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Thermodynamics of sodium aluminosilicate formation in aqueous alkaline solutions relevant to closed-cycle… Park, Hyeon 1999

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Thermodynamics of Sodium Aluminosilicate Formation in Aqueous Alkaline Solutions relevant to Closed-cycle Kraft Pulp Mills by  HYEON PARK B . S . , H a n y a n g U n i v e r s i t y , K o r e a , 1989 M . S . , H a n y a n g U n i v e r s i t y , K o r e a , 1993  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUESTMENTS FOR T H E DEGREE OF D O C T O R OF PHTLOSPHY in  THE F A C U L T Y OF G R A D U A T E STUDIES  D e p a r t m e n t o f C h e m i c a l and B i o - R e s o u r c e E n g i n e e r i n g  W e accept this thesis as c o n f o r m i n g to the required standard  THE UNIVERSITY OF BRITISH C O L U M B I A A u g u s t , 1999 © H y e o n P a r k , 1999  in  presenting this  thesis  in partial  fulfilment  of the requirements  for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by  his  or  her  representatives.  It  is  understood  that  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  0)CVY\ Iced?  W  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  /Uj.J^,  fifa-JxW-^u^  Krg<h ^jzr-l^j  11  ABSTRACT  Accumulation of A l and Si ions in the recovery cycle of a kraft pulp mill may cause sodium aluminosilicate scale formation. This glossy scale forms on process equipment and is very hard to remove. Thus, formation of the scale can create several operational problems in mills moving towards progressive system closure and should be prevented. The purpose of this study is to supply: (a) data on the precipitation conditions of sodium-aluminosilicates in green and white liquors of the recovery cycle; and (b) a model to predict such conditions. The data can either be used directly or to test process models for the design and optimization of progressive system closure strategies. The precipitation conditions of sodium aluminosilicates in synthetic green and white liquors at 368.15 K (95 °C) were determined. In the experiments, the effects of varying the Al/Si ratio and concentrations of OH", C0 ", S O 4 ' , and H S " were studied. 2  2  3  The structure of the precipitates was identified by X-ray diffraction, thermogravimetry and chemical  analysis.  The precipitates  were found to  have  the  structure of  hydroxysodalite dihydrate (Na8(AlSi04)6(OH) -2H20) except in a simulated green liquor 2  system  with  low  OH" and  high  Cf  concentrations  where  sodalite  dihydrate  (Nag(AlSi04)6Cl2-2H20) was formed. The precipitation conditions in mill green and white liquors at 368.15 K were also measured. The effects of varying the Al/Si ratio, NaOH, Na2C03, and Na2S concentrations were studied. The precipitates were found to have the structure of hydroxysodalite dihydrate. A thermodynamic model for sodium aluminosilicate formation in aqueous alkaline solutions was developed. Pitzer's method was adopted to calculate the activity of  Ill  water and the activity coefficients of the other species in solution. The system under consideration contained the ions of N a , Al(OH) ', S i 0 " , OH", C 0 " , S 0 ' , Cl', HS" +  2  4  2  3  2  3  4  dissolved in water and in equilibrium with two possible solid phases (sodalite dihydrate : Na8(AlSi04)6Cl2-2H 0 and hydroxysodalite dihydrate : Na (AlSi0 ) (OH)2- 2 H 0 ) at 2  8  4  6  2  368.15 K. The equilibrium constants of sodalite dihydrate and hydroxysodalite dihydrate formation reactions were determined using the thermodynamic properties of the species involved. Property values that were not available in the literature were estimated by group contribution methods. The model calculates the molality of all species at equilibrium including the amount of solid precipitates. The calculations were compared with published data and were found to be in good agreement. Meanwhile, since the system contains the Si03 " and Al(OH) " ions, knowledge of 2  4  the relevant Pitzer's model parameters is required. Osmotic coefficient and water activity data for Na2Si03 and mixed Na2Si03-NaOH aqueous solutions were obtained at 298.15 K by employing an isopiestic method. The binary Pitzer's parameters, P , f3 , and C*, for (0)  Na2Si03 and the mixing parameters,  Q  0 H  -  S i 0  2-  and  ¥  N  a  +  O  H  -  s  i  o  i - ,  (1)  were estimated using the  osmotic coefficient data. In addition, osmotic coefficient data were obtained for the aqueous solutions of N a O H - N a C l - N a A l ( O H ) . 4  The solutions were prepared by  dissolving AICI36H2O in aqueous N a O H solutions. The osmotic coefficients of the solutions were measured by the isopiestic method at 298.15 K. The osmotic coefficient data were used to evaluate the unknown binary and mixing parameters of Pitzer's model for the aqueous NaOH-NaCl-NaAl(OH) system. The experimental osmotic coefficient 4  data were correlated well with Pitzer's model using the parameters obtained.  iv  TABLE OF CONTENTS ABSTRACT  ii  T A B L E OF CONTENTS  iv  LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS  C H A P T E R 1. I N T R O D U C T I O N  viii xi xiv  1  1.1. E n v i r o n m e n t a l Impact o f the K r a f t P u l p i n g Industry  3  1.2. C l o s e d - c y c l e M i l l O p e r a t i o n  4  1.3. N o n - p r o c e s s E l e m e n t s i n the K r a f t P u l p i n g P r o c e s s  5  1.3.1. Sources and p r o f i l e o f non-process elements  5  1.3.2. A d v e r s e effects o f non-process elements  9  1.4. R e c e n t D e v e l o p m e n t s o f C l o s e d - c y c l e T e c h n o l o g y  10  1.5. Scale F o r m a t i o n i n the R e c o v e r y C y c l e  13  1.5.1. S o d i u m A l u m i n o s i l i c a t e Scale F o r m a t i o n 1.6. R e s e a r c h O b j e c t i v e s  15 19  C H A P T E R 2. T H E O R E T I C A L B A C K G R O U N D  21  2 . 1 . T h e r m o d y n a m i c E q u i l i b r i u m Constant  21  2.2. E q u i l i b r i u m Constant C a l c u l a t i o n at S p e c i f i c T e m p e r a t u r e  23  2.3. A c t i v i t y o f W a t e r , O s m o t i c C o e f f i c i e n t , and A c t i v i t y C o e f f i c i e n t  24  2.4. P i t z e r ' s A c t i v i t y C o e f f i c i e n t M o d e l  28  2.5. Isopiestic M e t h o d  32  C H A P T E R 3. M A T E R I A L S A N D M E T H O D S 3.1. S o l u b i l i t y E x p e r i m e n t s u s i n g Synthetic L i q u o r s o f S y s t e m A  35 35  3.1.1. E x p e r i m e n t a l d e s i g n  35  3.1.2. E x p e r i m e n t a l procedure  37  3.1.3. Identification o f the precipitates  39  V  3.2. Solubility Experiments using Synthetic Liquors o f System B  40  3.2.1. Experimental design  40  3.2.2. Experimental procedure and analysis  42  3.3. Solubility Experiments using M i l l Liquors  42  3.3.1. Experimental design  43  3.3.2. Experimental procedure and analysis  44  3.4. Osmotic Coefficient Measurement for Na2Si03 and Na2Si03-NaOH  45  Systems 3.4.1. Identification of silicic species by a titration method  45  3.4.2. Apparatus and chemicals  46  3.4.3. Experimental procedure  49  3.5. Osmotic Coefficient Measurement for N a O H - N a C l - N a A l ( O H ) System  50  4  3.5.1. Apparatus and chemicals  50  3.5.2. Experimental procedure  51  C H A P T E R 4. T H E R M O D Y N A M I C M O D E L I N G O F S O D I U M ALUMINOSILICATE  53  FORMATION  4.1. Model Equations  53  4.2. Structure of the Thermodynamic Model  55  C H A P T E R 5. O S M O T I C C O E F F I C I E N T D A T A F O R N a S i 0 , N a S i 0 - N a O H , 2  3  2  3  57  A N D NaOH-NaCl-NaAl(OH) A Q U E O U S S Y S T E M S 4  5.1. Identification of Metasilicic Species by Titration  57  5.2. M o l e Fraction of Metasilicic Species  63  5.3. Osmotic Coefficient Data for N a 2 S i 0 Aqueous System  63  5.4. Osmotic Coefficient Data for N a S i 0 - N a O H Aqueous System  65  5.5. Osmotic Coefficient Data for N a O H - N a C l - N a A l ( O H ) Aqueous System  70  3  2  3  4  C H A P T E R 6. D E T E R M I N A T I O N O F P I T Z E R ' S P A R A M E T E R S F O R N a S i 0 , 2  3  73  Na Si0 -NaOH, A N D NaOH-NaCl-NaAl(OH) A Q U E O U S S Y S T E M S 2  3  4  6.1. Pitzer's Parameters for N a 2 S i 0 and Na2Si0 -NaOH Aqueous Systems 3  3  73  vi  6.2. P i t z e r ' s Parameters f o r N a O H - N a C l - N a A l ( O H )  4  Aqueous System  6.3. R e l i a b i l i t y o f the P i t z e r ' s Parameter D e t e r m i n a t i o n  76 81  C H A P T E R 7. A P R I O R I D E T E R M I N A T I O N O F M O D E L P A R A M E T E R S  84  7.1. P i t z e r ' s Parameters  84  7.2. E q u i l i b r i u m Constants  86  7.3. E s t i m a t i o n o f T h e r m o d y n a m i c Properties  88  7.3.1. AHf° a n d AGf° o f sodalite dihydrate a n d h y d r o x y s o d a l i t e d i h y d r a t e  88  7.3.2. C ° o f Sodalite dihydrate a n d h y d r o x y s o d a l i t e dihydrate  91  7.3.3. S ° o f S i 0 '  93  p  2  3  ( a q  )  7.3.4. A H ° o f Si0 "(aq)  95  7.3.5. C ° o f S i 0 -  96  2  f  3  2  p  3  ( a q )  7.3.6. C a l c u l a t i o n o f K  s o d  at 368.15 K  97  7.3.7. C a l c u l a t i o n o f K  h s o  d at 368.15 K  98  7.4. C h a n g e o f In Khsod w i t h Temperature  99  C H A P T E R 8. S O L U B I L I T Y M A P S O F A l A N D S i I N G R E E N A N D W H I T E  101  LIQUORS 8.1. Synthetic G r e e n a n d W h i t e L i q u o r s o f S y s t e m A  101  8.2. Synthetic G r e e n a n d W h i t e L i q u o r s o f S y s t e m B  106  8.3. M i l l G r e e n a n d W h i t e L i q u o r s  112  8.4. Structure o f Precipitates f r o m synthetic l i q u o r s  118  8.5. Structure o f Precipitates f r o m m i l l l i q u o r s  122  8.6. M o r p h o l o g y o f Precipitates  122  C H A P T E R 9. P R E D I C T I O N O F T H E P R E C I P I T A T I O N C O N D I T I O N S O F  125  SODIUM ALUMTNOSILICATES 9.1. N a - A l ( O H ) " - S i 0 - - O F T - C 0 +  2  4  3  2 3  9.2. N a - A l ( O H ) " - S i 0 " - O H " - C 0 +  2  4  3  " - S0 2 _  3  2 4  - - C f - H 0 (System A ) 2  - C l ' - H S " - H 0 (System B ) 2  C H A P T E R 10. C O N C L U S I O N S A N D R E C O M M E N D A T I O N S  126 135  139  vii  NOMENCLATURE  142  BIBLOGRAPHY  146  A P P E N D I X I. Chemical Analysis by Atomic Absorption Spectrophotometer  159  A P P E N D I X II. Standard Errors and Confidence Intervals for Experimental  161  Solubility Data A P P E N D I X III. Tables o f Solubility Data  162  A P P E N D I X IV. Calculation o f Titration Curve  165  A P P E N D I X V. Uncertainty of the Measured Osmotic Coefficient  167  A P P E N D I X VI. Uncertainty o f the Estimated Thermodynamic Properties and  170  Equilibrium Constants A P P E N D I X VII. Comparison o f Pitzer's Parameters with Published Values  174  A P P E N D I X VIII. Sensitivity Analysis of Pitzer's Parameters  176  A P P E N D I X IX. Computational Source Codes in F O R T R A N 77  178  Determination o f Pitzer's binary parameters for single electrolyte system using  178  osmotic coefficient data Calculation o f osmotic coefficient and activity coefficient using Pitzer's binary  183  parameters for single electrolyte system Determination o f Pitzer's mixing parameters for multi-component electrolyte  186  system using osmotic coefficient data Calculation o f osmotic coefficient and activity coefficient using Pitzer's binary  193  and mixing parameters for multi-component electrolyte system Computation  o f equilibrium  state for NI^-NI^OH-Ff-HCl-NELiCl-Cr-Na*-  199  N a C l - K - K C l system at 573.15 K +  Computation o f equilibrium state for sodium aluminosilicate formation  205  viii  LIST OF TABLES  T a b l e 1.1 A m o u n t o f non-process elements from each source.  6  T a b l e 1.2. M e t a l contents i n the b l e a c h effluent.  8  T a b l e 1.3. C o n c e n t r a t i o n range o f process and non-process elements i n g r e e n a n d  8  white liquors. T a b l e 3.1. S o l u b i l i t y experiment d e s i g n for synthetic l i q u o r s o f system A .  36  T a b l e 3.2. S o l u b i l i t y e x p e r i m e n t design for synthetic l i q u o r s o f system B .  41  T a b l e 3.3. A n a l y s i s results o f m i l l l i q u o r s .  43  T a b l e 3.4. S o l u b i l i t y experiment d e s i g n for m i l l l i q u o r s .  44  T a b l e 5.1. O s m o t i c coefficients  66  and w a t e r activities for the N a 2 S i 0 3 aqueous  system at 298.15 K . Table  5.2.  Osmotic  coefficients  and  water  activities  for the  Na2Si0 -Na0H 3  68  aqueous system at 298.15 K . T a b l e 5.3. O s m o t i c coefficients  of NaCl  and K C 1 as reference and  standard  71  T a b l e 5.4. O s m o t i c coefficients o f N a O H - N a C l - N a A l ( O H ) 4 aqueous solutions at  72  solutions at 298.15 K .  298.15 K . T a b l e 6.1. T h e P i t z e r ' s parameters o f N a 2 S i 0  3  and N a S i 0 - N a O H systems at 2  3  75  298.15 K . T a b l e 6.2. T h e P i t z e r ' s parameters at 298.15 K available i n the literature.  79  T a b l e 6.3. T h e P i t z e r ' s parameters o f N a O H - N a C l - N a A l ( O H )  80  4  aqueous system at  2 9 8 . 1 5 K obtained i n this study. T a b l e 6.4. T h e P i t z e r ' s parameters o f N a T c 0 , N a T c 0 - N a C l , and N a B r - N a C 1 0  4  82  T a b l e 6.5. C o m p a r i s o n o f measured o s m o t i c coefficients w i t h c a l c u l a t e d those for  82  4  4  systems at 2 9 8 . 1 5 K .  the N a T c 0  4  system at 298.15 K .  ix  Table 7.1. Pitzer's binary parameters for the modeling of sodium aluminosilicate  85  formation. Table 7.2. Pitzer's mixing parameters for the modeling of sodium aluminosilicate  85  formation. Table 7.3. Thermodynamic data at 298.15 K and 1 bar published in the literature.  87  Table 7.4. Estimations of A H ° and A G ° o f anhydrous sodalite ( N a ( A l S i 0 ) C l ) .  89  Table 7.5. Estimated thermodynamic data at 298.15 K and 1 bar.  90  f  f  8  4  6  2  Table 7.6. Estimation o f C ° of anhydrous sodalite (Na (AlSi0 )6Cl ).  92  Table 7.7. Contribution by 2 H 0 for C ° estimation.  92  p  4  8  2  2  p  Table 7.8. Contributions by C l and ( O H ) 2  for C ° estimation.  2  93  p  Table 7.9. Prediction of the entropy of aqueous ions at 298.15 K, cal/mol K. Thermodynamic data o f Na SiC>3( ), N a ( a q ) ,  Table 7.10.  +  S  2  calculation of the AG , A H ° , and A S 0  and  Si03 "(aq) 2  94 for  the  95  of reaction (7.11).  0  Table 7.11. Heat capacities of aqueous oxy-anions at 298.15 K, cal/mol K.  96  Table 8.1. Repeatability of the experiments in three runs.  102  Table 9.1. Comparison o f the calculation results for the N H , - N H j O H - H* - H C l -  126  NH4CI - C f - N a  - NaCl - K  +  +  - KC1 system at 573.15 K.  Table 9.2. Example o f the modeling calculation results for the N a Si0 " - O f f - C0 " - S0 2  3  2  3  2 _ 4  -Cf -H 0 2  +  - Al(OH) " 4  129  system at 368.15 K.  Table A. 1.1. Analytical data for the analysis of liquid phase alkaline samples.  159  Table A. 1.2. Analytical data for the analysis of samples from the solid precipitates.  160  Table A.3.1. Solubility data for synthetic liquors o f system A.  162  Table A.3.2. Solubility data for synthetic liquors of system B.  163  Table A.3.3. Solubility data for mill liquors.  164  Table A.7.1. Comparison of Pitzer's parameters.  174  Table A.8.1. Sensitivity analysis o f Pitzer's parameters for N a S i 0 2  system.  3  aqueous  176  X  T a b l e A . 8 . 2 . S e n s i t i v i t y analysis o f P i t z e r ' s parameters f o r Na2SiC«3-NaOH aqueous  177  system. Table  A.8.3.  Sensitivity  analysis  N a A l ( O H ) 4 aqueous system.  o f Pitzer's  parameters  for  NaOH-NaCl-  177  xi  LIST OF FIGURES  F i g u r e 1.1. A d i a g r a m o f the kraft p u l p i n g process.  2  F i g u r e 1.2. M e t a l p r o f i l e o f p r e - o x y g e n stage kraft pulp.  7  F i g u r e 3.1. E q u i l i b r i u m vessel for the s o l u b i l i t y experiments.  38  F i g u r e 3.2. T h e isopiestic apparatus.  47  F i g u r e 4 . 1 . A b l o c k d i a g r a m o f the t h e r m o d y n a m i c m o d e l i n g .  56  F i g u r e 5.1. T i t r a t i o n c u r v e for the Na2SiC»3-NaOH s o l u t i o n w i t h H C 1 s o l u t i o n .  58  F i g u r e 5.2. C a l c u l a t e d titration c u r v e for the N a S i 0 - N a O H and N a C 0 - N a O H  62  2  3  2  3  solutions w i t h H C 1 solution. F i g u r e 5.3. M o l e fraction o f m e t a s i l i c i c species w i t h p H .  64  F i g u r e 5.4. O s m o t i c coefficients o f N a S i 0 and K C I aqueous solutions at 2 9 8 . 1 5  67  2  3  K. F i g u r e 5.5.  O s m o t i c coefficients  o f m i x e d N a S i 0 - N a O H and 2  K C I aqueous  69  aqueous s o l u t i o n at  77  and N a O H i n m i x e d N a S i 0 -  78  3  solutions at 298.15 K . F i g u r e 6.1. M e a n a c t i v i t y coefficients o f N a S i 0 2  3  in N a S i 0 2  3  298.15 K . F i g u r e 6.2. M e a n a c t i v i t y coefficients o f N a S i 0 2  3  2  3  N a O H aqueous solution at 2 9 8 . 1 5 K . F i g u r e 7.1. C h a n g e o f In K h s o d w i t h temperature. Figure  8.1.  A l and  S i ions a p p r o a c h i n g  e q u i l i b r i u m obtained  99 from  the  base  102  F i g u r e 8.2. S o l u b i l i t y map o f A l and S i i n synthetic green and w h i t e l i q u o r s o f  104  e x p e r i m e n t u s i n g synthetic green l i q u o r o f system A .  system A . F i g u r e 8.3. E f f e c t o f h y d r o x y l ions o n the s o l u b i l i t y l i m i t i n synthetic green and  105  w h i t e l i q u o r s o f system A . F i g u r e 8.4. E f f e c t o f carbonate ions o n the s o l u b i l i t y l i m i t i n synthetic green and  107  Xll  white liquors of system A. Figure 8.5. Effect of sulfate ions on the solubility limit in synthetic green and white  108  liquors of system A. Figure 8.6. Solubility map of Al and Si in synthetic green and white liquors of  110  system B . Figure 8.7. Effect of Na S on the solubility limit in synthetic green and white 2  111  liquors of system B . Figure 8.8. Solubility map of Al and Si in mill green and white liquors.  113  Figure 8.9. Effect of NaOH on the solubility limit of Al and Si in mill liquors.  114  Figure 8.10. Effect of N a  115  2  C03  on the solubility limit of Al and Si in mill liquors.  Figure 8.11. Effect of Na S on the solubility limit of Al and Si in mill liquors.  116  Figure 8.12. Solubility map comparing solubility limit of Al and Si in varying  117  2  liquors. Figure 8.13. X-ray diffraction pattern of precipitates in synthetic green liquor of  119  system A. Figure  8.14.  Thermogravimetric  analysis  of hydroxysodalite  dihydrate,  121  Na8(AlSi04)6(OH) -2H 0, precipitated in synthetic white liquor of system 2  2  A. Figure 8.15. Scanning electron micrographs of precipitates.  123  Figure 9.1. Equilibrium concentration of aluminum and silicon species.  127  Figure 9.2. Effect of hydroxyl ion concentration changes on the equilibrium  128  concentration of aluminum and silicon species. Figure 9.3. Effect of carbonate ion concentration changes on the equilibrium  130  concentration of aluminum and silicon species. Figure 9.4. Effect of sulfate ion concentration changes on the equilibrium  131  concentration of aluminum and silicon species. Figure 9.5. Effect of hydroxyl ion concentration changes on the equilibrium concentration of aluminum and silicon species.  132  xiii  Figure 9.6. Effect o f carbonate ion concentration changes on the equilibrium  133  concentration of aluminum and silicon species. Figure  9.7. Effect o f sulfate ion concentration  changes on the equilibrium  134  concentration o f aluminum and silicon species. Figure 9.8. Effect o f hydrosulfide ion concentration changes on the equilibrium  135  concentration of aluminum and silicon species. Figure 9.9. Effect o f hydrosulfide ion concentration changes on the equilibrium  136  concentration of aluminum and silicon species. Figure 9.10. Comparison o f model predictions with published correlations and  137  industrial data. Figure A.7.1. Osmotic coefficients for NaCl, N a S 0 , and N a S 0 2  4  2  2  3  systems.  175  xiv  ACKNOWLEDGEMENTS  The  author wishes to thank those who  friendship for this work. In particular, the  supplied the ideas, the time, and  author wishes to express his sincere  appreciation to his supervisor, Dr. Peter Englezos, who electrolyte thermodynamics. His  the  guided him  advice, patience, instruction and  to the sea  support are  of the  principal contributions to the successful completion o f this study. Sincere gratitude is extended to the thesis committee members, Dr.  Charles  Haynes for his fruitful discussions about the osmotic coefficient measurement as well as Dr. A. Paul Watkinson, and Dr. Chad P. J. Bennington for their valuable comments. The author is deeply indebted to Dr. Mati Raudsepp in the Department of Earth and Ocean Sciences for his kind help in performing the X-ray diffraction and  SEM  analysis. The author would like to acknowledge the help and support provided by M i k e Towers, V i c Uloth, Brian Richardson, and Jim Wearing from P A P R I C A N . Thanks are also expressed to Mr. Horace Lam, Ms.  Brenda Dutka, Mr. Ken  Ms. Rita Penco, Mr. Tim Paterson, Mr. Peter Taylor,  Wong and all the staff in the Department o f Chemical  Engineering and Pulp and Paper Centre. John Bates Centennial fellowship as well as University Graduate Fellowship are gratefully acknowledged.  On a more personal level, I wish to thank my  best friends met in Canada: Tazim  Rehmat for her kind friendship including a fortune chip from Las  Vegas, Khizyr  Khoultchaev for his unique instruction of titration methods, Peter Pang for his kind help in the lab, Geoff Bygrave for his useful discussion about thermodynamics, Isabelle  XV  P i n e a u l t for sweet c o o k i e s and muffins, O k H y u n A h n for his great help w i t h c o m p u t e r s , A h H y u n g P a r k for her kindness t o m y f a m i l y , D a l H o o n L e e for e n j o y i n g coffee breaks together, J o n g C h o o n L i m and W o o k D o n g K w o n for sharing fresh atmosphere o n the green at M c C l e e r y . I a m also grateful t o Prof. K y o n g O k Y o o , P r o f . D o o S u b K i m , P r o f . H e e T a i k K i m , P r o f . S a n g June C h o i , Prof. D a e W o n P a r k , Prof. T a e J o o C h o i , D r . D o n g H y u n L e e , and D r . B y o u n g M o o M i n for their grateful encouragement. I w o u l d p a y special tribute to m y mother, brothers, and parents i n l a w for their u n c o n d i t i o n a l l o v e and support f r o m m y h o m e , K o r e a . T w i n k l i n g eyes o f m y son, S i Y o u n g , have been a catalyst for this w o r k . M o s t o f a l l , I w o u l d l i k e to express s p e c i a l thanks to m y w i f e , S u n M e e L e e for her love, sacrifice and best dinners. She never d o u b t e d m y d e c i s i o n to study abroad for m a n y years.  I w o u l d l i k e to dedicate this w o r k to m y father i n heaven. H i s c o n f i d e n c e and encouragement i n m e have never w e a k e n e d . S i n c e r e l y hope he is n o w p r o u d o f his son.  1  CHAPTER 1. INTRODUCTION  Kraft pulp is made by reacting wood chips with a strongly alkaline solution. This process is called digestion in the pulp industry. The pulp fibres are then subjected to bleaching for brightness improvement. The kraft pulp process consists o f three streams; brown fibre line, bleach plant fibre line and chemical recovery cycle (Smook, 1992). A simplified diagram of the kraft pulping process is shown in Figure 1.1. W o o d chips are delignified in the digester by using a solution o f N a O H (sodium hydroxide) and N a S (sodium 2  sulfide). After digestion, the delignified  chips are  discharged into a blow tank to be disintegrated into individual fibres. Separated weak black liquor from the brown stock washer is evaporated and burnt in the recovery boiler. Most o f organic materials are incinerated. The remaining inorganic chemicals are entered into the smelt dissolving tank. Major portion of the smelt is a solid form o f  Na C03 2  (sodium carbonate), N a S and NaOH. The smelt is dissolved in water which forms green 2  liquor. The dissolved  Na C03 2  in green liquor is converted to N a O H in white liquor by the  reaction (1.1) in the causticizers.  Na C0 2  3  + C a ( O H ) -> 2 N a O H + C a C 0 2  (1.1)  3  White liquor containing the cooking chemicals, N a O H and Na S, is recycled to the 2  digester and used for cooking chips (Smook, 1992; Grace etal, 1989).  2  3  The fibres separated at the brown stock washer do not have enough brightness. The lignin content of the fibres is reduced by 50 %  in the oxygen delignification stage.  Dissolved solids are recovered by washing the oxygen-delignified stock and they are recycled to the recovery boiler. The pulp is discharged to the bleach plant to increase the brightness (Grace et al,  1989). Several different sequences of bleach stages are used in  modern kraft pulp mills. The conventional bleaching method using the chlorine gas is not used any more because of the dioxin formation problem. Most of kraft mills have E C F (Elementary Chlorine Free) or T C F (Totally Chlorine Free) bleach stages (Teder et  al,  1990; Chandra, 1997). The kraft pulp is used to make high quality papers such as printing paper because of its better strength and brightness compared to mechanical pulp (Grace et al,  1989).  1.1. Environmental Impact of the Kraft Pulping Industry Dioxin and furan detection in effluents from kraft mills has been reported (Servos et al,  1996; Norstrom et al,  1988; Bohn, 1998). In 1983, U.S. government reported that  dioxin was found in the downstream of pulp mills in Maine, Wisconsin and  Minnesota.  Biologists of Canadian Wildlife Service found some of the highest dioxin levels in the egg shells near the pulp mill at Crofton on Vancouver Island in 1987 Norstrom et al.  (Bohn, 1998).  (1988) reported that ecologically significant amounts o f chlorinated  dioxins and furans were present in sediments and fish in the vicinity o f B.C. mills. As a result o f these findings, stringent pollution standards were set by the government and more efforts to minimize the environmental impact have been requested from the kraft pulp mill industry (Martin, 1998).  4 The large amount of water consumption is another environmental concern of the kraft pulp mills. A few decades ago, it was common for a bleached kraft mill to use up to 400 m /ton pulp. In spite of the significant improvements in the water consumption, total 3  water use still ranges from 30 to 150 m /ton pulp (Bihani, 1996). 3  1.2. Closed-cycle Mill Operation  Closed-cycle mill operation has been considered as the ultimate method to achieve further effluent reduction and to minimize the environmental impact. Closedcycle in the context here means no liquid effluents from the mill. Of course, there might be some emissions as gaseous and solid wastes which can be handled in an environmentally safe manner. This is the concept of reducing pollution at the source by reusing more of the water, fibre, chemicals and energy contained in the waste stream. This may also reduce the load of the effluent treatment (Galloway et al, 1994). The first attempt at closed-cycle at the Great Lakes Forest Products Ltd. bleached kraft pulp mill at Thunder Bay, Ontario, Canada was unsuccessful due to corrosion in the white liquor evaporators, the recovery boiler superheater tubes, and the black liquor evaporator tubes, pitch deposition, scaling in the salt recovery process and other miscellaneous problems (Patrick et al, 1994). Several trials of closed-cycle kraft pulp production have been attempted but it has not been achieved yet (Galloway et al, 1994). The gradual move towards a closed mill is what the industry refers to a progressive system closure. Although closed-cycle operation of any kraft mill has not been achieved yet, a number of mills have stated this as their goal, and are working towards it. It should be noted that closed-cycle CTMP (chemi-thermomechanical pulp) mills are already a  5  c o m m e r c i a l r e a l i t y ( B a r n e s et al, CTMP  1995). S u c h t e c h n o l o g i c a l d e v e l o p m e n t o f c l o s e d - c y c l e  m i l l s o p e n e d the p o s s i b i l i t y o f v i r t u a l l y e l i m i n a t i n g l i q u i d d i s c h a r g e s  from  b l e a c h e d kraft p u l p m i l l s .  1.3. Non-process Elements in the Kraft Pulping Process O n e o f the issues that prevent c l o s e d - c y c l e kraft m i l l o p e r a t i o n is related to the p r o b l e m s caused b y the b u i l d - u p o f non-process elements ( N P E s ) . N P E s are i o n s s u c h as aluminum ( A l ) , silicon (Si), calcium (Ca), barium (Ba), potassium ( K ) , chloride ( C l ) , m a g n e s i u m ( M g ) , p h o s p h o r u s (P), manganese ( M n ) , i r o n (Fe), and c o p p e r ( C u ) . T h e y enter the s y s t e m as part o f the w o o d chips, water, and c h e m i c a l s a n d are not required to manufacture p u l p . I n a n o p e n m i l l N P E s are w i t h d r a w n but they a c c u m u l a t e i n a c l o s e d one ( G a l l o w a y et al,  1994). T h e b u i l d - u p o f N P E s c a n cause severe process p r o b l e m s  s u c h as s c a l i n g , c o r r o s i o n , and interference o f b l e a c h i n g ( G a l l o w a y et al, et al,  1997). T h e p r o p e r management  of NPEs  1994; G l e a d o w  is prerequisite f o r the  successful  implementation o f closed-cycle technology.  1.3.1. Sources and profile of non-process elements The  major sources o f the non-process elements are w o o d , m a k e - u p l i m e , a n d  water. T a b l e 1.1 s h o w s the amount o f non-process elements i n t r o d u c e d to the process. M o s t o f the non-process elements tend to concentrate i n the bark, roots, and foliage. Therefore, u n b a r k e d w o o d o r w h o l e tree c h i p s w i l l c o n t a i n h i g h e r concentrations o f n o n process elements. S a n d , clay and c o n t a m i n a t i o n attached o n the l o g s c o n t a i n s i g n i f i c a n t  6  amounts o f s i l i c o n and a l u m i n u m . L o g s transported b y sea a d d e x t r e m e l y large amounts o f chloride. T a b l e 1.1. A m o u n t o f non-process elements from each source ( G a l l o w a y et al,  1994).  W o o d chips  Make-up lime  Water  ( m g / k g a.d. pulp)  ( m g / k g a.d. pulp)  ( m g / k g a.d. pulp)  Al  29  23  <10  Si  724  400  120  Ca  2310  13400  86  K  1100  <10  22  Element  Cl  629  <10  74  Mg  352  139  32  Mn  159  <10  <10  Fe  76  29  16  T h e r e are n o major differences  in N P E s between  h a r d w o o d s and  softwoods  except for the c a l c i u m and p o t a s s i u m content. C a l c i u m is m u c h h i g h e r i n h a r d w o o d s , e s p e c i a l l y i n aspen. P o t a s s i u m appears to be a little h i g h e r i n h a r d w o o d . C a l c i u m and m a g n e s i u m are integral c o m p o n e n t s o f the w o o d ( M a g n u s s o n et al,  1979). M a k e - u p l i m e  is one o f the major sources for c a l c i u m . S i l i c o n and m a g n e s i u m contents i n the m a k e - u p l i m e are not n e g l i g i b l e . A b o u t 5 ~ 12.2 k g / t o n a.d. p u l p o f the m a k e - u p l i m e is u s e d for the kraft p u l p i n g . D i s s o l v e d o r g a n i c and i n o r g a n i c materials i n c l u d i n g non-process elements  are  w a s h e d i n b r o w n stock washer and enter into the r e c o v e r y line. A p o r t i o n o f non-process elements are attached to the p u l p , w h i c h is i n t r o d u c e d to the b l e a c h i n g l i n e w i t h p u l p . T h e metal p r o f i l e o f the p r e - o x y g e n stage kraft pulp o f 15.3 % consistency and p H 10.3 from a m i l l ( i n P r i n c e G e o r g e , B . C . ) w a s determined i n o u r laboratory. T h e results are s h o w n i n F i g u r e 1.2. T h e p u l p s a m p l e o f 2 0 g w a s d r i e d i n a n o v e n at 105 ° C and ashed i n a furnace at 575 ° C . T h e ash w a s digested i n 6 N H C 1 s o l u t i o n . T h e digested s o l u t i o n w a s  d i l u t e d w i t h d i s t i l l e d and d e i o n i z e d water and filtered t h r o u g h 0.45 p m m e m b r a n e filter. T h e filtrate w a s a n a l y z e d b y the I C P (Inductively C o u p l e d P l a s m a , A C M E  Analytical  L a b . V a n c o u v e r , B . C . ) to determine the metal contents i n the p u l p . M e a n w h i l e , a p o r t i o n o f the p u l p sample w a s squeezed to extract the l i q u o r . T h e l i q u o r w a s filtered t h r o u g h 0.45 p m membrane filter. T h e filtrate s a m p l e w a s a n a l y z e d b y I C P to determine the metal content i n the l i q u o r (shaded bars i n F i g u r e 1.2).  Metal  content i n the fibres ( w h i t e bars i n F i g u r e 1.2) w a s c a l c u l a t e d b y s u b t r a c t i n g the metal content i n the l i q u o r from that i n the pulp.  F i g u r e 1.2. M e t a l profile o f p r e - o x y g e n stage kraft p u l p .  600  25000  T  2000 500  3 20000  Pulp  1  Q.  -ri o  1500  Liquor Fibre  400  I? 15000 E,  § 10000 c o o •jjj  300 A  1000  200 500  5000  100 A  Na  K  Ca  Mg Si  Al Fe Mn P Cu Ba  In the p r e - o x y g e n stage kraft pulp, large amounts o f N a , K , C a , and M g elements w e r e present. A m o u n t s o f S i , A l , F e , M n , P , C u , and B a w e r e not n e g l i g i b l e . M o s t o f  8  elements w e r e distributed i n fibers a n d their content i n l i q u o r w a s v e r y l o w except f o r s o d i u m a n d potassium. T a b l e 1.2 s h o w s metal content i n a c i d a n d alkaline effluents o f an E C F b l e a c h i n g plant. M e t a l i o n level i n the a c i d b l e a c h effluent is h i g h e r than that i n alkaline effluent.  T a b l e 1.2. M e t a l contents i n the b l e a c h effluent, mg/kg o v e n dried pulp ( T o w e r s , 1995).  Na  Al  Si  Ca  K  Mg  Mn  Fe  Acid  1060  40  400  1650  250  300  50  125  Alkaline  ND  35  290  350  60  75  7  40  N D : not detected  T a b l e 1.3. C o n c e n t r a t i o n range o f process and non-process elements i n green a n d white liquors, mol/L. mol/L element  2.53 - 4 . 2 6  Na  3.2-4.5  1 5 1  Al  - 0.0029  [ 3 ]  Si  0 . 0 0 2 - 0.009  Mg  - 0.00003  K  0.11 - 0 . 3 2  co  3  S0  4  2  2  -  0.7-1.5  "  0.05 - 0.2  U  0.3 - 0.8  OH"  0.25 - 1.0 '  5  0.05-0.15  ]  m  [ 1 ]  1 2 1  0.18-0.42  [ 1 ]  l 4  m  '  6 ]  [ 4 > 6 ]  0.7 t > 5  [ 5 ]  [ 4  - 0.0004  0.12-0.22  [ 1 ]  4  0.003 - 0 . 0 0 6 1  - 0.000012  1 6 1  HS"  cr  [  [ 1 ]  [  1 1 1  0.00016-0.00056 1 3 1  0.0001 - 0 . 0 0 0 6  Ca  White liquor  Green liquor  2.3 - 2.75  5 ]  0.0513 - 0 . 5 9 1  m  1 3 , 4 1  0.0538-0.623  [ 1 ]  [1] Towers 1995, [2] Ulmgren 1995, [3] Ulmgren 1987, [4] Magnusson etal. 1979, [5] Lindberg and Ulmgren 1982, [6] Grace etal. 1989.  Table  1.3 s h o w s the concentration range o f non-process  elements as w e l l as  process elements i n molarity. T h e A l , S i , and K are soluble elements i n a l k a l i n e solutions and their concentration levels are higher than those o f C a a n d M g .  9  1.3.2. Adverse effects of non-process elements A l u m i n u m and s i l i c o n are found p a r t i c u l a r l y i n the b a r k o f the p u l p w o o d . T h e s e elements are a c o n c e r n i n the r e c o v e r y c y c l e since no large p u r g e points are available. A c c u m u l a t i o n o f a l u m i n u m and s i l i c o n i n the s o d i u m c y c l e c a n result i n the f o r m a t i o n o f s o d i u m a l u m i n o s i l i c a t e scales. F o r m a t i o n o f these scales l o w e r s heat transfer e f f i c i e n c y and reduces e v a p o r a t i o n capacity o f the b l a c k l i q u o r evaporators ( U l m g r e n , 1982). A n increase i n the s i l i c o n content o f l i m e m u d l o w e r s the r e a c t i v i t y o f the burnt l i m e because a l k a l i - s i l i c o n c o m p o u n d s c o u l d melt o n the surface o f the l i m e pellets thus r e d u c i n g the p o r o s i t y o f l i m e ( M a g n u s s o n et al, 1979). C a l c i u m is considered a non-process element except i n the r e c a u s t i c i z i n g and l i m e k i l n area. C a l c i u m c a n lead to s c a l i n g p r o b l e m s i n a n u m b e r o f m i l l areas ( G l e a d o w et al, 1996). R e c y c l i n g o f a c i d i c effluents  to the  alkaline brownstock  increases c a l c i u m  concentrations, w h i c h c a n cause equipment scales s u c h as c a l c i u m carbonate, c a l c i u m oxalate and c a l c i u m silicate. W h e n the c a l c i u m concentration i n a c i d b l e a c h i n g stages is h i g h , c a l c i u m sulfate scales are f o r m e d because c a l c i u m sulfate is r e l a t i v e l y i n s o l u b l e at l o w p H ( B r y a n t and E d w a r d s , 1996). A c c u m u l a t i o n o f b a r i u m results i n b a r i u m sulfate deposit p r o b l e m s i n a E C F o r T C F b l e a c h plant ( U l m g r e n , 1996). P o t a s s i u m enters the m i l l w i t h the w o o d chips. It c o m b i n e s w i t h c h l o r i d e a n d leads to p l u g g i n g related problems caused b y s t i c k y r e c o v e r y b o i l e r dust. P o t a s s i u m has the greatest tendency t o accumulate i n the s o d i u m c y c l e under c l o s e d - c y c l e operation. There is no effective purge for potassium since it is s o l u b l e i n a l k a l i n e solutions. T h e major undesirable i m p a c t o f potassium is i n the r e c o v e r y furnace w h e r e , i n c o m b i n a t i o n w i t h c h l o r i d e , it reduces the m e l t i n g point o f s o d i u m salts that are entrained i n the flue  10  gas and a c c u m u l a t e o n the tubes o f the boiler. S o d i u m and p o t a s s i u m p r o d u c e s l a b b i n g and r i n g f o r m a t i o n i n the l i m e k i l n at h i g h concentrations because o f the l o w m e l t i n g points o f s o d i u m and potassium carbonate i n the c a l c i u m c y c l e ( G i l b e r t and R a p s o n , 1980). H i g h c h l o r i d e l e v e l s i n the r e c o v e r y c y c l e cause e x c e s s i v e c o r r o s i o n o f the superheater tubes i n the r e c o v e r y b o i l e r , decreasing  r e c o v e r y b o i l e r capacity,  and  a l l o w i n g a c c u m u l a t i o n o f dust o n the b o i l e r tubes ( B l a c k w e l l and H i t z r o t h , 1992) M a g n e s i u m also enters as lime.  Magnesium  and  MgSCu  phosphorus  used i n the fiber l i n e and w i t h the m a k e - u p  levels  are  important  in  the  calcium  cycle.  A c c u m u l a t i o n o f these elements causes increased deadload, reduced settling rates, and poor  filterability  i n the c a l c i u m c y c l e ( G l e a d o w et al,  1996). F o r m a t i o n o f M g ( O H ) 2 , a  gelatinuous material, causes p l u g g i n g p r o b l e m s i n w h i t e l i q u o r and l i m e m u d  filters  ( G a l l o w a y et al,  with  1994). T r a n s i t i o n metals s u c h as M n , F e , and C u interfere  b l e a c h i n g b y c a t a l y s i n g d e c o m p o s i t i o n o f h y d r o g e n p e r o x i d e under a l k a l i n e c o n d i t i o n s ( U l m g r e n , 1996).  1.4. Recent Developments of Closed-cycle Technology A k e y element i n progressing t o w a r d s either a c l o s e d - c y c l e o r effluent-free m i l l i s the r e c y c l i n g o f b l e a c h plant effluents. G l e a d o w and his c o w o r k e r s ( 1 9 9 3 ) suggested a m e t h o d t o achieve c o m p l e t e r e c y c l i n g o f the effluents. I n this m e t h o d , the a l k a l i n e b l e a c h effluent is used i n b r o w n s t o c k w a s h i n g and the a c i d i c effluent is concentrated and added to the b l a c k l i q u o r . E v a p o r a t o r condensates are treated for reuse as process w a t e r supply. I f the a c i d i c b l e a c h effluent is r e c y c l e d to the b r o w n stock washers as s h o w e r water, some o f the metals c a n be redeposited onto the pulp. T h i s r e c y c l e o f metals results  11  i n a n increase i n transition metal content for the p u l p that is sent to the b l e a c h plant. I n a d d i t i o n , the concentration o f s c a l e - i n d u c i n g metal i o n s c a n be increased throughout the fiberline  and i n the w e a k b l a c k l i q u o r ( B r y a n t and E d w a r d s , 1996). R i c h a r d s o n et al. ( 1 9 9 5 ) suggested the r e c y c l i n g o f bleach-plant effluents to the  green l i q u o r line. A l t h o u g h fresh w a t e r o f 50 % w a s replaced w i t h a c i d i c b l e a c h i n g effluents(Dioo stage), c a u s t i c i z i n g e f f i c i e n c y w a s o n l y decreased from 81.7 % to 77.4 % . T h e replacement o f 50 % fresh water w i t h a l k a l i n e b l e a c h i n g effluents ( E  0  stage) just  decreased the c a u s t i c i z i n g e f f i c i e n c y from 81.7 % to 76.0 % . H o w e v e r , the r e c y c l i n g o f b l e a c h i n g effluents resulted i n the b u i l d u p o f non-process elements s u c h as s i l i c o n , a l u m i n u m , c a l c i u m , m a g n e s i u m , and potassium. M a p l e et al.  ( 1 9 9 4 ) reported the d e v e l o p m e n t  o f the b l e a c h  filtrate  recycle  ( B F R ™ ) process for b l e a c h plant closure. T h e important aspects o f the process  are  c h l o r i d e r e m o v a l and metal r e m o v a l . A l k a l i n e b l e a c h effluents are r e c y c l e d for b r o w n stock w a s h i n g . D i s s o l v e d s o l i d s i n the effluents are transported into the b l a c k l i q u o r evaporators and fired i n the r e c o v e r y b o i l e r . T h e c h l o r i d e c o m p o n e n t i n the electrostatic precipitator dust c a n be r e m o v e d . D u r i n g the c h l o r i d e r e m o v a l process, the dust is m i x e d w i t h hot water. B e c a u s e o f greater s o l u b i l i t y o f s o d i u m c h l o r i d e than that o f s o d i u m sulfate, the s o d i u m sulfate i n the dust is precipitated out and r e c y c l e d to the b l a c k l i q u o r . S o d i u m c h l o r i d e i n aqueous f o r m is disposed. M e t a l i o n s i n a c i d b l e a c h effluent  are  r e m o v e d b y c h e m i c a l p r e c i p i t a t i o n w i t h s o d i u m h y d r o x i d e and s o d i u m carbonate o r i o n exchange. T r e a t e d effluent is r e c y c l e d to the b l e a c h plant. U l m g r e n ( 1 9 9 6 ) suggested a r e c y c l i n g strategy for a c l o s e d b l e a c h plant. T h e a l k a l i n e b l e a c h effluents are taken to the b r o w n stock washer. T h e o r g a n i c material i n the  12  a l k a l i n e effluents c a n be r e m o v e d b y b u r n i n g i n the r e c o v e r y b o i l e r v i a the b r o w n s t o c k washer. T h e a c i d i c effluents can be taken into the c h e m i c a l r e c o v e r y c y c l e for w h i t e l i q u o r preparation. I n the case o f the a c i d effluent f r o m a n E C F b l e a c h plant, the effluent contains a h i g h l e v e l o f c h l o r i d e . These a c i d i c effluents, r i c h i n c h l o r i d e , s h o u l d be treated separately to prevent the intake o f c h l o r i d e i o n . G l e a d o w et al. ( 1 9 9 8 ) presented three c l o s e d - c y c l e case studies u s i n g process s i m u l a t i o n s f o l l o w e d b y the analysis o f elemental c o m p o n e n t b e h a v i o u r i n the  kraft  p u l p i n g process. P a r t i c i p a t i n g m i l l s w e r e a 1965 vintage B . C . coastal E C F kraft m i l l , a m o d e r n ( 1 9 9 0 s vintage) B . C . coastal E C F m i l l , and a 1965 vintage B . C . interior m i l l . T h e amount o f b l e a c h effluent, 2 4 - 5 4 m / a . d . metric ton, is a b i g p o r t i o n o f the total m i l l 3  effluent, 6 4 - 9 9 m / a . d . metric t o n . T h e y suggested c l o s e d - c y c l e designs i n w h i c h a part o r 3  all o f the b l e a c h plant effluent w a s concentrated i n a b l e a c h plant evaporator and the solids incinerated i n the e x i s t i n g b l a c k l i q u o r r e c o v e r y b o i l e r . R e c y c l e o f a l k a l i n e  filtrate  to b r o w n stock w a s also considered. A c c u m u l a t i o n o f K and C l c a n be c o n t r o l l e d b y p u r g i n g precipitator catch i n the r e c o v e r y b o i l e r . S i m u l a t i o n w i t h these d e s i g n options s h o w e d n o increase i n the corrosiveness o f the r e c o v e r y b o i l e r deposits and the potential for p l u g g i n g . P o t a s s i u m and c h l o r i d e l e v e l s w e r e constant o r decreased as a result o f process m o d i f i c a t i o n s . C a l c i u m and m a g n e s i u m levels, h o w e v e r , i n b l a c k l i q u o r raised a c o n c e r n . T h e concentration o f these elements w e r e increased up to 3 0 0 % . A  new  b l e a c h i n g plant evaporator and a r e c o v e r y b o i l e r precipitator catch l e a c h i n g system are required. A d d i t i o n a l b l e a c h i n g stages are be required to compensate for the decrease o f b l e a c h i n g e f f i c i e n c y i n s o m e cases. C a p i t a l cost requirements are s i m i l a r to those o f effluent treatment facilities.  13  1.5. Scale Formation in the Recovery Cycle Several types o f s c a l i n g o c c u r throughout the r e c o v e r y c y c l e o f kraft p u l p m i l l s . M a t e r i a l s i n s o l u b l e i n b l a c k l i q u o r are fibres, sand, o i l soap (at 2 5 - 3 0 % solids), l i g n i n (at p H b e l o w 11), c a l c i u m carbonate scale (at h i g h temperature), s o d i u m  carbonate-sodium  sulfate d o u b l e salt (usually about 5 0 % solids), and s o d i u m a l u m i n o s i l i c a t e scale. S a n d and fibres are u s u a l l y f o u n d to be c o m b i n e d w i t h deposits w h i c h p l u g tubes ( G r a c e et  al,  1989). C a l c i u m s c a l i n g is v e r y sensitive to temperature i n b l a c k l i q u o r evaporators. A c o m p l e x is f o r m e d b e t w e e n c a l c i u m i o n and l i g n i n sub-groups i n the l i q u o r . A t h i g h temperature, the  complex  breaks d o w n .  The  released  c a l c i u m ions  combine  with  carbonate ions o n the hot surface, w h e r e they f o r m c a l c i u m carbonate scale ( W e s t e r v e l t et al,  1982). Increased amount o f c a l c i u m oxalate i n b l a c k l i q u o r s i g n i f i c a n t l y increases the  tendency o f the c a l c i u m carbonate scale f o r m a t i o n ( G r a c e et al, Sodium  carbonate-sodium  sulfate  scales  are  also  1989). common  in black  liquor  evaporators. T h e scales are soluble i n b l a c k l i q u o r . I f their concentration exceeds the s o l u b i l i t y l i m i t , t h e y f o r m b y c r y s t a l l i z i n g from a supersaturated solution. T h e scales are u s u a l l y f o u n d to have a structure o f burkeite, 2Na2S04-Na2CC>3. T h e s o l u b i l i t y at h i g h temperature is s l i g h t l y l o w e r than that at l o w temperature i n the range 100 ~ 140 ° C O r g a n i c c o m p o u n d s i n l i q u o r d o not greatly i n f l u e n c e the s o l u b i l i t y ( G r a c e et al,  1989).  T h e s o d i u m carbonate-sulfate s c a l i n g can be aggravated b y soap. S o a p has a  strong  tendency t o precipitate o n fibre to f o r m a s t i c k y mass. T h u s , soap and fibre s h o u l d be kept out o f the b l a c k l i q u o r as m u c h as possible ( U l o t h and W o n g , 1985; G r a c e et 1989).  al,  14  S o d i u m oxalate  (Na2C204) s c a l i n g o c c u r s sometimes i n the kraft p u l p m i l l s u s i n g  h a r d w o o d species, e s p e c i a l l y if w e a k b l a c k l i q u o r o x i d a t i o n is used to prevent o d o r o u s e m i s s i o n s o f H 2 S gas . T h e s o d i u m oxalate is moderately s o l u b l e i n w a t e r (6.0 g / 1 0 0 g at 100 °C)  and  shows  a normal  s o l u b i l i t y temperature relationship.  increases w i t h i n c r e a s i n g temperature.  Thus,  solubility  S o l u b i l i t y o f the s o d i u m o x a l a t e v a r i e s  with  amounts o f other s o d i u m salts. It forms scales i n b l a c k l i q u o r evaporators b y p r e c i p i t a t i o n as the s o l i d content i n the l i q u o r increases ( G r a c e et al,  1989).  S o d i u m a l u m i n o s i l i c a t e scales are hard and g l o s s y . S i n c e they h a v e a v e r y l o w t h e r m a l c o n d u c t i v i t y , a v e r y t h i n l a y e r is e n o u g h to cause a serious r e d u c t i o n o f the evaporation capacity. A l t h o u g h these scales g r o w s l o w l y , they are v e r y tenacious and difficult to r e m o v e ( G r a c e et al, temperature i n the  range 95 ~  1989). S o l u b i l i t y increases s l i g h t l y w i t h i n c r e a s i n g 150 °C (Streisel,  1987).  A  higher  solids  content  ( d e c o m p o s i t i o n products o f l i g n i n ) i n the b l a c k l i q u o r results i n a h i g h e r s o l u b i l i t y . T h u s , the l i q u o r c a n tolerate m o r e soluble A l and S i before s o d i u m a l u m i n o s i l i c a t e precipitates. T h i s is p r o b a b l y due to the increased concentration o f d e c o m p o s i t i o n p r o d u c t s o f l i g n i n . T h e s e o r g a n i c c o m p o u n d s f o r m strong chelate c o m p l e x e s w i t h A l . S u c h structures o c c u r i n b l a c k l i q u o r as d e c o m p o s i t i o n products o f l i g n i n ( U l m g r e n , 1985). G r e e n l i q u o r systems also have s c a l i n g p r o b l e m s i n transfer lines, the clarifiers, and the d i s s o l v i n g tanks. These scales are u s u a l l y f o u n d to have structures o f p i r s o n n i t e (Na2C0 Na2C0 -2H 0) 3  3  2  and gaylussite ( N a C 0 N a C 0 - 5 H 0 ) . 2  3  2  3  2  Scales seem  to  be  f a v o r e d b y decreased temperatures ( F r e d e r i c k and K r i s h n a n , 1990). Increased intake o f a l u m i n u m and s i l i c o n c a n cause s o d i u m a l u m i n o s i l i c a t e f o r m a t i o n i n green and w h i t e l i q u o r lines ( W a n n e n m a c h e r et al,  1996).  15  1.5.1. Sodium aluminosilicate scale formation  The sodium aluminosilicate scales may form in the recovery cycle of a kraft pulp mill and during the Bayer process for aluminum production (Gasteiger et al,  1992;  Swaddle et al, 1994; Zheng et al, 1997; Gerson and Zheng, 1997). In the case of the kraft pulping process, aluminum and silicon ions enter the process with wood chips, water, and make-up lime as seen in Table 1.1. In particular, significant amounts of aluminum and silicon enter from unwashed chips since bark and soil on the chips are a major source of those ions (Galloway et al,  1994). If aluminum and silicon ions are  introduced to the recovery cycle, those ions can not be purged out easily from the cycle since they are soluble in alkaline aqueous solutions. The build up of aluminum and silicon results in sodium aluminosilicate scale formation in the recovery cycle. The scale is glossy and hard to remove. It may lower the efficiency of heat exchangers and evaporation capacity of a kraft pulp mill (Ulmgren, 1982). The scale formation becomes more severe in closed-cycle plant operation because the effluent is recycled and the aluminum and silicon ion concentrations increase rapidly. Recycling of bleach plant effluents carries a lot of non-process elements to the recovery cycle as seen in Table 1.2. The A l and Si are not removed easily by precipitator dust removal or green and white liquor clarifications (Gleadow et al, 1998). Ulmgren (1982) studied the Na-Al-Silicate scale formation in black liquors of the recovery cycle. He measured the solubilities of A l and Si using the synthetic black liquors made of NaOH, N a C 0 , N a S 0 , and C H C O O N a (sodium acetate) at 120 - 150 2  3  2  4  3  °C. The scale samples were found to have structures of NaAlSi04-l/3Na C03 and/or 2  16  NaAlSi04-l/3Na S04 which look like cancrinite. According to his results, one of the 2  main factors governing formation of aluminosilicates was the O f f concentration. More soluble species formed in solution as the O f f concentration increased in the range of the O f f concentration from 0.03 to 1.6 mol/L. In addition, high concentrations of O f f caused scale formation on the surface of vessels and low concentrations resulted in precipitation as particles. Addition of HS" of 0.4 mol/L did not make any significant change in the solubility of A l and Si. The effect of temperature on the formation of sodium aluminosilicate was not significant at 120 °C, 135 °C, and 150 °C. Solubility increased slightly with increasing temperature. Ulmgren also presented a model for the formation of Na-Al-Silicate scale in evaporators for black liquor in kraft pulp mills. For the chemical modeling, he assumed the Na-Al-Silicate in the evaporators were formed by precipitation from a solution saturated with ions involved such as Na , Al(OH)4\ +  S i 0 ( 0 H ) \ SiO(OH) \ Off, C 0 \ S 0 \ C f and HS". Finally, he determined the 2  2  2  2  3  2  3  4  equilibrium constant of the cancrinite formation using the experimental solubility data to correlate the precipitation conditions. Ulmgren (1987) suggested a method to reduce the concentration of aluminum in the recovery cycle by adding a magnesium salt such as magnesium sulfate and magnesium hydroxide carbonate to the smelt dissolving tank. The insoluble salt, hydrotalcite (Mgi. Al (0H) (C0 )x/ nH 0, 0.10 < x < 0.34), was formed which could be x  x  2  3  2  2  removed from the process together with the dregs by the green liquor clarification. In this way, sodium aluminosilicate scale formation by the build up of A l and Si could be avoided. He observed a decrease in the aluminum concentration from 1.5 to 0.5 mmol/L by the addition of magnesium salts with molar ratio of Mg/Al=6 into the mill green  17 liquor. He also observed that removal of aluminum by the addition of the magnesium salts could be expedited by reducing the OH" concentration and/or temperature of the liquor. Streisel (1987) studied the Na-Al-Silicate formation using synthetic liquors. He prepared the liquors using NaOH and NaCl. He measured the precipitation conditions of the sodium aluminosilicates by varying the following parameters: the Al/Si molar ratio from 0.08 to 275, the hydroxyl ion concentration from 0.1 to 4 N , and the ionic strength from 1 to 4 N . The temperature was set at 95 and 150 °C. According to the results, as the hydroxide ion concentration increased, more soluble aluminum and silicon species formed in solution. The apparent solubility product of A l and Si decreased with increasing ionic strength. The apparent solubility product, [Al][Si] at 150 °C was higher than the solubility product at 95 °C. He found that the precipitates had a structure of sodalite (Na8(AlSi0 )6Cl ) by the X-ray diffraction analysis. 4  2  Streisel (1987) also studied the effects of the cationic ions (K, V , Fe, Mn, Ca, Mg) addition on the solubility of Al and Si. The potassium and vanadium are very soluble in alkaline solution and neither potassium or vanadium had any significant influence on the apparent solubility product of A l and Si. Iron and manganese are insoluble in alkaline solution. Iron and manganese precipitated as iron oxide (Fe 03) and manganese 2  hydroxide (Mn(OH) ). Neither iron or manganese had any significant influence on the 2  apparent solubility product of Al and Si. Calcium is nearly insoluble in alkaline solution. The calcium has an effect on the rate of precipitation of Al and Si but not on the apparent solubility product. When the molar ratio of Al/Si is less than one, aluminum tobermorite (Ca5Si5Al(OH)n5H 0) was mainly formed. When the molar ratio was equal to one, 2  18  sodalite and calcium hydroxide were formed. By the addition of M g S 0 , hydrotalcite was 4  formed. The higher Mg/Al  ratios resulted in significantly  more precipitation of  aluminum. Streisel (1987) developed a model to predict the precipitation conditions in the concentration range of O f f from 0.1 to 1.0 N for N a - Cl" - Al(OH) " - HSi0 " - OH* +  3  4  H2O system. He adopted Meissner's method (Zemaitis et al,  4  1986) to calculate the  activity coefficients of species and extracted Meissner's model parameters from his experimental solubility data. His model was unable to calculate the concentration of aluminum at higher hydroxide concentrations because of a convergence problem. Gasteiger et al. (1992) upgraded Streisel's model. Pitzer's method (Pitzer, 1991) was adopted to calculate activity coefficients of the species and activity of water. The model  contained  five  adjustable  parameters,  an  equilibrium  constant  sodalite/hydroxysodalite formation and four Pitzer's parameters of J3 N a H S i 0 and p 4  (0)  and p  (1)  and  (0)  of for  for NaAl(OH) . They obtained the five adjustable parameters 4  by correlating Streisel's experimental solubility data. They found that the precipitates had the structure of sodalite (Na8(AlSi0 )6Cl2) and/or hydroxysodalite (Nas(AlSi0 )6(OH)2) 4  4  by X-ray diffraction analysis. Wannenmacher et al. (1996) reported the effect of CaO and M g S 0 addition on 4  the precipitation conditions of sodium aluminosilicate scale in an unclarified kraft mill green liquor at 95 °C. For the 1:1 addition of CaO ([CaO]:[Si]), no change in the aluminum and silicon solubility was observed. The addition of M g S 0  4  was found to  lower the solubility of Al. They presented graphs showing the precipitation conditions of the Na-Al-Silicates for black, green and white liquors based on their experimental and  19 literature data. T h e y also reported  several equations t o calculate apparent  solubility  product, [Al][Si] at e q u i l i b r i u m w i t h sodalite (Na8(AlSiC»4)6Cl2) and/or h y d r o x y s o d a l i t e ( N a 8 ( A l S i 0 4 ) 6 ( O H ) 2 ) , cancrinite, natrolite, a n d hydrotalcite. T h e correlations w e r e based on  experimental  s o l u b i l i t y data. A c t i v i t y  coefficients  were  not considered  f o r the  calculations.  1.6. R e s e a r c h O b j e c t i v e s Knowledge required  to d e s i g n  o f the s o d i u m closed-cycle  a l u m i n o s i l i c a t e scale pulp  mills.  precipitation  A l t h o u g h the  c o n d i t i o n s is  formation  o f sodium  a l u m i n o s i l i c a t e scales i n a l k a l i n e solutions has been studied i n the past ( U l m g r e n , 1982; Ulmgren,  1987; Streisel, 1987; W a n n e n m a c h e r et al, 1996), the effects o f N a C 0 , 2  3  Na2S04 and ISfoS concentration o n the p r e c i p i t a t i o n c o n d i t i o n s i n green a n d w h i t e l i q u o r s have n o t yet been investigated. T h u s , o n e objective o f this w o r k w a s to measure the s o l u b i l i t y o f A l a n d Si i n h i g h l y a l k a l i n e s o l u t i o n s at  368.15 K (95 ° C ) and determine the effects o f N a 2 C 0 , 3  Na2S04 a n d Na2S a d d i t i o n o n the p r e c i p i t a t i o n c o n d i t i o n s . W e used synthetic l i q u o r s o f t w o different  systems,  A and B , that s i m u l a t e d m i l l green a n d w h i t e l i q u o r s . T h e  synthetic green a n d w h i t e l i q u o r s o f system A w e r e prepared u s i n g N a O H ,  Na2C0 , 3  Na2S04, a n d N a C l . T h o s e o f system B w e r e prepared u s i n g N a O H , N a 2 C 0 , and Na2S. 3  T h e p r e c i p i t a t i o n c o n d i t i o n s o f s o d i u m a l u m i n o s i l i c a t e scale i n m i l l green a n d w h i t e l i q u o r s w e r e also measured.  T h e effects  of NaOH,  Na2C0  3  and  Na2S at different  concentrations o n the p r e c i p i t a t i o n c o n d i t i o n s i n m i l l l i q u o r s w e r e o b s e r v e d . M i l l green and w h i t e l i q u o r s r e c e i v e d f r o m a m i l l i n P r i n c e G e o r g e , B . C . w e r e used f o r the study. I n  20  addition, the structure of the precipitates were identified by X-ray,  chemical and  thermogravimetric analysis. The other objective of this work was to present a thermodynamics-based model for sodium aluminosilicate formation in aqueous alkaline solutions. Pitzer's activity coefficient method was used to calculate the activity of water and the activity coefficients of ions in the solution because it performs well even at high molalities (Pitzer, 1991; Zemaitis et al, 1986). All parameters needed by the model were obtained from independent experimental data or available property estimation methods. The effects of the anions of O H , C O 3 , SO4 ", and H S were taken into account. The model predicts the -  2  -  2  precipitation conditions of sodalite dihydrate and/or hydroxysodalite dihydrate. Since the system contains the Si03 ' and A l ( O H V ions, knowledge of the relevant 2  Pitzer's model parameters is required. Osmotic coefficient data for the Na2Si03 single electrolyte system and the Na2Si03-Na0H multi-component electrolyte system were obtained at 298.15 K by an isopiestic method. The binary parameters, P for N a S i 0 and the mixing parameters, 9 2  3  OH  -  siol  - and ^  Na+0H  (0)  ,  and C*,  - 2-, for Na2Si0 -Na0H Si0  3  system were determined using the osmotic coefficient data. In addition, the binary parameters, f3 , P (0)  e  crAi oH);. (  (1)  , and C*, for NaAl(OH) and the mixing parameters,  *N.-OH-AI(OH);»  4  A  N  D  ^N.-CTAKOHH  a  r  e n e e d e d  -  0  s  m  o  t  i  c  ©OH-^^- ,  coefficient data for  NaOH-NaCl-NaAl(OH)4 aqueous system were also obtained at 298.15 K. The unknown Pitzer's parameters relevant for the description of the system were obtained using these osmotic coefficient data.  21  CHAPTER 2. THEORETICAL BACKGROUND  T h i s chapter presents the fundamental t h e r m o d y n a m i c relations that g o v e r n the b e h a v i o u r o f electrolyte solutions as w e l l as P i t z e r ' s a c t i v i t y coefficient  model. In  a d d i t i o n , the i s o p i e s t i c m e t h o d for the measurement o f o s m o t i c coefficients is also presented.  2.1.  Thermodynamic Equilibrium Constant L e t us consider the f o l l o w i n g reaction i n an aqueous electrolyte s o l u t i o n . aA + bB = cC + dD  (2.1)  T h e c o n d i t i o n o f c h e m i c a l e q u i l i b r i u m c a n be denoted b y au,  A  + bu,  B  = cue + duo  (2.2)  w h e r e p. is a c h e m i c a l potential. It is c o n v e n i e n t i n aqueous s o l u t i o n t h e r m o d y n a m i c s to describe the c h e m i c a l potential o f a species i i n terms o f its a c t i v i t y ai. u =H?+RTta(a ) i  (2.3)  i  w h e r e u,° is a c h e m i c a l potential at an arbitrarily c h o s e n standard  state. W h e n  the  c o m p o s i t i o n o f the s o l u t i o n is described i n terms o f the m o l a l i t y scale, the standard state o f i o n species is that o f a h y p o t h e t i c a l one m o l a r s o l u t i o n at the same temperature and pressure as the s o l u t i o n (Pitzer, 1991). F o r the solvent (water), the standard state refers t o pure solvent (water) at the same temperature and pressure as the s o l u t i o n . T h e a c t i v i t y is  22 a measure of the difference between the component's chemical potential at the state of interest and its standard state. The deviation from ideality is defined by the activity coefficient, y = a/m. Substituting the activity of species i, ai to yjmj in equation (2.3) gives ^-ur+RTlnCy.mJ  (2.4)  Thus, the general expression of equation (2.2) for the equilibrium can be expanded as follows a(u° + R T l n ( m ) ) + b ( K +RTln(y m )) = YA  A  B  B  c(p.° + R T l n ( y m ) ) + d(u + R T l n ( y m ) ) c  c  D  D  (2.5)  D  By combining terms  au° +bu° -cn° A  B  -du° =RTln (Yc c) (V D) (Y m ) (Y m ) m  C  D  m  D  (2.6)  D  A  A  A  B  B  B  Since the partial molar Gibbs free energy is also defined as the chemical potential, the u,°, can be substituted by AG° (standard Gibbs free energy of formation). ;  (Yc c) (Y m ) (Y m ) (y m ) m  aAGf + b A G ° - c A G ° - d A G ° A  B  c  D  = RTln  C  D  D  B  B  A  A  A  D  B  (2.7)  The solubility of A, B, C, and D species at equilibrium are expressed in molality, ITIA, me, mc, and mo respectively. Since the thermodynamic equilibrium constant for this reaction is defined as  K = exp  aAG° + b A G ° - c A G ? A  the equation (2.8) can be written as follows  f  B  RT  c  -dAG ° f  t  (2.8)  23  K =  (Yc c) (YD m  C  m  )  D  D  - exp  .(YAm ) (YBm ) . A  A  B  - AG°  B  RT  (2.9)  w h e r e A G is the standard G i b b s free energy change o f r e a c t i o n (2.1). 0  2 . 2 . Equilibrium Constant Calculation at Specific Temperature T h e t h e r m o d y n a m i c e q u i l i b r i u m constant K i n equation (2.9) c a n also be w r i t t e n as f o l l o w s . AG  InK  0  (2.10)  RT  D i f f e r e n t i a t i n g the equation (2.10) w i t h T at constant P and c o m p o s i t i o n g i v e s  D  d l n K  d(AG°/T)  (2.11)  dT  dT T h e G i b b s - H e l m h o l t z equation is g i v e n b y d_  f  AG  0  AH  >  0  (2.12)  5T w h e r e A H is the standard enthalpy change o f reaction. 0  T h u s , the equation (2.11) can be w r i t t e n as f o l l o w s .  R  dlnK dT  =  AH: T  2  T h e A H ° c a n be expressed as a f u n c t i o n o f temperature i n terms o f heat capacity, ACp.  AH° = AH° + f A C d T «r  (2.14)  T  P  0  A s s u m i n g constant ACp i n the range o f the To and T g i v e s AH  0  = AH° + A C ° ( T - T ) 0  (2.15)  24  C o m b i n i n g (2.13) and (2.15) g i v e s d t a K  R  AH  =  dT  T  I +  ^ni]  \T  2  (2.16)  I) 2  Integrating the e q u a t i o n (2.16) between the l i m i t s o f the reference temperature, To, and T gives  lnK-lnK  n  AH  =  °-  T  It can be w r i t t e n as f o l l o w s since In K  lnK  AGJ  = V  R  T  n  i  0  oJ  AC;  0  X  0  1 1 l n T - l n T + T ( - - — ) V o j  f  0  1  N  (2.17)  A  = -AGQ / R T . 0  AH  R  o  c  I__L  AC  R  o  f V  l n ^ - 1 T T  (2.18)  0  E q u a t i o n (2.18) is u s e d to calculate the e q u i l i b r i u m constant at any temperature,  T  ( A n d e r s o n a n d C r e r a r , 1993).  2.3. Activity of Water, Osmotic Coefficient, a n d Activity coefficient Activity  a n d a c t i v i t y coefficients w e r e i n t r o d u c e d to describe the n o n - i d e a l  b e h a v i o u r o f a c o m p o n e n t i n a s o l u t i o n . B a s e d o n equation 2 . 3 , the a c t i v i t y o f solvent (water), a , can be expressed b y : w  exp  where p  w  RT  (2.19)  is the c h e m i c a l potential o f the solvent, p^, is the standard state c h e m i c a l  potential o f the solvent, R is the gas constant, and T is the absolute temperature. T h e standard state refers to pure solvent (water) at the same temperature and pressure as the s o l u t i o n ( P i t z e r 1991).  25  Activity,  however,  is not  sensitive  at  l o w m o l a l i t i e s and  requires  several  significant d i g i t s to express the b e h a v i o u r accurately. T h e p r a c t i c a l o s m o t i c coefficient w a s i n t r o d u c e d to a v o i d this p r o b l e m b y exaggerating the d e v i a t i o n between real and i d e a l b e h a v i o u r ( P i t z e r 1991, Z e m a i t i s et al. 1986). T h e practical o s m o t i c coefficient, <j>, is defined as f o l l o w s  -10001na w 2 > i  M  where, M  w  m  w  (2.20a)  i  is the m o l e c u l a r w e i g h t o f the solvent (water), Vi is n u m b e r o f i o n s p r o d u c e d  b y 1 m o l o f solute i , and  m ; is the m o l a l i t y o f solute i . F o r a single aqueous electrolyte  s o l u t i o n w i t h a solute m o l a l i t y equal t o m  s  and v i o n s p r o d u c e d w h e n the electrolyte is  d i s s o l v e d the above equation is w r i t t e n as -lOOOlna.,,  (2.20b)  M„,vm.  L e t us n o w consider s i n g l e electrolyte aqueous s o l u t i o n . T h e total G i b b s energy n G is a f u n c t i o n o f T , P , and the numbers o f m o l e s o f the c h e m i c a l species present (solute and water). T h u s , the n G is g i v e n b y nG = f(T,P,n ,n ) s  (2.21)  w  w h e r e n is n u m b e r o f m o l e s , subscript w stands for solvent (water), and subscript s denotes the solute (electrolyte). T h e total differential o f n G is  d(nG) =  d(nG)  ap  dP + T,n  d(nG)  err  dT + JP,n  d(nG) an.  dn. + P.T,n„  a(nG) an...  dn  w  (2.22)  P.T.n,  S i n c e the partial m o l a r G i b b s energy o f species i is defined as f o l l o w s ,  G: =  a(nG) an ;  (2.23) JT.P.tij  26  the e q u a t i o n (2.22) can be r e w r i t t e n as f o l l o w s . ~5(nG)~  d(nG) =  "d(nG)~  dP +  5T  T,n  dT + G„dn S  P,n  +G.„dn W W  3  (2.24)  M e a n w h i l e , a general differential equation for ( n G ) at constant T and P is g i v e n b y d(nG) = 2  and  d(nG) = n d G s  s  i  n  d  G ,  +n dG w  w  +2_G,dn  +G dn s  l  +G dn  s  w  (2.25)  w  C o m p a r i s o n o f this e q u a t i o n (2.25) w i t h (2.24) y i e l d s the G i b b s - D u h e m equation. g(nG)  cP  dP +  d(nG)  d T - n d G - n s  5T  -lT,n  s  w  d G  w  = 0  (2.26)  P.n  F o r the case o f 1 k g o f s o l v e n t (water) at constant T and P , the equation (2.26) b e c o m e s -m.dG  and where m  -m,dG,„ W W  m dG =-m s  s  and m  w  s  w  =0  dG  (2.27)  w  are the m o l a l i t i e s o f the electrolyte (solute) and w a t e r  (solvent)  respectively. S i n c e the c h e m i c a l potential is d e f i n e d as the partial m o l a r G i b b s energy, the e q u a t i o n (2.27) becomes m dp = - m d p s  s  w  (2.28)  w  T a k i n g the general f o r m u l a o f solute (electrolyte) to be C  v  A  V j  , the c h e m i c a l p o t e n t i a l o f  the solute is u.=v u. +v.u._ c  e  (2.29)  = v p : + v . u . + v . R T l n ( a ) + v R T ln(a.) c  c  a  = v p: +v p: +v RTln(m y ) + v RTln(m Y ) c  8  c  c  c  a  a  w h e r e subscript c stands for c a t i o n and subscript a denotes the a n i o n .  a  27  D i f f e r e n t i a t i n g the equation (2.29) g i v e s dn =RTdln(m^m:-y:'y:-)  (2.30)  s  The m e a n m o l a l i t y and m e a n a c t i v i t y coefficient are defined as  m  ±  = ( m > i - r = ( ™ > :  ™ > : - Y  c  Y -(Y. -Y. ) V  V ,  v  = ^ > : - Y  v  (2.31)  (2-32)  , , V  ±  w h e r e v = v + v . T h u s , equation (2.30) b e c o m e s c  a  dn =vRTdln(m s  ± Y ±  )  (2.33)  The c h e m i c a l potential o f solvent (water) is g i v e n b y U -U°+RTlna w  (2.34)  w  D i f f e r e n t i a t i n g the equation (2.34) g i v e s dp. =RTdlna w  (2.35)  w  Substituting equations (2.33) and (2.35) to equation (2.28) g i v e s v m R T d l n ( m Y ) = - m R T d In a ±  s  ±  w  vm dln(m Y ) = - m d l n a  and  ±  s  ±  w  w  w  (236)  A n o t h e r e x p r e s s i o n for equation (2.20b) is g i v e n as f o l l o w s for single electrolyte s y s t e m  lna  and  w  - M  v m -<b 1000  =  w  s  lna =^ ^(j) m m  w  w  where m  w  = 1000/M =55.509 moles/kg H 0 W  2  T h u s , substituting the equation (2.37) to the equation (2.36) g i v e s  vm dln(m s  ± Y ±  ) = -m d w  (2.37)  28  m d l n ( m Y ) = d(m <t>) s  and  ±  ±  3  m d In (m±y±) = (|)dm + m d<|) s  s  (2.38)  s  E q u a t i o n (2.38) b e c o m e s  dln(m y ) = — d m , ±  ±  s  +d<t>  m  dlnm  ±  +dlny  =-^-dm  ±  s  +d<J)  dm Since d l n ( m ) = d l n ( m ) = ±  f r o m equation (2.31), the above e q u a t i o n g i v e s  L  s  dlny  ±  = — m  The  above  relation between  mean  dm  s  +d<|>  (2.39)  s  a c t i v i t y coefficient  o f solute,  y±, and  osmotic  coefficient, <|>, c a n be obtained b y integration o f equation (2.39) from m = 0 (where y± = s  1 and <)| = 1) to m ( P i t z e r 1991).  lnY  ±  = r ^ d m + ( d ) - l ) m  (2.40)  s  J o  2.4. Pitzer's Activity Coefficient M o d e l P i t z e r d e v e l o p e d a m o d e l to p r o v i d e i m p r o v e d estimation o f electrolyte s o l u t i o n properties b y t a k i n g into account the effect o f short-range forces. T h e P i t z e r ' s m o d e l is based o n the v i r i a l e x p a n s i o n o f the excess G i b b s free energy. T h e first term i n P i t z e r ' s equation is a m o d i f i c a t i o n o f the D e b y e - H u c k e l m o d e l for the electrostatic effect. T h e second t e r m represents short range interaction i n the presence o f solvent between t w o solute  species  ( i o n - d i p o l e interaction). T h e t h i r d t e r m  represents t r i p l e  interaction  29  b e t w e e n solute species i n solvent. P i t z e r ' s m o d e l c a n p r e d i c t the a c t i v i t y coefficients o f i o n s accurately e v e n at h i g h m o l a l i t y o f i o n s ( P i t z e r , 1 9 9 1 ; Z e m a i t i s et al,  1986). P i t z e r  expressed the excess G i b b s energy as a series o f terms i n i n c r e a s i n g p o w e r s o f m o l a l i t y t o d e r i v e h i s e q u a t i o n ( P i t z e r , 1991).  — —  - f ( I ) + XSm m X (I) + X E Z . m  W,„K1  where,  W  j  1  j  J  ij  m  j k  i  m J  ^.jk+-  (2.41)  : number o f K g o f water  w  mi mj nik  : m o l a l i t y o f solute i j k  I  : i o n i c strength ( I =  f(I)  : i n c l u d e s the D e b y e - H i i c k e l l i m i t i n g l a w  ~^m;zf )  Xij(I) = X,ji(I) : short-range interaction b e t w e e n solute species i a n d j i n s o l v e n t : t r i p l e interaction between solute species i , j a n d k i n solvent  Uijic  The  a c t i v i t y coefficient, Yi o f solute species i a n d o s m o t i c c o e f f i c i e n t , <|) are  obtained b y differentiating equation (2.41) as f o l l o w s .  lny = [ 3 ( G V W R T ) / a n L i  4_l  w  _  =  (  a  G  e *  /  a  w  (2.42)  i  j  n  i  /  (  R  T  £  m  i  (2.43)  )  R e w r i t i n g e q u a t i o n (2.41) i n terms o f e x p e r i m e n t a l l y d e t e r m i n a b l e quantities B and C instead o f the i n d i v i d u a l i o n quantities X and p. g i v e s the f o l l o w i n g e q u a t i o n (2.44).  G W  e  RT  f(I) + 2 £ £ m  c  m  m z  (  r  r  •ZZ  C  r  C  +Z Z  mm.  mm, a a  aa  /  J  (2.44)  c caa  +2Y Y m ml„ + 2V Y m ra,L + 2V V m„m ,L , + y m X +• n  /  J  /  J  n  c  c nc  n  /  J  /  J  n  B  a na  f  J  / f tl  n  n  n nn  m  / *  n nm  30  Pitzer derived semi-empirical equations for y and (2.44). For single electrolyte system, y± and ln  by taking the derivative of equation  are given by  =|z z |f +m(2v v /v)B^ + m [ 2 ( v v ) / v ] C T  Y ±  M  2  x  M  3 / 2  x  M  4.-lHz z |f*+m(2v v /v)Bt +m [2(v v ) 2  M  where, y±  x  M  x  K  M  x  x  3 / 2  /v]C*  l x  M X  (2.45) (2.46)  : mean activity coefficient  z  : charge  M  : cation  X  : anion  v  : number of ions produced by 1 mole of the solute  f  = -A4[I /(l + bl ) + (2/b)ln(l + bl )]  f*  = -A4  A4  : Debye-Huckel osmotic coefficient parameter  b  : universal parameter with the value of 1.2 (kg.mol)  1/2  1/2  1/2  (2.47)  1/2  / ( l + bl )  (2.48)  1/2  1/2  B  = B X + B*MX  BMX  =PSc+P ^g(a,I )+PScg(a I )  BL  =P^x+3l!_ exp(-a r ) PS exp(-a I )  (2.51)  =3C* /2  (2.52)  Y  (2.49)  M  (  ,/2  (2.50)  ,/2  2  /2  <  x  i  1/2  +  c  2  The P MX, 3 MX, C'MX are tabulated binary parameters specific to the salt M X . (0)  (1)  The P MX is a parameter to account for the ion pairing effect of 2-2 salts. When either (2)  31 cation M or anion X is univalent, cti = 2.0. For 2-2, or higher valence pairs, cti = 1.4. The constant a is equal to 12. 2  For multi-component electrolyte solutions, y and § are given by 1°YM  _  Z  M  20 +2>/F Mca Mc  a  c  1  (2.54)  a a'  In y = z F + Z m [2B + ZC ] + Z m 2 0 x  x  c  cX  cX  c  +ZSm mJ , c  z  V  +|Z |_T_>>c a m  cc x  lnYMx = | M x | + — z  X a +  £m ¥ c  (  a  Z  F  (2.55)  C  x  m  <  2B +ZC +^0 Ma  Ma  2B +ZC +^0 v cX  ,  cXa  cX  Xa  Mc  (2.56)  x  + J J m m , v '[2v Z e  M  c a  d)-l = (2/Zm )[f*I i  i  ZZ o a(Bl m  +  m  c a  + ZZmm ,(Ot + X c  c  +ZCJ (2.57)  m  X a ) +Z Z  m  a ^ a « . + Z ^ c a a ) ]  c c'  The quantity F in thefirstterm of equations (2.54), (2.55), and (2.56) includes the DebyeHuckel term given by F=f  Y  +ZZmcm B; +ZZm m ,0: ,+ZZniama.O; . a  c  a  a  c  c < c'  c  c  a  (2.58)  a < a'  Also, z  = Z  m  i  l i z  (2.59)  32  B ,=fc g'(a I )+3L g'(a I )]/I  (2.60)  * = e + e (o  (2.61)  )  1/2  c  2)  1  1/2  2  B  i j  i j  ij  (2.62)  <D+=0> + K> IJ  IJ  (2.63)  IJ  Gij are tabulated mixing parameters specific to the cation-cation or anion-anion pairs. The  is also tabulated mixing parameter specific to the cation-anion-anion or  anion-cation-cation pairs. The parameters 6ij(I) and 0'ij(I) represent the effects of E  E  unsymmetrical mixing. These values are significant only for 3-1 or higher electrolytes (Pitzer, 1975). The g(x) and g'(x) are functions accounting for the ionic strength dependence of B x and B'MX given by M  g(x) =  (2.64)  g'(x) =  (2.65)  The binary parameters P , (0)  and C* have larger effects than the mixing parameters, *F  and 9 (Pitzer, 1991).  2.5. Isopiestic M e t h o d  There are several methods to determine the electrolyte thermodynamic properties such as activity coefficient, activity of solvent, and osmotic coefficient. The activity coefficient can be determined by the electromotive force (e.m.f.) method. The activity or osmotic coefficient of the solvent can be determined from the measurement of the vapor pressure of the solvent and from the isopiestic method. The e.m.f. method and vapor  33  pressure measurement  are not suitable for this study. T h e e.m.f. m e t h o d is one o f the  m o s t precise measurements, but, p r o p e r reversible electrodes are not a l w a y s a v a i l a b l e f o r m a n y i o n s i n c l u d i n g s i l i c i c ions. I n the case o f v a p o r pressure measurements b y the static m e t h o d , v e r y precise c o n t r o l o f temperature is r e q u i r e d because the v a p o r pressure o f the solvent varies r a p i d l y w i t h e v e n v e r y s m a l l temperature change. T h e i s o p i e s t i c m e t h o d is s i m p l e r to p e r f o r m and m o r e accurate than direct v a p o r measurements.  There  are,  h o w e v e r , s o m e l i m i t a t i o n s for the isopiestic method. T h e solvent s h o u l d be the o n l y v o l a t i l e c o m p o n e n t i n the system. F u r t h e r m o r e , measurements b e l o w a m o l a l i t y o f 0.1 d o not s h o w g o o d r e l i a b i l i t y (Pitzer, 1991; T h i e s s e n and W i l s o n , 1987). T h e o s m o t i c coefficient is p a r t i c u l a r l y useful for treating isopiestic data (Pitzer, 1991). S a m p l e s o l u t i o n s and one o r m o r e reference solutions are prepared i n separate o p e n containers. F o r this study, t w o sample solutions, one reference s o l u t i o n ( N a C l ) , and one standard s o l u t i o n ( K C 1 ) w e r e prepared. T h e i n i t i a l c o n c e n t r a t i o n and mass o f each s o l u t i o n s h o u l d be k n o w n . T h e reference  and standard  solutions are c h o s e n as  electrolytes w h o s e o s m o t i c coefficient data are already k n o w n at that temperature.  the The  data for the reference s o l u t i o n are u s e d to determine the o s m o t i c coefficients o f the s a m p l e solutions. T h e standard s o l u t i o n is u s e d to c h e c k the r e l i a b i l i t y o f the e x p e r i m e n t s and calculate e x p e r i m e n t a l errors. T h e containers are p l a c e d i n a c l o s e d c h a m b e r w h e r e a l l s o l u t i o n s share the same v a p o r phase. T h e v a p o r space o f the c h a m b e r is evacuated to c o n t a i n o n l y w a t e r v a p o r . S o l v e n t is transferred t h r o u g h the v a p o r phase. T h e chamber c o n t a i n i n g the solutions is kept at i s o t h e r m a l c o n d i t i o n s at specific temperature until no m o r e change  i n the  c o n c e n t r a t i o n o f the s o l u t i o n is observed, thus, t h e r m o d y n a m i c e q u i l i b r i u m is reached.  34  When the solutions are in thermodynamic equilibrium, then p*w  M" w  M*w M"w  (2.66)  where p. is the chemical potential of water and superscripts, 1, 2, R, and S, refer to w  sample solution 1, sample solution 2, reference solution, and standard solution, respectively. Thus, the activity of the solvent is the same. In a' = In a* = In a* = In a*  (2.67)  w  Substituting equation (2.67) to equation (2.20) gives the following relationship for the osmotic coefficients: (fr'^v.m, f =  i  £  V  j  j  m  .  =  ^ 2 v k  k  m  = 4> 5> m 1 8  k  1  1  (2.68)  where, <> | is the osmotic coefficient, v is the number of ions produced by 1 mole of the solute, and m is the molality of the solute. The subscripts, i, j , k, and 1, refer to each component in sample 1, sample 2, reference, and standard solutions. Following isopiestic equilibration, the solutions are weighed. The molality of each solution is calculated from the measured weight. Subsequently, the activity of solvent or osmotic coefficient of the standard solution at that molality is calculated by an activity coefficient model using known parameters from the literature. The activity of solvent and the osmotic coefficient of the other solutions at that molality can be determined using equations (2.67) and (2.68).  35  CHAPTER 3. MATERIALS AND METHODS  Solubility experiments were performed using two types of synthetic liquors (system A and B) and mill liquors to measure the precipitation conditions of sodium aluminosilicates at 368.15 K (95 °C). The concentration levels of NaOH, Na2C03, Na2S04, NaCl, and Na S in synthetic green and white liquors were designed based on 2  those in various mill liquors in Table 1.3. The structure of the precipitates was identified by X-ray diffraction, chemical and thermogravimetry analysis. An isopiestic method was used to measure the osmotic coefficients for the Na Si0 , Na Si0 -NaOH, and NaOH-NaCl-NaAl(OH) aqueous systems at 298.15 K . 2  3  2  3  4  3.1 Solubility Experiments Using Synthetic L i q u o r s of System A  The major difference in the chemical composition of green and white liquors is the concentration level of NaOH and N a C 0 2  (Smook, 1992). White liquor contains a  3  higher concentration of O H and lower of C 0 ' than those in green liquor as seen in -  2  3  Table 1.3. Two synthetic green and white liquor systems were prepared to study the precipitation conditions of sodium aluminosilicate complex in the systems.  3.1.1 Experimental design  System A was prepared by dissolving the following six salts (reagent grade, Fisher Scientific, Vancouver, B.C.) in water: A1C1 -6H 0, Na Si0 -9H 0, NaOH, NaCl, 3  2  2  3  2  N a C 0 , and N a S 0 . Distilled water was used in all experiments after it was deionized 2  3  2  4  36  andfilteredthrough a 0.05 umfilterin an E L G A S T A T U H P water purification apparatus (Fisher Scientific, Vancouver, B.C.). Based on typical mill concentration levels, a base concentration level was formulated and then perturbations around it gave the other compositions. The experimental design is shown in Table 3.1. The effects of the input molar ratio, Al/Si, and concentrations of N a O H , Na2C03, and N a 2 S 0 4 on the solubility of aluminum and silicon were determined by using system A.  T a b l e 3 . 1 . S o l u b i l i t y e x p e r i m e n t d e s i g n for synthetic l i q u o r s o f s y s t e m A . Synthetic g r e e n l i q u o r Experiment  C o n c e n t r a t i o n s i n i n i t i a l solutions ( m o l / k g H2O) A I C I 3 6 H 2 C»  Na SiO 9H 0  NaOH  0.025 0.04 0.01  1.0  1.0  0.1  0.25  1.0  1.0  0.1  0.25  A3*  0.025 0.01 0.04  1.0  1.0  0.1  0.25  A4  0.025  0.025  1.0  0.1  0.25  A5  0.025  0.025  0.25 2.0  1.0  0.1  0.25  0.1  0.25  Al* A2*  2  r  2  Na C0 2  A6  0.025  0.025  1.0  A7  0.025  0.025  1.0  0.5 1.5  A8  0.025  0.025  1.0  1.0  A9  0.025  0.025  1.0  A12*  0.05 0.02 0.08  0.05 0.08 0.02  A13  0.05  0.05  A14  0.05  A15  0.05  A16  3  Na S0 2  4  NaCl  0.1  0.25 0.25  1.0  0.05 0.2  2.5  0.3  0.1  0.1  2.5  0.3  0.1  0.1  2.5  0.3  0.1  0.1  0.3  0.1  0.1  0.05  2.0 3.0  0.3  0.1  0.1  0.05  2.5  0.05  0.1  0.05  0.05  2.5  0.1 0.5  0.15  0.1  A17  0.05  0.05  2.5  0.3  0.1  A18  0.05  0.05  2.5  0.3  0.05 0.15  0.25  Synthetic white liquor A10* All*  * base c o n c e n t r a t i o n l e v e l e x p e r i m e n t s  0.1  37  T h e amounts o f AICI36H2O and N a S i 0 3 - 9 H 2 0 that w e r e added into w h i t e l i q u o r 2  w e r e double those added i n green l i q u o r i n order to obtain e n o u g h precipitate samples for X - r a y diffraction, t h e r m o g r a v i m e t r i c , and c h e m i c a l analysis.  3.1.2 Experimental procedure T w o solutions w e r e prepared b y d i s s o l v i n g measured amounts o f A l C l 3 - 6 H 0 and 2  Na Si03-9H_C) i n 1 k g o f d e i o n i z e d w a t e r respectively. P r o p e r amounts o f N a O H , 2  Na2C03, Na2S04, and N a C l salts w e r e added to the solutions to m a k e the desired i n i t i a l c o n d i t i o n s for the experiments. T h e solutions w e r e stirred until a l l salts w e r e d i s s o l v e d c o m p l e t e l y and kept at 3 6 8 . 1 5 K (95 ° C ) . T h e solutions w e r e then p o u r e d into a vessel m a d e o f stainless steel t o create a supersaturated  s o l u t i o n at the b e g i n n i n g o f the  experiments. E q u i l i b r i u m vessels o f capacity 4 L and 2.5 L w e r e built for the experiments. A schematic o f the vessel is s h o w n i n F i g u r e 3.1. T h e inside o f each vessel w a s c o a t e d w i t h T e f l o n t o prevent any c h e m i c a l attack f r o m the a l k a l i n e solutions. A v a r i a b l e speed stirrer w a s attached to the vessel. T h e stirrer shaft and blade w e r e made o f T e f l o n - c o a t e d steel. A t h e r m o c o u p l e p r o b e and a s a m p l i n g port w e r e built into the l i d o f the vessel. A T e f l o n coated t h e r m o c o u p l e probe w a s used. A s a m p l i n g tube, w h i c h w a s also made o f T e f l o n , w a s passed t h r o u g h the s a m p l i n g port d u r i n g s a m p l i n g . A n o - r i n g w a s p l a c e d b e t w e e n the l i d and the vessel t o prevent evaporation o f the e x p e r i m e n t a l s o l u t i o n . A T e f l o n p a c k i n g g l a n d w a s used a r o u n d the stirrer shaft to prevent evaporation. T h e vessel c o n t a i n i n g the s o l u t i o n w a s c o v e r e d w i t h a l i d . T h e l i d o f one vessel w a s made o f stainless steel and coated w i t h T e f l o n and that o f the other vessel w a s made o f p l e x i g l a s s . T h e vessel w a s  38 then placed in a water bath at 368.15 K. The air inside the vessel was replaced with nitrogen gas to prevent undesirable reactions such as those with the carbon dioxide in the air. The solution was stirred during the experiments.  Figure 3.1. Equilibrium vessel for the solubility experiments.  Thermometer  Stirrer Packing Gland Sampling Tube  O-Ring  Shaft and Blade  39 Liquid phase samples were obtained from the vessel using a syringe. Each sample went through a Teflon pipe and a 0.5 um polyvinylidene fluoride membrane filter (Millipore Canada, Nepean, Ontario). It was found by dynamic light scattering (DLS) that all of the precipitate particles were larger than 3 um, meaning all portions of the precipitate were trapped by the filter. The D L S experiments were conducted by using a Malvern Zetasizer III apparatus (Malvern Instruments Inc., Malvern, UK). The filtrates were then analyzed by a G B C 904 Atomic Absorption Spectrophotometer (GBC Scientific Equipment Pty Ltd., Victoria, Australia) using the nitrous oxide-acetylene flame to measure the total soluble A l and Si. The procedure of Atomic Absorption analysis is explained in detail in APPENDIX I. The samples were taken over a period of time until no change in A l and Si concentration was observed. This was taken to be the equilibrium state of the system. It takes about seven days to reach equilibrium. The  other approach of solubility experiment by adding sodium aluminosilicate  precipitates into an unsaturated solution of Al and Si was not tried because dissolution of the solid precipitate was too slow as it was found by preliminary experiments. In particular, a small amount, 0.005 g, of precipitates could not be dissolved significantly in 100 mL of alkaline solution containing NaOH of 1 mol/kg H 0 after four weeks. 2  3.1.3. Identification of the precipitates  After equilibrium was reached, precipitates, which deposited on the wall, stirrer blade, and bottom of the vessel were collected, washed with deionized water several times and dried in an oven at 105 °C. The structure of the dried precipitates was identified by X-ray diffraction (D5000 Diffractometer, Siemens Aktiengesellschaft, Germany) and  40 thermal analysis using a TGS-2 thermogravimetric analyzer (Perkin-Elmer, Norwalk, Connecticut, USA).  The software, FIFFRAC / A T v.3.1 (Siemens Industrial Automation,  Inc., Madison, Wisconsin, USA),  was used to compare the X-ray patterns of samples with  those of reference minerals. A portion of the solid materials was dissolved in nitric acid solution for analysis to obtain the molar ratios of Na, A l , and Si using the Atomic Absorption Spectrophotometer (see APPENDIX I). The presence of chlorine and sulfate in the solid were tested by mixing samples of dissolved solid with a AgNC>3 and B a C l solution respectively (Greenberg et al,  2  1992; Masterton and Slowinski, 1972). The  presence of carbonate in the structure of the solids was tested by dissolving the solid in an acidic solution to observe formation of bubbles of CO2 gas (Masterton and Slowinski, 1972). Finally, images of the precipitates were obtained on carbon-coated samples using a Philips XL30  scanning  electron  microscope  (Philips Electronics, Eindhoven,  Netherlands).  3.2. Solubility Experiments using Synthetic Liquors of System B  3.2.1. Experimental design The synthetic liquors of system B were prepared to study the effect of Na S. The 2  liquor concentrations were chosen to resemble closely mill liquors from a Kraft pulp mill in B.C., Canada. Two salts, N a S 0 4 and NaCl, were not added into the liquors of system 2  B in order to make the system simpler with only major anions. It is also noted that the concentrations of SO4 - and Cl" were very small in the mill liquors compared with those 2  of other anions such as OH", HS", and CO3 ' (Magnusson et al, 1979). 2  41  System B was prepared similarly with the following salts: AICI36H2O, Na2Si03-9H20, NaOH, Na2C03, and Na2S. The perturbations around the base concentration level gave the other compositions at which experiments were conducted as seen in Table 3.2. The liquors were prepared by controlling the added amount of Na2S for both green and white liquors. The amount of input Na2S was variedfrom0 to 1.0 mol/kg H2O to observe the effects of H S and OH concentrations in synthetic green liquor. It is -  -  known that Na S dissociates to Na , H S and OH" in H 0 according to the following +  -  2  2  reaction (Smook, 1992): Na S + H 0 ->• 2 N a + H S " + O H " . +  2  2  T a b l e 3.2. S o l u b i l i t y experiment design for synthetic l i q u o r s o f system B .  Synthetic green liquor C o n c e n t r a t i o n s i n i n i t i a l solutions ( m o l / k g H2O)  Experiment  AICI36H2O  Na Si0 -9H 0  NaOH  Bl*  0.05  0.05  0.25  1.0  0.5  B2*  0.1  0.05  0.25  1.0  0.5  B3*  0.05  0.1  0.25  1.0  0.5  B4  0.05  0.05  0.25  1.0 1.0  2  3  2  Na C0 2  3  Na S 2  0.1  0.05  0.25  0.05  0.1  0.25  1.0  B7 B8  0.05  0.05  0.25  1.0  0.1  0.05  0.25  1.0  B9  0.05  0.1  0.25  1.0  0.0 0.0 0.0 1.0 1.0 1.0  B5 B6  Synthetic white liquor BIO*  0.05  0.05  2.0  0.25  0.5  Bll*  0.1  0.05  2.0  0.25  0.5  B12*  0.05  0.1  2.0  0.25  0.5  B13  0.05  0.05  2.0  0.25  B14  0.1  0.05  2.0  0.25  B15  0.05  0.1  2.0  0.25  B16  0.05  0.05  2.0  0.25  B17  0.1  0.05  2.0  0.25  B18  0.05  0.1  2.0  0.25  0.0 0.0 0.0 1.0 1.0 1.0  base concentration level experiments  42  3.2.2. Experimental procedure and analysis Two solutions were prepared by dissolving measured amounts of  AICI36H2O  and  Na2Si03-9H20 in 1 kg of deionized water respectively. Proper amounts of NaOH, Na2C03, and Na S salts were added to the solutions to make the desired initial conditions 2  for the experiments. The subsequent experiments and analysis procedures are similar to those in sections 3.1.2 and 3.1.3.  3.3. Solubility Experiments using Mill Liquors Prior to the solubility experiments, basic information on the mill liquors was obtained and is presented in Table 3.3. The liquor samples were passed through a 0.5 urn polyvinylidene fluoride membrane filter (Millipore Canada, Nepean, Ontario) to remove particles. The concentrations of Al, Si, and K were determined using a G B C 904 Atomic Absorption Spectrophotometer (GBC Scientific Equipment Pty Ltd., Victoria, Australia). The chlorine content was measured by titration with 0.1 M A g N 0  3  solution using a  Mettler Toledo DL25 titrator (Fisher Scientific, Vancouver, B.C.). A Mettler DM141 silver electrode (Fisher Scientific, Vancouver, B.C.) was used for the titration. The concentrations of NaOH, Na2C03, and Na2S were obtained from the A B C test (Grace et al, 1989) done by the Prince George Lab of the Pulp and Paper Research Institute of Canada. The A B C test is a titration method (TAPPI Standard Method T624 os-68) using HC1 solution to determine the amount of titratable alkali such as NaOH, Na2S, and Na2C03 in green and white liquors (Grace et al, 1989).  43  3.3.1. E x p e r i m e n t a l design E x p e r i m e n t s w e r e performed w i t h samples prepared u s i n g the m i l l green and w h i t e l i q u o r s and a d d i n g appropriate  c h e m i c a l s t o simulate: (a) progressive  system  closure: and (b) observed variations i n the concentrations o f carbonate and other i o n s i n m i l l liquors.  T a b l e 3.3. A n a l y s i s results o f m i l l l i q u o r s . C aemical concentrations ( m o l / k g H 0 ) 2  Green liquor  Al  Si  K  NaOH  Na C0  N.D.  0.0008  0.245  0.29  1.05  2  N.D.  0.0008  0.244  2.06 (NaOH* 2.63)  Na S  Cl  0.56  0.084  2  (NaHS* 0.56)  (NaOH* 0.85) White liquor  3  0.23  0.57  0.076  (NaHS* 0.57)  N . D . : not detected *  : T h e concentrations o f N a O H and N a S c a n also be expressed as N a O H * 2  and  N a H S * since 1 m o l o f N a S dissociates to 1 m o l o f N a H S and 1 m o l o f N a O H i n 2  w a t e r b y the f o l l o w i n g reaction : N a S + H 0 - > N a H S + N a O H ( S m o o k , 1992). 2  2  T h e detailed e x p e r i m e n t a l d e s i g n is s h o w n i n T a b l e 3.4. F i r s t , experiments w i t h base concentration l e v e l s w e r e p e r f o r m e d u s i n g the green l i q u o r s (experiments M 1 , M 2 , and M 3 ) i n T a b l e 3.4. Perturbations around the base-case concentration l e v e l g a v e the c o m p o s i t i o n for experiments M 4 to M 1 2 i n o r d e r t o observe the effects  of NaOH,  N a C 0 3 , and N a S o n the p r e c i p i t a t i o n c o n d i t i o n s o f s o d i u m a l u m i n o s i l i c a t e . In the case 2  2  o f e x p e r i m e n t s w i t h the m i l l w h i t e l i q u o r , the base concentration l e v e l is the c o m p o s i t i o n o f l i q u o r s i n e x p e r i m e n t s M 1 3 , M 1 4 , and M 1 5 . A g a i n , perturbations a r o u n d this base concentration l e v e l w e r e done and gave the c o m p o s i t i o n s for experiments M l 6 to M 2 4 .  3.3.2. Experimental procedure and analysis T h e subsequent  experiments and a n a l y s i s procedures are s i m i l a r to those i n  sections 3.1.2 and 3.1.3. T h e s o d i u m , a l u m i n u m , s i l i c o n , and p o t a s s i u m contents i n the s o l i d precipitates w e r e a n a l y z e d u s i n g the A t o m i c A b s o r p t i o n S p e c t r o p h o t o m e t e r after d i s s o l v i n g the s o l i d samples i n nitric a c i d s o l u t i o n .  T a b l e 3.4. S o l u b i l i t y experiment design for m i l l l i q u o r s . v l i l l green l i q u o r Exp.  C o n c e n t r a t i o n s i n i n i t i a l solutions  (mol/kg H 0 ) 2  A1C1 -6H 0  Na Si0 -9H 0  NaOH  Ml*  0.05  0.05  0.29  1.05  0.56  M2*  0.10  0.05  0.29  1.05  0.56  M3*  0.05  0.10  0.29  1.05  0.56  M4  0.05  0.05  1.05  0.56  M5  0.10  0.05  1.05  0.56  M6  0.05  0.10  1.29 1.29 1.29  1.05  0.56  M7  0.05  0.05  0.29  0.56  M8  0.10  0.05  0.29  M9  0.05  0.10  0.29  1.55 1.55 1.55  M10  0.05  0.05  0.29  1.05  M i l  0.10  0.05  0.29  1.05  M12  0.05  0.10  0.29  1.05  1.06 1.06 1.06  3  2  2  3  2  Na C0 2  3  Na S 2  0.56 0.56  M i l l w h i lte l i q u o r M13*  0.05  0.05  2.06  0.23  0.57  M14*  0.10  0.05  2.06  0.23  0.57  M15*  0.05  0.10  2.06  0.23  0.57  M16  0.05  0.05  0.57  0.10  0.05  0.23  0.57  M18  0.05  0.10  2.56 2.56 2.56  0.23  M17  0.23  0.57  M19  0.05  0.05  2.06  0.57  M20  0.10  0.05  2.06  M21  0.05  0.10  2.06  0.48 0.48 048  M22  0.05  0.05  2.06  0.23  M23  0.10  0.05  2.06  0.23  M24  0.05  0.10  2.06  0.23  1.07 1.07 1.07  * base c o n c e n t r a t i o n l e v e l e x p e r i m e n t s  0.57 0.57  45  3.4. Osmotic Coefficient Measurement for Na2Si03 and Na2Si03-Na0H Systems A q u e o u s a l k a l i n e silicate solutions contain a variety o f s i l i c i c ions, o r t h o s i l i c i c (Si0  4 4  \ HSi0  3 _ 4  , H Si0 2  2 4  \ H S i 0 \ a n d F L j S i O ^ o r m e t a s i l i c i c species ( S i 0 3  4  2 3  \  HSi0 ', 3  and H S i 0 3 ) . S e v e r a l reactions related t o the s i l i c i c species take place i n aqueous m e d i u m 2  (Jendoubi et al,  1997). A l t h o u g h t h e r m o d y n a m i c c a l c u l a t i o n s have been done t o c h e c k  the stability b e t w e e n o r t h o s i l i c i c a n d m e t a s i l i c i c species ( B a b u s h k i n , 1985), the nature o f stable s i l i c i c species i n a l k a l i n e solutions, w h e n metasilicate salt is d i s s o l v e d i n water, has n o t yet been e l u c i d a t e d e x p e r i m e n t a l l y . U n d e r s t a n d i n g the nature o f s i l i c i c i o n s i n a l k a l i n e solutions is a prerequisite t o the study o f electrolyte t h e r m o d y n a m i c properties o f those ions. A titration m e t h o d w a s used t o identify the species present w h e n the s o d i u m metasilicate i s d i s s o l v e d i n aqueous a l k a l i n e s o l u t i o n .  3.4.1. Identification of silicic species by a titration method An  aqueous s o l u t i o n o f N a 2 S i 0 - N a O H w a s prepared 3  a n d titrated u s i n g H C 1  s o l u t i o n . T h e concentration o f N a 2 S i 0 3 w a s 0.25 m o l / L a n d that o f N a O H w a s 1.00 m o l / L . T h e s o l u t i o n w a s prepared  b y d i s s o l v i n g p r o p e r amounts o f N a 2 S i 0 3 - 9 H 2 0  ( s o d i u m metasilicate, Reagent grade, F i s h e r Scientific, V a n c o u v e r , B . C . ) a n d N a O H (Reagent grade, F i s h e r S c i e n t i f i c , V a n c o u v e r , B . C . ) i n d i s t i l l e d a n d d e i o n i z e d water. T h e s o l u t i o n w a s then stirred u s i n g a magnetic b a r coated w i t h T e f l o n f o r a w e e k at r o o m temperature t o a l l o w f o r a n y p o s s i b l e reaction such as c o n v e r s i o n o f m e t a s i l i c i c species to o r t h o s i l i c i c species t o o c c u r (Gasteiger, 1988). T h e H C 1 s o l u t i o n o f 1 ± 0.005 m o l / L ( F i s h e r S c i e n t i f i c , V a n c o u v e r , B . C . ) w a s used as a titrant. T h e titration w a s c o n d u c t e d b y  46 using a Mettler Toledo DL25 titrator (Fisher Scientific, Vancouver, B.C.) equipped with a Mettler DG111-SC pH electrode (Fisher Scientific, Vancouver, B.C.). The pH electrode was calibrated using two buffer solutions of pH 4 and pH 7 purchased from Fisher Scientific. The measured pH values were 12.85 for NaOH solution of 0.1 mol/L and 11.92 for that of 0.01 mol/L respectively. Calculated pH values using Pitzer's equation (2.46) were 12.89 and 11.96 respectively. This result shows that a reliable measurement was available in high pH range using the calibrated electrode. The titration proceeded until the pH reached a value of 2.5 with an increment of the titrant of 0.05 mL.  3.4.2. A p p a r a t u s a n d c h e m i c a l s  The isopiestic apparatus of four-neck type for osmotic coefficient measurement was designed by modifying a known three-neck type apparatus (Thiessen and Wilson, 1987). One set of the isopiestic apparatus is shown in Figure 3.2. The neck-type apparatus has been used by other researchers also (Lin et al, 1996; Ochs et al, 1990). This neck-type apparatus has several advantages compared to the conventional one. It has smaller capacity (140 mL). The solutions are in good thermal contact since the heat can be transferred through the glass from the water of the water-bath to the sample solutions. In the case of the conventional isopiestic apparatus, the heat is transferred through the vacuum, and it takes long time to reach the equilibrium. The time to reach the equilibrium can be substantially reduced by using a neck-type apparatus.  47  F i g u r e 3.2. T h e isopiestic apparatus.  sample bottle  c a  P  48 Four sets of the isopiestic apparatus were built by the Canadian Blowing Company (Richmond, B.C.) in order to speed up the work. One set of the isopiestic apparatus consists of a four-neck flask equipped with a vacuum stopcock, four sample bottles, and their caps. The capacity of the four-neck flask is 100 mL and each neck has a 14/20 joint of female connector. The four-necks are attached symmetrically to the flask. The high vacuum stopcock is attached to the top center of the flask. The capacity of the flat-bottom sample bottle is 10 mL and the neck has a 14/20 compatible joint of male connector. The water-bath (Model 1187, V W R Scientific, Richmond, B.C.) equipped with a digital temperature controller was used to keep the temperature constant. A circulation unit of the water-bath can minimize the temperature gradient inside the water-bath. The temperature stability of the water-bath was + 0.01 °C. The readability of the temperature controller was 0.001 °C. Reagent grade salts (Fisher Scientific, Vancouver, B.C.) were used without further purification. The NaCl, KCI, and NaOH salts were dried in a oven at 105 °C for 24 hours before use. Sodium metasilicate, N a S i 0 3 - 9 H 2 0 , was used without further 2  drying. Distilled water was used in all experiments after it was deionized and filtered through a 0.05 um filter in an E L G A S T A T UHP water purification apparatus (Fisher Scientific, Vancouver, B.C.). The NaCl solution was used as a reference whereas the KCI solution was used as the standard to compare our results with data from the literature.  49 3.4.3. E x p e r i m e n t a l p r o c e d u r e  The salt solutions were prepared to the desired concentrations by weighing and dissolving. Thefirstbottle of each apparatus contained the reference (NaCl) solution. The second bottle contained the standard (KG) solution. The remaining two bottles contained the sample solutions of same initial concentration. The sample solution of Na2Si03 was prepared by dissolving the sodium metasilicate, Na.Si03-9H20, salt in the water. The sample solution of Na2SiC>3-NaOH was prepared by dissolving proper amounts of Na Si03-9H20 and NaOH salts. The molalities of Na2Si03 and NaOH were the same in 2  the sample solution. The presence of Si03 ', metasilicic ion in alkaline aqueous solution, 2  when the sodium metasilicate is dissolved, will be explained in section 5.1. The groundglass surfaces of each sample bottle were slightly coated by a silicon vacuum grease. The sample bottles were put into the four-neckflask.The apparatus was evacuated slowly to remove the air and the dissolved gas in the sample solutions using a vacuum pump. Four sets of the apparatus were available. In order to determine the equilibration time, the following procedure was used. The four sets were placed in the water-bath at 298.15 K. Aiter two days, one of them was taken outfromthe water-bath. The solutions of each sample bottle were weighed. The remaining sets were taken out after two or three more days until no change in the solute concentration was observed. It was then assumed that the total elapsed time is the required equilibrium time. It was found that the equilibrium was reached in five days. It was then decided to set the equilibrium time to seven days. Subsequently, all four sets were used to obtain data. Following equilibration, the solutions were weighed. The molality of each solution was calculatedfromthe measured weight. The osmotic coefficient of the sample  50  s o l u t i o n w a s c a l c u l a t e d from the m o l a l i t i e s o f the sample s o l u t i o n and o f the reference ( N a C l ) s o l u t i o n a n d from the o s m o t i c coefficient o f the reference ( N a C l ) s o l u t i o n . T h e o s m o t i c coefficient o f the reference N a C l s o l u t i o n w a s c a l c u l a t e d b y P i t z e r ' s m o d e l u s i n g equation (2.54) i n section 2.5 w i t h P i t z e r ' s parameters, p Naci (0)  =  0.0765 , P Naci = 0.2664 (1)  , and c W i = 0 . 0 0 1 2 7 at 2 9 8 . 1 5 K (Pitzer, 1991). T h e measured o s m o t i c c o e f f i c i e n t o f the K C 1 s o l u t i o n w a s c o m p a r e d to calculated data u s i n g p u b l i s h e d P i t z e r ' s parameters to ensure the a c c u r a c y o f the experiments (Pitzer, 1991).  3.5. Osmotic Coefficient Measurement for NaOH-NaCl-NaAl(OH)4 System  3.5.1. Apparatus and chemicals T h e apparatus w a s the same one used i n the p r e v i o u s o s m o t i c coefficient study for the Na2Si03 and Na2Si03-NaOH systems.  Reagent  grade  salts  (Fisher  Scientific,  V a n c o u v e r , B . C . ) w e r e used w i t h o u t further p u r i f i c a t i o n . T h e N a C l , K C 1 , and N a O H salts w e r e d r i e d i n an o v e n at 105 ° C for 2 4 hours before u s i n g . A l u m i n u m c h l o r i d e hydrate, A I C I 3 6 H 2 O , w a s used w i t h o u t further d r y i n g . D i s t i l l e d w a t e r w a s used i n a l l e x p e r i m e n t s after it w a s d e i o n i z e d a n d filtered t h r o u g h a 0.05 p m filter i n an E L G A S T A T H H P w a t e r p u r i f i c a t i o n apparatus ( F i s h e r Scientific, V a n c o u v e r , B . C . ) . T h e N a C l s o l u t i o n w a s u s e d as reference whereas the K C 1 s o l u t i o n w a s used as standard to c o m p a r e o u r results w i t h data from the literature. Aluminum  i o n s p e c i a t i o n i n aqueous  solutions changes  with  both  p H and  concentration. I n d i l u t e solutions at p H above 9, it is c o m m o n l y assumed that a l u m i n a t e i o n , A l ( O H V , is the p r e d o m i n a n t one. T h e f o r m a t i o n o f other a l u m i n u m i o n s such as  51  A l 2 0 ( O H ) 6 ' and A l ( O H ) 6 " w a s not c o n s i d e r e d f o r this study since these ions c a n be 2  3  present o n l y at concentrations o f a l u m i n u m a b o v e 1.5 m o l / L a n d at e x t r e m e l y h i g h p H (Swaddle  etal, 1994; P o k r o v s k i i  The dissolving  sample a  proper  a n d H e l g e s o n , 1995).  NaOH-NaCl-NaAl(OH)4 amount  o f A1C13-6H20  concentrations o f a l u m i n u m and h y d r o x y l  aqueous in  a  solution  NaOH  was  aqueous  prepared solution.  by The  i o n s w e r e s u c h that f o r m a t i o n o f other  a l u m i n u m i o n s except for A l ( O H ) 4 ' w a s prevented. In a l l s o l u t i o n s , the input m o l a l i t y ratio o f AICI36H2O to N a O H w a s less than 1 : 5 so that a l l a l u m i n u m salts w e r e c o m p l e t e l y d i s s o l v e d and w e r e present as A l ( O H ) 4 " i o n . T h u s , the species present i n the s a m p l e s o l u t i o n s w e r e assumed to be N a , O H " , C l " , and A l ( O H ) 4 " o n l y . +  3.5.2. E x p e r i m e n t a l p r o c e d u r e T h e e x p e r i m e n t a l p r o c e d u r e for N a O H - N a C l - N a A l ( O H ) 4 s y s t e m w a s s i m i l a r t o that o f the p r e v i o u s o s m o t i c coefficient study for the Na2Si03 and N a 2 S i 0 3 - N a O H systems. B r i e f l y , an e x p e r i m e n t p r o c e e d e d as f o l l o w s . T h e s o l u t i o n s w e r e prepared to the desired concentrations b y w e i g h i n g and d i s s o l v i n g . T h e first bottle o f e a c h apparatus c o n t a i n e d the reference ( N a C l ) solution. T h e s e c o n d bottle c o n t a i n e d the standard ( K C I ) s o l u t i o n . T h e r e m a i n i n g t w o bottles c o n t a i n e d the s a m p l e s o l u t i o n s o f the same i n i t i a l concentration. T h e g r o u n d - g l a s s surfaces o f each s a m p l e bottle w e r e s l i g h t l y c o a t e d b y a s i l i c o n v a c u u m grease. T h e s a m p l e bottles w e r e put into the f o u r - n e c k  flask.  The  apparatus w a s evacuated i n o r d e r to r e m o v e the air a n d the d i s s o l v e d gas in the s a m p l e s o l u t i o n s u s i n g a v a c u u m p u m p . T h e s o l u t i o n s i n the apparatus w e r e e q u i l i b r a t e d i n a w e l l thermostated c o n d i t i o n at 2 9 8 . 1 5 K .  52  A t e q u i l i b r i u m , the c h e m i c a l potential o f w a t e r is the same i n the t w o  sample  s o l u t i o n s and i n the reference and standard s o l u t i o n . T h i s c o n d i t i o n m a y be expressed as f o l l o w s ( P i t z e r , 1991)  • T  v  i  i  m  i  = *  2  I  v  i  m  i = *  j  R  k  I  v  A  =4 __>. . S  (2-54)  m  I  w h e r e , <J> is the o s m o t i c coefficient, v is the n u m b e r o f ions p r o d u c e d b y 1 m o l e o f the solute, and m is the m o l a l i t y o f the solute. T h e superscripts, s a m p l e s o l u t i o n 1, sample s o l u t i o n 2, reference  1, 2, R , and S, refer to  s o l u t i o n , and standard  solution. The  subscripts, i , j , k, and 1, refer to each c o m p o n e n t i n s a m p l e 1, s a m p l e 2, reference,  and  standard  The  solutions. E q u i l i b r i u m i n each e x p e r i m e n t w a s reached  i n s e v e n days.  measured o s m o t i c coefficient o f the K C 1 s o l u t i o n w a s c o m p a r e d to c a l c u l a t e d data u s i n g p u b l i s h e d P i t z e r ' s parameters to ensure the a c c u r a c y o f the e x p e r i m e n t s ( P i t z e r , 1991). F o l l o w i n g e q u i l i b r a t i o n , the s o l u t i o n s w e r e w e i g h e d . T h e m o l a l i t y o f the solutes i n each s o l u t i o n w a s c a l c u l a t e d from the measured w e i g h t . T h e o s m o t i c coefficients o f the sample s o l u t i o n s w e r e then c a l c u l a t e d from the measured m o l a l i t i e s o f the  sample  s o l u t i o n s and o f the reference ( N a C l ) s o l u t i o n , and from the o s m o t i c c o e f f i c i e n t o f the reference ( N a C l ) s o l u t i o n . T h e o s m o t i c coefficient o f the reference N a C l s o l u t i o n w a s c a l c u l a t e d b y P i t z e r ' s m o d e l u s i n g equation (2.54) i n section 2.5 w i t h P i t z e r ' s parameters, P  (0)  N a d = 0.0765 , P  (1) N  a c i = 0.2664 , and C * c i = 0 . 0 0 1 2 7 at 298.15 K ( P i t z e r , 1991). T h e N a  measured o s m o t i c coefficient o f the K C 1 s o l u t i o n w a s c o m p a r e d to c a l c u l a t e d data u s i n g p u b l i s h e d P i t z e r ' s parameters (Pitzer, 1991) to ensure the a c c u r a c y o f the experiments.  53  CHAPTER 4. THERMODYNAMIC MODELING OF SODIUM ALUMINOSILICATE FORMATION  A  thermodynamic  e q u i l i b r i u m m o d e l has been  d e v e l o p e d to predict  sodium  a l u m i n o s i l i c a t e p r e c i p i t a t i o n c o n d i t i o n s i n a l k a l i n e solutions at 368.15 K . A  method  based o n the e q u i l i b r i u m constants o f the s o l i d f o r m a t i o n reactions w a s used for this m o d e l i n g ( A n d e r s o n and C r e r a r , 1993). P i t z e r ' s m e t h o d w a s adopted to calculate the a c t i v i t y o f w a t e r and i o n a c t i v i t y coefficients.  4.1. M o d e l E q u a t i o n s T h e p r e d o m i n a n t a l u m i n u m and s i l i c o n species i n s o l u t i o n w e r e a s s u m e d to be A l ( O H ) 4 ' and S i 0 et al,  2 3  ' r e s p e c t i v e l y because the system is v e r y a l k a l i n e ( p H > 1 3 ) ( B a b u s h k i n  1985; P o k r o v s k i i and H e l g e s o n , 1995; S w a d d l e et al,  1994). T h u s , the m o d e l  considers that eleven species are present at e q u i l i b r i u m at 3 6 8 . 1 5 K and 1 atm: t w o s o l i d species ( N a ( A l S i 0 ) C l - 2 H 0 and N a ( A l S i 0 ) ( O H ) 2 - 2 H 0 ) , one l i q u i d ( H 0 ) , and 8  4  6  2  2  8  eight i o n s ( N a , A l ( O H ) \ S i 0 ' , O H ' , C 0 +  4  2  4  3  2 3  6  2  2  ' , S 0 " , H S " , and C l ) . T h e m o d e l equations 2  4  consist o f the reaction e q u i l i b r i u m equations for sodalite dihydrate and h y d r o x y s o d a l i t e dihydrate, one charge b a l a n c e equation, and the mass balance equations for the elements o f N a , A l , S i , C l , O , H , S, and C . F o r m u l a s for sodalite dihydrate and h y d r o x y s o d a l i t e dihydrate f o r m a t i o n i n a l k a l i n e aqueous solutions c a n be w r i t t e n as f o l l o w i n g ( Z h e n g et al, 1997).  54  8Na  +  8Na  (aq)  + 6Al(OH)  +  + 6Si0 2  4(aq)  3  + 6Al(OH)4 (aq)+ 6Si0 _  (aq)  (aq)  + 2Cr  2  3  (aq)  <-> Na_(AlSi0 ) Cl -2H 0 + 4 H 0 + 120H-  (aq)  4  20H"  +  6  2  2  (8)  2  (1)  (4.1)  (aq)  Na.(AlSi0 ) (OH) 2H O + 4H 0 ,)+ 120H-  (aq)  4  6  r  2  w  2  (4.2)  (aq)  (  Assuming the solids to be pure then their activity is unity and the thermodynamic equilibrium constant of sodalite dihydrate, K _ , can be written as follows s o  a K  « a - ) «  Hp( QH-'V'oH-)  ^  m  3)  O H ) , Y L H ) , ) « O > - ylo? X c r ylr ) m  (  3  ( 0  where, a is the activity, m is the molality, and y is the activity coefficient of the species. Similarly, the equilibrium constant of hydroxysodalite dihydrate, Khsod, can be written as follows A K  H Q 2  ( Na^  ("WVoH-)  m  (A N 4  X iO>-YiO?- ^ m  Na+ ) (  M A  1  (  O H ) , YAKOHK  S  OW )  S  The mass balance equations for the Na, Al, Si, Cl, O, H , S, and C elements are given by toui  n  =  ^  n  r  =  +  n r = 2n  = (  ^OOo7£oi5  + 26m  H 2 0  sod  +(  ^  ) ( N a  s o d  ^OOOnS.OlS^^^  =  "  "^o 1000/18.015  (  +28m  n 1 0 Q Q  H /  )(4m  hsod  2 1  °  id7^  ) ( m  ^°"><-  +  3  +  6  c.-  "W  +  ^  hsod  m  -  + 2 m  m  +  6  m  «  }  (  4  -)  o»-  +  3 m  6  )  ^ coi-  +  4 m  soJ-  .9)  (4  )  0 1 5  )(4m  A 1 ( O H )  , + m _ + m . +4m oH  H s  sod +  6  m h s o d  ) (4.10)  55  .OUl  ,  =  V  w  tow c  =  , V  v  soj  1000/18.015  s  "H^O  )  A  c o  4  Jjx  v  ^  (  1000/18.015  (  HS  (  ' ^  4  ;  1  2  )  '  V  T h e charge b a l a n c e equation c a n be w r i t t e n as f o l l o w s . m  +  Na  = m ,^  t i N  . +2rn  Al(OH)  +  + ni SiOJ  4  _ + 2m OH  ,_ + 2 m CO|  + m. SOJ  _ + ni HS  (4.13) Cl  v  '  where, n is the n u m b e r o f m o l e s , superscript total stands for total n u m b e r o f m o l e s o f element,  subscript  sod  indicates  sodalite  dihydrate,  subscript  hsod  indicates  h y d r o x y s o d a l i t e dihydrate, and m is the m o l a l i t y o f the species.  4.2. S t r u c t u r e o f t h e T h e r m o d y n a m i c M o d e l A  structure o f the m o d e l i n g is s h o w n i n F i g u r e 4 . 1 . T h e total a m o u n t  c h e m i c a l s , P i t z e r ' s parameters,  of  and e q u i l i b r i u m constants o f sodalite d i h y d r a t e and  h y d r o x y s o d a l i t e d i h y d r a t e formations w e r e g i v e n f o r the m o d e l i n g c a l c u l a t i o n . M o d e l parameters such as P i t z e r ' s parameters and e q u i l i b r i u m constants are d i s c u s s e d i n m o r e detail i n C h a p t e r 7. A n initial guess for the m o l a l i t y o f each species w a s also g i v e n as input. W a t e r a c t i v i t y a n d a c t i v i t y coefficients o f species w e r e c a l c u l a t e d u s i n g the P i t z e r ' s equation i n the subroutine A C T C O F . P i t z e r ' s parameters used for this m o d e l i n g w i l l be d i s c u s s e d i n section 7.1. T h e m o l a l i t i e s , activity coefficients, and w a t e r a c t i v i t y were  substituted  into the  m o d e l equations  i n the  subroutine F U N C V .  The model  equations w e r e a set o f n o n - l i n e a r equations. A N e w t o n - R a p h s o n m e t h o d ( N u m e r i c a l Recipies™,  1995) w a s used to solve the n o n - l i n e a r equations. A constraint that the  m o l a l i t y o f any species c a n not be negative w a s i n c l u d e d i n the m o d e l . T h e m o l a l i t i e s o f  56  species at e q u i l i b r i u m w e r e c a l c u l a t e d b y s o l v i n g the m o d e l equations. T h e m o l a l i t i e s o f A J ( O H V and S i 0 3 ' at e q u i l i b r i u m define the p r e c i p i t a t i o n c o n d i t i o n s . A c o m p u t a t i o n a l 2  source c o d e (kshsod.for) o f this m o d e l i n g is g i v e n i n A P P E N D I X I X together w i t h e x a m p l e s o f input and output.  F i g u r e 4 . 1 . A b l o c k d i a g r a m o f the t h e r m o d y n a m i c m o d e l i n g .  INPUT  • Total amount of chemicals • Pitzer's parameters • Equilibrium constants ( K ^ and K ^ ) • Initial guess for molalities of species  ACTCOF  FUNCV  • Calculation of activity of water and activity coefficients using Pitzer's equations (2.40)~(2.43)  • Model equations, (4.3)~{4.13)  OUTPUT  • Molalities of species ( N a \ AI(OH) ", Si032-, OH", C 0 - , S0 ", HS", CI-, H 0 , hsod, sod) 4  4  2  3  2  2  57  CHAPTER 5. OSMOTIC COEFFICIENT DATA FOR Na Si0 , 2  3  Na Si0 -NaOH, AND NaOH-NaCl-NaAI(OH) AQUEOUS SYSTEMS 2  3  4  Prior to the determination of Pitzer's parameters relevant to SiC»3 " and Al(OH)4', 2  the osmotic coefficient  data for the Na2SiC»3, Na Si0 -NaOH, and NaOH-NaCl2  3  NaAl(OH)4 aqueous systems were measured at 298.15 K and the identification of silicic species in solution was done.  5.1. Identification of Metasilicic Species by Titration  A titration curve of Na2Si0 -NaOH solution is shown in Figure 5.1. In the figure, 3  20 mL of the solution containing Na2SiC«3 of 0.25 mol/L and NaOH of 1.00 mol/L was titrated with a HC1 solution of 1+0.005 mol/L. If we assume that metasilicic ion, Si03", and hydroxyl ion, OH', are the 2  predominant ions in the solution and orthosilicic ion, HSi04 ', is not present, then the 3  strong base, OH', should be titrated first. The Si03" ion, then, should be converted to 2  HSi0 " ion which in turn should be converted to H2Si03 by the reactions (5.1) and (5.2) 3  with the addition of the titrant (Babushkin et al, 1985; Harris, 1991). Thus, three equivalence points should be displayed on the titration curve. S i 0 ' + It -> HSi0 "  (5.1)  H S i 0 ' + It -> H S i 0  (5.2)  2  3  3  3  2  3  The first equivalence point, VNaOH of 20 mL should correspond to the OFT since e  the OH" of 1.00 mol/L in the sample solution of 20 mL is titrated with 20 mL of HC1  58 solution of 1.00 mol/L. The second equivalence point, V i should be observed at 25 mL e  since 5 mL of HC1 solution of 1.00 mol/L is needed to convert 20 mL of SiC^ ' of 0.25 2  mol/L to the same amount of HSi0 '. The third equivalence point, V 2 should be 3  e  observed at 30 mL since 5 mL of HC1 solution of 1.00 mol/L is needed to convert 20 mL of HSiCV of 0.25 mol/L to the same amount of F^SiC^.  Figure 5.1. Titration curve for the Na2Si03-NaOH solution with HC1 solution.  14  5  10  15  20  HCI solution (mL)  25  30  59  The pH values corresponding to the volumes of HC1 at which [Si03 "] equals 2  [HSi0 '] and [HSi0 '] equals [H Si0 ] are the p K values of the reactions (5.1) and (5.2) 3  3  2  3  a  according to the Henderson-Hasselbalch equation (Harris, 1991). The p K values for the a  reactions (5.1) and (5.2) were calculated using the data of standard Gibbs free energy of formation, AGf° (Babushkin, 1985). The standard Gibbs free energy change, A G of the 0  reaction (5.1) is equal to A G ° ( H S i 0 ' ) - A G ° ( S i 0 ' ) = -240.7 kcal/mol - (-224.6 2  f  3  kcal/mol) = -16.1 kcal/mol. The p K  a2  f  3  of the reaction (5.1) is equal to log K(5.i) = -  AG7(2.3RT) = -(-16.1 kcal/mol)/(2.3 x 0.001987 kcal/mol K x 298.15 K) = 11.82. Similarly, the standard Gibbs free energy change, A G of reaction (5.2) is equal to 0  A G f ° ( H S i 0 ) - A G ° ( H S i 0 ' ) = - 253.9 kcal/mol - (-240.7 kcal/mol) = -13.2 kcal/mol. 2  The  3  pK i a  f  3  of the reaction (5.2)  is equal to log K<5.2) = -AG7(2.3RT) = -(-13.2  kcal/mol)/(2.3 x 0.001987 kcal/mol K x 298.15 K) = 9.69. Thus, the titration curve should pass from the following two points : (22.5 mL, pH 11.82), (27.5 mL, pH 9.69). If we assume that the metasilicic ion, S i 0 ' is converted to orthosilicic ion, 2  3  H S i 0 ' by the reaction, Si0 " + O H ' -> HSi0 " (Gasteiger, 1988), then the H S i 0 ' of 3  2  4  3  3  3  4  4  0.25 mol/L and the OH* of 0.75 mol/L are present. In this case, the strong base, OH" should be titrated first and the H S i 0 ' ion should be converted to H S i 0 " ion by the 3  2  4  2  4  reaction (5.3) with the addition of the titrant. Subsequently, the H S i 0 " ion is converted 2  2  4  to H S i 0 ' ion which in turn is converted to H S i 0 according to the reactions, (5.4) and 3  4  4  4  (5.5) with the addition of the titrant (Babushkin, 1985; Harris, 1991). Thus, four equivalence points should be present on the titration curve.  60 H S i 0 " + r f - > H S i 0 2-  (5.3)  H Si0  (5.4)  3  ;  4  2  2  2 4  " + H+ - > H S i 0 ' 3  H Si0 " + IT 3  4  4  H4Si0  4  (5.5)  4  T h e first e q u i v a l e n c e point o f 15 m L corresponds to the O F T since the O H " o f 0.75 m o l / L i n the s a m p l e s o l u t i o n o f 2 0 m L is titrated w i t h 15 m L o f H C l s o l u t i o n o f 1.00 m o l / L . T h e s e c o n d e q u i v a l e n c e p o i n t s h o u l d c o r r e s p o n d to 2 0 m L since 5 m L o f H C l s o l u t i o n o f 1.00 m o l / L is needed to convert 2 0 m L o f H S i 0  3 4  " o f 0.25 m o l / L to the same  amount o f H 2 S i 0 " . T h e t h i r d equivalence p o i n t s h o u l d be observed at 25 m L a c c o r d i n g 2  4  to the c o n v e r s i o n o f H 2 S i 0 " to H S i 0 " and the fourth e q u i v a l e n c e point s h o u l d be 2  4  3  4  s h o w n at 3 0 m L a c c o r d i n g t o the c o n v e r s i o n o f H S i 0 " t o H 4 S i 0 . T h e p K values o f the 3  4  4  a  reactions (5.3), (5.4), and (5.5) are 12.00, 11.70, and 9.77 respectively ( B a b u s h k i n , 1985). T h u s , the titration c u r v e s h o u l d pass f r o m the f o l l o w i n g three points: (17.5 m L , p H 12.00), (22.5 m L , p H 11.70), and (27.5 m L , p H 9.77). A s seen from F i g u r e 5.1, the titration c u r v e d i d not pass f r o m the points: (17.5 m L , p H 12.00), (22.5 m L , p H 11.70) w h i c h c o r r e s p o n d t o the p K values o f o r t h o s i l i c i c a  species ( H S i 0 " , H 2 S i 0 " , H S i 0 " , and H » S i 0 ) . T h e curve, h o w e v e r , passed f r o m (22.5 3  2  4  4  3  4  4  m L , p H 11.82) and (27.5 m L , p H 9.69) w h i c h c o r r e s p o n d to the p K values o f m e t a s i l i c i c a  species ( S i 0 " , H S i 0 " , and H 2 S i 0 ) . 2  3  3  3  O n l y t w o e q u i v a l e n c e points are s h o w n that  c o r r e s p o n d to the v o l u m e s o f 25 m L and 30 m L . T h e first e q u i v a l e n c e p o i n t at 2 0 m L is not significant. It c a n be e x p l a i n e d b y the reaction: S i 0  2 3  ' + H2O <-» H S i 0 " + O H " . T h e r e  are t w o p r e d o m i n a n t anions, O H " d i s s o c i a t e d from the N a O H ,  3  and S i 0  2 3  '  from  the  N a 2 S i 0 , i n the i n i t i a l s o l u t i o n . T h e concentration o f the strong base, O H " decreases w i t h 3  61 the addition of the titrant, hydrochloric acid. As the concentration of OH" decreases, more Si03 ions react with H_0 and produce HSiCV and OK to establish the equilibrium. The 2_  standard Gibbs free energy change, AG°, of the reaction: SiC>3 ' + H_0 <-> HSiCV + OH" 2  is equal to AG °(HSi0 ") + AG °(OH") - AG °(Si0 ") - A G ° ( H 0 ) = -240.7 kcal/mol + (2  f  3  f  f  3  f  2  37.59 kcal/mol) - (-224.6 kcal/mol) - (-56.69 kcal/mol) = +3.0 kcal/mol. The log K of the reaction is equal to - A G /(2.3RT ) = -3.0/(2.3 x 0.001987 kcal/mol K x 298.15K) = 0  0  2.2017. Thus the equilibrium constant, K is io' 2.2on f Q  t  n  e  r e a c t  j  o n  22017  . Since the equilibrium constant, 10"  i high, the amount of OH" ions produced by the above reaction is s  enough to hide an inflection of the titration curve at the equivalence point. A calculated titration curve by a method available in the literature (Harris, 1991) is shown in Figure 5.2 with explanations in APPENDIX IV. As seen in the figure, the inflection at the equivalence point is not significant. Another calculated titration curve, when 20 mL of a solution containing Na C03 of 0.25 mol/L and NaOH of 1.00 mol/L 2  was titrated with a H C l solution of 1 mol/L, is shown in the same figure. This curve shows the effect of the equilibrium constant on the inflection point. The equilibrium constant, 10"  36769  , of the reaction, C 0 " + H 0 <-> HC0 " + OH" gave a significant 2  3  2  3  inflection at the equivalence point. Based on the above analysis, we conclude that when sodium metasilicate (Na Si03-9H 0) is dissolved in water containing OH", the predominant species is 2  2  metasilicic ion, Si03". Furthermore the metasilicic ion is not converted to orthosilicic ion 2  (HSi04 ") under these conditions. 3  62  F i g u r e 5.2. C a l c u l a t e d titration c u r v e for the N a S i 0 - N a O H and N a C 0 - N a O H 2  solutions w i t h H C 1 solution.  3  2  3  63 5.2. M o l e Fraction of Metasilicic Species  In addition to SiC>3 ', other anions such as OFT and HSiGV are also present, when 2  the metasilicate salt (Na2Si03-9H20) is dissolved in water. The following equilibrium between  each metasilicic species in the solution is established.  Si0 " + H 0 <-> HSiCV + OH* 2  3  (5.6)  2  Mole fractions of metasilicic species at various pH levels for the two solutions used in the osmotic coefficient experiments, Na2Si03 and mixed Na2Si03-NaOH, are shown  in Figure 5.3. The pH values of the solutions were measured. The mole fractions  of metasilicic species with varying pH were calculated by the method described in the literature (Lindsay, 1979) using the calculated equilibrium constants for the reactions (5.1) and (5.2). The mole fractions of H2Si03 and HSi03* are very low compared to that of  Si03 ' in the concentration range of the osmotic coefficient experiments. Due to this 2  reason, the existence of H2Si03 and H S K V can be ignored. Thus, Na2Si03 solution can be assumed to behave as the single electrolyte system of Na -Si03 " and the mixed +  Na2Si03-NaOH  2  solution can be assumed to behave as a ternary electrolyte system of  Na -Si0 -*-OH\ +  3  5.3. Osmotic Coefficient Data for N a S i 0 Aqueous System 2  3  Tables 5.1 contains the osmotic coefficient and water activity data and their uncertainties (standard deviations, a$) from eight experiments respectively for KCI (standard solution), Na2Si03 (sample solution 1), and Na2Si03 (sample solution 2).  F i g u r e 5.3. M o l e fraction o f m e t a s i l i c i c species w i t h p H .  pH pH range of osmotic coefficient experiments llll  N a S i 0 system 2  3  Na Si0 -NaOH system 2  3  65 The  uncertainty of the  measured osmotic  coefficient  was  calculated in  APPENDIX V from the uncertainty of the weight measurement, ±0.00005 g, and uncertainty in osmotic coefficient of the reference NaCl solution, 0.01 (Pitzer, 1991), by a method available in the literature (Baird, 1995; Holman, 1994). The uncertainty was found to increase with decreasing molality of the standard KC1 and the sample solutions. The osmotic coefficient data and predictions by the Pitzer's model are shown in Figure 5.4. Comparison of the osmotic coefficient data of KC1 standard solutions with prediction by Pitzer's model using the published parameters shows the accuracy of the isopiestic method and our four-neck apparatus. The values of the published Pitzer's parameters are: P KCI= 0.04835, P KCI = 0.2122, and C* ci = -0.00084 at 298.15 K (Pitzer, 1991). The (0)  (1)  K  relative percent error, Rel Err %, was calculated by comparing the measured osmotic coefficients  of the KC1 solutions with the calculated ones. For the entire set of  experiments, the average relative percent error in the osmotic coefficients  of KC1  (standard solution) was 0.26 %.  5.4. Osmotic Coefficient Data for Na Si0 -NaOH Aqueous System 2  3  Table 5.2 contains the osmotic coefficient and water activity data and their uncertainties from thirteen experiments respectively for KC1 (standard solution), Na Si03 2  - NaOH (sample solution 1), and Na Si03 - NaOH (sample solution 2). The uncertainties 2  were also calculated and found to be increasing with decreasing molality. The osmotic coefficients are shown in Figure 5.5 together with values computed by using Pitzer's model. For the entire set of experiments, the average relative percent error in the osmotic coefficients of KC1 (standard solution) was 0.17 %.  66 Table 5.1. Osmotic coefficients and water activities for the Na2Si03 aqueous system at 298.15 K.  Salt 1  NaCl  0.0864  KCI  0.0863  0.9971  0.9971  0.0018 0.0028 0.0029  0.8837  0.9638  0.9971  Na Si0  3  0.0603  0.8926  0.0096  0.8837  0.9971  0.9971  0.9971  0.5125  0.8969  0.0065  0.8998  0.3233  0.9836  0.9835  0.0054  0.9212  0.4990  NaCl  0.9836  Na Si0  3  0.3674  0.8339  0.0091  0.8401  0.7435  0.9836  0.9835  0.0123  Na Si0  3  0.3690  0.8304  0.0090  0.8398  1.1320  0.9836  0.9834  0.0187  0.9258  0.9768  NaCl  0.7048  KCI  0.7287  0.8955  0.0064  0.8977  0.2457  0.9768  0.9767  0.0058  3  0.5313  0.8188  0.0088  0.8158  0.3664  0.9768  0.9768  0.0086  3  0.5313  0.8188  0.0088  0.8158  0.3664  0.9768  0.9768  0.0086  2  Na Si0 2  NaCl  0.9388  1.0750  0.9643  KCI  1.1226  0.8990  0.0064  0.8992  0.0222  0.9643  0.9643  0.0008  Na Si0  0.8637  0.7790  0.0083  0.7796  0.0770  0.9643  0.9643  0.0028  0.8629  0.7797  0.0083  0.7797  0.0000  0.9643  0.9643  0.0000  2  3  Na Si03 2  0.9516  0.9552  NaCl  1.4424  KCI  1.5278  0.9018  0.0063  0.9044  0.2883  0.9516  0.9514  0.0143  1.2063  0.7614  0.0080  0.7618  0.0525  0.9516  0.9515  0.0026  0.7617  0.0080  0.7618  0.0131  0.9516  0.9516  0.0007  Na Si0 2  Na Si0 2  3  3  1.2059  NaCl  1.7545  KCI  1.8747  0.9709 0.0062  0.9106  0.2201  0.9405  0.9403  0.0135  0.7594  0.1709  0.9405  0.9406  0.0105  0.7594  0.1840  0.9405  0.9406  0.0113  Na Si0  3  1.4928  0.7607  Na Si0  3  1.4927  0.7608  0.0078  2  NaCl  2.1187  KCI  2.2808  0.9405  0.9086  0.0078  2  0.9910  0.9271  0.9206  0.0062  0.9193  0.1412  0.9271  0.9272  0.0107  0.7679  0.0781  0.9271  0.9272  0.0059  0.0782  0.9271  0.9271  0.0059  Na Si0  3  1.8213  0.7685  0.0078  Na Si0  3  1.8241  0.7674  0.0077  0.7680  3.0501  0.9367  0.0061  0.9385  0.1922  0.9022  0.9020  0.0198  2  2  8  0.6309  0.0096  Na Si0  7  * * Rel Err, %  w  0.8923  2  6  0.9293  a 0.9971  0.0603  2  5  0.0067  cole  w  3  KCI  4  0.9343  a  Na Si0 2  3  0.9352  * Rel Err, %  °*  0.9971  2  2  Molality  1.0308  2.7716  NaCl KCI  0.9022  Na Si0  3  2.3745  0.8021  0.0078  0.8029  0.0997  0.9022  0.9021  0.0103  Na Si0  3  2.3725  0.8028  0.0078  0.8028  0.0000  0.9022  0.9022  0.0000  2  2  * Relative Percent Error (Rel Err, %) = I f " " - f H x 100 / ** Relative Percent Error (Rel Err, %) = | aw"* - a  w  I x 100 / a ' w  67  Figure 5.4. Osmotic coefficients ofNa2Si03 and KC1 aqueous solutions at 298.15 K.  Molality (mol/kg H 0) 2  68 Table 5.2. Osmotic coefficients and water activities for the Na Si0 -NaOH aqueous system at 298.15 K. 2  Salt  Molality  ^calc  o  3  * Rel Err, %  6  1  2  NaCl KC1 Na SiO NaOH Na SiO NaOH NaCl KC1 Na_SiO.-NaOH Na SiO NaOH NaCl KC1 Na Si0 -NaOH Na SiO NaOH NaCl KC1 Na SiOj-NaOH NajSiOj-NaOH NaCl KC1 Na Si0 -NaOH Na Si0 -NaOH NaCl KC1 Na SiO NaOH Na SiO NaOH NaCl KC1 Na SiO NaOH Na Si0 -NaOH NaCl KC1 Na Si0 -NaOH Na SiO NaOH NaCl KC1 Na SiO NaOH Na Si03-NaOH NaCl KC1 Na SiOj-NaOH Na SiO NaOH NaCl KC1 Na Si0 -NaOH Na Si0 -NaOH NaCl KC1 Na Si0 -NaOH Na SiO NaOH NaCl KC1 Na SiO NaOH Na Si0 -NaOH 2  r  2  r  2  3  2  r  3  2  4  r  2  5  6  7  2  3  2  3  2  r  2  r  2  8  9  r  2  3  2  3  2  r  2  r  2  10  2  2  11  12  13  r  2  3  2  3  2  3  2  r  2  r  2  3  0.1206 0.1216 0.0466 0.0468 0.2439 0.2475 0.0970 0.0973 0.3547 0.3636 0.1481 0.1465 0.5460 0.5604 0.2335 0.2338 0.7996 0.8282 0.3557 0.3519 1.0411 1.0831 0.4731 0.4740 1.1478 1.2008 0.5263 0.5289 1.6712 1.7735 0.7859 0.7846 2.0263 2.1824 0.9599 0.9582 2.1558 2.3274 1.0186 1.0181 2.8345 3.1171 1.3269 1.3246 3.1888 3.5465 1.4954 1.4967 3.5748 4.0204 1.6635 1.6629  0.9215 0.9625 0.9572  0.0066 0.0104 0.0103  0.9084 0.9267 0.9239  0.0066 0.0101 0.0100  0.8976 0.8816 0.8910  0.0065 0.0096 0.0097  0.8983 0.8624 0.8611  0.0065 0.0094 0.0093  0.8967 0.8352 0.8440  0.0064 0.0090 0.0091  0.9012 0.8253 0.8236  0.0064 0.0088 0.0088  0.9003 0.8216 0.8175  0.0064 0.0087 0.0087  0.9108 0.8222 0.8236  0.0063 0.0085 0.0085  0.9152 0.8323 0.8338  0.0062 0.0084 0.0085  0.9199 0.8408 0.8412  0.0062 0.0085 0.0085  0.9410 0.8843 0.8858  0.0061 0.0085 0.0086  0.9516 0.9027 0.9019  0.0060 0.0085 0.0085  0.9647 0.9326 0.9329  0.0059 0.0086 0.0086  0.9293 0.9225 0.8993 0.8993 0.9215 0.9094 0.8891 0.8891 0.9200 0.9034 0.8805 0.8808 0.9220 0.8991 0.8663 0.8663 0.9287 0.8976 0.8481 0.8487 0.9375 0.8989 0.8361 0.8350 0.9418 0.9000 0.8308 0.8306 0.9666 0.9087 0.8239 0.8239 0.9858 0.9171 0.8313 0.8312 0.9932 0.9203 0.8357 0.8357 1.0349 0.9403 0.8736 0.8732 1.0583 0.9522 0.9036 0.9038 1.0850 0.9658 0.9394 0.9393  0.1085 6.5662 6.0489  0.9960 0.9960 0.9960  0.1101 4.0574 3.7698  0.9919 0.9919 0.9919  0.6462 0.1248 1.1448  0.9883 0.9883 0.9883  0.0891 0.4522 0.6039  0.9820 0.9820 0.9820  0.1004 1.5445 0.5569  0.9736 0.9736 0.9736  0.2552 1.3086 1.3842  0.9654 0.9654 0.9654  0.0333 1.1198 1.6024  0.9618 0.9618 0.9618  0.2306 0.2068 0.0364  0.9435 0.9435 0.9435  0.2076 0.1201 0.3118  0.9306 0.9306 0.9306  0.0435 0.6066 0.6538  0.9258 0.9258 0.9258  0.0744 1.2100 1.4224  0.8997 0.8997 0.8997  0.0631 0.0997 0.2107  0.8855 0.8855 0.8855  0.1140 0.7291 0.6860  0.8696 0.8696 0.8696  * Relative Percent Error, (Rel Err, %) = | f ** - f H x 100 / f ** ••Relative Percent Error, (Rel Err, %) = | a -a I x 100 / a ' e x p  w  w  aw  w  calc  aw 0.9960 0.9960 0.9962 0.9962 0.9919 0.9919 0.9923 0.9922 0.9883 0.9882 0.9883 0.9884 0.9820 0.9820 0.9819 0.9819 0.9736 0.9736 0.9732 0.9735 0.9654 0.9655 0.9650 0.9650 0.9618 0.9618 0.9614 0.9612 0.9435 0.9436 0.9433 0.9434 0.9306 0.9304 0.9306 0.9308 0.9258 0.9257 0.9262 0.9262 0.8997 0.8998 0.9009 0.9011 0.8855 0.8854 0.8854 0.8853 0.8696 0.8694 0.8687 0.8688  *• Rel Err,% 0.0004 0.0265 0.0244 0.0009 0.0329 0.0305 0.0076 0.0015 0.0135 0.0016 0.0082 0.0110 0.0027 0.0413 0.0149 0.0090 0.0460 0.0487 0.0013 0.0436 0.0624 0.0134 0.0120 0.0021 0.0149 0.0086 0.0224 0.0034 0.0468 0.0505 0.0079 0.1280 0.1504 0.0077 0.0121 0.0256 0.0159 0.1018 0.0958  69  Figure 5.5 Osmotic coefficients of mixed Na2Si03-NaOH and K C I aqueous solutions at 298.15 K.  /  Na Si0 -NaOH 2  3  measured calculated by Pitzer's model with mixing parameters calculated by Pitzer's model (mixing parameters = 0)  • o  —|—i—i  0.0  i  i—|—i—i  0.5  i  i  |  i  1.0  i  i  I  |  I  1.5  I  I  I  |  I  2.0  I  I—I—|  i  i  i  2.5  i  |  i—i—i  3.0  Molality (mol/kg H 0) 2  i—|—i  3.5  i—i—r-p  4.0  70  5.5.  O s m o t i c Coefficient D a t a for N a O H - N a C l - N a A I ( O H )  4  Aqueous System  N i n e t e e n e x p e r i m e n t s w e r e performed. T h e o s m o t i c coefficient data f o r the K C I standard  s o l u t i o n and  experiments.  the  two  sample  solutions  were  obtained  from  each  set  T a b l e 5.3 s h o w s the o s m o t i c coefficients for the reference ( N a C l )  of and  standard ( K C I ) solutions. T a b l e 5.4 s h o w s the results for t w o sample solutions o f interest. T h e uncertainty (standard d e v i a t i o n ,  o f the measured o s m o t i c coefficient i n T a b l e s 5.3 and 5.4 w a s  c a l c u l a t e d f r o m the uncertainty o f the w e i g h t measurement, ± 0 . 0 0 0 0 5 g, and uncertainty i n o s m o t i c coefficient o f the reference N a C l s o l u t i o n , 0.01 (Pitzer, 1991), b y a m e t h o d a v a i l a b l e i n the literature ( B a i r d , 1995). I n b o t h tables, the c a l c u l a t e d o s m o t i c coefficients are also s h o w n . I n T a b l e 5.3, c o m p a r i s o n o f the o s m o t i c coefficient data o f K C I standard s o l u t i o n s w i t h c a l c u l a t e d v a l u e s obtained b y P i t z e r ' s m o d e l s h o w s the a c c u r a c y o f the i s o p i e s t i c m e t h o d o f this study. F o r the entire set o f experiments,  the o v e r a l l average relative  percent error i n the o s m o t i c coefficients o f K C I w a s about 0.20 % . T h e f o l l o w i n g v a l u e s o f p u b l i s h e d P i t z e r ' s parameters, P KCI = 0 . 0 4 8 3 5 , p (0)  ( 1 ) K  c i = 0 . 2 1 2 2 , and C * c i = - 0 . 0 0 0 8 4 K  at 2 9 8 . 1 5 K w e r e u s e d (Pitzer, 1991) to calculate the o s m o t i c coefficient for the K C I solution.  T a b l e 5.3. O s m o t i c coefficients o f N a C l and K C I as reference and standard solutions at 298.15 K .  Exp. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  Salt NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI NaCl KCI  Molality 0.9909 1.0288 1.0014 1.0417 0.9766 1.0151 1.9501 2.0850 1.9344 2.0789 1.9341 2.0722 11.9259 2.0627 1.9235 2.0654 2.9268 3.2185 2.8991 3.1965 2.8846 3.1622 2.8915 3.1796 2.8605 3.1472 3.9089 4.4280 3.9353 4.4575 3.8825 4.3859 3.8681 4.3722  NaCl KCI NaCl KCI  3.7891 4.2877 3.8034 4.2962  °*  ^calc  *Rel Err, %  0.8985  0.0064  0.8986  0.0064  0.8984  0.0064  0.9149  0.0062  0.9148  0.0062  0.9147  0.0062  0.9145  0.0062  0.9145  0.0062  0.9430  0.0061  0.9424  0.0060  0.9415  0.0061  0.9420  0.0061  0.9411  0.0061  0.9779  0.0059  0.9788  0.0059  0.9766  0.0059  0.9762  0.0059  0.9355 0.9010 0.9359 0.8997 0.9350 0.8995 0.9815 0.9180 0.9806 0.9125 0.9806 0.9153 0.9802 0.9152 0.9800 0.9127 1.0409 0.9465 1.0391 0.9424 1.0381 0.9470 1.0386 0.9445 1.0365 0.9421 1.1089 0.9789 1.1108 0.9807 1.1070 0.9799 1.1059 0.9784  0.9737  0.0059  1.1002 0.9723  0.1438  0.0059  1.1013 0.9749  0.0924  0.9740  * Relative Percent Error (Rel Err, %) = I f " " - f H x 100 / tf*  0.2782 0.1224 0.1224 0.3388 0.2514 0.0656 0.0765 0.1968 0.3712 0.0000 0.5842 0.2654 0.1063 0.1023 0.1941 0.3379 0.2254  72  T a b l e 5.4. O s m o t i c coefficients o f N a O H - N a C l - N a A l ( O H ) 4 aqueous solutions at 298.15 K .  Exp. No. **input ratio  Molality NaAl(OH) NaOH NaCl 0.0504 0.8080 0.1513 1 0.05 1 0.1508 0.0503 0.05 1 0.8051 0.6204 0.3110 0.1037 0.10 1 2 0.6171 0.3093 0.1031 0.10 1 0.4571 0.1524 0.4041 3 0.15 1 0.4042 0.4572 0.1524 0.15 1 0.2997 0.0999 0.10 2 1.5964 4 1.5943 0.2993 0.0998 0.10 2 0.4518 0.1506 0.15 2 1.3996 5 0.4509 0.1503 0.15 2 1.3970 1.2019 0.6019 0.2006 6 0.20 2 1.2030 0.6024 0.2008 0.20 2 1.0081 0.7556 0.2519 7 0.25 2 0.7553 0.2518 0.25 2 1.0076 0.8014 0.9056 0.3019 8 0.30 2 0.3027 0.8036 0.9080 0.30 2 2.5581 0.2948 0.0983 9 0.10 3 0.2947 2.5569 0.0982 0.10 3 2.3657 0.4435 0.1478 10 0.15 3 2.3678 0.4439 0.1480 0.15 3 2.1751 0.5940 0.1980 11 0.20 3 0.5932 0.1977 0.20 3 2.1722 0.7529 0.2510 0.25 3 1.9960 12 0.2504 1.9918 0.7513 0.25 3 1.7811 0.8985 0.2995 13 0.30 3 0.8980 0.2993 0.30 3 1.7802 0.2901 0.0967 14 0.10 4 3.4814 0.2901 0.0967 0.10 4 3.4813 0.4446 0.1482 15 0.15 4 3.3572 3.3585 0.4448 0.1483 0.15 4 0.5927 0.1976 16 0.20 4 3.1613 0.5927 0.1976 0.20 4 3.1609 2.9570 0.7420 0.2473 17 0.25 4 2.9560 0.7418 0.2473 0.25 4 0.8778 0.30 4 2.7236 0.2926 18 0.2926 0.30 4 2.7237 0.8779 0.35 4 2.5645 1.0397 0.3466 19 2.5636 1.0393 0.3464 0.35 4 * Relative Percent Error (Rel Err, % ) = | f " - f H x 100 / f " ** Input ratio : Input molality ratio of A1C1 -6H 0 to NaOH  *Rel Err, %  4  3  2  0.9180 0.9213 0.9054 0.9013 0.9008 0.9006 0.9590 0.9602 0.9476 0.9494 0.9462 0.9454 0.9366 0.9370 0.9384 0.9359 1.0323 1.0327 1.0187 1.0178 1.0092 1.0106 1.0011 1.0032 0.9953 0.9958 1.1205 1.1206 1.1067 1.1062 1.0876 1.0878 1.0840 1.0844 1.0706 1.0705 1.0602 1.0606  0.0098 0.0098 0.0097 0.0097 0.0096 0.0096 0.0098 0.0098 0.0097 0.0097 0.0096 0.0096 0.0096 0.0096 0.0096 0.0095 0.0099 0.0099 0.0098 0.0098 0.0097 0.0097 0.0096 0.0097 0.0096 0.0096 0.0101 0.0101 0.0100 0.0100 0.0098 0.0098 0.0098 0.0098 0.0097 0.0097 0.0096 0.0096  0.9223 0.9222 0.9060 0.9059 0.8977 0.8977 0.9635 0.9633 0.9480 0.9478 0.9391 0.9392 0.9373 0.9373 0.9414 0.9417 1.0398 1.0397 1.0199 1.0200 1.0060 1.0058 0.9994 0.9990 0.9955 0.9954 1.1264 1.1264 1.1091 1.1092 1.0904 1.0904 1.0766 1.0765 1.0649 1.0650 1.0671 1.0670  0.4684 0.0977 0.0663 0.5104 0.3441 0.3220 0.4692 0.3228 0.0422 0.1685 0.7504 0.6558 0.0747 0.0320 0.3197 0.6197 0.7265 0.6778 0.1178 0.2162 0.3171 0.4750 0.1698 0.4187 0.0201 0.0402 0.5266 0.5176 0.2169 0.2712 0.2574 0.2390 0.6827 0.7285 0.5324 0.5138 0.6508 0.6034  73  CHAPTER 6. DETERMINATION OF PITZER'S PARAMETERS FOR Na Si0 , Na Si0 -NaOH, AND NaOH-NaCl-NaAl(OH) 2  3  2  3  4  AQUEOUS SYSTEMS  Since the sodium aluminosilicate formation system contains the Si03 " and 2  Al(OH)4* ions, knowledge of the relevant Pitzer's model parameters is required for the thermodynamic modeling. Unknown binary and mixing parameters of Pitzer's model were obtained using the osmotic coefficient data described in the previous chapter 5. Pitzer derived the semi-empirical equations of the osmotic coefficients and activity coefficients for the single and multi-component electrolyte systems (Pitzer, 1991). Pitzer's method is one of the most popular ones that can be used to calculate electrolyte thermodynamic properties for single and multi-component systems. This method works well even at high molalities (Pitzer, 1991; Zemaitis et al., 1986). For this reason, the Pitzer's method was adopted for the modeling.  6.1. Pitzer's Parameters for Na2SiOs and N a i S i O s - N a O H Aqueous Systems  In Pitzer's model, there are four binary parameters,  P ,P , P (0) ca  (1)  ca  (2) ca  , and C*  c a  and eight mixing parameters, ( W , B^-, 6cc'(I), 9aa'(I), 6'cc'(I), ^'^'(I), ^cc* , and ^caa-. E  E  E  a  The parameter, P  (2)  is important only for 2-2 or higher valence electrolyte (Pitzer,  1991). The effects of the parameters, 9 <I), ^-(I), 9'cc<I), and ^ - ( l ) , are significant E  E  CC  only for 3-1 or more unsymmetrical types of mixing (Pitzer, 1975). These five  74  parameters, B ^ , 0 <I), Q^(l), 9'cc(I), and 0'aa-(I), were ignored for the modeling of E  E  E  E  CC  the systems N a S i 0 and Na Si0 -NaOH. 2  3  2  3  The three Pitzer's parameters, p , P , and C*, were determined by least squares (0)  (I)  optimization using the experimental osmotic coefficient data of Table 5.1 for the N a S i 0 2  3  system. The Gauss-Newton method (Bard, 1974; Englezos, 1996) was used to minimize the following least squares objective function  S(P ,p ,C+) = £ (0)  (1)  ( ( | ) d  2  (  6 1  >  d=l  where <|) is the measured and <J> is the calculated osmotic coefficient using equation exp  (2.46).  cac l  is the uncertainty. Sensitivity of Pitzer's parameters for N a S i 0 2  aqueous  3  system is described in APPENDIX VIII. The computational code (siwpam.for) for the optimization is given in APPENDIX IV together with input and output files. Two sets of the binary parameters of NaOH and N a S i 0 systems and two mixing 2  parameters,  and *F -„. ..j. are required for the modeling of Na Si0 -NaOH  6„„- ,i-  T+  ov  OH  3  2  c  Na OH  S1O3  3  S1O3  system. The binary parameters of Na2Si0 were already obtained as explained above and 3  p  l  those of NaOH,  NaOH  =  0.0864,  P NaOH (1)  0.253, and C* ,OH = 0.0044 at 298.15 K are N  available in the literature (Pitzer, 1991). The remaining two Pitzer's mixing parameters, 0 _ O H  s j o  i_  and  the osmotic  ^  N  l  l  +  O  H  -  s  i  o  i -  coefficient  were determined by the least squares optimization method using data of Table 5.2 for the Na2Si0 -NaOH system. The 3  computational code (nasiwpam.for) for the optimization is given in APPENDIX IX together with input and output files. The binary and mixing parameters that were obtained are given in Table 6.1 with their standard deviations. The standard deviations were calculated according to methods described in the literature (Box et al,  1978). The  75  calculated osmotic coefficients using Pitzer's parameters have an average relative percent error of 0.33 % for Na2SiC<3 and 1.74 % for the Na2Si03-NaOH system respectively. The computational source codes (siwcal.for and nasiwcal.for) used for the calculations are available in APPENDIX IX. In Figures 5.4 and 5.5 found in the previous chapter, the solid lines are the calculated osmotic coefficients using the Pitzer's parameters obtained in this work. Minor inflections on the curves of calculated osmotic coefficients  are observed at low  molalities, 0 to 0.1 mol/kg H2O in the figures. The osmotic coefficient curve of K_Pt(CN)4 by Pitzer's model also shows a similar inflection at low molalities (Pitzer, 1991). Furthermore, it is known that the isopiestic method does not give reliable results below a concentration of 0.1 mol/kg FfeO (Pitzer, 1991).  Table 6.1. The Pitzer's parameters of N a S i 0 and Na Si0 -NaOH systems at 298.15 K 2  3  2  3  Binary parameters for the Na^SiOs system Parameter  Standard Deviation  p  (0)  = 0.0577  0.0039  p  (1)  = 2.8965  0.0559 0.00176  C* = 0.00977 Mixing parameters for the Na2SiOs-NaOH system Parameter  t_i  n . - = -0.2703  Standard Deviation  0.0384  OH SiOJ  ¥  +  . = 0.0233  Na OH Siof  0.0095  76  Pitzer introduced the mixing parameters, 0 and *F to account for the differences of ion interactions between multi-component and single salt electrolyte solutions. Thus, the mixing parameters have smaller effects than the binary parameters, p , P , and C * have (0)  (1)  (Pitzer and Kim, 1974). The contribution of the mixing parameters, however, was not negligible for the NaOH-Na2Si03 system. The dashed line in Figure 5.5 represents the calculated osmotic coefficients when the values of the mixing parameters, 0__.-_.__- and  ^Na oH-siof+  a r e s e t e c  l  u a  l  t 0 z e r o  - As shown in this Figure, the mixing parameters should  be included for an improved calculation of the osmotic coefficient. Mean activity coefficients of Na2SiC»3 in water at 298.15 K were calculated and are shown in Figure 6.1. Mean activity coefficients of Na2SiC>3 and NaOH in the Na Si032  NaOH binary system were also calculated and are shown in Figure 6.2. Sensitivity of Pitzer's parameters for Na2Si03-Na0H aqueous system is described in Appendix VIII.  6.2. Pitzer's Parameters for NaOH-NaCI-NaAl(OH)4 Aqueous System Among the Pitzer's parameters, the parameter, P  (2) ca  , is important only for 2-2 or  higher valence electrolytes. The parameters, 0ee(I), 0aa*(I), 0'c (I), and 0'__'(I), are E  E  E  E  C  significant only for 3-1 or for cases with more unsymmetrical mixing (Pitzer, 1975). Thus, these five parameters, P c_, 0ec'(I), 0__'(I), 0'cc'(I), and 0'__'(I), were ignored for (2)  E  E  E  E  the modeling of the system N a O H - N a C l - N a A l ( O H ) 4 in water. The Gauss-Newton method was used to minimize the following least squares objective function N  / i exp  S(pW p(').C*) = _ r ^ >  d=i  d  icak\2  2  cr.  )  (6-1)  77  F i g u r e 6 . 1 . M e a n a c t i v i t y coefficients o f Na2SiC«3 i n Na2SiC«3 aqueous s o l u t i o n at 298.15 K .  1.2  _ C  10  Q) O §  0.8  O  O  0.6  c CU 5  0.4 H  Na Si0 2  0.2  "i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—|—i—i—i—i—|—i—i—f  0.0  0.5  1.0  1.5  2.0  Molality (mol/kg H 0) 2  2.5  3  -  3.0  Molality of Na Si0 -NaOH (mol/kg H 0) 2  3  2  79  w h e r e <J> is the measured and (j) ' is the c a l c u l a t e d o s m o t i c c o e f f i c i e n t u s i n g e q u a t i o n exp  03 0  (2.46). c$ is the uncertainty. T h r e e sets o f the b i n a r y parameters, NaAl(OH)4  ^oH-cr>  systems  and  VQH-AKOHK'  six  A N D  N a C l - N a A l ( O H ) 4 aqueous  mixing  B  ( 0 )  , p  ( 1 )  parameters,  "WAKOH);  , and C * o f N a O H , N a C l , and  Q  ,  0 OH"Al(OH); '  Q Cl-Al(OH)7 '  are required f o r the m o d e l i n g o f the N a O H -  system. T h e b i n a r y parameters  o f the N a O H  and  NaCl  systems and t w o m i x i n g parameters and are a v a i l a b l e i n the literature (Pitzer, 1991) as s h o w n i n T a b l e 6.2.  T a b l e 6.2. T h e P i t z e r ' s parameters at 298.15 K a v a i l a b l e i n the literature (Pitzer, 1991).  Binary parameters System  Parameter  NaOH  NaCl  3  (0)  = 0.0864  p  (1)  = 0.253  C*  = 0.0044  p  (0)  = 0.0765  p  (1)  = 0.2664  C*  -  0.00127  Mixing parameters 0 Y  oircr +  =  -0.05  =  -0.006  F i r s t , the three P i t z e r ' s parameters, P , (0)  p , (1)  and C * for the N a A l ( O H )  4  system  w e r e determined b y least squares o p t i m i z a t i o n u s i n g the e x p e r i m e n t a l data o f T a b l e 5.4  80  and taking into account the published Pitzer's parameters shown in Table 6.2. The estimated parameters are shown in Table 6.3 with their standard deviations. The mixing parameters, Q OH  -,  Q -  M(OH)  Ci  -,  M(0H)  ^  o  i  i  -  M  m  )  V  and  V  C R A 1 ( 0 H )  -  were set equal to  zero during this optimization.  Table 6.3. The Pitzer's parameters of NaOH-NaCl-NaAl(OH)4 aqueous system at 298.15 K obtained in this study. Binary parameters of NaAl(OH)4 Parameter  Standard deviation  P  (0)  = - 0.0083  0.0417  p  (1)  = 0.0710  0.3362 0.00977  C* = 0.00184 Mixing parameters Parameter 0  ¥  =-0.2255  0.0469  = - 0.2430  0.0816  OH-Al(OH);  0  Standard deviation  +  =-0.0388  0.0147  = 0.2377  0.0332  Na OH~AI(OH)i +  ¥  +  Na CPAl(OH)7 +  After the determination of the binary parameters, the four Pitzer's mixing parameters, Q 0H  -,  M(0H)  6  c r A 1 ( O H )  - , V^-^-,  and ^  N a + c r A 1 ( O H )  -  were determined by  81  least squares optimization method using the osmotic coefficient data of Table 5.4 for the aqueous NaOH-NaCl-NaAl(OH)4 system. It was necessary to follow this approach because the simultaneous minimization search for the binary and ternary parameters did not converge. The mixing parameters that were obtained are also given in Table 6.3 with their standard deviations. The standard deviations were calculated according to methods described in the literature (Box et al, 1978). The calculated osmotic coefficients using Pitzer's parameters have an average relative percent deviation of 0.37 % from the experimental values. Sensitivity of Pitzer's parameters for NaOH-NaCl-NaAl(OFf)4 aqueous system is described in APPENDIX VIII.  6 . 3 . Reliability of the Pitzer's Parameter Determination In order to check the reliability of the optimization procedure, Pitzer's parameters for the NaTcC«4, NaTcCVNaCl, and NaBr-NaC104 systems were obtained using the osmotic coefficient data from the literature (Hernandez-Luis, 1996; Konnecke, 1997). The parameters that we obtained were compared with the published ones. The published parameters for the systems are tabulated in Table 6.4 together with those obtained in this work. Except for the binary parameters for the NaTcC«4 system, all parameters obtained agree well with the published ones. Table 6.5 displays the published osmotic coefficient data and the calculated values for NaTcC>4 system. As seen from the table, the osmotic coefficients calculated by using the parameters obtained in this work match the experimental data slightly better than those obtained by using the published parameter values.  82  Table 6.4. The Pitzer's parameters of NaTcCu, NaTc0 -NaCl, and NaBr-NaClC>4 systems 4  at 298.15 K. Binary parameters for the NaTc04 system Parameter  Konnecke, 1997  T h i s work  (0)  0.01111  0.01510  3d)  0.1595  0.1145  c*  0.00236  0.00187  p  Mixing parameters for the NaTcO^NaCl system Parameter  Konnecke, 1997  T h i s work  0.067  0.067*  -0.0085  -0.0085*  6 TcO<Cl  »P Na TcOiCr +  Mixing parameters for the NaBr-NaCl04 Parameter  system  Hernandez-Luis, 1996  T h i s work  0.0350  0.0350  -0.0058  -0.0058  e Br'ClOi Na Br"C10; +  * The parameters were obtained using the binary parameters, P ' = 0.01 111, p = 0.1595, and C* = 0.00236 determined by Konnecke et a/.(1997). (  (1)  Table 6.5. Comparison of measured osmotic coefficients with calculated those for the N a T c 0 system at 298.15 K. 4  Konnecke, 1997  This work  ( P = 0.01111, P = 0.1595, C*=0.00236)  (P = 0.01510, P = 0.1145, C*= 0.00187) ^calc Rel Err, %  (0)  (0)  (0)  (0)  Molality  tf*f  7.3278  0.9598  0.9639  0.4272  0.9653  0.5730  6.5487  0.9395  0.9341  0.5748  0.9375  0.2129  6.4555  0.9376  0.9308  0.7253  0.9343  0.3520  5.2349  0.9021 0.8680  0.8923 0.8629  1.0864 0.5876  0.8973  0.5321  0.8677  0.0346  0.8463 0.8545  0.6661  0.8487  0.9516  1.1159  0.8407 0.8519  0.3052  0.8523  0.0470  0.5353  0.8749  0.8739  0.1143  0.8703  0.5258  Ave Rel Err,%  0.4036  3.9632 2.6048  Rel Err, %  0.5608 Ave Rel Err,% Relative Percent Error (Rel Err, %) = | f * - f H x 100 /  83  C a l c u l a t i o n s w e r e also p e r f o r m e d for the N a C l , Na2SC>4, Na2S2C>3 and N a C l N a S C » 4 (see A P P E N D I X V I I ) . T h e c a l c u l a t e d parameters w e r e f o u n d to g i v e e x a c t l y the 2  same v a l u e s f o r the o s m o t i c coefficient o f N a C l and s l i g h t l y better v a l u e s f o r the other systems.  84  CHAPTER 7. A PRIORI DETERMINATION OF MODEL PARAMETERS  M o d e l parameters such as P i t z e r ' s parameters and e q u i l i b r i u m constants o f sodalite d i h y d r a t e and h y d r o x y s o d a l i t e dihydrate f o r m a t i o n reactions are r e q u i r e d for the t h e r m o d y n a m i c m o d e l i n g o f the s o d i u m a l u m i n o s i l i c a t e f o r m a t i o n i n a l k a l i n e solutions.  7.1. Pitzer's parameters Pitzer's b i n a r y and m i x i n g relevant parameters for our system are s h o w n i n the T a b l e s 7.1 and 7.2. A v a l u e o f 0.455 at 368.15 K w a s used for the D e b y e - H u c k e l parameter (Pitzer, 1991). P i t z e r i n t r o d u c e d the m i x i n g parameters, 9 and *F to account for the differences o f i o n interactions between i n m u l t i - c o m p o n e n t and s i n g l e salt electrolyte solutions. T h u s , the m i x i n g parameters have s m a l l e r effects than the b i n a r y parameters, p  ( 0 )  , p  ( 1 )  , and C * have ( P i t z e r and K i m , 1974). T h e b i n a r y parameters for N a O H ,  NaCl,  and N a 2 C 0 3 for 3 6 8 . 1 5  K  were  determined u s i n g the n u m e r i c a l expressions a v a i l a b l e i n the literature (Pitzer,  1991;  S i l v e s t e r and P i t z e r , 1977; P e i p e r and P i t z e r , 1982). A l t h o u g h n u m e r i c a l expressions  for the b i n a r y parameters for  Na S04 2  were  a v a i l a b l e i n the literature, they w e r e not used because they w e r e based o n the v a l u e o f 1.4 for the " a . parameter" instead o f the usual v a l u e o f 2.0 for a 1-2 electrolyte ( P i t z e r , 1 9 9 1 ; P a b a l a n and P i t z e r , 1988). O s m o t i c coefficient data for  Na S04 2  3 2 3 . 1 5 , 3 4 8 . 1 5 , 3 7 3 . 1 5 , and 398.15 K ( P a b a l a n and P i t z e r , 1988).  are a v a i l a b l e at 2 9 8 . 1 5 ,  85  Table 7.1. Pitzer's binary parameters for the modeling of sodium aluminosilicate formation.  ion pair  3(0)  N a OH"  0.0847  N a Cl"  0.1008  +  +  Na  +  Na  +  C0  3  S0  4  Na  +  P  1  0.3882  m  0.00021  0.3207  [ 2 ]  -0.00337  1.2419  [ 3 ]  0.0052  1.4325  1 4 1  - 0.01462  1 1 1  1 2 1  '  0.05811  2  '  0.0988  [ 4 ]  0.1396  [ 1 ]  0.0 w  0.0577  [ 4 ]  2.8965  [ 4 ]  0.00977  [ 4 ]  0.0710  [ 4 ]  0.00184  [ 4 ]  +  +  1 1 1  2  N a HS" Na  c*  3d)  Si0 " 2  3  - 0.0083  A1(0H) " 4  [ 3 ]  1 4 1  -0.0127  1 3 1  [ 4 1  1 1 1  [1] Pitzer (1991), [2] Silvester and Pitzer (1977),  [3] Peiper and Pitzer (1982), [4] this study  Table 7.2. Pitzer's mixing parameters for the modeling of sodium aluminosilicate formation.  ion pair  aa'Na*  OH"Cl" OH" C 0  -0.05 PI  2 3  "  0.1  m  -0.006  [ 1 ]  -0.017  1 1 1  -0.009  1 1 1  [ 2 ]  OH" S 0 "  -0.013  OH" S i 0 "  -0.2703  1 2 1  0.0233  OH"Al(OH) "  -0.2255  [ 2 ]  -0.0388  1 2 1  0.0085  m  2  4  2  3  4  cr co" Cl" S 0  2  4  2 3 "  C1" Al(OH) " 4  C0  2 3  " S0  2 4  '  -0.02 0.03  [ 1 ]  [ 1 ]  [ 1 ]  -0.2430 0.02  [ 2 ]  m  0.000  1 1 1  0.2377  [ 2 ]  -0.005  [ 1 ]  [1] Pitzer (1991), [2] this study  These data were interpolated at 368.15 K and gave a set of values. The binary parameters of N a 2 S 0  4  at 368.15 K were then determined by using these interpolated osmotic  coefficient data and minimizing the following least squares objective function  86  s(p ,p ,c*)=|;(c -(|)r ) (o)  (i)  t  1  (7.i)  2  d=l  where the (J)"* is the interpolated and the (J)* is the calculated osmotic coefficients using 0 1  equation (2.46). Based on a study with NaCl, Pitzer noted that change in the parameter values from 298.15 to 573.15 K was very small. This justified the use of the values at 298.15 K whenever values at 368.15 K were not available. However, the Debye-Huckel parameter, A$, changes significantly and the value at 368.15 K was used (Zemaitis et al, 1986). In the case that no Pitzer's parameters at 368.15 K were available, those at 298.15 K were used. Binary parameters for NaHS and mixing parameters for OH"-Cl', O H - C O 3 ' , OFT2  S0 ', C1'-C0 ", C1'-S0 ", and C0 "-S0 " are available at 298.15 K in the reference of 2  4  2  2  3  2  4  2  3  4  Pitzer 1991. Finally, it is noted that binary parameters of Na SiC>3 and NaAl(OH) and 2  4  mixing parameters of Na Si0 -NaOH and NaAl(OH) -NaOH-NaCl systems at 298.15 K 2  3  4  were determined from the osmotic coefficient measurements using isopiestic method as explained in chapters 5 and 6.  7.2. E q u i l i b r i u m C o n s t a n t s  Values of the equilibrium constants for sodalite dihydrate and hydroxysodalite dihydrate formation at 368.15 K were not available in the literature. Assuming that heat capacity change of reaction, AC °, is not a function of temperature, the equilibrium P  constants at specific temperature can be calculated using by equation (2.18) (Anderson and Crerar, 1993)  lnK =  AG°  AH"  RT,  R  0j  1  1  AC"  T  T,  R  T  T  In ___ + _____! V T T 0  (2.18)  87  w h e r e K is e q u i l i b r i u m constant at temperature T , AGJJ is the G i b b s free energy change  o f r e a c t i o n at reference state, A H ° is the enthalpy change o f r e a c t i o n at reference state,  AC°  is the heat c a p a c i t y change o f r e a c t i o n at reference state, R is the gas constant, and  To is the reference temperature. V a l u e s for A G £ , A H ^ , and A C " c a n be obtained b y the f o l l o w i n g equations A G ° = E v A G f products " E v A G f reactants  (7.2)  AH° = EvAHf°products - EvAHfVeactants  (7.3)  A C " = I V C P products I v C c  -  c P  reactants  (7.4)  w h e r e the v is the n u m b e r o f m o l e s o f reactants o r products. T a b l e 7.3 s h o w s property v a l u e s f o r the species required to calculate the above e q u i l i b r i u m constants.  Property  v a l u e s that w e r e not a v a i l a b l e w e r e estimated i n this w o r k as f o l l o w s .  T a b l e 7.3. T h e r m o d y n a m i c data at 298.15 K and 1 bar p u b l i s h e d i n the literature. AH ° ( k J / m o l )  AG ° ( k J / m o l ) Na aq) (  -262.0 ± 0 . 1  Cl'(aq)  -131.2 ± 0 . 1  O H (aq)  -157.2 ± 0 . 1  H2O (1)  -237.14 ± 0 . 0 4  +  Al(OH) "  ( a q )  -939.73  S i 0 3 ( q) 2  8  Na (AlSi0 )6Cl -2H 0 8  4  2  2  w  NagtMSiOACOrD^rtO , fl  N/A  [ 5 ]  N/A  [ 5 ]  [ 2 ]  -240.34 ± 0 . 0 6  [ 1 ]  -167.1 ± 0 . 1  [ 1 ]  [1]  -285.83 ± 0 . 0 4  [ 1 ]  [ 3 ]  -1488.92 N/A  [ 4 ]  +46.43  121  m  -148.5  111  m  +75.351 ± 0 . 0 8 +241.44 N/A  N/A  1 5 1  N/A  [ 5 )  N/A  t 5 ]  N/A  151  N / A : not available i n the literature [1] Nordstrom and M u n o z (1994), [2] Babushkin et al. (1985), [3] M a y et al. (1979), [4] Raizman (1985), [5] Hemingway (1997).  [ 2 ]  -136.4  t l ]  -230.01 ± 0 . 0 4  ( 1 ]  -1311.684 ± 1.255  4  CP° ( J / m o l - K )  f  f  [ 4 ]  m  88 7.3. Estimation of Thermodynamic Properties  7.3.1.  AHf°  and  AGr°  of sodalite dihydrate and hydroxysodalite dihydrate  The AHf° and AGf° o f sodalite d i h y d r a t e and h y d r o x y s o d a l i t e d i h y d r a t e w e r e estimated by the m e t h o d o f M o s t a f a et al. (1995). A m e a n error o f their m e t h o d w a s reported as 2 . 5 7 % for the e s t i m a t i o n o f standard enthalpy o f f o r m a t i o n and 2 . 6 0 % f o r that o f standard G i b b s free energy o f f o r m a t i o n . T h e y u s e d the f o l l o w i n g f u n c t i o n a l f o r m s f o r the standard enthalpy o f f o r m a t i o n and standard G i b b s free energy o f f o r m a t i o n o f i n o r g a n i c salts: A H ° = £  n  j  A  H  (7.5)  j  j  AG^JXAo.  (7.6)  j  where, nj is the n u m b e r o f g r o u p s o f the j t h type and AHJ and AQJ are c o n t r i b u t i o n s for the jth  a t o m i c o r m o l e c u l a r g r o u p i n the enthalpy and G i b b s free energy o f f o r m a t i o n  respectively. The  e s t i m a t i o n procedure is quite s i m p l e . T h e m o l e c u l a r structural f o r m u l a is  b r o k e n into appropriate c a t i o n i c , a n i o n i c , o r l i g a n d m o l e c u l a r structural g r o u p s . T h e n the n u m e r i c a l c o n t r i b u t i o n o f each g r o u p is obtained and m u l t i p l i e d b y the n u m b e r o f occurences o f the same g r o u p i n the m o l e c u l a r structural f o r m u l a . S u m o f the n u m e r i c a l v a l u e s o f the v a r i o u s g r o u p s y i e l d s estimation for AHf° and AGf°. T a b l e 7.4 s h o w s the sequence o f c a l c u l a t i o n s for anhydrous sodalite. T h e p u b l i s h e d AHf° o f sodalite ( N a g l ^ A l S i O ^ C b ) is - 1 3 4 5 7 . 0 4 k J / m o l ( K o m a d a et al,  anhydrous  1995) and predicted one  is - 1 3 1 1 0 . 7 2 k J / m o l . T h u s , an error o f the e s t i m a t i o n is 2.57 % . T h e p u b l i s h e d AGf° o f  89 anhydrous sodalite (Na (AlSi0 ) Cl ) is -12702.96 kJ/mol (Komada et al, 1995) and 8  4  6  2  predicted one is -12369.05 kJ/mol. An error of the estimation of the Gibbs free energy is 2.63%. Table 7.4. Estimations of AHf° and AGf° of anhydrous sodalite (Na (AlSi0 )6Cl ). 8  Na (AlSi0 ) Cl 8  Na Al o  6 6 24 2  + 3  su  n 8  +  2  cr  X  -553.115 -575.556 -173.650 -118.794  6 6 24 2  X X X  = -13110.72 kJ/mol  AHf°  Aci  s  H  X  2  2  A j  8  +  6  -241.688  ni  group  4  4  -199.801  X  -420.023 -411.036 -229.836 -134.110  X X X X  = -12369.05 kJ/mol  AG ° f  Since the AHf° of anhydrous sodalite (Na (AlSi0 )6Cl ) is available and the only 8  4  2  difference in the chemical formula of anhydrous sodalite (Na (AlSi0 )6Cl ) and that of 8  sodalite dihydrate (Na (AlSi0 )6Cl -2H 0) 8  4  2  2  4  2  is two water molecules, the AHf° of  Na (AlSi0 )6Cl - 2 H 0 can be calculated by adding the contribution term of 2 H 0 to the 8  4  2  2  2  published AH ° of Na (AlSi0 ) Cl . The contribution by 2 H 0 is equal to 2 x -298.933 = f  8  4  6  2  2  -597.866 kJ/mol. The AH ° of Na (AlSi0 ) Cl - 2 H 0 is equal to AH ° (Na (AlSi0 ) Cl ) f  8  4  6  2  2  f  8  4  6  2  + Contribution by 2 H 0 = -13457.04 + (-597.866) = -14054.91 kJ/mol. The AG ° of 2  f  Na (AlSi0 ) Cl -2H 0 can be calculated by the same logic. The contribution by 2 H 0 for 8  4  6  2  2  2  the AG ° is equal to 2 x -244.317 = -488.634 kJ/mol. The AG ° of Na (AJSi0 ) Cl -2H 0 f  f  8  4  6  2  2  is equal to AG ° (Na (AlSi0 ) Cl ) + Contribution by 2 H 0 = -12702.96 + (-488.634) = f  8  4  6  2  2  13191.59 kJ/mol. The uncertainties of the AH ° and AG ° of the Na (AJSi0 ) Cl -2H 0 f  f  8  4  6  2  2  were calculated from the uncertainties of the AHf° and AGf° of the Na (AlSi0 )6Cl , ± 8  4  2  15.80 kJ/mol and + 16.63 kJ/mol (Komada et al, 1995) and the uncertainties of the  90  contributions by 2 H 0 by a method available in the literature (Baird, 1995; Holman, 2  1994). The uncertainties are shown in Table 7.5 together with the estimated values of the thermodynamic properties. Detailed calculations of the uncertainties  are given in  APPENDIX VI.  Table 7.5. Estimated thermodynamic data at 298.15 K and 1 bar. AGf° ( kJ/mol)  AHf° ( kJ/mol)  C ° (J/molK )  -1075.38 ± 1 . 1 4  -326.27 ± 8 2 . 7 1  -13191.59 ± 2 0 . 9 2  -14054.91 ± 2 2 . 0 4  886.28±4.69  -13384.23 ± 2 5 . 1 0  -14283.02 ± 25.82  895.01 ± 5 . 3 7  Si03 "( ) 2  aq  Na (AlSi0 ) Cl -2H 0 8  4  6  2  2  ( s )  Na (AlSi04) (OH) -2H 0 . 8  6  2  2  (  )  P  The AHf° and AG ° of hydrated hydroxysodalite dihydrate (Na (AlSi0 )6(OH) f  2H 0) 2  were  8  calculated  by  the  same  method.  The  4  AHf°  and  2  AGf°  of  Na (AlSi0 )6(OH) -2H 0 can be calculated by subtracting the contribution term of C l 8  4  2  2  and adding the contribution term of (OH)  2  and 2 H 0 to the published AHf° and AGf° of  2  2  Na (AlSi0 ) Cl . The contribution of C l for the AH ° is equal to 2 x -118.794 = -237.588 8  4  6  2  2  kJ/mol and that of (OH)  f  is equal to 2 x -232.849 = -465.698 kJ/mol. Thus, the A H / of  2  Na (AlSi0 )6(OH) -2H 0 is equal to AH ° (Na (AlSi0 ) Cl ) - Contribution by C l + 8  4  2  2  f  8  4  6  2  2  Contribution by (OH) + Contribution by 2 H 0 = -13457.04 - (-237.588) + (-465.698) + 2  2  (-597.866) = -14283.02 kJ/mol. The contribution of C l for the AG ° is equal to 2 x 2  f  134.110 = -268.220 kJ/mol and that by (OH) is equal to 2 x -230.428 = -460.856 kJ/mol. 2  Thus, the AG ° of Na (AlSi0 ) (OH) -2H 0 is equal to AG ° (Na (AlSi0 ) Cl ) f  8  4  6  2  2  f  8  4  6  2  Contribution by C l + Contribution by (OH) + Contribution by 2 H 0 = -12702.96 - (2  2  2  268.220) + (-460.856) + (-488.634) = -13384.23 kJ/mol. The uncertainties of the AH ° f  91  and AGf° of the Na8(AlSi04) (OH)2-2H 0 were also calculated and are shown in Table 6  2  7.5 from the uncertainties of the AHf° and AGf° of the NagfAlSiO^eCb and the uncertainties of the contributions by 2H2O, CI2, and (OFfy groups.  7.3.2. C ° of sodalite dihydrate and hydroxysodalite dihydrate p  Another group contribution technique was proposed by Mostafa et al. (1996) to predict the C for solid inorganic salts. A mean error of their method was reported as 3.18 p  % when predicted values were compared with literature values for heat capacity at 298.15 K. They used the following functional form for the heat capacities of solids:  C  =2>Ai  P  r  \  lZ i  +  n  A  xi ' 0  b  J  3  f  \  M2>A* ° V J xl  6  IT^ I V"1 J + S  JADJ X L  °  6  T  (7.7)  J  where j is atomic or molecular group, nj is the number of groups of the jth type, A is the contributions for the a, b, c, or d coefficient and T is in kelvin. A stepwise procedure for the estimation of C is similar that of AGf° and AHf° p  estimations. The molecular structural formula for the solid inorganic salt is broken into appropriate cationic, anionic, or ligand molecular structural groups. Then the numerical contributions of each group are calculated and multiplied by the number of occurrences of the same group in the molecular structural formula. The sum of the numerical values of the various groups yields estimation for EpjAaj, SjnjAbj, EjnjAcj, and SjnjAdj. The C can p  then be calculated by the equation (7.7) at the temperature of interest. Table 7.6 shows the  sequence  of  calculations  for  the  C ° estimation p  of  anhydrous  sodalite  (Na (AlSi0 )6Cl ). The published C ° of anhydrous sodalite is 812.28 J/mol K at 298.15 8  4  2  p  92 K (Komada et al, 1995) and predicted one is 808.39 J/mol K. Thus, the estimation error is 0.48 %.  Table 7.6. Estimation of C ° of anhydrous sodalite (Na (AJSi0 )6Ci2). p  step 1 step 2  group Na  8 x 14.186 6 x 10.306 6 x -2.308 24x28.152 2 x 26.609  +  Al  Si O  3 +  4+  2  Cl  ZjnjAij  step 3 step 4  C  0  8  A*  Acj  8 x 9.665 6 x 4.518 6 x 4.382 24 x 12.043 2 x 10.376  8 x 0.529 6 x -0.623 6 x -0.041 24 x -0.747 2 x-0.251  the  =  3  chemical  Na8(AlSi04)6Cl2-2H_0  Adj 8 x 4.851 6 x -3.701 6 x -3.301 24 x -4.023 2 x 0.657  890.342 440.504 -18.182 -98.442 890.342 + 440.504xl0- x298.15 + (-18.182)xl0 7298.15 + (-98.442)xl0' x298.15 = 808.39 J/mol K <  6  Since  4  by  formula two  of  2  2  Na (AlSi04)6C-2  differs  8  water  molecules,  the  heat  from  that  capacity  of of  Nag(AlSi04)6Cl2-2H20 can be calculated by adding the contribution term of 2H 0 to the 2  published heat capacity value of Na8(AlSi04)6C.2. The contribution by 2H2O is equal to 73.996 as shown in Table 7.7. The C ° of Na (AlSi0 )6Cl is 812.28 J/mol K. Thus, the p  8  4  2  C ° of Na (AlSi04)6Cl2-2H 0 is equal to C ° (Na (AlSi0 )6Cl ) + Contribution by 2 H 0 p  8  2  p  8  4  2  2  = 886.28 J/mol K.  Table 7.7. Contribution by 2 H 0 for C ° estimation 2  Group  Aaj  p  Abj  A_j  Acj  H 0 2 x 15.458 2 x66.593 2 x0.47 2 x-40.518 ZjnjAij 30.916 133.186 0.94 -81.036 Contribution of 2 H 0 = 30.916 + 133.186xl0 x298.15 + 0.94xl0 /298.15 +(-81.036)xl0^x298.15 = 73.996 J/mol K 2  3  6  2  2  2  93  Similarly, the heat capacity of Na (AlSi04)6(OH) -2H 0 can be calculated by 8  2  2  subtracting the contribution term of C l and adding the contribution term of (OH) and 2  2  2 H 0 to the published heat capacity of Na (AlSi04)6Cl . The contributions by C l and 2  8  2  2  (OH) are described in Table 7.8. The C ° of Na (AlSi0 )6(OH) -2H 0 is equal to C ° 2  p  8  4  2  2  p  (Na (AlSi0 )6Cl ) - Contribution by C l + Contribution by (OH) + Contribution by 8  4  2  2  2  2 H 0 = 812.28 - 53.875 + 62.608 + 73.996 = 895.01 J/mol K. The estimated C ° values 2  p  of Na (AlSi0 )6Cl -2H 0 and Na (AlSi0 )6(OH) -2H 0 are shown in Table 7.5 together 8  4  2  2  8  4  2  2  with their uncertainties. The uncertainties were calculated from the uncertainty of C ° ( ± p  4.06 J/mol K) for Na (AlSi04)eCl and the uncertainty of the contributions by the 2 H 0 , 8  2  2  C l , and (OH) groups following the method used before (Baird, 1995; Holman, 1994). 2  2  Table 7.8. Contributions by C l and (OH) for C ° estimation. 2  2  p  group  Ajj  Ay  Acj  Cl  2 x 26.609  2 x 10.376  2 x-0.251  53.218  20.752  -0.502  2  EjnjAij  Adj 2 x 0.657 1.314  Contribution of Cl = 53.218 + 20.752xl0 x298.15 + (-0.502)xl0 /298.15 3  6  2  2  + 1.314xl0^x298.15 = 53.875 J/mol K 2  (OH)  2  ZjnjAij  2 x28.917  2 x30.73  57.834  61.46  2 x-0.628  2 x 3.257  -1.256  6.514  Contribution of (OH) = 57.834 + 61.46xl0" x298.15 + (-1.256)xl0 /298.15 3  6  2  2  +6.514xlQ- x298.15 = 62.608 J/mol K 6  2  7.3.3. S° o f S i Q 3 % * ) Prior to determining the A H / and Cp° of Si03 *, the S° of SiC>3" was estimated by 2  2  the method of Couture and Laidler (1957). They found that the entropy of oxy-anions (XO " ) in aqueous solution at standard state is given by the following empirical m  n  relationship  94 S° = 5.5z + 40.2 + - R l n M — ? 1 ^ L _ w  2  0.25n •  (7 ) 8  r  oxy  w h e r e , z is the charge o f i o n , R is the gas constant ( 1 . 9 8 7 c a l / m o l K ) , M weight o f ion,  noxy  w  is the m o l e c u l a r  is the n u m b e r o f o x y g e n and r is the radius o f a sphere that c o m p l e t e l y  c i r c u m s c r i b e s the a n i o n (r = rn + 1.40). T h e 1.40 A is the v a n der W a a l s radius o f o x y g e n . T h e rn is the distance between the center o f the central a t o m and the center o f the s u r r o u n d i n g o x y g e n atoms. T h e units o f the calculated entropy b y equation (7.8) are c a l / m o l K . T h e p r e d i c t e d entropies o f several aqueous i o n s are c o m p a r e d w i t h p u b l i s h e d data i n the literature i n T a b l e 7.9. T h e p u b l i s h e d entropy data o f aqueous i o n s w e r e obtained f r o m B a b u s h k i n et al. (1985). T h e average error o f the estimation w a s 1 8 . 4 1 % . T h e rn data except for that o f SiC«3 ' are a v a i l a b l e i n the literature ( C o u t u r e and L a i d l e r , 1957). T h e rn o f S i 0 3 ' is also 2  2  a v a i l a b l e i n the literature ( B a i l e r et al,  1973). T h e entropy o f the S i C b ' aqueous i o n w a s 2  c a l c u l a t e d as - 4 . 9 9 c a l / m o l K ( = -20.87 J / m o l K ) . T h e uncertainty o f the entropy o f the Si0  2 3  ' w a s assumed t o be, 1 8 . 4 1 % ( ± 3.84 J / m o l K ) , w h i c h is the average error o f this  estimation m e t h o d f r o m T a b l e 7.9.  T a b l e 7.9. P r e d i c t i o n o f the entropy o f aqueous ions at 2 9 8 . 1 5 K , c a l / m o l K .  Calculated rn  r  M  w  fro xy  z  s°  Published S°  error  CIO  1.70  3.10  51.452  1  -1  11.35  10  13.48%  N0  1.24  2.64  62.004  3  -1  33.26  35.1  5.23%  1.26  2.66  60.008  3  -2  -13.13  -13.6  3.44%  1.39  2.79  80.057  3  -2  -9.73  -7  39.04%  1.65  3.05  142.956  4  -2  8.32  12.9  35.51%  1.55  2.95  94.97  4  -3  -45.71  -53  13.75%  1.68  3.08  76.082  3  -2  -4.99  3  C0  2 3  so  2  3  Se0 P0  2 4 3  4  Si0  2 3  95  7.3.4.  A H f ° Of Si03 "(aq) 2  The enthalpy of formation of SiC>3 ' aqueous ion was calculated by considering 2  the following equation AH° = A G + TAS°  (7.9)  0  where, AG° is the standard Gibbs free energy change of reaction, A H is the standard 0  enthalpy change of formation, and A S is the change of standard entropy. 0  Let us consider the dissociation reaction of sodium metasilicate, Na2Si03(s) at 298.15 K (Babushkin etal, 1985). Na Si03 ) -> 2Na q) + Si0 '( +  2  (s  (7.10)  2  (a  3  aq)  Table 7.10 shows the thermodynamic data for Na2Si03( ), Na ( ), and Si03 "( ) needed in +  S  2  aq  aq  the calculation of the A G , AH°, and AS° of the reaction (7.10). Substituting the 0  calculated AH°, AG°, and AS° into equation (7.9) gives a value of -1075.38 kJ/mol for AHf° of S.O3  2  ".  The uncertainty in the calculation of AHf° for  Si(_>3 " 2  was found to be ±  1.14 kJ/mol following a method available in the literature (Baird, 1995; Holman, 1994).  Table 7.10. Thermodynamic data of Na Si03( ), 2  S  Na (aq), +  and Si03 "( ) for the calculation 2  aq  of the A G , AH°, and A S of reaction (7.10). 0  0  AG ° (kJ/mol) f  Na Si0 )  -1469.67  Na aq) (  -262.0±0.1  Si03 "(aq)  -939.73  2  3(s  +  2  f  -1556.7  m  [ 1 ]  AH ° (kJ/mol)  [2]  113.8  1 , 1  -240.34 ± 0 . 0 6  S° (J/molK)  121  111  58.45  [ 2 ]  -20.87  131  [1] Babushkin etal. (1985), [2] Nordstrom and Munoz (1994), [3] calculated in section 7.3.3.  96  7.3.5. C ° Of Si03 "(aq) 2  p  The  e s t i m a t i o n e q u a t i o n (7.11) for the heat capacities i n c a l / m o l K for i o n i c  solutes w a s suggested b y C r i s s and C o b b l e ( 1 9 6 4 ) C °  =  p  C °abs p  - 28.0z  = a + b ( S ° - 5.0z) - 2 8 . 0 z  (7.11)  w h e r e , a is equal t o -145 and b is equal t o 2.20 for o x y - a n i o n s ( X O " ) at 2 9 8 . 1 5 K , and z m  n  is the charge o f the i o n . T h e C r i s s and C o b b l e ' s heat capacity e s t i m a t i o n m e t h o d w a s tested for several o x y - a n i o n s . T h e c a l c u l a t e d values are c o m p a r e d w i t h the p u b l i s h e d data i n T a b l e 7 . 1 1 . The  p u b l i s h e d entropy and heat c a p a c i t y data o f aqueous ions w e r e o b t a i n e d  from  B a b u s h k i n et a/.(1985). T h e estimation error w a s not n e g l i g i b l e for s o m e ions s u c h as N b 0 " and 3  CO3 ". 2  A n average error o f the estimations w a s 2 5 . 3 5 % . T h e C ° o f SiC>3 " i o n 2  p  is equal to -77.98 c a l / m o l K ( = - 3 2 6 . 2 7 J / m o l K ) . T h e uncertainty o f the C ° o f the S i 0 " 2  p  3  w a s a s s u m e d as the same, 25.35 % ( ± 82.71 J / m o l K ) , as the average e r r o r o f this estimation method from Table 7.11.  T a b l e 7 . 1 1 . H e a t capacities o f aqueous o x y - a n i o n s at 298.15 K , c a l / m o l K . Published  Calculated  r  0  z  S°  -1  35.10  abs -56.78  CKV  -1  39.10  Nb0  -1  36.00  -2  N0  C0 S0  3  3 2 3  Se0 S0  3 2  2 3 2  4  As0 Si0  3 4 2 3  c  0  Published  C  0  error  -28.78  -20.7  -47.98  -19.98  -19.7  1.42%  -54.80  -26.80  -18.4  45.65%  -13.60  -152.92  -96.92  -59.7  62.35%  -2  -7.00  -138.40  -82.40  -64.1  28.55%  -2  -1.70  -126.74  -70.74  -67.6  4.64%  -2  4.20  -113.76  -57.76  -71.6  19.33%  -3  -39.40  -198.68  -114.68  -116.9  1.90%  -2  -4.99  -133.98  -77.98  39.03%  97  7.3.6. C a l c u l a t i o n o f  at 368.15 K  Prior to calculating the equilibrium constant,  Ksod,  of sodalite dihydrate formation,  the A G Q , A H Q , and AC° of the reaction (4.1) were calculated with the thermodynamic data in Tables 7.3 and 7.5. The AG° of reaction (4.1) is equal to AGf (Na (AlSi0 )6Cl 0  8  4  2  2H 0) + 4 A G ° ( H 0 ) + 12AG °(OH) - SAG/fNa*) - 6AG °(Al(OH) ") - 6AG °(Si0 ") 2  2  f  2  f  f  4  f  3  2AG °(Cr) = -13191.59 + 4x(-237.14) + 12x(-157.2) - 8x(-262.0) - 6x(-1311.684) - 6x(f  939.73) - 2x(-131.2) = -159.666 kJ/mol from equation (7.2). The AH° is equal to AHf°(Na (AlSi04)6Cl -2H 0) 8  2  +  2  4AH °(H 0) f  +.  2  12AH °(OH-)  -  f  8AH °(Na )  -  +  f  6AHf (Al(OH) ") - 6AHf°(Si0 ") - 2AH °(Cl') = -14054.91 + 4x(-285.83) + 12x(-230.01) 0  2  4  3  f  - 8x(-240.34) - 6x(-1488.92) - 6x(-1075.38) - 2x(-167.1) = -315.63 kJ/mol from equation (7.3). The A C ; is equal to C °(Na (AlSi0 )6Cl -2H 0) p  8  2  4  2  + 4 C ° ( H 0 ) + 12C °(OrT) P  2  p  8C °(Na ) - 6C °(A1(0H) -) - 6C °(Si0 ") - 2C °(Cf) = 886.28 + 4x(75.351) + 12x(+  2  p  P  4  p  3  p  148.5) - 8x(46.43) - 6x(241.44) - 6x(-326.27) - 2x(-136.4) = -183.976 J/mol K = 0.183976 kJ/mol K from equation (7.4). Substituting A G ° , AH°, and AC° into equation (2.18) at T = 368.15 K and T = 0  298.15  K  formation,  gives In K  s o  d,  K  s o c  i  = 39.74. Thus, the equilibrium constant of sodalite dihydrate  is equal to 1.82E+17. The uncertainty in the calculated values for In K  s  o  _  was found to be ± 8.71 from the uncertainties of the estimated thermodynamic properties in Table 7.5 by the method of Baird (1995). The major contribution in the uncertainty of K od S  was due to the uncertainties in the estimated thermodynamic data, especially that of  the AGf°(Na8(AlSi0 )6Cl -2H 0). 4  2  2  98  7.3.7. C a l c u l a t i o n o f K  The  h s o d  at 368.15 K  AG° of reaction (4.2) is equal to AG (Na (AlSi04)6(OH)2-2H 0) + 0  f  8  2  4 A G ° ( H 0 ) + 12AG (OFT) - 8AG °(Na ) - 6AG °(AJ(OH) ) - 6AG °(Si0 ") - 2AGf°(OH") 0  f  2  +  f  2  f  f  4  f  3  = = -13384.23 + 4x(-237.14) + 12x(-157.2) - 8x(-262.0) - 6x(-1311.684) - 6x(-939.73) 2x(-157.2)  =  -300.306  kJ/mol.  AH (Na (AlSi0 )6(OH) -2H 0)  +  0  f  8  4  2  2  The  AH° of  4AH °(H 0) f  reaction  +  2  (4.2)  12AH °(OFT)  -  f  is  equal  to  8AH °(Na )  -  +  f  6 A H ° ( A l ( O H ) ) - 6 A H ° ( S i 0 ' ) - 2AH °(OH-) = -14283.02 + 4x(-285.83) + 12x(-230.01) 2  f  4  f  3  f  - 8x(-240.34) - 6x(-1488.92) - 6x(-1075.38) - 2x(-230.01) = -417.92 kJ/mol. The AC° of reaction (4.2) is equal to C (Na (AlSi0 ) (OH) -2H 0) + 4 C ° ( H 0 ) + 12C (OFT) 0  0  p  8  4  6  2  2  P  2  p  8 C ° ( N a ) - 6C °(A1(0H) -) - 6 C ° ( S i 0 ) - 2C °(OH") = 895.01 + 4x(75.351) + 12x(+  2  p  P  4  p  3  p  148.5) - 8x(46.43) - 6x(241.44) - 6x(-326.27) - 2x(-148.5) = -151.046 J/mol K = 0.151046 kJ/mol K . Substituting AG° , AH°, and AC° into equation (2.18) at T = 368.15 K and T = 0  298.15  gives In  K  0  = 88.71. Thus, the equilibrium constant of hydroxysodalite  Khsod  dihydrate formation,  Khsod,  is equal to 3.38E+38. The uncertainty in the calculated values  for In K h s o d was found to be ± 10.41. Detailed calculation of the uncertainty is described in APPENDIX VI. Again major contribution in the uncertainty of uncertainties  of  the  estimated  AGf (Na (AlSi0 ) (0H) -2H 0). O  8  4  6  2  2  thermodynamic  data,  K  n  s  o  d  especially  was due to the that  of  the  99  7.4. C h a n g e o f In Khsod w i t h T e m p e r a t u r e 1  Values of In  Khsod  were calculated with varying temperature from 298.15  K  to  368.15 K using equation (2.18). The results are shown in Figure 7.1. A solid line in the figure represents In K h s o d at the temperature of interest. As seen in the figure, the In  Khsod  decreases with increasing temperature.  Figure 7.1. Change of In  Khsod  with temperature.  130  I i 298.15  gQ  i  i  i  I  i  318.15  i  i  i  I  i  i  338.15  i  I i i I 358.15 368.15  i  Temperature (K)  The AC° of the hydroxysodalite dihydrate formation reaction (4.2) is known at 298.15 K as described in section 7.3.7 but not at higher temperature. In this case, it is  100  generally better to assume that AC° is constant as temperature increases from to  368.15 K  Khsod  (Anderson and Crerar,  at the reference temperature,  1993).  A dotted line in the Figure  298.15 K .  7.1  298.15  K  represents In  The area between the dotted line and the  dashed line represents the contribution by the AC° term in equation  (2.18)  on In  Kh  S O  d.  The area between the dashed line and the solid line represents the contribution by the AHQ  term in the equation. As seen in the figure, the AH° term has the largest  contribution on the value of In  Khsod-  The contribution by the AC° term is very small  compared to that by A H ° . Thus, the assumption of constant A C ° in the range of temperature from To to T in the equation (2.18) is acceptable.  101  CHAPTER 8. SOLUBILITY MAPS OF Al AND Si IN GREEN AND WHITE LIQUORS  Data of the solubility experiments using synthetic liquors (systems A and B) and mill liquors are shown in Tables A.3.1, A.3.2, and A.3.3. in APPENDIX U l together with their standard error.  8.1. Synthetic Green and White L i q u o r s of System A  A solid phase started forming in a supersaturated solution of A l and Si within several hours from the beginning of the experiment. The solid precipitates were formed on the wall, stirrer blade, and bottom of the vessel. During the experiment, the concentrations of the soluble A l and Si decreased with time but after four of five days, they reached a constant value. After seven days, the samples were taken and considered to be in their equilibrium state (Figure 8.1). The base case experiment (Experiment A l ) of synthetic green liquor of system A was carried out three times to check the repeatability of the experiments. The results of the experiment are tabulated on the Table 8.1. The standard deviations for A l and Si concentrations were found to be 6.37xl0' and 5  6.52xl0" , respectively. 5  102  Figure 8.1. A l and Si ions approaching equilibrium obtained from the base experiment using synthetic green liquor of system A. (Experimental data were obtained from experiment A l using synthetic green liquors of system A at 368.15 K and latm.)  800  • O  CL 00# Q_ U tn 600 \7  Total soluble Si Total soluble Al  c o  •(5  500 h 400  o  V)  c o 13  300  •t. 200  8 c o  O  o  100  o  3  4  5  Time, (days)  Table 8.1. Repeatability of the experiments in three runs  Al  Si  [Al][Si]  moles/kg H2O  moles/kg H2O  (moles/kg H 0 )  1  4.49E-3  5.01E-3  2.25E-5  2  4.51E-3  5.06E-3  2.28E-5  3  4.61E-3  4.93E-3  2.28E-5  run  2  2  103  It is customary to present precipitation results in the form of a graph which is known as the solubility map (Wannenmacher et al,  1996). Figure 8.2 shows the  solubility map for the synthetic green and white liquors of system A. In the solubility maps, the 95 % confidence interval for each data point has been plotted together with the experimental data points. The confidence interval calculations are explained in detail in APPENDIX II. This was calculated using the standard error of the five Atomic Absorption Spectrophotometer measurements for each sample. If the concentrations of Al and Si in the liquors correspond to a point on the right side of each line, precipitation will occur for this solution. The precipitation conditions in synthetic white liquor are higher than those in the synthetic green liquor. This result is attributed to the effect of [OFT]. White liquor contains more OFT. Higher [OFT] content makes A l and Si more soluble as we see in Figure 8.3 which shows the effect of changing the OFT concentration on the precipitation conditions. The change in the OH" concentration is accomplished by varying the input amount of NaOH during the preparation of the solution. The base concentration, given in Table 3.1, is 1.0 mol/kg H 0 in synthetic green liquor. The perturbations around 2  the base case are also given in the figure. As seen from the plot, as the hydroxyl ion concentration increases, precipitation occurs at higher Al and Si concentrations. Zheng and coworkers also studied sodium aluminosilicate crystallisation in relation to the Bayer process at 100 °C (Zheng et al,  1997). Their result is also plotted in Figure 8.3. The  chemical compositions of the Bayer liquors are not exactly the same as in this work. The synthetic Bayer liquor contains 4.53 mol/L of NaOH.  104  Figure 8.2. Solubility map of Al and Si in synthetic green and white liquors of system A. (Experimental data were obtained from experiments A l , A2, and A3 using green liquors and from experiments A10, A l 1, A12 using white liquors at 368.15 K and latm.)  105  Figure 8.3. Effect of hydroxyl ions on the solubility limit in synthetic green and white liquors of system A. (Experimental data were obtained at 368.15 K and latm. Initial concentrations of NaOH in green liquors were 0.25 mol/kg H 0 for experiment A4, 1.0 mol/kg H 0 for experiments A l , A2, and A3, and 2.0 mol/kg H 0 for experiment A5. Those in white liquors were 2.0 mol/kg H 0 for experiment A13, 2.5 mol/kg H 0 for experiments A10, A l 1, and A12, and 3.0 mol/kg H 0 for experiment A14.) 2  2  2  2  2  2  Si concentration (mol/kg H 0) 2  106  T h e effect o f c h a n g i n g the concentration o f the carbonate a n i o n is s h o w n i n F i g u r e 8.4. I n c r e a s i n g the i n i t i a l carbonate i o n concentration i n the synthetic green l i q u o r g i v e s a l o w e r s o l u b i l i t y o f A l and S i . I n the case o f synthetic w h i t e l i q u o r , n o significant change i n the s o l u b i l i t y w a s o b s e r v e d for the concentrations studied (0.1 to 0.5 m o l / k g H _ 0 ) . It is n o t e w o r t h y that even t h o u g h the  synthetic g r e e n l i q u o r contains  more  carbonate, it is sensitive t o a perturbation i n the carbonate concentrations whereas the w h i t e l i q u o r is not, at least f o r a ± 0.2 m o l / k g H2O change. T h e concentrations o f the sulfate ions i n real green and w h i t e l i q u o r s f r o m kraft m i l l s are i n the range o f 0.05 to 0.2 m o l / L and 0.05 to 0.15 m o l / L ( M a g n u s s o n et  al,  1979). T h e effect o f the sulfate ions o n the s o l u b i l i t y o f A l and S i w a s also measured at input s o d i u m sulfate concentrations o f 0.05, 0.1, and 0.2 m o l / k g H2O for the synthetic green l i q u o r and 0.05, 0.1, and 0.15 m o l / k g H2O f o r the synthetic w h i t e l i q u o r . A s seen from F i g u r e 8.5, n o significant change i n the s o l u b i l i t y w a s o b s e r v e d .  8.2. S y n t h e t i c G r e e n a n d W h i t e L i q u o r s o f S y s t e m B T h e p r e c i p i t a t i o n c o n d i t i o n s i n synthetic green and w h i t e l i q u o r s o f system B are s h o w n i n F i g u r e 8.6. T h e synthetic w h i t e l i q u o r o f h i g h e r [OFT] c o m p a r e d w i t h the green l i q u o r s h o w s that p r e c i p i t a t i o n o c c u r s at higher A l and S i concentrations. T h e effect o f input amount o f Na2S o n the p r e c i p i t a t i o n c o n d i t i o n is s h o w n i n F i g u r e 8.7. A s m o r e Na2S is added i n t o the system, p r e c i p i t a t i o n o c c u r s at higher A l and S i concentrations.  107  Figure 8.4. Effect of carbonate ions on the solubility limit in synthetic green and white liquors of system A. (Experimental data were obtained at 368.15 K and latm. Initial concentrations of Na2CC>3 in green liquors were 0.5 mol/kg H2O for experiment A6, 1.0 mol/kg H2O for experiments A l , A2, and A3, and 1.5 mol/kg H 0 for experiment A7. 2  Those in white liquors were 0.1 mol/kg H2O for experiment A15, 0.3 mol/kg H2O for experiments A10, A l 1, and A12, and 0.5 mol/kg H2O for experiment A16.)  0.1  0.001  0.01  0.1  Si concentration (mol/kg H 0) 2  108  Figure 8.5. Effect of sulfate ions on the solubility limit in synthetic green and white liquors of system A. (Experimental data were obtained at 368.15 K and latm. Initial concentrations of Na2S04 in green liquors were 0.05 mol/kg H 2 O for experiment A8, 0.1 mol/kg H 2 O for experiments A l , A2, and A3, and 0.2 mol/kg H 2 O for experiment A9. Those in white liquors were 0.05 mol/kg H 2 O for experiment A17, 0.1 mol/kg H 2 O for experiments A10, A l l , and A12, and 0.15 mol/kg H 0 for experiment A18.) 2  0.1  Si concentration (mol/kg H 0) 2  109  Hence, it becomes more difficult to precipitate solids. In other words, the window for normal operation expands. This may be attributed to the fact that Na S dissociates 2  when dissolved in water and releases OH" by the reaction: Na S + H 0 -> 2Na + HS' + +  2  2  OH" (Smook, 1992), that affects the precipitation conditions in a manner seen in Figure 8.3. The effect of [OFT] might be explained by considering the sodium aluminosilicate formation reaction as seen next. The sodium aluminosilicate precipitates were found to be hydroxysodalite dihydrate (Na (AlSi0 ) (OH) -2H 0) and/or sodalite dihydrate (Na (AlSi0 ) Cl -2H 0). 8  4  6  2  2  8  4  6  2  2  The identification of the precipitates is explained in section 8.4. The chemical reaction for sodium aluminosilicate formation of this study can be written as  8Na + 6A1(0H) " + 6Si0 " + 2X" <- Na (AlSi0 )6X -2H 0(s) + 4H 0 + 120H" +  2  4  3  8  4  2  2  2  (8.1)  where X" can be O H ' or Cl" (Zheng et al, 1997). The solubility product of Al and Si can be written as  (aAI(OH);  e<,(*W) (a -)  K  8  x  where a is the activity and K  e q  (8.2)  2  J  is the equilibrium constant". The solubility product  increases with increasing [OH"] at constant concentrations of the other ions.  110  Figure 8.6. Solubility map of Al and Si in synthetic green and white liquors of system B. (Experimental data were obtained from experiments B l , B2, and B3 using green liquors and from experiments BIO, B l 1, B12 using white liquors at 368.15 K and latm.)  0.1  \  \  \  oCM  \  D) O  E c  \ 0.01  \  Precipitation  \  \  <  \  \  Q\  o >  -•—<  <D O C O  0.001  \  \  \  \  X\  0.001  \ \  Input ratio green Iq. white Iq. Al/Si A 1/2 1/1 O 2/1  • • •  \  \  N  \  •  0.01  0.1  Si concentration (mol/kg H 0) 2  Ill  Figure 8.7. Effect of NajS on the solubility limit in synthetic green and white liquors of system B. (Experimental data were obtained at 368.15 K and latm. Initial concentrations of NazS in green liquors were 0.0 mol/kg H2O for experiments B4, B5, and B6, 0.5 mol/kg H2O for experiments B l , B2, and B3, and 1.0 mol/kg H2O for experiments B7, B8, and B9. Those in white liquors were 0.0 mol/kg H2O for experiments B13, B14, and B15, 0.5 mol/kg H 0 for experiments B10, B l l , and B12, and 1.0 mol/kg H 0 for experiments B16, B17, and B18.) 2  2  0.1  \  (moles/kg H-O)  0.5 (base}  •  \  0.01  white Iq. O 0.0  2  \  \ • - * \  CM  O  green Iq. Input Na S • 0.0  \  1.0  0.5 (base)  •  1.0  \ o \  q  \  \m  I  \ \  \  c  \ \  U  \  c  g  0.001  * _l  I  '  I  I I I  I  0.001  '  '  I  I  I I I I I  I  \  \ I  I  'Ns.  0.01  I  I I  I  0.1  Si concentration (mol/kg H 0) 2  112  8.3. M i l l G r e e n a n d W h i t e L i q u o r s  Figure 8.8 shows the solubility map for the green and white liquors. In the solubility maps, the 95 % confidence interval for each data point has been plotted together with the experimental point. As seen from the graph, the data at three different A/Si ratios fall on the same line. If the concentrations of A l and Si in the liquors correspond to a point located on the right side of each line, precipitation will occur in this liquor. As seen, the precipitation conditions in white liquor are higher than that in the green liquor. This result is attributed to the effect of OFT. Higher OFT concentration makes A l and Si more soluble as seen in Figure 8.9. White liquor contains more OH" (2.63 mol/kg H 0 ) than the green liquor (0.85 mol/kg H 0 ) . 2  2  Figure 8.9 shows the effect of changing the OH" concentration on the precipitation conditions. As seen from the plot, higher concentrations of A l and Si are required to induce precipitation as the hydroxyl ion concentration increases. Thus, the liquor can tolerate increased levels of dissolved A l and Si. Increasing initial carbonate ion concentration in the mill liquors gave a lower solubility of Al and Si, which can be seen in Figure 8.10. In other words, as the carbonate ion concentration increases, precipitation occurs at lower A l and Si concentrations. The effect of Na S on the precipitation 2  conditions is shown in Figure 8.11. As more Na S is added into the system^ precipitation 2  occurs at higher A l and Si concentrations. This effect may be attributed to the fact that Na S dissociates when dissolved in water and releases OH" (Ulmgren, 1982; Smook, 2  1992).  113  Figure 8.8. Solubility map of Al and Si in mill green and white liquors. (Experimental data were obtained from experiments M l , M2, and M3 using green liquors and from experiments M13, M14, M15 using white liquors at 368.15 K and latm.)  0.1  Precipitation  CM  o E  0.01  co TO  O  c  O  0.001 Green liquor (base)  o  White liquor (base) 0.001  0.01  0.1  Si concentration (mol/kg H 0) 2  114  Figure 8.9. Effect of NaOH on the solubility limit of A l and Si in mill liquors. (Experimental data were obtained at 368.15 K and latm. Initial concentrations of NaOH in green liquors were 0.29 mol/kg H2O for experiments M l , M2, and M3, and 1.29 mol/kg H2O for experiments M4, M5, and M6. Those in white liquors were 2.06 mol/kg H2O for experiments M13, M14, and M15 and 2.56 mol/kg H2O for experiments M16, M17, andM18.)  0.001  0.01  0.1  Si concentration (mol/kg H 0) 2  115  Figure 8.10. Effect of Na2C03 on the solubility limit of Al and Si in mill liquors. (Experimental data were obtained at 368.15 K and latm. Initial concentrations of Na2CC«3 in green liquors were 1.05 mol/kg H 0 for experiments M l , M2, and M3, and 1.55 mol/kg H_0 for experiments M7, M8, and M9. Those in white liquors were 0.23 mol/kg H 0 for experiments M13, M14, and M15 and 0.48 mol/kg H2O for experiments M19, M20, andM21.) 2  2  116  Figure 8.11. Effect of Na S on the solubility limit of Al and Si in mill liquors.(Experimental data were obtained at 368.15 K and latm. Initial concentrations of Na2S in green liquors were 0.56 mol/kg FfeO for experiments M l , M2, and M3, and 1.06 mol/kg H2O for experiments M10, M i l , and M12. Those in white liquors were 0.57 mol/kg H 0 for experiments M13, M14, and M l 5 and 1.07 mol/kg H 0 for experiments M22, M23, and M24.) 2  2  2  Green liquor •  2  1.06 0.56  White liauor Na S O 1.07 0.57  CM  2  C O  E,  -  2  0.1  o  [OH ] (mol/kg H 0)  Na S  1.35 0.85, base [OH"] (mol/kg H 0) 2  3.13 2.63, base  0.01  c o  '~t—>  CO  8 c o  0.001  _1  1  1 I I I I  0.001  _1  I  I  I  I  I I I  J  I  I  0.01  I  'Nl  I  I  0.1  Si concentration (mol/kg H 0) 2  117  The results for the mill liquors with base concentrations were compared with data available in the literature and found in good agreement as seen in Figure 8.12. The straight line on the graph represents a correlation of the precipitation conditions obtained from experiments with mill green liquors (Wannenmacher et al, 1996). The grey square in Figure 8.12 represents the concentrations of AJ and Si in unsaturated mill white liquors. These liquors contain A l and Si at  a concentration level that is near the  precipitation conditions.  Figure 8.12. Solubility map comparing solubility limit of A l and Si in varying liquors. (The data were obtained at 368.15 K and 1 atm)  0.1  Green liquor • This work (base concentration) Wannenmacher et. al.1996  :  -  •  D)  __. O  E  0.01  White liquor • This work (base concentration)  •  H  \  c o  I  Wannenmacher etal. 1996  D  •\  -  8 c  8  0.001  •  -  I  0.001  ' • '  0.01  0.1  S i concentration (mol/kg H 0 ) 2  118  8.4. Structure of the Precipitates from Synthetic L i q u o r s  X-ray diffraction analysis of the precipitates from the solutions of system A and B showed  that  only  sodalite  (Na (AlSi04)6Cl2nH 0) 8  2  and/or  hydroxysodalite  (Nag(AlSi04)6(OH)2nH20) were present (Figure 8.13). There is no significant difference in the X-ray diffraction patterns for the sodalite and hydroxysodalite (Gasteiger et al, 1992). Ulmgren (1982) reported that samples of scales from Swedish pulp mills consist of N a A l S i 0 4 l / 3 N a C 0 2  3  and/or N a A l S i 0 l / 3 N a S 0 4  2  4  which look like cancrinite.  Although the system of this study contained carbonate and sulfate ions, the X-ray diffraction patterns of the precipitates did not match to those of any minerals containing the carbonate and sulfate ions. A portion of the precipitates in the synthetic liquors of system A a n d B was dissolved in IN nitric acid and analyzed to determine the molar ratios of Na, A l , Si, Cl, and O H in the solid. If the precipitates contain carbonate in the structure, dissolving the solid in acid solution can cause release of carbonate ions to combine with hydrogen ions and be converted to C 0 gas. However, no bubbles of CO2 gas were detected during the 2  dissolution. Sulfate was not present in the precipitates obtained in the synthetic green and white liquors because the precipitation of B a S 0 4 was not observed by the addition of BaCb solution to the dissolved precipitate solutions. Chloride was not present in the white liquor precipitates of system A and green and white liquor precipitates of system B because the precipitation of AgCl was not observed by the addition of A g N 0 solution to 3  the dissolved precipitate solutions. The green liquor precipitates of system A, however, had chloride since AgCl precipitated when A g N 0 solution was added. The amount of 3  119 chloride ions in the dissolved precipitate solution was measured quantitatively using a titration method with a 0.1 N AgNC«3 solution.  Figure 8.13. X-ray diffraction pattern of precipitates in synthetic green liquor of system A.  Hydroxysodalite (reference)  I  100  • i  i  Sample  60  00 c 20  rpTrrp' ''' 'j' |  5  r  r r r  ' T* l  r r T !  i'VT!"i | i i  1rp'n'i  pT'n p  i  rr^^Trr^rrrT^'rrrp-TTTTTTTinrTrrrp  10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90  20  120  Thus, X-ray diffraction analysis and chemical analysis revealed that the precipitates of the synthetic green liquor of system A contain the structure of sodalite and hydroxysodalite whereas those of the synthetic white liquor of system A and green and white liquors of system B contain the structure of hydroxysodalite only. In the case of the synthetic green liquor of system A, approximately 25 % of the precipitates on a molar basis are sodalite which has the Cl group and 75 % of the precipitates are hydroxysodalite which has the O H group. The molar ratio of Na : A l : Si is 8 : 6.06 ± 0.05 : 6.05 ± 0.06. In the case of the synthetic white liquor of system A, the precipitate is hydroxysodalite. The molar ratio of Na : A l : Si is 8 : 5.96 ± 0.09 : 6.07 ± 0.07. The precipitates of synthetic green and white liquors of system B are hydroxysodalite. The molar ratios of Na : A l : Si  are 8 : 6.23 ± 0.20 : 6.15 ± 0.31 and 8 : 6.18 ± 0.13 : 5.89 ± 0.09,  respectively. Thermogravimetry analyses were performed for four precipitates, each from the synthetic green and white liquor, of systems A and B. The analyses proceeded from 105 to 900 °C at a heating rate of 10 °C/min under a N atmosphere. The data for synthetic 2  white liquor precipitates from system A are shown in Figure 8.14. Total weight loss was 5.73 % by heating up to 900 °C and the loss is equivalent to 3.1 H 0 ( « 3 H 0 ) molecules 2  2  per unit cell of the precipitate. Engelhardt et al. (1992) studied the hydroxysodalite system with thermal analysis. According to their result, a total of n+1 water molecules per unit cell leave the structure of N a 8 ( A l S i 0 4 ) 6 ( O H ) n H 0 by heating up to about 700 2  2  °C. First of all, n water molecules leave to form Nag(AlSi04)6(OH) and another water 2  molecule from the remaining O H groups is released to change to a carnegieite-type phase  121  Na 0-6NaAlSi04. Therefore, the total water loss, three water molecules per unit cell in 2  Figure 8.14, indicates that the structure of precipitate in synthetic white liquor is Na8(AlSi04)6(OF£)2-2H 0, hydroxysodalite dihydrate. Other precipitates showed similar 2  weight loss, 5.46 % of synthetic green liquor precipitate of system A, 5.22 % and 5.55 % of synthetic green and white liquor precipitates of system B. This fact means that all precipitates have the same number of hydrated water molecules, 2H2O, in their structure.  F i g u r e 8.14. T h e r m o g r a v i m e t r i c analysis o f h y d r o x y s o d a l i t e d i h y d r a t e , Na8(AlSi04)6(OH)2-2FJ.20,  100  precipitated i n synthetic w h i t e l i q u o r o f s y s t e m A .  X  99 -\ 98 H ^  -•—>  97  H  CO  'CD  96  95  H weight loss : 5.73 % • loss of H 0/unit cell: 3.1  94  — >  2  93 H T  T  100  200  300  400  500  600  temperature (°C)  T  700  800 900  122  8.5. Structure of the Precipitates from Mill Liquors X-ray diffraction analysis revealed that the precipitates could be sodalite (Na (AlSi0 )6Cl nH 0) 8  4  2  2  and/or  (Na (AlSiO )6(OF0 nH O).  hydroxysodalite  8  4  2  2  This  analysis cannot distinguish between these two solids (Gasteiger et al, 1992). Therefore, it was complemented with chemical analysis and thermogravimetry. The chemical tests described earlier showed that there was not any chloride, sulfate or carbonate present in the precipitated solids. In addition, the atomic absorption spectroscopy tests showed that there was not any potassium present in the solid. The molar ratios of Na : A l : Si in the precipitates from the green and white liquors were found to be 8 : 6.17 ± 0.16 : 5.86 ± 0.08 and 8 : 5.97 ± 0 . 1 1  : 5.99 ± 0.10 respectively. Thus, the chemical formula of the  precipitate is that of Na (AJSi04)6(OIT) nH 0. Finally, the number of the hydrated water 8  2  2  molecules was found to be equal to two by thermogravimetry. Hence the precipitate is hydroxysodalite dihydrate, Na8(AlSi04)6(OH) -2H 0. Structure of precipitates in mill 2  2  liquors was found to be similar to that in synthetic liquors.  8.6. Morphology of precipitates The precipitates in green and white liquors consist of particles 5 to 30 pm in diameter. Aggregated particles, as shown in Figure 8.15, were found to be suspended in the solution or present as scale on the wall of the vessel and the stir blade. Most of green liquor precipitates were suspended in solution. Homogeneous nucleation might be the dominant nucleation mechanism in the green liquors (Mullin, 1972). The green liquor precipitates formed on the wall of vessel could be easily removed. The image of the green  123  l i q u o r precipitates i n F i g u r e 8.15 (a), (b), and (c) s h o w s a less p a c k e d structure o f the particles. F i g u r e 8.15. S c a n n i n g electron m i c r o g r a p h s o f precipitates.  (a)  m  Precipitates in (a) synthetic green liquor of system A (experiment A l ) , (b) synthetic green liquor of system B (experiment Bl), (c) mill green liquor (experiment M l ) , (d) synthetic white liquor of system A (experiment A10), (e) synthetic white liquor of system B (experiment BIO), and (f) mill white liquor (experiment M13). All scale bars in the images have the same length, 10 um.  124  White liquor precipitates were formed mainly on the wall and bottom of the vessel and on the stir blade. Heterogeneous nucleation might be the dominant nucleation mechanism in the white liquors (Zettlemoyer, 1969). The scale on the wall and bottom of the vessel was very glassy. Thickness of the scale was less than 1 mm. Surface of scale consists of spherical cap type deposits. These precipitates could not be easily detached by scraping. The image in Figure 8.15 (d), (e), (f) shows a well packed structure of the particles in the white liquor. More precipitates were formed in green liquors than in white liquors when the same amount of Al and Si salts were added into the liquors. Amount of precipitates was approximately 7 to 8 g/kg H2O in the synthetic green liquors of system B when Na Si0 -9H 0 of 0.05 mol/kg H 0 and A1C1 -6H 0 of 0.05 mol/kg H 0 were used. The 2  3  2  2  3  2  2  amount of precipitates in synthetic white liquors of system B ranges from 5 to 6 g/kg H 0 2  when the same amounts of Na Si0 -9H 0 and A1C1 -6H 0 were used in the experiments. 2  3  2  3  2  125  CHAPTER 9. PREDICTION OF THE PRECIPITATION CONDITIONS OF SODIUM ALUMINOSILICATES  The  eleven model equations were solved by the Newton-Raphson method  (Numerical Recipies™,  1995) to give the molalities of the species. The activity  coefficients of species as well as the activity of water were also calculated. The product of the molalities of Al(OH)4" and  SiC<3 ' 2  at equilibrium was taken as the solubility  product. In order to check the reliability of the modeling procedure, calculations for the NH4 - N H 4 O H - If - HCl - NH4CI - C f - N a - NaCl - K - KC1 system were performed. +  +  The calculation results were compared with the published ones (Anderson and Crerar, 1993). For the exact comparison, the Davies revision of the Debye-Huckel equation (Anderson and Crerar, 1993) was used for the activity coefficient calculation since the same equation was used in the literature. The computational source code (heqbrm.for) is available in APPENDIX IX together with examples of input and output. As seen from the Table 9.1, the values obtained agree well with published ones. Calculations were performed at 368.15 K for the N a - Al(OH) ' - S i 0 ' - OH" +  2  4  3  C 0 " - S 0 ' - Cl" - H 0 system (system A) and the N a - Al(OH) * - Si0 " - OH" - CO3 ' 2  3  2  +  4  2  2  4  2  3  - C f - HS" - H 0 system (system B). The results were compared with the experimental 2  data described in chapter 8. The calculations showed that only hydroxysodalite dihydrate forms in both systems. During the experiments, most of the precipitates were found to have the structure of hydroxy sodalte dihydrate. Only in the solutions of low OH" and high Cl* concentrations of system A, a small amount of the sodalite dihydrate precipitates was  126 found together with hydroxysodalte dihydrate. A comparison of the calculated results with experimental data is presented next.  Table 9.1. Comparison of the calculation results for the NFL, - NH4OH - FT - HC1 NFL,C1 - Cl" - N a - NaCl - K - KCI system at 573.15 K +  +  Calculated molalities (mol/kg H20) Species  Anderson and Crerar, 1993  This work  NH4  Na NaCl K  1.630E-1 2.844E-3 1.206E-3 1.638E-3 8.416E-2 4.782E-1 1.385E-1 1.115E-1 1.755E-1  KCI  7.450E-2  1.630E-1 2.876E-3 1.220E-3 1.657E-3 8.415E-2 4.782E-1 1.385E-1 1.115E-1 1.755E-1 7.450E-2  NH4OH  FT HC1 NH4CI  cr  +  +  The molalities of the species at equilibrium were calculated using the following input amounts of chemicals: NH4CI of 0.25 moles, NaCl of 0.25 mol, KCI of 0.25 mol, and H Oofl.0kg. 2  9.1. N a - A l ( O H )  - Si0  +  4  2 3  - O H - C0  2 3  - SO4  2  - CI - H  2  0 (System A )  Figure 9.1 shows data and calculated values (solid line) for the concentration of the aluminum species versus that of the silicon at equilibrium. When the concentration of the A l and Si species in the solution correspond to a point on the right of the line then precipitation occurs. Calculations were also performed to test the sensitivity of the model to the value of  Kh  S O  d-  These calculations using values  Kh  S O  d  ± uncertainty are shown as  dotted lines in Figure 9.1. As seen the experimental data are located within the boundaries of the precipitation conditions computed by taking into account the uncertainty in  Khsod-  The value of  K  n s  od  was subsequently adjusted to 4.39E+36 (In  Khsod  127 = 84.37) instead of the calculated 3.38E+38 (In Khsod  =  88.71) and was used to give a  solubility product calculation in perfect agreement with the data (dotted-dashed line).  Figure 9.1. Equilibrium concentration of aluminum and silicon species. (Experimental data were obtained from experiments A l , A2, and A3 using synthetic green liquors of system A at 368.15 K and latm. For the model calculation, input amount of NaOH was 1.0 mol/kg H 0 , that of N a C 0 was 1.0 mol/kg H 0 , that of N a S 0 was 0.1 mol/kg H 0 , and that of NaCl was 0.25 mol/kg H 0 . Input amounts of A1C1 6H 0 and N a S i 0 9 H 0 were varied from 0.04 to 0.01 mol/kg H 0 andfrom0.01 to 0.04 mol/kg H 0 respectively.) 2  2  3  2  2  2  4  2  2  3  3  2  2  •  0.1  2  Experimental data Prediction using In K,,^ = 88.71 Prediction using In K = 88.71±10.41 Prediction using In K,^ = 84.37 hsod  J  iJ  i  i i 11 0.001  i  i i i i r-i 11  2  i  i i i i i i 11  0.01  0.1  Si concentration (mol/kg H 0) 2  128 Figure 9.2 shows the effect of varying the concentration of OFT on the precipitation conditions. As seen from the plot the solubilities of A l and Si increase with increasing hydroxyl ion concentration and the model is able to capture this behaviour.  Figure 9.2. Effect of hydroxyl ion concentration changes on the equilibrium concentration of aluminum and silicon species. (Experimental data were obtained from experiments A l , A2, A3, A4, and A5 using synthetic green liquors of system A at 368.15 K and latm. For model calculations, only input amount of NaOH was varied from 0.25 to 2.0 mol/kg H2O. Input amounts of other chemicals were same as those of Figure 9.1. A value of In K h d = 84.37 was used.) S O  NaOH (mol/kg H 0) 2  0.1  • • A  0.25 1.0 2.0 Prediction  j  0.001  1  1  L  0.1  0.01  Si concentration (mol/kg H 0 ) 2  The amount of hydroxysodalite scale was also calculated to be smaller. This calculation result shows that the solutions can tolerate more dissolved A l and Si species  129 by increasing the amount o f OH". Varying the total amount o f N a and OH" by changing +  the input amount o f N a O H affects ion-ion interactions reflected as activity o f water and activity coefficients o f ions in the system. Table 9.2 shows one example o f the calculation results with varying amounts o f NaOH. The activity o f water and activity coefficients showed significant change with varying input amounts o f N a O H .  Table 9.2. Example o f the modeling calculation results for the N a - A l ( O H ) 4 " - Si03 " +  OH" - C 0 " - S 0 ' - GI" - H 0 system at 2  2  3  4  2  368.15 K . In the table, m  2  is the molality, y is the  activity coefficient, a is the activity, and hsod denotes the hydroxysodalite dihydrate. The total amounts o f the chemicals except for the N a O H were AICI36H2O o f N a S i 0 9 H 0 o f 0.025 moi, N a C 0 3  2  2  2  3  of  1.0  moi, N a S 0 2  4  0.025 moi, 0.25 moi,  o f 0.1 moi, N a C l o f  and H 0 o f 1 kg in initial solution. 2  Input amount o f N a O H 0.25 mol/kg H 0  1.0 mol/kg H 0  2  Na  +  Al(OH) " 4  Si0 " 2  3  OH" C0 " 2  3  S0 " 2  4  Cl" H 0 2  hsod  2  2.0 mol/kg H 0 2  2.6990 0.0010 0.0010 0.1886 0.9930 0.0993 0.3227  Y 0.5057 0.2654 0.0519 0.6262 0.0192 0.0250 0.5706  3.4489 0.0047 0.0047 0.9272 0.9930 0.0993 0.3227  Y 0.5325 0.1694 0.0389 0.6701 0.0180 0.0235 0.6218  4.4520 0.0120 0.0120 1.9083 0.9931 0.0993 0.3228  Y 0.5782 0.0889 0.0281 0.7391 0.0173 0.0222 0.6996  m  a  m  a  m  a  55.9003 0.003969  0.9452 1  55.8978 0.003347  0.9170 1  55.8929 0.002137  0.8775 1  m  m  m  Figure 9.3 shows the effect o f carbonate ion on the precipitation conditions. The experimental data show that the solubility o f A l and Si decreases when the amount o f carbonate  ion increases. The calculations  concentration changes o f the carbonate ion.  show  a very  small  sensitivity  to  the  130  Figure 9.3. Effect of carbonate ion concentration changes on the equilibrium concentration of aluminum and silicon species.(Experimental data were obtained from experiments A l , A2, A3, A6, and A7 using synthetic green liquors of system A at 368.15 K and latm. For model calculations, only input amount of Na2C03 was varied from 0.5 to 1.5 mol/kg H2O. Input amounts of other chemicals were same as those of Figure 9.1. A value of In K h s o d = 84.37 was used.) 0.1  Na C0 2  o  • •  CM  A  CO  o  S  (mol/kg  3  H 0) 2  0.5 1.0 1.5  Prediction  0.01  c o  '•*->  CO  c  CD O  c  g  0.001  _i  1  1  1 1 1 1  0.001  0.01  0.1  Si concentration (mol/kg H 0) 2  Figure 9.4 shows that the model agrees well with the data that show that the sulfate ion did not change the precipitation conditions. Calculations at different concentrations of Al, Si and other species have shown similar agreement between the experimental data and the calculated results. For example, Figure 9.5 shows the effect of hydroxyl ion, Figure 9.6 that of the carbonate ion and Figure 9.7 that of the sulfate ion.  131  Figure 9.4. Effect of sulfate ion concentration changes on the equilibrium concentration of aluminum and silicon species.(Experimental data were obtained from experiments A l , A2, A3, A8, and A9 using synthetic green liquors of system A at 368.15 K and latm. For model calculations, only input amount of Na2SC<4 was varied from 0.05 to 0.2 mol/kg H_0. Input amounts of other chemicals were same as those of Figure 9.1. A value of In Khsod 84.37 was used.) =  0.001  0.1  0.01  Si concentration (mol/kg H 0) 2  132  Figure 9.5. Effect of hydroxyl ion concentration changes on the equilibrium concentration of aluminum and silicon species. (Experimental data were obtained from experiments A10, A l l , A12, A13, and A14 using synthetic white liquors of system A at 368.15 K and latm. For model calculations, Input amount of Na C03 was 0.3 mol/kg H 0, that of Na S0 was 0.1 mol/kg H 0, and that of NaCl was 0.1 mol/kg H 0. Input amount of NaOH was varied from 2.0 to 3.0 mol/kg H 0 Input amounts of A l C l 3 6 H 0 and Na Si0 9H 0 were varied from 0.08 to 0.02 mol/kg H 0 and from 0.02 to 0.08 mol/kg H 0 respectively. A value of In K h s o d = 84.37 was used.) 2  2  2  4  2  2  2  2  3  2  2  2  2  0.1  CM  CD O  E  c o 2 c  0.01  •  \  3.0  v  -  \  -  2.5  -»—«  8  C o o  2.0  NaOH (mol/kg H 0) • 2.0 0.001 h • 2.5 A 3.0 Prediction -  2  _  i  i  i  i i i i  1  0.001  •  i  I  I  i  1111  i  i  i  i  i  111  0.1  0.01  Si concentration (mol/kg H 0) 2  133  Figure 9.6. Effect of carbonate ion concentration changes on the equilibrium concentration of aluminum and silicon species. (Experimental data were obtained from experiments A10, A l l , A12, A15, A16 using synthetic white liquors of system A at 368.15 K and latm. For model calculations, only input amount of Na2C03 was varied from 0.1 to 0.5 mol/kg H 0 . Input amounts of other chemicals were same as those of Figure 9.5. A value of In K h s o d 84.37 was used.) 2  =  0.1  CM  o  £  0.01  c o CO  l_ -«—'  c  8 c o o  Na C0 (mol/kg H 0) • 0.1 • 0.3 A 0.5 Prediction 2  0.001  _i  i  3  i i  i ii  0.001  2  _i  i  i  i i  i ii  _i  i  i  0.01  i i i  ii  0.1  Si concentration (mol/kg H 0) 2  134  Figure 9.7. Effect of sulfate ion concentration changes on the equilibrium concentration of aluminum and silicon species.(Experimental data were obtained from experiments A10, A l l , A12, A17, and A18 using synthetic white liquors of system A at 368.15 K and latm. For model calculations, only input amount of Na2SC«4 was varied from 0.05 to 0.15 mol/kg H2O. Input amounts of other chemicals were same as those of Figure 9.5. A value of In K h s o d = 84.37 was used.)  0.1  0.15  CM  X  co o  E  0.01  c  o  2  8 C  o o  N a S 0 (mol/kg H 0 ) • 0.05 • 0.1 A 0.15 Prediction 2  0.001  4  0.001  2  0.1  0.01  Si concentration (mol/kg H 0) 2  135  9.2. N a  +  - Al(OH)  4  - Si0  2 3  - OH - C0  2 3  - C l - H S - H 0 (System B ) 2  In experiments w i t h system B, N a S was 2  water t o N a , OH",  used. S o d i u m  and HS" a c c o r d i n g to the reaction: N a S + H 0  +  2  2  sulfide dissociates i n  -> 2 N a  +  + HS" +  OH"  ( S m o o k 1992). T h e effect o f different HS" concentrations is s h o w n i n F i g u r e 9.8.  Figure  9.8.  Effect  o f hydrosulfide  i o n concentration  changes  on  the  equilibrium  concentration o f a l u m i n u m and s i l i c o n species. ( E x p e r i m e n t a l data w e r e o b t a i n e d f r o m experiments B 1 - B 9  u s i n g synthetic green l i q u o r s o f system B at 368.15 K  m o d e l calculations, input a m o u n t o f N a O H was was  1.0  mol/kg H 0 . 2  T h a t o f N a S was 2  0.25  mol/kg H 0 , 2  v a r i e d f r o m 0.0  and l a t m . F o r  and that o f N a C 0 2  to 1.0 mol/kg H 0 .  Input  2  amounts o f A 1 C 1 6 H 0 and N a S i 0 9 H 0 w e r e v a r i e d f r o m 0.1 to 0.05 mol/kg H 0 3  2  2  f r o m 0.05 to 0.1 mol/kg H 0 2  3  2  2  respectively. A v a l u e o f In K o d = 84.37 was used.) n S  Na S (mol/kg H 0) 2  0.001  2  0.1  0.01  Si concentration (mol/kg H 0) 2  3  and  136  As seen from the plot, model and data agree that increasing HS" concentration increases the solubility of Al and Si. The same agreement is also seen in Figure 9.9 that shows results at different total concentration of chemicals.  Figure 9 . 9 . Effect of hydrosulfide ion concentration changes on the equilibrium concentration of aluminum and silicon species. (Experimental data were obtained from experiments B10-B18 using synthetic white liquors of system B at 368.15 K and latm. For model calculations, input amount of NaOH was 2.0 mol/kg H 2 O , and that of Na2C03 was 0.25 mol/kg H 0 . That of N a 2 S was varied from 0.0 to 1.0 mol/kg H 0 . Input amounts of A J C 1 6 H 0 and N a 2 S i 0 9 H 0 were varied from 0.1 to 0.05 mol/kg H 0 and from 0.05 to 0.1 mol/kg H 2 O respectively. A value of In Kh d = 84.37 was used.) 2  3  2  2  3  2  2  S0  0.1  1.0 0.5  8 c  0.0  Na S (mol/kg H 0) 2  2  0.0 0.5 1.0  • •  0.001  A  Prediction j  1  1  11111  0.001  1  1  1  1 1 1 1  j  0.01  1  111  0.1  Si concentration (mol/kg H 0) 2  137 The thick line in Figure 9.10 represents experimental data at 368.15 K using kraft pulp mill green liquors containing 4.37 mol/L N a , 0.85 mol/L OFT, 1.49 mol/L CO3 ', +  2  0.44 mol/L HS' and 0.02 mol/L S 0 ' (Wannenmacher et al, 2  4  1996). The apparent  solubility product, [Al][Si], was calculated by using the correlation for sodalite or hydroxysodalite formation of Wannenmacher et al (1996) and is plotted in Figure 9.10 as dashed line. The [Al][Si] was also determined using a graph from Gasteiger et al (1992) and is shown in the Figure as dotted-dashed line. As seen from the figure, the calculations based on the model presented in this work are closer to the data than the calculations based on published correlations.  Figure 9.10. Comparison of model predictions with published correlations and industrial data. Experimental data  0.1  —  Wannenmacher et al. (1996)  Predictions  o  This work Gasteiger et al. (1992) Wannenmacher et al. (1996)  CN  j  0.001  1 1  •• I  0.01  0.1  Si concentration (mol/kg H 0) 2  138  According to the overall results of the modeling calculations, the calculated precipitation conditions agree with the experimental data well. The model takes into account the effects of anions on the precipitation conditions. Thus, it is able to calculate solubilities of A l and Si in the presence of sodium aluminosilicates in green and white liquors of kraft pulp mills. This work can be used to develop an upgraded model to predict the equilibrium state of liquors involving more complicated reactions. For example, magnesium salts are added to the green liquor containing A l species to form hydrotalcite (Mgi. Al (OH)2 x  x  (C03)x/2-nH20, 0.10 < x < 0.34) precipitates which can be removed by the green liquor clarification (Ulmgren, 1987). Thus, the aluminum content in the recovery cycle can be reduced and sodium aluminosilicate scale formation can be prevented. If the hydrotalcite formation reaction is incorporated into the model, amount of hydrotalcite formed, remaining aluminum concentration, and required input amount of magnesium salts to prevent the sodium aluminosilicate scale formation can be calculated. In order to do these calculations, knowledge of the thermodynamic properties such as equilibrium constant of hydrotalcite formation and parameters for ion activity coefficient calculation (Pitzer's parameters) are required. Calculations of the precipitation conditions with the proposed model can be used as a tool to design progressive system closure kraft mill configurations that prevent sodium aluminosilicate formation in the recovery cycle.  139  CHAPTER 10. CONCLUSIONS AND RECOMMENDATIONS  The precipitation conditions of sodium aluminosilicate scale were determined in two types of synthetic solutions which were prepared to simulate kraft pulp mill green and white liquors. The effects of the anions of OH", CO3 ", and SO4 " and the effect of 2  2  Na S on the precipitation conditions were investigated. The predominant aluminum and 2  silicon species in solutions were Al(OH)4" and Si03 " because the solutions were very 2  alkaline (pH>13). The solutions were found to tolerate more dissolved Al and Si species by increasing the amount of OH" and Na S. Increasing the concentration of Na C03 was 2  2  found to lower the solubility of Al and Si species in the synthetic green liquor thus making the scale precipitation conditions easier to achieve. No significant effect of the carbonate and sulfate ions on the solubility limit of Al and Si in the synthetic white liquor was observed. Most of the precipitates were found to have the structure of hydroxysodalte dihydrate. Only in the solutions of low OH" and high Cf concentrations of system A, a small amount (about 25 % on a molar basis) of the sodalite dihydrate precipitates was found together with hydroxysodalte dihydrate (about 75 % on a molar basis).  The above results were based  on X-ray  diffraction, chemical, and  thermogravimetric analysis. The precipitation conditions of sodium aluminosilicate scale were also determined in mill green and white liquors. The effects of varying the Al/Si ratio and the concentration of NaOH, Na C03, and Na S on the precipitation conditions were 2  2  investigated. The solubility limit of Al and Si was found to increase by increasing the  140  amount of NaOH and Na S and thus the liquor can tolerate more dissolved A l and Si. In 2  both cases the amount of hydroxyl ion in the system increases. On the other hand, increasing the concentration of N a C 0 lowers the solubility limit and the liquor tolerates 2  3  less A l and Si dissolved. The precipitates were found to have the structure of hydroxysodalite dihydrate, Na (AlSi0 )6(OH) -2H 0. 4  8  A  thermodynamics-based  2  model  2  to  predict  sodium  aluminosilicate  (hydroxysodalite dihydrate and/or sodalite dihydrate) precipitation conditions in aqueous alkaline solutions was presented. Activity coefficients  were calculated by Pitzer's  method. Comparison of the model-based calculated results with precipitation data showed good agreement. The effects of the OH", CO3 ', SO4 ", HS" ions were predicted 2  2  satisfactorily. The calculations were found to be sensitive to the value for the equilibrium constant for hydroxysodalite dihydrate. A simple isopiestic apparatus using a four-neck flask was built and employed to measure the osmotic coefficients of Na Si03 and mixed Na Si03-NaOH solutions at 2  2  298.15 K. The average relative percentage error of the osmotic coefficient measurements for the N a S i 0 and Na Si0 -NaOH systems was 0.215 ± 0.045 %. Pitzer's binary 2  3  2  3  parameters of Na -Si03 ' and mixing parameters for OH"-Si03 " and Na -0H"-Si03 ' +  2  2  +  2  were estimated using the above osmotic coefficient data. Finally, it was determined that when metasilicate is dissolved in an alkaline aqueous solution, the predominant silicic species is the metasilicic ion of Si0 ". 2  3  Osmotic coefficient data of the NaOH-NaCl-NaAl(OH)4 aqueous solutions were also obtained at 298.15 K. The results were successfully correlated with Pitzer's activity coefficient model. Pitzer's binary parameters for Na -Al(OH)4" and mixing parameters +  141 for  OFT-Al(OH) ", 4  Cr-Al(OH) ', 4  Na -OFr-Al(OH) ', +  4  and Na -Cl'-Al(OH) ' +  4  were  determined using the experimental osmotic coefficient data. The Pitzer's parameters obtained can be used to calculate activity coefficients in the system involving the Al(OH) " ion. 4  This work provides a tool based on thermodynamics that can be used to predict the equilibrium state of the green and white liquors involving undesirable sodium aluminosilicate formation caused by the accumulation of the non-process elements of Al and  Si. Thus, this work can aid the design of progressive system closure mill  configurations. Future studies may include the effect of Ca(OH)2 addition on the sodium aluminosilicate formation. This makes possible to study the interactions of Al and Si with Ca species during the causticizing reaction. In the case of the thermodynamic modeling of the sodium aluminosilicate formation, the temperature dependence on the precipitation conditions might be readily included by adding a subroutine to calculate the equilibrium constants of sodalite dihydrate and/or hydroxysodalite dihydrate formation reaction at specific temperature. In addition, more accurate prediction of the precipitation conditions might be possible if accurate thermodynamic properties such as AG£, AH£, and Cp of sodalite dihydrate and hydroxysodalite dihydrate are available. Finally, the model can be incorporated in process simulation package like a C A D S I M ™ to examine closed mill processing configuration.  142 NOMENCLATURE  a  activity  A4,  Debye-Huckel parameter  a.d.  air dried 1/2  b  universal parameter of Pitzer's equation, 1.2 (kg mol)  C°  standard heat capacity, J/mol K  C°abs  absolute heat capacity  AC °  heat capacity change of reaction, J/mol K  fn)  Debye-Hiickel limiting law term of Pitzer's equation  G  Gibbs free energy  p  p  P  G  excess Gibbs free energy  ex  AG  standard Gibbs free energy change of reaction, kJ/mol  AGf°  standard Gibbs free energy of formation, kJ/mol  AH°  standard enthalpy change of reaction, kJ/mol  AHf°  standard enthalpy of formation, kJ/mol  I  ionic strength, mol/kg H2O  K  thermodynamic equilibrium constant  Khsod  thermodynamic equilibrium constant of hydroxysodalite dihydrate  0  formation reaction Ksod  thermodynamic equilibrium constant of sodalite dihydrate formation reaction  m  molality, mol/kg H2O  143  M  molecular weight  w  n n  number of moles o x y  number of oxygen  nj  number of groups of the jth type  R  gas constant, 8.314 J/mol K  r  radius of a sphere that completely circumscribes the anion  ru  distance between the center of the central atom and the center of the surrounding oxygen atoms  S  objective function  S°  standard entropy, J/mol K  AS  0  standard entropy change of reaction, J/mol K  T  temperature  To  reference temperature  V  volume at equivalence point  e  W  w  number of kg of water  stderr  standard error  x  average value of x  z  charge of ion  Aj a  group contribution for a of jth ionic, atomic, or ligand molecule group, J/mol K  Abj  group contribution for b of jth ionic, atomic, or ligand molecule group, J/mol K  Aq  2  group contribution for c of jth ionic, atomic, or ligand molecule group,  144  JK/mol A<j  group contribution for d of jth ionic, atomic, or ligand molecule group, J/mol K  3  AHJ  contribution for group j in the prediction of AHf°, kJ/mol  Aqj  contribution for group j in the prediction of AG/, kJ/mol  Greek letters p ,P ,p ,C* Pitzer's binary parameters (0)  (1)  (2)  0, 0, 0', \|/ Pitzer's mixing parameters E  E  Xij(I)  the short-range interaction between solute species i and j in solvent of Pitzer's equation  u.  chemical potential, J mol"  Uijic  triple interaction between solute species i, j and k in solvent of Pitzer's  1  equation v  number of ions produced by 1 mol of solute  <> j  osmotic coefficient  o  uncertainty  a$  uncertainty of measured osmotic coefficient  cti, cti  numerical constant of Pitzer's equation  y  activity coefficient  Y±  mean activity coefficient  Subscripts a, X  anion  (aq)  aqueous  c, M  cation  contrib  contribution  d  index  f  formation  hsod  hydroxysodalite dihydrate, Na (AJSi04)6(OH) -2H 0  i  indicates solute i  i, j, k, 1  indicate each component in solutions  (1)  liquid  s  solute  (s)  solid  sod  sodalite dihydrate, Na (AlSi0 )6Cl -2H 0  w  solvent or water  8  8  4  2  2  2  Superscripts calc  calculated  exp  experimental  int  interpolated  o  standard state  total  total number of moles of element in the system  1, 2, R, S  indicate solutions  2  146  BIBLOGRAPHY  Anderson, G. 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Scatchard, "Osmotic and Activity Coefficients for Binary Mixtures of Sodium Chloride, Sodium Sulfate, Magnesium Sulfate, and Magnesium  158  Chloride in Water at 25°C. I. Isopiestic Measurements on the Four Systems with Common Ions", J. Phys. Chem., 72, 4048 (1968).  Zemaitis, J. F., D. M . Clark, M . Ratal, and N . C. Scrivner, Handbook of Aqueous Electrolyte Thermodynamics, AIChE, New York, 1986, pp. 13-23, 47-391.  Zettlemoyer, A. C , Nucleation, Marcel Dekker, Inc., New York, 1969.  Zheng, K., A. R. Gerson, J. Addai-Mensah, and R. St. C. Smart, "The influence of sodium carbonate on sodium aluminosilicate crystallisation and solubility in sodium aluminate solutions", J. Crystal Growth, 171, 197-208(1997).  159  APPENDIX I. Chemical Analysis by Atomic Absorption Spectrophotometer  Two types of samples containing metals were analyzed using a G B C 904 Atomic Absorption Spectrophotometer (GBC Scientific Equipment Pty Ltd., Victoria, Australia). The first type consisted of samples which were obtained from the vessel of solubility experiments. The samples were treated using a 0.5 pm pore sized polyvinylidene fluoride membrane filter (Millipore Canada, Nepean, Ontario) before analysis. In the case that metal content in sample was much higher than optimum concentration range of analysis, the sample solution was diluted with deionized. Standard solutions of Al, Si, and K analysis were prepared by dissolving AICI36H2O, Na2Si03-9H20, and KC1 in deionized water respectively. Since a lot of sodium salts were dissolved in the samples, proper amount of NaOH and Na2C03 were dissolved into the standard solutions to minimize the interference of the back matrix solution. Table A. 1.1 shows analytical data used for each element.  Table A. 1.1. Analytical data for the analysis of liquid phase alkaline samples. Element  Wavelength  Flame  (nm) Al  396.2  Nitrous oxide-  Optimum cone, range  Sensitivity  (pg/ml)  (pg/ml)  5 - 100  m  1  [ I ]  2  acetylene Si  251.6  Nitrous oxide-  5-150  acetylene ,J  404.4 145 - 580 K Air-acetylene Greenberg etal. (1992), Athanasopoulos (1993). 121  [ 2 ]  3.2  160 The other type consisted of samples prepared from the solid precipitates. Prior to the analysis, a portion (about 0.1 g) of the precipitate was added into 1 g of deionized water. Nitric acid of 1 mol/L was added to the solution. A small amount (about 1 g) of the nitric acid was enough to dissolve the solid precipitate completely. The solution was diluted with deionized water. Table A. 1.2 shows analytical data used for the analysis of precipitate dissolved samples. Commercial standard solutions from Fisher Scientific, Vancouver, B.C. were used for calibrations.  Table A. 1.2. Analytical data for the analysis of samples from the solid precipitates. Element  Wavelength  Flame  (nm)  Optimum cone, range (pg/ml)  Na  330.2  Air-acetylene  100-380  121  Al  396.2  Nitrous oxideacetylene  5 - 100  m  Si  251.6  Nitrous oxideacetylene  5-150 ^  K  404.4  766.5 Greenberg et al (1992),  Air-acetylene w  145 - 580  0.4-1.5 Athanasopoulos (1993).  121  [2]  Sensitivity (pg/ml) 2.1 1 2 3.2 0.008  161  APPENDIX II. Standard Errors and Confidence Intervals for Experimental Solubility Data  Each sample solution of solubility experiments was analyzed five times using an atomic absorption spectrophotometer. The average value of the analysis results was taken and its standard error and 95% confidence interval were calculated For example, A l content in a sample solution of experiment A l in Table 3.1 was analyzed using three standard solutions of 49.96, 131.65, and 201.27 mg Al/kg H2O prepared in our lab. The atomic absorption analysis gave five values, 121.22, 120.61, 120.61, 119.40, and 124.86 mg/kg H 0 . The values were converted to molality scale and 2  are 4.49E-3, 4.47E-3, 4.47E-3, 4.42E-3, and 4.62E-3 mol/kg H 0 . Average value was 2  given by _ 0.00449 + 0.00447 + 0.00447 + 0.00442 + 0.00462 ... ^ x= = 0.00449 mol/kg H 0 n  n  n  A  A  n  T T  2  (A.2.1)  Standard error of the value was given by  5>,-x) stderr =  2 ( X j -0.00449)  2  i=l  1  "(n-1)  K  =  5(5-1)  2  = 3.36E-5  (A.2.2)  A value of t for 4 degree of freedom (n-1) and 95% confidence interval was 2.776 (Box et al, 1978). Thus, 95% confidence interval of the value 0.00449 mol/kg H 0 is given by 2  95% confidence interval = ± txstderr = 9.33E-05  (A.2.3)  The calculated 95% confidence interval was plotted together with solubility data in Figure 8.2.  162  A P P E N D I X I H . Tables of Solubility Data  E x p e r i m e n t a l s o l u b i l i t y data are s h o w n i n the  following  Tables  A.3.1-A.3.3  together w i t h standard errors calculated b y a m e t h o d i n A P P E N D I X II.  T a b l e A . 3 . 1 . S o l u b i l i t y data for synthetic l i q u o r s o f system A . Synthetic green l i q u o r Experiment  stderr  Al (mol/kg H 0 )  stderr  Si (mol/kg H 0 )  2  2  Al  4.49E-03  3.36E-05  5.01E-03  8.55E-05  Al  4.51E-03  1.22E-04  5.06E-03  1.92E-04  Al  4.61E-03  5.89E-05  4.93E-03  9.11 E - 0 5  A2  1.01E-03  9.01E-06  2.37E-02  1.00E-03  A3  2.58E-02  9.17E-04  7.36E-04  2.58E-05  A4  1.76E-03  1.09E-05  1.41E-03  5.81E-05  A5  6.45E-03  2.68E-05  6.62E-03  2.86E-05  A6  5.91E-03  2.49E-04  6.19E-03  2.17E-04  A7  3.79E-03  6.97E-05  2.66E-03  1.08E-04  A8  6.09E-03  2.42E-05  4.79E-03  5.72E-05  A9  5.38E-03  2.88E-05  4.70E-03  2.12E-05  Si  stderr  Synthetic w h i t e l i q u o r Experiment  stderr  Al (mol/kg H 0 )  (mol/kg H 0 )  2  2  A10  1.40E-02  1.10E-04  1.47E-02  3.25E-04  All  5.05E-03  7.54E-05  3.72E-02  2.07E-04  A12  4.88E-02  3.45E-04  4.60E-03  1.30E-04  A13  7.97E-03  7.35E-05  8.31E-03  1.89E-04  A14  1.54E-02  8.93E-05  2.02E-02  3.09E-04  A15  1.32E-02  3.57E-05  1.55E-02  1.20E-04  A16  1.32E-02  1.53E-04  1.61E-02  2.02E-04  A17  1.37E-02  1.70E-04  1.37E-02  3.30E-04  A18  1.43E-02  5.61E-05  1.48E-02  1.07E-04  stderr : standard error o f measured m o l a l i t y  163  T a b l e A . 3 . 2 . S o l u b i l i t y data for synthetic l i q u o r s o f s y s t e m B . Synthetic green l i q u o r Experiment  Al  stderr  (mol/kg H 0 )  stderr  Si (mol/kg H 0 )  2  2  Bl  3.41E-03  8.99E-05  3.98E-03  1.79E-04  B2  3.20E-02  2.94E-04  2.70E-04  2.63E-05  B3  4.85E-04  1.55E-05  2.54E-02  7.12E-04  B4  3.03E-03  9.04E-05  2.56E-03  1.28E-04  B5  1.93E-02  2.04E-04  3.78E-04  1.70E-05  B6  3.92E-04  1.07E-05  1.99E-02  6.80E-04  B7  4.02E-03  1.33E-04  4.52E-03  1.78E-04  B8  2.98E-02  2.17E-04  6.51E-04  2.16E-05  B9  8.94E-04  1.81E-05  2.29E-02  4.91E-04  stderr  Si  stderr  Synthetic w h i t e l i q u o r Experiment  Al (mol/kg H 0 )  (mol/kg H 0 )  2  BIO  2  8.09E-03  2.77E-04  9.40E-03  Bll  3.01E-02  4.21E-04  2.55E-03  2.59E-05  B12  2.78E-03  3.15E-05  2.69E-02  4.36E-04  B13  9.02E-03  1.44E-04  7.22E-03  2.94E-04  B14  3.52E-02  2.64E-04  1.95E-03  5.12E-05  B15  2.13E-03  2.04E-05  2.88E-02  8.87E-04  B16  1.14E-02  9.85E-05  8.90E-03  2.72E-04  B17  3.57E-02  3.93E-04  2.76E-03  8.06E-05  B18  3.74E-03  2.62E-05  2.78E-02  7.36E-04  stderr : standard error o f measured m o l a l i t y  3.06E-04  164  T a b l e A . 3 . 3 . S o l u b i l i t y data for m i l l l i q u o r s . M i l l green l i q u o r Al  Experiment  stderr  (mol/kg H 0 )  stderr  Si  (mol/kg H 0 )  2  2  Ml  2.65E-03  1.41E-04  5.63E-03  2.24E-04  M2  1.87E-02  2.47E-04  7.80E-04  2.24E-05  M3  6.44E-04  2.55E-05  2.66E-02  5.37E-04  M4  5.54E-03  2.02E-04  5.42E-03  1.89E-04  M5  2.14E-02  3.22E-04  1.48E-03  3.57E-05  M6  1.09E-03  3.00E-05  2.65E-02  4.67E-04  M7  2.16E-03  1.00E-04  3.69E-03  1.93E-04  M8  1.92E-02  3.94E-04  3.87E-04  1.82E-05  M9  3.88E-04  1.74E-05  1.98E-02  6.36E-04  M10  5.54E-03  9.23E-05  5.33E-03  2.86E-04  M i l  3.02E-02  7.27E-04  7.78E-04  7.76E-05  M12  9.27E-04  3.09E-05  2.39E-02  3.80E-04  Al  stderr  Si  stderr  M i l l white liquor Experiment  (mol/kg H 0 )  (mol/kg H 0 )  2  2  M14  2.93E-02  4.42E-04  1.37E-03  5.37E-05  M15  1.38E-03  3.61E-05  2.94E-02  5.45E-04  M16  8.05E-03  2.19E-04  7.30E-03  2.85E-04  M17  3.19E-02  4.80E-04  1.83E-03  7.01E-05  M18  2.02E-03  4.91E-05  2.99E-02  4.04E-04  M19  5.22E-03  1.77E-04  4.54E-03  1.59E-04  M20  2.80E-02  5.38E-04  8.88E-04  3.03E-05  M21  8.35E-04  1.74E-05  2.52E-02  4.42E-04  M22  8.65E-03  8.45E-05  6.77E-03  2.40E-04  M23  3.08E-02  3.99E-04  1.89E-03  1.47E-04  M24  2.02E-03  8.58E-05  2.66E-02  3.45E-04  stderr : standard error o f measured m o l a l i t y  165  APPENDIX  I V . Calculation of Titration Curve  The titration curve shown in Figure 5.2 was constructed by a method available in the literature that shows how the pH changes as titrant is added (Harris, 1991). One example of the calculation for Na2Si03-NaOH solution titration with H C 1 solution is given below. Before any acid is added, the solution of 2 0 mL ( 0 . 0 2 L) contains 0.25 mol/L Na2Si03 and 1.0 mol/L N a O H . The amount of O H " in the initial solution is 0.02 mol ( 1 . 0 mol/L x 0.02 L) from the dissociation of N a O H . The amount of S i 0 " is 0.005 mol (0.25 2  3  mol/L x 0 . 0 2 L) from the dissociation of Na2Si03. A portion of S i 0 3 " is converted to 2  H S i 0 " and O H " by the following reaction. 3  Si0 " 2  3  +  H 0 2  <->  HSi0 "  +  x mol/L  (x + 0.02 mol/0.02 L )  3  (0.005 mol/0.02 L - x)  OH"  (A.4.1)  A value of O H " concentration at equilibrium can be calculated. Let x be the concentration of H S i 0 " . Since equilibrium constant, K(A.4.I) of the reaction ( A . 4 . 1 ) is equal to i 0 ' 3  x(x + 0 . 0 2 / 0.02)  =  1  0  .  M  0  1  2 2 0 1 7  .  7  (0.005/0.02-x)  The value of x is equal to 0.001559 mol/L by solving equation ( A . 4 . 2 ) . Thus, pH of the initial solution is equal to pH = 14 + log[OH"] = 14 + log ( 0 . 0 0 1 5 5 9 + 0.02/0.02) = 14.001  166 If the 1.0 mol/L HC1 of 10 mL (0.01 L) is added into the solution, the volume of the solution is equal to 0.02 L + 0.01 L = 0.03 L and the strong base OH" of 0.01 mol is titrated by the acid addition. Equation (A.4.1) can be rewritten as follows.  Si0 " 2  3  +  H 0  <-»  2  HSi0 "  +  3  (0.005 mol/0.03 L - x)  x mol/L  OH"  (A.4.3)  (x + (0.02-0.01) mol/0.03 L)  The value of x is equal to 0.003058 mol/L as calculated by equation (A.4.4). x(x + (0.02-0.01)/0.03)_ _ 10  22 0 1 7  (0.005/0.03-x) Thus, pH of the initial solution is equal to pH = 14 + log[OH"] = 14 + log (0.003058 + (0.02-0.01V0.03) = 13.527  Figure 5.2 was plotted with calculated pH at varying amounts of added HC1 varying from 0 to 24 mL. A similar titration curve for the Na2C0 -NaOH solution is 3  shown in Figure 5.2 and was generated by the same method using an equilibrium constant of 10"  36 7 6 9  for the reaction: C 0 " + H 0 +» HC0 " + OH". 2  3  2  3  167  A P P E N D I X V. Uncertainty of the Measured Osmotic Coefficient  Uncertainty of the measured osmotic coefficient in Tables 5.1-5.4 was calculated by the following equation available in the literature (Holman, 1994; Baird, 1995). If f is a function of the variables xi,  \2,x„, f=f(xi, x , x „ )  (A.5.1)  2  the uncertainty in the calculation of f is given by  af dx,  X ,  df  +  J  °"x  6\  K  2  •+  V^n  j  -|l/2  df  (A.5.2) J  where, a is uncertainty. An example of uncertainty calculation for the osmotic coefficient for Na2Si03 aqueous solution is given as follows. The Osmotic coefficient of Na2Si03 aqueous solution in Table 5.1 was calculated from the molality of solutes (Na2Si03) in sample solution, that (NaCl) in reference solution, and osmotic coefficient of reference solution by equation (A.5.3) ^sample N a S i 0 V  2  m 3  Na Si0 2  —  3  ^NaCI N a C i N a C l V  m  (A.5.3)  where, <> | is the osmotic coefficient, v is the number of ions produced by 1 mole of the solute, and m is the molality of the solute. Rearranging the equation (A.5.3) gives  4>sample  _  2<  l>NaCi NaCI m  3m Na Si0 2  3  Uncertainty of the osmotic coefficient of the sample solution, c r ^ , is given by  (A.5.4)  168  1/2 sample  sample NaCl  where,  <t>N«ci  f  a _  m  dm  N a C  N«ci  i  ^frsample 5m  j  L  (A.5.5) m  " Na SiOj  N.  l  S  i  oj  y  , ,  2  is the uncertainty of osmotic coefficient of NaCl solution and o  uncertainty of molality of the solute. A value of 0.01 was used for  Differentiating the equation (A.5.4) with <J>Naci, mwaci,  sample ^NaCl  2  sample  m  N  l  j  M  gi  o ,  is the  (Pitzer, 1991).  v e s  NaCl  (A.5.6)  3 NajSi0 m  ^'sample ^ N a C l  m  °  m  2<  3  l>NaCl  (A.5.7)  ^ NajSiO m  _  2 (  }  l>NaCi NaCl  ^NajSiO,  m  ^ Na Si0  (A.5.8)  m  2  3  The molality, mNaci, is calculated from the measured mass of NaCl and H 2 O as follows 8 NaCl  m NaCl  58-44 x g  (A.5.9) H j Q  where, gNaci is mass of NaCl, 58.44 is molecular weight, and g Differentiating the equation (A.5.9) with g  5m NaCl 3g aci N  d m NaCl _  dg , H  NaC  i and g  H j 0  H 2 0  2  gives  1  58.44 x g  is mass of H 0  (A.5.10) H 2 0  g NaCl  58.44 xg*  (A.5.11)  Since readability of the mass balance is 0.0001 g, the uncertainty of gNaci and g equal to 0.00005 and hence the uncertainty of mNaci is given by  H j 0  is  169  m  V  V (  dm NaCl N«CI  5e  8  -11/2  "° 2  il/2  ( 1^58.44 x g  •x 0.00005  gNaci  0.00005  x  (A.5.12)  58.44 x g H 0  H j  2  By the same logic, the uncertainty of m  N a S i 0 j  is given by 1/2  m  Nl#i03  ^122.06 x g  x 0.00005 H j 0  +  J  g Na,SiO,  (A.5.13)  x 0.00005  122.06 x g  J  where, a valuel22.06 is molecular weight of Na2SiC«3. The values of <j> ci, m ci, m Na  Na  N a 2 S i 0 j  , g ci, Na  g a N  j S  io  3  >  a  n  d  8H O 2  a  r  e  determined from  experiment. Substituting the equations (A.5.6), (A.5.7), (A.5.8), (A.5.12), and (A.5.13) to the equation (A.5.5) gives the uncertainty of the osmotic coefficient, sample solution.  , of the  170  APPENDIX VL Uncertainty of the Estimated Thermodynamic Properties and Equilibrium Constants  Uncertainty of AG ° of sodalite dihydrate (NarfAlSiO^Ch-l^O) f  The AGf° of sodalite dihydrate was estimated by the group contribution method in section 7.3.1. A simplified equation of the estimation was given by AG °(sod) = AG °(usod) + contribution by 2 H 0 f  f  (A.6.1)  2  where, the sod stands for sodalite dihydrate and the usod stands for unhydrous sodalite. Uncertainty of AGf°(sod) can be calculated using the equation (A.6.2). Aj  dAG°(sod) AGf(sod)  dAG °(usod) f  aAG  ?  (usod  >  2  f  12  dAG°(sod)  J [acontrib(2H 0) +  acon,rib(2Hj0)  2  (A.6.2)  J  where the contrib standards for contribution. The uncertainty for AGf°(usod) is equal to 16.63 kJ/mol (Komada et al, 1995). That of contrib(2H 0) is equal to contribution by 2  2 H 0 x uncertainty of the estimation method (%) = -488.634 kJ/molx2.60% = -12.70 2  kJ/mol. Thus, uncertainty of AGf°(sod) is equal to 20.92 kJ/mol.  Uncertainty of AG ° of hydroxysodalite dihydrate (Na (AlSi04) (OU) 2H 0) s  f  6  2  2  The AGf° of hydroxysodalite dihydrate was estimated by the group contribution method in section 7.3.1. A simplified equation of the estimation was given by AGf°(hsod) = AGf°(usod) - contribution by C l + contribution by (OH) 2  2  + contribution by 2H 2 0  (A.6.3)  where, the hsod stands for hydroxysodalite dihydrate and the usod stands for unhydrous sodalite. Uncertainty of AGf°(hsod) can be calculated using the equation (A.6.4).  171  f  f  ^AG°(usod)° AG? (hsod)  1/2  aAG °(hsod)  dAG °(hsod) A G  '°  2  V  dAG°(hsod) acontrib((OH) )  'contrib(Clj)  5contrib(Cl )  ( u s o d )  'contrib((OH) ) 2  (  J  2  (A.6.4)  aAG°(hsod) deontrib(2H 0)  'contrib(2H 0) 2  2  J  where the contrib standards for contribution. The uncertainty for AGf°(usod) is equal to 16.63 kJ/mol (Komada etal., 1995). That of contrib(Cl2) is equal to contribution by C b x uncertainty of the estimation method (%) = -268.220 kJ/molx2.60% = -6.97 kJ/mol. That of contrib((OH)2) is equal to contribution by (OH) x uncertainty of the estimation 2  method (%) = -460.856 kJ/molx2.60% = -11.98 kJ/mol. That of contrib(2H 0) is equal to 2  contribution by 2H2O x uncertainty of the estimation  method (%)  = -488.634  kJ/molx2.60% = -12.70 kJ/mol. Thus, uncertainty of AG °(hsod) is equal to (16.63 + (2  f  6.97) + (-11.98) + (-12.70) ) 2  2  2  1/2  = 25.10 kJ/mol. The same method was used to calculate  the uncertainties of A H / , and C ° of sodalite dihydrate (Na8(AlSi04)6Cl2-2H20) and p  hydroxysodalite dihydrate (Na (AlSi0 )6(OH)2 -2H 0) in Table 7.5. 8  Uncertainty of S° of  Si0  4  2  2 3  Average error of the S° estimation in Table 7.9 is equal to (13.48% + 5.23% + 3.44% + 39.04% + 35.51% + 13.75%) / 6 = 18.41%. Thus, uncertainty of S° for Si0 " is 2  3  equal to estimated S°(Si0 ") x 18.41% = 3.84 J/mol K =0.00384 kJ/mol K. 2  3  Uncertainty of C ° of P  Si0  2 3  Average error of the C ° estimation in Table 7.11 is equal to (39.03% + 1.42% + P  45.65% + 62.35% + 28.55% + 4.64%  +  19.33% +  1.90%) /  8 = 25.35%.  172  Thus, uncertainty of C (Si0 ') is equal to estimated C (Si0 ") x 25.35% = 82.71 J/mol 0  2  P  0  3  2  P  3  K.  Uncertainty of AH ° of Si0 " 2  r  3  The AHf° of S i 0 ' was calculated by the following equation in section 7.3.4. 2  3  A H ° ( S i 0 - ) = 2AGf°(Na ) + A G ° ( S i 0 - ) - A G ° ( N a S i 0 ) - 2AH °(Na ) + 2  f  +  2  3  f  +  3  f  2  3  f  A H ° ( N a S i 0 ) + T (2S°(Na ) + S (Si0 ") - S ° ( N a S i 0 ) ) +  f  2  0  (A.6.5)  2  3  3  2  3  Uncertainty of AH °(Si0 ") from estimated S ° ( S i 0 ' ) is given by 2  f  2  3  3  aAH°(SiQ -) ^ as°(Sio -) '  -|l/2  2  3  °AHf(SiOf-)  2  (A.6.6)  S"(SiOj") J  3  = 298.15K x 0.003 84kJ/moi K = 1.14kJ/mol  Uncertainty of In  Khsod  The equilibrium constant of hydroxysodalite dihydrate formaiton at 368.15 K was calculated using equation (2.18). f~  lnK =  \Q°  ^  RT,o J  AXJO AH°  f  1 1  11  T  T,  >  A r<° AC"  \  R  T  f  T  "N T -^-1  T  In — +  (2.18)  Uncertainty of In K is given by  ainK a  inK  = v  aAG°  G a g :  glnK + aAH° ^ J  V  'ainK  a  v  aAc;°  Differentiating the equation (2.18) with A G ° , A H ° , a n d AC° gives  ^ A C  v  1/2  (A.6.7)  173  r  ainK^ RT  = -0.4034mol/kJ 1  1  (A.6.9)  = 0.0767mol/kJ  f dlnK  2.4963molK/kJ  R  dAC°,  (A.6.8)  n  (A.6.10)  when R is the gas constant (8.314 kJ/kmol K), To is the reference temperature (298.15 K), and T is the temperature of interest (368.15 K).  The A G Q of hydroxy sodalite formation reaction (4.2) is given by AG° = AG °(hsod) + 4 A G ° ( H 0 ) + 12AG°(OFr) - 8AG °(Na ) -6AG °(Al(OH) ') +  f  f  2  f  f  f  (A.6.11)  6AGf°(Si0 ") - 2AGf (OH') 2  4  0  3  Uncertainty of AG£ from estimated AGf° (hsod) is given as follows with ignoring other uncertainties of published thermodynamic properties. -.1/2  dAG° a  AG  S  =  SAG °(hsod)  = 25.10kJ/mol  A G ? ( h s o d )  (A.6.12)  f  By the same method, uncertainty of AH° and AC° are calculated as 26.71 kJ/mol and 0.4963 kJ/mol K respectively. Substituting the values of equations (A.6.8), (A.6.9), (A.6.10), (A.6.12) and uncertainty values of AH^ and AC° to equation (A.6.7) gives uncertainty of In K is equal to ((-0.4034 mol/kJx25.10 kJ/mol) + (0.0767 mol/kJx26.71 2  kJ/mol) + (2.4963 mol K/kJx0.4963 kJ/mol K ) ) 2  dihydrate formation reaction. Uncertainty of In  2  1/2  K d, S O  = 10.41, for hydroxysodalite 8.71, for sodalite dihydrate  formation reaction (4.1) was calculated by the same method.  174 A P P E N D I X VII. Comparison of Pitzer's Parameters with Published Values  The reliability of the optimization method for the determination of Pitzer's parameters was checked for four systems, NaCl, N a S 0 , N a 2 S 2 0 2  4  3  and NaCl-Na2SC>4.  The systems were chosen since both experimental data and Pitzer's parameters were available in the literature. The same osmotic coefficient data were used to determine the parameters. The estimated parameters by Pitzer and in this work are given in Table A.7.1 together with standard deviations and sum (SUM)  ofOTP-f ' ) . 3  6  2  Table A.7.1. Comparison of Pitzer's parameters. system  parameter p  NaCl  (o)  m  c* SUM 0(0)  Na S0 2  m 4  c* SUM P  Na S 0 2  2  (0)  pd)  [ 1 ] 3  c* SUM crsoj-  NaCl-Na S0 2  121 4  *P Na Cl"SoJ" +  SUM  Pitzer (1991)  This work Parameter values Standard deviations  0.0765 0.2664 0.00127 0.00003 0.01958 1.113 0.00497 0.00456 0.06615 1.27575 0.00497 0.00015 -0.035  0.0767 0.2626 0.00121 0.00002 0.01739 1.127 0.00773 0.00007 0.06403 1.28655 0.00602 0.00006 -0.029  0.0003 0.0027 0.00005  0.007  0.007  0.001  0.00007  6.66064  References of osmotic coefficient data [1] Robinson and Stokes (1965), [2] Wu etal. (1968).  0.00092 0.018 0.00028 0.00108 0.01875 0.00037 0.004 1  175 Calculated curves of osmotic coefficient data using both parameters are shown in Figure A.7.1. As seen from the figure and the table, the parameters obtained in this work gave exactly same prediction for the NaCl system and slightly better for the NazSCu and Na2S2C«3 systems.  Figure A.7.1. Osmotic coefficients for NaCl, Na S04, and Na2S203 systems. 2  1-3  11  i  ~  i  c CO  D  £ co o o  0.6 H 0.5  0  1  2  3 molality  4  5  6  176  A P P E N D I X V I E . Sensitivity Analysis of Pitzer's Parameters  Sensitivities of Pitzer's parameters which were obtained in Chapter 6 were checked for N a S i 0 , Na Si0 -NaOH, and NaOH-NaCl-NaAl(OH) aqueous systems. 2  3  2  3  4  Values of the following least squares objective function, S, were calculated using parameter, parameter!-10%, and parameter-10%.  ±(*r-*rr  ..  s=  d=i  a  (A 8 0  +d  where (|> is the measured and (j) ' is the calculated osmotic coefficient using equation exp  03 6  (2.46). c$ is the uncertainty.  The results of the calculations are given in Tables A.8.1, A.8.2, and A.8.3. In the case of N a S i 0 aqueous system, the objective function value, S was more sensitive on 2  PSjSio,  a  n  d  3  P Na sio t an on C * (  h  2  3  a 2 S i 0 j  . The value, S, was very sensitive on 6 _ _ for OH  sio2  Na Si0 -NaOH aqueous system. For NaOH-NaCl-NaAl(OH)4 aqueous system, the value, 2  3  S, was more sensitive on P <  Na+cl  -  AI(OH)  -  and © O H - ^ ^ - than by other parameters.  Table A.8.1. Sensitivity analysis of Pitzer's parameters for N a S i 0 aqueous system. 2  Parameter o(0)  S value  0.0577  HNa SiOj  3  ParameteH-10%  S value  Parameter-10%  S value  0.06347  30.015  0.05193  29.9941  3.18615  32.960  2.60685  32.939  0.010747  6.374  0.008793  6.368  2  Od) MNa Si0 2  ,  2.8965  "Na Si0 2  3.556  3  0.00977 3  177  Table A . 8 . 2 . Sensitivity analysis of Pitzer's parameters for Na2Si03-NaOH aqueous system. Parameter  S value  Parameter+10%  S value  Parameter-10%  S value  O(0)  0.0577  0.06347  123.896  0.05193  123.840  pO)  2.8965  3.18615  116.719  2.60685  149.726  r"t>  0.00977  0.010747  113.799  0.008793  113.772  e  -0.2703  -0.29733  142.755  -0.24327  142.843  0.0233  0.02563  114.613  0.02097  114.583  HNajSiOj HNajSiOj ^NajSiOj  110.71  OH SiOj  Na OH"SiOj" +  T a b l e A . 8 . 3 . S e n s i t i v i t y analysis o f P i t z e r ' s parameters for N a O H - N a C l - N a A l ( O H ) 4 aqueous system. Parameter+10%  S value  Parameter-10%  S value  -0.0083  -0.00913  7.943  -0.00747  7.939  0.0710  0.0781  7.930  0.0639  7.931  0.00184  0.002024  7.933  0.001656  7.936  -0.24805  11.743  -0.20295  11.651  -0.2430  -0.2673  8.822  -0.2187  8.787  -0.0388  -0.04268  9.190  -0.03492  9.137  0.2377  0.26147  14.111  0.21393  14.218  Parameter O(0)  HNaAl(OH)  4  o(D  PNaAl(OH)  S value  4  P<t>  ^NaAl(OH)  4  e OH"Al(OH)i  6  -0.2255  7.929  CPAl(OH);  Na OH"Al(OH)i +  Na CrAl(OH)7 +  178  APPENDIX IX. Computational Source Codes in FORTRAN 7 7 Deternination of Pitzer's binary parameters for single electrolyte system using osmotic coefficient data Example of inputfile (shvpanuin) 'siwpam.in' •Na2Si03 s i n g l e e l e c t r o l y t e system' 'Charges o f c a t i o n and a n i o n ' 1 -2 ' s t o c h i o m e t r i c numbers o f c a t i o n & a n i o n ' 2 1 'Temperature(oC)' 25.00 'Debye-Huckel parameter a t T ( k g / m o l ) l / 2 ' 0.3915 ' i n i t i a l guess o f P i t z e r p a r a m e t e r s ' •BethaO B e t h a l C p h i • 0.0000 0.0000 0.0000 'number o f d a t a ' 16 ' M o l a l i t y , osm., Wr' 0 0603 0 8923 0 0096 0 0603 0 8926 0 0096 0 3674 0 8339 0 0091 0 8304 0 0090 0 3690 0 8188 0 0088 0 5313 0 5313 0 8188 0 0088 0 8637 0 7790 0 0083 0 8629 0 7797 0 0083 1 2063 0 7614 0 0080 1 2059 0 7617 0 0080 0 7607 0 0078 1 4928 1 4 927 0 7608 0 0078 1 8213 0 7685 0 0078 0 7674 0 0077 1 8241 2 3745 0 8021 0 0078 0 8028 0 0078 2 3725  Example of outputfile(siwpam. out) D a t a f i l e : siwpam.in Na2Si03 s i n g l e e l e c t r o l y t e Temperature : 298.15 K  system  i n i t i a l gue^s o f P i t z e r parameter : bethaO bethal cphi .00000 .00000 .00000 ite bethaO bethal cphi P(l) P(2) 1 .05770 2.89650 .00977 .0577 2.8965 2 .05770 2.89649 .00977 .0000 .0000 Iterations: 2 P i t z e r parameters obtained BethaO Bethal Cphi .05770 2.89649 .00977 S value at s o l u t i o n : 3.555965 E r r o r v a r i a n c e , sigma~2 = S/(N-P): .273536 V a r i a n c e - c o v a r i a n c e m a t r i x , COV=(inv A ) * ( s i g m a 2 ) COV(l,l)= .000015 COV(l,2)= -.000182 COV(l,3)= -.000007 COV(2,l)= -.000182 COV(2,2)= .003128 COV(2,3)= .000076 COV(3,l)= -.000007 COV(3,2)= .000076 COV(3,3)= .000003 A  S t a n d a r d d e v i a t i o n o f p a r a m e t e r s , STDEV=(diag stdev(betha0)= .003911  COVP0.5  P(3) S .009811833.6200 .0000 3.5560  stdev(bethal)= stdev(cphi) = molality 0603 0603 3674 3690 5313 5313 8637 8629 1 2063 1 2059 1 4928 1 4 927 1 8213 1 8241 2 3745 2 3725  .055932 .001764 osmexp .8923 .8926 .8339 . 8304 .8188 .8188 .7790 .7797 .7614 .7617 .7607 .7608 .7685 .7674 .8021 .8028  osmcal .8837 . 8837 . 8401 .8398 .8158 .8158 .7796 .7797 .7618 .7618 .7594 .7594 .7679 .7680 .8029 .8028  aH20cal .99712 .99712 .98346 .98339 .97685 .97685 .96427 .96430 .95156 .95157 .94058 .94058 .92721 .92709 .90210 .90220  Source code (siwpam.for) c Q c c c c c c c  siwpam.for ********************************************************** C a l c u l a t i n g P i t z e r ' s parameters(BethaO,Bethal,Cphi) a t g i v e n s e t o f m o l a l i t y and o s m o t i c c o e f f i c i e n t d a t a f o r S i n g l e e l e c t r o l y t e s o l u t i o n u s i n g a Gauss-Newton method with Weighting Factor Hyeon Park U n i v e r s i t y o f B r i t i s h Columbia March 05, 1998  Q  **********************************************************  i m p l i c i t r e a l (a-h, o-z) external g character*50 d a t a f i l e , h e a d l i n e parameter(npara=3,NP=100,MP=100,GT0L=1.OE-5,ITMAX=100) parameter(nunit=l1 r e a l f(NP),mol<NP),x(MP),osmexp(NP),osmcal(NP) r e a l JM (NP, MP) , J J (MP, MP), J f (NP), P (NP) r e a l i s (NP) , f p h i (NP) ,bphi (NP) , c p h i r e a l AI (MP,MP), xg (MP,MP) , ah2o(NP) r e a l errvar,COV(MP,MP),stdev _p(MP) r e a l wr(NP) c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Open I/O f i l e s open (5,file='siwpam.in',form='formatted') open (6,file='siwpam.out',form='formatted') c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Read i n p u t f i l e read(5,*) d a t a f i l e write(6,10) d a t a f i l e 10 f o r m a t ( / l x , ' D a t a f i l e : ',al2) read(5,*) h e a d l i n e write(6,15) headline 15 f o r m a t d x , a40) read(5,*) h e a d l i n e . r e a d ( 5 , * ) z c , za read(5,*) h e a d l i n e r e a d ( 5 , * ) v c , va v = v c + va read(5,*) h e a d l i n e read(5,*) t c t k = t c + 273.15 write(6,20) tk 20 f o r m a t ( l x , ' T e m p e r a t u r e : ' , f 6 . 2 , ' K') c Debye-Huckel parameter a t T oC read(5,*) h e a d l i n e read(5,*) aphi read(5,*) h e a d l i n e read(5,*) h e a d l i n e c  I n i t i a l guess o f b e t h a O , b e t h a l , c p h i read(5,*) x ( l ) , x ( 2 ) , x ( 3 ) write(6,25)  25  f o r m a t ( / l x , i n i t i a l guess o f P i t z e r parameter : ') write(6,30) 30 format(6x,'bethaO',3x,'bethal•,3x,'cphi') write(6,35) x ( 1 ) , x ( 2 ) , x ( 3 ) 35 format(5x,f7.5,2x,f7.5,2x,f7.5) c Number o f d a t a read(5,*) headline r e a d ( 5 , * ) ndata c Ready t o read t h e m o l a l i t y d a t a ! read(5,*) headline do 47 i = l , n d a t a read(5,*) moi(i),osmexp(i),wr(i) 47 continue c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c U n i v e r s i a l c o n s t a n t s o f P i t z e r ' s eqs b = 1.2 i f ((zc.eq.2).and.(za.eq.2)) then a l p h a l =1.4 alpha2 = 12.0 else alphal =2.0 a l p h a 2 = 0.0 end i f write(6,49)'iter','bethaO','bethal','cphi', & 'P(l)','P(2)','P(3)','S' 49 format(/Ix,a3,3(a9),2x,3(a9),lx,a6) ccccccccccccccccccccccccccccccccccccccccccccccccccccc Start iteration do 500 i t e r = l , I T M A X c I n i t i a l i z a t i o n o f S (value o f o b j e c t i v e f u n c t i o n ) S = O.OeO c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c osmotic c o e f f i c i e n t c a l c u l a t i o n do 51 i = l , n d a t a i s ( i ) = O.OeO i s ( i ) = 0.5*( m o i ( i ) * v c * ( z c * * 2 ) + m o i ( i ) * v a * ( z a * * 2 ) ) f p h i ( i ) = O.OeO fphi(i) = -aphi*(is(i)**0.5)/(l+b*is(i)**(0.5)) c I f i t i s n o t 2-2 s a l t , betha2 i s 0. bethaO = x ( l ) bethal = x(2) betha2 = O.OeO cphi = x(3) b p h i ( i ) = O.OeO b p h i ( i ) = bethaO bphi(i) = bphi(i) + bethal*exp(-alphal*(is(i)**0.5)) bphi(i) = bphi(i) + betha2*exp(-alpha2*(is(i)**0.5)) osmcal(i)=0.OeO osmcal(i)=abs(zc*za)*fphi(i)+mol(i)*(2*vc*va/v)*bphi(i) & +(mol(i)**2)*((2*(vc*va)**(3/2))/v)*cphi+l f ( i ) = O.OeO f(i) = (osmcal(i)-osmexp(i))/wr(i) S = S + f(i)**2. c c a l c u l a t e t h e a c t i v i t y o f water a h 2 o ( i ) = O.OeO ah2o(i) = 10**(-0.007823*(vc*mol(i)+va*mol(1))*osmcal(i)) 51 continue c Jacobian matrix c a l c u l a t i o n s do 54 i = l , N P do 53 j=l,MP JM(i,j)=0.0e0 53 continue 54 continue do 55 1=1,ndata JM(i,l) = mol(i)*(2*vc*va/v)/wr(i) JM(i,2) = m o l ( i ) * ( 2 * v c * v a / v ) * e x p ( - a l p h a l * ( i s ( i ) * * 0 . 5 ) ) / w r ( i ) JM(i,3) = ( m o i ( i ) * * 2 ) * ( 2 * ( ( v c * v a ) * * ( 3 / 2 ) ) / v ) / w r ( i ) • 55 continue c JJ initialization do 65 i=l,MP do 60 j=l,MP JJ(i,j1=0. 60 continue 65 continue 1  c  J J calculation do 130 i = l , n p a r a do 120 j = l , n p a r a do 110 k=l,ndata JJ(i,j)=JJ(i,j)+JM<k,i)*JM(k,j) 110 continue 120 continue 130 continue c Jf initialization do 150 i=l,MP Jf(i)=0. 150 continue c J f calculation do 180 i = l , n p a r a do 170 j = l , n d a t a J f ( i ) = J f ( i ) + J M ( j , i ) * f (j ) 170 continue Jf(i)=-Jf(i) 180 continue c c c c c c c c c c c c c c c c c c c c c c c c P c a l c u l a t i o n (to o b t a i n updated p a r a m e t e r s ) do 185 i=l,MP do 184 j=l,MP AI(1,j)=0.OeO xg(i,j)=0.0e0 184 continue 185 continue do  190 200  200 i = l , n p a r a do 190 j = l , n p a r a AI(i,j)=JJ(i,j) continue continue  do 210 c c c c  240  250  210 i = l , n p a r a xg(i,l)=Jf(i) continue  By p a s s i n g t h e s u b r o u t i n e " g a u s s j " , M a t r i x AI becomes I n v e r s e m a t r i x o f J J ( AI = and M a t r i x xg becomes P m a t r i x . ( J J * P = J f ) c a l l gaussj(AI,npara,NP,xg,nunit,MP) New x ( i ) s t e p _ l e n g t h = 1.0 do 240 1=1,npara p(i)=xg(i,l) x(i)=x(i)+p(i)*step_length continue  Inv J J )  w r i t e ( 6 , 2 5 0 ) i t e r , x ( l ) , x ( 2 ) , x ( 3 ) , P ( l ) , P(2) , P(3) ,S format(lx,i3,3(f9.5),2x,3(f9.4),fl0.4)  c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c S t a t i s t i c s o f parameters c E r r o r v a r i a n c e (errvar,sigma**2) e r r v a r = O.OeO e r r v a r = S/(ndata-npara) c V a r i a n c e - c o v a r l a n c e m a t r i x (V=(Inv A ) * ( s i g m a * * 2 ) ) do 271 1=1,MP do 270 j=l,MP COV(i,j)=0.0e0 270 continue 271 continue do 281 i = l , n p a r a do 280 j = l , n p a r a COV(i,j)=AI(i,j)*errvar 280 continue 281 continue do 290 i = l , n p a r a stdev _ p ( i ) = s q r t ( C O V ( i , i ) ) 290 continue if((abs(P(l)).LT.GTOL).AND.(abs(P(2)).LT.GTOL)) go t o 600 500 continue  p r i n t *, 'Exceeding maximum i t e r a t i o n s . . . ' stop ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 600 p r i n t *, ' ' write(6,'(//lx,a,i5)') 'Iterations: ',iter write!*,'(//lx,a,i5)') 'Iterations: ',iter w r i t e ( 6 , ' ( / l x , a ) ' ) ' P i t z e r parameters o b t a i n e d ' w r i t e ( * , ' ( / l x , a ) ' ) ' P i t z e r parameters obtained' w r i t e ( 6 , ' ( l x , a 9 , a l O , a l l ) • ) 'BethaO','Bethal','Cphi' w r i t e ! * , ' ( l x , a 9 , a l O , a l l ) • ) 'BethaO','Bethal','Cphi' write(6,610) x ( 1 ) , x ( 2 ) , x ( 3 ) 610 format(3x,f9.5,lx,f9.5,lx,f9.5) write!*,620) x(1),x(2),x(3) 620 format(lx,f9.5,2x,f9.5,2x,f9.5) w r i t e ( 6 , ' ( / l x , a , f 1 2 . 6 ) ' ) 'S v a l u e a t s o l u t i o n : ' , S w r i t e ! * , ' ( / l x , a , f 1 2 . 6 ) ' ) 'S v a l u e a t s o l u t i o n : ' , S w r i t e ( 6 , • ( / l x , a , f 1 2 . 6 ) ' ) ' E r r o r v a r i a n c e , sigma~2 = S/(N-P):', & errvar w r i t e ! * , ' ( / l x , a , f 1 2 . 6 ) ' ) ' E r r o r v a r i a n c e , sigma"2 = S/(N-P):', & errvar w r i t e ( 6 , ' ( / l x , 2 a ) ' ) ' V a r i a n c e - c o v a r i a n c e m a t r i x , ', S'COV=(inv A) * (sigma~2') ' w r i t e ( * , ' ( / l x , 2 a ) ' ) ' V a r i a n c e - c o v a r i a n c e m a t r i x , ', &'COV=(inv A ) * ( s i g m a ~ 2 ) ' do 631 i = l , n p a r a do 630 j = l , n p a r a w r i t e ( 6 , ' ( l x , a , i l , a , i l , a, f12 . 6) ' ) 'COV( ' , i , ', ' , j , ' ) = ' , C O V ( i , j ) w r i t e ( * , ' ( l x , a , i l , a , i l , a , f 1 2 . 6 ) ' ) 'COV(',i,',',j,')=',COV(i,j) 630 continue 631 continue w r i t e ( 6 , ' ( / l x , 2 a ) ' ) ' S t a n d a r d d e v i a t i o n o f p a r a m e t e r s , ', 5 ' s t d e v = ( d i a g COV)~0.5* w r i t e ( * , ' ( / l x , 2 a ) ' ) ' S t a n d a r d d e v i a t i o n o f p a r a m e t e r s , ', 6 ' s t d e v = ( d i a g COV)~0.5' write(6,'(lx,a,fl2.6) 'stdev(betha0)=',stdev _ p ( l ) write(*,'(lx,a,fl2.6) 'stdev(bethaO)=',stdev _ p ( l ) write(6,'(lx,a,fl2.6) ' s t d e v ( b e t h a l ) = ' , s t d e v _p(2) write!*,'(lx,a,fl2.6) ' s t d e v ( b e t h a l ) = ' , s t d e v _p(2) w r i t e ( 6 , • ( l x , a , f l 2 . 6 ) ' ] 'stdev(cphi) =',stdev _p(3) write)*,'(lx,a,fl2.6) 'stdev(cphi) =',stdev _p(3) w r i t e ( 6 , ' ! / l x , 4 ( a l 2 ) ) • ] 'molality','osmexp','osmcal', & 'aH20cal' do 640 i = l , n d a t a write(6,'(Ix,3(fl2.4),fl2.5)')mol(i),osmexp(i),osmcal(i), S ah2o(i) 640 continue p r i n t *, ' ' c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c C l o s e I/O F i l e s close(5) close(6,status='keep') end c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Function g(x) r e a l f u n c t i o n g(x) real x i f (x.eq.0) t h e n g = 0 else g = 2*(l-(l+x)*exp(-x))/(x**2) endif end ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc SUBROUTINE gaussj(a,n,np,b,m,mp) c. gaussj.for c : s u b r o u t i n e i m p o r t e d from "Numerical R e c i p e s F o r t r a n 77", c v e r s i o n 2.07 t o c a l c u l a t e an i n v e r s e m a t r i x o f A and s o l v e c a m a t r i x e q u a t i o n , AX=B. return END 1  c  Hyeon Park, UBC, 1998  183 Calculation of osmotic coefficient and activity coefficient using Pitzer's binary parameters for single electrolyte system Example of inputfile (sbvcaLin) •siwcal.in' 'Na2Si03 s i n g l e e l e c t r o l y t e system' 'Charges o f c a t i o n and a n i o n ' 1 -2 'stochiometric  numbers  of  cation  2 1 'Temperature(oC)' 25.00 'Debye-Huckel parameter at T 0.3915 'Pitzer parameters' 'BethaO B e t h a l Betha2 Cphi' 0.0577 2.8965 0.0000 0.00977 'number o f m o l a l i t y data' 129 •Molality' 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700  4  anion'  (kg/mol)1/2'  r  1.9000 2.0000 2.2000 2.4000 2.6000  Example of inputfile(siwcal out) Datafile: siwcal.in Na2Si03 s i n g l e e l e c t r o l y t e Temperature Pitzer  :  298.15  parameter  bethaO .05770  system  K  :  bethal 2.89650  betha2 .00000  cphi .00977  molality 0100 0200  osmcal . 9158 . 9006  aH20 .99951 .99903  act.coef .7415 .6852  0300  .8932  .99855  .6523  0400  .8888  .99808  .6293  0500 0600  .8858 .8837  .6119 .5979  0700  . 8821  .99761 .99714 .99667  9000  .7714 .7767  .92385 .91948  .2979  .7895  .91041  1 2  .5862  .2961 .2937  2  0000 2000  2  4000  .8051  .90085  .2931  2  6000  .8232  .89078  .2941  .  Source code (siwcalfor) c  siwcal.for  **********************************************************  c  c  Calculating  c  at  c  and P i t z e r ' s  c  for  given  osmotic  molality,  Single  coefficient  parameters(BethaO,  electrolyte  c j-  Bethal,  coefficient parameter),  Betha2,  Cphi)  solution  c c  and a c t i v i t y  temperature(Debye-Huckel  Hyeon University March  of  Park  British  10,  Columbia  1998  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  implicit real (a-h, o-z) external g character*50 datafile,headline r e a l m o i , i s , lngam c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Open I/O Files open (5,file='siwcal.in',form='formatted') open (6,file='siwcal.out',form='formatted') c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Read I n p u t File  10  15  20 c  c  25 30 35 c  read(5,*) datafile write(6,10) datafile format(/lx,'Datafile:  ',al2)  read(5,*) headline write(6,15) headline formatdx, a40) read(5,*) headline r e a d ( 5 , * ) z c , za read(5,*) headline r e a d ( 5 , * ) v c , va v = vc + va read(5,*) headline read(5,*) tc tk = t c + 273.15 write(6,20) tk format(lx,'Temperature : ',f6.2,' K') D e b y e - H u c k e l p a r a m e t e r at T oC read(5,*) headline read(5,*) aphi Read P i t z e r ' s parameters read(5,*) headline read(5,*) headline read(5,*) bethaO, b e t h a l , betha2, cphi write(6,25) format(/lx,'Pitzer parameter : ') write(6,30) format(6x,'bethaO',3x,'bethal',3x,'betha2',4x,'cphi') write(6,35) bethaO, b e t h a l , betha2, cphi format(5x,f7.5,2x,f7.5,2x,f7.5,2x,f7.5) Number o f d a t a  read(5,*) headline read(5,*) ndata c Ready to read the m o l a l i t y read(5,*) headline cccccccccccccccccccccccccccccccc b if  =  data  !  Universial  constants  of  Pitzer's  eqs  1.2 ((zc.eq.2).and.(za.eq.2))  alphal alpha2 else  then  =1.4 =12.0  alphal  =2.0  alpha2 endif  =0.0  write(6,50)'molality','osmcal','aH20','act.coef' 50  format(/lx,4(al2)) write!*,51) ' m o l a l i t y ' , 'osmcal', 'aH20',  'act.coef  51 format(/lx,4(al2)) ccccccccccccccccccccccccccccccccccccccccccccccccccccc do 1000 i t e r = 1, ndata r e a d ( 5 , * ) moi ccccccccccccccccccccccccccccccccccccc is = 0.0 is = fphi c  0.5*( mol*vc*(zc**2) =0.0  osmotic  coefficient  + mol*va*(za**2)  fphi = --aphi*(is**0.5)/(l+b*is**(0.5)) If i t i s n o t 2-2 s a l t , b e t h a 2 i s 0. bphi bphi  = =  0.0 bethaO  bphi = bphi + bphi = bphi + o s m c a l = O.OeO osmcal osmcal  bethal*exp(-alphal*(is**0.5)) betha2*exp(-alpha2*(is**0.5))  = osmcal + = osmcal +  abs(zc*za)*fphi moi*(2*vc*va/v)*bphi  Start  )  iteration  calculation  c  osmcal = osmcal + m o l * * 2 * ( ( 2 * ( v c * v a ) * * { 3 / 2 ) ) / v ) * c p h i osmcal = osmcal + 1.0 C a l c u l a t e the a c t i v i t y of water  ah2o = O.OeO ah2o = 1 0 * * ( - 0 . 0 0 7 8 2 3 * ( v c * m o l + v a * m o l ) * o s m c a l ) ccccccccccccccccccccccccccccccccccccccc activity coefficient fgam = 0.0 fgam = (is**0.5)/(1+b*(is**0.5)) fgam =  fgam  +  (2/b)*log(1+b*(is**0.5))  fgam = fgam*(-aphi) bmx = O . O e O bmx = b e t h a O bmx = bmx + b e t h a l * g ( a l p h a l * ( i s * * 0 . 5 ) ) bmx = bmx + b e t h a 2 * g ( a l p h a 2 * ( i s * * 0 . 5 ) ) b g a m = bmx + b p h i cgam = 3.0*cphi/2.0 l n g a m = O.OeO lngam = abs(zc*za)*fgam lngam = lngam + mol*(2*vc*va/v)*bgam lngam = lngam + (mol**2)*(2*((vc*va)**(3/2))/v)*cgam gam = exp(lngam) write(6,55) mol,osmcal,ah2o,gam 55 format(lx,2(fl2.4),fl2.5,fl2.4) write!*,56) mol,osmcal,ah2o,gam 56 format(lx,2(f12.4),f12.5,f12.4) 1000 continue c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c C l o s e I/O close(5) close(6,status='keep') end cccccccccccccccccccccccccccccccccccccccccccccccccc Function real function g(x) real x if  (x.eq.0) then g = 0 else g = 2*(l-(l+x)*exp(-x))/(x**2) endif end c  Hyeon  Park,  UBC,  1998  Files  g(x)  186 Deternination of Pitzer's mixing parameters for multi-component electrolyte system using osmotic coefficient data Example of inputfile (nasbvpam.in) ' nasiwpam.in' 'NaOH-Na2Si03 multi-component e l e c t r o l y t e system' ' C h a r g e s o f c a t i o n and a n i o n ( N a + , O H - , S i 0 3 2 - ) ' +1 - 1 -2 'Temperature (oC)' 25.00 'Debye-Huckel parameter at T ( k g / m o l ) l / 2 ' 0.3915 ' P i t z e r ' s parameters for s i n g l e e l e c t r o l y t e system' 'NaOH' •BethaO B e t h a l C p h i ' 0.0864 0.253 0.0044 •Na2Si03' 'BethaO Bethal C p h i ' 0.0577 2.8965 0.00977 ' I n i t i a l guess of P i t z e r ' s parameters f o r multicomponent 'Theta(OH,Si03) Psi(OH,Si03,Na)' 0.0000 0.0000 'Number o f d a t a ' 26 •Molality(Na+, OH-, Si032-), o s m , w r (No o f d a t a : 2 6 ) ' 0 0104 0 1397 0 0466 0 0466 0 9625 0 0103 0 1 4 0 5 0 0 4 6 8 0 0 4 6 8 0 9572 0 0101 0 2911 0 0970 0 0970 0. 9267 0 0100 0 2920 0 0973 0 0973 0 9239 0 0096 0 4 4 42 0 1 4 8 1 0 1 4 8 1 0 8 8 1 6 0 0097 0 4395 0 1465 0 1465 0 8910 0 0 1 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4  7005 7015 0670 0558 4192 4221 5789 5868 3577 3537 8798 8747 0557  0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1  2335 2338 3557 3519 4731 4740 5263 5289 7859 7846 9599  9582 0186 0181 0542 9807 3269 9739 3246 4861 4954 4 901 1 4 9 6 7 9904 1 6 6 3 5 9888 1 6 6 2 9  0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1  2335 2338 3557 3519 4731 4740 5263 5289 7859 7846 9599  9582 0186 0181 3269 3246 4954 1 4 967 1 6635 1 6629  0 0 0 0 0 0 0 0 0 0 0  8624 8611 8352 8440 8253 8236 8216 8175" 8222 8236 8323  0 0 0 0 0 0 0 0 0 0 0  0 0 0 0  8338 8408  0 0 0 0 0 0  8412 8843 0 8858 0 9027 0 9019 0 9326 0 9329  0 0 0  0094 0093 0090 0091 0088 0088 0087 0087 0085 0085 0084 0085 0085 0085 0085 0086 0085 0085 0086 0086  Example of outputfile(nasiwpam. out) Datafile: nasiwpam.in NaOH-Na2Si03 multi-component e l e c t r o l y t e system Temperature : 298.15 K i n i t i a l guess of P i t z e r parameter : thetaa psia .00000 .00000 iter thetaa psia P(l) P(2) 1 -.27031 .02330 2 -.27031 .02330 Iterations: 2 P i t z e r parameters obtained  -.27031 .00000  Theta(OH,Si03) Psi(OH,Si03,Na) -.27031 .02330 S value at s o l u t i o n : 110.705500 E r r o r v a r i a n c e , sigma~2 = S/(N-P):  S 02330********** 00000110.705500  4.612729  system'  Variance-covariance matrix, C0V(1,1)= .001472 COV(l,2)= -.000351 COV(2,l)= -.000351 COV(2,2)= .000090  COV=(inv A)*(sigma~2)  Standard deviation of parameters, stdev =(diag stdev thetaa(OH-,Si032-) = .038362 stdev psia(Na+,OH-,Si032-)= .009495 osmcal mOHmSi032osmexp mNa+ .8993 1397 .0466 .9625 .0466 .8993 . 0468 .9572 1405 .0468 .9267 .8891 .0970 2911 .0970 2920 4442 4395  .0973 .1481 .1465  .0973 .1481 .1465-  . 9239 .8816 .8910  .8891 .8805 .8808  7005  .2335 .2338 .3557  .2335  .8624 .8611  .8663 . 8663  .3519 .4731 . 4740 .5263 .5289 .7859 .7846 . 9599  .3519 . 4731  .8352 .8440 .8253 .8236 .8216 .8175 .8222 .8236 . 8323  . 8481 .8487  . 9582 1.0186 1.0181  . 9582 1.0186  . 8338 . 8408 .8412  .8312 .8357 .8357  1.3269  .8843  .8736  .8858 .9027  .8732 . 9036 . 9038 . 9394 . 9393  7015 1 1 1 1 1 1 2 2 2  0670 0558 4192 4221 5789 5868 3577 3537  8798 2 8747 3 0557 3 0542 3 9807  .2338 .3557  .4740 .5263 . 5289 .7859 .7846 . 9599  1.0181  3 9739 4 4861 4 4901 4 9904  1.3246 1.4954 1.4967  1.3269 1.3246 1.4954 1 . 4 967  1.6635  1.6635  4  1.6629  1.6629  9888  .8351 .8350 .8308 .8306 .8239 . 8239 . 8313  . 9019 . 9326 . 932 9  COV)"0.5 aH20cal .99623 .99622 .99226 .99224 .98833 .98845 .98195 .98192 .97320 .97346 .96504 .96498 .96138 .96120 .94335 .94344 .93065 .93078 .92620 .92624 .90087 .90107 .88542 .88529 .86871 .86877  Source code (nashvpanufor) c c  nasiwpam.for  ***************************************************************  c  Calculating  c  molalities  c  system  Pitzer's  p a r a m e t e r s ( t h e t a and p s i )  and o s m o t i c  coefficient  c  Hyeon  c  University  c c  of  March  data  for  at  given  set  of  multi-component  Park  British 09,  Columbia  1998  i m p l i c i t real (a-h, o-z) character*50 datafile,headline  c  parameter(npara=2,NP=100,MP=100,GTOL=l.OE-6,ITMAX=5000) parameter(nunit=l) parameter(ncat=l,nani=2) integer zc(neat),za(nani) r e a l a p h i , b, a l p h a l , alpha2, s r e a l bethaO(neat,nani),bethal(neat,nani),betha2(neat, nani) real cphi(neat,nani) real thetac(neat,neat),ethetac(neat,neat),ethetape(neat,neat) real  thetaa(nani,nani),ethetaa(nani,nani),ethetapa(nani,nani)  real psic(neat,neat,nani),psia(nani,nani,neat) real x(MP),mc(ncat,NP),ma(nani,NP),osmexp(NP) real is(NP),mt(NP),z(NP),bphi(neat,nani) real c(neat,nani),phic(neat,neat),phipc(neat,neat) real  phia(nani,nani),phipa(nani,nani),phiphic(neat,neat)  real real  phiphia(nani,nani),osml(NP),osm2(NP),osm3(NP) osm3a(NP),osm4(NP),osm4a(NP),osmcal(NP)  real  f ( N P ) , a h 2 o ( N P ) , JM ( N P , M P ) , J J ( M P , M P )  real real  J f (MP) , p ( M P ) , A I ( M P , M P ) , x g ( M P , M P ) e r r v a r , C O V ( M P , M P ) , s t d e v _p(MP)  real  wr(NP)  cccccccccccccccccccccccccccccccccccccccccccccccccccccc open ( 5 , f i l e = ' n a s i w p a m . i n ' , f o r m = ' f o r m a t t e d ' ) open ( 6 , f i l e = ' n a s i w p a m . o u t ' , f o r m = ' f o r m a t t e d ' )  Open  I/O  Files  c  Charge  of  do 10  species  10 i = 1 , zc(i) = 0 continue  neat  do  20 k = 1 , nani za(k) = 0 20 continue ccccccccccccccccccccccccccccccccccccccccccccccccccccc c Read '~.in'  30 c  read(5,*) datafile write(6,30) datafile format(/lx,"Datafile: ',al2) Read • - m u l t i - c o m p o n e n t e l e c t r o l y t e  40 c  read(5,*) headline write(6,40) headline format(lx,a) Read c h a r g e o f c a t i o n  and  52 53  input  file  system'  anion  read(5,*) headline read(5,*) zc(1),za(1),za(2) c Read t e m p e r a t u r e (oC) read(5,*) headline read(5,*) tc tk = t c + 273.15 write(6,45) tk 45 format(lx,'Temperature : ',f6.2,' K') c Read D e b y e - H u c k e l p a r a m e t e r at T oC read(5,*) headline read(5,*) aphi cccccccccccccccccccccc I n i t i a l i z a t i o n of P i t z e r ' s d o 51 i = 1 , neat d o 50 k = 1 , nani b e t h a 0 ( i , k ) = O.OeO b e t h a l ( i , k ) = O.OeO b e t h a 2 ( i , k ) = O.OeO cphi(i,k) = O.OeO 50 continue 51 continue d o 53 i = 1 , neat d o 52 j = 1 , neat thetacfi,j) = ethetacli,j) = ethetapefi,j) =  Read  parameters  as  O.OeO  O.OeO O.OeO O.OeO  continue continue d o 55 k = 1 , nani d o 54 1 = 1 , nani thetaa(k,1) ethetaa(k,l) ethetapa(k,l)  54 55  = 0.OeO = O.OeO = O.OeO :  continue continue d o 58 i = 1 , neat d o 57 j = 1 , neat d o 56 k = 1 , nani psic(i,j,k) = O.OeO  56 57 58  continue continue continue d o 61 k = 1 , nani d o 60 1 = 1 , nani d o 59 i = 1 , neat psia(k,l,i) = O.OeO  59  continue  60 continue 61 continue c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Reading P i t z e r ' s parameters c Read ' P i t z e r ' s p a r a m e t e r s f o r s i n g l e e l e c t r o l y t e s y s t e m ' c  read(5,*) headline Read b e t h a O , b e t h a l , c p h i read(5,*)  headline  read(5,*)  headline  of  Na+  OH-  c  read(5,*) bethaO(1,1),bethal(1,1),cphi(1,1) R e a d b e t h a O , b e t h a l , c p h i o f Na+ S i 0 3 2 read(5,*) read(5,*)  c  headline headline  read(5,*) bethaO(1,2),bethal(1,2), cphi(1,2) I n i t i a l guess o f t h e t a a ( O H - , S i 0 3 2 - ) & psia(OH-,S1032-,Na+) read(5,*) headline read(5,*) headline read(5,*) x(l),x(2) write(6,70)  70  format(/lx,'initial write(6,71)  71  c  format(6x,'thetaa',6x, 'psia') write(6,72) x(l),x(2) format(5x,f7.5,2x,f7.5) Number o f d a t a read(5,*) headline read(5,*) ndata Ready to read the m o l a l i t y d a t a  c c c c c  read(5,*) headline Molality of species mc(l,ndata) : Na+ ma(l,ndata) : OHma(2,ndata) : S1032osmexp(ndata): osmotic  72 c  guess  of  P i t z e r parameter  :  ')  !  coefficient  data  do  80 n = l , n d a t a read(5,*) mc(1,n),ma(1,n),ma(2,n), osmexp(n),wr(n) 80 continue c U n i v e r s a l c o n s t a n t s o f P i t z e r ' s e q . ( n o t 2-2 e l e c t r o l y t e ) b = 1.2 a l p h a l = 2.0 a l p h a 2 = O.OeO write(6,90) ' i t e r ' , ' t h e t a a ' , ' p s i a ' , • P ( 1 ) ' , ' P ( 2 ) ' , ' S ' 90 format(/lx,a5,5(a9)) cccccccccccccccccccccccccccccccccccccccccccccccccccc Start iteration do 500 i t e r = 1, itmax c I n i t i a l i z a t i o n of S (value of o b j e c t i v e function) c  c  S = O.OeO U p d a t i n g p a r a m e t e r s t o be o b t a i n e d thetaa(l,2) = x(l) p s i a ( l , 2 , l ) = x(2) do 100 n = l , n d a t a i o n i c s t r e n g t h and t o t a l m o l a l i t y i s ( n ) = O.OeO mt(n) do  110  110  = O.OeO  is(n)  i = 1, n e a t mc(i,n)*(zc(i)**2) = is(n) +  mt(n)  = mt (n)  + mc ( i , n)  continue do  111  is(n)  k = 1, n a n i ma(k,n)*(za(k)**2) = is(n) +  111  mt(n) = mt(n) + continue is(n)=0 5*is(n)  c  Calculation  of  ma(k,n)  z  z ( n ) = O.OeO do 120 i = 1, n e a t z(n) = z(n) + m c ( i , n ) * a b s ( z c ( i ) ) 120  121  continue d o 121 k = 1 , n a n i z(n) = z(n) + m a ( k , n ) * a b s ( z a ( k ) ) continue  cccccccccccc Calculation'of d o 131 i = 1 , n e a t do 130 k = 1, n a n i b p h i ( i , k ) = O.OeO  bphi(cat,ani)  and c ( c a t , a n i )  coefficients  bphi(i,k) = bethaO(i,k)+bethal(i,k)*exp(-alphal*sqrt(is(n))) bphi(i,k) = bphi(i,k)+betha2(i,k)*exp(-alpha2*sqrt(is(n))) c ( i , k ) = O.OeO 130  c(i,k) = continue  cphi(i,k)  /  ( 2*(  (abs(zc(i)*za(k)))**0.5  )  )  131 continue ccccccc Calculatiion of phic(cat,cat), c and p h i p a ( a n i , a n i )  phipc(cat,cat),  phia(ani,ani),  d o 141 i = 1 , neat d o 14 0 j = 1 , neat phic(i,j) = O.OeO phipc(i,j) = O.OeO phic(i,j) phipc(i,j)  = =  thetac(i,j) + ethetapc(i,j)  ethetac(i,j)  140 141  continue continue d o 151 k = 1 , nani do 150 1 = 1 , nani phia(k,l) - O.OeO phipa(k,l) = O.OeO phia(k,l) = thetaa(k,l) + ethetaa(k,l) phipa(k,l) = ethetapa(k,1) 150 continue 151 continue c c c c c c c c c c c c c c c c C a l c u l a t i o n o f p h i p h i c ( c a t , c a t ) and p h i p h i a ( a n i , a n i ) d o 161 1 = 1 , (ncat-1) d o 160 j = ( i + 1 ) , neat p h i p h i c d , j ) = O.OeO phiphic(i,j) =phic(i,j) + is(n)*(phipc(i,j)) 160 continue 161  continue  d o 171 k = 1 , (nani-1) do 170 1 = ( k + 1 ) , n a n i p h i p h i a ( k , l ) = O.OeO phiphia(k,l) = phia(k,l) + is(n)*(phipa(k,1)) 170 continue 171 continue ccccccccccccccccccccccccccccccccccccc C a l c u l a t i n g osmotic c o e f f i c i e n t o s m l ( n ) = O.OeO osml(n) aphi*(is(n)**(3./2.))/(1+b*{is(n)**0.5)) osm2(n) = O.OeO d o 181 i = l , n c a t do 180 k = 1, n a n i osm2(n)=osm2(n)+(mc(i,n)*ma(k,n))*(bphi(i,k)+z(n)*c(i,k)) 180 continue 181 continue osm3(n) = O.OeO d o 192 i = 1 , (ncat-1) d o 191 j = ( i + 1 ) , neat o s m 3 a ( n ) = O.OeO do 190 k = 1, nani osm3a(n) 190 191 192  continue osm3(n) =  =  osm3a(n)  + ma(k,n)  *  psic(i,j,k)  osm3(n)+((mc(i,n)*mc(j,n))*(phiphic(i,j)+osm3a(n)))  continue continue osm4(n) = 0.OeO d o 202 k = 1 , (nani-1) d o 201 1 = (k+1), n a n i o s m 4 a ( n ) = O.OeO do 200 i = 1, neat osm4a(n)  200  =  osm4a(n)  + mc(i,n)  *  psia(k,l,i)  continue osm4(n)  =  osm4(n)+((ma(k,n)*ma(1,n))*(phiphia(k,1)+osm4a(n)))  201 202  continue continue  c  o s m c a l ( n ) = O.OeO o s m c a l ( n ) = o s m l ( n ) + osm2(n) + osm3(n) osmcal(n) = (2.0/mt(n))*osmcal(n) o s m c a l ( n ) = o s m c a l ( n ) + 1. f(n) = (osmcal(n)-osmexp(n))/wr(n) S = S + f(n)**2. C a l c u l a t e the a c t i v i t y of water  100  ah2o(h) = ah2o(n) = continue  +  O.OeO 10**(-0.007823*mt(n)*osmcal(n))  osm4(n)  cccccccccccccccccccccccccccccccccccccccccccccccc c Jacobian matrix calculations  Gauss-Newton  routine  do  290  290 n = l , n d a t a J M ( n , l ) = O.OeO J M ( n , 2 ) = O.OeO continue  do  300 c  300 n = l , n d a t a JM(n,l) = (2.0/mt(n))*(ma(1,n)*ma(2,n))/wr(n) JM(n,2) = (2.0/mt(n))*(mc(1,n)*ma(1,n)*ma(2,n))/wr(n) continue JJ initialization  do  310 311 c  311 m = l , n p a r a do 310 m m = l , n p a r a JJ(m,mm) = O.OeO continue continue JJ calculation  do  320 321 322 c  330 c  340  322 m = l , n p a r a d o 321 m m = l , n p a r a d o 320 n = l , n d a t a JJ(m,mm) = JJ(m,mm) + J M ( n , m ) * J M { n , m m ) continue continue continue Jf initialization do 330 m = l , n p a r a Jf(m) = O.OeO continue Jf calculation d o 341 m = l , n p a r a d o 34 0 n = l , n d a t a Jf(m)=Jf(m)+JM(n,m)*f(n) continue Jf(m)=-Jf(m)  341 continue cccccccccccccccccccccccc P calculation d o 351 i = 1 , M P d o 350 j = 1 , M P A I ( i , j ) = O.OeO x g ( i , j ) = O.OeO 350 351  360 361  (to  obtain  updated  parameters)  continue continue d o 361 i=l,npara d o 360 j = l , n p a r a AI(i,j)=JJ(i,j) continue continue do  365  365 i=l,npara xg(i,l)=Jf(i) continue  c  By p a s s i n g  c c  M a t r i x A I b e c o m e s I n v e r s e m a t r i x o f J J (AI = and M a t r i x xg becomes P m a t r i x . (JJ*P = Jf)  the  subroutine  "gaussj",  c  call New  Inv  JJ)  gaussj(AI,npara,NP,xg,nunit,MP) x(i)  step_length = 1.0 do 370 i=l,npara p(i)=xg(i,l) 37 0 380  x(i)=x(i)+p(i)*step_length continue write(6,380) iter, x(1),x(2),p(1),p(2),s f o r m a t ( l x , 1 5 , 2 ( f 9 . 5 ) , 2 x , 2 ( f 9 . 5 ) , f 1 0 . 6)  cccccccccccccccccccccccccccccccccccccccccccc c Error variance (errvar,sigma**2)  c  e r r v a r = O.OeO errvar = S/(ndata-npara) Variance-covariance matrix  390  d o 391 i=l,MP d o 390 j = l , M P COV(i,j)=0.0e0 continue  (V=(Inv  Statistics  A)*(sigma**2))  of  parameters  192  391  continue  400  d o 401 1=1,npara d o 400 j = l , n p a r a COV(i,j)=AI(i,j)*errvar continue  401  410  continue d o 410 1=1,npara stdev _p(i)=sqrt(COV(i,i)) continue  500  if((abs(p(l)).LT.GTOL).AND.(abs(p(2)).LT.GTOL)) continue  go t o  ccccccccccccccccccccccccccccccccccccccccccccccccccccc print *, 'iter=',iter  600  610 620  600  End o f  loop  500  print *, ' E x c e e d i n g maximum i t e r a t i o n s . . . ' stop print *, ' • write(6,'(//lx,a,i5)') 'Iterations: ',iter w r i t e ! * , ' ( / / l x , a , 1 5 ) ') 'Iterations: ',iter write(6,'(/lx,a)') ' P i t z e r parameters obtained' write(*,'(/lx,a)') ' P i t z e r parameters obtained' write(6,•(lx,al5,2x,al6)•) 'Theta(OH,Si03)',' Psi(OH,S103,Na)' write!*,'(lx,al5,2x,al6)•) 'Theta(OH,Si03)',' Psi(OH,Si03,Na)' write(6,610) x(l),x(2) format(lx,f9.5,8x,f9.5) write(*,620) x(l),x(2) format(lx,f9.5,8x,f9.5) write(6, ' (/lx,a,f12.6)') 'S v a l u e at s o l u t i o n : ' , S write!*,'(/lx,a,f12.6)') 'S v a l u e at s o l u t i o n : ' , S w r i t e ( 6 , ' ( / l x , a , f l 2 . 6) ' ) ' E r r o r v a r i a n c e , s i g m a ' 2 = S / ( N - P ) : ' , & errvar write(*,'(/lx,a,f12.6)') ' E r r o r v a r i a n c e , sigma~2 = S / ( N - P ) : ' , & errvar write(6,'(/lx,2a)')'Variance-covariance matrix, ', S'COV=(inv A)*(sigma~2)' write(*,'(/lx,2a)')'Variance-covariance matrix, ', S ' C 0 V = ( i n v A) * ( s i g m a 2 ) ' d o 631 i=l,npara d o 630 j = l , n p a r a write(6,•(lx,a,il,a,il,a,f12.6)•) 'COV(',i,',',j,')=',COV(i,j) write(*,'(lx,a,il,a,il,a,fl2.6)•) •COV(',i,',',j,')=',COV(i,j) ,  / s  630 631  continue continue write(6,'(/lx,2a)')'Standard & 'stdev =(diag COV) 0.5' write(*,'(/lx,2a)')'Standard  deviation  of  parameters,  ',  deviation  of  parameters,  ',  A  & 'stdev =(diag COVl'-O.S' write(6,'(lx,a,fl2.6)') 'stdev thetaa(0H-,Si032-) =*,stdev write!*,*(lx,a,fl2.6)') 'stdev thetaa(OH-,Si032-) =',stdev write(6,'(lx,a,fl2.6)') 'stdev psia(Na+,0H-,S1032-)=',stdev write(*,'(lx,a,fl2.6)') 'stdev psia(Na+,0H-,Si032-)=',stdev write(6,'(/lx,6(a9))') 'mNa+','mOH-','mSi032-','osmexp',  _p(1) _p(1) _p(2) _p(2)  & 'osmcal','aH20cal' d o 640 n=l,ndata & 641 640  write(6,641) mc(l,n),ma(l,n),ma(2,n),osmexp(n),osmcal(n), ah2o(n) format(lx,5(f9.4),f9.5) continue  print  *,  '  '  ccccccccccccccccccccccccccccccccccccccccccccccccccccc close(5)  Close  I/O  Files  close(6,status='keep') end ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc SUBROUTINE g a u s s j ( a , n , n p , b , m , m p ) c g a u s s j . f o r s u b r o u t i n e imported from "Numerical Recipes Fortran c  version return END  c  Hyeon  2.07  Park,  to  1998  calculate  an  inverse  matrix  of  A and  solve  77",  a matrix  equation,  AX=B.  193 Calculation of osmotic coefficient and activity coefficient using Pitzer's binary and mixing parameters for multi-component electrolyte system Example of inputfile (nashvcaLin) 'nasiwcal.in' 'NaOH-Na2Si03 multi-component e l e c t r o l y t e system' ' C h a r g e s o f c a t i o n and a n i o n ( N a + , O H - , S i 0 3 2 - ) ' +1 - 1 -2 'Temperature(oC)' 25.00 'Debye-Huckel parameter at T ( k g / m o l ) l / 2 ' 0.3915 ' P i t z e r ' s parameters f o r s i n g l e e l e c t r o l y t e •NaOH' 'BethaO Bethal Cphi* 0.0864 0.253 0.0044 •Na2Si03* 'BethaO Bethal Cphi' 0.0577 2.8965 0.00977 •Theta(0H,Si03) Psi(OH,S103,Na)' -0.2703 0.0233  system'  'Number o f d a t a ' 80 'Molality(Na+, OH-, Si032-)' 0.0300 0.0100 0.0100 0.0600 0.0200 0.0200 0.0900 0.0300 0.0300 0.1200 0.0400 0.0400 0.1500 0.0500 0.0500 7.8000 8.1000 8.4000 8.7000 9.0000  2.6000 2.7000 2.8000 2.9000 3.0000  2.6000 2.7000 2.8000 2.9000 3.0000  Example of outputfile(nasiwcal.out) Datafile:  nasiwcal.in  Na0H-Na2Si03 multi-component e l e c t r o l y t e system Temperature : 298.15 K mNaOH g a m N a O H m N a 2 S i 0 3 g a m N a 2 S i 0 3 osmcal aH20 .7177 .99917 .0100 9250 .0100 8399  gamNa  gamOH g a m S i 0 3  .8569  .8233  .5035  9120  .99836  . 8301  .7721  .4192  .6065  9054 9013  .99756 .99676  .8163 . 8078  .7379 .7118  .3730 .3420  .0500  .5899  8984  .99596  . 8022  .6903  .3189  9347 9877  2.6000 2.7000  .5862 .6187  1 2334 1 2734  .74914 .73369  1 .5756 1 .6682  .5545 .5848  . 0812 . 0851  .0200  8006  .0200  .0300 . 0400  7761 7583  .0300 .0400  .0500  7442  2.6000 2.7000  . 6610 .6287  2.8000  1  0462  2.8000  .6546  1 3150  .71776  1 .7696  .6185  .0896  2.9000  1 1108  2.9000 3.0000  1 .8806 2 . 0021  .6561  1  1 3581 1 4028  .70137  3.0000  .6942 .7381  .0946 .1003  1822  .68453  .6980  Source code (nasiwcalfor) c  nasiwcal.for  c  c c  Calculating osmotic coefficientat given  c o e f f i c i e n t , water a c t i v i t y , and a c t i v i t y s e t o f m o l a l i t i e s and P i t z e r ' s parameters  c c  for  system Hyeon  multi-component  c  University  c  of  March implicit external  real g,gp  (a-h,  Park  British 10,  o-z)  character*50 datafile,headline parameter(NP=200) parameter(ncat=l,nani=2) integer zc(neat),za(nani)  Columbia  1998  real real real  bethaO(neat,nani),bethal(neat,nani),betha2(neat,nani) cphi(neat,nani) thetac(neat,neat),ethetac(neat,neat),ethetape(neat,neat)  real real  thetaa(nani,nani),ethetaa(nani,nani),ethetapa(nani, psic(neat,neat,nani),psia(nani,nani,neat)  real  nani)  mc(neat,NP),ma(nani,NP)  real real  is(NP),mt(NP),z(NP),bphi(neat, nani) c(neat,nani),phic(neat,neat),phipc(neat,neat)  real  phia(nani,nani),phipa(nani,nani),phiphic(neat,neat)  real real  phiphia(nani,nani),osml(NP),osm2(NP),osm3(NP) osm3a(NP),osm4(NP),osm4a(NP),osmcal(NP)  real  F l , F2, F3, F4,ah2o(NP)  real lngamc(neat),game(neat),lngama(nani),gama(nani) real bmx(neat,nani),bpact(neat,nani) r e a l mNaOH(NP),gamNaOH(NP) real mNa2S103(NP),gamNa2Si03(NP) c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Open I/O Files open (5,file='nasiwcaO.in',form='formatted') open (6,file='nasiwcaO.out',form='formatted') c Charge of species d o 10 i = 1 , neat zc(i) = 0 10 continue d o 20 k = 1 , nani za(k) = 0 20 continue c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Read i n p u t file c Read '-.in'  25 c  26 c  c  27 c  read(5,*) datafile write(6,25) datafile format(/lx,'Datafile: ',al2) Read ' - m u l t i - c o m p o n e n t s y s t e m ' read(5,*) headline write(6,26) headline format(/lx,a) Read c h a r g e o f c a t i o n and a n i o n read(5,*) headline read(5,*) zc(1),za(1),za(2) Read t e m p e r a t u r e (oC) read(5,*) headline read(5,*) tc tk = t c + 273.15 write(6,27) tk format(lx,'Temperature : ',f6.2,' K') Read D e b y e - H u c k e l p a r a m e t e r at T oC read(5,*) read(5,*)  headline aphi  cccccccccccccccccccccc Initialization d o 31 i = 1 , neat do  30  k =  1,  nani  betha0(i,k) = O.OeO bethal(i,k) = O.OeO betha2(i,k) = O.OeO cphi(i,k) = O.OeO 30 31  continue continue d o 41 i = do  1, j  neat =  1,  neat  thetacd, j ) ethetacd, j ) ethetapc(i,j) continue  40 41  40  O.OeO O.OeO O.OeO  = = =  O.OeO O.OeO O.OeO  continue do  51  k =  do  50  1, 1 =  nani 1,  nani  thetaa(k,l) ethetaa(k,l) ethetapa(k,l) 50 51  = = =  continue continue do  62  i  =  1,  neat  of  Pitzer's  parameters  as  O.OeO  do  61  j  =1,  do  60  neat  k =  1,  nani  psic(i,j,k) 60  =  O.OeO  continue  61  continue  62  continue do  72  k =  do  1,  71  nani  1 =  do  1,  70  nani  i  =  1,  neat  psia(k,l,i) 70  =  O.OeO  continue  71  continue  72  continue  ccccccccccccccccccccccccccccccecccccccccc c  cation-anion  :  bethaO(cation,anion),  c c  betha2(cation,anion), Read  'Pitzer's  read(5,*) c  Read b e t h a O , b e t h a l , c p h i  c  c  of  headline bethaO(1,1),bethal(1,1),cphi(1,1)  Read b e t h a O , b e t h a l , c p h i  of  Na2Si03  headline  read(5,*)  headline:  read(5,*)  bethaO(1,2),bethal(1,2),cphi{1,2)  Read  thetaa(OH-,Si032-),psia(OH-,Si032-,Na+)  read(5,*)  headline  read(5,*)  thetaa(1,2),psia(1,2,1)  Number  data  of  read(5,*)  headline  read(5,*)  ndata  Ready t o  read  the  molality  mc(l,ndata)  :  Na+  c  ma(l,ndata)  :  OH-  ma(2,ndata)  :  80  of  data  !  species  Si032-  n=l,ndata  read(5,*) 80  molality  headline  c  do  system'  NaOH  read(5,*)  c  c  cphi(cation,anion) electrolyte  read(5,*)  read(5,*)  c  single  parameters  headline  read(5,*)  c  for  Pitzer's  bethal(cation,anion)  headline  read(5,*)  c  parameters  Reading  mc(l,n),ma(l,n),ma(2,n)  continue Universal b  =  constants  of  Pitzer's  eq.(not  2-2  electrolyte)  1.2e0  alphal  =  2.0e0  alpha2  =  O.OeO  write(6,90)'mNaOH','gamNaOH','mNa2Si03',•gamNa2Si03', & 90  'osmcal','aH20','gamNa','gamOH','gamSi03' format(/lx,3(a8),al0,5(a8))  ccccccccccccccccccccccccccccccccccccccccccccc do c  100  ionic  strength  is(n)  =  mt(n)  =  do  110  110  molality  O.OeO i  =  1,  neat +  mt (n)  =  mt (n)  + mc ( i , n)  mc(i,n)*(zc(i)**2)  continue 111  k =  1,  nani  ls(n)  =  is(n)  +  mt (n)  =  mt (n)  + ma ( k , n)  ma(k,n)*(za(k)**2)  continue =  0 . 5 * i s (n)  Calculating do  =  z  O.OeO  120  z(n)  i =  =  1,  z(n)  neat +  mc(i,n)*abs(zc(i))  continue do z(n)  121  total  is(n)  z(n)  120  and  =  i s (n) c  iteration  O.OeO  is(n)  do  111  Start  n=l,ndata  121 =  k =  1,  z(n).  +  nani ma(k,n)*abs(za(k))  continue  ccccccccccccccc  Calculating  bphi(cat,ani)  and  c(cat,ani)  coefficients  do 131 1 = 1 , neat do 130 k = 1, n a n i b p h i ( i , k ) = O.OeO bphi(i,k) = bethaO(i,k)+bethal(i,k)*exp(-alphal*sqrt(is(n))) bphi(i,k) = bphi(i,k)+betha2(l,k)*exp(-alpha2*sqrt(is(n))) c ( i , k ) = O.OeO c ( i , k ) = c p h i ( i , k ) / ( 2*( ( a b s ( z c ( i ) * z a ( k ) ) ) * * 0 . 5 ) ) bmx(i,k) = O.OeO bmx(i,k) = b e t h a O ( i , k ) + b e t h a l ( i , k ) * g ( a l p h a l * s q r t ( ' i s ( n ) ) ) bmx(i,k) = bmx(i,k)+betha2(i,k)*g(alpha2*sqrt(is(n))) b p a c t ( i , k ) = O.OeO bpact(i,k) = bethal(i,k)*gp(alphal*sqrt(is(n))) bpact(i,k) = bpact(i,k)+betha2(i,k)*gp(alpha2*sqrt(is(n))) bpact(i,k) = bpact(i,k)/is(n) 130 continue 131 continue ccccccccccc Calculating phic(cat,cat), phipc(cat,cat), phia(ani,ani), c and p h i p a ( a n i , a n i ) do 141 1 = 1 , neat do 140 j = 1, neat phic(i,j) = O.OeO p h i p c ( i , j ) = O.OeO phic(i,j) = thetac(i,j) + ethetac(i,j) phipc(i,j) = ethetapc(i,j) 140 continue 141 continue do 151 k = 1, n a n i do 150 1 = 1 , n a n i phia(k,l) = O.OeO p h i p a ( k , l ) = O.OeO phia(k,l) = thetaa(k,l) + ethetaa(k,l) p h i p a ( k , l ) = ethetapa(k,1) 150 continue 151 continue c c c c c c C a l c u l a t i n g p h i p h i c ( c a t , c a t ) and p h i p h i a ( a n i , a n i ) c o e f f i c i e n t s do 161 i = 1, (ncat-1) do 160 j = ( i + 1 ) , neat p h i p h i c ( i , j ) = O.OeO phiphic(i,j) = phic(i,j) + is(n)*(phipc(i,j)) 160 continue 161 continue do 171 k = 1, (nani-1) do 170 1 = (k+1), n a n i p h i p h i a ( k , l ) = O.OeO phiphia(k,l) = phia(k,l) + is(n)*(phipa(k,1)) 170 continue 171 continue c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c C a l c u l a t i n g osmotic c o e f f i c i e n t osml(n) = O.OeO osml(n) = - a p h i * ( i s ( n ) * * ( 3 . / 2 . ) ) / ( 1 + b * ( i s ( n ) * * 0 . 5 ) ) osm2(n) = O.OeO do 181 i = l , n c a t do 180 k = 1, n a n i osm2(n)=osm2(n) + ( m c ( i , n ) * m a ( k , n ) ) * ( b p h i ( i , k ) + z ( n ) * c ( i , k ) ) 180 continue 181 continue osm3(n) = O.OeO do 192 1 = 1 , (ncat-1) do 191 j = ( i + 1 ) , neat osm3a(n) = O.OeO do 190 k = 1, n a n i osm3a(n) = osm3a(n) + ma(k,n) * p s i c ( i , j , k ) 190 continue osm3(n) = o s m 3 ( n ) + ( ( m c ( i , n ) * m c ( j , n ) ) * ( p h i p h i c ( i , j ) + o s m 3 a ( n ) ) 191 continue 192 continue osm4(n) = O.OeO do 202 k = 1, (nani-1) do 201 1 = (k+1), n a n i osm4a(n) = O.OeO do 200 1 = 1 , neat  osm4a(n) = osm4a(n) + rac(i,n) * p s i a ( k , l , i ) continue osm4(n) = osm4(n)+((ma(k,n)*ma(1,n))*(phiphia(k,1)+osm4a(n))) 201 continue 202 continue osmcal(n) = O.OeO osmcal(n) = osml(n) + osm2(n) + osm3(n) + osm4(n) osmcal(n) = (2.0/mt(n))*osmcal(n) osmcal(n) = osmcal(n) + 1. c C a l c u l a t e t h e a c t i v i t y o f water ah2o(n) = O.OeO ah2o(n) = 10**(-0.007823*mt(n)*osmcal(n)) c C a l c u l a t i n g F term F l = O.OeO Fl = (is(n)**0.5)/(1+b*(is(n)**0.5)) Fl = F l + (2/b)*log(l+b*(is(n)**0.5)) Fl = Fl*(-aphi) F2 = O.OeO do 211 i = l , n c a t do 210 k = l , n a n i F2 = F2 + m c ( i , n ) * m a ( k , n ) * b p a c t ( i , k ) 210 continue 211 continue F3 = O.OeO do 221 i = 1, (ncat-1) do 220 j = ( i + 1 ) , n c a t F3 = F3 + m c ( i , n ) * m c ( i , n ) * p h i p c ( i , j ) 220 continue 221 continue F4 = O.OeO do 231 k = 1, (nani-1) do 230 1 = (k+1),nani F4 = F4 + ma(k,n)*ma(k,n)*phipa(k,1) 230 continue 231 continue F = O.OeO F = F l + F2 + F3 + F4 ccccccccccccccccccccccccccccc Calculating cation a c t i v i t y coefficient do 790 i i = 1, neat csuml = O.OeO csuml = ( z c ( i i ) * * 2 ) * F csum2 = O.OeO do 700 k = 1, n a n i csum2 = csum2 + m a ( k , n ) * ( 2 * b m x ( i i , k ) + z ( n ) * c ( i i , k ) ) 700 continue csum3 = O.OeO do 720 j = 1, neat i f (j .eq. i i ) go t o 720 csum3a = O.OeO do 710 k = 1, n a n i csum3a = csum3a + ma(k,n) * p s i c ( i i , j , k ) 710 continue csum3 = csum3 + m c ( j , n ) * ( 2 * p h i c ( i i , j ) + c s u m 3 a ) 720 continue csum4 = O.OeO do 740 K = 1, (nani-1) do 730 L = (K+1), n a n i csum4 = csum4 + ma(k,n) * ma(l,n) * p s i a ( K , L , i i ) 730 continue 740 continue 200  750 760 c  csum5 = O.OeO do 760 i = 1, neat do 750 K = 1, n a n i csum5 = csum5 + mc(i,n) * ma(K,n) * C ( i , K ) csum5 = a b s ( Z C ( i i ) ) * csum5 continue continue game() : a c t i v i t y c o e f f i c i e n t o f c a t i o n by P i t z e r eq. l n g a m c ( i i ) = csuml + csum2 + csum3 + csum4 + csum5 gamc(ii) = exp(lngamc(ii))  790 continue ccccccccccccccccccccccccccccccc d o 890 kk = 1, nani a s u m l = O.OeO asuml = ( z a ( k k ) * * 2 )*F asum2 = O . O e O d o 800 i = 1, neat 800  asum2 = asum2 continue  +  Calculating.anion  activity  coeficient  mc(i,n)*(2*bmx(i,kk)+z(n)*C(i,kk))  asum3 = O.OeO d o 820 1 = 1 , nani if ( l . e q . k k ) go t o asum3a = O.OeO  820  do  810 820  830 840  850 860 c  890 c  810 1 = 1 , neat asum3a = asum3a + m c ( i , n ) * psia(kk,l,i) continue asum3 = asum3 + m a ( 1 , n ) * ( 2 * p h i a ( k k , 1 ) + asum3a) continue asum4 = O . O e O d o 840 1 = 1 , (ncat-1) do 830 J = ( i + 1 ) , neat asum4 = asum4 + m c ( i , n ) * m c ( j , n ) * psic(i,j,kk) continue continue asum5 = O.OeO do 860 1 = 1 , neat d o 850 K = 1 , nani asum5 = asum5 + m c ( i , n ) * m a { k , n ) * C(i,K) asum5 = abs(za(kk))*asum5 continue continue gama() : a c t i v i t y c o e f f i c i e n t o f a n i o n b y P i t z e r e q . l n g a m a ( k k ) = a s u m l + asum2 + asum3 + asum4 + a s u m 5 gama(kk) = e x p ( l n g a m a ( k k ) ) continue mean a c t i v i t y coefficient mNaOH(n) =( (1./3.)*mc(1,n) * ma(l,n) )**(l./2.) g a m N a O H ( n ) = (game {1) * g a m a (1) ) * * ( 1 . / 2 . )  380  390 100  mNa2Si03(n)=( ( ( ( 1 . / 3 . ) * m c ( 1 , n ) ) * * 2 . ) * m a ( 2 , n ) )**(l./3.) gamNa2Si03(n) = ( (game(1)**2.)*gama(2) )**(l./3.) write(6,380)mNaOH(n),gamNaOH(n),mNa2Si03(n),gamNa2Si03(n), & osmcal(n),ah2o(n),game(1),gama(1),gama(2) format(lx,3(f8.4),f10.4,f8.4,f8.5,3(f8.4)) write!*,390)mNaOH(n),gamNaOH(n),mNa2Si03(n),gamNa2Si03(n), & osmcal(n),ah2o(n),game(1),gama(1),gama(2) format(lx,3(f8.4),f10.4,f8.4,f8.5,3(f8.4)) continue  ccccccccccccccccccccccccccccccccccccccccccccccccccccc close(5)  Close  I/O  Files  close(6,status=•keep') end cccccccccccccccccccccccccccccccccccccccccccccccccc real function g(x) real x if  (x.eq.0)  g = else g = endif  if  Function  gp(x)  then  2*(l-(l+x)*exp(-x))/(x**2)  (x.eq.0) gp = 0 else gp  then  2*(1-  endif end Hyeon  g(x)  0  end cccccccccccccccccccccccccccccccccccccccccccccccccc real function gp(x) real x  c  Function  Park,  1998  (l+x+(x**2)/2.)  *exp(-x))/(x**2)  199 Computation of equilibrium state for NH -NH OH-H -HCl-NH Cl-Cr-Na -NaClK+-KC1 system at 573.15 K +  4  4  +  4  This code was written in order to check the reliability of the modeling procedure by comparing the calculation results with the published ones. Example of input and output  *************************************************  NH4-NH40H-H+-HC1-NH4C1-C1—Na+-NaCl-K+-KCl OCT , 1 9 9 8 Hyeon Park  system  ************************************************* System  : NH4+ H+ Na+ K+ C l - NH40H H C l NH4C1 N a C l K C l H 2 0 T e m p e r a t u r e : 300 C > I n p u t a m o u n t o f NH4C1 ? 0.25 > I n p u t amount o f N a C l ? 0.25 > I n p u t amount o f K C l ? 0.25 (Press  enter  key to see r e s u l t . . . )  *+****+****+*+++* Input  Result  *****************  chemicals(moles) .250000 .250000  NH4C1 NaCl  .250000  KCl Initial  guess  mNH4 mH mNa mK mCl mNH40H  for molalities .100000 .002000 .100000 .100000 .200000 .002000  mHCl mNH4Cl mNaCl mKCl F value  .005000 .150000 .150000 .150000  Fll) F(2)  .000080 .000000  F(3) F(4) F(5)  .000000  F(6) F(7)  .000000  .000000 .000000 .000000 .000000  F(8)  .000000  F(9) F(10)  .000000  Ionic Strength : .478185 M o l a l i t y [ m o l e s / K g H20] .162978 mNH4  gamNH4  .404252  mH  .001220  gamH  mNa mK  .138489 .175497  gamNa gamK  .404252 .404252  mCl  .478185  gamCl  mNH40H  .002876 .001657  mHCl mNH4Cl mNaCl  .404252 .404252  .084145 .111511 .074503  mKCl  Source code (heqbrntfor) c c  c c  heqbrm.for  ****************************************************** NH4-NH40H-H+-HC1-NH4C1-C1—Na+-NaCl-K+-KCl University  of British  Columbia  system  Oct Input  1998  Hyeon  Park  chemicals  NH4C1 NaCl KCI Species  at  Cation Anion  (4) (1)  No c h a r g e Unknowns molality molality molality molality molality molality molality molality molality molality Main  08,  NH4Clin NaClin KClin equilibrium  species  of of of of of of of of of of  NH4+ H+ Na+ K+ ClNH40H HC1 NH4C1 N a C l  (5)  NH4+ H+ Na+ K+ C l NH40H HC1 NH4C1 NaCl KCI  mNH4 mH mNa  KCI  mK mCl  xll) x(2) x(3) x(4) x(5)  mNH40H mHCl  x(7)  mNH4Cl mNaCl mKCl  x(8) x(9) x(10)  x(6)  routine  INTEGER N PARAMETER(N=10) XG(N) DOUBLE P R E C I S I O N x ( N ) , f ( N ) , DOUBLE P R E C I S I O N N H 4 C l i n , N a C l i n , K C l i n DOUBLE P R E C I S I O N g a m N H 4 , g a m H , g a m N a , g a m K , g a m C l DOUBLE P R E C I S I O N a H 2 0 , i s COMMON / C I N P U T / N H 4 C l i n , N a C l i n , K C l i n COMMON / R E S U L T / a H 2 0 , is COMMON / G A M / g a m N H 4 , g a m H , g a m N a , g a m K , g a m C l LOGICAL c h e c k N H 4 C l i n = 0.0D0 NaClin = 0.0D0 = 0.0D0 KClin PRINT PRINT PRINT PRINT  *  PRINT  +  PRINT  *  •itt t  * *r  PRINT  +  PRINT  * * *r  PRINT  OCT  t  ,  1998  Hyeon  HC1 NH4C1 N a C l  Park  KCI  H20  •  PRINT WRITE{ •itr  9  READ(*,*) NH4Clin =  WRITE!*,*) ' > Input READ(*,*) NaClin NaClin = 0.25  amount  of  NaCl  WRITE!*,*) ' > Input READ!*,*) KClin KClin = 0.25  amount  of  KCI  ?  key t o  see  result...)  PRINT READ  c  •  NH4Clin 0.25  *, ' (*,*)  (Press  Molality  of  mNH4  x(l) x(2)  c c  mH mNa  c  mK  c c  mCl mNH40H  c c  mHCl mNH4Cl  x(3) x(4) x(5) x(6) x(7) x(8)  enter  species  at  initial  ?  state  '  '  (Guess  1  values)  201  mNaCl x(9) mKCl x(10) 1000g/18.015Mw x(l) = 0.1 x(2) x(3) x(4)  = = =  0.002  x(5) x(6) x(7)  = = =  0.2 0.002  x(8)  =  0.005 0.15  x(9)  =  0.15  ->  55.509  0.1 0.1  x(10) = 0.15 T O SHOW I N I T I A L G U E S S V A L U E S A T R E S U L T XG(1)-XG(6) XG(1) = X ( l ) XG(2) = X{2) XG(3) = X(3) XG(4) = X(4) XG(5) = X(5) XG(6) = X(6) XG(7) = x ( 7 ) XG(8) = x ( 8 ) XG(9) = x ( 9 ) XG(10)= x(10) call newt(x,N,check) call funcv(N,x,f) if (check) then write!*,*) 'Convergence problems.' endif at f i n a l state  10  PRINT Result PRINT ***************** PRINT Input chemicals(moles)' WRITE (*,*) ' ,NH4Clin WRITE ( * , 1 0 ) ' NH4C1 ' ,NaClin WRITE ( * , 1 0 ) • NaCl • KCl ',KClin WRITE ( * , 1 0 ) FORMAT(3x,a, t 2 5 , f l 2 . 6 ) print * , ' ' WRITE (*,*) • I n i t i a l guess f o r m o l a l i t i e s WRITE ( * , 1 4 ) ' mNH4 ',XG(1) WRITE ( * , 1 4 ) ' mH •,XG(2) WRITE ( * , 1 4 ) • mNa *,XG(3) ' mK WRITE ( * , 1 4 ) ' , XG (4 ) WRITE  (*,14)  ' mCl  ',XG(5)  WRITE  (*,14)  '  mNH40H  WRITE WRITE  (*,14) (*,14)  '  mHCl  ',XG(6) ' , XG ( 7 )  '  mNH4Cl  ' , XG(8)  WRITE 14  ' mNaCl (*,14) WRITE ( * , 1 4 • mKCl FORMAT(3x,a, t 2 5 , f l 2 . 6 ) PRINT * , ' ' PRINT * , ' ( P r e s s e n t e r READ (*,*) WRITE (*,*) ' F value WRITE (*,15) ' F ( l ) WRITE (*,15) ' F(2) WRITE  (*,15) ' F(3) (*,15) ' F(4) WRITE ( * , 1 5 ) ' F(5) WRITE (*,15) ' F(6) WRITE (*,15) ' F(7) WRITE (*,15) ' F(8) WRITE (*,15) ' F(9) WRITE (*,15) ' F(10) FORMAT ( 3 x , a , t 2 5 , f l 2 . 6 ) PRINT * , ' ' PRINT * , ' ( P r e s s e n t e r READ (*,*) WRITE  15  *,XG(9) ',XG(10)  key to  see next  page...)  see next  page.  ,F(1) ,F(2) ,F(3) ,F(4) ,F(5) ,F(6) ,F(7) ,F(8) ,F(9) ,F(10)  key to  '  202  PRINT 19 20  * ,  '  '  WRITE ( * , 1 9 ) ' Ionic Strength : ' , i s F0RMAT(lx,a,fl2.6//) WRITE ( * , 2 0 ) ' Molality [moles/Kg H20]' FORMAT(lx,a) WRITE ( * , 2 1 ) ' mNH4 :•,X(1),'gamNH4: WRITE ( * , 2 1 ) ' mH :',X(2),•gamH : WRITE  (*,21)  • mNa  :•,X(3),•gamNa  :  ',gamNa  WRITE ( * , 2 1 ) • mK :',X(4),'gamK WRITE ( * , 2 1 ) mCl :',X(5),'gamCl FORMAT(3x,a,t20,fl2.6,5x,a,fl2.6) WRITE ( * , 2 2 ) ' mNH40H :',X(6) WRITE ( * , 2 2 ) • mHCl :',X(7) WRITE ( * , 2 2 ) • mNH4Cl :',X{8) WRITE ( * , 2 2 ) • mNaCl :',X(9) WRITE ( * , 2 2 ) * mKCl :',X(10) FORMAT(3x,a,t20,fl2.6) print * , ' ' END  : :  ',gamK ',gamCl  1  21  22  C C  funcv Subroutine =================== SUBROUTINE  funcv(n,x,f)  INTEGER n , m p a r a m e t e r (m=5) DOUBLE P R E C I S I O N DOUBLE DOUBLE DOUBLE DOUBLE DOUBLE DOUBLE COMMON COMMON COMMON mNH4 mH  = x(3) = x(4) = x(5)  mK mCl mNH40H mHCl  = x(6) = x(7)  mNH4Cl mNaCl  = x(8) = x(9)  mKCl  = x(10)  call  x(n),f(n),gam(m)  PRECISION N H 4 C l i n , N a C l i n , K C l i n P R E C I S I O N mNH4, mH, m N a , mK, m C l P R E C I S I O N mNH40H, m H C l , m N H 4 C l , m N a C l , PRECISION gamNH4,gamH,gamNa,gamK,gamCl PRECISION a H 2 0 , i s P R E C I S I O N K I , K 2 , K 3 , K 4 , K5 /CINPUT/ NH4Clin, N a C l i n , KClin / R E S U L T / aH20, i s / G A M / gamNH4,gamH,gamNa,gamK,gamCl = x(l) = x(2)  mNa  davies(n,m,x,gam)  gamNH4=  gam(1)  gamH = gam(2) gamNa = g a m ( 3 ) gamK gamCl c  c  = gam(4) = gam(5)  Reaction 1 KI = 4 . 6 6 7 KI = 1 0 * * K 1 f ( l ) = 0.0D0 f(1)= mNH4*gamNH4*aH20/(mNH40H*mH*gamH) f(l)= f(l)-Kl Reaction 2 K2 = - 0 . 8 2 K2 = 1 0 * * K 2 f ( 2 ) = 0.0D0  c  f ( 2 ) = mNH4*gamNH4*mCl*gamCl/(mNH4Cl) f(2)= f(2)-K2 Reaction 3 K3  1.013  K3 = 1 0 * * ( K 3 ) f ( 3 ) = 0.0D0  c  ',gamNH4 ',gamH  f ( 3 ) = mNa*gamNa*mCl*gamCl/(mNaCl) f(3)= f(3)-K3 Reaction 4 K4  = 1.24  mKCl  K4 = 1 0 * * ( K 4 ) f ( 4 ) = 0.0D0 f(4)= mHCl/(mH*gamH*mCl*gamCl) f(4)=  f(4)-K4  Reaction 5 K5 = - 0 . 7 3 5 K5 = 1 0 * * ( K 5 ) f(5)=  0.0D0  f(5)= mK*gamK*mCl*gamCl/(mKCl) f(5)= f(5)-K5 Mass b a l a n c e o f N f ( 6 ) = 0.0D0 f(6) f(6) Mass f(7) f(7) f(7) Mass f(8) f(8) f(8) Mass f(9) f(9) f(9)  = mNH4+mNH40H+mNH4Cl = 0.25-f(6) balance of C l = 0.0D0 = mHCl+mNH4Cl+mCl+mNaCl+mKCl = 0.75-f(7) b a l a n c e o f Na = 0.0D0 = mNa+mNaCl = 0.25-f(8) balance of K = 0.0D0 = mK+mKCl = 0.25-f(9)  Electroneutrality f ( 1 0 ) = O.OdO f ( 1 0 ) = mNH4 + mH + mNa + mK - m C l return END  Subroutine : Davies r e v i s i o n o f Calculate activity coefficients  the Debye-Huckel e q . S osmotic coefficients  subroutine davies(n,m,x,gam) i m p l i c i t double p r e c i s i o n (a-h, o-z) integer n,m,neat,nani parameter(ncat=4,nani=l) double p r e c i s i o n x(n),gam(m) integer zc(neat),za(nani) double p r e c i s i o n mc(neat),ma(nani) d o u b l e p r e c i s i o n i s , m t , z , AP double p r e c i s i o n loggamc(neat),game(neat),loggama(nani),gama(nani) common / r e s u l t / aH20, is Number 1 2 3 4 Number  cation NH4 + H+ Na+ K+ anion Clc a t i o n and  1 Moles of mc ( 1 ) = x ( 1 ) mc(2)=x(2) mc ( 3 ) = x ( 3 ) mc(4)=x(4) ma ( 1 ) = x ( 5 ) Charge o f zc(l)=l  cation  moles mc(1)=x(1) mc(2)=x(2) me (3) =x (3) mc(4)=x ( 4 ) moles ma ( 1 ) = x ( 5 ) anions  and a n i o n s  zc(2)=l zc(3)=l zc(4)=l za(1)=-1 ionic strength is  =  O.OdO  mt  =  O.OdO  do  and t o t a l  molality  110 i = 1, n e a t is = is + mc(i)*(zc(i)**2) mt  = mt + mc ( i )  charge zc(l)=+l zc(2)=+l zc(3)=+l zc(4)=+l charge za(1)=-1  204  110  continue do  111 c  111 k = 1 , nani is = is + ma(k)*(za(k)**2) mt = mt + ma (k) continue is = 0.5*is Calculating z  z do z 120  continue do z  121 c c c c c  7 90  890  c c  = O.OdO 120 1 = 1 , neat = z + mc(i)*abs(zc(i)) 121 = z  k = 1, nani + ma(k)*abs(za(k))  continue Assume t h e a c t i v i t y o f water as u n i t ah2o = l . O d O Debye-Huckel parameter Temp. 25 50 100 150 200 250 300 oC p a r a . 0.51 0.53 0.60 0.69 0.81 0.98 1.256 AP = 1.256 C a l c u l a t e c a t i o n and a n i o n a c t c o f d o 790 ii=l,ncat l o g g a m c ( i i ) = O.OdO loggamc(ii) = -(zc(ii)**2)*AP*DSQRT(is}/(1+DSQRT(is)) loggamc(ii) = loggamc(ii)+0.2*AP*(zc(ii)**2)*is gamc(ii) = 10**(loggamc(ii)) continue d o 890 kk = 1, nani l o g g a m a ( k k ) = O.OdO loggama(kk) = -(za(kk)**2)*AP*DSQRT(is)/(1+DSQRT(is)) loggama(kk) = loggama(kk)+0.2*AP*(za(kk)**2)*is gama(kk) = 10**(loggama(kk)) continue gam(1)=gamc(1) gam(2)=gamc(2) gam(3)=gamc(3) gam(4)=gamc(4) gam(5)=gama(1) R e t u r n aH20 and R e t u r n gam() t o  i s v a l u e s b y COMMON / R E S U L T / func subroutine  return end c  newt,ludemp,fdj ac,lubksb,lnsrch  c  subroutines  c  version  SUBROUTINE c  imported  2.07  PARAMETER PARAMETER  to  from  "Numerical  Recipes  calculate  non-linear  equations  Fortran  77",  newt(x,n,check) (NP=40,MAXITS=200,TOLF=l.e-4,TOLMIN=l.e-6,TOLX=l.e-7,STPMX=100.) (NP=40,MAXITS=200,TOLF=l.e-10,TOLMIN=l.e-6,TOLX=l.e-7,STPMX=100.)  END SUBROUTINE  ludemp(a,n,np,indx,d)  return END SUBROUTINE  fdjac(n,x,fvec,np,df)  return END SUBROUTINE  lubksb(a,n,np,indx,b)  return END SUBROUTINE l n s r c h ( n , x o l d , f o l d , g , p , x , f , s t p m a x , c h e c k , f u n c ) END c c c  fmin(x) : f u n c t i o n imported v e r s i o n 2.07 FUNCTION  from  fmin(x)  return END c  Hyeon  Park,  UBC,  1998  "Numerical  Recipes  Fortran  77",  205 Computation of equilibrium state for sodium aluminosilicate formation This code was written in order to compute the equilibrium state for the Na - Al(OH)4* Si0 * - OH" - C0 * - S0 ' - Cl" - H 0 system (system A) and the Na - Al(OH) " Si0 " - OH" - C O 3 " - Cl" - HS" - H 0 system (system B) at 368.15 K. +  2  2  3  2  3  2  +  4  2  2  3  2  Example of input and output N a - A l - S i l i c a t e formation system Nov. 1998 Hyeon Park ****++*********+*+********************** System  : Na+ O H - C l - C 0 3 2 - S 0 4 2 - H S A l ( O H ) 4 - S 1 0 3 2 - H20 Temperature: 95 C Pressure : 1 atm > Input 0.025 > Input 0.025 > Input 1.0 > Input 0.25  amount  o f A1C136H20  ? (0.01 - 0.1)  amount  o f Na2Si039H20  amount  o f NaOH  ? (0.25 ~ 3.0 moles)  amount  o f NaCl  ? ( 0 . 0 - 3 . 0  ? (0.01 ~ 0.1)  moles)  > I n p u t amount o f Na2C03 ? ( 0 . 0 - 2 . 0 m o l e s ) 1.0 > I n p u t amount o f Na2S04 ? ( 0 . 0 ~ 2 . 0 m o l e s ) 0.1 > I n p u t amount o f Na2S ? ( 0 . 0 ~ 1 . 5 m o l e s ) 0.0 > I n p u t amount o f H20 ? ( 1 . 0 Kg) 1.0 E n t e r i n i t i a l g u e s s o f msod (0.0001-0.002)? 0.001 E n t e r i n i t i a l g u e s s o f mhsod ( 0 . 0 0 1 - 0 . 0 0 9 d 0 ) ? 0.005 add_p add_p  1 2  add_p mhsodini  6 4.700000000000001E-003  By c o n s i d e r i n g  The  sodalite .000000  f( f(  1)= 2) =  f(  3) =  .000000  f(  4) =  .000000  f( f( f(  5) = 6) = 7) =  .000000 .000000  f(  8) =  .000000  f ( 9) = f(10)=  .000000 .460197  f(11)= mSOD :  -.467532  S hydroxysodalite...  .000000  .000000  .607041  .471669 mHSOD : mSOD h a s n e g a t i v e v a l u e  Recalculating  with  Enter  guess  initial  !  a s s u m i n g mSOD = 0 . o f m h s o d (0.001~O.009d0)?  0.005 add_p  1  add_p  2  add_p  17  add_p  18  mhsodini 4.100000000000001E-003 Calculated successfully ! f( 1)= .00000000 f( 2)= .00000000 f ( 3)= .00000000  4  .00000000 f t 4) = .00000000 f ( 5) = . 00000000 f t 6) = .00000000 f t 7) = .00000000 f t 8) = .00000000 f t 9) = .00061927 f (10) = P r e s s ENTER key t o see t h e r e s u l t . Result Input c h e m i c a l s ( m o l e s ) A1C13 .025000 .025000 Na2Si039H20 1.000000 NaOH 1.000000 Na2C03 .100000 Na2S04 .000000 Na2S .250000 NaCl A c t i v i t y c o e f f i c i e n t s and Water A c t i v i t y .532522 gamNa+ .169388 gamAl(OH)4.038886 gamSi032.670091 gamOH.017960 gamC032.023491 gamS042.580598 gamHS.621849 gamCl.917029 aH20 4.545978 Ionic strength P r e s s ENTER key t o s e e t h e next page. . . M o l a l i t y [moles/Kg H20] mNa+ 3.448883 mAl(OH)4.004746 mSi032.004746 mOH.927208 mC032.993045 mS042.099304 mHS.000000 mCl.322740 msodalite .000000 mhydroxysodalite .003347 mH20 55.897780 mAl*mSi .0000225  Source code (kshsodfor) c Q  c c c Q  kshsod.for * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  N a - A l - S i l i c a t e formation i n a l k a l i n e s o l u t i o n s U n i v e r s i t y o f B r i t i s h Columbia Nov.02, 1998 Hyeon Park * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  c  Input  c c c c c c c c c c c c c c c c c c  A1C136H20 AlClin Na2Si039H20 N a S i i n NaOH NaOHin Na2C03 NaCOin Na2S04 NaSOin Na2S Na2Sin NaCl NaClin H20 H20in S p e c i e s at e q u i l i b r i u m Cation Anion Solid  chemicals  (1) : (7) : (2) :  Na+ A l ( O H ) 4 - S1032- OH- C032- S042- HS- C l Na8(AlSi04)6C122H20 (sodalite) Na8(AlSi04)6(OH)22H20 ( h y d r o x y s o d a l i t e ) L i q u i d (1) : . H20 Unknowns  m o l a l i t y o f Na+  : mNa  x b ( l ) x s ( l ) xh  207  c  molality  of  mAl  xb(2)  xs(2)  xh(2)  c c c  molality molality  of of  Si032OH-  mSi mOH  xb(3) xb(4 )  x s (3) xs(4)  xh(3) xh(4 )  molality molality  of of of of  C032S042HSC l -  mCO mSO  xb(5) xb(6) xb(7)  x s (5) x s (6) xs(7)  xh(5) xh(6) xh(7)  sodalite hydroxysodalite  xb(8) xb(9)  xs(8) x s ( 9)  xh(8)  of of  c c c c c c  molality molality molality molality moles Main  Al(OH)4-  mHS mCl msod  o f H20  mhsod  xb(10)  mH20  xb(ll)  x h ( 9) xs(10)  xh(10  routine  INTEGER n b , n s , n h , i PARAMETER(nb=ll,ns=10,nh=10 ) INTEGER p s o d , p h s o d DOUBLE P R E C I S I O N x b ( n b ) , f b ( n b ) , x s ( n s ) , f s ( n s ) , x h ( n h ) , f h ( n h ) DOUBLE P R E C I S I O N x i ( n b ) DOUBLE P R E C I S I O N A l C l i n , N a S i i n , N a O H i n , N a C l i n , N a C O i n DOUBLE P R E C I S I O N N a S O i n , N a 2 S i n , H20in DOUBLE P R E C I S I O N m N a i n , m A l i n , m S i i n , m O H i n , m C l i n DOUBLE P R E C I S I O N m C O i n , m S O i n , m H S i n , mH20in DOUBLE P R E C I S I O N m N a , m A l , m S i , mOH, m C l , mCO, mSO DOUBLE P R E C I S I O N mHS, mSOD, mHSOD, mH20 DOUBLE P R E C I S I O N g a m N a , g a m A l , g a m S i , g a m O H , g a m C O , g a m S O DOUBLE P R E C I S I O N g a m H S , g a m C l DOUBLE P R E C I S I O N a H 2 0 , i s DOUBLE P R E C I S I O N m h s o d i n i , m s o d i n i , a d d _ v integer add_p, add_int COMMON / C I N P U T / A l C l i n , N a S i i n , N a O H i n , N a C l i n , N a C O i n , N a S O i n , N a 2 S i n , COMMON / P _ V A L U E / p s o d , p h s o d COMMON / r e s u l t / a H 2 0 , is COMMON / a c t c o e f / g a m N a , g a m A l , g a m S i , g a m O H , g a m C O , g a m S O , g a m H S , g a m C l LOGICAL c h e c k print print  *, *,  print *, p^.j_nt * ,  ' '  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' N a - A l - S i l i c a t e formation system  • '  N o v . 1998 Hyeon Park ' **************************************** i  print  *,  •  print print print  *, *, *,  • ' '  1  System  :  Na+  OH- C l - C032-  Al(OH)495 C ' 1 atm '  Temperature: Pressure :  Si032-  S042-  H20  write!*,*) ' > Input read(*,*) AlClin  amount  of  A1C136H20  write(*,*) ' > Input read(*,*) NaSiin  amount  of  Na2Si039H20  write!*,*) ' > Input r e a d ( * , * ) NaOHin  amount  of  NaOH ?  (0.25  write(*,*) ' > Input read(*,*) NaClin  amount  of  NaCl  (0.0  write(*,*) ' > Input r e a d ( * , * ) NaCOin  amount  of  Na2C03  ?  ?  ?  (0.01 ?  of  Na2S04  ?  write!*,*) ' > Input read!*,*) Na2Sin  amount  of  Na2S  (0.0  write!*,*) read!*,*) H20in  =  Moles  of  '  >  Input  amount  of  H20  ?  ?  ~  (1.0  3.0 3.0  (0.0  amount  ~  '  0.1)  (0.01  -  write!*,*) ' > Input r e a d ( * , * ) NaSOin  HS-  •  -  (0.0 -  Kg)  ~ 0.1)  '  moles) moles)  2.0  ' '  moles)  ~ 2.0 1.5  '  '  moles)  moles)  '  '  '  H20in H2Oin*1000/18.015 s p e c i e s at  initial  state  mNain:Na+ mOHin:OHmClin:ClmCOin:C032mSOin:S042mHSin:HSmAlin:Al(OH)4mSiin:Si032mH20in:H20 mNain = 2*NaSiin+NaOHin+2*NaCOin+2*NaSOin+2*Na2Sin+NaClin mAlin = A l C l i n mSiin = NaSiin mOHin = N a O H i n + N a 2 S i n mCOin = N a C O i n mSOin = N a S O i n  -  4*AlClin  H20in  208  mHSin = mClin = mH20in= C  Na2Sin 3*AlClin + NaClin H20in + 6 * A l C l i n +  Molality  of  species  at  9*NaSiin  initial  -  state  Na2Sin (Guess  values)  c  add_p = 1 write(*,*) 'Enter read(*,*) mhsod  320  write)*,*) 'Enter r e a d ( * , * ) mhsod continue mhsodini mNa = mAl = mSi = mOH =  mCl mH20 x i (1) x i (2) x i (3) xi(4) xi xi xi  (5) (6) (7)  xi  (8)  xb(l) xb(2) xb(3)  xb(8) x b ( 9) xb(10) xb(ll)  guess  of  mhsod  (0.001-0.009d0)? '  mOHin/(mH20in/55  509) - 8 * m s o d - 8 * m h s o d 509) - 6 * m s o d - 6 * m h s o d 509) - 6 * m s o d - 6 * m h s o d 509)+12*msod+10*mhsod  mCOin/(mH20in/55 mSOin/(mH20in/55 mHSin/(mH20in/55  509) 509) 509)  mCl msod mhsod mH20 mNa mAl mSi mOH mCO mSO mHS mCl  = = = =  msod mhsod mH20 1  =  phsod  initial  (0.0001-0.002)?'  mHS  = = =  psod =  msod  mCO mSO  = = = =  xb(4) xb(5) xb(6) xb(7)  of  m C l i n / ( m H 2 0 i n / 5 5 509) - 2 * m s o d mH20in+4*msod+4*mhsod mNa mAl mSi mOH  = = = = =  x i (9) xi(10) x i (11)  guess  = mhsod mNain/(mH20in/55 mAlin/(mH20in/55 mSiin/(mH20in/55  = = = = = = =  mCO mSO mHS  initial  1  call newt(xb,nb,check) call funcv(nb,xb,fb) if (check) then write(*,*) endif  'Convergence problems.'  if ((xb(2).LT.O.OdO).OR.(xb(3).LT.O.OdO)) add_int=(add_p/2)*2 add_v = add_p - a d d _ i n t if (add_v.eq.1.OdO) then print *, 'add_p',add_p mhsod = m h s o d i n i + add_p*(1.0d-4) add_p = add_p + 1 g o t o 320 else i f (add_v.eq.0.OdO) then print *, 'add_p',add_p mhsod = m h s o d i n i add_p*(1.0d-4) add_p = add_p + 1 g o t o 320 end i f end i f print mNa mAl mSi mOH  *, = = = =  'mhsodini',mhsodini xb(l) xb(2) xb(3) xb(4)  then  209  mCO = mSO = mHS = mCl = msod = mhsod= mH20 = print *  601  c  c  321  xb(5) xb(6) xb(7) xb(8) xb(9) xb(10) xb(ll) , ' '  write)*,*) 'By considering sodalite S h y d r o x y s o d a l i t e . . . ' d o 601 1 = 1 , n b write)*,'(6x,a,i2,a,fl2.6)')'f(',i,')=',fb(i) continue print *, ' ' write)*,'(6x,a,fl2.6)•)'mSOD :',msod write)*,'(6x,a,fl2.6)')'mHSOD :',mhsod print *, ' ' T e s t msod<0 o r m h s o d < 0 if (msod.LT.O.OdO) then print *, ' T h e mSOD h a s n e g a t i v e v a l u e !' print *, ' R e c a l c u l a t i n g w i t h a s s u m i n g mSOD =0.' read)*,*) psod = 0 msod = O.OdO add_p = 1 print *, ' ' write!*,*) ' E n t e r i n i t i a l g u e s s o f mhsod (0.001-0.009d0)?' r e a d ( * , * ) mhsod • continue mhsodini=mhsod xh(l) = m N a i n / ( m H 2 0 i n / 5 5 509) - 8 * m s o d - 8 * m h s o d xh(2) xh(3) xh(4) xh(5) xh(6) xh(7)  = = = = =  mAlin/(mH20in/55 mSiin/(mH20in/55  509) - 6 * m s o d - 6 * m h s o d 509) - 6 * m s o d - 6 * m h s o d  mOHin/(mH20in/55 mCOin/(mH20in/55  509)+12*msod+10*mhsod 509)  m S O i n / ( m H 2 0 i n / 5 5 509) m H S i n / ( m H 2 0 i n / 5 5 .509) xh(8) = m C l i n / ( m H 2 0 i n / 5 5 .509) - 2 * m s o d xh(9) = mhsod xh(10) = mH20in+4*msod+4*mhsod call newt(xh,nh,check) call funcv(nh,xh,fh) if (check) then write)*,*) endif  'Convergence problems.'  if ((xh(2).LT.O.OdO).OR.(xh(3).LT.O.OdO)) add_int=(add_p/2)*2 add_v = add_p - a d d _ i n t if (add_v.eq.l.0d0) then print *, 'add_p',add_p mhsod = m h s o d i n i + add_p*(1.0d-4) add_p = add_p + 1 goto 321 else i f (add_v.eq.0.OdO) then print *, 'add_p',add_p mhsod = m h s o d i n i add_p*(1.0d-4) add_p = add_p + 1 goto 321 end i f end i f  then  print *, 'mhsodini',mhsodini print *, ' ' print *, 'Calculated successfully d o 603 1 = 1 , n h 603  !'  write)*,'(6x,a,i2,a,f30.8)')'f(',i,')=',fh(i) continue mNa mAl mSi mOH mCO mSO  = xh(l) = xh(2) = xh(3) = x h ( 4) = xh(5) = xh(6)  210  mHS = x h ( 7 ) mCl = x h ( 8 ) mhsod= x h ( 9 ) mH20 = x h ( 1 0 ) else i f print print  (mhsod.LT.0.OdO) then * , ' T h e mHSOD h a s n e g a t i v e * ,  'Press  ENTER t o  value  !'  recalculate with  a s s u m i n g mHSOD =  read(*,*)  322  phsod = 0 mhsod = O.OdO add_p = 1 write!*,*) 'Enter r e a d ( * , * ) msod continue m s o d i n i = msod xs(l)  initial  xs(2) xs(3) xs(4)  = mNain/(mH20in/55 = mAlin/(mH20in/55 = mSiin/(mH20in/55 = mOHin/(mH20in/55  xs(5) xs(6) xs(7)  = mCOin/(mH20in/55 = mSOin/(mH20in/55 = mHSin/(mH20in/55  guess  o f msod ( O . O O O l d O ) ? '  5 0 9 ) - 8 * m s o d - 8*mhsod 5 0 9 ) - 6 * m s o d - 6*mhsod 5 0 9 ) - 6 * m s o d - 6*mhsod 509)+12*msod+10*mhsod 509) 509)  509) xs(8) = mClin/(mH20in/55 509)-2*msod xs(9) = msod x s ( 1 0 ) = mH20in+4*msod+4*mhsod c a l l newt(xs,ns,check) call funcv(ns,xs,fs) if ((xs(2).LT.O.OdO).OR.(xs(3).LT.O.OdO)) add_i nt=(add_p/2)* 2 add_v = add_p - a d d _ i n t if (add_v.eq.l.0d0) then print * , 'add_p',add_p msod = m s o d i n i + a d d _ p * ( 1 . 0 d - 4 ) add_p = add_p + 1 g o t o 322 else i f (add_v.eq.O.OdO) then print * , 'add_p',add_p msod = m s o d i n i add_p*(1.0d-4) add_p = add_p + 1 g o t o 322 end i f end i f  then  print * , 'msodini',msodini print * , * ' print * , 'Calculated successfully d o 605 1 = 1 , n s  !'  write(*,•(6x,a,i2,a,f12.6)•)•f(•,i,•)=•,fs(i) 605  continue mNa = x s (1) mAl mSi mOH mCO  = = = =  xs(2) xs(3) xs(4) xs(5)  mSO = x s ( 6 ) mHS = x s (7 ) mCl = x s ( 8 )  C  msod= x s ( 9 ) mH20= x s ( 1 0 ) end i f at f i n a l state  c  print  *,  '  '  print * , 'Press read(*,*) ' '  ENTER  key to see the  print print  *, *,  print write write  *, ' ' (*,*) (*,10)  ' Input 'A1C13  write  (*,10)  'Na2Si039H20  result...'  ' Result chemicals(moles)' :',AlClin :',NaSiin  0'  211  10  16  20  21 22  C C  ',NaOHin write *,10) 'NaOH ',NaCOin write *,10) 'Na2C03 ' ,NaSOin write *,10) 'Na2S04 ' ,Na2Sin write *,10) 'Na2S ' ,NaClin write *,10) 'NaCl format 6 x , a , t 2 5 , f l 2 . 6 ) print WRITE A c t i v i t y c o e f f i c i e n t s and Water A c t i v i t y ' *,*> WRITE gamNa+ ',gamNa *,16) WRITE ',gamAl gamAl(OH)4*,16) WRITE ',gamSi gamSi032*,16) WRITE gamOH',gamOH *,16) WRITE gamC032',gamCO *,16) WRITE gamS042',gamSO *,16) WRITE gamHS',gamHS *,16) WRITE ',gamCl gamCl*,16) WRITE aH20 ',aH20 *,16) WRITE Ionic strength ',is *,16) FORMAT fl2.6) print * print * ' P r e s s ENTER k e y t o s e e t h e n e x t p a g e . r e a d (*, ) w r i t e ( *,20) Molality [moles/Kg H20]' format( lx,a) • ,mNa write ( * , 2 1 ) •mNa+ ' ,mAl write (*,21) 'mAl(OH)4write (*,21) •mSi032' , mSi ' ,mOH write ( * , 2 1 ) •mOHwrite (*,21) 'mC032• ,mCO write (*,21) 'mS042• ,mSO ' ,mHS write ( * , 2 1 ) •mHS' ,mCl write (*,21) •mCl•,mSOD write (*,21) 'msodalite write (*,21) 'mhydroxysodalite ',mHSOD write ( * , 2 1 ) •mH20 ',mH20 format(6x,a,t25,f12.6) WRITE ( * , 2 2 ) 'mAl*mSi :',mAl*mSi FORMAT(3x,a,t26,fl2.7) END funcv Subroutine ===================  C SUBROUTINE f u n c v ( n , x , f ) integer n,m,psod,phsod p a r a m e t e r (m=8) DOUBLE P R E C I S I O N f s o d , fhsod DOUBLE P R E C I S I O N x ( n ) , f ( n ) , g a m ( m ) DOUBLE  PRECISION  AlClin,  NaSiin,  NaOHin,  DOUBLE  PRECISION  NaSOin,  Na2Sin,  H20in  DOUBLE  PRECISION  m N a , mOH, m C l , mCO,  DOUBLE DOUBLE  PRECISION PRECISION  m H S , m A l , m S i , mSOD, mHSOD, mH20 gamNa,gamAl,gamSi,gamOH,gamCO,gamSO  DOUBLE  PRECISION  gamHS,gamCl  DOUBLE  PRECISION  aH20,is,Ksod,  COMMON / C I N P U T / &  AlClin, NaSOin,  NaClin,  NaCOin  mSO  Khsod  NaSiin, Na2Sin,  NaOHin, H20in  NaClin,  NaCOin,  COMMON / P _ V A L U E / p s o d , p h s o d COMMON / R E S U L T / a H 2 0 , i s COMMON / a c t c o e f / &  gamNa,gamAl,gamSi,gamOH,gamCO,gamSO, gamHS,gamCl  mNa = x(l) mAl = x(2)  mSO mHS mCl if  mSi = x(3) mOH = x(4) mCO = x(5) = x(6) = x(7) = x(8) ((psod.eq.0).AND.(phsod.eq.1))  then  212  mSOD = O . O d O mHSOD= x ( 9 ) mH20 = x(10) else i f ((psod.eq.1).AND.(phsod.eq.0)) mSOD = x(9) mHSOD= O . O d O mH20 = x(10) else if ((psod.eq.1).AND.(phsod.eq.1)) mSOD =  then  x(9)  mHSOD= mH20 = else  x(10) x(ll)  w r i t e ! * , * ) "run e r r o r stop end i f call actcof(n,m,x,gam) gamNa = g a m ( l ) gamAl gam(2) gamSi gam(3) gamOH gam(4) gamCO gam(5) gamSO gam(6) gamHS gam(7) gamCl gam(8) C  then  in  funcv!"  Mass f(l) f(l) f(l) Mass  b a l a n c e o f Na = O.ODO = 2*NaSiin+NaOHin+2*NaCOin+2*NaSOin+2*Na2Sin+NaClin = f(l)-(mH2O/55.509)*(mNa+8*mSOD+8*mHSOD) balance of Al  f(2) f(2) f(2) Mass f(3) f(3) f(3) Mass  = O.ODO = AlClin = f(2)-(mH2O/55.509)*(mAl+6*mSOD+6*mHSOD) balance of Si = O.ODO = NaSiin = f(3)-(mH2O/55.509)*(mSi+6*mSOD+6*mHSOD) balance of Cl  C  f(4) f(4) f(4) Mass f(5) f(5) f(5) Mass  = O.ODO = 3*AlClin+NaClin = f(4)-(mH2O/55.509)*(mCl+2*mSOD) balance of S = O.OdO = NaSOin+Na2Sin = f(5)-(mH2O/55.509)*(mSO+mHS) balance of O  C  f(6) f(6) f(6) & Mass  = O.ODO = 12*NaSiin+6*AlClin+NaOHin+3*NaCOin+4*NaSOin+H20in = f(6)-mH2O-(mH2O/55.509)*(4*mAl+3*mSi+mOH+3*mCO+ 4*mSO+26*mSOD+28*mHSOD) balance of H  f(7)  =  f(7) f(7)  = =  C  C  C  C  C  C  c c c  O.ODO 18*NaSiin+12*AlClin+NaOHin+2*H20in f(7)-2*mH20-  & (mH2O/55.509)*(4*mAl+mOH+mHS+4*mSOD+6*mHSOD) Mass b a l a n c e o f C f(8) = f(8) = Electr f(9) =  O.OdO NaCOin (mH20/55.509)*(mCO) oneutrality O.OdO  f(9) = mNa (mOH+mCl+2*mCO+2*mSO+mHS+mAl+2*mSi) Sodalite & Hydroxysodalite formation A c t i v i t y o f p u r e s o l i d c a n be K s o d = 1 . 8 2 d + 1 7 (95 o C ) Ksod = 1.82d+17 fsod= fsod=  assumed as  O.ODO dlog(aH20**4)+dlog(mOH**12)+dlog(gamOH**12)  fsod=  fsod-dlog(mNa**8)-dlog(gamNa**8)  fsod= fsod= fsod=  fsod-dlog(mAl**6)-dlog(gamAl**6) fsod-dlog(mSi**6)-dlog(gamSi**6) fsod-dlog(mCl**2)-dlog(gamCl**2)  fsod=  1.  fsod-dlog(Ksod)  213  c c  Khsod = 3.38d+38 4.39d+36 Khsod = 4.39d+36 f h s o d = O.ODO  (95oC) (from f i t t i n g  to  exp.data)  fhsod= fhsod=  dlog(aH20**4)+dlog(mOH**12)+dlog(gamOH**12) fhsod-dlog(mNa**8)-dlog(gamNa**8)  fhsod=  f h s o d - d l o g ( m A l * * 6 ) - d l o g ( g a m A l * * 6)  fhsod= f h s o d - d l o g ( m S i * * 6 ) - d l o g ( g a m S i * * 6 ) f h s o d = f h s o d - d l o g ( m O H * * 2 ) - d l o g ( g a m O H * * 2) fhsod= fhsod-dlog(Khsod) if ((psod.eq.0).AND.(phsod.eq.1)) then f(10)= fhsod else i f ((psod.eq.1).AND.(phsod.eq.0)) f(10)= else i f f(10) f(ll) else write! stop end i f return end  c c  fsod ((psod.eq.1).AND.(phsod.eq.1)) =fsod =fhsod *,*)  "run error  in  then then  funcv!"  Subroutine o f P i t z e r ' s Model C a l c u l a t e a c t i v i t y c o e f f i c i e n t s S osmotic  coefficients  subroutine actcof(n,m,x,gam) i m p l i c i t double p r e c i s i o n (a-h, o-z) external g,gp integer n,m,neat,nani parameter(ncat=l,nani=7) double p r e c i s i o n x(n),gam(m) integer zc(neat),za(nani) double p r e c i s i o n bethaO(neat,nani),bethal(neat,nani) double p r e c i s i o n betha2(neat,nani),cphi(neat,nani) double p r e c i s i o n thetac(neat,neat),thetaa(nani,nani) double precision ethetac(neat,neat),ethetapc(neat,neat) double precision ethetaa(nani,nani),ethetapa(nani,nani) double precision psic(neat,neat,nani),psia(nani,nani,neat) double precision mc(neat),ma(nani) double precision is,mt,z,bphi(neat,nani) double double double double double  precision precision precision precision precision  c(neat,nani),phic(neat,neat),phipc(neat,neat) phia(nani,nani),phipa(nani,nani) phiphic(neat,neat),phiphia(nani,nani) osml,osm2,osm3,osm3a,osm4,osm4a,osmcal F l , F2,F3,F4,aH20,aphi  double p r e c i s i o n lngamc(neat),game(neat),lngama(nani),gama(nani) double p r e c i s i o n bmx(neat,nani),bpact(neat,nani) common / r e s u l t / a H 2 0 , i s charge zc(l)=+l  Number 1  charge  1  anion Al(OH)4-  moles  c  ma(1)=x(2)  c c  2 3  Si0320H-  ma(2)=x(3) ma(3)=x(4)  za(1)=-1 za(2)=-2  c  4 5  C032-  6 7  HSCl-  ma{4)=x(5) ma(5)=x(6) ma(6)=x(7 )  c c c c  cation Na+  moles mc ( 1 ) = x ( 1 )  c c c  Number  Moles  S042-  of cation  mc(1)=x(1) ma ( 1 ) = x ( 2 ) ma ( 2 ) = x ( 3 ) ma ( 3 ) = x ( 4 ) ma ( 4 ) = x ( 5 ) ma ( 5 ) = x ( 6 ) ma ( 6 ) = x ( 7 ) ma ( 7 ) = x ( 8 )  ma(7)=x(8) and a n i o n s  za(3)=-l za(4)=-2 za(5)=-2 za(6)=-l za(7)=-l  c  Charge  of  cation  and  anions  zc(l)=l za(l)—1 za(2)—2 za(3)—1 za(4)=-2 za(5)=-2 za(6)=-l za(7)=-l c  I n i t i a l i z a t i o n of d o 31 1 = 1 , neat  Pitzer's  parameters  as  O.OdO  do  30 31  40 41  30 k = 1 , nani b e t h a 0 ( i , k ) = O.OdO b e t h a l ( i , k ) = O.OdO b e t h a 2 ( i , k ) = O.OdO cphi(i,k) = O.OdO continue continue d o 41 i = 1 , neat do 4 0 j = 1, neat thetacli,j) = O.OdO ethetac(i,j) = O.OdO e t h e t a p c ( i , j ) = O.OdO continue continue do  50 51  60 61 62  70 71  51 k = 1 , nani d o 50 1 = 1 , nani thetaa(k,l) = ethetaa(k,l) = ethetapa(k,l) =  continue continue d o 62 i = 1 , neat d o 61 j = 1 , neat d o 60 k = 1 , psic(i,j,k continue continue continue d o 72 k = 1 , nani d o 71 1 = 1 , nani d o 70 i = 1 , psia(k,l,i continue  O.OdO O.OdO O.OdO  nani ) = O.OdO  neat ) =  O.OdO  continue  72 continue c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c Reading P i t z e r ' s parameters c cation-anion : bethaO(cation,anion), bethal(cation,anion) c c  betha2(cation,anion), Read b e t h a O , b e t h a l , c p h i betha0(l,l)= bethal(l,l)=  c  c  c  betha0(l,2)=  0.0577  bethal(l,2)=  2.8965  c p h i ( l , 2 ) = 0.00977 Read b e t h a O , b e t h a l , c p h i  c  cphi(l,5)=  of  Na2Si03  of  NaOH a t  95oC  of  Na2C03  at  95oC  of  Na2S04  at  95oC  0.0581 1.2419  c p h i ( 1 , 4 ) = 0.0052 Read b e t h a O , b e t h a l , c p h i betha0(l,5)= bethal(l,5)=  NaAl(OH)4  0.0847 0.3882  c p h i ( l , 3 ) = 0.00021 Read b e t h a O , b e t h a l , c p h i betha0(l,4)= bethal(l,4)=  of  -0.0083 0.0710  c p h i ( l , l ) = 0.00184 Read b e t h a O , b e t h a l , c p h i  betha0(l,3)= bethal(l,3)=  cphi(cation,anion)  0.0988 1.4325  -0.01462  c  Read  bethaO,bethal,cphi of  NaHS  c  betha0(l,6)= 0.1396 bethal(l,6)= 0.0 cphi(l,6)= -0.0127 Read b e t h a O , b e t h a l , c p h i o f  NaCl  c  betha0(l,7)= 0.1008 bethal(l,7)= 0.3207 cphi(l,7)= -0.00337 Read t h e t a a and p s i a  c  c  c  c  c  c  c  thetaa(Al(OH)4-,OH-) thetaa(l,3)= -0.2255  at  95oC  psia(Al(OH)4-,OH-,Na+)  psia(l,3,l)= -0.0388 thetaa(Al(OH)4-,Cl-) psia(Al(OH)4-,C1-,Na+) thetaa(l,7)= -0.2430 psia(l,7,l)= 0.2377 thetaa(Si032-,OH-) psia(Si032-,OH-,Na+) thetaa(2,3)= -0.2703 psia(2,3,l)= 0.0233 thetaa(OH-,C032-) psia(OH-,C032-,Na+) thetaa(3,4)= 0.1 psia(3,4,l)= -0.017 thetaa(OH-,S042-) psia(OH-,S042-,Na+) thetaa(3,5)= -0.013 psia(3,5,l)= -0.009 thetaa(OH-,Cl-) psia(OH-,Cl-,Na+) thetaa(3,7)= -0.05 psia(3,7,l)= -0.006 thetaa(C032-,S042-) psia(C032-,S042-,Na+) thetaa(4,5)= 0.02  c  psia(4,5,l)= -0.005 thetaa(C032-,C1-) psia(C032-,Cl-,Na+) thetaa(4,7)= -0.02 psia(4,7,l)= 0.0085 thetaa(S042-,C1-) psia(S042-,C1-,Na+) thetaa(5,7)= 0.03 psia(5,7,l)= 0.000 U n i v e r s a l constants of P i t z e r ' s eq.(not  c  b = 1.2d0 a l p h a l = 2.0d0 a l p h a 2 = O.OdO i o n i c s t r e n g t h and t o t a l  c  c  is  =  mt do  = O.OdO 110 i = 1, is mt  110  molality  = is = mt  neat  + mc(i)*(zc(i)**2) + mc ( i )  continue d o 111 k =  1,  nani  + ma(k)*(za(k)**2) + ma (k)  111  continue is = 0.5*is  c  Calculating z z = O.OdO do 120 i = 1, neat z = z + mc(i)*abs(zc(i)) continue do z  121  electrolyte)  O.OdO  is = is mt = mt  120  2-2  121 k = 1 , n a n i = z + ma(k)*abs(za(k))  continue  ccccccccccccccc Calculating bphi(cat,ani) d o 131 i = 1 , neat do 130 k = 1, n a n i b p h i ( i , k ) = O.OdO  and c ( c a t , a n i )  coefficients  bphi(i,k) = bethaO(i,k)+bethal(i,k)*dexp(-alphal*dsqrt(is)) bphi(i,k) = bphi(i,k)+betha2(i,k)*dexp(-alpha2*dsqrt(is)) c(i,k) = O.OdO c(i,k) = cphi(i,k) b m x ( i , k ) = O.OdO bmx(i,k)  =  /  (  2*(  (abs(zc(i)*za(k)))**0.5  )  )  bethaO(i,k)+bethal(i,k)*g(alphal*dsqrt(is))  bmx(i,lc)  =  bpact(i,k)  bmx(i,k)+betha2(i,k)*g(alpha2*dsqrt(is)) =  O.OdO  bpact(i,k) = bethal(i,k)*gp(alphal*dsqrt(is)) bpact(i,k) = bpact(i,k)+betha2(i,k)*gp(alpha2*dsqrt(is)) bpact(i,k) = bpact(i,k)/is 130 continue 131 continue ccccccccccc Calculating phic(cat,cat), phipc(cat,cat), phia(ani,ani), c and p h i p a ( a n i , a n i ) d o 141 1 = 1 , neat do 140 j = 1, n e a t phicfi,j) = O.OdO' phipc(i,j) = O.OdO phicfi,j) = thetac(i,j) + ethetac(i,j) phipc(i,j) = ethetapc(i,j) 140 continue 141 continue d o 151 k = 1, n a n i do 150 1 = 1 , nani phia(k,l) = O.OdO phipa(k,l) = O.OdO phia(k,l) = thetaa(k,l) + ethetaa(k,l) phipa(k,l) = ethetapa(k,1) 150 continue 151 continue c c c c c c C a l c u l a t i n g p h i p h i c ( c a t , c a t ) and p h i p h i a ( a n i , a n i ) c o e f f i c i e n t s do 161 i = 1 , (ncat-1) do 160 j = ( i + 1 ) , neat p h i p h i c ( i , j ) = O.OdO phiphic(i,j) = phic(i,j) + is*(phipc(i,j)) 160 continue 161 continue d o 171 k = 1 , (nani-1) do 170 1 = ( k + 1 ) , n a n i p h i p h i a ( k , l ) = O.OdO phiphia(k,l) = phia(k,l) + is*(phipa(k,1)) 170 continue 171 continue ccccccccccccccccccccccccccccccccccccc C a l c u l a t i n g osmotic c o e f f i c i e n t c a p h i : 0 . 3 9 1 5 a t 25oC 0 . 4 5 5 a t 95 o C aphi=0.455 o s m l = O.OdO osml = - a p h i * ( i s * * ( 3 . / 2 . ) ) / ( 1 + b * ( i s * * 0 . 5 ) ) osm2 = O . O d O d o 181 i = l , n c a t do 180 k = 1, n a n i osm2=osm2+(mc(i)*ma(k))*(bphi(i,k)+z*c(1, 180  continue  181  continue osm3 = O.OdO do 192 i = 1, do  190 191 192  (ncat-1)  191 j = ( i + i ) , osm3a = O.OdO do  190 k = 1, n a n i osm3a = osm3a + ma(k)  202 k = 1,  psic(i,j,k)  (nani-1)  201 1 = (k+1), nani osm4a = O.OdO do 200 i = 1, n e a t osm4a  202  *  continue continue osm4 = O . O d O do  201  neat  continue osm3 = osm3+((mc(i)*mc(j))*(phiphic(i,j)+osm3a))  do  200  k))  = osm4a + m c ( i )  *  psia(k,l,i)  continue osm4 = o s m 4 + ( ( m a ( k ) * m a ( 1 ) ) * ( p h i p h i a ( k , 1 ) + o s m 4 a ) ) continue continue  217  c  c  osmcal osmcal  = =  O.OdO osml +  osmcal osmcal  = =  (2.0/mt)*osmcal o s m c a l + 1.  Calculate ah2o ah2o  c  210 211  = =  the  + osm3  activity  of  +  osm4  water  O.OdO 10**(-0.007823*mt*osmcal)  Calculating  F  term  F l = O.OdO '(' Fl = (is**0.5)/(1+b*(is**0.5)) Fl = Fl + (2/b)*log(l+b*(is**0.5)) Fl = Fl*(-aphi) F2 = O . O d O d o 211 1 = l , n c a t d o 210 k = l , n a n i F2 = F2 + m c ( i ) * m a ( k ) * b p a c t ( i , k ) continue continue F3 = O . O d O do  220 221  osm2  221 1 = 1 , d o 220 j = F3 = F3 continue continue F4 = O . O d O  (ncat-1) (i+1),neat + mc(i)*mc(i)*phipc(i,j)  do  231 k = 1 , (nani-1) do 230 1 = (k+1),nani F4 = F4 + m a ( k ) * m a ( k ) * p h i p a ( k , l ) 230 continue 231 continue F = O.OdO F = F l + F2 + F 3 + F4 ccccccccccccccccccccccccccccc Calculating cation d o 790 i i = 1, neat c s u m l = O.OdO csuml = (zc(ii)**2)*F csum2 = O.OdO d o 700 k = 1, nani csum2 = csum2 + m a ( k ) * ( 2 * b m x ( i i , k ) + z * c ( i i , 700 continue csum3 = O.OdO d o 720 j = 1, neat if (j .eq. ii) go t o csum3a = O.OdO do 710 720  710 k = csum3a = continue  csum3 = csum3 continue  coefficient  k))  720  1, nani csum3a + ma(k) +  activity  *  psic(ii,j,k)  mc(j)*(2*phic(ii,j)+csum3a)  csum4 = O . O d O d o 740 K = 1, (nani-1) do 730 L = ( K + 1 ) , nani 730 740  csum4 = continue continue  csum4  + ma(k)  *  ma(l)  *  *  ma(K)  *  750 760  csum5 = O.OdO d o 760 1 = 1 , neat d o 750 K = 1, nani csum5 = csum5 + m c ( i ) continue continue  c  csum5 = a b s ( Z C ( i i ) ) * csum5 lngamct) : In a c t i v i t y c o e f f i c i e n t  c  7 90  psia(K,L,ii)  C(i,K)  of  cation  gamc() : a c t i v i t y c o e f f i c i e n t of c a t i o n by l n g a m c ( i i ) = c s u m l + c s u m 2 + c s u m 3 + csum4 gamc(ii) = dexp(lngamc(ii)) continue  by  Pitzer  Pitzer eq. + csum5  eq.  218  ccccccccccccccccccccccccccccccc do 890 kk = 1, nani a s u m l = O.OdO asuml = ( z a ( k k ) * * 2 )*F asum2 = O . O d O do 800 i = 1, n e a t 800  asum2 = asum2 continue  Calculating  anion  activity  coeficient  + m c ( i ) * ( 2 * b m x ( i , k k ) + z * C ( i , kk))  asum3 = O.OdO d o 820 1 = 1 , nani if ( l . e q . k k ) go t o asum3a = O.OdO  820  do  810 820  830 840  850 860 c c  c 890  c c  810 1 = 1 , n e a t < asum3a = asum3a + m c ( i ) * p s i a ( k k , l , i ) continue asum3 = asum3 + m a ( 1 ) * ( 2 * p h i a { k k , 1 ) + asum3a) continue asum4 = O . O d O do 840 i = 1, (ncat-1) do 830 J = ( i + 1 ) , neat asum4 = asum4 + m c ( i ) * m c ( j ) * p s i c ( i , j , k k ) continue continue asum5 = O . O d O do 860 1 = 1 , neat d o 850 K = 1, nani asum5 = asum5 + m c ( i ) * ma(k) * C ( i , K ) continue continue asum5 = a b s ( z a ( k k ) ) * a s u m 5 lngama() : In a c t i v i t y c o e f f i c i e n t o f anion by P i t z e r gama() : a c t i v i t y c o e f f i c i e n t o f a n i o n b y P i t z e r e q . l n g a m a ( k k ) = a s u m l + asum2 + a s u m 3 + asum4 + asum5 gama(kk) = d e x p ( l n g a m a ( k k ) )  eq.  continue gam(1)=gamc(1) gam(2)=gama(1) gam(3)=gama(2) gam(4)=gama(3) gam(5)=gama(4) gam(6)=gama(5) gam(7)=gama(6) gam(8)=gama(7) R e t u r n aH20 a n d i s v a l u e s Return return  gam() t o  func  b y COMMON  /RESULT/  subroutine  end cccccccccccccccccccccccccccccccccccccccccccccccccc double p r e c i s i o n function g(x) double p r e c i s i o n x if (x.eq.0) then g else  Function  g(x)  = 0  g = endif  2*(l-(l+x)*dexp(-x))/(x**2)  end cccccccccccccccccccccccccccccccccccccccccccccccccc double p r e c i s i o n function gp(x) double p r e c i s i o n x if (x.eq.0) then  Function gp(x)  gp = 0 else gp = - 2 * ( 1 endif  (l+x+(x**2)/2.)  *dexp(-x))/(x**2)  end  Q  ******************************************************  c  newt,ludemp,fdj  c  :subroutines  c  version  ac,lubksb,lnsrch  imported  2.07 t o  from  "Numerical  calculate  non-linear  Recipes  Fortran  equations  77",  219  c  SUBROUTINE PARAMETER  newt(x,n,check) (NP=40,MAXITS=200,TOLF=l.e-2,TOLMIN=l.e-6, TOLX=l.e-7,STPMX=100.)  * c c  *  PARAMETER  c  END SUBROUTINE PARAMETER PARAMETER return END  (NP=40,MAXITS=200,TOLF=l.e-10,TOLMIN=l.e-6, TOLX=l.e-7,STPMX=100.) ludemp(a,n,np,indx,d) (NMAX=500,TINY=1.Od-20) (NMAX=500, T I N Y = 1 . 0 d - 1 0 ) :  SUBROUTINE  fdjac(n,x,fvec,np,df)  return END SUBROUTINE  lubksb(a,n,np,indx,b)  return END SUBROUTINE l n s r c h ( n , x o l d , f o l d , g , p , x , f , s t p m a x , c h e c k , f u n c ) END c c c  fmin(x) :function imported v e r s i o n 2.07 FUNCTION f m i n ( x ) return END  c  Hyeon  Park,  1998  from  "Numerical  Recipes  Fortran  77",  

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