et al., 2001; Anderko et al., 2002; Jiang and Sandler, 2003). Accurate viscosity data are needed to calculate the viscosity A- and B-coefficients in the limiting law of viscosity and extended Jones-Dole viscosity equation, respectively. Furthermore, the Jones-Dole viscosity B-coefficient is important in the description and understanding of the structure and destruction of ionic processes, e.g. solvation effects of cation and anion (Stokes and Mills, 1965; Horne, 1972; Marcus, 1985; Horvath, 1985; Jenkins and Marcus, 1995; Anderko et al., 2002; Jiang and Sandler, 2003). The theory predicts only the values of viscosity A- coefficient of electrolyte solutions at infinite dilution (m → 0) (Falkenhagen and Dole, 1929). To accurately determine the higher-degree viscosity coefficients (e.g. B- and D- coefficients) in the extended Jones-Dole equation, very accurate viscosity data for electrolyte solutions at the high concentration range are required. Theoretical modeling (Lencka et al., 1998; Chandra and Bagchi, 2000a,b; Esteves et al., 2001; Anderko et. al., 2002; Jiang and Sandler, 2003; Wang et al., 2004 and Hu, 2004)

of the viscosity of electrolyte solutions still cannot describe the behavior of real systems. To develop better predictive models, more reliable viscosity measurements, and in a wider range, are required. A literature survey revealed that the number of measurements reported for the viscosity of such aqueous systems under pressure and at high temperature (above 200 °C), is rather limited. Furthermore, the scatter of the reported data is quite large (up to 10–20%) and far exceeds the quoted mutual uncertainties of the authors (about 1–2%). This chapter aims to provide the readers with a review of the available experimental data sets on the viscosity of aqueous systems at high temperatures (above 200 °C) and high pressures, to present a critical analysis of the estimation, correlation, and prediction methods, to select the most reliable data sets and to propose preliminary recommendations. In Table 6.1, a summary of all viscosity measurements at high temperatures (above 200 °C), to our knowledge, is presented. It is interesting to note that the majority of the investigators quote uncertainty between 1% and 2%. Correlation and prediction of these viscosity measurements as a function of temperature, pressure, and concentration is also briefly considered, mostly as a means of interpreting and comparing the different data sets. 6.2 EXPERIMENTAL TECHNIQUES The definition of the dynamic viscosity given by Equation (6.1) presumes the ability to measure local shear stresses. Since, however, it is impossible to measure local shear stresses, and viscometers undoubtedly do not have a constant shear rate, methods of measurement of the viscosity must be based on the determination of some integral effect of the stresses amenable to precise measurement in a known flow field. Inevitably, the imposition of a shear field generates small pressure differences, and dissipation causes local temperature gradients, both of which change slightly the reference thermodynamic state to which a measurement is assigned, from the initial, unperturbed, equilibrium state. The reference state for the measurement will be obtained by averaging so it is important that the system is disturbed as little as possible from equilibrium during measurement Techniques frequently employed to measure the viscosity of liquids are: 1. capillary flow (CF); 2. oscillating discs (OD); 3. oscillating cups (OC); 4. falling body (FB); 5. quartz viscometer (QV); and 6. vibrating wire (VW). In Table 6.1 all available measurements, to our knowledge, of the viscosity of aqueous solutions at high temperatures (above 200 °C) and high pressure are presented. It can be seen that almost all data were derived by a capillary-flow technique (CF), while only very few datasets were obtained by the oscillating-disc technique (OD), the falling-body method (FB) and a quartz viscometer (QV). Only one dataset, reported by Abaszade, 1971 for non-electrolyte solution, C2H5OH(aq), was measured with QV method. OC technique basically used to measure the viscosity for corrosive liquids such as liquid metals and molten salts at high temperatures. A disadvantage of the OC viscometer is the meniscus effect. It is not easy to determine the exact height

Viscosity

Figure 6.1 Schematic diagram of the experimental apparatus employed for the measurement of viscosity of aqueous solutions at high temperatures and high pressures by the capillary method (J. Chem Eng. Data, 48, 1549–1556. Abdulagatov and Azizov. Copyright 2003. American Chemical Society). 1: Working capillary; 2: two electrical heaters; 3: solid (substantial) red copper block; 4: high pressure autoclave; 5: thermocouple; 6: extension tube; 7: flange; 8: viewing windows; 9: movable cylinder; 10: flexible connecting tube; 11: unmovable (fixed) cylinder; 12: valve; 13: separating vessel; 14: dead-weight pressure gauge (MP-600); 15: heat exchanger; 16: PRT (Platinum Resistance Thermometer); 17: outer thermal screen; 18: heat insulation.

5

1

6

15

7

8 16

17

18 9

12

14 13

10

11 Hg filled

of liquid in the cup (Wakeham et al. eds., 1991). VW method have been applied at extremely high pressures and very low temperatures (for example, He at low temperatures) due to their mechanically simplicity. We further note that almost all investigators quote an uncertainty of better than 2%, with the exception of the falling-body data where the uncertainty quoted is 4%. In this section a brief analysis of these methods is presented. The theoretical bases of the methods, and the working equations employed are presented, together with a brief description of the experimental apparatus and the measurements procedure of each technique. For a more thorough discussion of the various techniques employed, the reader is referred to the monograph by Wakeham et al. (eds.), 1991. 6.2.1 Capillary-flow technique As seen in Table 6.1, capillary viscometers are the most extensively used instruments for the measurement of viscosity of aqueous electrolyte solutions at high temperature and pressure. They have the advantage of simplicity of construction and operation. 6.2.1.1 Theoretical The principle of the capillary viscometer is based on the Hagen-Poiseuille equation of fluid dynamics (first formulated by Hagen in 1839) and its alteration for practical viscometry by Barr (1931) in order to include the so-called kinetic-energy correction and the end correction. The resulting equation expresses the viscosity of a fluid flowing through a thin capillary, in terms of the capillary radius, R, the pressure drop along the tube, ∆P, the volumetric flow rate, Q, and the length of the tube, L, as mρQ π R 4 ∆P , η= − 8Q ( L + nR ) 8π ( L + nR )

2 34

253

(6.4)

where n is the end-correction factor and m is the kineticenergy correction factor with L >> R. The above equation is derived on the assumptions that, (a) the capillary is straight with a uniform circular cross section, (b) the fluid

is incompressible and Newtonian and (c) the flow is laminar and there is no slip at the capillary wall – to avoid turbulence (Reynolds number, Re, over 2000), viscometers are designed to operate where the Reynolds number is well bellow 300. The correction factors n and m reflect the fact that in a practical viscometer two chambers must be placed at either end of the capillary in order to measure the pressure drop. Thus, for example, the parabolic velocity distribution characteristic of most of the flow can only be realized some distance downstream from the inlet of the capillary. In the range of Reynolds numbers between 0.5 and 100, the theoretical values of the correction factors m and n are represented as m = m0 + 8n/Re with m0 = 1.17 ± 0.03 and n = 0.69 ± 0.04 (theoretical values by Kestin et al., 1973). The values of m and n can also be determined experimentally (Nagashima, 1975). The values of m proposed by Swindells et al. (1952) are m = 1.12 to 1.16 for Re between 106 and 648 and by Kawata et al. (1974) m = 1.08 to 1.16 for Re between 46 and 1466. The end correction factor reported by various authors is: n = 0.79 to 0.88 for Re < 0.14 (Kawata et al., 1969) and n = 1.16 for Re < 10 and n = 0.57 for Re > 10 (Bond, 1922). Other corrections – capillary shape and slip, non-uniform cross-sections (Barr, 1931), elliptical cross-section (Ito, 1951a), coiled capillaries (Ito, 1951b; Dawe and Smith, 1970), wall roughness (Kawata, 1961), fluid properties effects, compressibility, non-Newtonian (Van Wazer et al., 1963), and surface tension correction (Van Wazer et al., 1963; Goncalves et al., 1991; Kawata et al., 1991) – can be found in the respective literature. 6.2.1.2 Experimental Figure 6.1 shows a schematic diagram of a typical capillary viscometer (Pepinov et al. 1978, 1979a,b, 1983, 1986, 1988, 1989; Abdullaev et al. 1990, 1991a,b; Akhundov et al., 1990a,b, 1991b; Abdullaev, 1991; Zeynalova et al. 1990, 1991; Pepinov, 1992; Iskenderov, 1996; Azizov, 1996, 1999; Azizov and Akhundov, 1997; Abdulagatov and Azizov, 2003, 2005a–d, 2006a,b, and Abdulagatov et al. 2004, 2005, 2006a,b). They all employed a very similar

254

Hydrothermal Experimental Data

capillary viscometer, differing only in the actual capillary dimensions. The working capillary-1 with ID of 0.3 mm and length of 216 mm is made from stainless steel. The capillary-1 is soldered to the extension tube-6. The fluid under study flows to a cold zone through the extension tube-6. Capillary-1 with extension tube-6 located in the high temperature and high pressure autoclave-4. The extension tube-6 is connected to a movable cylinder-9, which in turn is connected to the fixed cylinder-11 by means of the flexible tube-10. Both cylinders (9 and 11) are supplied with identical expanded bottles, employed to stabilize the fluid efflux through the capillary. The input and output sections of the capillary have conical extensions. All parts of the experimental installation in contact with the sample are made out of stainless steel. The capillary tube-1 is filled with the fluid and when the movable cylinder is moved vertically at constant speed, the fluid flows through the capillary. To create and also measure accurately the pressure, the autoclave is connected to a dead-weight pressure gauge by means of separating vessel13. Mercury is used as the separating liquid. 6.2.1.3 Working equation and uncertainty In the capillary viscometer shown in Figure 6.1, if we denote by t the time required for a volume of fluid V to flow through the capillary, and take into consideration the variation of the geometrical size of the capillary, and that of mercury and sample densities, then Equation (6.4) becomes

η=

mρV π R4 ∆Pt , (1 + a∆T )3 − 8 ( L + nR )V 8π ( L + nR ) t

(6.5)

where, a is the linear expansion coefficient of the capillary material, ∆T the temperature difference between experimental temperature and room temperature. The pressure drop, ∆P, is determined from the relation: ∆ P = g ∆ H ( ρHg − ρ )

(6.6)

where, ∆H, is the average mercury level drop in the movable and fixed cylinders at the beginning and ending of the measurements, rHg, is the density of mercury at room temperature and experimental pressure, and r is the density of the fluid under study. Mercury level in the cylinders was measured with a cathetometer. Equation (6.5) in essence can be simplified to

η = − c1t −

c2 . t

(6.7)

where constants c1 and c2 can be obtained from Equation (6.5). In Equation (6.5) the viscosity obtained is proportional to the fourth power of the capillary radius. Hence a very accurate value of the radius is required. The inner surface of the capillary walls is perfectly polished with powders of successively smaller grain size (1 to 40 nm). The average

capillary radius is measured using a weighing technique or/and by calibration (relative method, see Abdulagatov and Azizov, 2003) from the viscosity of a standard fluid (pure water) with well-known viscosity values (IAPWS formulation, Kestin et al., 1984a). The correction for capillary radius, due to the meniscus curvature (surface forces in a capillary), is made. Typical values (obtained by Abdulagatov and Azizov, 2003) of the capillary radius determined with both weighing and by the calibration techniques are 0.15091 mm and 0.15048 mm, respectively, resulting in a value for R4 of (51.27 ± 0.59) × 10−5 mm4. The length, L, of the capillary is measured with a microscope with an uncertainty of ±0.005 mm. Typically the final value of the capillary length (obtained by Abdulagatov and Azizov, 2003), is 540.324 ± 0.005 mm. Flow time measurements are usually made electronically and the uncertainty in this value is never more than 0.1s (0.5%). To assess the uncertainty of the technique, the uncertainty of each quantity that enters into Equation (6.5) must also be taken into consideration. After a very careful analysis of the uncertainty of these quantities (Abdulagatov and Azizov, 2003), it is estimated that the combined relative uncertainty in measuring the viscosity (up to the highest temperature of 575 K) is 1.5% (in this chapter we use a coverage factor k = 2). Furthermore, the uncertainty associated with the measurement of the concentration is estimated to be 0.014%, while the maximum uncertainty in the pressure measurements is 0.05%. Another example of this type of viscometer was developed in the Leningrad Technological Institute by Semenyuk et al. (1977a,b) and Feodorov (1982). Semenyuk et al. (1977a,b) used a capillary viscometer (see Figure 6.2), made out of titanium, in order to perform viscosity measurements in aggressive aqueous NaCl, KCl, LiCl solutions at high temperatures (between 273 and 673 K) and high pressures (from vapor-pressure to 200 MPa). The apparatus consists of a titanium capillary – 1 welded in the top part of a cylindrical bulb. The bulb is placed in a high pressure titanium-alloy autoclave – 2, which in turn is placed in a copper block – 3, surrounded by the cylindrical electroheater – 4. When the high-pressure autoclave is turned by an angle of 90° and return to its initial vertical position, the difference of the mercury levels in the viscometer, flow of the fluid through the capillary takes place. Temperature is measured by a platinum resistance thermometer PRT – 5, while the pressure was recorded by a dead-weight pressure gauge – 11 connected via rubber bellows to the separating vessel – 6. In this case, the internal radius and length of the titanium capillary was 13.63 × 10−5 m and 14.83 × 10−2 m, respectively. The value of the viscometer constant c1 in Equation (6.7), at 298.15 K, was determined by calibration employing water as the viscosity reference fluid (IAPWS formulation, Kestin et al., 1984a). The maximum uncertainty in the viscosity measurements with this type of viscometer is estimated to be 2%. A very similar viscometric apparatus was previously designed in the same Institute by Mashovets et al. (1971) and Puchkov et al. (1973, 1974), and employed to measure the viscosity of aqueous Na2SO4, K2SO4, Li2SO4, NaNO3,

Viscosity

12

discussed in detail elsewhere (Verschaffelt, 1915; Kestin et al., 1957a, 1958, 1959, 1981a; Newell, 1959; Kestin and Khalifa, 1976 and Kestin and Shankland, 1981b).

7 8

13 14

R

255

5

6.2.2.1 Theoretical

1 11

10 2

A

9

3 4

6

The theoretical aspects of the technique are described by Verschaffelt (1915) and Kestin et al. (1957a, 1958). The characteristic equation which relates the motion of an oscillating body to that of the fluid is (Kestin and Newell, 1957b)

( s + ∆ 0 )2 + 1 + D ( s ) = 0,

Figure 6.2 High temperature and high pressure capillary viscometric system (Semenyuk et al., 1977b). 1: titanium viscometer; 2: high-pressure autoclave; 3: copper block; 4: cylindrical electroheater; 5: PRT; 6: separating vessel; 7: high-pressure electro-input unit; 8: removal (withdrawal); 9: electronic voltage stabilizer (Π71M); 10: auto-transformer; 11: dead-weight pressure gauge (MP-2500); 12: indicated circuit; 13: electronic oscillograph; 14: audio-frequency oscillator.

(6.8)

where ∆0 is the logarithmic decrement in a vacuum. Here, D(s) is the torque on the body, calculated from solutions for the fluid flow close to the oscillating body. It is therefore the torque D(s) that is characteristic of the particular type of oscillating viscometer employed. Apart from roots that are associated with the initial oscillatory behavior of the body, the roots associated with the long-time behavior can be written in the form s = ± (i − ∆ ) θ

(6.9)

where i is the imaginary unit and KNO3, LiNO3, NaOH, KOH, and LiOH solutions at temperatures up to 573 K and at pressures near the vapor pressure. They used nickel and glass viscometers. The uncertainty of the measured values of viscosity quoted is 1.5% for the glass viscometer and 1.0 to 1.5% for the nickel viscometer. The internal radius and length of the metallic capillary was 0.15 mm and 13.5 cm, respectively. Finally, Rivkin et al. (1986) also used the capillary flow technique to measure the viscosity of aqueous boron solutions, at temperatures up to 623 K and at pressures up to 30 MPa. In this case they employed a platinum capillary of 500 mm length and 0.3 mm ID, placed in a liquid thermostat in which temperature was controlled with an uncertainty of 0.03 K. A pump-flowmeter was used to measure the volume of the fluid flowing through the capillary tube at each given temperature and pressure. The pressure drop across the capillary ends was measured with a compensation-type differential mercury pressure gauge with a movable elbow. The details of the experimental apparatus and measurement procedure are given in Rivkin et al. (1979).

θ = T T0.

Here, T is the period of oscillation in the fluid and the subscript zero denotes the same quantity in vacuo. The function D(s) can be expressed as D (s) =

sM ( s ) , I ω [ sα ( s ) − α 0 ] 2 0

(6.11)

where M(s) is the Laplace transform of the torque function M(t) (torque exerted by the fluid on the body), t = w 0t is a dimensionless time, w 0 = 2pT0 is the angular frequency of oscillation in a vacuum, I is the moment of inertia of the oscillating system. The symbol, a0, denotes the initial angular displacement, while a(s) is the Laplace transform of the angular displacement a(t) of an axially symmetric body, defined as

α (τ ) = 6.2.2 Oscillating-disk technique Oscillating-disk viscometers consist of an axially symmetric disk placed between two fixed parallel plates and suspended from a torsion wire, so that it performs oscillations in the fluid about its axis of symmetry. Such a viscometer has been used by several researchers as an instrument for viscosity measurements (see, for example, DiPippo et al., 1966; Kestin et al., 1977, 1978a,b, 1980; Correia et al., 1979; Correia and Kestin, 1980; Kestin and Shankland, 1981b, 1984b and Krall et al., 1987, 1992). The theoretical and experimental problems of this technique have been

(6.10)

 sτ 1 + ∆ 02 α 0  1  −  e ds (6.12) 2 ∫ 2π i C  s s ( s + ∆ 0 ) + 1 + D ( s )  

or

α (τ ) = α 0 e − ∆θτ cos (θτ ) .

(6.13)

During an experiment, the logarithmic decrement ∆ and the period T, are determined from the motion of the body. The form of the torque functions D(s) for various oscillating-body viscometers are discussed in the literature (Kestin and Newell, 1957b; Newell, 1959; Azpeitia and Newell, 1959; Beckwith and Newell, 1959; Tørklep and Øye, 1982;

256

Hydrothermal Experimental Data

Nieuwoudt et al., 1987; Nieuwoudt et al., 1988 and Nieuwoudt, 1990). Before proceeding to examine different forms of the function D(s), it is important to introduce a natural length scale that appears in oscillatory systems in general, namely the boundary-layer thickness, d, defined as 12

 η  δ = .  ρω 0 

(6.14)

As it will be shown in the following paragraphs, this natural length scale is important in the selection of the dimensions of oscillating-disk viscometers. In the particular case of viscometers consisting of a disk of thickness d and radius R, oscillating between two fixed horizontal plates, and provided d >> 2b + d (where b is the separation between the disk and one of the fixed horizontal plates), the solution for D(s), is Kestin and Shankland (1981b) D ( s )=

πρ R 4δ 3 2  b ( C − 1) δ 1 2 s coth  s1 2  + N s , (6.15)   I b  δ 

where CN is calculated from the viscometer geometry (Newell, 1959; Iwasaki and Kestin, 1963). For the oscillating-disk viscometers consisting of a thick disk oscillating in an infinite fluid (i.e. a free thick disk), and provided that d << d/2 and R >> d, the analytical solution for D(s) is Kestin and Shankland (1981b)

πρ R4δ 3 2  2d K 2(ξ0 s1 2 )  s 1 + + ε ( s ) , 12 I R K s ξ ( ) 1 0  

D (s) =

(6.16)

where K1 and K2 are the modified Bessel functions of order 1 and 2, and j0 = R/d. The edge-effects e(s) for this type of geometry are given by

ε ( s) =

16  4π 1 17 1 − 1 + +
3π  3 3  ξ0 s1 2 9 ξ02 s

(6.17)

The solutions represented by Equations (6.14) and (6.17) are valid for oscillations of small amplitude. For all disks the general torque function can be expressed (Nieuwoudt et al., 1987) in the form of Dk ( s ) =

ρ 32 s ρ

[ Akξ0−1 + Bk s −1 2ξ0−2 + Ck s −1ξ0−3 + Dk s −3 2ξ0−4 + Qk ( s )], (6.18) _ where k denotes the type of configuration and r is the effective density of the oscillating body. The term Ak arises from the torque on the flat and cylindrical sides of the disk, while the high-order terms contain the effects of the sharp edges at the rims of the disk. The values of the coefficients Ak, Bk, Ck and Dk appearing in Equation (6.18) for various oscillating-body viscometers, can be found in literature (Wakeham et al., 1991).

6.2.2.2 Experimental During the last fifty years, many designs of oscillating-disk viscometers, operating in a relative or in an absolute way, have been reported and their theory has been developed (Kestin et al., 1957a, 1958, 1959, 1978a, 1980, 1981a; Newell, 1959; Kestin and Khalifa, 1976, Grimes et al., 1979, Kestin and Shankland, 1981b,c, 1984b). However, due to design limitations, absolute measurements of the viscosity of aqueous solutions with an oscillating-disk viscometer are almost impossible. Kestin and co-workers (Kestin et al., 1978a, 1980; Kestin and Shankland, 1981b, 1984b) employed relative methods, based upon the development of previous formulations (Kestin et al., 1957a, 1958, 1959; Newell, 1959), in order to measure the viscosity of aqueous NaCl and KCl solutions at temperatures up to 200 °C and pressures up to 30 MPa. Calibration of the viscometer involves measurement of the viscosity of distilled water, whose viscosity is well known, in order to determine the dependence of the edge-correction factor C upon the boundary-layer thickness d. Calibration was performed over the temperature range from 25 to 150 °C, which corresponds to a boundary-layer range from 0.73 to 1.53 mm. The oscillating-disc viscometer used by Kestin et al. (1977, 1981a); Grimes et al. (1979) and Kestin and Shankland (1984b), and to measure the viscosity for aqueous electrolyte solutions at high temperatures and high pressures, is schematically shown in Figure 6.3. The viscosity body is divided into a solid lower part-3 and hollow upper part-7 forming the viscometer cavity, effectively sealed against an internal pressure in excess of 30 MPa. The oscillating-disk-5 is suspended between two Hastelloy fixed plates-4 and -6 by means of a stress relieved 92 Pt thin strand-9. The upper end of the wire is gripped at the top of the suspension cartridge. The top suspension assembly-11 is designed to permit controlled adjustments in the elevation of the disk as well as in the angular orientation of the oscillating system. Two side windows at the lower part of the instrument provide access to the disk and the fixed plates. 6.2.2.3 Working equation and uncertainty As already mentioned, the value of the viscosity (obtained in a relative way), is derived from measurements of the logarithmic decrement ∆ and the period of oscillation T. The working equation for the viscometer reduces to (Kestin et al., 1978a, 1980)

πρ R 4δ 2 ∆   − ∆0  − C θ θ I   H K + H K + 2d  H + 3δ  1 2 1  1 2 2 Rθ R 

  = 0,  

(6.19)

where, q is the ratio of the period of oscillation in the liquid to that in vacuum, R is the radius of the disk, I its moment of inertia, and d is a measure of the boundary layer thickness (Equation (6.14), δ = η ( ρω 0 ) ). Parameter C is an edge-

Viscosity

11

10 9

12

8

13

7

14

6

15

5

16

4

17

3 18 2

19

1

Figure 6.3 Cross-section view of the viscometer of Kestin et al. (1980) employed for measuring the viscosity of aqueous electrolyte solutions at high temperatures and high pressures (Kestin J, Paul R, Shankland I.R. and Khalifa H.E. (1980) Ber Bunsenges. Phys Chem., 84, 1255–1260. Reproduced with permission from Deutsche Bunsen-Gesellschaft). 1: bearing for rotating viscometer; 2: window; 3: solid lower part of the viscometer; 4 and 6: fixed plates; 5: disk; 7: hollow upper part of the viscometer; 8: buttressthreaded stainless steel cap; 9: Pt/W thin strand; 10: alumina column; 11: suspension assembly; 12: ten bolts; 13: pressure ring; 14: suspension mounting plate; 15: thick-walled cylinder; 16: thermocouple; 17: O-ring seal; 18: mirror; 19: filling connection.

correction factor depended on the dimensionless boundarylayer thickness (d/b), determined by calibration. Finally, the functions H1,2 and K1,2 are defined by H1,2 = (1 ± 1.5∆ − 0.375∆ 2 )

2θ 3 2,

(6.20)

and K1 =

sin Y sinh X , K2 = , cosh X − cos Y cosh X − cos Y

2 2θ

[1 ± 0.5∆ + 0.125∆ 2 ]

b . δ

q. Kestin et al. (1980) used triple-distilled water as the calibration fluid. The precision of the viscometer depends both upon the accuracy of the mathematical model describing its operation and on the precision of each individual measurement involved in the overall determination. In this method the measurement of the following basic quantities are needed: temperature T, pressure P, a series of the times, and the period of oscillation. The temperature inside the viscometer is usually measured by means of a Pt/Pt-Rh thermocouple with an uncertainty of 0.05 K. The uncertainty in pressure measurements is 50 kPa. The time intervals were measured with the aid of digital timers and a photo-electric circuit (Kestin and Khalifa, 1976). The accuracy of the time interval measurements is 1 ms; this translates into a logarithmic decrement, known to within 0.1% and a period that is known to within 0.001% (Kestin and Khalifa, 1976). On the basis of these values the estimated uncertainty of the viscosity measurements does not exceed 0.4%. The uncertainty of the viscosity measurements for aqueous KCl solutions at 200 °C is 0.5% (Kestin et al., 1981a). This uncertainty is comparable with the precision claimed in similar works (Kestin et al., 1980; Kestin and Shankland, 1981c). However, in the case of aqueous KCl solutions the results are burdened with an additional uncertainty arising from inaccuracies in the values of density. Kestin et al. (1981a) numerically evaluated the sensitivity of the viscometer working equation to uncertainties in density. They found that at room temperatures, the viscosity is insensitive to any uncertainty in density, while at 200 °C, the relative uncertainty in density is amplified by a factor of approximately 2 in viscosity. As the density of aqueous KCl solutions reported in literature (Potter and Brown, 1976; Egorov et al. 1976; and Grimes et al. 1979) could possibly be burdened with uncertainties as great as 0.5%, the estimated uncertainty in viscosity data for the H2O + KCl solutions is within 0.5 to 1.5%. 6.2.3 Falling-body viscometer This method is usually employed to measure the viscosity of liquids and high-dense gases. The method is characterized by high uncertainty (3–4%), but has some advantages for measurements at high pressures. The theoretical and experimental problems of this technique have been discussed by Kawata et al. (1991).

(6.21) 6.2.3.1 Theoretical

with X,Y =

257

(6.22)

Equation (6.19) is first employed in combination with viscosity measurements of a liquid of ‘known’ viscosity, in order to obtain the edge-correction factor C(d). Consequently having obtained this factor, it is applied to measure the viscosity of other liquids from measured values of ∆ and

The method is based on Stoke’s law, according to which, the force, W, exerted by the liquid on a sphere of radius, r, falling in an infinite homogeneous liquid at a constant velocity n, is related to viscosity h of the liquid via the equation W = 6phrn. This relation is valid for very small Reynolds numbers, Re. At greater Reynolds numbers, this relation should be corrected for the effect of walls. Stoke’s law assumes that the following conditions are satisfied, during the free-fall under gravity of a sphere through the liquid of interest (Wakeham et al., 1991): (a) the motion of

258

Hydrothermal Experimental Data

the sphere is sufficiently slow; (b) the liquid is of infinite extent; (c) there is no slip between the liquid and the surface of the sphere; (d) the sphere is rigid; (e) the liquid is incompressible; and (f) the liquid is Newtonian. For falling bodies of various shapes (a cylinder, a cylinder with semispherical ends, or an arrow-like body), the viscosity is determined by measuring the time t of fall through a fixed distance at a constant velocity as

η = C ( ρ b − ρ1 ) t ,

(6.23)

where C is the instrument’s constant (function of the dimensions and the design of the apparatus), rb is the density of the falling body, and rl is the density of the liquid studied. The value of the instrument’s constant, C, is usually determined by a calibrating procedure, from the viscosity of a standard fluid (usually pure water) with well-known viscosity values (IAPWS formulation, Kestin et al., 1984a). For a free-fall of a sphere of radius r through a distance h, in a liquid enclosed in a tube of radius R, the viscosity equation is derived as

η=

2r 2 g ( ρ b − ρ1 ) tf w. 9h

(6.24)

In the above equation fw is the correction factor for the wall effect. The correction factor fw has been studied theoretically and experimentally (Faxen, 1923; Barr, 1931; Fidleris and Whitemore, 1961; Sutterby, 1973; and Kawata et al., 1991). Faxen (1923) expressed the factor fw as a function of the Reynolds number, Re, and the ratio (r/R) f w = 1 − 2.104 ( r R ) + 2.09 ( r R ) − 0.95 ( r R ) . 3

5

(6.25)

Stoke’s law is applicable provided the Reynolds number, Re, is much less than unity. Oseen (1913) derived the following working equation for a sphere moving with a velocity ν, which is applicable for a wide range of Re number

η=

2r 2 g 2 Rv ρ1 < 1 (6.26) ( ρ b − ρ1 ) for Re = 9ν (1 + 3Re 16 ) η

There are several modifications of the Stoke’s law for a wide range of Re numbers (see, for example, Goldstein, 1929; Proudmann and Pearson, 1957; Maxworthy, 1965; Chester and Breach, 1969; Sutterby, 1973; Huner and Hussey, 1977). Other corrections to the working equation of this technique, such as the effect of the fall-tube ends, the fall-tube dimensions, and the selection of spherical material, are well documented in literature (Maude, 1961; Tanner, 1963; Flude and Daborn, 1982). For a cylinder of mass m, radius r1 and length Lb, falling under the influence of gravity a distance h along the axis of a tube of radius r2, the viscosity of the liquid can be expressed as

η=

( ρ b − ρ1 ) Aρ b

t

(6.27)

where A=

2π Lb h . mg [ ln ( r2 r1 ) − [( r22 − r12 ) ( r22 + r12 )]]

(6.28)

In practice the value of the instrument’s constant A is determined by a calibration procedure employing fluids of well-known viscosity (pure water, for example). This method was used to measure the viscosity of water, alcohols, and their mixtures (Isdale et al., 1985; Tanaka et al., 1987).

6.2.3.2 Experimental Melikov (1996, 1999, 2000) employed the falling-body technique to measure the viscosity of aqueous electrolyte solutions at temperatures up to 300 °C and pressures up to 30 MPa. The apparatus used to measure the viscosity of aqueous electrolyte solutions is shown schematically in Figure 6.4a. The main part of the apparatus is a viscometric tube – the fall-tube (see Figure 6.4 b), with 40 mm OD, 10.33 mm ID, and a length of 500 mm, made out of stainless steel. The working section of the viscometric tube is 400 mm (see Figure 6.4a). The inner surface of the tube walls is perfectly polished with powders of successively smaller grain size (1 to 40 nm). On the outside surface of the fall-tube (50 mm from the ends), the two inductance coils (electromagnetic transducers) are mounted, connected to potentiometers. When the falling-body passes the inlet and outlet of the fall-tube, an induced signal triggers the appropriate timing circuitry (see Figure 6.4c). The cylindrical falling body with a diameter of 10.214 mm and a density rb = 6.290 g·cm−3, is made out of magnetic steel (3X13). The fall-tube is located in the high-pressure autoclave (see Figure 6.4b). The autoclave together with viscometric tube is located in a liquid thermostat with 7 heaters (see Figure 6.4a) and can be rotated upside down in order to let the ball return to its starting position. The temperature inside the thermostat was maintained uniform within 3 mK with the aid of guard and regulating heaters. Melikov (1996, 1999, 2000) measured the viscosities of binary aqueous NaCl + MgCl2 and ternary KCl + CaCl2 + MgCl2 solutions at temperatures up to 573 K and at pressures up to 30 MPa. To perform accurate viscosity measurements with the falling-body technique, various corrections (fall-tube dimensions, effect of fall-tube ends, terminal velocity, falling-body shape, position of the fall-tube) ought to still to be considered (Wakeham et al., 1991). 6.2.3.3 Uncertainty The uncertainty of the viscosity values is directly connected to the uncertainty associated with several other factors, including the measurement of the dimensions, mass and density of the falling body, the radius of the fall tube, the distance traveled and time taken, the density of the falling body and that of the liquid. These uncertainties are con-

Viscosity

259

(b)

(a) 1 8 3

2

9 5V

5

-12V

+ 12V

6

3500 Hz

20 mV

3

4

2

7

(c)

Figure 6.4 Schematic diagram of a falling-body viscometer (Melikov, 1996). Experimental apparatus (4a), fall-tube construction (4b), and fall-time measure unit (4c). (a): 1: high-pressure autoclave; 2: cover of the high-pressure vessel; 3: rotary encoder; 4: liquid thermostat; 5: mixer; 6: circulating pump; 7: thermostating liquid; 8: PRT-10; 9: patentiometer (P363/1); 10: high precise temperature regulator (HPTR-3); 11: manometer, (b): 1: falling-body; 2: high pressure autoclave; 3: cover of the high-pressure vessel; 4: fall-tube; 5: inductance coils (electromagnetic transducers); 6: filling tube, (c): 1: falling-body; 2: primary winding of the transducer; 3: secondary winding of the transducer; 4: generator of the signals; 5: amplifier; 6 and 7: direct current power supply unit; 8: frequency meter; 9: oscillograph.

nected through the corresponding working equation. In particular the radius of the falling body and that of the tube are of primary importance as they strongly affect the viscosity. For the instrument described here (Melikov 1996, 1999, 2000), the uncertainty in the radius of the falling cylinder and the tube is 0.001% in both cases. Density of falling body and liquid were measured with an uncertainty of 0.002% and 0.0052% respectively. The temperature and the pressure were measured with an uncertainty of 0.1 K and 0.005 MPa. Hence, the resulting total uncertainty in the viscosity measurements was about 3.3%. It should also be pointed out that as a test of the operation of his instrument, Melikov (1996, 1999, 2000) measured the viscosity of pure water at pressures between 0.1 and 40 MPa and over the temperature range from 298 to 573 K. His values agreed

with the IAPWS formulation values (Kestin et al., 1984a) within 1.5%.

6.2.4 Conclusion In this section the three techniques employed for the measurement of aqueous electrolyte solutions were discussed. These were the capillary-flow technique, the oscillatingdisc technique and the falling-body method. From the discussion of the techniques it is apparent that measurements performed with the capillary-flow viscometer and the oscillating-disc viscometer enjoy a low degree of uncertainty. Hence, measurements would be expected to attain an uncertainty of better than 2%. Measurements performed with the

260

Hydrothermal Experimental Data

falling-body viscometer would be expected to attain a higher uncertainty (3–4%). 6.3 AVAILABLE EXPERIMENTAL DATA As already stated in Table 6.1, a summary of all viscosity measurements of aqueous solutions at high temperatures (above 200 °C) is presented. In the same table, for every composition of non-aqueous components, the first author and the year published, the concentration ranges, the temperature and pressure, the experimental method employed, and the uncertainty claimed by the authors is also shown. A reference code assigned to each measurement set refers the reader to the original data set in the Appendix for easy access. The tables provide, to our knowledge, the largest and most useful collection of viscosity data at the present time for aqueous solutions at high temperatures (above 200 °C). All tables are accompanied by additional information related to the experimental methods employed and their uncertainties. It should further be mentioned that in cases

where an investigator has also performed measurements below 200 °C, these are shown in Table 6.1, but the actual values presented in the Appendix are restricted to above 200 °C. Detailed analyses of available experimental viscosity data of aqueous solutions at low temperatures (below 200 °C) and at atmospheric pressure are reported elsewhere in literature (Robinson and Stokes, 1959; Stokes and Mills, 1965; Horne, 1972; Horvath, 1985; Lobo, 1989; Zaytsev and Aseyev, 1992). Figures 6.5a–c shows the typical dependence of the viscosity of aqueous electrolyte solutions on temperature, pressure and concentration. The viscosity data of aqueous non-electrolyte solution, C2H5OH(aq), reported by Abaszade et al., 1971, shows almost the same temperature and pressure dependences, while the concentration dependence exhibit a maximum between 0.6 and 0.7 mass fraction (or 0.37 and 0.48 mole fraction) of ethanol (see Figure 6.5d). For water + methanol mixtures this maximum is occur at concentration between 0.3 and 0.35 mole fraction of metha-

0.58 H2O + NaCl P = 30 MPa x = 20 mass %

1270

0.54

255 18%

270

360

440

(a)

T/K

520

600

235 215

0.50

520

0.48

195

0.46

175

0.44

155

0.42 0

H2O + NaCl P = 20 MPa T = 473.15 K

η/mPa·s

0.52

770

20 280

275

η/mPa·s

η/mPa·s

1020

m = 10.1097 mol·kg–1 0.56 T = 473.15 K

10 20 30 40 50 60

(b)

P/MPa

135 0

(c)

5

10 15 20 25 30

x/mass %

0.30 0.27

T = 473.15 K H2O + C2H6O

η/mPa·s

0.24 0.21 0.18 0.15 0.12 0.0

(d)

0.2

0.4 0.6 0.8 x/ mass fraction of C2H6O

1.0

Figure 6.5 Measured and calculated values of viscosity (h) of aqueous electrolyte (5a–c) and aqueous ethanol (5d) solutions as a function of temperature (T) (5a), pressure (P) (5b) and concentration (m) (5c, d) reported by various authors (Abaszade et al., 1971). (a) NaCl(aq): ●, Akhundov et al. (1990a); 䉭, Kestin and Shankland (1984b); (——), by Kestin and Shankland (1984b) correlation. (b) LiCl(aq): ●, Abdulagatov et al. (2006a); 䊊, Abdullaev (1991); ⵧ, Semenyuk et al. (1977a); (-------), Zaytsev and Aseyev (1992); (c) NaCl(aq): ●, Akhundov et al. (1990a); 䊊, Pepinov et al. (1978, 1983, 1986, 1992); 䉭, Kestin and Shankland (1984b); ×, Semenyuk et al. (1977a,b); ♦, IAPWS (H2O, Kestin et al., 1984a). (d) C2H6O(aq): ●, 20 MPa; 䊏, 40 MPa; ⵧ, 60 MPa; ×, 80 MP; 䉱, 100 MPa; 䊊, 120 MPa (Abaszade et al., 1971).

Viscosity

0.2

H2O + NaBr

– 0.0

P = 0.1 MPa

– 0.2 In η

nol (Kubota et al., 1979). The maximum shifts to higher concentrations with pressure and dose not shift significantly with temperature. The following three sections will provide a brief outline of the available schemes describing the temperature, the pressure and the concentration dependence of the viscosity of aqueous solutions. These schemes will be employed in Section 6.4 in order to perform a preliminary comparison of the experimental data presented in Table 6.1.

261

– 0.4 – 0.6 – 0.8 –1.0 –1.2 0.0027

6.3.1 Temperature dependence The viscosity of aqueous solutions decreases considerably with temperature (see Figure 6.5a). For example, at constant pressures (30 MPa) between temperatures (285 and 630 K), the viscosity of the electrolyte solution H2O + NaCl, changes by a factor of 15. In the concentration range m > 1 mol·kg−1, the empirical equation of Arrhenius-Andrade (Glasstone et al., 1941; Stokes and Mills, 1965 and Erday-Grúz, 1974), describing the temperature dependence of viscosity, as b η = A exp   T 

(6.29)

is valid. In this equation, A and b = ea /R (ea is the flow activation energy) are functions of concentration. However, Equation (6.29) fails to represent the experimental data over the complete temperature range at high pressures (Grimes et al., 1979 and Kestin and Shankland, 1984b). The Eyring’s absolute rate theory (Glasstone et al., 1941) enables a much better description of the temperature dependence of the viscosity of concentrated aqueous electrolyte solutions, as

η=

+ hN  ∆G  exp   RT  V

+

 ∆H  or η = A exp  .  RT 

(6.30)

In the above equations ∆G+ and ∆H+ are the free enthalpy of activation and enthalpy of activation, h is Planck’s constant, N Avogadro’s constant, R the gas constant, and V is the molar volume of the hole in the liquid. The enthalpy of activation ∆H+/R can be calculated from the slope of the straight line by the ln h ≈ 1/T function (see Figure 6.6). In a more simplified form, for a 1 : 1 electrolyte, Equation (6.30) can be expressed as

η=

η0 exp ( xE ) , 1 + xV

(6.31)

where, h is the viscosity of the electrolyte solution at a concentration m and temperature T, h0 is the viscosity of the solvent (pure water) at temperature T, and x is the mole fraction of the cation or anion in solution. The individual ionic components of the V parameter is related to the ionic salvation numbers, and the individual ionic free energy of activation components of E is related to a surface free energy for the formation of a hole in the liquid. The temperature dependence of the viscosity of concentrated

0.0029

0.0031

0.0033

T–1/K–1

Figure 6.6 Measured values of ln h as a function of 1/T (Arrhenius plot, ln h vs. T−1) at three selected concentrations and at atmospheric pressure for H2O + NaBr solutions (Abdulagatov and Azizov, 2006a). ●, 2.961 mol·kg−1; ×, 1.496 mol·kg−1; 䊊, 0.049 mol·kg−1 (Journal of Solution Chemistry).

aqueous electrolyte solutions can be described in terms of the temperature dependence of the E and V parameters of Equation (6.31). Figure 6.7 illustrates the dependence of the temperature coefficient of viscosity, b T,

βT =

1  ∂η  η  ∂T  P , m

(6.32)

of H2O + NaBr solution, at 298.15 K, and at atmospheric pressure as a function of concentration and temperature reported by Isono (1980, 1984, 1985) and Abdulagatov and Azizov (2006a). As one can see from Figure 6.7a, the temperature coefficient bT increases with concentration, passes through a maximum near 4 mol·kg−1, and then decreases at higher concentrations. This maximum can be qualitatively interpreted in terms of a competition between specialized viscosity effects as long-range coulombic interaction, size and shape of effects or Einstein effect, alignment or orientation of polar molecules by the ionic field, and distortion of the solvent structure. These effects are governing the concentration and temperature behavior of viscosity of the aqueous electrolyte solutions (see Section 6.3.3). Figure 6.7b further shows the temperature dependency of the coefficient bT of H2O + NaBr solution, at 0.1 MPa and 2.961 mol·kg−1. In the same figure values for pure water are also shown (IAPWS formulation, Kestin et al., 1984a). It can be seen that the effect of temperature on the viscosity of the H2O + NaBr solutions is higher than that of pure water. 6.3.2 Pressure dependence The dependence of the viscosity on pressure is small (up to 7%, for a 1–40 MPa pressure increase) at high temperatures (473 K) and high concentrations (see Figure 6.5b), and even smaller (up to 0.5–1.0%) at low temperatures. We note that for pure water at the same temperature and pressure ranges, the pressure effect on viscosity is about 6% at high

262

Hydrothermal Experimental Data

H2O + NaBr –2.00 – 0.8 P = 0.1 MPa

–2.05 –1.0 –2.10 βT × 102/ K–1

–1.2 –2.15

–1.4

–2.20

P = 0.1 MPa

–2.25

T = 298.15 K

–106 –1.8

–2.30

–2.0

–2.35

–2.2

–2.40

0

2

4 6 m/ mol·kg–1

8

(a)

–2.4 290

310

330 T/K

350

370

(b)

Figure 6.7 The viscosity temperature coefficient, bT = h−1(∂h/∂T)PX, of H2O + NaBr solution and pure water as a function of concentration and temperature at atmospheric pressure. (a): ●, Abdulagatov and Azizov (2006a); 䊊, Isono (1984); ×, pure water (IAPWS, Kestin et al., 1984a); (b): ●, 2.961 mol·kg−1; 䊊, 0.049 mol·kg−1; (-------), pure water (IAPWS, Kestin et al., 1984a); (——), smoothed curves (Journal of Solution Chemistry).

temperatures and about 0.5% at low temperatures. The pressure dependence of the experimental viscosity of aqueous solutions in the range from 0.1 to 40 MPa is almost linear. Grimes et al. (1979) and Kestin and Shankland (1984b) developed a linear correlative equation to describe the effect of pressure on the viscosity of the systems H2O + NaCl and H2O + KCl, as

η (T , m, P ) = η0(T , m) [1 + β (T , m) P ],

(6.33)

where h0(T,m) represents the extrapolated to zero–pressure viscosity at constant temperature and concentration, and b(T,m) is the pressure coefficient of viscosity. An empirical polynomial expression of the form 3

(6.34)

i =0 j =0

was employed to correlate the pressure coefficient as a function of temperature and concentration for H2O + NaCl and H2O + KCl solutions (Grimes et al., 1979 and Kestin and Shankland, 1984b). The temperature and concentration dependences of h0(T,m) were described as

η(T , m) = 1 + d1m + d2 m 2 + d3 m3, η0(T )

(6.35)

where 3

j =0

(P) ηwis = ηw( Pe + P ),

(6.37)

3

β (T , m) = ∑ ∑ bij t i m j ,

di = ∑ dijT j.

The scheme described by Equations (6.33)–(6.36) reproduced the complete data sets for H2O + NaCl and H2O + KCl with an average standard deviation of 0.23% and 0.20% (and maximum deviation 1.0% and 0.8%), respectively. This equation was found to be valid in the temperature range 25 to 200 °C, at pressures up to 30 MPa, and at concentrations 0 to 6 mol·kg−1. Leyendekkers and Hunter (1977a,b) and Leyendekkers (1979) have applied the TTG (Tammann-Tait-Gibson) model to the prediction of the viscosity of aqueous electrolyte solutions at high pressures. According to this scheme, the value of the viscosity of water in solution hwis, is given by the relation

(6.36)

where hw is the viscosity of pure water, P is the external pressure, and Pe is the effective pressure due to the presence of the salt. Similarly, the viscosity of the solution at pressure P is given by

ηS( P ) ηw( Pe + P ) = . ηS(1) ηw( Pe +1)

(6.38)

This relation was employed by Kestin and Shankland (1984b) and Abdulagatov and Azizov (2006b) to compare viscosity values predicted with this scheme with experimental data for H2O + NaCl, H2O + KCl, and H2O + NaBr solutions (see Figure 6.8). As it can be seen the agreement between predicted and measured values of the viscosity of H2O + NaBr solutions, is good (deviations within 1.5–2.0%).

Viscosity

H2O + NaBr 1.9

1.9

P = 40 MPa

P = 10 MPa

η/mPa·s

1.7

1.7

T = 293.15 K

1.5

1.5

1.3

1.3

1.1

1.1

0.9

263

0

1

2

3 4 5 m/ mol·kg–1

6

0.9

7

(a)

T = 293.15 K

0

1

2

3 4 5 m/ mol·kg–1

6

7

(b)

Figure 6.8 Comparison between experimental viscosities at high pressures (10 and 40 MPa) and values predicted by TTG model (Equation 6.38) along isotherm of 293.15 K. ●, Abdulagatov and Azizov (2006a); (——), TTG model prediction (Leyendekkers, 1979 and Leyendekkers and Hunter, 1977a,b) (Journal of Solution Chemistry). H2O + NaBr

– 0.2 P = 0.1 MPa

– 0.3

P = 0.1 MPa

T = 298.15 K

1.05

– 0.4

βP × 104/ MPa–1

– 0.5 0.65 – 0.6 – 0.7 0.25 – 0.8 – 0.9

– 0.15

–1.0 –1.1 0.0

0.6

1.2 1.8 m/ mol·kg–1

2.4

(a)

3.0

– 0.55 290

310

330 T/ K

350

370

(b) −1

Figure 6.9 The viscosity pressure coefficient, bP = h (∂h/∂P)TX, of H2O + NaBr solution and pure water as a function of concentration and temperature at atmospheric pressure. (a): ●, Abdulagatov and Azizov (2006a); ×, pure water (IAPWS, Kestin et al., 1984a); (b): −1 −1 −1 ●, 0.049 mol·kg ; ×, 2.007 mol·kg ; 䊊, 2.961 mol·kg ; (-------), pure water (IAPWS, Kestin et al., 1984a); (——), smoothed curves (Journal of Solution Chemistry).

Finally, Figure 6.9 shows the concentration and temperature dependences of the experimental pressure coefficients

βP =

1  ∂η  η  ∂P  T , m

(6.39)

of the viscosity of H2O + NaBr solutions at the temperature of 298.15 K, together with pure water values (calculated

from the IAPWS formulation, Kestin et al., 1984a). The pressure coefficient bp of the viscosity of aqueous solutions can be both positive and negative (depending on temperature), changing sign from negative to positive at about 306 K (see also Kestin and Shankland, 1984b). As Figure 6.9 shows, the bP is strongly affected by concentration, while the pressure dependence of bP is very weak (almost independent on pressure).

264

Hydrothermal Experimental Data

T = 298.15 K P = 0.1 MPa 1.45 2.7 1.35

η/mPa·s

2.3

1.25 1.15

1.9

1.05 1.5 0.95 1.1 0.85 0.7 0

1

2

3 4 m/ mol·kg–1

5

6

(a)

0.75

0

1

2 3 m/ mol·kg–1

4

5

(b)

Figure 6.10 Viscosity of a series of aqueous solutions as a function of composition at a selected temperature 298.15 K and a pressure of 0.1 MPa reported by various authors. (a): ●, Na2SO4 (Isono, 1984); ⵧ, NaBr (Abdulagatov and Azizov, 2006a); ×, NaF (Goldsack and Franchetto, 1977, 1978); 䊊, NaI (Goldsack and Franchetto, 1977, 1978); ◊, NaNO3 (Isono, 1984); 䉭, Na2CO3 (Zaytsev and Aseyev, 1992); 䉱, NaH2PO4 (Zaytsev and Aseyev, 1992); 䊏, NaHSO4 (Zaytsev and Aseyev, 1992); ♦, NaCl (Afzal et al., 1989); 䉮, NH4Br (Goldsack and Franchetto, 1977, 1978). (b): 䉭, NaBr (Abdulagatov and Azizov, 2006a); ♦, CsBr (Maksimova et al., 1987); ●, KBr (Isono, 1984); ⵧ, LiBr (Zaytsev and Aseyev, 1992); ×, RbBr (Desnoyers and Perron, 1972).

6.3.3 Concentration dependence The concentration dependence of the viscosity of electrolyte solutions is quite anomalous (Chandra and Bagchi, 2000a,b), and clearly depends upon the nature of the solute ions. For some electrolyte solutions (see Figures 6.10a,b), such as H2O + CsF, H2O + KF, H2O + LiCl, H2O + LiBr, H2O + LiI, H2O + NaCl, H2O + NaF and H2O + RbF and the viscosity increases monotonically with the electrolyte concentration, while for other types of electrolyte solutions such as H2O + CsCl, H2O + KBr, H2O + KCl, H2O + KI and H2O + RbCl the viscosity decreases at low electrolyte concentrations, reaching a minimum value, and then increases at higher concentrations. Hence, the modeling of the electrolyte-solutions’ viscosity over the whole concentration range is rather difficult. Existing theoretical models, which describe the concentration dependence of the viscosity of ionic solutions, are valid only at infinite dilution. Falkenhagen-Onsager-Fuoss theory (Falkenhagen and Dole, 1929; Onsager and Fuoss, 1932; Falkenhagen, 1971) and Debye-Hückel-Onsager (Onsager, 1926; Debye and Hückel, 1924) predicts at infinite dilution (c → 0), a square-root concentration dependence, as

η = 1 + D c. η0

(6.40)

Equation (6.40) is also known as the limiting law. This theory correctly explains the rise of viscosity with concen-

tration in the limit of very dilute ion concentrations (c < 0.05 mol·L−1). However, as this model was based on macroscopic properties, it becomes inadequate when intermolecular considerations become important. Jones and Dole (1929) proposed an empirical extension of the Falkenhagen and Dole (1929) model for higher concentrations as

η = 1 + A c + Bc. η0

(6.41)

In the above equation, h and h0 are the viscosities of the electrolyte solution and the pure solvent (water), respectively, while c is the electrolyte molarity concentration (mol·L−1). Constant A is always a positive constant. Although this equation was found to provide a better description than the limiting law of Equation (6.40), it was still only applicable to concentrations below 0.1 mol·L−1. Usually, the values of the parameters of Equation (6.41) are determined by employing various fitting procedures over a wide concentration ranges. Furthermore, the optimal concentration range also depends on temperature. Hence the values of the viscosity A- and B-coefficients strongly depend on the concentration ranges employed in the fitting procedure. This is one of the reasons of the high discrepancies in the viscosity B-coefficient observed between the values reported by various authors. To extend the validity of Equation (6.41) to higher concentrations, Jones and Talley (1933), Kaminsky (1955, 1956, 1957), Feakins and Lawrence (1966), Robertson and

Viscosity

Tyrrell (1969), Desnoyers et al. (1969), Desnoyers and Perron (1972), Abdulagatov et al. (2004, 2005, 2006a,b) and Abdulagatov and Azizov, 2006a,b), added a quadratic term Dc2 (extended Jones-Dole equation), as

η = 1 + A c + Bc + Dc 2. η0

(6.42)

In this way, Equation (6.42) could be applied to more concentrated electrolyte solutions (c < 0.1–0.2 mol·L−1). It was proposed that the new term in Equation (6.42) accounted for solute-solvent and solute-solute structural interactions at high concentrations (Stokes and Mills, 1965; Desnoyers and Perron, 1972) such as: long-range Coulombic forces; high term hydrodynamic effects; and effects arising from changes in solute-solvent interactions due to concentration changes. Finally, Abdulagatov et al. (2004, 2005, 2006a,b) included one further term, Fc2.5, as

η = 1 + A c + Bc + Dc 2 + Fc 2.5. η0

(6.43)

and thus increased the validity of the equation up to saturated concentration. Grimes et al. (1979) and Kestin and Shankland (1984b) omitted the square-root term owing to its small magnitude, and proposed an equation of the form

η = 1 + d1m + d2 m2 + d3m3, η0

(6.44)

where 3

di = ∑ dijT j.

(6.47)

where Vk is the hydrodynamic molar volume in cm3·mol−1. Thomas (1965) has extended the Einstein Equation (6.47) for the hydrodynamic effect to high concentrations by showing that for suspensions, the relative viscosity is given by the relation

η = 1 + 2.5φ + 10.05φ 2 = 1 + 2.5Vk c + 10.05Vk2 c 2. η0

(6.48)

Breslau and Millero (1970) showed that this relation can be employed to describe the concentration dependence of the relative viscosity for concentrated electrolyte solutions, provided Vk is taken as an adjustable parameter. Abdulagatov and Azizov (2005c,d, 2006a) and Abdulagatov et al. (2006a,b) used Equation (6.48) and experimentally obtained viscosity values to determine the values of Vk as a function of the temperature for H2O + NaBr and H2O + LiI solutions. The value of Vk = 0.0239 l·mol−1 at 298.15 K for the H2O + NaBr solution is in agreement with the value 0.0222 l·mol−1 reported by Breslau and Millero (1970). Moulik and Rakshit (1975) also used Equation (6.48) to correlate the concentration dependence of the viscosity of 72 different electrolyte solutions at high concentrations. Finally, Sahu and Behera (1980) also represented experimental relative viscosity of electrolyte solutions by extending the limiting Einstein equation as

η (6.49) = 1 + 2.5Vc + k1V 2 c 2 + k2V 3c 3 + k3V 4 c 4, η0 – where V is the molar volume of the electrolyte in solution (dm3·mol−1), and c represents the concentration in mol·dm−3.

(6.45)

j =0

Grimes et al. (1979) and Kestin and Shankland (1984b) employed successfully the aforementioned equation to describe the behavior of the systems H2O + NaCl and H2O + KCl. Einstein (1911) has calculated the size effect (hydrodynamic effect) for an infinitely dilute suspension of rigid spherical particles in a continuum. He thus proceeded to propose the following limiting equation

η = 1 + kφ, η0

η = 1 + 2.5Vk c, η0

265

(6.46)

where f is the volume fraction of the solute molecules (f = (4/3)pR3NAc, and R is the effective solute ions radius, and c the salt concentration). For solid spheres with large diameters, compared to molecular dimensions, the commonly accepted value of k in Equation (6.46) is 2.5, although values as large as 5.5 have been suggested by Happel (1957). If f is expressed in terms of concentration in mol·l−1, then Equation (6.46) becomes

6.4 DISCUSSION OF EXPERIMENTAL VISCOSITY DATA The comparison of the datasets given in Table 6.1 was difficult due to the temperature, pressure, and concentration differences between the measurements. Therefore, a regression analysis based on the schemes discussed in Section 6.3 was employed for the temperature and composition dependence for each isobar. In the analysis that follows, a preliminary comparison is given between the various datasets, aiming to help the reader choose which values to use. It should be stressed, however, that the conclusions derived here are only based on a preliminary comparison, and should be viewed accordingly. Below the discrepancies between different datasets were examined statistically in terms of the absolute average deviation AAD =

100 N ∑ (ηexp − ηcal ) ηexp . N i =1 i

H2O+Ca(NO3)2: Two datasets were found (Zeynalova et al., 1991; Abdulagatov et al., 2004). The agreement between these data sets at atmospheric pressure and at temperatures from 298 to 348 K is within 0.1%, while at 373 K

266

Hydrothermal Experimental Data

the deviation rises to 0.7%. At high pressures (between 10 and 40 MPa) and at the concentrations 0.6721, 1.5236, and 2.6218 mol·kg−1 for temperatures from 298 to 423 K the deviations are (0.25–0.68)%, (0.02–0.07)%, and (0.37– 0.43)%, respectively. Hence, it seems that the deviations of these datasets are within the quoted mutual uncertainty of each investigator. H2O+KCl: Five datasets have been found, referring to four research groups (Semenyuk et al., 1977a; Kestin et al., 1981a; Feodorov, 1982; Pepinov et al., 1986; Pepinov, 1992). From these five sets, the papers by Semenyuk et al. (1977a) and Feodorov (1982), refer to the same experimental measurements. The agreement between the viscosity values reported by Semenyuk et al. (1977a) and the data reported by Pepinov et al. (1986) is within 1%, up to 623 K and 30 MPa. Furthermore, the values reported by Semenyuk et al. (1977a) deviate from the data reported by Kestin et al. (1981a) up to 0.9% at 473 K and 25 mass %, and up to 1.6% at 623 K. Hence, it seems that the deviations of these datasets are within the quoted mutual uncertainty of each investigator. H2O+K2SO4: Two datasets have been found (Puchkov and Sargaev, 1974; Abdulagatov and Azizov, 2005b). These two datasets were found to agree within 0.6% which is well within the mutual uncertainty of the two investigators. H2O+LiCl: Seven datasets have been found, referring to four research groups (Semenyuk et al., 1977a; Feodorov, 1982; Pepinov et al., 1989; Akhundov et al., 1990a; Abdullaev et al., 1991a; Abdullaev, 1991; Pepinov, 1992; Abdulagatov et al., 2006a). From these seven datasets, the papers by Semeyuk et al. (1977a) and Feodorov (1982), as well as the papers by Pepinov et al. (1989) and Pepinov (1992), and also the papers by Akhundov et al., 1990a, and Abdullaev et al. 1991a, all refer to the same experimental measurements in each case. At high temperatures and high pressures, large scatter (up to 20% and more) between the various data sets is observed, while the agreement is generally good near ambient temperatures and atmospheric pressure. The data of Pepinov et al. (1989), Akhundov et al. (1990a), Abdullaev (1991), Abdullaev et al. (1991a), Pepinov (1992), and Abdulagatov et al. (2006a), agree within 1.2% at atmospheric pressure, high temperatures, and for compositions up to 10 mol·kg−1. At high pressures and high temperatures however, the scatter between the aforementioned investigators rise up to 18%, Figure 6.5b). More analytically, the following can be noticed. The data of Semenyuk et al. (1977a) deviate from those of Abdulagatov et al. (2006a) by up to 13% at high concentrations (x > 10 mass %), while at low concentrations at the same temperature and pressure conditions, the deviations are within 2%. Good agreement within 2%, is also found between the data of Abdulagatov et al. (2006a) and the data of Akhundov et al. (1990a) and Abdullaev, 1991, Abdullaev et al., 1991a at temperatures up to 348.15 K and

at pressures up to 40 MPa, while at temperature above 348.15 K deviations between these two sets reached 18%. Finally, good agreement within 1.2% is observed between the data reported by Pepinov et al. (1989) and Abdulagatov et al. (2006a) with values of viscosity at temperatures up to 523.15 K and up to 30 MPa and compositions up to 30 mass %. Hence, it seems that although the agreement between the various datasets is generally good at ambient conditions, at high temperature and high pressures, scatter up to 20% is observed. H2O + LiI: Three datasets were found, referring to two research groups (Abdullaev et al., 1991a, b; Abulagatov and Azizov, 2005d). From these three sets, the papers by Abdullaev et al. (1991a) and Abdullaev et al. (1991b) refer to the same experimental measurements. The data of Abdullaev et al. (1991a,b) agree with the data of Abdulagatov and Azizov (2005d) within 1.2% at concentrations below 2.16 mol·kg−1, while at higher concentrations and high pressures the deviations rise up to 3.7%, which is just over the mutual uncertainty of the two investigators. Hence, it seems that the agreement between the two datasets is within the quoted mutual uncertainty of each investigator, rising to 3.7% at concentrations over 2.16 mol·kg−1 and high pressures. H2O + LiNO3: Three datasets were found, referring to two research groups (Puchkov and Sargaev, 1973; Azizov, 1999; Abdulagatov and Azizov, 2005a). The measurements of Abdulagatov and Azizov (2005a) and those reported by Puchkov and Sargaev (1973), were found to agree within 1.1%, which is well within the mutual uncertainty of the two investigators. H2O + Li2SO4: Three datasets were found, referring to two research groups (Puchkov and Sargaev, 1974; Azizov, 1999; Abdulagatov and Azizov, 2003). The measurements of Abdulagatov and Azizov (2003) and those reported by Puchkov and Sargaev (1974), Maksimova et al. (1987), and Cartón et al. (1995), were found to agree within 0.65%, at temperatures up to 323 K and at 0.1 mol·kg−1, while at higher concentrations and at temperatures up to 343 K the deviations rose up to 4–8%. H2O + MgCl2: Five datasets were found, referring to only two research groups (Pepinov et al., 1979b, 1983; Pepinov, 1992; Azizov, 1996, 1999; Azizov and Akhundov, 1997; Azizov 1996, 1999). The data by Azizov (1996, 1999) agree within 1.5% with the data of Pepinov et al. (1979b, 1983) and Pepinov 1992, which is well within the mutual uncertainty of the two investigators. H2O + NaBr: Two datasets were found (Iskenderov, 1996; Abdulagatov and Azizov, 2006a). The data of Iskenderov (1996) agree within 1.0% with the data of Abdulagatov and Azizov (2006b) at concentration below 1.5 mol·kg−1 and at atmospheric pressure, while at high concentrations the deviations rise to 2.6%, which is still well within the mutual uncertainty of the two investigators. H2O + NaCl: Eight datasets were found, referring to four research groups (Semenyuk et al., 1977a,b; Pepinov et al.,

Viscosity

1978, 1979a, 1983; Pepinov, 1992; Feodorov, 1982; Kestin and Shankland, 1984b; Akhundov et al., 1990b). From these eight sets, the papers by Semenyuk et al. (1977a,b) and Fedorov (1982) refer to the same experimental measurements. The data reported by Kestin and Shankland. (1984b) agree with the data of Akhundov et al. (1990b), Pepinov et al. (1978, 1979a, 1983), Pepinov (1992) within 2.3% at temperatures above 473 K, pressures up to 30 MPa and concentrations up to 10% by mass. Above this concentration, deviations between the values of Kestin et al. (1984b) and those of Akhundov et al. (1990b) rose up to 3.9%. The data by Semenyuk et al. (1977a,b) and Feodorov (1982) deviate from the those reported by Akhundov et al. (1990b) by 1.9% at low concentrations (2 mass %), rising to 6.8% at high concentrations (10 mass %) – Akhundov’s et al. (1990b) data are systematically higher than the data of Semenyuk et al. (1977a,b). Finally, the data of Semenyuk et al. (1977a,b) agree within 1.6% with the data by Pepinov et al. (1978, 1979a, 1983) at high temperatures and high pressures. Hence, it seems that although the agreement between the various datasets is generally good at low concentrations, care must be taken at higher concentrations where discrepancies rise up to 6.8%. H2O + NaNO3: Two datasets were found (Puchkov and Sargaev, 1973; Abdulagatov and Azizov, 2005c). The data of Puchkov and Sargaev (1973) agree with the viscosity data reported by Abdulagatov and Azizov (2005c) within 0.6% at atmospheric pressure, up to 348.15 K and compositions up to 6.3 mol·kg−1. At higher concentrations the disagreement rose to 1.6%, which is still well within the mutual uncertainty of the two instruments. H2O + Na2SO4: Four datasets were found, referring to three research groups (Puchkov and Sargaev, 1974; Pepinov et al., 1978; Pepinov, 1992; Abdulagatov et al., 2005). In this case, the agreement between the various data sets is generally good. The data of Abdulagatov et al. (2005) were found to agree within 1.5%, with the data reported by Pepinov et al. (1978) at high pressures (10 and 30 MPa) and concentrations of 5 and 10 mass %, while at low pressures the deviations were within 0.6%. Excellent agreement, 0.7% was found between the measurements of Abdulagatov et al. (2005) and those of Puchkov and Sargaev (1974) at concentrations of 15 and 20 mass % and at temperatures up to 348 K, while at low temperatures (298.15 K), deviations rose up to 2%. Hence, it seems that the deviations of these datasets are within the quoted mutual uncertainty of each investigator. REFERENCES Abaszade, A., Agaev, N.A. and Kerimov, A.M. (1971) Zh. Fizich. Khimii. 45: 2672–3. Abdulagatov, I.M. and Azizov, N.D. (2003) J. Chem. Eng. Data 48: 1549–56. Abdulagatov, I.M. and Azizov, N.D. (2005a) Ind. Eng. Chem. Res. 44: 416–25. Abdulagatov, I.M. and Azizov, N.D. (2005b) Int. J. Thermophys. 26: 593–635.

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7

Calorimetric Properties of Hydrothermal Solutions Vladimir M. Valyashko (Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow, Russia)

Miroslav S. Gruszkiewicz (Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA)

Calorimetric techniques for measuring the enthalpy changes and the heat capacities of fluid mixtures provide a convenient means for experimental determination and subsequent calculation of high-temperature thermodynamic properties in hydrothermal solutions such as activity and osmotic coefficients, or thermodynamic equilibrium constants of various processes including chemical reactions and phase changes. Development of accurate high-temperature, highpressure calorimeters made it practical to develop comprehensive models taking advantage of thermodynamic relations between volumetric and thermal properties over a wide range of conditions (Pitzer, 1995). The molar excess enthalpies (HE) of mixtures, enthalpies of vaporization (∆vapH), enthalpy increments (∆incH) relative to enthalpy in some chosen standard state, heats of mixing (∆mixH), heats of dilution (∆dilH), and heats of solution (∆solH), as well as the heat capacities at constant pressure (Cp) or at saturation pressure (Cs) and the heat capacities at constant volume (Cv), are the experimentally determined calorimetric quantities of considerable current use. Since thermal properties of aqueous solutions are often referenced and measured in relation to pure water, or extrapolated to the standard state of infinite dilution, the differences between the solution and the pure water it contains are often derived from experimental data. Apparent properties (such as apparent molar enthalpies Lf and heat capacities Jf) can be obtained as a natural result of measurements using twin-cell calorimeters. Depending on application, excess molar enthalpies or excess heat capacities and enthalpy or heat capacity changes of mixing can be used interchangeably. Sometimes molar excess enthalpies of mixtures have a fundamental importance (a deviation of from ideal behavior) and attest as primary calorimetric data, in other cases the enthalpies of mixing or dilution are a measure of the thermal effect during a mixing process and have a practical importance (Christensen et al., 1982, 1988; Grolier, 1990).

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

While the heat capacities at constant pressure are useful for calculation of various thermodynamic quantities, related to Gibbs free energy for aqueous species, and chemical equilibria involving aqueous species, the isochoric heat capacity measurements are useful in developing equations of state (EOS) because they yield valuable information about the second derivative of the pressure and of the Helmholtz energy with respect to temperature. Detailed comparisons of experimental Cv data with available EOS are needed to establish their accuracy. Cv experiments contain direct information on the curvature behavior of the p-T isochores, which are extremely important in the development of a reliable EOS. Furthermore, the temperature dependence of Cv at fixed density serves as a sensitive indicator of the phase transition boundary. Thus Cv measurements provide a tool for investigation of temperatures (Ts) and densities (ds) on the coexistence curve, especially near the critical point. Two techniques are used in the solution calorimetry for thermal properties measurements: batch techniques, in which no mass transfer with the surroundings occurs, and flow techniques, in which a solution or reaction is investigated under steady-state conditions of constant fluid flow. Although the flow techniques appeared much later than the batch ones, the volume of thermal data for high-temperature solutions measured with the batch methods is very limited. The development of flow calorimeters at the end of the seventies was an important advance in high-temperature solution calorimetry because of their great sensitivity, freedom from vapor-space corrections, and rapidity with which measurements could be made (Wood and SmithMagowan, 1980; Wood, 1989; Oscarson and Izatt, 1992; Chen et al., 1994a; Simonson and Mesmer, 1994). Since accurate measurements of enthalpy changes as a function of pressure are relatively straightforward with flow calorimeters, independently obtained thermal and volumetric data can be verified using the thermodynamic identity (∂H/∂p)T = V − T(∂V/∂T)p

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Hydrothermal Experimental Data

7.1 BATCH TECHNIQUES According to Chen et al. (1994a), there were no calorimetric data above 100 °C on aqueous systems until 1951 when Eigen and Wicke made batch heat capacity measurements of aqueous solutions of NaCl, LiBr, and MgCl2 up to 140 °C. In 1969, Gardner et al. measured heat of solution of NaCl in water from 100 to 200 °C with the average errors ∼24– 50 cal using the isoperibol-type batch calorimeter, and calculated the standard partial molal heat capacities and entropies of NaCl(aq). The same type calorimeter was used for measurements of enthalpies of solution to 573 K in aqueous systems with Na2SO4, CuCl2 + HCl and CoCl2 + HCl (Cobble and Murray, 1977). The first drop calorimeters for enthalpy measurements of aqueous solutions at high temperatures were used by Galinker and Belova (1963); Mashovets et al. (1970); Puchkov et al. (1972); Borodenko and Galinker (1975); Borodenko and Galinker (1976); Kasper et al. (1979). The enthalpy changes of concentrated aqueous electrolyte solutions (NaOH, LiOH, NaCl, KCl, K-Al-OH and CoCl2) were measured for temperatures up to 300 °C under saturated vapor pressure; only the paper of Kasper et al. (1979) contains/discusses the enthalpies of aqueous NaCl solutions at temperatures from 184 °C to 712 °C and pressures 51 MPa and 100 MPa. The calorimetric measurements were used to calculate heat capacities at the saturation and at constant pressure. Heat capacity measurements of LiCl, KCl, NaCl, CaCl2, BaCl2, MgCl2 solutions at temperatures up to 623 K using a drop calorimeter were continued at the Leningrad Technological Institute by Feodorov and Zarembo in the 1980s. Although the uncertainties of measured values estimated by the authors did not exceed a few per cent, it was mentioned by Simonson and Mesmer (1994) that even when the drop method is carefully calibrated, there are, apparently, systematic errors of unknown origin. A drop calorimeter was also used by Conti et al. (1984, 1985, 1986, 1989) for measurements of heat capacity of aqueous solutions of single electrolytes and their mixtures to 220 °C. The use of this instrument was limited to concentrated solutions and its precision was 10 times worse than that of the flow calorimeter constructed by the same research group (Conti et al., 1988). A thermal-rise calorimeter for batch measurements of heat capacities of solutions at temperatures to 200 °C was reported by Bromley et al. (1970) and used by Likke et al. (1973) to measure the heat capacities at saturated vapor pressure (with an uncertainty of ±0.2–0.3% (±0.003 cal/ g * K)) of a number of aqueous electrolytes (KCl, MgCl2, MgSO4, NaCl and Na2SO4) in the concentration range 2–10% by mass along the saturated vapor pressure curve. This level of precision does not give usefully accurate values of apparent molal heat capacity, particularly at lower molalities. In more recent studies using flow calorimeters (Roger and Duffy, 1989), improvements by about a factor of 10 have been made in experimental precision. Most measurements of the isochoric heat capacity were made using a high-temperature, high-pressure adiabatic

calorimeter originally designed by Amirkhanbov et al. (1974) and described with various modifications by Kerimov and Alieva (1976) and Abdulagatov et al. (1993). The calorimeter was a multilayer spherical system and consisted of an inner thin-walled vessel (thickness 0.8 mm) and an outer shell (thickness 8 mm). The calorimeter vessel was made of stainless steel. The adiabatic conditions were controlled by a semiconductor layer of Cu2O in the gap between the inner calorimeter vessel and the outer shell. This layer was used as a highly sensitive thermoelement for precise measurements of temperature difference between two coaxial vessels to regulate the heaters and to control the adiabatic conditions. For heat capacity studies, a precisely determined amount of electric energy (∆Q) was applied and the resulting temperature rise (∆T = T2 − T1) was measured. The isochoric heat capacity (Cv) is defined by the relation Cv = [(∆Q/∆T) − A]/m, where ∆Q = I*U*∆t is the energy released by the inner heater, ∆t is the heating time, ∆T is the temperature rise of the system, m is the mass of the sample in the calorimeter, A is the heat capacity of the calorimeter vessel with the stirrer and other devices included. The measurements of Cv, with the uncertainty of 1–2% in the liquid phase, 2–3% in the vapor phase and 4–5% near the critical point, cover the range from 300 K to 827 K at pressures up to 100 MPa. Twin-cell type adiabatic calorimeters for Cv measurements up to 420–520 K, and 20–30 MPa were described by Magee et al. (1998); Magee and Kagawa (1998); Kuroki et al. (2001) and Kitajima et al. (2003a). Both sample and reference cells, identical spherical vessels, were surrounded by high vacuum and positioned in a temperature-controlled adiabatic shield. The uncertainty in temperature measurement was 13–30 mK. The expanded relative uncertainty for Cv was estimated to be 1–2.2% for liquid phase and 4% for gaseous results. Information on the isochoric heat capacities at temperatures above 473 K is available for aqueous solutions of methanol, n-hexane, KCl, KNO3, KOH, NH3, Na2CO3, NaCl, NaOH, Na2SO4, etc. (see Summary Table 7.1). 7.2 FLOW TECHNIQUES After the pioneering work of Monk and Wadsö (1968) and Picker with co-authors (Picker et al., 1969, 1971; Picker, 1974) on flow calorimetry at room temperature, already in the years 1975–77 flow mixing calorimeters were developed for measurements at elevated temperatures (up to 70–150 °C) at the University of Delaware, USA (Messikomer and Wood, 1975), at Brigham Young University, Provo, USA (Christensen et al., 1976) and at the University of Bristol, UK (Wormald, 1977). The second generation of flow calorimeters for enthalpy of dilution measurements at temperatures between 348 and 473 K was described by (Wood and Smith-Magowan, 1980; Mayrath and Wood, 1982a,b; Archer et al., 1984) and used to study aqueous electrolyte (LiCl, NaCl, NaBr, NaI, Na2SO4, KCl, KBr, K2SO4, CsCl, MgCl2, MgSO4) and surfactant (decyltrimethylammonium bromide; dodecyltrimethylammonium bromide) solutions at pressures up to

Calorimetric Properties of Hydrothermal Solutions 273

2–3.5 MPa (Mayrath and Wood, 1982a,b, 1983; Archer et al., 1986a,b). The solutions passed through a countercurrent heat exchanger to an aluminum block situated inside a thermostatically controlled air bath. Input streams were preheated and equilibrated with a large aluminum block. Two streams (water and solution) were mixed, and the energy released was transferred to the thermostated block through the thermopiles connecting the tubing to the block. Calorimeter was operated at flow rates from 3 to 11 mm3/s. It was estimated that between 3 and 30 per cent of energy generated was not detected by the thermopiles or lost in the exit stream. The accuracy of the calorimeter was approximately ±1 per cent and temperatures of the experiments were accurate to about 0.3 K. After calibrations were made at each flow condition, identical (±0.05%) enthalpies were obtained. Differential heat flux calorimeters, consisting of mixing cells and thermostating devices, were used for measuring the enthalpy of mixing or reaction of two fluids, containing water and organic liquids (ethanol or methanol), at temperatures up to 573 K and pressures up to 20 MPa (Mathonat et al., 1994; Hynek et al., 1999). Christensen et al. (1976) constructed an isothermal flow mixing calorimeter consisting of a flat spiral of stainless steel tubing soldered to a circular brass plate. The center of the plate was in contact with a calibration heater and a Peltier cooling device. Isothermal calorimetry is based on measuring the energy required to maintain the reaction zone at a constant temperature during the course of a reaction. This condition is achieved in the calorimeter by adjusting the energy output of a controlled heater to balance the energy arising from the chemical reaction plus the energy removed by a constant heat-leak path. The method is equally applicable to endothermic and exothermic reactions. No heat capacity measurements are required and no corrections are necessary for the heat exchange between the reaction zone and the surroundings. The isothermal method has been applied at elevated and high temperatures (up to 773 K) and several versions of isothermal flow calorimeters with some modifications of design were built at Brigham Young University, Provo, USA (Ott et al., 1986; Christiansen et al., 1986; Oscarson et al., 1991; Chen et al., 1996) for measurements of excess enthalpy, heats of reactions, heats of mixing of two fluids and enthalpy of dilution at temperatures to 623 K and pressures to 20 MPa. The energy effects due to the heat of reaction from 0.15 to 120 J/min can be measured to an accuracy of ±0.8–1% at constant temperature and pressure. These mixing calorimeters were used to make an extensive study of ionic equilibria in binary and ternary aqueous solutions at high temperatures. Typically measurements would be made over a range of temperature on a triad of solutions such as (Na2SO4 + H2O), (H2SO4 + H2O) and (Na2SO4 + H2SO4), and values of log K, ∆H, ∆Cp and ∆S would be obtained as a function of the ionic strength. Busey et al. (1984) constructed a flow mixing device from a cylindrical coil of stainless steel tube which fitted into a high-temperature Tian-Calvet type, heat-flux calorimeter. Fluids were pumped at the same flow rate through both sample and reference cells. Platinum-rhodium capillary

tubing and a platinum-core high pressure valve were used to transfer the electrolyte solution from the reservoir to the heat exchanger, where it was mixed with water or another solution. High sensitivity of the calorimeter (3 microwatts) permitted measurements on very dilute solutions and small volumes, thus eliminating the need for the massive vessels previously used for such studies at high temperatures and pressures. The uncertainty of the measurements was estimated to be no greater than ±0.5%. The calorimeter was used to measure heats of dilution of electrolyte (NaCl (Busey et al., 1984), CaCl2 (Simonson et al., 1985; Holmes et al., 1994); HCl (Holmes et al., 1987); NaOH (Simonson et al., 1989); NH4Cl (Thiessen and Simonson, 1990); Na2CO3, NaHCO3 (Polya et al., 2001)) and nonelectrolyte (methanol) (Simonson et al., 1987)) solutions up to 673 K and 40 MPa. A high-temperature, high-pressure flow calorimeter was built at the University of California, Berkeley (Wang et al., 1997; Oakes et al., 1998) using the fundamental design elements of isothermal flow calorimeters built at Brigham Young University (Christiansen et al., 1986; Oscarson et al., 1991). The principal components of the calorimeter were a brass preheater cylinder, coaxially wound with two inlet tubes and a heater, a brass heat sink plate containing a second, independently controlled heater, a passively heated ceramic dowel wound in a countercurrent arrangement with the two inlet tubes and the effluent tube, and a copper isothermal cylinder which was coaxially wound with a heater and the tube in which mixing/dilution occurs. Solutions were delivered to the calorimeter using four independent syringe pumps filled with water that pushed the solutions of interest from Teflon bags contained within separate pressure vessels, in a manner similar to the ORNL flow calorimeter (Busey et al., 1984). The heat of mixing/dilution experiments were conducted by measuring the energy output provided by the isothermal controller to maintain the isothermal cylinder at constant temperature when the two inlet streams are mixed in the calorimeter. The uncertainties in the heat of mixing and the heat of dilution were estimated for this apparatus (Wang et al., 1997) using standard deviation of the Hart controller output recorded over a time period (typically, 45 min). The calculated uncertainty of the heat of mixing of NaCl and MgCl2 solutions at T = 473 K to 573 K and at p = 20.5 MPa varied from 2 to 40% with average values of 15 to 16% at 473 K and 523 K, and 6% at 573 K. The uncertainty of heat of dilution for MgCl2 solutions at T = (523 and 573) K and at p = 20.5 MPa varied from 5.6 to 0.2% with an average value 1.9%. The first measurements of the excess enthalpy of gaseous mixtures at elevated and high temperatures (up to 700 K) were made in the University of Bristol, England, using differential flow mixing calorimeters (Wormald, 1977; Wormald and Colling, 1983; Wormald and Lloyd, 1994; Wormald et al., 1996). Measurements were made for sub- and supercritical (up to 700 K and 30 MPa) aqueous mixtures containing Ar, CO, CO2, H2, N2, various alkanes, and other hydrocarbons (see Summary Table 7.1). The gases to be mixed were passed through heat exchange coils into a mixing calorimeter, causing temperature rise at the outlet. The mixture

274

Hydrothermal Experimental Data

passed through another heat exchange coil to equilibrate again with the bath temperature, and then was split into two streams and passed through a second calorimeter identical with the first one. The purpose of the second calorimeter was to automatically correct for the temperature change caused by the Joule-Thomson effect m = (∂T/∂p)H, using a serial connection of the two thermopiles. The subsequent calorimetric arrangements were much the same as that of the gas mixing calorimeter described above. Mixing occurred over a heater in the center of the calorimeter where concentric cylinders reversed the direction of the flow so that all temperature gradients were confined to the center and leaks were small. The calorimeter assemblies were mounted in a fluidized-alumina bath controlled to ±0.1 K (Wormald and Colling, 1983; Wormald and Lloyd, 1994) at temperatures up to 700 K, or in an air oven fitted with a powerful circulating fan that could be controlled to ±0.1 K at temperatures up to 550 K, ±0.3 K at temperatures up to 650 K, and ±0.6 K at higher temperatures (Wormald et al., 1996). The error in the measured excess molar enthalpy values arising from random fluctuations was 1–2%, but there could be an additional 1 per cent error arising from unidentified heat leaks. A flow-mixing calorimeter designed by Bottini and Saville (1985) was used to study the excess molar enthalpy of mixing of (H2O + N2) and of (H2O + CO2) in the vapor phase for temperature region 520 K to 620 K at pressures below the saturation pressure of water. The measured molar enthalpy change (∆Hm), or molar enthalpy difference between the mixture at po and the pure components at (po+∆p) is defined as ∆Hm = Hm(po, T, X) − Σi Xi*Hm,i (pI, T), where pI is the inlet pressure, po is the outlet pressure, with pI = (po + ∆p), Xi is the mole fraction of solution and the summation is over both pure components in the mixture. It was converted to the true isothermal-isobaric excess molar enthalpy of mixing (H mE ). H mE was calculated by use of the equation H mE (po,T,X) = ∆Hm − (pI − po)*Σi Xi*ϕi(p, T), where ϕi(p, T) is the isothermal Joule-Thomson coefficient, (∂H/∂p)T, for pure components at the mean pressure p = (pI + po)/2. The overall uncertainty in the measured enthalpy change (∆Hm) varied from 20 to 35 J/mol. An estimation of the overall uncertainty in the excess molar enthalpy of mixing gave values in the range 25 to 50 J/mol, with a mean of about 35 J/mol. An alternative to measuring the excess enthalpy is to measure the total enthalpy of the mixture relative to some chosen standard state. Details of a water-cooled heatexchange calorimeter for measurement of enthalpy increments of fluids up to 700 K and 15 MPa have been given by (Wormald and Yerlett, 1985). In this calorimeter a pure liquid or a liquid mixture was flash vaporized, passed through a column held at an accurately controlled temperature, and finally passed through a water-cooled heat exchanger into a reservoir back-pressurized with nitrogen. The incremental change of enthalpy relative to T = 298 K and p = 0.1 MPa was calculated from the flow rate and temperature rise of the water for [H2O + CH4O (methanol)], [H2O + C2H6O (ethanol)], [H2O + C3H6O (acetone)] systems (Wormald and Yerlett, 2000; Wormald and Vine, 2000;

Wormald and Yerlett, 2002). Systematic errors for most of the measurements were estimated to be no greater than ±0.2%. Random errors arose mainly from fluctuations in the operation of the metering pump. The uncertainty of the measurements was usually less than ±1%. The flow, heat capacity calorimeter, originally developed by Picker et al. (1971) for operation at room temperature, measured the ratio of electric powers delivered to the tubing in the sample and reference cells and required to maintain a constant temperature rise in the fluid passing the heaters. The ratio of heater powers (Ps/Pw) was proportional to the ratio of the heat capacity flux through the two cells where the subscripts ‘s’ and ‘w’ refer to sample and water, respectively. This ratio was used to calculate the heat capacity ratio cp,s/cp,w by using (cp,s/cp,w) = 1 + f *[∆Ps/Pw]/[dw/ds], where ∆Ps = (Ps − Pw), dw and ds are the water and solution densities at the temperature and pressure of the sample loop, and f is a heat loss correction factor, which must be determined at each temperature. The use of flow calorimeters for the measurement of heat capacities of aqueous solutions at high temperatures and pressures was pioneered by Wood and Smith-Magowan (1980), Smith-Magowan and Wood (1981), Rogers and Pitzer (1981), and Phutela and Pitzer (1986). The ratio of the heat capacity of water to the heat capacity of a solution was measured with an accuracy of 0.01 per cent. In 1988, Conti et al. described a flow calorimeter which can be used for both heat capacity and enthalpy of mixing measurements at high temperatures with the uncertainties of ±0.05% and ∼1/m (J/mol*K) for Cp and Cp,ϕ, respectively, where m is the molality (mol/kg). Several versions of the instrument originally designed in the Laboratory of Prof. Wood (the University of Delaware) in the early 1980s were developed during the following decades to extend this technique to 430 °C and 40 MPa, to improve the performance and accuracy of the calorimeter and to simplify and speed up the measurements (Biggerstaff and Wood, 1988; Carter and Wood, 1991; Hnedkovsky et al., 2002). Heat capacity measurements have been made by flow calorimetry for hydrothermal solutions containing a number of electrolytes including CaCl2, CsBr, HCl, H3PO4, FeCl2, MgCl2, MgSO4, KCl, LiCl, NaAl(OH)4, NaBr, NaCl, NaOH, Na2SO4, NiCl2, etc., and nonelectrolytes, such as methane, ethylene, organic acids, alanine, propionamide, propylamine, pyridine, 1,6-hexanediamine, propylene, phenol, dihydroxybenzenes, aminophenols, toluidine, cresols, Xe, etc. (see Summary Table 7.1). 7.3 SUMMARY TABLE Table 7.1 summarizes all the available experimental calorimetric data for aqueous solutions at high temperatures (usually above 200 °C). It consists of two parts; the first part contains information about the enthalpy measurements in hydrothermal solutions, whereas the second part contains the heat capacity measurements. The systems are arranged in alphabetical order of nonaqueous components for each of the two parts. The first two columns in the table show the chemical composition of the

methanol methanol methanol methanol methanol ethylene

ethane

ethane ethanol ethanol ethanol ethanol ethanol acetone

C2H6

C2H6 C2H6O C2H6O C2H6O C2H6O C2H6O C3H6O

x x x x x x x

x

x x x x x x

0.5 0.05 0.98 0.85 0.9 0.5 0.5

0.5

1.0 0.8 0.8 0.5 0.1 0.5

0.612 0.7

x x

CH4O CH4O CH4O CH4O CH4O C4H4

CH4 CH4

0.5

0.51 0.51 + 0.025

0.5

max

x

m m

barium chloride barium chloride + hydrochloric acid hexafluoro benzene methane methane

BaCl2 BaCl2 + HCl

C6F6

x

argon

Ar

unit

solute

formula

min

0.95 0.05 0.1 0.05

0.9

0.023 0.16 0.02

0.329 0.3

0.025 0.012 + 0.0125

Concentration

574 398.2 308 398 348 423 373

448

296 423 423 373 323 448

373 448

383

573 598

448

min

574 473 473 473 473 473 473

473

473 473 473 473 422 473

473

573 598

473

min Table

Temperature (K)

699 473 523 548 523 573 573

698

573 523 573 573 513 648

423 698

453

623

698

max

ENTHALPY

Summary of experimental data on enthalpies and heat capacities in hydrothermal solutions

Nonaqueous component

Table 7.1

5 5 5 15 5 V.pr. V.pr

0.6

7 7 7 V.pr. 5 0.6

0.1 0.35

0.1

11 15

0.42

min

20 11 12

25 15 20

13

42 20 20 13 10 5

13

18

13.3

max

Pressure (MPa)

Hexc Hexc Hmix Hexc Hmix Hinc; Hvap Hinc; Hvap

Hexc

Hdil Hexc Hmix Hinc; Hvap Hexc Hexc

Hexc Hexc

Hexc

Hdil Hdil

Hexc

Data

fc fc fc fc fc fc fc

fc

fc fc fc fc fc fc

fc fc

fc

fc fc

fc

Technique

Wormald and Wurzberger Smith et al. Wormald and Colling; Lancaster & Wormald; Wormald Simonson et al. Wormald et al. Hynek et al. Wormald and Yerlett Dettmann et al. Lancaster & Wormald; Lancaster & Wormald; Wormald Lancaster & Wormald; Lancaster & Wormald; Wormald Wormald et al. Ott et al. Mathonat et al. Wormald and Lloyd Hynek et al. Wormald and Vine Wormald and Yerlett

Wormald and Colling Oscarson et al. Oscarson et al.

Authors

2000 1987 1994 1996 1999 2000 2002

1987a; 1990; 1995

1987 1996 1999 2000 2006 1987a; 1990; 1995

1983 1984; 1990; 1995

2000

2001 2001

1993

Year

en-C2H6-2.1 en-C2H6O-1.1 en-C2H6O-2.1 en-C2H6O-3.1 en-C2H6O-4.1 en-C2H6O-5.1; 5.2 en-C3H6O-1.1; 1.2

en-C2H6-1.1

en-CH4O-1.1 en-CH4O-2.1; 2.2; 2.3 en-CH4O-3.1 en-CH4O-4.1; 4.2 en-CH4O-5.1 en-C2H4-1.1

en-CH4-1.1; 1.2

en-BaCl2-1.1 en-BaCl2 + HCl-1.1

en-Ar-1.1

Table codes for Appendix

Calorimetric Properties of Hydrothermal Solutions 275

Continued

solute

propane

butane

t-butanol n-pentane

pentane benzene

benzene benzene cyclohexane

cyclohexane hexane hexane

heptane heptane

octane octane

decyltrimethylammonium bromide

formula

C3H8

C4H10

C4H10O C5H12

C5H12 C6H6

C6H6 C6H6 C6H12

C6H12 C6H14 C6H14

C7H16 C7H16

C8H18 C8H18

C13H30NBr

Nonaqueous component

Table 7.1

m

x x

x x

x x x

x x x

x x

m x

x

x

unit

0.57

0.6 0.76

0.59 0.7

0.62 0.7

0.79 0.5 0.5

0.7 0.5

4.05 0.75

0.5

0.5

max

Concentration

0.002

0.37 0.24

0.37 0.3

0.5 0.39 0.3

0.01

0.41

0.096 0.2

min

323

363 498

363 448

403 363 448

503 403 448

363 448

348 448

448

448

min

498

423 648

423 698

433 423 698

592 433 698

423 698

424 698

698

698

max

ENTHALPY

498

498

473

473

473

503

473

473

473

473

min Table

Temperature (K)

ENTHALPY

3.5

10

12.6

11.5

13

14

0.8 14

13

13.7

max

Pressure

1.0

0.1 0.2

0.1 0.4

0.1 0.1 0.6

16.4 0.1 0.38

0.1 0.38

0.2 0.5

0.62

0.5

min

Pressure (MPa)

Hdil

Hexc Hexc

Hexc Hexc

Hexc Hexc Hexc

Hexc Hexc Hexc

Hexc Hexc

Hdil Hexc

Hexc

Hexc

Data

fc

fc fc

fc fc

fc fc fc

fc fc fc

fc fc

fc fc

fc

fc

Technique Lancaster & Wormald; Lancaster & Wormald; Wormald Lancaster & Wormald; Lancaster & Wormald; Wormald Mayrath and Wood Lancaster & Wormald; Wormald Smith and al. Colling et al.; Wormald Wormald and Slater Wormald et al. Colling et al.; Wormald Wormald et al. Smith and al. Al-Birzreh et al.; Wormald Smith and al. Al-Birzreh et al.; Wormald Smith and al. Wormald & Al-Bezeeh; Wormald Archer

Authors

1986a

1984 1993; 1995 1996 1997a 1993; 1995 1997a 1984 1989; 1995 1984 1989; 1995 1984 1990; 1995

1983a 1988; 1995

1987b; 1990; 1995

1987b; 1990; 1995

Year

en-C13H30NBr-1.1

en-C8H18-1.1; 1.2

en-C7H16-1.1; 1.2

en-C6H14-1.1; 1.2

en-C6H12-2.1

en-C6H6-1.1

en-C6H6-1.1

en-C5H12-1.1; 1.2

en-C4H10-1.1

en-C3H8-1.1

Table codes for Appendix

276 Hydrothermal Experimental Data

0.95 0.5 0.09x + 0.49m

0.1 7.3 6 1 + 2.2

x x

x x x m

m m m m

carbon dioxide carbon dioxide

carbon dioxide carbon dioxide carbon dioxide + sodium hydroxide calcium chloride calcium chloride calcium chloride calcium chloride + hydrochloric acid calcium chloride + hydrochloric acid calcium chloride + sodium chloride cobaltous chloride+ hydrochloric acid cesium chloride cesium chloride cesium hydroxide cupric chloride + hydrochloric acid hydrogen hydrogen

CO2 CO2

CO2 CO2 CO2 + NaOH

H2 H2

CsCl CsCl CsOH CuCl2 + HCl

CoCl2 + HCl

CaCl2 + NaCl

CaCl2 + HCl

CaCl2 CaCl2 CaCl2 CaCl2 + HCl

11 0.51 0.53 0.0015 + 0.01

0.599 0.3

x x

0.0027 + 0.01

1.9 + 1.9

0.50 + 0.011

0.78 0.7

0.5

13.4

m m m m

m

m

m

m

0.30

x

CO

C16H36NBr

m

dodecyltrimethylammonium bromide tetra-n-butyl ammonium bromide carbon monoxide

max

C15H34NBr

unit

solute

0.003

0.20 0.3

0.005

0.002

min

0.359 0.7

0.005 0.025 0.026

0.06 + 0.06 373

0.012 + 0.025

0.002 0.49 0.01 0.25 + 0.53

0.001x + 0.009m

Concentration

formula

Nonaqueous component

373 448

373 573 573 573

573

473

573

574 298 373 523

498 649 523

523 448

473

348

323

min

473

473 573 573 573

573

573

573

574 473 473 523

498 649 523

523 473

473

498

min Table

Temperature (K)

423 698

473 623 623

21

623

673 526 573 598

573 698 598

623 698

698

424

498

max

0.1 0.4

0.2 11 9 V.Pr.

V.Pr.

22

10.3

7 7 21 10.3

10 20 12

2 0.4

0.76

0.2

1.0

min

11.9 12

1.9 18 18

17.6

13.2

41 44

15 25.6 13.8

4.8 20

12

0.8

3.5

max

(MPa)

Hexc Hexc

Hdil Hdil Hdil Hsoln

Hsoln

Hmix

Hdil

Hdil Hdil Hdil Hreac; Hdil

Hmix Hexc Hmix

Hinc; Hexc Hexc

Hexc

Hdil

Hdil

Data

fc fc

fc fc fc bc

bc

fc

fc

fc fc fc fc

fc fc fc

fc fc

fc

fc

fc

Technique

Smith et al. Wormald and Colling; Lancaster & Wormald; Wormald

Mayrath and Wood Gillespie et al. Gillespie et al. Cobble and Murray

Cobble and Murray

Oakes et al.

Oscarson et al.

Simonson et al. Holmes et al. Oakes et al. Gillespie et al.

Wormald et al.; Lancaster & Wormald; Wormald Bottini and Saville Lancaster & Wormald; Wormald and Lioyd; Wormald Chen et al. Wormald et al. Chen et al.

Mayrath and Wood

Archer

Authors

1983 1985; 1990; 1995

1982b 1997 1998 1977

1977

1998

2001

1985 1994 1998 1992

1992 1997b 1992a

1985 1990; 1994; 1995

1986; 1990; 1995

1983a

1986b

Year

en-H2-1.1; 1.2

en-CsCl-1.1 en-CsCl-2.1 en-CsOH-1.1 en-CuCl2 + HCl-1.1

en-CoCl2 + HCl-1.1

en-CaCl2 + NaCl-1.1

en-CaCl2 + HCl-2.1

en-CaCl2-1.1 en-CaCl2-2.1 en-CaCl2-3.1 en-CaCl2 + HCl-1.1

en-CO2-3.1 en-CO2-4.1 en-CO2 + NaOH-1.1

en-CO2-1.1 en-CO2-2.1; 2.2

en-CO-1.1

en-C15H34NBr-1.1

Table codes for Appendix

Calorimetric Properties of Hydrothermal Solutions 277

hydrochloric acid hydrochloric acid hydrochloric acid hydrochloric acid hydrochloric acid + sodium acetate nitric acid hydrogen sulfide sulfuric acid + sodium sulfate potassium bromide potassium chloride potassium chloride potassium chloride potassium hydroxide potassium hydroxide potassium sulfate lithium chloride lithium chloride magnesium chloride magnesium chloride magnesium chloride + hydrochloric acid magnesium chloride + hydrochloric acid magnesium sulfate

HCl HCl HCl HCl HCl + NaC2H3O2

MgSO4

MgCl2 + HCl

MgCl2 + HCl

MgCl2

K2SO4 LiCl LiCl MgCl2

KOH

KOH

KCl

KCl

KCl

KBr

HNO3 H2S H2SO4 + Na2SO4

solute

formula

Nonaqueous component

Table 7.1 Continued

0.52 + 0.025

2.7

m

m

1+2

1.55

m

m

0.66 16.5 0.5 5.4

0.5

0.5

0.5

4.5

13.4

m m m m

m

m

m

m

m

4.5

1.55 0.5 1.2 + 1.4

m x m

m

15.6 0.51 0.97 0.5 1+1

max

m m m x m

unit 0.01 0.01 0.025

min

0.001

0.12 + 0.01

0.24 + 0.53

0.1

0.003 0.015 0.022 0.002

0.008

0.023

0.025

0.016

2

0.015

0.10 + 0.12

0.08

0.24 + 0.25

Concentration

373

573

523

523

373 373 573 373

573

573

573

373

573

373

523 383 423

298 573 523 383 548

min

573

523

523

473 573 473

573

573

573

473

573

473

523 453 473

473 573 523 453 548

min Table

Temperature (K)

424

623

598

573

424 473 623 473

643

623

623

473

473

592 483 593

648 643 623 483 593

max

ENTHALPY

0.2

10.3

10.3

20.5

0.2 0.2 11 0.2

11

11

11

0.2

V.pr

0.2

10 0.1 12.8

7 11 10 0.1 10

min

0.8

17.6

13.2

0.8 1.9 18 1.9

25

18

18

1.9

1.9

13

13

41 25 18

max

Pressure (MPa)

Hdil

Hdil

Hreac; Hdil

Hdil

Hdil Hdil Hdil Hdil

Hdil

Hdil

Hdil

Hdil

Hsoln

Hdil

Hdil Hexc Hreac; Hdil

Hdil Hdil Hdil Hexc Hreac; Hdil

Data

fc

fc

fc

fc

fc fc fc fc

fc

fc

fc

fc

dr/c

fc

fc fc fc

fc fc fc fc fc

Technique

Mayrath and Wood

Oscarson et al.

Gillespie et al.

Wang et al.

Mayrath and Wood Mayrath and Wood Gillespie et al. Mayrath and Wood

Fuangswasdi et al.

Gillespie et al.

Gillespie et al.

Borodenko and Galinker Mayrath and Wood

Mayrath and Wood

Oscarson et al. Wormald Oscarson et al.

Holmes et al. Fuangswasdi et al. Oscarson et al. Wormald Oscarson et al.

Authors

1983b

2001

1992

en-MgCl2 + HCl-2.1

en-MgCl2 + HCl-1.1

en-MgCl2-1.2

en-LiCl-1.1 en-LiCl-2.1 en-MgCl2-1.1

1983b 1982b 1997 1983b 1997

en-KOH-2.1

en-KOH-1.1

en-KCl-3.1

en-KCl-2.1

en-KCl-1.1

en-HNO3-1.1 en-H2S-1.1 en-H2SO4 + Na2SO4-1.1 en-KBr-1.1

en-HCl-1.1 en-HCl-2.1 en-HCl-3.1 en-HCl-4.1 en-HCl + NaC2H3O2-1.1

Table codes for Appendix

2000

1998

1997

1982b

1975

1982b

1992 2003c 1988

1987 2000 2001 2003b 1988

Year

278 Hydrothermal Experimental Data

ammonium chloride sodium carbonate sodium bromide sodium chloride sodium chloride

NH4Cl

Na2SO4 Na2SO4 SO2

NaOH + HCl

NaI NaOH NaOH NaOH NaOH NaOH NaOH NaOH + HCl

NaHSO4 + NaC2H3O2

NaHCO3

NaCl NaCl NaCl NaCl NaCl NaCl NaCl + MgCl2

sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride + magnesium chloride sodium bicarbonate sodium bisulfate + sodium acetate sodium iodide sodium hydroxide sodium hydroxide sodium hydroxide sodium hydroxide sodium hydroxide sodium hydroxide sodium hydroxide + hydrochloric acid sodium hydroxide + hydrochloric acid sodium sulfate sodium sulfate sulfur dioxide

x

ammonia

NH3

Na2CO3 NaBr NaCl NaCl

x x

nitrogen nitrogen

N2 N2

m m x

m

m m m m m m m m

0.0025 2.14 0.5

0.5 + 0.52

5 6.3 1.84 9.8 0.515 1.9 1.93 0.5 + 0.5

1+1

0.98

m

m

6 6 5.18 3.0 0.45 0.5 1.9 + 1.9

1.45 8.1 0.043 10.3

6

0.5

0.87 0.80

max

0.01 0.025 0.007 1.65

0.01

0.25 0.25

min

0.003

0.099 + 0.1

0.016 0.01 0.370 0.026 0.026 0.022 0.01 0.1 + 0.5

0.25 + 0.25

0.02

0 0.007 0.02 0.012 0.05 0.01 0.25 + 0.25

Concentration

w m m m m m m

m m m m

m

unit

solute

formula

Nonaqueous component

573 373 383

523

373 298 523 523 573 573 573 598

548

298

457 348 333 349 573 573 373

298 373 387 573

298

383

520 448

min

453

573

523

473 473 523 523 573 573 573 598

548

473

457 473 472 498 573 573 473

473 473 473 573

473

453

520 498

min Table

Temperature (K)

573 424 483

623

598 573 623 643 598

473 525

593

523

985 473 675 498 623 653 573

523 473 473 573

523

493

621 698

max

ENTHALPY

V.pr. 0.2 0.1

11.4

0.2 6.8 5.5 4.5 9.3 9 9.3 12.4

10

7

6.6 1.0 9.3 9.3 20.5

51

7 0.2 V.pr. V.pr.

6.9

0.1

2 4.24

min

0.8

17.4

18 25

12.4

1.5 41

13

41

100 1.9 42 3.4 17.6 25

41 1.5

35

6 12.6

max

Pressure (MPa)

Hsoln Hdil Hexc

Hmix

Hdil Hdil Hdil Hdil Hdil Hdil Hdil Hmix

Hreac. Hdil

Hdil

Hsoln Hdil Hdil Hdil Hdil Hdil Hmix

Hdil Hdil Hsoln Hsoln

Hdil

Hexc

Hinc; Hexc Hexc

Data

bc fc fc

fc

fc fc fc fc fc fc fc fc

fc

fc

bc fc fc fc fc fc fc

fc fc bc dr/c

fc

fc

fc fc

Technique

Cobble and Murray Mayrath and Wood Wormald

Chen et al.

Mayrath and Wood Simonson et al. Oscarson et al. Chen et al. Chen et al. Gillespie et al. Fuangswasdi et al. Chen et al.

Oscarson et al.

Polya et al.

Bottini and Saville Wormald and Colling; Lancaster & Wormald; Wormald Wormald & Wurzberger Thiessen and Simonson Polya et al. Mayrath and Wood Gardner et al. Borodenko and Galinker Kasper et al. Mayrath and Wood Busey et al. Archer Chen et al. Fuangswasdi et al. Wang et al.

Authors

1977 1983b 2003a

1994b

1982b 1989 1991 1992b 1996 1998 2000 1992b

1988

2001

1979 1982a 1984 1986b 1996 2001 1997

2001 1982b 1969 1975

1990

2001

1985 1983; 1990; 1995

Year

en-SO2-1.1

en-Na2SO4-1.1

en-NaOH + HCl-2.1

en-NaI-1.1 en-NaOH-1.1 en-NaOH-2.1 en-NaOH-3.1 en-NaOH-4.1 en-NaOH-5.1 en-NaOH-6.1 en-NaOH + HCl-1.1

en-NaHSO4 + NaC2H3O2-1.1

en-NaHCO3-1.1

en-NaCl-3.1 en-NaCl-4.1 en-NaCl-5.1 en-NaCl-6.1 en-NaCl-7.1 en-NaCl-8.1 en-NaCl + MgCl2-1.1

en-Na2CO3-1.1 en-NaBr-1.1 en-NaCl-1.1 en-NaCl-2.1

en-NH4Cl-1.1

en-NH3-1.1

en-N2-1.1 en-N2-2.1; 2.2

Table codes for Appendix

Calorimetric Properties of Hydrothermal Solutions 279

argon argon arsenious acid arsenic acid barium chloride methane

methanol methanol methanol methanol methanol ethylene acetic acid glycine glycine ethanol acetone propanoic acid propionamide a-alanine b-alanine 1-propanol propanol propylamine propylamine hydrochloride succinic acid glycylglycine diethyl ether 1,2-dimethoxyethane 1,4 butanediol 1-4, butanediamine pyridine proline phenol m-dihydroxybenzene o-dihydroxybenzene p-dihydroxybenzene aniline m-aminophenol o-aminophenol

Ar Ar As(OH)3 AsO(OH)3 BaCl2 CH4

CH4O CH4O CH4O CH4O CH4O C2H4 C2H4O2 C2H5NO2 C2H5NO2 C2H6O C3H6O C3H6O2 C3H7NO C3H7NO2 C3H7NO2 C3H8O C3H8O C3H9N C3H10NCl

C4H6O4 C4H8N2O3 C4H10O C4H10O2 C4H10O2 C4H12N2 C5H5N C5H9NO2 C6H6O C6H6O2 C6H6O2 C6H6O2 C6H7N C6H7NO C6H7NO

solute

formula

Nonaqueous components

Table 7.1 Continued

m m m m m m m m m m m m m m m

0.15 0.07 0.05 0.10 0.42 0.4 0.4 0.1 0.19 0.3 0.3 0.15 0.15 0.11 0.025

0.5 0.059 0.36 0.1 0.5 0.17 0.42 0.097 0.076 0.1 0.11 0.4 0.4 0.08 0.051 0.4 0.25 0.35 0.39

0.08 0.144

w m

x x x x w m m m m x m m m m m m x m m

0.08 0.070

min

m m

unit

Concentration

0.23 0.085 0.50 0.70 0.89 0.86 0.93 1.79 0.81 1.82 1.49 0.5 0.3 0.22

0.85 2.27 0.3 0.76 1.04 0.9 0.78 1.21 1.34 0.9 0.74 0.69 0.69

0.9

0.71

0.26

0.115 0.098

max

303 352 298 298 303 303 303 323 303 303 303 303 303 303 303

436 290 335 329 371 302 303 323 352 290 298 303 303 298 323 303 290 303 303

418 304

306 607

min

473 473 523 523 523 523 473.5 423 423 423 473.5 423 423

523

523 523

523

473 524 523 473

422 446 447 523 474

454

470 523

500 607

min Table

Temperature (K)

523 423 524 524 523 523 523 499 623.2 473 473 473 623.2 573 473

650 415 421 522 579 722 523 499 471 430 524 524 523 473 423 523 430 523 523

632 704

578 720

max

HEAT CAPACITY

28 10 0.1 0.1 28 28 28 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

d/304 5 0.09 5 d/214 18 28 0.1 10 5 0.1 28 28 0.1 0.1 28 8.4 28 28

V.pr. 28

17 32

min

30.6 30.2 2.2 2.2 2.2 30.2 30.2 2.2

28 28

30

30.2 30.3

30 28

30.6

d/339 28 18 10 d/395 32

max

Pressure (MPa)

Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp

Cv Cv Cv Cp Cv Cp Cp Cp Cp Cv Cp Cp Cp Cp Cp Cp Cv Cp Cp

Cp Cp Cp Cp Cs Cp

Data

fc fc fc fc fc fc fc fc fc fc fc fc fc fc fc

adiab adiab adiab fc adiab fc fc fc fc adiab fc fc fc fc fc fc adiab fc fc

fc fc fc fc dr/c fc

Technique

Inglese et al. Downes et al. Slavik et al. Slavik et al. Inglese and Wood Inglese et al. Inglese et al. Clarke et al. Censky et al. Censky et al. Censky et al. Censky et al. Censky et al. Censky et al. Censky et al.

Biggerstaff et al. Biggerstaff and Wood Perfettii et al. Perfettii et al. Zarembo Hnedkovsky and Wood Abdulagatov et al. Kitajima et al. Aliev et al. Dettmann et al. Polikhronidi et al. Biggerstaff and Wood Inglese et al. Clarke et al. Downes et al. Kitajima et al. Slavik et al. Inglese et al. Inglese et al. Clarke et al. Clarke et al. Inglese and Wood Kitajima et al. Inglese et al. Inglese et al.

Authors

1996 2001 2007 2007 1996 1997 1997 2000 2005a 2005b 2005b 2005b 2005a 2005b 2005b

2000a 2003 2003 2006 2007 1988 1996 2000 2001 2003b 2007 1996 1997 2000 2000 1996 2003a 1997 1997

1985 1988 2008 2008 1985 1997

Year

hc-C4H10O-1.1 hc-C4H10O2-1.1 hc-1,4-C4H10O2-1.1 hc-C4H12N2-1.1 hc-C5H5N-1.1 hc-C5H9NO2-1.1 hc-C6H6O-1.1 hc-m-C6H6O2-1.1 hc-o-C6H6O2-1.1 hc-p-C6H6O2-1.1 hc-C6H7N-1.1 hc-m-C6H7NO-1.1 hc-o-C6H7NO-1.1

hc-C4H6O4-1.1

hc-C3H9N-1.1 hc-C3H10NCl-1.1

hc-C3H8O-1.1

en-C3H6O-1.1 hc-C3H6O2-1.1 hc-C3H7NO-1.1 hc-C3H7NO2-1.1

hc-CH4O-2.1 hc-CH4O-3.1; 3.2 hc-C2H4O-1.1 hc-C2H4O2-1.1 hc-C3H7NO2-1.1

hc-CH4O-1.1

hc-Ar-1.1 hc-Ar-2.1 hc-As(OH)3-1.1 hc-AsO(OH)3-1.1 hc-BaCl2-1.1 hc-CH4-1.2

Table codes for Appendix

280 Hydrothermal Experimental Data

phosphoric acid phosphoric acid+ hydrochloric acid hydrogen sulfide potassium chloride potassium chloride potassium chloride potassium chloride potassium chloride potassium chloride potassium nitrate potassium hydroxide potassium hydroxide

potassium hydroxide

potassium aluminates

H3PO4 H3PO4 + HCl

KOH

K2O/Al2O3

H2S KCl KCl KCl KCl KCl KCl KNO3 KOH KOH

x K2O

w

m w w m m m x x w x

w m m x P2O5 m m

m m m m

calcium chloride cobaltous chloride cesium bromide ferrous chloride+ hydrochloric acid boric acid boric acid hydrochloric acid phosphoric acid

CaCl2 CoCl2 CsBr FeCl2 + HCL

H3BO3 H3BO3 HCl H3PO4

m m m m x x m m m m m m m m m m w

p-aminophenol o-diaminobenzene 2,5-hexanedione cyclohexanol n-hexane n-hexane 1,6-hexanediol 1,6-hexanediamine benzylalcohol m-cresol o-cresol p-cresol m-toluidine o-toluidine p-toluidine carbon dioxide calcium chloride

C6H7NO C6H8N2 C6H10O2 C6H12O C6H14 C6H14 C6H14O2 C6H16N2 C7H8O C7H8O C7H8O C7H8O C7H9N C7H9N C7H9N CO2 CaCl2

0.1

0.0009

0.369 0.02 0.025 0.8 0.1 0.05 0.0024 0.0018 0.001 0.0083

0.12 0.12 + 0.049

0.05 0.2 0.1 0.62

0.05 0.5 0.005 0.07

0.05 0.12 0.06 0.05 0.385 0.61 0.39 0.36 0.10 0.1 0.097 0.095 0.097 0.12 0.065 0.189 0.053

0.3

0.043

0.05 0.014

0.373 0.10 0.25 9.1 3.0 3

0.82

0.2 0.75 6.0 0.83

3.0 2.5 0.5 3.5

0.195 0.42

0.14

0.06 0.24 0.70 0.31 0.879 0.99 0.63 0.64 0.30 0.2 0.21 0.18

298

653

304 353 423 333 325 413 604 299 646 646

303 303

433 303 302 300

306 298 598 349

303 303 298 298 455 373 303 303 298 303 303 303 303 303 303 304 423

423

653

523 473 473 473 500 473 604 473 646 646

523 523

433 523 523 450

501 298 598 498

423 423 473 424 491 480 523 523 423 473.5 473.5 473.5 473.5 473.5 473.5 523 473

611

681

704 473 623 493 603 573 679 536 681 712

623 623

573 704 623 640

603 573 691 599

473 573 524 424 575 575 523 523 473 623.2 623.2 623.2 623.2 623.2 623.2 704 628

V.pr.

d/250

28 V.pr. V.pr. V.pr. 17.9 20 d/333 d/794 d/315 d/250

28 28

<20 28 28 V.pr.

2.1 V.pr. 28 18

0.1 0.1 0.1 0.1 d/263 d/259 28 28 0.1 0.1 0.1 0.1 0.1 0.1 0.1 28 V.pr.

d/315

d/315

d/598 d/1002

38

17.5

10 30.2 30.2 30.2 30.2 30.2 30.2

2 26 28 10 d/286 d/312

adiab dr/c

Cs

fc bc dr/c dr/c fc fc adiab adiab adiab adiab

fc fc

bc fc fc bc

fc dr/c fc fc

fc fc fc fc adiab adiab fc fc fc fc fc fc fc fc fc fc dr/c

Cv

Cp Cs; Cp Cs Cs Cp Cp Cv Cv Cv Cv

Cp Cp

Cp Cp Cp Cs

Cp Cs Cp Cp

Cp Cp Cp Cp Cv Cv Cp Cp Cp Cp Cp Cp Cp Cp Cp Cp Cs

Hnedkovsky & Wood Likke et al. Feodorov Conti et al. White et al. Pabalan and Pitzer Abdulagatov et al. Abdulagatov et al. Amirkhanov et al. Abdulagatov and Dvoryanchikov Abdulagatov and Dvoryanchikov Mashovets et al.

Sharygin et al. Sharygin et al.

Popov Hnedkovsky et al. Sharygin & Wood Luff

Censky et al. Censky et al. Slavik et al. Slavik et al. Kamilov et al. Kamilov et al. Inglese and Wood Inglese et al. Slavik et al. Censky et al. Censky et al. Censky et al. Censky et al. Censky et al. Censky et al. Hnedkovsky & Wood Soboleba et al.; Zarembo White et al. Galinker and Belova Carter Wood et al.

1970

1994

1997 1973 1982 1984 1987b 1988a 1998a 1997 1979 1993

1997 1997

1970 1995 1997 1981

2005b 2005b 2007 2007 1996 2001 1996 1997 2007 2005a 2005a 2005a 2005a 2005a 2005a 1997 1985; 1985 1987a 1963 1992 1988

hc-K2O/Al2O3-1.1

hc-KOH-3.1

hc-H2S-1.1 hc-KCl-1.1 hc-KCl-2.1 hc-KCl-3.1 hc-KCl-4.1 hc-KCl-5.1 hc-KCl-6.1; 6.2 hc-KNO3-1.1 hc-KOH-1.1 hc-KOH-2.1

hc–H3PO4–2.1 hc–H3PO4 + HCl–1.1

hc–H3BO3–1.1; 1.2 hc–H3BO3–2.1 hc–HCl–1.1 hc–H3PO4–1.1

hc-CaCl2-2.1 hc-CoCl2-1.1 hc-CsBr-1.1 hc-FeCl2 + HCl-1.1

hc-p-C6H7NO-1.1 hc-o-C6H8N2-1.1 hc-C6H10O2-1.1 hc-C6H12O-1.1 hc- C6H14-1.1 hc- C6H14-2.1 hc-C6H14O2-1.1 hc-C6H16N2-1.1 hc-C7H8O-1.1 hc-m-C7H8O-1.1 hc-o-C7H8O-1.1 hc-p-C7H8O-1.1 hc-m-C7H9N-1.1 hc-o-C7H9N-1.1 hc-p-C7H9N-1.1 hc-CO2-1.1 hc-CaCl2-1.1

Calorimetric Properties of Hydrothermal Solutions 281

Continued

lithium chloride lithium chloride lithium hydroxide magnesium chloride magnesium chloride magnesium chloride magnesium sulfate magnesium sulfate ammonia ammonia ammonium chloride sodium bromide sodium bromide sodium acetate sodium propanoate sodium benzenesulfonate sodium carbonate sodium chloride sodium chloride

sodium chloride sodium chloride

sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride sodium chloride

LiCl LiCl LiOH MgCl2 MgCl2 MgCl2 MgSO4 MgSO4 NH3 NH3 NH4Cl NaBr NaBr NaC2H3O2 NaC3H5O2 NaC6H5O3S

NaCl NaCl

NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl Na,K//Cl,SO4 Na,K//Cl,SO4 Na,K//Cl,SO4

Na2CO3 NaCl NaCl

solute

formula

Nonaqueous components

Table 7.1

w m m m m m m m x m m m m

w m

x w w

m m w w w m w m m w m m m m m m

unit

0.05 0.08 0.015 1 1 0.1 0.005 3 0.0009 0.015 0.6 0.6 0.6

0.01 0.1

0.0087 0.02 0.025

0.05 0.005 0.02 0.02 0.052 0.03 0.02 0.1 0.184 0.7 0.1 0.05 0.0097 0.12 0.4 0.3

min

Concentration

0.0932 2.99 5 5 5

3 6 2.0 3.0

0.2 3

3

0.11 0.26

0.9 0.67

3.0 3.0 0.1 0.08 0.35 2.26 0.10 2.1 3.09 0.9 6.0 3.0 3.0

max

369 349 604 358 323 348 599 303 473 303 333 333 333

615 320

331 353 423

306 598 298 353 421 349 353 348 304 301 303 306 599 303 303 303

min

477 498 604 574 499 473 599 524 473 473 453 473 453

615 491

473 473 473

470 498 473 473 523 469 524 501 599 523 524 523

501 598 471

min Table

Temperature (K)

587 598 720 574 598 548 691 524 713 632 493 493 493

667 603

661 473 623

603 676 616 453 626 598 473 473 704 522 623 603 676 523 524 523

max

HEAT CAPACITY

d/757 2 32 17.7 7 16.5 28 28 d/342 0.2 V.pr. V.pr. V.pr.

15 17.7

d/245 V.pr. V.pr.

17.5 28 V.pr. Psat V.pr. 2.3 V.pr. 2 28 3 28 17.5 28 28 28 28

min

d/1017 30

38

36

d/990 18

27.5

d/427

38

20

18

38

max

Pressure (MPa)

Cv Cp Cp Cp Cp Cp Cp Cp Cv Cp Cp?Cs Cs Cp?Cs

Cv Cp

Cv Cs; Cp Cs; Cp

Cp Cp Cs Cs; Cp Cs Cp Cs; Cp Cp Cp Cv Cp Cp Cp Cp Cp Cp

Data

adiab fc fc fc fc fc fc fc adiab fc dr/c dr/c dr/c

adiab fc

adiab bc dr/c

fc fc dr/c bc dr/c fc bc fc fc adiab fc fc fc fc fc fc

Technique

Abdulagatov et al. Likke and Bromley Puchkov et al.; Feodorov Mursalov et al. Smith-Magowan & Wood Mursalov & Bochkov Gates et al. White et al. White and Downes Roger and Dutty Coxam et al. Carter Inglese and Wood Abdulagatov et al. Hnedkovsky et al. Conti et al. Conti et al. Conti et al.

White et al. Carter Puchkov and Matveeva Likke et al. Zarembo White et al. Likke and Bromley Phutela & Pitzer Hnedkovsky & Wood Magee and Kagawa Sharygin and Wood White et al. Carter Inglese et al. Inglese et al. Inglese et al.

Authors

1984 1987 1988b 1988 1989 1991 1992 1996 1998a 2002 1985 1986 1989

1999 1973 1976; 1982 1979 1981

1987c 1992 1972 1973 1985 1988a 1973 1986 1997 1998 1996 1987d 1992 1996 1996 1997

Year

hc-NaCl-5.1 hc-NaCl-6.1 hc-NaCl-7.1 hc-NaCl-8.1 hc-NaCl-9.1 hc-NaCl-10.1 hc-NaCl-11.1 hc-NaCl-12.1 hc-NaCl-13.1; 13.2 hc-NaCl-14.1 hc-Na,K//Cl,SO4-1.1 hc-Na,K//Cl,SO4-2.1 hc-Na,K//Cl,SO4-3.1

hc-NaCl-3.1 hc-NaCl-4.1

hc-Na2CO3-1.1 hc-NaCl-1.1 hc-NaCl-2.1

hc-MgCl2-1.1 hc-MgCl2-2.1 hc-MgSO4-1.1 hc-MgSO4-2.1 hc-NH3-1.1 hc-NH3-2.1 hc-NH4Cl-1.1 hc-NaBr-1.1 hc-NaBr-2.1 hc- NaC2H3O2-1.1 hc- NaC3H5O2-1.1 hc-NaC6H5O3S-1.1

hc-LiCl-2.1 hc-LiCl-3.1 hc-LiOH-1.1

Table codes for Appendix

282 Hydrothermal Experimental Data

sodium hydroxide sodium hydroxide+ sodium hydroxyaluminate sodium sulfate sodium sulfate sodium sulfate sodium sulfate sodium sulfate sodium sulfate sodium sulfate sodium sulfate+ sodium chloride nickel chloride nickel chloride * 2 sodium chloride sulfur dioxide sulfur dioxide + hydrochloric acid xenon

NaOH NaOH + NaAl(OH)4

Xe

SO2 SO2 + HCl

Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 + NaCl NiCl2 NiCl2*2NaCl

sodium hydroxide sodium hydroxide sodium hydroxide sodium hydroxide sodium hydroxide

NaOH NaOH NaOH NaOH NaOH

0.2 0.18 + 0.05

m m

0.06

0.12 0.12

m m

m

0.02 0.05 0.1 0.05 1 0.0013 0.01 3

0.0045 0

0.05 0 0.1 0.0045 0.01

w m m m m x w m

x m

w m m x w

0.07

0.9

3 1

0.099 2.6 1 1.5 3 0.014 0.1 4.5

0.1 1.7

0.5 1.5 4.1 0.0091 0.05

319

303 303

323 322

353 305 323 413 333 460 350 333

661 326

396 325 323 619 612

486

524 524

499 498

475 473 473 453 460 350 453

661 470

473 470 523 619 612

720

623 623

573 573

453 475 473 573 493 668 670 493

827 518

675 522 523 735 695

31

28 28

17.7 17.7

V.pr. 0.1 4 20 V.pr. d/250 d/250 V.pr.

d/370 <6

V.pr. 4? 7 d/540 d/370

d/926 d/1073

20

d/960

36 d/680 d/720

Cp

Cp Cp

Cp Cp

Cs; Cp Cp Cp Cp Cp; Cs Cv Cv Cp; Cs

Cv Cp

Cs Cp Cp Cv Cv

fc

fc fc

fc fc

bc fc fc fc dr/c adiab adiab dr/c

adiab fc

dr/c fc fc adiab adiab

Biggerstaff and Wood

Sharygin et al. Sharygin et al.

Smith-Magowan et al. Smith-Magowan et al.

Likke et al. Roger and Pitzer Conti et al. Pabalan & Pitzer Conti et al. Abdulagatov et al. Abdulagatov et al. Conti et al.

Puchkov et al. Conti et al. Simonson et al. Abdulagatov et al. Abdulagatov and Dvoryanchikov Abdulagatov et al. Caiani et al.

1988

1997 1997

1982 1982

1973 1981 1988 1988b 1989 1998b 2000b 1989

1998a 1989

1972 1988 1989 1989 1994

hc-Xe-1.1

hc-SO2-1.1 hc-SO2 + HCl-1.1

hc-NiCl2-1.1 hc-NiCl2*2NaCl-1.1

hc-Na2SO4-1.1 hc-Na2SO4-2.1 hc-Na2SO4-3.1 hc-Na2SO4-4.1 hc-Na2SO4-5.1 hc-Na2SO4-6.1 hc-Na2SO4 + NaCl-1.1

hc-NaOH-6.1; 6.2 hc-NaOH + NaAl(OH)4-1.1

hc-NaOH-1.1 hc-NaOH-2.1 hc-NaOH-4.1 hc-NaOH-3.1 hc-NaOH-5.1

Calorimetric Properties of Hydrothermal Solutions 283

284

Hydrothermal Experimental Data

nonaqueous components in each aqueous system and indicate the general molecular formula (the first column) and the chemical names of the nonaqueous components (the second column). The concentration units, indicated in the 3rd column, are: molality (m); mass (w) or mole fractions (x) of nonaqueous component. The columns from 4th to 10th contain the minimal and maximal values for solution concentration (4th and 5th columns), temperature (6th, 7th and 8th columns) and pressure (9th and 10th columns) to indicate the ranges of the parameters of state studied. The 7th column shows the lowest temperatures starting from which the original experimental calorimetric data are available in the Appendix placed on the CD-ROM. In some cases the values of density are indicated in the 9th and 10th columns. V.pr. indicates that the experiment was made at the saturated vapor pressure and the values of pressure are not given. The experimental quantities (type of data) reported in the study publication are indicated in the 11th column: excess enthalpy (Hexc); enthalpy of mixing (dHmix); enthalpy of solution (Hsoln); enthalpy of vaporization (Hvap); enthalpy of dilution (dHdil); enthalpy increment (dHinc); enthalpy of reaction (dHreac), isobaric heat capacity (Cp), isochoric heat capacity (Cv), heat capacity under saturated vapor pressure (Cs). The 12th column indicates the experimental technique employed in the study: flow calorimetry (fc); batch calorimetry (bc); drop calorimeter (dr/c); adiabatic calorimeter (adiab) for Cv measurements. References are listed in the 13th column (names of the authors or the first author if there are more than two) and 14th column (year of publication). The 15th column indicates the cases where the experimental calorimetric data are available in the Appendix. Empty boxes in this column mean that the measurements have been made at temperatures below 200 °C. Acknowledgement Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC, for the U.S. Department of Energy. REFERENCES Abdulagatov, I.M., Dvoryanchikov, V.I., and Abdurakhmanov, I.M. (1990) In: M. Pichal and O. Sifner (eds), Properties of Water and Steam, Proceedings of the 11th Intern. Conference on the Properties of Steam. Hemisph. Publ. Corp., pp. 203–9. Abdulagatov, I.M. and Dvoryanchikov, V.I. (1993) J. Chem. Thermod. 25(7): 823–30. Abdulagatov, I.M. and Dvoryanchikov, V.I. (1994) Geokhimiya 1: 101–10. Abdulagatov, I.M., Dvoryanchikov, V.I. and Kamalov, A.N. (1997) J. Chem. Thermod. 29(12): 1387–1407. Abdulagatov, I.M., Dvoryanchikov, V.I., Mursalov, B.A. and Kamalov, A.N. (1998a) Fluid Phase Equil. 143, n.1–2, pp. 213–240.

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Calorimetric Properties of Hydrothermal Solutions 287

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Index

adiabatic calorimeters 272 ‘analytic’ methods 2, 3 apparent molar volume 135–6 excess volume 136 ionic solutes 140–3 non-ionic solutes 143 binary systems phase diagrams classification 87–91 critical phenomena in solid saturated solutions 93, 95, 97, 106 experimental examples 86, 88, 91–2, 95, 97, 100 graphical representation 91, 103 with liquid-liquid immiscibility 93 without liquid-liquid immiscibility 91–3 phase equilbria 86–7 pVTx data acids 185 ionic solutes 140, 143, 153, 157 non-ionic solutes 143 buffer solutions 200 buffers 81 calorimetric properties basic principles 271 batch techniques 272 experimental data 274–84 flow techniques 272–4 capillary-flow viscometers 253–5 capsule apparatus 73, 74 chemical equilibria and reactions 72 coaxial-cylinder thermal conductivity cell 236–9 cold-seal pressure vessels 81 conductivity see electrical conductivity; thermal conductivity constant volume piezometers (CVP) 136–7 cosolvency effect 114 critical phenomena/equilibria 1, 4, 74, 87–119, 148–52, 157–9, 271 crossover equation of state (CREOS) 148–52 Debye-Hückel (DH) theory 136 Debye-Hückel limiting law (DHLL) 140, 142 density measurement 84, 136–40 diamond window cells 73 differential heat flux calorimeters 273 differential thermal analysis (DTA) 85–6

diffusion potential 198, 199–200 dilatometers 137–8 drop calorimeters 272 dynamic (flow) methods, phase equilbria 3, 74 dynamic viscosity applications 249, 252 basic principles and definitions 249 concentration dependence 264 experimental data 250–1, 260–7 comparisons 265–7 experimental techniques 252–60 capillary-flow technique 253–5 falling-body technique 257–9 oscillating cups 252–3 oscillating-disk technique 255–7 vibrating wire 253 limiting law 252, 264 pressure dependence 261–4 temperature dependence 249, 261 Einstein (viscosity) equation 265 electrical conductivity basic principles and definitions 207, 215 concentration dependence 220, 221, 222, 223 data treatment associated electrolytes 219–21 dissociated electrolytes 219 density dependence 222, 222–3, 224 experimental data 208–14 obtaining information from 221 experimental methods 215 flow-through conductivity cell 217–18 measurement procedure 218 static high temperature conductivity cells 215–17 limiting law 220 molar conductivity 215 limiting 222–3 property-parameter curves 84 temperature dependence 221–2, 224 ternary systems 214, 224 electrochemical potential basic principles 195, 198 data treatment 203–5 diffusion potential 199–200 experimental data 196–7 experimental techniques buffer solutions 200 indicator electrodes 198–9 reference electrodes 198

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

reference solutions 200 streaming potential 199–200 thermal diffusion potential 199–200 thermoelectric potential 199–200 electrolytes see ionic solutes enthalpy activation energy 261 calorimetric techniques 271–4, 284 experimental data 275–9 ionization 204 property-parameter curves 84–5 entropy, ionization 154, 155 equations of state binary aqueous solutions 144–5 Helgeson and Kirkham (HKF) model 154 parametric crossover model 148–52 quasilattice equation of state for mixtures 145–8 water + hydrocarbon mixtures 143–4 eutonic equilibria 115 excess apparent molar volume 136, 140–3 ionic solutes 140–3 non-ionic solutes 143 excess molar enthalpies 271, 274 experimental methods, classification 3 Falkenhagen-Onsager-Fuoss theory 264 falling-body viscometer 257–9 Fernández- Prini equation (FHFP) 219, 220, 221, 223 fill coefficient 74 filtering materials 77 flow calorimeters 271, 272–4 flow methods, phase equilbria measurements 74 flow vibrating-tube densimeter (VTD) 139–40 flow-mixing calorimeters 273–4 flow-through conductivity cell 217–18 flow-through potentiometric cells 202–3 fluid inclusions method 79 Franck equations 143–4 Fuoss-Hsia equation 219 Fuoss-Kraus equation 221 Gibbs energy 141, 154 electrochemical potential 195, 198, 203, 204 heat capacity 271 calorimetric properties basic principles 271 batch techniques 272

290

Index

experimental data 274–84 flow techniques 272–4 property-parameter curves 85 heat capacity calorimeters 274 heat exchange calorimeters 274 heat-flux calorimeters 273 Helgeson and Kirkham (HKF) model 154–5 non-ionic solutes 157 ‘hot’ valves 78 hot-wire thermal conductivity cell 240–1 hydrogen-electrode concentration cell (HECC) 200–2 hydrostatic weighing technique (HWT) 138–9 hydrothermal bombs 76–7

non-ionic solutes dynamic viscosity 260 electrical conductivity in ternary systems 224 excess apparent molar volume 143–6 Helgeson and Kirkham (HKF) model 157 multi-component systems 153 pVTx properties binary systems – nonelectrolytes 172–81 ternary systems – nonelectrolytes 184 ternary systems – nonelectrolytes – electrolytes 184 standard partial molar volume 157 near critical conditions 157–9

immiscibility 87, 88 phase diagrams 93–100, 112–13, 114 indicator electrodes 198–9 internally heated pressure vessels 82 ionic solutes excess apparent molar volume 140–3 ion association effects 142–3, 219–21 ion-interaction model 141–2 multi-component systems 153 pVTx data binary systems 160–71 quaternary systems 184 ternary systems 183–4 standard partial molar volume 153–7 near critical conditions 157–9 isochoric heat capacity 271, 272 property-parameter curves 85 isopiestic method 72, 80 isothermal flow mixing calorimeter 273 isotope partitioning 3

Onsager’s law 219 optical cells 73–4 oscillating cup viscometers 252–3 oscillating-disk viscometers 255–7

Jones-Dole viscosity equation 252, 265 Kohlrausch’s law 215 Krichevskii parameter 156, 158 law of corresponding states (LCS) 150 Lee and Wheaton equation (LW) 219 limiting law Debye- Hückel limiting law (DHLL) 140, 142 dynamic viscosity 252, 264 electrical conductivity 219 limiting molar conductivity 222–3 mean spherical approximation (MSA) 142 metal bellows densimeter 138 molar conductivity 215 concentration dependence 220, 221, 223 density dependence 224 limiting molar conductivity 222–3 temperature dependence 224 molar enthalpy calorimetric techniques 271–4, 284 experimental data 275–9 molar excess enthalpies 271, 274 property-parameter curves 84–5 nonelectrolytes see non-ionic solutes non-ideal solutions 136

parallel-plate thermal conductivity cell 234–5 parametric crossover model 148–52 partial molar volume 135–6 absolute value 153 excess apparent molar volume 136 ionic solutes 140–3 non-ionic solutes 143–6 near critical conditions 157 standard state 136, 142 ionic solutes 153–7 near critical conditions 157–9 non-ionic solutes 157 p-∆H curves 4 property-parameter curves 84–5 phase boundaries 88–91 phase diagrams 2 binary systems boundary versions 88–91 classification 87–91 critical phenomena in solid saturated solutions 93 experimental examples 91–105 graphical representation 91–105 with liquid-liquid immiscibility 93–100 main types 86–7 topological transformation 88–91 without liquid-liquid immiscibility 91–3 ternary systems derivation and classification 105– 19 extrema on ternary critical curves and surfaces 113–14 fluid phase equilibria 112–15 graphical representation 103–19 influence of salts on ternary immiscibility regions 112–13 main types 106 p-T projections 105 solid solubility phenomena 115–19 three-dimensional T-x projection 104 topological transformation 105 transformation of immiscibility equilibria 114–15

two binary subsystems of types 1 and 2 115–18 two binary subsystems of types 2 118–19 topological schemes 91 two-dimensional representation 91 phase equilbria background 1–2 binary systems 86–103 experimental data 4–71 experimental methods 3, 72–86 ‘analytic’ methods 3 classification 3 dynamic (flow) methods 74–6 indirect methods 82–6 quenching methods 80–2 recirculation method 75 sampling methods 74–80 ‘synthetic’ methods 3 visual observation 3, 73–4 ternary systems 103–19 piston densimeter 138 Pitts equation (P) 219 Pitzer’s equation of state 146–8 Pitzer’s ion-interaction model 141–2, 142–3 Pitzer-Tanger-Hovey (PTH) EOS 146–7 plug-flow solubility apparatus 75 plugging 77 potentiometric method, solubility determination 73 potentiometry see electrochemical potential pressure determination 73–4 property-parameter curves 84–5 p-T curves 84, 86–7, 104, 105 p-T-x phase diagrams 91 pumps 75 p-V curves 84 p-V-T-x curves 82–3 pVTx properties background 2 basic principles and definitions 135–6 excess partial molar volume 140–53 experimental data 159–86 binary systems – electrolytes 160–71 binary systems – nonelectrolytes 172–83 quaternary systems – electrolytes 184 ternary systems – electrolytes 183–4 ternary systems – nonelectrolytes 184 ternary systems – nonelectrolytes – electrolytes 184 experimental methods 136–59 standard partial molar volume 153–9 p-x curves 83, 104 quasilattice equation of state for mixtures 145–6 quaternary systems, pVTx data 153, 184 quenching method 80–2 radioactive tracers, phase equilbria determination 3 Raman spectra 74 Redlich-Mayer equation 141 reference electrodes 198 reference solutions 200

Index

sampling methods 74–80 sapphire windows 73, 74 Scaled Particle Theory (SPT) 157 scanning force microscopy 74 sealed thick-walled capsules 73 Shedlovsky equation 220, 223 solubility determination 72–3 solute-solvent interaction 136, 156, 157 Soret effect 198 stainless steel vessels with quartz 73 Standard Hydrogen Electrode (SHE) scale 195 standard partial molar heat capacity of ionization 204 standard partial molar volume of ionization 204 standard state partial molar volume 135, 136 ionic solutes 153–7 near critical conditions 157 non-ionic solutes 157 static high temperature conductivity cells 215–17 static methods, phase equilbria measurements 3 streaming potential 198, 199–200 SUPCRT92 154 supercritical regions 146–51 models 156, 157 phase diagrams binary systems 90, 93, 103 ternary systems 116, 118 synthetic fluid inclusions method 79 fluid density measurement 139–40

‘synthetic’ methods, phase equilbria 3 Tammann-Tait-Gibson (TTG) model 262 ternary systems electrical conductivity 214, 224 phase diagrams classification 105–7 derivation 105–8 extrema on ternary critical curves and surfaces 113 fluid phase equilibria 112 graphical representation 103 influence of salts on ternary immiscibility regions 112 main types 106 p-T projections 105 solid solubility phenomena 115 three-dimensional T-x projection 104 topological transformation 105 transformation of immiscibility equilibria 114 two binary subsystems of types 1 and 2 118 two binary subsystems of types 2 118 pVTx data 183–4 thermal conductivity applications 228 basic principles 227 concentration dependence 245 experimental data 229–32, 242 comparisons 245–6

291

experimental techniques 228–42 coaxial-cylinder technique 235 parallel-plate technique 228, 233–5 transient hot-wire technique 239–41 pressure dependence 244–5 temperature dependence 242–4 thermal diffusion potential 198, 199–200 thermal-rise calorimeter 272 thermodynamic functions 72 thermoelectric potential 198, 199–200 thermostats 73 Turk-Blum-Bernard-Kunz equation (TBBK) 219, 220 T-V curves 84 T-x curves 82–3 vapor pressure determination 3, 72 variable volume piezometers (VVP) 137–8 vibrating tube densimeter (VTD) 139–40 vibrating wire viscometers 253 vibration response, property-parameter curves 84 visual cells 73–4 visual observation, phase equilbria 3, 73–4 volatility 92–3 weight-loss methods 80 X-ray absorption fine structure (XAFS) 74 X-ray diffraction measurements 74