modified co2 database carey 2006

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CO2 in PHREEQC and Geochemists Workbench July 13, 2006

Modifying the PHREEQC and Geochemists Workbench

Databases for a more accurate CO2 Solubility

Bill Carey

Background

Geochemical codes generally represent the solubility of CO2 in terms of the Henrys LawRelationship:

CO2(gas) CO2(aq) (1)

The equilibrium constant for this reaction (Ksp(1)) is :

Ksp(1) =aCO2(aq)

fCO2(g)= Kh(Henrys Law constant)

In Geochemists Workbench (GWB), the fundamental carbon species is HCO3 . To derivethe appropriate database reaction equation we take

CO2(aq) + H2O H+ + HCO3 (2)

for which the equilibrium constant is

Ksp(2) = aH+aHCO3

aCO2(aq)aH2O

and add Ksp(1) and Ksp(2) together to get

CO2(gas) + H2O H+ + HCO3 (3)

Ksp(3) =aH+aHCO

3

fCO2(gas)aH2O= Ksp(K1) Ksp(2) = Kh Ksp(2)

Implementation in GWB

If you look in the GWB database, youll see an entry like the following:

CO2(g)

mole wt.= 44.0098 g

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3 species in reaction

-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

-7.6765 -7.8136 -8.0527 -8.3574

-8.7692 -9.2165 -9.7202 -10.3393

* gflag = 1 [reported delG0f used]* extrapolation algorithm: supcrt92 [92joh/oel]

* reference-state data source = 82wag/eva

* delG0f = -94.254 kcal/mol

* delH0f = -94.051 kcal/mol

* S0PrTr = 51.085 cal/(mol*K)

The lines containing

-7.6765 -7.8136 -8.0527 -8.3574

-8.7692 -9.2165 -9.7202 -10.3393

are log Ksp(3) values given at

0, 25, 60, 100150, 200, 250, and 300 C

The problem with how GWB and PHREEQC handle CO2 is that Kh should be a functionof pressure (and therefore a function of fugacity). There is no simple way to correct thisproblem that we have found, but one approximation is to create new species of CO 2 thatare valid at a constant pressure. For example, we can copy into the GWB database a newspecies valid at a constant pressure of CO2 = 5 bar:

CO2p5(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8444 -8.0809 -8.3915

-8.8007 -9.2397 -9.7355 -10.3175

* Species valid at a constant pressure of 5 bars and from 15 to 300 C

* Henrys law and Poynting Correction combined with

* Duan and Sun (1993)s Fugacity-Pressure relations

* See Carey (2006) manuscript for further details

This species is simply copied into the database in the gas section (e.g., place this rightbelow the entry for CO2(g) in thermo.com.dat). It is also necessary to modify the linegiving the total number of gas species at the start of the section on gases.

To perform a calculation at a pressure of CO2 equal to 5 bars use the commands:

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swap HCO3- for CO2p50(g)fugacity of CO2p5(g) = 5

Note that you must still call this value a fugacity. In reaction calculations, it is notnecessary to suppress the other CO2 species. In activity diagrams, you may want tosuppress the other species:

suppress CO2(g) and other CO2p species

to prevent the most stable species from controlling the activity diagram.

Implementation in PHREEQC

In the PHREEQC llnl.dat database, the CO2 species appears as

CO2(g)

CO2 +1.0000 H2O = + 1.0000 H+ + 1.0000 HCO3-

log k -7.8136

-delta H -10.5855 kJ/mol # Calculated enthalpy of reaction CO2(g)

# Enthalpy of formation: -94.051 kcal/mol

-analytic -8.5938e+001 -3.0431e-002 2.0702e+003 3.2427e+001 3.2328e+001

# -Range: 0-300

Rather than an explicit tabulation of log Ksp values at specific temperatures, PHREEQCmakes direct use of an equation for log10 K:

log K = A1 + A2T +A3T

+ A4 log T +A5T2

(T in Kelvin) (4)

The five coefficients are given on the line following -analytic.

We can use the same approach as outlined for GWB and insert a new species into thedatabase. For example, a species valid at a constant pressure of 50 bars and from 15 to300 C:

CO2p50(g)

CO2 +1.0000 H2O = + 1.0000 H+ + 1.0000 HCO3-

log k -7.9971# Enthalpy of formation: -94.051 kcal/mol

-analytic -40.92349784 -0.021320754 483.8310143 15.2200071 0.0

# Species valid at a constant pressure of 100 bars and from 15 to 300 C

# Henrys law and Poynting Correction combined with

# Duan and Sun (1993)s Fugacity-Pressure relations

# See Carey (2006) manuscript for further details

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PHREEQC also has the flexibility to introduce this species only in the input file (withoutmodifying the database) as follows:

PHASES

CO2p100(g)

CO2 + H2O = H+ + HCO3-

log k -7.8425

-analytical expression 0.294236304 -0.014832354 -1220.102351 0.0 0.0

An example input file in PHREEQC would invoke a new CO2 species as follows:

PHASES

CO2p200(g)

CO2 + H2O = H+ + HCO3-

-log k -8.483251771

-analytical expression 0.842135999 -0.015193434 -1428.818729 0 0

# Species valid at a constant pressure of 200 bars and from 15 to 300 C# Henrys law and Poynting Correction combined with

# Duan and Sun (1993)s Fugacity-Pressure relations


TITLE Solubility of CO2 at 200 bar

SOLUTION 1

temp 25

pH 7 charge

EQUILIBRIUM PHASES

CO2p200(g) 2.30103 100

REACTION TEMPERATURE

25 300 in 56 steps

END

This would generate the solubility of CO2 at 200 bars pressure (log10(200) = 2.30103).

Methodology

This provides some information on the methodology used to generate the new CO2 speciesand provides some validation and discussion of the approach.

The solubility of CO2 was calculated using a Henrys Law method based on the Lichtneret al. (2003) modified approach of Crovetto (1991) with the addition of a Poyntingcorrection for pressure. The modified Henrys Law equation is:

XaqCO2 =

fgasCO2

Kh expPPo

Vaq

CO2RT

(5)

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The solubility of CO2 was calculated using Eq. 5, with a temperature-dependent HenrysLaw:

Kh =

272998.463142

T2 +

568.443483

T

0.00625205T+ 1.099025 log10(T) (6)

and a constant partial molar volume of CO2:

VaqCO2 = 30 cm

3/mol (7)

and the pressure-temperature-fugacity equation of state of Duan et al. (1992). Theserelations are embodied in a FORTRAN computer code, co2sol.f (Lichtner et al., 2003).

At each temperature, the molar volume of CO2 was assumed to be independent of pressure,simplifying the integral:

PPo

VaqCO2

RT=

VaqCO2(P Po)

RT(8)

The reference pressure Po is the saturation pressure for water at the given temperature.

The Poynting correction (the integral in Eq. 5) introduces pressure so that a relationshipbetween fugacity and pressure is required to calculate the solubility. This relationshipwas obtained from Duan et al. (1992). It could also be obtained from standard referencecompilations of CO2 properties.

The implementation procedure was as follows: At each temperature of interest (25, 60,100, 150, 200, 250, and 300 C), a set of pressure values were chosen. Duan et al. (1992)was used to calculate the corresponding fugacity. With temperature, pressure, and fugac-ity, Equation 5 together with Equations 6 and 7 were used to calculate the mol-fractionCO2. The mol-fraction was then converted to molality of CO2. An effective K

hwas cal-

culated using the molality of CO2 (with an activity coefficient of 1) and the fugacity atthe conditions of interest (based on Eq. 1). Then for each of the five temperatures, thevalue of Ksp(3) was calculated using K

hand the database value for Ksp(2). The values of

Ksp(3) were used as the log K entries for the new species of CO2 labeled by the appropriatepressure (cf. the example for CO2p50(g) above).

A comparison between experimental data and the calculated relations for constant pressureis given in Figure 1. The calculated solubility is reasonably accurate over these conditions.Differences are inevitable because we have not simultaneously optimized a fugacity equationof state and a Henrys Law formulation.

A comparison of the calculated solubility at constant temperature using the new CO 2species with the original CO2 species of Geochemists Workbench is shown in Figure 2. Thedifference in solubility is greatest at lowest temperature and at higher fugacities. GWB is

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Figure 1: Comparison of calculated (using Eq. 5) and measured solubility of CO2. Exper-imental data from various sources in the literature.

reasonably accurate for fugacities < 30 bars (this corresponds to about all temperaturesand pressure < 50 bar). The solubility errors are significant, for example, at 100 C and150 bars. [There is no simple way to make a comparison of the new CO2 species and theoriginal CO2 species as a function of temperature and pressure because the original speciesis defined in terms of fugacity. To aid the interpretation of Figure 2, pressure-fugacitycurves are superimposed. Thus for a temperature of 100 C at a fugacity of 100 bars, thepressure is approximately 250 bars with a difference in predicted solubility of about 0.007(33% error)].

A further comparison of the GWB standard database CO2 species [CO2(g)] with solubility

data is given in Figure 3. This shows more clearly the conditions where the original CO 2species over-predict the solubility of CO2.

A comparison of the modified species with experimental data at constant pressure is shownin Figure 4. The calculations reveal a slightly lower predicted solubility than is observed.Figure 4 demonstrates that GWB and PHREEQC using the same modified CO2 speciesproduce the same solubility in pure water. However, GWB and PHREEQC use a differentactivity coefficient model (GWB always uses an activity coefficient of 1.0 for all non-charged

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Figure 2: Comparison of calculated CO2 solubility (using Eq. 5) and solubility calculatedby Geochemists Workbench at constant temperature as a function of fugacity. The right-axis provides a means of translating fugacities into pressures.

species such as CO2(aq)). Consequently, GWB predicts no change in solubility in a 1 mNaCl solution (contrary to the well known fact that CO2 solubility decreases with theionic strength of a solution). PHREEQC does reproduce this lowered solubility by virtueof having an activity coefficient different than 1.0 for CO2(aq).

The modified CO2 species are also compared in Figure 4 to the study of Duan and Sun(2003) which is a more sophisticated model of CO2 solubility that includes the effect ofionic strength on solubility. The Duan and Sun model fits the observations more closely butis not reliable at temperatures above 225 C. The Duan and Sun 1 molal NaCl lowering

of solubility is similar to that predicted by PHREEQC (but I have not looked at thissystematically and may have fortuitously chosen a pressure at which PHREEQC doeswell).

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Figure 3: The same curves as shown in Figure 2 but with experimental solubility datasuperimposed.

Discussion

This method provides a more accurate representation of CO2 solubility at higher pressuresand lower temperatures. However, its other convenient feature is that it provides a meansof using CO2 pressure rather than fugacity when modeling geochemical systems. Thiseliminates the need to have a table (or program) of fugacity-pressure-temperature forinterpretation of CO2 fugacities. This also allows isobaric, polythermal calculations whichare impossible in a system based on a fugacity specification.

Note on interpretation

In situations where the CO2 pressure is not specified, but rather one wants to discover theCO2 pressure at which some reaction occurs there is some ambiguity in how to interpretthe program output. As an example, the following is an excerpt from the results of a

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Figure 4: Comparison of experimental solubility data for CO2 with the solubility calculatedusing the modified CO2 species approach in Geochemists Workbench and PHREEQC. Theeffect of 1 molal NaCl on the model predictions is also shown. Graphical representation of

the tabular results of Duan and Sun (2003) are shown for comparison.

calculation in PHREEQC on the CO2 pressure associated with a brine in equilibrium withcalcite. The second column of numbers is the log of the pressure. One can see that noneof the constant pressure species has a pressure value that is equal to its database value.Examination of the results shows that the species CO2p1 through CO2p10 have databasepressures less than that given in the second column. Species CO2p25 through CO2p1000have database pressures greater than that given in the second column. Clearly, the truepressure of the system lies between 10 and 25 bars. Additional species could be addedto make this a more precise calculation. However, in many instances an approximate

answer can be had by using the species closest in value to that in the second column (hereCO2p10(g)) and using that pressure (here 12.0 bars).

CO2(g) 1.04 -6.98 -8.02 CO2

CO2p1(g) 1.03 -6.98 -8.01 CO2

CO2p5(g) 1.03 -6.98 -8.02 CO2

CO2p10(g) 1.05 -6.98 -8.03 CO2

CO2p25(g) 1.08 -6.98 -8.06 CO2

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CO2p50(g) 1.13 -6.98 -8.12 CO2

CO2p75(g) 1.20 -6.98 -8.18 CO2

CO2p100(g) 1.26 -6.98 -8.25 CO2

CO2p125(g) 1.33 -6.98 -8.31 CO2

CO2p150(g) 1.40 -6.98 -8.38 CO2CO2p200(g) 1.50 -6.98 -8.48 CO2

CO2p500(g) 1.83 -6.98 -8.81 CO2

CO2p1000(g) 2.07 -6.98 -9.05 CO2

Attachments

I have included a listing of modified CO2 species in two attachments:

co2.gwb: is appropriate for insertion into the GWB database (e.g., directly below the entryfor CO2(g). It includes 22 new species and the number of gas species should be increasedby 22 in the database.

co2.phreeqc: is appropriate for including in an input file for a PHREEQC calculation. Seethe example in the text.

References

Crovetto, R. (1991) Evaluation of solubility data of the system CO 2-H2O from 273K to the

critical point of water. Journal of Physical and Chemical Reference Data 20: 575589.

Duan, Z. and Sun, R. (2003) An improved model calculating CO 2 solubility in pure waterand aqueous NaCl solutions from 273 to 533 k and from 0 to 2000 bar. Chemical Geology193: 257271.

Duan, Z. H., Mller, N., and Weare, J. H. (1992) An equation of state for the CH 4-CO2-H2O system .1. Pure systems from 0

oC to 1000 oC and 0 to 8000 bar. Geochimica etCosmochimica Acta 56: 26052617.

Lichtner, P. C., Carey, J. W., OConnor, W. K., Dahlin, D. C., and Guthrie, G. D., Jr.(2003) Geochemical mechanisms and models of olivine carbonation. In Proceedings ofthe 28th International Technical Conference on Coal Utilization & Fuel Systems, March9-13, 2003.

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Geochemists Workbench Database Entries

CO2p1(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8342 -8.0733 -8.3860

-8.7969 -9.2372 -9.7337 -10.3164


* Henry's law and Poynting Correction combined with

* Duan and Sun (1993)'s Fugacity-Pressure relations


CO2p2.5(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8380 -8.0762 -8.3880

-8.7983 -9.2381 -9.7344 -10.3168

* Species valid at a constant pressure of 2.5 bars and from 15 to 300 C


* Duan and Sun (1993)'s Fugacity-Pressure relations* See Carey (2006) manuscript for further details

CO2p5(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8444 -8.0809 -8.3915

-8.8007 -9.2397 -9.7355 -10.3175





CO2p7.5(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8508 -8.0857 -8.3949

-8.8030 -9.2413 -9.7366 -10.3182

* Species valid at a constant pressure of 7.5 bars and from 15 to 300 C




CO2p10(g)

mole wt.= 44.0098 g

3 species in reaction-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8573 -8.0905 -8.3983

-8.8053 -9.2430 -9.7377 -10.3189





CO2p15(g)


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mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8706 -8.1001 -8.4052

-8.8100 -9.2462 -9.7399 -10.3203





CO2p20(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.8842 -8.1099 -8.4121

-8.8147 -9.2494 -9.7421 -10.3217





CO2p30(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.9122 -8.1298 -8.4261

-8.8240 -9.2559 -9.7465 -10.3244





CO2p40(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.9417 -8.1500 -8.4401

-8.8334 -9.2623 -9.7509 -10.3272





CO2p50(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -7.9729 -8.1708 -8.4543-8.8428 -9.2687 -9.7552 -10.3299





CO2p75(g)

mole wt.= 44.0098 g



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-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.0815 -8.2249 -8.4902

-8.8662 -9.2847 -9.7661 -10.3368





CO2p100(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.1950 -8.2828 -8.5267

-8.8896 -9.3005 -9.7769 -10.3435





CO2p125(g)

mole wt.= 44.0098 g3 species in reaction

-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.2817 -8.3445 -8.5634

-8.9128 -9.3162 -9.7875 -10.3502





CO2p150(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.3514 -8.4038 -8.5999

-8.9357 -9.3316 -9.7979 -10.3568





CO2p175(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.4095 -8.4556 -8.6353

-8.9581 -9.3466 -9.8081 -10.3632

* Species valid at a constant pressure of 175 bars and from 15 to 300 C* Henry's law and Poynting Correction combined with



CO2p200(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.4591 -8.5006 -8.6690


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-8.9798 -9.3613 -9.8181 -10.3695





CO2p250(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.5403 -8.5750 -8.7291

-9.0208 -9.3894 -9.8374 -10.3818





CO2p300(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-500.0000 -8.6049 -8.6346 -8.7798

-9.0578 -9.4156 -9.8556 -10.3933





CO2p400(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.7034 -8.7257 -8.8593

-9.1199 -9.4614 -9.8882 -10.4142





CO2p500(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.7765 -8.7933 -8.9192

-9.1687 -9.4992 -9.9158 -10.4321



* Duan and Sun (1993)'s Fugacity-Pressure relations* See Carey (2006) manuscript for further details

CO2p750(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.9012 -8.9081 -9.0214

-9.2540 -9.5673 -9.9668 -10.4645



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CO2p1000(g)

mole wt.= 44.0098 g


-1.0000 H2O 1.0000 H+ 1.0000 HCO3-

500.0000 -8.9827 -8.9826 -9.0876

-9.3095 -9.6119 -9.9999 -10.4833






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Phreeqc Database Listing

CO2p1(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.858354842

-analytical_expression -52.92050292 -0.023213277 1016.570949 19.63057287 0


# Henry's law and Poynting Correction combined with

# Duan and Sun (1993)'s Fugacity-Pressure relations


CO2p2.5(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.862159991


# Species valid at a constant pressure of 2.5 bars and from 15 to 300 C




CO2p5(g)CO2 + H2O = H+ + HCO3-

-log_k -7.868556606






CO2p7.5(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.875014098


# Species valid at a constant pressure of 7.5 bars and from 15 to 300 C




CO2p10(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.881532431






CO2p15(g)CO2 + H2O = H+ + HCO3-

-log_k -7.894789945






CO2p20(g)


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CO2 + H2O = H+ + HCO3-

-log_k -7.908349864






CO2p30(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.93635034






CO2p40(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.965847968

-analytical_expression -45.28793776 -0.022046977 663.6020742 16.84044099 0# Species valid at a constant pressure of 40 bars and from 15 to 300 C




CO2p50(g)

CO2 + H2O = H+ + HCO3-

-log_k -7.997098061






CO2p75(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.105718616

-analytical_expression -0.330189095 -0.014217308 -1057.553905 0 0





CO2p100(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.219189351

-analytical_expression 0.294236304 -0.014832354 -1220.102351 0 0# Species valid at a constant pressure of 100 bars and from 15 to 300 C




CO2p125(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.305863469

-analytical_expression 0.617821238 -0.015118684 -1315.907383 0 0


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CO2p150(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.375585301






CO2p175(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.433653635




# Duan and Sun (1993)'s Fugacity-Pressure relations# See Carey (2006) manuscript for further details

CO2p200(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.483251771






CO2p250(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.564463604






CO2p300(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.62911869




# Duan and Sun (1993)'s Fugacity-Pressure relations# See Carey (2006) manuscript for further details

CO2p400(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.727617318






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CO2p500(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.800717615






CO2p750(g)

CO2 + H2O = H+ + HCO3-

-log_k -8.925339526






CO2p1000(g)CO2 + H2O = H+ + HCO3-

-log_k -9.006881434

-analytical_expression -0.138120225 -0.013672717 -1428.207057 0 0






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Please Cite this report as follows:

Carey, J. W. (2006) Modifying the PHREEQC and Geochemist's Workbench Databases

for a more accurate CO2 Solubility. Technical Report LA-UR-06-4676, Los

Alamos National Laboratory.

modified co2 database carey 2006

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