Monte Carlo predictions for the phase behavior of H2 S+n-alkane, H2 S+CO2, CO2+CH4 and H2 S+CO2+CH4 mixtures

Fluid Phase Equilibria 246 (2006) 71–78

Monte Carlo predictions for the phase behavior of H2 S + n-alkane, H2 S + CO2 , CO2 + CH4 and H2 S + CO2 + CH4 mixtures Ganesh Kamath, Jeffrey J. Potoff∗ Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, MI 48202, United States Received 24 April 2006; received in revised form 11 May 2006; accepted 11 May 2006 Available online 22 May 2006

Abstract Phase diagrams for binary mixtures of H2 S + n-alkanes, H2 S + CO2 , CO2 + CH4 and a ternary mixture containing H2 S, CH4 and CO2 are determined with atomistic simulations. Pressure–composition diagrams for each of the binary mixtures are determined with configurational-bias Monte Carlo simulations in the grand canonical ensemble, combined with histogram-reweighting techniques. Overall, the predicted phase diagrams for the H2 S + n-alkanes and CO2 + CH4 mixtures are found to be in excellent agreement with experiment, while significant deviations are found between simulation and experiment for the H2 S + CO2 mixture. Gibbs ensemble Monte Carlo simulations are used to determine the ternary phase diagram for the H2 S + CH4 + CO2 mixture at 310.93 K and 41.3 bar. Comparison of simulation to experiment shows a close agreement at the temperature and pressure studied in this work. © 2006 Elsevier B.V. All rights reserved. Keywords: Simulation; Vapor–liquid equilibria; Hydrogen sulfide

1. Introduction Raw crude oil contains significant quantities of sulfur compounds that must be removed during the processing of oil into gasoline or other fuels. In addition to hydrogen sulfide that is naturally found in these reservoirs, sulfur compounds such as thiols and sulfides are usually converted to hydrogen sulfide during processing (1), which later must be removed. Sulfur compounds are undesirable in refining processes as they deactivate catalysts, and cause corrosion problems in pipelines, as well as pumping and refining equipment. More stringent environmental standards on sulfur emissions, coupled with the need to process feed-stocks with increasing amounts of sulfur contaminants (2) have made sulfur management a critical aspect in the refining process (3). The need to separate H2 S from hydrocarbons has motivated the extensive study of H2 S+ hydrocarbon vapor–liquid equilibria over the last 60 years. Data can be found in the literature for binary mixtures of H2 S+ methane (4), ethane (5–7), propane (8– 14), butane, iso-butane (12), pentane (15), iso-pentane, neopen-

∗

Corresponding author. Tel.: +1 313 577 9357; fax: +1 313 577 3810. E-mail address: [email protected] (J.J. Potoff).

0378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2006.05.011

tane (16), hexane, cyclohexane, benzene, pentadecane (17), heptane (18), decane (19,20), n-eicosane (21), n-hexadecane, ntridecane, squalane (20), toluene (18), ethylcyclohexane, propylcyclohexane (22) and m-xylene (23). The phase envelopes for H2 S + CO2 (24) and H2 S + water (25) have also been determined by experiment. A common approach in the calculation of mixture phase equilibria is the use of equation of state models (EOS), such as Peng– Robinson (26), and such modeling has been used successfully for H2 S + alkane mixtures (27). A limitation of the EOS methodology, is that binary interaction parameters kij are usually needed for an accurate representation of fluid phase equilibria. These kij parameters are derived from experimental data, but are only relevant for the specific binary mixture that was used in the fitting process, limiting the predictive capability of the EOS technique. Molecular simulation provides another method of predicting the vapor–liquid equilibria of complex fluid mixtures. Given an appropriate simulation algorithm, such as Gibbs ensemble Monte Carlo (28–30) or histogram-reweighting (31–33), the primary limitation in the accuracy of the prediction rests on the molecular model or “force field” used to describe the interactions of atoms with each other. Modeling of fluids on the molecular level provides some advantages over typical cubic EOS models. If the interactions between atoms in the molecules of interest are

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known to sufficient accuracy, it is possible to avoid the use of kij ’s altogether (34). If one must resort to the use of kij parameters, they can, in many cases, be fit to a limited number of data and yield reliable results over a wide range of temperatures and pressures (35) as well as for mixtures containing components similar to those for which the kij ’s were fit. In this work, grand canonical histogram-reweighting Monte Carlo simulations are used to determine the pressure composition diagrams for binary mixtures of H2 S and various alkanes ranging from methane to heptane as well as H2 S + CO2 . Gibbs ensemble Monte Carlo simulations are used to determine the phase envelope for a ternary mixture of H2 S + CO2 + CH4 . Hydrogen sulfide has received considerable attention from the simulation community and a number of force fields exist in the literature (36–41). Recently, our group developed a new force field for H2 S that was parameterized specifically to complement the TraPPE-EH force field for alkanes (42) to yield a quantitative representation of the pressure composition behavior of H2 S + n-pentane mixtures. The calculations performed here are an extension to that work and are used to demonstrate the predictive capabilities of our force field for H2 S when combined in mixtures with other hydrocarbons, with CO2 , and a ternary mixture involving H2 S, CO2 and methane. The specific details regarding the implementation of the force fields used in this work are given in the following section, while the relevant simulation details are presented in Section 3. In Section 4, pressure composition diagrams for H2 S with various alkanes from methane to heptane, and H2 S + CO2 are presented as well as the ternary phase diagram for a mixture of H2 S + CO2 + CH4 . The conclusions of this work can be found in Section 5. 2. Force field In this section, the force fields used in this work are described. Non-bonded interactions between atoms in each of the molecules, H2 S, CO2 and n-alkanes, use a Lennard–Jones potential to describe dispersive interactions, while point charges are used to reproduce multipole moments found in H2 S and CO2 . Therefore, the interaction energy between a pair of atoms may be written as
   6  σij 12 qi qj σij + (1) − U(rij ) = 4εij rij rij 4πε0 rij where rij , εij , σij , qi , and qj are the separation, LJ well depth, LJ size, and partial charges, respectively, for the pair of interaction sites i and j. ε0 is the permittivity of vacuum. All interactions are treated as pairwise additive, and additional three-body and/or polarizable terms are not used. Interactions between unlike interaction sites are computed with the Lorentz-Berthelot combining rules (43–45): σij =

σii + σjj , 2

ij =

√ ii jj

(2)

No special binary interaction parameters have been used in this work.

2.1. Hydrogen sulfide A number of force fields have been proposed for H2 S (36– 41) over the last 10 years. These can be split into two groups based on the arrangement of the interaction sites. The Forester model utilizes four sites arranged in a TIP4P-like geometry (37). Charges are placed on each of the atomic sites, while a fourth charge is placed in the H–S–H plane a distance δ from the center of the sulfur atom along the bisector of the H–S–H bond angle. Dispersive interactions are modeled with a single Lennard– Jones site placed on the sulfur atom. Gibbs ensemble Monte Carlo simulations have shown that the Forester force field, originally parameterized for the study of low temperature liquid and solid phases, does not yield an accurate vapor–liquid coexistence curve, which motivated the successful reparameterization of the model as presented by Kristof and Liszi (38). The Kristof and Liszi force field has been used in a number of calculations, including the simulation of phase behavior for H2 S + water (46), and H2 S + n-propane (47). The second class of force fields for H2 S are based on the Jorgensen model, where three interaction sites are distributed amongst the three atoms present in H2 S according to the experimental geometry (36). Although the original parameterization by Jorgensen was not found to yield an accurate vapor–liquid coexistence curve (38), reparameterization of the model by three separate research groups has shown such an arrangement of interaction sites is capable of yielding accurate predictions for the vapor–liquid equilibria of H2 S (39–41). The force fields developed by Kristof and Liszi, Delhommelle et al. and Nath, while yielding pure component vapor–liquid coexistence curves for H2 S that were in close agreement with experiment, each displayed systematic deviations from experiment, for mixtures rich in H2 S, when used to predict the pressure composition behavior of H2 S + propane (47) or H2 S + pentane mixtures (39,40). Recently, however, simulations involving the Kristof and Liszi H2 S force field and the revised AUA-3 force field, denoted AUA-4, for n-alkanes were found to be in excellent agreement with experimental data for the H2 S + n-pentane mixture (48). The deviations of previous works from experiment motived the original development of a transferable force field for H2 S that was compatible with the TraPPE-EH series of force fields for n-alkanes (41). The H2 S force field used in this work is a three site model, similar to that of Jorgensen. Hydrogen and sulfur interaction ˚ The sites are connected with a fixed bond length of 1.34 A. H–S–H bond angle is defined by a harmonic potential: Ubend =

kθ (θ − θ0 )2 2

(3)

where θ0 = 92.5◦ is the equilibrium bond angle and kθ = 32780 K/rad2 is the bending constant. Dispersive interactions are represented by a single Lennard–Jones site placed at the location of the sulfur atom. No dispersive interactions are included for the hydrogen atoms. Point charges are placed on each of the hydrogen and sulfur atoms. Both the Lennard–Jones and partial charge parameters were optimized simultaneously to minimize the deviation of simulation predictions and experimental data for

G. Kamath, J.J. Potoff / Fluid Phase Equilibria 246 (2006) 71–78 Table 1 Parameters for non-bonded interactions used in this work

of dihedral angles involving hydrogen atoms bonded to a methyl carbon are given by

Molecule

Site

εii (K)

˚ σii (A)

H2 S

S H

232 0.0

3.72 0.00

− 0.380 0.190

n-Alkane

Ha C (in CH2 ) C (in CH3 ) C (in CH4 )

15.3 5.0 4.0 0.01

3.31 3.65 3.30 3.31

0.00 0.00 0.00 0.00

C (in CO2 ) O (in CO2 )

27.0 79.0

2.80 3.05

0.70 − 0.35

CO2 a

qi (e)

The site is placed at the midpoint of the C–H bond.

the saturated liquid densities and vapor pressure for pure H2 S and pressure vs composition behavior of the H2 S + n-pentane binary mixture. These optimized Lennard–Jones parameters and partial charges are listed in Table 1. 2.2. n-Alkanes As in the case of H2 S, a number of force fields exist in the literature for normal alkanes that yield accurate predictions in vapor–liquid equilibria calculations (42,49–52). To maintain consistency with our previous work for CO2 + alkane mixtures (34), the transferable potentials for phase equilibria explicit hydrogen (TraPPE-EH) force field (42) was used in this work. In the TraPPE-EH force field, non-bonded Lennard–Jones interactions are placed on the carbon atoms and at the midpoint of the carbon–hydrogen bond. No interaction sites are placed at the hydrogen nuclei. The parameters for all non-bonded interactions are listed in Table 1. The bond lengths, angles and bending constants for the TraPPE-EH force field are listed in Table 2. Carbon and hydrogen atoms are connected with fixed bond lengths. While the H–C–H and C–C–H bond angles are held constant at their equilibrium values, a harmonic potential is used to control the C–C–C bond angle: Ubend =

kθ (θ − θ0 )2 2

(4)

where θ0 = 112.7◦ is the equilibrium bond angle and kθ = 58, 765 K/rad2 . The motion of the C–C–C–C dihedral angles is governed by a three parameter cosine series Utorsion = c1 [1 + cos(φ)] + c2 [1 − cos(2φ)] + c3 [1 + cos(3φ)]

(5)

with the following values for each of the constants: c1 /kb = 355.03 K, c2 /kb = −68.19 K, c3 /kb = 791.32 K. The motion Table 2 Bond lengths, bond angles and force constants Vibration

Bond length (A˚ )

Bending

Bond angle

rH–S rC–H rC–C

1.34 1.10 1.535

rC–O

1.16

∠ HSH ∠ CCC ∠ CCH ∠ HCH ∠ OCO

92.5 112.7 110.7 107.8 180.0

73

(◦ )

kθ /kb (K) 32780 58765 Fixed Fixed Fixed

Utorsion = cx [1 − cos(3φ)]

(6)

where cx = 854 K (53) for C–C–C–H dihedrals and cx = 717 K (54) for H–C–C–H dihedrals. 2.3. Carbon dioxide Like the other molecules of interest in this work, multiple force fields for CO2 that have been optimized for vapor–liquid equilibria calculations can be found in the literature (34,55,56). In this work, the TraPPE force field for CO2 is used (34). This force field was parameterized specifically to yield accurate predictions of pure CO2 phase behavior as well as the phase behavior of CO2 + n-alkane mixtures when used with the TraPPE-EH alkane force field. In this force field, the C O bond length is ˚ and the O C O bond fixed at the experimental value of 1.16 A, angle is held constant at 180◦ . Non-bonded interactions are represented by Lennard–Jones potentials and partial charges placed at each of the atomic nuclei. These non-bonded parameters are listed in Table 1. 3. Simulation details 3.1. Grand canonical Monte Carlo Grand canonical histogram-reweighting Monte Carlo simulations (31–33,56) were used to determine the phase diagrams for each of the binary mixtures studied in this work. The insertion of molecules in the GCMC simulations were enhanced through the application of the coupled–decoupled configurational-bias algorithm method (57). The fractions of the various moves for each simulation were set to 15% for particle displacements, 15% for rotations, 10% configurational bias regrowths and 60% for insertions and deletions. Simulations were performed for a system ˚ except for the H2 S + n-heptane system where size of L = 25 A, ˚ was used. In all calculations, Lennard– a box length of 30 A ˚ and analytical tail Jones interactions were truncated at 10 A corrections were applied (43). Long range electrostatic interactions were calculated with the Ewald sum technique (tinfoil boundary conditions) (43,58). All simulations were equilibrated for (1–2) × 106 Monte Carlo steps (MCS) before run statistics were recorded. Statistics were collected after the equilibration period for an additional (1–5) × 107 MCS, where shorter runs were performed in the gas phase while longer simulations were required in the liquid phase and near critical points. 3.2. Gibbs ensemble Gibbs ensemble Monte Carlo (GEMC) (28–30) was used to determine the phase behavior of the ternary mixture H2 S + CO2 + CH4 . For ternary systems, four-dimensional histograms would be required for the determination of phase equilibria. Due to the complexity of mapping a four-dimensional phase space, the more direct Gibbs ensemble Monte Carlo approach was selected. GEMC simulations were performed for 600 molecules.

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Thirty million Monte Carlo steps were used for the equilibration periods, and results were averaged over the next 30 million MC steps. As in the grand canonical Monte Carlo simulations, ˚ and analytLennard–Jones interactions were truncated at 10 A ical tail corrections were applied. The electrostatic interactions were calculated via an Ewald summation technique identical to GCMC calculations. 4. Results and discussion 4.1. Mixtures of H2 S + n-alkanes Unlike mixtures of H2 S and other alkanes, the mixtures H2 S + ethane (6) and H2 S + propane (10–13) both exhibit maximum pressure azeotropy. This is due to the fact that the experimentally measured normal boiling points for ethane, propane and hydrogen sulfide are all within 15% of each other (Tbethane = propane = 231 K and TbH2 S = 212.9 K). The difference 185 K, Tb in normal boiling points between H2 S and other alkanes, which do not form azeotropic mixtures, is greater than 100 K. In Fig. 1 the predictions of simulation for the pressure– composition behavior of H2 S + ethane at 283.16 K are presented. The experimental data of Kalra et al. (6) and the predictions of the Benedict–Webb–Rubin–Starling (BWRS) equation of state (7) are included for comparison. Simulations predict a maximum pressure azeotrope with an azeotropic pressure and sim = 0.102, respectively. These composition of 30.52 bar and xH 2S values are in close agreement with the experimental values of expt 30.28 bar and xH2 S = 0.1. The agreement of simulation with experiment for the rest of the pressure–composition diagram is excellent. The maximum deviation of the compositions predicted by simulation for a given pressure was determined to be 1.4%. The results of simulation are a significant improvement over the predictions of the BWRS EOS. Although the BWRS EOS predicts a vapor pressure for pure ethane that is within 1% of experiment, the prediction of the pure H2 S vapor pressure is less robust, with an over prediction of approximately 10%. The result

Fig. 1. Pressure–composition diagram for H2 S(1) + ethane(2) at 283.16 K. Simulation results are shown as circles and the BWRS equation of state predictions are shown as dashed lines (7). The solid line represents experimental data (6).

is a shift in the entire H2 S + ethane pressure composition diagram to higher pressures. It should be noted, however, that Kalra et al. were able to achieve a good representation of H2 S + ethane phase behavior with the Peng–Robinson equation of state. The phase behavior of H2 S + propane has been investigated experimentally by a number of researchers (8–13). In the early 1990s, a critical assessment of existing VLE data revealed discrepancies between the published azeotropic compositions (27). In some cases, errors were traced to the use of impure materials (8,9). In other studies, discrepancies arose from the method used to predict the azeotropic point, since these points were not determined directly from experiment, but were instead inferred by interpolation between collected vapor–liquid equilibrium data. These discrepancies were later resolved by Carroll, who used the Peng–Robinson EOS to perform a more physically realistic interpolation between existing data points (27), and Jou et al. who measured the azeotropic compositions directly over a range of temperatures from 252 to 370.15 K (13). Fig. 2 shows the predictions of simulation for the pressure vs. composition behavior for a mixture of H2 S + n-propane at 299.85, 322 and 344.25 K. In comparison to previous simulations performed for this system with the Kristof and Liszi H2 S and the AUA-3 alkane force fields (not shown) (47), our calculations show minor improvements in the propane rich region of the phase diagram, but similar deviations from experiment as the H2 S mole fraction approaches 0.6. A direct comparison of results is not possible due to a lack of overlap in the TPx space covered by the work of Delhommelle et al. and our calculations. The simulations predict correctly the maximum pressure azeotrope for each of the isotherms. In each case, however, the azeotropic pressure is underpredicted by simulation ranging from a relative error of 3.0% for the 344 K data to 5.7% for the 299.85 K dataset. Since azeotropic compositions were not available for the isotherms studied, “experimental” results were determined by fitting a quadratic polynomial to the data of Jou et al.: azeo xC = 0.1588 + 0.0009287T − 3.371 × 10−6 T 2 3 H8

(7)

Fig. 2. Pressure–composition diagram for H2 S(1) + propane(2). Simulation results are represented as 299.85 K (triangle), 322 K (square) and 344.25 K (circle). The solid line represents experimental data (10).

G. Kamath, J.J. Potoff / Fluid Phase Equilibria 246 (2006) 71–78

and interpolating between experimentally measured data points. sim = 0.93 at Simulations predict azeotropic compositions of xH 2S sim sim 344 K, xH2 S = 0.91 at 322 K and xH2 S = 0.88 for 299.85 K, azeo = which compare favorably to the experimental values of xH 2S 0.91, 0.89 and 0.87 for the temperatures 344, 322 and 299.85 K, respectively. The pressure composition behavior of H2 S + pentane has been calculated with molecular simulation by a number of research groups (39–41), but with the exception of solubility calculations by Nath for H2 S in n-decane, n-hexadecane and neicosane (40), no other calculations have been performed for alkanes longer than pentane. In Fig. 3, the predictions of simulation for the pressure–composition behavior of H2 S + n-heptane at 394.26 and 477 K are presented. The experimental data of Ng et al. (18) are included for comparison. Over the majority of the pressures and compositions studied, the predictions of simulation are in close agreement with experiment. The only exception are minor deviations between simulation and experiment in the region near the critical point, which may be due in part to finite-size effects. 4.2. Mixtures of H2 S, CO2 and CH4 4.2.1. Binary constituents The H2 S + CO2 mixture is the most most important nonaqueous system in acid–gas injection (1). This system was investigated experimentally by Bierlein and Kay, who determined the vapor–liquid equilibria over a range of temperatures from 273 to 373 K (24). Robinson et al. experimentally measured a limited number of vapor–liquid equilibria data as part of their investigation of the phase behavior of a ternary mixture of H2 S + CO2 + CH4 (59,60). We note that the Robinson data for the H2 S + CO2 mixture show minor differences compared to that the earlier Bierlein and Kay data set. Recently, Ungerer et al. used Monte Carlo simulations to predict the densities of H2 S + CO2 mixtures (61). The effect of combining rule on the predicted densities was also investigated. Signifi-

Fig. 3. Pressure–composition diagram for H2 S(1) + heptane(2). Simulation results are represented as 394.26 K (circle) and 477 K (square). The solid line represents experimental data (18).

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Fig. 4. Pressure–composition diagram for H2 S(1) + CO2 (2). Simulation results are represented as 293.0 K (circle) and 313.15 K (square). The solid line represents experimental data (24).

cant deviations in the predicted densities were observed when Lorentz–Berthelot combining rules were used, while the Kong combining rules (62) were found to yield results that were in closer agreement with experiment. In this work, Monte Carlo simulations were used to determine the pressure composition behavior of the H2 S + CO2 mixture. The results of these calculations, performed at 293.15 and 313.15 K, are presented in Fig. 4 with the experimental data of Bierlein and Kay for comparison. At 293 K, the reproduction of the pure component vapor pressures is excellent. However, at intermediate pressures, the dew and bubble point H2 S mole fractions are underpredicted by up to 40% These results show that the H2 S CO2 pair interactions are overpredicted by the force fields used in this work. In our previous work with H2 S + n-pentane mixtures, multiple sets of Lennard–Jones and partial charge parameters were found to satisfy the constraint of reproducing accurately pure H2 S phase behavior, as well as the pressure–composition behavior of H2 S + n-pentane mixtures (41). It may be possible to improve the transferability of the H2 S force field presented in this work through a more exhaustive parameter search involving two or more selected binary mixtures. However, such a search is limited by available experimental VLE data as well as the accuracy of the other force fields that would be used in such calculations. For example, H2 S + water VLE data are available (25,63), but none of the current Lennard–Jones + fixed charge based water force fields are capable of reproducing the vapor–liquid coexistence curve and vapor pressure to an accuracy comparable to typical force fields developed for n-alkanes (64–68). In a future work, it would be instructive to simultaneously parameterize a force field for H2 S to reproduce both H2 S + nalkane and H2 S + CO2 phase behavior. Failure of a single force field to reproduce the phase behavior of both mixtures would illuminate physics that were missing from the modeling scheme. CO2 is only weakly attractive to most molecules and H2 S has a relatively small dipole moment of 1.0 D. Therefore, polariz-

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Fig. 5. Pressure–composition diagram for H2 S(1) + methane(2). Simulation results are represented as 277 K (circle), 311 K (square) and 343 K (triangle). The solid line represents experimental data (4). The simulation results of Ungerer et al. at 343 K are shown as (plus) (61).

Fig. 6. Pressure–composition diagram for CO2 (1) + CH4 (2). Simulation results are represented as 220.0 K (circle), 250 K (diamond) and 260 K (triangle). The solid line represents experimental data for each temperature (71). GEMC simulation results of Liu and Beck are represented as(plus) (80).

ability effects involving only fluctuations of charges are not expected to significantly improve the predicted phase behavior. However, a model that includes polarizibility effects in both the Coulombic and well as dispersive interactions may provide a viable, albeit significantly more complex, solution to this problem (69). The mixture H2 S + CH4 is another constituent binary for the H2 S + CO2 + CH4 ternary mixture. In Fig. 5 the predictions of simulation for the pressure–composition behavior of this mixture are presented at 277, 311 and 343 K. The experimental data of Reamer et al. are included for comparison (4). The agreement between simulation and experiment is excellent for mixtures rich in H2 S, but some deviations are present in the gas phase for the 277 K isotherm at pressures above 50 bar. At 343 K, our results are also in close agreement with recent Gibbs ensemble Monte Carlo simulations performed by Ungerer et al. who used the force fields of Kristof and Liszi (38), and M¨oller et al. (70) for modeling the interactions of H2 S and CH4 , respectively Mixtures of CO2 and n-alkanes have been studied extensively both by experiment (71–78) and more recently through Monte Carlo simulations (34,47,79–82). In Fig. 6, the results of our simulations for the CO2 + CH4 mixture are shown in comparison to experiment (71) at 220, 250 and 260 K. The predictions of simulation are in close agreement with experiment over the entire coexistence curve for 250 and 260 K. However, for the 220 K data, the liquid phase mole fractions of CO2 are overpredicted by approximately 13%. For comparison, we present the results of Gibbs ensemble Monte Carlo calculations performed by Liu and Beck at 250 K (80) with the potential models of Lotfi (70,83). In order to improve the agreement of simulation with experiment, Liu and Beck fit binary interaction parameters for both the Lennard–Jones collision diameter and well-depth. Even with the inclusion of binary interaction parameters, their results show a slight overprediction in the CO2 liquid phase mole fraction.

4.2.2. Ternary mixture of carbon dioxide + hydrogen sulfide + methane The H2 S + CH4 + CO2 mixture is one of the few systems involving H2 S where experimental ternary phase equilibrium data are available (59,60). To assess the performance of the TraPPE force fields, Gibbs ensemble Monte Carlo simulations were performed for this mixture at 310.93 K and 41.3 bar. The predicted coexistence data are presented in Fig. 7, while the experimental data of Robinson et al. (59) are included for comparison. At these conditions, both CO2 and CH4 are supercritical and H2 S is the only component that can exist as a pure liquid. Consequently two phase vapor–liquid equilibrium does not occur in the CH4 –CO2 branch of the phase diagram at these conditions. Overall, the simulation results compare well with experiment, with the maximum deviation in composition being under 2.5%. This is an inter-

Fig. 7. Ternary phase diagram for H2 S + CO2 + CH4 at 310.93 K and 41.3 bar. Simulation results are represented as symbols (circle) and experimental data (asterisk) (59).

G. Kamath, J.J. Potoff / Fluid Phase Equilibria 246 (2006) 71–78

77

esting result given the significant deviations of the predicted H2 S + CO2 pressure–composition behavior from experiment shown earlier. These results suggest that the prediction of accurate ternary vapor–liquid equilibria is less sensitive to intermolecular interactions than that of the constituent binary mixtures.

Acknowledgment

5. Conclusions

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In this work, a force field for H2 S originally optimized to reproduce the phase behavior of neat H2 S as well as the pressure– composition behavior of H2 S + n-pentane was used to determine the pressure–composition behavior for a range of systems including alkanes and CO2 . The ability of the H2 S force field used in this work to reproduce the pressure–composition behavior of H2 S + n-alkane mixtures is excellent, although some deviations are observed at certain temperatures and pressures for specific mixtures. These deviations tend to be the largest for temperatures closest to the critical temperature of the nalkane of interest. The predictions of simulation for the pressure– composition behavior of the H2 S + CO2 were less robust, showing significant deviations from experiment for both temperatures studied. These results demonstrate that the H2 S CO2 pair interactions are overpredicted by the force fields chosen in this work, and that further optmization of potential parameters for H2 S, and possibly CO2 , may be necessary to achieve a quantitative representation of experimental VLE data. Despite the deviations from experiment observed in the H2 S + CO2 system, simulations used to predict the ternary phase behavior of the H2 S + CO2 + CH4 mixture at 310.93 K and 41.3 bar were found to be in good agreement with experiment. These results show that the predicted phase behavior of ternary mixtures is less sensitive to the pair-wise interactions specified by the atomistic force fields than that of the constituent binary mixtures. List of symbols c1 , c2 , c3 Fourier constants kb Boltzmann’s constant kθ bond angle force constant P pressure qi partial charge of bead i rij separation between beads i and j T absolute temperature U(rij ) energy of interaction between beads i and j Ubend energy of bond angle bending Utorsion torsional potential Greek letters εii pseudo-atom well depth for the Lennard–Jones potential ε0 permittivity of vacuum θ bond angle θ0 equilibrium bond angle σii pseudo-atom diameter for the Lennard–Jones potential φ dihedral angle

Financial support from National Science Foundation CTS0522005 is gratefully acknowledged. References

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