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Phase Equilibria of Water/CO and Water/ n-Alkane Mixtures from Polarizable Models Hao Jiang, Ioannis George Economou, and Athanassios Z. Panagiotopoulos J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b12791 • Publication Date (Web): 20 Jan 2017 Downloaded from http://pubs.acs.org on January 24, 2017

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The Journal of Physical Chemistry

Phase Equilibria of Water/CO2 and Water/n-Alkane Mixtures from Polarizable Models Hao Jiang† , Ioannis G. Economou‡ , and Athanassios Z. Panagiotopoulos†∗ †

Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States

‡

Chemical Engineering Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Abstract Phase equilibria of water/CO2 and water/n-alkane mixtures over a range of temperatures and pressures were obtained from Monte Carlo simulations in the Gibbs ensemble. Three sets of Drude-type polarizable models for water, namely the BK3, GCP, and HBP models, were combined with a polarizable Gaussian charge CO2 (PGC) model to represent the water/CO2 mixture. The HBP water model describes hydrogen bonds between water and CO2 explicitly. All models underestimate CO2 solubility in water if standard combining rules are used for the dispersion interactions between water and CO2 . With the dispersion parameters optimized to phase compositions, the BK3 and GCP models were able to represent the CO2 solubility in water, however, the water composition in CO2 -rich phase is systematically underestimated. Accurate representation of compositions for both water- and CO2 -rich phases cannot be achieved even after optimizing the cross interaction parameters. By contrast, accurate compositions for both water- and CO2 -rich phases were obtained with hydrogen bonding parameters determined from the second virial coefficient for water/CO2 . Phase equilibria of water/n-alkane mixtures were also studied using the HBP water and an exponenial-6 united-atom n-alkanes model. The dispersion interactions between water and n-alkanes were optimized to Henry’s constants of methane and ethane in water. The HBP water and united-atom n-alkane models underestimate water content in the n-alkane-rich phase; this underestimation is likely due to the neglect of electrostatic and induction energies in the united-atom model.

I.

Introduction

CO2 is the most important greenhouse gas leading to global climate change. Sequestration of CO2 in geologic formations is a promising strategy to reduce emissions of CO2 . Underground ∗

Corresponding author. E-mail: [email protected]. Tel:609-258-4591.

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saline formations provide most of the CO2 geologic storage capacity, therefore understanding their thermophysical properties, and phase equilibria in particular, of water/CO2 mixtures over a wide range of temperature and pressure conditions is of great importance to the design of CO2 geologic sequestration processes. Thermodynamic properties of water/CO2 mixtures have been extensively measured, mostly at temperatures lower than 373 K, but important discrepancies remain in the phase equilibrium data at higher temperatures. 1 For phase equilibria at elevated temperatures (> 473 K) and pressures (> 200 bar), which are of particular interest for geochemical applications, there are mainly three sets of experimental measurements from Takenouchi and Kennedy, 2 Todheide and Frank, 3 and Capobianco et al. 4 Although these show consistent results for CO2 solubility in water, the reported equilibrium compositions of the CO2 -rich phase are in disagreement. A comprehensive review of experimental data for the water/CO2 mixture is available. 5 Numerous phenomenological models have been developed for the PVTx properties of the water/CO2 mixture, but most of these correlations were developed for the single-phase bulk fluid; only a few can be used to calculate phase equilibria. Duan et al. proposed a series of important correlations 6–8 to calculate CO2 solubility in water as well as in aqueous NaCl solutions up to 2000 bar. Equations of state have also been developed for the water/CO2 mixture. Models rooted in statistical mechanics, such as statistical associating fluid theory (SAFT) 9–15 and cubic plus association (CPA) equations of state, 16–18 are better suited for description of this system than purely empirical models, because of its highly non-ideal character. Although these equations of state show remarkable accuracy in calculation or prediction of phase equilibria for the water/CO2 mixture, temperature- or pressure-dependent model parameters are required, and these parameters need to be obtained by fitting to mixture experimental data. Molecular modeling and simulation using transferrable molecular models can provide useful information for thermophysical properties of the water/CO2 mixture. In an early Monte Carlo simulation study, Destrignevill et al. 19 calculated excess volumes of the water/CO2 mixture at 773 K and 1073 K in a pressure range of 0.2 to 30 kbar, and it was found that water molecules tend to form clusters in the mixture while the distribution of CO2 molecules is similar to that of ideally diluted CO2 fluid. Tafazzoli and Khanlarkhani 20 conducted Monte Carlo simulation using TIP4P water 21 and EPM2 CO2 22 models to calculate the solvation free energy of water in supercritical CO2 . The reported entropy change due to the solvation of water in CO2 is negative, which is consistent with the conclusion of Destrignevill et al. that water molecules form clusters in the CO2 -rich fluid phase. L˘isal et al. 23 used several non-polarizable water and CO2 models to calculate the Henry’s constant of CO2 in water by Monte Carlo simulations. Although all of the studied models predict a correct temperature dependence of the Henry’s constant, only the Exponential-6 (Exp-6) water and CO2 models 24,25 give values in agreement with experimental data. Vorholz et al. 26 predicted the vapor-liquid equilibrium of the water/CO2 mixture using Monte Carlo simulation in the Gibbs ensemble. With Lorentz-Berthelot combining rule, the TIP4P 21 and SPC 27 water models in conjunction with EPM2 CO2 model give satisfactory representation of CO2 solubility in H2 O for temperature and pressure up to 393 K and 200 bar, respectively. The phase equilibrium of the water/CO2 mixture at elevated temperatures (323 K < T < 523 K) and pressures (P < 1000 bar) was studied by Liu et al. 28 using various non-polarizable 2 ACS Paragon Plus Environment

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water and CO2 models. It was concluded that none of the existing non-polarizable models reproduces adequately experimental data over the entire temperature and pressure range using cross interaction of unlike-pair constructed from the Lorentz-Berthelot combining rule. Since the interaction between water and CO2 is highly non-ideal, satisfactory representation of phase equilibrium for the water/CO2 mixture requires an adequate description of cross interaction. Vlcek 29 optimized the unlike-pair interaction between SPC/E water and EPM2 CO2 models in order to account for the overpolarization of the SPC/E model in CO2 -rich phase. With optimized cross interaction, the predicted phase compositions are greatly improved, however, the water content in CO2 -rich phase at 348 K is still unsatisfactory. In a recent study, Orozco et al. 30 optimized the cross interactions between water and CO2 models to experimental phase equilibrium data over a range of temperatures and pressures. Lennard-Jones potential based fixed-point charge models, such as SPC/E water and TraPPE CO2 models, were found to have significant limitations in representing phase equilibrium for the water/CO2 mixture. The Exp-6 sets of non-polarizable water 24 and CO2 25 models gave accurate calculation of solubilities for both water- and CO2 -rich phases with optimized cross interaction parameters. However, the Exp-6 water model is inaccurate for the structure of liquid water and it gives poor performance with respect to the prediction of thermodynamic properties for the water+NaCl mixture, 31 which is also important to CO2 geological storage and other geochemical applications. Therefore, the success of the Exp-6 models for the water/CO2 mixture should be viewed as a fortuitous cancellation of errors. In addition to phase equilibrium, transport properties of the water/CO2 system have also been studied by molecular simulations. Moultos et al. performed molecular dynamics simulations to calculate diffusion coefficients of water and CO2 in their mixture. 32–34 The predicted diffusion coefficient are insensitive to the cross interactions between water and CO2 . First-principles based simulations were also used to study the water/CO2 mixture. Wheatley and Harvey 35 constructed the potential energy surface for the interaction of water and CO2 using Moller-Plesset perturbation theory and calculated the second virial coefficient for the water/CO2 dimer. The reported second virial coefficient is in good agreement with experimental data. 36 In an important study by Glezakou et al., 37 the structure, dynamics and vibrational spectrum of water clusters in supercritical CO2 fluid were investigated using DFTbased molecular dynamics simulation. It was found that CO2 may form hydrogen bonds with water although such hydrogen bonding interaction is not strong enough to break the water clusters. It was concluded in prior simulation studies 28,30 that none of the existing non-polarizable water and CO2 models can represent fully the phase equilibrium of water/CO2 mixture. The dielectric permittivities of water- and CO2 -rich phases differ significantly, but the non-polarizable models are unable to respond the change of the system electric environment, as they carry a fixed dipole moment. Therefore, the failure of fixed-point-charge models in literature may be attributed to the lack of polarizability. 29,30 However, another important intermolecular interaction that is missing in most of the existing models is the charge transfer or hydrogen bonding interaction between water and CO2 . In the present work, we obtain phase equilibrium of the water/CO2 mixture over a range of temperature and pressure conditions using several polarizable water and CO2 models, by Monte Carlo simulation in the Gibbs ensemble. The main 3 ACS Paragon Plus Environment


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objective of the work is to test the hypothesis that a recently proposed hydrogen bonding polarizable model for water (HBP) can improve on the performance of prior models for aqueous mixtures. We also obtain the Henry’s law constant and phase equilibria of water/n-alkane mixtures using the same model along with prior united-atom hydrocarbon models. The paper is organized as follows: polarizable molecular models used in the present study are briefly described in section II, simulation details and methodology of the Monte Carlo simulations are given in section III. Results for phase equilibria of the water/CO2 and water/n-alkane mixtures are presented in section IV, and the main conclusions are summarized in section V.

II.

Molecular Models

Several classical Drude oscillator based polarizable molecular models were evaluated, namely the BK3, 39 GCP 38 and HBP 40 models for water and the polarizable Gaussian charge model (PGC) for CO2 . 41 The original GCP model uses induced point dipoles to model polarization, but was recently found to be equivalent to a model with Drude oscillators 42 – this latter approach is adopted in the present work. For water, the three polarizable models have TIP4P-like rigid geometry. The PGC CO2 model also has a rigid geometry with polarization modeled by three Drude oscillators. All water and CO2 models studied use Gaussian charges to represent electrostatic interactions, U Coul (rij ) =

1 qi qj erf(αij rij ) 4π0 rij

1 αij = q 2σi2 + 2σj2

(1) (2)

where σi is the width of the charge distribution of Gaussian charge i, and the Buckingham Exp-6 potential was used to represent vdW interactions, 6 U Exp6 (rij ) = Aexp(−Brij ) − C/rij

(3)

where rij is the intermolecular distance between two Exp-6 potential sites, which are the center of oxygen atoms for water and centers of oxygen and carbon atoms for CO2 . The Exp-6 potential is more realistic than the Lennard-Jones 12-6 potential in describing short range repulsions. 39 For the HBP water model, a short-range and orientation-dependent hydrogen bonding term is included to account for the effect of charge transfer during the formation of hydrogen bond, σHB 12 σHB 10 HB U (rij ) = 4HB ( ) −( ) cos(θ)4 (4) rij rij where θ is the angle between the oxygen atom accepting the hydrogen bond, the hydrogen atom and the oxygen atom donating to the hydrogen bond, and rij is the intermolecular distance between oxygen atoms of two hydrogen-bonding molecules. HB and σHB are the energy and


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size parameters of the hydrogen bonding interactions. N -alkanes were represented by the Exp6 united-atom model of Errington and Panagiotopoulos, 43 which use the Exp-6 potential to represent intermolecular vdW interactions and do not include any electrostatic interactions. All models studied in the present work were parameterized to experimental data and the quantum effects on thermophysical properties are included implicitly in the model parameterization. The GCP and HBP models show excellent agreement with experimental data for VLE properties of pure water, the BK3 model also shows good performance for VLE properties of water, with slight overestimation of vapor pressure at high temperatures. The BK3, GCP and HBP models show significantly better performance than non-polarizable models, with a computational cost generally 5-10 times higher than their non-polarizable counterparts, for the BK3 and GCP models. The HBP model uses a single Drude site to handle polarization, and it can be simulated efficiently with extended Lagrangian approach in molecular dynamics simulations, which makes it 2-3 times faster than the BK3 and GCP models. The PGC CO2 model gives accurate representation of many fluid phase properties for CO2 , and its overall performance is better than non-polarizable TraPPE 44 and EPM2 22 models. Further details of the pure component molecular models can be found in the original publications. 38–41,43 When modeling mixtures, a key question is how to determine the unlike-pair interactions. For the highly non-ideal water/CO2 and water/n-alkane mixtures of interest, we chose to use as starting point the Kong combining rule for the Exp-6 type interactions between H2 O, CO2 and alkane sites. In this approach, unlike-pair dispersion interactions, for example those between the oxygen atom of water (1) and the oxygen atom of CO2 (2), are expressed as, A12

− B B+B − B B+B 1 2 1 2 1 2 A2 B2 A1 B1 1 + A2 = A1 2 A2 B2 A1 B1 2B1 B2 B12 = B1 + B2 p C12 = C1 C2

(5) (6) (7)

where Ai , Bi , Ci are the corresponding force field parameters of the Exp-6 potential. Scaling factors will be applied to Eqs. 5-7 to optimize the cross interactions, as shown in section IV. It is worth mentioning that other combining rules, such as Lorentz-Berthelot and geometric rules, can also be used to describe the unlike-pair dispersion interactions. In fact, the unlike-pair interaction parameters obtained from the Lorentz-Berthelot and geometric combining rules are similar to those from the Kong combining rule. It is noted that these commonly used combining rules are empirical and may be inadequate to represent intermolecular interactions of unlike pairs in real systems. 45,46 Poor prediction of phase compositions for mixtures can be caused by the faiure of combining rules, rather than the inadequacy of the molecular models used to describe the pure components. Since the presence of hydrogen bonds between water and CO2 was confirmed by first principles simulations of the water/CO2 mixture 37 , we explicitly modeled the hydrogen bonding interaction between water and CO2 using the hydrogen bonding term (Eq. 4) in the HBP water model. In particular, the hydrogen bonds between water (HBP) and CO2 (PGC) were modeled as interactions between the oxygen and hydrogen atoms of water molecules that donate hydrogen bonds and the oxygen atoms of CO2 molecules that 5 ACS Paragon Plus Environment


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accept hydrogen bonds. The PGC CO2 model does not explicitly have hydrogen bonding interaction, therefore the unlike-pair parameters (σHB and HB in Eq. 4) for the hydrogen bonding interaction between the HBP water and PGC CO2 models cannot be constructed from combining rules, and as discussed in section IV, such parameters were optimized to the second virial coefficient of the water/CO2 dimer.

III.

Simulation Details

Isothermal-isobaric Monte Carlo (MC) simulations in the Gibbs ensemble 47,48 were performed to calculate phase equilibria of the water/CO2 and water/n-alkane mixtures. Since the interactions of polarizable models are not pair-wise additive, a multi-particle move approach was used to efficiently sample phase space, 49 and all molecules were translated or rotated simultaneously in one MC step. The positions of the Drude (r D ) site(s) of molecule i were calculated at each MC step using the following iterative approach, r iD (n) = r iD (n − 1) + F iD /k

(8)

where F iD is the force acting on the Drude particle, and k is the spring constant of the harmonic spring connecting the Drude particle. The calculation was terminated at the nth iteration if the condition max |r iD (n) − r iD (n − 1)| < 10−4 nm

i=1...N

(9)

was satisfied. For simulation of the water and CO2 mixture, the base system size contains 256 water and 256 CO2 molecules. Finite-size effects were tested by doubling the number of molecules at 473 K and 200 bar, and phase compositions obtained were within statistical uncertainties of results obtained from the base system size. For simulations of the water and n-alkanes mixtures, 256 water and 128 n-alkane molecules were used. Finite-size effects were tested by doubling the number of molecules at 523 K and 1000 bar, and negligible finite-size effect was observed when comparing to results obtained from the base system size. The cutoff distance for the Exp-6 potential and real space Coulomb interactions were set to 9 ˚ A for the water-rich phase box and 11 ˚ A for CO2 (10 ˚ A for n-alkane)-rich phase box, respectively. Standard mean-field long-range corrections 50 were applied to the r−6 part of the Exp-6 potential for both phases. The long-range part of the electrostatic interactions was handled by Ewald summation. 51 The system was equilibrated for 1 million steps followed by a production of 5 million steps. The probabilities of performing multi-particle translation, multi-particle rotation, volume change and particle exchange moves were 0.1, 0.1, 0.1, 0.7, respectively. Statistical uncertainties of phase compositions were estimated by dividing the production runs into 5-8 blocks and calculated the standard deviations of the block averages. Further details of simulations can be found in our prior work. 52 All the MC simulations were performed using Cassandra, 53 an open source Monte Carlo software, with in-house modifications to handle polarization, hydrogen-bonding interactions and Gaussian electrostatics. Typical runs for the water/CO2 mixture took about 80-100 hours to complete on 16-core 2.6 GHz Intel Sandybridge processors. 6 ACS Paragon Plus Environment

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Henry’s constants of methane, ethane and propane in water were calculated from the excess chemical potential using the Widom insertion technique. 256 water (HBP) molecules were first equilibrated by Monte Carlo simulations in the isobaric-isothermal ensemble, and a production run of 3 million steps was performed. During the production period, 40000 trial insertions of n-alkane molecule were conducted every 10000 MC steps and the excess chemical potential of n-alkane in water was averaged. For n-butane and n-hexane, the Widom insertion technique was found to be less efficient, and the excess chemical potentials were estimated using molecular dynamics (MD) simulations. In MD simulations, the interactions between n-butane (or n-hexane) and water were scaled by a coupling parameter λ (=[0, 0.05, 0,1, ..., 0.25, 0.3, 0.4, ..., 1.0]). At each λ, 256 water and a single n-butane (or n-hexane) molecules were equilibrated for 1 ns (timestep is 1 fs) in the isobaric-isothermal ensemble followed by a 3 ns production period in the canonical ensemble. The free energy difference between two neighbouring states was estimated using the Bennett’s acceptance ratio method. 54 The temperature of MD simulations were controlled using the Langevin thermostat with the extended Lagrangian approach 55 to control the relative motion of Drude particles while the pressure was controlled using the Nose-Hoover barostat. 56 MD simulations were performed with the open-source simulator LAMMPS. 57

IV.

Results and Discussion

Phase compositions of the water/CO2 mixture were obtained from 323 K to 573 K and from 200 bar to 800 bar covering typical temperature and pressure conditions of CO2 geological sequestration processes. Phase equilibria of water/n-alkane mixtures and Henry’s constant of n-alkanes in water were also obtained from 320 K to 550 K and up to 3000 bar. Numerical data for the phase compositions and their associated simulation uncertainties are listed in the supporting information. The experimental data of Todheide and Frank 3 or water/CO2 phase compositions, which were confirmed to be reliable in our prior work 30 were used to validate simulation results.

A.

Unoptimized Potentials

The phase compositions of the water/CO2 mixture, i.e. CO2 solubility in water-rich phase (xCO2 ) and water solubility in CO2 -rich phase (yH2O ), were calculated using cross interaction parameters obtained from the Kong combining rule (Eqs. 5-7). As shown in Figure 1, all polarizable models studied significantly underestimate the compositions for both water- and CO2 -rich phases with the BK3 model slightly outperforming the GCP and HBP models. A similar underestimation of phase compositions was observed if Lorentz-Berthelot or geometric combining rules were used to establish the cross interaction of unlike pairs. Clearly, for this system the conventional combining rules do not adequately represent the unlike-pair interactions.



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Figure 1: Composition of the water-rich (left) and CO2 -rich (right) phases from the BK3, GCP, HBP water and PGC CO2 models with cross interaction parameters obtained from the Kong combining rule. Experimental data 3 are shown as solid lines. The simulation uncertainties are comparable with the symbol size.

B.

Optimized Potentials

Since the use of empirical combining rules leads to significant underestimation of phase compositions for the water/CO2 mixture, the next step involves adjusting the cross interaction parameters. In an important study, Schultz et al. 58 found that by adjusting the vdW cross interaction parameters between the GCP water and a Gaussian charge polarizable CO2 59 models, these classical models can represent satisfactorily the cross second virial coefficient (B2 ) of the water/CO2 dimer, in agreement with results from high level quantum chemical calculations. 35 In the present work, we adjusted the cross interaction parameters between the BK3, GCP, HBP water and PGC CO2 models to the cross second virial coefficients, as did Schultz et al. The second virial coefficient were obtained by numerical integration of the Mayer function, Z ∞ − k UT (10) B2 (T ) = −2π < e B > −1 r2 dr 0

where the upper limit of the integration was set to 20 ˚ A, beyond which the integrand is negligible. The average of Boltzmann factor was taken over 25000 randomly sampled molecular 8 ACS Paragon Plus Environment

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orientations at a certain intermolecular distance. It is noted that Eq. 10 is a classical calculation and quantum effects make important contribution to the second virial coefficient at low temperatures. 58 Quantum effects are included implicitly in the polarizable models, since these models were parameterized to experimental data, therefore we did not introduce any explicit correction to account for quantum effects in the calculation of the second virial coefficient, as did Schultz et al. 58 To adjust the cross interaction parameters between the BK3, GCP water and PGC CO2 models, two scaling factors (k12 and l12 ) were introduced to the Kong combining rule (i.e. Eqs. 5-6), A12

− B B+B − B B+B 1 2 1 2 1 2 A1 B1 A2 B2 1 + A2 (1 − k12 ) = A1 2 A2 B2 A1 B1

(11)

2B1 B2 (1 − l12 ) (12) B1 + B2 Scaling factors (k12 and l12 ) were only used to correct the dispersion interaction parameters between oxygen atoms of water and CO2 , since it was found that adjusting dispersion interaction parameters between oxygen atoms of water and carbon atoms of CO2 has only small impact on the phase equilibrium. A12 and C12 are the energy parameters for cross dispersion interactions, while B12 is the size parameter, and it is not necessary to use an additional scaling factor for Eq. 7. For the HBP water and PGC CO2 models, we explicitly considered the hydrogen bonds between water and CO2 . The interaction parameters (HB and σHB in Eq. 4) for hydrogen bonding between water and CO2 were adjusted to the second virial coefficient of the dimer, while the cross vdW interaction parameters follows the Kong combining rule (Eqs. 5-7) without any adjustment. As shown in Figure 2, all studied models overestimate the second virial coefficient without adjustment of cross interaction parameters indicating the Kong combining rule underestimate the strength of cross interactions, which is consistent with the underestimation of phase compositions (see Figure 1). With cross interaction corrected by the scaling factors (k12 and l12 , given in supporting information), the second virial coefficients from the BK3, GCP water and PGC CO2 models are in agreement with quantum chemical calculation. The HBP water and PGC CO2 models also represent accurately the second virial coefficient when considering the hydrogen bonding interaction between water and CO2 . Using the cross interaction parameters adjusted to the cross second virial coefficient, the BK3 and GCP water and PGC CO2 models significantly overestimate the CO2 solubility in water by a factor up to 6 (results shown in Supporting Information). In order to test if there exists a set of cross interaction parameters that can represent fully phase equilibrium of the water/CO2 mixture, we directly optimized the scaling factors (k12 and l12 ) for BK3, GCP water and PGC CO2 models to experimental phase composition data. 3 The optimization process is based on a least-square minimization of a weighted objective function F , B12 =

n

1X 1 |Asim,i (k12 , l12 ) − Aexpt,i | F = n i=1 δAsim,i

(13)

where Asim,i is the calculated phase composition from simulation and Aexp,i is the corresponding experimental data, including both the CO2 solubility in water and water solubility in CO2 -rich 9 ACS Paragon Plus Environment


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Figure 2: Second virial coefficient of the water/CO2 dimer from the BK3, HBP water and PGC CO2 models with and without adjustment of cross interaction parameters. Quantum chemical calculated second virial coefficient 35 is shown as solid line.

phase. The function F is weighted by the simulation uncertainty δAsim,i . The GaussianNewton approach was used to minimize the objective function F , and partial derivative of the objective function was approximated by a finite difference scheme. This optimization method has been successfully applied to parameterize the PGC CO2 model, and further details of the optimization process can be found in our prior work. 41 The optimization converged after several Gaussian-Newton iterations, and the optimized scaling factors (k12 and l12 ) are listed in Table 1. With the scaling factors directly optimized to phase composition data, the BK3 model represents accurately the CO2 solubility in water, as shown in Figure 3. A good representation of CO2 solubility in water was observed as well (results not shown for clarity) for the GCP water Table 1: Scaling factors (k12 and l12 ) for cross vdW and hydrogen bonding interaction parameters. Molecular model BK3/CO2 GCP/CO2 HBP/CO2

k12 l12 HB (kJ/mol) σHB (˚ A) 0.34 0.036 0.031 0.024 0 0 6.86 3.45


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model when using scaling factors given in Table 1. With cross hydrogen bonding interaction parameters adjusted to the second virial coefficient, the HBP water and PGC CO2 models predict accurately the CO2 solubility in water. The non-polarizable SPC/E water and TraPPE CO2 models overestimate the CO2 solubility with optimized cross interaction parameters. 30

Figure 3: Composition of the water-rich phase from the BK3, HBP water and PGC CO2 models with optimized cross interaction parameters. Stars are phase composition data at 423 K from non-polarizable SPC/E water + TraPPE CO2 models with optimized cross interactions. 30 Experimental data 3 are shown as solid lines.

The accurate representation of water-rich phase composition from the BK3 and GCP models does not extend to the CO2 -rich phase with optimized cross interaction parameters. As shown in Figure 4, the BK3 water model underestimates the water content in CO2 -rich phase and an underestimation of phase composition was also observed for the GCP water model (not shown for clarity). One may argue that the poor performance of the BK3 and GCP models for the CO2 -rich phase reflects that the scaling factors listed in Table 1 do not give the “truly” optimized cross interaction provided the optimization procedure can only find local minimum of the objective function F . We performed a sensitivity analysis with respect to the effects of cross interaction parameters on the phase compositions by calculating the phase compositions for a range of scaling factors. Details of this analysis is given in the supporting information. It was found that the composition of the CO2 -rich phase is significantly less sensitive to the cross interaction parameters than that of the water-rich phase, and it is not possible to achieve accurate representation of compositions for both phases simultaneously by simply adjusting dispersion cross interaction parameters. Although the performance of the BK3 (or GCP) model is unsatisfactory, polarizable models outperform non-polarizable SPC/E-TraPPE models. 11 ACS Paragon Plus Environment


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The HBP water plus PGC CO2 model combination satisfactorily predicts the compositions for both water- and CO2 -rich phases up to 573 K and 800 bar using hydrogen bonding parameters listed in Table 1 (results at 573 K are given in Fig 5). No phase composition data were used to find the hydrogen bonding interaction parameters, therefore, the calculation from the HBP water model was purely predictive. At 573 K, the representation of phase equilibrium from the HBP water model is in a reasonable agreement with experimental data 3 , while the BK3 and GCP water models overestimate the composition of CO2 -rich phase, consistent with their underestimation of water content in CO2 -rich phase at lower temperatures. The accurate prediction of composition from the HBP model indicates the hydrogen bonds between water and CO2 have important effects on thermodynamic properties of the water/CO2 mixture. It is noted that the PGC CO2 model underestimates polarizability of CO2 along its molecular axis, and such underestimation may contribute to the need of the hydrogen bonding interaction. The inclusion of hydrogen bond, i.e. association, between water and CO2 was also found to improve the accuracy of CPA equation of state for the water-CO2 mixture. 17

Figure 4: Composition of the CO2 -rich phase from the BK3, HBP water and PGC CO2 models with optimized cross interaction parameters. Stars are phase composition data at 423 K from non-polarizable SPC/E water + TraPPE CO2 models with optimized cross interactions. 30 Experimental data 3 are shown as solid lines.


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Figure 5: Phase equilibrium of the water/CO2 mixture at 573 K from the BK3, GCP and HBP water and PGC CO2 models with optimized cross interaction parameters. Experimental data 2 are shown as solid lines.

C.

Phase Equilibria of Water/n-Alkane Mixture

Since the HBP water model does well for phase equilibrium of the water/CO2 mixture, it is interesting to evaluate its performance with respect to H2 O/n-alkane mixtures. Henry’s constants of n-alkanes up to 6 carbon atoms in HBP water were calculated. As shown in Figure 6, the HBP water and united-atom methane and ethane models overestimate the Henry’s constant over the entire temperature range using the Kong combining rule. Since the n-alkanes molecules were represented by united-atom model neglecting the intramolecular degrees of freedom, it is expected the models cannot represent the second virial coefficients of dimers, although such information is available from quantum chemical calculations. 60 Therefore, the dispersion interaction parameters between water and n-alkanes were adjusted, p (14) C12 = C1 C2 (1 − p) The scaling factors (p12 ), -0.07 and -0.08 for water/CH4 and water/CH3 cross interactions, respectively, were adjusted to the Henry’s constants of methane and ethane in water. With adjusted cross interaction parameters, the united-atom n-alkane and HBP water models show reasonable agreement for the Henry’s law constants of methane and ethane in water, as shown in Figure 6. The models show reasonable representation for the Henry’s constant of propane and n-butane in water, and the water/CH2 cross interaction follows the Kong combining rule without adjustment. However, larger deviations to experimental data were observed for the case 13 ACS Paragon Plus Environment


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of n-hexane, as shown in Figure 7, possibly due to the larger conformation space of n-hexane in water.

Figure 6: Henry’s constant of methane (bottom) and ethane (top) in water from the HBP water and united-atom methane and ethane models. Stars are results using the Kong combining rule, circles are results with cross interaction optimized to the experimental Henry’s constant. Experimental data 61 are shown as solid lines.


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Figure 7: Henry’s constant of propane (bottom), n-butane (middle) and hexane (top) in water from the HBP water and united-atom models with optimized cross interaction parameters. Experimental data 62–64 are shown as solid lines.

The phase equilibria of water in mixture with methane and ethane were obtained at elevated temperatures and pressures. Figure 8 shows the prediction of phase equilibrium for the water/methane mixture from the HBP water and united-atom methane models using cross interaction parameters adjusted to the Henry’s constant of methane in water. The overall agreement between simulation data and experimental data is reasonable, however, the methane solubility in water is overestimated at high pressures. Figure 9 shows the prediction of phase compositions for water/ethane mixture with cross interaction parameters adjusted to the Henry’s constant. While the prediction of ethane solubility in water from low to intermediate pressure range is reasonable, the water content in ethane-rich phase is underestimated. The inclusion of polarizability into water does not improve the overall accuracy of simulations compared to phase equilibria obtained in prior simulations using non-polarizable water models. 66,67 The less satisfactory representation of phase equilibria for water/n-alkane mixtures, especially the underestimation of water content in n-alkane-rich phase, can be attributed to the use of united-atom model for n-alkane. The electrostatic and induction interaction between water and n-alkanes were omitted due to the use of united-atom model, however, such interactions strongly affect the properties of water/n-alkanes mixtures. 68–70



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Figure 8: Phase equilibrium of the water/methane mixture at 423 K and 523 K with cross interaction parameter optimized to the Henry’s constant. Experimental data 65 are shown as solid lines.

Figure 9: Phase equilibrium of the water/ethane mixture at 523 K and 573 K with cross interaction parameter optimized to the Henry’s constant. Experimental data 65 are shown as solid lines. 16 ACS Paragon Plus Environment

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V.


Conclusions

The performance of several Drude-type polarizable water and CO2 models, namely BK3, GCP, HBP and PGC models, were evaluated with respect to their representation of phase equilibrium for the water/CO2 mixture. With commonly used combining rules for the cross interactions between unlike pairs, all the studied models underestimate the phase compositions, consistent with their overestimation of second virial coefficient of the water/CO2 dimer. The cross interaction between BK3, GCP water and PGC CO2 models were optimized to experimental phase composition data of the mixture, however, the water solubility in CO2 -rich phase is still underestimated with optimized cross interaction parameters. For the BK3, GCP H2 O and PGC CO2 models, inclusion of polarizability into molecular models only slightly improves the representation of phase composition relative to non-polarizable models. For the HBP water plus PGC CO2 model combination, we explicitly modeled the hydrogen bonding interaction between water and CO2 , and parameters of such hydrogen bonding interaction were fitted to the second virial coefficient without including any phase composition data into the fitting. The HBP water and PGC CO2 models give excellent prediction of compositions for both water- and CO2 -rich phases simultaneously. The phase equilibria of water/n-alkanes mixtures were also studied by using the HBP water and Exp-6 united-atom n-alkane models. With cross interaction parameters between water and n-alkanes optimized to Henry’s constants of methane and ethane in water, the HBP and Exp-6 models show reasonable prediction of phase equilibrium with underestimation of water content in n-alkane-rich phase. The underestimation of water content is likely due to the neglect of electrostatic and induction energies in the united-atom model.

VI.

Acknowledgments

This publication was made possible by NPRP grant number 6-1157-2-471 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. Additional support was provided by the Office of Basic Energy Sciences, U.S. Department of Energy, under Award DE-SC0002128, and by the Carbon Mitigation Initiative at Princeton University. Computational resources were provided by the Princeton Institute for Computational Science and Engineering. Supporting Information. Force field parameters, numerical values and statistical uncertainties of phase compositions for water/CO2 , water/methane, water/ethane and Henry’s constant; CO2 solubility in water predicted from BK3, GCP models using cross interaction parameters adjusted to the second virial coefficient; details of sensitivity analysis for the calculation of phase compositions with different cross interaction parameters.

References [1] Diamond, L. W.; Akinfiev, N. N. Solubility of CO2 in water from -1.5 to 100 C and from 0.1 to 100 MPa: Evaluation of Literature Data and Thermodynamic Modelling. Fluid Phase Equilib. 2003, 208, 265-290.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 22

[2] Takenouchi, S.; Kennedy, G. C. The Binary System H2O-CO2 at High Temperatures and Pressures. Am. J. Sci. 1964, 262, 1055-1074. [3] Todheide, K.; Frank, E. U. Das Zweiphasengebie Und Die Kritische Kurve Im System Kohlenoxid-Wasser Bis Zu Drucken Von 3500 Bar. Z. Phys. Chem. Neue Folge. 1963, 37, 387-401. [4] Capobianco, R.; Guszkiewicz, M.; Bodnar, R.; Rimstidt, J. D. PVTx Properties of CO2-H2O from 150 C250 C and from 200-800 bar; European Current Research On Fluid Inclusions (ECCROFIXXII), Antalya, Turkey, June 4-9, 2013. [5] Hu, J.; Duan, Z.; Zhu, C.; and Chou, I. M. PVTx properties of the CO2-H2O and CO2-H2O-NaCl systems below 647 K: Assessment of experimental data and thermodynamic models. Chem. Geol. 2007, 238, 249267. [6] Duan, Z.; Moller, N.; Weare, J. H. An Equation of State for the CH4-CO2-H2O System: I. Pure Systems from 0 to 1000 C and 0 to 8000 Bar. Geochim. Cosmochim. Acta. 1992, 56, 2605-2617. [7] Duan, Z.; Moller, N.; Weare, J. H. An Equation of State for the CH4-CO2-H2O System: II. Mixtures from 50 to 1000 C and 0 to 1000 Bar. Geochim. Cosmochim. Acta. 1992, 56, 2619-2631. [8] Duan, Z. H.; Sun, R. An Improved Model Calculating CO2 Solubility in Pure Water and Aqueous NaCl Solutions from 273 to 533 K and from 0 to 2000 bar. Chem. Geol. 2003, 193, 257-271. [9] Lobanova, O.; Mejia, A.; Jackson, G.; Muller, E. A. SAFT-γ Force Field for the Simulation of Molecular Fluids: 6. Binary and Ternary Mixtures Comprising Water, Carbon dioxide, and N-alkanes. J. Chem. Thermodyn. 2016, 93, 320-336. [10] Llovell, F.; Vega, L. F. Accurate Modeling of Supercritical CO2 for Sustainable Processes: Water + CO2 and CO2 + Fatty Acid Esters Mixtures. J. Supercrit. Fluids. 2015, 96, 86-95. [11] Vega, L. F.; Llovell, F. Review and New Insights into the Application of Molecular-Based Equations of State to Water and Aqueous Solutions. Fluid Phase Equilib. 2016, 416, 150-173. [12] Fouad, W. A.; Yarrison, M.; Song, K. Y.; Cox, K. R.; Chapman, W. G. High Pressure Measurements and Molecular Modeling of the Water Content of Acid Gas Containing Mixtures. AIChE J. 2015, 61, 3038-3052. [13] Ji, X.; Tan, S. P.; Adidharma, H.; Radosz, M. SAFT1-RPM Approximation Extended to Phase Equilibria and Densities of CO2-H2O and CO2-H2O-NaCl Systems. Ind. Eng. Chem. Res. 2005, 44, 8419-8427. [14] 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. [15] Jiang, H.; Panagiotopoulos, A. Z.; Economou I. G. Modeling of CO2 solubility in Single and Mixed Electrolyte Solutions using Statistical Associating Fluid Theory. Geochim. Cosmochim. Acta. 2016, 176, 185-197. [16] Li, Z.; Firoozabadi, A.; Cubic-Plus-Association Equation of State for Water-Containing Mixtures: Is “Cross Association” Necessary? AIChE J. 2009, 55, 1803-1813. [17] Tsivintzelis, I.; Kontogeorgis, G. M.; Michelsen, M. L.; Stenby, E. H. Modeling Phase Equilibria for Acid Gas Mixtures Using the CPA Equation of State. Part II: Binary Mixtures with CO2. Fluid Phase Equilib. 2011, 306, 38-56.


Page 19 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[18] Tsivintzelis, I.; Kontogeorgis, G. M. Modelling Phase Equilibria for Acid Gas Mixtures Using the CPA Equation of State. Part V: Multicomponent Mixtures Containing CO2 and Alcohols. J. Supercrit. Fluids. 2015, 104, 29-39. [19] Destrigneville, C. M.; Brodholt, J. P.; Wood, B. J. Monte Carlo Simulation of H2 O-CO2 Mixtures to 1073.15 K and 30 kbar. Chem. Geol. 1996, 133, 53-65. [20] Tafazzoli, M.; Khanlarkhani, A. Study of Self-Association of Water in Supercritical CO2 by Monte Carlo Simulation: Does Water Have a Specific Interaction with CO2 ? Fluid Phase Equilib. 2008, 267, 181-187. [21] Jorgensen, W. L.; Chandrasekhar J.;, Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79, 926. [22] Harris, J. G.; Yung, K. H. Carbon Dioxide’s Liquid-Vapor Coexistence Curve and Critical Properties as Predicted by a Simple Molecular Model. J. Phys. Chem. 1995, 99, 12021. [23] Li˘sal, M.; Smith, W. R.; Aim, K. Analysis of Henry’s Constant for Carbon Dioxide in Water via Monte Carlo Simulation. Fluid Phase Equilib. 2005, 226, 345-356. [24] Errington, J. R.; Panagiotopoulos, A. Z. A Fixed Point Charge Model for Water Optimized to the VaporLiquid Coexistence Properties. J. Phys. Chem. B 1998, 102, 7470-7475. [25] Potoff, J. J.; Errington, J. R.; Panagiotopoulos, A. Z. Molecular Simulation of Phase Equilibria for Mixtures of Polar and Non-Polar Components. Mol. Phys. 1999, 97, 1073-1083. [26] Vorholz, J.; Harismiadis, V. I.; Rumpf, B.; Panagiotopoulos, A. Z.; Maurer, G. Vapor + Liquid Equilibrium of Water, Carbon Dioxide, and the Binary System, Water + Carbon dioxide, from Molecular Simulation. Fluid Phase Equilib. 2000, 170, 203-234. [27] Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials, J. Phys. Chem. 1987, 79, 926. [28] Liu, Y.; Panagiotopoulos, A. Z.; Debenedetti, P. G. Monte Carlo Simulations of High-Pressure Phase Equilibria of CO2-H2O Mixtures. J. Phys. Chem. B 2011, 115, 6629-6635. [29] Vlcek, L.; Chialvo, A. A.; Cole, D. R. Optimized Unlike-Pair Interactions for Water-Carbon Dioxide Mixtures Described by the SPC/E and EPM2 Models. J. Phys. Chem. B 2011, 115, 8775-8784. [30] Orozco, G. A.; Economou, I. G.; Panagiotopoulos, A. Z. Optimization of Intermolecular Potential Parameters for the CO2/H2O Mixture. J. Phys. Chem. B 2014, 118, 11504-11511. [31] Orozco, G. A.; Moultos, O. A.; Jiang, H.; Economou, I. G.; Panagiotopoulos, A. Z. Molecular Simulation of Thermodynamic and Transport Properties for the H2O+NaCl System. J. Chem. Phys. 2014, 141, 234507. [32] Moultos, O. A.; Tsimpanogiannis, I. N.; Panagiotopoulos, A. Z.; Economou, I. G. Atomistic Molecular Dynamics Simulations of CO2 Diffusivity in H2O for a Wide Range of Temperatures and Pressures. J. Phys. Chem. B 2014, 118, 5532-5541. [33] Moultos, O. A.; Tsimpanogiannis, I. N.; Panagiotopoulos, A. Z.; Economou, I. G. Atomistic Molecular Dynamics Simulations of H2O Diffusivity in Liquid and Supercritical CO2 Mol. Phys. 2015, 113, 28052814. [34] Moultos, O. A.; Tsimpanogiannis, I. N.; Panagiotopoulos, A. Z.; Economou, I. G. Self-Diffusion Coefficients of the Binary (H2 O+CO2 ) Mixture at High Temperatures and Pressures. J. Chem. Thermodyn. 2016, 93, 424-429.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 22

[35] Wheatley, R. J.; Harvey, A. H. Intermolecular Potential Energy Surface and Second Virial Coefficients for the Water-CO2 Dimer. J. Chem. Phys. 2011, 134, 134309. [36] Meyer, C. W.; Harvey, A. H. Dew-Point Measurements for Water in Compressed Carbon Dioxide. AIChE J. 2015, 61, 2913. [37] Glezakou, V. A.; Rousseau, R.; Dang, L. X.; McGrail, B. P. Structure, Dynamics and Vibrational Spectrum of Supercritical CO2/H2O Mixtures from Ab Initio Molecular Dynamics as a Function of Water Cluster Formation. Phys. Chem. Chem. Phys. 2010, 12, 8759-8771. [38] Paricaud, P.; Predota, M.; Chialvo, A. A.; Cummings, P. T. From dimer to Condensed Phases at Extreme Conditions: Accurate Predictions of the Properties of Water by a Gaussian Charge Polarizable Model. J. Chem. Phys. 2005, 122, 244511-14. [39] Kiss, P. T.; Baranyai, A. A Systematic Development of a Polarizable Potential of Water. J. Chem. Phys. 2013, 138, 204507-17. [40] Jiang, H.; Moultos, O. A.; Economou I. G.; Panagiotopoulos, A. Z. Hydrogen-Bonding Polarizable Intermolecular Potential Model for Water. J. Phys. Chem. B 2016, 120, 12358-12370. [41] Jiang, H.; Moultos, O. A.; Economou I. G.; Panagiotopoulos, A. Z. Gaussian-Charge Polarizable and Nonpolarizable Models for CO2 . J. Phys. Chem. B 2016, 120, 984-994. [42] Chialvo, A. A.; Moucka, F.; Vlcek, L.; Nezbeda, I. Vapor-Liquid Equilibrium and Polarization Behavior of the GCP Water Model: Gaussian Charge-on-Spring versus Dipole Self-Consistent Field Approaches to Induced Polarization. J. Phys. Chem. B 2015, 119, 5010-5019. [43] Errington, J. R.; Panagiotopoulos, A. Z. A New Intermolecular Potential Model for the N-Alkane Homologous Series. J. Phys. Chem. B 1999, 103, 6314-6322. [44] Potoff, J. J.; Siepmann, J. I. Vapor-Liquid Equilibria of Mixtures Containing Alkanes, Carbon Dioxide and Nitrogen. AIChE J. 2001, 47, 1676-1682. [45] Boda, D.; Henderson, D. The Effects of Deviations from Lorentz-Berthelot Rules on the Properties of a Simple Mixture. Mol. Phys. 2008, 106, 2367-2370. [46] Delhommelle, J.; Millie, P. Inadequacy of the Lorentz-Berthelot Combining Rules for Accurate of Equilibrium Properties by Molecular Simulation. Mol. Phys. 2001, 99, 619-625. [47] Panagiotopoulos, A. Z. Direct Determination of Phase Coexistence Properties of Fluids by Monte Carlo Simulation in a New Ensemble. Mol. Phys. 1987, 61, 813-826. [48] Panagiotopoulos, A. Z.; Quirke, N.; Stapleton, M.; and Tildesley, D. J. Phase Equilibria by Simulation in the Gibbs Ensemble. Mol. Phys. 1988, 63, 527-545. [49] Mou˘cka, F.; Nezbeda, I.; Smith, W. R. Computationally Efficient Monte Carlo Simulations for Polarisable Models: Multi-Particle Move Method for Water and Aqueous Electrolytes. Mol. Sim. 2013, 39, 1125-1134. [50] Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press: San Diego, CA, 2002. [51] Kiss, P. T.; Sega, M.; Baranyai, A. Efficient Handling of Gaussian Charge Distributions: An Application to Polarizable Molecular Models. J. Chem. Theory. Comput. 2014, 10, 5513-5519. [52] Jiang, H.; Moultos, O. A.; Economou I. G.; Panagiotopoulos, A. Z. Thermodynamic and Transport Properties of H2O+NaCl from Polarizable Force Fields. J. Chem. Theory. Comput. 2015, 11, 3802-3810.


Page 21 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[53] Shah, J.; Maginn, E. A General and Efficient Monte Carlo Method for Sampling Intramolecular Degrees of Freedom of Branched and Cyclic Molecules. J. Chem. Phys. 2011, 135, 134121-11. [54] C. H. Bennett, Efficient Estimation of Free Energy Differences from Monte Carlo Data. J. Comput. Phys. 1976, 22, 245-268. [55] Dequidt, A.; Devemy, J.; Padua, A. A. H. Thermalized Drude Oscillators with the LAMMPS Molecular Dynamics Simulator. J. Chem. Inf. Model. 2016, 56, 260-268. [56] Kamberaj, H.; Low, R. H.; Neal, M. P. Time Reversible and Symplectic Integrators for Molecular Dynamics Simulations of Rigid Molecules. J. Chem. Phys. 2005, 122, 224114-30. [57] Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics J. Comput. Phys. 1995, 117, 1. [58] Schultz, A. J.; Kofke, D. A.; Harvey, A. H. Molecular-Based Virial Coefficients of CO2-H2O Mixtures. AIChE J. 2015, 61, 3029-3037. [59] Persson, R. A. X. Gaussian Charge Polarizable Interaction Potential for Carbon Dioxide. J. Chem. Phys. 2011, 134, 034312. [60] Akin-Ojo, O; Szalewicz, K. Potential Energy Surface and Second Virial Coefficient of Methane-Water from Ab Initio Calculations. J. Chem. Phys. 2005, 123, 134311. [61] Harvey, A. H. Semiempirical Correlation for Henry’s Constants over Large Temperature Ranges. AIChE J. 1996, 42, 1491-1491. [62] Chapoy, A.; Mokraouia, S.; Valtza, A.; Richon, D.; Mohammadi, A. H.; Tohidi, B. Solubility Measurement and Modeling for the System Propane-Water from 277.62 to 368.16 K. Fluid Phase Equilib. 2004, 226, 213-220. [63] Carroll, J. J.; Jou, F. Y.; Mather, A. E. Fluid Phase Equilibria in the System N-butane + Water. Fluid Phase Equilib. 1997, 140, 157 [64] Tsonopoulos, C.l Wilson, G. M. High-temperature Mutual Solubilities of Hydrocarbons and Water. Part I: Benzene, Cyclohexane and N-hexane. AIChE J. 1983, 129, 990-999. [65] Sultanov, R. G.; Skripka, V. G.; Yu, N. A. Zh. Fiz. Khim. 1972, 46, 2160. [66] Errington, J. R.; Boulougouris, G. C.; Economou, I. G.; Panagiotopoulos A. Z.; Theodorou, D. N. Molecular Simulation of Phase Equilibria for Water-Methane and Water-Ethane. J. Phys. Chem. B 1998, 102, 88658873. [67] Boulougouris, G. C.; Errington, J. R.; Economou, I. G.; Panagiotopoulos A. Z.; Theodorou, D. N. Molecular Simulation of Phase Equilibria for Water-n-Butane and Water-n-Hexane Mixtures. J. Phys. Chem. B 2000, 104, 4958-4963. [68] Ballal, D.; Venkataraman, P.;Fouad, W. A.; Cox, K. R.; Chapman, W. G. Isolating the Non-Polar Contributions to the Intermolecular Potential for Water-Alkane Interactions. J. Chem. Phys. 2014, 141, 064905. [69] McDaniel, J. G.; Yethiraj, A. Comment on “Isolating the Non-Polar Contributions to the Intermolecular Potential for Water-Alkane Interactions”. J. Chem. Phys. 2016, 144, 137101. [70] Asthagiri, D.; Ballal, D.; Venkataraman, P.;Fouad, W. A.; Cox, K. R.; Chapman, W. G. Response to “Comment on ’Isolating the non-polar contributions to the intermolecular potential for water-alkane interactions”’ J. Chem. Phys. 2016, 144, 137102.



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