Monte Carlo Simulations Probing the Adsorptive Separation of

Oct 16, 2015 - Alberto Fraccarollo , Lorenzo Canti , Leonardo Marchese , and Maurizio Cossi. Journal of Chemical Theory and Computation 2017 13 (4), ...
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Monte Carlo Simulations Probing the Adsorptive Separation of Hydrogen Sulfide/Methane Mixtures Using All-Silica Zeolites Mansi S. Shah,†,§ Michael Tsapatsis,† and J. Ilja Siepmann*,†,‡,§ †

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States ‡ Department of Chemistry and §Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States S Supporting Information *

ABSTRACT: Selective removal of hydrogen sulfide (H2S) from sour natural gas mixtures is one of the key challenges facing the natural gas industry. Adsorption and pervaporation processes utilizing nanoporous materials, such as zeolites, can be alternatives to highly energyintensive amine-based absorption processes. In this work, the adsorption behavior of binary mixtures containing H2S and methane (CH4) in seven different all-silica zeolite frameworks (CHA, DDR, FER, IFR, MFI, MOR, and MWW) is investigated using Gibbs ensemble Monte Carlo simulations at two temperatures (298 and 343 K) and pressures ranging from 1 to 50 bar. The simulations demonstrate high selectivities that, with the exception of MOR, increase with increasing H2S concentration due to favorable sorbate−sorbate interactions. The simulations indicate significant inaccuracies of predictions using unary adsorption data and ideal adsorbed solution theory. In addition, the adsorption of binary H2S/H2O mixtures in MFI is considered to probe whether the presence of H2S induces coadsorption and reduces the hydrophobic character of all-silica zeolites. The simulations show preferential adsorption of H2S from moist gases with a selectivity of about 18 over H2O.

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INTRODUCTION Hydrogen sulfide is a very toxic gas, and causes irritation to eyes, nose, and throat at concentrations as low as 5 ppm, and results in an almost instantaneous death at concentrations above 1000 ppm.1 Large reserves of natural gas are untapped today due to the difficulties involved in processing low-quality sour gas. The development of alkanolamines for acid gas absorption dates back to as early as 1930.2 Since then, aminebased regenerative absorption processes, that employ aqueous solutions of organic amines, have been used for large-scale acid gas sweetening.3,4 The H2S-rich stream, generated as a result of this process, is subjected to sulfur recovery in the Claus unit, where H2S is converted to elemental sulfur. Present-day natural gas industries are facing two main challenges as regards to the sweetening of sour gas. First, with an increase in the H2S content of newer gas fields, the load on the acid gas treatment unit is expected to increase dramatically. Second, increasingly stringent government regulations on permissible sulfur emissions may lead to current H2S cleanup strategies becoming technologically and/or economically insufficient. Thus, as demand for cleaner energy resources continues to rise and also as the need to explore more difficult, that is, sourer, natural gas reservoirs becomes more pressing, better technologies for efficient H2S removal will become pivotal. Adsorptive separations have numerous advantages over absorptive separations: Smaller foot-print, less exorbitant materials of construction for equipment, and lower pumping © XXXX American Chemical Society

costs are among them. In the past few years, applications of newly discovered nanoporous materials such as zeolites and metal−organic frameworks (MOFs) have demonstrated the potential for adsorptive separations.5−7 The structural and chemical stability of zeolites over vast ranges of temperature and pressure makes them potential candidates for separations involving highly corrosive sour natural gas streams. Raw natural gas emerging from wells often contains a significant amount of water. The gas-phase dipole moment of water (1.85 D) is about twice that of hydrogen sulfide (0.98 D), and water forms much stronger hydrogen bonds. Hence, there is a large enthalpic gain for water to adsorb preferentially over H2S on polar solids, particularly those with the ability to act as hydrogen bond acceptor or donor, thereby making the adsorption sites largely unavailable to H2S. However, highly siliceous zeolites (Si/Al ratio tending to infinity) made with specialized synthesis methods8 contain negligible amounts of polar cations and silanol groups, and these materials are extremely hydrophobic. Hence, there is a potential for all-silica zeolites to selectively capture H2S from natural gas streams. In this work, adsorption of H2S in seven all-silica zeolite frameworks is investigated via particle-based Monte Carlo simulations. Selectivity data for H2S over CH4 adsorption at Received: August 13, 2015 Revised: October 13, 2015

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Langmuir Table 1. Zeolite Unit Cell Parameters and Simulation Box Sizes Used in This Work zeolite

a [Å]

b [Å]

c [Å]

α [deg]

β [deg]

γ [deg]

ref

CHA DDR FER IFR MFI MOR MWW

13.5292 13.860 18.7202 18.496 20.022 18.11 14.2081

13.5295 13.860 14.0702 13.4406 19.899 20.53 14.2081

14.748 40.891 7.4197 7.7111 13.383 7.528 24.945

90.00 90.00 90.00 90.00 90.00 90.00 90.00

90.00 90.00 90.00 101.58 90.00 90.00 90.00

120.00 120.00 90.00 90.00 90.00 90.00 120.00

́ Diaz-Cabañ as et al.23 Gies24 Morris et al.25 Barrett et al.26 Van Koningsveld et al.27 Gramlich28 Camblor et al.29

METHODOLOGY

Molecular Models. All force fields used in this work are nonpolarizable and have a rigid geometry. Nonbonded interactions are modeled using pairwise-additive potentials consisting of Lennard− Jones (LJ) 12−6 and Coulomb terms: ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj σij σij U (rij) = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ 4πε0rij ⎣⎝ ij ⎠

3 3 2 2 2 2 3

× × × × × × ×

3 3 3 3 2 2 3

× × × × × × ×

3 1 4 5 3 4 2

positions for the purpose of this work. The zeolite framework is treated as rigid during the course of the simulation, with Si and O atoms fixed at their crystallographically determined positions. The LJ potentials for the sorbate−sorbate interactions in the zeolite and liquid phases are truncated at 14 Å, whereas the cutoff distance is set to approximately 40% of the box length for the vapor phase (to achieve a computationally efficient balance between direct and reciprocal space parts of the Ewald summation). Analytical tail corrections to energy and pressure are applied for the sorbate−sorbate LJ interactions in all phases.14 The Ewald summation method with a screening parameter of κ = 3.2/rcut and an upper bound of the reciprocal space summation at Kmax = int(κ Lbox) + 1 is used for the calculation of the Coulomb energy.14 In order to improve the simulation efficiency, all sorbate−sorbent LJ and Coulomb interactions (using periodic lattice sums to convergence) are pretabulated with a grid spacing of ≈0.2 Å and interpolated during the simulation for any position of an interaction site belonging to a sorbate molecule.30,31 Four different types of Monte Carlo moves, including translational, rotational, volume exchange (only applied between explicitly modeled reservoir phase and ideal gas bath and not for the zeolite phase), and particle transfer moves, are used to sample the statistical-mechanical phase space. The coupled−decoupled configurational-bias Monte Carlo algorithm16 with the dual cutoff approach32 is used to enhance the acceptance rate for particle transfer moves. The probabilities for volume and transfer moves are adjusted to have approximately one accepted move per Monte Carlo cycle (MCC),33 where an MCC consists of a number of randomly selected moves that is equal to the total number of sorbet molecules in the system. In case of binary mixtures, the probability to choose a molecule type for transfer move is set to allow the ratio of accepted transfers for the two molecule types to be approximately proportional to the overall composition. The remaining moves are divided equally between translations and rotations. Production periods consisting of 25 000−50 000 MCCs are used to obtain the unary adsorption isotherms for CH4 and H2S, while 150 000 MCCs are used for the binary simulations in order to obtain better statistics even for the dilute compositions. We used 400 000 MCCs for the adsorption simulations from an extremely dilute liquid phase containing trace amounts of H2S in H2O; 150 000 MCCs are used for simulating the vapor−liquid equilibrium of the H2S/H2O mixture. For binary mixtures, the partial molar enthalpies of adsorption for the two components can be quite different and can provide greater insight than simply the overall enthalpy of adsorption. These are computed from the differences between the total adsorption enthalpies of configurations that differ in the number of only one species. For all adsorption systems investigated in this work, eight independent Monte Carlo simulations are carried out and the statistical uncertainties reported in the following sections correspond to the standard error of the mean calculated from these independent simulations.

varying compositions, pressures, and temperatures are presented. The applicability of ideal adsorbed solution theory (IAST) to H2S/CH4/all-silica zeolite systems at different thermodynamic state points is tested. Finally, to assess the hydrophobicity of all-silica zeolites in the presence of H2S, the adsorption of binary H2S/H2O mixtures is investigated.

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box [cells]

(1)

where rij, εij, σij, qi, and qj are the site−site separation, LJ well depth, LJ diameter, and partial charges on beads i and j, respectively. The Transferable Potentials for Phase Equilibria (TraPPE) force field is used for the zeolites,9 H2S,10 and CH4,11 whereas water is described using the TIP4P model.12 In the TraPPE-zeo force field, LJ interaction sites and partial charges are placed on both silicon and oxygen atoms. H2S is represented by the recently developed 4-site TraPPE model where LJ sites are placed on the S and H atoms and partial charges are placed on H atoms and an off-atom site.10 CH4 is represented by the 5-site TraPPE-EH model where LJ interaction sites are located at the carbon atom and the four C−H bond centers.11 The TIP4P model represents water by a single LJ site on the oxygen atom and partial charges are placed on H atoms and an off-center site. The standard Lorentz−Berthelot combining rules13 are used to determine the LJ parameters for all unlike interactions. Analytical tail corrections and the Ewald summation method (see below) are applied to account for the long-range interactions.14 Simulation Details. Configurational-bias Monte Carlo simulations15,16 in the isobaric−isothermal (NpT) version of the Gibbs ensemble17−19 are used to compute pure (H2S and CH4) and binary (H2S/CH4 and H2S/H2O) adsorption isotherms in all-silica frameworks at T = 298 and 343 K and p ≤ 50 bar, and also for the vapor− liquid equilibrium between H2S and H2O at T = 298 K and p = 1 bar. The osmotic version of the Gibbs ensemble20−22 where only the sorbate compounds transfer between reservoir and zeolite phases is used here for two reasons: (i) it does not require one to determine the chemical potentials for the selected molecular models in compressed gas or liquid solution phases from a presimulation, and (ii) it more closely resembles the experimental setup. A system size of 500 molecules in total is used for all unary and binary simulations probing adsorption from a gas phase, whereas a total of 1000 molecules is used for probing the adsorption from a liquid-phase H2S/H2O mixture and also for the vapor−liquid equilibrium of this mixture. For the zeolite phase, the number of unit cells in each dimension is chosen to yield a simulation box sufficiently large to encompass a sphere with a diameter of 28 Å. The unit cell dimensions and the number of unit cells in each direction for the different zeolite frameworks studied here are listed in Table 1. With the exception of MOR, all framework structures studied in this work are available in their all-silica form. Aluminum atoms in the MOR crystal structure are replaced by silicon atoms at the same

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RESULTS AND DISCUSSION Unary Adsorption. The adsorption of H2S in an all-silica zeolite was investigated experimentally for the first time in 2013 by Maghsoudi et al.34 for the CHA-type framework. To our knowledge, this is the only available experimental data for H2S adsorption in any crystalline all-silica material. Figure 1 shows B

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particular framework at a given fugacity (approximated by pressure for near-atmospheric conditions). The ratio of the Henry’s constants of two species is a good metric to quantify their binary selectivity at low loadings. As can be seen from Table 2, MOR has the highest selectivity toward H2S while CHA is the least selective. As illustrated by the data in Figure 1, the adsorption capacities, which depend on the accessible pore volume for a framework type, are also quite different; CHA and MWW exhibit much higher values of loading near saturation than those found for FER, MFI, and MOR. As can be seen from the adsorption isotherms for CHA, there is a very good agreement between the experimental and simulation data for both H2S and CH4. Together with the fact that the TraPPE force field describes the interactions between CH4 and H2S very accurately, as judged from the binary vapor− liquid equilibria for H2S/CH4,10 this suggests that binary simulations using the TraPPE force field for these molecules in all-silica zeolites should provide accurate estimates for binary loadings and selectivities. Binary Adsorption of H2S/CH4 Mixtures. In gas reservoirs, natural gas exists in a considerable variety of compositions; especially, the sourness of the gas stream can vary from a few ppm of H2S to as high as 90 vol % in some cases.36 Hence, to design processes for natural gas sweetening, it is of value to understand the adsorption behavior over a wide range of H2S mole fractions. Binary adsorption selectivities of H2S over CH4 in different zeolite frameworks at varying gasphase compositions, overall pressures, and temperatures are presented in Figure 2. The selectivity is defined here as a measure of the enrichment gained at equilibrium by contacting a gas mixture with the zeolite,

Figure 1. Unary adsorption isotherms for H2S (top) and CH4 (bottom) in different zeolite framework types. The filled symbols show the experimental data of Maghsoudi et al.34 for CHA. The legend denotes framework type and temperature in Kelvin. The statistical uncertainties are smaller than symbol size.

the unary adsorption isotherms for H2S and CH4 in the CHA, FER, MFI, MOR, and MWW frameworks. The saturated vapor pressure of H2S is 20 and 53 bar at T = 298 and 343 K, respectively.10,35 In the present work, the focus is on gas-phase adsorption and, hence, H2S adsorption isotherms are computed only up to 10 bar at 298 K and up to 50 bar at 343 K. At T = 298 K, there is practically no adsorption of H2S below p < 10−3 bar, while CH4 does not adsorb appreciably below 0.1 bar. This difference of about 2 orders of magnitude in the onset pressures for H2S and CH4 adsorption and the fact that 50% of the H2S saturation capacity is reached for all five frameworks at p < 1 bar and T = 298 K suggest a fairly high potential for the separation of these two compounds using all-silica zeolites. In the low pressure zone, loading is largely determined by the strength of the sorbate−sorbent interactions. At T = 298 K, FER exhibits the highest loadings at low pressures, and it can be inferred that both H2S and CH4 bind more strongly to the FER-type framework. This is also reflected in the Henry’s constants, /H2S and /CH4 , that are summarized in Table 2. As zero loading is approached, the Henry’s constant helps to quantify the extent of adsorption of a particular species in a

α H 2S =

x H2S/xCH4 yH S /yCH 2

(2)

4

where xH2S and xCH4 are mole fractions in the adsorbed phase, and yH2S and yCH4 are mole fractions in the gas phase. At T = 298 K and 1 bar total pressure, the selectivities range from a value of 12.2 for DDR at yH2S = 0.007 to a value of 44.4 for MOR at y H 2 S = 0.004. For all temperature/pressure combinations, the simulation data show that the composition dependencies of the selectivity for preferential H2S adsorption vary significantly for different zeolites. At T = 298 K and 1 bar total pressure, the selectivity nearly doubles for MFI when the H2S gas-phase concentration is changed from very dilute to about 90 mol %, increases by a factor of 1.6 for CHA, 1.4 for DDR, 1.3 for IFR, 1.2 for FER and MWW, and decreases by close to a factor of 2 for MOR. The peculiar behavior for MOR is due to a few highly selective adsorption sites that are exhausted beyond a certain H2S loading, and this leads to a sharp fall in selectivity. At T = 298 K and 1 bar total pressure,

Table 2. Calculated Henry’s Constants for Hydrogen Sulfide and Methane in All-Silica Zeolites zeolite

T [K]

/H2S [(mmol)/(g·bar)]

/CH4 [(mmol)/(g·bar)]

/H2S//CH4

CHA FER MFI

298 298 298 343 298 298

8.184 21.74 9.81 2.262 16.875 11.32

0.7025 1.241 0.601 0.2191 0.4253 0.611

11.71 181 16.34 10.31 39.74 191

MOR MWW

C

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Figure 2. H2S versus CH4 selectivity as a function of vapor-phase composition. The legend denotes framework type, temperature in Kelvin, and total pressure in bar. The statistical uncertainties are smaller than the symbol size.

Figure 3. H2S versus CH4 selectivity as a function of H2S loading. The legend denotes framework type, temperature in Kelvin, and total pressure in bar. The statistical uncertainties are smaller than the symbol size.

and CH4 with the zeolite framework play a larger role for determining the selectivity. At the higher temperature (343 K), entropic contributions become more important, and differences in the strengths of interactions with the adsorbent play a smaller role for determining selectivities. This issue will be revisited when discussing the partial molar enthalpies of adsorption at different state points. For selecting higher performing zeolites for natural gas sweetening from all candidate structures, in addition to the binary selectivity, it is also important for these zeolites to provide higher loading levels. The dependence of the selectivity on H2S loading is depicted in Figure 3. It can be seen that the selectivity curves for different overall pressures, but for a given framework type and temperature, nearly collapse onto one another. This implies that at a given temperature, the selectivity is mainly dependent on the H2S loading. MFI is found to possess the highest selectivity at loadings above ≈1.6 mmol/g,

MOR exhibits the highest selectivity up to about 35 mol % H2S in the gas phase, beyond this concentration MFI yields the highest selectivity. At 10 bar overall pressure, this switchover between the most selective zeolite happens at lower H2S concentration, below 10 mol %. Once again, this shift can be explained by the limited number of very favorable sites in MOR that get filled at lower concentration when the total pressure is higher. A very encouraging result for the application of all-silica zeolites for natural gas sweetening is that the selectivities in FER and MFI increase as the total pressure increases from 1 to 10 bar at both T = 298 and 343 K. It is clear from Figure 2 that the selectivity is strongly affected by changes in the temperature. For FER, the selectivity decreases by a factor of 1.8 as T is increased from 298 to 343 K, and the decrease is close to a factor of 2.3 and 2.0 for MFI at a total pressure of 1 and 10 bar. At the lower temperature (298 K), enthalpic factors due to the different interactions of H2S D

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gas-phase compositions low and high in H2S (yH2S ≈ 0.015 and ≈0.5, respectively). At this state point, the loadings for unary adsorption of H2S are 3.1 and 3.0 mmol/g in MFI and MOR, respectively, and 1.9 and 1.7 mmol/g for CH4 in MFI and MOR, respectively. These values correspond to about 90 and 50% of the saturation loading for H2S and CH4, respectively. In MFI, straight channels along the b-direction and sinusoidal channels along the a-direction form intersections that provide a larger free volume than the channels. Both types of sorbate molecules exhibit a modest preference to adsorb near the mouth of the sinusoidal channels, but also near the center of the straight channels and in the low-curvature segments of the sinusoidal channels. At yH2S = 0.015, H2S molecules are found throughout the entire two-dimensional channel system of MFI, whereas CH4 is almost entirely displaced at yH2S = 0.51 and is found only in the intersections. Note that unary adsorption of CH4 at low pressure yields a preference for channel locations in agreement with previous simulations.30 The density distributions in MOR differ markedly from those found in MFI. In MOR, both compounds exhibit a very strong preference for adsorption in the smaller pores that are confined by 4- and 8-membered rings. At yH2S = 0.015, the densities for H2S and CH4 are similar in these smaller pores, whereas a larger amount of CH4 is adsorbed in the larger pores formed by 12-membered rings. Thus, H2S displaces CH4 from the most favorable sites. At yH2S = 0.47, the density of CH4 in the smaller pores becomes negligible and these pores are almost exclusively filled by H2S molecules (the densities differ by more than 2 orders of magnitude). In the larger MOR pores, there is a slight preference to locate closer toward the walls parallel to the b-axis and the H2S density exceeds that for CH4 by a factor of ≈15 at yH2S = 0.47. Snapshots of the adsorbed phases (T = 298 K, p = 1 bar, and yH2S ≈ 0.05) in all framework types investigated here, and a brief description of the adsorption sites are provided in the Supporting Information. In addition to the capacity and selectivity of an adsorbent toward the desired component, there are a few other attributes that also play a role in determining the optimal adsorbent for a given application. Among these factors, the enthalpy of adsorption is extremely important because it determines the heating and cooling duties and, hence, to a large extent the operating cost of an adsorption unit. Figure 5 shows the partial molar enthalpies of adsorption, ΔHads, for H2S and CH4 as a function of H2S loading computed from binary adsorption simulations. Enthalpies of adsorption for both compounds in the majority of zeolites, with MOR and MWW being the exceptions, become increasingly more favorable (larger in magnitude) with increasing H2S loading. The ΔHads values include contributions from interactions of the sorbate with the bare framework and with other sorbate molecules. In general, as loading decreases, sorbate molecules are able to find sites providing more favorable interactions with the framework, that is, the contribution of sorbate−sorbent interactions can only cause a decrease in |ΔHads| with increasing loading (see Figure 6 in the Supporting Information). Therefore, the increase in |ΔHads| with qH2S must be a result of favorable interactions with guest H2S molecules (see Figure 7 in the Supporting Information). The increase of |ΔHads| with qH2S is largest (≈ 20%) for CHA, the zeolite with the highest saturation

whereas MOR shows a much higher selectivity at lower qH2S. In general, the selectivities are found to increase with qH2S. The exceptions are MOR, where the number of highly favorable H2S adsorption sizes is limited and a minimum is observerd at qH2S ≈ 2.2 mmol/g that is followed by the usual increase in selectivity, and FER and MFI at T = 343 K and a total pressure of 50 bar (and less pronounced for FER at T = 298 K and p = 10 bar), where a maximum is found near saturation loading. This latter feature will be discussed further below. Figure 4 shows the spatial distribution of CH4 and H2S in MFI and MOR at T = 298 K and p = 10 bar for equilibrium

Figure 4. Number density distribution (in units of Å−3) for H2S (left) and CH4 (right) at T = 298 K, p = 10 bar: (a) yH2S = 0.015 in MFI, (b) yH2S = 0.51 in MFI, (c) yH2S = 0.015 in MOR, and (d) yH2S = 0.47 in MOR. The number densities are shown in the ab-plane for the entire simulation box with the number of units cells provided in Table 1 and averaged along the c-axis. For MOR, the small pores are located in the dense region of the framework and yield sharp density enhancements, whereas the large 12-membered ring channels along the c-axis yield more diffuse density enhancements. E

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Figure 5. Partial molar enthalpies of adsorption of H2S (larger |ΔHads|) and CH4 (smaller |ΔHads|) as a function of H2S loading from binary mixtures of various compositions. The legend denotes framework type, temperature in Kelvin, and total pressure in bar.

Figure 6. H2S versus CH4 selectivity (on logarithmic scale) as a function of the difference in adsorption enthalpies of CH4 and H2S. The legend denotes framework type, temperature in Kelvin, and total pressure in bar. The statistical uncertainties are smaller than the symbol size.

decrease of favorable sorbate−sorbent interactions caused by the limited availability of smaller pores in MOR. Adsorption in the MWW framework constitutes an intermediate case, where a decrease of favorable sorbate−sorbent interactions is balanced by an increase in favorable sorbate−sorbate interactions. As a result, ΔHads for both compounds and αH2S (see Figure 3) do not change appreciably over a wide range of qH2S. The adsorption selectivity reflects the difference of the Gibbs free energies of transfer of the two sorbate molecules from the vapor phase to the zeolite. The Gibbs free energy can be separated into enthalpic and entropic terms. Figure 6 depicts the adsorption selectivity for H2S over CH4 as a function of the difference in adsorption enthalpies. With the exception of the data for FER and MFI at T = 343 K and p = 50 bar, αH2S values are linearly correlated with ΔΔHads. Thus, changes in the adsorption enthalpies govern changes in the selectivity. At low qH2S, ΔΔHads ≈ 6 kBT for MOR and αH2S > 40 is achieved. In

loading and a relatively constant sorbate−sorbent interaction energy. For MOR, the adsorption entalpies for both H2S and CH4 are most favorable for gas streams very dilute in H2S. As qH2S increases, |ΔHads| decreases for both H2S and CH4, but the absolute change in |ΔHads| is significantly larger for H2S than for CH4. That is, the adsorption enthalpies mirror the trend of decreasing selectivity with increasing qH2S. The reason for this behavior is the strong preference to adsorb in the smaller pores of MOR (see Figure 4). The |ΔHads| values for H2S at low qH2S are about 2 kJ/mol smaller at p = 10 bar than those at p = 1 bar because the higher pressure reduces the availability of the small pores for H2S due to more of them being occupied by CH4. The adsorption enthalpies reach a maximum at qH2S ≈ 2.2 mmol/g for H2S and qH2S ≈ 1.6 mmol/g for CH4. At this point favorable sorbate−sorbate interactions are able to overcome the F

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Langmuir contrast, the ΔΔHads values for the other zeolites fall into the range from 3 to 4 kBT and the selectivities fall into the range from 12 to 22. For FER and MFI, the data at p = 1 and 10 bar nearly coincide; an indication that entropic effects due to pore crowding are not significant for this pressure range. In contrast, crowding of the smaller pores is important for adsorption in MOR and, for a given ΔΔHads value, the selectivity is larger at p = 10 bar because the entropic penalty for CH4 to reside in the smaller pores is larger than at p = 1 bar. As shown in Figures 2 and 3, the zeolite frameworks FER and MFI exhibit a significant decrease in the selectivity for H2S over CH4 as the temperature is increased from 298 to 343 K. For FER, the change in temperature does not affect the ΔHads values for both compounds to any significant extent (see Figure 5). In contrast, for MFI, the shift in ΔHads is larger for H2S than for CH4 and ΔΔHads is increased by ≈0.5 kJ/mol. Nevertheless, the distribution of the sorbate molecules is not altered appreciably by the temperature increase, and the main reason for the decrease in selectivity is the increased importance of entropic factors that disfavor preferential adsorption of H2S. An interesting feature observed for these binary mixtures is the maximum in the adsorption selectivity at T = 343 K and p = 50 bar for the FER and MFI frameworks (see Figures 2 and 3), which is reflected in the very nonlinear behavior of the αH2S versus ΔΔHads correlation (see Figure 6). A possible explanation would be that the pore architecture limits the number of sorbate−sorbate contacts. Figure 7 shows the loading dependence of the number of H2S neighbors in the first

solvation shell of H2S. The sorbate packings differ significantly between FER and MFI with the latter allowing about twice as many molecules in the solvation shell at a given loading. Nevertheless, the number of nearest neighbors are linearly correlated with the loading in both frameworks and there is no indication of a decrease in the slope at higher loading. At the qH2S values corresponding to the maximum in αH2S (qH2S ≈ 2.2 mmol/g for FER and ≈2.6 mmol/g for MFI), the H2S adsorption isotherms reach their flat region as the saturation loading is approached. Calculation of the partial molar sorbate− sorbate energy of adsorption (see Figure 7 in the Supporting Information) indicates a change in the slope as saturation loading is approached. The reason for this change in slope is not so much that sorbate−sorbate interactions in the zeolite phase become less favorable, but a significant increase in sorbate−sorbate interactions in the H2S-rich gas phase as indicated by an exponential increase of the number of neighbors in the first solvation shell (see Figure 7). A large αH2S value requires a large ΔΔHads value which in turn requires a large |ΔHads| for H2S. With respect to the heating and cooling duties for sorption-based separations, however, one would like a sorbent that for a given |ΔHHads2S| yields a higher αH2S (or for a given αH2S requires a smaller H 2S |ΔHads |). The data in Figure 8 demonstrate significant

Figure 8. H2S versus CH4 selectivity as a function of |ΔHads| for H2S at T = 298 K and p = 1 bar. The statistical uncertainties are smaller than the symbol size.

variations that can be exploited for finding an optimal sorbent material. For example, for |ΔHHads2S| ≈ 32 kJ/mol, αH2S values of ≈22, 27, and 34 are found for the FER, MFI, and MOR frameworks, and αH2S ≈ 24 requires |ΔHHads2S| ≈ 33, 31, and 28 kJ/mol for these three zeolites. That is, one may achieve an increase in αH2S by 50% or a decrease in |ΔHHads2S| by 20% by judicious choice of the framework. Overall, the data for MOR are found closest to the upper left corner of Figure 8 indicating that this framework may be optimal under many conditions, whereas the data for CHA, DDR, and FER fall closest to the lower right corner. However, these data do not reflect the different trends with increasing loading that are observed for MOR compared to the other frameworks (see Figure 3).

Figure 7. Number of [S]H2S−[S]H2S neighbors within the first solvation shell (rS−S ≤ 5.4 Å) in the zeolite (top) and the corresponding gas phase (bottom) at T = 343 K and p = 10 and 50 bar. The legend denotes framework type, temperature in Kelvin, and total pressure in bar. The statistical uncertainties are smaller than the symbol size. G

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Figure 9. Comparison of H2S and CH4 loadings from binary simulations and predicted using IAST as a function of partial pressure. Data for H2S obtained from binary simulations are represented by red, green, and magenta squares for overall pressures of 1, 10, and 50 bar, respectively. Data for CH4 obtained from binary simulations are represented by blue, black, and violet circles for overall pressures of 1, 10, and 50 bar, respectively. The lines of the same colors denote the H2S and CH4 loadings obtained from IAST. Framework type and temperature are indicated for each subfigure.

Figure 10. Ratio of loadings predicted using IAST and obtained directly from simulations for binary mixtures. Data for H2S are shown as red squares, orange up triangles, and magenta circles for p = 1, 10, and 50 bar, respectively. Data for CH4 are shown as blue diamonds, cyan down triangles, and violet crosses for p = 1, 10, and 50 bar, respectively. Framework type and temperature are indicated for each subfigure.

Assessment of Ideal Adsorbed Solution Theory. Experimental measurements of multicomponent adsorption isotherms with a high degree of accuracy and precision still remain a challenge, whereas unary adsorption measurements are comparably easy to carry out. Thus, numerous approaches have been suggested to predict mixture adsorption from the knowledge of pure-component adsorption isotherms.5 The most widely used approach, called ideal adsorbed solution

theory (IAST), was proposed by Myers and Prausnitz in 1965.37 IAST treats the adsorbed phase akin to a liquid by using equations analogous to the thermodynamics for multicomponent vapor−liquid equilibria. IAST is thermodynamically consistent and also quite easy to apply. The adsorption selectivity is defined analogous to the inverse of the relative volatility. Under conditions where Raoult’s law is applicable, the H

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Langmuir relative volatility is simply equal to the ratio of the purecomponent vapor pressures at the temperature of interest, RL αVLE =

p1sat p2sat

(3)

and, hence, the separation factor for binary vapor−liquid equilibria is independent of composition. For binary adsorption, this separation factor is defined as37 IAST αads =

p20 (π ) p10 (π )

(4)

where p0i (π) is the equilibrium gas-phase pressure corresponding to the solution spreading pressure, π, for the adsorption of pure component i. Since π can be a function of adsorbed-phase composition and loading, contrary to ideal vapor−liquid equilibria, αIAST can vary with the fluid-phase composition. ads The dependence of the separation factor on the gas-phase composition is determined by the shapes and locations of the single-component adsorption isotherms for the species constituting the multicomponent mixture.37 In Figure 9, qH2S and qCH4 obtained directly from simulations for binary mixtures and predicted using IAST (with input from simulations for unary systems) are compared for five different zeolite frameworks (CHA, FER, MFI, MOR, and MWW). The data indicate that there is very good agreement for the overall shape of the adsorption isotherms and near quantitative agreement for the loading of the species found in higher concentration in the zeolite phase. Such an agreement between IAST predictions and binary measurements indicates that (i) there are no adsorption sites that are inaccessible to either CH4 or to H2S in any of the investigated zeolites (both molecules are mostly spherical and have very similar sizes) and (ii) that the interactions between adsorbates are smaller in magnitude than the sorbate−sorbent interactions. The absolute scale used in Figure 9 hides to some extent the deviations that are found for compositions where one component is only sparingly adsorbed. Relative data (see Figure 10) provide a better assessment of IAST’s shortcomings for the systems investigated in this work. With the exception of the data for MOR at higher pressure, IAST overpredicts qH2S for reservoir phases dilute in H2S, and the extent of the overprediction is ≈40% for CHA, MFI, and MWW at T = 298 K. The underestimation of qH2S for MOR at T = 298 K and p = 10 bar is likely caused by the competition for the smaller pores (see Figure 4). In addition, IAST is found to unpredict qCH4 at intermediate qH2S where IAST does not reflect the significant effects of H2S coadsorption. For MOR, qCH4 is underestimated by up to a factor of 1.6. A comparison of the selectivities predicted from IAST versus those determined from binary simulations is illustrated in Figure 11. Although IAST predicts correctly that MOR exhibits the highest αH2S values for low yH2S and that αH2S values increase with increasing yH2S (with the exception of MOR), IAST yields deviations of more than 10% for about half of the data points. In the low H2S mole fraction regime, IAST overpredicts αH2S for MFI, CHA, FER, and MWW by 10 to 40%, and the αIAST/ αbinary values decrease with increasing yH2S. For MOR at T = 298 K and p = 1 bar, the deviation is about 10% at low yH2S, but

Figure 11. Ratio of adsorption selectivities predicted using IAST and obtained directly from binary simulations as a function of gas-phase mole fraction. The legend denotes framework type, temperature in Kelvin, and total pressure in bar.

increases with yH2S and reaches values in excess of 50% at high yH2S. Overall, application of IAST holds some promise for the initial screening of zeolites for natural gas sweetening, but its margin of error is too large to rely on it to distinguish better performing zeolites, and extensive computations/measurements of multicomponent adsorption remain necessary. Binary Adsorption of H2S/H2O Mixtures. The synthesis of silicalite, a silica polymorph with the MFI framework, by Flanigen and Patton38 was a remarkable milestone in the history of zeolite synthesis. They introduced the use of fluoride anions as mineralizers instead of the conventional hydroxide anions. This enabled a low-pH synthesis that greatly reduces the extent of silanol (Si−OH) defects by condensation of adjacent groups. The fluoride ions also serve as substitutes for the siloxy ions (Si−O−) to neutralize the cationic structuredirecting agents, and in turn reduce these defects. As a result, Flanigan and Patton were successful in synthesizing a highly defect-free silica material that is extremely hydrophobic. The all-silica analogues of zeolites are very good candidates for separations requiring the selective exclusion of water. However, this will only be possible if water is not entrained into the zeolite by the species that are the target of the adsorption. For example, the adsorption of ethanol or other hydrogen-bonding compounds induces significant coadsorption of water.22,39 In order to investigate whether the assumption about hydrophobicity holds true for natural gas sweetening with allsilica zeolites, the binary H2S/H2O adsorption is studied in MFI at T = 298 K and p = 1 bar. MFI is chosen because of its availability in the nearly defect-free silicalite form and because it exhibits the highest αH2S at higher qH2S for the binary H2S/CH4 mixture (see Figure 3). At the selected state point, the H2S/ H2O mixture exists as a two-phase system with a very low H2S solubility in the liquid phase and a very low partial pressure of H2O in the vapor phase. In order to avoid computing I

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approaches 20 and is promising for sour-gas sweetening even in the presence of moisture.

adsorption selectivities in the large part of the composition range that falls into the vapor−liquid coexistence region, the coexistence compositions are determined here as a first step. Subsequent adsorption simulations are carried out at four different fluid-phase compositions (two in the one-phase vapor region and another two in the one-phase liquid region). The simulation data are listed in Table 3, where the selectivity is

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b03015. Numerical values of the simulation data in tabular form, snapshots of the adsorbed phases (T = 298 K, p = 1 bar, and yH2S ≈ 0.05) in all framework types, and data for the enthalpy decomposition into sorbate−sorbent and sorbate−sorbate contributions (PDF)

Table 3. Compositions and Selectivities for Vapor−Liquid and Adsorption Equilibria in MFI Calculated for the Binary H2S/H2O Mixture at T = 298 K and p = 1 bar phase 1

phase 2

x1H2S

x2H2S

α12 H2 S

vapor zeolite

liquid vapor

zeolite

liquid

0.9511 0.99831 0.99721 0.98643 0.9681

0.000421 0.96971 0.95471 0.0000804 0.0000351

4.62 × 104 181 171 916 × 104 863 × 104

ASSOCIATED CONTENT

S Supporting Information *

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 612-624-1844. Fax: 612626-7541.

αH122S

= (xH1 2S/xH1 2O)/(xH2 2S/xH2 2O). the simulations yield αH122S =

given by For the vapor−liquid equilibrium, 46 000. This value is ≈2.7 times larger than the corresponding experimental value,40 because use of nonpolarizable models leads to an underestimation of the H2S concentration in the liquid phase. For adsorption from the vapor phase, the selectivity for H2S over H2O is found to be 18, that is, only about a factor of 2 smaller than the selectivity for H2S over CH4 at similarly high H2S concentrations in the gas phase. A selectivity of 18 is more than sufficient to allow for the use of all-silica MFI for the sweetening of moisture-laden natural gas streams. At first glance, it might appear that MFI is exceedingly hydrophobic when adsorption occurs from the liquid phase, but this difference is entirely due to the large relative volatility of H2S in binary H2S/H2O mixtures. That is, when the selectivity for adsorption from the liquid phase is divided by the relative volatility, then one obtains a value that within statistical uncertainites agrees with the selecivity for adsorption from the gas phase: (91 + 86) × 104/(2 × 4.6 × 104) = 19.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences under Award DE-FG0212ER16362. The authors thank the Minnesota Supercomputing Institute for part of the computer resources used in this work.

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REFERENCES

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CONCLUSIONS Adsorption of H2S and CH4 in seven different all-silica zeolite frameworks is probed over a wide range of H2S partial pressures. Although all of the investigated frameworks are of the all-silica form, there is a considerable variation in selectivity toward H2S that falls into the range from 12 for DDR to 44 for MOR at yH2S < 0.007, T = 298 K, and p = 1 bar. At low H2S equilibrium concentrations in the vapor phase (below ≈10% but depending on the phase ratio, the initial feed concentration could be significantly higher), MOR has the highest selectivity and also the most favorable enthalpy of adsorption for H2S due to very favorable sorbate−sorbent interactions in its smaller pores. At high H2S equilibrium concentrations, MFI exhibits the highest selectivity and also the most favorable enthalpy of adsorption for H 2 S due to favorable sorbate−sorbate interactions. The precise point where the adsorption selectivities in MOR and MFI cross over depends on temperature and total pressure but, for a given value ot ΔHHads2S, MOR yields a larger αH2S. Ideal adsorbed solution theory is found to predict the salient features for binary H2S/CH4 mixtures, but it lacks the quantitative accuracy to select between high-performing zeolites. For gas-phase adsorption, silicalite provides a selectivity for H2S over H2O that J

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K

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