Phase Equilibrium Modeling for Carbon Dioxide Solubility in Aqueous

May 24, 2019 - Then, a noniterative equation was presented by Duan et al. ... to determine CO2 solubility within NaCl solutions below 573 K. Dubacq et...
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Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 10570−10578

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Phase Equilibrium Modeling for Carbon Dioxide Solubility in Aqueous Sodium Chloride Solutions Using an Association Equation of State Xiao-Qiang Bian,* Wei Xiong, Don Thisal Kaushika Kasthuriarachchi, and Yong-Bing Liu Petroleum Engineering School, Southwest Petroleum University, Chengdu 610500, China

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S Supporting Information *

ABSTRACT: The model, i.e., the thermodynamic model, focused on the cubic-plus-association equation of state combined with the Wong− Sandler mixing rule with six parameters is presented (CPA-WS). The model confirmed that the inert association scheme is more suitable for carbon dioxide (CO2) than the 3B association scheme, for the level equilibrium in the carbon dioxide−water (H2O) system. Meanwhile, the CO2−H2O−sodium chloride (NaCl) system can be reasonably well predicted by using two adjustable parameters of the H2O−NaCl and CO2−NaCl systems. The average absolute relative deviations of the predicted CO2 solubility in H2O and aqueous NaCl solutions of the CPA-WS model are 5.31 and 3.56%, respectively.

association of water. Yan and Chen11 presented the PC-SAFT EoS coupled with an activity coefficient equation for determination of the CO2 solubility in NaCl solutions over valid pressures and temperatures up to 150 MPa and 473 K. Sun and Dubessy12 used the SAFT-LJ model to determine CO2 solubility within NaCl solutions below 573 K. Dubacq et al.13 constructed the activity−composition model for phase equilibrium in the CO2−H2O−NaCl tertiary system with a valid T−P range of 283−653 K and 0.1−350 MPa. Nomeli et al.14,15 presented a new model by calculation of the dissolved CO2 partial molar volume to capture the impacts of pressure, temperature, and salinity on CCS. Mao et al.16,17 determined the CO2 solubility in NaCl solutions with a Helmholtz free energy model within a wide temperature range (273−1273 K) and wide pressure range (0−500 MPa). Lloret et al.18,19 predicted CO2 solubility in monoethanolamine solutions using the soft-SAFT EoS. Xu et al.20,21 studied CO2 capture using EPPR78 and PC-SAFT EoSs. Li et al.22 studied CO2 diffusion coefficients with different permeabilities using the PR EoS. However, these models are either very complex or have various adjustable parameters. Kontogeorgis et al.23 first presented a cubic-plus-association of state (CPA EoS), which was widely used to calculate the vapor−liquid equilibria (VLE) and liquid−liquid equilibria (LLE) for hydrocarbon + N-formylmorpholine, esters + ethanol + water, biodiesel, amino acid solutions, fatty acid

1. INTRODUCTION Carbon capture and storage (CCS) technologies have become more important in dealing with global carbon dioxide (CO2) emissions. The dissolution of CO2 in formation water or seawater is one of the efficient CCS methods at high temperature and pressure. Knowledge of CO2 solubility in seawater is of great significance for CO2 storage in seawater. It is acknowledged that experimental determination of CO2 solubility is time-consuming and expensive. Thus, thermodynamic models have been developed on the basis of experimental data and phase equilibria to exceed the limitations of experimental methods. Duan and Sun1 developed a thermodynamic model based on the equation of state (EoS) of Duan et al.2 and the theory of Pitzer3 to predict the solubility of CO2 in pure water and in aqueous NaCl solutions. Then, a noniterative equation was presented by Duan et al.4 to improve the performance of Duan and Sun’s1 model. However, Duan’s model is complex with 15 adjustable parameters, and it does not take into consideration the interaction between CO2 and H2O. Spycher and Pruess5 used a solubility model with activity coefficients for CO2 and water (H2O) to account for the effects of dissolved salts. Dubessy et al.6 constructed an asymmetric thermodynamic model with Redlich−Kister’s method for the activity coefficients of water and gas components in the CO2−H2O− sodium chloride (NaCl) system. Hassanzadeh et al.7−10 presented a similar activity coefficient−fugacity coefficient (γ−φ) type thermodynamic model like Duan’s model, which is based on the Redlich−Kwong (RK) or Peng−Robinson (PR) EoS. Nevertheless, these simple EoSs cannot describe the interaction between CO2 and H2O as well as the self© 2019 American Chemical Society

Received: Revised: Accepted: Published: 10570

March 29, 2019 May 10, 2019 May 24, 2019 May 24, 2019 DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

Article

Industrial & Engineering Chemistry Research Table 1. CPA Parameters for CO2−H2O Binary System Used in This Worka fluid

assn scheme

assn sites in fluid

a0 (cm2·MPa/mol2)

b (cm3/mol)

c1

ε (cm·MPa/mol)

β

ref

CO2 CO2 H2O

inert 3B 4C

0ed−1ea 2ed−1ea 2ed−2ea

350 790 305 580 122 770

27.2 28.1 14.5

0.7602 0.6703 0.6736

− 5168 16655

− 0.0411 0.0692

31 31 31

a

ed, electron donor; ea, electron acceptor.

repulsive force; xi is considered the mole fraction of a given component i; A and B indicate the bonding sites; XAi is the fraction of A-sites of the molecule i that are not in bonds with any other active sites; εAB and βAB are the association of energy and volume of interaction; η is the determined reduced fluid density. In this work, in order to increase the performance of the CPA EoS, the vdW one-fluid mixing rule is replaced with the WS mixing rule as follows:

ester + alcohol, solid solute solutions, isopropyl alcohol + propylene, petroleum fractions, and heavy crude systems.24−30 Tsivintzelis et al.31 used the CPA EoS to study CO2 solubility in the H2O−CO2 system with different association schemes including inert, 2B, 3B, and 4C association schemes, and CO2 was considered as solvating to get better results. Bjørner and Kontogeorgis32 studied quadrupolar interactions for CO2 + hydrocarbon mixtures with less adjustable parameters than other CPA EoSs. Muro-Sune et al.33 acquired more satisfactory results with the new CPA-HV model at the cost of high interaction parameters in the water−acetic acid system. All in all, a single CPA EoS has been applied to complex systems and a few satisfied results have been acquired. However, poor performance is apparent, such as low accuracy, limiting temperature, and pressure. In this work, a phase equilibrium model is presented that is based on the CPA EoS and the Wong and Sandler34 (WS) mixing rule (CPA-WS). The performance of the CPA-WS in the description of the CO2 solubility in pure water and/or in aqueous NaCl solutions is evaluated with experimental data. Meanwhile, a comparison of the model of the CPA EoS coupled with the van der Waals one-fluid mixing rule (CPAvdW)31 and CPA-WS model is given for the solubility of CO2 in pure water and H2O content in CO2-rich phase using the inert and 3B association scheme approaches.

amL = RTQ L

a(T ) RT − v−b v(v + b) n i 1 RT jj 1 ∂ ln g yzz − jj1 + zz ∑ xi ∑ (1 − X A i) 2 v k v ∂(1/v) { i = 1 A i

a(T ) = a0(1 + c1(1 −

2

Tr ))

ij yz j z X = jjjj1 + (1/v) ∑ xj ∑ X BjΔA iBj zzzz jj zz j Bj k { ÄÅ É ÑÑ ÅÅ ij ε A iBj yz Ñ zz − 1ÑÑÑbijβ A iBj ΔA iBj = g (v)ÅÅÅÅexpjjj z ÑÑ ÅÅ k RT { ÑÑÖ ÅÇ

1 η= b 4v

DL =

∑ xi

(7)

(8)

ai A E(L) + ∞ biRT CRT

i k

∑ ∑ xixjjjjb − i

j

(9)

a zy zz RT {ij

(10)

AE∞

where is the excess Helmholtz energy (approximated the excess Gibbs energy); C is a constant (−1.414 for the Soave− Redlich−Kwong (SRK) EoS). The cross second virial term was modified by Zhao and Lvov35 to promote the performance in WS mixing rule as follows: bi + bj a yz ij jjb − zz = − RT {ij 2 k

aiaj [1 − kij + (kij − kji)xi ] RT (11)

where k is the binary interaction parameter (kij ≠ kji). Huron and Vidal36 modified the NRTL model as follows:

(1) (2)

GE = RT

−1

1 1 − 1.9η

QL 1 − DL

QL =

Ai

g (v ) =

bmL =

i

2. CPA-WS APPROACH The CPA EoS is presented by Kontogeorgis et al.23 as follows: P=

DL 1 − DL

n

n

∑ xi i=1

∑ j = 1 xjEjiGji n

∑k = 1 xkGki

(12)

Gji = bj exp( −αjiEji),

(3)

Gki = bk exp(−αkiEki)

n

ln γi =

(4)

(5)

∑ j = 1 xjEjiGji n ∑k = 1 xkGki

(13)

n

+

xjGij n j = 1 ∑k = 1 xkGkj

∑

n ij y jjE − ∑l = 1 xlEljGlj zzz jj ij z n j ∑k = 1 xkGkj zz k {

(14)

(6)

where αji and αki are constant (αji = αij); Eij is the interaction parameter of component between i and j.

Herein, P is the system pressure, MPa; T is the system temperature, K; Tr is the reduced temperature (Tr = T/Tc); Tc is the critical temperature, K; v is the mole volume, cm3·mol−1; R is the universal gas constant, 8.314 MPa·cm3·mol−1·K−1; a and b are related to the intermolecular attraction force and

3. CO2−H2O SYSTEM There are five association schemes for CO2, including inert, 2B, 3B, 4C, and quadrupolar. Many researchers proved that CO2 is appropriate for modeling as inert and 3B association 10571

DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

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Industrial & Engineering Chemistry Research Table 2. Experimental Data for CO2−H2O System and CO2−H2O−NaCl System Used in This Work M (mol·kg−1)

T (K)

P (MPa)

Np

ref

288.15−433.15 288.15−313.15 288.15−298.15 298.15−423.15 304.19−313.15 304.19

10−120 5.17−24.32 0.5−5.59 1.09−17.55 1.76−5.83 0.69−20.27

0 0 0 0 0 0

63 41 22 21 10 8

313.15−373.15

5.07−70.93

0

25

298.15−323.15

2.53−70.93

0

26

323.15−523.15

20−350

0

80

323.15 323.15 323.15 323.15−353.15 373.15 393.15

6.82−17.68 10.13−15.2 2.1−15.99 4.05−14.11 7.21−27.26 6.89−70.32

0 0 0 0 0 0

14 4 7 58 5 10

393.15−473.15

3.91−10.21

0

18

423.15−523.15

10−140

0

30

473.15−523.15 323.15 373.15 303.15−333.15 323.15−413.15

9.81−58.84 10.1−30.1 0.32−2.31 10−20 5−40

0 0 0 0.17−0.53 1.00−5.00

70 3 7 36 36

Guo et al.37 King et al.38 Valtz et al.39 Hou et al.40 Gu41 Gillespie and Wilson42 Wiebe and Gaddy43 Wiebe and Gaddy44 Toedheide and Franck45 Briones et al.46 D’souza et al.47 Liu et al.48 Bamberger et al.49 Tong et al.50 Prutton and Savage51 Nighswander et al.52 Takenouchi and Kennedy53 Malinin54 Dohrn et al.55 Müller et al.56 Bando et al.57 Yan et al.58

Table 4. CPA-vdW Model Parameters Optimized for CO2− H2O System Used in This Worka assn sites in CO2

kij

εcross (cm·MPa/mol)

βcross

ref

0ed−1ea 2ed−1ea

−0.15508 + 0.000877T −0.10517 + 0.000389T

8328 14200

0.1836 0.004

31 31

a

ed, electron donor; ea, electron acceptor. kij, binary interaction parameters; εcross, βcross, cross-associating strength parameters.

cross-association with H2O. Therefore, the cross-associating strength is only related to the association strength of H2O. In this work, a combining rule (eq 15) for the cross-associating strength of the CO2−H2O system is presented with an adjustable binary interaction parameter (F). The fraction of one electron acceptor site (A-site) of CO2 that is not bonded with any other active sites is related to the cross-association strength of CO2−H2O and the fraction of two electron donor sites (B-sites) of H2O, that are not in bonds with other active sites, which can be calculated by eq 16. ΔA iBj = Fij ΔA iBi −1 + X Aj =

(15)

1 + 4ρ2 X BiΔAjBi 2ρ2 X BiΔAjBi

(16)

where i is H2O and j is CO2, ρ is the molar density, and F is the binary interaction parameter (Fij = Fji). CO2, as a self-associating compound (3B), accepts two pairs of electrons and donate a pair of electrons to other compounds. Previous combining rules about association energy are not satisfied for the CPA-WS model. A modified Elliott combining rule is presented with an adjustable binary interaction parameter (F) as follows:

schemes, while H2O is considered as 4C. In the present work, association schemes of inert (only one electron acceptor site in CO2) and 3B (one electron acceptor site and two electron donor sites in CO2) are used for CO2 and the association scheme of 4C (two electron donor sites and two electron acceptor sites in H2O) is used for H2O to develop the CPAWS (NRTL) model. The parameters of the CPA EoS for the CO2−H2O system are listed in Table 1. CO2, as a non-self-associating compound, only accepts a pair of electrons to solvate in water. It is necessary to consider

ΔA iBj = Fij ΔA iBi ΔAjBj

(17)

where F is a binary interaction parameter (Fij = Fji). Herein, six adjustable parameters are employed for the presented CPA-WS model; they are respectively α, kij, kji, Eij, Eji, and F (subscripts i and j stand for H2O and CO2). The optimized results are acquired by setting α = 0.1 for the CO2−

Table 3. CPA-WS Model Parameters Optimized for H2O−CO2 Systema inert assn scheme

3B assn scheme

T (K)

kij

kji

Eij

Eji

F

kij

kji

Eij

Eji

F

288.15 298.15 304.19 313.15 323.15 333.15 353.15 373.15 393.15 413.15 423.15 433.15 473.15 523.15

0.08 0.05 0.09 0.13 0.19 0.24 0.28 0.22 0.31 0.33 0.27 0.28 0.28 0.27

0.09 0.09 0.09 0.17 0.18 0.17 0.18 0.26 0.27 0.28 0.3 0.31 0.3 0.26

0.31 0.34 0.31 0.46 0.6 0.63 0.63 1.21 1.2 1.16 1.23 1.2 1.15 0.97

0.5 0.51 0.54 0.65 0.62 0.58 0.59 0.43 0.42 0.42 0.4 0.39 0.33 0.27

3.58 3.68 3.79 4.28 4.63 4.65 4.65 5.79 5.81 5.86 5.91 5.93 6.15 6.91

0.15 0.04 0.07 0.12 0.12 0.1 0.08 0.25 0.29 0.3 0.38 0.39 0.45 0.63

0.15 0.27 0.29 0.17 0.17 0.18 0.19 0.3 0.29 0.35 0.39 0.36 0.43 0.6

0.02 0.03 0.04 0.11 0.14 0.15 0.14 0.41 0.3 0.47 0.49 0.47 0.5 0.68

0.61 0.85 0.88 0.77 0.82 0.83 0.86 1.03 1.04 1.03 1.09 1.05 1.07 1.11

0.33 0.37 0.39 0.43 0.48 0.5 0.53 0.76 0.79 0.9 0.95 1.06 1.27 1.75

a

Subscripts i and j stand for H2O and CO2, respectively. 10572

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Figure 2. CO2−H2O VEL at 323.15 K. CPA-WS calculations (black lines), CPA-vdW calculations (red lines), and PRSV-WS calculations (blue lines) for liquid (a) and vapor (b) compositions using inert and 3B association scheme approaches. Experimental data taken from Wiebe and Gaddy,44 Hou et al.,40 Wiebe and Gaddy,43 Toedheide and Franck,45 Briones et al.,46 Liu et al.,48 Bamberger et al.,49 D’souza et al.,47 and Dohrn et al.55

Figure 1. CO2−H2O VEL and LLE at 298.15 K. CPA-WS calculations (black lines), CPA-vdW calculations (red lines), and PRSV-WS calculations (blue lines) for liquid (a) and vapor (b) compositions using inert and 3B association scheme approaches. Experimental data taken from Guo et al.,37 King et al.,38 Hou et al.,40 Valtz et al.,39 and Wiebe and Gaddy.44

H2O binary system. The phase boundary line between two phase regions and the CO2-rich phase is mainly affected by the parameters kji and Eji, while parameter F is very important to improve the water content line within the CO2-rich gas phase. The experimental data of CO2 within H2O and within aqueous NaCl solutions are obtained from many literature sources (Table 2). The CPA-WS model parameters are optimized over large ranges of pressure (0.1−350 MPa) and temperature (288−523 K). These results are listed in Table 3. Meanwhile, the CPA-vdW parameters are also optimized in Table 4. The CPA-vdW31 and PRSV-WS35 models are used to compare with the proposed CPA-WS model. It can be determined from Figure 1 that the performance of CPA-WS calculations for liquid (Figure 1a) and vapor (Figure 1b) compositions using inert and 3B association scheme approaches are better than that of the CPA-vdW model at 298.15 K. The results of the CPA-WS model for the solubility of CO2 in H2O by means of the inert association scheme are better than that of the 3B association scheme. The calculated results of the CPA-vdW model are apparently larger than experimental data especially at pressure above 20 MPa. The

performance of the CPA-WS model for H2O content in CO2rich phase is better than that of the CPA-vdW model at pressure above 10 MPa. CPA-WS calculations have a correct trend to describe H2O content in CO2-rich phase, while CPAvdW calculations are larger, especially with the inert association scheme approach. The performance of the PRSVWS model is better than that of CPA-vdW, but its accuracy is lower than that of CPA-WS. It is mentioned that a jump in data for H2O content in Figure 1b is seen. The reason is that the phase behavior has been transited from the CO2-rich vapor phase to the liquid phase with a slight pressure increase. Thus, water content in the CO2-rich phase jumps. It can be seen from Figures 2−4 that CPA-WS has the ability to predict CO2−H2O VLE over a wide T−P range of 288.15− 523.15 K and 0.1−350 MPa, and the calculated results of CPAWS are satisfied compared against experimental data. Apparently, the CPA-WS model is more accurate than the CPA-vdW model for the CO2 solubility within pure water at pressure higher than 50 MPa and the H2O content in CO2-rich gas phase at pressure above 30 MPa. With the pressure 10573

DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

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Industrial & Engineering Chemistry Research

Figure 4. CO2−H2O VEL at 473.15 K. CPA-WS calculations (black lines), CPA-vdW calculations (red lines), and PRSV-WS calculations (blue lines) for liquid (a) and vapor (b) compositions using inert and 3B association scheme approaches. Experimental data taken from Nighswander et al.,52 Takenouchi and Kennedy,53 Malinin,54 and Toedheide and Franck.45

Figure 3. CO2−H2O VEL at 373.15 K. CPA-WS calculations (black lines), CPA-vdW calculations (red lines), and PRSV-WS calculations (blue lines) for liquid (a) and vapor (b) compositions using inert and 3B association scheme approaches. Experimental data taken from Guo et al.,37 Hou et al.,40 Wiebe and Gaddy,43 Toedheide and Franck,45 Tong et al.,50 and Müller et al.56

temperatures and pressures higher than 373.15 K and 200 MPa. It can be seen from Table 5 that the average absolute relative deviation (AARD) between CPA-WS calculations and experimental data for the H2O−CO2 system is acceptable, while the CPA-vdW and PRSV-WS models yield larger AARDs. The AARDs of predicted CO2 solubility in the H2O-rich phase of CPA-WS (inert), CPA-WS (3B), CPA-vdW (inert), CPA-vdW (3B), and PRSV-WS models are 5.31, 4.9, 9.54, 10.88, and 6.32%, respectively. The AARDs of predicted H2O content in the CO2-rich phase of CPA-WS (inert), CPAWS (3B), CPA-vdW (inert), CPA-vdW (3B), and PRSV-WS models are 5.14, 6.13, 16.29, 32.35, and 11.07%, respectively.

continually increasing, the errors of CPA-vdW calculations incessantly increase, which leads to an incorrect trend compared with experimental data. With the temperature continually increasing, the errors of CPA-vdW for the H2O content in CO2-rich phase are lower than experimental data, because it is not modified cross-associating strength. Meanwhile, the inert association scheme is more suitable to CO2 than the 3B association scheme for the CPA-WS and CPAvdW models. With the pressure continually increasing, the predicted solubility of CO2 in pure water (CO2 as 3B association scheme) is larger than experimental data at low temperatures (e.g., T = 323.15 K), and lower than experimental data at high temperatures (e.g., T = 473.15 K). However, with the pressure continuously increasing, the predicted H2O content in CO2-rich phase (CO2 as 3B association scheme) is always lower than experimental data at all temperatures. The PRSV-WS model can exactly determine or predict the solubility of CO2 in pure water, but it does not reflect the H2O content in CO2-rich phase at

4. CO2−H2O−NaCl SYSTEM The solubility of CO2 within NaCl solutions is also calculated by using the presented CPA-WS model. It can be thought of nonassociating in the CO2−NaCl and H2O−NaCl systems. Therefore, the CPA-WS physical term parameters of NaCl can be estimated from the SRK EoS (eqs 18−21). 10574

DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

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Table 5. AARDs of CPA-WS, CPA-vdW, and PRSV-WS Models for H2O−CO2 System with 0ed−1ea and 3B Association Schemesa AARD (%) CPA-WS

CPA-vdW

x2

y1

x2

y1

PRSV-WS

T (K)

0ed−1ea

3B

0ed−1ea

3B

0ed−1ea

3B

0ed−1ea

3B

x2

y1

288.15 298.15 304.19 313.15 323.15 333.15 353.15 373.15 393.15 413.15 423.15 433.15 473.15 523.15 mean AARD (%)

5.62 6.35 5.9 5.17 3.57 2.77 3.1 3.05 9.17 2.06 4.92 6.45 5.8 7.72 5.31

5.83 8.12 6.54 5.12 3.47 2.58 2.75 2.83 7.92 1.95 3.87 6.8 5.19 5.47 4.9

15.18 5.53 1.44 2.63 6.09 3.61 2.81 4.82 − − 1.65 − 3.58 5.04 5.14

13.89 5.54 2.47 1.93 8.57 3.1 2.43 6.55 − − 2.79 − 3.7 7.89 6.13

11.14 8.26 7.19 6.19 7.03 5.32 6.8 10.03 10.55 6.72 9.63 6.05 9.93 19.17 9.54

8.33 7.51 6.32 6.25 7.42 4.65 4.06 8.34 7.11 4.3 7.01 9.94 15.67 28.84 10.88

28.74 13.17 9.54 1.94 9.76 5.76 4.21 29.62 − − 32.86 − 29.98 31.63 16.29

29.29 8.62 8.73 27.22 32.66 21.98 18.5 65.81 − − 64.83 − 49.88 52.15 32.35

4.81 8.73 6.72 4.74 4.94 6.77 7.9 4.53 9.85 8.86 4.72 10.48 6.52 5.3 6.32

13.91 9.75 3.29 10.23 8.57 6.67 9.65 15.67 − − 6.76 − 11.76 25.96 11.07

ed, electron donor; ea, electron acceptor. Subscripts “1” and “2” stand for H2O and CO2 respectively. x2 and y1 denote the solubility of CO2 in

a

pure water and the H2O content in CO2-rich gas phase, respectively. AARD = cal

pure water in mole fraction; x

1 n

n

∑i = 1

|xiexp − xical| , xiexp

where xexp is the experimental solubility of CO2 in

is the calculated solubility of CO2 in pure water. “−” stands for lack of experimental data.

Table 6. CPA-WS Model Parameters for H2O−NaCl and CO2−NaCl Systems and AARDs of CPA-WS for H2O− CO2−NaCl System D T (K)

H2O−NaCl

CO2−NaCl

H2O−CO2−NaCl AARD (%)

303.15 313.15 323.15 333.15 373.15 413.15

0.21 0.13 0.02 −0.11 −0.57 −1.75

1.00 0.99 0.99 1.00 1.00 1.00

3.35 2.04 3.36 2.08 5.84 4.01 3.56a

a

Mean AARD (%).

a = 0.42748

(RTc)2 α (T ) Pc

b = 0.08664

RTc Pc

(19)

α(T ) = [1 + m(1 − Tr 0.5)]2

(20)

m = 0.48 + 1.574ω − 0.176ω 2

(21)

(18) Figure 5. CO2−H2O−NaCl VEL at 323.15 K. CPA-WS calculations (black lines) for liquid compositions using inert association scheme approach. Experimental data taken from Bando et al.57 and Yan et al.58

ÅÄÅ ÑÉ aj ÑÑÑÑ C ÅÅÅÅ aiaj(1 − Dij) Eij = − ÑÑÑ Å RT ÅÅÅÅ bi bj ÑÑÑ ÅÇ ÑÖ

Dij = 1 − kij + (kij − kji)x

Herein, Pc is the critical pressure of a component, MPa; ω is the acentric factor, dimensionless; and α(T) is a function of the reduced temperature (Tr) and eccentric factor (ω) and equals unity at the critical temperature (Tc). In this work, a simplified CPA-WS model is presented to reduce CPA-WS parameters of the H2O−NaCl and CO2− NaCl systems. A new interaction parameter (D) is presented to replace kij and kji for the CO2−NaCl and H2O−NaCl binary systems (eq 22). The energy parameters of CO2−NaCl and H2O−NaCl can be calculated from interaction parameters (D) by choosing α = 0 (eq 23).

(22)

(23)

There are only two parameters for the H2O−NaCl and CO2−NaCl systems (we choose α = 0). The interaction parameters (D) of the H2O−NaCl and CO2−NaCl systems need to be regressed from the literature experimental data (Table 2) with the definite interaction parameters of CO2− H2O (using the inert association scheme approach) presented above. The results of fitted parameters are listed in Table 6. 10575

DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

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Figure 8. CO2−H2O−NaCl VEL at 413.15 K. CPA-WS calculations (black lines) for liquid compositions using inert association scheme approach. Experimental data taken from Yan et al.58

Figure 6. CO2−H2O−NaCl VEL at 333.15 K. CPA-WS calculations (black lines) for liquid compositions using inert association scheme approach. Experimental data taken from Bando et al.57

Figure 9. CO2−H2O−NaCl VEL at 4.795 MPa. CPA-WS calculations (black lines) for liquid compositions using inert association scheme approach. Experimental data taken from Malinin and Savelyeva59 and Malinin and Kurovskaya.60

Figure 7. CO2−H2O−NaCl VEL at 373.15 K. CPA-WS calculations (black lines) for liquid compositions using inert association scheme approach. Experimental data taken from Yan et al.58

NaCl system are 0.66 and −0.4, while those for the CO2− NaCl system are respectively 1 and 0.997 at 298.15 and 348.15 K. Other parameter values are listed in Table 6 (the CPA-WS model parameters of kij, kji, Eij, Eji, and F for the H2O−CO2 system are 0.26, 0.17, 0.63, 0.59, and 4.64 at 348.15 K, respectively). The AARD of predicted CO2 solubility in aqueous NaCl solutions is 5.99%. However, it is worth mentioning that experimental data from Malinin and Savelyeva59 and Malinin and Kurovskaya60 have some disagreements among these data.1 Because their experimental apparatus was designed principally to measure the difference in CO2 solubility between pure H2O and aqueous salt solutions, their solubilities in pure H2O may not be very accurate.61

It can be determined from Figures 5−8 that the simplified CPA-WS model can easily and well predict CO2 solubility in aqueous solutions for different NaCl concentrations with two adjustable parameters (D) of CO2−NaCl and H2O−NaCl over a valid range of temperature and pressure from 303 to 413 K and from 0.1 to 50 MPa. Moreover, CPA-WS has a stable performance and it can increase adjustable parameters to gain a better performance. The AARD of predicted CO2 solubility in aqueous NaCl solutions of the simplified CPA-WS model is 3.56% (Table 6). In order to further verify the accuracy and reliability of the presented method, a comparison of the predictions with the data reported by Malinin and Savelyeva59 and Malinin and Kurovskaya60 has been made. It can be indicated from Figure 9 that the simplified CPA-WS model can accurately predict CO2 solubility in aqueous solutions for different NaCl concentrations at 4.795 MPa. The parameters of D for the H2O−

5. CONCLUSIONS The new CPA-WS model is proposed for the CO2−H2O− NaCl tertiary system and the CO2−H2O binary system. This results confirmed that the inert association scheme is more suitable for CO2 than the 3B association scheme for the phase 10576

DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

Article

Industrial & Engineering Chemistry Research equilibrium of the CO2−H2O system, and the tertiary system (CO2−H2O−NaCl) can be reasonably well predicted by using two adjustable parameters of the H2O−NaCl and CO2−NaCl systems. The overall CPA-WS model performance was validated by using a large number of experimental data of the CO2−H2O and CO2−H2O−NaCl systems. Compared with the CPA-vdW model, the performance of CPA-WS was better satisfied, and it is necessary to improve physical term performance and modify cross-associating strength. Over a wide T−P range from 288.15 to 523.15 K and from 0.1 to 350.0 MPa, The AARDs of predicted CO2 solubility in the H2O-rich phase of CPA-WS (inert), CPA-WS (3B), CPA-vdW (inert), CPA-vdW (3B), and PRSV-WS models are 5.31, 4.9, 9.54, 10.88, and 6.32%, respectively. The AARDs of predicted H2O content in the CO2-rich phase of CPA-WS (inert), CPA-WS (3B), CPA-vdW (inert), CPA-vdW (3B), and PRSV-WS models are 5.14, 6.13, 16.29, 32.35, and 11.07%, respectively. In other words, the performance of the CPA-WS model is better than that of CPAvdW and PRSV-WS, and the PRSV-WS model is better than the CPA-vdW model. The CPA-WS can accurately predict CO2 solubility in brine with different NaCl contents with two adjustable parameters (D) with AARD = 3.56% within a range of temperatures and pressures from 303.15 to 413.15 K and from 0.1 to 50 MPa.

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(4) Duan, Z.; Sun, R.; Zhu, C.; Chou, I. An improved model for the calculation of CO2 solubility in aqueous solutions containing Na+, K+, Ca2+, Mg2+, Cl−, and SO42‑. Mar. Chem. 2006, 98, 131−139. (5) Spycher, N.; Pruess, K. CO2-H2O mixtures in the geological sequestration of CO2. II. Partitioning in chloride brines at 12−100°C and up to 600 bar. Geochim. Cosmochim. Acta 2005, 69, 3309−3320. (6) Dubessy, J.; Tarantola, A.; Sterpenich, J. Modelling of liquidvapour equilibria in the H2O-CO2-NaCl and H2O-H2S-NaCl Systems to 270°C. Oil Gas Sci. Technol. 2005, 60, 339−355. (7) Hassanzadeh, H.; Pooladi-Darvish, M.; Elsharkawy, A. M.; Keith, D. W.; Leonenko, Y. Predicting PVT data for CO2-brine mixtures for black-oil simulation of CO2 geological storage. Int. J. Greenhouse Gas Control 2008, 2, 65−77. (8) Zirrahi, M.; Azin, R.; Hassanzadeh, H.; Moshfeghian, M. Prediction of water content of sour and acid gases. Fluid Phase Equilib. 2010, 299, 171−179. (9) Salari, H.; Hassanzadeh, H.; Gerami, S.; Abedi, J. On estimating the water content of CO2 in equilibrium with formation brine. Pet. Sci. Technol. 2011, 29, 2037−2051. (10) Zirrahi, M.; Azin, R.; Hassanzadeh, H.; Moshfeghian, M. Mutual solubility of CH4, CO2, H2S, and their mixtures in brine under subsurface disposal conditions. Fluid Phase Equilib. 2012, 324, 80−93. (11) Yan, Y.; Chen, C. Thermodynamic modeling of CO2 solubility in aqueous solutions of NaCl and Na2SO4. J. Supercrit. Fluids 2010, 55, 623−634. (12) Sun, R.; Dubessy, J. Prediction of vapor-liquid equilibrium and PVTx properties of geological fluid system with SAFT-LJ EOS including multi-polar contribution. Part II: Application to H2O-NaCl and CO2-H2O-NaCl System. Geochim. Cosmochim. Acta 2012, 88, 130−145. (13) Dubacq, B.; Bickle, M. J.; Evans, K. A. An activity model for phase equilibria in the H2O-CO2-NaCl system. Geochim. Cosmochim. Acta 2013, 110, 229−252. (14) Nomeli, M. A.; Tilton, N.; Riaz, A. A new model for the density of saturated solutions of CO2-H2O-NaCl in saline aquifers. Int. J. Greenhouse Gas Control 2014, 31, 192−204. (15) Nomeli, M. A.; Riaz, A. A data driven model for the impact of IFT and density variations on CO2 storage capacity in geologic formations. Adv. Water Resour. 2017, 107, 83−92. (16) Mao, S.; Zhang, D.; Li, Y.; Liu, N. An improved model for calculating CO2 solubility in aqueous NaCl solutions and the application to CO2-H2O-NaCl fluid inclusions. Chem. Geol. 2013, 347, 43−58. (17) Mao, S.; Hu, J.; Zhang, Y.; Lü, M. A predictive model for the PVTx properties of CO2-H2O-NaCl fluid mixture up to high temperature and high pressure. Appl. Geochem. 2015, 54, 54−64. (18) Lloret, J. O.; Vega, L. F.; Llovell, F. A consistent and transferable thermodynamic model to accurately describe CO2 capture with monoethanolamine. J. CO2 Util. 2017, 21, 521−533. (19) Llovell, F.; Vega, L. F. Accurate modeling of supercritical CO2 for sustainable processes: Water + CO2 and CO2 + fatty acid esters mixtures. J. Supercrit. Fluids 2015, 96, 86−95. (20) Xu, X. C.; Lasala, S.; Privat, R.; Jaubert, J. N. E-PPR78: A proper cubic EoS for modelling fluids involved in the design and operation of carbon dioxide capture and storage (CCS) processes. Int. J. Greenhouse Gas Control 2017, 56, 126−154. (21) Xu, X. C.; Privat, R.; Jaubert, J. N.; Lachet, V.; Creton, B. Phase equilibrium of CCS mixtures: Equation of state modeling and Monte Carlo simulation. J. Supercrit. Fluids 2017, 119, 169−202. (22) Li, S. Y.; Qiao, C. Y.; Li, Z. M.; Hui, Y. T. The effect of permeability on supercritical CO2 diffusion coefficient and determination of diffusive tortuosity of porous media under reservoir conditions. J. CO2 Util. 2018, 28, 1−14. (23) Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. An equation of state for associating fluids. Ind. Eng. Chem. Res. 1996, 35, 4310−4318. (24) Mahmoudjanloo, H.; Izadpanah, A. A.; Osfouri, S.; Mohammadi, A. H. Modeling liquid-liquid and vapor-liquid equilibria

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b01736.

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Calculated CO2 solubility in pure water using CPA and PRSV model; calculated water content in CO2-rich gas phase using CPA and PRSV models; calculated CO2 solubility in NaCl aqueous solutions using CPA model (XLSX)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Xiao-Qiang Bian: 0000-0003-4995-8159 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 51404205) and the Program for Innovative Research Team of the Education Department of Sichuan Province, ChinaThe Greenhouse Gas Carbon Dioxide Storage and Resource Utilization (No. 16TD0010).

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REFERENCES

(1) Duan, Z.; Sun, R. An improved model calculating CO2 solubility in pure water and aqueous NaCl solutions from 273 to 533 K and from 0 to 2000 bar. Chem. Geol. 2003, 193, 257−271. (2) Duan, Z.; Møller, N.; Weare, J. H. An equation of state for the CH4−CO2−H2O system: I. Pure systems for 0 to 1000 °C and 0 to 8000 bar. Geochim. Cosmochim. Acta 1992, 56, 2605−2617. (3) Pitzer, K. S. Thermodynamics of electrolytes: I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. 10577

DOI: 10.1021/acs.iecr.9b01736 Ind. Eng. Chem. Res. 2019, 58, 10570−10578

Article

Industrial & Engineering Chemistry Research for the hydrocarbon + N-formylmorpholine system using the CPA equation of state. Chem. Eng. Sci. 2013, 98, 152−159. (25) Follegatti-Romero, L. A.; Oliveira, M. B.; Batista, E. A.C.; Coutinho, J. A.P.; Meirelles, A. J.A. Liquid-liquid equilibria for ethyl esters + ethanol + water systems: Experimental measurements and CPA EoS modeling. Fuel 2012, 96, 327−334. (26) Oliveira, M. B.; Follegatti-Romero, L. A.; Lanza, M.; Batista, F. R.M.; Batista, E. A.C.; Meirelles, A. J.A. Low pressure vapor-liquid equilibria modeling of biodiesel related systems with the Cubic-PlusAssociation (CPA) equation of state. Fuel 2014, 133, 224−231. (27) Oliveira, M. B.; Queimada, A. J.; Kontogeorgis, G. M.; Coutinho, J. A.P. Evaluation of the CO2 behavior in binary mixtures with alkanes, alcohols, acids and esters using the cubic-plusassociation equation of state. J. Supercrit. Fluids 2011, 55, 876−892. (28) Zirrahi, M.; Hassanzadeh, H.; Abedi, J. Prediction of water solubility in petroleum fractions and heavy crudes using cubic-plusassociation equation of state (CPA-EoS). Fuel 2015, 159, 894−899. (29) Zirrahi, M.; Hassanzadeh, H.; Abedi, J. Prediction of CO2 solubility in bitumen using the cubic-plus-association equation of state (CPA-EoS). J. Supercrit. Fluids 2015, 98, 44−49. (30) Keshtkari, S.; Haghbakhsh, R.; Raeissi, S.; Florusse, L.; Peters, C. J. Vapor-liquid equilibria of isopropyl alcohol + propylene at high pressures: Experimental measurement and modeling with the CPA EoS. J. Supercrit. Fluids 2013, 84, 182−189. (31) Tsivintzelis, I.; Kontogeorgis, G. M.; Michelsen, M. L.; Stenby, E. H. Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part II: Binary mixtures with CO2. Fluid Phase Equilib. 2011, 306, 38−56. (32) Bjørner, M. G.; Kontogeorgis, G. M. Modeling derivative properties and binary mixtures with CO2 using the CPA and the quadrupolar CPA equations of state. Fluid Phase Equilib. 2016, 408, 151−169. (33) Muro-Sune, N.; Kontogeorgis, G. M.; Solms, N. V.; Michelsen, M. L. Phase equilibrium modelling for mixtures with acetic acid using an association equation of state. Ind. Eng. Chem. Res. 2008, 47, 5660− 5668. (34) Wong, D. S. H.; Sandler, S. I. A theoretically correct mixing rule for cubic equations of state. AIChE J. 1992, 38, 671−680. (35) Zhao, H.; Lvov, S. N. Phase behavior of the CO2-H2O system at temperatures of 273−623 K and pressures of 0.1−200 MPa using Peng-Robinson-Stryjek-Vera equation of state with a modified WongSandler mixing rule: An extension to the CO2-CH4-H2O system. Fluid Phase Equilib. 2016, 417, 96−108. (36) Huron, M. J.; Vidal, J. New mixing rules in simple equations of state for representing vapour-liquid equlibria of strongly non-ideal mixtures. Fluid Phase Equilib. 1979, 3, 255−271. (37) Guo, H.; Chen, Y.; Hu, Q.; Lu, W.; Ou, W.; Geng, L. Quantitative Raman spectroscopic investigation of geo-fluids highpressure phase equilibria: Part I. Accurate calibration and determination of CO2 solubility in water from 273.15 to 573.15 K and from 10 to 120 MPa. Fluid Phase Equilib. 2014, 382, 70−79. (38) King, M. B.; Mubarak, A.; Kim, J. D.; Bott, T. R. The mutual solubilities of water with supercritical and liquid carbon dioxides. J. Supercrit. Fluids 1992, 5, 296−302. (39) Valtz, A.; Chapoy, A.; Coquelet, C.; Paricaud, P.; Richon, D. Vapour-liquid equilibria in the carbon dioxide-water system, measurement and modelling from 278.2 to 318.2 K. Fluid Phase Equilib. 2004, 226, 333−344. (40) Hou, S. X.; Maitland, G. C.; Trusler, J. M. Measurement and modeling of the phase behavior of the (carbon dioxide+ water) mixture at temperatures from 298.15 to 448.15 K. J. Supercrit. Fluids 2013, 73, 87−96. (41) Gu, F. Solubility of carbon dioxide in aqueous sodium chloride solution under high pressure. J. Chem. Eng. Chin. Univ. 1998, 12, 118−123. (42) Gillespie, P. C.; Wilson, G. M. Vapor-liquid and liquid-liquid equilibria, Water-methane, water-carbon dioxide, water-hydrogen sulphide, water-pentane. GPA Research Report; Gas Processors Association: Tulsa, OK, 1982.

(43) Wiebe, R.; Gaddy, V. L. The solubility of carbon dioxide in water at various temperatures from 12 to 40 and at pressures to 500 atm. Critical phenomena. J. Am. Chem. Soc. 1940, 62, 815−817. (44) Wiebe, R.; Gaddy, V. L. Vapor phase composition of carbon dioxide-water mixtures at various temperatures and at pressures to 700 atm. J. Am. Chem. Soc. 1941, 63, 475−477. (45) Toedheide, K.; Franck, E. U. Two-phase range and the critical curve in the system carbon dioxide-water up to 3500 bar. Z. Phys. Chem. 1963, 37, 387−401. (46) Briones, J. A.; Mullins, J. C.; Thies, M. C.; Kim, B. U. Ternary phase equilibria for acetic acid-water mixtures with supercritical carbon dioxide. Fluid Phase Equilib. 1987, 36, 235−246. (47) D’souza, R.; Patrick, J. R.; Teja, A. S. High pressure phase equilibria in the carbon dioxide-n-Hexadecane and carbon dioxidewater systems. Can. J. Chem. Eng. 1988, 66, 319−323. (48) Liu, Y.; Hou, M.; Yang, G.; Han, B. Solubility of CO2 in aqueous solutions of NaCl, KCl, CaCl2 and their mixed salts at different temperatures and pressures. J. Supercrit. Fluids 2011, 56, 125−129. (49) Bamberger, A.; Sieder, G.; Maurer, G. High-pressure (vapor+ liquid) equilibrium in binary mixtures of (carbon dioxide+ water or acetic acid) at temperatures from 313 to 353 K. J. Supercrit. Fluids 2000, 17, 97−110. (50) Tong, D.; Trusler, J. M.; Vega-Maza, D. Solubility of CO2 in aqueous solutions of CaCl2 or MgCl2 and in a synthetic formation brine at temperatures up to 423 K and pressures up to 40 MPa. J. Chem. Eng. Data 2013, 58, 2116−2124. (51) Prutton, C. F.; Savage, R. L. The solubility of carbon dioxide in calcium chloride-water solutions at 75, 100, 120 and high pressures. J. Am. Chem. Soc. 1945, 67, 1550−1554. (52) Nighswander, J. A.; Kalogerakis, N.; Mehrotra, A. K. Solubilities of carbon dioxide in water and 1 wt.% sodium chloride solution at pressures up to 10 MPa and temperatures from 80 to 200 °C. J. Chem. Eng. Data 1989, 34, 355−360. (53) Takenouchi, S.; Kennedy, G. C. The solubility of carbon dioxide in NaCl solutions at high temperatures and pressures. Am. J. Sci. 1965, 263, 445−454. (54) Malinin, S. D. The system water-carbon dioxide at high temperatures and pressures. Geokhimiya 1959, 3, 292−306. (55) Dohrn, R.; Bü nz, A. P.; Devlieghere, F.; Thelen, D. Experimental measurements of phase equilibria for ternary and quaternary systems of glucose, water, CO2 and ethanol with a novel apparatus. Fluid Phase Equilib. 1993, 83, 149−158. (56) Müller, G.; Bender, E.; Maurer, G. Vapor-liquid-equilibrium in the ternary-system ammonia-carbon dioxide-water at high water contents in the range 373 to 473 K. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 148−160. (57) Bando, S.; Takemura, F.; Nishio, M.; Hihara, E.; Akai, M. Solubility of CO2 in aqueous solutions of NaCl at (30 to 60) °C and (10 to 20) MPa. J. Chem. Eng. Data 2003, 48, 576−579. (58) Yan, W.; Huang, S.; Stenby, E. H. Measurement and modeling of CO2 solubility in NaCl brine and CO2-saturated NaCl brine density. Int. J. Greenhouse Gas Control 2011, 5, 1460−1477. (59) Malinin, S. D.; Savelyeva, N. I. The solubility of CO2 in NaCl and CaCl2 solutions at 25, 50, and 75° under elevated CO2 pressures. Geokhimiya 1972, 6, 643−653. (60) Malinin, S. D.; Kurovskaya, N. A. Solubility of CO2 in chloride solutions at elevated temperatures and CO2 pressures. Geokhimiya 1975, 4, 547−550. (61) Diamond, L. W.; Akinfiev, N. N. Solubility of CO2 in water from − 1.5 to 100 °C and from 0.1 to 100 MPa: evaluation of literature data and thermodynamic modelling. Fluid Phase Equilib. 2003, 208, 265−290.

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