Solubility of Methane and Carbon Dioxide in the Aqueous Phase of

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Solubility of Methane and Carbon Dioxide in the Aqueous Phase of the Ternary (Methane + Carbon Dioxide + Water) Mixture: Experimental Measurements and Molecular Dynamics Simulations Panagiotis Kastanidis,† Vasileios K. Michalis,‡ George E. Romanos,† Athanassios K. Stubos,§ Ioannis G. Economou,*,‡ and Ioannis N. Tsimpanogiannis*,§ †

Institute of Nanoscience and Nanotechnology, and §Environmental Research Laboratory, National Center for Scientific Research “Demokritos”, Aghia Paraskevi Attikis, 15310, Greece ‡ Chemical Engineering Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar S Supporting Information *

ABSTRACT: New experimental measurements (at 10 MPa and 323.15 K) and molecular dynamics (MD) simulations (at 10 MPa and 323.15 K, 50 MPa and 344.25 K, and 50 MPa and 375.5 K) are reported in order to measure/predict the aqueous solubilities of the ternary methane−carbon dioxide−water system under two-phase (vapor−liquid) equilibrium conditions. The TIP4P/ice, TraPPE-UA, and OPLS-UA force fields for water, carbon dioxide, and methane, respectively, are used, according to the modifications introduced in the recent study by Michalis et al. (Phys. Chem. Chem. Phys., 2016, 18, 23538−23548) for the binary methane−carbon dioxide hydrate. The MD calculated values for the solubility are in good agreement with the newly available experimental measurements. The molecular dynamics simulations clearly indicate that the solubility of each gas decreases by the addition of the other gas. The particular conclusion is in excellent agreement with the conclusion obtained from the new experimental measurements reported in the current study, as well as the analysis of previously reported experimental measurements. The new experimental solubility measurements are found to be in very good agreement with the limited available experimental data in the literature for the ternary mixture.

1. INTRODUCTION The ternary methane−carbon dioxide−water system is encountered in a number of applications of significant industrial interest. They include energy-related applications such as oil/ gas production during enhanced oil recovery,1 and flow assurance (i.e., gas hydrate formation control) during oil/gas production and transportation within pipelines2 or environmentally related applications associated with carbon capture and sequestration.3−5 In all the aforementioned cases it is essential to be able to describe accurately the phase behavior of the ternary system in order to proceed with the design of the required processes involved. Despite the significant importance of the particular system, only a very limited number of experimental studies have been reported in the open literature that examine the solubility of the carbon dioxide and methane in the water-rich phase of the ternary system at vapor−liquid equilibrium (VLE) conditions. In particular, Dhima et al.6 reported experimental solubilities for the system at 344.25 K and pressure range 10 to 100 MPa. Qin et al.7 reported VLE experimental measurements for three different gas-mixture compositions and temperatures from 324 up to 375 K and pressures in the range of 10 to 50 MPa. Al Ghafri et al.8 examined the carbon dioxide and methane mixture with equimolar composition and reported extensive © XXXX American Chemical Society

VLE experimental measurements for temperatures in the range 323.15 to 423.15 K and for pressures up to 20 MPa. In addition, they reported VLLE experimental measurements for temperatures in the range 285.15 to 303.5 K and pressures up to the upper critical end point (UCEP). A second group of experimental studies involved those measuring aqueous solubilities, however, focusing primarily at three-phase equilibrium conditions. Namely, such studies consider phase equilibrium in the presence of solid hydrates. Bruusgaard et al.9 reported experimental solubility measurements, for the particular ternary system. In addition to VLE conditions, they also measured solubilities under three-phase hydrate equilibrium conditions (hydrate−liquid−vapor; HLwV) for pressures lower than 4.1 MPa. Belandria et al.10 reported three-phase equilibrium conditions and the corresponding aqueous solubility calculations for a number of initial gas mixture compositions and temperatures from 273.6 up to 285.5 K and pressures in the range of 1.51 to 7.19 MPa. Bi et al.11 Special Issue: In Honor of Cor Peters Received: August 31, 2017 Accepted: March 12, 2018

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DOI: 10.1021/acs.jced.7b00777 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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ternary system methane−carbon dioxide−water by combining experimental and computational approaches at conditions where hydrates are not forming. To this purpose (i) initially we reevaluate reported experimental measurements, (ii) subsequently we report a limited number of new experimental measurements, and (iii) finally we report novel MD simulations with the purpose to further extend the comparison between the MD-calculated solubilities and experimental measurements at additional pressure and temperature conditions. No further optimization of the force field parameters is performed in the current study, since one of the objectives is to examine the parameters reported in ref 21 at a number of different conditions. The current paper is organized as follows: initially, the experimental methodology and the current measurements, along with the discussion of the previous experimental measurements are presented. Next, details of the MD methodology used are presented, including the preparation of structures and implemented force fields. Then, the results are presented and discussed, and finally, the conclusions are summarized.

reported compositional measurements at the upper quadruple point. Eslamimanesh et al.12 presented and discussed a thermodynamic consistency test for the reported solubility experimental data for the methane−carbon dioxide−water hydrate system. It should be noted that in the absence of experimental data molecular dynamics (MD) simulations13,14 have often been used as an alternative approach to obtain thermodynamic properties. The ternary system of interest was considered by simulation studies including those by Miguez et al.15 who discussed phase equilibria properties, and Miguez et al.16 who examined the interfacial behavior of the ternary system. Earlier MD studies have shown that both water−water and water−guest interactions are essential for the accuracy of predictions of the three-phase (HLwV) equilibrium conditions of pure gas hydrates. In particular, in a series of studies using the direct phase coexistence methodology,17 it has been shown18−21 that it is advantageous to use the TIP4P/ice water force field,22 mainly because the good performance at predicting the melting temperature of ice23 is also reflected in the prediction of the hydrate equilibrium conditions. Furthermore, regarding the water−guest interactions, it has been shown that the ability of the guest force field to provide accurate predictions of the guest solubility in the liquid waterrich phase is of critical importance to the three-phase (HLwV) equilibrium conditions. When the OPLS-UA24 model is used for the case of methane, it is found that the calculated solubilities at hydrate forming conditions are quite accurate.25 On the other hand, for the case of carbon dioxide, it has been found that when the TraPPE-UA model26 is used, a modification in the water−carbon dioxide energy crossinteraction parameter between the oxygens of unlike molecules was necessary in order to correct the predicted solubility of carbon dioxide in water. Such a modification further results in the improvement of the predictions of the three-phase equilibrium conditions of the hydrate system.21 Subsequently, Michalis et al.27 considered the case of mixed methane−carbon dioxide hydrate and reported calculations: (i) for three-phase (HLwV) equilibrium conditions, and (ii) for guest solubilities in the aqueous phase. They reported comparison of the MD results with the experimental measurement of the solubilities in the aqueous phase of the VLE ternary system (methane−carbon dioxide−water) at 10 MPa and 323.15 K of Al Ghafri et al.8 In particular, Michalis et al.27 reported the dependence of carbon dioxide and methane solubilities on methane mole fraction in the gas-rich phase (methane−carbon dioxide). The agreement for the particular temperature and pressure was found to be satisfactory, as was also the agreement with the aqueous solubilities given by the models of Sun and Duan28 and Duan et al.29 for the case of the binary systems (methane−water, and carbon dioxide−water, respectively). This computational study concluded that the combination of these particular force fields can predict correctly the solubilities of both gases in the aqueous phase close to the hydrate equilibrium conditions. Furthermore, the solubility of each gas decreases by the addition of the other gas, a conclusion which was however in disagreement with the main conclusion reported in the experimental studies by Qin et al.,7 and Al Ghafri et al.,8 namely, that carbon dioxide and methane become more soluble in the presence of methane and carbon dioxide, respectively. The main objective of the current study is to provide additional insight into the aqueous solubility behavior of the

2. EXPERIMENTAL SECTION 2.1. Analysis of Literature Experimental Data. compare the solubility of methane and carbon dioxide in liquid aqueous phase in the ternary system with that in binary system, Qin et al.7 defined an apparent Henry’s constant, H*, as follows: H * = Pyi /xi

To the the law (1)

where the subscript i denotes methane or carbon dioxide, y denotes the mole fraction in the vapor phase, and x denotes the gas solubility in the liquid aqueous phase (mole fraction). This apparent constant represents the distribution of a gas between the vapor phase and liquid phase. According to Qin et al.,7 a larger apparent Henry’s law constant represents a smaller solubility of the gas in the liquid. Subsequently, Qin et al. proceeded to plot the apparent Henry’s law constants as a function of the ratio: nCO2/(nCO2 + nCH4), where n denotes the total number of moles in the experimental cell. They observed that an increase of the ratio carbon dioxide to methane in the system results in an appreciable increase in the Henry’s law constant of carbon dioxide. Therefore, the higher the methane amount is in the system, the lower the Henry’s law constant is. Essentially, as the amount of methane increases, carbon dioxide becomes more soluble in the aqueous phase. Similarly, an increase of the ratio carbon dioxide to methane in the system results in a substantial decrease in the Henry’s law constant of methane. Following a similar pattern, as the amount of carbon dioxide increases, methane becomes more soluble in the aqueous phase. A similar approach was followed by Al Ghafri et al.8 in order to analyze their experimental solubility measurements for the particular ternary system considering an equimolar gas mixture. The authors plotted, however, the apparent Henry’s law constant as a function of the gas phase mole fractions. It should be noted that they observed that the presence of carbon dioxide enhances the solubility of methane; however, the effect was found to be “quite small”. Michalis et al.27 used MD simulation in order to calculate gas solubilities in the aqueous phase. Specifically, they reported the dependence of carbon dioxide and methane solubilities in the B



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Figure 1. Experimental carbon dioxide solubility in the aqueous phase for the ternary system methane−carbon dioxide−water plotted as a function of the methane mole fraction in the gas phase and for three temperatures: (a) 324.50 K,7 (b) 344.25 K,6 and (c) 375.50 K.7 Solid lines are guides to the eye only.

aqueous phase on methane mole fraction in the gas-rich phase (methane−carbon dioxide). From the particular plot it becomes evident that the solubility of each gas in water decreases by the addition of the other gas. More specifically, the mole fraction of carbon dioxide in water for a ternary methane−carbon dioxide−water system can vary between 0 and 0.0204. The former value corresponds to the case of methane−water system, while the latter to the carbon dioxide− water system (i.e., cases of binary mixtures). Similarly, for methane mole fraction the corresponding range is 0−0.0014. This is a conclusion in disagreement with the main conclusion reported in the experimental studies by Qin et al.,7 and Al Ghafri et al.8 To further explore the issue we used reported experimental measurements from different studies and plotted the experimental data in a similar mode as the plot given in Michalis et al.27 In particular, we used the experimental data from Dhima et al.6 for the temperature 344.25 K and from Qin et al.7 for the temperatures 324.5 and 375.5 K. Figure 1 shows the resulting plots for the case of carbon dioxide solubilities. From Figure 1, we can reach a conclusion that is similar to the one reported by Michalis et al.27 (i.e., that the solubility of each gas decreases by the addition of the other gas). A similar conclusion is also reached if the aqueous methane solubilities are used. 2.2. New Experimental Measurements. 2.2.1. High Pressure Experimental Apparatus. In a recent study30 a novel experimental apparatus was designed, built, and validated with the purpose of measuring hydrate equilibria and performing quantitative analysis of the liquid phase at equilibrium conditions. The particular apparatus was used here for solubility measurements. While the detailed description of the experimental apparatus can be found in Kastanidis et al.,30 a brief description is presented below for the sake of completeness. In particular, the apparatus (a schematic shown in Figure 2) consists of a high pressure PVT cell (Parr autoclave constructed from Alloy 20) with a gas and a liquid sampling branch, enclosed in a thermostated air cabinet, along with electronics and monitoring equipment. The gas sampling branch consists of a sample loop between two valves, while the liquid sample branch consists of a similar sampling loop and an adjacently placed pressure relief cell, where the liquid sample is flashed and left to expand. Both sampling branches are connected to a gas chromatograph (GC) through a three-way valve for the analysis of the gas mixture composition. A temperature control sleeve is firmly mounted around the PVT cell and is connected

Figure 2. Schematic diagram of the high pressure PVT experimental cell and the gas preparation manifold. The top part of the diagram shows all the equipment located at the constant-temperature air bath, while the bottom part shows all the equipment of the gas-mixture preparation manifold. A modification adapted from ref 30.

to a temperature control system. The PVT cell is fed by the gas preparation manifold. A gas mixture of the desired composition is prepared in the primary vessel and compressed to the PVT cell by a gas booster. The sampling branches, the PVT cell, the GC branch, as well as the primary vessel are connected to a high vacuum turbomolecular pump assisted by a rotary pump so that they can be evacuated when necessary. 2.2.2. Gas Chromatograph. For the case of experiments with binary gas mixtures the use of a GC is necessary, so that the composition of gas mixtures could be accurately measured. In particular, GC analysis was performed for the following three cases: (i) During the preparation of the initial gas mixture that is fed to the PVT cell, the composition of the gas mixture in the preparation manifold was obtained. (ii) The final gas phase composition (i.e., after full equilibration is attained) was also obtained through GC analysis. (iii) A liquid sample that was obtained after full equilibration was attained was expanded in the pressure relief cell and the resulting gas phase is analyzed with GC. C



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The first and second cases were facilitated through the gas sample branch, while the third case through the liquid sample branch. To this purpose, a SRI 8610c GC apparatus was used, connected via serial bus on a computer running the PeakSimple software (developed by SRI Instruments) that is used to operate the GC apparatus.31 The “sample in” line of the GC’s gas sampling loop is connected to the experimental apparatus directly after the gas and liquid sample branches, through a three-way valve, so the selection between the sample branches toward the GC or toward high vacuum can be made. The “sample out” line of the GC’s gas sampling loop is either exposed to atmosphere or high vacuum via another three-way valve. Hence, the sampling at atmospheric pressure or under vacuum is possible. The GC runs are performed using the low sensitivity mode of the thermal conductivity detector (TCD). The gas sample was analyzed by flashing the sample through the GC, until the sample pressure was equal to atmospheric. In such a way the GC results are pressure independent. The results were obtained in molar gas percentage form. The liquid sample was obtained by expansion of the vapor phase from the pressure relief cell to the GC loop, which is under high vacuum. The resulting pressure is often lower than atmospheric pressure. The GC results are obtained in partial gas pressures form. For the GC results to be precise, a calibration of the GC had to be performed. Several gas mixtures of different constitutions were prepared and measurements were made through both the sample loops. Two different operation files were created, one for each sample branch. The prepared gas mixtures consisted of methane, carbon dioxide, and nitrogen, in different concentrations extending from large to low concentration for each specific gas. The calibration was carried out using the PeakSimple software and verified by calculation performed separately. 2.2.3. Fluid Properties. For the current experiments, the water was deionized to a resistivity of 18 MΩ cm, by an “inhouse” reverse osmosis device. Furthermore, the water was degassed under high vacuum for a substantial amount of time. The methane used by the current experiments was supplied by Messer−Greisheim with a minimum listed purity of 99.95 vol % and the impurities included oxygen, nitrogen, hydrogen, carbon monoxide, carbon dioxide, and water. The carbon dioxide was supplied by SOL with a minimum listed purity of 99.998 vol %. Values for purities are those reported by the supplier, and no further purification was carried out for all chemicals. The purities are reported at 20 MPa and 288.15 K (see also Table S1 of the Supporting Information). On the basis of the reported purities it is estimated that the minimum mole fraction of methane and carbon dioxide in the supply gases are 0.999467 and 0.999983, respectively. 2.2.4. Two-Phase (Lw−V) Equilibrium Measurements. For every experimental run considered, the gas preparation manifold was filled with methane and carbon dioxide in the desired concentration ratio, and the binary gas mixture composition was verified through GC analysis performed through the gas sampling branch of the device. Then, the PVT cell was cleaned with ethanol and subsequently with deionized water. This procedure was repeated for a number of times and the cell was subsequently dried with compressed air. After the cleaning step was completed, the cell was filled with approximately 200 mL of water, attached on the apparatus and subjected to high vacuum. Then the binary gas mixture was

inserted up to a pressure value that is slightly higher (i.e., 0.2 MPa higher than the 10 MPa target value) than the desired pressure and the temperature control system was set to the desired temperature. The fluid mixture was then left to equilibrate for at least 48 h, so that a uniform composition can be obtained. During this step, the temperature was stabilized and the pressure was decreasing as the binary gas mixture keeps dissolving into the liquid water, until the solubility limit was reached which is indicated by reaching a constant pressure value. Then additional gas was injected, and the procedure is repeated until the fluid mixture has equilibrated at the desired temperature. The thermocouples have a measurement precision of δT= ±0.1 °C, while the pressure transducers have an accuracy that is equal to 0.1% of the scale. In particular, the cell pressure transducer has a range of 0−20 MPa, and therefore the accuracy is ±0.02 MPa. In a similar manner, the press relief cell transducer has a range of 0− 2 MPa, and therefore the accuracy is ±0.002 MPa. 2.2.5. Quantitative Analysis of the Liquid Phase. Kastanidis et al.30 described in detail the procedure that was followed in order to measure the guest gas solubility in water. Kastanidis et al.30 performed experiments using pure, hydrate-forming, gas− water systems. For experiments performed with a binary gas mixture, the solubility calculation method is similar to the necessary modifications, however, to account for the binary gas mixture. The required modifications to account for binary gas mixtures have also been discussed in the recent study by Kastanidis et al.32 Further details are reported in the Supporting Information for completeness.

3. MOLECULAR DYNAMICS SIMULATIONS 3.1. Methodology. For the determination of the two-phase aqueous solubility of the ternary system the direct phase coexistence method was used.17 In this methodology, we allow the two different phases to coexist in our simulation box, namely a liquid water phase and a gas-rich phase. MD simulations were carried out in the isobaric−isothermal ensemble (NPT) at different temperatures and pressures. The initial two-phase configuration consists of a liquid water slab which is in contact with the mixed gas-rich phase, resulting in a two-slab configuration ordered as water−gas (WG). The gas-rich phase consists of a mixture containing methane and carbon dioxide. Initially, water and methane−carbon dioxide slabs are constructed with their tangential dimensions equal. After equilibration of each slab, the two slabs are connected with a 0.1 nm buffer distance, followed by energy minimization to avoid overlaps, while keeping the oxygen positions frozen. The solubilities were calculated with MD at the following pressure and temperature conditions: (i) 323.15 K and 10 MPa, (ii) 344.25 K and 50 MPa, and (iii) 375.50 K and 50 MPa. Different initial gas mixture compositions were examined for each set of conditions. It should be noted that the initial feed composition of the methane−carbon dioxide mixture does not correspond to the equilibrium gas-rich phase composition due to the different solubilities of the two species in the aqueous phase and primarily due to the strong adsorption of the carbon dioxide molecules on the water interface, so that the initial load is always significantly different from the equilibrium composition. The strong adsorption of carbon dioxide on the water interface has been previously reported in various studies.33,34 In the current study we used the rigid, nonpolarizable models TIP4P/ice,22 OPLS-UA,24 and TraPPE26 in order to describe water, methane and carbon dioxide, respectively. Table 1 shows D



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Table 1. Force Field Parametersa for TIP4P/Ice (Water),22 OPLS-UA (Methane),24 and TraPPE (Carbon Dioxide)26 force field TIP4P/ice (water)

OPLS-UA (methane) TraPPE (carbon dioxide)

atom

σ (Å)

ε/kB (K)

q (e)

O H M CH4 C O

3.1668 0.0 0.0 3.73 2.800 3.050

106.1 0.0 0.0 148 27.0 79.0

0.0 0.5897 −1.1794 0.0 0.700 −0.350

geometry dOH (Å) ∠H−O−H dOM (Å)

0.9572 104.5 0.1577

dCO (Å) ∠O−C−O

1.16 180

a The distance between atoms A and B is denoted dAB. The angle, in degrees, formed at a central atom B separating two A atoms is denoted ∠A−B− A. The Lennard-Jones parameters are denoted σ (size parameter) and ε/kB (energy parameter), with kB being the Boltzmann constant. The charge is denoted q.

Figure 3. Initial (top) and final (bottom) snapshots for the MD simulations. Water and gas mixture molecules are located at the left side and right side of the simulation box, respectively. Light blue spheres denote methane molecules and dark blue spheres denote the carbon atom of the carbon dioxide molecules

dimensions were kept fixed and equal to 2.4 nm. In all cases, the pressure component normal to the interface calculated through the virial theorem was exactly the same as the reference pressure. The leapfrog integration algorithm was employed with a time step of 2 fs and periodic boundary conditions were applied in all directions. The LJ potential was truncated at 11 Å without employing any dispersion corrections as the system is anisotropic and inhomogeneous. The long-range Coulombic interactions were handled with the Particle Mesh Ewald (PME) method.39 The solubilities were calculated with a 2 ns blockaveraging scheme over a 200 ns long trajectory. Figure 3 shows two different snapshots that depict the initial (Figure 3a) and the final (Figure 3b) states of an MD simulation run at 344.25 K and 50 MPa. The methodology described above has been successfully applied in a series of previous works20,21,27 where the solubility in the aqueous phase of methane and carbon dioxide, as well as their mixture is correctly predicted at the three-phase hydrate equilibrium conditions. Without further parametrization, we applied this methodology in this work beyond hydrate forming conditions for comparison. Given that a 1.1 nm cutoff is a medium-sized distance, for a limited number of cases a 1.5 nm cutoff was also used, and additionally, all the simulations at 50 MPa have been repeated using the PME method for the LJ interactions as well (using GROMACS version 2016.4) to evaluate the effect of these parameters in the calculations.

the values for the parameters for these models. The OPLS-UA methane model is essentially identical to the TraPPE methane model. The Lennard−Jones (LJ) cross-interaction parameters were calculated using the Lorentz−Berthelot13 combining rules, with the following exception. As in our previous work,21 the cross interaction energy parameter between the oxygen of the water and the oxygens of the carbon dioxide was modified by a factor of χ = 1.08, according to the equation: εO(CO2) − O(H2O) = χ εO(CO2)εO(H 2O)

(2)

where εO(CO2) and εO(H2O) are the LJ energy parameters for oxygen in carbon dioxide and water, respectively. In the earlier study21 the particular modification was found essential in order to correct the predicted solubility of carbon dioxide in the aqueous phase. Furthermore, it was found that it also corrects the predicted three-phase equilibrium temperature of the pure carbon dioxide hydrate system in the whole range of pressures above the quadruple point up to 500 MPa. A series of simulations was performed at the NPT ensemble using the open-source GROMACS MD simulation package (version 4.6.5).35−37 The water slab contained 1104 molecules while the gas slab contained 400 molecules in total. The Berendsen38 temperature and pressure coupling schemes were employed with time constants of 1 ps. Semianisotropic pressure coupling was used allowing fluctuations only in the direction normal to the interface. The tangential to the interface E



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imental data from Dhima et al.6 at 344.25 K and from Qin et al.7 at 324.5 and 375.5 K that are shown in Figure 1. 4.2. Molecular Simulations. Initially a series of MD simulations were performed at 10 MPa, 323.15 K in order to calculate the aqueous solubilities for binary gas mixtures with methane gas compositions that have a mole fraction that is higher than 0.5. This was essential in order to extend the previous work by Michalis et al.27 who reported solubilities for gas mixtures with methane compositions lower than 0.5. A comparison of the MD-calculated solubilities with the new experimental measurements is shown in Figure 5.

4. RESULTS AND DISCUSSION 4.1. Experimental Measurements. Experiments for the solubility measurement were performed at 10 MPa, 323.15 K and various compositions of the gas mixture. The solubilities of the pure gases in the aqueous phase have been also measured and are presented in Tables S2 and S3 of the Supporting Information for the cases of carbon dioxide and methane, respectively. The new experiments for the aqueous solubilities (expressed as mole fractions) of the pure gases deviate by only 2.8% and 3.6% for carbon dioxide and methane, respectively, from the values calculated with the correlative models of reported experimental data by Duan et al.,29 and Sun and Duan28 for carbon dioxide and methane, respectively. Furthermore, Table S4 of the Supporting Information presents details of the measured values for all cases of gas mixtures considered. Also given are the statistical uncertainties for the measured aqueous solubilities. Figure 4 shows the results obtained from the current experiments for the solubilities of carbon dioxide and methane

Figure 5. Solubilities of carbon dioxide (denoted with squares) and methane (denoted with circles) in the aqueous phase as a function of the methane composition in the gas phase, at 10 MPa and 323.15 K. Comparison of the MD calculated values (empty black symbols are MD simulations by ref 27 and solid black symbols are current simulations) with experimental measurements by the current study. Lines show 2nd degree polynomial fits of the new experimental measurements (solid black line corresponds to carbon dioxide, while dashed black line corresponds to methane). For most cases, the error bars are smaller than the symbol sizes.

Figure 4. Solubilities of carbon dioxide and methane in the aqueous phase as a function of the methane composition in the gas phase, at 10 MPa and 323.15 K. Comparison of the current experiments (denoted with circles) with the experimental measurements by Al Ghafri et al.8 at equimolar gas composition (denoted with triangles). Shown also are the results of the correlation models by Duan et al.,29 and Sun and Duan28 for the respective binary mixtures with water (denoted with triangles). Statistical uncertainties for the solubilities can be found in the Supporting Information. Solid lines show a second degree polynomial fit to the new experimental measurements.

Subsequently, MD simulations were performed at 50 MPa and two different temperatures (344.25 and 375.50 K). The results from the simulations are compared with the experimental measurements that were reported by Dhima et al.6 for the case of 344.35 K, and by Qin et al.7 for the case of 375.50 K. The comparison between the MD simulations and the experimental measurements is shown in Figure 6. An interesting observation should be pointed out. For the aqueous solubility of methane (Figure 6a,b) we observe that as the methane composition in the gas mixture increases, the agreement between the MD simulations and the experimental measurements deteriorates. The reason for this could be attributed to an inherent inadequacy of the methane model which obviously appears not to behave correctly away from the three-phase equilibrium conditions. On the other hand, for the aqueous solubility of carbon dioxide (Figure 6c,d) we observe that as the methane composition in the gas mixture increases, the agreement between the MD simulations and the experimental measurements improves. As pointed out in the Introduction no further optimization of the force field parameters is performed in the current study, since one of

in the aqueous phase, as a function of the methane composition in the gas phase at 10 MPa, 323.15 K. The figure shows a comparison of the current experiments with the experimental measurements by Al Ghafri et al.8 performed at equimolar gas composition. Solid lines show a second degree polynomial-fit of the new experimental measurements. We observe good agreement between the new experiments and the measurements by Al Ghafri et al.8 performed at equimolar gas composition. Shown also are the results of the correlation models by Duan et al.,29 and Sun and Duan28 for the respective binary mixtures with water and good agreement is observed. It should be noted, that the new experimental measurements that are shown in Figure 4 clearly indicate that the solubility of each gas decreases by the addition of the other gas. The particular conclusion is in excellent agreement with the conclusion obtained from the re-examination of the experF



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Figure 6. Solubilities of methane (a,b) and carbon dioxide (c,d) in the aqueous phase as a function of the methane composition in the gas phase, at 50 MPa and two temperatures (344.25 and 375.50 K). Comparison of the MD calculated values with experimental measurements reported by Dhima et al.6 for the case of 344.35 K, and by Qin et al.7 for the case of 375.50 K. Error bars for the case of carbon dioxide are smaller than the symbol sizes. Lines are guides to the eye only.

conditions. In addition, very good agreement was found for the case of the comparison with the results of the experimental data correlation models by Duan et al.,29 for the carbon dioxide− water system, and Sun and Duan28 for the methane−water system. Subsequently, the direct phase coexistence methodology was implemented for the determination of gas solubilities in the aqueous phase of the ternary system methane−carbon dioxide− water at VLE conditions. The calculated solubility of both gas molecules in the aqueous phase was found to be in good agreement with existing and new experimental data. Both the new experimental and the MD studies clearly indicated that the increase of methane in the initial gas mixture results in the reduction of the solubility of carbon dioxide, while, similarly, the addition of carbon dioxide reduces the solubility of methane. In general, the combination of the guest force fields, that were successfully used for the case of the binary hydrate systems in our earlier studies,20,21 was shown to be adequate for the description of the ternary system. This is reflected by the accurate calculation of the gas solubilities in the water-rich phase under VLE conditions. The agreement with the experimental measurements is better close to the threephase equilibrium line of the respective ternary hydrate system. It should be recalled that the parameter optimization was performed by Costandy et al.21 using only one experimental data point for carbon dioxide solubility at 40 MPa and 286 K. Therefore, further improvements could be obtained if additional experimental data are used.

the main objectives here was to examine the parameters reported in ref 21 at a number of different conditions. Apart from calculations carried out with a 1.1 nm cutoff distance for the LJ interactions, in Figure 6 results are also presented where a 1.5 nm cutoff distance has been used (only at the 50% mole fraction), as well as calculations where the PME method has been used for the LJ interactions (for all conditions). It is interesting to point out that the results obtained with the cutoff of 1.1 nm are similar to those of 1.5 nm. At the same time, the PME treatment of LJ interactions appears to affect more the carbon dioxide solubility, and thus it improves the results only when the carbon dioxide content is high while it practically does not affect the results when the methane composition is higher than that of carbon dioxide. It should be noted, however, that new MD simulations that are shown in Figures 5 and 6 clearly indicate that the solubility of each gas decreases by the addition of the other gas. The particular conclusion is in excellent agreement with the conclusion obtained from the new experimental measurements at 10 MPa, 323.15 K, and the conclusions reported by Michalis et al.27

5. CONCLUSIONS A series of experimental measurements at 10 MPa and 323.15 K are performed, using a recently introduced experimental apparatus,30 in order to measure the aqueous solubilities of the ternary methane−carbon dioxide−water system, as well as the binary methane−water and the carbon dioxide−water systems. The new experimental measurements were found to be in very good agreement with the limited available experimental data in the literature for the ternary mixture8 at the particular P and T G



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(11) Bi, Y.; Yang, T.; Guo, K. Determination of the upper-quadruplephase equilibrium region for carbon dioxide and methane mixed gas hydrates. J. Pet. Sci. Eng. 2013, 101, 62−67. (12) Eslamimanesh, A.; Babaee, S.; Mohammadi, A. H.; Javanmardi, J.; Richon, D. Experimental data assessment test for composition of vapor phase in equilibrium with gas hydrate and liquid water for carbon dioxide + methane or nitrogen + water system. Ind. Eng. Chem. Res. 2012, 51, 3819−3825. (13) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications; Academic Press: San Diego, California, USA, 2nd edn, 2002. (14) English, N. J.; MacElroy, J. M. D. Perspectives on molecular simulation of clathrate hydrates: Progress, prospects and challenges. Chem. Eng. Sci. 2015, 121, 133−156. (15) Míguez, J. M.; dos Ramos, M. C.; Pineiro, M. M.; Blas, F. J. An Examination of the Ternary Methane + Carbon Dioxide + Water Phase Diagram using the SAFT-VR Approach. J. Phys. Chem. B 2011, 115, 9604−9617. (16) Míguez, J. M.; Garrido, J. M.; Blas, F. J.; Segura, H.; Mejía, A.; Piñeiro, M. M. Comprehensive characterization of interfacial behavior for the mixture CO2 + H2O + CH4: Comparison between atomistic and coarse grained molecular simulation models and density gradient theory. J. Phys. Chem. C 2014, 118, 24504−24519. (17) Ladd, A. J. C.; Woodcock, L. V. Triple-point coexistence properties of the Lennard-Jones system. Chem. Phys. Lett. 1977, 51, 155−159. (18) Conde, M. M.; Vega, C. Determining the three-phase coexistence line in methane hydrates using computer simulations. J. Chem. Phys. 2010, 133, 064507. (19) Míguez, J. M.; Conde, M. M.; Torré, J.-P.; Blas, F. J.; Piñeiro, M. M.; Vega, C. Molecular dynamics simulation of CO2 hydrates: Prediction of three phase coexistence line. J. Chem. Phys. 2015, 142, 124505. (20) Michalis, V. K.; Costandy, J.; Tsimpanogiannis, I. N.; Stubos, A. K.; Economou, I. G. Prediction of the phase equilibria of methane hydrates using the direct phase coexistence methodology. J. Chem. Phys. 2015, 142, 044501. (21) Costandy, J.; Michalis, V. K.; Tsimpanogiannis, I. N.; Stubos, A. K.; Economou, I. G. The role of intermolecular interactions in the prediction of the phase equilibria of carbon dioxide hydrates. J. Chem. Phys. 2015, 143, 094506. (22) Abascal, J. L. F.; Sanz, E.; García Fernández, R.; Vega, C. A potential model for the study of ices and amorphous water: TIP4P/ Ice. J. Chem. Phys. 2005, 122, 234511. (23) García Fernández, R.; Abascal, J. L. F.; Vega, C. The melting point of ice Ih for common water models calculated from direct coexistence of the solid-liquid interface. J. Chem. Phys. 2006, 124, 144506. (24) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. Optimized Intermolecular Potential Functions for Liquid Hydrocarbons. J. Am. Chem. Soc. 1984, 106, 6638. (25) Docherty, H.; Galindo, A.; Vega, C.; Sanz, E. A potential model for methane in water describing correctly the solubility of the gas and the properties of the methane hydrate. J. Chem. Phys. 2006, 125, 074510. (26) Potoff, J. J.; Siepmann, J. I. Vapor−liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen. AIChE J. 2001, 47, 1676−1682. (27) Michalis, V. K.; Tsimpanogiannis, I. N.; Stubos, A. K.; Economou, I. G. Direct phase coexistence molecular dynamics study of the phase equilibria of the ternary methane− carbon dioxide−water hydrate system. Phys. Chem. Chem. Phys. 2016, 18, 23538−23548. (28) Sun, R.; Duan, Z. An accurate model to predict the thermodynamic stability of methane hydrate and methane solubility in marine environments. Chem. Geol. 2007, 244, 248−262. (29) Duan, Z.; Sun, R.; Zhu, C.; Chou, I.-M. 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.

ASSOCIATED CONTENT

S Supporting Information *

. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00777. Discussion of the qualitative analysis of the liquid phase and Tables with experimental measurements and MDcalculated values for the solubilities (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Ioannis G. Economou: 0000-0002-2409-6831 Ioannis N. Tsimpanogiannis: 0000-0002-3466-1873 Funding

This publication was made possible by NPRP Grant No. 61547-2-632 from the Qatar National Research fund (a member of the Qatar Foundation). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The paper is dedicated to Prof. Cor Peters who has been a great friend, colleague and mentor for more than two decades. The statements made herein are solely the responsibility of the authors. We are grateful to the High Performance Computing Center of Texas A&M University at Qatar for generous resource allocation.

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REFERENCES

(1) Lake, L. W. Enhanced Oil Recovery; Prentice Hall: Old Tappan, NJ, 1989. (2) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press, Taylor & Francis Group: New York, 2008. (3) Eslamimanesh, A.; Mohammadi, A. H.; Richon, D.; Naidoo, P.; Ramjugernath, D. Application of gas hydrate formation in separation processes: A review of experimental studies. J. Chem. Thermodyn. 2012, 46, 62−71. (4) Tomita, S.; Akatsu, S.; Ohmura, R. Experiments and thermodynamic simulations for continuous separation of CO2 from CH4+CO2 gas mixture utilizing hydrate formation. Appl. Energy 2015, 146, 104−110. (5) Wang, F.; Fu, S.; Guo, G.; Jia, Z.-Z.; Luo, S.-J.; Guo, R.-B. Experimental study on hydrate-based CO2 removal from CH4/CO2 mixture. Energy 2016, 104, 76−84. (6) Dhima, A.; De Hemptinne, J.-C.; Jose, J. Solubility of hydrocarbons and CO2 mixtures in water under high pressure. Ind. Eng. Chem. Res. 1999, 38, 3144−3161. (7) Qin, J.; Rosenbauer, R. J.; Duan, Z. Experimental measurements of vapor-liquid equilibria of the H2O + CO2 + CH4 ternary system. J. Chem. Eng. Data 2008, 53, 1246−1249. (8) Al Ghafri, S. Z. S.; Forte, E.; Maitland, G. C.; RodriguezHenríquez, J. J.; Trusler, J. P. M. Experimental and modeling study of the phase behavior of (methane + CO2 + water) mixtures. J. Phys. Chem. B 2014, 118, 14461−14478. (9) Bruusgaard, H.; Beltrán, J. G.; Servio, P. Solubility measurements for the CH4 + CO2 + H2O system under hydrate-liquid-vapor equilibrium. Fluid Phase Equilib. 2010, 296, 106−109. (10) Belandria, V.; Eslamimanesh, A.; Mohammadi, A. H.; Théveneau, P.; Legendre, H.; Richon, D. Compositional analysis and hydrate dissociation conditions measurements for carbon dioxide + methane + water system. Ind. Eng. Chem. Res. 2011, 50, 5783−5794. H



Article

(30) Kastanidis, P.; Romanos, G. E.; Michalis, V. K.; Economou, I. G.; Stubos, A. K.; Tsimpanogiannis, I. N. Development of a novel experimental apparatus for hydrate equilibrium measurements. Fluid Phase Equilib. 2016, 424, 152−161. (31) PeakSimple for Windows Software (accessed November 20, 2014).http://www.sri-instruments-europe.com/en/products/ software/peak-simple.php. (32) Kastanidis, P.; Romanos, G. E.; Economou, I. G.; Stubos, A. K.; Tsimpanogiannis, I. N. Two- and three-phase equilibrium experimental measurements for the ternary CH4 + CO2 + H2O mixture. Fluid Phase Equilib. 2017, 451, 96−105. (33) Lehmkuhler, F.; Paulus, M.; Sternemann, C.; Lietz, D.; Venturini, F.; Gutt, C.; Tolan, M. The Carbon Dioxide-Water Interface at Conditions of Gas Hydrate Formation. J. Am. Chem. Soc. 2009, 131, 585−589. (34) Zhang, H.; Singer, S. J. Analysis of the subcritical carbon dioxide-water interface. J. Phys. Chem. A 2011, 115, 6285−6296. (35) Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701−1718. (36) Hess, B.; Kutzner, C.; Van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable Molecular Simulations. J. Chem. Theory Comput. 2008, 4, 435−447. (37) Pronk, S.; Pall, S.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; Van der Spoel, D.; Hess, B.; Lindahl, E.; Schultz, R. GROMACS 4.5: A high-throughput and highly parallel open source Molecular Simulation toolkit. Bioinformatics 2013, 29, 845−854. (38) Berendsen, H. J. C.; Postma, J. P. M.; Van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984, 81, 3684−3690. (39) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577−8593.

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Solubility of Methane and Carbon Dioxide in the Aqueous Phase of

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