Quantitative Raman Spectroscopic Measurements of CO2 Solubility in

Dec 31, 2015 - In this study, a noninvasive technique, quantitative Raman spectroscopy, was used to investigate the high pressure equilibria of the CO...
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Quantitative Raman Spectroscopic Measurements of CO2 Solubility in NaCl Solution from (273.15 to 473.15) K at p = (10.0, 20.0, 30.0, and 40.0) MPa Huirong Guo,* Yiqi Huang, Ying Chen, and Qian Zhou School of Environmental Studies, China University of Geosciences, Wuhan 430074, China S Supporting Information *

ABSTRACT: The knowledge of high pressure phase behavior of the CO2−H2O−NaCl system in a wide T−P−mNaCl range is of great interest in the injection of CO2 to deep reservoir for storage or enhancement of oil recovery (EOR). The calculation of CO2 solubility in brine is very important to predict the CO2 storage capacity in saline aquifers. However, CO2 solubility data at high salinity and high pressure are limited, and few thermodynamic models can accurately predict CO2 solubility when salinity is higher than 4.5 mol/kg. In this study, a noninvasive technique, quantitative Raman spectroscopy, was used to investigate the high pressure equilibria of the CO2−H2O−NaCl system. A total of 180 solubility data points were obtained for carbon dioxide in (1, 3, and 5) mol/kg NaCl solutions from (273.15 to 473.15) K up to 40 MPa. New parameters were derived to improve the Duan-type solubility model, thus it can be applied in CO2 sequestration and EOR to accurately calculate the solubility of CO2 in NaCl aqueous solution up to 6 mol NaCl/kg H2O from (273 to 473) K, (3 to 60) MPa.

1. INTRODUCTION The ternary system H2O−NaCl−CO2 is one of the most important fluid systems in geochemistry and petrology; the phase equilibrium and PVT properties of this system covering a wide range of temperature, pressure, and salinity are the key information to solve many geological problems.1−3 In geological storage of CO2 in deep saline aquifer and injection of CO2 to deep reservoir to enhance oil recovery, the knowledge of high pressure phase behavior of the CO2−H2O−NaCl system is necessary. A wide T−P−mNaCl range (e.g., temperature from 273 K to 473 K, pressure up to 40 MPa, and mNaCl up to 5 m) of CO2 solubility data is of great interest. Since 1940, over 30 experimental studies have been made on the phase equilibrium of the CO2−H2O−NaCl system; however, CO2 solubility data at high pressure (p > 10 MPa) and high salinity (NaCl molality to 5 mol/kg) are limited (Table 1, Figure 1), and few thermodynamic models are valid for salinity higher than 4.5 mol/kg.4 Raman spectroscopy can be used as a noninvasive technique to investigate high pressure phase equilibria. In our previous work,5 we developed an unsaturated homogenized solution method (UHSM) to accurately calibrate the Raman system for in situ measurments of dissolved gas under high pressure and a wide temperature range, and measured the solubility data of CO2 in water from 273.15 to 573.15 K and from 10 to 120 MPa. The main aim of the present work is to extend the measurements of CO2 solubility in NaCl aqueous solutions. © XXXX American Chemical Society

2. EXPERIMENTAL SECTION The apparatus and the procedures to accurately calibrate the Raman system for in situ measurments of gas solubility have been reported previously in detail.5,6 Compound, formula, source, and purity of all materials used in the experiments are listed in Table 2. NaCl aqueous solutions were gravimetrically prepared. For calibration, homogeneous solution samples with constant CO2 and NaCl concentration (mCO2 and mNaCl, in mol·kg−1) were prepared (Table 3) at high pressure and showed no immiscibility under any temperatures. The concentration of CO2 in solution in the capillary cell (mCO2in mol/kg water) was determined with the following equation: mCO2 = (πr 2LCO2 /Vm,CO2)/[(ρbrine πr 2L brine)(1 − S)] = (LCO2 /Vm,CO2)/[(ρbrine L brine)(1 − S)]

(1)

where r is the radius of the cell which was assumed to be constant; LCO2 is the length of CO2 column measured by a ruler with accuracy of 1.0 mm; Vm,CO2 is the molar volume of CO2; ρbrine is the density of NaCl solution; Lbrine is the length of NaCl Received: July 27, 2015 Accepted: December 22, 2015

A

DOI: 10.1021/acs.jced.5b00651 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. CO2 Solubility Measurements in Aqueous NaCl Solutions at High Pressure authors 1

Schmidt and Bodnar Takenouchi and Kennedy8 Yan et al.9 Koschel et al.10 Rumpf et al.12 Bando et al.13 Ferrentino et al.14 Liu et al.15 Kiepe et al.16 Zhao et al.17 Ellis and Golding18 Malinin and Savelyeva19 Malinin and Kurorskaya20 Drummond21 Cramer22 Gehrig et al.23 Nighswander et al.24 Gu25 Hou et al.26 Carvalho et al.27 a

T (K)

p (MPa)

mNaCl (mol/kg)

Na

548.1−923.15 423.15−723.15 323.2−413.2 323.1−373.1 313.14−433.12 303.15−333.15 313 318.15 313.38−353.07 325.15−423.15 445−607 298.15−358.15 298.15−423.15 293.65−673.15 296.75−511.75 415−783 353.65−473.65 303.15−323.15 323.15−423.15 293.15−353.15

450−3500 10−140 5−40 5−20.2 0.15−9.6 10−20 10−15 2.1−15.8 0.1−10.1 15.0 2.5−21.3 4.8 4.8 3.4−29.3 0.8−6.2 3.0−271.7 2.0−10.2 1.8−5.9 2.8−18.2 1.0−14.29

1.09−11.41 0−4.28 0−5 1−3 0−5.999 0.18−0.56 0.18 1.93−1.98 0.52−4.34 0−6.0 0−2.822 0−5.09 0−7.081 0−6.48 0−1.95 1.09−4.28 0−0.18 0.5−2.0 2.5, 4.0 0−2

42 123 54 14 76 36 2 8 64 18 54 37 36 506 20 64 67 60 36 44

Number of experimental data points.

liquid system was maintained, and the formation of gas hydrates should be avoided); (4) decrease pressure to 40 MPa (or other lower pressures to be studied); parts of CO2 were exsoluted from the solution and CO2 liquid drops (or bubbles) were generated in the long column of NaCl solution; (5) adjust temperature and/or pressure and wait for about 30 min to make sure the CO2 liquid drops and nearby solution are in equilibrium (equilibrium can be reached fast in the small section of water column with a length less than 0.4 mm in between CO2 bubbles; since the diffusion path is very short, usually no concentration difference at various distances in the whole water column can be detected some minutes after the adjusting temperature or pressure), then collect Raman spectra of CO2-saturated solution between small CO2 bubbles (about 0.020 mm away from the edge of bubble, Figure 2) with a JY/ Horiba LabRam HR800 system equipped with a frequency doubled Nd:YAG laser. During the Raman spectroscopic study, the temperature of the samples in the high-pressure cell was maintained by a heating−cooling stage and measured by a K-type thermocouple. The accuracy of the temperature control is ±0.1 K from 273 to 373 K, and 0.3 K from 373 to 473 K. The pressure in the cell was maintained by water in the line and adjusted by pressure generator, and read from a Setra 204D digital pressure transducer (69 MPa full scale; accurate to ±0.14%) with Datum 2000 manometer.

Figure 1. p−T region covered by the data of CO2 in pure water (△) and NaCl solution (■), T = (273 to 473) K, p = (5 to 60) MPa.

Table 2. Source and Purities of the Compounds Used in This Work compound

formula

source

purity

carbon dioxide water

CO2

Air Product

0.9999a

H2O

DDI (18.24 MΩ·cm)

sodium chloride

NaCl

From Millipore water filtering system Shanghai Shanpu Chemical Co.

a

0.9995a

Mass percentage purity declared by the manufacturer.

3. RESULTS AND DISCUSSION 3.1. Effects of Temperature, Salinity, Pressure, And Concentration on Hr/mCO2. Raman spectra were collected for homogeneous solution samples from 273.15 to 473.15 K at elevated pressures to establish the relationship between CO2 concentration and Raman peak height ratio (Hr) of the vu at 1385 cm−1 of CO2 Fermi dyad to the OH stretching band at 3400 cm−1 of water. The Raman peak height ratio (Hr) is directly proportional to the concentration (mCO2) of aqueous CO2,5 and also depends on temperature T and salinity S.

solution column measured by a with a screw micrometer (0.01 mm accuracy); S is the salinity in weight percent. For solubility measurements, CO2 saturated NaCl solutions were prepared: (1) First, load a column (∼1.5 cm long) of NaCl solutions to the closed end of the capillary cell; (2) evacuate the line once and introduce CO2 into the cell; (3) diffuse CO2 into the NaCl solution under ∼50 MPa at 274 K for 2 days, until the total CO2 concentration in the solution is close to the saturated concentration (a metastable of liquid− B

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Table 3. Parameters of Samples at Initial State after Being Loaded and Sealed with Mercury in the Capillary Tube, and the Calculated CO2 Concentration in the NaCl Solution after Homogenization at High Pressurea no.

mNaCl (mol/kg)

P (MPa)

T (K)

LCO2 (mm)

Lbrine (mm)

Vm,CO2b (cm3/mol)

ρbrinec (g/cm3)

mCO2 (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.0 1.0 1.0 1.0 1.0 3.0 3.0 3.0 3.0 3.0 5.0 5.0 5.0 5.0 5.0

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

293.05 292.35 294.55 292.85 289.85 293.45 290.15 290.15 288.75 289.05 290.55 291.65 292.05 291.55 293.35

147.2 106.0 133.0 61.4 185.0 123.8 100.7 82.9 74.3 136.3 73.8 107.0 104.6 138.2 92.0

9.267 9.788 9.339 9.969 9.033 10.058 10.257 9.633 11.842 9.634 11.635 8.957 10.830 10.698 11.540

24232.56 24171.71 24359.58 24215.20 23964.19 24264.81 23988.99 23988.99 23867.39 23895.12 24022.07 24113.01 24146.08 24104.74 24256.54

1.0379 1.0381 1.0375 1.0380 1.0389 1.1078 1.1093 1.1093 1.1099 1.1097 1.1701 1.1695 1.1693 1.1696 1.1687

0.6697 0.4576 0.5975 0.2598 0.8724 0.5382 0.4337 0.3802 0.2784 0.6271 0.2917 0.5475 0.4421 0.5922 0.3635

a

Standard uncertainties u are u(mNaCl) = 0.01 mol/kg, u(T) = 0.1 K, u(p) = 0.001 MPa, u(LCO2) = 0.5 mm, u(Lbrine) = 0.01 mm, u(Vm,CO2) = 0.001, u(ρbrine) = 0.0010 g/cm3. The relative uncertainty of calculated mCO2 with eq 1 is ur(mCO2) = 0.57%. bVm,CO2 was calculated with the model of Duan et al.28 cρbrine was calculated with the model of Duan et al.28

Figure 3. Dependence of Hr0 on temperature (T) and salinity (S) for CO2 homogeneous solutions with different mCO2 at various pressures: (◆) 1 m NaCl solution, 30 MPa, 0.2598 mol/kg CO2; (■) 1 m NaCl solution, 15 MPa, 0.4576 mol/kg CO2; (▲) 1 m NaCl solution, 15 MPa, 0.5975 mol/kg CO2; (●) 1 m NaCl solution, 30 MPa, 0.6697 mol/kg CO2; (◇) 3 m NaCl solution, 10 MPa, 0.2784 mol/kg CO2; (□) 3 m NaCl solution, 30 MPa, 0.3802 mol/kg CO2; (△) 3 m NaCl solution, 30 MPa, 0.4337 mol/kg CO2; (○) 3 m NaCl solution, 30 MPa, 0.5382 mol/kg CO2; (+) 3 m NaCl solution, 40 MPa, 0.6271 mol/kg CO2; (long filled rectangle) 5 m NaCl solution, 10 MPa, 0.2917 mol/kg CO2; (short filled rectangle) 5 m NaCl solution, 30 MPa, 0.3635 mol/kg CO2; (×) 5 m NaCl solution, 30 MPa, 0.4421 mol/kg CO2; (bold ×) 5 m NaCl solution, 30 MPa, 0.5475 mol/kg CO2; (bold +) 5 m NaCl solution, 40 MPa, 0.5922 mol/kg CO2.

Figure 2. Schematic diagrams showing preparation for CO 2 unsaturated solutions initially at 0.1 MPa (a) and later homogenized at high pressure (b), and CO2 saturated solutions (c) for quantitative Raman spectroscopic study.

However, at constant S and T, the ratios of Hr to mCO2 (Hr/ mCO2) do not change with concentration mCO2 and pressure (Figure 3). Therefore, the relationship between Hr/mCO2 and temperature T (in K) could be fitted regardless of pressure. We obtained the temperature-dependent standard peak height ratio Hr0 at standard molality (1.0 mCO2) at each salinity condition:

where

1 m NaCl: Hr 0 = −0.020473(T /T0)2 + 0.033024(T /T0) + 0.09053

2

(R = 0.97)

Hr 0 = Hr /mCO2 ·mCO2 0

(2a)

where mCO2 = 1.0 mol/kg is reference concentration, T0 = 273.15 K is the reference temperature. The Hr0 in these formulas was used to determine solubility of CO2 (mCO2s) in NaCl solutions from the Raman peak height ratio Hrs of CO2 saturated NaCl solution:

3 m NaCl: Hr 0 = −0.008804(T /T0)2 + 0.0072958(T /T0) + 0.09280

(R2 = 0.99)

(2b)

5 m NaCl: Hr 0 = − 0.00025815(T /T0)2 − 0.0099017 (T /T0) + 0.09028

(R2 = 0.99)

(2d)

0

mCO2 s = (Hr s/Hr 0) ·mCO2 0

(2c) C

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Table 4. CO2 Solubility (mCO2) in NaCl Solutions Determined by Raman Spectroscopya mNaCl = 1.0 mol/kg

mNaCl = 3.0 mol/kg

mNaCl = 5.0 mol/kg

p (MPa)

T (K)

mCO2 (mol/kg)

U(mCO2) (mol/kg)

mCO2 (mol/kg)

U(mCO2) (mol/kg)

mCO2 (mol/kg)

U(mCO2) (mol/kg)

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 40 40

273.15 278.15 283.15 288.15 293.15 298.15 313.15 333.15 353.15 373.15 393.15 413.15 433.15 453.15 473.15 273.15 278.15 283.15 288.15 293.15 298.15 313.15 333.15 353.15 373.15 393.15 413.15 433.15 453.15 473.15 273.15 278.15 283.15 288.15 293.15 298.15 313.15 333.15 353.15 373.15 393.15 413.15 433.15 453.15 473.15 273.15 278.15 283.15 288.15 293.15 298.15 313.15 333.15 353.15 373.15 393.15 413.15 433.15 453.15

1.465 1.405 1.334 1.267 1.208 1.162 1.024 0.854 0.740 0.658 0.613 0.592 0.569 0.551 0.547 1.604 1.509 1.422 1.347 1.270 1.223 1.102 1.009 0.948 0.937 0.926 0.935 0.952 0.990 1.029 1.672 1.588 1.503 1.422 1.364 1.313 1.189 1.107 1.084 1.075 1.105 1.160 1.230 1.304 1.385 1.755 1.659 1.569 1.492 1.429 1.394 1.270 1.190 1.165 1.177 1.228 1.313 1.425 1.540

0.018 0.019 0.017 0.018 0.017 0.016 0.016 0.012 0.011 0.008 0.011 0.010 0.008 0.007 0.009 0.022 0.021 0.018 0.025 0.017 0.016 0.015 0.015 0.014 0.013 0.017 0.014 0.013 0.013 0.016 0.020 0.022 0.018 0.020 0.018 0.017 0.016 0.016 0.015 0.014 0.018 0.017 0.016 0.017 0.022 0.021 0.023 0.019 0.021 0.018 0.018 0.018 0.017 0.016 0.015 0.021 0.019 0.019 0.020

1.007 0.953 0.912 0.876 0.842 0.795 0.702 0.597 0.517 0.467 0.433 0.417 0.400 0.401 0.402 1.089 1.042 0.990 0.955 0.885 0.852 0.768 0.723 0.695 0.681 0.671 0.682 0.683 0.693 0.722 1.167 1.110 1.058 1.019 0.982 0.944 0.843 0.805 0.781 0.764 0.786 0.805 0.846 0.896 0.945 1.181 1.115 1.068 1.023 0.996 0.969 0.920 0.862 0.852 0.821 0.867 0.905 0.966 1.038

0.012 0.011 0.012 0.010 0.011 0.012 0.009 0.007 0.007 0.007 0.007 0.007 0.005 0.006 0.009 0.013 0.012 0.014 0.011 0.011 0.013 0.010 0.010 0.009 0.009 0.009 0.009 0.009 0.010 0.009 0.014 0.014 0.013 0.012 0.012 0.013 0.011 0.012 0.010 0.011 0.010 0.010 0.011 0.011 0.016 0.014 0.013 0.013 0.012 0.013 0.015 0.011 0.011 0.011 0.010 0.013 0.014 0.011 0.013

0.706 0.669 0.646 0.632 0.618 0.597 0.554 0.491 0.429 0.390 0.368 0.345 0.336 0.330 0.313 0.743 0.718 0.686 0.675 0.652 0.645 0.613 0.571 0.553 0.547 0.533 0.535 0.537 0.541 0.553 0.796 0.767 0.737 0.711 0.700 0.687 0.647 0.626 0.612 0.618 0.633 0.657 0.675 0.701 0.728 0.822 0.801 0.776 0.763 0.743 0.730 0.703 0.679 0.671 0.680 0.709 0.731 0.759 0.806

0.009 0.009 0.008 0.008 0.009 0.009 0.007 0.007 0.006 0.005 0.007 0.005 0.008 0.007 0.006 0.010 0.008 0.008 0.008 0.009 0.010 0.009 0.007 0.008 0.008 0.008 0.011 0.006 0.008 0.006 0.009 0.010 0.009 0.008 0.009 0.009 0.008 0.009 0.008 0.008 0.009 0.009 0.008 0.009 0.009 0.010 0.010 0.010 0.010 0.009 0.010 0.009 0.011 0.008 0.010 0.009 0.010 0.009 0.011

D

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Table 4. continued mNaCl = 1.0 mol/kg

mNaCl = 3.0 mol/kg

mNaCl = 5.0 mol/kg

p (MPa)

T (K)

mCO2 (mol/kg)

U(mCO2) (mol/kg)

mCO2 (mol/kg)

U(mCO2) (mol/kg)

mCO2 (mol/kg)

U(mCO2) (mol/kg)

40

473.15

1.691

0.026

1.122

0.022

0.852

0.010

a

Standard uncertainties u are u(T) = 0.1 K for 273 K < T < 373 K, u(T) = 0.3 K for 373 K < T < 473 K, u(p) = 0.097 MPa for p < 60 MPa, u(mNaCl = 0.01 mol/kg), and the combined expanded uncertainties U(mCO2) at 95% confidence were calculated with U(mCO2) = 1.96 u(mCO2), where the combined standard uncertainties u(mCO2) were estimated from all input uncertainties, such as the uncertainty of phase-equilibrium determination, the uncertainty of the measurements of Raman peak height ratio, the uncertainty of fitting calibration equations, and the uncertainties of determination of LCO2, Lbrine, Vm,CO2, ρbrine, and S in the calibration procedure, see the text for details.

3.2. Determination of CO 2 Solubility in NaCl Solutions. CO2 solubility in 1, 3, and 5 m NaCl solutions were measured at temperature from 273 to 473 K and pressure from 10 to 40 MPa. A total of 180 data points were obtained, and the results are listed in Table 4. As it has already been reported in much of the literature,8−27 CO2 solubility decreases with increasing salinity and decreasing pressure. At temperatures below 353 K, CO2 solubility in NaCl solutions increases with decreasing temperature. It is noted that the equilibrium is metastable for the CO2−H2O−NaCl fluid at low-temperature− high-pressure ranges where CO2 gas hydrates could form; the metastable data of CO2 solubility in NaCl solutions measured here are useful in calculating the driving force of the kinetic nucleation of hydrate.7 3.3. Uncertainty of the Obtained Solubility Data. The accuracy of mCO2s at a certain pressure and temperature is mainly affected by the determination of Hr0 and Hrs in eq 2b. Substituting eq 1 in eq 2d, we have

4d are evaluated. The relative uncertainties of the measurement and determination for LCO2, Lbrine, Vm,CO2, ρbrine, and S are 0.5%, 0.05%, 0.1%, 0.1%, and 0.05% respectively (estimated from the accuracy of the measurements of the length of CO2 column and NaCl solution column during the sample preparation, and the accuracy of the calculation of Vm,CO2 and ρbrine with equation of state). The relative uncertainty of Hr is 0.24% (estimated from the standard deviation of measurements of Raman peak high ratio of CO 2 homogeneous aqueous solutions). The uncertainty of phase-equilibrium determination of Hrs (the standard uncertainty u(Hrs)) equals to the standard deviation of Hrs divided by the square root of the number of measurements N at each T−P−mNaCl condition. We then estimated the expanded combined uncertainty U(mCO2) (Table 4) at 95% confidence of the solubility measurement for each T−P−mNaCl condition: U (mCO2) = ku(mCO2 s) = kmCO2 s[u(mCO2 s)/mCO2 s]

mCO2 s = (Hr s/HrmCO2) = (Hr s/Hr)LCO2 /(Vm,CO2ρbrine L brine(1 − S))

where k = 1.96 is the coverage factor at 95% confidence, u(mCO2s) is the combined standard uncertainty, mCO2s is the solubility determined with eq 2b, and u(mCO2s)/mCO2s is the relative uncertainty derived from eq 4d. 3.4. Comparison with Previous Work. We compared the solubility data of CO2 in NaCl solutions in this study with those from some previous experimental investigation and model prediction. Figure 4 shows that our data for 1.0 mol/kg NaCl

(4a)

The natural logarithm of mCO2s can be obtained as ln(mCO2 s) = ln Hr s − ln Hr + ln LCO2 − ln Vm,CO2 − ln ρbrine − ln L brine − ln(1 − S)

(4e)

(4b)

s

The total differential of ln(mCO2 ) can be derived in the following forms: d(mCO2 s)/mCO2 s = d(Hr s)/Hr s − d(Hr )/Hr + d(LCO2)/LCO2 − d(Vm,CO2)/Vm,CO2 − d(ρbrine )/ρbrine − d(L brine)/L brine − d(1 − S)/(1 − S) s

(4c) s

Thus, the relative uncertainty of u(mCO2 )/mCO2 can be written in the forms of the relative uncertainties of measured variables, Hrs, Hr, LCO2, Vm,CO2, ρbrine, Lbrine, and S: [u(mCO2 s)/mCO2 s]2 = [u(Hr s)/Hr s]2 + [u(Hr)/Hr]2 + [u(LCO2)/LCO2]2

Figure 4. Temperature-depended CO2 solubility in 1 mol/kg NaCl solutions (mCO2) measured by quantitative Raman spectroscopy, plotted with previous measurements for comparison: filled symbols, measured in this work at (◆) 10 MPa, (■) 20 MPa, (▲) 30 MPa, (●) 40 MPa. Unfilled symbols, Takenouchi & Kennedy8 at (short rectangle) 10 MPa, (long rectangle) 20 MPa, (×) 30 MPa, (bold ×) 40 MPa. Yan et al.9 at (◇) 10 MPa, (□) 20 MPa, (△) 30 MPa, (○) 40 MPa. Koschelet al.10 at (•) 10 MPa, (large bold ×) 20 MPa.

+ [u(Vm,CO2)/Vm,CO2]2 + [u(ρbrine )/ρbrine ]2 + [u(L brine)/L brine]2 + [u(1 − S)/(1 − S)]2 s

(4d)

s

The relative uncertainty u(mCO2 )/mCO2 of solubility is the square root of the sum of the right-side items, and can be calculated when the relative uncertainties in the right side of eq E

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solutions show good agreement with those determined by Takenouchi and Kennedy,8 Yan et al.,9 and Koschel et al.,10 except that two data points at 40 MPa and one at 30 MPa of Takenouchi and Kennedy8 are about 7% smaller than ours. Data of Yan et al.9 in 5.0 mol/kg NaCl solutions from 323.15 to 413.15 K are generally 2 to 5% smaller than ours (Figure 5),

(average absolute deviation is 2.76% and 2.42% for 1 and 3 mol/kg NaCl solutions, respectively) and by the model Mao et al.4 (average absolute deviation is 2.06% and 1.98% for 1 and 3 mol/kg NaCl solutions, respectively), except for data at the temperatures below 298 K which have about 10% maximum deviations (Figure 6). Noting that extending the models to calculate the solubility above 4.5 mol/kg NaCl was not recommended by authors, we tested two models to 5 mol/kg and found that the average deviations to our data are generally small, for example, 3.27% and 2.68%, respectively. But the deviations are relatively bigger (may reach 7 and 10%, respectively) at temperatures below 348 K for 5 mol/kg NaCl. This is because previously few experimental data at 5 mol/kg NaCl and pressures higher than 10 MPa could be used to fit the parameters of the models. The solubility of CO2 in NaCl aqueous solution is a function of salt concentration, temperature, and pressure. It decreases with increasing salinity, which is the so-called salting out effect. Following Koschel et al.,10 we can calculate the percentage decrease (d in %) of solubility of CO2 in aqueous NaCl solution (m) relative to CO2 solubility in pure water (m0) at the same temperature and pressure:

Figure 5. Temperature-depended CO2 solubility in 5 mol/kg NaCl solutions (mCO2) measured by quantitative Raman spectroscopy, plotted with previous measurements for comparison: filled symbols, measured in this work at (◆) 10 MPa, (■) 20 MPa, (▲) 30 MPa, (●) 40 MPa; Unfilled symbols, Yan et al.9 at (◇) 10 MPa, (□) 20 MPa, (△) 30 MPa, (○) 40 MPa.

d = 100(m0 − m)/m0

(5)

The salting out effect is a function of salt concentration, temperature, and pressure (Figure 7). Our results suggest that there is no noticeable pressure dependence of the salting out effect, which agrees with Koschel et al.10 However, our results clearly show that there is significant temperature dependence of the salting out effect (Figure 7); for constant salt concentration, d increases with decreasing temperature below 353 K, and increases with increasing temperature above 373 K. 3.5. Refining the Parameters of the Thermodynamic Model. There are numerous solubility models that allow

except two data at 20 MPa and 373.15 and 413.15 K are 7 to 11% larger than ours; this probably arises from unpredictable random errors. We did not find experimental data for 3.0 mol/ kg NaCl solution in the literature to make a comparison. The solubility data obtained in this work are consistent with those solubility calculated by the model of Duan and Sun11

Figure 6. CO2 solubility in 1 m (a and b) and 3 m (c and d) NaCl solutions (mCO2) measured by quantitative Raman spectroscopy at (◆) 10 MPa, (■) 20 MPa, (▲) 30 MPa, (●) 40 MPa; plotted with the values calculated from thermodynamic models of Duan et al.11 (lines, a and c) and Mao et al.4 (lines, b and d) for comparison. F

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not be extrapolated to pressures higher than 60 MPa and temperatures higher than 473.15 K. In the near future, we will perform more measurements at high pressure and high temperature, and improve the model accordingly.

4. CONCLUSION CO2 solubility in NaCl solutions at molalities of (1, 3, and 5) mol/kg, temperatures of (273.15 to 473.15) K, and pressures up to 40 MPa were systematically measured with in situ Raman spectroscopy. Significant temperature dependence of the salting out effect was found at different temperatures. The commonly used solubility models were then evaluated, and new parameters were derived for the Duan-type solubility model. This new model can be used to calculate the CO2 solubility from (273 to 473) K, (3 to 60) MPa, and NaCl molalities up to 6 mol/kg, covered almost the entire T−P−mNaCl range likely to be encountered during injection of CO2 to deep reservoir for storage or enhancement of oil recovery.

Figure 7. Percentage decrease (d = 100(1 − m/m0)) of CO2 solubility in NaCl solutions m, related to CO2 solubility in pure water m0, at same temperature and pressure: mNaCl = 1 and (◇) 10 MPa, (□) 20 MPa, (△) 30 MPa, (○) 40 MPa; mNaCl = 3 and (◆) 10 MPa, (■) 20 MPa, (▲) 30 MPa, (●) 40 MPa; mNaCl = 5 and (×) 10 MPa, (long rectangle) 20 MPa, (short rectangle) 30 MPa, (bold ×) 40 MPa.

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APPENDIX A. DUAN-TYPE GAS SOLUBILITY MODEL For CO2 saturated solution, the chemical potential of CO2 in the liquid phase μlCO2 equals to that in the vapor phase μvCO2. The chemical potential can be written in terms of fugacity in the vapor phase and activity in the liquid phase:4,11

calculation of CO2 solubility in aqueous NaCl solution. Among them, the model developed by Duan and Sun11covers a wider P−T range than other models, and becomes the most cited and used in the geological scientific community. Because of the limitation of accurate experimental data at high salinity (e.g., 5 mol/kg NaCl) to fit the model parameters, the commonly used thermodynamic model of Duan and Sun11 and Mao et al.4 for temperatures below 313.15 K substantially deviate from the new measurements, suggesting that new or refined parameters are needed to improve these models. Following the procedures of Duan et al.,11 we refined the parameters (Table 5) of the thermodynamic model (Appendix A) with the solubility data we measured. We compared with 288 experimental data points in the literature from (273 to 473) K, (2 to 60) MPa, and NaCl molalities up to 6 mol/kg (Supplementary S1), and found that 17 data of Ellis and Golding,18 6 data at 423 K for 4.27 m NaCl of Takenouchi and Kennedy,8 11 data of Hou et al.26 and 8 data of Liu et al.15 are (100 to 360%), (17 to 70%), (10 to 13%), and (6 to 8%) systematically lower than the values calculated by the model, respectively. However, 200 of the remainder 245 data (including 10 data of Takenouchi and Kennedy8) have a deviation less than 7%, and the calculations of the model are in good agreement (127/133 of data) with Bando et al.,13Rumpf et al.,12Yan et al.,9 and Zhao et al.17 The model with new parameters seems to be able to accurately calculate the CO2 solubility from (273 to 473) K, (3 to 60) MPa, and NaCl molalities up to 6 mol/kg. However, the current model could

l l(0) (T , P , m) = μCO (T , P) + RT ln aCO2(T , P , m) μCO 2

2

=

l(0) (T , μCO 2

P) + RT ln mCO2

+ RT ln γCO (T , P , m)

(A1)

2

v v(0) μCO (T , P , y) = μCO (T ) + RTfCO (T , P , y) 2

2

=

v(0) μCO (T ) 2

2

+ RT ln yCO P 2

+ RT ln ϕCO (T , P , y)

(A2)

2

where μl(0) CO2 is the standard chemical potential of CO2 in liquid, μv(0) is the standard chemical potential in vapor, yCO2 is the CO2 mole fraction of CO2 in the vapor phase. γCO2 and φCO2 are activity coefficient of CO2 in liquid phase and fugacity coefficient of CO2 in vapor phase, respectively. yCO = (P − PH2O)/P

(A3)

2

Table 5. Interaction Parameters Fitted for Solubility Model parameters c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11

μl(0) CO2/(RT) 2.52671156 −2.99024399 −4.11129437 1.23091891 −4.86804783 9.66527036 −1.43035525 −4.28379454 2.70920374 −1.64011109 −1.24611227

× × × × × × × × × × ×

λCO2−Na 1001 10−02 1003 10−05 1001 10−02 10−02 1000 10−01 10−02 10−04

2.32329297 −5.52304993 −3.21472657 1.82754454 8.16653987 −4.06006390 6.10232321 1.88150995 −2.50830982 2.48768009 1.01658267 G

× × × × × × × × × × ×

ζCO2−Na−Cl 1000 10−03 1002 10−06 1001 10−02 10−03 1000 10−01 10−02 10−04

−1.10067716 2.58535943 1.61555536 −9.67677864 −3.24768654 1.30813929 −1.97407284 −6.02020260 9.35464931 −9.06376267 −3.63798082

× × × × × × × × × × ×

1000 10−03 1002 10−07 1001 10−02 10−03 10−01 10−02 10−03 10−05

DOI: 10.1021/acs.jced.5b00651 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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PH2O is approximated as the saturated pressure of pure H2O. γCO2 is expressed as a virial expansion of excess Gibbs energy: ln γCO = 2

2

+

*E-mail: [email protected]. Tel.: +86 13995565446. Fax: +86 27 87436235.

2

a

Funding

∑ ∑ ξCO − a− cmcma 2

c

This work was partly supported by the National Sciences Foundation of China (No. 41102154, 41472218).

(A4)

a

Notes

where λ and ξ are second-order and third-order interaction parameters, respectively; c and a refer to cation and anion, respectively. At phase equilibrium μlCO2 = μvCO2, and we obtained ln

yCO P 2

mCO2

=

l(0) v(0) (T , P) − μCO (T ) μCO 2

2

RT

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Wanjun Lu and Mr. Lantao Geng for their kind help on the experimental and thermodynamic studies.

− ln ϕCO (T , P , y) 2

+ ln γCO (T , P , m)

and ln

2

mCO2

=

l(0) μCO 2

RT +

− ln ϕCO + 2

∑ 2λCO − cmc 2

c

∑ 2λCO − ama + ∑ ∑ ξCO − a− cmcma 2

a

2

c

a

(A6)

where λ, ξ, and μl(0) CO2/(RT)are T−P depended parameters (v) in the following form: v(T , P) = c1 + c 2T + c3/T + c4T 2 + c5/(630 − T ) + c6P + c 7P ln T + c8P /T + c 9P /(630 − T ) + c10P 2/(630 − T )2 + c11T ln P

(A7)

Equations A6 and A7 form the basis of our model parametrization. Since measurements can only be made in electronically neutral solutions, one of the parameters in eq A6 must be assigned arbitrarily.11 λCO2_Cl is set to zero and then the remaining parameters are fit to the experimental solubility data measured in this study. Approximations were made during the calculation: (1) The fugacity coefficient of CO2 in the CO2−H2O gas mixtures is equal to that of pure CO2 at the same P−T condition, so that ϕCO2 in eq A5 was calculated from the EOS of Duan et al. for pure CO2. (2) The partial pressure of H2O in the CO2−H2O gas mixture is equal to the saturation pressure of pure water. Thus, yCO2 was calculated from eq A3. (3) The standard chemical potential of CO2 in the gas phase, μv(0) CO2, is the hypothetically ideal gas chemical potential when the pressure is equal to 1 bar. The standard chemical potential of CO2 in liquid phase, μl(0) CO2, is the chemical potential in hypothetically ideal solution of unit molality. These approximations will lead to errors (up to 5%) for μl(0) CO2/(RT) and ln γCO2. However, these errors can be canceled to a large extent in the parametrization, and the effect on the calculation of CO2 solubility is negligible.

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REFERENCES

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(A5)

2

yCO P

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Corresponding Author

∑ 2λCO − cmc + ∑ 2λCO − ama c

Article

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00651. Data from the references in spreadsheet form (XLS) H

DOI: 10.1021/acs.jced.5b00651 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

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DOI: 10.1021/acs.jced.5b00651 J. Chem. Eng. Data XXXX, XXX, XXX−XXX