U. S. GEOLOGICAL SURVEY

MIX2: A COMPUTER PROGRAM FOR MODELING CHEMICAL REACTIONS IN NATURAL WATERS

U. S. GEOLOGICAL SURVEY

Water-Resources Investigations 75-61

LIOGRAPHIC DATA 1. Report No. 2.

ET

itle and Subtitle

MIX2: A Computer Program for Modeling Chemical Reactions in Natural Waters

uithor(s) L. Niel Plummer, David L. Parkhurst, and David R. Kosiu Department of Geology, Univ. of California, Los Angeles, Ca

'erforzning Organization Name and Address

U.S. Geological Survey Water Resources Division

12201 Sunrise Valley Drive Reston, VA. 22092

Sponsoring Organization Name and Address

U.S. Geological Survey Water Resources Division

12201 Sunrise Valley Drive Reston, Va. 22092

3. Recipient's Accession No.

5. Report Date

February 1976 6.

————————————————————

. Performing Organization RCRU

No-usGS/WRD/WRI-75/061

10. Project/Task/Work Unit No.

11. Contract/Grant No.

13. Type of Report & Period Covered

Final . ' . 14.

Supplementary Notes

Abstracts MIX2 is a FORTRAN IV computer program that utilizes an aqueous model and the nstraints of mass balance and electrical balance to compute the pH and equilibrium stribution of inorganic species as a result of net reaction progress in the closed stem: CaO-MgO-Na2 0-K2O-C0 2 -H2 SO,-HCl-H2 0. The program considers three general classes

problems involving net reaction progress: 1) mixing of two solutions in fixed volume titration of one solution into another (variable volume), and 3) the addition or .btraction of a net stoichiometric reaction to or from an aqueous solution. In additior X2 will follow one phase boundary through any of the above classes of problems. This port presents the theory and method of calculation used by MIX2, describes the input

the program, presents results of two test cases, and provides a program listing.

Key Words and Document Analysis. 17o. Descriptors

* * *

Computer models, Geochemistry, Chemical Reactions

*Water Chemistry, Mixing, Volumetric Analysis, solubility Aqueous Solutions, Chemical Precipitation, Solvation, Saturation, Equilibrium

Identifiers/Open-Ended Terms

MIX2: A COMPUTER PROGRAM FOR MODELING CHEMICAL REACTIONS IN NATURAL WATERS

By L. Niel Plummer, David L. Parkhurst, and David R. Kosiur

U. S. GEOLOGICAL SURVEY

Water-Resources Investigations 75-61

December 1975

UNITED STATES DEPARTMENT OF THE INTERIOR Thomas S. Kleppe, Secretary

GEOLOGICAL SURVEY V. E. McKelvey, Director

For additional information write to:

U.S. Geological Survey National Center

Office of Regional Hydrologist, MS 432

Reston, Virginia 22092

CONTENTS

Page

Abstract- --- 1

Introduction- Methods --- 2

Aqueous Model --- 2

Numerical Convergence --- 3

case 2 --- 4

case 3 --- 5

General Calculation Procedure --- 6

Input --- 8

Description of input variables- --- 9

optional Input- ---11

Selected References ---12

ii

TABLES

Page

Table 1. Thermochemical Data ---13

2. Parameters of the Debye-HUckel equation- ---15

3. Test Cases- ---16

Example 1- --- 16

Example 2 — ___-.-.__»____»_-.___ 15 List of data cards for example 1---17

List of data cards for example 2--- 17

Output from example 1- --- 18

Output from example 2- --- 35

4. Program listing ---47

MIX2: A Computer Program for Modeling Chemical Reactions

in Natural Waters By

L. Niel Plummer and David L. Parkhurst U.S. Geological Survey

National Center Reston, Virginia 22Q92

and

David R. Kosiur Department of Geology University of California Los Angeles, California 90024

ABSTRACT

MIX2 is a FORTRAN IV computer program that utilizes an aqueous model and the constraints of mass balance and electrical balance to compute the pH and equilibrium distribution of inorganic species as a result of net reaction progress in the closed system: CaO-MgO-Na^O- K^O-CO^-H-SO.-HCl-H^O. The program considers three general classes of problems involving net reaction progress: 1) mixing of two solu- tions in fixed volume, 2) titration of one solution into another

(variable volume) , and 3) the addition or subtraction of a net stoichio- metric reaction to or from an aqueous solution. In addition, MIX2 will follow one phase boundary through any of the above classes of problems.

This report presents the theory and method of calculation used by MIX2, describes the input to the program, presents results of two test cases, and provides a program listing.

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INTRODUCTION

MIX2 is a FORTRAN IV computer program that utilizes an aqueous model and the constraints of mass balance and electrical balance to compute the pH and equilibrium distribution of inorganic species as a result of net reaction progress in the closed system: CaO-MgO- Na 0-K2 0-C02 -H2 SO,-HC1-H2 0. The program considers three general classes of problems involving net reaction progress: 1) mixing of two solutions in fixed volume, 2) titration of one solution into another (variable volume), and 3) the addition or subtraction of a net stoichiometric reaction to or from an aqueous solution, In addi- tion, MIX2 will follow one phase boundary through any of the above classes of probelms.

There are a number of problems in natural water systems, and in the laboratory, that can be modeled by MIX2. For example, MIX2 can model chemical reactions in problems such as sea water encroachment of a fresh water aquifer, Plummer (1975), the testing of proposed inorganic reaction paths in heterogeneous evolving systems, predicting the amount of accompanying mineralogic transfer in reacting hetero- geneous systems, predicting the solubility of minerals in aqueous solutions, and testing proposed aqueous models by simulating labora- tory experiments.

The purpose of this report is to briefly present the theory and method of calculation used by MIX2, describe the input to the program, present test cases suitable for comparison (Table 3), and make avail- able a listing of M1X2 (Table 4).

METHODS Aqueous Model

The aqueous model of MIX2 is similar to that of WATEQ (Truesdell and Jones, 1974),, except that fewer species are used. The species considered and t'hermochemical data (which are valid from 0 to 50°C (Celsius) at one atmosphere total pressure) are shown in Table 1.

Individual ion activity coefficients of changed species are computed

where z is the ion charge and I is ionic strength. In equation (1), the parameters a and b have been estimated for the major ions by Truesdell and Jones (1974) and are given in Table 2. The constants A and B of equation (1) are calculated from the density and dielec- tric constant of water as a function of temperature (Hamer, 1968;

see also Truesdell and Jones, 1974). As shown by Truesdell and Jones (1974, p. 242), the computed activity coefficients for the major ions (Table 2) are near the mean salt values to ionic strengths of 4.0.

Activity coefficients of neutral species are estimated from the relation

log Y ° - 0.11, (2)

except for YT, ™ which has been computed £rom the Henry's Law con- H2 C03

stants of Harned and Davis (1943) (for the solubility of C02 in NaCl solutions) by Wigley and Plummer (1975). The analytical expres- sion for YTT ™ is given as a footnote to Table 1.

H2 C03

The mass action and mass balance equations in the aqueous model of MIX2 are programmed in a manner similar to WATEQ (Truesdell and Jones, 1974). An advantage of this programming method (see Truesdell and Jones, 1974) is that important changes in the model can be accom- plished quite simply. The only significant programming difference between the aqueous models of MIX2 and WATEQ is the method of con- vergence on mass balance for the anions used by MIX2 which is as much as 10 times faster than that of WATEQ. MIX2 solves both cation and anion mass balance in the manner described for cation mass bal- ance by Truesdell and Jones (1974); a method similar to that of Wigley (1971).

Numerical Convergence

MIX2 performs three functions that require an iterative procedure:

1) Solving mass action and mass balance equations in the aqueous model given pE and total compo- sition of the solution.

2) Finding the pH of a solution necessary for both mass and charge balance.

3) Finding the number of moles of a specified mineral to be dissolved or precipitated in order to bring the solution to equilibrium with the mineral and accompanying mass and charge balance.

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Because of the number of iterative calculations made by MIX2, it is essential that the speed of these calculations be optimized.

Probably little can be done to speed convergence on mass action and mass balance in the aqueous model. For example, MIX2 solves the aqueous model for a simple carbonate solution to better than 1.0x10 moles per lOOOg H^O (molality difference between computed mass of carbon and actual carbon) in six iterations, and seawater is solved to the same precision in 14 iterations (see Table 3). These required iterations on the aqueous model compound rapidly, however, in solving for solution pH following chemical reaction (case 2) and particularly in finding phase boundaries (case 3).

In solving cases (2) and (3) above, MIX2 uses an optimized nu- merical convergence scheme of scanning functional relationships until roots are crossed, followed by linear and second order approximation.

As shown in Table 3, this method of convergence is quite rapid, re- quiring roughly 4 to 7 iterations each for cases (2) and (3). The number of iterations on the aqueous model compound rapidly, however, when phase boundaries are solved, because each iteration on the phase boundary necessitates iteration on pH - charge balance which in turn requires iteration on mass action - mass balance in the aqueous model.

Thus, for example, in finding the number of moles of a specified mineral to be dissolved or precipitated (to 3 significant figures) and defining the pH of that solution (to 3 decimal places) can require as many as 686 iterations (7x7x14) of the aqueous model for solutions similar to seawater (when convergence to better than 10~15 On mass balance is required). The test cases of Table 3 show that this esti- mate of number of iterations is an extreme value. Many cases can be solved to high precision in several hundred iterations of the aqueous model, and this estimate of required iterations can be reduced fur- ther when less accuracy of computed results is warranted. We discuss in more detail below the numerical convergence procedure in solving cases (2) and (3).

Case 2. There is one unique value of pH of a solution that, through convergence on mass balance in the aqueous model, will result in perfect charge balance. Perfect charge balance is defined by the equation

I m.z. = 0 (3)

MIX2 uses the following procedure to find the value of pH re- sulting in perfect charge balance, within the prescribed limits of the calculation:

1) Scan pH as a function of charge balance (an approximately parabolic function for most natural waters) until the root is crossed, as indicated by a change in sign of electrical balance and converging on mass balance in the aqueous model with each new estimate of pH.

2) Obtain a first order estimate of the unique value of pH from a linear relation between the point (point (X,Y) = point (pH, electrical balance)) above the root and the point below the root, and return to the aqueous model for convergence on mass balance to find the new corresponding value of charge balance.

3) Obtain a second order estimate of the unique value of pH using a parabolic solution to the three values from step 2 (above), and return to the aqueous model for convergence on mass balance to find the corresponding charge balance.

At this point, MIX2 has knowledge of four points on the pH - electrical balance curve. Because of the nature of the pH - electrical balance curve, the 4th point, obtained by the second order approximation, is closer to the root than any of the other 3 points, and is therefore retained.

Two of the remaining 3 points lie on the same side of the root. The absolute values of the electrical balance of these two points are compared and the point farthest from the root is discarded.

4) Repeat step 3 (above) until the required precision is ob- tained.

Once the root is crossed, this procedure usually finds pH to 3 decimal places in 2-3 steps, which compares with 20 or more steps by interval halving techniques. It is important that the root be crossed in as few steps as possible; MIX2 scans initially at 0.2pH (in the direction of the root based on the sign of electrical balance), and if not crossed on the first step, the scanning increment is in- creased to l.OpH unit.

Case 3.

Case 3, that of locating a phase boundary, is essentially iden- tical (mathematically) to that of finding the unique value of pH

(case 2), where pH is replaced by the term "XMOL", the number of moles of the appropriate mineral to be added to or removed from the solution to bring the solution to equilibrium with the mineral, and electrical balance is replaced by the corresponding saturation index

—5—

(SI) of the mineral. Saturation index is defined by

SI = log +f- TAP (4)

where IAP is the ion activity product of the mineral in solution and K is the thermodynamic equilibrium constant. Negative values of SI correspond to undersaturation and positive values indicate super- saturation. In finding a phase boundary, each new estimate of XMOL revises the total masses of appropriate species in solution which requires iteration on mass and charge balance (case 2) to define the new pH, distribution of species and resultant mineral saturation index corresponding to the estimate of XMOL.

General Calculation Procedure

Having described some of the details of the aqueous model and numerical convergence procedure of MIX2, we can discuss the overall calculation scheme of the program. All calculations of MIX2 are performed in double precision, necessary for the required convergence on an IBM 370/155. The initial data to MIX2 define the various op- tions and required parameters for the job to follow. The total mass composition, pH, temperature and density of initial solution is read and the units of concentration are converted to molality, if not entered as molality. All equilibrium constants and other temperature dependent data are computed at the temperature of the input solution.

Because the constraint of charge balance will be utilized later in the program to determine solution pH, it is essential that the initial solution be balanced in charge through the aqueous model in accordance with the initial pH. Charge balance in the initial solu- tion is accomplished by adding^ chloride OIL potassium (as determined by the initial charge imbalance) using the same numerical procedure described above for finding the pH of solutions.

So that any possible errors in later solutions, owing to dif-

ferences in extent of convergence, will be negligible, the initial

solutions are converged on mass balance and charge balance to _< +

10~~15. Also with the choice of the appropriate input option (de-

scribed in a later section of this report), the pH of an initial

solution can_be adjusted rather than total chloride"or potassium

content in determining initial charge balance.

temperature effects resulting from heats of reaction are not consid- ered.

If a net reaction is to be added to the initial solution, the

^toichiometric coefficients of each component in the net reaction, X, are entered along with values of total moles of that net reaction to be added to the solution. The net stoichiometric reaction must be perfectly charge balanced, that is,

V + V " V + 2 <^o~ + foo-> (8)

except for the cases of adding acids ojr bases to solution, such as in the oxidation of organic matter where X— — is taken as Xpn .

L.U- L.U«

For example, suppose that along a presumed flow path in an aqui- fer, analytical data suggest that the net reaction is, relatively, 2.7 moles of calcite +0.5 moles of dolomite +0.1 moles of CHLO

(organic matter) per mole of gypsum. The stoichiometric coefficients for the net reaction could be written X ++ =4.2, \++ * 0.5, X — 3.8, and X — = 1.0, with the remaining X values equal to zero. The

oU , 4

total mass composition of the solution is computed at any point in reaction progress from the total concentrations in the initial solu- tion, the stoichiometric coefficients of the net reaction, and the number of moles of the net reaction to be added to the solution, XMIX; i.e.,

CTOT (a) = CTOT (initial) + XMIX - X (9) where CTOT is the total molality of the species in solution and a

indicates the desired amount of reaction progress. If, based on the net stoichiometric reaction, the total molality of sulfate added to

the initial solution at a is to be 3.0 mmoles, XMIX (equation 9) be- comes 0.003. After the step in reaction progress is taken, MIX2 returns to the iterative convergence procedure of finding pH result- ing in both charge and mass balance.

If the appropriate options are specified in the input data, MIX2 will follow any mineral phase boundary that can be defined in

the chemical system of the aqueous model. The phase boundary is defined by entering the number of moles of each component in one mole of the mineral, PHAS (I), and the desired value of the equilibrium constant to be followed. For example, if it is desired to maintain

—1 6 85

the ion activity product of dolomite at 10 , one would enter PHAS (Ca++) =1.0, PHAS (Mg++) =1.0, PHAS (C0"~) = 2.0 and a log value of the "equilibrium" constant, KPHAS, of -16.85. All other

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values of PHAS(I) would be zero. MIX2 is capable of following one phase boundary during, mixing, titrating, or dissolution - precip- itation reaction steps.

INPUT

The number of data cards required by MIX2 is variable and de- pends on the nature of the problem being solved. We have listed below the data requirements for all possible situations considered by MIX2 in the sequence in which the cards would be input. The actu- al input cards required for a particular problem should be evident from the description of the input variables.

Card

2 3 4 5 6 7 7 + n

8 + n

Variables

IOPT1, IOPT2, IOPT3, IOPT4, IOPT5, IOPT6, IOPT8, IOPT9, IOPT10, NMIX, VO, CLOSE, HCLOSE, STPSIZ

COEF(I), (I * 1,7)

PHAS (I), (I * 1,7), KPHAS XMIX (I), (I » 1, NMIX) TITLE

TEMP, PH, DENS, FLAG, IHOLD, IOPT7, CUNITS(7)

CUNITS (I), (I * 1,6)

n cards containing optional input pertaining to Solution 1 are read here

Blank card required to denote

Format (911, 15 4D10.3)

(7D10.3) (8D10.3) (8D10.3) (20A4)

(3D10.3, IX, 311, IX, D12.5)

(6D12.5)

(A4, IX, 5(13,

D12.5))

Description of Input Variables

IOPT1 IOPT2 IOPT3 IOPT4

TOPT5 IOPT6

IOPT8 IOPT9

IOPT10 NMIX

VO

Equals 0 prints thermochemical data, equals 1 omits print of thermochemical data.

Equals 0 prints convergence iterations on electrical balance for initial solutions, equals 1 to omit print.

Equals 0 prints convergence iterations on pH, equals 1 to omit print.

Equals 0 if solution 1 is to be mixed with solution 2 in a fixed volume system. Equals 1 if solution 2 is to be titrated into solution 1, (VO must be specified), equals 2 if any net stoichio- metric reaction is to be added to or removed from solution.

Equals 0 prints summary of titration pH curve (if IOPT4 equals 1).

Equals 1 omits summary of pH titration curve.

Equals 0, roots are found by scanning, linear, and parabolic

approximation. Equals 1, roots are found by scanning and interval halving. Note that IOPT6 equals 0 is significantly faster than IOPT6 equals 1.

Equals 0 if no phase boundary is to be followed, phase boundary is to be followed.

Equals 1 if one Equals 0 if phase boundary is to be followed at all points in the reaction, (provided IOPT8 equals 1). Equals 1, phase boundary will be followed if solution supersaturates with specified phase

(PHAS(I), KPHAS), provided IOPT8 equals 1. Thus, if IOPT9 equals 0, the specified mineral will either dissolve or precipitate in maintaining "equilibrium". If equal to 1, the mineral will pre- cipitate only in maintaining SI-KPHAS.

Equals 0, causes printout of convergence iterations on the phase boundary search (if IOPT8 equals 1). Equals 1 omits print.

Total number of mixtures to be made if IOPT4 equals 0, or total number of titration additions (of defined solution 2 into solution 1), if IOPT4 equals 1, or total number of additions or removals of a net stoichiometric reaction, if IOPT4 equals 2.

Initial volume of solution 1 if IOPT4 equals 1, otherwise leave VO blank. If IOPT4 equals 1, VO must be greater than zero and have the same units as XMIX (I).

-9-

CLOSE Absolute value of SI desired in following phase boundary.

Reasonable value is 0.001. Leave blank if IOPT8 is not equal to 1.

HCLOSE A factor that is multiplied times the absolute value of

electrical balance to determine the closure on mass balance.

l.OD-08 is reasonable. If the electrical balance is l.OD-04, convergence on mass balance would be to l.OD-32 for HCLOSE of l.OD-08. All initial solutions converge to l.OD-15 regardless of the value of HCLOSE. Larger values of HCLOSE decrease the

time for convergence on mass balance, and increase the error of the aqueous speciation.

STPSIZ A factor that is multiplied times the total limiting concen- tration of species in the phase-boundary mineral in order to determine the step size in searching for the phase boundary.

STPSIZ must be greater than 0.0 and less than 1.0. Values of 0.3 to 0.6 are reasonable. Large values of STPSIZ usually increase the speed of convergence on saturation.

COEF (I) Stoichiometric coefficients of the net reaction being added to or removed from solution. Omit card if IOPT4 is not equal to 2. Order is Ca Mg Na Cl , SO, CO,

PHAS (I) Number of moles of each major species in one mole of the

mineral for which the phase boundary is to be followed. Order is Ca Mg Na Cl , SO, and

KPHAS

XMIX (I)

The log of the equilibrium constant for the mineral PHAS (I) ++ +•

written in terms of mineral = ions, where ions are Ca , Mg Na , K Cl , SO, , and CO

Percent of solution 2 to be mixed with solution 1, if IOPT4 equals 0. If IOPT4 equals 1, XMIX is the volume of solution 2 (same units as VO) to be added to solution 1. If IOPT4

equals 2, XMIX is the total number of moles of the net reaction

(COEF (I)) to be added to the solution for each desired point

along the proposed reaction path. XMIX (I) is negative if

PH Negative log activity H . DENS Density of Solution (g/cc).

FLAG Signal for units of input concentration. 1 equals meq/1, 2 equals mg/1, 3 equals ppm, 4 equals molality.

IHOLD Signal used to hold a previous end-member solution constant on successive mixing or titrating cases. IHOLD must be zero for the first 2 end-member solutions input. On additional mixing cases, IHOLD may be 0, 1, or 2. If IHOLD equals 0,

2 new end-member solutions are read in. If IHOLD equals 1, the previous defined solution 1 is saved and solution 2 is redefined by input. The opposite is true if IHOLD equals 2.

IOPT7 Equals 0 if chloride or potassium are to be adjusted in the initial solution for charge balance. Equals 1 if the pH of the initial solution is to be adjusted for charge balance.

CUNITS (7) Total concentration of carbon in solution.

CUNITS (I) Total concentrations of Ca , Mg , (1-1,6) (in order) in initial solution.

Na"*", K4", Cl", and S0~

Optional Input

Optional input cards can be used to (1) input the total concen- trations of species not included on cards 6 and 7 ("CONC" card (s));

(2) change AH' ("DELH" card (s)); (3) change log K at 25 C ("TABL"

card (s)); or (4) input a value of log K that overrides all previous values of log K and will not be corrected for temperature ("LOCK"

card (s)). n option cards fit in the data stream between card 7 and the blank card 8+n. There is no limit to the number of option cards used. However, the order in which option cards appear must be that as described above (1-4), that is, 1., "CONC", 2., "DELH", 3., "TABL", 4., "LOCK". It is possible to use none, 1, 2, 3, or all 4 types of option cards in a single data set provided the sequencing is that shown above. Information coded on option cards must follow a fixed format:

Variables

WORD, (INT(I), VAL(I), I - 1,5)

Format

(A4, IX, 5(13,E12.5)) Where WORD is either "CONC", "DELH", "TABL", or "LOCK". INT (I) is the subscripting number in the program and VAL(I) is the appropriate new value. As many as 5 values may be input on each option card.

Subscript numbers for reactions in the aqueous model are~ given in Table 1, and subscript numbers for ions appear in Table 2. If IOPT4 is

not equal to 2 and thermodynamic data are overridden with optional input for solution 1, similar appropriate input should follow with solution 2.

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SELECTED REFERENCES

Back, W. and Hansahw, B. B., 1970, Comparison of chemical hydro- geology of the carbonate peninsulas of Florida and Yucatan:

Jour. Hydrology 10, 330-368.

Hamer, W. J., 1968, Theoretical mean activity coefficients of strong electrolytes in aqueous solutions from 0 to 100°C: U.S. Natl.

Bur. Standards, Natl. Standard Reference Data Ser. 24, 271 p.

Harned, H. S. and Davis, R., Jr., 1943, The ionization constant of carbonic acid in water and the solubility of carbon dioxide in water and aqueous salt solutions from 0 to 50°: Am. Chem. Soc.

Jour. j>5, 2030-2037.

Harned, H. S. and Scholes, S. R., Jr., 1941, The ionization constant of HCO" from 0 to 50°: Am. Chem. Soc. Jour. 63, 706-1709.

Jacobson, R. L., and Langmuir, D., 1974, Dissociation constants of calcite and CaHCO"t from 0 to 50 C: Geochim. et Cosmochim.

Acta, 38, 301-318.

Kielland, J., 1937, Individual activity coefficients of ions in aqueous solutions: Am. Chem. Soc. Jour. 59, 1675-1678.

Plummer, L. N., 1975, Mixing of sea water with calcium carbonate ground water, in E.H.T. Whitten, Ed., Geol. Soc. America, Memoir 142, 219-236.

Reardon, E. J., and Langmuir, D., 1974, Thermodynamic properties of the ion pairs MgCO~ and CaCO° from 10 to 50°C: Am. Jour. Sci.

274, 599-612. J

Robinson, R. A., and Stokes, R. H., 1955, Electrolyte Solutions:

London, Butterworths Scientific Publications, 559 p.

Siebert. R. M., 1974, The stability of Mgl:a+ and MgCO° from 10°C to 90 C: Ph.D. Dissertation, Univ. of Missouri.

Truesdell, A. H., and Jones, B. F., 1974, WATEQ, A computer program for calculating chemical equilibrium in natural waters: Jour.

Research, U.S. Geol. Survey, 2_, 233-248.

Wigley, T.M.L., 1971, Ion pairing and water quality measurements:

Can. J. Earth Sci., 8, 468-476.

Wigley, T.M.L., 1973, Chemical evolution in the system calcite- gypsum-water: Can. J. Earth Sci., 10, 306-315.

Wigley, T.M.L., and Plummer, L. N., 1975, Mixing of Carbonate waters:

Geochim. et Cosmochim. Acta, in press.

TABLE 1 Thermochemical Data 1

Reaction AH° 2 LogK^.v 3

(6) CaOH4 - Ca44 + OH*

(9) CaSO? - Ca44 + S0~~

H H

(2) MgOH4 - Mg44 + OH"

(5) MgSO° - Mg44 + S0~~

(12) NaSO~ - Na4 + S0~~

(16) Na 2 SO° - 2Na4 + SO™

(11) NaHCo" - Na4 + HCO~

(10) NaCO~ - Na4 + C0~

(14) N« 2CO° - 2Na + C0~~

(20) NaCl° - Na4 + Cl~

(21) KC1° - K4 + Cl~

(19)HC1° - H4 + Cl"

. (17)H20 - H + OH"

(22)H2 SO° - 2H4 + S0~

(26)CaMg (C0 3 ) 2 dolo-lt .) -Ca44 - (24)CaC03(.ragonite) - Ca++ <

(25)MgC03(iMgne||lte) - Mg4*- (27)CaS°4 (anhydrite) - <*" '

-1.19 -1.50 -2.14 -1.27 -2.229

3.657

———

-8.911 14

<4

>4

-18.630 -13.345

WM»«4

* Mg44 + 200^ -«.29

k C0~ -2.959

*• C0~ -6.169

^ S0~ -3.769

-1.40 -2.309 -2.60 -2.238 -0.226 -1.512 0.250 -1.268 -O.672 1.602 1.585 +6.10 -13.998

1.00

-17.00 -8.215 -8.24 -4.548 Analytical Expression (7.) CaHCO4 - Ca44 + VCO~

(8) CaCO° - Ca44 + C0~

(4) MgHCO4 - Mg44 + VCO~

(3) MgCO° - Mg44 + C0 3 "

(18)H2CO° - H4 + HC03 (1) HC0 3 - H4 + C0~

(13) K804 - K4 + 30~

(15) HSO^ - H4 + 30~

°°2 4 *2° " "z^a

(23) CaCO

-Ca44 + CO"

(28) c* s°it (gyfBvm )

« Ca •*• SO.

LogK(T) 5 - 2.95 - LogK(T) - 27.393 -

7

LogK(T) - -2.319 + LogK(T) - 8 -.991 - LogK(T) - 14.8435 LogK(T) - 6.498 - LogK(T) - -3.106 4 LogK(T) - 5.3505

9 f U

*** *H^C0 3 - PCO - 2

LogK(T) S - 13.870 -

12

LogK(T) - -*.6535 .0133T

4114/T - .05617T

1.1056xlO"2T + 2.29812xlO"5T 2 .00667T

- 0.032786T - 3404. 71/T 0.02379T - 2902. 39/T 673. 6/T

- 0.0183412T - 557.2461/T 14.0184 + 0.015264T + 2385. 73/T

• 0.04035T - 3059/T

+ 4.545xlO~3T - 1.01x10 TZ

(footnotes, see next page)

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Footnotes to Table JL

I/ Thermochemical data used in the aqueous model, except where noted have been taken from the recent compilation of Truesdell and Jones (1974). Numbers in parentheses indicate appropriate reaction numbers required for optional input of thermochemical data.

2/ Standard enthalpy of reaction (Kcal/mole).

3/ Log of equilibrium constant, K, for the reaction at 25 C.

4/ No value of AH is available. The temperature dependence of log K has been ignored.

5/ Jacobson and Langmuir (1974).

6/ Reardon and Langmuir (1974).

11 Least squares fit to the data of Siebert (1974).

8/ Siebert (1974).

9/ Harned and Davis (1943).

107 Harned and Scholes (1941).

ll/ Based on the assumption that Y^CO- is unity in C02 saturated aqueous solutions. The temperature and ionic strength depend- ence of YH~CO.j in the presence of dissolved solids has been estimated from the solubility of CO- in Nad solutions (Harned and Davis, 1943), and is log yH0 C0 0 = I (a - bl) where

2 3 ~T~

I is ionic strength, T is temperature in °K, a = 33.5 - 0.1099 + 0.00149 2 , and b = 1.5 + 0.0159 - 0.00492 where 9 is temperature in °C.

12/ Wigley (1973).

Table 2—parameters of the Debye^Huckel equation Major ions

Ca-(l)

Mg^d)

Na+ (3) K+ (4) cr<5) S0~~(6) HCO~(7) C0~"(8)

Minor ions OH~ (24) MgHCO+dl) HSO~(22)

NaCO~(17), NaSO~(19), KSO~(20) CaOH+ (13), CaHCO^(14)

MgOH+ (9) H+ (23)

&

5.0 5.5 4.0 3.5 3.5 5.0 5.4 5.4 a 3.5 4.0 4.5 5.4 6.0 6.5

b 0.165

.20 .075 .015 ,015 -.04 0.0 0.0

Numbers in parentheses are the subscript numbers for the ions ±n KTX2.

Subscription for the neutral species is as follows: MgCO_(10), >s gSO,(12), HC1°(27), NaCl°(28), KC1°(29), H SC

2/ a and b values calculated from experimental mean salt single - ion activity coefficients by Truesdell and Jones (1974).

3/ a values from Kielland (1937); b values set to zero.

-15-

TABLE 3

Two test cases are presented below that serve as examples of input data sets for MIX2, and provide output from MIX2 suitable for comparison.

Example 1

The first case is that of mixing sea water with a solution saturated with calcite at a P _ of 1CT 2 atmospheres and 10°C.

L«Urt

After each mixture is solved, the solubility of calcite in the solu- tion is computed. The CaHCO+ ion pair is ignored via the optional

"LOCK" card. The input data set provides for 3 mixtures to be com- puted (10%, 30% and 50% sea water).

Example 2

The second case simulates a proposed closed system reaction path in the Floridian aquifer (based upon the field data of Back and Hanshaw, 1970). It is assumed that the chemical path of the ground water results from the net stoichiometric reaction

starting water + XMIX (Ca 0 , 0Mg rtCft SO. C0_ ) •*• groundwater .873 .059 4 3

+ XMOL

where "starting water" is the Polk City analysis of Back and Hanshaw

(1970), and XMIX is the moles of the net stoichiometric reaction

dissolved. A 2 mole percent magnesian calcite is precipitated at

approximately 2-fold saturation (pK^S^) where XMOL is the number of

moles of calcite precipitated along the path. Two points along the

proposed reaction path (XMIX - 10""^ and 10"^ moles) are presented.

List of data cards for example 1

1 r i 3 l.OOOD 00

l.OOOD 01 3.0000 01

SOLUTION NUMBER

1.0000 01 7.3350 00 2.16600D-03

LOOK 7-3.000000 01

l.OOOD-03 1.0000-00 5.0000-01 GOOD 01

0000 00 400 4.86028D-03

l.OOOD 00-8.359D 00

SEA WATER SOLUTION NUtfRER 2 DRYSSE* AND WEOBCRQ (] 974 ) 35 PPT. C l_* 1 <«• 3 74PF T 1.0000 01 8.1500 00 l.OOOD 00 400 2.368200-03

1.066000-02 5.508000-02 4.846300-01 1.058000-02 5.657200-01 2.926000-02 LOGK 7-3.000000 01

List of data cards for example 2

000200110 2 0.6730 00 0,0590 00 0.9800 00 0.0200 00 1.0000-03 1.0000-02

SIMULATION OF CENTRAL FLORIDA GROUND tuATER CHEMISTRY, 2.5000 01 8.0000 00 l.OOOD 00 400 1.270000-04

8.400000-04 2.300000-04 1.390000-04 1.300000-04 2.500000-04 2.10000D-03 1.0000-03 1.0000-08 5.0000-01

0.0930 00 0.907H 00

1.0000 00-8.2000 00

START

DATA I NWEACTLOGKTOLOGKT

1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ?3 2* 25 26 27 28 29 30

KHCC3 KVGCH KMGC03 KMGHC03 KMGS04

KCACH

KCAHC03 KCAC03 KCAS04 KNAC03 KNAHC03 KNAS04 KKSC4 KNA?C03 KHSC4 KN42S04 KM KH3C03 KHCL KNACL KKCL KH2S04 CALCITE AR AGON IT *AGNESIT DOLOMITE AKHYDRIT GYPSUM BRUCITE MUNTITE 3.5500 ?.1400 0.0580 10.3700 1.2700 1.1900 6.3310 3.1300 1.5000 8.9110 0.0 2.2290 3.08?0 0.0 4.9100 -3.6570 13.3450 1.9760 18.6300 0.0 0.0 0.0 -3.1900 -2. 9590 -6.1690 -8.2900 -3.7690 0.2610 0.8500 -25.7600 -10.3296 2.6000 3.3980 0.9280 2.2380 1.4000 1.2600 3.2000 2.3090 1.2680 -0.2500 0.2260 0.8470 0.6720 1.9870 1.5120 -13.9980 -6.3510 -6.1000 -1.6020 -1.5850 -1.0000 -8.4100 -8.2150 -8.2400 -17.0000 -4.5480 -4.7590 -11.4100 -30.5100 -10.4884 2.5169 2.8797 1.0310 2.1887 1.3538 -30.0000« 3.0410 2.2508 0.9220 -0.2500 0.1395 0.7271 0.6720 1.8109 1.6540 -14.5162 -6.4642 -6.8234 -1.6020 -1.5850 -1.0000 -8.3586 -8.1001 -8.0005 -16.6781 -4.4017 -4.7691 -11.4430 -29.5098

I 1 ?

3 4

«;

6 7 8 9 10 11 12 13 14 15 1ft 17 1« 19 20 21 22 23 24 25 26 27 28 29 30

NSPEC CA** KG** NA + K* CL- S04— HC03- C03-- MGOH* MGC03 WGMCC3* MGS04 CAOH* CAHC03* CAC03 CAS04 NAC03- NAHC03 NAS04- KS04- NA2C03 HS04- H* OH- NA2S04 H2C03 HCL NACL KCL H2S04

Z 2. 2. 1. 1. -1. -2. -1. -2. 1. 0. 1. 0. 1. 1. 0. 0. -1. 0.

-1. -1.

0.

-1. 1. -1.

0. 0. 0. 0. 0. 0.

DHA 5.0 5.5 4.0 3.5 3.5 5.0 5.4 5.4 6.5 0.0 4.0

o;o

6.0 6.0 0.0 0.0 5.4 0.0 5.4 5.4 0.0 4.5 9.0 3.5 0.0 0.0 0.0 0.0 0.0 0.0

GFW 40.0800 24.3120 22.9898 39.1020 35.4530 96.0616 61.0173 60.0094 41.3194 84.3214 85.3293 120.3736 57.0874 101.0973 100.0890 136.1416 82.9992 83.9909 119.0514 135.1636 105.9890 97.0696 1.0080 17.0074 142.0412 62.0253 36.4610 58.4428 74.5550 98.07T5 • DENOTES VALUES CHANGED IN INPUT

SOLUTION NUMBER 1

SOLUTION NUMBER i

TEMPERATURE * 10.00 DEGREES CPI- » 7.335ANALYTICAL EPMCAT •4.3ANALYTICAL EPMAN >4.9 —— TOTAL CONCENTRATIONS OF INPUT SPECIES —— SPECIESTOTAL KOLALITYLOG TOTAL MOLALITYTOTAL GRAMS/KGM H20 CATOT

MGTOT NATOT KTOT

CLTOT S04TOT -2 C02TOT -1 0.2166000-02 0.0 0.0 0.0 0.0 0.0 0.4860280-02

•2.6643 0.0

o.o

0.0 0.0 0.0 •2^3133

0.8681330-01 0.0 0.0 0.0 0.0 0.0 0.2965610 00 ITERATION 1 2 3 4

—— CONVERGENCE ITERATIONS —— S1-C02TOT S2-S04TOT S3-CLTOT -0.4050580-15 -0.4050580-15 -0.4050580-15 -0.4050580-15

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

ELECTRICAL BALANCE N MODEL -0.19029230170023100-05 6 -0.25343926827361840-08 6 0,18970544599018890-05 6 -0.15210119017775240-15 6 ——DESCRIPTION OF SOLUTION ANALYTICAL COMPUTED PH EPMCAT 4.33 4.32 7.335 EPMAN 4.86 4.32 IONIC STRENGTH « 0.6489440-02 TEMPERATURE DENSITY • 1.0000 10.00 OEG C CLTOT > 0.0 KTOT « 0.1905460-05

ACTIVITY H20 * 0.9999 PCC2 • 0.1000040-01 LOG PC02 • -2.0000 UNCOUPLE* C02 « 0.4855490-02 C02TOT * 0.4860280-02 ELECT * -0.1521010-15 ALKALINITY • 4.334 MEG/LITRE

DISTRIBUTION OF 2. 1. -1. -2. 1. 1. 0. 1.

-1.

0.

PPM 0.865B8P 02 0,74*790-01 0.263?8D 03 0.231940 00 0.143670-03 0.680670-30 0.47955D 00 0. 502100-04 0.121010-02 0.331740 02 UP 0. 43680-08 0.43680-08 0.0 0.0 0.0 MOLALITY 0. 216120-02 0.190550-05 0.431660-02 0.386660-05 0. 251760-08 0. 673540-35 0. 479310-05 0. 498300-07 0.717090-07 0.535060-03 KT LOG 0. 43790-08 -8 0.79410-08 -6 0.99890-08 -100 0.20980-16 -100 0. 17020-04 -100

LOG -2. -5. -2. -5. -8. -35. -5. -7. -7. -3. IAP .3597 .3597 .0000 .0000 .0000

MOL 6653 7200 3649 4127 5990 1716 3194 3025 1444 2716 LOG -8 -8 -8 -16 -4

0 0 0 0 0 0 0 0 0 0 KT .3586 .1001 .0005 .6781 .7691

SPECIES ACTIVITY .156P1D-0? .175110-05 .398060-02 .279620-05 .232420-0* .621*10-35 .460030-05 .462380-07 .658840-07 .535980-03 IAP/KT 0.99740 00 0.5500D 00 0.10000-49 0. 10000-49 0. 10000-49

LOG ACT -2 -5 -2 -5 -8 -35

.8063 .7567 .4000 .5534 .6337 .2063 -5.3187 -7 -7 -3

.3350 .1812 .2709

ACT. COEFF. 0 0 0 0 0 0 0 0 0 0.722790 00 .918970 00 .922170 00 .723180 00 .923190 00 .923190 00 .100150 01 .927910 00 .918760 00 .100170 01 LOG IAP/KT -0 -0 -100 -100 -100

.00113 .25961 .00000 .00000 .00000 LOG A COF -0.1410 -0,0367 -0.0352 -0.1408 -0.0347 -0.0347 0.0006 -0.0325 -0.0368 0.0007

SEA WATEH SOLUTION NUMBER 2 DRYSSEN AND WEDBORG<1974) 35 PPT. CL«19.374PPT SOLUTION NUMBER 2 TEMPER«TURF10.00 DEGREES C PH » 8.150 ANALYTICAL EPMCAT • 626.7 ANALYTICAL EPMAN • 626.6 —— TOTAL CONCENTRATIONS OF INPUT SPECIES —- TOTAL LOG TOTAL SPECIES fOLALirr MOLALITYTOTAL GHAMS/KGM H20 CATOT MGTOT NATOT KTOT CLTOT S04TOT

2. 2. 1. 1. -I. -2. C02TOT -1.

0,1066000.01 0.5508000-01 0.4846300 00 0.1058000-01 0.5657200 00 0.2926000.01 0.2368200-02

•1.9722 •1.2590 •0.3146 •1.9755 •0.2474 •1.5337 •2.6256

0.4272530 00 0.1339100 01 0.1114150 02 0.4136990 00 0.2005650 02 0.2810760 01 0.1445010 00 ITERATION 1 2 3 4

—— CONVERGENCE ITERATIONS —— S1-C02TOT S2-S04TOT S3-CLTnT 0.1820090-13 0.1109550-12 0.1337820-12 0.3398970-16 0.3035770-16 -0.6938890-16 0.1808860-13 0.1116210-12 0.1268430-12 0.3355610-16 0.2775560-16 -0.1387780-16

ELECTRICAL BALANCE N MODEL -0,16558240124489430-04 12 -0.61719184795461450-11 IS 0.16558227018393360-04 12 0.27326937239648830-16 15 ——-DESCRIPTION OF SOLUTION ANALYTICAL COMPUTED PH EP"CAT 626.69 591.38 8.150 EPMAN 626.61 591.38 IONIC STRENGTH > 0.6636430 00 TEMPERATURE DENSITY > 1.0000 10.00 OE6 C CLTOT • O.S65720D 00 KTOT > 0.1059660-01

ACTIVITY H20 * 0.9808 PC02 * 0.4570760-03 LOG PCC2 * -3.3400 CNCOMPLEX C02 « 0.1790900-02 CD2TOT * 0.2360200-02 ELECT « 0.2732690-16

ALKALIMTY • 2.464 MEQ/LITRE

DISTRIBUTION OF SPECIES

1 ^

SPECIES CA + + 2. f<5 + + 2. NA + 1. K+ 1. CL- -1. S04 — -2. HCC3- -1. C03 — -2.

PGOH+ i.

KGC03 0. f6HC03+ 1. I*GS04 0.

CAGH+ i.

CAHC03+ 1. C&C03 0. CAS04 0. NAC03- -1. NAHC03 0. NAS04- -1. KS04- -1. NS2C03 0. (-S04- -1. h+ 1. CH- -1. NA2S04 0. H2C03 0. HCL 0. NACL 0.

KCL o.

H2S04 0. PHASE 23 CALCITE 24 ARA60NIT 25 MAGNESIT 26 DOLOMITE 28 GYPSUH

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

PPM .376590 03 .117440 04 .102110 05 .392810 03 .192*10 05 .114430 04 .102600 03 .146580 01 .115880 00 .428900 01 .245760 02 .53346D 03 .189210-02 .417680-30 .12478C 01 .117670 03 .175720 01 .152460 02 .177860 03 .156300 02 .248240 00 .152990-03 .906080-05 .112330-01 .133210 04 .123540 01 .113790-10 .140870 03 .373810 01 .948040-15 IAP 0.13720-07 0. 13720-07 0 0 0.61130-07 .11130-14 .58660-05 MOLALITY 0.975010-02 0.501270-01 0.460900 00 0.104250-01 0.563170 00 0.123620-01 0.174490-02 0.253470-04 0.291010-05 0.527820-04 0. 298880-03 0.4598BP-02 0.343930-07 0.428730-35 0.129370-04 0.896920-03 0.219700-04 0.188360-03 0.155030-02 0.120000-03 0.237170-05 0.163550-08 0.932780-08 0.685350-06 0.973210-02 0.206680-04 0.323850-15 0.250130-02 0.520290-04 0. 100310-19 KT LOG 0.43790-08 -7 0.79410-08 -7 0.99890-08 -7 0.20980-16 -14 0.17020-04 -5

LOG MOL -2 -1 -0 -1 -0

-1

-2 -4 -5 -4 -3 -2 -7 -35 -4

-3

-4 -3 -2 -3 -5 -8 -8 -6 -2 -4 -15 -2 -4 -19 IAP .8628 .8628 .0908 .9536 .2316

.0110 .2999 .3364 .9819 .2494 .9079 .7582 .5961 .5361 .2775 .5245 .3374 .4635 .3678 .888? .0472 .6582 .7250 .8096 .9208 .6249 .7863 .0302 .1641 .0118 .6847 .4897 .6018 .2838 .9987 LOG -8 -8 -8 -16 -4

0 0 0

ACTIVITY . 251580-02 .148P1D-01 .328430 00 0.656920-02 0.354H9D 00 0.233180-0? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KT .3586 .1001 .0005 .6781 .7691

.118830-02 .545190-05 .206510-05 .614970-04 .189910-03 .535010-02 .239820-07 .298940-35 .150730-04 .104500-0? .149*20-04 .219460-03 .105580-02 .817220-04 .276330-05 .106820-08 .707950-08 .422100-06 .113390-01 .244970-04 .377320-15 .291430-02 .606190-04 .116870-19 I«P/KT 0.3132D 01 0.17270 01 O.H122D 01 0.53030 02 0.34470 00 LOG ACT -2.5993 -1.8274 - -0.4836 -2.1825 -0.4499 -2.6323 -2.9251 -5.2635 -5.6850 -4.2111 -3.7214 -2.2710 -7.6201 -35.5244 -4.8218 -2.9809 -4.8250 -3.6586 -2.9764 -4.0877 -5.5586 -8.9714 -8.1500 -6.3746 -1.9454 -4.6109 -15.4233 -2.5355 -4.2174 -19.9323 LOG IAP/KT 0.49580 0.23732 0.90964 1.72450 -0.46250 ACT. COEFF. 0.258020 0.296870 0.712560 0.630170 0.630170 0.188630 0.681010 0.21509D 0.70965D 0.116510 0.635420 0.116510 0.697290 0.697290 0.116510 0.116510 0.681010 0.116510 0.681010 0.681010 0.116510 0.65310D 0.758970 0.615890 0.116510 0.118530 0.116510 0.116510 0.116510 0.116510

00 00 00 00 00 00 00 00 00 01 00 01 00 00 01 01 00 01 00 00 01 00 00 00 01 01 01 01 01 01

LOG A COF -0.5883 -0.5274 -0.1472 -0.2005 -0.2005 -0.7244 -0.1666 -0.6674 -0.1490 0.0664 -0.1969 0.0664 -0.1566 -0.1566 0.0664 0.0664 -0.1668 0.0664 -0.1668 -0.1666 0.0664 -0.1850 -0.1196 -0.2105 0.0664 0.0738 0.0664 0.0664 0.0664 0.0664 MXTURE NUMBER 1 CONTAINING 90.00 PERCENT OF SOLUTION 1 AND 10.00 PERCENT OF SOLUTION 2 —— TOTAL CONCENTRATIONS OF INPUT SPECIES —— TOTAL LOG TOTAL SPECIES l-OLALITVTCTAL GRAHS/KGM H20

CATOT

MGTOT

NATOT

KTOT

CLTOT

S04TOT C02TOT 2.

2. 1. 1. -I.

-2. -1.

0.3015400-02 0.5508000-02 0.4046300-01 0.1061370-02 O.SA57200-01 0.2926000-02 0.4611070-02

•2.5207 •2.2590 •1.3146 •P.9741 •1.2474 •2.5337 •2.3913

0.1208570 00 0.1339100 00 0.1114150 01 0.4150170-01 0.20056SO 01 0.2810760 00 0.2478140 00 MSTFP 1PHPH

—— CONVERGENCE ITERATIONS —— ELECTRICAL BALANCE S1-CO?TOT S?-S04TOTS3-CLTOT 7.335000 -0.498345D-04 7.135000 0.1712190-03 7.289912 -0.6290360-05 7.2B3620 0.4861380-07 -0.3261280-14 -0.742212C-13 0.6328790-13 0.4106530-12 -0.954410C-13 0.5099130-13 -0.64?2*»10-14 -O.I!30304C-14 0.5097050-13 -0.9671080-15 -0.565411C-16 -0.1708700-15

N MODEL 8 8 9 10 -——DESCRIPTION OF SOLUTION ——

I NJ ANALYTICAL COMPUTED PH EPMCAT 66.57 65.11 7.?84 EPPAN 67.04 65.11 IONIC STRENGTH s 0.7527820-01 TEMPERATURE DENSITY * 1.0000 10.00 DEC C CLTOT x 0.5657200-01 KTOT « 0.1061370-02

ACTIVITY H20 « 0.9979 PCC2 • 0.9049670-02 LOG PCC2 * -2.0434 UNCOMPLEX C02 * 0.4437840-02 C02TOT « 0.4611070-02 ELECT « 0.4861380-07 ALKALINITY « 4.147 MEQ/LITRE I SPECIES 1 C»*« 2 Kfi** 3 N»» 4 K« 5 CL- 6 S04— 7 HC03- «» COS— 9 l»r,CH« 10 K6C03 11 K6HC03* 12 *GS04 13 CAOH* 14 CAHC03* IS CAC03 16 CAS04 17 NAC03-

2. 2. 1. 1. -It -2. -It -2. 1. 0. 1. 0.

1. 1.

0. 0.

-1.

PPM 0.10B63D 03 0.119080 03 0.106700 04 0.397630 02 0.193130 04 0.210370 03 0.232710 03 0.270140 00 0.211050-02 0.273380 00 0.805960 01 0.375920 02 0.107<»5D-03 0.463710-30 0.252090 00 0.262820 02 0.638670-01 MOLALITY 0.2A125D-02 0.508250-02 0.481640-01 0. 105520-02 0.565290-01 0.227150-02 0.395770-02 0.46714D-05 0.530030-07 0. 336440-05 0.980140-04 0.374070-03 0.196220-08 0.475970-35 0.261370-05 0.200330-03 0.798510-06 DISTRIBUTION LOG MOL -2.5S09 -2.2939 -1.3173 -2.9767 -1.2477 -2.6437 -2.4026 -5.3305 -7.2757 -5.4731 -4.0087 -3.4894 -8.7073 -35.3224 -5.5828 -3.6983 -6.0977 OF SPECIES ACTIVITY 0.121160-02 O.?26110-0? 0.366000-0) 0.832?9D-03 0.445*60-01 0.944190-03 0.320030-0? 0.199720-05 0.434300-07 0.34232D-OS 0.777180-04 0.329740-03 0.1S9R5D-OA 0.387740-35 0,266930-0^ 0.203430-03 0.645690-06 LOG ACT -2.9166 -2.6457 -1.4124 -3.0797 -1.3508 -3.0248 -2.4948 -5.6996 -7.3622 -5.4656 -4.1095 -3.4818 -8.7963 -35.4115 -5.5752 -3.6907 -6.1900 ACT. COEFF. 0.430800 00 0.44489D 00 0.803300 00 0.788720 00 0.788720 00 0.415760 00 0.808620 00 0.427540 00 0.819390 00 0.101750 01 0.79292D 00 0.101750 01 0.81465D 00 0.81465D 00 0.10175D 01 0.101750 01 0.80862D 00 LOG A COF -0.3657 -0.3517 -0.0951 -0.1031 -0.1031 -0.3812 -0.0923 -0.3690 -0.0865 0.0075 -0.1008 0.0075 -0.0890 -0.0890 0.0075 0.0075 -0.0923

0. 0.553880 01 0.68432D-04 -1. 0.714680 01 0.6?295D-04 -1. 0.675460 00 0.516580-05 0. 0.141020-02 0.13807D-07 -1. 0.37243D-03 0.39614D-08 1. 0. 6019*0-04 0.619660-07 -1. 0.12171D-02 0.742600-07 0. 0.85734D 01 0.626350-04 0. 0.284200 02 0.475470-03 0. 0. 120340-10 0.342500-15 0. 0.23874U 01 0.423900-04 0. 0. 661310-01 0.948290-06 0. 0.237620-13 0.251410-16 IAP KT 0.24200-08 0.43790-08 0.24200-08 0.79410-08 0.45160-08 0.99890-08 0.10930-16 0.20980-16 0.11440-05 0.17020-04

LOG -8 -6 -6 -16 -5

-4.1647 0.696380-04 -4.2055 0.503730-04 -5.2852 0.419330-05 -7.8599 0.140480-07 -8.4000 0.316040-08 -7.2078 0.520450-07 -7.1292 0. 584190-07 -4.2032 0.637300-04 -3.3229 0.485030-03 -15.4653 0.348490-15 -4.3727 0. 431310-04 -6.0231 0.964870-06 -18.5996 0.255«1D-18 IAP .6162 .6162 .3452 .9615 .9415 ON PHASE BOUNDARY —— MOLES SI PH -0.2570 00 0.7260 01 0.1870-03 0.1810 01 0.9120 01 0.1610-03 0.4130-01 0.7520 01 0.1640-03 -0.5750-02 0.7480 01

IPH 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 1 2 3 4

PH 7.284 6.284 9.284 9.006 9.141 9.125 9.122 9.122 8.122 7.122 7.703 7.501 7.522 7.521 7.521 7.321 7.488 7.482 7.482 7.682 7.488 7.487

LOG KT -8.3586 -8.1001 -8.0005 -16.6781 -4.7691 -4.1572 -4.2976 -5.3774 -7.8524 -8.4975 -7.2836 -7.2334 -4.1957 -3.3142 -15.4576 -4.3652 -6.0155 -18.5921

0.10175D 01 0.808620 00 0.808620 00 0.10175D 01 0.798810 00 0.839870 00 0.78668D 00 0.10175D 01 0.102010 01 0.101750 01 0.101750 01 0.101750 01 0.101750 01

1 -( -( 1 •1 •1 -( 1 ( 1 1 1 I I*P/KT LOG IAP/KT 0.55260 00 0.3047D 00 0.45210 00 0.12060 00 O.A724D-01 —— CONVERGENCE ON ELECT 0.1660-02 0. 9300-03 -0.3570-03 0.2130-03 -0.3630-04 -0.4360-05 0.6410-08 -0. 1040-02 -0.2900-03 0.4010-03 -0.1100-03 0. 1470-04 -0.8100-06 0. 2370-08 -0.2600-04 0.1380-03 -0.3850-05 0.2130-07 0.3500-05 -0.1230-03 -0. 5930-06 0. 4680-09

S1-C02TOT 0.989C-12 0.262C-11 0.780C-13 0.9560-12 -0.3650-13 -0.303C-14 -0.3790-15 0.2840-12 0.901C-12 0.463C-12 0.604C-12 -0.7170-14 -0.512016 -0.2430-16 -0. 7120-14 0.489C-12 -0.8120-14 -0.226D-16 -0.8100-14 0.5880-12 -0.1210-14 -0.2430-16 -0.25762 -0.51610 -0.34478 -0.28334 -1.17236 MASS AND PH—— S2-S04TOT 0. 6110-11 0. 8420-11 0. 2840-13 0.1010-11 -0.4930-13 -0.1300-13 -0.2960-15 0. 8830-11 -0.1150-12 0.3560-11 -0.1070-12 -0. 1020-12 -0.2180-15 -0.7520-16 -0. 1000-12 -0.1040-12 -0.9250-14 -0.7330-16 -0.9260-14 -0.1060-12 -0.6360-16 -0.7380-16 S3-CLTOT N 0.1390-10 0.4240-11 -0.1750-11 0.5020-12 0.2710-13 0.2380-13 -0.2220-15 0.2060-11 0.2700-11 0.2580-11 0.5690-13 0.5560-13 -0.3260-14 -0.1850-15 0.5520-13 0.5440-13 -0.3210-14 -0.1890-15 -0.3220-14 0.5630-13 -0.3220-14 -0.1810-15

MODEL 7 7 9 8 9 11 11 8 8 7 8 8 10 10 8 8 9 10 9 8 10 10

THE PHASE BOUNDARY HAS BEEN FOUND 0.164110-03 MOLfcS OF CA (1.000)MG(0.0 )NA(0.0)K(0.0 )CL(0.0 )S04(0.0 IC03U.OOO) HAVE BEEN ADDED TO SOLUTION NO. 1 —— TOTAL CONCENTRATIONS OF INPUT SPECIES —— SPECIES CATOT MGTOT NATOT KTOT CLTOT S04TOT C02TOT

2.

2.

i. i. -i.

-2. -1.

TOTAL KOLALITY 0. 3179510-02 0.5508000-02 0.48*6300-01 0.106137D-02 0.5657200-01 0.2926000-02 0. 4775180-02

LOG TOTAL HOLALITY •2.5280 •2.2945 •1.3173 •2.9766 •1.2477 •2.6449 •2.3709

TOTAL GRANS/K6H H20 0.1188340 00 0.1233930 00 0.1107170 01 0.4126290-01 0.2004110 01 0.2175850 00 0.259733D 00 ——DESCRIPTION OF SOLUTION —— I CO Ln I

ANALYTICAL EPMCAT 66.57 EPMAK 67.04 IONIC STRENGTH « COMPUTED 65.40 65.40 0.7571370-01 DENSITY • 1.0000 CLTOT • 0.5657200-01 KTOT * 0.106137D-02 PH 7.487 TEMPERATURE 10.00 DE6 C

ACTIVITY H20 • 0.9979 PC02 • 0.6089010-02 LOG PCC2 • -2.2155 UNCOMPLEX C02 • 0.4564640-02 C02TOT • 0.477S18D-02 ELECT • 0.4680610-09 ALKALINITY • 4.475 MEO/LITRE I SPECIES 1 CA*+ 2 *G* + 3 NA* 4 K + 5 CL- 6 S04— 7 HC03- 8 C03— 9 KGOH* 10 KGC03 11 KGHC03* 12 KGS04 13 CAOH + 14 C4HC03* 15 CAC03 16 CAS04 17 NAC03- 18 NAHC03

PPM 0.114520 03 0.118910 03 0.106690 04 0.397640 02 0.19313D 04 0.20968D 03 0.25030D 03 0.464840 00 0.336390-02 0.46827D 00 0.864470 01 0.373100 02 0.181620-03 0.524940-30 0.455780 00 0.275330 02 0.109710 00 0.595120 01 MOLALITY 0.296490-02 0.507540-02 0.481590-01 0.105530-02 0.565290-01 0.226510-02 0.425670-02 0.803830-05 0.844820-07 0,576270-05 0.105130-03 0.321630-03 0.330130-08 0.538820-35 0.472540-05 0.209860-03 0.137160-05 0.735260-04

DISTRIBUTION LOG MOL -2.5280 -2.2945 -1.3173 -2.9766 -1.2477 -2.6449 -2.3709 -5.0948 -7.0732 -5.2394 -3.9783 -3.4926 -8.4813 -35.2686 -5.3256 -3.6781 -5.8628 -4.1336

OF SPECIES ACTIVITY 0.12753D-0? 0.225470-02 0.386700-01 0.831880-03 0.445630-01 0.940050-03 0.344060-02 0.343100-05 0.691980-07 0.586410-05 0.833190-04 0. 327290-03 0.268840-08 0.438780-35 0.480850-05 0. 213550-03 0.110860-05 0.748190-04

L08 ACT -2.8944 -2.6469 -1.4126 -3.0799 -1.3510 -3.0269 -2.4634 -5.4646 -7.1599 -5.2318 -4.0793 -3.4851 -8.5705 -35.3578 -5.3180 •3.6705 -5.9552 -4.1260

ACT. COEFF. 0.430120 00 0.444250 00 0.802960 00 0.788320 00 0.788320 00 0.415020 00 0.808290 00 0.426840 00 0.819090 00 0.101760 01 0.792530 00 0.101760 01 0.814330 00 0.814330 00 0.101760 01 0.101760 01 0.808290 00 0.101760 01

LOG A COF -0.3664 -0.3524 -0.0953 -0.1033 -0.1033 -0.3819 -0.0924 -0.3697 -0.0867 0.0076 -0.1010 0.0076 -0.0892 -0.0892 0.0076 0.0076 -0.0924 0.0076

-1. -1. 0. -1. 1. -1. 0. 0. 0. 0. 0. 0.

0. 0. 0.

u.

0. 0. 0. 0. 0. 0. 0. 0.

711330 01 672300 00 241990-02 232110-03 376820-04 194580-02 652440 01 191200 02 752680-11 23847D 01 6B0560-01 926300-14 0.620020-04 0.516150-05 0.23692D-07 0.246140-08 0.387930-07 0. 118720-06 0.622760-04 0.319880-03 0.214220-15 0.423420-04 0.947250-06 0.960070-19 -4.2076 -5.2872 -7.6254 -8.6053 -7.4113 -6.9255 -4.2057 -3.4950 -15.6691 -4.3732 -6.0235 -19.0087

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

501160-04 41720D-05 241090-07 19812D-08 325720-07 93345D-07 633710-04 326150-03 217990-15 430H70-04 963910-0* 99711D-10 -4.3000 •5.3797 -7.6178 -8.7031 -7.4872 -7.0299 -4.1981 -3.4863 -15.6616 -4.3657 -6.0160 -19.0012 0.808290 0.80829D 0.10176D 0.798450 0.839640 0.786260 0.101760 0.102020 0.101760 0.101760 0.101760 0.101760

00 00 01 00 00 00 01 01 01 01 01 01

-0.0924 -0.0924 0.0076 -0.0978 -0.0759 •0.1044 0.0076 0.0087 0.0076 0.0076 0.0076 0.0076 IAP 0.43750-08 0.43750-08 0.7736D-08 0.33850-16 0.11990-05

KT 0.4379D-08 0.79410-08 0.9989D-08 0.20980-16 0.17020-04 LOG UP -8.3590 -6.3590 -P.1115 -16.4705 -5.9212 LOG KT -8.3586 -8.1001 -8.0005 -16.6781 UP/KT 0.99910 00 0.55100 00 0.77440 00 0.16130 01 -4.7691 0.70450-01

LOG IAP/KT -0.00039 -0.25887 -0.11101 0.20766 -1.15211 MJH6EP 2 CONTAINING 70.00 PERCENT OF SOLUTION 1 AND 30.00 PERCENT OF SOLUTION 2 ••*•*•**** —- TOTAL CONCENTRATIONS OF INPUT SPECIES —— LOG TOTAL SPECIES CATOT

MGTDT

NATOT KTOT CLTOT S04TOT COZTOT

2. 2. 1. 1. -1. -2. -I.

TOTAL fOLALITY 0.4714200-02 0.1652400-01 0.1453890 00 0.3180300-02 0.1697160 00 0.8778000-02 0.4112660-02

•2.3266 •1.7819 •0.8375 •2.4975 •0.7703 •2.0566 •2.4256

TOTAL GRAMS/K6M H20 0.1889450 00 0.4Q1731D 00 0.3342460 01 0.1243560 00 0.6016940 01 0.8432290 00 0.2269950 00 NSTEP IPHPH

—— CONVERGENCE ITERATIONS —— ELECTRICAL BALANCE S1-C02TOT S2-S04TOTS3-CLTOT 7.487161 -0.1296690-03 7.287161 0.6363170-05 7.296516 -0.1065520-05 7.295163 0.1570040-08 -0.7829410-13 -0.8937990-12 -0.3851090-12 -0.2810250-15 -0.1153240-13 -0.3688720-13 -0.1700900-14 -0.100987C-13 -0.1526560-15 0.1110220-15 0.1543900-15 -0.1387780-16

N MODEL 9 11 10 12

———DESCRIPTION OF SOLUTION ——— ANALYTICAL COMPUTED PH EP«CAT 191.05 164.66 7.P95 EPMAK 191.38 184.86 IONIC STRENGTH « 0.2100370 00 TEMPERATURE DENSITY « 1.0000 10.00 DE6 C CLTOT « 0.1697160 00 KTOT « 0.3180300-02

ACTIVITY H20 « 0.99*1 PC02 » 0.6995950-02 LOG PCC2 * -2.1552 LNCOMPLEX C02 « 0.3759550-02 C02TOT * 0.4112660-02 ELECT * 0.1570040-08 ALKALINITY » 3.774 MEQ/LITRE DISTRIBUTION OF I 1 2 3 4 5 6 7

e

9 10

11

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

SPECIES

C*+* 2. »G++ 2. NA+ 1. K* 1. CL- -1. SD4-- -?. HC03- -1. C03-- -2.

CGOH+ i.

*GC03 0. *GHC03* 1. KGS04 0.

CACH* i. CAHC03+ i.

CAC03 0. CAS04 0. NAC03- -1. NAHC03 0. NAS04- -1. KS04- -1. NA2C03 0. HS04- -1. h+ 1. Ch- -1. NA2S04 0. H2C03 0. hCL 0. NACL 0.

KCL o.

h2S04 0. PHASE 23 CALCITE 24 ARAGOMT 25 MA6NESIT 2ft DOLOMITE 28 GYPSU*

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

PPM .166240 03 .351*10 03 .316630 04 .118550 03 .578760 04 .541360 03 .199890 03 .301820 00 .531850-02 .497440 00 .162360 02 .152770 03 .136930-03 .456490-30 .229810 00 .535080 02 .155240 00 .117460 02 .387970 02 .358640 01 0. 846290-02 0 0.722530-03 .616120-04 0, 138370-02 0 0 0 0 0 0 0 0 0 0 0.11491D 03 .212100 02 .307760-10 .172770 02 .482250 00 .397720-13 IAP .22750-08 .22750-08 .84760-08 .19290-16 .24030-05 MOLALITY 0.430400-02 0.150030-01 0.142920 00 0.314610-02 0.169400 00 0.584800-02 0.339950-02 0.521920-05 0.133570-06 0.612180-05 0.197450-03 0.131700-02 0.248900-08 0.468560-35 0.238260-05 0.407850-03 0.194090-05 0.145130-03 0.338170-03 0.275340-04 0.828560-07 0.772400-08 0.634280-07 0.844250-07 0. 839490-03 0.354850-03 0.875920-15 0.306770-03 0.671220-05 0.420610-16 KT LOG 0.43790-06 -8 0.79410-08 -B 0.99890-08 -6 0.20980-16 -16 0.17020-04 -5

LOG MOL -2 -1 -0 -2 -0 -2 -2 -5 -6 -5 -3 -2 -8 -35 -5 -3 -5 -3 -3 -4

.3661 .8238 .8449 .5022 .7711 .2330 .4686 .2824 .8743 .2131 .7045 .8804 .6040 .3292 .6230 .3895 .7120 .8383 .4709 .5601 -7.0817 -8 -7 -7 -3 -3 -15 -3 -5 -18 IAP .6429 .6429 .0718 .7147 .6192

.1122 .1977 .0735 .0760 .4500 .0575 .5132 .1731 .3759 LOG -8 -8 -6 -16 -4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

KT

.3566 .1001 .0005 .6781 .7691

SPECIES ACTIVITY .139740-02 .520560-02 .106MO 00 .22*320-02 .120780 00 .171960-02 .254060-02 .162«30-05 .102?8D-06 .642510-05 .142040-03 .136220-02 .168600-08 .355040-35 .250060-05 .428060-03 .145050-05 .152320-03 .252740-03 .205780-04 .869IS30-07 .563900-08 .506800-07 .597MD-07 .881080-03 .374950-03 .919320-15 .321470-03 .704^80-05 .441660-18 IftP/KT 0.51960 00 0.28650 00 O.B485D 00 0.91910 00 0.14120 00 LOG ACT -2.8547 -2.2635 -0.9722 -2.6491 -0.9160 -2.7646 -2.5951 -5.7883 -6.9902 -5.1921 -3.6476 -2.8594 -8.7245 -35.4497 -5.6019 -3.3665 -5.6385 -3.6173 -3.5973 -4.6666 -7.0607 -8.2488 -7.2952 -7.2236 -3.0550 -3.4260 -15.0365 -3.4922 -5.1521 -16.3549 LOG IAP/KT -0.28435 -0.54283 -0.07133 -0.03662 -0.65012 ACT. COEFF. 0.324690 0.346960 0.745960 0.713010 0.71301D 0.29404'D 0.747360 0.311980 0.765740 0.104960 0.719390 0.104960 0,757730 0.757730 0.104960 0.104960 0.747360 0.104960 0.747360 0.74736D 0.104960 0.730060 0.799020 0.707850 0.104960 0.105660 0.104960 0.104960 0.104960 0.104960

00 00 00 00 00 00 00 00 00 01 00 01 00 00 01 01 00 01 00 00 01 00 00 00 01 01 01 01 01 01

LOG A COF -0.4885 -0.4597 -0.1273 -0.1469 -0.1469 -0.5316 -0.1265 -0.5059 -0.1159 0.0210 -0.1430 0.0210 -0.1205 -0.1205 0.0210 0.0210 -0.1265 0.0210 -0.1265 -0.1265 0.0210 -0.1366 -0.0974 -0.1501 0.0210 0.0239 0.0210 0.0210 0.0210 0.0210

ON PHASE BOUNDARY-— MOLES SI PH 0.2060-02 -0.2640 00 0.7300 01 0.2710-03 0.1870 01 0.924D 01

IPH——CONVERGENCE ON MASS AND PH- ELECT S1-C02TOT S2-S04TOTS3-CLTOT N MODEL 0.10RO-03 0.2930 00 0.7600 01 0.1510-03 -0.673D-01 0.7460 01 0.1500-03 0.1470-02 0.7540 01

1

2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 1 2 3 4 1 2 3

7.295 8.295 9.295 9.191 9.238 9.236 9.236 8.236 7.236 7.896 7.809 7.798 7.799 7.799 7.599 7.399 7.467 7.460 7.460 7.660 7.544 7.537 7.537 7.337 7.536

0.2220-0? 0.1510-02 -0.1750-03 0.1240-03 -0.7310-05 -0.3260-06 -0.1250-02 -0.1780-03 0.3460-03 -0.3930-04 -0. 4440-05 0.1440-06 -0.4960-09 -0.1660-03 -0. 7690-04 0.3970-04 -0.4170-05 0.22RO-07 0.451C-04 -0.6240-04 -0.3650-05 0.1570-07 -0.7060-06 0.1290-03 -0.1060-06 0.210C-10 -0.27f.C-12 -0.14AC-11 -0.116C-11 0.2220-14 0. 2840-14 0.659C-12 -0.2290-12 -0.65RC-13 -0.136C-12 -0.224D-14 0.159C-15 0.158C-15 -0.1100-12 -0.879C-13 -0.725C-13 -0.225O14 0.123C-15 -0.77SC-13 -0.95«D-13 -0.23AC-14 0.130C-15 -0.182C-1* -0.6820-13 0.130C-15 -0.9160-11 -0.8830-11 -0.1710-12 -0.8260-13 0.8960-14 0.1510-14 -0.3180-11 -0.1010*11 -0.9370-12 -0.1310-13 -0.1160-13 0.1730-15 0.1730-15 -0.926C-12 -0.103O13 -0.1000-13 -0.1*30-13 0.1600-15 -0.1020-13 -0.1060-13 -0.1*70-13 0.1640-15 0.31*0-1* -0.9170-12 0.1620-15 0.7080-11 0.8060-11 -0.3560-12 -0.*55D-12 -0.5220-1* 0.5690-15 -0.3*80-12 -0.4080-12 -0.3970-12 -0.2640-15 -0.3940-13 -0.6940-16 -0.5550-16 -0.3900-12 -0.3880-12 -0.3880-12 -0.3780-13 -0.1390-16 -0.3900-12 -0.3910-12 -0.3810-13 -0.2780-16 -0.1390-16 -0.3900-12 -0.1390-16

8 8 10 10 11 12 8 9 9 10 10 12 12 9 10 10 10 12 10 10 10 12 11 9 12

THE PHASE, BOUNDARY HAS BEEN FOUND 0.149890-03 HOLES OF CA(1.000)MG(0.0 INAIO.O )K(0.0 )CL(0.0 >S04<0.0 )C03(1.000) HAVE BEEN ADDED TO SOLUTION NO. 1 —— TOTAl CONCENTRATIONS OF INPUT SPECIES —— SPECIES CATOT MGTOT NATOT KTOT CLTOT S04TOT C02TOT

2. 2. 1. 1. -1. -2. -1.

TOTAL "OLALITY 0.4864090-02 0.1652400-01 0.1453890 00 0.3180300-02 0.1697160 00 0.8778000-02 0.4262550-02 LOG TOTAL HOLALITY •3.3536 •1.8243 •0.8449 •2.5022 •0.77H •2.2334 •2.4381

TOTAL GRAPS/KGM H20 0.177943D 00 0.3643860 00 0.3265460 01 0.1230190 00 0.600583D 01 0.5612290 00 0.222534D 00 ———DESCRIPTION OF SOLITIOw ——— VO I

ANALYTICAL COMPUTED PH EPMCAT 151.05 185.12 7.535 EPMAN 191.38 185.12 IONIC STRENGTH = 0.210403D 00 TEMPERATURE DENSITY * 1.0000 10.00 DEG C CLTOT = 0.1697160 00 KTOT = 0.3180300-02

ACTIVITY H2r « 0.9941 PC02 = 0.431421D-02 LOG PCC2 = -2.3651 INCOMPLEX C02 * 0.3875610-02 C02TOT = 0.4262550-02 ELECT = -0.1056240-06 ALKALINITY = 4.073 MEG/LITRE I SPECIESMOLALITYLOG ACTACT. COEFF.LOG A COF

1 CA*»

2 *G** 3 NA» 4 K» 5 CL- 6 S04-- 7 HC03- 8 COS—

9 CGOH*

10 PGCQ3 11 KGHC03* 12 *GS04

13 CACH*

14 CAHC03* 15 CAC03 16 CAS04 17 NAC03- 18 NAHC03

2. 2. 1. 1. -1. -2. -1. -2. 1. 0. 1. 0.

1. 1.

0. 0.

-1.

0.

0.171480 03 0.35115D 03 0.31661D 04 0.11855D 03 0.57876D 04 0.540H4D 03 0.21445D 03 0.563480 00 0.523940-02 0.92678D 00 0.173950 02 0.152300 03 0. 245610-03 0.504940-30 0.442070 00 0.550780 02 0. 289650 00 0.125970 02

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

.443970-02 .149880-01 .142910 00 .314610-02 .169400 00 .584240-02 .364710-02 .974390-05 .232040-06 .114050-04 .211540-03 .131290-02 .446460-08 .518290-35 .45fl33D-05 .419820-03 .362130-05 .155630-03

-2 -1 -0 -2 -0 -2 -2 -5 -6 -4 -3 -2 -8 -35 -5 -3 -5 -3

.3526 .8243 .8449 .5022 .7711 .2334 .4381 .0113 .6344 .9429 .6746 .8818 .3502 .2854 .3388 .3769 .4411 .8079

0.14409D-0? 0.5l9fl3D-02 0.106S9D 00 0.22*?8D-0? 0.120760 00 0.171*80-02 0.272530-02 0. 303820-05 0.177660-06 0.119720-04 0. 152150-03 0.137810-02 0.338?50-08 0.352*70-35 0.481080-05 0.440660-03 0.270MD-0* 0.163360-03 -2.8414 -2.2841 -0.9723 -2.6492 -0.9181 -2.7653 -2.5646 -5.5174 -6.7504 -4.9218 -3.8177 -2.8607 -8.4708 -35.4060 -5.3178 -3.3559 -5.5677 -3.7869 0.324540 0.346830 0.745870 0.712870 0.712870 0.293860 0.747260 0.311800 0.765650 0.104960 0.719260 0.104960 0.757630 0.757630 0.104960 0.104960 0.747260 0.10496D

00 00 00 00 00 00 00 00 00 01 00 01 00 00 01 01 00 01

-0.4887 -0.4599 -0.1273 -0.1470 -0.1470 -0.5319 -0.1265 -0.5061 -0.1160 0.0210 -0.1431 0.0210 -0.1205 -0.1205 0.0210 0.0210 -0.1265 0.0210

-1. -1.

n. -1. 1. -1.

0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

387340 02 358060 01 15784D-01 414780-03 354230-04 24073D-02 114*80 03 130780 02 176fl80-10 172690 02 482040 00 131230-13

0 0 0 0 0 0 0 0 0 0 0 0

.337620-03 .274900-04 .154540-06 .443410-08 .364670-07 .146880-06 .837790-03 .218B10-03 .503420-15 .306630-03 .670930-05 .138840-18 -3.4716 -4.5608 -6.8110 -8.3532 -7.4381 -6.8330 -3.0769 -3.6599 -15.2981 -3.5134 -5.1733 -18.8575 0.252?90-03 0.205420-04 0.162?1D-06 0.323660-08 0. 291350-07 0.103950-06 0.879380-03 0.231220-03 0.528410-15 0.321*50-03 0.704?4D-05 0.14574D-lfl -3.5981 -4.6874 -6.7899 -8.4899 -7.5356 -6.9832 -3.0558 -3.6360 -15.2770 -3.4923 -5.1523 -18.8364 0.74726D 0.747260 0.10496D 0.72994D 0.79895D 0.70771D 0.10496D 0.10567D 0.10496D 0.10496D 0.10496D 0.104960

00 00 01 00 00 00 01 01 01 01 01 01

-0*1265 -0.1265 0.0210 -0.1367 -0.0975 -0.1501 0.0210 0.0240 0.0210 0.0210 0.0210 0.0210 IAP 0. 43780-08 0.43780-08 0.15790-07 0.69140-16 0.24740-05

KT 0.43790-08 0.79410-08 0.99890-08 0.20980-16 0.17020-04 LOG UP -8.3588 -8.3588 -7.8015 -16.1603 -5.6067 LOG KT -8.3586 -8.1001 -8.0005 -16.6781 -4.7691 IAP/KT 0.99960 00 0.55120 00 0.15810 01 0.32950 01 0.14540 00

LOG IAP/KT -0.00018 -0.25866 0.19894 0.51782 -0.83752 MJMBEH 3 CONTAINING 50.00 PERCENT OF SOLUTION 1 AND 50.00 PERCENT OF SOLUTION 2 —— TOTAL CONCENTRATIONS OF INPUT SPECIES —— SPECIES CATOT

MGTOT

NATOT KTOT CLTOT S04TOT C02TOT

2. 2. 1. 1. -1. -2. -1.

TOTAL *OLALITY 0.6413000-02 0.2754000-01 0.2423150 00 0.5299230-02 0.2828600 00 0.1463000-01 0.3614240-02

LOG TOTAL fOLALlTY •2.1929 •1.5600 •0.6156 •2.2758 •0.5484 •1.8348 •2.4778

TOTAL GRAHS/KGM H20

0.2570330 00 0.669552D 00 0.557077D 01 0.207211D 00 0.1002820 02 0.1405380 01 0.203068D 00 NSTEP IPH

PH

—— CONVERGENCE ITERATIONS ——

ELECTRICAL BALANCE S1-C02TOT S2-S04TOT

S3-CLTOT 7.535387 -0.8015860-04 7.335387 0.2266140-04 7.379467 -0.2814000-05 7.374421 0.1144860-07

-0.1918130-12 -0.174938D-13 -0.5264120-12 -0.1093220-12 -0.1965880-13 -0.3191890-15 -0.1471780-13 -0.228012C-13 -0*3885780-15 0.1734720-17 -0.1526560-15 0.1387780-15

N MODEL 10 10 10 13