Density Measurement and Modeling of CO2−Brine System at

Article pubs.acs.org/jced

Density Measurement and Modeling of CO2−Brine System at Temperature and Pressure Corresponding to Storage Conditions Yi Zhang,†,∥ Tongtong Li,†,∥ Baixin Chen,*,‡ Masahiro Nishio,§ and Yongchen Song*,† †

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People’s Republic of China ‡ School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom § National Institute of Advanced Industrial Science and Technology, 1-2-1, Namiki, Tsukuba, Ibaraki 305-8564, Japan ABSTRACT: The densities of CO2 solution of the brine from Teikoku Oil Field located at Niigata Prefecture in Japan are measured by a magnetic suspension balance at temperatures from 303.15 to 323.15 K, pressures from 10 to 20 MPa, and CO2 mole fractions of 0, 0.0038, 0.0040, 0.0087, 0.0100, and 0.0160. Results show that the densities of CO2−brine solution increase to 0.86% from that of brine and linearly increases with pressure at a gradient of 0.411 kg·m−3·MPa−1 and with CO2 mole fraction at an average gradient of 514 kg·m−3·mol−1 at a temperature of 303.15 K. On the other hand, the density of CO2−brine solution decreases with increasing temperature at an average rate of −0.377 kg·m−3·K−1 under our experimental conditions. The ePC-PSAFT model is applied to predict the data obtained from this study and those from literature. It is demonstrated that the model works well with average relative deviation (ARD) of 0.27%. A correlation of density ratio of CO2−brine solution to brine is provided and validated by data used in the ePC-PSAFT model, which is convenient for engineering application in comparison with that by the ePC-PSAFT. The ARDs for density ratio predicted by ePC-PSAFT and correlation are 0.075% and 0.019% for this work, respectively. CO 2 −H 2 O solutions at 293 K and 6.44−29.49 MPa corresponding to ocean depths of 500−3000 m. The effect of saline has been investigated by directly measuring the density change of CO2 saline water solution. Data have been reported at temperatures ranging from 353.15 to 473.15 K and pressures up to 10 MPa by Nighswander et al.9 at the NaCl mass fraction of 0.001 and from 333.15 to 413.15 K and at 10 MPa at mass fractions of 0.055−0.189 by Song et al.10 Yan et al.11 measured the saturated CO2−brine density at temperatures of 323, 373, and 413 K and pressures from 5 to 40 MPa. For high-temperature and -pressure states, Schmidt et al.12 measured the PVT properties of CO2−H2O−NaCl solution with the NaCl mass fraction of 0.4 as solvent at temperatures from 623.15 to 973.15 K and pressure from 200 to 400 MPa in a cold-seal pressure vessel, in which it was attempted to simulate the conditions of metamorphic rocks. For CO2 seawater and brine solutions, Li et al.13 reported the data of solubility and density of CO2−Weyburn formation at a temperature of 332.15 K and pressures up to 29 MPa. Song et al.14 measured the density of CO2−seawater solution at low temperatures from 276.15 to 283.15 K and high pressures from 4 to 12 MPa simulating deep ocean conditions. Also, Zhang et al. measured the densities of CO2 solution of brine from Tianjin

1. INTRODUCTION Global warming due to the greenhouse effect has been widely recognized as one of the most significant issues that human beings have to face. Since the utilization of fossil fuels after the Industrial Revolution, manufacturing activities have induced numerous greenhouse gas emissions, in which CO2 is considered as one of the most important anthropogenic greenhouse gases leading to natural disasters. 1−3 CO 2 sequestration as liquid or supercritical phase in saline aquifers or oceans is regarded as a promising technology to reduce the CO2 concentration in the atmosphere.4 The buoyancy due to the density difference between brine and CO2−brine solution caused by CO2 dissolution is the driving force for the fluids flow, which is one of the key properties for prediction of the evolution of CO2 and CO2 solution plumes underground and for the risk assessment of CO2 storage technology.5 Studies have been carried out for both the density measurement and modeling of CO2 aqueous solutions. In early studies with regard to CO2 water solution, Drange and Haugan4 proposed a simple model based on Henry’s modified law,6 for injection of CO2 into shallow water at ocean depths of 200−400 m. Ohsumi et al.7 preliminarily measured the density of liquid CO2−H2O solution at 276.15 K and 34.3 MPa by a vibrating-tube-type densitometer, and demonstrated that CO2 deposit would form a CO2 lake in seawater at the depth of 3000 m. Later on, Teng et al.8 extended measurements of liquid © XXXX American Chemical Society

Received: August 26, 2015 Accepted: January 14, 2016

A

DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 1. Schematic diagram of the experimental system.

Tanggu Reservoir15 and supercritical CO2−Dagang brine solution16 under sequestration conditions in the pressure range from 10 to 18 MPa and at temperatures from 313 to 353 K. The literature, as discussed by Duan et al.,17 show that the available data from the literature are inconsistent, especially for those of CO2−brine solutions; therefore, more data from field brine will benefit both the academics and engineers in CCS studies and designs. Increasing research interest has been found in modeling and predicting the densities of CO2−H2O and CO2−brine solutions. Statistical association fluid theory (SAFT) was applied in the aqueous solution modeling which was proposed by Chapman et al.18 and Huang and Radosz.19 SAFT has been used to evaluate physical, thermodynamic, and transport properties, such as solubility, heat conductivity,20 and viscosity.21 In comparison with the traditional equation of state (EOS), the SAFT model is a more predictive and physically realistic alternative for predicting the properties of CO2 solutions relevant to oil recovery and CO2 sequestration, which takes electrolytes, association sites and polar component, mixing rules, and ionic forces into consideration. SAFT1-RPM (SAFT with restricted primitive model) was presented by Ji et al.22 to predict the density and equilibrium data for the CO2− H2O and CO2−H2O−NaCl systems. PC-SAFT (perturbed chain SAFT) is the modification of SAFT EOS by introducing the perturbation theory, which was applied to the mixture of small spherical molecules and, in principle, is also applicable to the prediction of the densities of CO2 and CO2−alkane systems.23,24 As one of the fundamental physical−chemical properties for CO2 geological storage, comprehensive data on the density of CO2−brine solutions are needed to understand how the CO2− brine solution will behave at temperature and pressure corresponding to the storage conditions. In this work, we first report the new data of densities of brine in the Teikoku Oil Field with the salinity (the mass fraction of NaCl (g) to brine (g)) of 0.008 and its CO2 solution measured at temperatures from 303.15 to 323.15 K and pressures from 10 to 20 MPa with CO2 mole fractions from 0 to 0.0160. We then present an improved ePC-PSAFT model, based on the studies of Gross and Sadowski,24 Ji et al.,22 Cametetti,25 and Diamantonis and Economou26 to predict the density of CO2−brine solutions and

its ratio to that of brine. For convenience in engineering application, a simple version of the correlation of density ratio model27 is modified to predict the data obtained from this study.

2. EXPERIMENTAL APPARATUS AND PERFORMANCE In this study, a magnetic suspension balance (MSB) is applied to measure the density of brine and its solution. The experimental system is schematically shown in Figure 1. The details about the measurement principles and measurement characteristics of the MSB are presented in the previous research of Zhang et al.28 The system resolutions of the measured quantities are 0.01 K for temperature, 10−5 g for mass, and a reproducibility of 0.0008 MPa at 20 MPa for pressure. Density measurements of pure water were used to test the accuracy and reliability of the experimental system. The average relative error was within 0.002% compared with the data from the National Institute of Standards and Technology (NIST) database established by the EOS and presented by Wagner and Pruss29 The experiment is performed as follows. Before the measurement, a leakage test is carried out by injecting highpressure N2 gas into the high-pressure vessel. The sealed measurement vessel is evacuated and equilibrated at the desired temperature. Then, CO2 is injected into the vessel to measure the density of CO2 and calculate its mass. Finally, brine is injected to form CO2−brine solution. In the high-pressure vessel, a circulating pump is used to accelerate the dissolution of CO2, and when the temperature, pressure, and MSB readouts remain stable, it shows that CO2 is totally dissolved into the brine solution. As such, the solution density can be measured with given pressures, temperatures, and CO 2 concentrations. The CO2 mass fraction xm and mole fraction x in the solution can be calculated with xm =

ρCO V0 2

ρsol V

=

ρCO (V − ΔV ) 2

ρsol V

=

ρCO

2

ρsol (1 − ΔV /V )

≈

ρCO

2

ρsol (1)

B

DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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against pressure, at five temperatures in Figure 2 and at six mole fractions at a temperature of 313.5 K in Figure 3. As a liquid, the CO2 brine solution behaves, as shown in Figure 3, the same as that of the brine, shown in Figure 2; the density is linearly proportional to the pressure with an average gradient of 0.418 kg·m−3·MPa−1 for brine and 0.411 kg·m−3· MPa−1 for solutions with all CO2 mole fractions at the temperature of 313.15 K. The same behavior is seen in both with regard to the temperature in that the density is approximately linearly inversely proportional to temperature as shown in Figure 4. However, the absolute value of the gradient of CO2 solution density with respect to temperature under a given pressure (10 MPa) decreases with increasing of the mole fraction from −0.406 kg·m−3·K−1 at a CO2 mole fraction of 0.0160 to −0.319 kg·m−3·K−1 for the brine (zero mole fraction). The repeatability and the resolution of the experimental measurements are checked by setting the measurements with CO2 mole fractions of 0.0038 and 0.0040. As shown in Figure 3 and the data listed in Table 4, the densities under all pressures are distinguished with a density difference of about 0.12 kg·m−3, which verifies the satisfactory repeatability of the experiments. The dissolution of CO2 causes the increase of the density of the CO2−brine solution. From this study, as shown in Figure 5, the relationship between CO2−brine solution density and CO2 mole fraction is nearly linear with an average rate of 514 kg· m−3·mol−1 at the temperature of 303.15 K for all pressures. For temperatures of 313.15 and 323.15 K, the average gradients are 467 and 437 kg·m−3·mol−1, respectively. The gradients decrease as the temperature rises; therefore, the equal density temperature phenomenon may appear at higher temperature according to the study of Lu et al.30

xm MCO2 xm MCO2

+

s(1 − xm) MNaCl

+

(1 − s)(1 − xm) M H2O

(2)

where V0 is the volume of the measuring cell after CO2 is injected and V is the volume after brine is injected. ΔV is the volume change due to the injection of brine, which can be ignored in the calculation.27 ρCO2 is the density of CO2 injected into the measuring cell, and ρsol is the density of the CO2 solution when the CO2 dissolves completely into the brine. s is the salinity of brine, and MCO2, MNaCl, and MH2O are the molar masses of CO2, NaCl, and H2O respectively. The materials used in this study are listed in Table 1. The brine was taken from Teikoku Oil Field at the depth of 1000− Table 1. Details of the Chemicals Used in the Experiment chemicals

mole fraction purity

CAS no.

source

nitrogen

7727-37-9

carbon dioxide deionized water

124-40-3

Dalian Da-te Gas Co., Ltd. Dalian Da-te Gas Co., Ltd. Dalian University of Technology Teikoku Oil Field

7732-18-5

brine a

molecular weight

0.99999

28.01

0.9999

44.01

1−10 μs/cma

18.02

The resistivity of deionized water is from 1 to 10 μs/cm.

1100 m with salinity of 0.008. The basic characteristics of Teikoku Oil Field for CO2 injection are shown in Table 2 and Table 3. Table 2. Characteristics of Teikoku Oil Field injection rate (ton/day)

pressure (MPa)

4. VALIDATION OF DENSITY MODELS The data obtained from this study are used, together with those selected from previous measurements, to test the density prediction models. The ePC-PSAFT model is selected, which has been developed by Gross and Sadowski,24 Ji et al.,22 Cametetti,25 and Diamantonis and Economou26 to calculate both the CO2−brine solution density and the density ratio of CO2−brine solution to brine. Meanwhile, a correlation of density ratio previously proposed by Song et al.27 is corrected and tested as a simple alterative version in comparison to the ePC-PSAFT model. In general, ePC-PSAFT in terms of Helmholtz energy considers the energy contributions from hard sphere, chain, dispersion, association, ion interactions, polar, and induced polar interactions. The residual Helmholtz free energy can also be estimated by the compressibility factor which is used to calculate the density in EOS,23 which was clearly demonstrated in previous studies.31,32

temperature (K)

range

ordinary rate

well head

well bottom

well head

well bottom

10−48

20−40

7−11

19

305.15

321.15

3. RESULTS AND DISCUSSION The experiments were conducted at temperatures from 303.15 to 323.15 K, pressures from 10 to 20 MPa, and CO2 mole fractions from 0 to 0.0160 to cover most of the storage conditions in the experimental field, where CO2 storage was implemented in the selected reservoir in Teikoku Oil Field at a depth of approximately 1100 m. Analysis of Experimental Densities of CO2−Brine Solution. The measured densities of brine and the densities of CO2−brine solutions are listed in the Table 4 and plotted Table 3. Brine Composition of Teikoku Oil Field composition +

Na K+ Ca2+ Mg2+ Al3+ Mn2+

concentration (mg·L−1)

composition 2+

1699.7 250.4 399.2 17.8 0.1 0.6

Sr Ba2+ Cl− SO42− HCO3− SiO2 C

concentration (mg·L−1) 1.2 0.6 3418.7 74.0 494.0 109.0 DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Density Data of Brine (Mole Fraction x = 0) and CO2−Brine Solution (Mole Fraction x > 0)a T/K

p/MPa

303.11 303.15 303.13 303.14 303.16 303.15 303.12 303.13 303.14 308.15 308.12 308.12 308.14 308.15 308.13 308.16 308.15 308.14 313.14 313.12 313.13 313.15 313.16

5.022 5.977 7.997 10.044 12.009 14.056 15.993 18.013 19.951 4.885 6.032 7.969 10.071 12.036 14.001 16.075 17.931 19.924 5.049 6.004 7.969 10.153 12.063

303.15 303.14 303.15 303.16 303.12 303.17 313.13 313.14 313.12

10.087 12.106 14.058 16.111 18.029 19.914 10.029 12.024 13.918

303.16 303.14 303.18 303.16

10.019 12.005 14.024 15.942

ρ/(kg·m−3)

T/K

x=0 1005.10 313.12 1005.53 313.13 1006.38 313.14 1007.24 313.16 1008.15 318.12 1008.95 318.15 1009.81 318.16 1010.77 318.14 1011.52 318.16 1003.87 318.17 1004.30 318.12 1005.10 318.15 1006.06 318.16 1006.92 323.14 1007.72 323.16 1008.52 323.17 1009.33 323.13 1010.24 323.15 1002.53 323.14 1002.96 323.13 1003.76 323.14 1004.67 323.12 1005.42 x = 0.0038 1009.43 313.14 1010.13 313.16 1010.97 313.14 1011.71 323.12 1012.64 323.15 1013.34 323.12 1005.93 323.15 1006.65 323.16 1007.52 323.12 x = 0.0040 1009.52 313.15 1010.26 313.14 1011.05 323.12 1011.85 323.18

p/MPa

ρ/(kg·m−3)

T/K

p/MPa

14.083 15.912 17.986 19.951 5.049 6.032 8.024 10.016 11.954 13.919 15.966 17.986 19.896 5.213 6.195 7.997 9.853 12.145 14.110 16.048 18.040 19.814

1006.28 1007.03 1007.94 1008.74 1000.98 1001.51 1002.26 1002.96 1003.87 1004.67 1005.69 1006.38 1007.03 999.00 999.43 1000.18 1000.87 1001.89 1002.74 1003.60 1004.35 1004.99

303.15 303.12 313.17 313.16 313.10

17.928 19.914 10.029 14.019 15.981

303.16 303.16 303.12 303.15 303.14 303.17 313.17 313.16 313.17

9.986 11.971 13.990 15.909 17.995 19.981 9.961 11.990 14.019

15.947 17.976 19.937 10.024 12.082 14.106 15.961 17.952 19.942

1008.31 1009.18 1009.94 1001.82 1002.64 1003.38 1004.20 1004.98 1005.79

303.15 303.14 303.15 303.16 303.14 303.13 313.15 313.14 313.12

10.000 12.039 13.923 15.875 17.962 19.914 9.928 11.957 14.019

303.15 303.15 303.15 303.17 303.14 303.15 313.15 313.14

10.010 12.039 13.957 15.909 17.894 19.947 9.986 11.990

17.942 19.903 9.990 12.015

1009.26 1010.09 1001.97 1002.71

ρ/(kg·m−3) x= 1012.68 1013.47 1006.04 1007.75 1008.43 x= 1011.27 1012.02 1012.90 1013.78 1014.53 1015.36 1007.75 1008.62 1009.34 x= 1012.20 1013.03 1013.69 1014.53 1015.45 1016.29 1008.50 1009.41 1010.36 x= 1015.88 1016.46 1017.25 1018.18 1018.84 1019.58 1012.11 1012.97

T/K 0.0040 323.16 323.17 323.16 323.14 0.0087 313.14 313.15 313.16 323.14 323.15 323.15 323.12 323.14 323.16 0.0100 313.13 313.15 313.15 323.14 323.16 323.17 323.14 323.16 323.15 0.0160 313.12 313.15 313.16 323.16 323.15 323.16 323.12 323.17

p/MPa

ρ/(kg·m−3)

13.971 15.928 17.952 19.976

1003.46 1004.35 1005.13 1005.94

15.981 17.942 19.937 9.990 12.015 14.072 16.029 17.918 19.976

1010.13 1010.96 1011.83 1003.58 1004.36 1005.17 1005.99 1006.88 1007.55

15.981 17.874 19.971 9.990 11.947 13.971 16.063 17.986 19.976

1011.19 1011.95 1012.78 1004.36 1005.25 1005.96 1007.00 1007.74 1008.44

15.981 18.010 19.903 10.058 11.947 13.971 16.029 19.942

1014.56 1015.39 1016.11 1007.76 1008.95 1009.73 1010.51 1011.99

a

Standard uncertainties U are U(T) = 0.01 K, U(p) = 0.002 MPa, and U(x) = 0.0002, and the expanded uncertainties of measured densities are U(ρ) = 0.27 kg·m−3. Confidence level = 95%; k = 2.

ePC-PSAFT contains five parameters for the association component, which are the number of segments in the chain molecule, m; the chain segment diameter, σ; the energy dispersion interactions between segments, ε/k; the association energy between site A in component i and site B in component j, εAiBj/k; and the volume of the association interactions between site A in component i and site B in component j, kAiBj. In this study, as suggested by previous studies,10,25 CO2 is regarded as a molecule without consideration of association effect but with the effect of quadrupole, and H2O is modeled as a molecule with four association sites and dipole effect. kAB is optimized by the experimental density data33 of pure water according to the research of Diamantonis and Economou.26 The details of each parameter in solution are listed in Table 5.26 To determine the interaction of chain segment diameter and energy dispersion between different segments, the conventional combining rules are applied in this work. Figure 2. Density of brine (salinity = 0.008) as a function of pressure. Temperatures of the experiment: □, 303.15 K; ▲, 308.15 K; ○, 313.15 K; ■, 318.15 K; △, 323.15 K.

σij = D

1 (σi + σj) 2

(3) DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 5. Densities of CO2−brine solution as a function of CO2 mole fraction (temperature = 303.15 K). Experimental pressures: □, 12 MPa; ▲, 14 MPa; ○, 16 MPa; ■, 18 MPa; △, 20 MPa.

Figure 3. Densities of CO2−brine solution as a function of pressure (temperature = 313.15 K). Mole fractions of CO2: □, 0; ○, 0.0038; △, 0.0040; ■, 0.0087; ●, 0.0100; ▲, 0.0160.

εij = (εi + εj)1/2 (1 − kij)

where k13, k23, and k34 stand for the binary interaction parameters of Na+−H2O, Cl−−H2O, and CO2−H2O, respectively, T is the temperature of CO2−H2O−NaCl solution (K). To apply the aforementioned model to predict the CO2− brine solution density, the CO2−brine solution, which may contain other components but is represented by an overall salinity, in this work, is converted to CO2−H2O−NaCl solution, in which the salinity of solution was represented by the mole fraction of NaCl as

(4)

where i and j = 1, 2, 3, 4 stand for Na+, Cl−, H2O, and CO2 respectively. For the CO2−H2O−NaCl mixture, the binary interactions between CO2−Na+ and Cl−−Na+ are considered to be negligibly weak and those of Cl−−H2O and Na+−H2O are equal. The binary interaction parameters for Na+−H2O (Cl−− H2O) and CO2−H2O are optimized in this study by the previous experimental density data10 of the NaCl−H2O system and CO2−H2O solution from 333.15 to 413.15 K. The obtained interaction parameters as a function of temperature are

x NaCl =

s(1 − xm) MNaCl xm MCO2

+

s(1 − xm) MNaCl

+

(1 − s)(1 − xm) M H2O

(6)

where xNaCl is the mole fraction of NaCl and xm is the mass fraction of CO2, s is the overall salinity of brine, and MCO2, MNaCl, and MH2O are the molar masses of CO2, NaCl, and H2O, respectively. The measured density data of CO2−brine solution from this study are predicted by the ePC-PSAFT model discussed previously. To further validate the model, the experimental data

k13 = k 23 = − 24.9562 + 0.2056T − 0.0005T 2 + 5.5789 × 10−7T 3 − 8.7153 × 10−11T 4 k 34 = − 6948.3119 − 55.0485T + 0.1015T 2 − 6.3902T 3 − 1.2078 × 107 /T + 8.7508 × 105/T 0.5 + 5.2102 × 108/T 2

(5)

Figure 4. Densities of CO2−brine solution as a function of temperature: a, experimental pressure at 10 MPa; b, experimental pressure at 20 MPa. Mole fractions of CO2: □, 0; ○, 0.0038; △, 0.0040; ■, 0.0087; ●, 0.0100; ▲, 0.0160. E

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Table 5. Parameters for CO2−H2O−NaCl of ePC-PSAFT Equations of State Used in This Work component a

H2O (4C and dipole ) CO2 (quadrupolec) Na+ Cl−

m

σ (Å)

ε/k (K)

εAB/k (K)

kAB

2.815 1.912 1 1

2.037 2.854 1.6262 3.5991

150.71 157.97 119.8060 359.6604

1575.20

(a0 + a1T + a2T2 + a3T3)b

For H2O, μ = 1.85 D, σp = 3.093 Å, and α = 1.49 Å. ba0 = 4.5384, a1 = −0.0423, a2 = 0.0001, and a3 = −1.2051 × 10−7. cFor CO2, Q = 4.3D Å and σp = 2.974 Å.

a

In engineering applications and modeling coding, a density ratio, the ratio of the density of the CO2−brine solution to that of brine, is more convenient and widely applied to calculate the density changes and buoyancy driving the movement of CO2− brine solution in a geoformation. The data listed in Table 4 are recalculated as the density ratio, as illustrated in Figure 7 and Figure 8. It seems that the

in previous literature are calculated, which are listed in Table 6. The average relative deviation (ARD) between the modeling Table 6. Average Relative Deviation, ARD (%),a for Density of the CO2−H2O−NaCl Solutions from Literature Predicted by ePC-PSAFT literature

T/K

p/MPa

ARD/%

this work Li et al.13 Yan et al.11 Zhang et al.16 Song et al.10

303.15−323.15 332.15 323−413 313−353 333.15−413.15

10−20 0.45−29 5−40 10−18 10−18

0.27 0.69 0.21 0.03 0.19

ARD/% = ∑Ni ((|ρcal − ρexp|)/ρexp) × (100/N), where N is the number of data points, ρcal is the density calculated by the ePC-PSAFT model (kg·m−3), and ρexp is the experimental density in this work (kg· m−3). a

results and data is used to assess the capability of the model. It is found that ARD of densities between the modeling results and our data in CO2−brine solution is 0.27%. The ARD of model and data reported by Li et al.13 is relatively larger (0.69%), which may be due to the measurement system errors as discussed by Duan et al.17 For all other data sets, the predictive ARDs are all less than 0.21%. Therefore, it may deduce that the ePC-PSAFT model has decent predictability in CO2−brine solution over a certain range of temperature and pressure. The details of the results of modeling predictions and the data can be found from Figure 6 for reference.

Figure 7. Density ratio as a function of temperature calculated by experimental data of CO2−brine solution (CO2 mole fraction = 0.0040). Experimental pressures: ■, 10 MPa; ○, 14 MPa; ▲, 16 MPa; ▽, 18 MPa; ☆, 20 MPa.

Figure 6. Calculation results of CO2−H2O−NaCl densities by ePCPSAFT from this work and literature: dashed line, calculated by ePCPSAFT. Scatter points are experimental data: ▲, Li et al.13▼, Yan et al.11 ●, Song et al.10 ■, Zhang et al.16 □, this work (303.15 K); ○, this work (313.15 K); ◇, this work (323.15 K).

Figure 8. Density ratio as a function of CO2 mole fraction. The lines show the density ratio results under different temperatures by eqs 7 and (8): dashed line, 303.15 K; dotted line, 313.15 K; dashed−dotted line, 323.15 K. Symbols ●, ■, and ▲ stand for data under 303.15, 313.15, and 323.15 K, respectively. F

DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 7. Parameters of Density Ratio Correlations in Equations 7 and 8

a

parameter

correlationa

b0 b1 b2 b3 c0 c1

1 8.12659 − 0.0246T −880.93453 + 2.7462T 31562.0465 − 96.11T 633.755 + 2.65T − 4.7285 × 10−3T2 −1695.3 + 2.15T − 0.10257T2 + 2.1686 × 10−4T3 − 1.7182 × 10−7T4

T = the experimental temperature (K).

Table 8. Average Relative Deviation, ARD (%),a for Density Ratio of the CO2−Brine Solutions from Literature Predicted by the ePC-PSAFT Model and Density Ratio Correlation

behavior of CO2 solution can be demonstrated rather explicitly in terms of the density ratio. For instance, the ratio decreases almost linearly with the temperature increase and becomes more independent of pressure. In terms of mole fraction, the ratio increases nonlinearly with more CO2 dissolved (larger CO2 mole fraction). In the CO2−brine solution, as temperature increases, the density ratio (the ratio of density of CO2−brine solution to that of brine) decreasingly approaches 1. As such, it is reasonable to estimate that the density of CO2−brine solution could be smaller than that of brine as a further increase in temperature. The temperature at the turning point, with density ratio of 1, is referred to as equal density temperature for CO2 and its solution system. The density ratio smaller than 1, may occur in the reservoirs with temperature higher than the equal density temperature, which means that the CO2−brine solution would move upward, rather than sink, driven by the negative buoyancy, which would provide an additional factor to enhance the leakage of stored CO2.30 It is straightforward to calculate the density ratio by the ePCPSAFT model, for which the brine density can be calculated by setting the CO2 mole fraction to zero. The correlations developed by using data are simple, in general, in comparison with that of the ePC-PSAFT model, for engineering applications. A simple version of correlations of density ratio and the brine density27 is modified by using the data listed in Table 4, which are ρs ρw

= b0 + b1x + b2x 2 + b3x 3

ρw = c0 + c1p

literature

T/K

p/MPa

ARD/%b

ARD/%c

this work Li et al.13 Zhang et al.16 Song et al.10

303.15−323.15 332.15 313−353 333.15−413.15

10−20 0.45−29 10−18 10−18

0.075 0.071 0.057 0.097

0.019 0.086 0.093 0.471

a ARD/% = ∑Ni ((|ρcal − ρexp|)/ρexp) × (100/N), where N is the number of data points, ρcal is the density calculated by the ePC-PSAFT model (kg·m−3), and ρexp is the experimental density in this work (kg· m−3). bCalculated by the ePC-PSAFT model. cCalculated by density ratio correlation.a

5. CONCLUSIONS The densities of the CO2−brine solution are measured at temperatures from 303.15 to 323.15 K and pressures from 10 to 20 MPa with CO2 mole fractions up to 0.0160. The ePC-PSAFT model is improved by resetting the binary interaction parameters (kij) and validated by the data from this study and literature in terms of the average relative deviation (ARD). The ARD between the modeling predictions and data from this work is 0.27%, and those from literature are less than 0.21% except from that of Li et al.13 The data from this study are analyzed in terms of the density ratio of the CO2−brine solution to that of brine, which shows that the density ratio describes the physical behavior of CO2− brine solution in a straightforward manner. Based on the analysis, a correlation of density ratio is proposed and validated, along with the ePC-PSAFT model by the data from literature. It is found that both work well in the point of view of engineering applications. In this work, the average relative deviation calculated by ePC-PSAFT (0.075%) is relatively larger than that by the density ratio correlation (0.019%). However, the ePC-PASFT model is better than the correlation in terms of predictive ability for other literature data.

(7) (8)

where ρs is the density of the CO2−brine solution (kg·m−3), ρw the density of brine (kg·m−3), x the CO2 mole fraction, and p the pressure (MPa). The parameters of the correlations are listed in Table 7, and the fitting results are shown in Figure 8. Both the ePC-PSAFT model and the correlation proposed in this study are validated by the data from this study and available data from literature in terms of ARD, as listed in Table 8. Compared with the data of this study, the ARD of the modeling density ratio by the ePC-PSAFT model is 0.075% and the ARD by the correlation is 0.019%. Applying both to calculate the density ratio from literature, the ARDs of the ePCPSAFT model is less than 0.097%, while that of density ratio model is relatively higher (less than 0.471%). Obviously, the better prediction of correlation to the data from this study in comparison with that from the ePC-PSAFT model is because the correlation was established by the data curve fitting, while, to the data from other literature, the ePC-PSAFT model has better predictive ability than that of the correlation, which demonstrated the weakness of the correlation.

■

AUTHOR INFORMATION

Corresponding Authors

*(B.C.) E-mail: [email protected]. *(Y.S.) E-mail: [email protected]. Author Contributions

∥ Y.Z. and T.L. contributed equally to this work and should be regarded as co-first authors.

Funding

The study is supported by National Natural Science Foundation of China (51576031), Fundamental Research Funds for the Central Universities (DUT15LAB22), and the RSE-NSFC Joint Project (443570/NNS/INT). G

DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Notes

(20) Kiselev, S. B.; Ely, J. F.; Abdulagatov, I. M.; Huber, M. L. Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols. Ind. Eng. Chem. Res. 2005, 44, 6916−6927. (21) Quinones-Cisneros, S. E.; Zeberg-Mikkelsen, C. K.; Stenby, E. H. The friction theory (f-theory) for viscosity modeling. Fluid Phase Equilib. 2000, 169, 249−276. (22) Ji, X.; Tan, S. P.; Adidharma, H.; Radosz, M. SAFT1-RPM Approximation Extended to Phase Equilibria and Densities of CO2H2O and CO2-H2O-NaCl Systems. Ind. Eng. Chem. Res. 2005, 44, 8419−8427. (23) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41, 5510−5515. (24) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244−1260. (25) Cameretti, L. F.; Sadowski, G.; Mollerup, J. M. Modeling of Aqueous Electrolyte Solutions with Perturbed-Chain Statistical Associated Fluid Theory. Ind. Eng. Chem. Res. 2005, 44, 3355−3362. (26) Diamantonis, N. I.; Economou, I. G. Modeling the phase equilibria of a H2O−CO2 mixture with PC-SAFT and tPC-PSAFT equations of state. Mol. Phys. 2012, 110, 1205−1212. (27) Song, Y.; Chen, B.; Shen, S. Density and state function of CO2 salt water in underground conditon. J. Therm. Sci. Technol. (Tokyo, Jpn.) 2003, 2, 358−364. (28) Zhang, Y.; Liu, Z.; Liu, W.; Zhao, J.; Yang, M.; Liu, Y.; Wang, D.; Song, Y. Measurement and Modeling of the Densities for CO2+ Dodecane System from 313.55 to 353.55 K and Pressures up to 18 MPa. J. Chem. Eng. Data 2014, 59, 3668−3676. (29) Wagner, W.; Pruss, A. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 2002, 31, 387. (30) Lu, C.; Han, W. S.; Lee, S. Y.; Mcpherson, B. J.; Lichtner, P. C. Effects of density and mutual solubility of a CO2−brine system on CO2 storage in geological formations: “warm” vs. “cold” formations. Adv. Water Resour. 2009, 32, 1685−1702. (31) Aungier, R. H. A fast, accurate real gas equation of state for fluid dynamic analysis applications. J. Fluids Eng. 1995, 117, 277−281. (32) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The properties of gases and liquids. McGraw-Hill: New York, NY, USA, 2001. (33) Olivella, S.; Carrera, J.; Gens, A.; Alonso, E. E. Nonisothermal multiphase flow of brine and gas through saline media. Transp. Porous Media 1994, 15, 271−293.

The authors declare no competing financial interest.

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DOI: 10.1021/acs.jced.5b00719 J. Chem. Eng. Data XXXX, XXX, XXX−XXX