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Highlighting the Influence of Thermodynamic Coupling on Kinetic Separations with Microporous Crystalline Materials

Cite this: ACS Omega 2019, 4, 2, 3409-3419
Publication Date (Web):February 15, 2019
https://doi.org/10.1021/acsomega.8b03480
Copyright © 2019 American Chemical Society
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Abstract

The main focus of this article is on mixture separations that are driven by differences in intracrystalline diffusivities of guest molecules in microporous crystalline adsorbent materials. Such “kinetic” separations serve to over-ride, and reverse, the selectivities dictated by mixture adsorption equilibrium. The Maxwell–Stefan formulation for the description of intracrystalline fluxes shows that the flux of each species is coupled with that of the partner species. For n-component mixtures, the coupling is quantified by a n × n dimensional matrix of thermodynamic correction factors with elements Γij; these elements can be determined from the model used to describe the mixture adsorption equilibrium. If the thermodynamic coupling effects are essentially ignored, i.e., the Γij is assumed to be equal to δij, the Kronecker delta, the Maxwell–Stefan formulation degenerates to yield uncoupled flux relations. The significance of thermodynamic coupling is highlighted by detailed analysis of separations of five different mixtures: N2/CH4, CO2/C2H6, O2/N2, C3H6/C3H8, and hexane isomers. In all cases, the productivity of the purified raffinate, containing the tardier species, is found to be significantly larger than that anticipated if the simplification Γij = δij is assumed. The reason for the strong influence of Γij on transient breakthroughs is traceable to the phenomenon of uphill intracrystalline diffusion of more mobile species. The major conclusion to emerge from this study is that modeling of kinetic separations needs to properly account for the thermodynamic coupling effects.

1. Introduction

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Most commonly, the driver for mixture separations in fixed-bed adsorbers is the selectivity based on mixture adsorption equilibrium. Industrially important examples of such equilibrium-based separations include H2 purification, production of purified oxygen, and separation of xylene isomers.(1−8) However, there are practical instances of kinetic separations in which diffusional effects over-ride the influence of mixture adsorption equilibrium and are the prime driver for separations;(9) examples include production of N2 from air and removal of N2 from natural gas.(2−4)
In recent years, there has been substantial progress in the development of novel materials for industrially important separations(10) that are primarily driven by diffusion selectivities and size exclusion. For industrially important separation of C2H4/C2H6 mixtures, the pore dimensions of UTSA-280, an ultra-microporous molecular sieve [Ca(C4O4)(H2O)], are tuned to only allow C2H4 to enter the channels, resulting in almost total exclusion of the saturated alkane.(11) Pimentel and Lively(12) demonstrate the potential of ZIF-8/cellulose acetate fiber sorbents for the kinetic separation of C3H6/C3H8 mixtures. Several other examples of kinetic separations are discussed in the review by Wang and Zhao.(13)
For the design and development of pressure swing adsorption (PSA) technologies exploiting diffusion-selective separations, it is of vital importance to use mathematical models for transient uptakes and breakthroughs in fixed adsorbers that properly describe both mixture adsorption equilibrium and the intracrystalline diffusion characteristics.(14) Commonly, the ideal adsorbed solution theory (IAST)(15) is the appropriate model to describe mixture adsorption equilibrium.(9) In the simple case of single-site Langmuir isotherms, with equal saturation capacities of guest species, the IAST degenerates to yield the mixed-gas Langmuir model(1)In eq 1, pi are the component partial pressures, qi are the component loadings defined in terms of moles per kg of framework, qi,sat are the saturation capacities, and bi are Langmuir binding constants, with units of Pa–1.
The most practical approach to modeling n-component diffusion in porous materials is the Maxwell–Stefan (M–S) formulation that has its basis in irreversible thermodynamics. The M–S formulation relates the intracrystalline molar fluxes Ni to the chemical potential gradients(16−20)(2)In eq 2, R is the gas constant, T is the temperature, ρ represents the framework density of the microporous crystalline material, r is the radial distance coordinate, and the component loadings qi are defined in terms of moles per kg of framework. The xi in eq 2 are the component mole fractions of the adsorbed phase within the micropores(3)Đi characterize and quantify the interaction between species i and pore walls. The advantage of using eq 2 is that the M–S diffusivity Đi equals the corresponding diffusivity for a unary system, determined at the same pore occupancy.(19) Furthermore, the M–S diffusivity Đi for any species i in a mixture remains invariant to the choice of the partner(s) species.(19)
Đij, defined in the first right member of eq 2, reflect how the facility for transport of species i correlates with that of species j. The Onsager reciprocal relations demand the symmetry constraint(4)The magnitude of Đi relative to that of Đij determines the extent to which the flux of species i is influenced by the driving force of species j. The degree of correlations, defined by Đi/Đij, is governed by a wide variety of factors such as pore size, channel topology, and connectivity.(21,22) Generally speaking, the tardier-more-strongly-adsorbed species will have the effect of slowing down the more-mobile-less-strongly-adsorbed partner in the mixture.(21) In other words, the presence of the first term on the right of eq 2 serves to reduce the differences in the effective mobilities of the constituent species within the pores. Therefore, correlation effects are undesirable for kinetic separations that seek to exploit the differences in the mobilities. In practice, we aim to select materials for which Đi/Đij → ∞ is a good approximation and the first right member of eq 2 can be ignored, resulting in(5)Examples of materials for which the flux expression 5 provides a good description of intracrystalline fluxes are cage-type structures such as CHA, DDR, ERI, LTA, and ZIF-8 that have narrow windows in the 3–4.2 Å size range.(23) In such structures, the windows allow the intercage hopping of only one molecule at a time; consequently, the jumps are practically uncorrelated.(24)
The chemical potential gradients ∂μi/∂r can be related to the gradients of the molar loadings, qi, by defining the thermodynamic correction factors Γij(6)The thermodynamic correction factors Γij can be calculated by differenting the model describing the mixture adsorption equilibrium,(25) such as eq 1. Combining eqs 5 and 6, we get(7)Finite magnitudes of the off-diagonal elements Γij (ij) cause the flux of species i to be also influenced by the gradient of the molar loading of species j.(26) To appreciate the significance of such thermodynamic “coupling”, Figure 1 presents the calculations of the thermodynamic correction factors Γij for 50:50 C3H6(1)/C3H8(2) mixture adsorption within the crystals of all-silica CHA zeolite at 353 K. We note that at a total pressure of 100 kPa, the cross-coefficients are about 60–80% of the magnitudes of the diagonal elements, indicating that thermodynamic coupling effects are extremely significant.

Figure 1

Figure 1. Calculations of the matrix of thermodynamic factors for 50:50 C3H6(1)/C3H8(2) mixture adsorption within the crystals of all-silica CHA at 353 K. Further details and input data are provided in Chapter 9 of the Supporting Information.

In the Henry regime of adsorption, at low pore occupancies, Γij → δij, the Kronecker delta, and eq 7 degenerates to yield a set of n uncoupled flux expressions(27)(8)Even though eq 8 is strictly valid at low pore occupancies, a large number of implementations of intracrystalline diffusion in models for fixed-bed adsorbers ignore the contribution of Γij; see the comprehensive review of Shafeeyan et al.(28) The primary objective of this article is to investigate and highlight the strong influence of thermodynamic coupling effects, engendered by Γij (ij), on the effectiveness of kinetic separations. We aim to show that the use of the simpler uncoupled flux expression 8 often leads to significant errors in the prediction of recoveries and productivities of the purified raffinate during the adsorption cycle of PSA operations. To meet our objective, we investigate the kinetically driven separation of five different mixtures N2/CH4, CO2/C2H6, O2/N2, C3H6/C3H8, and hexane isomers. In each case, we compare the separation effectiveness predicted by breakthrough simulations incorporating eqs 7 and 8.
The Supporting Information accompanying this publication provides (a) details of the methodology used for modeling of the transient breakthroughs in fixed-bed adsorbers, with incorporation of the IAST and the Maxwell–Stefan diffusion formulations, (b) input data on unary isotherms, and M–S diffusivities, for each of the five cases studies investigated, and (c) structural details of the zeolites and metal–organic frameworks (MOFs).

2. Modeling Transient Uptakes and Breakthroughs

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For an n-component gas mixture flowing through a fixed-bed adsorber maintained under isothermal, isobaric conditions, the molar concentrations in the gas phase at any position and instance of time are obtained by solving the following set of partial differential equations for each of the species i in the gas mixture(4,18,26)(9)In eq 9, t is the time, z is the distance along the adsorber, ε is the bed voidage, Dax is the axial dispersion coefficient, v is the interstitial gas velocity, and is the spatially averaged molar loading within the crystallites of radius rc, monitored at position z and at time t.(18) Ruthven et al.(4) state, “when mass transfer resistance is significantly greater than axial dispersion, one may neglect the axial dispersion term and assume plug flow”. The assumption of plug flow is appropriate for kinetically controlled separations and is invoked in all the simulation results presented in this article.
The radial distribution of molar loadings, qi, is obtained from a solution of a set of differential equations describing the transient uptake within a spherical crystallite of radius rc(10)The intracrystalline fluxes Ni, in turn, are related to the radial gradients in the molar loadings by eq 7. At any time t, the component loadings at the surface of the particle qi(rc, t) = qi* is in equilibrium with the bulk phase gas mixture.(29) The loadings qi* are determined by the IAST or mixed-gas Langmuir model, as appropriate.(30)
At any time t, during the transient approach to thermodynamic equilibrium, the spatial-averaged component loading within the crystallites of radius rc is calculated using(11)In all of the simulations reported in this article, the entire bed of crystalline particles is considered to be devoid of adsorbates at time t = 0, i.e., we have the initial condition(12)At time, t = 0, the inlet to the adsorber, z = 0, is subject to a step input of the feed gas mixture, with inlet partial pressures pi0, and this step input is maintained till the end of the adsorption cycle when steady-state conditions are reached.(13)Combination of the discretized partial differential equations along with the algebraic equations describing mixture adsorption equilibrium (IAST or mixed-gas Langmuir model) results in a set of differential–algebraic equations, which are solved using a sparse matrix solver based on the semi-implicit Runge–Kutta method;(30) further numerical details are provided in the Supporting Information.
Validation of the simulation methodology for transient uptakes and breakthroughs by comparison with published experimental works is available in earlier works.(9,18,29,31−34) As an illustration, Figure 2 presents the experimental data of Jolimaître et al.(35) for transient breakthrough of a ternary mixture of 2-methylbutane (2MB), 2-methylpentane (2MP), and 2,2-dimethylbutane (22DMB) at 473 K in a fixed bed packed with MFI zeolite that has a topology consisting of a set of intersecting straight channels and zig-zag channels approximately 5.5 Å in size.(8) Branched alkanes are located preferentially at the channel intersections. The hierarchy of adsorption strengths is 2MP > 22DMB > 2MB, whereas the diffusion hierarchy is 2MB > 2MP ≫ 22DMB. Due to the diffusional penalty, 22DMB breaks through earlier than the more mobile 2MB. The experimental breakthroughs are quantitatively captured by simulations that adopt the flux expressions including Γij.(18) If the assumption Γij = δij is invoked, the agreement is significantly worse.(18) Similar good agreement of the breakthrough simulations based on eq 7 is obtained for the complete set of seven experimental runs, with different entering feed mixture compositions, using the same set of isotherm and diffusivity parameters;(18) details are provided in Chapter 10 of the Supporting Information.

Figure 2

Figure 2. Transient breakthrough experiments of run 20 of Jolimaître et al.(35) for 2MB/2MP/22DMB ternary mixtures at 473 K.(18) The continuous solid lines are simulations based on eq 7. The dashed lines are the simulations based on eq 8. Further details and input data are provided in Chapter 10 of the Supporting Information, which also contains the rationale for ignoring correlation effects.

3. Results and Discussions on Five Mixture Separations

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3.1. Separation of N2/CH4 Mixtures

Many natural gas reserves contain nitrogen in concentrations ranging to about 20%.(36) To meet pipeline specifications, the nitrogen level must be reduced to below 4%.(37) A large majority of nitrogen removal facilities use cryogenic distillation, but such units are economical only for large-capacity wells. For smaller reserves, PSA technology has economic benefits, especially because the feed mixtures are available at high pressures.(36−38) It is desirable to use adsorbents in PSA units that are selective to N2. For most known adsorbents, the selectivity for the separation of N2/CH4 mixtures is in favor of CH4 due to its higher polarizability.(18)
In a classic paper published in 1958, Habgood(39) reported experimental data on transient uptake of N2(1)/CH4(2) mixtures in crystallites of LTA-4A zeolite at 194 K. The data measured with partial pressures (a) p1 = 50.9 kPa, p2 = 49.1 kPa and (b) p1 = 10 kPa, p2 = 90 kPa are shown in Figure 3a,b.(40) The nitrogen molecule has a “pencil-like” shape with dimensions of 4.4 Å × 3.3 Å; it can hop length-wise across the narrow 4.1 Å × 4.5 Å 8-ring windows of LTA-4A.(41) The methane molecule is spherical with dimensions of 3.7 Å; it is much more severely constrained and has a diffusivity that is 22 times lower than that of N2.(29,42) The adsorption strength of CH4 is higher than that of N2 by a factor 2.2. During the early stages of the transient uptake process, the pores of LTA-4A are significantly richer in the more mobile N2. With increasing time, the nitrogen contained within the pores is progressively displaced by the more strongly adsorbed, tardier CH4 molecules.(18) The net result is an overshoot in the N2 uptake in both experimental uptake campaigns. The continuous solid lines in Figure 3a,b are uptake simulations based on eq 7; these simulations successfully capture the overshoot in the uptake of the more mobile N2. The dashed lines are the simulations based on eq 8, ignoring thermodynamic coupling, i.e., Γij = δij; in this scenario, no N2 overshoot is experienced. The attainment of supraequilibrium loadings of N2 during the early transience signals the phenomena of uphill diffusion, which can be exploited to achieve kinetic separations in fixed-bed adsorption devices.(7,20,29)

Figure 3

Figure 3. (a, b) Experimental data of Habgood(39) on transient uptake of N2(1)/CH4(2) mixture within LTA-4A crystals exposed to binary gas mixtures at partial pressures (a) p1 = 50.9 kPa, p2 = 49.1 kPa and (b) p1 = 10 kPa, p2 = 90 kPa at 194 K.(18) (c) Transient breakthrough of 20:80 N2(1)/CH4(2) mixture in a fixed-bed adsorber packed with LTA-4A crystals operating at 194 K and total pressure pt = 100 kPa. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 6 of the Supporting Information.

Figure 3c shows the transient breakthrough simulations for 20:80 N2/CH4 mixtures through fixed-bed adsorber packed with LTA-4A crystals operating at 194 K and total pressure pt = 100 kPa.(29) The x-axis is the dimensionless time, τ = tv/L, obtained by dividing the actual time, t, by the characteristic time, L/v, where L is the length of the adsorber.(5,6,30) The continuous solid lines are simulations based on eq 7; the dashed lines are simulations based on eq 8. For the target purity of CH4 is 96%, corresponding to prescribed pipeline specification, we can determine the moles of 96% + pure CH4 produced. Expressed per kg of LTA-4A zeolite in the packed bed, the respective productivities are 0.09 and 0.002 mol kg–1. Ignoring the thermodynamic coupling effects severely underestimates the separation performance by a factor of about 50.
N2/CH4 separations with LTA-4A zeolite are effective only at low temperatures, and other materials such as Ba-ETS-4 and clinoptilolites are more suitable for kinetic separations at ambient conditions.(3,36−38) The experimental data of Majumdar et al.(43) on transient uptake of N2/CH4 mixtures in Ba-ETS-4 show overshoots in N2 loading, confirming the manifestation of uphill diffusion and thermodynamic coupling effects.(18,29)

3.2. Separation of CO2/C2H6 Mixtures

The separation of CO2/C2H6 mixtures is relevant in the context of natural gas processing. Current technologies for CO2/C2H6 separations use extractive distillation because of CO2/C2H6 azeotrope formation.(44) Another alternative is to combine distillation technology with membrane separations; for this purpose, cross-linked poly(ethylene oxide) membranes have demonstrated to have good separation potential.(45−47)
Figure 4a–c shows the experimental data of Binder et al.(48) and Lauerer et al.(49) for spatial-averaged transient uptake of (a) 1:1, (b) 2:1, and (c) 3:1 CO2/C2H6 gas mixtures within the crystals of DDR zeolite at 298 K.(9) The DDR zeolite consists of cages of 277.8 Å3 volume separated by 3.65 Å × 4.37 Å 8-ring windows.(41,50) Both guest molecules, CO2 and C2H6, jump length-wise across the 8-ring windows of the DDR zeolite.(51) The cross-sectional dimension of CO2 is smaller than that of C2H6,(5) and therefore, the intracrystalline M–S diffusivity of CO2 is significantly higher than that of C2H6 by about 2–3 orders of magnitude; for further details, see Chapter 7 of the Supporting Information.

Figure 4

Figure 4. (a–c) Experimental data of Binder et al.(48) and Lauerer et al.(49) (indicated by symbols) for spatial-averaged transient uptake of (a) 1:1, (b) 2:1, and (c) 3:1 CO2(1)/C2H6(2) gas mixtures within the crystals of DDR zeolite at 298 K.(9,29) (b) Transient breakthrough of 1:1 CO2/C2H6 mixtures through fixed-bed adsorber packed with DDR crystals operating at 298 K and total pressure pt = 40 kPa. The continuous solid lines in are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 7 of the Supporting Information.

The Maxwell–Stefan flux expression including thermodynamic coupling quantitatively captures the overshoots in CO2 loadings with good accuracy for all three experiments.(29) If thermodynamic coupling effects are ignored and the assumption Γij = δij is invoked, no overshoots in CO2 uptake are experienced, and the simulations show poor agreement with experiments during the early transience.(29)
Figure 4d shows the transient breakthrough simulations for 1:1 CO2/C2H6 mixtures through fixed-bed adsorber packed with DDR crystals operating at 298 K and total pressure pt = 40 kPa.(29) Assuming that target purity of C2H6 is 90%, we can determine the moles of more than 90% pure C2H6 produced. The productivities of more than 90% pure C2H6 are 0.18 and 0.054 mol kg–1, respectively, for the two scenarios in which thermodynamic coupling is accounted for, or ignored. Ignoring the thermodynamic coupling effects underestimates the separation performance by a factor of about three.

3.3. Separation of O2/N2 Mixtures

For the production of purified N2 from air, it is desirable to have an adsorbent that is selective to O2, which constitutes 21% of the feed mixture; purified N2 can be recovered as a raffinate during the initial transience of the adsorption cycle.(4,18,52) However, for most adsorbents, the mixture adsorption equilibrium is in favor of N2, which has a higher quadrupole moment compared to O2. Oxygen-selective separations are achieved with LTA-4A zeolite and carbon molecular sieve (CMS); in these materials, O2 has higher diffusivity due to its smaller size.(3,53−56)
Simulations of transient uptake of O2/N2 mixture in LTA-4A zeolite at 298 K and total pressure of 600 kPa, display an overshoot in the O2 uptake (see Figure 5a). The overshoot in the O2 loading disappears with the simplification Γij = δij. The experimental data of Chen et al.(55) for transient O2/N2 uptake in CMS also show an overshoot in the O2 uptake, confirming the occurrence of uphill diffusion and attainment of supraequilibrium O2 loadings for a short time span.(20,29)

Figure 5

Figure 5. (a) Transient uptake of O2(1)/N2(2) mixture in LTA-4A zeolite at 298 K and total pressure of 600 kPa. The partial pressures of the components in the bulk gas phase are p1 = 126 kPa and p2 = 474 kPa. (b) Transient breakthrough characteristics of O2(1)/N2(2) mixture in a fixed-bed adsorber packed with LTA-4A operating at a total pressure of 600 kPa and 298 K. The partial pressures of the components in the bulk gas phase at the inlet are p1 = 126 kPa and p2 = 474 kPa. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 8 of the Supporting Information.

Figure 5b presents transient breakthrough simulations for a fixed-bed operating at 298 K and total pressure of 600 kPa. For an assumed target purity of more than 95% N2, we can determine the moles of more than 95% pure N2 produced; expressed per kg of LTA-4A zeolite in the packed bed, the productivities are 0.066 and 0.036 mol kg–1 for the respective models including and ignoring thermodynamic coupling influences. Ignoring thermodynamic coupling effects underestimates the separation performance by a factor of 50%.

3.4. Separation of C3H6/C3H8 Mixtures

Cryogenic distillation of C3H6/C3H8 mixtures is the currently used technology for making polymer-grade propene with more than 99.5% purity. Propane of more than 90% purity is used for various purposes such as fuel for engines, oxy-gas torches, and barbecues; this can be obtained as the bottoms product of the cryogenic distillation column.(57) The boiling points are close to each other: propene (226 K) and propane (231.3 K). Consequently, the distillation columns are some of the largest and tallest distillation columns used in the petrochemical industries with about 150–200 trays and operate at reflux ratios of about 15.(58) A PSA process can be an attractive alternative for C3H6/C3H8 separations because of its expected low energy demand. A variety of adsorbents have been investigated for this separation task.(57,59−61) Promising good potential for alkene/alkane separations are MOFs with coordinatively unsaturated metal centers that may be created by evacuation of frameworks that have metal-bound solvent molecules. This strategy has been employed to expose M2+ cation sites in M2(dobdc) [M = Mg, Mn, Co, Ni, Zn, Fe; dobdc4– = 2,5-dioxido-1,4-benzenedicarboxylate].(62) Unsaturated alkynes and alkenes such as C2H2, C2H4, and C3H6 can bind with M2+ of M2(dobdc), with side-on attachment and π-coordination.(5,63,64) The potential of M2(dobdc) for the technologically important separations of C2H2/C2H4, C2H4/C2H6, and C3H6/C3H8 mixtures has been established in laboratory studies.(32,63−65) Other adsorbents that also exhibit adsorption selectivity in favor of the unsaturated propene include CuBTC,(66) LTA-4A zeolite,(59,60) and NaX (=13X) zeolite.(59,61) An important disadvantage of the C3H6/C3H8 separations with the adsorbents listed above is that the desired alkene product, required for the production of polymer-grade feedstock, can only be recovered in the desorption phase. It becomes necessary to operate PSA units with multiple beds, involving five different steps; the C3H6 product of desired purity is recovered in the final step by counter-current vacuum blowdown.(34,60,61,67)
The recovery of high-purity C3H6 product in the final vacuum blowdown step is expected to be enhanced if C3H8 is (almost) excluded from the pores during the high-pressure adsorption cycle. Near-total exclusion of C3H8 is achievable by kinetically based separations using cage-type zeolites with 8-ring windows.(51) Due to the smaller cross section of the propene molecule (the dimensions are provided by Chng et al.(68)), kinetic separations selective to propene are possible using all-silica CHA zeolite that consists of cages of volume 316 Å3 and separated by 3.8 Å × 4.2 Å 8-ring windows.(8,57,69−71)
Using the input data on isotherms and diffusivities provided by Khalighi et al.,(57) we first examine the influence of thermodynamic coupling on transient uptake within a single spherical crystallite of CHA zeolite, initially devoid of guest molecules, exposed to a bulk 50:50 C3H6/C3H8 mixture at 100 kPa and T = 353 K. For the uptake simulations using eq 7, the more mobile C3H6 exhibits a pronounced overshoot in its approach to thermodynamic equilibrium (see Figure 6a).(20,29) If thermodynamic coupling is ignored, no C3H6 overshoot is detected.

Figure 6

Figure 6. (a) Simulations of transient uptake of 50:50 C3H6(1)/C3H8(2) mixtures within crystals of all-silica CHA at 353 K. (b) Simulations of transient breakthrough of 50:50 C3H6(1)/C3H8(2) mixtures in a fixed-bed adsorber packed with crystals of all-silica CHA at 353 K and operating at a total pressure of 100 kPa. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 9 of the Supporting Information.

We should expect the transient overshoot phenomena, and uphill diffusion, to have a beneficial effect on the transient breakthrough characteristics in fixed beds.(29)Figure 6b shows the simulations for transient breakthrough of 50:50 C3H6/C3H8 mixtures in a fixed bed adsorber packed with crystals of all-silica CHA at 353 K and operating at a total pressure of 100 kPa. The simulations clearly show that more than 90% pure C3H8 can be collected during the earlier stages of transience. If thermodynamic coupling effects are ignored and simplified eq 8 are invoked, the time interval during which more than 90% pure C3H8 can be recovered is reduced by about an order of magnitude. Expressed per kg of CHA zeolite in the packed bed, the respective productivities of more than 90% pure C3H8 are 0.62 and 0.06 mol kg–1, a reduction by a factor of about 10 due to neglect of thermodynamic coupling.
It must be remarked that the model used by Khalighi et al.(57) takes due account of thermodynamic coupling effects, whereas more simplified approach using the linear driving force approximation is adopted by Da Silva and Rodrigues(61) for modeling kinetic separations of C3H6/C3H8 mixtures using LTA-4A zeolite.
Cadiau et al.(72) report the synthesis of NbOFFIVE-1-Ni (also named KAUST-7), a customized MOF for C3H6/C3H8 separations that belongs to the class of SIFSIX materials,(73) using pyrazine as the organic linker. The (SiF6)2– pillars in the cage are replaced with somewhat bulkier (NbOF5)2– pillars. This causes tilting of the pyrazine molecule on the linker, effectively reducing the aperture opening from 0.50 nm [with (SiF6)2– pillars] to 0.30 nm. The small aperture permits ingress of the smaller C3H6 molecules but practically excludes C3H8 on the basis of subtle differences in bond lengths, bond angles, and molecular conformations.(5)Figure 7 presents a comparison of the percentage C3H8 in the outlet gas leaving fixed-bed adsorbers packed with KAUST-7 and CHA zeolite. Both of these adsorbents appear to be equally effective in near-total exclusion of C3H8. Further investigation and detailed PSA simulations such as that presented by Khalighi et al.(67) are required to determine whether KAUST-7 offers significant improvements over CHA zeolite for the production of more than 99.5% pure C3H6. It is worth mentioning that in Figure S12 of Cadiau et al.,(72) breakthroughs of KAUST-7 are compared with data on LTA-4A and LTA-5A zeolites but not with all-silica CHA.

Figure 7

Figure 7. Comparison of the percentage C3H8 in the outlet gas leaving fixed-bed adsorbers packed with KAUST-7 and CHA zeolite. Both simulations are based on eq 7. Further details and input data are provided in Chapter 9 of the Supporting Information.

3.5. Separation of Mixtures of Hexane Isomers

An important step in the production of high-octane gasoline is the separation of hexane isomers, n-hexane (nC6), 2-methylpentane (2MP), 3-methylpentane (3MP), 2,2-dimethylbutane (22DMB), and 2,3-dimethylbutane (23DMB). The values of the Research Octane Number (RON) increases with the degree of branching: nC6 = 30, 2MP = 74.5, 3MP = 75.5, 22DMB = 94, and 23DMB = 105. Due to their higher RON values, di-branched isomers are preferred products for inclusion in the high-octane gasoline pool.(18,74,75) There are a number of adsorbents that have potential use in the separation of hexane isomers.(18,76) Separations using MFI zeolite(18) have some unique characteristics; these features arise from the preferential location of the mono- and di-branched isomers at the channel intersections, whereas the linear nC6 can locate anywhere within the channel network.(6,77,78) As a consequence, the hierarchy of adsorption strengths, dictated by configurational entropy considerations,(6,79,80) is nC6 > 2MP ≈ 3MP > 22DMB ≈ 23DMB. The hierarchy of the magnitudes of intracrystalline diffusivities is nC6 ≫ 2MP ≈ 3MP ≫ 22DMB ≈ 23DMB.(58) Consequently, both adsorption and diffusion act synergistically.(18,81)
The transient uptake of nC6/2MP mixtures in MFI crystals, exposed to an equimolar gas-phase mixture at constant total pressure (=2.6 Pa) have been reported by Titze et al.(29,81) (see Figure 8a). The transient equilibration of nC6 displays a pronounced overshoot, achieving supraequilibrium loadings during transient equilibration. The origin of the nC6 overshoot is traceable to the contribution of finite off-diagonal elements of Γij; if the assumption Γij = δij is invoked, the overshoot disappears.

Figure 8

Figure 8. (a) Experimental data of Titze et al.(81) for the transient uptake of nC6/2MP mixtures in MFI zeolite at 298 K.(29) (b) RON of product gas mixture leaving fixed-bed adsorber packed with MFI operating at a total pressure of 100 kPa and 433 K; the feed is a 5-component nC6/2MP/3MP/22DMB/23DMB mixture with partial pressure of 20 kPa for each component. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 10 of the Supporting Information, which also contains the rationale for ignoring correlation effects.

Uphill diffusion of nC6 is beneficial to the hexane isomer separations in fixed beds because the desired raffinate phase will be richer in the branched isomers that have high octane numbers. To confirm this expectation, transient breakthrough simulations were performed for a 5-component nC6/2MP/3MP/22DMB/23DMB mixture. The transient variations of the RON values of the gas mixture exiting the adsorber are plotted in Figure 8b.(7,18,29) Assuming that the target RON value of the raffinate is 92+ RON, we can determine the number of moles of 92+ RON product that can be recovered during the initial transience. The 92+ RON productivity is 0.36 mol kg–1 for the scenario in which thermodynamic coupling is included. The 92+ RON productivity is lowered to a value of 0.28 mol kg–1 for invoking the simplification Γij = δij.

4. Conclusions

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The major conclusion that emerges from our investigation of kinetic separations of five different mixtures is the need for proper modeling of the intracrystalline diffusion, which takes proper account of thermodynamic coupling influences.(51) The off-diagonal elements Γij (ij) engender overshoots in the loading of the more mobile partner species during transient uptakes within a microporous particle. Such overshoots, signifying uphill diffusion, are beneficial, resulting in increasing productivity of the tardier component that is recovered in purified form as raffinate during the high-pressure adsorption cycle of PSA operations.
Although the inclusion of thermodynamic coupling influences for kinetic separations in adsorbers is properly recognized by Ruthven, Farooq, and others,(4,37,43,52,54,57,67) there are several other published works that adopt much simpler approaches employing eq 8;(28) the simulations presented in this article demonstrate that such simplified approaches may lead to severely pessimistic estimates of the effectiveness of kinetic separations.
Thermodynamic coupling effects should also be expected to have strong influences on the selectivity and conversion of diffusion-limited zeolite-catalyzed reactions carried in fixed-bed reactors;(78) this aspect deserves further investigation.

Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b03480.

  • Calculation procedure for mixture adsorption equilibrium, along with derivations of the mixed-gas Langmuir model, summary of the Maxwell–Stefan theory of diffusion in microporous materials, methodology adopted for numerical solutions to transient uptake within single crystalline particle, methodology used for transient breakthroughs in fixed-bed adsorbers, and simulation details and input data on unary isotherms, and Maxwell–Stefan diffusivities are provided for each of the five case studies (PDF)

The author declares no competing financial interest.

Terms & Conditions

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Acknowledgments

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The simulation code for transient breakthroughs was developed by Dr Richard Baur and Dr Jasper van Baten; their assistance and help is gratefully acknowledged.

Nomenclature
Latin Alphabet
bi

Langmuir binding constant, Pa–1

ci

molar concentration of species i, mol m–3

ci0

molar concentration of species i in fluid mixture at inlet, mol m–3

Dax

axial dispersion coefficient, m2 s–1

Đi

Maxwell–Stefan diffusivity for molecule–wall interaction, m2 s–1

Đij

M–S exchange coefficient for n-component mixture, m2 s–1

n

number of species in the mixture, dimensionless

L

length of packed-bed adsorber, m

Ni

molar flux of species i with respect to framework, mol m–2 s–1

pi

partial pressure of species i in mixture, Pa

pt

total system pressure, Pa

qi

component molar loading of species i, mol kg–1

qi,sat

molar loading of species i at saturation, mol kg–1

qt

total molar loading in mixture, mol kg–1

spatial-averaged component uptake of species i, mol kg–1

r

radial direction coordinate, m

rc

radius of crystallite, m

R

gas constant, 8.314 J mol–1 K–1

t

time, s

T

absolute temperature, K

v

interstitial gas velocity in packed bed, m s–1

xi

mole fraction of species i in adsorbed phase, dimensionless

z

distance along the adsorber, m

Greek Alphabet
Γij

thermodynamic factors, dimensionless

δij

Kronecker delta, dimensionless

ε

voidage of packed bed, dimensionless

μi

molar chemical potential, J mol–1

ρ

framework density, kg m–3

τ

time, dimensionless

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  2. Ilona van Zandvoort, Erik-Jan Ras, Robbert de Graaf, Rajamani Krishna. Using transient breakthrough experiments for screening of adsorbents for separation of C2H4/CO2 mixtures. Separation and Purification Technology 2020, 241, 116706. DOI: 10.1016/j.seppur.2020.116706.
  3. Rajamani Krishna. Maxwell-Stefan modelling of mixture desorption kinetics in microporous crystalline materials. Separation and Purification Technology 2019, 229, 115790. DOI: 10.1016/j.seppur.2019.115790.
  4. Ilona van Zandvoort, Jan Kees van der Waal, Erik-Jan Ras, Robbert de Graaf, Rajamani Krishna. Highlighting non-idealities in C2H4/CO2 mixture adsorption in 5A zeolite. Separation and Purification Technology 2019, 227, 115730. DOI: 10.1016/j.seppur.2019.115730.
  • Abstract

    Figure 1

    Figure 1. Calculations of the matrix of thermodynamic factors for 50:50 C3H6(1)/C3H8(2) mixture adsorption within the crystals of all-silica CHA at 353 K. Further details and input data are provided in Chapter 9 of the Supporting Information.

    Figure 2

    Figure 2. Transient breakthrough experiments of run 20 of Jolimaître et al.(35) for 2MB/2MP/22DMB ternary mixtures at 473 K.(18) The continuous solid lines are simulations based on eq 7. The dashed lines are the simulations based on eq 8. Further details and input data are provided in Chapter 10 of the Supporting Information, which also contains the rationale for ignoring correlation effects.

    Figure 3

    Figure 3. (a, b) Experimental data of Habgood(39) on transient uptake of N2(1)/CH4(2) mixture within LTA-4A crystals exposed to binary gas mixtures at partial pressures (a) p1 = 50.9 kPa, p2 = 49.1 kPa and (b) p1 = 10 kPa, p2 = 90 kPa at 194 K.(18) (c) Transient breakthrough of 20:80 N2(1)/CH4(2) mixture in a fixed-bed adsorber packed with LTA-4A crystals operating at 194 K and total pressure pt = 100 kPa. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 6 of the Supporting Information.

    Figure 4

    Figure 4. (a–c) Experimental data of Binder et al.(48) and Lauerer et al.(49) (indicated by symbols) for spatial-averaged transient uptake of (a) 1:1, (b) 2:1, and (c) 3:1 CO2(1)/C2H6(2) gas mixtures within the crystals of DDR zeolite at 298 K.(9,29) (b) Transient breakthrough of 1:1 CO2/C2H6 mixtures through fixed-bed adsorber packed with DDR crystals operating at 298 K and total pressure pt = 40 kPa. The continuous solid lines in are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 7 of the Supporting Information.

    Figure 5

    Figure 5. (a) Transient uptake of O2(1)/N2(2) mixture in LTA-4A zeolite at 298 K and total pressure of 600 kPa. The partial pressures of the components in the bulk gas phase are p1 = 126 kPa and p2 = 474 kPa. (b) Transient breakthrough characteristics of O2(1)/N2(2) mixture in a fixed-bed adsorber packed with LTA-4A operating at a total pressure of 600 kPa and 298 K. The partial pressures of the components in the bulk gas phase at the inlet are p1 = 126 kPa and p2 = 474 kPa. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 8 of the Supporting Information.

    Figure 6

    Figure 6. (a) Simulations of transient uptake of 50:50 C3H6(1)/C3H8(2) mixtures within crystals of all-silica CHA at 353 K. (b) Simulations of transient breakthrough of 50:50 C3H6(1)/C3H8(2) mixtures in a fixed-bed adsorber packed with crystals of all-silica CHA at 353 K and operating at a total pressure of 100 kPa. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 9 of the Supporting Information.

    Figure 7

    Figure 7. Comparison of the percentage C3H8 in the outlet gas leaving fixed-bed adsorbers packed with KAUST-7 and CHA zeolite. Both simulations are based on eq 7. Further details and input data are provided in Chapter 9 of the Supporting Information.

    Figure 8

    Figure 8. (a) Experimental data of Titze et al.(81) for the transient uptake of nC6/2MP mixtures in MFI zeolite at 298 K.(29) (b) RON of product gas mixture leaving fixed-bed adsorber packed with MFI operating at a total pressure of 100 kPa and 433 K; the feed is a 5-component nC6/2MP/3MP/22DMB/23DMB mixture with partial pressure of 20 kPa for each component. The continuous solid lines are simulations based on eq 7. The dashed lines are simulations based on eq 8. Further details and input data are provided in Chapter 10 of the Supporting Information, which also contains the rationale for ignoring correlation effects.

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    • Calculation procedure for mixture adsorption equilibrium, along with derivations of the mixed-gas Langmuir model, summary of the Maxwell–Stefan theory of diffusion in microporous materials, methodology adopted for numerical solutions to transient uptake within single crystalline particle, methodology used for transient breakthroughs in fixed-bed adsorbers, and simulation details and input data on unary isotherms, and Maxwell–Stefan diffusivities are provided for each of the five case studies (PDF)

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Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

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