Supporting Information
Experimental studies and modeling of CO2 solubility in high temperature aqueous CaCl2, MgCl2,
Na2SO4, and KCl solutions
Haining Zhao, Robert M. Dilmore, and Serguei N. Lvov,
1. Web-based computational interface of PSUCO2 model.
We developed a web-based computational interface for the proposed PSUCO2 model, please use
the link: http://www.carbonlab.org/psuco2/.
The calculation procedure is:
(1). Select a system
(2). Input pressure, temperature and salt concentration
(3). Click "Calculate" button, then the results will come out shortly
Figure S1. Web-based computational interface of the proposed PSUCO2 model. (Can be accessed via the
link: http://www.carbonlab.org/psuco2/)
2. Procedure to evaluate coefficients 𝒂𝟏 ~𝒂𝟓 in Eqs. (10) and (11)
We starting from Eq. (9),
𝑜
ln(𝑚CO2 𝛾CO2 ) = ln(𝑚CO
𝛾𝑜 )
2 CO2
𝑜
𝑚CO
2
ln (𝑚
CO2
o
) = ln𝛾CO2 − ln𝛾CO
2
(9)
(S2.1)
Substituting Eqs. (7) and (8) into the right side of Eq. (S2.1), we obtain:
𝑜
𝑚CO
2
ln (𝑚
CO2
) − 𝐶 = 2𝑚salt 𝐹
(S2.2)
where C and F in Eq.(S2.2) are given by Eqs. (S2.3) and (S2.4) as below:
o
2
o
𝐶 = 2𝜆nn (𝑚CO2 − 𝑚CO
) + 3𝜇𝑛𝑛𝑛 (𝑚CO
− (𝑚CO
)2 )
2
2
2
𝐹 = 𝐵CO2−salt +
𝑣+𝑣−
2
𝑚salt 𝜉𝑛𝑐𝑎 + 3𝑚CO2 𝐶CO2 −CO2−salt
(S2.3)
(S2.4)
and, from Eq. (S2.2)
𝑜
𝑚CO
2
𝐹 = (𝑙𝑛 (𝑚
CO2
) − C) /(2𝑚salt )
(S2.5)
By equating Eqs. (S2.4) and (S2.5), we obtain
𝐹 = 𝐵CO2−salt +
𝑣+𝑣−
2
𝑚𝑜
CO2
)−C)
𝑚CO
2
(ln(
𝑚salt 𝜉𝑛𝑐𝑎 + 3𝑚CO2 𝐶CO2 −CO2−salt =
(2𝑚salt )
(S2.6)
The parameter C can be calculated by Eq. (S2.3) using experimental CO2 solubility data in both
the CO2-H2O and CO2-salt-H2O systems. In order to determine the combined Pitzer interaction
parameters 𝐵𝐶𝑂2 −𝑠𝑎𝑙𝑡 and 𝐶𝐶𝑂2 −𝐶𝑂2 −𝑠𝑎𝑙𝑡 in Eq. (7), a function for F was chosen for the data
fitting process as shown in Eq. (S2.7).21
100
𝑇
𝐹 = 𝑎1 + 𝑎2 𝑇−𝜃 + 𝑎3 1000 + 𝑎4 𝑔(𝑥) + 𝑎5 3𝑚𝐶𝑂2 + 𝑎6
𝑣+𝑣−
2
𝑚𝑠𝑎𝑙𝑡
(S2.7)
For each salt species, 𝑎1 to 𝑎6 are coefficients determined by fitting of Eq. (S2.7) to the
corresponding experimental data. Comparing Eqs. (S2.6) and (S2.7), we obtain
100
𝑇
𝐵𝐶𝑂2 −𝑠𝑎𝑙𝑡 = 𝑎1 + 𝑎2 𝑇−𝜃 + 𝑎3 1000 + 𝑎4 𝑔(𝑥)
(S2.8)
𝐶𝐶𝑂2−𝐶𝑂2 −𝑠𝑎𝑙𝑡 = 𝑎5
(S2.9)
2
where 𝜃=228K, 𝑔(𝑥) = 𝑥 2 (1 − (1 + 𝑥)𝑒 −𝑥 ) , 𝑥 = 𝛼1 𝐼 0.5 , and 𝛼1 = 2.0 kg0.5 mol-0.5. For each
CO2-salt-H2O system, suppose the number of available experimental CO2 solubility data is n (at
different P-T-x points), Eq. (S2.7) can then be written in matrix form as:
𝐴𝑥 = 𝑓
(S2.8)
where
1(1)
𝐴=
1(2)
..
.
(𝑛)
(1
100
𝑇 (1)
𝑇 (1) −θ
100
1000
𝑇 (2)
𝑇 (2) −θ
1000
100
𝑇 (𝑛)
𝑇 (𝑛) −θ
1000
..
.
..
.
(1)
𝑣+𝑣−
(2)
2
𝑣+𝑣−
𝑔(1) (𝑥)
3𝑚CO2
𝑔(2) (𝑥)
.
.
.
3𝑚CO2
.
.
.
𝑔(𝑛) (𝑥)
3𝑚CO2
(𝑛)
2
𝑣+𝑣−
2
(1)
𝑚salt
𝑎1
𝐹 (1)
𝑎2
𝐹 (2)
𝑎3
..
;𝑥= 𝑎
;𝑓=
4
𝑎5
.
(𝐹 (𝑛) )𝑛×1
(𝑎6 )6×1
(2)
𝑚salt
.
.
.
(𝑛)
𝑚salt )
𝑛×6
The least-squares solution (𝑥̂) for Eq. (S2.8) is
[𝐴𝑇 𝐴]6×6 [𝑥̂]6×1 = [𝐴𝑇 𝑓]6×1
(S2.9)
where 𝐴𝑇 is the transpose of matrix A. The parameters (𝑎1 ~𝑎6 ) for each CO2-salt-H2O system
are obtained by solving Eq. (S2.9). The results are shown in Table 2. As a result, the parameters
𝐵𝐶𝑂2 −𝑠𝑎𝑙𝑡 and 𝐶𝐶𝑂2 −𝐶𝑂2−𝑠𝑎𝑙𝑡 can be calculated by Eqs. (10) and (11). Following Eqs. (S2.6) and
(S2.7), it appears that 𝜉𝑛𝑐𝑎 equals 𝑎6 , which means 𝜉𝑛𝑐𝑎 is a constant at any P-T-x condition for a
CO2-salt-H2O system. However, we can better correlate our experimental CO2 solubility data by
adjusting 𝜉𝑛𝑐𝑎 at different temperatures and salt concentrations as described in the paper.
3. Pitzer ion-ion interaction parameters for aqueous CaCl2, MgCl2, Na2SO4, and KCl
solutions.
(0)
(1)
The empirical function f(T,P) to calculate Pitzer ion-ion interaction parameters (𝛽𝑐𝑎 , 𝛽𝑐𝑎 and
𝜑
𝐶𝑐𝑎 ) at the desired temperatures and pressures for the system of CaCl2-H2O, Na2SO4-H2O,
MgCl2-H2O and KCl-H2O are summarized as below:
3.1. CaCl2-H2O system1
𝑓(𝑇, 𝑃) = 𝐹0 + 𝐹1 (𝑃) + 𝐹2 (𝑃)2
(S3.1)
where P is the system pressure in bar. Fo, F1 and F2 are functions of temperature only and given
by Eqs. (S3.2) to (S3.4),
1
1
1
1
5
𝑇
𝐹0 = 𝑞1 + 2 𝑞2 𝑇 + 6 𝑞3 𝑇 2 + 12 𝑞4 𝑇 3 + 6 𝑞5 𝑇 2 {ln𝑇 − 6} + 𝑞6 {2 +
𝑞7 {2
𝑇𝑦
𝑇
+ 1} ln𝑇y
1
𝐹1 = 𝑞8 + 𝑞9 𝑇 + 𝑞10 𝑇 + 𝑞11 𝑇 2 + 𝑇𝑥−1 𝑃12 + 𝑇𝑦−1 𝑃13
1
𝐹2 = 𝑞14 + 𝑞15 𝑇 + 𝑞16 𝑇 + 𝑞17 𝑇 2
3𝑇22
2𝑇
+
𝑇2 𝑇𝑥
𝑇
ln𝑇𝑥 } +
(S3.2)
(S3.3)
(S3.4)
where T1 = 647K, T2 = 227 K, Tx = (T-T2), and Ty = (T1-T). The constants q1~q17 were listed in
Table S1.
3.2. Na2SO4-H2O system2,3
𝑇
1
𝑓(𝑇) = 𝑞1 + 𝑞2 (𝑇 2 − 𝑇𝑅2 ) + 𝑞3 (𝑇 − 𝑇𝑅 ) + 𝑞4 ln (𝑇 ) + 𝑞5 (𝑇−𝑇 − 𝑇
𝑅
1
𝑇𝑅 (𝑇𝑅
1
1
1
1
𝑅 −𝑇1
) + 𝑞6 𝑇2 (𝑇(𝑇−𝑇 ) −
2
1
) + 𝐴 (𝑇 − 𝑇 )
−𝑇 )
2
(S3.5)
𝑅
𝐴 = 𝑞7 + 𝑞8 𝑇𝑅 + 𝑞9 𝑇𝑅2 + 𝑞10 𝑇𝑅3 + 2𝑇1 𝑞11 (𝑇
1
𝑅 −𝑇1
+ 2(𝑇
𝑇1
𝑅 −𝑇1
)2
) + 2𝑇2 𝑞12 (2(𝑇
𝑇2
𝑅 −𝑇2
1
)2
− 𝑇 −𝑇 )
2
𝑅
(S3.6)
where 𝑇𝑅 is the reference temperature which is conveniently set at 298.15𝐾. 𝑇1 is 263𝐾 and 𝑇2
is 263 or 680 K depending on which ion-interaction parameter is to be calculated (Table S2).
3.3. MgCl2-H2O system4
Wang and Pitzer (1998) developed a general model that describes the thermodynamic properties
of MgCl2(aq) based on an ion-interaction treatment of a variety of thermodynamic properties.
(0)
(1)
(0)
(1)
The equations for calculating the ion interaction parameters (𝛽𝑐𝑎 , 𝛽𝑐𝑎 ,𝐶𝑐𝑎 , 𝐶𝑐𝑎 ) are given
below,
𝑃
𝑃 2
𝑓(𝑇, 𝑃) = 𝐹0 + 𝐹1 (10) + 𝐹2 (10) /2
(S3.7)
where P is the system pressure in bar. F0, F1 and F2 are functions of temperature only and given
by Eqs. (S3.8) to (S3.11)
1
𝐹0 = 𝑞1 + 𝑞2 ln𝑇 + 𝑞3 𝑇 + 𝑞4 𝑇 2 + 𝑞5 𝑇 3 + 𝑞6 𝑇 10 + 𝑞7 (𝑇 −𝑇)
2
(S3.8)
1
2
1
𝐹1 = 𝑞8 + 𝑞9 ln𝑇 + 𝑞10 𝑇 + 𝑞11 𝑇 2 + 𝑞12 𝑇 3 + 𝑞13 𝑇 10 + 𝑞14 (𝑇 −𝑇)
(S3.9)
1
1
2
𝐹2 = 𝑞15 + 𝑞16 ln𝑇 + 𝑞17 𝑇 + 𝑞18 𝑇 2 + 𝑞19 𝑇 3 + 𝑞20 𝑇 10 + 𝑞21 (𝑇 −𝑇)
1
𝜙
(0)
(1)
(2)
𝐶𝑐𝑎 = 2[𝐶𝑐𝑎 + 𝐶𝑐𝑎 exp(−𝑥𝑐1 ) + 𝐶𝑐𝑎 exp(−𝑥𝑐2 )]
(S3.10)
(S3.11)
where 𝑥𝑐1 = 𝛼𝑐1 𝐼; 𝑥𝑐2 = 𝛼𝑐2 𝐼, 𝛼𝑐1 = 0.4 kg mol−1, 𝛼𝑐2 = 0.28 kg mol−1 , and T1 = 647K. The
constants q1~q21 are shown in Table S3.
3.4. KCl-H2O system5
1
1
𝑇
𝑓(𝑇) = 𝑞1 + 𝑞1 (𝑇 − 𝑇 ) + 𝑞3 ln (𝑇 ) + 𝑞4 (𝑇 − 𝑇𝑅 ) + 𝑞5 (𝑇 2 − 𝑇𝑅2 ) + 𝑞6 ln(𝑇 − 260)
𝑅
𝑅
where 𝑞1 -𝑞6 are constants listed in Table S4, and 𝑇𝑅 is 298.15 K.
(S3.12)
(0)
(1)
Table S1. Constants of Eqs. (S3.1) to (S3.4) for calculating Pitzer ion-interaction parameters (𝛽𝑐𝑎 , 𝛽𝑐𝑎
𝜙
and 𝐶𝑐𝑎 ) of CaCl2(aq).1
(0)
Const.
(1)
𝑓(𝑇, 𝑃) = 𝛽𝑐𝑎
𝜙
𝑓(𝑇, 𝑃) = 𝐶𝑐𝑎
𝑓(𝑇, 𝑃) = 𝛽𝑐𝑎
𝑞1
0
0
-1.3455 10-1
𝑞2
4.9213 10-3
-1.3814 10-1
0
𝑞3
-3.5512 10-5
1.6522 10-2
3.0401 10-4
𝑞4
4.7629 10-8
6.3784 10-6
1.3136 10-7
𝑞5
0
-3.1030 10-3
-5.8863 10-5
𝑞6
0
-2.0329 10-2
-6.4986 10-4
𝑞7
-3.5549 10-4
0
0
𝑞8
1.1021 10-3
0
-9.0317 10-7
𝑞9
-1.3924 10-1
0
0
𝑞10
-2.8663 10-6
1.0935 10-6
0
𝑞11
2.9609 10-9
-4.0084 10-9
5.9573 10-12
𝑞12
2.3285 10-3
0
0
𝑞13
-2.1508 10-2
0
0
𝑞14
0
0
-5.5630 10-9
𝑞15
0
0
1.7685 10-6
𝑞16
-1.2534 10-10
0
0
𝑞17
3.5462 10-13
0
0
(0)
(1)
Table S2. Constants in Eqs. (S3.5) – (S3.6) for calculating Pitzer ion-interaction parameters (𝛽𝑐𝑎 , 𝛽𝑐𝑎
𝜙
and 𝐶𝑐𝑎 ) of Na2SO4(aq).3
(0)
Const.
𝑓(𝑇) = 𝛽𝑐𝑎
(1)
𝜙
𝑓(𝑇) = 𝐶𝑐𝑎
𝑓(𝑇) = 𝛽𝑐𝑎 *
𝑞1
1.869 10-2
1.0994
5.54900 10-3
𝑞2
-1.03611 10-5
-3.2355 10-4
0
𝑞3
3.00299 10-2
5.76552 10-1
5.14316 10-5
𝑞4
-1.43441 10+1
-1.88769 10+2
0
𝑞5
-6.66894 10-1
-2.05974 10-1
0
𝑞6
0
-1.46744 10+3
3.45791 10-1
𝑞7
-2.081437 10+2
-5.29421 10+2
4.25799 10+1
𝑞8
-1.43441 10+1
-1.88769 10+2
0
𝑞9
3.00299 10-2
5.76552 10-1
5.14316 10-5
𝑞10
-2.07222 10-5
-6.471 10-4
0
𝑞11
6.66894 10-1
2.05974 10-1
-3.45791 10-1
𝑞12
0
1.46744 10+3
0
(1)
*When calculating 𝛽𝑐𝑎 , T2 in Eqs. (A5) and (A6) is 680K, otherwise T2 is 263K
(0)
(1)
𝜙
Table S3. Constants of Eqs. (S3.7) – (S3.10) for calculating Pitzer ion-interaction parameters (𝛽𝑐𝑎 , 𝛽𝑐𝑎 and 𝐶𝑐𝑎 ) of MgCl2 (aq).4
(0)
Coeff.
(1)
𝑓(𝑇, 𝑃) = 𝛽𝑐𝑎
𝜙
𝑓(𝑇, 𝑃) = 𝛽𝑐𝑎
(0)
(1)
(2)
𝐶𝑐𝑎 = 2 [𝐶𝑐𝑎 + 𝐶𝑐𝑎 exp(−𝑥𝑐1 ) + 𝐶𝑐𝑎 exp(−𝑥𝑐2 )] (Eq. (A11))
(0)
(1)
𝑓(𝑇, 𝑃) = 𝐶𝑐𝑎
(2)
𝑓(𝑇, 𝑃) = 𝐶𝑐𝑎
𝑓(𝑇, 𝑃) = 𝐶𝑐𝑎
𝑞1
-5.50111455 10+1
7.21220552 10+1
5.92428240
0
0
𝑞2
1.50130326 10+1
-1.77145085 10+1
-1.65126386
-1.02256042
0
𝑞3
-1.58107430 10-1
1.14397153 10-1
1.89399822 10-2
3.77018617 10-2
-2.28040769 10-3
𝑞4
2.30409919 10-4
0
-2.99972128 10-5
-7.91682934 10-5
1.37425889 10-5
𝑞5
-1.31768095 10-7
-1.43588435 10-7
1.89174291 10-8
5.91314258 10-8
-1.94821902 10-8
𝑞6
-1.26699609 10-28
1.72952766 10-27
0
0
1.04649784 10-28
𝑞7
2.82197499 10+2
3.41920714 10+3
5.49030201 10+1
-2.28493084 10+2
0
𝑞8
0
0
4.50114048 10-2
0
0
𝑞9
0
2.28440612 10-4
-1.08427926 10-2
0
0
𝑞10
8.39661960 10-5
0
7.41041864 10-5
-7.79259941 10-5
0
𝑞11
-4.60207270 10-7
0
-5.99961498 10-8
4.28675876 10-7
0
𝑞12
6.21165614 10-10
0
0
-5.77509662 10-10
0
𝑞13
8.43555937 10-31
-1.77573402 10-29
0
0
0
𝑞14
0
-2.29668879 10+2
-4.60562847
0
0
𝑞15
0
0
0
-5.13962051 10-4
0
𝑞16
0
0
0
9.30761142 10-5
0
𝑞17
0
-2.71485086 10-7
0
0
0
𝑞18
0
0
0
0
0
𝑞19
0
0
-1.39016981 10-15
-7.43350922 10-13
0
𝑞20
0
0
0
0
0
𝑞21
-1.11176553
1.01000272 10+1
1.40556304 10-1
1.12721557
0
(0)
(1)
𝜙
Table S4. Constants of Eq. (S3.12) for calculating Pitzer ion-interaction parameters (𝛽𝑐𝑎 , 𝛽𝑐𝑎 and 𝐶𝑐𝑎 )
of KCl(aq).5
(0)
Const.
(1)
𝑓(𝑇) = 𝛽𝑐𝑎
𝜙
𝑓(𝑇) = 𝐶𝑐𝑎
𝑓(𝑇) = 𝛽𝑐𝑎
𝑞1
4.808 10-2
4.76 10-2
-7.88 10-4
𝑞2
-7.5848 10+2
3.039 10+2
9.127 10+1
𝑞3
-4.7062
1.066
5.8643 10-1
𝑞4
1.0072 10-2
0
-1.298 10-3
𝑞5
-3.7599 10-6
0
4.9567 10-7
𝑞6
0
4.7 10-2
0
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in
Aqueous
Solutions
of
Strong
Electrolytes.
Berichte
der
Bunsengesellschaft für physikalische Chemie. 1993;97:85-97.
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