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Experimental control of H-O-S gas mixtures with applications to Fe-Ni sulfideoxide-silicate reactions Lecheminant, Anthony Norman 1973

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EXPERIMENTAL CONTROL OF H-O-S GAS MIXTURES WITH APPLICATIONS TO ' F e-Ni SULFIDE-OXIDE-SILICATE REACTIONS . . by ANTHONY NORMAN LECHEMINANT B.Sc, C a r l e t o n U n i v e r s i t y , 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of GEOLOGY We accept t h i s t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1973 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C olumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p urposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Geology Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date Cjuu^ 4 / >3> i ABSTRACT S u l f i d e - o x i d e and s u l f i d e - o x i d e - s i l i c a t e r e a c t i o n s commonly i n v o l v e gas species i n the H-O-S system. Experimental i n v e s t i g a t i o n of such r e a c t i o n s r e q u i r e s c o n t r o l of H-O-S gas mixture compositions. The r e a c t i o n : F e 3 0 4 + 3/2 S 2 t 3 FeS + 2 0 2 has been s t u d i e d using s o l i d phase b u f f e r s i n nested noble metal capsules to c o n t r o l the H-O-S vapour phase at temperatures between 550 and 700°C and t o t a l pressures to 3000 bars. Results f o r IW, QFM, and NNO b u f f e r s correspond c l o s e l y to those p r e d i c t e d from thermochemical data. Reaction r a t e s allow p y r r h o t i t e compositions to be bracketed i n experiments l a s t i n g l e s s than 100 hours. Platinum and t h i n - w a l l e d Au capsules have been s u c c e s s f u l l y used as hydrogen membranes at f j ^ values s p e c i f i e d by QFM or NNO e x t e r n a l b u f f e r s . At s u l f u r and oxygen f u g a c i t i e s higher than those defined i n NNO b u f f e r experiments d i f f i c u l t i e s a r i s e due to low f j ^ v a l u e s , quench s u l f i d e phases, and r e a c t i o n between the H-O-S vapour phase and Pt capsules. Computer programs and data used to compute 0-H and H-O-S gas mixture compositions c o n t r o l l e d by b u f f e r systems t e s t e d i n t h i s study are t a b u l a t e d . C a r e f u l d i s t i n c t i o n must be made between c o n f i g u r a t i o n s that c o n t r o l f ( j 2 i n t e r n a l l y by s o l i d phase oxygen b u f f e r s and those i n which fQ i s s p e c i f i e d i n d i r e c t l y through hydrogen d i f f u s i o n . In the l a t t e r case f ( j 2 i n the charge capsule may d i f f e r s i g n i f i c a n t l y from f g 2 i n the e x t e r n a l b u f f e r . Computations show H 20, H 2, H 2S, and S 0 2 are ii q u a n t i t a t i v e l y the important species w i t h i n g e o l o g i c a l l y s i g n i f i c a n t regions of io,^ - f g - P - T space. Experimental evidence supports c a l c u l a t i o n s that p r e d i c t hematite cannot c o e x i s t w i t h e i t h e r p y r i t e or p y r r h o t i t e above 550°C at P ^ o t a l = 500 bars or 600°C at P t o t a l >2000 bars. The f e a s i b i l i t y of using QFM or NNO b u f f e r s to i n v e s t i g a t e s u l f i d e - o x i d e r e a c t i o n s i n the Ee-Ni-H-O-S system has been e s t a b l i s h e d . Results demonstrate the importance of £Q i n d e f i n i n g the m e t a l : s u l f u r r a t i o i n ( F e , N i ) j monosulfide s o l i d s o l u t i o n c o e x i s t i n g w i t h an Fe-bearing s p i n e l and vapour. iii TABLE OF CONTENTS ABSTRACT . i TABLE OF CONTENTS •• Hi LIST OF TABLES ; v LIST, OF FIGURES vii NOMENCLATURE List of symbols and abbreviations ix Greek letters % Notation for oxygen buffers - xi Notation for buffering systems • ' xi ACKNOWLEDGEMENTS xii 1. INTRODUCTION 1 2. THE 0-H SYSTEM 2.1 Theory 4 2.2 Temperature-Composition Diagrams 10 3. THE H-O-S SYSTEM 3.1 Theory . 17 3.2 I o n i z a t i o n E q u i l i b r i a 25 4. EXPERIMENTAL PROCEDURES 4.1 S t a r t i n g M a t e r i a l s and P r e l i m i n a r y M i n e r a l Syntheses C r i s t o b a l i t e 27 F a y a l i t e 27 N i c k e l - I r o n O l i v i n e S o l i d S o l u t i o n 27 N i c k e l O l i v i n e 28 Magnetite 28 Monosulfide S o l i d S o l u t i o n s 28 Bu f f e r Mixes ,. 29 .4.2 General Experimental Equipment and Procedures Pressure Systems 29 Pressure Vessels 32 Furnaces 32 • Temperature Measurement and C a l i b r a t i o n .. 32 Quench Procedures 3 3 Capsules 34 Bu f f e r Systems 35 iv 4.3 I d e n t i f i c a t i o n and Analysis of Phases 38 5. THE Fe-Si-H-O-S AND Fe-H-O-S SYSTEMS 5.1 Introduction 40 Choice of Reaction Vessel 41 Phase Rule 42 5.2 Thermochemical Calculations Magnetite-Pyrrhotite Equilibrium 43 Pressure Corrections 49 5.3 Experimental Results . . 56 WI External Buffer 56 QFM Internal Buffer 65 QFM External Buffer 74 NNO External Buffer 82 HM External Buffer 84 S t a b i l i t y of Platinum Sulfides 87 Electron Microprobe Analyses 92 6. NICKEL-BEARING SYSTEMS 6.1 Introduction and Theoretical Considerations ... 95 6.2 Experimental Results QFM and NNO External Buffers 96 6.3 Discussion and Geologic Implications 114 7. SUMMARY AND CONCLUSIONS 120 REFERENCES 125 Appendix 1. Input Data for Computer Programs 133 Appendix 2. 0-H System Computer Programs 140 Appendix 3. H-O-S System Computer Programs 155 Appendix 4. S-0 System Computer Program 188 Appendix 5. Gas Mixture Experiments - 0-H System .... 193 Experimental Procedures 193 Theory 194 • Experimental Results 196 Appendix 6. Fe-Ni Olivines 200 V LIST OF TABLES (2-1) Log f n 2 defined by MI, WI, and MW b u f f e r s 15 (1000 bars) (3-1) E q u i l i b r i u m Constants f o r Sg, Sg, and S4 20 (5-2) C r i t i c a l Constants f o r Molecular Species i n the H-O-S System 24 (4-1) Compositions of Mss used i n experiments 30 (4-2) Experimental B u f f e r i n g Systems: H-O-S Gas Mixtures 36 (5-1) Experimental Results Fe-H-O-S System 57 (5-2) Experimental Results Fe-Si-H-O-S System 59 (5-3) Experimental Results - C a l c u l a t e d log f ^ and Pressure C o r r e c t i o n s 61 (5-4) C a l c u l a t e d P o s i t i o n s of the F a y a l i t e + P y r r h o t i t e + Magnetite + Quartz + Vapour I n v a r i a n t P o i n t .. 71 (Fe-Si-H-O-S System - 1 atm.) (5-5) Thermochemical C a l c u l a t i o n s 73 (QFM I n t e r n a l B u f f e r ) (5-6) H-O-S Gas Mixture Compositions i n e q u i l i b r i u m with Quartz + F a y a l i t e + Magnetite + P y r r h o t i t e . 75 (5-7) Thermochemical C a l c u l a t i o n s ' 81 (QFM E x t e r n a l Buffer) (5-8) Thermochemical C a l c u l a t i o n s 83 (NNO E x t e r n a l Buffer) (5-9) Microprobe Analyses 93 (6-1) Experimental Results 100 (6-2) Analyses of Monosulfide S o l i d S o l u t i o n (Mss) ... 105 (6-3) C a l c u l a t e d log f o 2 values based on the Magnetite - P y r r h o t i t e E q u i l i b r i u m f o r Pumice flows from the Rabaul Caldera, Papua, New Guinea 119 (Al-1) C o e f f i c i e n t s f o r oxygen b u f f e r s 134 (Al-2) Fugacity C o e f f i c i e n t s f o r gas species i n the H-O-S system 135 (Al-3) Log K f o r gas species i n the H-O-S system 139 vi (A5-1) Experimental Results Fe-O-H System 197 (A5-2) O-H Gas Mixture C a l c u l a t i o n s 199 (A6-1) Fe-Ni O l i v i n e Syntheses 201 (A6-2) d(130) Values f o r F a y a l i t e 203 v i i LIST OF FIGURES (2-1) Fe-O-H System I s o b a r i c T-X Diagram 11 (1000 bars, MW1, WI1, M i l b u f f e r s ) (2-2) Fe-O-H System I s o b a r i c T-X Diagram 12 (1000 bars, MW2, WI2, MI2 b u f f e r s ) (2-3) Fe-O-H System I s o b a r i c T-X Diagram 13 (2000 bars, MW1, WI1, M i l b u f f e r s ) (3-1) Log f s 8 , log f s 6 , and log f S 4 as a f u n c t i o n of log f§2 i n s u l f u r vapour 22 (4-1) 7 K i l o b a r Argon Pressure System 31 (4-2) QFM B u f f e r L i f e t i m e 37 (5-1) I s o b a r i c , isothermal log f s 2 - log ffJ2 diagram. . 45 (Fe-S-0 System - 627°C, 1 atm.) (5-2) P r e d i c t e d P y r r h o t i t e Compositions i n e q u i l i b r i u m w i t h Magnetite 47 (5-3) Molar Volume of- P y r r h o t i t e as a f u n c t i o n of Composition 51 (5-4) Experimental Results Fe-Si-H-O-S System 67 (5-5A) Topology r e s u l t i n g from the Quartz + F a y a l i t e + Magnetite + P y r r h o t i t e + Vapour I n v a r i a n t P o i n t . 69 (627°C - 1 atm.) (5-5B) Experimental Bracket d e f i n i n g the Quartz + F a y a l i t e + Magnetite + P y r r h o t i t e + Vapour I n v a r i a n t P o i n t 69 (5-6) Experimental Results Fe-H-O-S System 78 (5-7) P t o t a l ~ T c u r v e f ° r the 'assemblage Hematite + Magnetite + P y r i t e + Vapour 88 (5-8) S t a b i l i t y of Platinum S u l f i d e s 89 (1 atm.) (6-1) H y p o t h e t i c a l path across the Mss d e f i n i n g compositions of Mss i n e q u i l i b r i u m w i t h magnetite at constant f g 2 97 (6-2) Mss and p y r r h o t i t e compositions as a f u n c t i o n of d(102) 102 via (6-3) Mss and p y r r h o t i t e compositions i n experiments defined by QFM or NNO e x t e r n a l b u f f e r 108 (6-4) Path across the Mss defined by compositions of Mss i n e q u i l i b r i u m w i t h magnetite ss at constant oxygen f u g a c i t y c o n t r o l l e d by QFM e x t e r n a l b u f f e r 112 ( P t o t a l - 2000 bars) (A5-1) Gas Mixture Compositions i n E q u i l i b r i u m w i t h i r o n + magnetite 198 (Fe-O-H System T-X Diagram 2000 bars) (A6-1) Fe-Ni O l i v i n e X-ray Determinative Curve 202 ix NOMENCLATURE L i s t of Symbols and Ab b r e v i a t i o n s a c t i v i t y of species i atm. atmosphere atom % atomic percent C number of components cm. centimeter F f a y a l i t e F number of degrees of freedom f{, f u g a c i t y of gas species i f° f u g a c i t y of pure i at the temperature and t o t a l pressure % of i n t e r e s t G g r a p h i t e AG° standard Gibbs f r e e energy of r e a c t i o n H hematite I i r o n I.D. i n n e r diameter K thermodynamic e q u i l i b r i u m constant Kb. k i l o b a r K c a l . k i l o c a l o r i e KV. k i l o v o l t l o g logarithm to the base 10 In logarithm to the base e M magnetite M number of elements Mss monosulfide s o l i d s o l u t i o n ( F e ,Ni)^_ xS N n i c k e l NO n i c k e l oxide (bunsenite) Np e s p y r r h o t i t e composition (equation 4-2) O.D. outer diameter X c r i t i c a l pressure. h p a r t i a l pressure of gas species i Pr reduced pressure ( P r = P-total/Pc) p t o t a l t o t a l pressure a c t i n g on the s o l i d phases (= t o t a l pressure of the gas phase) Pn p e n t l a n d i t e Po p y r r h o t i t e Py p y r i t e Q quartz R gas constant ss s o l i d s o l u t i o n T • temperature °C degrees Centigrade °K degrees K e l v i n T c c r i t i c a l temperature T r reduced temperature ( T r = T°K/T C) v c c r i t i c a l volume AV S volume change of the s o l i d phases v f p a r t i a l molar volume of species i i n phase <j> W wt l s t i t e wgt % weight percent X. mole f r a c t i o n of species i c r i t i c a l c o m p r e s s i b i l i t y Greek L e t t e r s a. ^ a c t i v i t y c o e f f i c i e n t of species i Y . ^ f u g a c i t y c o e f f i c i e n t of gas species i ( f . = Is y microns v i chemical p o t e n t i a l of species i yamps microamperes y l m i c r o l i t e r s number of phases * temperature f u n c t i o n r e l a t e d to molecular i n i n H 2 - H 2 O gas mixtures (Shaw 1967) to a c e n t r i c f a c t o r ( P i t z e r and Brewer 1961) xi N o t a t i o n f o r Oxygen B u f f e r s QFI Quartz + F a y a l i t e + Iron MI Magnetite + Iron WI Wustite + Iron MW . Magnetite + Wustite QFM Quartz + F a y a l i t e + Magnetite NNO N i c k e l + N i c k e l Oxide (Bunsenite) HM Hematite + Magnetite Notation f o r B u f f e r i n g Systems The shorthand n o t a t i o n developed by Skippen (1967) has been adopted: Og any solid-phase oxygen b u f f e r Sg any solid-phase s u l f u r b u f f e r X " the charge ( ) welded capsule (permeable to W^) | | crimped capsule (permeable to the e x t e r n a l gas mixture) The Og symbol may be rep l a c e d by the n o t a t i o n f o r a p a r t i c u l a r oxygen b u f f e r . The arrangement of parenthesis r e f l e c t s the capsule c o n f i g u r a t i o n . Gas phase components are s p e c i f i e d , separated from the s o l i d s by a comma. In a d d i t i o n to Skippen's n o t a t i o n , square brackets [ ] represent a welded Au capsule separating the b u f f e r assemblage from the pressure medium. xii ACKNOWLEDGMENTS This research was supported through N a t i o n a l Research C o u n c i l of Canada Grant A-4222 held by Dr. H.J. Greenwood, and N.R.C. Post-graduate S c h o l a r s h i p s , 1968-1971. The support, i n t e r e s t , and s u p e r v i s i o n of Dr. H.J. Greenwood i s g r e a t l y appreciated. Dr. T.M. Gordon ( G e o l o g i c a l Survey of Canada) and Dr. P. Metz ( M i n e r a l o g i s c h - P e t r o l o g i s c h e s I n s t i t u t der U n i v e r s i t a t GOttingen) have given me the b e n e f i t of numerous d i s c u s s i o n s of problems encountered during t h i s study. I would a l s o l i k e to thank Mr. J . Harakal f o r a s s i s t a n c e w i t h microprobe work, and Mr. T. Cl a r k ( U n i v e r s i t y of Toronto) f o r supplying some of the s u l f i d e samples used i n t h i s work. Dr. G.B. Skippen (Carleton U n i v e r s i t y ) made a v a i l a b l e h i s computer program f o r c a l c u l a t i o n s on C-O-H gases. This program proved to be an i n v a l u a b l e model f o r s e v e r a l of the H-O-S programs w r i t t e n f o r t h i s study. 1 CHAPTER I INTRODUCTION The past f i f t e e n years have seen a s i g n i f i c a n t expansion and improvement of the thermodynamic b a s i s f o r the s o l u t i o n of pi-oblems i n m i neral e q u i l i b r i a . Major t h e o r e t i c a l c o n t r i b u t i o n s by Thompson (1955, 1959), Eugster (1959), Holland (1959), and K o r z h i n s k i i (1959) provided important i n s i g h t s which could be t e s t e d only f o l l o w i n g the development of new experimental techniques. This impetus was f o l l o w e d by the s u c c e s s f u l development of s e v e r a l independent methods to study e q u i l i b r i a i n v o l v i n g gas mixtures i n the metamorphic pressure and temperature range (Eugster, 1957; Greenwood, 1961; Eugster and Wones, 1962; Shaw, 1963). The use of s o l i d phase b u f f e r s to c o n t r o l i n d i v i d u a l gas f u g a c i t i e s (Eugster, 1957; Eugster and Wones, 1962; French and Eugster, 1965; Munoz and Eugster, 1969) has r e s u l t e d i n numerous experimental s t u d i e s of r e a c t i o n s i n two-component and three-component gas systems. S u l f i d e - o x i d e and s u l f i d e - o x i d e - s i l i c a t e r e a c t i o n s commonly i n v o l v e gas species i n the three-component H-O-S system. Eugster and Skippen (1967) o u t l i n e the theory and b u f f e r system c o n f i g u r a t i o n s which make p o s s i b l e determination of phase e q u i l i b r i a i n H-O-S gas mixtures. The present study i s an experimental i n v e s t i g a t i o n of a number of r e a c t i o n s i n v o l v i n g i r o n and n i c k e l - b e a r i n g s u l f i d e s , o x i d e s , and s i l i c a t e s . H-O-S gas mixture compositions are c o n t r o l l e d through solid-phase oxygen and s u l f u r b u f f e r s . C o n s i d e r a t i o n i s given to s i l i c a t e - s u l f i d e - o x i d e r e l a t i o n s and the c o n t r o l exerted by r e a c t i o n s among these groups of minerals on vapour phase compositions. The term 2 gas mixture or vapour phase r e f e r s to the s u p e r c r i t i c a l f l u i d phase present at the pressure-temperature c o n d i t i o n s of i n t e r e s t i n these experiments (2000-3000 bars, 550-750°C). Previous experimental s t u d i e s u s i n g r i g i d s i l i c a g l a s s tubes have been s u c c e s s f u l l y a p p l i e d to a l a r g e number of s u l f i d e systems ( K u l l e r u d , 1967; Barton and Skinner, 1967). A number of s t u d i e s i n v o l v i n g s u l f i d e - o x i d e and s u l f i d e - o x i d e - s i l i c a t e e q u i l i b r i a have a l s o been conducted ( K u l l e r u d and Yoder, 1963, 1964; N a l d r e t t , 1969; C l a r k and N a l d r e t t , 1972). Unbuffered experiments i n c o l l a p s i b l e gold or platinum tubes have been attempted by a few authors ( K u l l e r u d and Yoder, 1963, 1964, 1968; MacRae and K u l l e r u d , 1971, 1972). C o l l a p s i b l e gold and platinum capsules serve as r e a c t i o n v e s s e l s f o r both b u f f e r and charge assemblages i n t h i s study. The a p p l i c a t i o n of t h i s method i s r e s t r i c t e d to c o n d i t i o n s over which the vapour phase does not r e a c t w i t h the noble metal capsules and over which hydrogen d i f f u s i o n may be used to c o n t r o l oxygen f u g a c i t i e s . ' A number of experiments were designed to provide i n f o r m a t i o n on the l i m i t s imposed by t h i s experimental arrangement. Chapters 2 and 3 o u t l i n e the theory and equations that e s t a b l i s h a q u a n t i t a t i v e b a s i s f o r experimental study of r e a c t i o n s i n H-O-S gas mixtures. Gas mixture compositions i n the 0-H and H-O-S systems are considered as a f u n c t i o n of the e x p e r i m e n t a l l y c o n t r o l l e d v a r i a b l e s temperature, t o t a l p r e s s u r e , and the f u g a c i t i e s of i n d i v i d u a l gas s pecies. Data and computer programs necessary f o r these computations are t a b u l a t e d i n the appendices. Thermochemical data f o r phases i n the Fe-H-O-S system provide a s o l i d b a s i s to t e s t the range of c o n d i t i o n s t h a t can be s p e c i f i e d by the experimental techniques. The e f f e c t of v a r i a b l e oxygen 3 f u g a c i t y on the p y r r h o t i t e - m a g n e t i t e e q u i l i b r i u m has been measured. Experimental r e s u l t s compare fa v o u r a b l y w i t h thermochemical c o n s i d e r a t i o n s . These experiments e s t a b l i s h the background f o r a p r e l i m i n a r y i n v e s t i g a t i o n of n i c k e l - b e a r i n g systems. The study i s designed to e s t a b l i s h the importance of 'gangue' s i l i c a t e - o x i d e assemblages i n d e f i n i n g the composition of phases i n the Fe-Ni-S system. 4 CHAPTER 2 THE 0-H SYSTEM 2.1 Theory The 0-H b i n a r y has r e c e i v e d c o n s i d e r a b l e a t t e n t i o n w i t h the widespread use of s o l i d phase b u f f e r i n g techniques to d e f i n e £Q i n hydrothermal experiments. Accurate experimental determination of the P-V-T p r o p e r t i e s of gas mixtures i n t h i s system are c r i t i c a l to c a l c u l a t i o n of the f ( ) 2 > % 2 ' A N C * ^ 2 0 d e f i n e d by the b u f f e r assemblages. The same comment a p p l i e s even more f o r c e f u l l y to experiments i n which f j . ^ i s defined by means of d i f f u s i o n through a m e t a l l i c membrane (Shaw, 1963, 1967) . H 2, O 2 and H 2 0 are assumed to be the only s i g n i f i c a n t , gas species present i n the 0-H system (Eugster and Wones, 1 9 6 2 ) . These gas species are commonly assumed to be non-ideal r e a l gases t h a t mix i d e a l l y . For any t o t a l pressure; P t o t a l = P H 2 0 + P H 2 + P 0 2 = ~ ^ + T 1 + T 1 ( 2 _ 1 ) Y H 2 0 Y H 2 Y 0 2 The equation f o r the thermal d i s s o c i a t i o n of water i s : H 2 + 1/2 0 2 t- H 2 0 K H 2 Q = ! l 2 ^ ( 2 - 2 ) f H 2 ' f 0 2 Oxygen f u g a c i t y i s many orders of magnitude l e s s than % 2 0 A R I < ^ % 2 u n < ^ e r m o s ' t g e o l o g i c c o n d i t i o n s . P Q ^ may t h e r e f o r e be neglected i n the P t o t a l summation (equation 2 - 1 ) , and s u b s t i t u t i n g (2-2) i n 5 (2-1) r e s u l t s i n the f o l l o w i n g equations f o r f j ^ o a n ^ ^ 2 (Eugster and Wones, 1962): p t o t a l ' K H 2 0 ' foY2 ' Y H 2 ' Y H 2 0 f H 2 Q = 7 ~ = (2-3) K H 2 0 • F 0 / • Y F i 2 + Y H 2 0 P t o t a l • Y H 2 Y H 2 0 f = ( 2 _ 4 ) 1 / 2 K H 2 0 ' F 0 2 ' Y H 2 + Y H 2 0 A FORTRAN IV program ( 0 - H V e r s i o n 1, Appendix 2) has been w r i t t e n to s o l v e equations (2-3) and (2-4) . A v a i l a b l e data f o r Y H . 2 > Y H 2 0 > log % 2o> a n c* c o e f f i c i e n t s to c a l c u l a t e l og f g ^ d e f i n e d by v a r i o u s s o l i d phase b u f f e r s are t a b u l a t e d i n Appendix 1. Y H 2 has been c a l c u l a t e d from the e m p i r i c a l equation of s t a t e d e r i v e d by Shaw and Wones (1964) and from the experimental data of P r e s n a l l (1969). E x p e r i m e n t a l l y determined values of Y H 2 0 are from Burnham, et a l . (1969) and log % 2 o n a s been t a b u l a t e d from the c o m p i l a t i o n of Robie and Waldbaum (1968). C o e f f i c i e n t s f o r oxygen b u f f e r s have been compiled from s e v e r a l sources (Table A l - 1 ) . These data are used to c a l c u l a t e f u g a c i t i e s , p a r t i a l p r e s s u r e s , and mole percent of 0 2 , H 2 , and H 2 O over a range of temperature and pressure (327-1027°C, 1-3000 b a r s ) . The 0 - H V e r s i o n 1 output permits easy comparison of values generated by d i f f e r e n t sets o f source data. 0 - H V e r s i o n 1 i s based on the assumption of i d e a l mixing of r e a l gases and hence the p r o p o r t i o n s of H 2 and H 2 O are c a l c u l a t e d from the Lewis and Randall rule."** o . . . . . t f^ - f^ The fugacity of gas species i in a mtxture is equal to its mole fraction times the fugacity of the pure gas at the temperature and total pressure of the mixture. (Note: in non-ideal mixtures f^ = a^f^ where a^ is the activity of gas species i. See equations 2-9, 2-10) 6 Thus: £H 2° = XH2° ' FH2° = XLI2° ' Y H2° ' P T O T A ] (-2"5-' f H 2 = X H 2 • f H 2 = X H 2 ' Y H 2 • Ptotal C2"6) fH20 £ H 2 Since P H 0 = , and P H = : 1 THoO 1 YH2-P H20 p t o t a l = XH,0 ^ H 2 = Xo (2-8) P t o t a l " H 2 Programs s p e c i f y output i n mole percent r a t h e r than mole f r a c t i o n , where mole percent i = 100.0 ' X^. The Lewis and Randall r u l e i s rig o r o u s f o r an i d e a l gas mixture and i s t h e r e f o r e a good approximation only i f molecular i n t e r a c t i o n s among d i f f e r e n t species i n the gas mixture cause i n s i g n i f i c a n t d e v i a t i o n from i d e a l i t y . In general the r u l e provides reasonable accuracy at low t o t a l pressures and f o r mixtures i n which £ i s present i n excess over alt other s p e c i e s . I f molecular species present i n the gas mixture have s i m i l a r p h y s i c a l p r o p e r t i e s then the behaviour of the mixture should be s i m i l a r to th a t of the pure gases. F a i r accuracy can then be expected f o r a wide compositional range. Consequently the r u l e can a l s o be u s e f u l i f 5 X^ of p h y s i c a l l y s i m i l a r molecular species i s i n excess over alt t other s p e c i e s . I n t e r m o l e c u l a r f o r c e s t h a t are important i n determining how a gas deviates from i d e a l behaviour a l s o govern p h y s i c a l p r o p e r t i e s 7 such as c r i t i c a l constants. The c r i t i c a l constants f o r pure H 2 and pure H 2 O are: T c P c V c Z c (°K) (bars) (cm3/gm.mole) H 2 33.3 12.97 65.0 0.304. H 20 647.25 221.2 56 0.230 (Handbook of Chemistry and P h y s i c s , 1970) The s i g n i f i c a r t t d i f f e r e n c e s between the p r o p e r t i e s of these two gases suggest a p p l i c a t i o n of the Lewis and Randall r u l e w i l l be r e l i a b l e only at low pressures or when one species i s present i n excess. Gas mixture compositions d e f i n e d by QFM, NNO, and HM b u f f e r s are very l ^ O - r i c h and the i d e a l mixing assumption i s adequate given other experimental l i m i t s . 0-H gas mixtures defined by IM, IW, and WM b u f f e r s have much higher values of f j - ^ and f o r experiments using these b u f f e r s account should be taken of non-ideal mixing e f f e c t s . D i r e c t experimental measurement of the P-V-T p r o p e r t i e s of H 2 - H 2 O mixtures provides the data necessary to c a l c u l a t e exact f u g a c i t i e s of H 2 J H 20, and O 2 i n the mixtures. I f such data i s not a v a i l a b l e approximations can be made using the p r i n c i p l e of corresponding s t a t e s or an equation of s t a t e such as the v i r i a l equation ( P r a u s n i t z , 1969). The t h e o r e t i c a l approach i s l i m i t e d f o r mixtures c o n t a i n i n g p o l a r molecules (eg. H 2 O ) and u n t i l c o n s i d e r a b l y more i s known concerning i n t e r m o l e c u l a r f o r c e s at high temperatures and pressures d i r e c t measurement of the p h y s i c a l p r o p e r t i e s of such mixtures remains the only accurate way to determine f u g a c i t i e s . Shaw (1963) measured the compositions of H 2 - H 2 O mixtures at c o n t r o l l e d values of fj.[ (700°C, P t o t a l ~ ^00 b a r s ) . Measured compositions show s i g n i f i c a n t d e v i a t i o n from an i d e a l mixing model. For non-ideal mixing, equations (2-5) and (2-6) must be r e w r i t t e n s u b s t i t u t i n g a c t i v i t y f o r mole f r a c t i o n : fH20 = aH20 ' fH20 = aH20 ' YH20 * P t o t a l C 2 " 9 ) fH2 = aH2 ' fH2 = aH2 * YH2 * p t o t a l " (2-10) The a c t i v i t y c o e f f i c i e n t (a^) f o r species, i i n the mixture i s de f i n e d by a^ = X^-a-i. S u b s t i t u t i n g i n t o (2-2): XH?0 " aH20 - YH20 * p t o t a l KH2O= — 1 rr2 • ^ XH2 ' aH2 * YH2 * p t o t a l * f02 I f P Q ^ i s i n s i g n i f i c a n t i n the gas mixture then: XH20 - 1 " XH2 C 2 - 1 2 ) and s i m p l i f y i n g (2-11): (1 - X H 2 ) • AH20 • H^20 . . KH2O 7777 <2-13) XH 2 ' «H2 • YH2 • f02' Shaw (1967) has c a l c u l a t e d an e m p i r i c a l expression which c o r r e c t s f o r non-ideal mixing over a l i m i t e d P-T range f o r each component i n the mixture. The expressions f o r a ^ and a r e : a H 2 . X„ exp [ O j j H j l l J l . ] ( 2. 1 4 ) ^ RT aH20 = *H20 - P t iijliH20 L^ ] (2-15) RT where H' = 0.0098 + 54.5/T°K, and P = P t o t a l ( b a r s ) . 9 Substituting x H 0 = ^ (1 - xH 2) 2 a H 2 X H 2 exp [ ] — = _ (2-16) H 2 ° r ( X H 2 ) 2 PV. (1 - XH ) exp[ — ] Setting — = Z, and simplifying: RT aH 2 XH 2 exp [ (1 - 2XU ) Z ] (2-17) A H 20 (1 - X H 2 ) Substituting into (2-13) recalling a^ = X ^ • : (1 - X H 2 ) * Y H 2 0 XH 2 H2 f 0 2 (2-18) XH 7 YH70 i = i exp [-(1 - 2XH ) Z ] (2-19) C 1 - V % 2 0 • YH 2 • f Q 2 / 2 Defining Gf= _ _ , then from (2-13): v a Y -p */2 KH20 ' H2 • TH 2 • *0 2 Ho G G, or X H = (2.20) 2 1 + G c i - v This is a temporary iteration parameter not to be confused with Gibbs free energy. 10 S u b s t i t u t i n g i n (2-19): G = YH 20 exp [-(1 - 2 X H 2 ) Z] (2-21) KH20 " YH2 ' f02 1/2 Taking logarithms to the base 10: log G = - [ l o g K H 2 Q + log Y H 2 YH 20 + 1/2 log f 0 z + (1 - 2 X H 2 ) Z ] (2-22) 2.303 Equations (2-22) and (2-20) have been solved f o r XJ.J by i t e r a t i o n through s u c c e s s i v e s u b s t i t u t i o n s f o r Xj.^ converging on a value that s a t i s f i e s both equations. Non-ideal mixing equations are i n c o r p o r a t e d 0-H gas mixture compositions d e f i n e d by v a r i o u s oxygen b u f f e r s assuming both i d e a l and non-ideal mixing of H 2 and H 20. Input data are t a b u l a t e d i n Appendix 1. Shaw (1967) cautions that the accuracy of the non-ideal mixing expressions (equations 2-14 and 2-15) f a l l s o f f s i g n i f i c a n t l y at temperatures below 500°C or pressures g r e a t e r than 1000 bars. 2.2 Temperature - Composition Diagrams Temperature - composition (T-X) diagrams have been con s t r u c t e d f o r a p o r t i o n of the Fe-O-H system assuming both i d e a l and non-ideal mixing of H 2 and H 20 (Figures 2-1 to 2-3). The 0-H system i s t r e a t e d as a b i n a r y mixture of H 2 and H 20. M a g n e t i t e - i r o n (MI), w i i s t i t e - i r o n (WI) , and ma g n e t i t e - w i i s t i t e (MW) b u f f e r curves have been c a l c u l a t e d u s i n g the 0-H Vers i o n 2 program (Appendix 2). Shaw and Wones' (1964) Y j ^ values i n t o the 0-H V e r s i o n 2 program (Appendix 2) . This p.rogram computes 11 FIGURE (2-1) Fe-O-H System I s o b a r i c T-X Diagram D o t t e d - l i n e s i n d i c a t e log T Q 12 FIGURE (2-2) Fe-O-H System Isobaric. T-X Diagram Dotted l i n e s i n d i c a t e l og £Q 1000 B « . R i ( Idcul M i » i n 9 ) 1000 EAP.S ( N o n - i d e o t M i x i n g Shew C o r r e c t i o n ) 13 FIGURE (2-3) Fe-O-H System I s o b a r i c T-X Diagram Dotted l i l i e s i n d i c a t e log' 2 0 0 0 BARS ( Idea l M i . i n g ) MOlf FRACTION Mj 14 are used throughout (Table A l - 2 ) . Log f g ^ contours are drawn from values computed by the 0-H V e r s i o n 3 program (Appendix 2). Non-ideal mixing, as c a l c u l a t e d by the Shaw c o r r e c t i o n , r e s u l t s i n a systematic s h i f t of contours. Log f g 2 i s more s t r o n g l y dependent on temperature than p r e d i c t e d by the i d e a l mixing model. Small isothermal changes i n log f g r e s u l t i n extreme compositional v a r i a t i o n i n H 2 - H 2 O gas mixtures under reducing c o n d i t i o n s ( i e . when both H 2 and H 2 O are important s p e c i e s ) . S i m i l a r l y small temperature changes at constant log f g are r e f l e c t e d by s u b s t a n t i a l d i f f e r e n c e s i n the gas mixture composition (Figures 2-1 to 2-3). Log f g ^ may be estimated from Fig u r e s (2-1) and (2-3) f o r H 2 - H 2 0 gas mixtures at t o t a l pressures of 1000 and 2000 bars r e s p e c t i v e l y (300-1000°C). Two i n t e r n a l l y c o n s i s t e n t s e t s of curves f o r MI, WI, and MW b u f f e r s have been p l o t t e d f o r a t o t a l pressure of 1000 bars (Figures 2-1 and 2-2) . D i f f e r e n c e s i n the t a b u l a t e d f r e e energies f o r i r o n , w i i s t i t e , and magnetite are m i r r o r e d by the c a l c u l a t e d s t a b i l i t y f i e l d s . Table (2-1) d i s p l a y s these d i f f e r e n c e s i n terms of l o g f g and records the p r e d i c t e d p o s i t i o n o f the i r o n - w i l s t i t e - m a g n e t i t e t r i p l e p o i n t f o r each set of data. Dis c r e p a n c i e s i n current t a b u l a t i o n s of AG° f o r i r o n , w t i s t i t e , and magnetite, coupled w i t h non-ideal mixing e f f e c t s r e s u l t i n l a r g e u n c e r t a i n t i e s i n X H and T°C. Experiments to determine the composition of H 2 - H 2 O gas mixtures i n e q u i l i b r i u m w i t h i r o n and magnetite (MI b u f f e r ) at t o t a l pressures of 1000 and 2000 bars are described i n Appendix 5 . Measured compositions i n d i c a t e a s i g n i f i c a n t p o s i t i v e d e v i a t i o n from i d e a l i t y (Appendix 5, Fig u r e A5-1). Compositions p r e d i c t e d by the Shaw c o r r e c t i o n are not c o r r e c t , c l e a r l y showing equations (2-14) and (2-15) cannot be e x t r a p o l a t e d 15 TABLE (2-1) Log £Q defined by MI, WI, and MW buffers Total pressure = 1000 bars Coefficients tabulated in Appendix 1 (Table Al-1) Buffer Identification Mil WI1, MW1 MI 2, WI2, MW2 W13, MW3 Reference Norton (1955) Darken and Gurry (1945) Robie and Waldbaum (1968) Charette and Flengas (1968) T°K T°C Mil MI2 600 327 -39.68 -39.79 700 427 -32.72 -32.99 800 527 -27.51 -27.89 900 627 -23.45 -23.93 1000 727 -20.21 -20.76 1100 827 -17.55 -18.16 1200 927 -15.34 -16.00 1300 1027 -13.47 -14.17 T°K T°C WI1 WI2 WI3 600 327 -38.70 -39.07 -39.00 700 427 -32.23 -32.54 -32.46 800 527 -27.38 -27.64 -27.55 900 627 -23.61 -23.83 -23.74 1000 727 -20.59 -20.78 -20.69 1100 827 -18.12 -18.27 -18.19 1200 927 -16.06 -16.21 -16.11 1300 1027 -14.32 -14.46 -14.35 T°K T°C MW1 MW2 MW3 600 327 -41.29 -42.50 -41.33 700 427 -33.52 -34.69 -33.59 800 527 -27.69 -28.84 -27.79 900 627 -23.15 -24.29 -23.27 1000 727 -19.53 -20.65 -19.66 1100 827 -16.56 -17.67 -16.71 1200 927 -14.09 -15.19 -14.25 1300 1027 -11.99 -13.09 -12.16 Calculated position of the iron--wiistite-magnetite triple poii T°C *H2 *H2 (ideal mixing) (Shaw c o r r e i Mil, WI1, MW1 565 0.51 0.52 MI2, WI2, MW2 700 0.59 0.64 WI3, MW3 555 0.56 0.62 16 beyond t h e i r quoted range (T>500°C, t o t a l pressure <1000 b a r s ) . C a l c u l a t e d £ u values f o r MI, WI, and MW b u f f e r s assuming 2 i d e a l mixing are i n a c c u r a t e , and the Shaw c o r r e c t i o n i s a p p l i c a b l e only over a narrow P-T range. F u g a c i t i e s of H 2 and K 2 O computed f o r b u f f e r i n g c o n f i g u r a t i o n s such as [MI,0H(SgX,HOS)] must be considered approximate u n t i l r e l i a b l e a c t i v i t y c o e f f i c i e n t s f o r H 2 and H 20 are a v a i l a b l e . Measurement of 0-H gas mixture compositions d e f i n e d by solid-phase oxygen b u f f e r s when combined w i t h known a H 2 and aF^O values would a l l o w extremely accurate determination of log ^ c^ ' ^ e l e v e r a £ e a f f o r d e d by t h i s procedure r e f l e c t s the marked temperature dependence of log £Q over a wide range of gas compositions. 17 CHAPTER 3 THE H-O-S SYSTEM  3.1 Theory Eugster and Skippen (1967) summarize the procedures necessary to c o n t r o l the composition of gas mixtures i n multicomponent gas systems. In the three-component H-O-S system at f i x e d P t o t a l a n d T the phase r u l e i n d i c a t e s t h a t two a d d i t i o n a l parameters must be c o n t r o l l e d i f the s t a t e of the system i s to be completely c h a r a c t e r i z e d . In t h i s study was defi n e d w i t h i n the charge capsule by means of i r o n s u l f i d e assemblages. The second s p e c i f i e d parameter was e i t h e r f ^ ( c o n t r o l l e d by an e x t e r n a l oxygen b u f f e r ) or f o 2 ( i n t e r n a l l y c o n t r o l l e d ) . The b u f f e r i n g c o n f i g u r a t i o n s found to be p r a c t i c a l f o r t h i s work are summarized i n Table (4-2). The f o l l o w i n g equations provide the b a s i s f o r the c a l c u l a t i o n of gas mixture compositions i n the H-O-S system. £H 20 (3-1) 1/2 K, £H2S (3-2) f l H2 18 F S 0 3 S 0 ^ * ' * 2 " U 2 ' f 1/2 . r 3/2 (3-5) F S ? 0 KS o = Z~ (3-6) * s 2 • *o\/2 F H S K H S = _ ( 3 - 7 ) M / 2 • f s 2 / 2 P t o t a l = P S 2 + P ° 2 + P H 2 + P H 2 0 + P H 2 S + P S 0 2 + P S 0 + P S O 3 + P S 2 0 + P H S f S 2 F 0 2 F H 2 F H 2 0 F H 2 S F S 0 2 F S 0 F S 0 3 F S 2 0 F H S p t o t a l = + + + + + + + + +  Y S 2 ^ 0 2 Y H 2 Y H 2 0 Y H 2 S Y S 0 2 Y S 0 Y S 0 3 Y S 2 0 Y H S ( 3 - 8 ) S u b s t i t u t i n g equations ( 3 - 1 ) , ( 3 - 2 ) , and ( 3 - 7 ) i n t o equation ( 3 - 8 ) , and rearr a n g i n g to give an expression i n K H 2 0 * f o / 2 1 K H 2 S * F S 2 ^ 2 K H S ' F S 2 / 2 , / , ^ H 2 0 Vti2 Y H 2 S 1 Y H S 12 F S 0 2 F S 0 F S 0 3 F S 2 0 F S 2 F 0 2 ( + + + + + p t a l ) = 0 ( 3 - 9 ) ' ^ S 0 2 Yso Yso 3 Y s 2 0 Ys 2 Y Q 2 Equations (3-1) to (3-9) have been solved (H-O-S V e r s i o n 1 and 1A programs) f o r f g values defined by solid-phase oxygen b u f f e r s over a s p e c i f i e d range of fS2> temperature, and t o t a l pressure. Programs are l i s t e d i n Appendix 3, and input data i s t a b u l a t e d i n Appendix 1. The program l i s t i n g i n c l u d e s comment cards to o u t l i n e the sequence of s u b s t i t u t i o n s used to s o l v e the preceding set of equations. 19 U n c e r t a i n t y e x i s t s as to the r e l a t i v e importance of SO and S2O at high temperatures and high f s 2 - B l u k i s and Myers (1965) demonstrate that S2O has been i n c o r r e c t l y i d e n t i f i e d as SO i n s e v e r a l experimental s t u d i e s . The e q u i l i b r i u m constants KgQ and Kg 2Q as compiled i n the JANAF Tables (addendum, 1966) have l a r g e e r r o r l i m i t s . C a l c u l a t i o n of fgg and f ^ O m u s t be considered approximate u n t i l new experimental data are a v a i l a b l e . I n v e s t i g a t i o n of the molecular composition of s u l f u r vapour has been conducted by numerous authors. Measurement of s u l f u r vapour d e n s i t i e s over a range of temperatures and pressures r e s u l t e d i n the e a r l y c h a r a c t e r i z a t i o n of Sg, Sg, and S 2 as important species (Preuner and Schupp, 1909) . Braune, P e t e r , and Neveling (1951) i n c l u d e the species S 4 to provide a b e t t e r f i t to t h e i r data. Mass-spectrometric s t u d i e s demonstrate Sy, S 5 , and S 3 may a l s o be present i n s u l f u r vapour (Berkowitz, 1965). E q u i l i b r i u m constants f o r r e a c t i o n s i n v o l v i n g Sg, Sg, and S4 have been c a l c u l a t e d f o r temperatures of 800, 900, and 1000°K (Table 3-1). 4S 2 t Sg Ks = (3-10) CS 2 3S„ t S, Kc = f s 6 (3-11) b f c ? CS 2 2S 9 t SA Kq = f S 4 (3-12) 4 f 2 H-O-S computer programs assume S 2 i s the only molecular species present i n the gas mixtures. This assumption i s v a l i d f o r f g 2 20 TABLE (3-1) E q u i l i b r i u m Constants f o r Sg, S^, and S 4 : s 8 log K s = log f S g - 4 log f s ^ log K S g 800°K 900°K 1000°K (527°C) (627°C) (727°C) 2.33 -0.71 -3.16 3.09 0.29 -i;95 2.41 -0.47 -2.76 2.477 -0.408 -2.699* Reference K e l l e y (1937) Braune, P e t e r , and Neveling (1951) Gu t h r i e , S c o t t , and Waddington (1954) {JANAF (1965) LRobie and Waldbaum (1968) log Kg = log f s - 3 log f s log 800°K 900°K 1000°K (527°C) (627°C) (727°C) Reference 2.00 -0.05 -1.70* 2.21 0.27 -1.28 K e l l e y (1937) Braune, P e t e r , and Neveling (1951) f 2 r c log Kc log f c - 2 log f c b4 b2 log K S 4 800°K 900°K 1000°K (527°C) (627°C) (727°C) Reference 0.80 -0.07 -0.72* Braune, P e t e r , and Neveling (1951) Source data f o r Figure (3-1) 21 values more than a few orders o f magnitude below the s u l f u r condensation curve. F i g u r e (3-1) may be u t i l i z e d to estimate log ^ Sgj £S ' a n c* log f g f o r log f g 2 values c l o s e to the s u l f u r condensation curve. When the p a r t i a l pressures of these species represent a s i g n i f i c a n t c o n t r i b u t i o n to the t o t a l p r essure, equation (3-8) must be modifie d to i n c l u d e ( £§2 + £S4 + £§6. + £Sg j i n p i a c e 0 f t n e £s_2 term. Equations (3-10) Y S 2 Y S 4 Ys 6 YS 8 YS 2 to (3-12) provide the a d d i t i o n a l c o n s t r a i n t s necessary to s o l v e the new p t o t a l equation. H-O-S Ve r s i o n 2 and 2A programs exclude e q u i l i b r i a i n v o l v i n g SO, SOg, S 2 O , and HS. Ve r s i o n 1 c a l c u l a t i o n s i n d i c a t e that these species may be neglected i n the P t o t a j summation (equation 3--8) s i n c e the magnitudes of Pgg, PS03» P S 2 0 ' a n c * P H S A R E S M A - H over the e n t i r e range of g e o l o g i c a l l y important values of f g and f g . This r e s t r i c t i o n s i m p l i f i e s equation (3-8) t o : P t o t a l = PSo + P0o + PHo + PH90 + P S 0 o + PH0S p - f S ? f 0 2 fH-> fHoO fS0o fH2S P t o t a l —± + —L + —L + __£_ + f- + — ± - ( 3_ 1 3) YS 2 Y o 2 Y H 2 Y H 2 0 Y S 0 2 YH2S S u b s t i t u t i n g equations (3-1) to (3-3) i n t o equation (3-13), and re a r r a n g i n g to g i v e an expression i n £ H 2 : CS2P ' f ° 2 / 2 + JUL + M2£_liSp).f + (£S02 + £S2 + £0_2_ _ a 0 YH20 YH2 Y H 2 S Y S 0 2 Y g 2 Y Q 2 (3-14) H-O-S Ve r s i o n 4 and 4A programs (Appendix 3) permit c a l c u l a t i o n of the composition of H-O-S gas mixtures when the de f i n e d 22 i r e f e r s to the species Sg, S^, or 23 f u g a c i t i e s are f ^ and fg r a t h e r than fg^ and f s 2 " ^ o r t n ^ - s c a s e equations (3-1) and (3-3) have been r e s u b s t i t u t e d i n t o equation (3-13) to g i v e an expression i n f o 2 : K S 0 2 • f S 2 / 2 ! > 2 0 • % l / 2 ( + — ) - f o 2 + c yfo/ * Y S 0 2 Y 0 2 YH 20 1 f H 2 f S 2 fH 2S + _A + _ J _ . P t o t a l ) = 0 (3-15) Y H 2 Y S 2 YH 2S Equation (3-15) has been solved f o r values d e f i n e d by s o l i d phase oxygen b u f f e r s (0-H V e r s i o n 1 or 2 c a l c u l a t i o n s ) over a range of f s 2 - Gas mixture compositions computed i n t h i s way apply to b u f f e r c o n f i g u r a t i o n s i n which f ^ o i s c o n t r o l l e d e x t e r n a l l y , f o r example [0 B,OH(S BX,HOS)]. Ex p e r i m e n t a l l y d e r i v e d f u g a c i t y c o e f f i c i e n t s f o r s u l f u r -bearing gas species are not a v a i l a b l e and estimates have been made from reduced v a r i a b l e c harts (Appendix 1). C r i t i c a l constants f o r pure gas species i n the H-O-S system (Table 3-2) have been used to c a l c u l a t e the r e q u i r e d reduced temperatures and reduced pressures. Non-ideal mixing of H 2 and H 20 can be c o r r e c t e d f o r temperatures >500°C and t o t a l pressure <1000 bars (Shaw c o r r e c t i o n , see S e c t i o n 2.2). Outside t h i s P-T range c a l c u l a t i o n s f o r MI, WI, and WM b u f f e r s must be considered approximate. No c o r r e c t i o n can be made f o r non-ideal mixing among species other than H 2 and H 20. The Lewis and Randall r u l e employed t o compute the mole percent of each species i s only r e l i a b l e when a s i n g l e gas species dominates the vapour phase (see d i s c u s s i o n , S e c t i o n 2.1). In other cases values c a l c u l a t e d f o r the mole percent of each gas species must be i n t e r p r e t e d with c a u t i o n . 24 TABLE (3-2) C r i t i c a l Constants f o r Pure Mole c u l a r Species i n the H-O-S System ec u l a r lec i e s °K Pc bars cm3/g mole Z c H 2 "'•33.3 12.97 6 5 . 0 0. ,304 0 02 1 5 4 . 8 5 0 . 7 6 7 4 . 4 0. ,292 0. ,021 s 2 1313 117.5 - • - 0. ,070 H 2S 3 7 3 . 5 5 9 0 . 0 8 95 0. ,268 0. ,100 s o 2 4 3 0 . 9 5 7 8 . 7 3 122 0. 268 0 . ,273 s o 3 4 9 1 . 4 8 1 . 4 126 0. ,262 0. 510 H 2 0 6 4 7 . 2 5 221.2 56 0. ,230 0. ,348 Data compiled from the Handbook of Chemistry and Physics (1970) and Reid and Sherwood (1966). t a c e n t r i c f a c t o r (Pi.tzer and Brewer, 1961): co = - l o g P s / P c - 1.000 where P s = vapour pressure at T r = 0.700 to = 0 f o r simple f l u i d s w i t h s p h e r i c a l l y symmetric molecules (Ar, Kr, and Xe) . to provides a measure of the d e v i a t i o n of i n t e r m o l e c u l a r f o r c e s from those of the simple s p h e r i c a l molecules. Complete r e s u l t s of c a l c u l a t i o n s using H - O - S programs are not t a b u l a t e d owing to the massive amount of output i n v o l v e d and the need to c o n s t a n t l y reassess the input parameters i n the l i g h t of new experimental data. The programs, a l l a v a i l a b l e input data, and example pages of output are to be found i n Appendix 1 and 3 . C a l c u l a t i o n s a p p l y i n g to the r e a c t i o n s s t u d i e d are t a b u l a t e d i n Chapter 5 . 3 . 2 I o n i z a t i o n E q u i l i b r i a E q u i l i b r i a i n the H - O - S system must a l s o be considered i n terms of r e a c t i o n s i n v o l v i n g i o n i c s p e c i e s . Important r e a c t i o n s are: H O t H + + O H " % 0 = — + ' & 0 H - ( 3 - ] 6 ) 2 a H 2 0 H S O 4 t H + + S 0 4 2 " K H S 0 J = f H l l i S O ^ ( 3 _ 1 7 ) A H S 0 4 ~ H 2 S t H + + HS PIS" t H + + S 2 The e q u i l i b r i a expressed by equations ( 3 - 1 6 ) to ( 3 - 1 9 ) do not change the f u g a c i t y r a t i o s d e f i n e d by equations ( 3 - 1 ) to ( 3 - 7 ) . I o n i z e d species however do c o n t r i b u t e to the P t o t a l e cl u a ti° n ( 3 - 8 ) . I f molecular species completely overshadow i o n i z e d species i n abundance the P t o r a ] _ equation w i l l not change s i g n i f i c a n t l y and the c a l c u l a t e d f u g a c i t i e s w i l l not be a f f e c t e d . H 2 S a H + ' a H S ~  a H 9 S ' ( 3 - 1 8 ) K H S " " a H + • a s 2 -a H S " ( 3 - 1 9 ) 26 Munoz and Eugster (1969)' consider the e f f e c t of i o n i z e d species on c a l c u l a t i o n s i n the H-O-F system. At a t o t a l pressure of 2000 bars (T = 450, 550, and 650°C) the gas phase i s dominantly molecular. The p r o p o r t i o n of i o n i z e d to molecular species i s small enough t h a t the c o n t r i b u t i o n of i o n i z e d species to the P t 0 ^ a ^ equation may be s a f e l y ignored. I o n i z a t i o n constants f o r H?0 i n the s u p e r c r i t i c a l temperature and pressure range are t a b u l a t e d by Barnes et a l (1966) f o r temperatures up to 700°C. Constants f o r HSO^ , H^S, and HS have been compiled by Ohmoto (1972) f o r temperatures below 350°C but no data i s a v a i l a b l e f o r temperatures i n the s u p e r c r i t i c a l , range. Barnes and -Czamanske (1967) di s c u s s e q u i l i b r i u m r e l a t i o n s among molecular and i o n i c s u l f u r - c o n t a i n i n g species i n aqueous s o l u t i o n (T<250°C) and i n the c o e x i s t i n g vapour phase. Raymahashay and Holland (1968, 1969) and Ohmoto (1972) d i s c u s s a d d i t i o n a l aspects of r e a c t i o n s i n v o l v i n g s u l f u r - b e a r i n g species i n aqueous s o l u t i o n s at temperatures up to 350°C. J The degree of i o n i z a t i o n decreases w i t h i n c r e a s i n g temperature (at constant d e n s i t y ) and in c r e a s e s w i t h i n c r e a s i n g pressure at constant temperature (Barnes and E l l i s , 1967). A d d i t i o n a l data i s needed before the importance o f i o n i z e d species i n s u p e r c r i t i c a l H-O-S gas mixtures can be q u a n t i t a t i v e l y evaluated. A v a i l a b l e evidence i s against i o n i c species c o n t r i b u t i n g s i g n i f i c a n t l y to the P t o t a l equation except perhaps f o r mixtures at pressures and temperatures near c r i t i c a l c o n d i t i o n s . 27 CHAPTER 4 EXPERIMENTAL PROCEDURES 4.1 S t a r t i n g M a t e r i a l s and P r e l i m i n a r y M i n e r a l Syntheses C r i s t o b a l i t e : C r i s t o b a l i t e was prepared by dehydrating s i l i c i c a c i d (H 2Si03-nH20) i n a platinum c r u c i b l e f o r s i x hours at 1300°C i n a globar furnace ( F i s h e r C e r t i f i e d Reagent Lot #730944. A n a l y s i s : n o n - v o l a t i l e w i t h HF 0.20%, c h l o r i d e 0.005%, s u l f a t e 0.020%, heavy metals (as Pb) 0.005%, and i r o n (Fe) 0.003%). Powder X-ray d i f f r a c t i o n i d e n t i f i e d only a c r i s t o b a l i t e . F a y a l i t e : F a y a l i t e was synthesized from a f e r r o u s o x a l a t e - a c r i s t o b a l i t e mix. Ferrous o x a l a t e was s u p p l i e d by the C i t y Chemical Corporation of New York ( p u r i f i e d Lot #SA714. A n a l y s i s by Coast E l d r i d g e , L t d . , Vancouver detected 0.11% Mn as a major i m p u r i t y ) . The dry mix was sealed i n a s i l v e r capsule and heated to 700°C f o r peri o d s of 12 to 120 hours ( P t o t a l = 2000 b a r s ) . 100% f a y a l i t e was produced f o r a l l time p e r i o d s (X-ray and o p t i c a l v e r i f i c a t i o n . ) X-ray data are t a b u l a t e d i n Appendix 6. N i c k e l - I r o n O l i v i n e S o l i d S o l u t i o n s : Three o x a l a t e - a c r i s t o b a l i t e mixes were prepared corresponding to 10.5, 20.0, and 50.0 mole % N i - o l i v i n e . N i c k e l o x a l a t e used i n these mixes was s u p p l i e d by Johnson Matthey Chemicals, L t d . ( s p e c t r o g r a p h i c a l l y standardized Lot #S 50384 B p u r i t y 99.999 weight % ) . Syntheses were run i n sealed s i l v e r capsules at temperatures ranging from 750-800°C f o r times of 13 to 97 hours ( P t o t ? 1 = 2000 b a r s ) . In a l l cases 28 the f i n a l run product c o n s i s t e d of a Fe-Ni o l i v i n e + N i + quart z . The composition o f the o l i v i n e s o l i d s o l u t i o n i n each s y n t h e s i s was determined from the d(130) spacing (Appendix 6). N i c k e l O l i v i n e ( N i 2 S i 0 4 ) : S e v e r a l u n s u c c e s s f u l attempts were made to s y n t h e s i z e Ni2Si04 at P t o t a l " 2000 bars. An oxide mix (NiO + a c r i s t o b a l i t e ) sealed i n s i l v e r capsules r e a c t e d to N i - t a l c + N i + NiO at 700°C and 825°C. Oxalic-a c i d ( H 2 C 2 O 4 • 2 H 2 O ) was added to each run to produce a high XQQ^ This method was not s u c c e s s f u l i n s t a b i l i z i n g N i 2 S i 0 4 r e l a t i v e to the hydrous phase ( N i - t a l c ) . A N i - o x a l a t e + a c r i s t o b a l i t e mix rea c t e d to N i - t a l c + Ni at 750°C and P„. ^  . = 2000 bars, t o t a l Magnetite: Magnetite powder was s u p p l i e d by F i s h e r S c i e n t i f i c ( p u r i f i e d Lot #763881. A n a l y s i s by Coast E l d r i d g e , L t d . , Vancouver detected 1.00% Mn, 0.08% Ca, and 0.01% Mg as major i m p u r i t i e s ) . Monosulfide S o l i d S o l u t i o n s (Mss): P y r r h o t i t e , NiS, and s e v e r a l intermediate (Fe,Ni)S compositions were prepared by r e a c t i n g the pure metals w i t h s u l f u r i n cl o s e d , evacuated s i l i c a g l a s s tubes f o r 24 to 48 hours at 600°C (±10 PC). P y r r h o t i t e was prepared w i t h s e v e r a l d i f f e r e n t Fe:S r a t i o s . Products were reground under a l c o h o l and homogenized 5-10 days at 600°C i n evacuated s i l i c a g l a s s tubes. The m e t a l : s u l f u r r a t i o of the Mss was measured from i t s (102) X-ray r e f l e c t i o n (methods see S e c t i o n 4.3). A sharp (102) r e f l e c t i o n was taken to i n d i c a t e homogeneity. S p e c t r o g r a p h i c a l l y standardized sponge Fe and Ni wire were obtained from Johnson Matthey Chemicals, L t d . , (Lots #G 4294 and #W 6707, p u r i t y 99.99S weight % ) . 29 High p u r i t y lump s u l f u r was obtained from the United M i n e r a l and Chemical Corporation of New York. The compositions of Mss a v a i l a b l e f o r experiments are l i s t e d i n Table (4-1). B u f f e r Mixes: The f o l l o w i n g m a t e r i a l s were used f o r b u f f e r assemblages which were not i n p h y s i c a l contact w i t h the charge i n a run: Fe - powder, Baker Analysed Reagent (Lot #39363) F e 3 0 4 - powder, F i s h e r ' F e r r i c Oxide Black' P u r i f i e d (Lot #763881) F e 2 0 3 - powder, F i s h e r C e r t i f i e d Reagent (Lot #725030) Ni - powder, F i s h e r (Lot #755139) NiO - powder, F i s h e r C e r t i f i e d Reagent -(Lot #753646) F a y a l i t e s y n t h e s i z e d f o r QFM b u f f e r mixes was prepared as described p r e v i o u s l y . i 4,2_ General Experimental Equipment and Procedures Pressure Systems Two separate pressure systems were a v a i l a b l e f o r these experiments. (1) Water System: An a i r - o p e r a t e d Sprague h y d r a u l i c pump produced a maximum water pressure of 2000 bars. Pressures were measured on a c a l i b r a t e d A s h c r o f t Bourdon Tube gauge and are accurate to ±25 bars. (2) Argon System: Figure (4-1) diagrams the 7 k i l o b a r argon system. An a i r - o p e r a t e d SC h y d r a u l i c pump was used to pump o i l ( I m p e r i a l O i l Nuto H-54) to e i t h e r the se p a r a t i n g c y l i n d e r or to the low pressure s i d e of the i n t e n s i f i e r (maximum 2000 b a r s ) . Argon was introduced i n t o the se p a r a t i n g TABLE (4-1) Compositions of Mss used in Experiments Identification Number Wgt% Fe Wgt% Ni Wgt% S Atom% Fe Atom% Ni Atom% S d(102) NFeS Po#l 61.22 0.00 38.78 47.54 0.00 52.46 2.0685 0.9508 Po#2 62.10 0.00 37.90 48.48 0.00 51.52 2.0784 0.9695 Po#3 60.89 0.00 39.11 47.20 0.00 52.80 2.0648 0.9439 FNS1 51.49 10.00 38.51 40.20 7.43 52.37 • 2.0524 --FNS2 41.62 19.96 38.42 32.64 14.89 52.47 2.0441 --FNS3 31.00 31.09 . 37.90 24.49 23.36 52.15 2.0377; ' --FNS106* 30.0 31.0 39.0 23.5 23.1 53.3 -- — FNS109* 20.0 41:5 38.5 15.8 31.2 53.0 -- --FNS113* 10.0 52.75 37.25 8.0 40.1 51.9 -- — NS1 0.00 63.27 36.73 0.00 48.47 51.53 • 1.9861, Samples provided by T. Clark, University of Toronto. 7 kb Heise gauge 2 kb gouge N 2 or Air tank Ar tank FIGURE (4-1) 7 K i l o b a r Argon Pressure System 32 c y l i n d e r at tank pressure, prepumped to 2000 bars, and f i n a l l y pumped to run pressure by the i n t e n s i f i e r (maximum 7000 b a r s ) . Pressures were measured on a c a l i b r a t e d 15-inch Heise Bourdon Tube gauge ( s c a l e reading 7000 bars, accuracy +7 b a r s ) . Runs were l e f t open to the gauge f o r an i n i t i a l p e r i o d of one to two hours. A f t e r the temperature has s t a b i l i z e d the gauge was cl o s e d o f f from the run and the pressure was subsequently checked f o r a few seconds each day f o r the d u r a t i o n of the run. Pressures were g e n e r a l l y constant to ±10 bars. The r e s u l t i n g u n c e r t a i n t y i n the quoted pressures i s ±20 bars. Pressure Vessels Ren£ 41 c o l d - s e a l pressure v e s s e l s of the type o r i g i n a l l y d escribed by T u t t l e (1949) were used f o r a l l experiments (1 1/4" O.D., 1/4" I.D., length 12"). Furnaces (1) Water Pressure System: H o r i z o n t a l l y mounted 9" x 9" x 12" furnaces constructed of i n s u l a t i n g f i r e b r i c k s were used f o r a l l runs (furnace cores: 1 5/16" I.D., c y l i n d r i c a l , h e l i c a l l y wound w i t h nichrome w i r e ) . (2) Argon Pressure System: 10" O.D. c y l i n d r i c a l furnaces were suspended v e r t i c a l l y on cables w i t h i n a r o t a t i n g s a f e t y s h i e l d (furnace cores: 1 5/16" I.D., s e m i - c y l i n d r i c a l , l o n g i t u d i n a l l y wound w i t h nichrome w i r e ) . The furnaces were f i l l e d w i t h P l i c a s t A i r - l i t e c a s t a b l e r e f r a c t o r y . A small winch was used to p o s i t i o n the furnace w i t h i n the s a f e t y s h i e l d . Temperature Measurement and C a l i b r a t i o n Each bomb-furnace combination was c a l i b r a t e d to determine 33 the shape and l o c a t i o n of the thermal p l a t e a u w i t h i n the bomb. Temperatures were measured with steel-sheathed chromel-alumel thermocouples i n s e r t e d i n t o w e l l s i n the end of each bomb. These bomb thermocouples were c a l i b r a t e d i n pl a c e against a standard thermocouple p o s i t i o n e d i n the main bore of the bomb. The standard thermocouple had been p r e v i o u s l y c a l i b r a t e d a g ainst NBS t e s t thermocouple #179300 and against the melti n g p o i n t s of NBS standard Pb, Zn, and A l . For both v e r t i c a l l y and h o r i z o n t a l l y mounted furnaces i t was p o s s i b l e to p o s i t i o n the bomb so as to d e f i n e a thermal p l a t e a u 3 to 4 cm. long centered 1.5 to 2 cm. from the end of the main bore w i t h a maximum 2°C temperature d i f f e r e n c e over the p l a t e a u length. F i l l e r rods i n s e r t e d f o r experimental runs and the e x c e l l e n t heat c o n d u c t i v i t y of the run capsules should f u r t h e r reduce the thermal g r a d i e n t . Convection of water may s l i g h t l y i n f l u e n c e thermal g r a d i e n t s i n the h o r i z o n t a l furnaces. Convection i s considered i n s i g n i f i c a n t i n v e r t i c a T furnaces when argon i s used as the pressure medium (Boettcher and K e r r i c k , 1971). The temperature of each run was continuously monitored by a Leeds and Northrup 16 p o i n t recorder. A Leeds and Northrup K~3 potentiometer provided accurate d a i l y checks. S o l i d s t a t e temperature c o n t r o l l e r s (Hadidiacos, 1969) maintained run temperatures to ±2°C f o r most runs. Recorded run temperatures are g e n e r a l l y accurate to ±5°C ( c a l i b r a t i o n ±1°C, thermal g r a d i e n t s ±2°C, c o n t r o l f l u c t u a t i o n s ±2°C). U n c e r t a i n t i e s f o r i n d i v i d u a l experiments are l i s t e d i n run t a b l e s . Quench Procedures Runs i n h o r i z o n t a l furnaces were quenched d i r e c t l y i n t o a water bath ( T r u n < 600°C). Runs at temperatures >600°C were allowed to 34 cool i n a i r f o r two to three minutes before quenching. Runs i n v e r t i c a l furnaces could not be quenched w i t h the r o t a t i n g s a f e t y s h i e l d c l o s e d during e a r l y s e t s o f experiments. A c o i l was subsequently fastened beneath each furnace a l l o w i n g a i r or water quenches w i t h the s h i e l d c l o s e d . Quench procedures when used are i n d i c a t e d i n run t a b l e s . C o oling times are approximately 4 minutes f o r a i r or water quenched runs and 15 minutes f o r a l l others ( T f i n a i = room temperature). Capsules The normal experimental arrangement r e q u i r e d an outer Au capsule e n c l o s i n g an inner Au or Pt capsule. Appropriate lengths of Au and Pt tubing were annealed at '800°C i n a globar furnace (30-60 minutes). The tubing was then cleaned i n b o i l i n g HC1 (1M) and washed i n d i s t i l l e d water. I n d i v i d u a l tube dimensions are t a b u l a t e d below. Length O.D. Wall Thickness Au (outer) 3.0 cm. (1.1.8") 0.445 cm. (0.175") 0.025 cm. (0.010") (inner) 1.5 cm. (0.59") 0.241 cm. (0.095") 0.015 cm. (0.006") Pt (inner) 1.5 cm. (0.59") 0.305 cm. (0.120") 0.025 cm. (0.010") The charge, c o n s i s t i n g of d i s t i l l e d water p l u s the c r y s t a l l i n e phases under study, was contained i n the inner Au or Pt capsule. The oxygen b u f f e r assemblage, d i s t i l l e d water, and the charge capsule were sealed i n the outer Au capsule. To preserve v o l a t i l e s , capsules were immersed i n a small ice-water bath during welding w i t h a D.C. carbon a r c . Weighings were recorded during the e n t i r e l o a d i n g sequence and the f i n a l s ealed and weighed capsule p l a c e d i n a c o l d - s e a l bomb (see Huebner, 1971 f o r d e t a i l s of the weighing sequence). A f t e r a run the capsule was reweighed, then opened. I f the 35 capsule had remained sealed f o r the d u r a t i o n of the run the weight change was u s u a l l y l e s s than 1 mg. Observations such as the a u d i b l e or v i s i b l e v e n t i n g of gas, the presence of l i q u i d , and the c o l o u r and t e x t u r a l homogeneity of run products provide f u r t h e r evidence regarding the success or f a i l u r e of an experiment. B u f f e r Systems The b u f f e r i n g systems used i n t h i s study are summarized i n Table (4-2). A f t e r each run the b u f f e r assemblage was X-rayed and r e l a t i v e peak i n t e n s i t y r a t i o s were measured to provide an estimate of modal p r o p o r t i o n s of phases i n the b u f f e r . These estimates were u s e f u l i n determining the l i f e t i m e of b u f f e r mixes. The weight change during a run ( p o s i t i v e f o r a modal, s h i f t towards the reduced phase(s), negative f o r a s h i f t towards the o x i d i z e d phase(s)) l a r g e l y r e f l e c t s H 2 exchange w i t h the pressure medium. The weight change c o r r e l a t e s w e l l w i t h the modal change estimated from peak i n t e n s i t y r a t i o s . T r a n s f e r of Fe between the outer capsule and the w a l l s of the bomb may al s o r e s u l t i n weight change, but t h i s e f f e c t i s apparently small f o r experiments i n an Ar pressure medium. Hydrogen d i f f u s i o n i n t o the Ar pressure medium caused r a p i d o x i d a t i o n of IM, IW, and WM b u f f e r s (time <1 day above 500°C). The high f u j 2 i n these runs e v i d e n t l y should be balanced as c l o s e l y as p o s s i b l e by an Ar-H 2 pressure medium i n p l a c e of pure Ar i n order to in c r e a s e b u f f e r l i f e . QFM b u f f e r a l s o showed a d i s t u r b i n g l y short l i f e t i m e at higher temperatures. F i g u r e (4-2) provides a guide to estimate maximum run times f o r QFM b u f f e r at va r i o u s temperatures. No s i g n i f i c a n t d i f f e r e n c e was detected f o r runs at 2 or 3 k i l o b a r s . NNO b u f f e r o x i d i z e d only s l i g h t l y a f t e r TABLE (4-2) Experimental Buffering Systems: H-O-S Gas Mixtures £°2 £ h2 Buffer Fugacities Fugacities Internal(i) Internal(i) Computer programs Comments Symbol imposed imposed and and to calculate gas externally internally External(e) External(e) mixture compositions inner and outer < H-O-S Version 4, 4A welded [0 B ,OH(S B X,H0S)] f H ? . f s ? £o® * f 0 2 f H o = £ H o 0 _ H V e r s i o n 1 o r 2 o u t e r capsules inner capsule [0B,HOSlsBX,HOS|] f 0 f s f0Q = f0i = f H o H-O-S Version 1, 1A crimped, outer 1 L 2 1 1 1 H-O-S Version 2, 2A capsule welded inner and [0B,OH(0BSBX,HOS)] - f 0 , f S 9 f o ! = f0; £Ho * £H* H-O-S Version 1, 1A outer capsules 2 2 2 2 2 n 2 H-O-S.Version 2, 2A welded [n these runs the charge itself is a buffering system. The external fjj^ is controlled at a value :lose to that of the charge capsule in order to prolong the l i f e of the internal buffering system. 37 450-? 400 D o I 350 300 250 200 150 100 50 • 19 - 17 15 H 3 ° 11 550 600 650 700 750 — — > T e m p e r a t u r e °C FIGURE (4-2) QFM B u f f e r L i f e t i m e Ar pressure medium (2000 or 3000 bars) Au capsule (0.010" w a l l t h i c k n e s s ) S t a r t i n g assemblage: f a y a l i t e + H 2 O F i n a l assemblage: QFM + vapour ( f a y a l i t e detected by X-ray) o QM + vapour ( t r a c e f a y a l i t e detected o p t i c a l l y ) x QM + vapour Many runs i n the QFM + vapour f i e l d are not p l o t t e d . The b u f f e r l i f e t i m e i s l e s s f o r s t a r t i n g mixtures of QFM + H 2 O . A 3:3:2 mix (molar p r o p o r t i o n s ) of QFM contained only t r a c e amounts of f a y a l i t e a f t e r 96 hours at 660°C. 38 I I .1 /I 150 ,hours at 670 C, and longer runs are clearly practical. HM buffer showed very l i t t l e change after 300 hours at 665°C. Observations on buffer l i f e expectancy in a water pressure medium closely parallel those detailed by Huebner (1971). 4.3 Identification and Analysis of Phases Standard petrographic and X-ray diffraction techniques were employed to study al l run products and phases synthesized for charges or buffers. X-ray slides (smear mounts) were prepared by mounting samples on glass slides with Duco cement dissolved in acetone. Silicon was mixed in as an internal standard (a = 5.43054 +0.00017, Parrish, 1960). Each sample was scanned at 2° 26 per minute on a Phillips X-ray diffractometer using Ni-filtered Cu radiation (chart speed 5x240 mm./hour). Accurate measurement of an individual peak was obtained by oscillating a smear mount at least three times (six measurements) between the sample peak and the nearest Si peak (scan speed 0.5° 26 per minute). The distance between peaks on the strip chart was measured from midpoints located at two-thirds peak height when K j and K a 2 components were clearly resolved, and at one-half peak height for poorly resolved maxima. 26 values for 'up' and 'down' scans commonly differ slightly. This difference is compensated by averaging equal numbers of 'up' and 'down' measurements. 29 for the (102) peak of hexagonal pyrrhotite was obtained by oscillation between the (102) pyrrhotite peak and the (220) silicon peak. The composition of hexagonal pyrrhotite was determined from the equation calculated by Yund and Hall (1970) expressing d(102) as a function of atomic percent 'iron: 39 Atomic % Fe - 45.212 + 72.86(d(102) - 2.0400) + 311.5(d(102) - 2.0400) 2 (4-1) The standard e r r o r of estimate f o r t h i s equation i s quoted as 0.06 atomic percent i r o n . Np eg, de f i n e d as the mole f r a c t i o n of FeS i n the system FeS-S2 by Toulmin and Barton (1964), i s r e l a t e d to atomic percent i r o n by the f o l l o w i n g expression: N F e S = 2(Atomic % Fe) / 100.0 (4-2) 26 f o r the (130) peak of o l i v i n e was obtained by o s c i l l a t i o n between the (130) o l i v i n e peak and the (111) s i l i c o n peak. The composition of Fe-Ni o l i v i n e was c a l c u l a t e d from equations (A6-1) and (A6-2). These equations are discussed i n Appendix 6. Iron and n i c k e l analyses were determined on a J e o l c o JXA - 3A e l e c t r o n microprobe ( a c c e l e r a t i n g v o l t a g e 25KV., sample cu r r e n t 0.08 yamps measured on b r a s s , t a k e o f f angle 20 degrees). The background l e v e l was taken as the average of counts recorded one degree above and one degree below the Fe and Ni peaks. Standards were pure Fe and pure N i . Standard c o r r e c t i o n s f o r dead-time and i o n i z a t i o n -p e n e t r a t i o n l o s s e s , absorption and f l u o r e s c e n c e e f f e c t s were computed on an IBM 360/67 computer us i n g a program s u p p l i e d by the Department of M e t a l l u r g y , U.B.C. (MAGIC - Microprobe A n a l y s i s General I n t e n s i t y C o r r e c t i o n s ) . 40 CHAPTER 5 THE Fe-Si-H-O-S AND Fe-H-O-S SYSTEMS 5.1 Introduction Geologic interest in the Fe-Si-H-O-S system and its subsystem Fe-H-O-S reflects the natural abundance of iron-bearing silicates and their common attendance by iron oxides and iron sulfides. Iron sulfide and iron oxide reactions have been discussed through the application of thermochemical data in significant papers by Holland (1959, 1965), and Barnes and Kullerud (1961). Advances to 1967 are summarized by Kullerud (1967) and Barton and Skinner (1967). The theoretical and experimental study by Toulmin and Barton (1964) has resulted in the calibration of pyrrhotite as a useful indicator of sulfur fugacity in natural and experimental systems. The following equations, derived by Toulmin and Barton, have been used in this Po work to calculate log fg^ and log ap gg from measured pyrrhotite compositions (Npeg) a n d T°K: log fg = (70.03 - 85.83 N p e S) (1000/T°K - 1) + 39.30 / l - 0.9981 N p e S - 11.91 (5-1) log a P ° s = 85.83 (1000/T°K - 1) (1 - N + In N p e S) + 39.30 0.9981 N - 39.23 tanh"1 A - 0.9981 N - 0.002 (5-2) 41 The r e a c t i o n : Fe 30 4 3/2 S 2 t 3 FeS + 2 0 2 (5-3) has been s t u d i e d over a range of s u l f u r and oxygen f u g a c i t i e s . Oxygen f u g a c i t y was c o n t r o l l e d i n t e r n a l l y by QFM b u f f e r (Fe-Si-H-O-S System) or e x t e r n a l l y by WI, QFM, or NNO b u f f e r s (Fe-H-O-S I n t e r n a l System). The p y r r h o t i t e composition i n d i c a t e s the s u l f u r f u g a c i t y i n each experiment. study r e a c t i o n s at high f s 2 - Results however when combined w i t h thermochemical c o n s i d e r a t i o n s bear on the s t a b i l i t y of the important assemblages p y r i t e - p y r r h o t i t e - magnetite and p y r i t e - magnetite -hematite. Choice of Reaction V e s s e l : C o l l a p s i b l e noble metal capsules (Pt and Au) serve as r e a c t i o n v e s s e l s f o r these experiments. These capsules permit experimental c o n t r o l of t o t a l pressure and i n d i v i d u a l gas f u g a c i t i e s i n a d d i t i o n to the v a r i a b l e s temperature and bulk composition c o n v e n t i o n a l l y s p e c i f i e d i n s t u d i e s of s u l f i d e - b e a r i n g systems. Capsule c o n f i g u r a t i o n s and b u f f e r i n g systems are summarized i n Table (4-2) . The maximum s u l f u r f u g a c i t i e s d e f i n a b l e i n Pt and Au capsules are c o n t r o l l e d by the r e a c t i o n s * : Experimental problems were encountered i n attempting to 2 Pt + . S 2 t 2 PtS (5-4) log f s 2 = [0.1365 ( P t o t a l " 1•°) " 14,993] / T°K + 9.86 (derived from Larson and E l l i o t , 1967) 4 Au + S 2 t 2 Au 2S (5-5) * See a l s o S e c t i o n 5.3; S t a b i l i t y of Platinum S u l f i d e s . 42 The log f g defined by equation (5-5) l i e s i n the metastable region above the s u l f u r condensation curve (Barton, 1970). K u l l e r u d (1971) and Barnes (1971) d i s c u s s experimental methods c u r r e n t l y employed to study s u l f i d e - b e a r i n g systems. The small number of c a l i b r a t e d s o l i d phase b u f f e r s r e s t r i c t s the scope of s t u d i e s that may be t a c k l e d through c o n t r o l of the vapour phase composition. The b u f f e r method however o f f e r s s o l u t i o n s to problems which cannot be approached through conventional s i l i c a g l a s s tube experiments. B u f f e r i n g the gas phase composition may a l l o w experimental e v a l u a t i o n of the g e o l o g i c s i g n i f i c a n c e of internal versus external b u f f e r i n g . * This study shows that r e a c t i o n r a t e s i n i r o n - b e a r i n g s u l f i d e - s i l i c a t e - o x i d e systems are enhanced by the preserice of an H-O-S vapour phase. Experiments of r e l a t i v e l y short d u r a t i o n may t h e r e f o r e be undertaken at lower temperatures than i s f e a s i b l e u s i n g s i l i c a g l a s s tubes. Phase Rule: The Gibb's phase r u l e s t a t e s : F = C - * + 2 where F = . number of degrees of freedom C = number of components $ = number of phases The number of components may equal, but cannot exceed, the number of chemical elements (A/) i n a system. Exceptions to the equivalence * In an internally buffered system the composition of the condensed phases defines the vapour phase composition. In the case of external buffering the gas phase controls the composition of solid phases. 43 'M=C. are summarized by Van Zeggeren and Storey (1970). A p p l i c a t i o n of the phase r u l e to the Fe-H-O-S system i n d i c a t e s that an e q u i l i b r i u m assemblage of two condensed phases + vapour has three degrees of freedom (M=t7=4; thus when $=3, F=3) . The assemblage p y r r h o t i t e + magnetite + an H-O-S gas mixture t h e r e f o r e i s i n v a r i a n t at f i x e d P t o t a l J ^' and fo2' S p e c i f i c a t i o n of these three v a r i a b l e s d e f i n e s the composition of each phase and the e q u i l i b r i u m p y r r h o t i t e composition serves to i n d i c a t e the s u l f u r f u g a c i t y i n the vapour phase. Given Ptotal> £ 0 2 5 £ S 2 ' a n <^ ^ f u g a c i t i e s of a l l other gas species i n the vapour phase can be computed (H-O-S programs, Appendix 3). A f i v e phase assemblage (eg. p y r r h o t i t e , f a y a l i t e , q u a r t z , magnetite, and vapour) i s i n v a r i a n t at f i x e d P^ota] a n c^ T t n e Fe-Si-H-0-S system (M=C=5; thus when $=5, F-2~) . Four phase assemblages are i n v a r i a n t under the same c o n d i t i o n s w i t h the a d d i t i o n a l experimental c o n t r o l of f c ^ -5.2 Thermochemical C a l c u l a t i o n s Magnetite - P y r r h o t i t e E q u i l i b r i u m : The composition of p y r r h o t i t e i n e q u i l i b r i u m w i t h magnetite has been-computed from thermochemical data. R e c a l l i n g r e a c t i o n (5-3): F e 3 0 4 + 3/2 S 2 * 3 FeS + 2 0 2 , Po , 3 , f 2 R , T " M- . 3/2 a F e 3 0 4 S2 thus; M Po log f 0 2 = (log K R ; T + log a + 3/2 log f g 2 - 3 log a p e S ) /2 (5-6) 44 Values of log K and AG° f o r t h i s r e a c t i o n have been c a l c u l a t e d using ' K y I K, 1 both Robie and Waldbaum (1968) and JANAF (1966) data. T°K T°K log K R > T AG^ T * ( K c a l . ) R $ Wt JANAF§ R § Wt JANAF§ 800 527 -34.572 -34.387 126.551 125.874 900 627 -30.013 -29.814 123.595 122.776 1000 727 -26.389 -26.176 120.746 119.771 1100 827 -23.430 -23.208 117.928 116.810 1200 927 -20.964 -20.731 115.108 113.829 * A GR,T = -4.57562 T log K R ? t Robie and Waldbaum (1968) thermochemical data. § JANAF (1966) magnetite data s u b s t i t u t e d f o r the Robie and Waldbaum (1968) values. R '§ W log K D = 6.253 - 32,651/T°K K, 1 (5-(800-1200°K, standard e r r o r i n l o g K „ = 0.010) K, 1 JANAF log K =• 6.580 - 32,765/T°K K, 1 (5-( 8 0 0 - 1 2 0 0 % standard e r r o r i n log K = 0.009) R, 1 -Equations (5-7) and (5-8) are l i n e a r r e g r e s s i o n equations based on the c a l c u l a t e d log K data. These equations are used i n S e c t i o n K, 1 5.3 to t e s t and compare experimental r e s u l t s . Equation (5-6) permits l o c a t i o n of the p y r r h o t i t e - m a g n e t i t e boundary i n terms o f the e q u i l i b r i u m £Q^ f o r a s p e c i f i c p y r r h o t i t e Po composition and temperature. Log f g and l o g ap g C, values are c a l c u l a t e d i n i t i a l l y from equations (5-1) and (5-2). Results shown i n F i g u r e (5-1) M and (5-2) are based on log a p e 3 Q 4 = °" 0 , I n F i 2 u r e ( 5 _ 1 ) t n e p y r r h o t i t e -magnetite boundary based on Robie and Waldbaum (1968) data would be s h i f t e d approximately +0.10 i n log £Q (at constant log fg ) by s u b s t i t u t i o n of the JANAF (1966) log K R T values. A s h i f t of +0.30 to +0.40 i n log £Q2 i s 45 FIGURE (5-1) I s o b a r i c , isothermal log f Q - log f n diagram ^2 2 (Fe-S-0 System) 627°C 1 atm. S o l i d l i n e s d e l i m i t s t a b i l i t y f i e l d s c a l c u l a t e d from thermodynamic data compiled by Robie and Waldbaum (1968). Dashed l i n e s d e f i n e the m o d i f i c a t i o n s to the f i e l d s necessary f o r agreement with the s t u d i e s by Darken and Gurry (1945) and Norton (1955). Oxygen b u f f e r s i n t h i s f i g u r e are l a b e l e d according to the i d e n t i f i c a t i o n code employed i n Appendix 1 (Table A l - 1 ) . Log values c a l c u l a t e d f o r QFM and NNO b u f f e r s are shown f o r comparison. The t e r m i n a t i o n p o i n t against the p y r r h o t i t e - m a g n e t i t e boundary determines the p r e d i c t e d log f $ 2 value f o r the e q u i l i b r i u m assemblage p y r r h o t i t e + magnetite when internally b u f f e r e d by e i t h e r QFM or NNO b u f f e r s . Dotted l i n e s d e f i n e the p y r r h o t i t e composition ( i n Np eg) as c a l c u l a t e d from equation (5-1) (Toulmin and Barton, 1964). 47 FIGURE (5-2) Predicted pyrrhotite compositions in equilibrium with magnetite. 1 arm. The 1 atm. log fg^ - log £Q^ diagrams for temperatures of 527, 627, and 727°C have been projected on to a common log fg^ -log fQ^ plane. At each temperature the pyrrhotite compositions (in Npeg) calculated from equation (5-1) are shown as dotted lines. Dashed lines define the log fg and log fg at which pyrrhotites of a specific composit 2 2 are in equilibrium with magnetite (T between 500 and 750°C). The temperature at any point along each dashed line may be calculated from equation (5-1) since both log fg and ^-peS a r e known. Trace of the intersection of QFM buffer (QFM1, Wones and Gilbert, 1969) with the pyrrhotite --magnetite boundary. The equation for QFM1 buffer (Table Al-1) allows recovery of the temperature at any point along the line. Npeg m a y be estimated by comparison with the dashed Npgg contours or accurately calculated from equation (5-1) (log fg^ read from the diagram and temperature calculated from the QFM1 equation). Trace of the intersection of QFM buffer (QFM2, Skippen, 1967) with the pyrrhotite - magnetite boundary. Pyrrhotite compositions and temperatures along the line may be recovered as discussed for QFM1, substituting the QFM2 equation as appropriate. 49 necessary f o r agreement with the WI1 and MW1 b u f f e r c a l i b r a t i o n s (Appendix 1). The temperature (between 500 and 750°C), log a n c* log f g at which a s p e c i f i c composition of p y r r h o t i t e i s i n e q u i l i b r i u m w i t h magnetite may be deduced from F i g u r e (5-2). The c a l c u l a t e d p y r r h o t i t e -magnetite curves are based on Robie and Waldbaum (1968) thermochemical data. The s u l f u r f u g a c i t y i n the vapour phase i n e q u i l i b r i u m w i t h p y r r h o t i t e + g n e t i t e i s i n d i c a t e d f o r £Q values internally defined by QFM b u f f e r . ma Pressure C o r r e c t i o n s : Equation (5-1) define s l og f g as a f u n c t i o n of p y r r h o t i t e composition and temperature w i t h r e f e r e n c e to the i d e a l diatomic gas at a t o t a l pressure on the s o l i d s o f 1 atm. A c o r r e c t i o n must be a p p l i e d to t h i s equation i n order to c a l c u l a t e log f q at t o t a l pressures other 2 than 1 atm. At any temperature and t o t a l p r e ssure: gas . Po rc 01 V% = V c (5-9) b 2 b 2 defines the e q u i l i b r i u m c o n d i t i o n when p y r r h o t i t e c o e x i s t s w i t h a vapour phase. By d e f i n i t i o n , f o r a non-ide a l gas: y | a s = y° (T) + RT In f g S 2 S 2 ^2 where y° i s a f u n c t i o n of temperature only. Consequently i f e q u i l i b r i u m 2 i s maintained during an isothermal pressure change: RT d In f s = d \ £ 0 (5-10) 2 b 2 At constant composition the d e r i v a t i v e i s : Po 9 In f S o 3 ] i ° 2 , S?, —Po RT (— ) = ( = VL U (5-11) 8 P T,N F e S 3 P T,Np eg S 2 50 and: 9 log f s VP° ( 2 = ( 5 _ 1 2 ) 9 P T,Np e S 2.303 RT -Po The p a r t i a l molar volume of S ? i n p y r r h o t i t e , V , ^ o 2 was estimated by f i t t i n g a l i n e a r r e g r e s s i o n equation to molar volume data c a l c u l a t e d from the l a t t i c e parameters of s y n t h e t i c p y r r h o t i t e s r e p o r t e d by F l e e t (1968). Molar volume (cm 3) = 11.637 + 6.534 (N p g ) (5-13) (standard e r r o r i n molar volume = 0.021 cm 3/mole) Thus : V P° • = 11.637 cm 3 T 7 P 0 o i ; P ° T O n i 3 V„ _ = V = 18.171 cm3 FeS S i g n i f i c a n t d i f f e r e n c e s i n p u b l i s h e d molar volume data are apparent i n F i g ure (5-3) ; The equation d e r i v e d by Toulmin and Barton (1964) does not agree w e l l w i t h the molar volume data from Robie, et a l . (1967) or F l e e t (1968). These l a t e r data are reasonably represented by equation (5-13) f o r compositions more i r o n - r i c h than N p e g = 0.96, but t h i s equation must be used w i t h r e s e r v a t i o n f o r more s u l f u r - r i c h compositions. New data are r e q u i r e d before a more extensive treatment of the molar volume data i s warranted. Equation (5-1) can now be c o r r e c t e d to permit c a l c u l a t i o n of log f$2 at any t o t a l pressure ( P 2 , i n b a r s ) : —Po log f g 2 (P 2,T) = log fs2(l>V + VS2 C P 2 " 1 , 0 ) (5-14) 2.303 RT where, l°g £ s (1>T) i s c a l c u l a t e d from equation (5-1) 51 FIGURE (5-3) Molar Volume of P y r r h o t i t e as a f u n c t i o n of Composition (N „) — i • 1 1 1 1 i 1 1 i 1 1.0 0 0.98 0.96 0.94 0.92 0.90 > N F E S The equation Molar volume (cm 3) = 16.420 + 1.841 ( N p e g ) was d e r i v e d by Toulmin and Barton (1964) based on c e l l edge data from Haraldsen (1941). [ Note: Toulmin and Barton, 1964, Table 7, p.665 i n c o r r e c t l y d e f i n e s t h i s equation as 16.420 - 1.841 ( N p e S ) ] o Molar volumes t a b u l a t e d by Robie, et a l . (1967) c Molar volumes c a l c u l a t e d from the l a t t i c e parameters of F l e e t (1968) The equation Molar volume (cm 3) = 11.637 + 6.534 ( N p e S ) (5-13) represents a l i n e a r r e g r e s s i o n f i t to t h i s data. [ The v e r t i c a l bar at. N p e S = 0.9760 marks a d i s c o n t i n u i t y c o r r e l a t e d to a s t r u c t u r a l rearrangement i n the hexagonal c e l l at t h i s composition. F l e e t , 1968 ] vl° = 11.637 cm 3  s 2 R = 83.1398 cm 3 bars °K _ 1 m o l e - 1 The e f f e c t o f pressure on the p y r r h o t i t e - magnetite e q u i l i b r i u m must now be considered. To maintain e q u i l i b r i u m f o r r e a c t i o n (5-3) F e 3 0 4 + 3/2 S 2 t 3 FeS + 2 0 2 the v a r i a t i o n of AGR at constant temperature must equal zero f o r changes i n t o t a l pressure and composition of p y r r h o t i t e . Therefore: 3 AGn 3 AGn d (AG R ) T) = 0 = ( — f ) d P + ( — J i ) d Npeg 3 P T,N F e S 9 N F e S P,T and: 3 AGR fd NFeS. * ^ ( 5 _ 1 5 ) d P T,AGR=0 9 AGR 3 N F e S }P,T The numerator of equation (5-15) i s : 3 AGn „ Po M ,3 In fn-x ( H) = (3 °V - V ) + 2 RT ( U 2 ) 3 P 1 , ^ ^ 3 P T,N F e S ~ i Po 3 In f S o 9 In a 3/2 D T ( Ti) + 3 RT ( t^L) 3 / 2 3 P J T , N F e S 3 P T,N F e S Now: 3 In f g _ p n RT C— -) = v (equation 5-11) 3 P T,N F e S b2 53 and: , 3 l n aFeS. VFeS " V ( ) = (5-16) 8 P T,N F e S RT Equation (5-16) i s equal to zero i f a l i n e a r r e l a t i o n e x i s t s between molar volume and p y r r h o t i t e composition (eg. equation 5-13). 3 In f Q 2 The oxygen b u f f e r determines the value of RT ( ) 3 P T,N F e S i n these experiments: 3 In f n ? RT ( -) = AV C D f r 3 P T,Np es S,Buffer AVg g u f f e r ^ s t n e volume change of the s o l i d s i n v o l v e d i n the b u f f e r r e a c t i o n per mole of 0 2. Therefore: ( ii) = (3 °V - V M ) + 2 A V C „ „ - 3/2 V ' ° (5-17) 3 P T,N F e S S,Buffer S 2 The denominator of equation (5-15) becomes: P n 3 AGn 9 l n aFeS 8 l n f S 2 ( — - - ) p T = 3 RT ( - 3/2 RT ( l-) (5-18) 3 % e S P ' T 3 N F e S P > T 3 N F e S P,T The Gibbs - Duhem equation at constant T and P i s : | d H = 0 Thus f o r any phase i n the FeS - S 2 system (constant T,P); NFeS d l 0 g aFeS = ( NFeS " ^ d l 0 g f S 2 (Toulmin and Barton, 1964, p.658) Therefore: 3 log a d log f s ( ,: ( £) ( i _ i — ) ( 5 _ i 9 ) 3 N F e S P j T 3 N F e S P,T N F e S 54 S u b s t i t u t i n g (5-19) i n t o (5-18) and s i m p l i f y i n g : ( 9 AG R ). 9 N F e S P,T * 3 log f s ? 2.303 RT (3/2 - — — ) ( -) N F e S ' 9 N F e S 'P,' (5-20) S u b s t i t u t i n g (5-17) and (5-20) i n t o (5-15) ,M d N (" FeS (3 °V P° V") + 2 A V S > B u f f e r " 3 / 2 ^ 2 d P T,AGR=0 3 9 log f s ? 2.303 RT (3/2 - — — ) ( - ^ - t r — ), (5-21) % e S ^ N F e S P,T Equation (5-21) can be evaluated f o r any experiment d e f i n i n g the p y r r h o t i t e - magnetite e q u i l i b r i u m upon determination of N g and temperature. The f o l l o w i n g values were used f o r c a l c u l a t i o n s i n S e c t i o n 5.3. Value N o t a t i o n ,Po v1 AV ,M S, B u f f e r S 2 R 3 log f S 2 3 N F e S 3P,T 18.171 cm 3 44.524 cm3 (WI) 10.64 cm3 (QFM - aqtz) 17.945 cm 3 (QFM - Bqtz) 21.035 cm 3* (NNO) 8.764 cm 3 (HM) 3.548 cm 3 11.637 cm3 83.1398 cm 3 bars °K _ 1 mole" 1 85.83(1-1000/T) 1 9 - 6 1 / l - 0.9981 N Source equation (5-13) Robie, et a l . (1967) Robie, et a l . (1967) equation (5-13) D i f f e r e n t i a t i o n of equation (5-1) at constant T and P * This value a p p l i e s f o r experiments i n which 6 quartz i s the s t a b l e phase i n the b u f f e r assemblage. Experimental r e s u l t s at any t o t a l pressure (1?2> ^ n bars) can now be co r r e c t e d to a standard pressure of 1 atm. d Nr N FeS FeS U,T) = N F e S ( P 2 , T ) + ( ^ - ^ o ( i . o i 3 - P 2) (5-22) 55 The pressure effect on the equilibrium log fg and Po log ap eg m a y be obtained by dividing the total differentials of these terms by d P at constant T, noting that AGR for the magnetite - pyrrhotite equilibrium must equal zero.* d log f g 2 3 log f s 2 3 log f s 2 d N p e S ( d P \,LGR=0~ ( 3 P ^T^peg + C 3 N F e S d P )T,AGR=0 (5-23) and j i Po ^ i P° - , Po ... d l 0 g aFeS _ 8 l o g aFeS + 3 l 0 g aFeS d NFeS d P T,AGR=0~ 3 P T>NFeS+ 3 N F e S ?>T d P T,AGR=0 Po 3 l 0 g aFeS 3 l 0 g f s2 1 d NFeS 3 P T,N F e S 3 N F e S P,T N F e S d P T,AGR=0 (5-24) The terms on the right side of equations (5-23) and (5-24) have a l l been evaluated previously (equations 5-12, 5-16, and 5-21). These equations may be used directly to correct experimental data to any standard pressure. Po The pressure effect on log fg and log a F e g c a n also be calculated from N F eg values determined using equation (5-22). For Po Npeg(l,T), log fg and log ap gg are calculated from equations (5-1) and Po (5-2). For Npeg(P2,T), log fg and log ap g g are calculated from equations Po (5-14) and (5-2). Alog fg and Alog a calculated by this method are identical to those calculated directly using equations (5-23) and (5-24). * Toulmin and Barton (1964, p.666) employ this method to calculate the Po pressure effect on ln apgg for the pyrite - pyrrhotite equilibrium. 56 5.3 Experimental R e s u l t s The r e s u l t s of experiments i n the Fe-H-O-S and Fe-Si-H-O-S systems are grouped on the b a s i s of common b u f f e r c o n f i g u r a t i o n (Tables 5-1 and 5-2). P y r r h o t i t e s used i n these experiments (Po#l, Po#2, and .Po#3) are c h a r a c t e r i z e d i n Table (4-1). The measured f i n a l p y r r h o t i t e composition i n d i c a t e s the log f g i n each experiment. Equation (5-14) was used to c a l c u l a t e log f g 2 at the experimental temperature and pressure. A l l r e s u l t s were c o r r e c t e d to a reference pressure of 1 atm.(equation 5-22). The r e s u l t s of these c a l c u l a t i o n s are presented i n Table (5-3). WI E x t e r n a l B u f f e r [WI,OH(SgX,HOS)]: The high fj.j imposed by WI b u f f e r caused s i g n i f i c a n t hydrogen d i f f u s i o n through the w a l l s of the outer Au capsule i n t o the argon pressure medium. The consequent r a p i d o x i d a t i o n of the b u f f e r assemblage l i m i t e d experiments to times of l e s s than two days. Under these reducing c o n d i t i o n s d i f f u s i o n of f e r r o u s i r o n from b u f f e r and charge assemblages h e a v i l y t a r n i s h e d both Au and Pt capsules. Magnetite + s u l f u r - r i c h p y r r h o t i t e r e a c t to form w i i s t i t e + t r o i l i t e i n 46 hours at 669°C and 2000 bars t o t a l pressure (Table 5-1). The measured composition (Np eg = 1.0026 ±0.003) l i e s at the i r o n - r i c h l i m i t o f the p y r r h o t i t e s o l i d s o l u t i o n and t h e r e f o r e cannot be bracketed through the use of s t a r t i n g mixtures c o n t a i n i n g p y r r h o t i t e s more i r o n - r i c h than the e q u i l i b r i u m composition. The e f f e c t of pressure on the e q u i l i b r i u m d NppS - i composition ( — ) i s -0.0001 Kb. 1 at 669 C (equation 5-21). d P T,AGR=0 This e f f e c t i s too small to be d e t e c t a b l e at pressures w i t h i n the range of the experimental equipment (7 Kb.). C a l c u l a t e d log f g values presented TABLE (5-1) Experimental Results Fe-H-O-S System Run Temperature Pressure Duration Bars Hours Charge Assemblage Original Final Inner Capsule Remarks M Po* M Po d(102) NFeS WI External Buffer [WI,0H(SDX,H0S)] D SN29 668±4 2070±25 39 X #2 x X 2.0938 1.0006 Pt SN32 669±4 2000±20 46 X #1 X 2.0947 1.0026 Pt QFM External Buffer [QFM,OH(SDX,HOS)] D SN71 651±5 2050±25 116 X #3 x X 2.0744 0.9617. Pt SN67, SN7V 663±4 2000±20 96 { x X #3 x X 2.0719 0.9570 Pt #3 x X 2.0734 0.9598 Au S37 665±6 3000±30 274 X #1 X X 2.0735 0.9601 Pt S38 665±6 3000±30 273 X #2 x X 2.0728 0.9588 Pt SN75 665±4 2000±20 93 X ' #3 x X 2.0737 0.9604 Au S21 666±4 3000±20 70 X #2 x X 2.0734 0.9598 Pt S24 666±4 3000120 91 - #2 ? X 2.0736 0.9603 Pt S17, S19^ 669±5 3000±20 90 <x #2 #2 x X X 2.0735 2.0736 0.9600 0.9603 Pt Pt S26 670±4 3000±20 92 X #1§#2 x X 2.0748 0.9624 Pt S22 672±4 3000±20 .95 X #1 X X 2.0734 0.9598 Pt S25 673±4 3000±20 90 X #2 x X 2.0734 0.9598 Pt [QFM,H0S|SBX,H0S|] S35 676±4 3000±20 90 X #2 x X 2.0739 0.9608 Pt +wtlstite in final assemblage +wtlstite in final assemblage water quench air quench, the same Au outer capsule contained both experiments 3 buffer changes 3 buffer changes air quench the same Au outer capsule contained both experiments crimped Pt inner capsule Identification number only - compositions listed in Table (4-1) corit1 d. TABLE (5-1) cont'd: Run Temperature Pressure Duration °C Bars Hours Charge Assemblage Original Final Inner Capsule Remarks M Po* M Po d(102) NFeS NNO External Buffer [NN0,0H(SBX,H0S)] S30 609±5 3000±20 114 x #1 x X 2.0725 0.9582 Pt SN72 663±5 2000±20 163 x #3 X X 2.0730 0.9592 Au air quench SN65 664±4 2030±25 148 x #3 X X 2.0731 0.9594 Pt water quench SN73 664±4 2000120 142 -.- #3 - X 2.0729 0.9590 Au air quench S27 666±4 5000120 76 #2 tr? X 2.0729 0.9589 Pt S29 666±5 3000120 91 x #1 X X 2.0727 0.9585 Pt S28 673±4 3000120 75 x #2 X X 2.0727 0.9585 Pt SN69 678±4 2000120 100 #3 - X 2.0718 0.9569 Pt air quench Original Final M H Po* M Py Po d(102) NFeS HM External Buffer [HM,0H(SBX,H0S)] SN79 662±5 2000120 240 x x #3 X X X 2.0563 0.9296 Au air quench SN76 663+4 2000120 118 x - . #3 X X X 2.0588 0.9338 Au air quench SN70 664±5 2000120 311 x - #3 x tr? X • 2.0571 0.9310 Pt air quench, PtS lining inner capsule SN66 673±5 2000120 132 x - #3 x tr? X 2.0545 0.9266 Pt. air quench, PtS lining inner capsule [HM,H0S|SBX,H0S|] SN78 665±4 2000120 216 x - #3 x tr? X 2.0537 0.9253 Pt air quench, Pt capsule * Identification number only - compositions listed in Table (4-1) no hematite remaining in buffer, PtS lining on capsule TABLE (5-2) Experimental Results Fe-Si-H-O-S System Run Temperature °C Pressure Bars Duration Charge Assemblage Hours Original Final F Po* F Q M Po d(102) NFeS Remarks QFM : Internal Buff er [QFM,OH(QFMSgX,HOS)] Pt inner capsules S7 562±5 3000120 312 x #1 X X X X 2.0745 0.9619 S2 595±4 3000120 215 x . #1 X X X X 2.0740 0.9610 S12 61415 3000120 114 X #2 x X X X 2.0739 0.9608 S59 62714 2000120 117 X #2 x X X X 2.0749 0.9626 S40 62814 2000120 117 X #1 X X X X 2.0760 0.9647 S15 65614 1975125 137 X #2 x X X X 2.0756 0.9640 SI 65715 3000120 97 X #1 X X X X 2.0751 0.9631 S13 66514 3000120 93 X #2 x X X X 2.0757 0.9642 S14 66714 3000120 113 X #2 x X X X 2.0756 0.9640 SN41 67015 2070125 13 X #3 x tr ? X 2.0774 0.9675 [0H(QFMSBX,H0S)] SN31 66914 2070125 94 X #1 X X X X 2.0772 0.9671 QFM External Buffer [QFM,OH(SBX,HOS)] Pt inner capsules SN68 64915 2050125 120 X #3 X X X 2.0741 0.9611 water quench SN77 66114 2000120 93 X #3 X X X 2.0739 0.9607 air quench, Au inner cap S33 ' 66614 3000120 80 - #1 X X X 2.0741 0.9612 Q + M in original assem. S34 67014 3000120 79 - #2 X X X 2.0737 0.9605 Q + M in original assem. SN42 70114 2000120 45 X #3 X X X 2.0721 0.9574 S23 70615 3000120 49 X #1 X X X 2.0736 0.9603 cont'd. TABLE (5-2) cont'd: Run Temperature °C Pressure Bars Duration Charge Assemblage Hours Original Final NNO External Buffer F Po* F [NN0,0H(SBX,H0S)] Q M Po d(102) N F e S Remarks Pt inner capsules Sol 664±4 3010±30 95 X #2 - X X X 2.0733 0. ,9596 S32 673±4 3000±20 80 X #1 - X X X 2.0726 0. ,9584 lo Internal or External Oxygen . Buffer after Run [QM,0H(SBX,H0S)] t Pt inner capsules S6 657±6 2980±30 408 X #1 - X X X 2.0587 0. ,9337 trace pyrite in final ass err. S5 711+5 2980±30 349 X #1 - X X X 2.0597 0. ,9353 pyrite in final assemblage SIS 729±5 3000±20 71 X #2 - X X X 2.0576 0. ,9318 S16 75C±5 3000±20 75 X #2 - X X X 2.0593 0. ,9347 * Identification number only - compositions listed in Table (4-1) t PtS formed a thin lining on the inside of these capsules during the experiments. TABLE (5-3) Experimental Results Calculated log fg and Pressure Corrections Run Temperature 103/°K Log f s 2 at Measured experimental T and P* NpeS (equation 5-14) WI External Buffer SN29 1.0627 SN32 1.0616 QFM External Buffer SN71 SN67 SN74 S37 S38 SN75 S21 S24 S17 S19 S26 S22 S25 S35 1.0823 1.0684 1.0684 1.0661 1.0661 1.0661 i.0650 1.0650 1.0616 1.0616 1.0604 1.0582 1.0571 1.0537 [WI,OH(SBS,HOS)] -11.05 1.000 -11.04 • 1.000 [QFM,0H(SBX,H0S)] -4.93 0.9617 -4.29 0.9570 -4.57 0.9598 -4.51 0.9601 -4.37 0.9588 -4.60 0.9604 -4.46 0.9598 -4.51 0.9603 -4.44 0.9600 -4.47 0.9603 -4.67 0.9624 -4.38 0.9598 -4.37 0.9598 [QFM,H0S|SBX,H0S|] -4.43 0.9608 NpeS at T and 1 atm.t (equation 5-22) Log f s 2 at T and 1 atm. (equation 5-1) Fe-H-O-S System 1.000 -11.19 1.000 -11.17 Fe-H-0-S System 0.9641 -5.32 0.9594 -4.66 0.9621 -4.94 0.9636 -5.06 0.9623 -4.93 0.9627 -4.97 0.9633 -5.02 0.9638 -5.07 0.9635 -5.00 0.9638 -5.03 0.9658 -5.23 0.9633 -4.93 0.9633 -4.92 0.9643 -4.98 Po L°S aFeS a t T and 1 atm. (equation 5-2) 0.000 0.000 -0.0913 -0.1098 -0.0983 -0.0922 -0.0973 -0.0957 -0.0933 -0.0914 -0.0923 -0.0912 -0.0831 -0.0929 -0.0929 -0.0888 cont'd. TABLE (5-3) cont'd: Run Temperature Log fg, a t Measured 103/°K • experimental T and P* NpeS (equation 5-14) NNO External Buffer [NN0,0H(SBX,H0S)] S30 1.1338 -5. 13 0.9582 SN72 1.0684 -4. 51 0.9592 SN65 1.0672 -4. 51. 0.9594 SN73 1.0672 -4. 47 0.9590 S27 1.0650 -4. 37 0.9589 S29 1.0650 -4. 33 0.9585 S28 1.0571 -4. 24 0.9585 SN69 1.0515 . -4. 08 0.9569 HM External Buffer [HM,0H(SBX,H0S)] SN79 1.0695 -1. 90 0.9296 SN76 1.0684 -2. 23 0.9338 SN70 1.0672 -1. 99 0.9310 SN66 1.0571 -1. 55 0.9266 [HM,H0S|SBX,HOS|] SN78 1.0661 -1. 53 0.9253 Npes at T Log f g ? at T and 1 atm.f and 1 atm. (equation 5-22) (equation 5-1) Fe-H-O-S System 0.9592 -5.45 0.9599 -4.71 0.9601 -4.71 0.9597 -4.67 0.9599 -4.67 0.9595 -4.63 0.9595 -4.53 0.9576 -4.27 Fe-H-O-S System 0.9296 -2.03 0.9338 -2.35 0.9310 -2.12 0.9266 -1.68 0.9253 -1.66 Log a F e S at T and 1 atm. (equation 5-2). -0.1153 -0.1077 , -0.1068 -0.1085 -0.1073 -0.1090 -0.1084 -0.1163 -0.2640 -0.2390 -0.2551 -0.2792 -0.2894 cont'd. TABLE (5-3) cont'd: Run Temperature Log f s 2 at Measured 103/°K experimental T and P* NpeS (equation 5-14) QFM Internal Buffer [QFM,OH(QFMSBX,HOS)] S7 1.1976 -6.31 0.9619 S2 1.1521 -5.65 0.9610 S12 1.1274 -5.33 0.9608 S39 1.1111 -5.39 0.9626 S40 1.1099 -5.61 0.9647 S15 1.0764 -5.11 0.9640 SI 1.0753 -4.93 0.9631 S13 1.0661 -4.93 0.9642 S14 1.0638 -4.88 0.9640 SN41 1.0604 -5.28 0.9675 [0H(QFMSBX,H0S)] SN31 1.0616 -5.25 0.9671 QFM External Buffer [QFM,0H(SBX,H0S); SN68 1.0846 -4.90 . 0.9611 SN77 1.0707 -4.69 0.9607 S33 1.0650 -4.60 0.9612 S34 1.0604 -4.48 0.9605 SN42 1.0267 -3.83 0.9574 S23 1.0215 -3.98 0.9603 NFeS at T and 1 atm.t (equation 5-22) • Fe-Si-H-0 0.9648 0.9639 0.9637 0.9645 . 0.9665 0.9662 0.9659 0.9676 0.9674 0.9697 Log f s 2 at T and 1 atm. (equation 5-1) S System -6.87 -6.18 -5.85 -5.73 -5.95 -5.48 -5.43 -5.49 -5.44 -5.67 Log a F e S at T and 1 atm, (equation 5-2) -0.0948 -0.0960 ' -0.0955 -0.0912 -0.0828 -0.0S24 -0.0836 -0.0768 -0.0774 -0.0686 0.9693 -5.64 -0.0700 Fe-Si-H-O-S System 0.9635 -5.28 -0.0938 0.9630 -5.06 -0.0948 0.9647 -5.16 -0.0879 0.9640 "-5.03 -0.0904 0.9598 -4.18 -0.1052 0.9638 -4.52 -0.0889 cont'd. TABLE (5-3) cont'd: Run Temperature Log f s 2 a t Measured 103/°K experimental T and P* NpeS (equation 5-14) NNO External Buffer [NNO,OH(SBX,IIOS)] NFeS a t T L oS fS2 a t T and 1 atm.t and 1 atm. (equation 5-22) (equation 5-1) Fe-Si-H-O-S System S31 S32 1.0672 1.0571 -4.47 -4.23 No Internal or External Buffer after Run S6 S5 S18 S16 1.0753 1.0163 0.9980 0.9970 -2.22 -1.76 -1.31 -1.52 0.9596 0.9584 [QM,0H(SBX,H0S)] 0.9337 0.9353 0.9318 0.9347 0.9606 -4.77 0.9594 -4.52 Fe-Si-H-O-S System 0.9337 -2.41 0.9353 -1.94 0.9318 -1.49 0.9347 -1.70 r PO j . r r -Log a F e S at T and 1 atm. (equation 5-2) -0.1045 -0.1088 -0.2411 -0.2207 -0.2360 -0.2203 * The uncertainty in log fg^ calculated from equation (5-14) is approximately ±0.7. i The uncertainty in N„ Q calculated from equation (5-22) is approximately ±0.004. These estimates include the following sources of error: Source of Error equation (4-1) X-ray measurement of d(102) —Po s2 equation (5-1) Uncertainty log £S 2 ±0.12 ±0.03 ±0.15 ±0.10 (3Kb.) ±0.07 (2Kb.) ±0.35 Uncertainty NFeS ±0.0012 ±0.0003 ±0.0015 ±0.0010 (3Kb.) ±0.0007 (2Kb.) Not applicable References / Comments Yund and Hall (1970) Section 4.3 Figure (5-3) - the uncertainty reflects inconsistencies in the molar volume data. Toulmin and Barton (1964) 65 in Table (5-3) are based on Npeg = 1.000. The final assemblage corresponds to that predicted from thermochemical data (Figure 5-2). The rapid change in pyrrhotite composition in response to the imposed conditions is encouraging in view of the severe experimental restrictions imposed by the buffer system. QFM Internal Buffer [QFM,OH(QFMSBX,HOS)]: The equilibrium assemblage quartz + fayalite + magnetite + pyrrhotite + vapour defines an invariant point in the Fe-Si-H-O-S system at fixed Ptotal a n d temperature• Under these conditions the composition of.each condensed phase and the fugacity of each gas species in the vapour phase is fixed. This invariant point is determined by the intersection of three equilibria: Fe 30 4 + 3/2 S 2 * 3 FeS + 2 0 2 (5-3) 3 Fe2Si04 + 0 2 t 2 Fe304 + 3 Si0 2 (5-25) Fe 2Si0 4 + S 2 2 2 FeS + Si0 2 + 0 2 (5-26) The resulting topology is illustrated in Figure (5-5A). The equilibrium at the isobaric isothermal invariant uoint may be expressed as: Fe 2Si0 4 + FeS + 0 2 t Fe 30 4 + Si0 2 + 1/2 S 2 (5-27) The external QFM buffer in these experiments serves to define fpj in the outer system at values close to that controlled internally. This reduces H2 diffusion, prolonging the effective l i f e of the internal buffer assemblage. Experimental results are presented in Tables (5-2) and (5-3). The pyrrhotite composition at the invariant point has been bracketed at 66 s e v e r a l temperatures through the use of s t a r t i n g mixtures c o n t a i n i n g p y r r h o t i t e s more s u l f u r - r i c h (Po#l and Po#3) or more s u l f u r - p o o r (Po#2) than the e q u i l i b r i u m composition (Figures 5-4 and 5-5B). Measured compositions i n some cases overstep the average composition d e f i n e d by a p a i r of experiments (eg. S39 and S40, Table 5-3). This apparent overstepping i s not s i g n i f i c a n t s i n c e the u n c e r t a i n t y i n Np eg i s ±0.004 and ANp eg i n such cases i s <0.002. The log fs2> 1°S £ 0 2 > a n c* p y r r h o t i t e composition at the OFMPo + vapour i n v a r i a n t p o i n t has been c a l c u l a t e d at 527, 627, and 727°C using f i v e d i f f e r e n t combinations of thermochemical data (Table 5-4). I n c o n s i s t e n c i e s are r e f l e c t e d as d i f f e r e n c e s of 1.5 i n log f s 2 ' l ' 2 i - n log f"02> a n c* 0.012 i n Np eg. Each data set shows a s h i f t to more s u l f u r -r i c h p y r r h o t i t e compositions w i t h decreasing temperature. The p r e d i c t e d ANpeS over the 200 degree temperature i n t e r v a l between 727 and 527°C i s s m a l l . Estimates range from -0.0036 to -0.0012 (Table 5-4). Experimental r e s u l t s were c o n s i s t e n t and r e p r o d u c i b l e w i t h i n narrow e r r o r l i m i t s . Results l i e between those c a l c u l a t e d based on the QFM b u f f e r c a l i b r a t i o n s of Wones and G i l b e r t (1969) and Skippen (1967) (Figure 5-4). Measured p y r r h o t i t e compositions are v i r t u a l l y independent of temperature between 560 and 670°C. Experiments at the lower temperatures c o n t a i n s l i g h t l y more s u l f u r - r i c h p y r r h o t i t e s (Table 5-3) but the ±0.004 u n c e r t a i n t y i n Np eg i s g r e a t e r than the measured ANp eg. P y r r h o t i t e changes composition r a p i d l y i n response to the imposed c o n d i t i o n s . The d u r a t i o n of experiments ranges between 13 and 312 hours (Table 5-2). The composition change ( N p e S '= 0.9439 to Np eg = 0.9675) i n SN41 occurred i n l e s s than 13 hours. 67 FIGURE (5-4) Experimental Results Fe-Si-H-O-S System All results corrected to a standard pressure of 1 atm. Buffer Systems © [QFM,OH(QFMSBX,HOS)] A [QFM,OH(SBX,HOS)] • [NNO,OH(SBX,HOS)] Isocompositional lines (Npeg) calculated from equation (5-1) Trace of the intersection of QFM buffer (QFM1, Wones and Gilbert, 1969) with the pyrrhotite-magnetite boundary. For further details refer to Figures (5-1) and (5-2) -Trace of the intersection of QFM buffer (QFM2, Skippen, 1967) with the pyrrhotite-magnetite boundary * I Arrows define the direction of compositional change 1 from the original to the final pyrrhotite composition .0.9400 .0.9450 . 0.9500 . 0.9550 •0.9600 A SN42 - 4.4 0.9650 S32 m.--' , - A S 2 3 . -O - 4.8 O - 5.2 5.6 E3S31 SN 77 A kS34 5 3 3 ^ ASN68 ..• SI © S14© .•' S15© S13©f f I. S39© •" sN3iQ: • -QSN41 . 0.9700 0.9750 - 6.0 S12© ©S40 , 0.9800 S2© - 6.4 - 6.8 H S7. 1.20 1.16 1.12 600 C 650 1.08 o 1.04 700 C 0.9850 1.00 69 FIGURE (5-5A) Topology r e s u l t i n g from the Quartz + F a y a l i t e + Magnetite + P y r r h o t i t e + Vapour I n v a r i a n t P o i n t . (627°C - 1 atm.) S o l i d l i n e s d e f i n e the p o s i t i o n of e q u i l i b r i a c a l c u l a t e d using Robie and Waldbaum (1968) data. The p r e d i c t e d p o s i t i o n of the i n v a r i a n t p o i n t i s l a b e l l e d 1. Numbers 2 to 5 i d e n t i f y c a l c u l a t e d p o s i t i o n s of the i n v a r i a n t p o i n t based on other thermochemical data (Table 5-4) . FIGURE (5-5B) Experimental Bracket d e f i n i n g the Quartz + F a y a l i t e + Magnetite + P y r r h o t i t e + Vapour I n v a r i a n t P o i n t . (627°C - 1 atm.) e P y r r h o t i t e composition i n s t a r t i n g mixture O F i n a l p y r r h o t i t e composition Isocompositional l i n e s (Np eg) c a l c u l a t e d from equation (5-1) 70 71 TABLE (5-4) . Calculated Positions of the Quartz + Fayalite + Magnetite + Pyrrhotite + Vapour Invariant Point (Fe-Si-H-O-S System - standard pressure 1 atm.) Pyrrhotite composition at the invariant point log f S 2 log f Q 2 Fig.(5-5A)* N p e S a P ° s Robie and Waldbaum (1968) Thermochemical Data 527 -8. 65 -23.68 0. .9733 0.8669 627 -6. 98 -20.13 1 0. ,9749 0.8867 727 -5. 70 -17.36 - 0. 9769 0.9051 Position Gilbert, defined by the 1969) and QFM2 intersections buffer (Skipp of QFMl en, 1967) buffer (Wones with reaction and (5-26) Fe2Si04 + s 2 i 2 FeS + Si0 2 + °2 QFMl 527 -8. 16 -23.17 0. 9697 0.8386 627 -6. 40 -19.60 2 0. ,9703 0.8539 727 -5. 00 -16.74 0. 9709 0.8668 QFM 2 527 -7. 47 -22.43 0. .9642 0.7941 627 -5. 85 -18.99 3 0. ,9655 0.8187 727 -4. 64 -16.25 0. ,9676 0.8442 Position reaction defined by the C 5 " 3 ) : Fe 30 4 intersections + 3/2 S 2 t 3 of QFMl FeS + 2 C and QFM2 buffers with »2 QFMl 527 -7. 97 -23.17 0. .9682 0.8268 627 -6. 26 -19.60 4 0. .9691 .0.8453 727 -4. 89 -16.74 0. .9699 0.8601 QFM 2 527 -7. 10 -22.43 0. .9611 0.7683 627 -5. 50 -18.99 5 0. .9624 0.7943 727 -4. 28 -16.25 0, ,9641 0.8198 Numbers 1-5 identify points plotted on Fig. (5-5A). 72 Log i n each experiment has been c a l c u l a t e d u t i l i z i n g l o g K R T data f o r r e a c t i o n (5-3) (equations 5-7 and 5-8) plu s e x p e r i m e n t a l l y Po determined log fg and log a p e g values (Table 5-3). Equation (5-6) M has been solved assuming log ape^Q^ = 0.0. S i m i l a r procedures are employed to c a l c u l a t e log f r ^ f ° r r e a c t i o n s (5-26) and (5-27). Results are compared to log fQ^ values computed from QFM b u f f e r c a l i b r a t i o n s (Table 5-5). The e r r o r i n determining l o g f o 2 based on r e a c t i o n s (5-3), (5-26), and (5-27) depends on i n t e r r e l a t e d source data. A r e a l i s t i c estimate f o r r e a c t i o n (5-3) i s ±0.8 i n log f ( ) 2 - These data t h e r e f o r e cannot be used to r e f i n e the a v a i l a b l e c a l i b r a t i o n s f o r QFM b u f f e r . The r e s u l t s of a l l c a l c u l a t i o n s agree w i t h i n l i m i t s of ±0.4 f o r each experiment. K u l l e r u d , Donnay, and Donnay (1968, 1969) show th a t omission s o l i d s o l u t i o n of i r o n i n magnetite occurs i n the presence of M a s u l f u r - b e a r i n g vapour phase. Equation (5-6) can be solved f o r l o g ap but the combined u n c e r t a i n t y i n the input data (approximately ±1.0) i s much l a r g e r than the e f f e c t that omission s o l i d s o l u t i o n could have on t h i s a c t i v i t y term. C a l c u l a t e d pressure e f f e c t s at the QFMPo + vapour i n v a r i a n t p o i n t (627°C) are: d N 0 — ) = -0.00091 Kb" 1 v d P T,AGR=0 i Po d aFeS r Lh£.) = -0.00688 Kb 1 d P T,AGR=0 d log f g ( £) = 0.170 Kb 1 d P T,AGR=0 TABLE (5-5) Thermochemical Calculations QFM Internal Buffer Log f 0 2 calculated at run temperature and a standard pressure of M 1 atm. (log a ^ ^ and log ; olivine Fe2SiC>4 Run Temperature °C Log f 0 reaction QFMl* ?5-25) QFM 2* Log f 0 reaction R § Wt ?5-3) JANAF§ Log f o 2 reaction (5-26) R § Wt Log f 0 reaction R § Wt ?5-27) JANAF S7 562 -21.82 -21.13 -21.43 -21.34 • -21.13 -21.74 -21.54 S2 595 • -20.65 -20.01 -20.18 -20.08 -19.84 -20..51 -20.32 S12 614 -20.02 -19.40 -19.52 -19.42 -19.17 -19.87 -19.67 S39 627 -19.60 -18.99 -19.17 -19.07 -18.84 -19.50 -19.30 S40 628 -19.57 -18.96 -19.33 -19.23 -19.06 -19.59 -19.39 S15 656 -18.71 -18.14 -18.43 -18.33 -18.14 -18.71 -18.51 SI 657 -18.68 -18.11- -18.37 -18.27 -18.08 -18.66 -18.46 S13 665 -18.44 -17.88 -18.28 -18.18 -18.03 -18.52 -18.32 S14 667 -18.38 -17.83 -18.21 -18.10 -17.95 -18.45 -18.25 SN41 670 -18.29 -17.74 -18.33 -18.23 -18.15 -18.51 -18.30 SN31 669 -18.32 -17.77 .-18.33 -18.22 -18.13 . -18.51 -18.31 * Table (Al-1) Appendix 1 t Log KR j based on Robie and Waldbaum (1968) thermochemical data § JANAF (1966) magnetite data substituted for the Robie and Waldbaum (1968) values 74 d log f 0 ( -) = 0.104 Kb 1 d P T ,AGR=0 Combining these predicted pressure dependencies with the experimental Po results for 627°C (S39, S40) defines Npeg, apeg> log ^S2> a n c* °^g ^ 02 a t the QFMPo + vapour invariant point as a function of total pressure. L1 Pressure (bars) NFeS Po aFeS log f s 2 log f o 2 QFMl 1 0.9655 0.8184 -5.85 -19.60 1000 0.9646 0.8115 -5.68 -19.49 2000 0.9637 0.8046 -5.51 -19.39 3000 0.9628 0.7978 -5.34 - 1 9 . 2 9 4000 0.9619 0.7909 -5.17 -19.18 5000 0.9610 0.7840 -5.00 -19.08 Log fQ 2 is based on the Wones and Gilbert (1969) calibration of QFM buffer. These results have been used to calculate the composition of the H-O-S gas phase in equilibrium with quartz + fayalite + magnetite + pyrrhotite at 627°C and P = 2000 bars (Table 5-6). The range of total log fg^ considered (-5.1 to -5.8) brackets the experimentally determined value of -5.5. The dominance of F^ O in the fluid phase makes the Lewis and Randall rule a good approximation for this calculation. QFM External Buffer [QFM,0H(SBX,H0S)]: Reaction (5-3) has been investigated in both the Fe-Si-H-O-S and Fe-H-O-S systems. The experimental configuration is identical for both systems. Quartz is present as an additional phase in Fe-Si-H-O-S system experiments. At a specified pressure, temperature, and fc>2 the pyrrhotite composition in equilibrium with magnetite should be identical in either system. Equilibrium compositions were bracketed by using mixtures containing pyrrhotites of different compositions (Tables 75 TABLE (5-6) H-O-S Gas Mixture Composition in equilibrium with Quartz + Fayalite + Magnetite + Pyrrhotite. (627°C - 2000 bars total pressure) Output from H-O-S Version 2A program (Appendix 3). Calculations assume ideal mixing of non-ideal gases. Species considered are O 2 , S 2 , S O 2 , H 2 O , l^S, and I ^ . Log fr^  is defined by the QFM buffer calibration of Wones and Gilbert (1969). The experimentally determined log f g 2 is -5.5 ±0.7. Calculations cover the range -5.1 to -5.8. 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J^ON-» O O O O O O O O • • • • ! • • * u i u i u i c n u i u i u i m CCiCCCOCOCO^lOO _ j _ . _ . O O v O « O C O vj j : j CD f ; vO I ; CO v l CC 0"i o O U l U l CO O N O N O I O N O N L I U I U I W W W - 1 O lO CO v l ui ^ C J cr. co vo to O p) P3 P I !fl td P ) P I II .— ra O O O O O O O O NJ u i c n c n u i u i c n c i c n v O C C v ) 0 > U l W W O K) f r f r CO. _* - J to U l ON o C J U l CO - J U l f r td W rt P I rt M M O O O O O O O O f r f r f r f r c f r c f r Ui Ln c c f w u w LO—' CO ON 'jj >0 (Jl -* COtOCO — -^--JUD-O o 9/1 77 5-1 and 5-2). The experimentally determined pyrrhotite composition (Npeg = 0.963 ±0.004, at 1 atm.) is independent of temperature between 650 and 700°C (Table 5-3). Consistent results were obtained for both the Fe-Si-H-O-S and Fe-H-O-S systems (Figure 5-4 and 5-6). The bracketed composition is more sulfur-rich than that defined by QFM internal buffer (AN F e S - 0.004). Results are not influenced by different quench times, or by substitution of Au in place of Pt inner capsules (Tables 5-1 and 5-2). The latter observation implies: (1) H 2 diffusion is rapid enough that QFM buffer effectively controls fj-^ in the charge system under the experimental conditions (Note: capsule wall thickness - Pt 0.025 cm.; Au 0.015 cm.). (2) Interactions between noble metal capsules and the charge assemblage (eg. reactions 5-4 or 5-5) are not a factor in these experiments. The duration of successful experiments ranges from 45 to 274 hours. QFM buffer lifetime is short under the conditions of these runs (Figure 4-2). In the longest experiments (Table 5-1; S37, S38) the buffer was renewed three times. The buffer assemblage in the outer capsule enclosing experiments SN67 and SN74 contained only a trace amount of fayalite after the run. More sulfur-rich pyrrhotite in SN67 may reflect loss of buffer control. The charge assemblage in the Pt inner capsule (SN67) apparently reacted more rapidly to the changed f}^ than the assemblage in the Au inner capsule (SN74). 78 FIGURE (5-6) Experimental Results Fe-H-O-S System All results corrected to a standard pressure of 1 atm. Buffer Systems © [QFM,H0S|SBX,H0S|] A [QFM,OH(SBX,HOS)] m [NNO,OH(SBX,HOS)] Isocompositional lines (Npeg) calculated from equation (5-1). -4.0 0.9450 -4.4 o -4.8 A o o - 5 - 2 1' -5.6 •6.0 •6.4 4 - 6.8 S30 B 1.15 1.13 600 °C 620 1.11 .. • 0.9500 . • • 0.9550 SN71 A I SN69 S28 0 .. • S24 A 5 2 6 0.9600 SN S29 S N"A 7 b 3.8,---" SN72g@ S 2 7 . ••• SN65 S38 S25 SN74 A A c „ A* . 0.9650 SNA75^AS21SA17 5 2 2 © S 3 5 . . . . -S 3 7 A A AS19 0.9700 0.9750 0.9800 1.09 1-07 1-05 640 660 680°C > 103/T°K CD 80 Differences between internal log fg (log f o 2 ) a n d external log fg^ (log f o 2 ) have been computed on the basis of data for the 0-H and H-O-S systems tabulated in Appendix 1. Alog fr^ between internally and externally buffered systems is determined by comparison of values generated by H-O-S Version 2 and Version 4 programs (Note: example output, Appendix 3). H20 dominates the external 0-H and the internal H-O-S gas mixtures under the conditions of these experiments ( pH 2 o/ ptotal >0.96). The calculated Alog f o 2 is less than 0.02 (log f g 2 < log frj2) . This small value reflects the extremely low fugacities of species present in the internal H-O-S gas mixture but not in the external 0-H gas mixture. Table (5-7) compares log fg^ values based on QFM buffer calibrations to log fQ 2 data computed from experimental results. Log f g 2 values are higher than those computed for equivalent experiments in which log f o 2 w a s defined by QFM internal buffer (compare Table 5-5 and 5-7). Alog f o 2 between the two groups of experiments is 0.3 to 0.4. This difference is larger and in the opposite sense than that predicted by i e the H-O-S calculations (ie. log fg^ > log fg 2). This effect is small relative to uncertainties in the thermochemical data. Pressure corrections are of the same magnitude as those presented for QFM internal buffer. Since changes in external log f g 2 are closely mirrored by the internal log £Q the A V g j D U f f e r term required to solve equation (5-21) can be considered equal to the volume change of the solids involved in the external buffer reaction. 81 TABLE (5-7) Thermochemical Calculations QFM External Buffer Log f o 9 calculated at run temperature and a standard pressure M of 1 atm. (log a = 0.0) Fe 3U 4 Run Temperature Log f Q 2 Log f o 2 °C QFM1* QFM2* reaction (5-3) Fe-H-O-S System R § Wt JANAF § SN71 651 -18. .85 -18. ,28 -18. ,39 -18. ,29 SN67 663 -18. ,50 -17. ,94 -17. ,64 -17. ,54 SN74 663 -18. .50 -17. ,94 -17, .87 -17. .77 S37 665 -18. 44 -17. ,88 -17. ,94 -17. ,84 S38 665 -18. ,44 -17. 88 -17. ,83 -17. ,73 SN75 665 -18. ,44 -17. ,88 -17. ,86 -17. ,76 S21 666 -18. ,41 -17. ,85 -17. ,88 -17. .78 S24 666 -18. 41 -17. ,85 -17. ,93 -17. ,82 S17 669 -18. ,32 -17. ,77 -17. ,81 -17. ,71 S19 669 -18. ,32 -17. ,77 -17. ,84 -17. ,73 S26 670 -18. ,29 -17. ,74 -17. ,98 -17. .88 S22 672 -18. ,24 -17. ,69 -17. ,71 -17. ,61 S25 673 -18. .21 -17. ,66 -17. ,68 -17. .58 S35 676 -18. . 12 -17. ,58 -17. .68 -17. .57 Fe-Si-H-O-S System SN68 649 -18. ,92 -18. ,34 -18. .40 -18. .30 SN77 661 -18. ,56 -18, ,00 -18, ,01 -17, .90 S33 666 -18, ,41 -17, ,85 -18, ,00 -17, ,90 S34 670 -18, ,29 -17. .74 -17. ,83 -17, .72 SN42 701 -17, ,43 -16, ,91 -16, ,61 -16, ,51 S23 706 -17. ,29 -16. ,78 -16, ,80 -16. , 70 * Table (Al-1) Appendix 1 f Log K R jy based on Robie and Waldbaum (1968) thermochemical data § JANAF (1966) magnetite data substituted for the Robie and Waldbaum (1968) values 82 NNO External Buffer [NNO,OH(SBS,HOS)]: Experimental configuration and procedures are identical to those employed for QFM external buffer. The pyrrhotite composition in equilibrium with magnetite (Npeg = 0.960 ±0.004, at 1 atm.) is independent of temperature between 600 and 680°C. Identical results were obtained for the Fe-Si-H-0-S and Fe-H-O-S systems (Figures 5-4 and 5-6). This conclusion is not changed by different quench procedures or use of Au in place of Pt inner capsules. Nickel from the buffer assemblage tarnishes the walls of Au and Pt capsules with which i t is in physical contact. This tarnish is only a few microns thick and does not cause embrittlement of the capsule or significant restriction of H2 diffusion. Pt reacts with the H-O-S vapour phase to produce a thin uniform grey lining (PtS) on the inner walls of Pt capsules. A pronounced odour was noted on puncturing the run capsules (H2'S?). Table (5-8) compares log fg® values based on NNO buffer calibrations to log f o 2 data calculated from experimental results. Computations (H-O-S Version 2 and Version 4, Appendix 3) predict a difference between log f g 2 and log fg^ of less than 0.01. Assuming i e log fg 2 = log fg all determinations of log f g 2 agree within limits of ±0.2 for each experiment. The uncertainty in log fg 2 calculated by equation (5-6) (±0.8) and discrepancies in NNO buffer calibrations overshadow the tabulated differences. Pressure effects are less pronounced than those calculated for QFM buffer. Values necessary to correct experiment SN65 to any standard pressure are: 83 TABLE (5-8) Thermochemical Calculations NNO External Buffer Log fo^ calculated at run temperature and a standard pressure of 1 atm. (log ap =0.0) e i Run Temperature Log fQ 2 Log f o 2 °C x,>Tr> n* M x m o * reaction (5-3) NN01* NN02V R $ Wt JANAF§ Fe-H-O-S System 530 609 -18.91 -19.07 -19.29 -19.20 SN72 663 -17.27 -17.46 -17.68 -17.58 SN65 664 -17.25 -17.43 -17.67 -17.57 SN73 664 -17.25 -17.43 -17.64 -17.54 527 666 -17.19 -17.37 -17.60 -17.50 S29 666 -17.19 -17.37 -17.57 -17.47 528 673 -16.99 -17.18 -17.37 -17.26 SN69 678 -16.85 -17.04 -17.07 -16.97 Fe-Si-H-O-S System 531 664 -17.25 -17.43 -17.72 -17.61 532 673 -16.99 -17.18 -17.36 -17.26 * Table (Al-1) Appendix 1 t Log KR T based on Robie and Waldbaum (1968) thermochemical data § JANAF (1966) magnetite data substituted for the Robie and Waldbaum (1968) values 84 d N ( — ) = -0.00034 Kb" d P T,AGR=0 A P° d aFeS ( — ) = -0.00260 Kb 1 d P T,AGR=0 d log f s ( £.) = 0.099 Kb"1 d P .T,AGR=0 d log f 0 (— -) = 0.049 Kb 1 d P T,AGR=0 Pressure effects predict that the compositions of pyrrhotite in equilibrium with magnetite as defined by QFM and NNO buffers converge with increasing pressure (constant T). Results support this contention but experiments at higher total pressures are required to adequately demonstrate the shift in composition. HM External Buffer [HM,0H(SBX,H0S)] : Charge assemblages did not equilibrate with HM external buffer. Magnetite + pyrrhotite reacted to pyrite + sulfur-rich pyrrhotite + magnetite (Table 5-1). This final assemblage, invariant at fixed P-totai and temperature, defines condensed phase and H-O-S vapour phase compositions in the inner system. Internal £Q is approximately two orders of magnitude less than the external fg defined by HM buffer (Figure 5-1). The calculated Af 0 ? ( f Q e - fQ\) is slightly less than one order of magnitude at 670°C, 2000 bars, and fg values appropriate to the Po-Py boundary (0-H Version 1, H-O-S Version 4A). 85 This discrepancy indicates H2 diffusion is ineffective in defining fj.j| = fpj^ at the very low f^ values present under these experimental conditions. This applies equally to Au and Pt capsules (Table 5-1). Pyrite occurs in small amounts (5-10% of the sulfide in the run) as discrete 5-15y grains and as discontinuous rims on pyrrhotite. Final pyrrhotite compositions are governed by the extent of pyrite exsolution during quenching. All runs were air-quenched but this was insufficient to prevent exsolution. On the basis of Toulmin and Barton's (1964) determination of pyrrhotite compositions along the Po-Py curve exsolution is inferred to have ceased at a temperature of approximately 500°C (±50°C) in all runs. Problems of pyrite exsolution from pyrrhotite during quenching were encountered by Arnold (1957,1959) and Kullerud and Yoder (1959) in experiments at total pressures of 1000 and 2000 bars. The extent of quench reaction increases with increasing total pressure. Au and Pt capsules in contact with the MM buffer assemblage are untarnished. Pt capsules reacted with the H-O-S vapour phase to produce a thin coating of PtS (PtS stability is discussed in the next subsection). Au capsules were not affected by reaction with the H-O-S vapour phase. A strong H2S odour was evident on puncturing run capsules. Results of experiments in which external £Q was undefined were similar to HM buffer experiments (Table 5-2). The experimental conditions for these runs, originally controlled by QFM buffer, exceeded the buffering capacity of the external system (Figure 4-2). No fayalite remained in the final 'buffer' assemblage. The charge assemblage was sulfur-rich pyrrhotite + magnetite + quartz ± pyrite. Pyrite exsolution 86 affected the final pyrrhotite composition. Compositions indicate equilibrium with pyrite at a temperature of approximately 480°C (±20°C). Attempts to use HM as an internal buffer were unsuccessful (SN78, S N 7 9 ; Table 5-1). The final charge assemblage in each experiment was pyrite + pyrrhotite + magnetite. S-0 Version 1 computations (Appendix 4) provide an explanation for the antipathy between hematite and iron sulfides at the P-T conditions of these experiments. The maximum fg^ and fg^' at any temperature and total pressure is defined by the condition that the sum of the partial pressures of gas species in the S-0 system equals the total pressure (^P^(g_o) = ptotal^" This condition specifies the limit at which the ternary H-O-S system (or any S-0 bearing gas system) degenerates to the S-0 binary. S O 2 is quantitatively the most important species when ?P^ -^g g) = ^total a n d the restriction may be stated as Pgf^ ~ ptotal ^ o r m o s - t considerations. Sulfur and oxygen fugacities defined by the assemblage hematite + magnetite + pyrite equal those specified by the condition ? pi(g_0) = Ptotal a t ge°i°gicaliy significant temperatures and pressures. P total' ^' * o g 0^2» a n d * o g ^S2 v a l u e s a t points of coincidence are: bars 500 2000 5000 10000 Log 'fg is computed for HM1 buffer (Appendix 1; Norton, 1955) and log fg is defined by: 3 Fe 30 4 + S 2 t 4 Fe 20 3 + FeS2 where log f s = [0.05988 (P t otal - 1-0) - 12678] /T°K + 13.90 (derived from Barton and Skinner, 1967) Temperature °C log % log b2 553 -15. .74 -1. ,41 595 -14. 25 -0. ,57 602 -13. ,95 -0. ,25 602 -13. .84 + 0. ,10 87 The assemblage hematite + magnetite + pyrite is stable at temperatures and pressures to the left of the curve plotted in Figure (5-7). The fg and £Q^ in this region are specified by the coexistence of al l three phases + vapour at any T and Ptotal• o^ the right of the curve the three phases cannot coexist and pyrite or hematite disappears. Two possibilities exist: (1) Pyrite is lost through oxidation. The assemblage hematite + magnetite buffers fg^ at P-T conditions to the right of the curve, fg must be equal to or less than values defined by the condition fi(S-O) = ptotal-(2) Hematite is reduced to magnetite and the assemblage magnetite + pyrite coexists to the right of the curve. fg and values are undefined but must lie along the magnetite - pyrite boundary (eg. Figure 5-1) and cannot exceed values specified by ?Pirg-0) ~ Ptotal* The assemblage pyrite + hematite cannot exist to the right of the curve. • This analysis explains the experiments of Taylor and Kullerud (1971) who observe that hematite is apparently unstable in the presence of pyrite or pyrrhotite at temperatures above 550°C. Computations for the assemblage pyrrhotite + pyrite + magnetite indicate these phases constitute a stable assemblage to at least 727°C at 2000 bars. Stability of Platinum Sulfides: Sulfur fugacities determined for experiments on QFM, NNO, and HM buffers lie within the calculated stability field of PtS (Figure 5-8). A thin uniform lining of PtS coated the inner walls of 10.0 8.0 -6.0 • 4.0 -2.0 -400 500 600 700 FIGURE (5-7) P-T Curve marking the Upper Stability Limit for the Assemblage Hematite + Magnetite + Pyrite 89 F I G U R E (5-8) Stability of Platinum Sulfides (sta.nd.ard pressure - 1 atm.) P t S , 2 Pt + S 9 t 2 PtS reaction (5-4) log f-s2 = [0.1365 ( P t o t a i - 1.0)- 14,993]/T°K + 9.86 (derived from Larson and Elliot, 1967) P t S 2 P t S 2 PtS + S 2 2 2 PtS 2 log f S 2 = -9,562.3 / T°K + 9.57 (derived from Richardson and Jeffes, 1952) Calculated stability fields (Pt, PtS, PtS2) are superimposed on pyrrhotite compositions calculated from equation (5-1). The intersection of QFM buffer with the pyrrhotite -magnetite boundary is shown (recall Figure 5-2). Isocompositional lines (Npes) calculated from equation (5-1) . QFM1, Wones and Gilbert (1969). QFM2, Skippen (1967). Experimental Buffer Systems A [ Q F M , 0 H ( S B X , H 0 S ) ] n [NN0,0H(SBX,H0S)] A [HM,0H(SBX,H0S)] 90 -10.0 1.12 1.08 1.04 627°C 677°C 1.00 727°C » 103/ T°K 91 Pt capsules in NNO and HM buffer experiments. Platinum capsules in QFM buffer experiments were generally free of PtS tarnish. Kjekshus (1961) demonstrated that reaction between Pt plate and sulfur resulted in a thin PtS layer the thickness of which remained constant with time (10-50 day experiments; T=700° and 825°C). The barrier to reaction presented by a thin PtS layer ensures the survival of Pt capsules in experiments of long duration at sulfur pressures within the PtS stability field (eg. SN70, Table 5-1). Four experiments (SN71, SN69, SN70, SN68; Table 5-1 and 5-2) were conducted in which a small Pt foil capsule was f i l l e d with Pt powder, crimped, and enclosed in the inner capsule with the charge assemblage. Run products were analysed in the normal manner and the Pt powder X-rayed. Small amounts of PtS were present in a l l four experiments (Figure 5-8). Experimental and theoretical studies (Biltz and Juza, 1930; Anderson, 1946) suggest 'PtS' is stable over a composition range bracketing the ideal PtS formula and extending significantly towards more sulfur-rich compositions. This conclusion was contested by Kjekshus (1966) who reports a very limited homogeneity range for PtS. Lattice parameters of PtS synthesized from starting mixtures with variable Pt:S ratios were found to be constant by Gr^nvold, et al. (1960) and Kjekshus (1966). PtS in the present experiments should display a compositional variation reflecting different sulfur fugacities (Figure 5-8) i f the homogeneity range of PtS extends appreciably towards more sulfur-rich compositions. No shift in 26 values for PtS peaks was detected, supporting the contention that PtS has a limited homogeneity 92 range. PtS therefore cannot serve as an experimentally useful indicator of f S 2 . Platinum capsules in QFM buffer experiments are usually free of PtS tarnish. Pt powder and Pt fo i l exposed to the H-O-S vapour phase but not in physical contact with the charge assemblage were coated with a thin grey layer of PtS (eg. SN71, SN68). Sulfur fugacities in these experiments are close to the Pt-PtS boundary (Figure 5-8). Recalling reaction (5-4): 2 Pt + S 2 t 2 PtS a 2 v -R ' T a 2 • f o a p t f s 2 thus; log f S 2 = 2 log a p t s - log K R j T - 2 log a p t Iron diffusion from the charge assemblage into the Pt capsule lowers the a , therefore raising the equilibrium log fg at which PtS coexists with the Pt-Fe alloy. This effect is enhanced since Pt-Fe alloys display significant negative departures from ideality resulting in aPt^°^ v a l u e s considerably less than X a l l ° ^ (Alcock and Kubik, 1969). Diffusion of iron may account for observed differences in the physical appearance and reactivity of Pt surfaces in QFM buffer experiments. Electron Microprobe Analyses: Analytical procedures are described in Section 4.3. Pyrite and pyrrhotite analyses (Table 5-9) are considered accurate to ±1% of the quoted values.. No contamination of run products by platinum or gold from the reaction capsules was detected. Individual pyrrhotite TABLE ( 5 - 9 ) Microprobe Analyses Run Wgt% Atom% Wgt%+ Fe Fe S Pyrrhotite Analyses Fe-H-O-S System S 3 7 61.53±0.26* 4 7 . 8 7 1 0 . 2 7 3 8 . 4 7 S 5 5 6 1 . 5 1 1 0 . 2 1 4 7 . 8 5 1 0 . 2 1 3 8 . , 4 9 S 5 0 6 1 . 4 1 1 0 . 3 1 4 7 . 7 7 1 0 . 3 3 3 8 . , 5 7 SN29 6 2 . 8 4 1 0 . 3 2 4 9 . 2 6 1 0 . 3 4 3 7 . , 1 6 S N 3 2 6 2 . 8 5 1 0 . 2 1 4 9 . 2 8 1 0 . 2 0 3 7 . , 1 5 Pyrrhotit e Analyses Fe -Si-H-O-S System S 2 6 1 . 5 5 1 0 . 4 4 4 7 . 8 9 1 0 . 4 6 3 8 . 4 5 S 5 5 9 . 7 2 1 0 . 4 7 4 5 . 9 8 1 0 . 4 8 4 0 . 2 8 S 1 6 5 9 . 6 4 1 0 . 1 3 4 5 . 8 9 1 0 . 1 3 4 0 . 3 6 Pyrite Analysis Fe-Si-H-O-S System S 5 4 7 . 2 7 1 0 . 3 8 3 3 . 9 8 1 0 . 3 4 . 5 2 . 7 3 * Counting precision at the 9 5 % confidence level t Sulfur by difference Atom%"i" %eS Buffer Configuration S Microprobe X-ray 5 2 . 1 3 0 . 9 5 7 4 0 . 9 6 0 1 [ Q F M , 0 H ( S B X , H 0 S ) ] 5 2 . 1 5 0 . 9 5 7 0 0 . 9 6 0 8 [ Q F M , H 0 S | S B X , H 0 S | ] 5 2 . 2 3 0 . 9 5 5 4 0 . 9 5 8 2 [ N N 0 , 0 H ( S B X , H 0 S ) ] 5 0 . 7 4 . 0 . 9 8 5 2 1 . 0 0 0 6 [ I W , 0 H ( S B X , H 0 S ) ] 5 0 . 7 2 0 . 9 8 5 6 1 . 0 0 2 6 [ I W , 0 H ( S B X , H 0 S ) ] 5 2 . 1 1 0 . 9 5 7 8 0 . 9 6 1 0 [ Q F M , O H ( Q F M S B X , H O S 5 4 . 0 2 0 . 9 1 9 6 0 . 9 3 5 3 [ Q M , 0 H ( S B X , H 0 S ) ] 5 4 . 1 1 0 . 9 1 7 8 0 . 9 3 4 7 [ Q M , 0 H ( S B X , H 0 S ) ] 6 6 . 0 2 [ Q M , 0 H ( S B X , H 0 S ) ] :a) 94 grains (subhedral, 20-100y) are not zoned. The uncertainty in the composition of pyrrhotite determined from microprobe analyses is approximately five times greater than the uncertainty in the X-ray method (Section 4.3). Small differences in pyrrhotite composition, important to the interpretation of experimental results, cannot be measured accurately on the microprobe. Kullerud, Donnay, and Donnay (1968, 1969) show omission solid solution of iron in magnetite occurs at high sulfur fugacities. The 5-15y grain size of magnetite in these experiments precluded accurate analyses. Fragmentary results obtained are insufficient to determine the importance of this effect. 95 CHAPTER 6 NICKEL-BEARING SYSTEMS 6.1 Introduction and Theoretical Consideration: Reactions involving iron oxides and iron-bearing silicates may play an important role in controlling Fe-Ni sulfide compositions and assemblages. Sulfide nickel ores associated with mafic intrusive rocks commonly coexist with magnetite or another iron-bearing spinel. In terms of the ternary Fe-Ni-S system many of these ores have bulk compositions that plot within the experimentally determined 500°C compositional limits of the homogeneous (Fe,Ni)i_xS monosulfide solid solution (Naldrett, et al., 1967). Examples include the Alexo mine, Ontario (Naldrett, et al., 1967) and the Kambalda deposits of Western Australia (Ewers and Hudson, 1972). The sulfide-oxide phase assemblage in these ores above 500°C would consist of homogeneous Mss + magnetite (or spinel) ss. Nickel has been added to the systems treated in Chapter 5 to allow study of equilibria in the Fe-Ni-H-O-S and Fe-Ni-Si-H-O-S systems. Experimental methods are identical to those used in Chapter 5. Equation (5-3) can be rewritten to take account of nickel solid solution in the condensed phases: F e 3 0 4 S p i n e l + 3/2 S 2 * 3 FeS M s S + 2 0 2 (6-1) KR,T , MSS.3 . - 2 aspinel . ^ 3/2 Fe 30 4 S 2 96 thus; log = (log K R j X j + log + 3/2 log - 3 log a ^ ) /2 (6-2) The assemblage Mss + magnetite ss + vapour has four degrees of freedom in the Fe-Ni-H-O-S system (M=C=5; thus when $=3, F=4). The equilibrium compositions of these three phases are defined by the bulk composition of the charge when £Q , >^ a n c* ptotal a r e controlled experimentally. Compositions of Mss coexisting with magnetite ss trace out a specific path across the Mss as the nickel content of the system is changed. The path is uniquely defined for a specific f g 2 at each Ptotal a n d temperature. A hypothetical path is shown in Figure (6-1). Paths intersecting either the sulfur-rich or sulfur-poor limits of the Mss field are terminated by the appearance of another phase and the Mss composition is fixed (at fixed f o 2 > ^> a n ^ ptotal coexistence of 4 phases constitutes an invariant assemblage in the Fe-Ni-H-O-S system). 6.2 Experimental Results QFM and NNO Buffers [0B,0H(SBX,H0S)]: Mss - magnetite equilibrium (reaction 6-1) has been investigated using both QFM and NNO external buffers. QFM has also been used as an external buffer in an attempt to study the reaction: r olivine _ ^ 0 „ cMss _._ _ ' Fe2Si04 + S 2 ? 2 FeS + Si0 2 + 0 2 (6-3) Clark and Naldrett (1972) determined the partitioning of nickel and iron between Fe-Ni olivine and Mss at 900°C (Fe-Ni-Si-S-0 system; evacuated silica glass tube techniques). Their experiments were confined to a single temperature (900°C) by the occurrence of 97 FIGURE (6-1) Hypothetical path across the Mss defining compositions of Mss in equilibrium with magnetite at constant fQ^- Dashed tie lines between Mss and magnetite ss are schematic. The extent of nickel substitution in magnetite is exaggerated. 98 Fe-Ni-S-0 liquids at temperatures above 900°C and by prohibitively slow reaction rates at lower temperatures. Thermochemical calculations by Clark and Naldrett suggest nickel partitioning between Fe-Ni olivine and Mss is strongly temperature dependent. The favourable reaction rates observed in experiments reported in Section 5.3 prompted investigation of the feasibility of using buffer techniques to equilibrate Fe-Ni olivine with Mss in H-O-S gas mixtures. Various compositions of Fe-Ni olivine were synthesized hydrothermally (Appendix 6). The grain size of synthesized olivines (<2p) permitted only X-ray determination of composition. Experiments defining reaction (6-3) must be controlled at £Q values lower than the fr^ at which Fe-Ni olivine breaks down to magnetite ss + quartz. This breakdown is determined by: 3 F e 2 S i 0 4 ° l i v l n e + 0 2 t 2 Fe 3 0 4 S P i n e l + 3 Si0 2 (6-4) KR,T, , spinel, o ' r \3 C aFe 30 4 } ( aSiQ 2) , olivine.3 -l aFe 2Si04 J ' *02 thus; log f 0 2 = (2 log a ^ J * 1 + 3 log a s i 0 2 - 3 log a J ^ J ™ - log K R j T) (6-5) At any temperature and pressure QFM buffer defines a log fg that differs from equation (6-5) by a value equal to (2 log a p g 3 o 4 ^ ~ 3 ^e^SiC) 6^ assuming a s i o 2 ^ s n o t affected by Ni in the system. Nickel solid solution lowers both log a^1"6"'" and log a^ 1 1^ 1" 6. Little information on the ° Fe304 " Fe 2Si0 4 partitioning of nickel and iron between Fe-Ni olivine and magnetite is 99 available. Clark (1970) has shown the nickel content of coexisting magnetite and Fe-Ni olivine is similar for compositions containing less than 1 weight percent nickel (900°C, log asi02 = 0.0). Log f g 2 defined by equation (6-5) should be approximately equal to that defined by QFM buffer since the activity terms will tend to cancel. Mixtures of olivine (fayalite or Fe-Ni olivine) + Mss + were reacted in Pt capsules using the buffer configuration [QFM,0H(S3X,H0S)]. The final assemblage in all experiments was Mss + magnetite ss + quartz + vapour (Table 6-1). This assemblage indicates the internal f g 2 controlled by this configuration must be higher than that defined by equation (6-5). Reaction (6-3) therefore cannot be studied using QFM or a more oxidizing buffer assemblage. The results of these experiments apply however to the Mss - magnetite equilibrium. These results and the results of experiments in the Fe-Ni-H-O-S system using QFM and NNO external buffers to study the Mss - magnetite equilibrium are presented in Table (6-1). Microprobe analyses of run products could be obtained for only a limited number of experiments due to difficulties with sample preparation and fine grain size. Mss compositions were measured by combining microprobe analyses for Fe and Ni with sulfur determinations based on X-ray measurement of d(102). Figure (6-2) defines d(102) and weight percent S for various Ni:Fe ratios in Mss. The Ni:Fe =0.0 boundary was calculated from equation (4-1). Other curves are derived from Mss composition - d(102) data published by Naldrett, et al. (1967). Figure (6-2) provides the data required to determine weight percent S graphically for any Ni:Fe ratio and d(102) value. Results for various TABLE (6-1) Experimental Results Run Temperature Pressure Duration °C Bars Hours QFM External Buffer [QFM,OH(SBX,HOS)] SN1 670±4 2000±20 97 SN4 668±4 2000±20 90 SN2 683±4 2000±20 78 SN5 668±4 2000±20 92 SN36 661±5 2070±25 87 SN44 671±5 2000±30 17 SN6 663±4 2000±20 91 SN43 654±4 2070+25 18 SN45 605±5 2070±25 139 SN37 658±4 2070±25 87 SN35 668±4 2000±20 90 SN52 649±4 2050±25 79 SM55 65915 2000130 115 NNO External Buffer [NNO,OH(SB: SN23 665±4 2000120 97 SN22 665±4 2000120 115 SN24 663±4 2000120 97 SN53 669±4 2000120 108 Charge Assemblage Original Final M Mss* M Mss d(102) X FNS1 X X 2. 0653 X FNS1 X X 2. 0652 X FNS2 X X 2. 0561 X FNS2 X X 2. 0557 X FNS106 X X 2. 0474 X FNS3 X X 2. 0449 X FNS3 X X 2. 0446 X FNS3 X X 2. 0431 X FNS3 . X X 2. 0404 X FNS109 X X 2. 0385 X FNS113 X X 2. 0246 X NS1 X X 2. 0220 X NS1 X X 2. 0202 X FNS'2 X X 2. 0554 X FNS2 X X 2. 0548 X FNS3 X X 2. 0447 X NS1 X X 2. 0183 Identification number - compositions listed in Table (4-1) Remarks Fe-Ni-H-O-S Syst Pt inner capsule water quench +3Ni7S6 +8Ni7S6 +3Ni7S6 TABLE (6-1) cont'd: Run Temperature °C Pressure Duration Bars Hours Charge Assemblage Original olivine Mss* Final Q M Mss d(102) QFM External Buffer [QFM,OH(SgX,HOS)] SN16 685±4 2000+20 70 .Ai #1 X X X 2.0710 SN15 627±4 2000±20 115 A§ #1 X X X 2.0702 SN7 668±4 2000±20 96 F- FNS1 X X X 2.0655 SN8 656+4 2000±20 96 F FNS1 X X X 2.0651 SN10 666±4 2000±20 93 F FNS2 X X X 2.0564 SN9 66S±4 2000±20 94 F FNS2 X X X 2.0561 SN11 668±4 2000±20 97 F FNS3 X X X 2.0465 SN12 671±4 2000120 97 F FNS3 X X X 2.0456 Pn Remarks Fe-Ni-Si-H-O-S System Pt inner capsules Trace amounts of Ni and quartz in the original assemblage * Identification number - composition listed in Table (4-1) § Synthesized from oxalate + a cristobalite mix corresponding to 10.5 mole' % Ni2Si0 4 (Appendix 6) 102 FIGURE (6-2) Mss and pyrrhotite compositions as a function of d(102) Data for pyrrhotite (Ni:Fe = 0.0) are from the equation of Yund and Hall (1970). Other curves of constant Ni:Fe weight ratio ( ) are based on the data of Naldrett, et al., (1967). A Mss composition (QFM buffer) O Mss composition (QFM buffer) - Pn exsolution H Mss composition (NNO buffer) 600°C limits of the Mss (Naldrett, et al. , 1967) '.•'•.'.•!•' Area where quench problems were encountered by Naldrett, et al., (1967) in silica glass tube experiments 104 experiments are plotted on Figure (6-2). Complete analyses are presented in Table (6-2). Magnetite is a ubiquitous fine-grained phase in these experiments. Partial microprobe analyses of magnetite could be obtained for only four experiments. Run Wgt% Fe Wgt% Ni Remarks SN23 70.75±0.19 0.3310.01 10-20y SN36 70.48 0.51 10-15y, subhedral SN35 69.94±0.19 1.14±0.08 10-15y SN52 69.14±0.74 1.17±0.22 lOy Pentlandite (Pn) occurs in all experiments in which the Mss contains more than 25 weight percent Ni. The phase forms a fine intergrowth in Mss (l-3y grain size). Pn is known to break down to a heazlewoodite (aHz) + Mss at temperatures above 610±2°C (Kullerud, 1963). The breakdown temperature is approximately 7° lower at Ptotal = 2000 bars (Bell, et al., 1964). All experiments in which Pn was identified were run at temperatures >603°C. Pn must form 071 quenching either by exsolution from homogeneous Mss or by reaction between Mss and a more sulfur-deficient high temperature phase. Special quench techniques were not successful in preventing Pn formation. Experiment SN43 contained Pn even though the capsule was quenched in a few seconds. The experiment was run in a horizontal furnace with no f i l l e r rod inserted. The run was terminated by tapping the capsule to the cold end of the bomb and quenching in a water bath. Naldrett and Craig (1968) report a similar problem in rapidly quenched silica-glass tube experiments. They found sulfur-deficient nickel-rich Mss compositions break down to Pn, NiySg, or Hz. TABLE (6-2) Analyses of Monosulfide Solid Solution (Mss) QFM and NNO Buffers Run Wgt% Fe + Wc lt% Ni t Ni .:Fe d(102) Wgt% i S§ Total Remarks SN16 58. ,75±0. 20* 2. ,44±0. 32 0. 0415 2.0710 38. 32 99. ,51 Fine grained, 10-20u SN8 51. ,61±0. 17 9. ,37±0. 07 • 0. 1816 2.0651 37. 98 98. .96 50y grains, associated with magnetite too fine for analysis (<5y) SN10 43. ,60±0. 36 18. ,89±0. 30 0. 4333 2.0564 37. 53 100. .02 Fine grained, 5-20u SN23 42. ,63±0. 54 19. ,48±0. 34 0. 4570 2.0554 37. 55 99. ,66 30-60y SN36 35. 19±0. 22 27. ,67+0. 08 0. 7863 2.0474 37. 00 99. ,86 20-70y, subhedral, associated with Pn SN12 32. 79±0. 24 29. ,07±0. 53 0. 8866 2.0456 36. 91 98. ,77 Magnetite rims some grains - intergrc with Pn SN35 15. ,85±0. 16 48. ,51±0. 16 3. 061 2.0246 36. 47 100. ,83 40-100p, associated with Pn * Counting precision at the 95% confidence level (2a) t Determined by microprobe § Determined on the basis of Ni:Fe ratio and d(102) spacing (see text) uncertainty ±0.3 106 Pn lamellae were too fine for microprobe analysis and in many nickel-rich experiments (eg. SN52, SN53) neither Mss nor Pn could be analysed in the intergrowths. The d(115) spacing of Pn was determined when Pn occurred in sufficient quantities to give a sharply defined peak on the X-ray trace. Run d(115) a 0 SN44 1.9440 ±0.0008 10.101 ±0.004 SN37 1.9438 ±0.0006 10.100 ±0.003 SN52 1.9455 ±0.0015 10.109 ±0.008 SN55 1.9439 ±0.0012 10.101 ±0.006 SN53 1.9461 ±0.0020 10.112 ±0.010 Pn compositions are not uniquely defined by d(115) since variation in either Ni:Fe ratio or S content can change the unit cell (Shewman and Clark, 1970). Nevertheless since Pn coexists with Mss the variation in sulfur content should be small and the narrow range in d(115) apparently reflects a narrow range of Ni:Fe ratio in these pentlandites. An expression derived by Shewman and Clark (1970) defines Fe:Ni weight ratios (X) in Pn at a constant sulfur content of 33.05 weight percent: d(115) = 1.9407 - 0.0023 X + 0.0077 X2 - (6-6) On the basis of equation (6-6) the measured d(115) values reflect Pn compositions containing 34-37 weight percent Ni. BNiyS^ (godlevskite) was identified in experiments SN52, SN53, and SN55. This phase apparently forms on quenching below 400°C since BNiyS6 inverts to cxNiySg at 400°C when in equilibrium with cxNiS (Kullerud and Yund, 1962). Solid solution of iron may change this inversion temperature slightly. Mss, Pn, and 8NJ7S5 are associated in 107 irregular intergrowths up to 100y in maximum dimension. Microprobe analyses were obtained for SNiySg occurring as 5-10y patches within the sulfide intergrowth. Atomic Run Weight % Fe Weight % Ni Weight % St Metal:Sulfur SN52 3.56 64.35 32.06 6.95 : 6 SN53 3.33 64.45 32.22 6.91 : 6 t Sulfur by difference Compositions of Mss coexisting with magnetite ss are plotted in Figure (6-3). Analyses from Table (6-2) have been normalized retaining constant Ni:Fe weight ratio. The bracketed composition (QFM ) on the Fe - S join is the composition of pyrrhotite coexisting with magnetite at oxygen fugacities controlled by QFM external buffer ( ptotal = 2 0 0 0 bars; N F e S = 0.961, 61.70 weight percent Fe). NNO external buffer defines a more sulfur-rich pyrrhotite composition ( P t o t a l = 2000 bars; N F e S = 0.958, 61.56 weight percent Fe). These compositions overlap on the scale of Figure (6-3) and the NNO point has been omitted for clarity. The difference in composition increases slightly with decreasing pressure and is almost insensitive to temperature (Section 5.3). Mss compositions coexisting with magnetite ss become progressively more sulfur-poor as the nickel content of the Mss increases (Figure 6-2, Figure 6-3). Difficulties with quench phases (Pn or BNiySg) appear to be unavoidable in experiments containing sulfur-poor Mss with nickel contents greater than 25 weight percent. The stippled region in Figure (6-3) is the area in which quench problems were encountered by Naldrett, et al., (1967) in rapidly cooled sil i c a glass 108 FIGURE (6-3) Mss and pyrrhotite compositions in experiments defined by QFM or NNO external buffer. (2000 bars total pressure) • Initial pyrrhotite compositions (in order of decreasing sulfur content Po#3, Po#l, Po#2; Table 4-1) © Initial Mss compositions A Final Mss composition (QFM buffer) O Final Mss composition (QFMe buffer) - Pn exsolution^ O Final Mss composition (NNO buffer) Initial and final Mss compositions are joined by a dashed line. 600°C limits of the Mss (Naldrett, et al., 1967) Area v\'here quench problems were encountered by Naldrett, et al., (1967) in silica glass tube experiments Inset indicates area of figure within the Fe-Ni-S system 110 tube experiments at 600°C. The presence of quench phases limits study of the Mss - magnetite ss equilibrium to relatively nickel-poor bulk compositions at the oxygen fugacities controlled by QFM or NNO external buffers. Mss compositions are not constant in experiments containing Pn or BNiySg suggesting these phases form by exsolution and the sulfur-poor base of the Mss was not intersected at run conditions. d(102) values for Mss in experiments using the same buffer and starting mixture are identical (uncertainty ±0.0008) although both temperature and duration of experiments varied (Table 6-1). Some scatter occurs i f Pn or 3NiySg exsolved during cooling. All experiments were run at a total pressure of 2 Kb. QFM and NNO buffers theoretically define two separate paths across the Mss reflecting the different oxygen fugacities controlled by these buffers at any temperature and total pressure. The two paths are indistinguishable within the Mss since the difference in metal:sulfur ratio is small relative to uncertainty in measurement of Mss compositions. On the Fe - S join the difference in composition defined by these buffers is only 0.14 weight percent S at 2000 bars total pressure. Compositions within the Mss are not bracketed. Mss compositions in the starting mixtures are more sulfur-rich than final compositions in all experiments. Constancy of d(102) values in experiments with identical starting compositions but run for different durations and temperatures suggests final Mss compositions approach equilibrium values and compositions are not temperature dependent. Analysis of the pyrrhotite - magnetite equilibrium has shown pressure effects are small (Section 5.2, Section 5.3). I l l Figure (6-4) shows the approximate position of the path across the Mss defined by QFM external buffer. Further experiments are required to bracket the path and to test the suggested temperature independence. The oxygen fugacity defining this path can be assumed to be the value specified by QFM buffer. In Section 5.3 i t was shown i e that log f.Q - log f g 2 under the conditions of these experiments. Calculated log f0 values are -22.94, -19.39 and -16.55 at 527, 627, and 727°C respectively (Ptotal = 2000 bars). As nickel substitutes for iron in magnetite and pyrrhotite both log a^1"6"'" and log a^S^ decrease. Nickel partitions strongly Fe304 FeS 1 to the sulfide rather than the oxide phase (eg. SN35 - 1.14 weight percent Ni in magnetite compared to 48.51 weight percent Ni in Mss). Clark (1970) reports less than 1 weight percent Ni in magnetites coexisting with Mss containing up to 20 weight percent Ni (900°C, f g 2 defined by tridymite - fayalite - magnetite buffer). From equation (6-2) i t follows that i f the variation in log ^ g ^ o ^ ^ s n e g l i s i b l e Ms s then log f s 2 decreases by twice the change in log ap gg (constant log f j ^ * temperature, and Ptotal)-e The log f o isobar represented by the QFM path in Figure (6-4) has been compared to log f§2 isobars across the Mss determined by Naldrett and Craig (1968) at 600°C. Figure (6-4) shows the path across the Mss at Ptotal - 2000 bars. Corrected to 1 atm. the pyrrhotite composition in equilibrium with magnetite shifts to slightly more sulfur-poor compositions (38.3 to 38.2 weight percent S). Pressure corrections are assumed to be the same magnitude for other Mss compositions 112 FIGURE (6-4) Path across the Mss defined by compositions of Mss in equilibrium with magnetite ss at constant oxygen fugacity • controlled by QFM external buffer (P = 2000 bars; tota J. the path is independent of temperature - see text) — Limits of the Mss (Naldrett, et al., 1967) 300°C, 400°C, 500°C, 600°C. Average composition of typical Fe-Ni sulfide ore at; o Alexo Mine, Ontario. Naldrett et al., (1967). © Lunnon Shoot, Kambalda. Ewers and Hudson, (1972). A Sudbury, Ontario. Craig and Naldrett, (1971). (Abstract) Weight percent Fe 114 along the QFMe line. At 600°C and 1 atm. the calculated log f g 2 e defined by QFM buffer and equilibrium between pyrrhotite and magnetite is -6.0 (log f o 2 ~ -20.5). The log f g 2 = -6 isobar determined by Naldrett and Craig (1968) at 600°C coincides closely with the log fg = -20.5 isobar. Weight percent S in Mss at various nickel contents along the two isobars are: log £ s 2 = ~ 6 - 0 !°g £ 0 2 = " 2 0 - 5 (Naldrett and Craig, 1968) (QFM6 path - 1 atm.) Weight % Ni Weight % S Weight, % S 0.0 38.2 38.2 5.0 38.1 . 3 8 . 1 10.0 38.0 37.9 15.0 37.8 37.7 20.0 37.5 37.4 The agreement between these two paths determined by different experimental techniques is excellent in view of the preliminary nature of both data sets. The small difference in sulfur content with increasing nickel in the Mss is appropriate to a small decrease in log fg,, at constant Ms s log f g 2 caused by a decrease in log ap eg- This difference is however not significant in view of the ±0.3 uncertainty in the measurement of Mss compositions along the QFM line and cannot be used to estimate Mss l 0 g aFeS-6.3 Discussion and Geologic Implications Reaction (6-1) defines the relationship between the composition of Mss and iron-bearing spinel and the fugacities of sulfur and oxygen in the coexisting vapour phase. Experiments in the 115 Fe-H-O-S and Fe-Ni-H-O-S systems demonstrate that the metal:sulfur ratio in pyrrhotite or Mss coexisting with magnetite and vapour is extremely sensitive to variations in f g 2 at constant temperature. At oxygen fugacities controlled by QFM or NNO synthetic buffers the metal:sulfur ratio in pyrrhotite or Mss is virtually independent of temperature. Thermochemical calculations (Section 5.2) demonstrate this result reflects the manner in which log fQ - T curves defined by these buffers intersect the log f Q 2 " l°g f s 2 " ^  surface which describes equilibrium conditions among coexisting pyrrhotite, magnetite, and vapour. Figure (5-2) shows such intersections closely parallel lines of constant pyrrhotite composition. Many rocks contain assemblages which buffer f o 2 -Oxygen barometers such as the pair ilmenite + magnetite (Buddington and Lindsley, 1964), the assemblage biotite + K-feldspar + magnetite (Wones and Eugster, 1965), or the assemblage spinel + olivine + orthopyroxene (Irvine', 1965, 1967) can be used to estimate the fg,, at which these assemblages equilibrated. Application of these oxygen barometers suggest the change in f o 2 with temperature in many igneous and metamorphic rocks closely parallels curves defined by synthetic oxygen buffers (Carmichael and Nicholls, 1967; Nash and Wilkinson, 1970; Eugster, 1972). Carmichael and Nicholls (1967) estimate the range of f g 2 in basaltic lavas straddles QFM buffer with a band width of approximately three log units (T = 1000-1200°C). Kullerud and Yoder (1968) conducted experiments (Ptotal = 10 Kb., T = 1075°C and 1150°C) which demonstrate that the pyrrhotite composition in equilibrium with magnetite is buffered by a coexisting 116 ferrogabbro liquid. The measured pyrrhotite composition Fe^gSc^ (Npeg = 0.96) reflects an f g 2 close to that defined by QFM buffer. Kullerud and Yoder suggest that noritic or peridotitic magmas would exert a similar buffering mechanism with respect to the pyrrhotite + magnetite assemblage. Fe-Ni sulfide deposits are. characterized by close association with ultramafic or related mafic igneous rocks (Naldrett and Gasparrini, 1971). Bulk compositions of Fe-Ni sulfide ores containing magnetite show a narrow variation in sulfur content (37.5 -39.0 weight percent sulfur, Kullerud and Yoder, 1968). These compositions plot within the high temperature limits of homogeneous Mss (Figure 6-4). This regularity implies a common mechanism was responsible for setting the in i t i a l metal:sulfur ratio. Experiments in this study show buffering of f o 2 effectively controls the metal: sulfur ratio in pyrrhotite or Mss at temperatures as low as 550°C. In the presence of a natural assemblage which buffers f g 2 the presence of magnetite fixes the metal:sulfur ratio in coexisting Mss i f the sulfide, oxide and vapour phase are in equilibrium. The presence of additional components in solid solution in either magnetite or Mss -r . . spinel Mss , . .. . . , affects the a„r _ or the a„ „ and can cause variation in metal: Fe3C"4 FeS sulfur ratio at constant f o 2 -Difficulties arise in attempts to estimate the original bulk composition of Fe-Ni sulfides in ore deposits. The importance of low-temperature re-equilibration in establishing observed associations and phase compositions in natural, nickel-iron sulfide assemblages is apparent from recent studies (Graterol and 1 1 7 Naldrett, 1971; Page, 1972; Harris and Nickel, 1972). These papers demonstrate present sulfide assemblages represent temperatures <135°C and the compositions of coexisting phases reflect the specific associations in which they occur. It is suggested that the original metal:sulfur ratio of sulfides in many Fe-Ni sulfide deposits was established through local buffering of fg 2 by the host rocks. The Fe:Ni ratio in the Mss is determined by the partitioning of nickel and iron between coexisting sulfides, oxides, and silicates. Experiments to equilibrate Fe-Ni olivine with Mss at oxygen fugacities defined by Q F M buffer were not successful. Study of this equilibrium (reaction 6-3) should be feasible at lower oxygen fugacities than those defined by Q F M buffer. Two buffer configurations that may prove useful are [ W M G , O H ( S B X , H O S ) ] or [G,0H(SBX,H0S)1. Figure (6-4) shows that Mss compositions along the path defined by Q F M external buffer will exsolve pentlandite with decrease in temperature. The sulfur-poor limit of the Mss is intersected at approximately 400°C for compositions containing 25 weight percent nickel and 300°C for compositions containing 10 weight percent nickel. At these low temperatures the subsequent progression of reactions will be primarily determined by equilibria among the sulfide phases rather than by controls exerted by buffered conditions imposed by the host rocks. The significance of local buffering can perhaps be best established by determination of the bulk composition of sulfides present in trace amounts in volcanic rocks. Small sulfide grains in volcanics may be expected, to retain their original bulk composition 118 since assemblages are rapidly quenched and the small grain size of sulfide blebs permits accurate estimate of bulk composition even i f low-temperature sulfide phases are present. Heming and Carmichael (1973) measured the compositions of coexisting titanomagnetite, ilmenite, and pyrrhotite in a series of pumice flows from the Rabaul Caldera, Papua, New Guinea. Equation (5-6) has been solved using values derived from this data assuming the TM activity of Fe304 in titanomagnetite ( a p e ^ Q ^ equals the mole fraction xIM n ."1" Computed log fn„ values are in excellent agreement with Heming 10304 U Z and Carmichael's log f g 2 estimates based on coexisting iron-titanium oxide pairs (Table 5-10). Pyrrhotite and titanomagnetite are an t equilibrium assemblage in these lavas under the inferred conditions of fo 2> £$2> a n <^ temperature (sample 8000 may be an exception). Oxygen and sulfur fugacities decrease systematically with decreasing temperature along a path parallel to those defined by synthetic oxygen buffers. Pyrrhotite compositions in the Rabaul lavas appear to reflect internal buffering of f g 2 and f g 2 by the local mineral assemblage. Additional information of this type can be expected to place limits on the variation of f g 2 in many natural assemblages. t Heming and Carmichael use an expression ea^uivalent to equation TM TM (5-6) to test the assumption a^Q^Q^ = ^ 5 3 0 4 ' This approach, though theoretically valid, is not a reliable test of the ideality of the spinel solid solution since the combined uncertainty in temperature, ffio) fs->j and af° is veru larqe. The scatter in calcv.lo.ted a™ „ w leS " Fe304 values is more than three orders of magnitude. TABLE (6-3) Calculated log f g 2 values based on the Magnetite-Pyrrhotite Equilibrium for Pumice Flows from the Rabaul Caldera, Papua, New Guinea. Samplet Number Pyrrhotitet Composition (NFeS) Temp.t °C Fe 30 4 log f s 2 eqn.(5-1) i Po l 0 g aFeS eqn.(5-2) log f o 2 t log f o 2 equation (5-6' R § W* JANAF' 6820 • 0.9447 940 -0.180 -0.58 -0.146 -10.60 -10.64 -10.52 6S30A 0.9469 880 -0.111 -1.21 -0.143 -11.20 -11.78 -11.67 6830B 0.9469 995 -0.190 -0.33 -0.133 - 9.60 - 9.89 - 9.77 6831 0.9449 990 -0.178 -0.23 -0.141 - 9.60 - 9.85 - 9.73 6833 0.9308 990 -0.187 0.61 -0.197 - 9.70 - 9.14 - 9.02 8000A 0.9708 970 -0.240 -2.39 -0.055 -10.50 -11.83 -11.72 8000B 0.9708 870 -0.174 -3.32 -0.058 -12.00 -13.65 -13.53 8031 0.944S 910 -0.187 -0.82 -0.148 -11.20 -11.16 -11.04 8049 0.9347 955 -0.157 0.16 -0.185 -10.20 - 9.85 - 9.73 t Data from Heming and Carmichael (1973)• * Log j based on . Robie and Waldbaum (1968) thermochemical data § JANAF (1966) magnetite data substituted for the Robie and ' Waldbaum (1968) values 120 C H A P T E R 7 SUMMARY AND CONCLUSIONS Solid phase buffering techniques have been applied to study reactions involving gas species in the H-O-S system. This approach permits H-O-S gas mixture compositions to be controlled as a function of the experimentally defined variables temperature, total pressure, f s 2 > a n d either f g 2 o r R " H 2 " Calculations show H20, H 2 , H 2 S , and SO2 are quantitatively the important species within geologically significant regions of fs2 - f o 2 - P - T space. The mole fractions of molecular species in the gas mixtures have been calculated assuming ideal mixing. This assumption is reliable when a single gas species dominates the vapour phase. Non-ideality has been shown to seriously affect computation of gas mixture composition in the H2-rich vapour phase defined by MI, WI, or WM buffers. Successful application of these buffers requires measurement of activity coefficients for H 2 - H2O gas mixtures. Pyrrhotite is the only adequately calibrated sliding point indicator of sulfur fugacity. The reaction: F e 3 0 4 + 3 / 2 S 2 t 3 FeS + 2 0 2 has been investigated to test the applicability of solid-phase buffering techniques to reactions involving gas species in the H-O-S system. The experimental arrangement consisted of an inner Au or Pt capsule enclosed within an outer Au capsule. The following three buffer systems have been tested: [ 0 B , 0 H ( S B X , H 0 S ) ] [0B,HOS|SBX,HOS|] [ O B S B X , H O S ] 121 The first configuration controls f g 2 indirectly by hydrogen diffusion through the walls of the inner capsule. The latter two configurations Pyrrhotite provides an internal indicator of Programs for computing gas mixture compositions applicable to these experimental configurations are listed in Appendices 2 to 4. Supporting data (fugacity coefficients, equilibrium constants, and oxygen buffer coefficients) are tabulated in Appendix 1. The relationship between the buffer systems and the various programs are summarized in Table (4-2). The programs and data provide a quantitative base for defining regions currently accessible to experimental studies in H-O-S gas mixtures. Data for the C-O-H system have been compiled as part of theoretical and experimental work by French (1966) and Skippen (1967, 1971). Ultimately, combination of theoretical and experimental studies in C-O-H and H-O-S gas mixtures will provide the basis for investigation of the important four component C-O-H-S system. establishing pyrrhotite compositions in equilibrium with magnetite (or wilstite) and vapour to results predicted from thermochemical data: specify f o 2 internally by means of a solid phase oxygen buffer. The following table compares experimental results Oxygen Buffer Internal (i) External (e) Experimental Results * Pyrrhotite Composition (Npgg) 627°C - 1 atm. Thermochemical Calculations t 0.966 1.002 0.969 (QFM1) 0.962 (QFM2) 1.000 (WI1) QFM6 0.963 0.969 (QFM1) 0.962 (QFM2) NNO e 0.960 0.955 (NNOI) 0.957 (NN02) * ±0.004 (Table 5-3) • t Section 5.2 (Figure 5-1, Table 5-4) 122 Pyrrhotite compositions defined by QFM buffer lie between the theoretical compositions calculated using QFM1 (Wones and Gilbert, 1969) and QFM2 (Skippen, 1967) buffer calibrations. The calculated composition of the H-O-S vapour phase in these experiments at P-total = 2000 bars is: log f o 2 -19.39 f H z 0 1119 P H 2 Q 1977 log f S 2 - 5.50 f H 2 S 15.2 P H 2 s 11.3 log f S o 2 - 4.93 f H 2 17.6 P„ 2 11.6 (T = 627°C, fugacities and partial pressures in bars) H20 dominates the vapour phase in experiments using either NNO or QFM buffer. Pyrrhotite compositions bracketed at oxygen fugacities controlled by these buffers are virtually independent of temperature. The effect of total pressure on the pyrrhotite - magnetite equilibrium has been evaluated theoretically. Experimental results have been corrected to a standard pressure of 1 atm. by equation (5-21). Reaction rates are sufficiently rapid to allow pyrrhotite compositions to be bracketed in experiments lasting less than 100 hours (QFM and NNO buffers, Ptotal = 2000 bars, T = 650°C). No contamination of run products by platinum or gold from the reaction capsules was detected in Fe-H-O-S or Fe-Si-H-O-S system experiments. H2 diffusion into the external Ar pressure medium limited the duration of WI and QFM buffer experiments. Both platinum and thin-walled Au inner capsules have been successfully used as hydrogen membranes at fpj2 values specified by QFM or NNO external buffers. Different quench times did not affect results for these buffers. 123 Experimental results combined with thermochemical data for the magnetite - pyrrhotite equilibrium are used to calculate the log f g 2 imposed by the various oxygen buffers. Calculations agree with existing buffer calibrations. All log f o 2 values calculated for QFM1 experiments f a l l within limits of ±0.4. Log f o 2 calculations for NNO experiments agree within limits of ±0.2. In both cases uncertainties are approximately equal to existing discrepancies in the buffer calibrations. At sulfur and oxygen fugacities higher than those defined in NNO buffer experiments difficulties with the buffering technique arise as the result of: (1) lack of equilibration of f^j 2 between charge and external buffer assemblage. (2) quench exsolution of pyrite from pyrrhotite in experiments containing sulfur-rich pyrrhotite or both pyrite and pyrrhotite. (3) reaction between the H-O-S vapour phase and Pt capsules to produce PtS. The thin lining of PtS formed in these experiments prevents significant further reaction between the Pt capsule and the vapour phase. As a result successful experiments can be conducted within the stability field of PtS. The maximum f s 2 and f02 that is accessible to experimental control at any temperature and total pressure is defined when the total pressure equals the sum of partial pressures of gas species in the S-0 system. The common assemblage hematite + magnetite + pyrite defines sulfur and oxygen fugacities which intersect this condition at 124 geologixally significant temperatures and pressures (Figure 5-7). Hematite is not stable in the presence of either pyrite or pyrrhotite above approximately 550°C at Ptotal = 500 bars or 600°C at Ptotal^OOO bars. These temperatures are lowered by the presence of gas species other than those in the S-0 system. The feasibility of using QFM or NNO buffer to study sulfide-oxide relations in the Fe-Ni-H-O-S system has been established. Preliminary investigation of the reaction: F e 3 0 4 S p i n e l + 3/2 S 2 t 3 FeS M s S + 2 0 2 indicates compositions of Mss coexisting with magnetite ss at constant f g 2 become progressively more sulfur-poor as the nickel content of the Mss increases. The metal:sulfur ratio in Mss or pyrrhotite coexisting with magnetite is extremely sensitive to variations in f g 2 a t constant temperature. Changes in total pressure or variation of f g 2 with temperature along the QFM or NNO buffer curves cause l i t t l e variation in the metal:sulfur ratio. The path across the Mss at constant fg 2 determined by QFM buffer is consistent with log f g 2 isobars determined by Naldrett and Craig (1968). An attempt to determine the partitioning of nickel and iron between coexisting Fe-Ni olivine and Mss was not successful using QFM as an external buffer. Two buffer configurations which should prove useful in establishing nickel and iron partitioning between coexisting sulfides, oxides and silicates are . [WMG,0H(SBX,H0S)] or [G,0H(SBX,H0S)]. It is suggested that many natural assemblages are internally buffered with respect to f g 2 and f o 2 - Determination of the metal:sulfur ratio in Fe-Ni sulfides or pyrrhotite coexisting with an Fe-bearing spinel can provide estimates of f g 2 and f g 2 when an independent estimate of temperature is available. 125 REFERENCES Alcock, C.A., and Kubik, A., 1969. A thermodynamic study of the alpha-phase solid solutions formed between palladium, platinum, and iron. Acta Met., 17, 437-442. Anderson, G.M., 1964. The calculated fugacity of water to 1000°C and 10,000 bars. Geochim. Cosmochim. Acta, 28, 713-715. Anderson, J.S., 1946. The conditions of equilibrium of 'non-stoichiometric1 chemical compounds. Proc. Roy. Soc. (London), 185(A), 69-89. Arnold, R.G., 1957. The FeS - S "join. Carnegie Inst. Wash. 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Equations are of the form: log f o 2 = [C(Ptotal " 1-0) - A] / T°K + B (Al-1) Except for noted modifications to the C term, pre-1962 values were compiled by Eugster and Wones (1962). The A, B, and C terms are in the FORMAT designated by 0-H and H-O-S programs but the identification term (ID) as READ by the programs is entered on a separate card (see examples, Appendix 2 and 3). The log £Q equation with A, B, and C coefficients inserted and the ID term are printed as part of the heading for each page of output. Fugacity coefficients calculated for gas species in the H-O-S system are listed in Table (Al-2). The listing is in the FORMAT specified by 0-H and H-O-S programs (Appendix 2 and 3). Where two sets of data for a single gas species are tabulated, the second set is the preferred compilation. Fugacity coefficients for H 2 O and H2 are based in part on experimental P-V-T measurements. Experimentally derived fugacity coefficients for sulfur-bearing gas species are not available and estimates have been made from reduced variable charts (Hougen, et al., 1960; Newton, 1935). The Hougen, et al. (1960) chart of reduced pressure (Pr) versus has been replotted on a larger scale using the data of Lydersen, Greenkorn, and Hougen (1955) as tabulated in Reid and Sherwood (1966) . Points have 134 TABLE (Al-1) Coefficients for Oxygen Buffers C O E F F I C I E N T S F O R O X Y G E N B U F F E R S U S E D 111 O - H M I D H - O - S P R O G R A M S . P R O G R A M S S P E C I F Y A , B , C . F O R M A T ( 3 F 1 5 . D ) A L L O T H E R C O L U M N S A R E N O R M A L L Y B L A N K O H D A T A C A R D S P R E 1 9 6 2 R E F E R E N C E S C D H P I L E D B Y E N G S T E R & . W O M E 3 ( 1 9 6 2 ) L O G F ( 0 2 ) - = ( C ( P T - l . O ) - A ) / T E H P + D T E M P E R A T U R E I N D E G R E E S K E L V I N . P R E S S U R E I N B A R S . A B c I D R E F E R E N C E 3 0 0 3 0 , 0 8 . 0 2 0 . 0 5 0 Q F 1 1 D A R K E N (1 9 4 8 ) 2 9 3 8 2 . 0 7 . 5 1 0 . 0 5 0 Q F I 2 E U G S T E R 6 W D S E S ( 1 9 6 2 ) 2 9 2 & 0 . 0 8 . 9 9 Q . 0 6 1 0 0 M I 1 N O R T O N ( 1 9 5 5 ) 2 8 6 0 0 . 0 7 . 7 8 0 . 0 6 0 7 3 M I 2 R O B I E 5 W A L D B A U M ( 1 9 6 8 ) t 2 7 2 1 5 . 0 6 . 5 7 0 . 0 5 5 0 0 WI 1 D A R K E N & G U R R Y ( 1 9 4 5 ) 2 7 4 8 0 . . 0 ' 6 . 6 4 0 . 5 5 5 6 3 WI 2 3 O B I E > W A L D B A U M (1 9 6 0 ) i 2 7 5 1 6 . 0 6 . 7 7 2 0 . 0 5 5 6 3 WI 3 C H AR E 1 T F." G F L E N G A S ( 1 9 5 3 ) 3 2 7 3 0 . 0 1 3 . 1 2 0 . 5 8 3 MW 1 D A R K E N S G U R R Y (1 9 4 5 ) 3 2 8 5 0 . 0 1 2 . 1 2 0 . 0 8 0 . 1 3 MW 2 R O B I E D W A L D B A U M ( 1 9 6 8 ) fr 3 2 5 8 1 . 0 1 2 . 8 3 9 0 . 0 8 0 1 3 MW 3 C H A R E T T E & F L E N G A S ( 1 9 5 3 ) 2 5 7 3 0 . 0 9 . 0 0 0 . 0 D 3 7 4 Q F M 1 W O N S 5 > G I L B E R T ( 1 9 6 9 ) 2 U 7 0 0 . 0 8 . 4 5 0 . 0 9 3 7 Q F M 2 S K I P P E N ( 1 9 6 7 ) 2 6 4 9 4 . 0 9 . 6 9 0 . 0 9 2 Q F M 3 E U G S T E R & W D N S S ( 1 9 6 2 ) 2 6 4 9 4 . 0 9 . 6 9 0 . 0 9 3 7 4 Q F M 3 * E U G S T E R C W O N E S ( 1 9 6 2 ) 2 7 3 0 0 . 0 1 0 . 3 0 0 . 0 9 2 Q F M 4 M U A N ( 1 9 5 5 ) ; S C H E N C K E T i L ( 1 9 3 2 ) 2 7 1 0 0 . 0 1 0 . 3 0 . 0 . . 0 9 3 7 4 Q F M 4 * MU A H ( 1 9 5 5 ) ; S C H E N C K E T A L ( 1 9 3 2 ) 2 7 6 1 9 . 0 1 0 . 5 5 0 . 0 9 2 Q F i l 5 M U A N ( 1 9 5 5 ) A N N I T E E Q U I L 2 7 6 1 9 . 0 1 0 . 5 5 0. . 0 9 3 7 4 Q F M 5 * M U A N ( 1 9 5 5 ) A N N I T E E Q U I L 2 4 9 3 0 . 0 9 . 3 6 0 . 0 4 6 0 0 ' N N 0 1 H U E B N E R & S A T D ( 1 9 7 0 ) 2 4 9 3 0 . 0 9 . 3 6 0 . 0 4 5 7 8 N K 0 1 * H U E B N E R C S A T D (1 9 7 0 ) 2 4 7 0 9 . 0 8 . 9 4 0 . 0 4 6 N N 0 2 E U G S T E R & H D S E S ( 1 9 6 2 ) 2 4 7 0 9 . 0 8 . 9 4 0 . 0 4 5 7 8 H N 0 2 * E U G S T E R & H O N E S ( 1 9 6 2 ) 2 5 8 6 0 . 0 9 . 9 9 0 . 0 4 6 MHO 3 B O G A T 5 < I I ( 1 9 3 8 ) . 2 5 8 6 Q . 0 9 . 9 9 0 . 0 4 5 7 8 N S 0 3 * B O G A T S K I I ( 1 9 3 8 ) 2 4 4 0 9 . 0 8 . 8 6 9 0 . 0 4 5 7 8 11N 0 4 C H A R E T T E £ F L E N G A S ( 1 9 5 3 ) 2 4 9 1 2 . 0 1 4 . 4 1 0 . 0 1 9 HM 1 N O R T O N ( 1 9 5 5 ) 2 4 9 1 2 . 0 1 4 . 4 1 0 . 5 1 8 5 3 HM 1 * N O R T O N ( 1 9 5 5 ) 2 5 7 9 0 . 0 1 6 . 0 7 0 . 5 1 8 5 3 HM 2 R O B I E > W A L D B A U M ( 1 9 6 8 ) t 2 5 8 0 9 . 0 1 4 . 8 0 1 0 . 0 1 8 5 3 HM 3 C H A R E T T E & F L E N G A S ( 1 9 5 3 ) * C T E R f l M O D I F I E D - A V S O L I D S C A L CO L A T E D F S 3 * i T H E M O L A R V O L U . 1 B D A T A O F R O B I E , B E T I I K K , & B E A R D S * . , E Y (1 9 6 7 ) I D A T A O F R O B I S 6 W A L D B A U M ( 1 9 5 8 ) F I T T D A L I S E A R E D . U A T I O N B Y U B C T R I P ( T R I A N G U L A R R E G R E S S I O N P A C K A G E ) TA3LE (Al-2) Fugacity coefficients for gas species in the H-O-S system. DATA C A R D S USED T C ENTER F U G A C I T Y C O E F F I C I E N T S IN OH AND HCS PROGRAMS THE P R E S S U R E I N K I L O B A R S I S I N D I C A T E D IN C O I U K N S 1 - 3 . T H E S E 3 COLUMNS ARE B L A N K ON THE DATA CARDS USED I N T H E PROGRAM. (FORMAT 8 F 1 0 . 0 ) T H E E I G H T S P E C I F I E D F I E L D S L I S T F U G A C I T Y C O E F F I C I E N T S FRO M 6 0 0 TO 1 3 0 0 D E G R E E S K E L V I N . 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 F U G A C I T Y C O E F F I C I E N T S FOR H 2 0 (HOLSER 1 9 5 4 - P R E S S U R E S UP TO AND I N C L U D I N G 2 0 0 0 BARS - AND ERSON 1964 - P R E S S U R E S G R E A T E R THAN 2 0 0 0 BARS ) 0 . 5 0 . 2 4 5 0 . 4 7 8 0 . 7 0 1 0 . 8 1 2 0 . 875 0 . 9 1 3 0 . 9 4 8 0 . 9 57 1. 0 0 . 154 0 . 3 0 6 0 . 5 1 2 0 . 6 7 9 0 . 791 0 . 8 6 9 0 . 9 2 0 0 . 94 9 2 . 0 0 . 1 17 0 . 2 3 8 0 . 4 0 5 0 . 5 7 2 0 . 7 1 0 0 . 8 2 9 0 . 9 16 0 . 973 3 . 0 0 . 1 12 0 . 2 3 1 0 . 3 8 6 0 . 5 26 0 . 6 66 0 . 7 8 9 0 . 8 67 0 . 919 F U G A C I T Y C O E F F I C I E N T S FOR H 2 0 l (BUSNHAM, i lCLLOWAY AND D A V I S 1 9 6 9 ) 0 . 5 0 . 2 2 4 0 . 4 81 0 . 69 1 0 . 8 10 0 . 879 0 . 9 2 3 0 . 947 0 . 9 57 i m 0 0 . 140 0 . 3 1 3 0 . 50 9 0 . 6 7 5 0 . 7 89 0 . 8 6 4 0 . 9 15 0 . 9 50 1. 5 0 . 1 17 0 . 2 6 1 0 . 43 6 0 . 6 0 0 0 . 7 3 3 . 0 .831 0 . 8 9 6 0 . 94 0 2 . 0 0 . 1 10 0 . 2 4 2 0 . 4 0 6 0 . 5 6 6 0 . 7 0 7 0 . 8 1 6 0 . 8 9 3 0 . 9 « 6 3 . 0 0 . 1 10 0 . 2 3 8 0 . 3 9 5 0 . 5 5 5 0 . 6 9 9 0 . 8 2 3 . 0 . 9 1 4 0 . 979 F U G A C I T Y C O E F F I C I E N T S FOR H2 (SHAW AND WONES 1 9 6 4 ) 0 . 5 1. 178 1 . 1 4 9 1 . 1 2 7 1 . 111 1 . 0 9 8 1. 08 8 1 . 0 7 9 1. 0 72 1. 0 1. 384 1 . 3 1 7 1 . 2 6 9 1 . 2 3 3 1 . 2 0 4 1. 182 1 . 1 6 3 1. 148 1 . c 1.6 23 1. 5 0 7 1 . 4 2 7 1. 36 7 1 . 3 1 9 1. 2 8 2 1. 2 5 2 1. 231 2 . 0 • 1 . 8 9 6 1. 7 2 2 1 . 6 0 1 1 . 5 1 2 1. 44 5 1 . 39 2 1 . 3 4 9 1. 314 3 . 0 2 . 5 7 2 2 . 2 3 3 2 . 0 0 7 1. 846 1. 726 1 . 6 3 3 1 . 5 6 0 1. 501 F U G A C I T Y C O E F F I C I E N T S FOR H2 ( P R E S N A L L , 1 9 6 9 • SHAW AND WONES 1964 ) 0 . 5 1. 170 1. 135 1 . 1 1 5 1. 100 1 . 0 9 8 1 . 0 8 8 1 . 0 7 9 1. 072 1. 0 1 . 3 6 9 1 . 2 9 8 1 . 2 5 1 1 . 2 1 5 1. 204 1 . 1 8 2 1 . 16.3 1. 148 1. 5 1 . 6 0 5 1. 4 8 0 1 . 4 0 5 1. 344 1. 3 19 1 . 2 8 2 1 . 2 5 2 1. 2 31 2 . 0 1. 8 6 5 1. 684 1 . 5 6 6 1 . 4 8 0 1 . 4 4 5 1 . 3 42 1 . 3 4 9 1. 314 3 . 0 2 . 5 7 2 2 . 2 3 3 2 . 0 0 7 1 . 8 4 6 1. 726 1. 6 3 3 1 . 5 6 0 1. 501 cont'd TABLE (Al-2) cont'd: 0.5 1.0 1-5 2.0 3.0 F U G A C I T Y C O E F F I C I E N T S F O R S2 ( R E I D A N D S H E R K C O D 1966) 0.C01 0.C0 1 0.C0 1 0.001 0.C0 1 0.001 0.001 0.001 0. 002 0. 004 0.005 0.005 0.008 0.0 1 1 C .028 0. 023 0.021 0.026 0. 037 0.075 0. 052 0. 0 4 5 0.055 0. 073 0.1U2 0.099 0.035 0.097 0. 124 0. 233 0. 166 0. 142 0. 158 0. 197 0.352 0. 246 0.211 0. 23 1 0. 283 0.479 0.5 1.0 2.0 F U G A C I T Y C O E F F I C I E N T S F O R H2S ( N E W T O N 1935 + H C U G E N A N D W A T S O N G R A P H 1960) 0.781 0. 8 15 1. 150 0. 884 0. 942 1.287 0.958 1.038 1.427 1.012 1. 105 1.489 1. 046 1. 150 1. 525 1. 067 1.177 1. 533 1.080 1.194 1.546 1. 089 1. 205 1. 552 F U G A C I T Y C O E F F I C I E N T S F O R H2S ( R E I D A N D S H E R W C C C 1966) 0.5 0.782 0.887 0.937 0.963 0.978. 0.986 0.987 C.988 1.0 0.798 0.926 0.987 1.016 1.028 1.032 1.033 1.034 1 . 5 0. 925 1. 067 1 . 124 1. 144 1. 149 1. 149 1. 146 1. 142 2.0 1.141 1.292 1.336 1.339 1.330 1.317 1.306 1.291 0.5 1.0 2.0 F U G A C I T Y C O E F F I C I E N T S F O R S02 (NEWTON - 1935 + H O U G E N A N D W A T S O N G R A P H 1 960) 0.6 35 0.685 1.075 0. 793 0. 855 1.301 0.875 0.970 1.432 0. 945 1.06 1 1.495 1. COO 1.128 1.500 1.041 1.171 1. 500 1.06 6 1. 202 1.500 1. 080 1.213 1. 500 F U G A C I T Y C O E F F I C I E N T S F O R S02 ( R E I D A N D S H E R W C O D 1966) 0.5 0.630 0.780 0.880 0.929 0.957 0.974 0-983 0-987 1.0 0.670 0.832 0.955 1.011 1.040 1.055 1.060 1.060 1.5 0.832 1.015 1.144 1.200 1.218 1.222 1.217 1.212 2.0 1.100 1.300 1.439 1.472 1.469 1.455 1.437' 1.420 F U G A C I T Y C O E F F I C I E N T S F O R S03 ( R E I D A N D S H E R W C C E 1966) 0.5 0.465 0.665 0.784 0.870 0.922 0.952 0.967 0.978 1.0 0.475 0.694 0.828 0.932 0.991 1.021 1.037 1.046 1 .5 0.595 0. 842 0.991 1. 104 1. 160 1. 182 1. 188 1. 1 92 2.0 0.805 1.089 1.256 1.381 1.417 1.420 1.415 1.406 137 been extracted from this graph defining T r (reduced temperature) and Y^  at P r values corresponding to total pressures of 500, 1000, and 2000 bars for each gas species. Graphing T r versus Y^  at constant P r produced smooth curves from which has been estimated at 100-degree temperature intervals. The maximum total pressure for which may be obtained depends on the critical pressure of the individual gas species (P, must be <30.0 for T r <15.0). This limit is approximately 2700 bars for H2S, 2360 bars for S02, and 2440 bars for S O 3 . Reduced variable charts are based on a critical compressibility (Zc) of 0.27. This compares favourably with Z c values of 0.268 for H2S and S02, and 0.262 for S03. Ryzhenko and Volkov (1971) have derived equations which express Y^  as a function of the two variables T r and Pr. yi = 1 + 0.014986 P r - 0.0007015 T rP r + 0.00001024 T r 2P r + 0.00010787 P r 2 - 0.000006007 T rP r 2 + 0.000000087 T r 2P r 2 (Al-2) [range: T r = 12-35, P r - 0-100; error <10% of Y^] •Yi = 1 + 0.0124 P r + 0.000254 T rP r - 0.00005104 T r 2P r + 0.0011089 P r 2 - 0.0001998 T rP r 2 + 0.000009393 T r 2P r 2 (Al-3) [range: T r = 3-12, Pr = 0-60; error <10% of Y-£] Yi = 1 - 0.2242 Pr + 0.14667 T rP r - 0.02276 T r 2P r + 0.008899 P r 2 - 0.005119 T rP r 2 + 0.000786 T r 2P r 2 (Al-4) [range: T r = 1.5-3, P r = 0-20; error <10% of Y^] ^H2S' Y S 0 2 > A N C ' ^ 8 0 3 values generated by these expressions are within 5% of the equivalent values estimated from reduced variable charts. These equations have not been incorporated into the H-O-S programs 1 3 8 (Appendix 3 ) since the stated range restricts calculation of ^ I - ^ S J Y S 0 2 > and Y S O 3 to pressures < 2 0 0 0 bars, and no solutions are possible for ' ' ' s 2 -No estimates of Y.£ for S O , S 2 O , or H S are possible in the absence of critical constants for these gas species. Equilibrium constants for H 2 O , S O 2 , S O 3 , and H 2 S are tabulated by Robie and Waldbaum ( 1 9 6 8 ) . H S is tabulated in the J A N A F Thermochemical Tables ( 1 9 6 5 ) , and S O and S 2 O are included in the addendum ( 1 9 6 6 ) . Table (Al - 3 ) lists the values for 100-degree temperature increments from 3 2 7 -1 0 2 7 ° C in the order specified by H - O - S Version 1 . The values appear in the F O R M A T designated for specific 0 - H or H - O - S programs in data listings included in Appendix 2 and 3 . S 2 gas has been defined as the reference state for the tabulated equilibrium constants of all sulfur-bearing gas species both above and below the boiling point of S 2 liquid ( 7 1 7 . 7 5 ° K ) . This convention is necessary for calculations in the H - O - S system since fg values of geologic importance are below the equilibrium fg on the sulfur condensation curve for a l l temperatures considered ( 3 2 7 - 1 0 2 7 ° C ) . TABLE (Al-3) Log K for Gas Species in the H-O-S System T°K T°C SO S0o S0T S„0 H„0 H0S HS 2 3 2 z 2 600 327 5.290 27.711 31.397 12.807 18.633 5.272 -5.186 700 427 4.571 23.207 25.664 10.497 15.585 4.168 -4.325 800 527 4.032 19.828 21.366 8.766 13.289 3.338 -3.681 900 627 3.613 17.208 18.033 7.419 11.499 2.687 -3.181 1000 727 3.278 15.098 15.355 6.342 10.062 2.163 -2.781 1100 827 3.004 13.378 13.173 5.463 8.883 1.734 -2.454 12C0 927 2.775 11.946 . 11.357 4.730 7.899 . 1.375 -2.182 1300 1027 2.581 10.734 9.822 4.109 7.065 1.070 -1.952 140 APPENDIX 2 0-H SYSTEM COMPUTER PROGRAMS Programs written for calculations in the 0-H gas system are listed with typical data setups and a representative page of output. All computations were run on an IBM/360 Model 67 computer located at the University of British Columbia and operated under control of the Michigan Terminal System (MTS). Programs were compiled on a WATFIV compiler (a FORTRAN IV compiler modified to operate under MTS at the University of Waterloo). 0-H Version 1: The program calculates fugacities and partial pressures of H2 and H20 for log values defined by solid phase oxygen buffers. The computation assumes ideal mixing of non-ideal gases. Theory and equations are developed in Chapter 2. Printed output fits a standard 8 1/2" x 11" page. 0-H Version 2: The program makes use of Shaw's (1967) equation which corrects for the non-ideal mixing of H 2 and H20 (Chapter 2, equations 2-14, 2-15). Version 1 calculations are duplicated and the output provides easy comparison between the assumption of ideal mixing and the non-ideal mixing term proposed by Shaw (1967) . Note that, the correction may not be valid for temperatures less than 500°C or pressures greater than 1000 bars. 1 4 1 0 - H Version 3 : The third 0 - H program provides the data needed to contour log £Q on temperature-composition diagrams for the 0 - H system (dotted lines Figures 2 - 1 to 2 - 3 ) . The calculations are similar to those of 0 - H Version 2 . Log fo may be defined at any desired value. Small changes in temperature result in large changes in the composition of the gas mixture at constant log f c ^ - The temperature increment is therefore 1 0 degrees in contrast to the 100-degree intervals set for a l l other programs. The listed data deck needs no modification for temperatures from 3 0 0 - 1 0 1 0 ° C ( P T O T A ] = 5 0 0 , 1 0 0 0 , 1 5 0 0 , 2 0 0 0 , and 3 0 0 0 bars). y H 2 0 values must be compiled at 10-degree intervals from Table 6 , Burnham, et al. ( 1 9 6 9 ) for computations at other pressures. 142 SCOKPILE TIHF,= 20,PACES-MO C C 0-H VERSION 1 IDEAL MIX I US CF NON-IDEAL GASES C C IN MAKING V A R IA iiLKS THE FOLLOW T MG PREFIXES KERB USED C (1) FC FOH FUGACITY COEFFICIENTS C (2) FL FOR LOG 10 FUGACITIES C (3) F FOR FUGACITIES C (4) P FOR PRESSURES C (5) PCT OR PC FOR PER CVAVt CF A GAS SPECIES C N (6) CL FOR THE LOG OF THE EQUILIBRIUM CONSTANT C C " GAS SPECIES WERE NAMED BY FORMULA (SG 02 HOT OX FOR OXYGEN) C 1 DIMENSION PT(5) , F C H 2 0 ( 3 , 5 ) , FCH2(8,5), A(S) , B (5) , C (5 ) , 1DUK (5) , CLH20(8), T EK PC (8) , FLO 2 (8) , FLM20(8) , FLH2(8), 2F02 (8) , F H 2 0 ( 3 ) , F!I2(8), P02 (8) , PK20(8), PH2(8), P C T 0 2 ( 3 ) , 3PCTH2C (8) , PCTH2 (8) C 2 READ (5,500) (PI (I) ,1=1,5) 3 500 FORMAT (5F10.0) H READ (5,501) ((FCH2C (K,I) ,K=1 , 3 ) ,1=1,5) 5 RKAD(5,501) ((FCH2 (K,I) , K = 1, 8) , 1=1,5) 6 READ (5,501) (CLi!20 (K) ,K=1 ,8) 7 501 FORMAT (8F10.0) 8 HEAL (5,512) (A (.1) , !3 (J ) ,C (J) , J= 1 ,5) 9 512 FORMAT (3F10.0) 10 READ (5,5 13) (B !IF (J ) , J = 1 , 5) 11 513 FOH MAT (5A4) C CHANGE TOTAL PRESSURE 12 DO 100 1-1,5 C C CHANGE BUFFER C 13 DO 200 J = 1 ,5 14 F A C=- A (J ) t C ( J) * (PT (I) - 1.0) C C SET T EK P IN DEGREES KELVIN - I NCR EKE i.'T BY 100.0 (8 riHES) 15 TEMP-500.0 16 • DO 4 00 K=1,8 17 T E "i P=T EH P+ 100.0 18 TEMPC (K)=TEKP-273.0 C C CALCULATE F (02) FROM AN EQUATION OF THE FORK (C (PT- 1.0)-A)/TEMP +B C 19 FL02 (K) =FAC/TEMP IB (.1) 20 FL02RT=FL02(K)/2.0 21 F02 (K)=10.0**FL02(K) 22 P02 (K) =F02 (K) 23 F02R?= 10.0**FL02RT 24 Cli20 = 10.0**CLH2C) (K) C C SOLVE FOR F(H2) A tl C F(!I20) 25 D-PT (I) *FC!!2 (K, I) *FC*i20 (K , I.) 26 E-C!!2 0*F 02 RT* FCI!2 (K, I) + FCH20 (K, I) 27 FH20 {K) -0*Ci!2O*I'02RT/E 143 28 PH20 ( K ) = FH20 ( K ) /PCH20 (i( ,1) 29 FH2 (K ) = D / E 30 P H2 (K ) = Fil 2 (K) /FCH2 (K , I) 3 1 FLH2 (K) =ALOG 10 (Fl!2 (K) ) 32 FLH20 (K)=ALOG10 (FH20 ( K ) ) C C CALCULATE THE PES CEUT OF EACH GAS SPECIES 33 PCT02 (ft) =P02 ( K ) * 1 00. 0/PT (I) 34 PCTH2 ( K ) =PH2 (K) *1 00. O/PT (I) 35 PCTH 2 0 (i\) = PH20 ( K) * 1 00. 0/PT (I) 36 400 CONTINUE C 3 7 WRITE (6 ,6 00) PT (I) 38 600 FOR RAT (1111/2 5X15!! TOTAL P HESS UREF 1 0. 0 , 8 H . BARS/2X23H OXYGEN BtlFF 1ER,OH (X.OH)) 39 WRITE (5,601) BUF(J) 40 601 FORMAT (1H02XA4, 71i BUFFER) 4 1 WRITE (6,608) C (.7) , A (J ) ,11 (J) 42 608 FORMAT (11102X13 HLOG F (02) = (F8. 5 , 1 OH (PT- 1.0) - F9 . 1,1011 J/TEMP +F5 1.2) • ,43 WRITE(6,602) ('f E MP C (K ) , FL02 ( K) , F I.H2 0 (K ) , FL H2 ( K ) , K= 1 , 8 ) 44 602 FORMAT ( 1 H 0 / 2 X 8 H TE HP (C) 5X 10 !i LOG F (02)4X11 H LOG F (i! 20) 5X10H LOG F( 1 H2)// (F10.0,3F15. 5) ) 45 WHITE (5 ,603) ( T F, MP C (K ) , FO 2 ( K) , F!!20 (K ) ,'FH2 ( K) , K~ 1, 8) 46 603 FORMAT (1H0/2X0H TEMP ( C ) 9X6H F (02) 8X71! F (H2b) 9 X6H F (il 2)//(0 P F 10 . 0, 1 1P3E15.5)) 47 WRITE (6 ,604) (T3MPC (K) ,P02 ( K ) , P1I20 (K ) , Fl!2 ( K) , K- 1 , 8) 48 604 FORMAT (1H0/2X8II TE MP (C ) 9X6 H P (02)8X711 P(H2D)9X6H P (il 2)//(0 P F 1 0 . 0, 1 1P3E15.5)) 49 WRITE (5 ,605) (TEMPC (K) ,PCT02 (K) , PCTfl20(K) ,PCTH2 (K) , K = 1,8) 50" 505 FORMAT (1H0/2X8H TEMP (C ) 3X1211 PER CENT 022X 1311 PER CENT H203X12H PE 1R CENT 1!2// (F10. 0, 3F15 .5) ) C 51 200 CONTINUE 52 100 CONTINUE 53 STOP 54 END . . • • $ D A T A TYPICAL DATA EHCK 500.0 1000.0 0.224 0.481 0. 140 0. 3 13 0.117 0.261 0. 1 10 0. 242 0. 110 0.23 3 1. 178 1. 149 1.384 . 1.317 1.6 23 1 . 507 1.896 1. 722 2.572 2.233 18.633 15.585 29260.0 8. 99 27215.0 5.57 25738.0 9. 00 24930.0 9.36 24912.0 . 14.41 MI 1KI 1CFM1NN01HM 1 0-H VERSIONS 1500.0 2000.0 0.691 0.810 0.509 " 0.675 ' 0.436 0.600 0.40 6 0.566 0. 395 0.555 1.127 1.111 1.269 1.233 1. 427 1. 367 1.601 1.512 2.007 1.846 13.289 11.499 0.06100 0.05500 0.09374 0.04578 0.019 1 5 2 3000.0 0. 879 0. 923 0. 789 0. 864 0. 733 0. 831 0. 707 0. 816 0. 699' 0. 8 23 1.098 1. 088 1. 204 1. 182 1.319 1. 282 1.445 1 ^ 392 1. 726 1. 633 10.062 8. 883 0. 947 0. 957 0. 915 0. S50 0. 896 0. 940 0. 893 0. 946 0. 9 14 0. 979 1. 079 1. 072 1. 163 1. 148 1. 25 2 1. 231 1. 349 1. 314 1. 560 1. 501 7. 899 7. 065 -3 TO . A c?. —- cs o SO CC -J cr. xr Co -3 o SO CO u> tu K) to to ro tO to to No tO to t o to t o r o , — , -~j - J ~0 ~ J vo v j vo v j - J o _> X T X T 1 to Ul co t o ' _ i is CO to CO to to CO CC -0 Cr-. cr. c-. o o — • —' o O o o o o o o r, -V* CO so CO C C —1 CO • • 4 • » • • • U l o c s o CO CT-. to o o o o o o o o — o j0 U l -JO OS U l o o o o o o o o •-3 M C-J ra . o o o o c o o o 1 1 1 1 1 1 1 1 c o o o o o c o o o — . —i —» 1 to to ro CO ro o o o o o o o o to u> m ~J o J= CO — C*j CO so U0 » • • • • • • • CC cc cc CO o '.3 UD o so o O J U l CT\ CO o o" co 2D co CO CC -0 so .0 so CO o XT to XT o SO to to cr, —1 o JO U l Ul' CO U l en Co C u> Ul CO i-3 \-i to CO , C> cc —J Cs _ a o cr tO X T o SO r o Z'l LT: r-J "J l-J ro fO OS . o o ui ui to NO _ co o U l cr- Xr to o o o o o o o o o ui cc o cr. c . 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CO ! i I Y i i 1 c Cs c CO xr CO Ul Xr o c ~o G _» _^ . ro ro to CO r o xr ro o Co -0 xr U"' ro xr so Ul o X : cc xr \iC co Ul — xr CO SO •— »-3 1 o . o CO - J Ul CO —- • o r-« Co O '•^ 1 '»j o — •CO C •— XT ro J3 cc u. — i -tr-c. to CO Ci Ul XT i r o r j ro to ro ro to t o 1 p-r Co o sC to co CO Ul ~A •n ro c^ xr CO X r Ul cn , • o cc CO Xr X CI t-: cC CT3 " rd cc U"' Lo ro o xr zrc t o CI ISO o xr o . Ul 'CO Co Ul to U*l cc; o O O o o o o c o c^. co Ui so _ i v j -J ui ' c- ^L; to to to to ro ro *— xr -^j Ui to _* CO -J ^—* U) cc o Ul ro • • • • • • \ . C- Ul XT —. CO xr o U! XT o —. cc Ui ro — i b ro o ' .o sO ro cc CO CO o o O o —> cc sD CO o XT ro Ul I"v • IS Ui —: ^ . J X T .SO to to . o sd -J Co —j ?c C"i Xr o Ul xr to CC c^ CO _ i xr to ro to CS to + o o o o o o o o ro CO O . . JD Xr . Oi to — -• - » -> o o o Ui — -* U) Co Cs —' o CO o o 0-) 146 SCOHPILE TIHE=15,PACES=30 C C 0-1! VERSION 2 C THE CALCULATION IS P EH FORMED ASSUMING BOTH IDEAL A >i I NON-IDEAL C MIXING OF 82 AND H20 (BOTH GASES ASSUMED TO BE NON-IDEAL) C C IN NAMING VARIABLES THE FOLLOWING PREFIXES WERE USED C (1) FC FOR FUGACITY COEFFICIENTS C (2) FL FOR LOG 10 FUGACITIES C (3) F FOR FUGACITIES C (It) P FOR PRESSURES C (5) PCT OR PC FOR PER CENT CF A GAS SPECIES C (6) X FOR MOLE FRACTION C (7) ACT FOR ACTIVITY C ' (ci) AC FOR ACTIVITY COEFFICIENT C (9) CL FOR THE LOG OF THE EQUILIBRIUM CONSTANT C GAS SPECIES WERE NAMED BY FORMULA (EG C2 NOT OX FOR OXYGEN) C 1 DIMENSION PT(5 ) , FCI!20(rt,5), FCII2.(8,5), A (5), F. (5) , C (5 ) , 1BUF(5), CLH20(8), TEMPC(8), FL02(8) , Fi,H20(8), FLH2(8) , 2F02 (8) , FH20(3), FII2(8), P02 (8) , P!I2C(8), PM2(8), PCV02(8), 3PC?H20(8), PCTR2(8), PH2NI(8), PH20NI(8), 1IXH2 (8) , XH20(3), ACTH2(8), ACTH20(8), Fi!2HI(8), FH20MI(8), 5ACH2 (8) , ACH20(8), PCH2(8), PCH20(8) C 2 READ(5,500) (PT (I) , 1= 1 , 5) 3 500 FORMAT (5F10.0) l| READ (5,501) ( ( FCH2 C (K , I j , K= 1, 8) , 1=1,5) 5 READ (5,501) ((FCH2 (K,I) , K = 1 , 8) ,1=1,5) 6 READ (5,501) (CLH20 (K) ,K = 1,8) 7 • 501 FORMAT (8F10.0) 8 READ (5,5 12) ( A (J) , B (.1 ) , C (J) , J= 1, 5) 9 5 12 FOR MAT (3F10.0) 10 READ (5,5 13) (BUF (J) , J= 1 ,5) 11 513 FORMAT (5 A 4) C C CHANGE TOTAL PRESSURE C 12 DO 10 0 1=1,5 C C CHANGE BUFFER C 13 DO 200 J=1,5 Hi FAC=-A (J) +C (J) * (PT ( I ) - 1.0) C C SET TEMP IN DEGREES KELVIN - INCREMENT BY 100.0 (8 TIMES) C 15 TEMP=5 00.0 16 DO 400 K=1 ,8 17 TSKP=TEHP+100.0 18 TEMPC (K)=TEMP-2 73.0 C CALCULATE F(02) FROM AN EQUATION OF THE FORM (C (PT- 1.0)-A)/TEMP +B C 19 F L02 (K ) = ?AC/'IE tl P + B (J ) . 20 FL02RT = FL02 (K)/2.0 21 F02 (K) = 10.0**FLO2 (K) 22 P02 (K)=F0 2 (K) 23 F02RT= 10.0**ELO2RT 2 47 24 CH20--10.0**CJ,H20 ( K ) C C SOLVE FOR F(!!2) MiD F(!l20) C 25 D=PT (I ) *FCfl2 (K, I) *FCH20 (K , T) 26 F.= Ctl2C*F02RT*FC!!2 (K,I) +ICH20 (K, I) 27 FH2 0 (K ) = D*C II20 ~ F02 RT/E 20 PH20 (K) --FII20 (K) /FCH20 (K ,1) 2 9 FII2 (K) =D/E 30 . PH2 (K) =FH2(K) /FCH2 (K/I) 3 1 FLH2 (K) =ALOG10 (FH2 (X) ) 32 F 1.112C (K) =A LOG 10 (FK 20 (K ) ) C C . CALCULATE THE PER CENT OF EACH GAS SEICIES C 33 PCT02 (K)=P02(K) * 100.0/PT (I) 3H PCTH2 ( K ) =PH2 (K) * 10 0. 0/PT (I) 35 PCT112C (K) =P 1120 (K) *100. 0/PT (I) C C BEGIN CALCULATION FOR NON-IDEAl MIXING OF 112 AND 1120 C 36 PS 1 = 0.0090+(51.5)/TEMP 3 7 R=0.083147 38 Z = PT ( I ) * P S I / (R * T K H P) 39 RATFC=FCH2(K,I)/FCH20 ( K , I ) 40 H=CL!!20 (K) +ALOG10 (R AT FC) +FL02RT C C CALCULATE THE HOLE FRACTION OF 112 BY ITERATION C 41 XCORR=0.0 42 XVA»=0.0 4 3 10 CONTINUE 44 XVAR=XVAK+XCORR 45 GLOG=-tl- ( 1 .0-2. 0*XVAR) *Z/2. 302505 46 G=10.0**GLOG 4 7 XNEK=G/(1 ,0+G) 48 XTKST=XNEW-XVAR 49 IF (XTF.ST.LE.0.000001) GO TO 11 50 XC03R=XTEST 51 GO TO 10 52 11 XH2 (K)=XNEW C C CALCULATE REMAINING VARIABLES 53 XH20 (K.) = 1 .0-XH2 (X) 54 ACH2 (K)= E X P (XH20 (K) * XH20 (K)*Z) 55 AC 1120 (K) = EXP (XH2 (K) * XH 2 (K) *Z) 56 ACTH 2 (K) =X 112 ( K) * ACH 2 ( A ) 57 ACTH 2 0 (K)=X H20 { K) * ACH 2 0 ( K ) 58 FU2 i l l ( K ) =ACTU2 ( K) *FCil2 (K ,1) *PT (I) 59 FH20NI (K) = ACT:!20 (K) *FCH20 (K, I) *PT (I) 60 P112NI ( K ) =XH2 (K) *PT (I) 61 PH20NI (K) =X;120 ( K ) *PT (I) 62 PC112 (K) =XH2 (K) * 100. 0 63 PC1I20 (K) =XH20 ( K) * 1 00. 0 64 400 CONTINUE C 65 HRITE(6,600) P1(I) 66 600 FORMAT ( 111 1/25X 1 51! TOTAL PRSSSUREF ! 0. 0,OH BARS/2X2311 OXYGEN BUFF 1ER.OH (X,OH) ) 148 67 WHITE (5,60 1) !5UF(."I) 68 601 FORMAT (1II02XA';, 7i! SUFFER) 6') WRITE (5 ,6 00) C (J) , A (J ) ,n (J) 70. 608 FOR MAT ( 1 HO 2/ 1 3 ii LOG F (02) = (F8. 5, 1 OH ( FT- 1. 0) - F9 . 1,1011 )/TBMP + F5 1.2) 7 1 WRITE (6 ,602) (TEMPC (K) ,FL02 (S) , FLH20 (K) , FLM2 (K) , F02 (K ) , FH20 (K) ,FH2 1 (K) ,K=1,8) 72 602 FOR MAT ( 1H0/2X8H TSMP {C) 5X10 51 LOG F(02) ' iX11i i LOG F (K20)SX 1011 LOG F( 1112) 9X6H F (02) 8X71! F (!!20) 9X611 F (112)// (OPF 10.0,3F15. 5, 1P3215. 5) ) 73 WRTTS(6 ,60'!) (tEMPC (K ) ,P02 (K) ,P!I20 (K ) ,tt!2 (K) ,PCT02 (K ) ,PCT1!20 (K) ,PC 1TH2 (K) ,K=1 ,8) 7't 60'i FORMAT (1H0/2X8H TEMP(C)9X6li P (02) 8X7II F (1120) 9X611 ,P (112)3X121! PER CE 1 NT 022X 13H PER CENT H203X 12H PER CENT H 2// (OP F 10.0, 1P3E15.5,0P3F15 2.5)) 75 WRITE (5 ,605) 76 605 FORMAT ( 1110/2X52 H RECALCULATE ASSUMING NON-IDEAL MIXING OF I! 2 AND II 120) 77 ' WRITE (6,6 10) (1E MP C ( K ) , X I! 20 ( K) , XH2 (K ) , A CT (120 (K) , A CT II 2 (K) , F H20M I (K ) 1,Fii2\'I ( K ) ,K=1, 8) 78 6 10 FORMAT (1H0/2X8H TEMP (C) 1X 1 '1 !l MOLE FR AC H202X13H MOLE FRAC H22X13H 1ACTI.VI1'Y H203X 1 2H ACTIVITY H23X12I! F (i! 20) S H A W 4 X 1 1H F(il2) SHAW//(0 2PF10.0,2F15.7,1P4E15.5)) 79 WRITE (6,6 12) (TEMPC ( K ) .ACII20 (K) , ACH2 (K ) ,PII20!1I ( K ) , PIl2iiI (K) ,PCH20 (K 1) ,PCH2 (K) ,K=1,8) 80 612 FORMAT ( 1H0/2X8H TUMP (C) 1X11II ACT COSFF 1120 2X1311 ACT COEFF H23X12H •1P(!120) SIIAW4X1111 P (H 2) SHAW2X13H PER CENT . 11203 X 12 Ii PER CENT 112// (0 2PF10. 0, 1P4E 1 5. 5, OP 2 F 15 .5) ) C 81 200 CONTINUE 82 100 CONTINUE 83 STOP 84 END $ D A T A 149 to to M to to to ro t: ~y c~- u~\ <n m ng rf cr cr* co — r-. 5c c-sj cr cr- r - r -fS' L l r - CJ i n rj- c i r - T - in r - tu N i n T- -- t - i - r -( N ( N ( N t N ( M ( N ( N t N o o c o o o o o to to to [.J i-"- I:: to u D i n r - i j a o - j ' ^ f ^ iTi iO pj o C' n f^r^-cr in ^ n N *o err - i n c o c r - ' C N - - — ;r r - r n i r o r ^ C D O M T ' i l I i I re to o i to ;o tu iTi ^ O IT fT C cf fM 'O n O O O Lf1 •~ o o «o '-O S D n X C M I N X f j C O r - fN CO n N - T y r -*— CJ CT1 O * <N vC fN' C N CN zt *~ CO X (N rt r - L", C \ 0 r-, r - cr o *- CN c\j o C O O ' r - . c c ' - r N f - . a - r ^ - ^ IT. r , r IT . r " c a o Z J cr o CN c -***• KT. r -• ^ ^ r ^ c o c o c r c r c r rv" fs] iN (N (N (N (N rj-. cr D ^ p •** fJ ^ ro * : i *r; i.T > ^ ' i o cr ro ro r - r-» r - o P i j i s j i c -*- n o CT «- -|- •£} O O O O r - i ~ r - t -cr r- -t o o co I D •j o M I c n r - tN lA li -! 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O y M if C CO o o o o o o o o o o o o o o o o o o o o o o c o o o o o o o o o o o o o o o o o o o o o o o o o to c-.: ro co to pa to to t~ r - -/l at »- rN CN r- o cT> •-* co d r^-T- J >J3 <yi *~ f - •— o o c o o o o o to co to to ui to to to vc B \£ n CM n in to cr o i— \o CN CN ( N C ' O - J M J O C O co ir. r-» o co in m c r c r c r c r . c r c r c r c r -o o o «— l— ---o o o c: o o o fc. to ro tl) to to to t l f-> <n '— c< r-j ul r-. r" Cr- i n CN r - o o <h o CN CO .11 o CN •n •.o ir ro CO T—~ -I r~ ro CN m CO CN r-j CN CN CN CN rsi CN O o o O O o o o to tO to to lO to CO r - CO r - T— cr- i~- •—-\D T -o : i '— p-O r - C ' i»- <-o O f*^  CN CN r - f\l vj r- r - o a: f i r— o r - CO in o CJ *~ ro m >-o r - CD o> er-CNI cn ro ro ro CN CN CN rs O o o o o o O o to to to tc to CO to O o r- -S) O m M vC CO CO r>j vO ZJ o CN r-"U tn ro o .-N r- o Cr w •si s£J O «e =3 O O o o o o O o O :c i 1 t I 1 1 1 1 to to ro CO to Iti CO >* r— cr in »— C-J H vD cr •~ o vD M rr- o CO u1^ CN UJ o- a« r - CN r— cr. M cr cr* cr cr X E- • • • t • • • O cr c-. cr cr <r cr < CN v£) r - o ^ CO CO in cr-a: C N ^~ o •o o ~y ro o •X) o- CN to in CD u <N cr I— r- in r~ *< o o rN r" u l CO o o o o o O o o tl- o o o o o o o o to o o o c o o o o o^ r-- o *-~ ro :T> in cr-o .c ^ c -> m o o cr CN co m » M o- — -n r~ O O O O O O O r -m M o c * •* c r - cc O (••  cO r i cr e j e r - r r O r - ' - ^ ' -r - o vo C N ;* cc C N co c cr. r— C N cr. cr !? cr <r ^ c- o oj c r i O ^ c r c r c r c r c r i c r i i :o co to to co to ro cr vo cr «JD -O *~ cr CTi v c c N O o r — c O r * n in r- o vo '-JO o O J fNt-'OC^-N-Oir--f . o »— r - in «— r - o IN CM 1.1 r* M r -to to co ro to to to c-j r - co o cr co (••-! o tn ^ c> j o r- «— u*> T~ r - o c o " N - : tu CN uj c> c r - 'JD cr fN r- cr C^CTCTC>CTC\CT>CO cr c- cr cr- cr cr cr cr to to J,T t i ; r»3 to t«.: c-1 r-. vc cr -n. r - o o r~ vn CN in cr o vfi o CN cc LT, r i cc r - c r T - i r a - c r r N C r m =y rj in »— co r> in cr co =r *— u*i *•'*> cr m r ^ - 3 - r - c n o c N c T h I O C - J sC n r ; h n r» n c> y r s i O r O < N C N « - » - » ~ r - t -I I I I I I I I I tO CO tO til |J] CO CO to t n ^ D o o o ^ c r - C i r (N L i -c n C >0 O ' j i co «*- co cc i". rt r-r - T - O O ' f i ' O ^ ^ C C r v ^ X C N C N C O f N C O h a? o ^ ro m cr - A ^ c . r o -N t - ; t r -r* o m N a C O C N . C O tr c r~ v£ y CN cr c r c ^ c r c r c r c r c r c o cr cr cr cr cr cr- o cr o o o o o o o o o to to CO to w to to to o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o CNCNfNfNCNCNrNrN r ^ c r i n ^ D f ^ c c c r o CNCNCNrsifNCNCNrN f n c r i n ^ o r ^ - c o c r o C N r s i r N f N f N C N f N C N n 3 '/mo r- c o o o to C J fN .-N CN r a CN rg r-j n c T i n ^ r - j O c r o 150 $ C O H P I I . E T I H E = 2 0 , P A G E S = '»5 C C 0 - H V E R S I O H 3 CONSTANT LOG F 0 2 C T H E C A L C U L A T I O N I S P E R F O R M E D A S S U M I N G BOTH I D E A L AND N O N - I D E A L C M I X I N G OF 112 AND 1120 (BOTH GASES AS SUMED TO BE H O N - 1 DEAL ) C C III NAM ING V A R I A B L E S T H E F O L L O W I N G P R E F I X E S WERE USED C (1 ) FC FOR F U G A C I T Y C O E F F I C I E N T S . C (2) F L FOR LOG 10 F U G A C I T I E S C (3 ) F FOR F U G A C I T I E S C (1 ) P FOR P R E S S U R E S C ( 5 ) PCT OR PC FOR PER C E N T OF A GAS S P E C I E S C (6 ) X FOR HOLE F R A C T I O N C (7 ) ACT FOR A C T I V I T Y C (8) AC FOR A C T I V I T Y C O E F F I C I E N T C (9) C L FOR THE LOG OF THE E Q U I L I B R I U M C O N S T A N T C C GAS S P E C I E S WERE NAMED BY FORMULA (EG 0 2 NOT OX FOR OXYGEN) C 1 DOUBLE P R E C I S I O N C 1 , C 2 , C 3 , D E X P , T E M P , D S Q R T , P T , F C H 2 L , PTATM 2 D I M E N S I O N P T ( 5 ) , F C H 2 0 ( 7 2 , 5 ) , F C H 2 ( 1 0 ) , F C H 2 L { 1 0 ) , T E M P C ( 1 0 ) , 1 C I .H20 ( 1 0 ) ,. F L O 2 ( 1 0 ) , F L 0 2 B ( 7 ) , F L H 2 O ( 1 0 ) , F L 1 1 2 ( 1 0 ) , 2 F 0 2 ( 1 0 ) , F H 2 O ( 1 0 ) , F H 2 ( 1 0 ) , P O 2 ( 1 0 ) , P H 2 0 ( 1 0 ) , P H 2 ( 1 0 ) , 3 P C T 1 1 2 0 ( 1 0 ) , P C T H 2 ( 1 0 ) , P H 2 ! i I ( 1 0 ) , P1120 NT ( 1 0 ) , U X 1 I 2 ( 1 0 ) , X H 2 O ( 1 0 ) , A C T H 2 ( 1 0 ) , A C T H 2 O ( 1 0 ) r F H 2 N I ( 1 0 ) , F H 2 O H I { 1 0 ) , 5 A C H 2 ( 1 0 ) , A C 1 1 2 O ( 1 0 ) , P C H 2 ( 1 0 ) , P C H 2 O ( 1 0 ) , PTATM (5) C 3 R E A D ( 5 , 5 0 0 ) (PT ( I ) , 1= 1 , 5) U 500 F O R M A T ( 5 F 1 0 , 0 ) 5 R E A D ( S , 5 0 1 ) ( ( F C H 2 0 ( K , I ) ,K= 1 ,72 ) ,1=1 , 5) 6 5 0 1 F O R M A T ( 0 F 1 0 . 0 ) c C CHANGE T O T A L P R E S S U R E . . • C 7 DO 100 1=1,5 C C S E T LOG F 0 2 - I N C R E M E N T BY 2.0 C 8 F L O 2 A = - 2 8.0 9 DO 300 L=1,2 10 F L O 2 A = F L O 2 A + 2.0 11 F L 0 2 B ( L ) = F L 0 2 A 12 F L 0 2 R T = F L 0 2 B (L )/2.0 C C S E T TEMP I N D E G R E E S K E L V I N . TEMP CAN EE V A R I E D B E T W E E N 5 6 3 . 1 5 AND C 1 1 8 3 . 1 5 D E G R E E S K E L V I N (10 DEGREE I N C R E M E N T S - MAX IMUM RANGE FOR C ANY RUN I S 100 D E G R E E S ) . CARD 15 MUST R E A D M=I+K WHERE I N T E G E R C I = ( T E M P - 5 6 3 . 1 5 ) / 1 0 . 0 ( 0 <= I <= 62 ) C 13 T E H P = 7 6 3 . 1 5 1U DO 1100 K=1,10 15 M=20<K 16 TEMP=TF.KP+10.0 17 TEMPC (K) - T E M P - 27 3 . 15 18 F L 0 2 ( K) = F L 0 2 B (L ) 19 F 0 2 (K) = 1 0 . 0 * * F L O 2 (K) 20 P 0 2 (K) =F02 (K) '21 F 0 2 R T = 1 0 . 0 + * F L O 2 R T C C C A L C U L A T E LOG K 1120 FROM LS Q F I T TO R O B I E AND WALDBAUM ( 1 9 6 0 ) 151 c 22 C L H 2 0 (K) = ~ 3 . 0 0 5 8 5 9 + 1 3 . 1 8 7 0 1 (1 0 0 0 . 0 / T E M P ) - 0. 12 1 5 8 2 * (1 000. 0/1 E SP ) * ( 11000.O/TEMP) 23 C H 2 O = 1 0 . 0 * * C L H 2 O (K) C C C A L C U L A T E FUG C O E F F FOR H2 FROM E Q U A T I O N OF SHAH AND WOHES (19 61) C 24 C1 = DEXP ( - 3 . 8 4 0 2 * ( T E M P * * 0 . 125 ) 1-0.5410 ) 25 C2 = DEXP ( - 0 . 1 2 6 3 * D S Q R T ( T E M P ) - 1 5 . 9 8 0 ) 26 C 3 = 3 0 0 . 0 *DSXP ( - 0 . 0 1190 l * T E M P - 5 . 9 4 1 ) 27 P T A T M ( I ) = P T ( I ) * 0 . 9 8 6 9 2 4 28 FC112L (K) = C1 * PTATM ( I ) - C 2 * P T A T M ( I ) * P TATM ( I ) + C 3 * ( D E X P { - P T A T M ( I ) /300.0 D-1.0) 29 F C H 2 (K) =DEXP ( F C H 2 L (K) ) C C S O L V E FOR F ( H 2 ) AND F (H20 ) C • . 30 D=PT ( I ) * F C H 2 ( K ) * F C H 2 0 ( H , I ) 31 E = C H 2 0 * F 0 2 R T * F C H 2 ( K ) +FCH20 ( M , I ) 32 F H 2 0 (K) = D*CH 2 0 * F 0 2 RT/E 33 P H 2 0 (K) = F l l 2 0 (K) / F C H 2 0 (ti, I ) 34 F H 2 ( K ) = D / E 35 P1I2 (K) - F H 2 (K )/FCH2 ( K) 36 F L H 2 (K) = ALOG 10 ( FH2 (K) ) 37 FL1120 (K) = A L O G 1 0 ( F H 2 0 (K) ) C C C A L C U L A T E T H E PER CENT OF EACH GAS S P E C I E S C 38 P C T H 2 (K) =PH2 (K) * 1 0 0.0 / P T ( I ) 39 P C T H 2 0 ( K ) = P H 2 0 ( K ) * 1 0 0.0 / P T ( I ) C •C B E G I N C A L C U L A T I O N FOR N O N - I D E A L M I X I N G OF 112 AND 1120 C 40 P S I = 0. 0 0 9 8 + ( 5 4 . 5 ) / T E M P K1 R=0.083147 12 Z = P T ( I ) <:PS 1 / ( R * T E M P ) 13' R A T F C - F C H 2 (K )/FC! I20 ( H , I ) «4 H=CLH2D ( K ) + A L O G 1 0 ( R A T F C ) + F L 0 2 R T C C C A L C U L A T E T H E MOLE F R A C T I O N OF 112 B I I T E R A T I O N C 1»5 XCORR=0.0 H6 XVAR=0.0 U7 ' 10 C O N T I N U E «8 X V A R = X V A R + X C O R R «19 G L O G = - H - ( 1 . 0-2. 0 *XVAR) * Z / 2 . 3 0 2 5 8 5 50 G = 1 0.0 * * G L O G 51 X N E W = G / ( 1 .0 + G) 52 XTEST=XNEV/ -XVAR 53 I F ( X T E S T . L E . 0 . 0 0 0 0 0 1 ) G O T O 11 54 X C O R R = X T E S T 55 GO TO 10 56 11 XH2 (K )=XNE " r f C C C A L C U L A T E R E M A I N I N G V A R I A B L E S C 57 X H 2 0 (K) = 1 . 0-XH2 (K) 58 AC 112 (K) =EXP (XH 20 (K) * X H 2 0 (K) * Z ) 59 AC 1120 ( K ) =EXP (XH2 (K) * X H 2 (K) * Z ) 60 A C T H 2 (K) =XH2 (K) * A C H 2 (K) 152 61 ACTII20 (K) = Xii 20 (K) *AC!I2 0 (K) 62 FH2N I (K) = A CT U 2 (K) *FCH2 (K) *PT (I) 63 FH20NI (K) = ACTH 20 (K) * FCI12 0 (M , 1} *PT ( I) 64 PH2NI(K)=XH2.(K)*PT(I) 65 PII2OU I ( K) = Xii 20 (K) * PT (I) 66 PCH2 (K) = XH2 (K) +100.0 67 PCH20 (K) =XH2C(K) * 100 . 0 68 4 00 p CONTINUE 69 WRITE (6, 600) PT(I) 70 600 FORMAT(1H1/25X1SH TOTAL PRESSDREF10.0,8H BARS) 71 WRITE (6, 602) (T EH PC (K) , FJ.02 (K) , FLU 20 (K) , FLI! 2 (K ) , F0 2 (K) , Fli 20 (K) , F112 1 (K) ,K=1,10) 72 602 FORMAT (1H0/2X8H TEMP(C)5X10H LOG FQ2)4X11H LOG F(H20)5X10H LOG F( 1H2J9X6H F (02)8X711 F(I120)9X6H F (H2) // (0PF10.0, 3F15. 5, 1P3E15.5) ) 73 WRITE (6, 6 04 ) (T EM PC (K) , P02 (K) , PII2D (K) , PH 2 (K) ,FCII2 (K) , PCTH20 (K) ,PCT 1112 (K) , K=1 , 10) 74 : 6 04 FORM AT (1 H 0/2X0 H TEMP (C) 9X6II P(02)3X7H P(H20)9X6H P (112)2X131! FUG CO 1EFF H22X13H PER CENT H203X12H PER CENT H2// (0PF10.0,1P3E15.5,0P3F1 25.5)) 75 WRITE (6, 605) 76 6 05 FORMAT (1H0 2X5 2H RECALCULATE ASSUMING NON-IDEAL MIXING OF 1(2 AND H 120) 77 WRITE (6,610) (TEH PC (K) ,XH20 (K) ,XH2 ( K) , ACTH 20 (K) , AC Til 2 (K) , FI! 20N I (K) 1 , FH2M I ( K) , K= 1 , 10) 78 610 FORM AT (1 H 0 2X8H TEMP (C) 1X141! MOLE FR AC H202X13H MOLE FR AC H22X13H 1ACTIVITY H203X12H ACTIVITY H23X12H F(!I20) SHAW 4X1 1 H F(H2) SHAW//(0 2PF10.0,2F15.7, 1P4E15.5)) 79 WRITE (6, 612) (TEMPC ( K) , ACH2 0 (K) , ACH2 (K) , PH20NI (K) , P112 NI (K ) ,PCH20 £K 1) ,PCH2 (K) ,K=1, 10) RO 612 FORMA.T(1H.0/2X8H TEMP (CL 1 X 14 H. ACT COEFF H202X13H ACT COEFF H23X12H 1P(H20) SHAW4X11H P(H2) SHAW2X1311 PER CENT H203X12H PER CENT H2//(0 2PF10.O,1P4 E15.5,0P2F15.5)) 81 Q 300 CONTINUE 82 ' 100 CONTINUE 83 STOP 84 EH D $DATA TYPICAL DATA DECK 5 0 0 . 0 1 0 0 0 . 0 0 . 167 0 . 1 87 0 . 3 5 5 0 . 3 8 0 0 . 5 5 5 0 . 5 8 6 0 . 7 1 1 0 . 7 2 5 0 . 8 0 3 0 . 8 1 2 0 . 8 6 4 0 . 8 6 9 0 . 9 0 " 0 . 9 0 9 0 . 9 3 3 0 . 9 3 5 0 . 9 5 0 0 . 9 5 1 0 . 105 0 . 1 16 0 . 226 0 . 2 3 9 0 . 3 7 9 o . u o o 0 . 5 3 3 0 . 5 5 2 0 . 0 6 2 0 . 6 7 8 0 . 7 6 2 0 . 7 7 2 0 . 0 3 1 o . e u o 0 . 0 8 5 0 . 8 9 0 0 . 9 2 1 0 . 9 2 5 0 . 0 8 B 0 . 0 9 8 0 . 188 0 . 2 0 2 0 . 3 18 0 . 3 3 4 0 . 4 5 8 0 . 4 7 7 0 . 5 88 0 . 6 00 C . 7 0 0 0 . 7 1 2 C . 7 8 6 0 . 7 9 7 0 . 8 5 6 0 . 86 3 0 . 9 0 4 0 . 9 0 3 0 . 0 8 2 0 . 0 9 2 0 . 17 it 0 . 1 87 0 . 2 9 4 0 . 3 1 1 0 . " 26 0 . 4 4 5 0 . 5 5 5 0 . 5 7 0 0 . 6 7 1 . 0 . 6 8 5 0 . 7 6 5 0 . 7 7 9 0 . 8 4 4 0 . 8 5 2 0 . 9 0 1 0 . 9 0 7 C . 0 8 3 0 . 0 9 3 0 . 1 7 2 0 . 1 85 0 . 288 0 . 3 05 0 . 4 16 0 . 4 3 4 0 . 5 4 3 0 . 5 5 9 0 . 6 6 4 0 . 6 7 8 0 . 7 6 3 0 . 7 8 1 0 . 8 5 8 0 . 8 6 7 0 . 9 2 6 0 . 9 3 2 0-H VERSION 3 1 5 0 0 . 0 2 C C 0 . 0 0 . 2 0 6 0 . 230 0 . 4 0 9 0 . 4 3 5 0 . 6 0 9 0 . 6 3 0 0 . 7 3 9 0 . 7 5 1 0 . 8 2 1 0 . 8 2 8 0 . 8 7 5 0 . 8 8 0 0 . 9 1 3 0 . 9 17 0 . 9 3 8 0 . 9 4 0 0 . 9 5 2 0 . 9 5 3 0 . 1 3 1 0 . 140 0 . 2 6 3 0 . 2 3 2 0 . 4 19 0 . 4 39 0 . 570 0 . 5 3 7 0 . 6 9 0 0 . 7 0 5 0 . 7 0 1 0 . 7 9 1 0 . 8 4 8 . 0 . 8 5 4 0 . 8 9 5 0 . 9 0 0 0 . 9 2 8 0 . 9 3 2 0 . 1 0 9 0 . 1 20 0 . 2 1 9 0 . 23 2 0 . 3 5 3 0 . 3 6 9 0 . 1 9 . 3 0 . 5 0 9 0 . 6 1 9 0 - 6 34 0 . 7 2 4 0 . 7 3 6 0 . 0 0 7 ' 0 . 0 15 0 . 8 7 0 0 . 3 7 7 0 . 9 1 3 0 . 9 17 0 . 1 0 1 C . 1 14 0 . 2 0 2 0 . 2 1 7 0 . 326 0 . 34 5 0 . 061 0 . 4 7 7 0 . 5 0 6 C . 6 0 1 0 . 6 9 7 C . 7 10 0 . 7 0 8 C . 7 9 7 0 . 0 6 0 0 . 8 6 7 0 . 9 1 2 0 . 9 1 7 0 . 102 0 . 1 13 0 . 1 9 9 0 . 214 0 . 3 1 9 0 . 3 3 7 0 . 4 5 0 0 . 4 6 6 0 . 0 7 5 0 . 5 9 0 0 . 6 9 2 C . 7 0 7 0 . 7 9 5 0 . 3 0 5 0 . 8 7 7 0 . 8 3 5 0 . 9 3 9 0 . 9 4 5 3 0 0 0 . 0 0 . 2 5 3 0 . 2 7 8 0 . 4 6 3 0 . 4 9 0 0 . 6 4 7 0 . 6 6 5 0 . 7 6 2 0 . 7 7 3 0 . £34 0 . 8 4 2 0 . 8 8 7 0 . 8 9 1 0 . 9 2 0 0 . 9 2 4 0 . 9 4 2 0 . 9 4 4 0 . 9 5 4 C . 9 5 5 0 . 1 6 0 0 . 1 7 5 0 . 3 0 1 0 . 320 0 . 4 5 9 0 . 4 7 8 0 . 601 0 . 6 1 7 0 . 7 1 6 0 . 7 2 9 0 . £00 0 . 8 0 8 0 . 8 6 1 . . 0 . 8 6 7 0 . 9 0 5 0 . 9 0 9 0 . 93 5 0 . 9 3 8 0 . 1 3 3 0 . 1 4 5 0 . 2 5 1 0 . 2 6 5 0 . 3 8 9 ' 0 . 4 0 5 0 . 5 2 5 0 . 5 4 2 0 . 6 4 7 0 . 6 6 2 0 . 747 0 . 7 5 9 0 . £24 0 . 8 3 3 0 . 8 83 0 . 8 3 8 0 . 9 2 2 0 . 9 2 6 0 . 123 0 . 136 0 . 2 3 2 " 0 . 2 4 3 0 . 3 6 1 0 . 3 7 3 0 . 4 9 2 0 . 507 0 . 6 1 5 0 . 6 2 9 0 . 7 2 1 • . 0 . 7 3 4 0 . 8 0 8 0 . 8 1 8 0 . £75 0 . 0 8 2 0 . 9 2 2 0 . 9 2 7 0 . 123 0 . 1 3 5 0 . 2 2 8 0 . 2 4 4 0 . 3 5 3 0 . 369 0 . 4 8 1 0 . 4 9 5 0 . 6 0 5 0 . 619 0 . 7 1 9 0 . 7 . 3 3 0 . £17 0 . 8 2 8 0 . 8 9 5 0 . 9 0 2 0 . 9 5 2 0 . 9 5 8 0 . 3 0 2 0 . 3 3 0 0 . 5 17 0 . 5 4 2 0 . 6 8 1 0 . 697 0 . 7 3 1 0 . 793 0 . 0 4 9 0 . £56 0 . 8 9 6 0 . 9 0 1 0 . 9 2 7 0 . 93 0 0 . 9 4 6 0 . 9 4 8 0 . 9 5 6 0 . 957 0 . 192 0 . 20 9 0 . 3 4 0 0 . 36 0 0 . 4 9 8 0 . 5 15 0 . 6 32 •0 . 6 5 0 0 . 7 3 9 0 . 7 5 2 0 . 8 19 0 . £25 C . 8 7 4 0 . £79 0 . 9 13 0 . 9 1 7 0 . 9 4 0 0 . 94 3 0 . 159 0 . 173 0 . 2 8 4 0 . 300 0 . 4 2 4 0 . 4 4 0 0 . 5 5 7 0 . 5 7 3 0 . 6 7 4 0 . 6 8 8 0 . 7 7 0 0 . 779 0 . 3 4 1 0 . £4 9 0 . 3 9 4 . 0 . £99 0 . 9 3 0 0 . 93 4 0 . 147 0 . 161 0 . 2 6 2 0 . 2 7 9 0 . 3 9 4 0 . 4 1 0 0 . 5 2 3 ' 0 . 5 3 9 0 . 6 4 3 0 . 6 5 7 0 . 7 4 7 0 . 757 0 . 3 26 0 . £35 0 . 8 8 8 0 . 8 9 5 0 . 9 3 2 ' 0 . 9 3 7 0 . 146 0 . 160 0 . 2 5 7 0 . 2 7 2 0 . 3 3 5 0 . 4 0 0 0 . 5 1 2 0 . 5 2 8 0 . 6 34 0 . 64 8 0 . 7 4 7 0 . 7 5 8 0 . 8 3 9 0 . £4 8 0 . 9 1 0 0 . 9 1 7 0 . 9 6 4 0 . 5 6 9 yi ui w m in (ji L T O i_n co ~ j cn i_n ir L.J to o O O O O O O O O O O ui L ~ m ui u". ui u~< u"1 L P ul O CO Cn Ul -P" ro o o o o o o o o o o o U~- Ul U' Ln Ul Ui U1 U> Ul '-'i o c: - J ^ Ji j : U w .4 o o o o o o o o o o o Ul U i Ui Ul Ui U". 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M ^ D c o - - J c n x r L j r o — » — » c n C O f D - J U J ^ O U l f r c n ^ r O co ~-> ui m -o ro ro _* co fo o to o K ~ i ui o tu W j r a- U" f ; -P - o O ir ui o cn ui ui P o >j w ro :TJ to co io ;o n to ro co o o o o o o o o o o to ro ro ro ro ro N ; ro to —• 1 5 5 APPENDIX 3_ H-O-S SYSTEM COMPUTER PROGRAMS Programs have been written to calculate the compositions of gas mixtures in the H-O-S system. Several versions of these programs are listed together with examples of data setups and output. Primary programs are designed to write output for a specified oxygen buffer at constant Ptotal a n d log f s 2 f o r 8 values of T (327-1027°C). Version A programs provide output at constant Ptotal a n ^ T ^ o r 8 values of log f s 2 (0.0 to -14.0). The data setup is identical for both primary and Version A programs. The range of any DO statement may be varied within the limits set by the DIMENSION statement to provide calculations for limited ranges of PtotalJ t a n d log f s 2 - The DIMENSION statement or the statement defining the increments used in the DO loops may be respecified i f greater versitility is needed. H-O-S Version 1 and 1A: The programs calculate the fugacities and partial pressures of H2, H20, SO, S02, S03, S20, H2S, and HS for values of log f o 2 defined by solid phase buffers at values of log f$ 2 from 0.0 to -14.0. Calculations assume ideal mixing of non-ideal real gases. Data have been compiled for pressures of 1, 500, 1000, 2000, and 3000 bars in the temperature range from 327-1027°C (Appendix 1). If fugacity coefficients are not available for a particular gas species the value 1.0 must be defined where appropriate in the data deck (see listing for examples). 156 H-O-S Version 2 and 2A: Version 2 and 2A programs have been simplified by considering only H2, H 2 O , S02, and H2S to be significant gas species for the range of log f Q and log f s 2 under consideration (Section 3.1). Comments for Version 1 are applicable in other regards. H-O-S Version 4 and 4A: The same gas species are considered as for Version 2 but log fjj is specified rather than log f o 2 - Values for log f j ^ must be calculated (0-H Version 1 or 2). The example listing uses data calculated for MI, WI, QFM, NNO, and HM buffers. It is possible to use log f ^ values calculated assuming either ideal or non-ideal mixing 'in the 0-H system. 157 SPILE TIHE=50,PAGES=175 H-O-S SYSTEM - VERSION 1 IN NAMING VARIABLES IN THE PROGRAM THE FOLLOWING RULES WERE FOLLOWED (1) FUGACITY COEFFICIENTS WERE PREFIXED BY FC (2) LOG 10 FUGACITIES WERE PREFIXED BY FL (3) FUGACITIES WERE PREFIXED BY F (4) PRESSURES WERE PREFIXED BY P (5) Til E PER CENT OF A GAS SPECIES WAS PREFIXED EY PCT (6) GAS SPECIES WERE NAMED BY FORMULA (EG 32 HOT OX FOR OXYGEN) DIMENSION PT (5 ) , FCH20(8,5), FCH2(3,5), FCH2S(0,5), FCHS(8,5), 1 FCS03(8,5), FCS02(8,5), FCS0(8,5) , FCS2(8,5) , FCS2D(8,5), 2 A (2) , B (2) , C (2) , BUF (2) , 3 CLSO(3), CLS02 (8) , CLS03(8), CLS20(B), CLH20(8), CLH2S(8), 4 C1.HS(8) , TEMPC(8), FL02(8) , FT.S2(8), FLSO(8), 1 :LS02(8), FLS03(8) 5 FLS20(8), FLH20(8), FL(12S(8), FLHS(8), FLH2(8) DIMENSION F02 (R) , rr.2(0), FSO(8), FS02(8), FS03(8) , FS20(8), 1 FH20(B), FH2S (8) , FHS (8), FH2(8), 2 P02(8) , PS2 (8) , PSO(B), PS02(8 ) , PS03 (8) , PS2C(8), PH20(8), 3 PH2S (8) , PUS (8) PH2 (8) DIMENSION PCT02 ( 3 ) , PCTS2 (0) , PCTSO(8) , PCTS02 (8) , PCTS03 (8) , 1 PCTS2D(8), PCTH20(8), PCTH2S(8), PCTH5(8), PCTH2(8), 2 FLS21 (7) , FS2 1 (7) READ (5, 500) (PT (I) , 1 = 1 , 5) FORMAT(5F10.0) READ (5, 501) ( (FCH20 (K, I) , K= 1 , 8 ) ,1 = 1,5) ( (FCH 2 (K, I) , K= 1, 8) ,1=1,5) ( (FCH2S(K, I) , K= 1 , 8 ) ,1=1,5) ( (FCHS (K, I) , K=1, 8) ,1=1 ,5) ( (FCG03 ( K , I) ,K=1,8) ,1=1,5) ((FCS02(K,I) , K=1,8) ,1=1,5) ((FCSO(K,I) ,K=1,8) ,1 = 1,5) ((FCS2(K,I) , K= 1, 0) ,1=1,5) ( (FCS20 (K , I ) ,K=1,8) ,1 = 1,5) 0) (CLSO (K) ,CLS02 (K) , CLS0 3 ( K ) ,CLS20 (K ) , CI. 1120 (K) , CLH2S (K) READ(5,501) R FA f) (5, 50 1) READ (5,50 1) READ (5, 501) READ(5,501) RFA D(5,501) R E A D (5 ,501) R FA D ( 5, 501) FORMAT(8F10 READ (5, 51 1) 1CLHS (K) ,K=1,8) FORMAT(7F10.0) READ (5, 5 I 2) (A (J ) , B (.1) ,C (J) , 3 = 1, 2) FORMAT(3F10.0) READ(5,513) (BU F (J ) , J= 1, 2) FORMAT(2A4) CHANGE TOTAL PRESSURE DO 100 1 = 3 , 5 CHANGE BUFFER DO 200 J = 1 , 2 FAC = -A (J) +C (J) * (PT (I) - 1 . 0 ) SET LOG F ( S 2 ) - INCREMENT BY - 2 . 0 (7 TIMES) F L S 2 2 = 2 . 0 DO 300 L=1,7 FLS22=FLS22-2.0 FLS2 1 (L) =F LS22 FLS2RT--FI.52 1 (L) / 2. 0 FS21 (L) =10.0**FLS21 (L) SET TEMP IN DEGREES KELVIN - INCREMENT BY 100.0 (8 TIMES) TENP = L>00.0 DO 400 K= 1 , 8 TF.KP=TF.MP+ 100.0 TEMPO(K)=TEMP-273.0 CALCULATE F(02) FROM AN EQUATION OF THE FORM (C (PT-1.0) - A)/T EH P +B FL02 (K) = F AC/TEM P+ B (J) FLO2 RT= FLO2 ( K J / 2 . 0 ' F02 (K) =10.0**FLO2 (K) P02 (K) --F02 (K) FLS2 (K)=FLS21 (L) FS2 (K) =FS21 (I.) PS 2 ( K ) =FS2 (K) /FCS 2 (K , I) CALCULATE THE" FUGACITIES OF SO, S02, 503, AND S 20 FLSO (K)=C LSO (K) + FLS2RT + FL02RT FSO(K)=10.0**FLSO(K) PSO ( K ) = FSO (K ) / FCS 0 (K , I) FLS02(K) =CLS02 ( K ) + FLS2RT + FL02 (K) FS02(K)=10.0**FLSO2 (K) PS 02 (K) =FS02 (K) / FCS02 ( K , I) FLS0 3 (K)=CLS03 (K ) + FLS2RT+3.0*FLO2RT FS03(K) =10.0**FLSO3 (K) P S 0 3 ( K ) = F S 0 3 (K)/FCS03 (K, I) FLS20 (K) =CLS20 (K) + FLS2 ( K) +FL02RT FS20 (K)-10.0**FLS2O(K) PS 20 (K) =FS20 (K ) / FCS 20 ( K, I) SET REMAINING VALUES TO ZERO IF THE SUM OF PRESSURES CALCULATED TO THIS POINT IS GREATER THAtf THE TOTAL PRESSURE (PT) SUM = PSD (K) +PS02 (K) +PS03 (K) +PS20 ( K ) +PS2 (K) +P02 ( K ) I F (PT( I ) -SUM) 10, 10,20 SOLVE FOR F(H2) (QUACKATIC EQUATION) AL 1 = CL1I20 ( K ) +FL02RT ft1=10.3**AL1 AL2=CLH2S ( K ) +FLS2RT A2=10.0**AL2 BL 1=CLH5 (K) +FLS2RT B1=10.D**BL1 D=A 1/FCH20 (K,I)+1.0/FC H2 ( K , I) + A 2/FC H2 S ( K, I) E=B 1/FC:1S (K, I) F=5UK-PT(I) KC0T=(-S+SQRT (2* S-4 . 0* D* F ) ) / (2.0*D) FH2 (K) =ROOT*ROCT IF (FH2 ( K ) ) 12, 12,22 FL II 2 ( K) = A LOG 10 (Fii 2 ( K ) ) PH 2 ( K ) =FH2 ( K ) /FCI12 (K, I) 159 70 SUKA=PH2 (K) + SIK1 71 I F (PT (I.) -SOMA) 11,11,21 C 72 10 FH2(K)=0.0 73 12 FLH2 (K) =0.0 7 4 PH 2 (K)=0.0 7 5 11 FLII20(K) =0.0 76 FLC2S (K) =0.0 77 FL1IS(K)=0.0 '78 FH2O(K)=0.0 79 F1I2S (K) =0.0 80 FHS(K)=0.0 81 PH2O{K)=0.0 82 PH 2S (K)=0.0 8 3 PUS (K) =0.0 84 POT H 20 (K) = 0 . 0 85 PCT H2S ( K) =0.0 86 PCTHS(K}=0.0 87 PCTH2(K)=0.0 88 GO TO 23 C C CALCULATE TH3 FUGACITIES OF H20, H2S, AND US C 89 21 FLH20 (K)=CLH20 (K)+FLH2 (K) +FL02KT 90 FH20(K) = 10.0**FI.!!2O (K) 91 P1120 (K) =FH20 (K)/FCH20 (K, I) 92 FL1I2S (K) =CLH2S (K) + FLH2 ( K) +FLS2KT 93 FH2S (K)=10.0**FLH2S(K) 9 4 PU2S (K) - FH2S (K) /FC1I2S ( K, I) 95 PLUS (K) = CL!:S (K) + FLH2 (K) /?.. O + FLS 2RT 96 FHS (K) = 1 0 . 0* *F LIIS (K) 97 PUS (K) =F1IS (K)/FCHS (K, I) C C CALCULATE THE PER CENT OF EACH GAS SPECIES C 98 PCTH20 (K) = PII2 0 (K ) *100.0/PT (I) 99 PCTK2 S (K) =PH2S (K ) * 100 . 0/PT (I) 100 PCT IIS (K) = PUS (K ) * 100 .0/PT (I) 101 PCTH2 (K) =Pli2 (K) * 100 .0/PT (I) 102 23 PCT02 (K)=P02 (K)* 100.0/PT(I) 103 PCTS2 (K) =P32 (K) * 100.0/PT (I) 104 PCTSO (K)=PSO (K)* 100.0/PT (I) 105 PCTS02(K) =PS02 (K)MOO.O/PT (I) 106 PCTSO3 ( K) = PS03 (K ) * 100 . 0/PT (I) 107 PCTS20(K) =PS20 (K)*1O0.0/PT (I) 108 400 CONTINUE C 109 WRITE (6, 600) PT (I) 1 10 600 FORMAT ( 1 H1/50X 15!I TOTAL PRESSUREF10.0,8H BARS/2X 1 4 H (OP SB X , HO 1S) ) 111 HRITE(b,601) BUF(J) 1 12 601 FORK A T ( 1 H02 X Vl ,811 BUFFER) 113 WRITE(6, 608) C (,1) ,A (J) , 3 (J) 1 14 608 FORM AT (1H 02X13 II LOG F(32) = (F8 . 5 , 10H '(P7-- 1. 0) -F9.1.10H J/TEKP +F5 1.2) 115 WRITE (6, 602) (T 3,1 PC (K) , FL02 (K) , FLS2 ( K) , FLSO (K) , FLSJ2 (F.) , FLS03 (K) , 1FLS20(K) ,FLH20(K) ,K=1,8) 1 16 602 FORMAT(1 HO/2 X8H V EH? (C) 5X10H LOG F(02)5X10H LOG F(S2)5X10H LOG F(S 10)4X1111 LOG F(S02)4X11H LOG F(S03)4X11H LOG F(S20)4X11H LOG F(H20) 2//(F10.0,7F15.5)) 160 117 S1UTE{6, 603) (T EM PC (K) ,FLH2S (K) , FLHS ( K) , V L H 2 (K ) , F02 ( K) , FS2 (K) , 1FS0(K) ,PS02 (K) ,K=1,8) 1 18 603 FORKAT ( 1 110/2 X8H T EM P (C) 4X1 11I LOG ?(H2S) 5X1 OH LOG F(I!S) 5X1011 LOG F( 1112)0X611 F(02)9X6"I F(S2)9XGll F(SO)U!T/H F (S02) // (OPF 1 0 . 0 , 3F 1 5 . 5 , 1 P 4E 215.5)) 119 WRITS (6, 60 4) (TEH PC (K) ,FS0 3 (K) ,FS20(K) ,FH20(K) ,PH2S(K) , r IIS (K ) ,FH2( IK) ,P02(K) ,K=1,8) 120 604 FORMAT (1H0/2X8H TEMP(C)8X7ll F (SO 3) 8X7H F (S20) 8X7H F(H20) 8X711 F (H2S 1)9X611 F(HS)9X6H F(il2)9Xbll P (02 ) // (0 P F1 0 . 0 , 1 P7 F. 15 . 5) ) 121 WRITE (6, 605) (T EM PC (K)• , P S2 (K) , PSO (K) , P SO 2 (K) , PSO 3 ( K) , P S20 (K ) , PI120 ( IK) ,PH2S(K) ,K=1,8) 122 605 FORMAT ( 1 H0/2X8H T EH P (") 9 X6H P(S2)9X6H P(SO)8X7H P(S02)8X7H P(S03)8 1 X71I P (S2D) 0X7H . P (1120) 8X7I1 P (112S ) / / (0 PF1 0 . 0 , 1 P7 115. 5) ) 123 WRITE (6, 606) (T EM PC (K) , PUS (K ) , Pi! 2 (K) , PC TO 2 (K),PCTS2(K) , P CTS 0 (K ) , PC 1TS02 (K) ,PCT303 (K) ,K = 1,8) 1,24 606 FORMAT (1 H1 / /// / 2 X 3 II TSHP (C) 9X6U P(HS)9X6H P (112) 3X12H PER CENT 023X 112H PEH CENT S23X12H PER CENT S02X13H PER CENT S022X13H PER CENT S 2 03//(OPF10.0,1P2E15.5,DP5F15.5)) 125 WRITE (6, 60 7) (TEH PC (K) ,PCTS2 0 (K) ,PCTH20 ( K) , PCIH2S (K) , PCT IIS (K) , PCT II 12 (K) ,K=1 ,8) 126 607 FORi1AT(1H0/2X8II T EMP (C) 2 X1 3II PER CENT S202X13H PER CENT II202X 13H P 1 ER CENT H2S3X1211 PER CENT 1153X1211 PER CENT I! 2//( F 10 . 0 , 5F 1 5. 5 ) ) C 127 300 CONTINUE 128 200 CONTINUE 129 100 CONTINUE 130 STOP 131 END $ DAT A T Y P I C A L DATA DECK H- •0 -S VERSIONS 1 I 1A 1.0 5 0 0 . 0 1 C 0 C . 0 2000 .0 3000 .0 0 . -"98 0 . 9 9 9 0 . 999 1.000 1.000 1. COO 1.000 1.000 0 . 7.21 0 .181 0 . 6 9 1 0 . 810 0 .879 , 0 . 9 2 3 0 . 9 1 7 0 .957 0 . 110 0 . 3 1 3 0 . 5 0 9 0 . 675 0 .789 0. 861 0 . 9 1 5 0 .9 50 0 . 1 1 0 0 . 2 1 2 0 .106 0 . 566 0 .707 0. 8 16 ' 0 . 893 0 . 9 1 6 0 . 1 10 0 . 2 3 8 0 . 3 9 5 0. 555 0 .699 0. 823 0 .911 0 .979 1. 000 1.000 1. COO 1.000 1 .000 1. 000 1.000 1 .000 1 .178 1. 119 1. 127 1.111 1 .098 1. 088 1 .079 1.072 1. 381 1.317 1. 269 1.233 1 .201 1. 182 1. 163 1. 1 K8 1. 896 1 .722 1.60 1 1.512 1. 115 1. 392 1 .319 1 .311 2. 572 2 . 2 3 3 2 . C07 1. 816 1 .726 1.6 33 1. 560 1. 50 1 1 .000 1.000 1. COO 1. 000 1.000 1. COO 1 . 000 1.000 0 . 782 0 . 8 8 7 0 . 937 0 . 963 0 . « 7 8 0. 986 0 . 9 8 7 0 .988 0 . 798 0 . 9 2 6 0 . 9 8 7 1.016 1.0 28 1. 03 2 1.03 3 1.031 1.111 1. 292 1.336 1. 339 1. 330 1.3 17 1.306 1. 29 1 1 .000 1.000 1.000 1. 000 1.000 1. COO 1 . 0 0 0 1 .000 1 .000 1 . 000 1. C 0 C 1 .000 1.000 1. 000 1 .000 1.000 1. 000 1.000 1.000 1.000 1.000 • 1 . c o o 1. 000 1.000 1 .000 1 .000 1. COC 1. 000 1 .000 1. 000 1. 000 1.000 1 . 000 1.000 1. COO 1.000 1.000 1. CCO 1. 000 1.000 1 .000 1 .000 1. COC 1 .000 1.000 • 1 .000 1.000 1.000 1 .000 ' 1 .000 1. 000 • 1.000 1.000 1. CCO 1.000 1. COO 0 . 1465 0 . 6 6 5 0 . 7 8 1 0. 870 0 .922 C. 952 0 . 9 6 7 0 .978 0 . 175 0 . 691 0 . 828 0 . 9 3 2 0.99 1 1. 02 1 1 . 037 1.016 0 . 805 1.089 1. 256 1.361 1.117 1.120 1 .115 1. 10 6 1 . 0 0 0 1.000 1.C00 1. 000 1.000 ' 1.C0O 1. 000 1.000 1 .000 1 .000 1. COC 1 .000 1.000 1. COO 1. 00 0 1.000 0 . 63 0 0 . 780 0. 880 0 . 929 0 . 9 57 C. 971 0 . 983 0 .987 0 . 670 0 . 8 3 2 0 . 9 5 5 1 . 0 1 1 1 .010 1. 055 1.060 1.060 1. 100 1. 300 1.139 1 .172 1. 169 1. 155 1 . 137 1. 120 1.000 1 . 0 0 0 1. CCC 1 . 000 1 .000 1.000 1 .000 1.000 • 1 .000 1.000 1. 000 1. OCO 1.000 1. COO 1. 00 0 1.000 1 .000 1.000 1. COO 1.000 1.000 .1 . CCO 1 . 000 1.000 1. 000 1.000 1.-000 1. 000 1.000 • 1. COO 1.000 1 .000 1.000 1.000 1. COC 1. 000 1.000 1.000 1.000 1.000 1 .000 1.000 1. COO 1 .00 0 1.000 1 . CCO 1. 000 1. OCO 1. o c o 1.000 1.C00 1.00 0 1.000 1. 000 •1 .000 1.0CO 0 .001 0 . 0 0 1 - 0 . 005 ' 0 . 0 2 3 0 .052 C. 099 0 . 1 66 0 .216 0 . 001 0 . 0 0 1 C . COS 0 .021 0 . 0 1 5 0. 085 0 . 112 0 .211 0 .001 0 . 0 0 2 0 .011 0 . 037 0 . 0 7 3 0. 121 0 . 1 9 7 0 . 283 0 . 0 0 1 0 .001 C. 028 0 . 075 0 .112 0. 233 0 . 3 52 0 . 179 1 .000 1.000 1. 000 1. 000 1 .000 1. COO 1 . 000 • 1 .000 1 .000 1. 000 1. CCO 1 .000 , 1 .000 ' 1. COO 1. 000 1.000 1. 000 1.000 1.000 1.000 1.000 1. CCO 1 .000 1.000 1 .000 1.000 1. CCC 1 .000 1.000 1. COO 1. 000 1.000 1 . 000 1. 000 1.000 1.000 1.000 1. CCO 1. 000 1.000 5. 290 2 7 . 7 1 1 3 1 . 3 9 7 12. U07 18.633 5 . 2 7 2 - 5 . 1 0 6 1. 571 2 3 . 207 2 5 . 6 6 1 '10. 197 15. 585 1. 168 - 1 . 3 2 5 1.0 32 19 .828 2 1.366 8. 766 13.289 3 . 338 - 3 . 6 8 1 3. 613 1 7 . 2 0 8 1 8 . 0 3 3 7. 119 1 1. 199 2 .687 - 3 . 1 8 1 3. 278 1 5 . 0 9 8 1 5 . 3 5 5 6 .312 10 .062 2 . 163 - 2 . 781 3. 0 01 1 3. 378 13. 173 5. 163 8 . 8 8 3 1.731 - 2 . 1 5 1 2 . 775 11 .916 1 1 .357 1. 730 7 .899 1.375 - 2 . 1 82 2 .531 10 .731 9 . 822 1. 10S 7 . 0 6 5 1. 070 - 1 . 9 5 2 2 5 7 3 8 . 0 9 . 0 0 0 . 0 9 3 7 1 2 1 9 3 0 . 0 9 . 36 0 . 0 1 5 7 8 C7N QFK1HN01 TOTAL PRESSURE 1000. B U S (OB SB X,HOS> QFM1 BUFFER L O G F ( 0 2 ) = ( 0 .09374 ( P T - 1 . 0 ) - 2 5 7 3 8 . 0 ) / r E M P • 9 . 0 0 TEflP (C) LOG F(02) LOG F(S2) LOG F(SO). LCG F(S02) LOG F(S03) LOG F(S20) LOG F(l!20) 327. - 3 3 . 7 4 0 5 9 - 4 .00000 - 13 .53029 - 8 . 0 2 9 5 9 - 2 1 . 21385 - 8 . 0 6 3 2 8 1 .32198 427 . - 2 7 . 6 3 4 7 8 - 4 . 0 0 0 0 0 - 1 1. 24639 - 6 . 4 2 7 7 8 - 17 .78816 - 7 . 3 2 0 3 9 2 .22741 527 . - 2 3 . 0 5 5 4 4 -4 .00000 - 9 . 4 9 572 • - 5 . 2 2 7 4 3 - 1 5 . 2 1 7 1 5 - 6 . 7 6 1 7 2 2 .02697 627 . - 1 9 . 4 9 3 7 1 - 4 . 0 0 0 0 0 - 8 . 13 336 - 4 . 2 8 572 - 1 3 .20757 - 5 . 3273 6 2 .83119 7 2 7 . - 16 .64U35 -4 .00000 - 7 . 0 4 417 - 3 . 5 4 6 3 5 - 1 1.6 1 1 52 - 5 .9801 7 2 . 8 3 3 2 8 827 . - 1 4 . 3 " , 303 - 4 . 0 0 0 0 0 - 6 . 15 2 52 - 2.9 3503 - 10 .29654 - 5 .69 352 2 . 9 2 6 9 6 9 2 7 . - 12 . 37029 -4 .00000 - 5 . 4 1 0 1 4 - 2 . 4 2 4 2 8 - 9 . 19842 - 5 . 4551 4 2 .95313 1027 . - 10.72641 - 4 . 0 0 0 0 0 - 4 . 7 3 2 2 0 - 1.99241 - 8 . 2 6 7 6 2 - 5 . 2 5 4 2 0 2 .96972 TEKP (C) LOG F(K2S) LOG F(i!S) LCG F(H2) F(02) F(S2) F(SO) F (S02) 327. 2 . 8 3 1 2 8 -7 . 40 636 - 0 . 4 4 0 7 2 1. 8 1725E-34 1. 000002 -04 2 . 6 28542-14 S . 341422 -09 127. 2 .62781 - 6 . 0 9 509 0 .45931 2 . 3 18562-28 1. C00OOE-04 5 . 670352 -12 3 . 7 34 39 2 -0 7 527 . 2 .20369 - 5 . 2 4 3 1 5 0 .36569 8. 80 166E-24 1. 000002-04 3 . 193612-10 5 . o - " 5 2 - 0 6 627 . 1 .73605 - 4 . 6 5 6 4 8 1.04905 3 . 20839E-20 1. C00002-04 7 . 34756E-09 5 . 179402-05 7 2 7 . 1. 30646 - 4 . 2 0 9 2 7 1. 14 346 2 . 2 6 3 0 5 E - 1 7 1. 000O0E-04 n _ 03287S-08 2 . 84 2182-04 8 2 7 . 0 .93UU8 - 3 . 8 5 3 7 6 1. 20048 4 . 86 3692-15 1. 00000E-04 7. 0 3 8 5 4 E - 0 7 1. 16 1362-03. 9 2 7 . 0 . 6 1 4 2 7 - 3 . 5 5 2 3 6 1 .23927 4 . 26300E-13 1. 0 0 0 0 0 E - 0 4 3 . 889 172-0 6 3 . 7 6 4 5 7 2 - 0 3 1027. 0 . 33792 - 3 . 3 1 B 0 4 .1. 26 79 2 1. 377542-11 1. COOCOE-04 1. 651 18E-0 5 1. 0176 32-02 TEMP (C) F (S03) F (S2C) ' F(H20) F(H2S) F(!iS) F f H2) P(02) 327. 6 . 1 ! 150E-22 8. 5440DE-09 2. 09882E 0 1 6 . 780752 02 3 . 9 2 3 1 9 2 - 0 8 3 . 624752-0 1 1. 817252 -34 427. 1. 628692 -18 t) . 7 8 2 0 0 E - 0 8 1. 63814E 02 4 . 244342 02 8. 03.353E-07 2 . 882762 00 2 . 3 1856 2 -28 527 . 6. 0 6 5 3 0 E - 1 6 1. 7 3 0 9 4 3 - 0 7 4 . 2 36 1 4E 0 2 1. 5 984 12 0 2 5 . 6 4 7 3 6 E - 0 6 7. 3 3988E 00 8. 80 16 6 2 - 2 4 627 . 6 . 2 0 0 6 1 E - 1 4 4 . 7 0 0 4 0 E - 0 7 6. 3 26882 0 2 . 5 . 4 4 56 IE 01 2 . 2 0 5 5 9 S - 0 5 1. 1 19562 0 1 3 . 208392-20 7 2 7 . 2 . 4 4 6 1 2 E - 1 2 1. 0467 12-06 7. 64 3352 02 2. 025152 01 6 . 176 30E-0 5 1. 39 14 2 2 0 1 2 . 263052-1 7 827 . 5 . 05 1922-11 2 . 025272 -06 8. 4 5 199E 0 2 8. 59955E 00 1. 400352 -04 1. 5866 32 01 4 . 86 35 9 2-1 5 9 27 . 6. 3 3 2 5 7 E - 1 0 3 . 506 3 6 E - 0 6 8. 976992 02 4 . 1 14032- 00 2 . 739 28E-0 4 1. 734902 0 1 4 . 26 3002-1.3 1027. 5. 399392 -09 5 . 5 5 9 2 3 S - 0 6 9. 3 26502 0 2 2 . 177332 00 4 . 307982-04 1. 85321E 01 1. 877542-11 TE.IP (C) P(S2) P(f,0) ?(S02) P(f.03) P(S2E>) P(H20) P (H2S) 327. 1. OOOOOE-01 2 . 6 2 8 5 4 E - 1 4 1. 394242-08 1. 286632-21 8 . 6 4 4 0 0 E - 0 9 1. 49916E 02 8. 497 18E 02 427 . 1. OOOOOE-01 5 . 6 7 0 3 5 E - 1 2 4 . 4 8 3 U 5 E - 0 7 2 . 346812-18 U . 7 8 2 0 0 E - 0 8 5 . 39343E 0 2 u . 58 352E 02 527 . 2 . OOOOOE-02 3 . 19361E-10 6. 2024&E-0 6 7 . 32524 2-1 6 1. 7 3 0 9 4 E - 0 7 8. 322472 02 1. 6 1946E 02 627 . 1 . 76 1 9 0 E - 0 3 7 . 3 4 7 5 6 E - 0 9 5. 12304S-05 6. 653022-14 , 4 . 7 0 0 4 9 E - 0 7 9. 37 3152 0 2 5 . 359S6E 01 7 2 7 . 2 . 2 2 2 2 2 E - 0 3 9 . 0 3 2 3 7 E - 0 8 2 . 7 3236K-04 2 . 468 33 2 -12 1 . 0467 1E-06 9 . 667392 02 1. 969992 01 8 2 7 . 1. 176472-03 7 . 0 3 3 5 4 E - 0 7 1. 1008 1E-03 4 . 948022-1 1 2 . 0 2 5 2 7 E - 0 6 9. 78240E 02 8. 3329CS 00 9 2 7 . 7. 0 4 2 2 5 E - 0 4 3 . 839 17E-06 3 . 55 148E-03 6. 106632-10 3 . 5 0 6 3 6 E - 0 6 9. 3109 12 0 2 9S2652 00 1027. H. 7 3 9 3 4 S - 0 4 1. 65 1 1 8 E - 0 5 - 9 . 6 0 0 2 9 E - 0 3 5 . 16242E-09 5 . 5 6 9 2 3 2 - 0 6 9. 8 17 37 E 0 2 2 . 1057 3E 00 OU5CO-ocnuifr<^i N J W N J N J f O f O W W -O-O-O-J-O-g-O-J o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o _> o CO U l o CO CO •o Ol u» U l f r to 1- _1 CO CO t o o o r o •o r o U l w U l U l —» * r fr _* as cn —» o CC fr cn r o U l r o CC ro U l *-" U l -oj v£) o ~ CO O o o o U l cn U i f r to IO U l CO - 0 -j cc O —> *£> u> o- U i _ J U l -o o CO ~D c U l 2^ U"- J O t o o CO c> —' l o U l fr fr CO O o CO -o cn U l f r U l *3 ro ro ro to t o ro ro ro -o •o; •o, -J *o -J -o n f r ro _j Cn ro U l CO U l CO -o fr ro cr. o u> o U l O •o o f r U l ro - J •o O cn U l •O U l U l ro U l U l U l U l U l —* CO CO U l o O cn _ J o t i ro ro CO to CO ro CO —» | i I 1 1 i I 1 o o o o o o o o f r f r f r U l U l cn CO _» •-O U l ro ro cn f r o cn —* O fr U l - J Co CO _ » f r . JO U l u * cc -O U l -o UJ ~1 o _> _> o o f r wJ C l o f r ;1 :o CO :o CO :*i CO s 1 CC o o o o o o o o to —» -* —* —» o o o - » o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o M 33 o o o o o o o o o .ro o o o o o o o o o o o o o o o o *-J o o o o o o o o o o o o o o o o ic cn u> —» o o o o o o o o o o o o o o o o o o o o c o o o o o —* —* o o o o o r o o o 0 0 — » N j f r O O O u i - j t o r o c o o o o o o o o o o o o o o o o o o ro • • * • « * 1 • 1 0 cn fr U l — V \C U l ro o s_ o o o o o o o o —; _j •£> fr U l o -4 _j ro -3 o o o o o o o o >-J fr — i ro U i CC CO CO cn o o o o o o o o - J U l cn o cr CO — i rr; o o o o o o o o o f r Ul cn o O •JD o ro o o o o o o o o o to o o o o o o o o o CO * < • * • 1 • • v: o o o o o o o o ••3 o o o o o o o o o o o o o o o o CO v_ U l —* o o o o o o cn cn Uj ~ « o o o ro o o o o o o o o o o o o o o o o o o o o o o o o o o o O O o o o o o o o o o o o o o o o o o o o £91 164 $C0(5 c PlL K TI HE = 5 0 , I?A GES = 1 V'" ll-O-S SYSTEM - VERSION 1 A 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 C C C I N H A M I N C F O L L O W E D V A R I A B L E S 111 T H E P R O G R A M T H E F O L L O W I N G R O L E S H E R E C 5 0 0 501 51 1 512 513 C C c c ( 1 ) F U G A C I T Y C O E F F I C I E N T S il "AX?. P R E F I X E D B Y F C ( 2 ) L O G 10 F U G A C I T I E S W E R E P R E F I X E D B Y F L ( 3 ) F U G A C I T I E S W E R E P R " F l /. E D B Y F ( 4 ) P R E S S U R E S W E R E P R E F I X E D B Y P ( 5 ) T H E P E R C E N T O F A G A S S P E C I E S W A S P R E F I X E D B Y P C T ( 6 ) G A S S P E C I E S W E R E N A M E D B Y F O R M U L A ( E G 0 2 N O T O X F O R O X Y G E N ) D I M E N S I O N P ' P ( 5 ) , F C H 2 0 ( 8 , 5 ) , F C H 2 ( 8 , 5 ) , F C ! ! 2 S ( 8 , 5 ) , F C H S ( 8 , 5 ) , 1 F C S 0 3 ( 8 , 5 ) , F C S 0 2 ( 8 , 5 ) , F C S O ( 3 , 5 ) , F C S 2 ( 3 , 5 ) , F C S 2 3 ( 8 , 5 ) , 2 A ( 2 ) , B ( 2 ) , C ( 2 ) , B U F ( 2 ) , 3 C L S O ( S ) , C L S 0 2 ( 8 ) , C L S 0 3 ( 8 ) , C L S 2 0 ( 3 ) , C L 1 1 2 0 ( 8 ) , C L H 2 S ( 8 ) , 4 C L H S ( 3 ) , T 3 , " 1 P C ( B ) , F L 0 2 { 8 ) , F L S 2 ( B ) , F L S O ( 8 ) , F L S 3 2 ( 8 ) ; F L S 0 3 ( 8 ) , 5 F L S 2 0 ( 8 ) , F L H 2 0 ( 8 ) , F L H 2 S ( 3 ) , F L H S ( 8 ) , F L H 2 ( 8 ) D I M E N S I O N F 0 2 ( 3 ) , F S 2 ( 8 ) , F S 0 ( 8 ) , F S 0 2 ( 8 ) , F S 0 3 ( 8 ) , F S 2 3 ( 8 ) , 1 F H 2 0 ( b ) , F H 2 S ( 8 ) , F H 5 ( 8 ) , F H 2 ( 8 ) , 2 P 0 2 ( 8 ) , P S 2 ( 8 ) , P S O ( 3 ) , P S 0 2 ( 8 ) , P S 0 3 ( 8 ) , P S 2 0 ( 8 ) , P H 2 3 ( 8 ) , 3 P H 2 S ( 8 ) , P H S ( 8 ) , P H 2 ( 8 ) D I M E N S I O N P C T 0 2 ( 8 ) , P C T S 2 ( 3 ) , . P C T S O ( 0 ) , P C T S 0 2 ( 8 ) , P C T S 0 3 { 8 ) , 1 P C T S 2 3 ( 8 ) , P C T H 2 0 ( 8 ) , P C T H 2 S ( 8 ) , P C T H S ( 8 ) , P C T H 2 { 8 ) , 2 F L 0 2 1 ( 8 ) , T E H P C 1 ( 8 ) R E A D ( 5 , 5 0 1 ) R E A D ( 5 , 5 0 1 ) . R E A D ( 5 , 5 0 1 ) R E A 0 ( 5 , 5 0 1 ) R K A D ( 5 , 5 0 1 ) R E A D ( 5 , 5 0 1 ) R E A D ( 5 , 5 0 1 ) R E A D ( 5 , 5 0 1 ) R E A D ( 5 , 5 0 1 ) F O R K A T ( 8 F 1 0 R E A D ( 5 , 5 1 1 ) 1 C L H S ( K | , K = 1 R E A D ( 5 , 5 0 0 ) ( P T ( I ) , 1 = 1 , 5 ) F O R M A T ( 5 F 1 0 . 0 ) ( ( F C H 2 0 ( K , I ) , K = 1 , 8 ) , 1 = 1 , 5 ) ( ( F C I I 2 ( K , I ) , K = 1 , 8 ) , 1 = 1 , 5 ) ( ( F C H 2 S ( K , I ) , K= 1 , 8 ) ,1= 1 , 5 ) ( ( F C H S ( K , I ) , K = 1 , 8 ) ,1 = 1 , 5 ) < ( F C S 0 3 ( K , I ) , K = 1 , 8 ) , 1 = 1 , 5 ) ( ( F C S 0 2 ( K , I ) , K = 1 , 8 ) ,1 = 1 , 5 ) ( ( F C S O ( K , I ) , K = 1 , 3 ) , 1 = 1 , 5 ) ( ( F C S 2 ( K , I ) , K = 1 , 8 ) , 1 = 1 , 5 ) ( ( F C S 2 0 ( K , I ) , K = 1 , 8 ) , 1 = 1 , 5 ) . 0 ) ( C L S O ( K ) , C L S 0 2 ( K ) , C L S O 3 ( K ) , C L S 2 0 ( K ) , C L H 2 3 ( K ) , C L H 2 S (K) , 3 ) F O R M A T ( 7 F 1 0 . 0 ) R E A D ( 5 , 5 1 2 ) ( A ( J ) , B ( J ) , C ( J ) , J = 1 , 2 ) F O R M A T ( 3 F 1 0 . 0 ) R E A D ( 5 , 5 1 3 ) ( B U F ( J ) , J = 1 , 2 ) F O R M A T ( 2 A 4 ) C H A N G E T O T A L P R E S S U R E D O 1 0 0 1 = 4 , 5 C H A N G E B U F F E R D O 2 0 0 J = 1 , 2 F A C = - A ( J ) + C ( J ) * ( P T ( I ) - 1 . 0 ) S E T T E B P I N D E G R E E S K E L V I N T E M P = 7 0 0 . 0 I N C R E M E N T B Y 100.0 165 26 DO 300 L = 3 , 5 27 T E M P = T E H P + 1 0 0 . 0 20 T E H P C 1 (L) = T E M P - 2 7 3 . 0 C C • C A L C U L A T E F ( 0 2 ) FROM AH E2U A l ' 10 !l OF THE FORM (C (PT - 1 . 0) - A ) / T E H P + B C 29 F L 0 2 1 (L) = F A C / T E K P+C ( J ) 30 F L 0 2 R T - F L 0 2 1 ( L ) / ? . . 0 C C S E T LOG F ( 5 2 ) - I i iCH E H E ?! T BY - 2 . 0 (8 T I M E S ) C 31 F L S 2 2 = 2 . 0 32 DO '100 K = 1 , 8 33 F L S 2 2 = F L S 2 2 - 2 . 0 314 FI.S2 (K) = F L S 2 2 3b F L S 2 S T = F L S 2 ( K ) / 2 . 0 36 F S 2 ( K ) = 1 0 . 0 * * F L S 2 (K) 37 P S 2 ( K ) =FS2 ( K ) / F C S 2 ( L , I ) 38 T E H P C ( K ) = TEr1PC1 (L) 39 F L O 2 ( K) = F L 0 2 1 (T,) UO F 0 2 (K) = 1 0 . 0 * * F L O 2 (K) 41 P 0 2 (K) =F02 (K) C C C A L C U L A T E T H E F U G A C I T I E S OF S O , S 0 2 , S 0 3 , AND S 2 0 C 42 F L S O (K| = CLSO. (L ) + F I . S 2 R T + F L 0 2 RT 43 F SO (K) = 1 0 . 0 * * F L S O (K) . 4 4 P S O ( K ) =FSO ( K ) / F C S O ( L , I) 1 5 F L S 0 2 (K) = C L S 0 2 (L) + F I . S 2 R T + F L 0 2 (K) 46 F S 0 2 ( K ) = 1 0 . 0 * * F L S O 2 ( K ) 47 P 5 0 2 (K) = F S 0 2 ( K ) / F C S 0 2 ( L , I) 48 F L S O 3 ( K) - C L S 0 3 ( L ) + F L S 2 R T + 3 . 0 * F L O 2 R T 49 F S 0 3 ( K ) = 1 0 . 0 * * F L S O 3 (K) 50 P S 0 3 ( K ) - F S 0 3 ( K ) / F C S O 3 ( L , I ) • 51 F L S 2 0 ( K ) = C L S 2 0 ( L ) * F L S 2 (K) + F L02RT 52 FS 20 ( K) = 1 0 . 0 * * F L S 20 (K) 53 P 5 2 0 (K) = F S 2 0 ( K J / F C 5 2 0 ( L , I) C C S E T R E M A I N I N G V A L U E S TO ZERO I F THE SUM OF P R E S S U R E S C A L C U L A T E D C TO T H I S P O I N T I S G R E A T E R THAN T H E T O T A L P R E S S U R E (PT) 5 4 S U « = P S 0 ( K ) +P S02 ( K ) + P S03 ( K) + P S 2 0 ( K ) +PS2 ( K) +P02 ( K ) 55 I F (PT ( I ) - S U M ) 1 0 , 1 0 , 2 0 C C S O L V E FOR F ( H 2 ) ( Q U A D R A T I C E Q U A T I O N ) C 56 2 0 A L 1 = C L H 2 0 ( L ) + F L 0 2 R T 57 A 1 = 1 0 . 0 * * A I . 1 50 A L 2 = C L I ' 2 S (L ) + F L S 2 H T 59 A 2 = 1 0 . 0 * * A L 2 60 Bl 1 = CL!!S (L ) + F L S 2 R T 61 B 1 = 1 0 . 0 * * B L 1 6 2 D = A 1/FC1I20 ( L , I ) + 1 . 0 / F C H 2 ( L , T ) + A 2 / F C H 2 S ( L , I ) 6 3 E = B 1 / F C H S ( L , I ) 64 F = SI)H - PT ( I ) 6 5 KOOT= (-F.+SQRT ( E * E - 4 . 0 * D * F ) ) / ( 2 . 0 *D ) 6 6 F H 2 ( K ) = R O O T * R O C T 6 7 I F (F!12 (K) ) 12 , 1 2 , 22 68 22 FL I i 2 (K) = A LOG 1 0 (FH 2 (K) ) 69 I'H 2 (K) =FH2 (K) / FCH 2 (L , I ) 166 70 SUKA=PH2 (K) + SUN 71 I F (PT ( I ) -5UMA) 11,11,21 C 72 10 FH2(K)=0.0 73 12 FLH2(K)=0.0 74 PH2(K) =0.0 75 11 FLU 20 (K) =0.0 76 FL!I2S(K) =0.0 77 FL1?S(K)=0.0 78 FI!20 (K) =0.0 79 FU2S(K)=0.0 e0 FILS (K) =0.0 81 PH2O(K)=0.0 82 P1I2S(K) =0.0 83 PUS (K)=0.0 81 PCTH20 (K) =0 . 0 8 5 PCFH2S (K) =0.0 86 PCTHS(K)=0.0 87 PCTH2 (K)=0.0 88 GO TO 23 C C CALCULATE THE FUGACITIES OF 1120, H2S, AND I'.S 89 21 FLH20 (K) =CLH20 (L) + FLH2 (K) +FL02RT 90 FH20 (K)=10.0**FLH2O (K) 9 1 P1I20 (K) - F1I2 0 (K)/FCI120 (L, I ) 92 FLH2S (K) =CLH2S (L) + FLH2 (K) +FLS2RT 93 FH2S (K) =10.0**FLH2S (K) 94 PH2S (K) =FH2S (K)/FCH2S (L, I) 95 FL IIS (K) =CLHS (L) + FL 112 (K) /2 . 0 + FI.5 2RT 96 FllS (K) =10. 0**FLtlS (K) 97 PHS (K) =FUS(K)/FCHS (L,I) C C CALCULATE THE PER CENT OF EACH GAS SPECIES 98 PCTH20 ( K) =PH2 0 (K) * 100 . 0/PT (I) 99 PCTII2S (K) =PH25 (K) * 100. 0/PT (I) 100 PCTHS (K) =PHS (K) * 100.0/PT (I) 101 PCTH2 (K) = PI!2 (K) * 100.0/PT (I) 102 23 PCT02 (K)=P02 (N) * 100.0/PT (I) 103 PCTS2 (K) =PS2 (K)* 100.0/PT (I) 101 PCTSO (K) =PS0 (K) * 100 .0 /PT (I) 105 PCTS02 (K)=PS02 ( K ) * 100.0/PT (I) 106 PCTS03(K) =PS03 ( K ) * 1 0 0 . 0 / P T (I) 107 PCTS20(K)=PS20 (K)* 100.0/PT (I) 108 400 CONTINUE ' C 109 WRITE(6, 600) PT (I) 110 600 FORK AT (1 [11 / 5 0 X 15 H TOTAL PRESS 3 R EF 10. 0 , 811 BARS/2X14H (OB SB X,IIO 1S)) 111 WRITE (6,601) BUF(O) 112 601 FORMAT (1 H02 XA'I , 8ll BUFFER) 113 WRITE (6, 608) C (J ) , A (J) , 3 (J) 114 608 FOI!KAT(1H02X13IILOG F(02) = (F8 . 5 , 10 II (PT- 1. 0) -F9.1,10H ) / T E « P +F5 1.2) 115 WRITE (6, 602) (TEHPC (K) ,FL02 (K) , FL32 ( K) , F LS 0 (K ) , FLSD2 (K) , FLS 03 (K) , 1FLS20 (K) ,FLH20 (K) ,K=1,8) 1 16 602 FORM A T (1 110/2 X8II r EtlP (C) 5X1 Oil LOG F(02)5X10H LOG F(S2)5X10H LOG F (S 10)4X1111 LOG F (502) 4X 1 1 il LOG F(S03)4X11H LOG F(S20)4X11II LOG F(!!20) 2 / / (F10 .0 ,7F15 .5 ) ) 167 117 WRITS (6, 603) (T EH PC (K) ,FLH2S ( K ) , FL HS (K) , F L I! 2 (K ) , F0 2 ( K ) , FS2 (K ) , 1FSO ( K ) , FS02 (K) , K= 1 ,8)' 118 603 FOR;iAT(1Ii0/2X8t! t E H P ( C ) 4X1 1H LOG F (1! 25) 5X1 OH LOG F (HS) 5X10:1 LOG F ( 1112)9X611 F (02) 9X611 F(S2)9X6H F(SO)8X71l F (502)// (OPF 10.0, 3F15.5 , 1P4E 215.5)) 119 WRITE (6, 60 4) (T EM PC (K) ,F503 (K) , FS20(K) , FH2 0 (K ) , TH2S (K) , FilS (K) , FH2 ( I K ) , P 0 2 ( K ) , K = 1 , 8 ) 120 604 FORHAT(1H0/2XH!I TEKP(C)SX7H F(S03)8X7H F (52.0)8X711 F(H20) 8X711 F (H2S 1)9X611 F(HS)9X6H F(ii2) 9X6II P (02) // (OP V 1 0 . 0, 1 P7 E 15 . 5) ) 121 WRITS (6, 60 5) (TEMPC (K) ,pr . 2 ( K ) , P50 (K) ,PS02 (K) , PS 03 (K) , PS2 0 (K ) , PH20 ( 1K) ,FH2S (K) , K = 1 ,8) 122 605 FORHAT(1H0/2X8!l T Eel P (C) 9 X6H P(S2)9X6!l P(S0)8X7H P(S02)8X7I1 P(S03)8 1X7H P(S20)8X7II P(H20)8X7ll P (!1 25 )//(0 PF 1 0 . 0 ,. 1 ?7 S 15 . 5) ) 1 2 3 WRITE(b,60 6) (TEM PC (K) ,PH5 ( K ) , PII2 (K) ,PCT02 (K ) , PCTS2 (K) , P CTS 0 (K ) , PC 1TS02 (K) ,PCTS03 (K) ,K=1,8) 124 606 FORKAT(1H1/////2X8!l TEMP (C) 9X5 H P(H5)9X6H P(H2)3X12H PER CENT 023X 112H PER CENT S23X12H PER CENT S02X1311 PER CENT S022X1 3H PER CENT S 2O3//(0PF1 0. 0, 1 P2F.15. 5,0P5F15.5 ) ) 125 WRITE (6, 607) (TEHPC (K) , PCTS2 0 ( K ) , PCT [120 (K) , PCT 11 2S (K) , PCTHS (K ) , PCTH 12(K),K = 1,8) 126 607 FORMAT (1 HO/2 X8H I EM P (C) 2X13 H PER CEUT S202X13H PER CENT I1202X1 3H P 1 ER CENT 112 -S3 X 1 2 H PER CENT H53X12H PER CENT H2//( F1 0 . 0 , 5F1 5 . 5 ) ) 127 300 CONTINUE 128 200 CONTINUE 129 100 CONTINUE 130 STOP 131 END $DATA TOTAL PRESSURE 2000. BARS (OB SB X.HOS) QFt! 1 BUFFER LOG F (02 ) = ( 0 .09374 (PT - 1 .0) - • 25738. 0 )/rEHP + 9.00 TEHP(C) LOG F(32) LOG F(S2) LOG F(SO) LOG F(S02) LOG F(S03) LOG F(S20) LOG F(K20) 627. - 19. 38956 0.00000 - 6 . 0 8 1 7 8 - 2 . 181 56 -1 1.05133 - 2 . 2 7 5 7 8 2.42129 627. - 19. 38956 - 2 . 0 0 0 0 0 - 7 . 0 8 1 7 8 - 3 . 18 156 - 12.05133 - 4 . 27578 2.9 3040 627 . - 19. 38956 - 4 .00000 - 3 . 0 3 1 7 8 - 4 . 1 3 1 5 6 - 13.0 5133 -6 . 27578 3.03759 627. - 19. 38956 -6 .00000 - 9 . 0 3 1 7 8 - 5 . 1 3 1 5 6 - 14.051 33 - 8 . 2 7 5 7 8 3.0499 1 627 . - 19 . 38956 - 8 .00000 - 10.03178 - 5 . I S 156 - 15.0 51 33 - 10. 27578 3.0511 6 627. - 19 . 389 56 - 1 0 . 0 0 0 0 0 - 1 1.08 178 - 7 . 1 8 1 5 6 - 16.05133 - 12.27578 3.0 5129 627. - 19.38956 - 12.00000 - 1 2 . 0 8 1 7 8 - 8 . 1 8 156 - 17.05133 - 14. 27573 3.051 30 627 . - 1 9 . 3 8 9 5 6 - 14.00000 - 1 3.08 178- - 9 . 1 8 1 5 6 - 13.05133 - 16 .27 57 7 3.05130 TEMP (C) LOG F(H2S) LOG F(HS) LOG F(H2) F (02) F (S2) F (2.0) F ( SO 2) 627. 3 .30407 - 2 . 8 7 2 4 7 0 .61707 4. 07796E-20 1 .0O0OOE 00 8. 283542-07 6. 583 13E-03 627. 2 .81318 - 3 . 6 1 7 9 1 1.12 617 • 4 . 077962-20 1 . C0000 2-02 8. 2836 42 -08 6. 583182 -04 627. 1.92037 - 4 . 5 6 4 3 2 1 . 2 3 337 4. 077962-20 1 .C00002 -04 S. 233642-09 6. 5 8 3 1 8 2 - 0 5 627 . 0.9 3269 - 5 . 5 5 8 1 6 1 .24569 4 . 077962-20 . 9 . 9 9 9 9 9 2 - 0 7 8. 2636 42-10 5 • 5 8 3 1 8 2 - 0 6 627. - 0 . 0 6 6 0 6 - 6 . 5 5 7 53 1. 24694 4. 07796E-20 1 . 00000 2-03 8. 2836 4 2-11 6. 5 S 3 1 3 E - 0 7 627 . - 1 . 0 6 59 3 - 7 .55747 1 .24707 4 . 077962-20 1 . 0 0 0 0 0 2 - 1 0 3. 263642-12 6. 583182 -08 627. - 2 . 0 6 5 9 2 - 8 . 5 5 7 4 6 1. 24708 4. 07796E-20 1 . 0 0 0 0 0 2 - 1 2 8. 283642-13 6. 58 318E-09 627 . - 3.06592 - 9 . 5 5 7 4 6 1.24708 4 . 077952-20 1 . 000002 -14 8. 283&4E-14 6. 5S31C2-10 TEHP (C) F(S33) F (S20) F(i!20) F (H2S) F(HS) F (32) ? ('J 2) 627 . 8. 88524E -12 5. 299 332-03 2. 63807E 02 2. O1403E 03 1 . 3 4 1 3 2 2 - 0 3 4. 140632 00 4. 077962-20 627. 8 . 8 3 5 2 5 E - 1 3 5. 299 33E-0 5 8. 51915E 02 6. 5 0 39 22 3 2 2 . 4 10 39E-0 4 1. 337 1 42 0 1 4. 077962-20 627. 3 .885242-1 4 5. 2 9 9 3 3 2 - 0 7 1. 09040E 03 8.32464E 01 2 . 726992-05 1. 7 1 1452 0 1 4 . 07796 2-20 627 . 8. 885242-1 5 5. 29933E-09 1. 1 2 179 E 0 3 3. 564262 00 2 . 76 59 5 2-0 6 1. 760722 01 4. 077962-20 627. 8 .8U524E -16 5. 299 3 3 2-11 1. 1 2502E 03 8. 588972-01 2 . 7 6 9 9 4 2 - 0 7 1. 765302 01 4. 077962-20 627 . 8. 8 8 5 2 « E - 1 7 5. 299 3 3E-13 1. 12535E 03 8. 59 1462-02 2 . 770342 -08 1. 766 312 0 1 4 . 077962-20 627. 3. 885242-1 8 5. 299 3 32 -15 1. 1 25 3HE 0 3 a. 59170E-03 2 . 770392 -09 1. 76636E 01 4. 077962-20 627. 8. 88524E-.19 5. 29941E -17 1 - 125 33E 0 3 8. 59 1722-04 2 . 7 7 0 3 8 2 - 1 0 1. 766 37 2 0 1 4 . 0779b2-20 TEMP(C) P(S2) P(SO) P (S02) P (S03) • P(S20) P (K20) ? (!!2S) 627 . 2 .70270E 01 8. 28 36 4E -0 7 4. 472262 -03 6. 433922-12 5 . 29933E-03 • 4. 660902 02 1. 5 04 132 0 3 627. 2 .70270E -01 8. 23364E-0B 4 . 47 226S-04 6. 4 3392E-1 3 5 . 299 33E -05 1. 5 05 15E 0 3 4 . 85729E 02 627. 2 . 7 0 2 7 0 E - 0 3 8. 2S364E-09 4. 47 227E -05 6. 4 3 3922-1 4 5 . 2 9 9 3 3 2 - 0 7 1. 926502 0 3 6. 2 1706 2 0 1 627. 2 . 7 0 2 7 0 E - 0 5 8. 28 364E-10 4 . 47227E -06 6. 4 3 3 9 2 E - 1 5 5 . 2 9 9 3 3 2 - 0 9 ' 1. 981962 03 6. 39601E 00 627. 2 . 7 0 2 7 0 2 - 0 7 8. 28364E-11 4. 4 7 2 2 7 E - 0 7 6. 4 3 3922-1 6. 5 . 299332 -11 1. 987672 03 6 . 4 14 462-01 627 . 2 . 7 0 2 7 0 E - 0 9 8. 28364E-12 4. 47227E -0S 6. 433922 -17 5 . 2 9 9 3 3 2 - 1 3 1. 983252 03 6. 4 16 322-02 627. 2 .70270E -11 8. 23364E -13 4. 47227E -09 6. 43392E -18 5 . 2 9 9 3 3 2 - 1 5 1. 98831E 03 6. 4 16502-03 627 . 2 . 7 0 2 7 0 E - 1 3 8. 28364E -14 4 . 47227E-10 6. 4 3 39 2 E-1 9 5 . 2 9 9 4 1 E - 1 7 1. 98831E 03 6. 4 16522-04 o ^ c r c r o ^ c r c r > c r . c r > o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o r o o o o o o o o c n o o o v O < - n c n o _ » cc c x; ji o u) w ITJ C=J f-. tr-i M a ti H i i i i i i • o o o o o o o . CO • *3 vO NJ O -O Ul L O v. 4= O t\) L O H3 —» _ » cn tsj Ul O Ln tU w -J *r in Ln *-J CD —* {= Ui Cr. "* U> cr. o O T3 rt PO rO o o o O O O C u> ni 2: o o O O —k N J N i -3 o o O U J (_> <JO o o o •^J tvj -D X cn o o o CC U"' -C K> M —» -J o y^J -J *- 01 g\ C i 01 C M ^ w e C J W C r C D s J . p _ , u » C D N J N J - ' OD vD LTI LO LO O C> O _* O _» M c i C1! r=i t q :<j i-d o o o o o o o o o o o o o o o o o o o 1 -> o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 0 0 0 0 0 0 — . - j O O O O O O O - * o o o o o o o o O O O O O O — . ( j i O O O O O O L O - * O O O O O - J I J I L O O O O O O - f r — « t _ n o o o o o o o o Ul Ul Ul ui Ul I.H r: -* CO CO 03 W K cr- c w •n- fr *7 LO N J m ro cr _» j O NJ J vO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O o o o o o o o o o c o o O O O \) O O O O O O N J f s J O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 691 1 7 0 SCOHPlLE TlME=50,PAGES=2G0 C C H-O-S CALCULATION - SIMPLIFIED VERSION 2 C IH NAMING VARIABLES IN THE PROGRAM THE FOLLOWING RULES HIRE C FOLLOWED C (1) FUGACITY COEFFICIENTS WERE PREFIXED EY FC C (2) LOG 10 FIIGACITV.ES WERE PREFIXED BY FL C (3) FUGACITIES WERE PREFIXED BY F C (4) PRESSURES WERE PREFIXED BY P C ( 5 ) THE PER CENT OF A GAS SPECIES WAS PREFIXFC BY PCT C (6) GAS SPECIES WERE NAMED 13Y FORMULA (EG 02 HOT OX FOR C OXYGEN) C 1 DIMENSION PT(5) , FCH20 (8 ,5) , FC!I2(8,5), FCH2S(8,5), FCS02(8,5) , 1 F C S 2 ( 8 , 5 ) , A ( 5 ) , B (5 ) , C (5) , B!1F(5), 2CLS02(8), CLH2O(0), CLH2S(8), 3TEKPC{8), FL02(8), FLS2(8) , FLS02{8), FLH20(8), FLf!2S(8), FLII2(8), 4F02 (8) , FS2(8) , FS02(8), FH20(8), F l i 2S (8 ) , F112(8), 5P02 (8) , PS2(8), PS02(8), FI120(8), PH2S(8), PH2(8) 2 DIMENSION PCT02(8), PCTS2(8), PCTS02|8), PCTH20(8), PCTH2S{8), 1PCTH2(8), FLS2 1(7), FS2 1(7) C 3 READ(5,500) (PT (I) , 1=1 ,5) 4 500 FORMAT (5 F 1 0 . 0) 5 BEAD(5,501) ( (FCH20 (K, I) ,K = 1,8) , 1=1, 5) 6 RERD(5,501) (. (FCH2 (K, I) ,K=1 ,8) , 1=1 ,5) ' 7 READ(5,501) ( ( FCH2S ( K , I) ,K= 1, 8) , 1= 1, 5) 0 READ(5,501) ((FCS02 (K, I) ,K=1 ,8) ,1=1,5) 9 READ(5,501) ( ( FCS2 (K,I),K= 1,8) , 1=1,5) 10 501 FORMAT (8F10.0) 11 READ (5,511) (CLS02 (K) ,CLU20(K) ,CLH2S (K) ,K=1,0) 12 5 11 FOR I'i AT (3 F1 0 .0) 13 READ (5,512) (A (J) , B (J) , C (J) , J= 1, 5) 14 512 FORMAT (3F10.0) 15 READ(5,513) (BU F (J) , J = 1,5) 16 513 FOR HAT (5A4) C C CHANGE TOTAL PRESSURE C 17 DO 100 1=4,5 C C CHANGE BUFFER C 18 DO 200 J = 3 , 5 19 FAC=-A (J) +C (J) * (PT (I) - 1. 0) C C SET LOS F(S2) - INCREMENT BY - 2 . 0 (7 TIMES) C 20 FLS22=-2.0 21 DO 300 L=1,7 22 FLS22=FLS22-2.0 23 FLS21 (L)=FLS22 24 FLS2RT=FLS21(L)/2.0 25 FS21 (L)=10.0 * *FLS21 (I) C C SET TEKP IN DEGREES KELVIN - INCREMENT BY 1 0 0 . 0 (8 TIMES) C 26 TEHP=500.0 27 DO 4 00 K=1,8 28 TEMP=TEHP+100.0 171 29 TEHPC (K)=TEHP-273.0 C C CALCULATE F(02) FROM AN EQUATION OF THE FORM (C(PT-1.0)-A)/TENP to C 30 FL02 (K)=FAC/TEMP+B (J) 31 FL02RT = FL02 (K)/2.0 32 . F02 (K) = 10.0**FL02 (K) 33 P02 (K)=F02 (K) 31 FLS2 (K)=FL52 1 (L) 35 FS2 (K) = FS2 1 (L) 36 PS2 (K) ~"FS 2 (KJ/FCS2 (K, I) C C CALCULATE THE FUGACITY OF S02 C 37 FLS02 (K)-CLS02 (K) +FLS2RT + FL02 (K) 38 FS02 (K) = 10.0**FLSO2 (K) 3 9 PS02 (K) =FS02 (K) / FCS02 (K , I) C C SET REMAINING VALUES TO ZERO IF THE SUM OF PRESSURES CALCULATED C TO THIS POINT IS GREATER THAU THE TOTAL PRESSURE (PT) C UO SUM=PS02 (K)+PS2 (K) +P02 (K) 41 IF (PT (I)-SUM) 10, 10,20 C C SOLVE FOR F (112) C 42 20 AL1 = CLH20 (K)+FL02RT 43 A1=10.0**AL1 44 AL2 = CLH2S (K)+FLS2RT 45 A2=10.0**AL2 4 6 D=A1/FCH20(K,1) +1.0/FCH2 (K,1)+A2/FCH2S (K,1) 47 F=SUH-PT (I) 4 8 FH2 (K)=-F/D 49 FLH2 (K)=ALOG10 (FU2 (K)) 50 PH2 (K)=FH2 (K)/FCH2 (K,I) - ' 51 SUHA=PH2 (K)+ SIJH 52 IF (PT(I) -5UMA) 11,11,21 C 53 10 FLH2(K)=0.0 54 FH2(K)=0.0 55 PH2(K)=0.0 56 11 FLH20 (K)=0.0 57 FLH2S (K)=0.0 58 FH2O(K)=0.0 59 FH2S(K)=0.0 60 PH2O(K)=0.0 61 PH2S (K)=0.0 62 PCTO2(K)=0.0 63 PCTS2 (K)=0.0 64 PCTS02 (K)=0.0 65 PCTH20 (K)=0.0 66 PCTH2S (K)=0.0 67 PCTH2(K)=0.0 68 GO TO 400 C C CALCULATE THE FUGACITIES OF H20 AND H2S C 69 21 FLH20 (K)=CLH20 (K) +FLH2 (K)+ FL02RT 70 FH20 (K)=10.0**FLH2O (K) 71 PH20 (K)=FH20 (K)/FCH20 (K,I) 172 72 FLII2S ( K ) =CLH2S(K) +FLH2 (K)+FLS2RT 73 FH2S ( K ) = 1 0 . 0 * * F L H 2 S ( K ) 74 PH25 (K)=FH2S (K)/FCH2S ( K , I ) C C CALCULATE THE PER CENT OF EACH GAS SPECIES C 75 PCT02 (K)=P02 (K)* 100.0/PT (I) 76 PC TS2 (K)= PS 2 (K) * 10 0.0/PT (I) 77 PCTS02 ( K ) = PS02(K) * 100.0/PT (I) 78 PCTH20 (K)=PH20 (K) * 100.0/IT (I) 79 PCTH2S (K)=PH2S(K)* 100.0/FT (I) 80 PCTH2 (K)=PH2(K)* 100.0/PT (I) 81 4 00 CONTINUE C 82 WRITE (6,600) PT (I) 83 600 FORV:AT (1 H 1/5OX 1 511 TOTAL PRESSUREF10. 0, 8H BARS/2 X 1 4 H (OB SB X, HO 1S)) 84 WRITE (6,601) BUF(J) 85 601 FORMAT (1H02XA4,7H BUFFER) 86 WRITE (6, 608) C (J) , A (0) , B (J ) 87 608 FORMAT (1H02X13 FLOG F(02) = (F8.5,10H (PT- 1.0) -F9.1.10H )/TEMP +F5 1.2) 88 WRITE (6,602) (TEMP C (K) , FLO 2 (K) , FLS2 (K ) , FLSO 2 (K) , FLH 2 0 (K) , FL 112S (K) , 1FLH2 ( K ) ,K=1 ,8) 89 602 FORM AT (1110/2X8 F TEHP(C)5X10H LOG F (02)5X1011 LOG F{S2)4X11H LOG F (S 102)4X1111 LOG F(H20)4X11H LOG F(H2S)5X101I LOG F ( H2)// (F 10 . 0 , 6 F 1 5. 5) 2) 90 WRITE (6, 603) (TEMPC (K) ,FC2 (K) , FS2 (K) , FSC2 (K) , F 1120 (K) , FH2S (K ) , FH2 (K 1 ) ,K = 1 r 8 ) 91 603 FORMAT (1H0/2X8H TEMP(C)9X6H F(02)9X6H F(S2 ) 8 X 7 E F(S02)8X7H F(H20)8 1X71! F(II2S)9X6H F (112) // (OFF 10.0, 1P6E1 5.5) ) 92 WRITE (6,6 04) (TE'IPC ( K ) , PC2 (K ) , PS2 (K) , PS 02 (K) , P K20 ( K ) , PH2S (K) ,PH2 ( K 1),K=1,8) 93 604 FORMAT (1H0/2X8H TEMP(C)9X6H F(02)9X6Il F(S2)8X7F. P(S02)8X7H P(H20)8 1X7H P (112S) 9X6H P (II2) // (OFF 10 . 0 , 1P 6E 1 5. 5) ) 94 WRITE (6, 6 05) (TE!1PC ( K ) , PCT 0 2 (K) ,PCTS2 (K) , PCTS02 ( K ) , PCTH20 (K ) , PCT 112 1S(K) ,PCTH2 ( K ) ,K=1 , 8) 95 605 FORMAT (1H0/2X8H TEMP (C) 3 X 1211 PER CENT C23X12I1 PER CENT S22X13H PER 1 CENT S022X 13H PER CE NT H 20 2X 1 311 PER CENT H2S3X12I1 PER CENT H2//(F .210.0,6F15.5)) C 96 300 CONTINUE 97 200 CONTINUE 98 100 CONTINUE 99 STOP 100 END SDATA T Y P I C A L EATA DECK H - O - S VERSIONS 2 5 2A 1.0 500 .0 • 1C0C.0 2000.0 3000.0 0 .998 0 .999 0. 999 1. 000 1.000 1. COO 1.000 1.000 . 0 . 2 2 4 0.481 - 0.691 0 .810 0.879 0.923 0 .947 0 .957 0 . 1 4 0 0 . 3 1 3 0.509 0. 6 75 0.789 0. 864 0 .915 0.9 50 0 . 1 1 0 0 .242 0.4 06 0. 566 0.707 0.8 16 0. 893 0 .946 0 . 1 1 0 0 . 2 3 8 0.3 95 0. 555 0. 699 0. 82 3 0.914 0.979 1.000 1.000 1.C00 1.000 1.000 1. COO 1.000 1.000 1. 178 1. 149 1. 127 1.111 1.098 1. 038 1.079 1.072 1. 384 1.317 1. 269 1.233 1.204 1. 182 1. 163 1. 148 1. 896 1. 722 1.601 1.512 1. 445 1.392 1. 349 1.314 2. 572 2. 233 2. C07 1. 846 1 .726 1.633 1.560 1. 50 1 1.000 1.000 1.C00 1.000 1.000 1. COO 1.000 1.000 0 . 782 0 . 8 8 7 0. 937 0. 963 0.978 0. 936 0. 987 0.9B3 0. 798 0 .926 0. 987 1.016 1.028 1. 032 1 .03 3 1.034 1.14 1 1. 29 2 1.336 1.339 1.330 1.317 1.306 1.291 1.000 1 .000 1.000 1.000 1.000 1. COO 1. 000 1.000 1.000 1.000 1. ccc 1.000 1.000 1. COO 1. 000 1.000 0 . 6 3 0 0 . 7 8 0 0 .080 0. 929 0.9 57 C. 974 0.983 0 .987 0. 670 0 .832 0.955 1.011 1.040 1. 055 1.060 1.060 1. 1 00 1. 300 1.4 39 1. 472 1. 469 1. 455 1.437 • 1.420 1.000 1.000 1. COO 1.000 1 .000 1. 000 • 1.000 1.000 1. 000 1.000 1. 000 1.000 1.000 1. COO 1. 000 1.000 0.001 0 .00 1 0. C05 0.023 0.052 0. 099 0. 166 0 .246 0. 00 1 0.00 1 0. 005 0.021 0 .045 C. 085 0. 142 0.211 0 .00 1 0.002 0.011 0 .037 0.073 0. 124 0 .197 0 .283 0.001 0 .004 0 .028 0 .075 0 . 142 0. 233 0 .352 0.479 27. 711 18.633 5.272 2 3 . 2 0 7 15 .585 4 .168 19.828 13.289 3 .338 17.208 11.499 2.6 87 1 5. 098 10.062 2. 153 13.378 8 .883 1.734 11.946 7.899 1.375 10.734 7 . 0 5 5 1.070 29260 .0 8.99 0.061CO . 27215 . 0 6. 57 0 .05500 25718. 0 9 .00 0 .09374 2 4 9 3 0 . 0 9 . 36 0. 04578 24912 .0 14.41 O.C19 MI 1WI 1QFHIN NO 1 tin 1 TOTAL PRESSURE 2000. BASS (OB SB X,ROS) QFM1 BUFFER LOG F (02) = ( 0 .09371 (PT- 1. 0) - 2 5 7 3 8 . C ) / T E K P • 9 . 00 TEMP (C) LOG F (02) LOG F (S 2) LOG F (S 02 ) LOG F (K20) LOG F (H2S ) LOG F (H 2 ) 3 2 7 . - 3 3 . 58135 - U . 0 0 0 0 0 - 7 . 87335 1 .78577 . 3 . 2 1 6 9 5 - 0 . 0 5 5 0 5 1 2 7 . - 2 7 . 50087 - 1 . 0 0 0 0 0 - 6 . 29387 2. 53 6 93 2. 87033 0 . 7 0 2 3 8 5 2 7 . - 2 2 . 93826 - 1 . 0 0 0 0 0 - 5 . 11026 2 .86657 2. 3 817 0 1 .01670 6 2 7 . - 1 9 . 3 8 9 5 6 - 1 . 0 0 0 0 0 -1 . 18156 3 .03759 1. 92037 1 .23337 7 2 7 . -1 6. 55060 - 1 . 0 0 0 0 0 - 3 . 15260 3. 11158 1. 51787 1 .35187 827 . - 1 1 . 22783 - 1 . 0 0 0 0 0 - 2 . 81 983 3 .20596 1. 1 7087 1.13687 9 2 7 . - 1 2 . 292 18 - 1 . 0 0 0 0 0 - 2 . 316 18 3 .21560 0 . 8 6 7 6 9 1. 19269 1 0 2 7 . - 1 0 . 6 5 1 3 1 • - 1 . 0 0 0 0 0 - 1 . 92 03 1 3 .27056 0 . 60272 1 .53272 TEMP (C) F (02) F <S2) • F (S02) F (H20) F (H2S ) F (H2) 3 2 7 . 2. 6 0 1 0 5 E - 3 1 1 .OOOOOE-01 1. 33859E-08 6 . 1 0 6 1 1 E 01 1. 61797" 03 8 . 8 C 9 1 9 E - 0 1 « 2 7 . 3. 1 5 5 9 5 E - 2 8 1 .OOOOOE-01 5 . 0831 3 E - 0 7 3 .11297K 02 7 . 11958E 02 5 . 03911E 00 5 2 7 . 1. 15276E-23 1 .OOOOOE-01 7 . 7 5783E-.C6 . 7 •35179E 02 2 . 12195E 02 1. 1 1353E 0 1 627 . 1 . 0 7 7 9 6 E - 2 0 1 .OOOOOE-01 6 . 58 31 3 E - 0 5 1 . 0 9 0 1 0 E 03 8 . 32161E 01 1. 71116E 0 1 727 . 2 . 8 1 1 5 0 E - 1 7 1 . OOOOOE-01 3. 5269 7E-01 1 . 3 8 5 1 0 E 03 3. 2951 5E 01 . 2 . 26100E 01 8 2 7 . 5.9 1 7 9 1 E - 15 1 .OOOOOE-01 1. 11 309S-03 1 . 6 C 6 7 8 S 03 1. 18208E 01 2 . 731162 0 1 9 2 7 . 5. 10299E-13 1 .O0OO0F.-01 . 1. 50635E-03 1 .760372 03 7 . 37379S 00 3. 10951E 01 1 0 2 7 . 2. 21 660E-1 1 1 .OOOOOE-01 1. 2 0 1 1 0 E - 0 2 1 . 8 6 1 5 1 E 03 1. 00 609E 00 3 . 10971S 01 TEMP (C) P (02) P (S2) P (S02) P (M20) P [H2S ) P !H2) 3 2 7 . 2. 60105E-.31 1 .OOOOOE-01 1. 21690E-08 5 . 5 5 1 0 3 E 02 1. .11132E 03 1. 61635E-01 1 2 7 . 3. 1 S 5 9 5 E - 2 8 5 . 0 0 0 0 0 E - 0 2 3. 9 1 0 1 0 E - 0 7 1 . 1 2 2 7 2 E 03 5 . 71271E 02 2 . 92619" 00 5 2 7 . 1. 15276E-23 9 . 0 9 0 9 1 E - 0 3 5. 39112E-C6 1 . 8 U 5 3 E 03 1. 81 5082 02 6 . 9 5523E 00 6 2 7 . 1 . 0 7 7 9 6 E - 2 0 2 . 7 0 2 7 0 E - 0 3 1. 1722 72-05 1 .925502 03 6 . 21 70 6E 01 1. 13192" C1 7 2 7 . 2 . 8 1 1 5 0 E - 1 7 1 . 36986E-03 2. 1009 3E-01 1 .9 59 552 03 2 . 17755E 0 1 1. 56678E 01 8 2 7 . 5 . 9 1 7 9 U E - 1 5 8 . 0 6 1 5 1 E - 0 1 9 . 71 199E-01 1 . 9 6910E 03 1. 12535S 01 1. 96111" 01 9 2 7 . 5. 10299E- 13 5 .0.761 IE -01 3. 1 3591E-03 1 . 9 7 1 3 0 E 03 5 . 6160 9E 00 2 . 30505" 01 1027 . 2.21 6 6 0 E - 1 1 3 . 533 57E-01 8 . 16057E-03 1 . 9 7 0 9 1 2 03 3. 10 309E 00 2 . 59193E 01 TEMP (C) P E R . C E N T 02 P ER CENT S2 PER CENT S02 PER CENT H20 PER CENT H2S PES CENT H2 3 2 7 . 0 . 0 0 0 0 0 0 . 0 0 5 0 0 0 . 0 0 0 0 0 2 7 . 75516 72. 2 1622 0 .02 32 3 1 2 7 . 0 . 0 0 0 0 0 0 . 0 0 2 5 0 0 . 0 0 0 0 0 7 1 . 1 3 5 8 0 28 .71353 0 . 116.32 5 2 7 . 0 . 0 0 0 0 0 0 . 0 0 0 1 5 0 . 0 0 0 0 0 90 .57625 9 .07510 0 . 3 1 7 7 6 6 2 7 . 0 . 0 0 0 0 0 0 .00011 O.OOCCO 9 6 . 32515 3. 10 853 0 . 5 6 5 9 6 7 2 7 . 0 . 0 0 0 0 0 0 . 00007 0 .00001 97 .97716 1 .23878 0 . 78339 827 . 0 . 00000 0 .00001 0 .00005 98 .15183 0 . 56267 0 . 9 8 2 2 1 9 2 7 . 0 . 0 0 0 0 0 0 . 0 0 0 0 3 0 . 0 0 0 1 6 9 3 . 56183 0 . 2 S 2 3 0 1 .15252 1 0 2 7 . 0.00000 0 . 0 0 0 0 2 0 .00012 98.51688 0 . 1 5 5 1 5 1 . 2 9 7 1 6 175 SCOHPILE TINE=GO, PAGES=210 C C H-O-S CALCULATION - SIMPLIFIED VERS TO!.' 2A C IN NAMING VARIABLES IN THE PR OG R A M THE FOLLOWING RULES WERE C FOLLOWED C (1) FUGACITY COEFFICIENTS W7.RB PREFIXED BY FC C (2) LOG 10 FUGACITIES WERE PREFIXED BY FL C (3) FUGACITIES WERE PREFIXED BY F C ('I) PRESSURES WERE PREFIXED BY P C (5) THE PER CENT OF A GAS SPECIES WAS PREFIXED BY PCT C (6) GAS SPECIES WERE NAMED BY FORMULA (EG 32 NOT OX FOR C OXYGEN) 1 DIMENSION PT (5 ) , FCH20(8,5), FCH2(>3,5), FCII25 (8,5) , FCS02{8,5), 1FCS2(8,5), A (5), P, (5) , C (5) , BUF(5), 2CLS02(B), CLH2C(fi), CLH2S(8), 3TEHPC(3), FL02 (8 ) , FLS2(8), FLS02(8), FLH20(8) , FLH2S(8), FLH2(8 ) , <1F02(8), FS2 (8) , FSO2(0), FH2 0 ( b ) , E112S (8) , FH2(3) , 5PC2(8), PS2 (8) , PS02(8), Pi!20(8), P!12S(8), Pi! 2 (B) 2 DIMENSION PCT02 (0) , . PCTS2 (8) , PCTS02(8), PCr i l 2C(8 ) , PCTH2S(8), 1PCTI(2{3), FL02 1(B), THKPC1(8) C 3 READ(5, 500) (PT (I) ,1=1,5) 1 500 FORMAT(5F10.0) 5 READ(5,501) ( (FCH 20 (K, I) , K= 1, 8) ,1=1, 5) 6 READ(5,501) ( (FCH 2 (K , I) , K = 1 , 8) , I •= 1 , 5) . 7 READ(5,501) ( (FCH2S (K, I) , K= 1, 8) ,1= 1, 5) 8 READ(5,501) ( (FCS02 ( K , I) , K= 1 , 8) ,1 = 1 , 5) 9 READ(5,501) ((FCS2(K,I) , K = 1 , 8) ,1=1,5) 10 501 FORMAT(8F10.0) 11 RBAD(5,511) (CLS02 (K) , CLH20 (K) , CI.U2S (K) , K= 1, 8) 12 511 FORMAT(3F10.0) 13 READ(5,512) (A (3 ) , B (J) ,C(J),J=1,5) 14 512 FORMAT(3F10. 0) 15 READ(5,513) (BU F (J) , J= 1, 5) 16 513 FORMAT(5A4) C C CHANGE TOTAL PRESSURE C 17 DO 100 1=4,5 C CHANGE BUFFER 18 DO 200 J=1,5 19 FAC = -A(J) +C ( J ) * (PT ( I ) -1.0) C SET TEMP IN DEGREES KELVIN - INCREMENT BY 100.C C 20 TEMP=700.0 21 DO 300 I.= 3,5 22 TEMP=TEMP+100.0 23 TEMPC1 (I.) = TF.MP-273.0 C C CALCULATE F (02) FROM AN EQUATION OF THE FORM (C (PT-1.0) - A)/TEMP +B C 21 FLO21 (L) =FAC/TEMP+B (J) 25 FL02RT=FL021 (L)/2.0 C C SET LOG F(S2) - INCREMENT BY -2.0 (8 TIMES) C 176 FLS22=2.0 DO '4 00 K=1,8 FL522=FL522-2. 0 FL52(K)=FLS22 FLS 2 RT= F LS2 (K)/2.0 F.S 2 (K) = 1 0 . 0 * * F L 5 2 (K) PS 2 (K) = FS2 (K ) / F CS 2 (I,, I) TEIU'C (K) =TEMPC1 (I.) FL02 (K) = FL02 1 (I,) F02 (K) =10.0**FLO2 (K) P02 ( K ) =F02 (K) CALCULATE THE FUGACITY OF S02 FLS02 (K)=CL502 (L) + FL S2 RT + FL02 ( K ) FS 0 2 ( K) = 1 0 . 0 * <; F L 5 0 2 (K) PS02 ( K ) =FS02 (K)/FC502 (L, I) SET REMAINING VALUES TO ZERO IF THE SUM OF PRESSURES CALCULATED TO THIS POINT IS GREATER THAN THE TOTAL PRESSURE (PT) SUM=PS02 (K) +PS2 (K) + P02 ( K ) IF (PT (I) -SUK) 10, 10,20 SOLVE FOR F (i!2) AL 1=CLII20 (L) +FL02RT A1=10.0**AL1 AL2=CLI'2S (L)+FLS2RT A2=10.0**AL2 D=A 1/F^I120 (L,I) + 1. 0/FCH2 (L, I)+A2/FCH2S (L, I) F = S U H - P T (I) FH2(K)=-F/D FL H 2(K) = A LOG 10 ( FH2 ( K ) ) PH2 (K) =FH2 (K)/FCH2 (L, I) SUHA = PH2 ( K ) + SUH IF (PT (I) -SUfiA) 11, 1 1 ,21 FLH2(K)=0.0 FH2 (K)=0.0 PH 2 ( K ) =0.0 FLH20 (K) =0.0 FLH2S(K)=0.0 FH20 ( K ) =0.0 FH2S(K)=0.0 PH20 (K) =0.0 PH2S(K)=0.0 PCT02 ( K ) =0.0 PCTS2 (K)=0.0 PCTS02(K)=0.0 PCTH20 (K)=0.0 PCTH2S(K) =0.0 PCTH.2 (K) =0.0 GO TO U00 CALCULATE THE FUGACITIES OF H20 AND II25 FLH20 ( K ) =CL!!20 (I.) + FLH2 ( K) +FL02RT FH 2 0 (K) =10 . 0 * * FLU 20 (K) PH20 (K) =FH2 0 (K) /FCH20 (L, I) 177 72 FLH2S (K) =CLI12S (L)+FLH2(K) +FLS2RT 73 FH2S (K) =10.0**FLN2S (K) 7'l • PH2S (K) -FH2S (K)/FCH2S (I., T) C C CALCULATE THE PER CENT OF EACH GAS SPECIES C 75 FCT02 (K)=P02 (K)*100.0/PT (I) 76 PCTS 2 ( K) -PS2 (K) * 1 00 .0/PT (I) 77 PCTS02 (K) =PS02 (K)* 100.0/PT (I) 7U PCTII 20 ( K) = P li2 0 (K) * 100 . 0/PT (I) 79 PCT1I2S (h) =PH2S (K) * 100.0/PT (I) 80 PCT1I2 (K) =Pli2 (K) * 100 .0/PT (I) 8 1 400 CONTINUE C 82 WRITE (6, 600) PT (I) 83 600 FORHAT(1H1/50X15M TOTAL PRESS U R E F 10 . 0 , 811 BARS/2X14H (OD SB X , HO IS)) 84 WRITE(6,601) RUF(J) 85 601 FORMAT (1H02XAU ,711 BUFFER) 86 WRITE (6, 603) C (.1) , A (J) , B (J) 87 608 FORMAT(1H02X13HLOG F(02) = (F8.5,10H(PT-1.0) -F9.1,10H )/TEHP +F5 1.2) 88 WItITE(6, 602) (TKMPC(K) ,FL02 (K) ,FLS2(K) ,FLS02 (K ) ,FLH23 (K) ,FLH2S (K) , 1FLH2 (K) , K=1 , 8) 89 602 FORMAT (1 H0/2X3H TEMP(C) 5X101! LOG F (0 2). 5X 1 0 fi LOG F(S2)4X11H LOG F(S 102)4X1111 LOG F (Ii 20) 4 X 1 1 II LOG F (II2S) 5X 1 0II LOG F (H2) // ( F1 0. 0, 6 F 15 . 5) 2) • • 9 0 WRITE (6, 603) (T EM PC (K) ,F02 (K) ,FS2 (K) ,FS02 (K) , FH20 (K) , FII2S (K ) , FH 2 (K 1),K=1,8) 9 1 603 FORMAT(1HO/2XOII TEnP (C)9X6H F(02)9X6H F(S2)8X7I1 F(S02)8X7H F(H20)8 1X7H F(H2S)9X6Ii F (!) 2) // (0 PF 1 0. 0 , IP 6 S 1 5. 5) ) 9 2 WRITE (6, 604) (T EM PC (K) ,?02 (K) , PS 2 (K) , PS02 (K) , PH 20 (K) , P 112 S (K ) , P1I2 (K 1),K=1,8) 93 604 FORMAT(1H0/2X8!( TEHP(C)9X6H P(02)9X6H P(S2)0X711 P(S02)8X7H P (H 20) 8 1X7H P(H2S) 9X6II P (H2) // (OPF10. 0, 1P6E1 5. 5) ) 94 WRIT2(6, 605) (TEr':PC(K) , PCT02 (K ) , PCTS2 ( K) , P CIS 02 (K) , PCTII20 (K ) , PCT 112 IS (K) ,PCT!I2 (K) ,K=1,8) 95 605 FORMAT (1 HO/2 X3H ?EMP(C)3X12H PER CENT 023X12H PEE CENT S22X13I! PER 1 CENT S022X13H PER CENT H202X13I1 PER CENT H2S3X12H PER CENT H2//(F 2 10 .0,6n 5. 5) ) -C 96 300 CONTINUE 97 200 CONTINUE 98 100 CONTINUE 99 STOP 100 END C C $D AT A TOTAL PRESSURE 2000. BURS (OB SB X.HOS) QFM1 BUFFER LOG F(02) = ( 0.0937«(PT-1.0) - 25738.0 )/rE«P + 9.00 TEMP (C) LOG F(02) LOG F(S2) LOG F(S02) LOG F(H23) LOG F (H.2S) LOG F(H2) 527 . - 2 2 . 9 3 8 2 6 0 .00000 - 3 . 11026 1 .81703 3 .3651 7 0 . 0 2 7 1 7 527 . - 2 2 . 9 3 8 2 6 - 2 . 0 0 0 0 0 - 1 . 1 1 0 2 6 2 .60707 3.12520 0 . 78720 527 . - 2 2 . 9 3 3 2 6 - 1 . 0 0 3 0 0 - 5 . 1 1 0 2 6 2 .86657 2 .38170 1 .01670 527 . - 2 2 . 9 3 8 2 6 - 6 . 0 0 0 0 0 -6 . 11026 2 .90358 1. "2171 1.03371 527 . - 2 2 . 9 3 3 2 6 - 8 . 0 0 0 0 0 - 7 . 1 1 0 2 6 2 .90716 0 . 12559 1 .087 59 527 . - 2 2 . 9 3 8 2 6 - 10 .00000 - 8 . 1 1 0 2 6 2 .90 785 - 0 . 5 7 1 0 2 1 . 08798 527 . - 2 2 . 9 3 3 2 6 - 1 2 . 0 0 0 0 0 - 9 . 1 1 0 2 6 2 .90789 - 1.57 39 8 1 .08802 527 . - 2 2 . 9 3 8 2 6 -11 .00000 - 10.11026 2 .90789 - 2 . 5 7 39 8 1.08802 TEMP (C) ' F (02) F(S2) F (S02) F (iI2D) F (H2S) F (H2) 527 . 1. 1 5 2 7 6 E - 2 3 1. CCOOOE 00 7 . 7 5 7 8 2 E - 0 1 • 7 . 03 127E 01 2 . 3 18282 03 1. 06155E 00 527 . 1. 15276E-23 1. O0OOOE-02 7 . 7 5 7 8 2 E - 0 5 1. 0'I611 E 02 1 . 3 3 1 1 1 2 03 6. 1 26 36E 00 527 . 1. 15276E-23 1. 000002-0 « 7 . 7578 32 -06 7 . 35179E 02 2 . 1 2 1 9 5 E 02 1. 1 135 3E 01 527 . 1. 15276E-23 9. 9 9 9 9 9 2 - 0 7 7 . 7 5 7 3 2 E - 0 7 8. 00899 E 02 2 . 6 1 0 6 1 " 01 1. 2 1258E 01 527 . 1. 15276E-23 1. 000002 -08 7. 757822 -08 8. 080H7E 02 2 .661312 00 1. 22316S 01 527 . 1. 15276E-23 1. 000002-10 7 . 757822-09 3. 038132 02 2 . 6 6 6 7 1 2 - 0 1 ' 1. 221 56E 01 527 . 1. 15276E-23 1. 000002 -12 7 . 757822-10 8. 038862 02 2 . 6 6 6 9 S E - 0 2 1. 221672 01 527. 15276E-23 1. 0CO00E-11 7 - 757322-11 8. 088932 02 2 . 6 6 7 0 0 2 - 0 3 1. 221682 01 TEMP (C) P(02) P(S2) P(S02) • P(H20) P (H2S) P (H2) 527. 1. 15276E-23 9. 09091E 01 5. 39 112E-01 1. 73181E 02 1 . 7 3 5 2 1 E 03 6. 619282-01 527 . 1. 15276E-23 9. 090912-01 5. 39 1 1 22-0 5 9. 966522 02 9 . 9 8 6 0 9 E 02 •5 82658" 00 527 . 1. 15276E-23 9. 090912 -03 5. 39 1 1 22 -06 1. 8 1 1532 03 1 .815082 02 6. 955232 00 527. 1. 15276E-23 9. 0 9 0 9 0 2 - 0 5 5. 3 9 1 1 2 E - 0 7 1. 97 26 6 2 0 3 1 .976532 01 7 . 573892 00 527 . 1. 152763-23 9. 0 9 0 9 1 2 - 0 7 5. 39 1 122 -08 1. 990362 03 1 . 9 9 1 2 7 E 00 7. 611362 00 527 . 1. 152762-23 9. 090912-09 5. 39 1122-09 • 1. 99215K 03 1 . 9 9 6 0 6 2 - 0 1 7 . 61873E 00 527 . 1. 1 5 2 7 6 E - 2 3 9. 090'I02-11 5 . 39112E-10 1. 992332 03 1 . 9 9 6 2 1 2 - 0 2 7. 61911E 0 0 527 . 1. 15276E-23 9. 090912 -13 5. 39 112E-11 1. 992352 03 1 . 9 9 6 2 6 2 - 0 3 7. 619182 00 TEMP(C) .PER CENT 02 PER CENT S2 PER CENT SO2 PER CENT H20 PS R CENT H2S PER CENT I!2 527 . 0 . 0 0 0 0 0 1.51515 0 .C0O03 8 .659 19 8 6 . 7 6 1 3 7 O.C332 5 527 . 0 . 0 0 0 0 0 0 . 0 1 5 1 5 0.00000 19.83258 19.9 3011 0 . 19 133 527 . 0 . 00000 0 . 0 0 0 1 5 0.00000 9 0 . 5 7 6 2 5 9 .07510 0 . 3 1 7 7 6 527 . 0 . 0 0 0 0 0 0 .00000 0.00000 9 8 . 6 3 2 8 1 0 . 9 8 8 2 6 0 . 37869 527 . 0 . 00000 0 .00000 0.00000 99.51808 0 .09971 0 . 3820 9 527 . 0 . 0 0 0 0 0 0 .00000 0.00000 99.60 753 0 . 0 0 9 9 8 0 . 3 8 2 1 1 527 . 0 . 00000 0 .00000 0.00000 99.6 1619 0 . 00100 0 .38217 527 . 0 . 0 0 0 0 0 0 .00000 0.00000 99.61737 0 . 00010 0 . 3 8 2 1 7 CO 179 $COMPILE TIME=50,PAGEr> = 200 C H-O-f. VERSION 4 - VALUES FOR LOG F(H2) FROM O-ll PROGRAM C - SOLVED FDR 1120, 302, 112S, AND 02 C - VALUES FOR LOG F(S2) VARY FROM 0 .0 TO - 1 2 . 0 f C IN NAMING VARIABLES IN THE PROGRAM THE FOLLOWING RULES WERE C FOLLOWED C (1) FUGACITY COEFFICIENTS WERE PREFIXED BY FC C (2) LOG 10 FUGACITIES WERE PREFIXED BY FL C (3) FUGACITIES WERE PREFIXEC BY F C (1) PRESSURES WERE PREFIXED BY P C (5) THE PER C KMT OF A GAS SPECIES WAS PREFIXED BY PCT C (6) GAS SPECIES WERE NAMED BY FORMULA (EG 02 NOT OX FOR C OXYGEN) 1 DOUBLE PRECISION A1, A2, B1, B2, C2, F, Q, ROOT, DSQRT C 2 DIMENSION PT(5) , F C H 2 0 ( 8 , S ) , F C H 2 ( 8 , 5 ) , FC!12S (8 ,5 ) , F C S 0 2 ( 8 , 5 ) , 1 F C S 2 ( « , 5 ) , HUP (5), C A F L H 2 ( 8 , 5 , 5 ) , 2CLS02 (8) , C L H 2 0 ( 8 ) , C L H 2 S ( 8 ) , 3TEMPC (8 ) , F L 0 2 ( 8 ) , F L S 2 ( 8 ) , F L S 0 2 ( 8 ) , FL H2D (8) , F L H 2 S ( 8 ) , F L H 2 ( 8 ) , 4F02 ( 8 ) , F S 2 ( 8 ) , F S 0 2 ( 8 ) , F I !20 (8), FH2S(0) , F H 2 ( 8 ) , 5 P 0 2 ( 8 ) , P S 2 ( 8 ) , P S 0 2 ( 8 ) , P H 2 0 ( 8 ) , Pil 2S (8) , -P112 (8) 3 DIMENSION PC.T02 (8) , P C T S 2 ( 8 ) , P C T S 0 2 ( 8 ) , PCTH20 ( 8 ) , PCT112S(8), 1PCTH2 (8 ) , FLS21(7) , FS2 1(7) C . '4 READ(5 ,500) (PT (I) ,1=1 ,5) 5 5 0 0 FORMAT (5F10.0) 6 READ(5,501) ( ( FCH2 0 (K,I) ,K=1,8) ,1=1,5) 7 READ(5,501) ( ( F C H 2 (K , I) , K = 1 , 8) ,1=1,5) 8 READ(5,501) { ( FC H2S (K,I) ,K. = 1,8) ,1=1,5) 9 RKAD(5,501) ((FCS02 (K,I) ,K=1,8) ,1=1,5)-10 READ(5,501) ((FCS2 (K, I) ,K=1,8) , 1=1,5) 11 501 FORMAT (8F10.0) 12 READ (5,511) (C LS02 (K) , CL H 20 ( K) , CI.H 25 (K ) , K = 1, 8) 13 5 1 1 FORMAT(3F10.0) 14 READ (5,513) (BUF (0 ) , J = 1,5) 15 513 FOR MAT (5 A 4) 16 READ(5,514) (( (CAFLH2 (K , 0 ,1) , K = 1 , 8 ) , J= 1 , 5 ) ,1=1 ,5) 17 514 FORMAT ( 8 F 1 0 . 0 ) C CHANGE TOTAL PRESSURE 18 DO 100 1=1 ,5 C CHANGE BUFFER 19 DO 200 J = 1 , 5 C SET LOG F(S2) - INCREMENT BY - 2 . 0 (7 TIMES) 2 0 FLS22=2.0 ' 21 DO 3 0 0 1=1 ,7 22 FLS22=FLS22-2.0 23 FLS21 (L)=FLS22 24 F LS2 RT = FLS2 1 ( L ) / 2 . 0 25 FS21 (L) = 10 .0**FLS21 (L) C C SET TEMP IN DEGREES KELVIN - INCREMENT BY 100.0 (8 TIMES) 1 8 0 c 26 TEMP=500.0 2 7 DO '100 K = 1,8 28 TEMP=TEMP+100.0 2 9 TEMPC (K) =TEMP-273.0 30 FLS2 (K)=FLS21 (I.) 3 1 FS2 (K) = FS21 (I.) 32 PS2 (K) = FS 2 (K) /FCS2 (K, I) C C CALCULATE THE FUGACITY OF H2S C 33 FLH25 (K) =CL!l2S (K) -ICAFLH2 (K, J , I) +FLS2RT 31 FH2S (K) =10.0**FI.H2S (K) 35 PH2S (K)=FH2S (K)/FCH25 (K,I) 36 FLII2 (K)=CAFLH2 (K, J , I ) 37 FH2 (K) = 10.0**FLi l2 (K) 38 PII2 (K) = FI!2 (K) /FCII2 (K,I) C C SET REMAINING VALUES TO ZERO IF THE SUM OF PRESSURES CALCULATED C TO THIS POINT IS GREATER THAN THE TOTAL PRESSURE (PT) C 39 SUH = PB2 (K ) + PS2 ( K ) + PH2S ( K ) 4 0 IF (PT (I)-SUM) 10,10,20 C C SOLVE FOR F(02) (QUADRATIC EQUATION) r* • * 1 1 20 AL1 = CLS02 (K) +FLS2RT 42 A1=10.0**AL1 43 A2 = A1/FCS02 (K,I) +1 .0 44 BL1=CLH20(K) +FLII2 (K) 45 B1=10.0**BL1 46 B2=B1/FCH20(K,I) 47 C2 = SUM-PT (I) -4 8 P=B2/A2 49 Q=C2/A2 5 0 ROOT=-P/2.0+DSQRT (P*P/4,0-Q) 51 F02 (K)=ROOT*ROOT 5 2 IF (F02 (K) ) 12, 12, 22 53 22 FL02 (K) =ALOG 10 (F02 ( K ) ) 54 P02 ( K ) = F02(K) 55 SUKA=P02 (K) + SUM 56 IF (PT (I) -SUM A) 11,11,21 C 5 7 10 F02 (K)=0.0 5 8 12 FLO2(K)=0.0 5 9 P02 (K)=0.0 6 0 11 FLH20(K)=0.0 61 FH2O(K)=0.0 6 2 PH2O(K)=0.0 63 FLSO2(K)=0.0 64 FS02 (K)=0.0 65 PS02 (K)=0.0 66 PCTO2(K)=0.0 67 PCTS2 (S)=0.0 68 PCTS02 (K) =0.0 69 PCTII20 (K) =0.0 7 0 PCTH2S ( K ) = 0 . 0 71 PCT112(K)=0.0 72 GO TO 400 C 181 " C C A L C U L A T E THE F U G A C I T I E S OF 1120 AMD S 0 2 C 73 2 i F L I I 2 0 (K) =CLH20 (K) + F L H 2 (K) + FL02 ( K ) / 2 . 0 74 FH 2 0 (K ) = 1 0 . 0 * * K L H 2 0 (K ) 75 . PI120 (K) =F1120 (K) / F C H 2 0 (K , I ) 76 F L S 0 2 ( K ) = C L S 0 2 (K) + F L S 2 R T +FLO 2 ( K ) 77 F S 0 2 (K) =10 . 0 * * F T . S O 2 (K ) 78 P S 0 2 ( K ) = F S 0 2 ( K ) / F C S 0 2 ( K , I ) C C C A L C U L A T E THE PER CENT OF EACH GAS S P E C I E S C 7 9 P C T 0 2 (K) =P02 (K) * 1 0 0 . 0 /PT ( I ) 8 0 P C T S 2 (K) = P S 2 (K) * 1 0 0 . 0/PT ( I ) 81 P C T S 0 2 (K) = P S 0 2 (K) * 1 0 0 . 0 / P T ( I ) 82 P C T H 2 0 (K) = PH20 ( K) * 1 0 0 . 0 / P T ( I ) 83 P C T H 2 S ( K ) = P H 2 S ( K ) * 1 0 0 . 0 / P T ( I ) 84 P C T H 2 (K) = PH2 (K) * 1 0 0 . 0 /PT ( I ) 85 4 00 C O W T I I O E 86 WR ITE (a , 6 0 0 ) P T ( I ) 87 6 0 0 FORMAT (1 H 1 / 5 0 X 1 5 H T O T A L P R E S S U R E F 1 0 . 0 , 8 H B A R S / 2 X 1 S H O B , O H ( SB X , 1 H O S ) ) 88 WR ITE ( 6 , 6 0 1 ) BUF (0) 89 6 0 1 FORMAT ( 1 H 0 2 X A 4 , 7 H B U F F E R ) 90 WR ITE (6 , 6 0 2) ( T E M P C (K) , F L 0 2 (K) , F L S 2 (K) , F L S 0 2 (K) , F L U 2 0 (K) , FL H2S (K ) , I F L l i 2 (K) ,K = 1 ,8) 91 6 0 2 FORMAT (1 H0/2 X 8 H TEMP (C) 5X 1 01] LOG F ( O 2 ) 5 X 1 0 1 I LOG F ( S 2 ) 4 X 1 1 H LOG F (S 102 ) 4X1111 L C G F (1120) 4 X 1 1H LOG F ( l i 2 3 ) 5 X 1 0 H LDG F (H 2) / / (F 10 . 0 , 6F 1 5. 5 ) 2) '. . ' 92 WR ITE (5 , 6 0 3) {TE MP C (K ) , FO 2 (K) , FS 2 (K) , FSO 2 ( X) , F 112 0 (K ) , FH 2S (K) , F Ii 2 (K 1 ) , K = 1 , 8 ) 93 6 0 3 FORMAT (1110/2X8 H T E H P ( C ) 9 X b H F ( 3 2 ) 9 X 6 I ! F ( S 2 ) 8 X 7 H F ( S 0 2 ) 8 X 7 ! i F (1120)8 1X7H F ( I I 2 S ) 9 X 6 H F (8 2 ) / / ( 0 P F 1 0 . 0 , 1 P 6 E 1 5 . 5 ) ) 94 WR ITE (5 , 6 0 4) ( T E M P C (K) , P 0 2 ( K ) , P S 2 (K) , P S 0 2 ( K ) , P H2 0 (K) , P H 2 S ( K ) , P H 2 (K 1 ) . K = 1 , 8 ) 95 6 0 4 FORMAT ( 1 H 0 / 2 X 8 H T E H P ( C ) 9 X 6 H P ( 0 2 ) 9 X 6 l l P ( S 2 ) 8 X 7 H P ( S 0 2 ) 8 X 7 H P ( H 2 0 ) 8 1X7K P ( H 2 S ) 9 X 6 I I P ( H 2 ) / / ( O P F 1 0 . 3 , 1 P 6 E1 5 . 5 ) ) 96 W R I T E ( 5 , 6 0 5 ) (TE MPC (K ) , PCTO 2 (K) , PCT3 2 (K ) , PC T S 0 2 (K) , PCTH 20 (K) , PCTH 2 1 S (K) , PCT H2 (K) , K= 1 , 8) 97 6 0 5 FORMAT ( 1 H 0 / 2 X 8 H T E K P ( C ) 3 X 1 2 H PEK CENT 0 2 3 X 1211 PER CENT S 2 2 X 1 3 H PER 1 CENT S 0 2 2 X 1 3 H PER CENT H 2 0 2 X 1 3 H PER CENT I12S3X12H PER CENT 112// (F 2 1 0 . 0 , 6 F 1 5 . 5 ) ) 98 300 C O N T I N U E 99 2 0 0 C O N T I N U E 1 0 0 100 C O N T I N U E 101 S T O P 102 " . END SDATA 182 T Y P I C A L D A T A D E C K H-O-S V E R S I O N S 4 £ 4A 5 0 0 . n 100 0 .0 2CO0.0 3 COO.0 1. 0 0 . 221 0 . 1 8 1 0 . 6 9 1 0 . 8 10 0. 6 79 0 . 9 2 3 0 . 9 1 7 0 . 957 0 . 140 0 . 3 13 0. 50 9 0 . 6 75 0. 739 0 . 8 61 0.9 15 0 . 950 0 . 1 10 0 . 2 1 2 0 .106 0.56 6 0. 707 0 . 8 1 6 0 .89 3 0 . 916 0. 110 0 . 2 3 8 0 . 39 5 0. 555 0. 699 0 .823 0 .911 0 . 979 0 . 998 0 . 999 0 . 9 1 9 1. COO 1. COO 1.000 1. COO 1. COO 1. 17 8 1.119 1.127 1.111 1.0 93 1. 08 3 1.079 1. 072 1.334 1.317 1.269 1.233 1. 201 1.132 1. 16 3 1. 118 1.896 1. 72 2 1.601 1.512 1. 115 1. 39 2 1. 319 1.311 2 . 5 7 2 2. 2 33 2.007 1. 816 1. 726 1.633 1.560 1. 50 1 1. COO 1. 000 1.000 1. COO 1.. 000 1. 000 1. COO 1. 0 0 0 0 . 7 8 2 0 . 867 0 . 9 3 7 0 . 963 0 . 978 0 .936 0.987 0 . 988 . 0 .798 0 . 926 0 .987 1.0 16 1.028 1. 032 1.033 1. 031 1. VI 1 1. 292 1.336 1. 339 1.330 1.317 1.306 1. 29 1 1.000 1. 000 1.000 1. 000 1.000 1. 000 1. COO 1. COO 1. COO 1.000 1.000 1. 000 1. 000 1. 000 1. 000 1 . 0 0 0 0 . 6 3 0 0 . 780 0 . 8 8 0 0. 9 29 0 . 957 0 . 9 7 1 0. 933 0 . 987 0 . 6 7 0 0 . 83 2 0 .955 1.011 1. 010 1.055 1. 060 1. 060 1. 100 1. 300 1.139 1. 17 2 1. 169 1. 155 1.1 37 1. 120 1. COO 1.000 1.000 1. COO 1. 000 1. 000 1. 000 1. 0 0 0 1. 000 1. 000 1.000 1. 000 1.000 1. 000 1. COO 1. 0 0 0 0 .C01 0 . 0 0 1 0 .00 5 0 .023 0 . C52 0 . 0 9 9 0. 166 0 . 216 0. CO 1 0. 00 1 0 . 0 0 5 0.021 0 . 0 1 5 0. 085 0. 112 0 . 2 1 1 0. CO 1 0 . 0 0 2 0.011 0. 037 0.073 0. 121 0. 197 0 . 283 0 . 00 1 0 . 001 0 .028 0 .075 0 . 112 0 . 233 0. 352 0 . 1 7 9 1.C0O 1.000 1 .000 1. COO 1. 000 1.000 1.000 1. 0 0 0 2 7 . 7 11 1 8. 633 5.272 2 3 . 2 0 7 1 5. 585 1. 160 19.8 28 1 3. 289 3.338 17.208 1 1. 1 S 9 2 .687 15.098 1 0 . 0 6 2 2. 163 13.378 • 8.683 1 . 7 31 1 1.916 7. 899 1. 375 1 0 . 7 3 ft 7. 065 1.070 1KI 1CFM1H?I0II1M 1 2 . 6 5 2 9 1 2 .61937 2 . 5 6 1 9 2 ' 2. 1910 5 2. 1 186 9 2. 31530 2. 271 2 1 2. 20687 2 . 1 7 7 6 9 2. 53 560 2 .51067 2. 52557 2. 5071 6 2. 1393 1 2. 1 7.25 0 2. 15592 0 . 3210 1 0. 61361 • 0 .80 155 0. 87511 0. 91993 0. 95179 0. 97 3 36 0 . 98616 0 .503 11 • - 0 . 0 9 3 7 5 0 .13529 0. 261 26 0. 35269 • 0. 12011 0. 17 18 6 0 . 51 1 87 3. 03619 • - 2 . 6212 1 - 2 . 39131 - 2 . 26 169 - 2 . 1 7268 - 2 . 10111 - 2 . 05 251 - 2 . 012 15 2 . 9 3 2 36 2.88811 2 .8 351 1 2. 77 26 2 2. 70 3 3 8 2 . 6 3106 2. 56761 2. 50 5 92 2 . 678 16 • 2. 7690 1 2 .80157 2. 8110 2 2. 80363 2. 7 9 178 2. 77353 2. 76563 0 . 3 8 266 0 . 7 2 6 1 8 0 .9 1213 1. 07297 1. 15210 1. 20111 1. 21 10 1 1 . 2 6 £85 0 .130 28 0 .00153 0 . 28957 0 . 1 7 37 2 0. 59567 0. 63 267 0 .71367 0 . 80 11 1 2 .917 30 • - 2 . 5 1 3 1 0 - 2 .22386 - 2 . 0119 9 - 1. 9 2 31 9 - 1. 8 3628 - 1. 77030 - 1 . 717 87 3 .2315 1 3. 1 7228 3 .1119 7 3. 01 76 5 2. 9 8551 2. 92 360 2. 86 2 15 2. 80 35 1 2 . 9 0 7 7 9 3.0 1 873 3 .07181 3. 09 67 1 3. 10121 3. 10208 3. 0939 3 3. 08311 0 . 50 121 0..8193 9 1 .0380 2 1. 21708 1. 3 6 029 1. 1 39 32 1. 1 9 39 2 1. 53310 0. 272 28 0 . 1 6 1 1 2 0 . 16 391 0. 6 7 303 .0. 8 2 61 5 0. 93838 1. 0 20 37 1 . 0830 1 2 .76615 • - 2 . 33 73 1 - 2 .03750 - 1. 3 3 071 - 1. 6/908 - 1. 55319 - 1 . 16756 - 1. 12 580 3.13 330 3. 36003 3 . 29 197 3. 2216 3 3. 160 70 3. 10 17 5 3. 01 27 3 2. 9 e 6 1 9 3.07 010 3. 1 90 71 3 .25279 3. 28 1 36 3. 29271 3. 29 571 3. 29050 3. 28163 0 . 5 9 9 35 0 . 9 3 1 6 0 1 . 19113 1. 36 3 30 1. 1 6 516 1. 57716 1. 61 200 1. 68926 0. 13119 0. 29716 0 .59916 0. 8 15 2 5 0. 9 71 8 2 1. 09751 1. 18765 1. 2 5 656 2 . 60580 • - 2 . 1 8 1 7 2 - 1 . 8 3 50 2 - 1. 67 317 - 1. 5 1720 - 1. 39 71 1 - 1. 3 09C9 - 1 . 21 191 0 . 0 2 3 5 2 • - 0 . 0 6 1 2 7 - 0 .1 I860 - 0 . 18 965 - 0 . 26606 - 0 . 31 173 - 0 . 1 1388 - 0 . 18051 0. 06951 • - 0 . 103 76 - 0 . 1 3 58 8 - 0 . 1619 2 - 0 . 19001 - 0 . 21150 - 0 . 230 17 - 0 . 21 633 1.1,9111 • - 1. 70 9 7 1 . -1 .71171 - 1 . 7 0 370 - 1 . 70172 - 1. 6 9 231 - 1. 6 3 3 9 3 - 1 . 67505 2 . 5 1 0 13 • - 2 . 1 5 0 8 1 - 2 . 3399 6 - 2 . 3 3 10 3 - 2, 2 7 92 9 ~ £ . 2 3 37 3 - 2 . 191 29 - 2 . 15 556 5.07838 • - 1. 996 16 -1 .92111 - 1 . 8610 1 -1. 8110 1 - 1 . 7 613 8 - 1 . 7 210 1 - 1 . 68617 f v J N J t O N J W W W W - 4 - J - J - J ~~J O O C O v l O > i n C W w w N j w r o r o r o w - J « O ; - O . - O - O . N 1 - O , * - I o co o> m X T L O O^OCOvJOUiCU p) N) Ln Ul W U) ^  • C 4 ro o CO CO Ul o ro O CO CO -o o o X T —* Ul ro o o -J U"- xr _-t Ul ro o o o o o o o o o LO o Ul Ul ro o -O _o o Ul -O ro o ;d LP Ul -J o u> u» o U> o Ul _o o o o o o o o o o CO CO CO CO ro > Ui o CO' CO CO CO ro _• o -o o o o o o o o o H P J P J P I P I to P I t l C'J m pi pi P I pj P I p] o o o o o o c o 1 1 1 1 1 1 1 1 c 1 i t i i 1 i t o o o o o C o o o o . _- _- ro ro ro o ro ! _* ro ro ro o ro o o o o o o o o Ul -o o X T CO —• ~— —* Ui ui -j o fr CO —» •— t I I I I I I —. ~. ro ro O W C (T> O W o ro ro m o o o U > O W C J W « 0 U I c N ; J cc . c o o cr. 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TIME = f>0,PAGEM = 210 C C H-O-S VERSION It A - VALUES FOR LCG E(H2) FROM C-H PROGRAM C - SOLVED FOR 1120, S02, II2S, AND 02 C - VALUES FOR LCG F(S2) VARY FROM 0.0 TO -11.0 C IN NAMING VARIABLES IH THE PROGRAM THE FOLLOWING RULES WERE C FCLLOVi Ei) C (1) FUCACITY COEFFICIENTS WERE PREFIXED BY F C C (2) LCG 10 FUGACITIES WERE FREFIXEC BY FL C . (3) FUGACITIES WERE PREFIXED BY F C ('I) PRESSURES WERE PREFIXED BY P C (5) THE PER CENT OF A GAS SPECIES WAS PREFIXED BY PCT C (6) GAS SPECIES WERE NAMED BY FORMULA (EG 02 NOT CX IOR C OXYGEN) C 1 DCUBLE PRECISION A l , A2, B1, B2, C2, P, Q, ROOT, DSQRT C 2 ET MENS CON PT (5 ) , FCH20(8,5), FCH2(8,S), FCH2S(8,5), FCS02(8 , 5 ) , 1FCS2(8,S), EUF (5) , CA FL II2 (8 ,5,5) , 2CLS02(8), C.LII2C (8) , CLH2S(8), 3TEMPC(8), FL02 ( 3 ) , FLS2(G), FLSC2(8), FLU20|8), FLI:2S(8), FLH2(8) , UFC2(8), FS2 (8) , FS02(8), FH20 (8) , FH2S(8), FH2(8), 5PC2(8), PS2 (8) , PS02(8), PI!2C(8), PH2S(8), PH2|8) 3 DIMENSION PCT02 (8) , PCTS2(8), PCTS02(8), PCTH2C(8), PCTH2S(8), 1PCTH2(8) , TEMPC 1 (8) C 1 READ(5, 500) (PT (I) , 1= 1 , 5) 5 500' FCRMAT(5F10.0) 6 REAC(5,501) ( (FCH 20 (K , I) , K= 1,8) ,1=1,5) 7 READ(5,501) ( (FCH2 (K, I) , K= 1 , 8) ,1=1,5) 8 REAL(5,501) ( (FCI!2S (K , I) , K= 1 , 8) ,1 = 1,5) 9 READ(5,501) ( (FCS02 (K, I) , K= 1, 8 ) , 1= 1, 5) 10 READ(5,501) ( (FCS2(K,I) ,K=1,8) ,1=1,5) 11 501 FORMAT (8F10.0) 12 READ(5,511) (CLS02 (K) , CL 1120 (K) , CL H2S ( K) , K= 1 , 8 ) 13 511 FORMAT(3F10.0) 11 READ (5, 51 3) (Ell F (J) , 0 = 1 , 5) 15' 513 FCRMAT (5A1) 16 READ(5,51'i) | ( (CAFLH2(K, 0,1) ,K=1,8) ,0=1,5) ,1=1,5) 17 514 FORMAT(8F10.0) C C CHANGE TOTAL PRESSURE C 18 CC 100 1=3,5 . C C CHANGE BUFFER C 19 DC 200 0=1,5 C C • SET TEMP IN DEGREES KELVIN - INCREMENT BY 10C.C (8 TIMES) C 20 TEMP=700.0 21 EC 300 L=3,5 22 TEMF=TEMP+100.0 23 TEMPC1 (L) =TEMP-273.0 C C SET LOG F(S2) - INCREMENT BY -2.0 (8 TIMES) C 24 FLS22=2.0 25 DC 100 K=1,8 185 26 FLS22=FLS22-2. C 27 FLS 2 (K) =- F L52 2 28 F L S 2 R T = F L S 2 (K) / 2 . 0 29 FS2 (K) = 10.0**FL32 (K) 30 PS 2 (K) = FS2 (K) / F CS 2 (L , I) 31 TEH FC (K) =TEMPC 1 (L) -32 FL112 (K) =CAFLH2 (L , J ,1) 33 FH2 (K ) = 10 . 0 * * F L ! I 2 (K) 34 PH 2 (K) = FH2 (K) / F CH 2 (L , I) C C CALCULATE THE FUGACITY OF H2S C 35 FLH2S (K) =CI.H2S (L) +CAFLH2 (L, J , I) + ELS2 RT 36 FH2S ( K ) = 10.'0**FLli2S ( K ) 37 PH2S (K) = F112S (K)/FC1I2S (L, 1) C C SET REMAINING VALUES TO ZERO IF THE SUM OF PRESSURES CALCULATED C TC THIS POINT IS GREATER THAN THE TOTAL PRESSURE (PT) C 38 SUM=PH2(K) +PS2 (K)+PH2S(K) 39 I F (PT ( I) -SUM) 1 C , 1 0 , 20 C C SOLVE FOR F (02) (QUADRATIC EQUATION) C 40 20 AL 1 = CLS02 (I) +FLS2RT 41 A1=10.0**AL1 42 A2=A 1/FCS02 (L,I) + 1 .0 43 BL 1=CL 1120 (I) +FLH2 (K) 44 ' B1=10.0**BL1 45 ' B2 = B1/FCH2 0 (L, I) 46 C2=SUM-PT(I) 47 P=B2/A2 48 Q=C2/A2 49 RC0T = -P/2.0+DSQRT(P*P/4. 0-Q) 50 FG2 ( K ) =ROOT*RCCT • 51 IF (F02 (K)) 12,12,22 52 22 FL02 (K)= A LOG 1 0 (F02 (K)) 53 PC2 (K) = F02 (K) 54 S1IMA = P02 (K) +SUM 55 IF (FT (I)-SUMA) 11,11,21 C 56 10 FC2(K)=0.0 57 12 FLO2(K)=0.0 58 PC2 (K)=0.0 59 11 FLH20(K)=0.0 60 FH20(K)=0.0 61 PH2O(K)=0.0 62 FLSO2(K)=0.0 ' 63 FSO2(K)=0.0 . ' 64 PSO2(K)=0.0 65 PCTO2(K)=0.0 66 PCTS2(K)=0.0 67 PCTSO2 ( K) =0.0 68 PCTH20 (K)=0.0 69 PCTH 2 S ( K) =0. 0 70 PCTH2(K)=0.0 71 GC TO 400 C C CALCULATE THE FUGACITIES OF H20 Z S02 C 186 72 21 FLH20 ( K) =CLH2C (I.) + FT.H2 ( fc) + FLC2 (K)/?.. 0 7 3 Fli 20 (K) =10. 0 * *FI.H 2C (K) 71 P1120 (K) =Fii20 (K)/FCH20 (1, 1) 75 FLS02 (K) =C LS02 (L) + FLS2R'JMFL02 (K) 76 F502(K) =10.0**FLS02 (K) '77 PS02 (K) =FS02 (KJ/FCS02 (L, I) C C CALCULATE THE P EH CENT OF EACH GAS SPECIES C 78 PCT02 (K)=P02 (K)* 100.0/PT (I) 79 PCTS2 (K) =PS2 (K) * 100 .0/PT (I) 80 PCTS02 (K)=PS02 (K)* 100.0/PT (I) 81 PCTH20(K) =PH2C (K) * 100.0/PT (I) 82 PCTH2S (K)=PH2S (K)* 100.0/PT (I) 83 PCTH 2 (K) =PH2 (K) * 1C0 .O/PT (I) 84 400 CONTINUE C 85 WRITE(6,600) PT (I) 86 600 FORMAT(1H1/50X15H TOTAL PRESS U R E F10. 0 , 8 U BARS/2X16H OE,OH(SB X, 1H CS)) 87 WRITE(6,601) EU F (J)' 88 601 FORMAT (1H02XA4 ,711 BUFFER) 89 WRITE(6, 602) (T EM PC (K) ,F102 (K ) , FLS2(K) ,FLS02 |K ) ,FLK20 {K) , FLH2S (K) , 1FLH2 (K)<i'K=1 , 8) 90-. 602 FCRMAT(1H0/2X8H TENP(C)5X10H LOG F (02)5X1011 LCG F(S2) 4X1111 LCG I (S 1C2J4X11H LOG F- (II 20) 4X 1 1 !1 LOG F(H2S) 5X10H LOG F (H 2)//(F 10. 0, 6 F 15 . 5) 2) . 9 1 WRITE (6, 60 3) (TEMPC (K) ,F02 (K) , FS 2 (K) ,FS0 2 (K) , FH 20 (K) ,FH2S (K ) , FH 2 (K 1),K=1,8) 92 603 FORMAT (1 H0/2 X811 TEMP(C)9X6H F(02)9X6H F(S2)8X7il F(S02)8X7H F (H 20) 8 1X7H F(H2S)9XGH F (H2) // (0PF1 0. 0, 11:6 El 5.5) ) 93 WRITE(5, 604) (T EM PC (K) , P02 (K) , PS 2 (K) , PSO 2 (K) , PH 20 (K) , P112 S (K ) , P!12 (K 1) ,K=1,8) 94 604 FCRMAT (1110/2X8H TEMP(C)9X6I! P(02)9X6F. P(S2)8X7H P(S02)8X7H P (H 20) 8 1X71! P(I!2S) 9X611 P (112) // (0PF1 0. 0 , 11-6 E1 5. 5) ) 95 WRITE (6, 605) (T EM PC (K) , PCT02 (K ) , PCTS 2 ( K) , P CTS02 (K) , PC TH20 (K) , PCTH 2 1S (K) ,PCTH2 (K) ,K=1 ,8) 96 605 FCRMAT (1 HO/2 X 81] TFMP(C) 3X1211 PER CENT 023X1211 PER CENT S22X13I1 PER 1 CENT S022X13H. PER CENT H202X13H PER CENT H2S3X12H PER CENT 112// (F 210.0,6F15.5)) C 97 300 CONTINUE 98 200 CONTINUE 99 100 CONTINUE 100 STOP 101 END $DAT A TOTAL PRESSURE 2000. OARS O B ,0 ! ! [ S B X.HOS) QFM1 BUFFER TEMP<C) LCG F(02) LOG F(S2) ICG F(S02) LCG F(F20) LCG F(H2S) LCG F(H2) 527 . 0 . 0 0 0 0 0 0.OOOOO 0 .00000 0 .00000 4 .42602 1 .08802 527 . 0 . 00000 - 2 . 0 0 0 0 0 0 .00000 0 .00000 3 .42602 1.08802 527 . - 2 3 . 0 2 9 9 5 - 4 . 0 0 0 0 0 - 5 . 2 0 195 2 .86204 2.4 260 2 1 .03302 527 . - 2 2 . 9 4 6 9 9 - 6 .00000 - 6 . 1 1 8 9 9 2 .90352 1.4260 2 1.03802 527 . - 2 2 . 9 3 9 1 2 - 8 . C 0 0 0 0 - 7 . 1 1 1 1 1 2 .90746 0 .42602 1.C880 2 527 . - 2 2 . 9 3 3 3 4 - 10.00000 - 3 . 11034 2 .90785 - 0 .57 393 1.08802 527 . - 2 2 . 9 3 8 3 5 - 12 .00000 - 9 . 1 1 0 3 5 2 .90784 - 1 .57398 1 .08802 527 . - 2 2 . 9 3886 - 14.00000 - 1 0 . 1 1 0 8 6 2 .90759 - 2 .57398 1.08802 TEMP (C) F(02) F(S2) F (SC2) F(K20) F(K2S) F(H2) 527 . 0. COOOOE-O 1 1. OCOOOE 00 0. Cf.OOOE-O 1 0. OCCOOS-O 1 2 . 66699E 04 1. 224672 01 527. 0. COOOOE-01 1. 0O00OE-O2 0. COCOOS-01 " 0. CCC002-01 2 . 666992 03 1. 224672 01 527 . 9. 3 3 3 3 1 E - 2 4 1. CCCC0F.-04 6. 28131E-0 6 7 . 27852E 02 . 2 - 66698E 02 1. 224672 0 1 ' 527 . 1. 12979E-23 9 . 9999QE-07 7 . 603472 -07 ' 8. CC8012 02 2 . 656982 01 1. 224672 01 527 . 1. 15046E-23 1. CCOCOE-08 7 . 7 4 2 5 7 E - 0 8 8. C8C93E 02 2 . 6669BE .00 i m 224672 01 527 . 1. 15252E-23 1. COOOOE- 10 7 . 7 5 6 4 6 E - 0 9 8. C88172 02 '2 . 66698S-01 1. 224672 01 527 . 1. 15.249E-23 1. CCC00E-12 7. 756 19E-10 8. 088032 02 2 . 66699 2-02 1. 224672 01 5 2 7 . 1 * 15 1 142-23 1. COOOOE-14 7. 74720E-11 8. 08334E 02 2 . 666992 -03 1. 224672 01 TEMP (C) P(02) P (S2) P(S02) P(E20) P(K2S) P(82) 527 . 0. CC00OE-O1 9 . C9091E 01 C. CCCOOS-01 0. CCOOOE-0 1 1. 99625E OU 7. 649432 00 527 . 0. OOOOOE-01 9 . C9091E-01 0. COCOOE-O 1 0. CCC002-01 1. 99625S 03 7. 6494 32- 00 '. 527 . 9. 3 3 3 3 1 E - 2 4 9. C9091E-03 4 . 365052-0 6 1. 792742 03 1 . 99625E 02 ' 7. 64943E 00 527 . 1. 12979E-23 9 . 0 9 0 9 0 E - 0 5 5. 283862-07 1. 97 24 1E 0 3 1. 99624E 01 7. 64943E 00 527. 1. 15046E-23 9. C 9 0 9 1 E - 0 7 5 . 380522-08 1. 99033 E 03 1. 99624E 00 7. 64943E 00 527 . 1. 1 5 2 5 2 E - 2 3 9. 09091E-09 5. 390 172-09 1. 992 162 03 1. 996252-01 7 . 64943E 00 527 . 1. 152492-23 9 . C9090E-11 5 . 389982-10 1. 992122 03 1. 9 9 6 2 5 E - 0 2 7. 64943E 00 527 . 15 1 1UE-23 9 . 090912-13 5. 333742-1 1 1. 990972 03 1. 996252-03 7 . 6494 3E 00 TEMP (C) PER CENT 02 PER CENT S2' PER CENT 202 PER CENT K20 PE? CENT H2S PI R CENT 22 527 . 0 . 00000 0 . 0 0 0 0 0 .0 .00000 • 0 .00000 0 .00000 0.OOOOO 527 . 0 . 0 0 0 0 0 0 .00000 0 .00000 0 .00000 C.OOOOO 0 .00000 5 2 7 . O.COOOO 0 .000 4 5 0 .00000 8 9 . 6 369 6 9 . 9 8 1 2 3 0 .38247 527 . 0 . 00000 0 .00000 0 .00000 93 .62071 0 .99812 0 . 38247 527 . O.COOOO 0 .00000 0 .00000 99 .51874 0 .09981 0 .33247 527 . 0 . 0 0 0 0 0 0 .00000 0.OOOOO 9 9 . 5 0 7 9 6 0 .00990 0 .38247 527 . O.COOOO 0 .00000 C.OOOOO 99.6062.2 0 .00 100 0 .33247 527 . 0 . 0 0 0 0 0 0 .00000 0 .00000 99 .54849 0 .00010 0 .38247 188 APPENDIX 4 S-0 SYSTEM COMPUTER PROGRAM The H-O-S Version 1 program has been modified for calculations in the S-0 system. Fugacities and partial pressures of molecular gas species in the S-0 system (O2, S2, SO, SO2, SO3, and S2Q) are calculated for values of log fQ2 defined by solid phase buffers at constant Ptotal a n <^ 1°£ S^2 for 8 temperatures (327-1027°C). Calculations assume ideal mixing of non-ideal real gases. Data for pressures of 1, 500, 1000, 2000, and 3000 bars in the temperature range from 327-1027°C are tabulated in Appendix 1. Fugacity coefficients at other temperatures and pressures must be calculated, or defined at 1.0 (a condition which adds the assumption of ideal gas behaviour). The sum of the partial pressures of gas species in the S-0 system is calculated (PT SO SPECIES) and compared to the total pressure (P TOTAL RATIO). The PER CENT of each gas species is computed relative to the sum of the partial pressures of all species in the S-0 system, providing a measure of the relative importance of each species in the S-0 system. 189 SCOHPILF, TIME=60,PAGES=200 C C S-0 SYSTEM - VERSION 1 C C IN NAMING VARIABLES IH THE PROGRAM THE FOLLOWING RULES WERE C FOLLOWED C (1) FUGACITY COEFFICIENTS WERE PREFIXED BY FC C (2) LCG 10 FUGACITIES WERE PREFIXED BY FL C (3) FUGACITIES WERE PREFIXED BY F . C (4) PRESSURES WERE PREFIXED BY P C (5) THE PER CENT OF A GAS SPECIES WAS PREFIXED BY PCT' C (6) GAS SPECIES WERE NAMED BY FORMULA (EG 02 HOT OX FOR C OXYGEN) C 1 DIMENSION PT(5) , A (5), B(5) , C (5 ) , BUF(5), PTS0(8), RATIO (8), 1 FCS03(8,5), FCS02(8,5), FCS0(8,5), FCS2(8,5 ) , FCS20(8,5) , 2 CLS0(8), CLS02(8), CLS03 (8) , CLS20(8), FLS20(8) , 3 TEMPC (8), FL02(8) , FLS2 (8) , FLS0(8), FLS02(8 ) , FLS03 (8) , 4 P02(8) , PS2(8), PS0(8), PS02(8), PS03 (8) , PS20(8), 5 F02(8) , FS2 (8 ) , FSO (8) , FS02(8), FS03(8), FS20(8) 2 DIMENSION PCT02(8), PCTS2 (8) , PCTS0(8), PCTS02 (8) , PCTS03 (8) , 1 PCTS20(8), FLS21( 7 ) , FS21(7) C 3 READ(5,500) (PT (I) ,1=1,5) 4 500 FORMAT (5F10.0) 5 READ(5,501) ((FCS03(K,I),K=1 ,8),1=1,5) 6 READ(5,501) ( (FCS02(K, I ) ,K=1,0) ,1=1,5) 7 READ(5,501) ((FCSO(K,I) ,K=1,8) ,1=1,5) ' 8 READ(5,501) ( ( FCS2 (K,I),K= 1,8) , 1=1,5) 9 READ(5,501) ( (FCS20 (K , I ) , K = 1 , 8 ) ,1=1,5) 10 501 FORMAT (8F10.0) 11 READ (5,511) (CLSO ( K) ,CLS02 ( K ) ,CLS03(K) ,CLS 20 ( K ) ,K=1,8) 12 511 FORMAT (4F10.0) 13 READ(5,512) (A (J) , B (J) , C (J ) , J= 1 , 2) 14 512 FORMAT (3F10.0) 15 READ(5,513) (BUF(J),J=1,2) 16 513 FORM AT (2 A4 ) c C CHANGE TOTAL PRESSURE C 17 DO 100 1=4,5 C C CHANGE BUFFER C 18 ' DO 200 J=1 ,2 19 FAC=-A (J)+C (J) * (PT ( I ) - 1 . 0 ) ' C C SET LOG F (S2) C 20 F.LS2 2 = 1 . 0 21 DO 300 L=1,5 22 FLS22=FLS22-1.0 23 FLS21 (L)=FLS22 24 FL52RT=FLS21 (LJ/2.0 25 FS21 (L) = 10.0**FLS21 (L) C C SET TEMP IN DEGREES KELVIN - INCREMENT BY 100.0 (8 TIMES) C 26 TEMP=500.0 27 DO 400 K=1,8 190 28 TEMP=TEMP+100.0 29 TEMPC (K) =TEMP~27 3.0 C C CALCULATE T(02) FROM AH EQUATION OF THE FORM (C(PT -I .O)-A)/T EM P + B C 30 FL02 (K)=FAC/TEHP + B(J) 31 FL02RT=FL02(K)/2.0 32 F02 (K) =10. 0**FL02 (K) 33 P02 (K)=F02 (K) 34 FLS2 (K) =FLS2 1 (I.) 35 FS2 (K)=FS2 1 (L) 36 PS2 ( K ) =FS2 (KJ/FCS2 (K,I) C C CALCULATE THE FUGACITIES OF SO, S02, S03, AND S20 C 37 FLSO(K)=CLSC (K) +FLS2RT+FL02RT 38 FSO (K) =10.0* *FLSO (K) 39 PSO(K) =FSO(K)/FCSO ( K , I ) 40 FLSO2 (K)=CLS02 (K)+FLS2RT + F L 0 2 (K ) 41 FS02 (K)=10.0**FLSO2(K) 42 PS02 (K)=FS02 (K)/FCS02 (K,I) 43 FLS03 (K)=CLSC3 ( K ) +FLS2RT + 3.0*FLO2RT 44 FS03 ( K ) = 1 0. 0**FI.S03 (K) 45 PS03 (K)=FS03 (K)/FCS03(K,I) 46 FLS20 (K )= C L S 2 0 (K ) +FLS2 (K)+FL02RT 47 FS20 (K ) = 1 0 . 0 * * F L S 2 O (K ) 48 PS20 (K)=FS20(K)/FCS20(K, I) C C SUM PRESSURES OF GAS SPECIES IN THE S-0 SYSTEM C 49 PTSO (K) =PS0 (K) +PS0 2 ( K ) +PS03 (K) +PS20 (K) + PS 2 ( K ) * P02 ( K ) C C . CALCULATE THE PER CENT OF" EACH GAS' SPECIES RELATIVE TO THE TOTAL C PRESSURE OF SPECIES IN.THE S-0 SYSTEM C 50 PCT02 (K)=P02 ( K ) * 1 0 0 . 0 / P T S O ( K ) 51 PCTS2 (K)=PS2 ( K ) * 100.0/PTSO (K) . 52 PCTSO(K)=PSC (K)*100.0/PTSO (K) 53 PCTS02 (K)=PSO2(K)*100.0/PTSO(K) 54 PCTS03 (K)=PSC3 (K)*100.0/PTSO (K) 55 PCTS20 (K)=PS20 (K)* 100. 0/PTSO(K) C C CALCULATE THE RATIO ( IN PER CENT ) OF THE TOATL PRESSURE OF GAS C SPECIES IN THE S-0 SYSTEM TC THE TOTAL PRESSURE C 56 RATIO(K)=PTSO(K)*100.Q/PT (I) 57 400 CONTINUE C 58 WRITE(6, 600) PT (I) 59 600 FORMAT (1H1/50X15H TOTAL PRESSU REF10.0, 8H BARS) 60 WSITE(6,601) BUF(J) 61 601 FORMAT (1H02XA4,8H BUFFER) 62 WRITE(6, 608) C (J) , A (J) , B (J ) 63 608 FORMAT (1H02X13HLOG F(02) = (F8.5,1 OH (PT-1.0) -F9.1,10H )/TEMP +F5 1.2) 64 WRITE(6,602) (TEMPC (K) ,FL02 (K) ,FLS2(K) ,FLS0(K) ,FLSO2 (K),FLSO3 (K) , 1FLS20 (K),K=1,8) 65 602 FORMAT(1H0/2X8H TEMP(C)5X10H LOG F(02)5X10H LOG F(S2)5X10H LOG F (S 10)4X11H LOG F(S02)4X11H LOG F (SO 3) 4X 1 1 H LOG F (S20)//(F 10. 0 , 6 F1 5. 5) 2) 191 66 WRITE (6, 60 3) (TEHPC {K) , PTSO (K) , FS2 (K) , PSO (K) , FS0 2 (K) , FS03 (K) ,FS23 ( 1K),K=1,8) 67 603 FORMAT (IH 0/2X8 H TEMP (C) 2 X 1 3H PI SO Sp EC 1 ES 9 X6 11 F (S2) 9X611 F(SO)8X7H 1F(S02)8X7H F(S03)8X7H F (S2 C)//(0 PF10 . 0 , 1 P6 E15 . 5) ) 68 WRITE(6,604) (TEMPC (K) ,RATI 0 (K) ,PS2(K) , PS 0 ( K ) , P S 0 2 (K ) ,PS 03(K) ,PS20 1(K),K=1,8) 69 604 FORM AT (1110/2X8 H TSHP (C) 2 X 1 311P TOTAL RAT 109X6 11 P(S2)9X6H P(S0)8X7H 1P(S02)8X7H P(S03)8X7ll P (S20)//(OPF10.0,1P6E15.5)) 70 WRITE(6,605) (T EMPC (K) , PCT02 (K ) , PCTS 2 (K) , PCTSO (K) , PCTS02 (K ) , PC TSO 3 1 ( K ) ,PCTS20 (K) , K = 1,8) 71 605 FORMAT (1H0/2X8H TEMP (C)3 X12 H PER CENT 023X12H PER CENT S23X12H PER 1 CENT S02X13H PER CENT S022X13H PER CENT S032X13H PER CENT S20//(F 210.0,6F15. 5) ) 72 300 CONTINUE 73 200 CONTINUE 74 100 CONTINUE 75 STOP 76 END $DATA \ TOTAL PRESSURE 2 0 0 0 . BARS 6n 1 BUFFER LOG F (02) = i ! 0 . 0 1 9 0 0 (PT- 1. 0) - 2 1 9 1 2 . 0 ) / T E H P +11. 11 TEMP (C) LOG F(02) LOG F ( S 2 ) LOG F(SO) LOG F(S02) LOG F (S03 ) LOG F(S20) 327 . -27.014668 - 2 . 0 0 0 0 0 - 9 . 2 3 3 3 1 - 0 . 3 3 5 6 8 - 1 0 . 1 7 3 0 0 - 2 . 7 1 6 3 1 142 7. -21.121430 - 2 . 0 0 0 0 0 - 6 . 9 9 1 15 1.08270 - 7 . 0 2 2 1 5 - 2 . 0 6 5 1 5 527 . - 1 6 . 68251 - 2 . 0 0 0 0 0 - 5 . 30926 2. 11519 - 1 . 65776 - 1 . 57526 .62 7 . -1 3 .22779 - 2 . 0 C 0 0 0 - 1 . 0 0 0 8 9 2 .98021 - 2 . 80867 - 1 . 1 9 1 8 9 727 . - 1 0 . 1 6 1 0 1 - - 2 . 0 0 0 0 0 - 2 . 9 5 1 0 0 3. 63399 - 1 . 3 1 1 0 1 - 0 . 8 9 0 0 0 82 7. - 8 . 2 0 2 7 3 - 2 . 0 0 0 0 0 - 2 . 09 737 1. 1 7527 - 0 . 1 3 1 1 0 -0 . 63 83 7 92 7. - 6 . 31 833 - 2 . 0 0 0 0 0 - 1 . 3 8 1 1 7 1. 62767 0. 87950 - 0 . 1 2 9 1 7 1027 . - 14 . 72385 - 2 . 0 0 0 0 0 - 0 . 7 3 0 9 2 5 .01015 1. 73622 - 0 . 2 5 2 9 2 TERP (C) PT S 0 SPECIES F (S2) F(SO) F (S02) F (S03) F(S20) 327 . 1. 01216K 01 1 .OOOOOE-02 5 . 8 1 3 3 5 E - 1 0 1 . 61660E-01 6 . 71122E-11 1. 9 21 59E-03 <42 7. 1. 13115E 01 1 . 0 0 0 0 0 E - 0 2 1. 0 2 0 5 9 E - 0 7 1. 209772 01 9 . 1 9 6 3 0 E - 0 8 8 . 60698E-03 527. 9 . 80832E 01 1 . 0 0 0 0 0 2 - 0 2 14. 9 0 6 1 9 E - 0 6 1. 39795E 02 2 . 199072-05 2 . 6 59 1 62-02 627 . 6 . 19111S 02 1 .OOOOOE-02 9 . 97911F.-05 9 . 551152 02 1. 5 5 3 5 7 E - 0 3 6 . 38119E-02 72 7. 2. 93098E 03 1 . 0 0 0 0 0 2 - 0 2 1. 11 172S-03 1 . 30518E 03 - 1 . 550232 -02 . 1. 23B21E-01 827 . 1. 02906E 01 1 .OOOOOE-02 7 . 99 160E-03 1. 19716E 01 7 . 39 1392-0 1 2 . 29950E-01 927 . 2 . 95322E 0« 1 . 0 0 0 0 0 2 - 0 2 . Ii. 12889E-02 1 . 21291E 01 7 . 577072 00 7 22192-01 102 7. 7 . 212712 01 1 . 0 0 O O 0 E - 0 2 1. 65606E-01 .1. 02365E 05 5 . 117812 01 5 . 585672-01 TEMP (C) P T 0 T 1 L RATIO P(S2) P (SO) P(S02) P (S03) P(S20) 327 . 5 . 21080E-01 1 . 0 0 0 0 0 E 01 5 . 8 1 3 3 5 E - 1 0 1 . 19690E-01 8 . 31065E-11 1. 921 59E-03 <427. 7 . 15726E-01 5 .OOOOOE 00 1. 0 2 0 5 9 E - 0 7 9 . 30592E 00 8 . 7 2 0 2 0 2 - 0 8 8 . 606982-03 527. <4. 901162 00 9 - 0 9 0 9 1 E - 0 1 1 . 906192 -06 9 . 71175E 01 1. 7 5 0 8 5 E - 0 5 2 . 659 16E-02 627 . . 3 . 217072 01 2 . 7 0 2 7 0 E - 0 1 9 . 9 7 9 1 1 E - 0 5 6 . 190792 02 1. 1 219 62-03 6 . 3S119E-02 727 . 1. 16519E 02 1 . 3 6 9 8 6 E - 0 1 1. 11172E-03 2 . 9 30 68"E 03 3 . 21823E-02 1. 2S321E-01 82 7. 5 . 11529E 02 , 8 . 0 6 1 5 1 E - 0 2 7 . 99 1602-03 1. 02898E 01 5 . 20731E-01 2 . 299502-01 927 . 1. 17661S 03 5 . 0 7 6 1 1 2 - 0 2 1 . 12889E-02 2 . 95261E 01 5 . 35182E 00 3. 72219E-01 1027 . 3 . C0635E 03 3 . 5 3 3 5 7 E - 0 2 1. 6 5 6 0 6 E - 0 1 7 . 20878E 01 S7171E 01 5 . 58567E-01 TEKP (C) PER CENT 02 PER CENT S2 PE R CENT SO PEE CEK'T S02 PES " E S T S03 PER CENT S20 327 . 0 . 0 0 0 0 0 9 5 . 9 5 1 1 1 0 .00000 1.0271 1 0 .00000 0 .01811 U27. 0 . 0 0 0 0 0 31 .92953 0 .00000 65 .01030 0 . 0 0 0 0 0 0 .0 601 3 52 7. 0 . 0 0 0 0 0 0 . 9 2 6 8 6 0 .00001 9 9 . 0 1 6 0 2 0 .00002 0 .02711 627 . • 0 . 00000 0 . 0 1 1 6 2 0 .00002 99 .91811 0 . 0 0 0 1 7 0 .00983 727 . 0 . 0 0 0 0 0 0 . 0 0 1 6 7 0 .00001 9 9 . 9 8 9 7 9 0 . 0 0 1 1 0 C.00110 827 . 0 . 00000 0 . 0 0 0 7 8 0 . 0 0 0 0 8 9 9 . 9 9 1 9 0 0 . 0 0 5 0 6 0 .00223 9 2 7 . 0 . 0 0 0 0 0 0 . 0 0 0 1 7 0 .000 11 9 9 . 9 8 0 3 2 0 .01813 . 0 .00126 1 0 2 7 . 0 . 00000 0 . 0 0 0 0 5 0 .00023 9 9 . 9 1 5 1 8 0.0 5372 0 . 0 0 0 7 7 t-o 193 APPENDIX 5 GAS MIXTURE EXPERIMENTS - 0-H SYSTEM A preliminary set of experiments was undertaken to measure the composition of H 2 - H 2 O gas mixtures in equilibrium with iron and magnetite (MI buffer) at total pressures of 1000 and 2000 bars. The study was designed to determine the extent of non-ideal mixing in a portion of the 0-H system. Results place restrictions on the ideal mixing assumption commonly employed in the computation of equilibrium gas mixture compositions. in this system (Chapter 2 and Appendix 2). Experimental Procedures: Chargesj consisting of iron + 1^ 0 or iron + magnetite + 1^ 0, were sealed in Au or Pt capsules (dimensions tabulated in Section 4.2). The experimental configurations are [MI,OH] or [MI,OH(MI,OH)]. Starting materials, loading procedures, and calibrations are described in Sections 4.1 and 4.2. All experiments were quenched (air and water) and cooling times to room temperature were generally less than 4 minutes. The cold-seal bomb was cooled below room temperature with ice or dry ice before the pressure was released. After each'experiment the capsule was weighed, frozen on dry ice, washed with acetone, and carefully punctured with a sharp needle. The weight change on puncture was recorded and the capsule placed into a drying oven at 90°C. Constant weig?it was attained after 2-3 hours. Run products after each experiment were X-rayed and the modal proportions of iron and magnetite estimated from measurement of a peak intensity ratio. 194 Theory: The mole fractions of H 2 ( XH 2^ a n c l H 2 ° ( X H 2 0 ' ' * n t' i e v a P o u r phase at the termination of each run has been calculated in two ways. Method 1: moles H2 = ^ ^ _ i £ i L ^ i U ^ I £ t u r e = A 2.01594 moles H20 = weight loss on drying = g 18.01534 vmeas A , vmeas n meas X „ = — — — - , and X . T „ = 1 - X , . H2 A+B H 2 O H ? This calculation assumes only hydrogen is released on puncturing the run capsule, and the drying loss is due solely to water, meas X J J is not affected by H 2 diffusion during the experiment or by l-^ O loss on sealing the run capsule. Method 2: moles H - o r i g i n a l weight of H 2 O - weight loss on drying 2 18.01534 YC A L C C , Y c a l c , vcalc X = , and X = 1 - X „ H2 B + C H2° H2 This calculation is based on equating the number of moles of H 2 O unaccounted for after each experiment to the number of moles of H 2 in the final gas mixture. The overall reaction expressing the dissociation of H 2 0 in these experiments is; 4 H 2 0 + 3Fe % 4 H 2 + Fe 30 4 (A5-1) 195 Diffusion of hydrogen into the pressure medium during an experiment or loss of H 2 O on welding the capsule influences this calculation. Corrections have been applied where necessary. Loss of H 2 O in addition to H 2 on puncturing the run capsule necessitates an iterative calculation in order to estimate X j ^ l c . In this case method 1 calculations determine only an upper boundary on . Error limits for X^  are approximately ±0.10 for 2 2 method 1 and ±0.05 for method 2. The validity of assumptions for the two methods of computing X[< are effectively checked for each experiment by comparison of Xj„. and Cet 1C Xu . The configuration [MI,011 (MI,OH)] allows for two determinations of H2 X™ e a s and x£a-'-c. All values should f a l l within the error limits quoted H2 H2 above. The oxygen fugacity in each experiment has been calculated from thermochemical data for M I buffer (Table Al-1) and from experimentally determined values of Xu . H2 Assuming ideal mixing, f^ has been calculated by equation (2-6) and fQ 2 by rearranging equation (2-4): f 0 2 = ( Ptotal • YH20 • YH 2 - YH20 ' fH 2 )2 (A5-2) KH20 * fH 2 " YH 2 This expression on addition of a non-ideal mixing term becomes: f n = ( ptotal ' TH20 * aH20 " YH2 ' aH2 ~ Y"20 ' aH20 ' fH 2 ) 2 0 2  K H 20 ' fH 2 • YH 2 ' aH 2 (A5-3) 196 Experimental Results; 0-H gas mixture compositions in equilibrium with iron + magnetite at total pressures of 1000 and 2000 bars are listed in Table (A5-1). Results at 1000 bars are fragmentary. At T>550°C capsules either leaked during the run or exploded (apparently when pressure was released from the bomb) . The two measured X.J_J values (Table A5-1) show a positive deviation from ideality in comparison to Xj.^  calculated for MI buffer (see Figure 2-1 for Mil, Figure 2-2 for MI2). Measured XJ.J^ values for experiments at 2000 bars are plotted in Figure (A5-1). Log f Q o contours and Mil, WI1, and MW1 buffer curves (Figure A5-1) have been calculated assuming ideal mixing of H2 and H 2 O (Section 2.2). The extent of non-ideal mixing is strongly reflected in XJ_J . Measured X^  values differ from the predicted Xj_j values on the 2 2 . 2 Mil buffer curve (ideal mixing) by -0.33 at 327°C and -0.22 at 527°C (Figure A5-1, Table A5-2). The resulting error in log fQ (calculated by equation A5-2) is +1.5 at 327°C and +0.9 at 527°C (Table A5-2). The difference for each experiment may be estimated from Figure (A5-1). The Shaw correction (equation 2-14 and 2-15) does not extend to the P-T conditions of these experiments. Reliable activity coefficients for H2 and H20 are therefore not available and equation (A5-3) cannot be solved for these experiments. Results predicted by the Shaw correction are shown for comparison in Figure (2-3) and specific values for X ^ ^ , , and PH are tabulated (Table A5-2). TABLE (A5-1) Experimental Results Fe-O-H System Final assemblage in all experiments: iron + magnetite + vapour Argon pressure medium Run Temperature Duration Original Assemblage Gas Mixture Composition Capsule Experimental °C Hours Fe M yl H 2 O vmeas* vcalc* v Configuratio XH 2 H 2 XH 2 (average) 2 0 0 0 bars total pressure M H O 3 1 5 ± 3 2 2 X - 9 0 0 . 0 9 3 0 . 1 3 6 0 . 1 1 + 0 . 0 5 Au [MI,OH] M I 2 0 3 4 5 ± 3 7 1 x - 7 0 0 . 0 7 9 0 . 1 3 2 0 . .11+0. 0 6 Au [MI,OH] Mil 7 3 8 0 + 3 2 1 x - 5 0 0 . 1 2 5 0 . 2 0 4 0 . 1 6 ± 0 . 0 7 Au [MI,OH] M I S 4 7 0 + 4 2 3 x X 3 0 _ 0 . 1 5 2 , 0 . 1 6 ± 0 . 0 5 Pt [ M I ,OH ( M I ,OH)] X X 5 0 0 . 1 5 9 / Au Ml 5 4 7 0 ± 4 2 1 x X 3 0 0 . 2 2 2 \ 0 . . 2 1 + 0 . 0 5 Pt [ M I ,OH ( M I ,OH)] x X 5 0 0 . 1 9 7 0 . 2 0 3 ; Au M I 6 5 0 4 ± 4 1 4 x X 7 0 0 . 1 8 3 0 . 1 6 2 0 . 1 7 ± 0 . 0 5 Au [ M I , O H ] 1 0 0 0 bars total pressure • M I 2 3 3 0 9 ± 3 2 3 x - 5 0 < 0 . 2 5 6 F 0 . 2 1 7 0 . 2 2 + 0 . 0 5 Au [MI,OH] M I 1 2 3 1 8 ± 3 2 3 X - 6 0 < 0 . f 4 1 3 0 . 3 1 4 0 . 3 1 ± 0 . 0 7 Au [MI,OH] * . vmeas . vmeas vcalc . vcalc Note X H z 0 = 1 - X H z , X H 2 Q = 1 " X H 2 t High values reflect H20 loss on puncture FIGURE (A5-1) Gas Mixture Compositions in Equilibrium with iron + magnetite. Fe-O-H System Isobaric T-X Diagram. Dotted lines indicate log fQ2-2 0 0 0 &ARS ( I d o o l M i 1 0 0 0 • 9 0 0 -3 0 0 -7 0 0 -6 0 0 4 ' 5 0 0 /.00 i : 30C H-.O CO 199 TABLE (A5-2) 0-H Gas Mixture Calculations 2000 bars total pressure Y H 2 and Y H 2 0 values tabulated in Table (Al-2) log Kj.|2o from Table (Al-3) 0 -H Version 2 Calculations Buffer T°C log f 0 2 (defined) 4 l 2 £H 2 l 0S F H 2 ideal mixing H2 ) MI 1 327 -39.57 0.453 1716 3. 234 905 427 -32.64 0.432 1487 3. 172 863 527 -27.43 0.404 1294 3. 112 808 MI 2 327 -39.68 0.484 1836 3. 264 969 427 -32.90 0.508 1751 3. 243 1017 527 -27.82 0.514 1646 3. 216 1028 .iff er T ° C log f o 2 X H 2 fH2 l°g F H 2 P H 2 (defined) (non-•ideal mixing, , Shaw c o r r i Mil 327 -39.57 0.02 3086 3. 489 33 427 -32.64 0.05 2510 3. 400 95 527 -27.43 0.09 2014 3. 304 181 Ml 2 327 -39.68 0.02 3499 3. 544 38 427 -32.90 0.07 3355 3. 526 147 527 -27.82 0.23 2952 3. 470 458 Calculations based on experimental Xj.^  measurements Buffer T°C log £ 0 2 X H 2 % 2 l oS F H 2 P H , (eqn.A5-2) (Fig.A5-l) ( ideal mixing ) Ml 327 -38, ,05 0. ,125 474 2. ,676 250 427 -31, ,40 0. 155 534 2, ,727 310 527 -26, ,53 0, ,185 592 2. ,773 370 t outside valid range 200 APPENDIX 6 Fe-Ni OLIVINES Hydrothermal recrystallization of mixtures of ferrous oxalate + nickel oxalate + a cristobalite results in assemblages of Fe-Ni olivine + Ni + quartz (Table A6-1) . The intensity ratios 1quartz(101)/-1-olivine('130) and lNi(100)/Iolivine(130) measured from X-ray diffraction charts provide an estimate of the relative amounts of olivine, Ni, and quartz in each synthesis. Recrystallized assemblages corresponding to a mixture of 10.5 mole % Ni-olivine (Series A experiments - Table A6-1) contain amounts of Ni and quartz detectable only by optical study. The d(130) spacing varies strongly with composition in Fe-Ni olivines (Figure A6-1). Clark and Naldrett (1972) report d(130) for seven compositions of Fe-Ni olivines. A linear regression f i t to these data yields the following expression: Mole % Ni 2Si0 4 = 3336.29 - 1178.37 d(130) (A6-1) Equation (A6-1) is plotted as a dotted line on Figure (A6-1). Differences exist among reported d(130) values for fayalite (Table A6-2). Hydrothermally synthesized fayalites generally have d(130) values 0.003-0.005 lower than those reported by Clark and Naldrett (1972) or Jahanbagloo (1969). This difference adds an uncertainty of as much as 5 mole % Ni2Si04 to the X-ray determination of Fe-Ni olivine compositions. d(130) for each of the synthesized olivines was measured (see Section 4.3 for method) and the mole % Ni2Si04 calculated from equation (A6-1). Olivines synthesized from the mixture corresponding TABLE (A6-1) Fe-Ni Olivine Syntheses' Run Temperature Duration quartz(101)/ ^' iClOO)/ Hours Iolivine(130) JolivineflSO) d(130) Mole % Ni2Si04 equation equation (A6-1) (A6-2) F38 700 44 - - 2.827810.0009 - -Al 770 49 - - 2.820910.0007 12.23 8.46 A3 762 48 - - 2.8224±0.0008 10.46 6.69 A4 770 97 - - 2.820110.0008 13.17 9.40 Bl 760 61 0.17 0.43 2.817910.0005 15.76 11.99 B2 ' 796 37 0.10 0.16 2.8170+0.0005 16.82 13.05 B3 749 74 0.05 0.24 2.818510.0007 15.05 11.28 B4 751 97 0.10 0.31 2.8196+0.0009 13.76 9.99 Cl 750 52 0.66 1.33 2.8077+0.0011 27.78 24.01 C2 798 45 0.52 . 1.20 2.8047+0.0009 31.32 27.55 C3 754 74 0.72 1.84 2.8149+0.0005 19.30 15.53 C4 782 13 0.8.8 1.95 2.816610.0007 17.29 13.52 * All experiments at a total pressure of 2000 bars. The final assemblage for ail A,B, and C series experiments was Fe-Ni olivine + Ni + quartz. t Prefixes F, A, B, and C indicate starting oxalate + a cristobalite mixtures corresponding to 0.0, 10.5, 20.0, and 50.0 mole % Ni2Si04 respectively. F38 is a representative fayalite synthesis. O FIGURE (A6-1) Fe-Ni Olivine X-ray Determinative Curve 2.86 2.84 4 O. L .82 2.80 o n •o 2.7£ 2.76 1 2.74 1 F e 2 S I 0 4 1 0 •.0 30 5 0 © Clark and Naldrett (1972) A Fisher and Medaris (1969) A Pistorius (1963) equation (A6-1) equation (A6-2) '•Q "•A 70 90 M O L E % N i 2 s ; o 4 TABLE (A6-2) d(130) Values for Fayalite Source of Fayalite d(130) O A Reference Crystallized hydrothermally from a mixture of Si0 2 glass + ferrous oxalate (FeC204•2H20). Synthesized in a 1 atm. reducing furnace from a mixture of quartz + hematite. Crystallized hydrothermally under buffered f 0 2 [0B,OH(X,OH)] Ag7QPd30 inner capsule, Au outer capsule. Mixture of metallic iron + cristobalite held for 3 weeks at 900°C C ptotal = 5 0 0 b a r s ) • Crystallized hydrothermally in sealed Ag capsules from a mixture of metallic iron + quartz. Held for 2 weeks at 730°C (P t otal = 2 0 0 0 b a r s ) • Crystallized hydrothermally in sealed Ag capsules from a mixture of ferrous oxalate + a cristobalite. Held for 2 days at 700°C (P t otal = 2 0 0 0 bars). Prepared by dry fusion at 1 atm. (T>1000°C). Prepared in a blast furnace at 1 atm. (T>1000°C). Synthesized in Ag f o i l in evacuated sil i c a tubes from a mixture of metallic iron + hematite + quartz. Held for 1 week at 900°C. 2.826 2.8266 2.826 2.8280 2.8265 (QFM buffer) 2.8268 (QFI buffer) 2.8274 2.8278 2.8291 2.8292 2.8295 2.831 Wones and Gilbert (1969) Wones and Gilbert (1969) Fisher and Medaris (1969) (synthesized by Medaris) Fisher and Medaris (1969) (synthesized by Fisher) this study (Table A6-1) Yoder and Sahama (1957) Yoder and Sahama (1957) Clark and Naldrett (1972) Calculated d spacing based on X-ray diffraction study of 16 natural olivines. 2.831 Jahanbagloo (1969) 204 to 10.5 mole % Ni2SiO^ yield apparent compositions up to 2.7% higher than this value even though not a l l the Ni in the mixture went into the olivine structure. Taking d(130) for fayalite to be 2.8278 (Table A6-1) in place of the Clark and Naldrett (1972) value of 2.831 and keeping the slope of equation (A6-1) constant results in the following expression: Mole % Ni 2Si0 4 = 3332.52 - 1178.37 d(130) (A6-2) Equation (A6-2) yields values 3.77 mole % N^SiC^ lower than equation (A6-1) and gives more reasonable results for mole % Ni2Si04 (Table A6-1, Figure A6-1). 

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