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A COMPUTER PROGRAM INCORPORATING PITZER'S I;QUATIONS FOR CALCULATION OF GEOCHEMICAL REACTIONS IN BRINES

By L.N. Plummer, D.L. Parkhurst, G.W. Fleming, and S.A. Dunkle

U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 88-4153

Reston, Virginia

1988

DEPARTMENT OF THE INTERIOR DONALD PAUL HODEL, Secretary U.S. GEOLOGICAL SURVEY Dallas L. Peck, Director

For additional information write to:

Copies of this report can be purchased from:

Chief, Branch of Regional Research, Northeastern Region U.S. Geological Survey 432 National Center 12201 Sunrise Valley Drive Reston, Virginia 22092

U.S. Geological Survey Books and Open-File Reports Section Federal Center, Bldg. 810 P.O. Box 25425 Denver, Colorado 80225

Additional copies of the software described in this report are available from: WATSTORE PROGRAM OFFICE U.S. Geological Survey 437 National Center Reston, VA 22092

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CONTENTS page Abstract -----------------------------------------------------------------Introduction - - - - - -- - - - - -- - -- - - --- - --- - - - -- - - - -- - - --- - -- - --- - -- - - -- - -- - ---Pitzer equations -- - - - - - - - - - - -- - - - - - - --- - - --- - - --- - - - -- - -- - -- - -- - - -- - - -- - - - - 2 Data base ----------------------------------------------------------------- 5 Extensions of the data base ---------------------------------------------- 6 Internal consistency of the data base -------------------------------------- 6 Literature sources of Pitzer interaction parameters -------------------------- I I Scale convention of activity coefficients -------------------------------------- II Precautions and limitations -------------------------------------------------- 14 Numerical method --------- ---------------------------------------------- -- 15 Basic equations --------------------------------------------------------- 15 Restrictions on the Newton-Raphson approach ----------------------------- 17 Scaling the Newton-Raphson results --------------------------------------- 17 Description of input ------------------------------------------------------- 18 Title and option line ---------------------------------------------------- 19 Keywords ------------------------------------------------------------- 21 ELEMENTS - - - - - - - - - - - -- - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - --- - - - - - 21 SPECIES ----------------------------------------------------------- 22 SOLUTION - - -- - - - - -- - - - - - - - --- - - - -- - - - - -- - - -- - - -- - - - - --- - -- - - - - --- - 23 MINERALS - --- - - - - - - - - - -- - - - - - - - ---- - - -- - - - - - - -- - - - - - - - - - -- - - - - - - - 25 LOOK MIN ---------------------------------- ----------------- ---- - 27 MEAN GAM ------------------------------------------------------- 27 TEMP ------------------------------------------------------------- 28 STEPS ------------------------------------------------------------- 28 REACTION -------------- ------------------------------------- ---- - 29 NEUTRAL - - - - - - - - - - - - - - -- - - - -- - - ---- - - - - - - --- - -- - - -- - - --- - - - -- - - - - 30 SUMS -------------------------------------------------------------- 31 END --------------------------------------------------------------- 31 Description of PHRQPITZ.DATA file ---------------------------------------- 31 Description of PITZER.DA T A file ---- --------------------------------------- 32 -111-

Test problems -- - - - - -- - -- - -- - - --- - - ---- - ----- - - --- - - ---- --- --- - --- - -- - --- - - 34 -- Speciate a brine sample and examine effects of changing activitycoefficient scale -- - --- - -- - - - - ---- - - ----- ---- - --- ---- --- - --- - -- - - -- - 34 2 -- Equilibration of pure water with a set of minerals accompanied by an irreversible reaction - --- - ----- - ---- - - - --- - - -- -- -- - - --- --- - ------- -- 59 3 -- The anhydrite-gypsum phase boundary in the system NaCI-H2 0 at 25 ·Celsius ----------------------------------------------------- 75 4 -- Solubility with incremental temperature variation: halite-water system ----- 83 5 -- Fresh water-brine mixing in a closed system --------------------------- 98 6 -- Simulation of reaction path accompanying the evaporation of sea water --- 120 Program source code ------------------------------------------------------- 140 Interactive construction of input files for the computer program ----------------- 140 Acknowledgment ---------------------------------------------------------- 141 References --------------------------------------------------------------- 141 Attachments: A

Listing of the file PHRQPITZ.DATA ----------------------- 144

B

Listing of the file PITZER.DATA -------------------------- 149

C

Summary of published Pitzer interaction parameters ----------- 154

C.I

List of references cited in Attachments C.2. C.3. CA. and C.6-------------------------------------------------- 155

C.2

Summary of literature values of Pitzer interaction parameters for single salts ----------------------------------------------- 164

C.3

Summary of literature values of Pitzer interaction parameters for mixed-salt solutions --------------------------------------- 173

CA

Temperature dependence of single-salt parameters ------------ 181

C.5

Summary of analytical expressions for temperature (and pressure) dependence of selected single-salt Pitzer interaction parameters ----------------------------------------------- 184

C.6

Sources of data in the file PITZER.DATA ------------------- 189

D

Listing of source code to program PHRQPITZ ---------------- 194

E

Listing of source code to the interactive input program PITZINPT ----------------------------------------------- 261

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F

Listing of the file MINERALS.2.DAT A read by interactive input program PITZINPT --------------------------------------- 303

G

Example of use of interactive input program PITZINPT to . construct the input file for test problem 3 ------------------- 306

ILL USTRAnONS

Figure I.

Comparison of calculated solubility of nahcolite in aqueous solutions of Na2C03 ------------------------------------------------------- 9

TABLES

Table I.

2.

Temperature dependence of equilibria in program PHRQPITZ ------- 7 Comparison of two internally consistent sets of Pitzer interaction parameters for the system NaHC03-Na2C03-H20 at 25 "Celsius ------ 10

3.

Sea water in equilibrium with aragonite at a PC02 of 10-3 atmospheres and 25 "Celsius on two different activity-coefficient scales ---------- 12

4.

Comparison of individual-ion activities using the measured pH ------ 13

5.

Analytical data for Canadian Shield brine T -93 -------------------- 34

6.

Line images of input file to test problem I ------------------------ 35

7.

Listing of printout from test problem 1 --------------------------- 39

8.

Line images of input file to test problem 2 ------------------------ 60

9.


10.


II.


12.


13.


14.


15.


16.


17.

Listing of printout from test problem 6 --------------------------- 123 -v-

DISKETTES (Back Pocket)

Diskette containing a machine-readl,lble copy of the PHRQPITZ source code, the files COMMON.BLOCKS, PITZER.DATA, and PHRQPITZ.DATA, and input files to test problems 1-6. 2

Diskette containing a machine-readable copy of the source code to the interactive input program PITZINPT, and the files MINERALS.2.DAT A and PHRQPITZ.DAT A.

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A COMPUTER PROGRAM INCORPORATING PITZER'S EQUATIONS FOR CALCULATION OF GEOCHEMICAL REACTIONS IN BRINESl

L. Niel Plummer, D.L. Parkhurst, G.W. Fleming, and S.A. Dunkle

ABSTRACT The program named PHRQPITZ is a computer code capable of making geochemical calculations in brines and other electrolyte solutions to high concentrations using the Pitzer virial-coefficient approach for activity-coefficient corrections. Reaction-modeling capabilities include calculation of (I) aqueous speciation and mineral-saturation index, (2) mineral solubility, (3) mixing and titration of aqueous solutions, (4) irreversible reactions and mineral-water mass transfer, and (5) reaction path. The computed results for each aqueous solution include the osmotic coefficient, water activity, mineral saturation indices, mean activity coefficients, total activity coefficients, and scaledependent values of pH, individual-ion activities and individual-ion activity coefficients. A data base of Pitzer interaction parameters is provided at 25 "C (Celsius) for the system: Na-K-Mg-Ca-H-Cl-S04-OH-HCOTC03-CO.,-H:t0, and extended to include largely untested literature data for Fe(I1), Mn\I1), Sr, Ba, Li, and Br with provision for calculations at temperatures other than 25 "C. An extensive literature review of published Pitzer interaction parameters for many inorganic salts is given. Also described is an interactive input code for PHRQPITZ called PITZINPT.

INTRODUCTION PHRQPITZ2 is a FORTRAN 77 3 computer program that makes geochemical calculations in brines and other electrolyte solutions to high concentrations. PHRQPITZ has been adapted from the U.S. Geological Survey geochemical simulation computer code PHREEQE4 of Parkhurst and others (1980) in which the aqueous model of PHREEQE has been replaced with the Pitzer virial coefficient approach (Pitzer, 1973; Pitzer and Mayorga, 1973, 1974; Pitzer and Kim, 1974; Pitzer, 1975). The PHRQPITZ code contains most of the reaction-modeling capabilities of the original PHREEQE code, including calculation of (I) aqueous speciation and mineral-saturation index, (2) mmeral solubility, (3) mixing or titration of aqueous solutions, (4) irreversible reactions and mineral-water mass transfer, and (5) reaction path. The computed results for each aqueous solution include the osmotic coefficient, water activity, mineral saturation indices, mean-activity coefficients, total-activity coefficients, and scale-dependent values of pH, individual-ion activities and individual-ion activity coefficients. The Pitzer treatment of the aqueous model is based largely on the equations as presented by Harvie and Weare (1980) and Harvie and others (1984). An expanded data base of Pitzer interaction parameters is provided that is identical to the partially validated data base of Harvie and others (1984) at 25 "C (Celsius) for the system Na-K-Mg-Ca-H-CI-SO -OH-HC03C0 3-C02-H 20, and extended to include largely untested literature data for Fe( I), Mn(II), Sr, Ba, Li, and Br with provision for calculations at temperatures other than 25 "C. An extensive

t

1 Manuscript approved for publication October 5, 1988. 2 PH-Redox-eQuilibrium-equations incorporating the PITZer equations. 3 The use of trade names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey. 4 PH- REdox- EQuilibrium- Equations

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literature review of published Pitzer interaction parameters for many inorganic salts is also given that may serve as a guide in selection of additional data for inclusion in PHRQPITZ. Some new data for the temperature dependence of mineral equilibrium constants accompanies the additional (untested) data. As with PHREEQE, the aqueous model and thermodynamic data of PHRQPITZ are user-definable and external to the code. This report also describes an interactive input code for PHRQPITZ called PITZINPT, which is analogous to the PHREEQE input code, PHRQINPT (Fleming and Plummer, 1984). PITZINPT contains the mineral thermodynamic data base taken largely from Harvie and others (1984) and is used interactively to construct input data sets to PHRQPITZ. Because most modeling aspects of PHRQPITZ are identical to the original PHREEQE treatment, the reader is referred to the PHREEQE documentation (Parkhurst and others, 1980) for background and modeling information. The current report focuses on extensions to the PHREEQE code including documentation of the Pitzer data base, explanation of the Pitzer equations as incorporated in PHRQPITZ, program limitations and instructions for use.

PITZER EQUATIONS The osmotic coefficient, q" and activity coefficients of the cations, "1M and anions, "Ix are given by Harvie and Weare, 1980; Harvie and others, 1984), • , 2

(~-l)~(~mi) + L Lm,m,.(:,,+ Lmalji"'a) c
> Ca 2> > 3S04 2M9S04·4HZO = Mg2+ + S04 Zw + 4HZO

31 34 35 40 76 85 86

I

-..l I

Mineral name

-------

--

log KI1l 6.H~ 25 °c 25 0c (keal! moL)

-13.997 10.339 16.677 1.979 3.151 -11.809 2.928

-4.362 -8.220 -1.776 4.455 -2.347 -10.884 - .772 -8.406 4.330 -17.083 -1. 881 -9.421 -3.803 -5.245 Gypsum -4.581 Halite 1.570 Hexahydrate -1.635 + 3H20 Kainite - .193 Kal icinite -10.058 Kieserite -.123 + 2H20 Labile SaL t -5.672 leonhadi te - .887

Anhydri te Aragonite Arcanite Bischofite + 4H20 Bloedite Brucite Burkeite Calcite Carnall ite Dolomite Epsomite + 5H20 Gaylussite Glaserite Glauberite

13.345

----15.419

Al (1)

--

A2 (T)

--

107.8975 464.1925 -5.3585 -1228.806

0.03252849 .09344813 .0183412 -.299440

--

---

--

-32.225

---. ---

422.950 --171.8607 - .077993 2.823 -3.524 --

.85

----9.436

-------------

----

--

---

-171.8329 -.077993

--1.718

.-

---

-------

90.318 --713.4616 -.1201241 -62.666 --

------

--

-----

A3 (1!T)

--

A4 (LogT)

--

A5 (lIT2)

--

-5151.79 -38.92561 563713.9 -26986.16 -165.75951 2248628.9 -557.2461 -35512.75 485.818 -----1093.486 12.72433 -18431. 2903.293 -1371.2 277.6

---

--

2839.319

---

-147.708 71.595

------

--

71. 595

--

--

--------

--

-1073.

--

----

--

-4213. 37302.21 1828.

------

--. -----

---32.641 262.4583 22.187

-2106915.

--

.-

--

---

--

--

--

----

Source [1]

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

Table 1 -- Temperature dependence of equilibria in program PHRQPITZ (continued) [_., no data: oe, degrees Celsius; keel/mol, kilocalories per mole] Reaction

MineraL

name K2Mg(S04)2'4H20 = 2K+ + Mg2+ + 2S04 2- + 4H20 MgCQ3 = Mg2+ + C032Na2S04'10H20 = 2Na+ + S04 2- + 10H20 K8H6(S04)7 =8K+ 6H++ 7S04 2NaHC03 = Na+ + H+ + C03 2 Na2CQ3'10H20 = 2Na+ + CQ32- + 10H20 MgCQ3'3H20 = Mg2+ + C032- + 3H20 C02(9) = C02(aq) MgS04·5H20 = Mg2+ + 5°42- + 5H20 Na2Ca(CQ3)2'2H20 = 2Na+ + Ca 2+ + 2CQ32- + 2H20 KZMgCaZ(S04>4"ZHZO = 2K+ + Mg2+ + 2Ca 2+ + 4504 C8(OH)2=ca 2+ + 20HI 00 I

K2M9(S04)2·6H20 = 2K+ + Mg2+ + 2S04 2 - + 6H20 KCl

= K+

+

ct-

K2Ca(S04)2·H20 = 2K+ + Ca 2+ + 2S04 2- + H2O Na3H(C03)2'2H20 = 3Na+ + H+ + 2CQ32- + 2H20

-3.979 - 7.834 Mirabil ite -1.214 -10.806 Misenite Nahcolite -10.742 -.825 Natron Nesquehonite -5.167 -1.468 PC02 Pentahydrite -1.285 Pirssonite -9.234 2H20 Polyhalite -13.744 Portlandite -5.190 -4.328 Schoenite Sylvite .900 Syngenite -7.448 Trona -11.384

Leonite

Magnesl te

+

log K[1] D.H~ 25 0c 25 0c (keal/ mol)

--6.169

--

--------------

Al (1)

---

A2 (T)

---

-3862.234 -1. 19856

----108.3865 --

----3.984

---

(1l References to values of log KT: 1. Harvie and others (1984) unless otherwise indicated. 2. Parkhurst and others (1980). 3. Plummer and Busenberg (1982) with A1 adjusted for consistency with (1). 4. Parkhurst and others (1980) with A1 Adjusted for consistency with (1). 5. Solubility data from Linke (1965), speciated in PHRQPITZ, log K fitted to analytical expression as f(T) with A1 adjusted to be consistent with (1). 6. PLummer and others (1976). 7. HaLite solubility from Pitzer and others (1984) treated as in 5 (above). 8. Solubility data from Linke (1965) and Plummer and Busenberg (unpub. data, 1987). The revised value of log K at 25 C for mirabilite (-1.214) compares to -1.228 of Harvie and others (1984).

----

--

A3 (l/T)

--

--

A4 (logT)

---

93713_54 1577.756

-----

-----

A5 (1/T2)

--------

--

1 6 8 1 1 1 1 3 1 1 1 1

----. --

5 1 1

.01985076 -6919.53 -40.45154 669365. -------

-------

----919.55

--

--

-------

Source [1]

--

1

1.3 , - - - - - - - - - - - - - - - ,

oC\l :c ::2

1.2

~

...,

(!)

9

~

....

\~\..

1. 1

..

~

a:

UJ D-

en

\

.... \ \ .. \ . '. , , \

1.0

UJ

::2

0.9

z

~ ~

\

. ....

\ ...J

oen

0.7

UJ

1

I~

o () J: « Z

0.6 •

o ,5

Hill and Bacon (1927)

LLL-L-LL--'---L...L.L...L.L---'--l-LJ-LLLLLL.L-'-J.-'

0.0

0.5

1.5

1.0

2.0

2.5

Figure I - Comparison of calculated solubility of nahcolite in aqueous solutions of Na2C03 to 2 molal. (I) Calculated using the model of Harvie and others (1984), (2) Parameters po, pI, and C¢ of NaHC03 changed to those of Sarbar and others (1982), (3) Same as curve 2 but with KNahcoli!e changed to be consistent with Sarbar and others (1982), and (4) Same as curve 3 but with 8 and'" for NaHC03-Na2C03 mixtures changed to the values of Roy and others (1984) reported for KHC03-K 2C0 3 mixtures, Solid points are the experimental data of Hill and Bacon (1927),

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The Na+-HCOs - interaction parameters in the Harvie and others (1984) data base were originally taken from Pitzer and Peiper (1980) based on an evaluation of the original electrochemical measurements of Harned and Davis (1943) and Harned and Bonner (1945) in NaHCOs-NaCI aqueous solutions. Alternatively we have the Pitzer interaction parameters for NaHCOs of Sarbar and others (1982) determined from isopiestic measurements of mixed aqueous solutions of NaHCOs and Na2COj! at 25°C. Curve 2 of figure I shows the resulting calculated solubility of nahcolite in N~CUs solutions if the single-salt parameters of NaHCOs are arbitrarily changed from those of Pitzer and Peiper (1980) to those of Sarbar and others (1982). Curve 3 of figure I retains the Sarbar and others (1982) parameters for NaHCOs and adjusts the equilibrium constant of nahcolite to be internally consistent with the Sarbar and others (1982) parameters. Still the agreement is poor with the Harvie and others (1984) calculation (and experimental data). One final adjustment is to change e and ¢ for COi- - HC0J!- - Na+ interactions. Because no other values of e and ¢ are known for NaHCOs-Na2CUS mixtures, we have substituted values of e and ¢ determined by Roy and others (1984) for KHCOs-K 2COs-KCI aqueous salt mixtures. Curve 4 of figure I shows marked improvement, but further adjustments in these parameters are clearly needed to obtain a revised data set for the NaHCOs - Na2COS system consistent with the data of Sarbar and others (1982). New values of e and ¢ for COs2- - HCOs - - Na+ interactions that are internally consistent with the NaHCO s data of Sarbar and others (1982) and the known solubility of nahcolite in Na2CO~ solutions (Hill and Bacon, 1927) are compared with the Harvie and others (1984) data base III table 2. Both sets of parameters in table 2 will reproduce the experimental data for the solubility of nahcolite in Na2COS solutions (curve I, fig. I). This example demonstrates the need for internal consistency of all Pitzer interaction parameters and thermodynamic data for the given chemical system when changes to the Harvie and others (1984) data base are contemplated. Table 2. -- Comparison of two internally consistent sets of Pitzer interaction parameters for the system NaHCOs-Na2COs-H20 at 25 °Celsius 1 Harvie and others (1984)

Alternate parameter set

NaHCOS2 (P = 0.0277 (31 = .0411 C¢ = 0 Na2COs 4 (30 = .0399 (31 = 1.389 C¢ = .0044

NaHCOsS (30 = -0.04096 (31 = .5062 C¢ = .005250 Na2COs4 (30 = .0399 (31 = 1.389 C¢ = .0044

eCOS-HCOS = -.04 ¢Na-COS-HCOS = .002 Log KNahcolite = -10.742

eCOS-HCOS = .111 ¢Na-COS-HCOS = -.025 Log KNahcolite = -10.696

A¢ = .392. Higher-order electrostatic terms included in calculation of e and ¢. 2 Pitzer and Peiper (1980). S Sarbar and others (1982). 4 Harvie and others (1984). 1

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I,iterature Sources of Pitzer Interactjon parameters

As an aid to future improvement of the Pitzer data base, and guide to interpretation of uncertainties of model results, a computer search of literature values of single and mixed inorganic salt data was conducted through March, 1988. The results are summarized in Attachment C, where Attachment C.I lists a bibliography of 131 articles from which the data were selected. Attachment C.2 lists published values found for the single-salt parameters ,8(0), ,8(1), ,8(2), and C¢. Attachment C.3 summarizes data for binary salt systems, e and,p. The asterisks assijSned to values of e on Attachment C.3 denote parameters for which higher-order electrostatIc terms were not included in fitting to experimental data. Because PHRQPITZ automatically includes the higher-order electrostatic terms, these mixed-salt parameters cannot be used in PHRQPITZ without modification of the code. Attachment C.3 also summarizes values of the single-salt parameters used to define the mixed-salt parameters. Values of e and'" from Attachment C.3 should not be used in PHRQPITZ unless they are consistent with the same single-salt parameters found in PITZER.DATA. Attachment CA summarizes published values of the temperature derivative of the singlesalt parameters. Additional temperature-dependent data are given in Attachment C.5. Numbers in parentheses on Attachments Co2-C.5 refer to bibliographic citations listed in Attachment C.l. Several advanced formulations of the temperature dependence of single-salt parameters have been proposed for NaCI, CaCI2, NaOH, KCl, CsCI, HCI, LiCI, MgS04, Na2S04, K 2S0 4, MgCl 2, and CaS04' Attachment C.5 lists these equations, fitted constants and sources of data. The reader is also referred to the recent papers of Pabalan and Pitzer (1987), Pitzer (1987) and Moller (1988) for additional high temperature data. PHRQPITZ currently calculates values of the single-salt interaction parameters either using the 25 ·C value and its first derivative with respect to temperature, or utilizes an expression of the form given by Silvester and Pitzer (1977) for NaCI (only). For more extensive data on NaCI the reader is referred to Pitzer and others (1984) and Weres and others (1987). Because of our dependence in PHRQPITZ on the Harvie and others (1984) data base and its extensive origins from Pitzer and Mayorga (1973, 1974), and Pitzer and Kim (1974), Attachments C.2-CA are arranged to list single-salt parameters at 25 ·C in the order: Harvie and others (1984), Harvie and Weare (1980), followed by Pitzer sources, and then the remaining literature. Attachment C.6 lists the. PITZER.DATA file read by PHRQPITZ (see Attachment B) indicating sources of parameters in parentheses keyed to citations given in Attachment C.l.

SCALE CONVENTION OF ACTIVITY COEFFICIENTS As has long been recognized, individual-ion activities and activity coefficients cannot be measured independently. Equations 2 and 3 are valid only when individual-ion activity coefficients are combined to define properties of neutral combinations of ions such as in the calculation of mean activity coefficients, saturation indices, solubility, etc. Therefore, values of individual-ion activities and activity coefficients have meaning only in a relative sense and individual values depend on a particular choice of scale convention. The subject has received recent attention as applies to interpretation of pH in seawater (Bates, 1975; Bates and Culberson, 1977; Millero, 1979; Millero and Schreiber, 1982; Plummer and Sundquist, 1982; Millero, 1983; Dickson, 1984; Covington, Bates and Durst, 1985). PHRQPITZ offers two scaling conventions based on the work of Harvie and others (1984). In the first case (IOPT(10)=O, see Description of Input) no scaling is performed and individual-ion activity coefficients are as computed by equations 2 and 3. In the second case, all individual-ion activity coefficients are scaled according to the Macinnes (1919) convention (IOPT(1 0)=1, see Description of Input). In this case the activity coefficient of CI is defined to be equal to the mean activity coefficient of KCI in a KCI solution of equivalent ionic strength, 'YCl(Mac)='Y±KCl' The scaling factor for the ith ion is computed from the term ("(Cl(e~IJ.3)h±KCl)Zi and is multiplied through all other individual-ion activity coefficients computed tr6m equations 2 and 3. That is

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(24) where 'Ii(Ma~) is the individual ion activity coefficient of the ilh ion converted to the Macinnes scale, 'Ii IS tfie activity coefficient of the ion consistent with some other convention, such as equations 2 and 3, 'IC) is the activity coefficient of CI- according to the alternate convention, 'I±KCl is the mean activity coefficient of KCI in a pure KCI solution of equivalent ionic strength and zi is the charge of the ilh ion (+ for cations, - for anions). The activity coefficients could be placed on other scales by substituting for 'I±Kcl or 'IClI'I±KCI in equation 24. As an example, table 3 compares log values of the molality, activity, and activity coefficient of individual ions computed for sea water in equilibrium with aragonite at 25 ·C and a CO2 partial pressure of 10-3 atm. The results are presented for the problem computed on the MacInnes scale and without scalinll as given by equations 2 and 3. In the problem, pH was calculated from the given equilibna and is therefore internally consistent with the aqueous model and respective scale. For this particular case, when all individual-ion activity coefficients are consistent with a single scale, the individual-ion molalities are independent of choice of scale, while the computed individual-ion activities and activity coefficients are scale-dependent. For example, the pH of sea water in equilibrium with aragonite at 25 ·C and 10-3 atm. Pco~ (using the Harvie and others (1984) data base) is 7.871 on the MacInnes scale and 7.828 without scaling equations 2 and 3, as shown in table 3.

Table 3. -- Sea water in equilibrium with aragonite at a Pf10.2 of 10- 3 atmospheres and 25 ·Celsius on two different activity-coef IClent scales MacInnes scale

Unscaled

Species

Log molality

Log activity

Log gamma

Log molality

Log activity

Log gamma

H+ H2O Ca2 + M g 2+ Na+ K+ CICO 2-

-7.694 -.008 -1.981 -1.259 -.313 -1.973 -.246 -4.513 -1.532 -5.938 -2.781 -4.535 -8.204 -5.068 -5.890 -4.530

- 7.871 -.008 -2.795 -2.034 -.552 -2.248 -.363 -5.424 -2.419 -6.134 -2.956 -4.482 -8.312 -5.068 -5.980 -4.530

-0.178 .000 -.814 -.775 -.239 -.274 -.118 -.911 -.887 -.196 -.176 .053 -.108 .000 -.100 .000

-7.694 -.008 -1.981 - 1.259 -.313 -1.973 -.246 -4.513 -1.532 -5.938 -2.781 -4.535 -8.204 -5.068 -5.890 -4.530

-7.828 -.008 -2.708 - 1.946 -.508 -2.204 -.407 -5.512 -2.507 -6.178 -3.000 -4.482 -8.356 -5.068 -5.936 -4.529

-0.134 .000 -.726 -.687 -.195 -.230 -.162 -.999 -.975 -.240 -.219 .053 -.152 .000 -.056 .000

soZl.!-

011HC03-

H~F03 H 0CaC

C'-

C'-

V> I

lH

C'-

Mg8(OH)4+ ClCaB(OH)4+ C1$r+2

Cs+

NH4+

(1-

(1-

C \-

Summary of Literature Values of P1tzer Interaction Parameters for Single Salts BO .0765 (4B) .07650 (49) .0765 (B9) .07670 (B3) .0754 (93) .0754 (85) .07669 ( , 29) .0757 (46) .08305 ( 5 ) .0765 (26) .0765 (25) .0765 (35) .10820 ( 10) .0765 (24) .04835 (48) .04835 (49) .04835 (89) .04827 (83) .0481 (85) .0464 (46) .04453 (5 ) .04808 (54) .04626 (68) .06577 ( , 0) .05041176 ( '23) .1775 (48) · 1775 (89) · 18352 (B3) .1775 (85) .18029 (5 ) · 17527 (71 ) .18104 (65) .3729 ( 61) .1494 (89) .1485 (85) · 16832 ( 5 ) .14847 (54) · 16 (18) .244 (50) · , 2 ( , 8) .204 (50) .28575 (B9) .2834 (B5) .27967 (5 ) .28994 (72) .27948 (72) .28344 (99) .0300 (B9) .03449 (83) .0335 (85) .03352 (54) .03478 (99) .03917 (99) .03131 ( 4 ) .03178 (5) .0522 (89) .03603 ( 5 ) .04568 ( 10)

Bl .2644 (4B) .2664 (49) .2664 (89) .26495 (B3) .2770 (93) .2770 (B5) .26461 ( , 29) .2795 (46) .21900 (5 ) .2665 (26) .2664 (25) .2664 (35) .03127 ( , 0) .2664 (24) .2122 (4B) .2122 (49) .2122 (89) .20887 (B3) .2187 (85) .2274 (46) .22839 ( 5 ) .0476 (54) .21844 (68) .09351 ( 10) .195522 ( I 23) .2945 (48) .2945 (89) .25503 (83) .2945 (85) .27837 ( 5 ) .30197 ( 71) .27779 (65) -.3886(61) .3074 (B9) .3070 (85) .17721 ( 5 ) .307 (54)

1.66725

(89) '.626 (B5) 1.72429 (5) 1 .5795 (72) 1.6745 ( 72) 1.625625 (99) .055B (B9) .01336 (83) .0429 (85) .0429 (54) .03974 (99) -.002984 (99) .065925 (4) .02762 ( 5 ) .1918 (89) .29619 (5) .20431 ( I 0 )

CO

B2

.00127 (4B) .00127 (49) .00127 (89) .00122 (83) .0014 (93) .0007 (85) .0012193 ( '29) .0014 (46) -----

.00062 (26) .00121 (25) .000126 (35) -.002469 ( 10) .00124 ( 24) -.00084 (48) -.00084 (49) .00080 (89) .00082 (83) -.000394 (85) -.0004 (46) -----

-.000788 (54) -.000398 (68) -.002160 ( 10) .001355442 ( 1 23) .0008 (48) .00080 (89) -.00059 (83) .0004 (85)

-----

.0014670 ( 7 1 ) -.00007307 (65) .0008 ( 61) .00359 (B9) .00186 (85) -----

.003710

(54)

-.00130461 (B9) -.000315 (85) -----

-.003755 ( 72) .0003532 ( 7 2 ) -.000890954 (99)

.00038 (89) -.00049 (83) -.000131 (85)

-.000262 (54) -.000496 (99) -.001183 (99) .00030705 (4) -----.00301 (89) -----

-.001731

( 10)

.0

(49)

Attachment C.2 INTERACTION Cu+2 ClCd+2 Fe+ 2

C1C1-

Rb+

C1-

UD+2 Zn+2 Mn+2

C1C1C1-

Ba+ 2 Mg+2

N1+2

C1C1-

C1-

~ ~

,

Co+2

Ca+2

C1-

[1-

A 1+ 3

C1[1-

MgOH+ Cr+3

[1-

Na+

Br-

K+

Br-

H+

Br-

Mg+ 2

Br-

80 .308025 (B9) .2817 (26) .296625 ( '4) -.0169 ( 27) .335925 (B9) .31583 ( , 0) .0441 (89) .03934 ( 5 ) .42735 (B9) .260175 (B9) .327225 (B9) .3420 (35) .25811 ( , 0 ) .2628 (B9) .21638 ( 5 ) 1 .2556 (60) .35235 (4B) .35235 (49) .35235 (B9) .3509 (85) .38110 ( 5 ) .35093 (9B) .3509 (25 ) 1.4680 (58) .347925 (B9) .4456 (26) .44104 (28) 1.3969 (61 ) .364275 (B9) .3454 (35) .41908 (2B) .3582 ( 13) 1. 343 1 (62) .4108 (24) .3159 (4B) .31590 (49 ) .3159 (B9 ) .30534 (B 2) .3053 (B5) .31231 ( 5 ) .41328 ( 10 ) -.10(4B) .6993333 (B9) .70632 (5 ) .7364 (89) .65169 ( 5 ) .0973 (89) .10164 ( 5 ) • T 3523 ( 10) .0569 (B9) .04792 (5 ) .0629"2 ( 10 ) .1960 (89) .22156 ( 5 ) .1905 (64) .432675 (89) .45016 ( 5 )

-

continued

81 1.37625 (B9) 1 .4677 (26) 1 .39125 ( 14) .3468 ( 27) 1.53225 (B9) 10.4224 ( 10) .1483 (89) . 17280 ( 5 ) 1.644 (B9) 1.6425 (B9) 1.55025 (B9) 1.4091 (35) 2.31108 ( 10) 1.49625 (B9) 1.84591 ( 5 ) -1.9783 (60) 1.6815 (4B) 1.6815

(49)

1.6815 (B9) 1 .651 (B5) 1 .21197 ( 5 ) 1.65075 (98) 1.6508 (25) -2.2231 (5B) 1 .581 (B9) 2.4076 (26) 2.34470 (28) -2.0903 (61 ) 1.47525 (B9) 1.625 (35) 2.06641 (28) 1 .44975 ( '3) -1.9504 (62 ) 2.0664 (24) 1. 614 (4B) 1.6140 (49) 1.614 (B9) 1 .7083 (B 2) 1 .708 (B 5) 1 .64585 ( 5 ) .53043 ( 10) 1.658 (4B) 5.8446667 (89) 5.63756 (5 ) 5.2553333 (B9) 6.14389 ( 5 ) .2791 (89) .25274 ( 5 ) .02917 ( 10) .2212 (B9) .27445 (5 ) .16046 ( 10) .3564 (B9) .23087 ( 5 ) .3975 (64) 1.75275 (B9) 1 .44995 ( 5 )

82

CO

-.0404323 (89) -.01395 (26) .03602 ( , 4) .00747 (27)

.0023 (26) -5.829

( 27)

-.00B60725 (B9) -.010078 ( 10 ) -.00101 (89)

-----

-.0368632 (89) -.0879817 (B9) -.0204972 (B9) -.0298 (35) -.010540 ( 10 ) -.0193782 (B9)

(35)

.00102

-----

-.01938 (60) .00519 (4B) .00519 (49) .00519193 (89) .002301 (B5) -

(49)

----

.006507 (98) .00610 (25) .0051919 (58) -.00372291 (89) -.00784 (26) -.02156 (2B) -.0037 ( 61) -.0152151 (B9) .00179 (35) -.02429 (2B) .012537 ( , 3 ) -.01522 ( 62) -.02430 (24) -.00034 (4B) -.00034 (49) -.000339411 (89) .002153 (B2) .000761 (B5) -

.0

----

-.014250

( 10 )

----.00273279 (B9) - - - --

-.0451103

-----

(89)

.00116 (B9) --- --.003478 ( 10) -.00180 (89) -----.001981 ( , 0 ) .00827 (89)

-----

.009687 (64) .00312364 (B9)

.5680 (26) -.53354 (2B) -.00329 -.35136 -.0351

(35) (2B) (24)

Attachment INTERACTION Ca+2 Br-

U+

Br-

Rb+

Br-

Cs+ NH4+ Ba+2

BrBrBr-

5r+2

Br-

Co+2 Zn+2

8 rBr-

Na+

504-2

I ~

'" ..... I

K+

Mg+2

$04-2

504-2

(89) .40950 (5 ) .3648 (63) .3562 ( , 25) .1748 (89) .20243 ( 5 ) .0396 (89) .03297 ( 5 ) .0279 (89) .0624 (89) .31455 (89) .3143 (64) .331125 (89) .3303 (70 ) .426975 (89) .465975 (89) .01958 (4B) .01958 (49) .019575 (89 ) .0148 (83) .019575 (86) .0181 (85 ) .04210 (5 ) .01869 ( 106) .01869 (97) .0187 ( 37) .01957 (45) .0187 (40) .08610 ( , 0 ) .04995 (48) .04995 (49) .0500 (89 ) .000 (85) .04432 (68 ) .0927 (55)

(48)

.22100 (49) .2150 (85 ) .21499 (97) Ca+2

H+

504-2

504-2

Ni+ Cu+2

504-2 504-2

Zn+2 Cd+ 2

$04-2 504-2

-

continued

B,

BO .3816

.2210

C.2

.20 (48) .20000 (49) .20 (90) .15 ( 77) .0298 (48) .0027 (94) -7.59 (66) -7.08 (66 ) .1702 (90) .2358 (90) .2340 (14 ) .21757 (74) .1949 (90) .2053 (90) .2081 (20)

1.61325 (89) .84275 (5 ) 1.7269 (63) 1.872 ( , 25) .2547 (89) .06713 ( 5 ) .1530 (89) .18897 ( 5 ) .0139 (89) .1947 (89) 1.56975 (89) 1

(64)

.5853

1. 7 115 (89) 1. 7 1 4 (70 )

1.65975 (89) 1.63425 (B9) 1. 1 13 (48)

(49) (89) (B3) 1 . 113 (86) 1.0559 (85) .77712 ( 5 )

1. 1 13 1. 113 1. 218

1.0994 ( 106) 1 .099425 ( 97) 1.0094 ( 37) 1. 1 13 (45) 1.0994 (40) . 13037 ( , D) .7793 (48) .7793 (49) .77925 (89) 1. 1023 (85 ) .7365 (68 )

.603

(55)

3.343 (48) 3.3430 (49) 3.3636 (85) 3.3646 (97)

-----

--

---

-.00144

.00004 (89) -.00436 (89) -.0159576 (89 ) -.02257 (64) -.01579 (64) .00122506 (89) .001749 (70) -.000673519 (89) -.1079221 (B9) .00497 (48) .00497 (49) .00497449 (89) .00634 (83) .00570104 (86) .00202 (85) ----.005549 ( 106) .0055488 (97) .00550 (37) .001758 (45) .00553 (40) -.003104 ( 10)

.0 (48) .0 (49) .0 (89 )

.00665 (85) .00181 (68) -.03661 (55) .025 (48) .025 (49) .006993 (85) .02797 ( 97)

----.0

3.0 (77) .0 (48)

.0

( 77)

(66) (66) 2.907 (90) 2.485 (90) 2.527 (14 ) 2.62597 (74) 2.883 (90) 2.6170 (90) 2.6023 (20 )

(89)

-----

(49)

-----

(89)

-.004572 (63) .005291 ( , 25) .0053 (89)

3.1973 (48) 2.650 (49) 2:65 (90)

.0 .0

B2

CO -.0025721

- ----

.0438 (48) .0416 (94) 1 .735 (66) 1.60 (66) .0366 (90) -.0012 (90) .0044 ( , 4) .013756 (74) .02896 (90) .01140 (90) .01032 (20)

.0 ( 97)

.0 (49)

-37.25 (49) -3.74 (85 ) -32.743 (97) -37.23 (90)

-39.23

(75 )

-54.24.(48) -57.70 (49) -55.7 (90)

-40.06 (90 ) -47.35 (90 ) -48.33 ( , 4) -56.2413 (74 ) -32.81 (90) -48.07 (90)

Attachment INTERACTION Co+2 504-2 Mn+ 2

Cs·

504-2 504-2 504-2 504-2 504-2

U·

504-2

Rb·

504-2

Be·

U02+2 Sr+2 Fe+2

NH4+

I ~

'" 00 I

504-2

504-2

Na.

H504-

K.

H5Q4H5Q4H$Q4HSQ4-

Mg+2 Ca+2

H. Fe+2

H504-

Na.

OH-

K.

OH-

Ba+2

OHOHOHOHOH-

Na·

HC03-

Ca+2 L;'+

Cs· M9·

K.

HC03-

BO .20 (90) .16310 (2B.3B) .1631 (3B) .2010 (90) .2065 (40) .201 (B6) .330B9 ( , 0 ) .3170 (90) .3220 (90) .220 ( 102) .2568 ( , 03) .OBBB (B9) .0882 (55) .0714 (44) .136275 (B9) .1308 (B5) .1339 (55) .0579 (B9) .05772 (20) .0579 (34) .040875 (B9) .03369 (5 ) .03905 (29) .04888 ( , 0 ) .04763 ( , 0 ) .0454 (48) .0554 (94) -.0003 (48) .4746 (48) .2145 (4B) .2065 (4B) .2103 (94) .4273 ( 103) .0864 (4B) .0864 (B9) .0864 (B5) .10691 ( 5 ) · 1298 (4B) · 1298 (89) .14982 (5 ) -.1747 (4B) .015 (89 ) · 150 (89 ) -7.6 ( , 5 ) .17175 (B9) .0277 (4B) .028 (B 1) -.04096 ( 1 , 6) -.0490 ( 16) .0277 (92) .0296 (4B) -.0005 (92) -.022 ( 11 3) -.0107 ( 11 2) -.011 ( 114)

C.2 -

B'

2.70 (90) 3.3458 (2B.3B) 3.3460 (3B) 2.9511 (90) 2.9511 (40) 2.980 (B6) 3.14630 (10) 2.914 (90) 1. 8 27 (90) 2.88 ( , 02) 3.063 ( 103) 1.11075 (B9) 1 . 105 (55) 1.2010 (44) 1.2705 (B9) , .2913 (85) 1 .282 (55) 1 • 11075 (B9) 1 . 1105 ( 20) 1 . 1108 (34)

(89)

.65B5

.74799 (5 ) .66379 ( 29) .6585 ( 1 0 ) .44459 ( 1 0 )

.39B

(4B)

.2755 (94) . 1735 (4B) 1 .729 (4B) 2.53 (4B) .5556 (48) .4711 (94) 3.48 ( '03) .253 (4B) .253 (89) .2530 (85 ) . 17653 (5 ) .320 (4B)

.32

(B9 ) .22070 (5 ) -.2303 (4B) .14 (B9) .30 (B9)

continued

CO

-----

.00926 (2B.3B) .03704 (3B) .0182 (90) .01636 (40) .0182 (B 6) -.014731 ( 10 ) .0062 (90) -.0176 (90) .019 ( '02) .0209 (' 03) -.00599803 (B9) -.00795 (55)

0.0

(40)

-41.8+/- 9.2 -42.0+/- 9.2

(20 )

-----

-.00082 (29) -.00116 ( 10) -.001311 ( '0) ---

--

-.00118

(94)

.0044 .0044 .00205 - - --.0041 .0041

(4B) (B9) (85) (48) (B9)

-----

-----

-5.72

.005250

( 11 6)

-----

.0411 (92) -.013 (48) -.013 (92) .09 ( 11 3) .0478 ( 11 2) .049 ( 11 4)

-40.0

-.000036 (34) -.00116142 (B9)

(89)

.0411 (4B) .044 (B 1) .5062 ( 116)

B2 (90)

.00291 (44) .00399338 (B9) -.000894 (85) -.00333 (55 ) -.000100762 (B9)

-----

1 .2

-30.7

-.OOB

(4B)

(48)

( , 02) ( '03)

Attachment INTERACTION Mg+2 HC03-

C8+2

NH4+ Sr+2

Na+

K+

Mg+2

HC03-

HC03HC03C03-2

C03-2

C03-2

~

,

'D

Ca+2

C03-2

NH4+ Sr+2

C03-2 C03-2

Na+

BO (4B) (91 ) .46 ( , 5 ) .019 (76) · , 8 ( , 27) .49 ( , 07) .33 (96) .4 (48) .4 ( 91) .28 ( 9 1 ) .440 ( 107) · 12 (96) -.038 ( 1 14 ) · 12 (75) .0399 (48) · 18975 (89) .0362 (8' ) .040822 ( , 05) .1488 (48) · 138 ( "3) · 1288 ( "2) .075 ( , 07) -9.7 ( , 5 ) 2.833 (76) .180 ( 107) -3.9 (96) -6.8 (75) .160 ( 107) - 11. 9 (75 ) .329 .033

.1288 - 11. 9

(114)

(75 )

H+

1-

Li+

1-

Rb+

I -

Cs+

1-

Sr+2 8a+2 Co+2 Zn+2 Na+2

11I-

.1195 (89) • 1 195 (85) · '2549 ( 5 ) .0746 (89) .05708 (5 ) .4902 (89) .53450 (5 ) .437925 (89) .43524 (5 ) .2362 (89) .23777 (5 ) .2104 (89) .21024 (5 ) .0397 (89) .03461 (5 ) .0244 (89) .0244 (85) .40125 (89) .421875 (89) .52125 (89)

I -

.4821

F-

.0215 (89) .02147 (5 )

I -

K+

I -

Mg+2

1-

Ca+ 2

I -

K+ Mg+2

FF-

(89)

.08089 (89) (75 ) ( , 7)

-10.6 -10.6

C.2 -

continued

B1

CO

(4B) .85 ( 91) .6072

B2

-----

(76) .49 ( , 27) 1.90 ( , 07) .584

-- ---

(48) 3.0 (91 ) .3 ( 9 1 ) 2.977 1 .70

( 107)

- ---.070 ( "4)

----1 .389 (48)

(89) (8 1) '.46790 ( 105) 1.43 (48) 1 • 48 1 ( , 13) .846

1 .51

1 •

433

( 112 )

.66 (107)

.0044 (48) -.0480319 (89) .0052 ( 81) .0042374 ( , 05) -.0015 (48) -----

.00050 ( , , 2 )

- ----

-15.069 (76 ) 2.70 ( 107) 2. 10

( 107)

- - --1.433 ( 1 1 4 ) - ----

.3439 (89) .3439 (85) .31106 (5 ) .2517 (89) .34662 ( 5 ) 1.804125 (89) 1.80454 (5 ) '.80675 (89) 1.81137 (5 )

.392 (89) .39920 (5 ) .373 (89) .36981 (5 ) . , 330 (89) .15964 (5 ) .0262 (89 ) .0262 (85 ) 1.86 (89) 1.68675 (89 ) 1.6725 (89) 1 .9455 (89) .2107 (89) .20690 (5 ) .2021 (89)

- - ---- ---

-.970

(76)

-204.90 (76) -46.0 ( 107)

- ----

-69.0

-----

-----

.00050 ( "4) ----.0018 (89) .0009 (85)

----(89) -----

-.00414

.00793373

-----

(89)

-.000837921

(89)

-----

.0011

(89)

-.00108 (89) -----.00365 (89) -.00192 (85) .00265695 (89) -.0174266 (89) -.0046669 (89) -.0142658 (89)

.00093 (89) 10.0 (75) 10.01 (' 7)

( 107)

Attachment C.2 INTERACTION C8+2

F-

CS·

F-

Rb·

FF-

$r+2 Ne+2 K. Mg+2 Ca+2 H.

u·

.....

,

0

C104C104Cl04Cl04Cl04-

NH4+ Sr+2 8a+2 Zn+2 Pb+2

C104Cl04CI04C104Cl04C104-

U02+2

C104-

Na+2 K• Mg+2 C8+2 Na+2

C103C103C103C103N03-

K.

N03-

Mg+2

N03-

C8+2

N03-

H.

N03-

U·

N03-

'::b+

N03-

Cs· '9·

N03N03-

NH4+

N03-

Cu+2

N03-

Sr+2 8a+2

N03N03-

80 -2.3 (75 ) -2.3 (17) -2.3 ( 1 7 ) .1306 (89) .1306 (85) · 1141 (89) -2.3 (75) .0554 (89) -.040 ( 107) .496125 (89) .451125 (89) .1747 (89) · 1853 ( 1 26) .1998 ( 126) .1634 ( 6) .21795 (5 ) .1973 (89) -.0103 (89) .4269 (89 ) .361425 (89) .506025 (89) .333225 (89) .27386 ( 5 ) .611325 (89) .61785 (6 ) .0249 (89) -.0960 (89) .490 ( 107) .438 ( 107) .0066 (89) .00661 (83) .003 (46) .00351 ( 5 ) -.08155 (83) -.0802 (46) -.05771 ( 5 ) .367125 (89) .29978 ( 23) .3628425 ( 1 1 7 ) .210825 (89) · t 2920 (23) .1119 (89) .11477 ( 5 ) .1420 (89) .12274 (5 ) · 1421 ( 2 ) -.0789 (89 ) -.07885 (83) -.0758 (89) -.0856 (89) -.05431 (5 ) -.0154 (89) -.01561 ( 5 ) .3168 (89) .28076 ( 21) .34782 ( 117) · 134625 (89) -.03225 (89)

-

81 ---

--

----- ---.2570 .2570 .2842

-- - - -

(89) (85) (89)

.2755 (89) .08 ( 107) 2.0085 (89) 1.7565 (89) .2931 (89) .2329 ( 126) .2695 ( 126) .3465 ( 6 ) -.00041 ( 5 ) .3996 (89) -.0194 (89) 1.56675 (89) 1.57575 (89) 1 .797 (89) 1.722 (89) 2.71678 ( 5 ) 2.14425 (89) 2.06175 ( 6 ) .2455 (89) .2481 (89) 1 .804 ( 107) 1.76 ( 107) · 1783 (89) · 17939 (83) .2037 (46) .18642 ( 5 ) .04939 (83) .0722 (46) -.05759 ( 5 ) 1.58475 (89) 1.19260 (23) 1. 5944175 ( 1 1 7 ) 1.40925 (89) .79437 (23) .3206 (89) .30437 ( 5 ) .2780 (89) .36821 ( 5 ) .2772 ( 2 ) -.0172 (89) -.01736 (83) -.0669 (89) .0025 (89) -.21042 (5) · 1120 (89) .10898 ( 5 ) 1.43025 (89) 1.73230 (21) 1.369185 ( 11 7) 1.38 (89) .8025 (89)

continued

CO 1.9 (75) 1.92 ( 1 7 ) .81 ( 17) -.0043 (89) -.00215 (85) -.0105 (89) 1.9 (75) -.00118 (89)

82

----.00957776 (89) -.005001 (89) .00819 (89)

.0117

(6 )

----.0008 (89) - ---- .0131097 (89) -.0312576 (89) .0113172 (89) -.0088406 (89)

---- -

.0216851 (89) .0153795 ( 6 ) .0004 (89)

-.00072 (89) -.00067 (83) .00013 (46) ----.00660 (89) .0065 (46)

-----

-.0206245 (89) -.00181 (23) -.0166947 ( 11 7) -.0201419 (89) -.00263 (23) .0010 (89) -----

-.00551

(89)

--- --

-.0055 (2) .00529 (89) .00528 (83)

-----

.00591 -----.00003 ---

--

(89 ) (89)

-.0219344 (89) -.008372 ( 2 1 ) -.0300697 ( 117) -.0199245 (89)

.30453

(23)

.42877

(23)

Attachment C.2 INTERACTION Co+2 N03Zn+2 Cd+2 Pb+2 U02+2 Cr+5 Mn+2 Ni+2

NB+

-I

K+ Li+ Rb+ Cs+ NB+ K+ Mg+2 Ca+2 NH4+ NB+ K+ Mg+2

-.l I

Ca+2

NB+ K+ Mg+2 C8+2

NB+ K+ Na+ K+ NB+ K+ NB+ K+ Mg+2 C8+2 Sr+2

NB+ K+ NB+ K+ NB+ K+ Na+

BO .311925

(B9) .356025 ( "7) N03.348075 (89) ,3015 ( 2 1 ) .36915 ( "7) N03.2865 (89) N03-.03615 (89) N03.460725 (89) N03.704 (89) N03.337005 ( , 17) N03.28790 (22) .353475 ( " 7) N02.0641 (89) .051 (46) N02.0151 (89) N02. 1336 (89) N02,0269 (B9) N02.0427 (B9) H2P04-.0533 (89) H2P04-.0678 (89) H2PQ4-.41 ( 3 ) H2PQ4-.29 ( 3 ) H2P04-.07043 (29) HP04-2 -.058275 (B9) HP04-2 .02475 (89) HP04-2 -3.6 ( 3 ) -4.1 ( 57) HP04-2 -1.6 (3 ) -2.0 ( 57) P04-3 .1781333 (89) P04-3 .3729333 (B9) P04-3 -62.0 ( 3 ) -43.0 ( 57) P04-3 -67.0 ( 3 ) -56.0 ( 57) -,0442 (B9) H2As04H2As04-.0584 (89) HAs04-2 .030525 (89) HAs04-2 .1296 (89) As04-3 .23BB (89) As04-3 .4994 (B9) 8(OH)4-.0526 (50) -.0427 ( 1B ) 8(OH)4.035 ( 18) .20 (75) . , 9 (7) -.21 (50) B(OH)4-.93 (7) B(OH)4-1.57 (50) -2.35 ( 7 ) 8(OH)4-2.35 (75) 8303(OH)4 -.056 ( , 8 ) -.13 ( 18 ) B303(OH)4 -.11 ( 1B ) B405(OH)4 -.022 ( 18) B405(OH)4 Br03-.0205 (B9) Br03-.1290 (89) 802-.0526 (86)

continued

Bl 1.6905 (89) 1 .577175 ( "7) 1.69125 (89) 1.2012 ( 21) 1.4663475 ( " 7) 1.66B (89)

.285 (89) (89) (89) 1.54236 ( 11 7) 1.43724 ( 22 ) 1 . 60485 ( 117) .1015 (89) .1625 (46) .015 (89) .325 (89) -, 1553 (B9) ,060 (89) .0396 (89) -.1042 (B9) 1.61325

5, 1846667

-.41564 (29) 1.4655 (89) 1.27425 (89)

CO -.00761554 (89) -,0195797 ( "7) -.0156712 (89) -.005798 ( 21) -.0241247 ( "7) -,0256467 (89) ,00532981 (89) -.031544 (89) -,0590051 (89) -.0155439 ( 117) -.00189 ( 22) -.0194525 ( 117) -.0049 (89)

-.0023

(46) (89) (B9) -.00366 (B9) -.0051 (89) ,00795 (89)

.0007 -,0053

.00669 (29) .0293802 (B9) .0163872 (B9)

3.8513333 (89) 3.972 (89)

-.0515381 -.0867949

.2895 (89) .0626 (89) 1.62975 (B9) 1.6485 (B9) 3.93 (89) 4.3406667 (89) .1104 (50) .089 ( '8) .14 ( 18 )

.00180312 (89) -.017819 (89) -.0477276 (89) .1299423 (89) .0154 (50) .0114 ( 18 )

-4.98 (50) -----4,49 (50)

(89) (89)

-.36 (50) -----

-.17

(50)

-.910 ( 18) -----

-.40

( 1B)

-----

. , 91 0 (89) .2565 (89) . , 104 (86)

.0059 (89) --- --

.0154

(B6)

B2

.26536 ( 2 1 )

.30331

(22)

Attachment

INTERACTION Cr04-2 Na+ K+ Cr04-2 Na+ H$03K+ H503Mg+2 H503Ca+2 H503-

I

-..J

N I

Na+

503-2

K+

503-2

Mg+2

$03-2

Ca+2

503-2

Na+ Na+ K+

5203-2 5205-2

Mg+2

5205-2

Ca+2

5205-2

$205-2

BO .09375 (B9) .075B25 (B9) .0249 (107) -.096 (107) .490 (107) .438 ('07) .021 (108) .065 (108) .200 (107) .24 (lOB) .180 (107) .18 (lOB) .06615 (B9) .07 (107) .10 (107) .24 (107) .22

(l07)

C.2

Bl 1.3695 (89) 1.239 (89) .2455 (107) .24Bl (107) l.B04 (107) 1. 76 (107) 1. (108) 1.

°°

-

continued

CO -.00215844

B2

(89)

-.0007795B5 (89) .0004 (107)

(1 DB)

3.00 (107) 3.60 (lOB) 2.38 (107) 2.38 (lOB) 1.27575 (89) .9 (107) 1.1 (107) 3.7 (107) 3.0 (107)

.003738B2

-41.0 -33.0

(107) (lOB)

-61.3

(107)

-40.0

(108)

-34.0 -50.0

(107) (107)

(B9l

Attachment C.3. -- Summary of literature values of Pitzer interaction parametes for mixed-salt solutions

-173-

Attachment C.3 - Summary of Literature Values I NTERACTI ON Na+

Na+ Na+

Na+ Na+ Na+ Na+

-..., -..l

Na+

Na+

Na+

K+

K+ K+

K+ K+ K+ Ca+2

Ca+2

Mg+2

Mg+2

THETA Cl-

8r504-2

NC03C03-2 N03-2 Cl-

504-2

Cl-

504-2

Na+ Na+ Na+ Na+

N+

H+ H+ H+ Cl-

C!-

8rCI04HS04N03-2

P5I

Pitzer Parameters for Mixed Salt Solutions

-.0018 (48) -.0018 (49) -.0018 (88) -.00078 (51) -.004 (46)

-.012 (88) -.012 (48) -.012 (49) -.012 (88) .0 (47) -.0303 (31)

-.0022 (88) -.010 (48) -.010 (49) .010 (88) .0 (47) -.0066 (31)

-.0322 (31) - .012 (48) -.012 (48) -.012 (88) .07 (48) .07 (49) .0 (88). -.0078 (52). .05 (77) .07 (48) .07 (49) .0 (47).

.0085 (31) -.003 (48) .003 (48) -.0012 (88) -.007 (48) -.014 (49) .0 (88) .0029 (52) -.003 (77) -.055 (48) -.023 (49) .0 (47)

Na2S04+K2S04

.05 (77) .07 (48) .07 (49) .07 (84) .0 (88). .050 (30). .016130 (101).

-.012 (77) -.0122 (48) - .0122 (49) -.010 (84) .0 (88) -.01 (30) -.004633 (101)

Na2S04+CaS04

.07 (48) .07 (49) .07 (84) .0 (88). .0 (25).

-.015 (48) -.015 (49) -.023 (84) .0 (88) .00566 (25)

Na2S04+MgS04 Na2S04+MgS04 Na2S04+MgS04

.0224 (30)

Na2S04+MgS04

.036 (48) .036 (88) .0279 (9) .036 (88) .036 (56) .036 (48) .016 (88) -.0279 (46)

SINGLE SALT COMPATIBILITV DATA 80 81 CO

MEDIA

-.012 (48) -.012 (49) -.012 (88) - .0154 (51) -.0203 (46)

.050 (30). Na+

01

NaCl+KCl NaC1+KCl NaCl+KCl

NaCl KCl

.0757 .0464

.2795 .2274

.0014 -.0004

Na2S04 K2S04

.0187 .050

, .0994 .779

.0055 .0

Na2S04 CaS04

.01869 .15

1.0994 3.0

.0055488 .0

NaCI MgC12

.0765 .35093

.2664 1.65075

.00127 .006507

Na2S04 MgS04 Na2S04 "g504

.0187 .3150 .0187 .2150

1. 0994 3.3646 1. 0994 3.3646

.00550 .02797 .00550 .02797

NaCl HC!

.0765 .1775

.2664 .2945

.00127 .00080

NaCl NaN03

.0757 .003

.2795 .2037

.0014 .00013

82

Na2S04+K2S04 Na2S04+K2S04

NaN03+KN03 NaCl+CaC12 NaCl+CaCI2

Na2S04+CaS04

.0

NaC1+MgC12 NaC1HlgC12 NaCl+MgC12

-.004 (48) -.004 (88) .0105 (9)

NaCl+HCl HC1+NaCl

-.012 (88) .0 (56) -.0129 (48) -.006 (88) -.0035 (46)

NaC1+NaN03 NaCl+NaN03

-32.74 -32.74

Attachment C.3 - continued INTERACTION

-, ,

THETA

No. No' No' No' No' No' Na.

ClClClClClClCl-

No'

Cl-

8303(OH)4-

No'

Cl-

8405(OH)4-2 .074 (18)

No' No'

BrBa+2

ClCl-

No' No.

CS' Mn+2

ClCl-

Na' Na'

Mn+2 Co+2

H2P04H2As04HAs04-2 As04-3

Ac.

8(OH)38(OH)4-

Na'

Cu+2

In+2

- .024 (18)

NaCl+NaB303(OH)4

.026 (18)

NaC1+NaB405(OH)4

-.02155 (40) - .001 (13)

NaCl+CoC12

-.01289 (35)"

-.0589 (35)

NaCl+CoC12

S04-2

-.01939 (24) -.001413 (45)"

-.00845 (24) -.008986 (45)

NaCl+CoC12 Na2S04+CoS04

Cl-

-.01939 (24) .0 (14)"

-.01738 (24) -.014 (14)

Na2S04+CoS04 NaC1+CuC12

-.026 (14)

NaCl+CuCl2

- .00358 (26)

NaCl+CuC12

.0 (14)"

-.011 ( 14)

Na2S04+CuS04

.0031 (39) " .077 (14)

-.0125 (39) -.049 (14)

Na2S04+CuS04 Na2SD4+CuS04

.0 (88)" .05073 (41)"

----- (8S) -.03089 (41)

NaBr+ZnBr2 Na2S04+ZnSD4

- . 00032 (27) -.00032 (41)"

.14913 (27) -.01521 (41)

NaCl+CdC12 Na2S04+CdS04

.05917 (26)"

.01152 (26)

-.06404 (26)" Cu+2

NaCl+NaH2P04 NaCl+NaH2As04 NaCl+NaHAs04 NaCl+NaAs04 NaCl+NaAc NaC1+NaB(OH)3 NaCl+NaB(OH)4

.04320 (40)-.016 (13)"

S04-2 Cl-

.077 (14)

No·

.0 (131) .0 (75) .0 (75) .0 (75) .0 (75) .0 (75) -.0073 (18)

.0 (88) .0 (88) -.012 (84) -.003 (88) -.003 (88) -.0174 (84) -.01275 (35)

V>

Na'

.12 (18)

MEDIA

.0 (88) -.003 (88)" .067 (84) -.033 (88) .0 (88)" .082 (84) .03687 (35)"

->

Co+2

.1004 (131) .228 (75) .122 (75)" .060 (75)" - .017 (75) .0 (75)" -.065 (18)

PSI

S04-2

No· No'

Ln+2

8r504-2

No' No'

Cd+2 Cd+2

ClS04-2

Na'

Ni+2

Cl-

No·

CS'

S04-2

No·

N1+2

S04-2

- .0153 (37) .0027 (43)"

NaC1+NaBr NaC1+BaC 12 NaC1+BaC12 NaCl+CsCl NaCl+MnCl2 NaCl+MnC12 NaCl+MnC12

NaC1+NiC12

-.0035 (37)

Na2S04+Cs2SD4

-.0128 (43)

Na2S04+NiS04

SINGLE SALT COMPATIBILITY DATA 80 81 CO

NaCl NaB(OH)4 -.0427 NaC1 NaB303(OH)4 -.056 NaCl NaB405(OH)4 -.11

.089 -.910

.0765 .3420

NaCl CoC12 NaC1 CoC12

Ref.(89) .3582 1.44975 .0765 .2664 .3454 1.625

Na2S04 CoS04

.01957 .16310

NaCl CuC12 NaCl CuC12 NaCl CuC12 Na2S04 CuS04

Ref. (89) .2966 1.391 Ref. (89) .2966 1.391 .0765 .2665 .2817 1.4677 Ref. (89) .2340 2.527

Na2S04 CuS04

Ref.(89) .2340 2.527 .0187 .1949 -.0169 .0187 .2053 .0765 .4456 .0187 .0714 .0187 .1702

.0114

.0

-.40

NaCl MnC12

Na2S04 ZnS04 CdC1 Na2S04 CdS04 NaCl NiC12 Na2S04 (52S04 Na2S04 NiS04

82

.2664 1.4091

1.113 3.3458

1.0994 2.8830 .3468 1.0994 2.6170 .2665 2.4076 1. 0094 1.2010 1.0994 2.9070

.000126 -.0298

.00102

-.012537 .000126 .00179

-.00329

.001758 .00926

-30.7

-.03602

-.03602 .00062 -.01395

.0 .0023

.0044

-48.33

.0044

-48.33

.00553 .0290 .00747 .00553 .01140 .00062 -.00784 .00550 .00291 .0053 .03660

-32.81 -5.829 -48.07 .0 .5680

-40.06

Attachment C.3 - cont1nued INTERACTION

THETA

P5I

No+

N03-

N02-

-.0144 (46)

-.0012 (46)

K+

Ca+2

C,-

K+

Ca+2

504-2

K+

Mg+2

Cl-

.032 (48) .032 (49) -.040 (88).032 (49) -.040 (47).0 (48) .0 (49) .0 (47).0 (73).0 (48) .0 (49) .0 (47)-

-.025 (48) -.025 (49) -.015 (88) .0 (49) .0 (47) -.022 (48) -.022 (49) .0 (47) - .05 (73) -.048 (48) -.048 (49) .0 (47)

K+

K+

I.Ig"'2

H+

504-2

Cl-

.005 (48) .005 (88) .0049 (8) .0068 (8) .0074 (9)

I

...,

-.011 (48) -.007 (88) -.0081 (8) -.0106 (8) -.0105 (9)

MEDIA NaN03+NaN02

.0088 (9)

I

K+ K+ K+ K+

H+ H+ H+ Cl-

Br504-2 H504-

N03-2

.005 (88) .005 (48) .005 (48) .016 (88) -.000815 (46)

-.0131 (9) - .021 (88) .197 (48) -.0265 (48) -.006 (88) -.00023 (46)

NaN03 NaN02

C,-

H2P04-

.1004 (131) .1004 (95) .10 (86)

.06 (131) -.0105 (95) -.01 (86)

K2504.....lg504 HC1+KC1 HC1+KC1 HCHKCl HCHKCl HC1+KCl

KC1+KN03 KC HKN03

K2S04 Mg504

Ref. (88) HCI KCI HCI KC, HCI KCI HC, KC,

KCI

KC1"'KH2P04 KC HKH2P04 KC 1"'KH2P04

Ref. (89) KC, KH2P04

K+ K+

88+2

C'C'-

K+ K+

Cs+ Cs+

C,504-2

Br-

K+

Co+2

504-2

C8+2

1.19+2

Cl-

Ca+2

1.19+2

504-2

Ca+2

C'-

N03-

.0 (88) -.072 (88).010 (84) .0 (88) -.0049 (36) -.0982 (19)-.0819 (19).007 (48) .007 (49) .010 (88) .007 (48) .007 (49) .01 (47) .016 (88)

.0 (88) .0 (88) -.017 (84) -.0013 (88) -.0016 (36) -.0328 (19) -.0411 (19) -.012 (48) -.012 (49) .0 (88) .024 (48) .05 (49) .0 (47) -.017 (88)

B1

.051

.1625

.2037

CO .00013 -.0023

B2

KC1+NgC12 KC1+MgC12

KN03

K+

BO .003

KC1+CaC12 K2S04+Ca504

~

0-.

SINGLE SALT COMPATIBILITY DATA

KC1+KBr KC1+BaC12 KC1+BaC12 KC1+C5Cl K2S04+Cs2504

.04995 .21499 .1775 .04835 .1775 .04835 .1775

.04835 .1775 .04835

.0464

-.0802 .04835

-.0678

.7793 3.3646 .2945 .2122 .2945 .2122 .2945 .2122 .2945 .2122

.2274 .0722 .2122 -.1042

.0 .02797

-32.743

.00080 -.00094

.00080 -.00084

.00080 - .00084 .00080 -.00084

-.0004 .0065

-.00084

K2504

.0500

.7790

C52S04

.0714

1.2010

.00291

Ca2504 M9 S04

.200

2.65 3.3646

.0 .02797

M9C12+C8C12 C82504+M9 250 4 CaC12+Ca(N03)2

.21499

-57.70

-32.743

Attachment C.3 - continued INTERACTION Ca+2

H+

THETA

C'-

Ca+2 Mg+2

Co+2 C'MgOH+ C1-

Mg+2 Mg+2

C'H+

Mg+2 H+

H+ Na+

N03C'-

HS04C104-

PSI

MEDIA

.092 (4B) -.0333 (110)' .0612 (110) .0600 (110) .0739 (61) .0628 (59)' -.055 (9,76)

-.015 (48) .016 (110) .0008 (110) .0163 (110) .0030 (61) .0467 (59) .013 (9,76) .028 (48)

.016 (88) .10 (48) .062 (109) -.2257 (130) -.024 (109)' -.459 (58)' .0897 (61) .0459 (58). .0 (63)' .10 (48) .036 (88) .107 (126)

.0 (88) -.011 (48) .001 (109) .2775 (130) .0122 (109) .039 (58) - .0014 (61) .0396 (58) -.0298 (63) -.0178 (48) -.016 (88) -.113 (126)

HC104+NaCl04 HC104+NaC104

.069 (110) .0600 (63) .073 (70) .072 (84) -.036 (88)' .074 (110) .0616 (61). .0763 (61) .0719 (64) -.019 (86)

-.005 (110) .0163 (63) .0 (70) .0 (84) .024 (88) .0137 (110) .0424 (61) -.0001 (61 ) .0057 (64) .0 (86)

HBr+MgBr2 HBr+CaBr2 HBr+CaBr2 HC1+BaC12 HC1+BaC12 HC1+BaC12 HC1+BaC12 HC1+BaC12 HBr+BaBr2 HBr+NH4Br

.0787 (61) .0597 (61). .0 (103) .015 (88) .015 (88) .015 (88) -.044 (88) -.016 (88) -.0127 (9)

.0064 (61) .0493 (61) .0143 (103) .0 (88) .0 (88) -.0017 (88) -.019 (88) .0 (88) -.0091 (9)

HC1+CoC12

-.005 (9)

-.0125 (9)

HC1+NH4C1

-- ---

CaC12+HC1 HC1+CaC12 HC1+CaC12 CaC12+CoCI2 MgC12+Mg(N03)2 MgC12+HCl HC1+MgC12 MgC12+HCl MgC12+HCl HC1+MgC12 HC1+MgC12

I ~

-J -J

H+ H+

"9-2 C8+2

BrBr-

H+

Ba+2

C'-

H+ H+

8a+2 Br-

BrNH4+

H+

Co+2

C'-

H+ H+ H+ H+ H+ H+

Fe+2 Li+ Li+ Li+ Cs+ NH4+

HS04C'BrC'04C'C'-

I

H+

Sr+2

C'-

-.020 (88)' .065 (84) .0311 (61)' .0720 (62)

.018 (88) .003 (84) .0178 (61) .0007 (B2)

SINGLE SALT COMPATIBILITY DATA B1 BO CO

H2S04+FeHS04 HC1+L1C1 HBr+L1Br HC104+l1C104 HC1+CsCl HC1+NH4C1 HC1+NH4C1

HC1+SrC12 HC1+SrC12 HC1+SrC12 HC1+SrC12

Ref.(89) but CO=O

HC104 NaCl04

216 Ref.(89)

HBr NH4Br

.1960 .0624

.3564 .1947

.00B27 -.00436

HC' NH4Cl HC' NH4Cl

.1775 .0522 .1775 .0522

.2945 .1918 .2945 .1918

.00080 -.00301 .00080 -.00301

B2


THETA

H+

Mn+2

Cl-

H+

Ni+2

Cl-

H+

U02+2 C104-

C,-

Na+

Sr+2

C'-

H+

C,-

504-2 Na+

AH3

- -J

00

PSI

.0 (B8). .0834 (111) .075 (84) .0694 (61) .0666 (6n. .0818 (61) .0559 (6n -.0732 (6).

.0 (88) -.0090 (111) -.007 (84) -.0006 (61) .0386 (61) .0051 (61) .0475 (61) .0434 (6)

HC1+MnC12 HC1+MnC12 HC1+MnC12 HC1+t.lnC12 HC 1HlnC 12 HC1+NiC12

.051 (102)

-.0021 (102)

NaC1+SrC12

.0036 (72) -.00323 (100) .013 (84)

NaC1+$rC12 NaC1+5rC12 HC1+A1C13

.216 (2) .02 (48) .02 (49) .030 (14) -.02 (14).

.004 (2) .0014 (48) .0014 (49) .000 (14) .004 (14)

HC1+A1C13

-.035 (88).

.007 (88)

NaC1+Na2S04

-.045 (25).

.007 (25)

NaC1+Na2S04

.030 (79) -.035 (88). .02 (84) -.045 (25). -.045 (33). -.02 (86).

.0 (79) .0 (88) .0 (84) .014 (25) .018 (33) -.007 (86)

.030 (14) .030 (79) .02 (48) .02 (49) - .02 (47).

-.005 (14) -5.0 (79) -.018 (48) .0 (49) .0 (47)

-.0084 (72). .00940 (100). .185 (84)

HC'04+U02(CI04}2

NaCl+Na2504 NaC1+Na2504

I

C'-

C'-

C'-

504-2 K+

504-2 C8+2

$04-2 Mg+2

SINGLE SALT COMPATIBILITY DATA BD B1 CO

MEDIA

HC'04 U02(C104}2 NaCl SrC12

.1634 .61785 .0765 .2858

.3465 2.06175 .2664 1.667

.0117 .0153795 .00127 -.00130

.2664 1.0994

.00127 .00550

B2

HC' A1C13

NaCl Na2S04

Rof.(89) Rof.(89}

NaCl Na2S04

.0765 .0187

Pitz.Param. KCI K2S04 Rof.(14}

.04835 .04995

Cse12 C8504

.3159 .200

1.614 2.65

MgC12 MgS04

.35235 .2210

1.6815 3.343

.00519193 .0250 -37.23

M9Cl2 M9S0 4 Rof.(14} M9C12 M9S04

.3509 .2150

1.6508 3.3646

.00651 .02797

-32.74

.3509 .3150

1.6508 3.3646

,00610 .02797

-32.74

KC1+K2S04 KC1+K2S04 KC1+K2S04 KC1+K2S04

CaC12+CaS04

.02 (48) .02 (49) -.035 (88). -.02 (86).

-.004 (48) -.004 (49) .0 (88) -.007 (86)

I.IgC12+Mg504 MgC12+MgS04

.02 (84) -.056 (32).

-.014 (84) .0129 (32)

MgC12+MgS04 1.19C12+Mg504

.030 (14) - .045 (20,27).

-.020 (14) .007 (20,27)

MgC 12+1.Ig504 1.19 C12+l.IgS04

.2122 .77925

-.00084

-.00034 .0

-57.70


Cl-

ClClClClClCl-

S04-2 Cu+2

H$04- Na+ HS04- H+

OHOH-

P5I

MEDIA

.030 (14)

.031 (14)

CuC12+CuS04

-.02 (14)"

.043 (14)

CuC12+CuS04

-.006 (48) -.006 (48) -.050 (88) -.050 (48) -.050 (88) - .050 (48) .03 (48) .0359 (81)

-.006 (48) .013 (48) -.006 (88) -.006 (48) -.008 (88) -.025 (48) -.015 (48) -.0143 (81)

THETA

Na+ K+

OH-

Ca+2 HC03- Na+

.030 (92)

----- (92)

SINGLE SALT COMPATIBILITY DATA CuC12 CuS04 CuC12 CuS04

BO .2966 .2340 .2966

.2340

NaCl+NaHC03 NaCl+NaHC03

NaCl NaHC03 NaCl NaHC03

.0277

.0411 .2122 .0478

KC1+KHC03

KCl KHC03

ClCl-

HC03- Mg+2 C03-2 Na+

.03 (48) - .02 (48) -.1605 (129)"

-.096 (48) .0085 (48) .0503 (129)

NaCl+Na2C03

.07669

-.2343 (47)"

.0431 (47)

NaCl+Na2C03

-.053 (81)

.016 (81)

NaC1+Na2C03

-.092 (81)"

.006 (B1)

NaC1+Na2C03

NaCl Na2C03 NaCl Na2CC3 NaCl Na2C03 NaCl Na2C03

KCl K2C03 KCl

.04835 .1288

C03-2 K+

- .02 (48) - .053 (112) -.092 (112)"

ClCl-

Co+2 Ni+2

504-2

504-2

S04-2 H504- Na+ S04-2 HS04- K+ 504-2 HS04- Mg+2

504-2 OH504-2 OH-

Na+ K+

504-2 504-2 S04-2 S04-2

Ha+ Mg+2 Na+ K+ Na+

OHOHOHOH-

HC03HC03C03-2 C03-2 C03-2

C03-2 K+

BrBr-

Na+ K+

-.18140 (28)" -.045 (24) -.16242 (28)" .0 (48) .0 (48) .0 (48) -.013 (48) -.013 (48) .01 (48) .01 (48) .02 (48) .02 (48) .10 (48) .0 (78)" .10 (48) -.065 (88) -.065 (88)

.004 (48) .024 (112) .0073 (112) .08718 (28) .02911 (24) .07202 (28) -.0094 (48) -.0677 (48) -.0425 (48) -.009 (48) -.050 (48) -.005 (4B) -.161 (48) -.005 (48) -.009 (4B) -.017 (48) .0 (78) - .01 (49) -.018 (88) -.014 (88)

-.03602

.2664

-.0037 (112)

Cl-

.0044

1.391 2.527

.0765 .028

-.063 (112)

'"

2.527

,0044

B2 -48.33 -48.33

KC l+KOH

HC03- K+

I

CO -.03602

NaCl+NaOH

Cl-

-J

B1 1.391

KC l+K2C03 KC l+K2C03

.04835 -.0107

.026461 .040822 1.4679 .07669 .26461 .040822 1.4679 .0765 .2664 1.510 .0362 .0765 .2664 1.510 .0362

.0012193 .0042374 .0012193

.0042374 .00127 .0052 .00127

.0052

1.433 2.06641

-.02429

-.35136

N1CJ2 NiS04

.44104 2.34470 Ref. (90)

-.02156

-.53354

NaOH Na2C03

.0864 .0362

.04835 .1288 .41908

Ref.(90)

N1C12+N12S04

NaOH+Na2C03

.2122

-.00084

-.00084 .00050 -.00084 .00050

K2C03 CoC12 CoS04

CoC12+CoS04

.00127

.044

1.433 .2122

.253 1.51

.0044

.0052

Attachment C.3 - continued

INTERACTION

THETA

HC03- C03-2 Na+ HCQ3- C03-2 K+

-.04 (48) -.04 (48) .089 (112) - .063 (112).

I

00

0

P5I .002 (48) .012 (48) -.036 (112)

KHC03+K2C03

.013 (112)

KHC03+K2C03

L1+ L1+ L1+ L1+ L1+ L1+

Na+ No+ Na+ K+ CI8a+2

C,N03-2 C'04ClN03-2 Cl-

L1+ L1+

Cs+ Cs+

Cl504-2

.012 (88) .012 (88) .012 (88) - .022 (88) .016 (88) -.070 (88). .0 (84) - .095 (88) -.1242 (37)

L1+

Cd+2

504-2

.0 (42).

L1+ L1+

Ni+2 Mn+2

C'504-2

-.059 (69). .0 (40).

Cu+2

Ni+2

N03-2

.01314 (22)

-.003909 (22)

Cu+2

1n+2

N03-2

.00664 (21)

-.00141 (21)

Cs+

B8+2

C'-

Rb+

Cd+2

Rb+

Co+2

NH4+

504-2 H2P04-

-.003 (88) -.0072 (88) -.0080 (88) -.010 (88) -.003 (88) .019 (88) .009 (84) -.0094 (68) .0088 (37) .0 (42) .047 (69) .0 (40)

I

504-2

-.150 (88). - .070 (84) -.1226 (20).

.0 (88) .015 (84) .3730 (20)

504-2

-.3058 (34).

.0466 (34)

.01837 (29).

MEDIA

-.00427 (29)

• - Higher prder electrostatic terms not included.

liCl+NaCl LiN03+NaN03 LiC104+NaC104 LiCl +KC I LiCl+llN03 liCl+BaC12 liC1+BaC12 liCl+CsCl li2S04+Cs2S04

SINGLE SALT COMPATIBILITY DATA 61 60 CO KHC03 K2C03 KHC03 K2C03

-.0107 .1288 -.0107 .1288

Li 2504 1.1363 C52S04 .0714 Li2504+CdS04 Li2S04 .1363 Cd2S04 .2053 LiCl+NiC12 Ref.(89) but CO=O Li2S04+MnS04 li2504 .1363 MnS04 .2065 Cu(N03)2+Nl(N03)2 Cu(N03)2 .28076 N1(N03)2 .28790 Cu(N03)2+Zn(N03)2 Cu(N03)2 .28076 Zn(N03)2 .3015 C5Cl+BaC12 CsCl+BaC12 Rb2504+CdS04 Rb2S04 .05772 Cd504 .2081 Rb2S04+CoS04 Rb2S04 .0579 C0504 .1631 NH4H2P04+(NH4)2S04 NH4H2P04 -.07043 (NH4)2S04 .03905

.0478 1.433 .0478 1.433

62

.00050 .00050

1.2705 1.2010 1.2705 2.6170

- .00399 .00291 .00399 _01140

1.2705 2.9511 1.73230 1.43724 1.73230 1.2012

-.00399 .01636 - .00838 -.00189 -.008372 -.005798

1.1105 2.6023 1.1108 3.3458 - .41564 .66379

.0 .01032 -.000036 .00926 .00669 - .00082

Values of theta and psi not consistent with PHRQPITZ.

-48.07 -40.0

.30381 .26536

-48.07

-30.7

Attachment CA. -- Temperature dependence of single-salt parameters

-181-

Attachment

C.4

dBO/dT

I

00 N I

Cl-

Na. Na·

Br-

7.159E-4 ( 1 2 1 ) .008946 ( 1 20) 7.692E-4 ( 1 21)

504-2

2.367E-3

1-

Na· Na. Na· Na· Na. Na· Na· Na· Na·

FOH-

K+ K+ K+ K+ K+ K+ K+

HC03C03-2 C104N03C103Br03103C1Br-

504-2 1-

FHC03C03-2

K+

C104-

K+ K+ K+ K+ H+

N03C103H2P04103-

H+ H+ H+ Mg+2

Br1-

Mg+2 Mg+2 Mg+2 Mg+2 Ca+ 2

Br-

Ca+2 Ca+2 Ca+2 Ca+2 NH4+ NH4+ NH4+ NH4+ Rb+ Rb+ Rb+ Rb+

C1-

C104C1-

504-2 Cl04N03C1Br-

504-2 C104N03ClC03-2

HC03H2P04ClBr$04-2 1-

Temperature dependence of single salt dB 1 /dT

Na·

Na·

-

( 12 1)

.002349 ( 106) 8.355E-4 ( 121 ) 9.163E-4 (118 ) 5.361E-4 ( 121 ) 7.00E-4 ( 1 2 1 ) 1.00E-3 (B 1) 1.79E-3 rB 1) 12.96E-4 ( 1 2 1 ) 12.66E-4 ( 121 ) 10.35E-4 ( 1 2 1 ) 5.59E-4 ( 1 21) 20.66E-4 ( 1 21) 11.79E-4 ( 1 1 8 ) 5.794E-4 ( 121 ) 7.39E-4 ( 1 2 1 ) 1.44E-3 ( 1 2 1 ) 9.914E-4 ( 1 2 1 ) 2.14E-4 ( 121 ) .996E-3 (B 1 ) 1. 1 E-3 ( "2) 1.788E-3 ( 8 1 ) .60E-4 ( 1 21) 4.98E-4 ( "8) 2.06E-4 ( 1 2 1 ) 19.87E-4 ( 1 21) 6.045E-4 ( 1 21) 21.10E-4 ( "8) -3.081E-4 ( 1 21) -3.081E-4 ( 1 1 8 ) -2.049E-4 ( 1 2 1 ) -.230E-4 ( 1 2 1 ) 4.905E-4 ( 121 ) -.19425E-3 ( 121 ) -.429E-3 (86) -.05625E-3 ( 121 ) -.69E-3 ( 1 21) .52275E-3 ( 121 ) .51525E-3 ( 121 ) -.1725E-3 ( 1 2 1 ) 1.049E-4 (82) -.52275E-3 ( 1 21)

--- -- ( 1 2 1 ) .8925E-3 ( 121 ) .5295E-3 ( 121) .779E-4 ( 121 ) .5794E-3 ( "4) 1.1E-3 ( 1 14)

-12.6E-3 (114) 1.5'E-4 ( 1 2 1 ) 5.522E-4 ( 1 2 1 ) 6.780E-4 ( 1 2 1 ) .9375E-3 ( 121 ) 8.578E-4 ( 1 21)

7.005E-4 ( 1 2 1 ) 6.1608E-5 ( 120) 10.79E-4 ( 121 ) 5.6325E-3 ( 121 ) .005958 ( 1 06) 8.28E-4 ( 1 2 1 ) 9.964E-4 ( 1 1 B) 8.70E-4 ( 1 2 1 ) 1.34E-4 ( 1 2 1 ) 1. 10E-3 ( 81) 2.05E-3 (81) 22.97E-4 ( 1 21) 20.60E-4 ( 1 21 ) 19.07E-4 ( 1 21) 34.37E-4 ( 1 21) 60.57E-4 ( 1 21) 59.38E-4 ( "8) 10.71E-4 ( 121) 17.40E-4 ( 1 2 1 ) 6.6975E-3 ( 1 21) '1.86E-4 ( 1 21 ) 5.44E-4 ( 121 ) 1.104E-3 (81) 4.36E-3 ( 1 T 2 ) 2.051E-3 (B 1 ) 10.07E-3 ( 1 2 1 ) 95.19E-4 ( "8) 64.5E-4 ( 1 2 1 ) 31.8E-4 ( 1 21) 28.6E-4 ( 1 21) 45.36E-4 ( "8) 1.419E-4 ( 1 21) 1.419E-4 ( "8) 4.467E-4 ( 1 2 1 ) 8.86E-4 ( 1 2 1 ) 19.31E-4 ( 1 21) 2.775E-3 ( 121 ) 3.6525E-3 (B6) 3.8625E-3 ( 121) 1.53E-2 ( 121) 4.5E-3 ( 1 2 1 ) 4.4925E-3 ( 121) 3.9E-3 ( 1 2 1 ) 3.54E-3 (82) 6.0375E-3 ( 121) 5.46E-2 ( 121 ) 5.0775E-3 ( 1 21) 9.1875E-3 ( 121 ) 12.58E-4 ( 1 2 1 ) 1.071E-3 ( 1 14) 4.36E-3 ( "4) -l.75E-3 ( 1 1 4 ) 22.8E-4 ( 1 2 1 ) 15.06E-4 ( 121 ) 20.35E-4 ( 1 2 1 ) 8.64E-3 ( , 21) 23.83E-4 ( 1 2 1 )

parameters

dCO/dT

dB2/dT

-10.54E-5 ( 121 ) -4.655E-5 ( 1 20) -9.30E-5 ( 121 ) -4.879037 ( 1 2 1 ) -.00479 ( 106) -B.35E-5 -5.58E-5

( 12 1 ) ( "8)

-18.94E-5

( 121 )

-16.23E-5 -23.16E-5 -9.29£-5

( 1 21) ( 12 1) ( 1 21)

( 12 1) ( 1 21)

-5.095E-5 -7.004E-5

( 121) ( 121 )

-9.44E-5 -5.95E-5

39.7E-5

( 12 1)

-10.11E-5

( 121 )

6.213E-5 ( 1 21) 3.106E-5 ( 1 1 B ) -5.685E-5 ( 1 2 1 ) -7.32E-5 ( 1 2 1 ) -11.77E-5 ( 1 2 1 ) - 1.6493266 ( 121 ) .523E-3 ( 121) -3.5266952 ( 1 21)

( 1 21) ( 12 1 )

-3.0918245 -.05E-3

( 1 21 ) ( 1 14)

-2.84E-5

( 121)

2.10E-5

( 12 1 )

-5.16E-1

( 1 21)

(82)

-1.565E-4 -----

-2.53E-1

Attachment C.4 dBO/dT Rb+ Cs+ Co+ Cs+ Cs+ Cs+

,

00 W

,

N1+2 Cu+2 Cu+2 Zn+2 Zn+2 Cd+2 Co+2 Sr+2 $r+2 Sr+2 Sr+2 5r+ 2 8a+2 8a+2 8a+2 Mn+2 L1+2 L1+2 Li+2 L1+2

FCI8r-

$04-2 1-

FC104C'-

504-2 504-2 (104$04-2 C104C'8r-

504-2 C104N03C'8r-

N03CI04C'8r-

504-2 CI04-

-.76E-4 ( B.2BE-4 ( 7.030E-4 7.80E-4 ( .8925E-3 9.75E-4 ( .95E-4 (

1 21) 1 21) ( 118) , 21) ( '21) , 21) '21) .666E-3 ( 1 2 1 ) -2.715E-3 ( 1 21 ) -4.4E-3 ( , 21)

-3.66E-3 ( 1 2 1 ) .59625£-3 ( 12' ) -2.79£-3 ( 1 2 , ) .54525E-3 ( 1 21) .717E-3 ( 121) -.32775£-3 ( , 2 1 ) -2.9£-3 ( 102) 1.143E-3 ( 121) .177E-3 ( 121) .6405E-3 ( '2' ) -.33825E-3 ( 1 2 , ) -2.91£-3 ( 1 21) .39675E-3 ( 121) -1.685E-4 ( 1 2 1 ) -1.819E-4 ( 1 2 1 ) .5055£-3 ( 1 21) .386E-4 ( 1 21 )

dB1/dT

dCO/dT

14.7E-4 ( 1 21) 15.0E-4 ( 1 21 ) 21.07E-4 ( , 18 ) 2B.44E-4 ( , 2 1 ) 14.4825E-3 ( 1 2 , ) 34.77E-4 ( 1 21) 5.97E-4 ( 1 2 1 ) 4.7625E-3 ( '2' ) 8.475E-3 ( 121) 2.3BE-2 ( 1 21) 2.33£-2 ( , 2 1 ) 5.0925E-3 ( 1 21 ) 1 .71 E- 2 ( 1 2 1 ) 5.3625E-3 ( 12' ) 2.8425£-3 ( 1 2' ) 6.5325£-3 ( 1 2 1 ) 27.0£-3 ( 102) 5.3925£-3 ( 12' ) 12.4725£-3 ( '21) 3.2325E-3 ( '2' ) 6.78£-3 ( , 21) 29.1E-3 ( , 5.025E-3 5.366E-4 6.636£-4 1.41 £-3 ( 7.009E-4

continued

-12.25E-5 -4.06E-5

dB2/dT ( 121 )

( , ,8 )

-3.8236801

( 1 21)

4.80E-3 ( 121) 3.97E-3 ( 12' ) -3.8554999 ( 121) 2.61E-3 ( 1 2 1 ) -3.5903348 ( 121) ----- ( 1 21 )

3.0E-3 ( 102) -3.1077344 ( 1 21) -1.5379573

( 1 21)

-3.3357764 -4.520E-5 ( -2.813E-5 ( -2.3334525 -7.712E-5 (

( , 2 1)

21)

( 121 ) ( 121) ( 12 1 )

121) ( 121)

12 1 )

121) ( 121 ) 12 1 )

-4.73E-1 -3.33E-1

( 12' )

-5.22E-1

( 12 1 )

-.42

( 12' )

( 102)

Attachment C.S. -- Summary of analytical expressions for temperature (and pressure) dependence of selected single-salt Pitzer interaction parameters

-184-

Attachment C.5 - Summary of analytical expressions for temperature (and pressure) dependence of selected single salt Pitzer interaction parameters $ Parameter Number 1

2 3 4

5

6

Solution NBCl (120,5) .0765 -777.03 -4.4706 .008946 -3.3158E-6 .2664

CaC12 (1,n 3.39701E-1 5.10778E+3 4.64785E+1 -1.38971E-1 6.82557E-5 1.50481 -4.98241E+2 .0 -1.64685E-2 2.34630E-5 -2.67882E-2 -9.67633E+3 -8.48338E+1 2.46219E-1 -1.18352E-4

7

8 9

10 11

12 13 14 15 16 17 18 19

6.1608E-5 1.0715E-6 .00127 33.317 .09421 -4.655E-5 41587.11 -315.90 .8514 -8.3637E-4

I

00 V> I

80

1 2 3 4

5 6 81

1

2

3 4

5 6

CO

1 2 3 4

5 6

KCl (54,2) .04808 -758.48 -4.7062 .010072 -3.7599E-6 .0 .0476 303.9 1.066 .0 .0 .0470 -7.88E-4 91. 270 .58643 -.0012980 4.9567E-7 .0

CsCl (54,2) .03352 -1290.0 -8.4279 .018502 -6.7942E-6

Parameter Number NaOH (80,3) 6 -2.8'3'778E-3 7 3.70'2540E-, 8 7.'788733E-6 9 -5.8847404E-9 10 -4.8217410E~3 11 4.0534778e~4 12 -5.1714017E-2 13 -1.0553037E-B '4 8.9893405E-10 17 -4.9359970E+1 20 1.1931122E+1 22 4.6286977E~2 23 -1.02941S1E+4 24 -8.5960581E+1 25 2. 3905969E-1 26 -1.0795894E-4 29 2.9680772E-0 32 -6.8923899E-1 33 -8.1156286E-2 34 2.7682478E+2 35 -7.3755443E+3 36 1.0945106E-1 37 -4.0218506E-5 38 2.4824963E-O 39 -1.6686897E+1 40 4.5364961E+2 41 -6.5161667E-3 42 2.3765786E-6 HCl (115,4) .17416 -773.62 -4.5174 8.1556E-3 -2.8525E-6

.0 .0429 -38.0

.0 .00'306 .0 .0 -2.62E-4 157.13 1.0860 -.0025242 9.840E-7 .0

.28799 -374.50 -4.1319 1.0855E-2 -9.2990E-7

LiCl (54,2) .14847 ,0

.0 -1.546E-4 .0 .0 .307 .0 .0 6.36E-4 .0 .0 .0037'0 4.'15 .0 .0 -3.71E-9 .0


BO

1

B1

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

2

CO

1

2 3 4 5 6 7 B2

1

2 3 4 5 6

-'" 00 I

U9504 (79,6) -1.0282 8.4790E-3 -2.33667E-5 2.1575E-8 6.8402E-4 .21499 -----

-2.9596E-1 9.4564E-1 .0 .0 1.1028E-2

3.3646

-----

1.0541E-1 -8.9316E-4

2.51E-6

B1

CO

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 5 6 7

.7534

5.61E-3 -5.7513E-4 1.11068 -378.82 .0 1861.3 , .1745E-2

-3.3038E-4 1.85794E-5

-2.3436E-9

-3.9200E-2

-8.7899E-5 .006993

14.2130

----1.0541E-1 1.2121E-1 -2.7642E-4

.0 -24.950

K2504 (79,7) .0 7.476E-4

.0 -3.088 .0 .0 .6179 6.85E-3 5.576E-5 -5.841E-2

.0 - .90 .0 9.1547E-3

.0 .0 -1.81E-4

.0 .0 .0

.0 -32.743 5.93915E-7 -9.31654E-4

.576066 --------2.60169E-5

-1.09438E-2 2.60135

---------

HCI (53) .17690 -9.140E-2

.0 -4.034E-4

6.02E-6 .2973 16.147 -1.7631E-2

.0 7.20E-5 2.41831E-7 (2**3/2C) .362E-3 -2.49949E-4 (2**3/2C) .0 5.95320E-2 (2**3/2C) .0 -----3.036E-5 ----.0 NaCI (79,8) BO -656.81518 24.86913 5.3812753E-5 -5.5887470E-8 6.589326E-12 -4.4640952 1.1109914E-2

81 119.31966

-4.8309327E-1 .0 .0 .0 .0 1.4068095E-3

UgCl2 (79,9) 5.93915E-7 -9.316S4E-4

.576066

4.265E-3

-2.1515E-1

UgC12 (11) BO

N02504 (79,10) -1.727E-2 1.7828E-3 9.133E-6 .0 -6.552 .0 -96.90

CO -6.1084589 4.0217793E-1 2. 2902837E-5 .0 .0 -7.5354649E-2 1.5317673E-8

2.60169E-5 -1.09438E-2 2.60135

2.41831E-7 -2.49949E-4 5.95320E-2


8 9 10 11 12 13 14 15 16 17 18 19 20 21

NaCl (79,8) BO -2,6573399E-7 1.7460Q70E-10 1.0462619E-14

-5.3070129E-6 8.6340233E-10 -4.1785962E-13 -1.579366 2.2022821E-3

-1.3105503E-7 -6.3813683E-11 9.7065780 -2.6860396E-2 1.5344744E-5 -3,2153983E-9 NoOH (79,11) BO

1 2 3 4 5 6 7 8 9 10 11 12

I

00 -.J I

B1

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

-4.2345814

.0 .0 .0 .0 .0 .0 .0 B1

2.7682478E+2 -2.8131778E-3 -7.3755443E+3 3.7012540E-1 -4.9359970E+1 1.0945106E-1

-8.5960581E+1 2. 3905969E-1

7. 1788733E-6 -4.0218506E-5

-1.079584E-4

-5.8847404E-9 1.1931122E-1

2.4824963 -4.8217410E-3

NaCl (77)

BO

B1 .0 .0 .0 .0 .0 .0

1.43783204d+01

5.60767406d-03 -4.22185236d+02

-2.51226677dOO .0 -2.61718135d-06 4.43854508dOO -1.70502337dOO

-4.83060685d-01 1.40677479d-03 1.19311989d+02 .0 .0 .0 .0 -4. 23433299dOO

4.6286977E+2

.0 -1.0294181E+4

.0 .0 .0 .0 .0 .0 N02S04 (77) 8. 16920027d+01 3.011049570d-02 -2.32193726d+03 -1.43780207d+01 -6.66496111d-01

-.1.03923656d-05 .0 .0

CO -9.0550901E-8 .0 .0 -1.5386008E-8 8.6926600E-11 .0 3.5310414E-1 -4.3314252E-4

.0 .0 -9.1871455E-2

5. 1904777E-4 .0 .0

CO -1.6686897E+1 4.0534778E-4 4.5364961E+2 -5.1714017E-2 2.9680772 -6.5161667E-3 -1.05530373E-6

2.3765786E-6 8.9893405E-10

-6.8923899E-1 -8.1156286E-2

.0 eoe12 (77) -9.41895832d+01 -4.04750026d-02

2. 34550368d+03 1.70912300d+01 -9.22885841d-01 1.51488122d-05

1.00463018d+03

-1.39082000dOO .0 3.47870000dOO

5~77453682d-01

-1.54170000d-02

-2. 19434467d+04 -1.89110656d+02

-2.035505488-01 -3. 23949532d-04 1.46772243d+03

.0

.0 .0 .0 3. 17910000d-05 .0 .0

eoS04 (77) .15dOO

.0 .0 .0 .0 .0 .0 .0 3.0dOO .0 .0 .0 .0 .0 .0 .0


CO

1 2

3 4

NaCl (77) -1.005BB714d-01

Na2504 (77) -B.07S1SBB6d+01

-1.B0529413d-05 B.61185543dOO 1.24880954d-02

-3.54521126d-02 2.02438B30d+03 1.46197730d+01 -9.16974740d-02 1.43946005d-05 -2.42272049dOO

5 6 7 B

B2

.0 3.41172108d-OB

6.B3040995d-02 2.939226'1d-01

.0

CaCl2 (77) -3.03578731d+01 -1.36264728d-02 7.6458223Bd+02

5.5045B061dOO -3.27377782d-01

5. 69405B69d-06 -5.3623110Gd-01

.0

1

2 3 4

5 6 7

B

Equat10ns 1) B(O)=q1+q2(1/T-1/Tr)+q3 In(TITr)+q4(T-Tr)+q5(T •• 2-Tr**2)

I

2)

3)

00 00 I

4)

5) 6) 7)

B(1)=qG+q7(1/T-1/Tr)+q9(T-Tr)+q10(T·*2-Tr·*Z) CO=q11+q12(1/T-1/Tr)+q13 In(TITr)+q14(T-Tr)+q1S(T.*2-Tr •• 2) f(T)=p1+p2(1/T-1/Tr)+p3 In(TITr)+p4(T-Tr)+p5(T •• 2-Tr**2)+pG 1n(1-260) B(O)=U34+U6P+(U35+U7P)/T+U17 1n T+(U36+UBP)T+(U37+U9P)T •• 2+U20/(T-227)+(U38+U10P)/(647-T) B(1)=U2Z+U23/T+U24 ln T+U25T+UZ6T**2 CO=U39+U11P+(U40+U1ZP)/T+U29 In T+(U41+U13P)T+(U4Z+U14P)T**2+U32/(T-227)+U33/(647-T) B*=Q1+QZ(1/T-1/Tr)+Q3 In(TITr)+Q4(T-Tr)+Q5(T**Z-Tr.*Z) B(0)=q1+q2(1/T-1/Tr)+q3 In(T/Tr)+q4(T-Tr)+q5(T*.2-Tr**Z) B(1)=q6+q9(T-Tr)+q10(T*·2-Tr**Z) CO=q11+q12(1/T-1/Tr)+q13 In(TITr)+q14(T-Tr) MgS04 f(T)=Q1(T/2+298 •• Z/2T-298)+Q2(T**Z/6+29S**3/3T-298**212)+Q3(T**3/12+298**4/4T-298**3/3) +Q4(T**4/Z0+Z98**5/5T-298**4/4)+(Z98-298**Z/T)Q5+Q6

.2504 f(T)=Q1+QZ(Tr-Tr.*Z/T)+Q3(T**Z+ZTr**3/T-3Tr.*Z)+Q4(T+Tr**2/T-2Tr)+QS[ln(T/Tr)+Tr/T-1]

+Q6(1/(T-263)+(263T-Tr**2)/[T(Tr-263)*2jj+Q7(1/(6BO-T)+(Tr**2-6BOT)/[T(6BO-Tr)**2Jj B) NaCl f(T)=Q1/T+QZ+Q3P+Q4p.*Z+QSP**3+Q6In(T)+(Q7+Q8P+Q9P*.2+Q10P.*3)T+(Q11+Q1ZP+Q13P**Z)T.*2 +(Q14+Q15P+Q16P**Z+Q17P •• 3)/(T-227)+(Q18+Q19P+QZOP.*2+Q21P*.3)/(630-T)

9) MgC12 f(T)=Q1T·*Z+QZT+Q3

10) NaZS04 f(T)=Q1+Q2(Tr-Tr.*ZIT)+Q3(T*.Z+ZTr**3/T-3Tr**2)+Q4(T+Tr*.Z/T-ZTr)+QS(ln(T/Tr)+Tr/T-1] +Q6{1/(T-263)+(Z63T-Tr •• Z)/[T(Tr-263).*Z]}+Q7{1/(680-T )+(Tr*.Z-680T)/[T(680-Tr)*.Z]} 11) NaOH

f(T)=Q1+Q2P+(Q3+Q4P)/T+Q51n(T)+(Q6+Q7P)T+(QB+Q9P)T**2+ Q10/(T-227)+(Q11+Q12P)/(647-T) • numbers in parentheses following designation of a salt correspond to reference number (Attachment C.1) and equation number given below.

Ca504 (77) .0 .0 .0 .0 .0 .0 .0 .0

Attachment C.6. -- Sources of data in the file PITZER.DATA

-189-

Attachment C.6 - Sources of data in file PITZER.DATA SPECIES 1

4

21 5

6

7

B

9

11 12 14 15 16 21 22 31 34 35 40 76 B5 B6

BO NA+ K+

IdG+2 CA+2 IdGOH+ H+ 1I+

SR+2 FE+2 IdN+2 BA+2 NA+ K+ H+

IdG+2 CA+2 1I+ SR+ BA+ NA+ K+

,

-

t.lG+2 CA+2

'", 0

H+ Ll>

SR+2 FE+2 MN+2 NA+ K+

MG+2 CA+2 H+

FE+2 NA+ K+

CA+2 1I+

BA+2 NA+ K+

MG+2 CA+2 SR+2 NA+ K+

SR+2

CLCLCLCLCLCLCLCLCLCLCLBRBRBRBRBRBRBRBR-

S04-2 S04-2 S04-2 S04-2 S04-2 S04-2 504-2 S04-2 504-2 H504HS04HS04HS04HS04HS04OHOHOHOHOH-

HCQ3HC03HC03HC03HC03C03-2 C03-2 C03-2

0.0765 (4B) 0.04B35 (4B) 0.35235 (4B) 0.3159 (4B) -0.1 (4B) 0.1775 (4B)

0.1494 (89) 0.2B575 (B9) 0.335925 (B9) 0.327225 (B9) 0.262B (B9) 0.0973 (B9) 0.0569 (B9) 0.1960 (B9) 0.4326B (B9) 0.3B16 (B9) 0.174B (B9) 0.331125 (B9) 0.31455 (B9) 0.0195B (4B) 0.04995 (4B) 0.221 (4B) 0.2 (4B)

-777.03 (120)

-4.4706 (120)

0.00B946 (120) -3.315BE-6 (120) 5.794E-4 (121)

-1.943E-4 (121) -1.725E-4 (121) -3.0B1E-4 (121)

-1.6BSE-4 (121) 0.717E-3 (121)

0.6405E-3 (121)

7.692E-4 (121) 7.39E-4 (121)

-2.049E-4 (121) -S.62SE-S (121) -S.227SE-4 (121) -1.819E-4 (121) -O.32775E-3 (121) -0.33825E-3 (121) 2.367E-3 (121) 1.44E-3 (121) -0.69E-3 (121)

0.0298 (48) 0.136275 (B9)

0.220 (102)

0.5055E-3 (121)

-2.9E-3 (102)

0.256B (103)

0.2065 (40) 0.04S4 (48) -0.0003 (4B) 0.4746 (4B)

0.2145 (48) 0.2065 (4B)

0.4273 (103) 0.OB64 (4B) 0.129B (4B) -0.1747 (4B) 0.015 (B9) 0.17175 (B9) 0.0277 (4B)

7.00E-4 (121)

0.0296 (48)

1.00E-3 (B1) 0.996E-3 (B1)

0.329 (4B) 0.4 (4B) 0.12 (75) 0.0399 (4B)

1.79E-3 (B1)

0.1488 (48)

1.78BE-3 (81)

-11.9 (75)

B1 NA+ K+

MG+2

CLCLCL-

0.2664 (49)

0.2122 (48) 1.6B15 (4B)

6.160BE-5 (120) 1.0715E-6 (120)

10.71E-4 (121) 3.6525E-3 (B6)

Attachment C.6 - continued CA+2 MGOH+

H+ LI+ SR+2 FE+2 MN+2 BA+2

HA+ K+ H+ t.lG+2 CA+2

LI+ SR+2 BA+2

NA+ K+ MG+2 CA+2

LI+ SR+2 FE+2 MN+2

--

NA+ K+

I

'D

MG+2 CA+2

I

H+ fE+2

NA+ K+ CA+2

LI+ BA+2

NA+ K+ M6+2 CA+2

NA+ K+

CLCLCLCLCLCLCLCLBRBRBRBRBRBRBRBRS04-2 504-2 504-2 504-2 504-2 504-2 504-2 504-2 HS04HS04HS04H504H504H504-

OHOHOHOHOHHC03HC03HC03HC03C03-2

1.614 (4B) 1.65B (4B) 0.2945 (4B) 0.3074 (B9)

5.366E-4 (121)

1.66725 (B9)

2.8425E-3 (121)

3.9E-3 (121) 1.419E-4 (121)

1.53225 (B9) 1.55025 (89)

1.49625 (B9) 0.2791 (B9) 0.2212 (B9) 0.3564 (B9) 1.75275 (B9) 1.613 (B9)

3.2325E-3 (121) 10.79E-4 (121) 17 .40E-4 (121) 4.467E-4 (121) 3.8625E-3 (121) 6.0375E-3 (121) 6.636E-4 (121) 6.5325E-3 (121) 6.78E-3 (121) 5.6325E-3 (121) 6.6975E-3 (121) 1.53E-2 (121) 5.46E-2 (121) 1.41E-3 (121) 27.0 (102)

0.2547 (B9) 1.7115 (89)

1.56975 (B9) 1.113 (48) 0.77925 (48)

3.343 (4B) 3.1973 (48) 1,2705 (89) 2.88 (102)

3.063 (103) 2.951' (40)

0.39B (4B) 0.1735 (48)

1.729 (4B) 2.53 (4B) 0.5556 (4B) 3.4B (103) 0.253 (4B) 0.32 (4B) -0.2303 (4B) 0.14 (B9) 1.2 (B9) 0.0411 (4B) -0.013 (4B) 0.6072 (4B)

1,34E-4 (121)

1.10E-3 (Bl) 1.104E-3 (81)

2.977 (48) 1.389 (48)

2,05E-3 (81)

C03-2

1.43 (4B)

2.051E-3 (B1)

504-2 504-2 504-2 504-2 504-2

-37.23 (4B)

-0.253 (121)

-54.24 (48)

-0.516 (121) -0.42 (102)

B2 MG+2 CA+2 SR+2 FE+2 MN+2 CA+2

-41.B (4B) -42.0 (103) -40.0 (40)

OH-

-5.72 (4B)

CLCLCLCLCLCL-

0.00127 (4B) -0.000B4 (4B) 0.00519 (4B) -0.00034 (4B) O.OOOB (4B) 0.00359 (B9)

CO NA+ K+ 1.16+2 CA+2

H+ LI+

33,317 (120)

0.09421 (120)

-4.655E-5 (120) -5,095E-5 (121)

-1.6493266 (121) 6.213E-5 (121) -4.520E-5 (121)

Attachment C.6 - continued SR+2 FE+2 MN+2 BA+2

NA+ K+ H+ MG+2 CA+2

L1+ SR+2 BA+2

NA+ MG+2

H+ L1+ 5R+2 FE+2 I.4N+2

-,,

'0

tv

NA+ K+ K+ NA+ K+

CLCLCLCLBRBRBRBRBRBRBRBR504-2 S04-2 504-2 504-2 504-2 504-2 504-2

OHOHHC03C03-2 C03-2

-0.00130461 (89) -0.00860725 (89) -0.0204972 (89) -0.0193782 (89) 0.00116 (B9) -0.00180 (89) 0.00827 (89) 0.00312 (89) -0.00257 (89) 0.0053 (89) 0.00122506 (89) -0.0159578 (89) 0.00497 (48) 0.025 (48) 0.0438 (48) 0.00399338 (89) 0.019 (102) 0.0209 (103) 0.01636 (40) 0.0044 (48) 0.0041 (48) -0.008 (48) 0.0044 (48) -0.0015 (48)

THETA

K+ MG+2 CA+2

H+ CA+2

H+ CA+2

H+ H+ 504-2 H504-

OHHC03C03-2

OHOHHC03C03-2 C03-2 C03-2 LAMDA

NA+ K+ I.4G+2 CA+2

CL504-2 HS04PSI

NA+

NA+ NA+ NA+ NA+ K+ K+

HCQ3-

-0.012 (48) 0.07 (48) 0.07 (48) 0.036 (48) 0.032 (48) 0.005 (48) 0.007 (48) 0.1 (48) 0.092 (48) 0.02 (48) -0.006 (48) -0.05 (48) 0.03 (4B) -0.02 (4B) -0.065 (B8) -0.013 (48) 0.01 (48) 0.02 (48) 0.1 (48) -0.04 (48)

H2CQ3 H2C03 H2C03 H2C03 H2C03 H2C03 H2C03

0.1 (48) 0.051 (48) 0.183 (48) 0.183 (48) -0.005 (48) 0.097 (48) -0.003·(48)

MG+2 I.4G+2 CA+2

CLCLCLCLCLBR504-2 504-2 504-2

OH-

K+

CL-

-0.001B (48)

-1.5379573 (121) -9.30E-5 (121) -7.004E-5 (121) -5.685E-5 (121) -2.813E-5 (121) -4.879037E-4 (121) 0.523E-3 (121) -2.3334525 (121) 3.0E-3 (102) -18.94E-S (121)


'" I

W I

HA+ HA+ HA+ HA+ HA+ HA+ HA+ HA+ HA+ HA+ HA+ K+ K+ K+ K+ K+ K+ K+

K+ K+ K+ K+

CA+2 CA+2 CA+2 MG+2 MG+2 MG+2

MG+2 MG+2

CLCLCLCLCLCLCLCL CLCLCLCLCL504-2 504-2 504-2 504-2 504-2 504-2 504-2 504-2 504-2

oHoHoHoHHC03HC03-

BR-

CA+2 CA+2 MG+2 MG+2

CL504-2 CL-

H+ H+ H+

CLBR-

CA+2 MG+2 MG+2

CLCL-

H+ H+ H+ H+

CLBR-

-0.0022 (BB) -0.010 (4B) -0.003 (4B) 0.003 (4B) -0.007 (48) -0.055 (48) -0.012 (4B) -0.015 (48) -0.004 (48) -0.012 (8B) -0.0129 (48) -0.025 (48) -0.022 (48) -0.048 (4B) -0. 011 (4B) -0. 021 (BB)

504-2 H504-

-0.0265 (4B)

CL-

-0.012 (48)

H+ MGOH+

H+ H+ BR504-2 504-2 504-2 HS04H504-

oHoHoHHC03HC03C03-2 C03-2 H504H504H504-

oHoHHC03HC03-

C03-2 C03-2 C03-2 C03-2 BRBRC03-2 C03-2

504-2

HC03C03-2

504-2 H504504-2

504-2

0.197 (48)

0.024 (4B)

CLCLCL-

0.028 (4B) -0.011 (4B)

H5Q4-

-0.0178 (48)

K+ HA+ CA+2 MG+2

HA+ H+ HA+ K+ CA+2

HA+ MG+2

HA+ K+ HA+ K+

-0.015 (48)

0.0000 (BB) 0.0014 (48) -0.018 (48)

-0.004 (4B) -0.006 (48) 0.013 (48)

-0.006 (4B) -0.006 (4B) -0.025 (4B) -0.015 (4B) -0.096 (4B) 0.00B5 (4B) 0.004 (4B) -0.0094 (48)

-0.0677 (4B)

MG+2

-0.0425 (48)

NA+ K+ HA+

-0.009 (4B) -0.050 (4B) -0.005 (4B)

MG+2

HA+ K+ HA+ K+ HA+ K+ HA+ K+

-0.161 (48)

-0.005 (4B) -0.009 (48) -0.017 (48) -0.01 (48) -0.018 (8B) -0.014 (8B) 0.002 (4B) 0.012 (4B)

NotePages 195-302 contain a listing of the PHRQPITZ source code that have been omitted in this copy. The source code can be obtained from http://water.usgs.gov or by anonymous ftp to brrcrftp.cr.usgs.gov (136.177.112.5) where the programs reside in the directory geochem/pc (for PC versions), or geochem/unix (for unix versions).

Attachment F. -- Listing of the file MINERALS.2.DATA read by the interactive input program PITZINPT

-303-

ANHYDRIT 4 422.950 ARAGONIT 15 1.0 -171. 8607 ARCANITE 7 2.823 BISCHOFI 5 3.524 BLOEDITE 6 BRUCITE 5 BURKEITE 6 CALCITE 15 1.0 -171. 8329 CARNALLI 7 DOLOMITE 4 1.0 EPSOMITE 5 1. 718 GAYLUSSI 4 GLASERIT 6 GLAUBER I 6 GYPSUM 4 1.0 90.318 HALITE 6 -713.4616 HEXAHYDR 5 -62.666 KAINITE 7 KALICINI 7 KIESERIT 5 LABILE S 6 LEONHARD 5 LEONITE

-4.362 1.000 -147.708 -18431. -8.220 4.00 4 1.0 2903.293 71.595 - .077993 6.00 2 -1.776 1.000 2.000 16 -1371.2 0.0 0.00 4.455 3 6.000 2.000 1.000 14 3 277 .6 0.0 12.00 -2.347 4 2.000 16 1.000 2.000 5 0.00 -10.884.85 2 2.000 1.000 31 -.772 16.00 3 2.000 1.000 16 6.000 15 4.00 -8.406 2 4 1.0 71.595 2839.319 - .077993 0.00 4.330 4 3.000 1.000 14 1.000 5 8.00 -17.083 -9.436 3 15 2.0 5 1.0 6.00 -1.881 3 7.000 1.000 1.000 16 3 0.0 -1073 . 8.00 -9.421 4 2.000 2.000 15 6 1.000 24.00 -3.803 3 2.000 3.000 16 1.000 7 12.00 -5.245 3 2.000 1.000 16 2.000 4 6.00 -4.581 3 3 2.0 16 1.0 -32.641 -4213. 0.0 1.570 0.00 2 1.000 1.000 14 262.4583 -.1201241 37302.21 6.00 -1. 635 3 6.000 1.000 3 1.000 16 22.187 1828. 0.0 6.00 -0.193 5 1.000 1.000 14 1.000 5 4.00 -10.058 3 1.000 1 1.000 15 1.000 6.00 -0.123 3 1.000 1.000 1.000 16 3 18.00 -5.672 4 3.000 1.000 16 4 4.000 6.00 -0.887 3 4.000 1.000 1.000 16 3 12.00 4 -3.979 2 1.000 0.0 2

6.00

16

-304-

1

0 4.000

3 0 0

0 6.000

3 0

0 5.000

3 0 0

-2106915. 1 0 16

1.000 0 0 0

3

2.000 0 0

3

3.000

7 MAGNESIT 5 MIRABILI 6 -3862.234 MISENITE 7 NAHCOLIT 6 NATRON 6 NESQUEHO 5 PC02 35 1.0 108.3865 PENTAHYD 5 PIRSSONI 6 POLYHALI 7 PORTLAND 4 SCHOENIT 7 SYLVITE 7 3.984 SYNGENIT 7 TRONA 6

2.000 1.000 16 2.000 5 -6.169 4.00 -7.834 2 1.000 1.000 15 6.00-1.214 3 10.000 1.000 3 2.000 16 1577.756 93713.54 -1.19856 42.00 -10.806 3 7.000 6.000 16 8.000 4.00 -10.742 3 1.000 1.000 15 1.000 4.00 -0.825 3 10.000 1.000 3 2.000 15 4.00 -5.167 3 3.000 1.000 3 1.000 15 -1.468 -4.776 4.0 1 -40.45154 0.01985076 -6919.53 6.00 -1.285 3 5.000 1.000 3 1.000 16 8.00 -9.234 4 2.000 1.000 15 4 2.000 24.00 -13.744 5 2.000 1.000 4 2.000 5 0.00 -5.190 2 2.000 1.000 31 12.00 -4.328 4 2.000 1.000 16 2.000 5 0.00 .900 2 1.000 1.000 14 0.0 -919.55 12.00 -7.448 4 2.000 4 1.000 16 2.000 8.00 -11.384 4 2.000 1.000 15 3.000

-305-

3

4.000 0

0 0 0 0

669365.0 0 0 3

2.000 0 4.000

16 0 0

6.000

3

0 3 3

1.000 0 2.000

3

2.000

Attachment G. -- Example of use of the interactive input program PITZINPT to construct the input file for

test problem 3

-306-

ENTER OUTPUT FILE NAME TEST. 3 ENTER REFERENCE FILE NAME:

(HIT TO OMJT)

I NPUT THE TITLE Test Problem 3: Find the anhydr' i te-gypsum phase boundary \oIi th NaCI addition. Test Problem 3: Find the anhydrite-gypsum phase boundary \oIith NaCI addition. O.K.? Y INPUT IOPT( 1) 0

INPUT IOPT(2) 0

INPUT IOPT(3) 6

INPUT

IOPT(~)

0

INPUT IOPT(7) 0

INPUT IOPT(B) 0

INPUT IOPT(9) 0

INPUT IOPT( 10) 0

INPUT NCOMPS 2

0060020000 0 2

0.0

O.K.? Y

*******************

KEYWORD DATA BLOCKS *******************

ENTER KEYWORD. SOLUTION 1

-307-

SOLUTION

INPUT HEAD

* Pure water O.K.? Y

000 O.K.?

7.0

4.0

25.0

1.0

Y

*******************

KEYWORD DATA BLOCKS *******************

ENTER KEYWORD. MINERALS

MINERALS

PRE-CONSTRUCTED MINERAL DATA ARE AVAILABLE. DO YOU WISH TO HAVE ANY OF THEM? Y

1 6 11 16 21 26 31 36

ANHYDRIT BRUCITE EPSOMITE HALITE LABILE S MISENITE PENTAHYD SYLVITE

2 7 12 17 22 27 32 37

ARAGONIT BURKEITE GAYLUSSI HEXAHYDR LEONHARD NAHCOLIT PIRSSONI SYNGENIT

3 8 13 18 23 28 33 38

ARCANITE CALCITE GLASERIT KAINITE LEONITE NATRON POLYHALI TRONA

4 9 14 19 24 29 34

BISCHon CARNALLI GLAUBERI KALICINI MAGNESIT NESQUEHO PORTLAND

ENTER THE INDEX NUMBER OF MINERAL. (TYPE TO EXIT) 1

ANHYDRIT 4

422.950 O.K.?

6.00

2

1.000 0.0

16

-4.362 1.000 -18431. -147.708

Y

ENTER THE INDEX NUMBER OF MINERAL. (TYPE TO EXIT) -308-

5 10 15 20 25 30 35

BLOEDITE DOLOMITE GYPSUM KIESERIT MIRABILI PC02 SCHOENIT

15

GYPSUM

3

4 1.0

90.318 O.K.?

0.0

6.00 -4.581 161.0 32.0 -4213. -32.641

Y

ENTER THE INDEX NUMBER OF MINERAL. (TYPE TO EXIT) STOP MORE MINERALS TO BE TYPED IN FROM THE TERMINAL? N

*******************

KEYWORD DATA BLOCKS ***1****1**11******

ENTER KEYWORD. REACTION

REACTION

INPUT LREAC( 1) 6 INPUT CREAC ( 1) 1.

INPUT THMEAN(

o.

1)

INPUT LREAC(2) 14 INPUT CREAC(2) 1.

INPUT THMEAN(2)

o.

61.

o.

141.

o.

O.K. ? Y

*****1*************

KEYWORD DATA

BLO~KS

*******************

-309-

ENTER KEYWORD. END

END

MORE SIMULATIONS? N

nn STOP

-310-

~U.S.GOV£RNmENT

PRINTING

or,IC(t19~8-242-339:aaa47

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