Propylene Separation by Gas Phase

May 7, 2010 - Phone: +351 22 508 1671. ... Simulated Moving Bed Strategies and Designs: From Established Systems to the Latest Developments ... Gas ph...
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Potential Desorbents for Propane/Propylene Separation by Gas Phase Simulated Moving Bed: A Molecular Simulation Study Miguel A. Granato,† Thijs J. H. Vlugt,‡ and Alı´rio E. Rodrigues*,† Laboratory of Separation and Reaction Engineering (LSRE), Department of Chemical Engineering, Faculty of Engineering, UniVersity of Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal, and Delft UniVersity of Technology, Process & Energy Laboratory, Leeghwaterstraat 44, 2628 CA-Delft, The Netherlands

This paper is focused on using molecular simulation as a tool to guide the choice of desorbent for the separation propane/propylene by simulated moving bed (SMB) processes. Equilibrium adsorption isotherms of n-butane and neopentane on zeolite 13X and adsorption equilibria of binary mixtures of each one of these adsorbates with propane and with propylene were obtained by molecular simulation, in a predictive screening of an adequate desorbent for the separation of propane/propylene by the SMB technology. Comparisons of experimental isotherms with grand canonical Monte Carlo simulations in zeolite 13X showed that the results of n-butane are in excellent agreement with reported simulations and experimental data. The carbon-cation interactions for the quaternary carbon atom of neopentane were established and validated through determination of adsorption properties of binary mixtures of neopentane with propane and with propylene. The lack of experimental data of neopentane adsorption motivated the present study, providing the opportunity to predict the single adsorption isotherms over a temperature range from 273 to 423 K and pressures up to 150 kPa. From the simulated isotherms of neopentane in 13X zeolite, the isosteric heat of adsorption of 39.19 kJ/mol was calculated by using the Clausius-Clapeyron equation, in close agreement with the published value of 41.7 kJ/mol. Additionally, the simulation results of the binary mixtures with propane and with propylene showed that neopentane and propane have similar affinities to the adsorbent, which indicates a less favorable desorption effect for neopentane, compared with that of n-butane. 1. Introduction One of the most energy consuming operations in the petrochemical industry is the separation of propane/propylene mixtures. Cryogenic distillation is very energy intensive because of the small difference in their relative volatilities. A typical distillation column used to separate propane and propylene operates at -30 °C and 30 psig (0.308 MPa); contains more than 100 theoretical stages and can be up to 10 m high; and consumes about 1.7 MW h per ton of polymer grade propylene.1,2 Various studies have been initiated to replace the cryogenic distillation usually used for this separation, and cyclic adsorption processes appeared to be a promising option. The simulated moving bed (SMB) is an interesting and competitive alternative for separating gas mixtures. In order to develop a design strategy for this separation by SMB, one should consider different approaches, starting from equilibrium assumptions through more detailed models, accounting for mass transfer resistances, temperature, and pressure drop effects. Recent published results show that this separation is possible with the SMB technology, providing high purity propylene (>99.5%), at high recovery (>99.0%), and promising productivity values, above 1000 kg of propylene/mads3 · h. In comparison to other fixed bed adsorption systems, the SMB can achieve higher efficiency.3 As an example, vacuum pressure swing adsorption (VPSA) technology requires two coupled VPSA units to produce polymer-grade propylene (>99.6%) with 94% propylene recovering. This VPSA process has advantages over fractional distillation in terms of decrease in the separation volume. However, the power consumption of VPSA is still slightly higher than that for distillation.4 * To whom correspondence should be addressed. Phone: +351 22 508 1671. Fax: +351 22 508 1674. E-mail: [email protected]. † Faculty of Engineering, University of Porto. ‡ Delft University of Technology.

Furthermore, an SMB unit has to be coupled to distillation columns in order to concentrate the extract/raffinate, and to recover the desorbent. The difference between the boiling points of the desorbent and those of the raffinate (or the extract) is of key importance for the efficiency of the distillation step. Several potential desorbents for propane/propylene separation by SMB have been proposed in the literature. Lamia5 presented a review of selected hydrocarbons, which are suitable to be applied in cyclic separation processes to the propane/propylene system. This list comprises isobutane, butene-1, n-butane, n-pentane, neopentane, cyclopropane, cyclobutene, and cyclopentane.5 The linear alkanes have been already suggested as desorbents.6,7 n-Butane was taken as representative of the linear alkanes, and neopentane, which from the molecular simulation point of view represents a new contribution since the molecule contains a quaternary carbon and a new force field has to be developed and validated. At 1 atm, propane has a boiling point of -42.1 °C, and propylene has one of -47.8 °C. The boiling point of n-butane is -0.5 °C and that of neopentane is 10 °C.1 The design of an SMB unit requires not only the choice of a good solid adsorbent, but the selection of an efficient desorbent as well. The separation of a propane/propylene mixture over a column packed with 13X zeolite using isobutane and 1-butene as desorbents has been studied by Lamia et al.8,9 Multicomponent breakthrough experiments confirmed that isobutane was able to displace propane and propylene from 13X zeolite as it was itself easily displaced from the adsorbent, so that the zeolite could be reused in a cyclic gas separation processes such SMB.8–10 In addition, equilibrium adsorption isotherms of isobutane and 1-butene and x-y diagrams of binary mixtures of these components with propane and propylene in Zeolite 13X were calculated by using the configurational-bias Monte Carlo technique in the grand-canonical ensemble. The result of this study was a new set of force field parameters, extended for

10.1021/ie901732s  2010 American Chemical Society Published on Web 05/07/2010

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branched alkanes, that successfully reproduces experimental data that can be used to guide further development of SMB processes.11 The use of molecular simulations is very useful as a prediction tool, replacing expensive and long-time experiments. Our study encompasses data-driVen simulations, in which calculations are made to predict properties with little or no input from experiment. Simulations are used to interpolate between experimental data, extrapolate outside the range where data are available, or predict properties for compounds for which little or no data are available.12 The choice of a specific force field has several aspects to be considered. The all-atom (AA) force fields consider each atom individually. The united-atom (UA) and anisotropic-united-atom (AUA) force fields treat carbon atoms and their bonded hydrogens as a single interaction site. The UA models consider interactions to act on the center of the site, while for the AUA models, the interaction center is shifted to an intermediate position between the central atom and the connected hydrogen atoms.13,14 In this work, we applied the UA model, which gives effective estimates of adsorption properties that can be applied to engineering problems, such as projects of SMB or PSA (pressure swing adsorption). A reasonably accurate prediction of adsorption properties of single-component and binary mixtures can be obtained by grand-canonical Monte Carlo (GCMC) simulations with a suitable force field.15–17 The present work is focused on using molecular simulation as a tool to guide the choice of desorbent (n-butane and neopentane) for the separation propane/propylene by the SMB process and includes the following steps: (1) applying molecular simulations to provide information of chemical species in order to predict properties which can be used for engineering purposes; (2) developing a new set of force field parameters for the quaternary carbon interactions of neopentane with the sodium cations; (3) reproducing experimental data of equilibrium adsorption properties of neopentane in 13X zeolite and predicting the adsorption properties of binary mixtures of neopentane with propane and with propylene, in order to validate the force field parameters; (4) confirming previously published force fields by reproducing recent experimental data on adsorption of butane in 13X zeolite, single component, and finally, (5) using this force field to predict its binary mixtures with propane and with propylene. The paper is organized as follows. Details of the simulation method are given in section 2. Section 3 presents our results

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on adsorption equilibrium of n-butane and neopentane in the zeolite 13X framework. Finally, the main conclusions are summarized in section 4. 2. Simulation Methodology Adsorption isotherms were calculated by using the configurational-bias Monte Carlo (CBMC) technique in the grandcanonical (µVT) ensemble. In this ensemble, the zeolite crystals are allowed to exchange molecules with a reservoir of molecules at a fixed chemical potential and temperature. The simulations are performed in cycles, and in each cycle, one move is chosen at random with a fixed probability of four types of moves: molecule translation (0.15), rotation around the center of mass (0.15), exchange with the reservoir (0.55), and partial regrowth of a molecule (0.15). For mixtures, the number of exchanges was reduced to 0.50, and identity change moves have been included (0.05). The number of cycles was 2 × 106. For a more detailed explanation of this simulation technique, the reader is referred to refs 16 and 18. The extension of the CBMC algorithm to branched molecules is described in refs 16, 19, and 20. The alkane/alkene molecules were simulated using the united atom (UA) model. In this model, each CHn group is treated as a single interaction center. For calculations of adsorption properties, such as isotherms and heats of sorption, the UA model is appropriate because of its reduced set of parameters to describe the interand intramolecular interactions between the pseudoatoms. The UA force field requires only two optimized Lennard-Jones (LJ) parameters per pseudoatom: the strength parameter ε and the size parameter σ. For simple hydrocarbons, such as alkanes or alkenes, the computational demands of a simulation with UA force fields are considerably smaller than those of an all-atom calculation.13,20 The zeolite structure is considered to be rigid, as the flexibility of the framework has a negligible influence on adsorption properties,21 but the Na+ cations are fully mobile. It was demonstrated by Calero et al.,22 that simulations using fixed Na+ cations overestimate the adsorption of alkanes at low pressures and underestimate the adsorption of alkanes at high pressures. The zeolite framework model is described as the sodium form of Faujasite type zeolites, obtained by randomly substituting silicon by aluminum, satisfying the Lo¨wenstein rule. We used a cation density of 88 Na+ per unit cell, which yields a Na88Al88Si104O384 unit cell composition. Periodic boundary conditions were applied in all directions.

Table 1. Intermolecular Parameters for United Atom (UA) Force Fielda Lennard-Jones CH3

ε/kB [K] σ [Å] ε/kB [K] σ [Å] ε/kB [K] σ [Å] ε/kB [K] σ [Å] ε/kB [K] σ [Å] ε/kB [K] σ [Å]

CH2 sp3 CH2 sp2 C sp3 CH sp2 Na

a

OAl

OSi

Na

CH3

CH2 sp3

CH2 sp2

C sp3

CH sp2

93.00 3.48 60.50 3.58 77.30 3.50 10.00 4.56 62.50 3.46 23.00 3.40

93.00 3.48 60.50 3.58 77.30 3.50 10.00 4.56 62.50 3.46 23.00 3.40

443.73 2.65 310.00 2.95 398.40 3.14 0.25 6.70 289.02 3.17 124.40 2.16

108.00 3.76 77.70 3.86 95.81 3.72 9.03 5.07 71.25 3.75 443.73 2.65

77.70 3.86 56.00 3.96 68.99 3.82 6.69 5.17 51.30 3.85 310.00 2.95

95.81 3.72 68.99 3.82 85.00 3.68 8.25 5.03 63.21 3.70 398.40 3.14

32.86 4.22 23.66 4.32 29.15 4.18 0.80 6.38 21.68 4.21 6.70 0.25

71.25 3.75 51.30 3.85 63.21 3.70 6.13 5.06 47.00 3.73 289.02 3.17

point charges

OAl

OSi

Na

Si

Al

q [e]

-1.20

-1.025

+1.00

+2.05

+1.75

The partial charges [e] of the framework and the sodium cations are given at the bottom of the table. Most parameters are taken from the work of Calero et al.22 The parameters of sp2-bonded atoms are taken from our previous work.25 The LJ parameters of quaternary-carbon/nonframework cation interactions (in italics) were obtained by adjusting the force field through fitting a full isotherm. The methodology is described in ref 22. OAl are oxygens bridging one silicon and one aluminum atom, and OSi are oxygens bridging two silicon atoms.

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Table 2. Intramolecular Parameters for the United Atom (UA) Force Field bond energy constant reference bond length bend energy constant reference bend angle

CHisCHj CHidCHj alkane alkene alkane alkene

k1/kB ) 96500 K/Å2 r0 ) 1.54 Å r0 ) 1.33 Å k2/kB ) 62500 K/rad2 k2/kB ) 70400 K/rad2 θ0 ) 114° θ0 ) 119.7°

The inter- and intramolecular parameters used in this work are listed in Tables 1 and 2. It is noteworthy to mention that the LJ interaction parameters of the quaternary carbon with the nonframework cations were established by fitting a full isotherm of neopentane at 273 K and pressures from 1 × 10-4 to 150 kPa, taking as reference the experimental data from Bu¨low et al. and from Hathaway and Davis.23,24 The other interaction parameters between the sp2 carbons, the nonframework cations, and the zeolite atoms were taken from our previous work on adsorption of propane and propylene in zeolite 13X.25 The Lorentz-Berthelot mixing rules are used to calculate most cross interactions between different pseudoatoms, except for the interactions with the nonframework cations.21,26 The Ewald summation is used for calculating electrostatic interactions. The Ewald technique is widely described elsewhere.18,27

3. Simulations Results 3.1. Adsorption of n-Butane in Zeolite 13X. A recently developed united atom force field successfully reproduces experimental adsorption properties of n-alkanes, from methane to dodecane. The results of molecular simulations on n-butane adsorption have found that n-butane redistributes the sodium cations and induces a smaller sodium migration from the sodalite cages to the supercages. Calero and co-workers22 studied cation redistribution upon alkane adsorption in FAU. This study was made for n-butane in FAU-58-Na and FAU-96-Na, in two steps: first, simulations for the adsorbate-free zeolites were performed, in order to give information about the sodium cations occupancies, and the results have shown a good agreement with experimental data. Subsequently, n-butane adsorption was simulated. The effect of n-butane loadings is shown in Table 4 of ref 22. On the basis of this study, it is expected that the same effect can occur for other alkanes. Equilibrium adsorption isotherms of n-butane in zeolite 13X were calculated by CBMC simulations in the grand-canonical (µVT) ensemble, for a pressure range of 0.01-150 kPa and temperatures of 300, 333, 353, and 373 K. The simulations have been performed for a nonframework cation density of 88 Na+ per unit cell. Additional calculations have been made for

Figure 1. Adsorption isotherms of n-butane on zeolite 13X: comparison between simulations (open symbols)22 and experimental data (closed symbols).28

Figure 2. Simulated adsorption isotherms of n-butane on zeolite 13X.

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Figure 3. Equilibrium x-y diagrams of n-butane/propane in zeolite 13X at 348 K and a total pressure of 106.7 kPa. Closed squares are experimental data,29 and open triangles are simulations results. Errors are smaller than symbol size.

Figure 5. Simulations of binary equilibrium adsorption: (a) n-butane/propane and (b) n-butane/propylene in zeolite 13X at 373 K and a total pressure of 110 kPa.

Figure 4. Simulation results of n-butane/propane and n-butane/propylene in zeolite 13X: equilibrium x-y diagrams at 373 K and a total pressure of 110 kPa. Errors are smaller than symbol size.

comparison with experimental data from the work of Tarek et al.28 and simulation results from the work of Calero et al.22 The results are presented in Figures 1 and 2. The agreement between simulations and the results from Tarek et al. is very good, which confirms once more the applicability of the force field parameters. 3.2. Binary Adsorption of n-Butane/Propane and n-Butane/ Propylene in Zeolite 13X. In order to validate the results of n-butane adsorption in zeolite 13X, we performed simulations of binary mixtures of n-butane/propane and n-butane/propylene in 13X framework for several mole fractions of n-butane. The results of the n-butane/propane mixture in zeolite 13X at 348 K and a total pressure of 106.7 kPa show a very good agreement with experimental data from Hamad,29 as shown in Figure 3. However, no experimental studies on n-butane/propylene adsorption in zeolite 13X have been found in the literature. Thus,

we performed the simulations of binary mixtures of n-butane/ propylene as a predictive screening based on the reliability of our previous results. The corresponding x-y diagrams (Figure 4) and the equilibrium gas phase/adsorbed phase compositionss Figures 5a and bsshow the results of our calculations. From the binary diagrams, it is seen that n-butane exhibits a very good performance to be used as a desorbent for propane/propylene separation, because n-butane readily displaces propane and propylene. The boiling point of -0.5 °C is an additional favorable feature that makes n-butane very promising as a desorbent for propane/propylene separation by the SMB technology. 3.3. Adsorption of Neopentane in Zeolite 13X. Neopentane has been successfully used as a probe molecule to assess microporosity determinations in microporous carbons30 and to investigate intracrystalline diffusivities by sorption kinetics in zeolites.23 For the purpose of application to propane/propylene separation by SMB, as a potential desorbent for propane and propylene removal from the adsorbent bed, neopentane is seen to be very interesting, due to its higher boiling point, which facilitates its removal in the subsequent distillation step. Because adsorption data of neopentane on 13X zeolite are scarce, equilibrium isotherms of this molecule over 13X zeolite have been calculated

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Figure 6. Adsorption isotherms of neopentane on zeolite 13X at 273 K: comparison between simulations (open symbols) and experimental data (closed symbols).23,24

Figure 7. Simulated adsorption isotherms of neopentane on zeolite 13X.

by CBMC simulations in the µVT ensemble for a wide range of pressures and for temperatures of 273, 333, 353, 373, and 423 K. The interactions of the quaternary C with the sodium cations have been determined by adjustment of the simulation results to experimental data for the adsorption of neopentane.23,24 The weak interactions between the quaternary carbon and the nonframework sodium cations are due to the steric hindrance effect. Simulations were carried out for a pressure range of 10-4 to 150 kPa at 273 K and are shown in Figure 6, in excellent agreement with the experiments. The simulations of equilibrium adsorption isotherms of neopentane at temperatures of 333, 353, 373, and 423 K were performed using the force field parameters listed in Tables 1 and 2, in a predictive screening of the adsorption capacities in zeolite 13X. With these results, we calculated the value of -39.19 kJ/mol for the isosteric heat of adsorption at low coverage by means of the Clausius-Clapeyron relationship,

which agrees very well with the value of -41.7 kJ/mol, reported by Bu¨low et al.23 The simulated isotherms are presented in Figure 7. 3.4. Binary Adsorption of Neopentane/Propane and Neopentane/Propylene in Zeolite 13X. The binary adsorption equilibria of neopentane with propane and propylene, respectively, have been simulated by CBMC technique at 373 K and several mole fractions of neopentane. The resulting x-y diagrams are shown in Figure 8, and the equilibrium gas phase/ adsorbed phase compositions are shown in Figure 9a and b. Our simulations show that neopentane is less preferred to adsorb in 13X zeolite than both propane and propylene, but the pair neopentane-propane has almost equal selectivities at the studied conditions (373 K, 110 kPa total pressure). It turns out that neopentane is able to desorb more propylene than propane, which makes this separation more difficult than that using n-butane as desorbent. However, due to its higher boiling point,

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Figure 8. Simulation results of neopentane/propane and neopentane/propylene in zeolite 13X: equilibrium x-y diagrams at 373 K and a total pressure of 110 kPa. Errors are smaller than symbol size.

Figure 9. Simulations of binary equilibrium adsorption: (a) neopentane/propane and (b) neopentane/propylene in zeolite 13X at 373 K and a total pressure of 110 kPa.

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Figure 10. Isotherms in zeolite 13X of propylene (triangles), propane (circles), n-butane (squares), and neopentane (diamonds) at 373 K: simulations (closed symbols) and experimental data from the work of Lamia et al. (open symbols).5,8

neopentane still remains as a desorbent for propane/propylene separation by SMB to be experimentally tested.

Therefore, n-butane is a better desorbent than neopentane in SMB process for the separation propane/propylene.

4. Conclusions

Acknowledgment

The adsorption isotherms of n-butane and neopentane and the x-y diagrams of binary mixtures of these components with propane and propylene in zeolite 13X have been calculated by using the configurational-bias technique in the grand-canonical ensemble. For n-butane, the single component isotherms and the x-y diagrams are in excellent agreement with published experimental data. In the case of neopentane, experimental studies are scarce and there is no available data of binary mixtures with propane or propylene. However, the calculated isosteric heat of adsorption of neopentane in 13X zeolite at low coverage (-39.19 kJ/mol) is in excellent agreement with the value of -41.7 kJ/mol reported by Bu¨low et al.23 and validates the force field parameters established by fitting the available experimental isotherms. The loadings of n-butane in zeolite 13X are higher than the loadings of propane, propylene, and neopentane, up to a pressure of 50 kPa, at 373 K (Figure 10). At higher pressures, the loadings of butane go to intermediate values between propylene and propane, but higher than neopentane. On the other way, neopentane exhibits intermediate adsorption capacities between propane and propylene at pressures up to 40 kPa and becomes less adsorbed than these hydrocarbons at higher pressures. This behavior, associated with the higher boiling points of n-butane and neopentane, indicates that these are potential desorbent candidates for application in the separation of propane/propylene by SMB. From the simulation results of binary mixtures of n-butane with propane and with propylene, it follows that n-butane is able to replace both C3 hydrocarbons with a good desorption effect. However, neopentane exhibits a poor capability for desorbing propane from the adsorption bed. The Henry coefficient of neopentane is much smaller than that of n-butane, as shown in Figure 10, and it is of the same order of magnitude as those of propane/propylene. Additionally, at the applied pressure of 110 kPa (Figures 5, 8, and 9), in the case of a pure component neopentane, the zeolite is already saturated (see Figure 10), and the maximum loading is much smaller than for propane/propylene and n-butane. So the packing efficiency of neopentane is poor; this has to do with the fact that it is quite a bulky molecule.

M.A.G. acknowledges Fundac¸a˜o para a Cieˆncia e a Tecnologia (FCT, Portugal) for a research grant, ref SFRH/BPD/ 47432/2008. Literature Cited (1) Rodrigues, A. E.; da Silva, F. A.; Granato, M. A.; Lamia, N.; Grande, C.; Gomes, P. S. Development of Propane/Propylene Separations: From Molecular Simulation to Processes. Engineering Conference International (ECI) - The Role of Structure in Biological, Chemical and EnVironmental Separations: From the Molecular to the Macro, Costa Rica, January 611, 2008. (2) Rege, S. U.; Padin, J.; Yang, R. T. Olefin/ Paraffin Separations by Adsorption: π-Complexation vs. Kinetic Separation. AIChE J. 1998, 44, 799. (3) Gomes, P. S.; Lamia, N.; Rodrigues, A. E. Design of a Gas Phase Simulated Moving Bed for Propane/Propylene Separation. Chem. Eng. Sci. 2009, 64, 1336. (4) Grande, C. A.: Poplow, F.; Rodrigues, A. E. Vacuum Pressure Swing Adsorption to Produce Polymer-Grade Propylene. Sep. Sci. Technol., in press. (5) Lamia, N. Mode´lisation de la Se´paration du Me´lange Propane/ Propyle`ne par Adsorption en Lit Mobile Simule´. Ph.D. Thesis, University of Porto, Portugal, 2008. (6) Peterson, D. L.; Hefferich, F.; Griep, R. K. Thermodynamics of Mixed-Gas Adsorption. Proc. 1st Int. Conf. On Molecular SieVes, 217229, London, April 4-6, 1967, published by Soc. Chem. Ind. 1968. (7) Stine, L. O.; Hardison, L. C.; Lickus, A. G. Fluid Solid Contacting Process. U. S. Patent 3.231.492, 1966. (8) Lamia, N.; Wolff, L.; Leflaive, P.; Gomes, P. S.; Grande, C. A.; Rodrigues, A. E. Propane/Propylene Separation by Simulated Moving Bed I. Adsorption of Propane, Propylene and Isobutane in Pellets of 13X Zeolite. Sep. Sci. Technol. 2007, 42, 2539. (9) Lamia, N.; Granato, M. A.; Sa´ Gomes, P.; Grande, C. A.; Wolff, L.; Leflaive, P.; Leinekugel-le-Cocq, D.; Rodrigues, A. E. Propane/Propylene Separation by Simulated Moving Bed II. Measurement and Prediction of Binary Adsorption Equilibria of Propane, Propylene, Isobutane, and 1-Butene on 13X Zeolite. Sep. Sci. Technol. 2009, 44, 1485. (10) Rodrigues, A. E.; Lamia, N.; Grande, C. A.; Wolff, L.; Leflaive, P.; Leinekugel le-Coq, D. Proce´de´ de Se´paration du Propyle`ne en Me´lange Avec du Propane par Adsorption en Lit Mobile Simule´ en Phase Gaz ou Liquide Utilisant une Ze´olithe de Type Faujasite 13X Comme Solide Adsorbant. FR. Patent 2.903.981, July, 2006; INT. Patent WO/2008/.12410, January, 2008. (11) Granato, M. A.; Lamia, N.; Vlugt, T. J. H.; Rodrigues, A. E. Adsorption Equilibrium of Isobutane and 1-Butene in Zeolite 13X by Molecular Simulation. Ind. Eng. Chem. Res. 2008, 47, 6166.

Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 (12) Maginn, E. J. From Discovery to Data: What Must Happen for Molecular Simulation. AIChE J. 2009, 55, 1304. (13) Martin, M. G.; Siepmann, J. I. Transferable Potentials for Phase Equilibria - 1: United-Atom Description of n-Alkanes. J. Phys. Chem. B 1998, 102, 25569. (14) Ungerer, P.; Beauvais, C.; Delhommelle, J.; Boutin, A.; Rousseau, B.; Fuchs, A. H. Optimization of the Anisotropic United Atoms Intermolecular Potential for n-Alkanes. J. Chem. Phys. 2000, 112, 5499. (15) Du, Z.; Manos, G.; Vlugt, T. J. H.; Smit, B. Molecular Simulation of Adsorption of Short Linear Alkanes and Their Mixtures in Silicalite. AIChE J. 1998, 44, 1756. (16) Vlugt, T. J. H.; Krishna, R.; Smit, B. Molecular Simulations of Adsorption Isotherms for Linear and Branched Alkanes and Their Mixtures in Silicalite. J. Phys. Chem. B. 1999, 103, 1102. (17) Smit, B.; Krishna, R. Monte Carlo Simulations in Zeolites. Curr. Opin. Solid State Mater. Sci. 2001, 5, 455. (18) Frenkel, D.; Smit, B. Understanding Molecular Simulations: From Algorithms to Applications, 2nd ed.; Academic Press: San Diego, 2002. (19) Macedonia, M. D.; Maginn, E. J. A Biased Grand-canonical Monte Carlo Method for Simulating Adsorption Using All-atom and Branched United Atom Models. Mol. Phys. 1999, 96, 1375. (20) Martin, M. G.; Siepmann, J. I. Novel Configurational-Bias Monte Carlo Method for Branched Molecules. Transferable Potentials for Phase Equilibria. 2. United-Atom Description of Branched Alkanes. J. Phys. Chem. B. 1999, 103, 4508. (21) Vlugt, T. J. H.; Schenk, M. Influence of Framework Flexibility on the Adsorption Properties of Hydrocarbons in the Zeolite Silicalite. J. Phys. Chem. B. 2002, 106, 12757.

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(22) Calero, S.; Dubbeldam, D.; Krishna, R.; Smit, B.; Vlugt, T. J. H.; Denayer, J. F. M.; Martens, J. A.; Maesen, T. L. M. Understanding the Role of Sodium During Adsorption: A Force Field for Alkanes in sodiumExchanged Faujasites. J. Am. Chem. Soc. 2004, 126, 11377. (23) Bu¨low, M.; Lorentz, P.; Mietk, W.; Struve, P.; Samulevicˇ, N. N. Sorption Kinetics of Neopentane on NaX Zeolites of Different Crystal Sizes. J. Chem. Soc., Faraday Trans. I 1983, 79, 109. (24) Hathaway, P. E.; Davis, M. E. High Resolution, Quasi-Equilibrium Sorption Studies of Molecular Sieves. Catal. Lett. 1990, 5, 333. (25) Granato, M. A.; Vlugt, T. J. H.; Rodrigues, A. E. Molecular Simulation of Propane-Propylene Binary Adsorption Equilibrium in Zeolite 13X. Ind. Eng. Chem. Res. 2007, 46, 7239. (26) Beerdsen, E.; Smit, B.; Calero, S. The Influence of Non-framework Sodium Cations on the Adsorption of Alkanes in MFI- and MOR-Type Zeolites. J. Phys. Chem. B. 2002, 106, 10659. (27) Alllen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (28) Tarek, M.; Kahn, R.; de Lara, E. C. Modelization of Experimental Isotherms of n-Alkanes in NaX Zeolite. Zeolites 1995, 15, 67. (29) Hamad, E.-Al-D. Z. Comparison of Binary Sorption of Propane and N-Butane on 5A and 13X Zeolites. M.Sc. Thesis, King Fahd University of Petroleum and Minerals, Saudi Arabia, 1984. (30) Roberts, R. A.; Sing, K. S. W.; Tripathi, V. Adsorption of Nitrogen and Neopentane Vapor by Microporous Carbons. Langmuir 1987, 3, 331.

ReceiVed for reView November 2, 2009 ReVised manuscript receiVed April 12, 2010 Accepted April 26, 2010 IE901732S