Feasibility of Temperature Swing Adsorption in Adsorbent-Coated

Article pubs.acs.org/IECR

Feasibility of Temperature Swing Adsorption in Adsorbent-Coated Microchannels for Natural Gas Purification Darshan G. Pahinkar,† Srinivas Garimella,*,† and Thomas R. Robbins‡ †

Sustainable Thermal Systems Laboratory, GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ‡ UES, Inc., Laser-Hardened Materials Evaluation Laboratory Facility (RXAP), Dayton, Ohio 45432, United States ABSTRACT: The feasibility of the use of adsorbent-coated microchannels in temperature swing adsorption (TSA) processes for natural gas purification is investigated by analyzing fluid flow and heat and mass transfer within the monolithic structure containing microchannels. It is found that the operational difficulties in heating commonly used adsorbent beds for the TSA process, due to very low adsorbent thermal conductivity and void space within the bed, can be minimized by introducing the adsorbent as a thin layer coating the microchannel walls. The adsorption, desorption, cooling, and purge stage performances are enhanced by the sharp species and thermal waves in the microchannels. The overall performance of the TSA-based purification process in the present study is found to be competitive with existing PSA-based cycles, yielding similar or higher product purities and recoveries and at least an order of magnitude greater purification capacity. The energy requirement for the process is also found comparable with documented bed-based processes.

1. INTRODUCTION Natural gas is an increasingly important energy source for automobiles and power generation. As diverse sources of natural gas become available, there is a growing need to investigate purification technologies with smaller footprints and higher capacities, preferably with lower capital investments. Before purification, natural gas contains impurities such as N2, CO, CO2, and H2S in concentrations of up to 30% depending on the source, and these impurities must be removed as they pose serious risks, such as generating harmful environmental emissions and reducing the combustion potential of methane (CH4).1 For large scale methane (CH4) purification, absorption, adsorption, and membrane separation technologies are commonly used.2 The absorption-based gas separation system relies on preferential absorption of acid gas impurities in liquid solvents such as monoethanolamine (MEA).3 The continuous nature of the process and high-purity product streams make absorption systems viable for large-scale implementation, although they suffer from limitations such as solvent degradation and large capital cost.3,4 Membrane separation systems are gaining importance in small and medium-scale separation applications (up to 105 kg h−1) due to low energy requirements5 and simplicity of operation. During implementation, however, conventional membrane materials face thermal and chemical stability issues in the presence of heavier hydrocarbons.1,6,7 Of the adsorption-based gas separation technologies, pressure swing adsorption (PSA) is preferred over temperature swing adsorption (TSA) because of low energy requirements, © XXXX American Chemical Society

simplicity in operation, and low capital costs. Various adsorbents including zeolite 5A,8 LTA-zeolites,9 silica molecular sieve,10 sepiolite,11 silicalite,12 metal organic frameworks (MOFs),13 and activated carbon14 have been studied to determine their N2, CH4, and CO2 adsorption capacities, and their applications have been documented for use in PSA-based gas separation systems. While the analysis of adsorption capacities in terms of adsorption isotherms is also applicable for TSA applications, the most important limitation in implementing a TSA-based gas separation process is the difficulty associated with heating and cooling adsorbent materials,15 which typically have low thermal conductivity and high porosity. Therefore, the adsorbent bedbased TSA processes have thus far not been considered viable. Such an implementation of TSA process would need extremely high heating and cooling rates and large cycle times to allow the heat to diffuse through the adsorbent or would have very low capacity. Although heat transfer through adsorbent beds has been proven difficult, TSA-based cycles in gas separation have advantages over PSA processes, including reduced compressor loads. Additionally, as the thermodynamic state of an adsorbent can be altered by manipulating only its temperature, the TSAbased processes can utilize low-grade heat input for their Received: January 26, 2017 Revised: April 13, 2017 Accepted: April 14, 2017

A

DOI: 10.1021/acs.iecr.7b00389 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

can take place. During adsorption, cold water flows through the HTF channel assisting the adsorption of CO2 on the outer hollow fiber, whereas during desorption, hot water flows through the HTF channel, desorbing CO2 from the adsorbent. This design proved feasible from a process standpoint; however, as the flue gas flows through the space between hollow fibers, the footprint of such a system is larger than that of a monolithic array. A monolithic array of microchannels, which consists of alternating rows of HTF channels and adsorbent-coated gas channels, could lead to an improvement over the design implemented by Determan et al.25 The present study investigates the use of an adsorbent-coated microchannel monolith for purification of natural gas, addressing the key challenges in implementation of a TSA process discussed above. A schematic of the microchannel monolith used for the simulation in the present investigation is shown in Figure 1.

operation that may be provided by waste heat from other applications. Efforts to make TSA processes viable for general applications including gas separation have included the incorporation of finned adsorbent beds16 and heat recovery using process gas from parallel, out-of-phase cycles.17,18 Moete and LeVan19 performed a theoretical analysis of adsorption and desorption half cycles for CO2 separation from air using electric heaters inserted at the center of a zeolite 5A bed. They found that the thermal conductivity of the adsorbent influences the heat distribution during desorption, in turn significantly affecting operating capacity of the bed under a constant rate of heat supplied, reiterating the difficulties associated with heating and cooling of the adsorbent bed. As a result of low thermal conductivities of the adsorbent materials, the location of electric heaters plays a very important role in determining the performance of the adsorbent bed during the desorption stage. Lee et al.20 demonstrated the use of electrically driven TSA for CO2 removal from indoor air using a pair of honeycomb carbon monoliths and found that the energy requirement for such a system can be as high as 28 MJ kgCO2−1 (the documented energy requirement21 for advanced MEA absorption is 3.7 MJ kg-CO2−1) with the potential reasons for low performance being low CO2 concentration (1.5 μm), so that molecular diffusion equations can be used safely to determine the diffusion coefficients, and the effect of Knudsen diffusion on the diffusion of gases at near atmospheric pressure in the adsorbent layer can be neglected. The system considered here has a ternary mixture consisting of N2, CH4, and CO2. The effective binary diffusion coefficients for each of the pairs in the ternary mixture are employed to calculate the transport of each species in the mixture. Such an effective diffusion coefficient is also dependent on instantaneous mass fractions of the species to account for bulk flow in concentrated solutions. More complex iterative procedures for determination of ternary diffusion coefficients exist, but this simplified approach is chosen to enable the use of the mass transfer resistance analogy. A sample formulation for calculation of the effective diffusivity of A in ternary mixture (A + B + C) is shown in eq 14.30

15·Dcrystal, i rcrystal

2

(12)

Dcrystal, i = Do,crystal, i e(−Ei / Ru·Tw)

(13)

Table 2. Auxiliary Parameters for Competitive DSL Equation Used for Estimation of Zeolite 5A Adsorbent Capacity and Intracrystalline Diffusion Coefficient29 factor

CH4

CO2

N2

A1, mol K kg−1 A2, mol kg−1 A3, mol K kg−1 A4, mol kg−1 b0, kPa−1 QB, J mol−1 d0, kPa−1 QD, J mol−1 Do,crystal, m2 s−1 E, J mol−1 ρads, kg m−3

348.971 0.542 348.971 0.542 6.77 × 10−6 −13672.21 6.13 × 10−7 −20307.22 7.2 × 10−12 12551.94

516.743 −0.794 −932.131 6.083 3.32 × 10−7 −41077.1 6.43 × 10−7 −29812.29 5.9 × 10−11 26334 1480

605.423 −0.582 605.423 −0.582 3.73 × 10−5 −7528.09 3.18 × 10−5 −7941.248 5.2 × 10−13 6275

DA,eff,Mixture =

(1 − yA )

(

yB DAB,eff

+

yC DAC,eff

)

(14)

A unidirectional flow is assumed in the microchannel and variation of species and energy in the lateral direction in the adsorbent layer is neglected. The adsorbent layer is comprised of adsorbent material and the binding polymer (PEI). The thermophysical properties of this composite are calculated using the appropriate weighting techniques described in detail by Pahinkar et al.27 For calculating the HT and MT resistances, a repeating control volume as shown in Figure 3 is chosen. The underlying concept

It can be seen from Figure 2 that at high system pressure, the temperature swing is less effective than that at low pressures. The operating adsorbent capacity indicated by vertical distance from A to B at 120 kPa is about three times that of the capacity (C to D) at 1000 kPa and becomes negligible at 5000 kPa. The desorption temperature is selected as 90 °C, so that liquid water at atmospheric pressure can be used as the HTF and the excellent heat transfer characteristics of the liquid phase can be utilized. During the desorption stage, a purge gas is required to drive the desorbed gases out of the microchannel, so that the channel can be refreshed for the next feed stage. Feed gas, product gas, and pure nitrogen are some of the candidates for the desorption stage purge gas. For the present study, a pure N2 purge is selected, as it lowers the partial pressure of CO2, aiding desorption without any expenditure of the feed or the product gas. Feed gas purge to enrich the gas collected during desorption with more CO2 is possible, but the operating capacity of the adsorbent then relies only on temperature swing, which needs to be greater for a higher swing capacity. Product purge (purified CH4) results in higher swing capacity at the cost of highly reduced process capacity, as the CH4 used to purge will be lost. Hence, pure N2 purge is selected for gas removal during the desorption and cooling stages. After the desorbed gases are removed and the temperature of the monolith decreases to that of the ambient, the N2 stream is replaced by the purified CH4 stream bled from the product tank so that the microchannel flow region, adsorbent layer void spaces, and the adsorbent sites are filled by CH4 and the product collection can start as soon as the feed stage commences. It must be noted that the desorption and cooling stage purge and actual product purge at the end of the cooling stage are two different purging steps. Nitrogen is used a representative gas for the desorption and cooling stages; other alternatives may be possible. 2.2. Mass and Heat Transfer Resistances. For modeling the mass transfer within the microchannel and adsorbent layer, an approach similar to that followed by Pahinkar et al.27 that involves determination of binary and effective diffusion coefficients of gas mixtures in void spaces in the adsorbent layer30 and calculation of mass transfer coefficients and friction factor using Churchill correlations31 is adopted. The macro-

Figure 3. Schematic of the repeating geometry showing the extended surface approach to estimate heat and mass transfer resistances between material nodes.

involves modeling the HT and MT across a composite block, with the side walls of the channels idealized as indirect heat transfer surfaces. Thus, the vertical walls shown by yellow lines in Figure 3 act as fin edges with adiabatic boundary conditions at their ends (due to symmetry at all edges, there is no HT and MT across this control volume.) From the microchannel node to the adsorbent layer node, gases are transferred by mass convection at the horizontal base surface (edges shown as black lines) and at the fin surfaces (edges shown as yellow lines). It must be noted that mass transfer takes place only between the adsorbent layer and the microchannel, while the rest of the nodes are associated with only heat transfer. To estimate the convective mass transfer resistance, the MT efficiency of the adsorbent layer fin is calculated as shown in eq 15. This MT fin efficiency accounts for the increased convective D


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conduction resistance in the monolith wall. Finally, the HT resistance between the monolith wall node and the HTF channel node is calculated as shown in eq 21, wherein effective convection HT resistance from the HTF channel node to the monolith surface and conduction resistance from the monolith base surface are summed.

mass transfer resistance at the vertical walls, while a simple linear diffusion resistance can be used to calculate the diffusion resistance in the horizontal walls. Thus, the overall mass transfer resistance between the adsorbent layer node and the microchannel is calculated using eq 16. DG dz 2 D = 2 × G dz 2

AB,G = 2 × A f,G

1 h T,G ·(AB,G + ηf,G,HT,adiabaticA f,G)

R heat,G ↔ W =

+

A f,G,CS = (2 × th + thML) dz

kW

th × 2 × (DG + 2 × th + thML) dz (19)

perif,G = 2 dz mG,MT,i =

R heat,W ↔ ML =

hm,G,i perif,G Deff, iA f,G,CS

ηf,G,MT,adiabatic,i = R mass,G ↔ W, i =

tanh(mG,MT,iLf ) (mG,MT,iLf )

(20)

(15)

1

R heat,ML ↔ L =

hm,G, i ·(AB,G + ηf,G,MT,adiabatic, iA f,G) +

Deff, i

th k W × 2 × (DG + 2 × th × thML) dz thML + kML × 2 × (DG + 2 × th + thML) dz

th × 2 × (DG + 2 × th + thML) dz

1 h T,L ·(AB,L + ηf,L,HT,adiabaticA f,L ) +

thML kML × 2 × (DG + 2 × th + thML) dz

(16)

(21)

Heat transfer resistances are calculated in a similar fashion. For the adsorbent layer fin with an adiabatic tip, eq 17 is used to calculate the HT fin efficiency. Equation 18 is used to calculate the HT fin efficiency of the HTF channel.

2.3. Governing Equations for Microchannel Gas Region. The mass, species, momentum, and energy equations solved for the microchannel gas flow region are shown in eqs 22−25,27 respectively, where the heat and mass transfer resistances are utilized in calculating the source terms. The total mass balance shown in eq 22 calculates the gas velocity in the microchannel, which is also a function of the rate of exchange of total mass with the adsorbent layer, as seen on the right-hand side (RHS) of the equation.

mG,HT =

h T,G perif,G k WA f,G,CS

ηf,G,HT,adiabatic =

tanh(mG,HTLf ) (mG,HTLf )

Cg, i − Cw, i ∂(ρu) ∂ρ + = −∑ ∂t ∂z Ag ·R eq,mass,g ↔ w, i i

(17)

(DG + 2 × th) dz 2 D = 2 × L dz 2

AB,L = 2 × A f,L

The species conservation equation, which is shown in eq 23, calculates mass fractions of each species in the ternary mixture. While the first two terms on the left-hand side (LHS) are for the material derivative of the mass fraction, y, the third term represents the total mass balance derived using the chain rule for derivatives. The two terms on the RHS represent the axial diffusion of species in the microchannel and individual species exchange with the adsorbent layer.

A f,L,CS = (thML) dz perif,L = 2 dz mL,HT =

h T,L perif,L kMLA f,L,CS

ηf,L,HT,adiabatic =

ρ

tanh(mL,HTLf,L) (mL,HTLf,L)

(22)

(18)

∂yg, i ∂t

DA, i

On the basis of these fin HT efficiencies, HT resistances are calculated using eqs 19−21. The HT resistance between the microchannel node and the adsorbent layer node is the sum of the effective convection HT resistance at the finned surface and the conduction resistance in the adsorbent layer, as shown in eq 19. The HT resistance between the adsorbent layer node and the monolith wall node is calculated using eq 20, which is the sum of the conduction resistance in the adsorbent layer and the

+ ρu

∂yg, i ∂z

− yg, i ∑ i

Cg, i − Cw, i Ag ·R eq,mass,g ↔ w, i

Cg, i − Cw, i ∂ ⎛⎜ ∂yg, i ⎞⎟ + ρ ⎟ ⎜ Ag ·R eq,mass,g ↔ w, i ∂z ⎝ ∂z ⎠

=

(23)

Equation 24 is the standard form of the momentum conservation equation with the third term on the LHS analogous to that in the species conservation equation. The last term on the RHS substitutes the shear stress in the lateral direction, wherein the Churchill equations for friction factor calculation can be employed.32 E


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Industrial & Engineering Chemistry Research ρ

∂u ∂u + ρu − ∂t ∂z =−

∑ i

Cg, i − Cw, i Ag ·R eq,mass,g ↔ w, i

u

ρFS cp ,FS

ρu 2 ∂P ∂ 2u +μ 2 −f 2D h ∂z ∂z

+ (24)

∂t

+

∂(u·hg ) ∂z

=

Tg − Tw ∂ ⎛ ∂Tg ⎞ ⎜k g ⎟− ∂z ⎝ ∂z ⎠ Ag ·R eq,heat,g ↔ w

(25)

The dispersion coefficient, DA,i, which is dependent on channel velocity as well as diffusion coefficient, is calculated using eq 26.30

(30) 2⎞

⎛ Pe DA, i = DAB, i⎜1 + i ⎟ 192 ⎝ ⎠

2 32μL uL ΔP 64 ρL uL = = L ReL 2D h,L D h,L 2

(26)

2.4. Governing Equations for Adsorbent Layer. The governing equations for the adsorbent layer involve the species and energy balance, which are shown in eqs 27 and 28, respectively. The species conservation equation shown in eq 27 consists of the rates of change of gaseous and adsorbed concentration on the LHS and the terms for ternary axial gas diffusion and species exchange with the microchannel on the RHS. Equation 28 shows the energy equation for the adsorbent layer, wherein the temperature of the adsorbent layer node on the LHS is monitored and is a combined function of axial conduction, energy exchange with the microchannel node, heat of adsorption, and energy exchange with the monolith wall, respectively, on the RHS.

∂t

Deff

kw

Cg, i − Cw, i ∂Cw, i ⎞ ω ∂CA, i ∂⎛ + = ⎜Deff, i ⎟+ ε ∂t ∂z ⎝ ∂z ⎠ A w ·R eq,mass,g ↔ w, i

∑ ω·ΔHads, i i

∂CA, i ∂t

−

∂Cw, i ∂z

∂Tw ∂z

kFS

∂TFS ∂z

= Deff

∂Cw, i

z=0

= kw z=0

∂Tw ∂z

= kFS z=0

∂z

=0 (32)

z=L

=0 (33)

z=L

∂TFS ∂z

=0 (34)

z=L

2.8. Boundary Conditions for the Gas Microchannel, HTF Channel, and Simulation Procedure. Finally, the boundary conditions for the gas microchannel and the HTF microchannel are applied based on the stage that is in progress in the full process cycle. Equations 35−37 are required to close the problem solution for species balance, mass balance, and energy balance, respectively, of the microchannel domain. Equation 38 is used to close the energy balance solution for the HTF channel. While inlet and outlet pressures for all the headers are fixed at 120 and 100 kPa, respectively, the mass fractions at the inlet of the microchannel domain and temperatures at the inlet of the HTF channel domain are decided based on the active stage of the cycle, in accordance with Figure 4 and Table 3.

Tg − Tw ∂Tw ∂ 2T = k w 2w + A w ·R eq,heat,g ↔ w ∂t ∂z +

(31)

2.7. Boundary Conditions for Adsorbent Layer and Monolith Wall. The adsorbent layer and the monolith wall are assumed to be insulated at the inlet and outlet headers to improve the computational stability of the model.27 The boundary conditions for the species and energy balances are then given by eqs 32 and 33 for the adsorbent layer and eq 34 for the monolith wall.

(27)

ρw cp ,w

(29)

TFS − TL ∂(hL) ∂(uL ·hL) ∂ ⎛ ∂TL ⎞ ⎜k L ⎟+ + = ⎝ ⎠ AL ·R eq,heat,FS ↔ L ∂t ∂z ∂z ∂z

uD h Pei = DAB, i

∂Cw, i

TL − TFS AFS ·R eq,heat,FS, ↔ L

2.6. Governing Equations for the HTF Channel. The energy equation for the HTF channel is shown in eq 30, which is coupled with the monolith wall energy equation shown in eq 29. For water, because of its low specific volume, the specific enthalpy becomes nearly equal to the specific internal energy; hence, only hL is used in the transient and convection terms. For example, the internal energy of HTF water at a pressure of 100 kPa and a temperature of 90 °C is 376.85 kJ kg−1, whereas the enthalpy of water for these conditions is 376.95 kJ kg−1.33 For the HTF, laminar flow is expected for 120 kPa inlet and 100 kPa outlet pressures. Hence, liquid HTF velocity is determined by the laminar friction factor formulation as shown in eq 31. For a ΔP of 20 kPa, the liquid HTF flows at 0.10 m s−1 at 90 °C with Re = 62.

Finally, the energy conservation equation for the microchannel region as shown in eq 25 consists of the terms for rate of change of internal energy for the microchannel node and enthalpy exchange with the adjacent nodes on the LHS, with the terms for axial conduction and energy exchange with the adsorbent layer on the RHS. ∂(Ug)

∂TFS ∂ 2T Tw − TFS = kFS 2FS + ∂t AFS ·R eq,heat,w ↔ FS ∂z

Tw − TFS A w ·R eq,heat,w ↔ FS (28)

2.5. Governing Equation for the Fused Silica Monolith Wall. The adsorbent layer is attached to the fused silica monolith wall. Although the fused silica wall is impermeable to species, the thermal mass of fused silica must be incorporated for analyzing heat transfer from the adsorbent layer and the HTF channel. The energy equation used for the fused silica wall is shown in eq 29, which is coupled with the energy equation for the adsorbent layer as shown in eq 28 and with the HTF channel energy equation as shown in eq 30.

∂(ρuyi ) ∂z F

= z=0

∂(ρuyi ) ∂z

=0 z=L

(35) DOI: 10.1021/acs.iecr.7b00389 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 4. Model architecture for the TSA process cycle in the present work.

∂(ρu) ∂z

= z=0

∂(hg ) ∂z ∂(hL) ∂z

= z=0

= z=0

∂(ρu) ∂z

∂(hL) ∂z

(36)

z=L

∂(hg ) ∂z

property package. The gPROMS ModelBuilder interface also allows the components to be connected graphically with each other, thus avoiding the need to manually write the equations for boundary conditions between different components. Table 3 shows the details of the valve opening and closing procedure required for the cyclic simulation and corresponding stage times in the cycle. These times are selected based on the extent of completion of the requisite stage and are discussed in detail in the next section. For the baseline case considered, the total cycle time is 128 s, which is shorter than most of the PSAbased gas separation cycles27,35,36 (∼1200 s) and much shorter than the TSA-based cycle studied by Merel et al.16 (4020 s).

=0

=0 (37)

z=L

=0 (38)

z=L

Table 3. Simulation Procedure for the TSA-Based Purification Cycle and Stage Times stage

valves open

valves closed

stage time (s)

adsorption desorption cooling purge total cycle

V1, V5, V6, V8 V2, V4, V7 V2, V4, V6, V8 V3, V4, V6, V8

V2, V3, V4, V7 V1, V3, V5, V6, V8 V1, V3, V5, V7 V1, V2, V5, V7

40 60 20 8 128

3. RESULTS AND DISCUSSION The full process model described in the previous section is simulated as detailed above. The heat and mass transfer results in a cyclic steady state of the process are described first, followed by the assessment of full process performance. Figure 5 shows the gaseous concentration in the microchannel (a) and the adsorbed concentration in the adsorbent layer (b) during the adsorption or feed stage. At the start of the adsorption stage, the adsorbent microchannel is filled with near pure CH4, which is bled from the product tank as shown in Figure 4, and corresponding residual adsorbed concentrations can be seen in Figure 5b. The average residual adsorbed concentrations at the start of the adsorption stage are 636, 969, and 1 mol m−3 for CH4, CO2, and N2, respectively. As the feed gas enters the microchannel, CH4 desorbs from the adsorbent and flows out of the microchannel to be collected as the product. CO2 diffuses into the adsorbent layer and is adsorbed quickly due to high selectivity. Also, as the equilibrium adsorbed concentration for CO2 is about 50 times that of CH4 for the feed gas composition at 120 kPa, the CO2 adsorption wavefront progresses slowly through the microchannel. Meanwhile, purified CH4 collection can continue. The feed gas supply is stopped at 40 s after the start of the adsorption stage, when the CO2 adsorption wavefront is about to reach the microchannel outlet. At this instance in the process, although the adsorbent layer is not saturated fully at all axial locations, which is attributed to gas dispersion in the microchannel, the feed gas supply must

Figure 4 shows the model architecture developed for the complete simulation of the TSA-based purification cycle. The fully coupled FD/MT/HT equations described in earlier sections are embedded in the microchannel and HTF channel models in this schematic.34 The gas and liquid headers connected to the microchannel and HTF channel simply provide species, mass and energy mixing, the equations for which are omitted for brevity. The valves in the models are also assumed as a simple linear opening type (mass flow rate increases linearly with pressure drop), with the valve time constants CT and flow coefficient CV listed in Table 1. The source and sink models list the pressures and mass fractions considered for the system simulation. Additionally, the HTF recirculation loop employs a perfectly insulated path back to the HTF channel inlet. The purge gas, which is bled from the product tank, undergoes compression to be fed to the microchannel inlet. These equations and component models are implemented and simulated in gPROMS ModelBuilder,34 and the fluid properties required for the simulation are imported from the Multiflash G


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HTF channel, it takes about 20 s for all the axial locations to reach 90 °C. However, the desorption stage is continued until 60 s for efficient removal of the desorbed gases, because heating the monolith for 20 s does not accomplish the removal of CO2 from the gas channel instantaneously, as seen in Figure 7.

Figure 5. (a) Gaseous concentrations and (b) adsorbed concentrations of CH4 and CO2 during the adsorption stage simulated for 40 s. CO2 concentrations are shown by solid lines while CH4 concentrations at the same time instances are shown by dashed lines with the same color.

be cutoff to prevent product contamination. At the end of the adsorption stage, the average adsorbed concentration of CH4 drops to 180 mol m−3, while that of CO2 increases to 3230 mol m−3, thus generating an operating adsorption capacity of 2261 mol m−3 for CO2 with a regeneration ability of 70%. The theoretical maximum regeneration ability under the considered operating conditions is 80%, which is achievable if the entire adsorbent layer is allowed to saturate with CO2 during the adsorption stage. However, this will result in product contamination and the purification process will lose its utility. The N2 concentration does not change over the duration of the adsorption stage in either phase and is therefore not shown in Figure 5. At the end of the adsorption stage, N2 enters the microchannel displacing the residual feed gas, and hot water enters the HTF channel at 90 °C. Figure 6 shows the variations of adsorbent layer temperature and HTF temperature during the desorption stage. As the hot water enters the HTF microchannel, heat is readily transferred across the monolith wall. The difference between the temperature of the adsorbent layer and the HTF channel is imperceptible due to negligible heat transfer resistances across the thin material layers. For a pressure drop of 20 kPa across the

Figure 7. (a) Gaseous concentration and (b) adsorbed concentration during the desorption stage. Solid lines indicate CO2 concentrations, and dashed-dotted lines indicate corresponding N2 concentrations for the same instant with the same color. Gaseous and adsorbed concentration curves for the first 2 s are shown to display major changes in the channel gaseous concentrations due to gas flow and insignificant changes in adsorbed concentrations for the same period.

Figure 7a,b shows the gaseous and adsorbed concentrations during the desorption stage. The N2 stream entering the microchannel quickly mixes with the feed gas present in the microchannel; therefore, product collection may not be feasible after the start of desorption. The first two seconds of the process demonstrate significant change in the gas concentration profiles (Figure 7a); however, changes in the adsorbed concentration are small as the heating and desorption does not start until then (Figure 7b). Gas dispersion in the microchannel plays a major role in mixing of gases, thereby avoiding a clean displacement of residual feed gas with the entering N2. After N2 occupies the entire channel and desorption of gases in the adsorbent layer commences due to temperature rise, the adsorbed CO 2 concentration starts falling gradually at all axial locations, with a corresponding increase in CO2 gaseous concentration as seen in Figure 7 until about 20 s. The flowing N2 carries this gaseous CO2 out of the microchannel, and both Cg and CA for CO2 simultaneously drop as a result of continuous decrease in partial pressure of CO2. At the end of the desorption stage, when the rates of decrease in average adsorbed concentrations for the component gases are negligible, the supply of hot water is discontinued with the final average adsorbed concentrations of CH4, CO2, and N2 of 3 mol m−3, 1128 mol m−3, and 96 mol m−3, respectively. Because of low N2 adsorption capacity of zeolite 5A at 90 °C, the N2 adsorbed concentration does not increase to a significant value. At the end of the desorption stage, cold water supply replaces the hot water supply in the HTF channel, whereas the N2 flow in

Figure 6. Variation of adsorbent layer and HTF channel temperature during the desorption stage. The temperatures for the two layers are identical due to negligible heat transfer resistances. H


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the axial locations. The purge stage is continued until the product CH4 occupies the last node of the microchannel, while is adsorbed in the adsorbent layer locally. It takes nearly 8 s for the purge stage to complete. Afterward, no change in gaseous or adsorbed concentrations is observed and supply of purified CH4 can be terminated. At the end of the purge stage, the CO2 concentration remains nearly unchanged at 969 mol m−3, while the CH 4 concentration rises to 636 mol m −3 . The N 2 concentration simply reduces to 1 mol m−3 due to drop in its partial pressure, finally restoring the original thermodynamic state of the microchannel and the HTF channel. The next adsorption stage can start at the end of the purge stage, continuing the cycle. For process performance estimation, cyclic steady state product purity, CH4 recovery, process capacity, and energy requirements are evaluated for the purification process. The process delivers product output during the adsorption stage, while losing a fraction of the product during the purge stage. By monitoring the net product, its composition, and the amount of feed gas entering the microchannel per cycle, the first three of the performance parameters can be calculated. The net product collection is estimated using eq 39, while the product purity is estimated using eq 40. The CH4 recovery is calculated using eq 41.

the microchannel is continued. Figure 8 shows the temperature response of the adsorbent layer and the HTF channel during the

Figure 8. Variation of adsorbent layer and HTF channel temperature during the cooling stage. The temperatures for the two layers are nearly identical due to negligible heat transfer resistance.

cooling stage, which is found to be a mirror image of the temperature response during the desorption stage, because the driving temperature differences and pressure drops are equal. As with the desorption stage, it takes about 20 s for the cold water to lower the adsorbent temperature to 25 °C. The final values of adsorbed concentrations for CH4, CO2, and N2 are 13, 972, 217 mol m−3, respectively. Because of continuous flow of N2 through the microchannel and continued desorption of CO2 due to partial pressure reduction at downstream locations, where the temperature is still high, CO2 average concentration drops marginally. For all the gases including CO2, readsorption of trapped gases is observed as the temperature drops. At the end of the cooling stage, part of the purified product is sent through the microchannel to replace the N2 stream. Figure 9 shows the gaseous (a) and adsorbed concentrations (b) during the purge stage. As the product CH4 enters the microchannel, it occupies the void spaces replacing N2 and also fills up the adsorbent sites, raising the CH4 adsorbed concentration for all

dM net, i dt

•

•

= Mads, i − M purge, i

purityi ,kg =

M net, i ∑i M net, i

purityi ,mole =

ηrecovery =

(39)

cycle

(purityi ,kg /MW) i ∑i (purityi ,kg /MW) i

(40)

M net,CH4 M feed,CH4

cycle

(41)

Figure 10 shows the product tank CH4 mass compared with the feed CH4 (a) and the cyclic steady state purity variation with time (b). It can be seen that at the end of the adsorption stage, CH4 mass collected in the product tank is greater than the feed CH4 entering the microchannel by the amount of CH4 present in the microchannel at the start of the adsorption stage. At the start of the purge stage, a fraction of this purified product is sent back to the microchannel after recompression; hence, the net product collected decreases and becomes smaller than the feed CH4 for each cycle. For the baseline case shown in Table 3, with the cycle time of 128 s, the point for calculation of net purification capacity is shown as B, while point A marks the amount of CH4 sent in for purification, indicating the numerator and denominator in eq 41, respectively. While Figure 10a is shown for illustration purposes, the cyclic steady state values for purity and recovery are reported in later sections. The net product collection for the baseline case is 0.054 kg kg-ads−1. The adsorbent mass, which is dependent on void fraction, adsorbent mass loading, and thermo-physical properties of the adsorbent layer, is found to be 1.07 × 10−5 kg, which is used for normalizing the net product collected from one microchannel. The CH4 recovery for this case is then found to be 93.4%. Finally, as shown in Figure 10b, the product purity in a cyclic steady state is found to be 97.05%. The high purity and recovery factors are attributed to a small purge-to-feed ratio,

Figure 9. (a) Gaseous concentration and (b) adsorbed concentration during the purge stage. Dashed lines indicate CH4 concentrations and dashed-dotted lines indicate corresponding N2 concentrations for the same time instances with the same color. I


Article


of the basic stages and small adsorbent mass per microchannel required for gas separation. Figure 12 shows the product purity plotted against CH4 recovery and compared with the data in the literature. Not

Figure 12. Variation of product purity with CH4 recovery, compared with the literature.36,37

only does the product purity stay competitive with the PSAbased processes, but the recovery factor for CH4 is also found to be very high for the three cases considered in the present work. One of the reasons for the high recovery factors is the requirement of a small mass of purge gas for refreshing the microchannel before the start of adsorption. At low system pressures, the current process capitalizes on very high CO2 adsorption capacity and low CH4 adsorption capacity; hence, the adsorption stage can be longer and purge stage can be shorter. An increase in system pressure may not yield better performance because at high pressures, the mass flow rate and density of the gases increase and the adsorption wavefront becomes less sharp. Thus, the product collection must be stopped much before the wavefront reaches the outlet to prevent CO2 reaching the product tank. Additionally, the mass of CH4 required for refreshing the channel during the purge stage is greater at high pressure than that at low pressure. For the calculation of the total energy required for process operation, the sensible heat required for heating the adsorbent layer−monolith wall assembly, heat of desorption, compressor power required during the purge stage, and HTF recirculation energy must be estimated. Although the desorption stage is continued for 60 s in the present work, it is assumed that the hot water is recirculated through insulated tubes as shown in Figure 4, so that the additional heat required during the desorption process is only the heat lost by the HTF in the microchannel monolith. The equations used to estimate these components of energy and the total energy requirement are shown in eqs 42−46, respectively. In these equations, Ṅ cyc is the number of cycles per hour, which is 28.12 for the baseline case (128 s) and reduces to 26 for the case with a cycle time of 138 s. The sensible energy requirement, which is a function of adsorbent layer thermal mass, monolith wall thermal mass, and the temperature swing considered (65 °C), is calculated using eq 46.

Figure 10. (a) Normalized cyclic net CH4 collection compared with feed CH4 (b) cyclic steady state product purity for the baseline case.

sharp adsorption wavefront at low pressure, and high CO2/CH4 selectivity for zeolite 5A. This process performance is compared with the PSA processes in the literature for CO2 separation. Kapoor and Yang37 investigated kinetic separation using molecular sieve carbon (MSC) and equilibrium separation using zeolite 5A for the CH4−CO2 gas pair. Olajossy et al.36 investigated CH4 separation from coal mine gas using activated carbon (AC). Both of these studies have described the process performance in terms of the parameters discussed above and can provide adequate background for feasibility of the purification process in the present work. The purification cycle in the present work is simulated for two more cases of adsorption stage times (45 and 50 s), with a total cycle time of 133 and 138 s, so that a broader spectrum of results can be compared with the literature. Figure 11 shows the product purity plotted against process capacity and compared with the PSA-based processes described by Kapoor and Yang37 and Olajossy et al.36 It can be seen from Figure 11 that the process capacity normalized with the adsorbent mass and time is at least an order of magnitude higher than the PSA-based processes at comparable or greater purity values. This performance improvement is attributed to not only the reasons listed in the previous paragraph but also to a convection-based design resulting in quick execution

•

•

Esens = Ncyc·(ρw ·c p,w ·A w + ρFS ·c FS·AFS) ·L ·ΔT

(42)

The heat of desorption is calculated using eq 43, wherein volumetric rates of heat of desorption for each species are added to estimate the net desorption energy requirement. •

•

Edeso = Ncyc·A w ·L ·∑ ω·hads, i ·ΔCA, i

Figure 11. Variation of product purity with process capacity, compared with the literature.36,37

i

J

(43)


Article

Industrial & Engineering Chemistry Research Table 4. Component-Wise Energy Requirement Calculations for the Present Work tcycle [s]

Ė sens [MJ kg−1h−1]

Ė deso [MJ kg−1h−1]

Ė purge [MJ kg−1h−1]

Ė HTF [MJ kg−1h−1]

Ė total [MJ kg−1h−1]

Ṁ product [kg kg−1h−1]

Etotal [MJ kg−1]

128 133 138

11.1 10.7 10.3

1.33 1.42 1.50

0.163 0.157 0.151

0.014 0.014 0.014

12.48 12.16 11.85

1.52 1.70 1.87

8.21 7.15 6.33

The energy required for the flow of purge gases through the monolith, which is a function of mass flow rate through the compressor and pressure drop across it (20 kPa), is calculated using eq 44. •

•

Epurge = Ncyc·M purge ·ΔHcom

(44)

Finally, the energy required for the flow of HTF through the monolith is calculated in a similar fashion as shown in eq 45. With the other notations carrying their usual meanings, Table 4 shows the energy requirement calculation for the three cases considered in the present work. •

•

Figure 13. Comparison of energy requirement values normalized with mass of CO2 with those in the literature.

•

E HTF,recir = Ncyc·MHTF,cyc ·vHTF·ΔP •

•

•

(45)

•

Etotal = Esens + Edeso + Epurge + E HTF,recir

The thermal mass of the system used to calculate the sensible energy includes that of the adsorbent layer and the monolith wall and is calculated to be 0.065 J K−1. The monolith wall accounts for 75% of the thermal mass. The total sensible heat and heat of desorption required for the present work is 11.8 MJ kg−1 h−1. When normalized with rate of product collection, 1.87 kgproduct kg−1 h−1, this energy requirement is 6.31 MJ kgproduct−1. However, if the sensible heat fraction for the supporting monolith wall is subtracted, this value decreases to 2.17 MJ kg-product−1 or 1.97 MJ kg-CO2−1. This value is comparable with the minimum energy requirements (sum of adsorbent sensible energy not including monolith wall and heat of desorption) for MOFs reported by Li et al.22 (1.33−2.46 MJ kg-CO2−1) and smaller than that discussed by Pirngruber et al.21 of 2.5 MJ kg-CO2−1. The impurity level considered in the present study, 30%, is one of the higher fractions. However, as the impurity fraction decreases, it takes more time for the adsorbent layer to be saturated with CO2 and thus, even more product can be collected in a single adsorption stage. This prediction is attributed to a sharp favorable isotherm for the CO2 and zeolite 5A pair. The adsorbent capacity decreases sharply only after CO2 partial pressure decreases to a trace value in the feed stream. The advantage of the TSA-based process in the present work, when compared with the adsorbent-bed based PSA and TSA gas separation processes in the literature, lies in processing greater magnitudes of feed gas using smaller footprint and producing a high purity gas at a high recovery efficiency, at a faster rate and at a competitive operating cost.

(46)

The process capacities, product purities and CH4 recoveries can be compared with those reported in the CH4 separation studies by Kapoor and Yang37 and Olajossy et al.36 as shown in Figures 11 and 12; however, energy requirement values normalized with purified CH4 are not reported in these studies. Therefore, the total energy requirement values shown in Table 4 are modified to reflect the mass of CO2 removed, for which data are available. The energy requirement for CO2 separation from N2 is reported by Clausse et al.38 and Merel et al.16 for an indirect TSA process using adsorbent beds with fins. Kulkarni and Sholl39 reported the energy requirement for CO2 separation from air using a TSA process employing a structured monolith contactor. Krishnamurthy et al.40 reported a wide range of energy utilization as a function of process capacity for a bed-based vacuum-pressure swing adsorption (VPSA). CO2 separation costs for MEA absorption-based systems are reported by Luis,41 Pirngruber et al.,21 and Bounaceur et al.42 To enable a comparison of the energy requirement of the present concept with these studies, the energy requirement estimated for the present concept for removal of CH4 is recalculated as the energy requirement for separating CO2 from the feed mixture. The mass of CO2 removed during the adsorption stage is used to normalize the actual energy requirement per cycle, and the energy requirement values are plotted against the mass of CO2 removed per unit adsorbent mass per hour in Figure 13. The CO2-specific energy requirement for the present concept is found to be better than that of the bed-based TSA processes. For better economic viability, the lower right corner of Figure 13 is desired, which indicates higher gas removal capacities with low energy requirements. The present concept yields better performance than the bed-based PSA process for which the energy requirement is marginally lower; however, the process capacity is smaller for Krishnamurthy et al.40 by at least an order of magnitude than that estimated for the present concept. Additionally, the energy requirement for the present concept is also comparable with the MEA absorption processes for CO2 removal. The present concept yields at least an order of magnitude greater CO2 removal capacity than bed-based PSA and TSA processes at similar or competitive operating costs.

4. CONCLUSIONS The feasibility of using adsorbent-coated microchannels for a TSA process for natural gas purification is investigated by analyzing the fluid dynamics and heat and mass transfer within a microchannel monolith consisting of repeating arrays of adsorbent-coated microchannels for feed gas and heat transfer fluid. The TSA-based process is designed and simulated, and the adsorbent layer response, gas concentration, and temperature variations during the sequential execution of adsorption, desorption, cooling, and purge stages of the cycle are reported. Cyclic steady state process performance along with comparisons with the literature are presented. K


Article

Industrial & Engineering Chemistry Research DA = Axial dispersion coefficient [m2 s−1] Dcrystal = Intracrystalline diffusion coefficient [m2 s−1] Deff = Effective diffusion coefficient [m2 s−1] Dh = Diameter [m] ΔHads = Heat of adsorption [J mol−1] ΔHcom = Compressor energy requirement [J mol−1] E = Activation energy [J mol−1] Ė = Energy requirement [MJ kg−1 h−1] eps = Gas channel surface roughness [m] f = Friction factor [−] h = Enthalpy [J m−3] hm = Mass transfer coefficient [m s−1] hT = Heat transfer coefficient [W m−2 K−1] k = Thermal conductivity [W m−1 K−1] KLDF = Linear driving force constant [s−1] L = Length [m] LL = HTF channel width [m] m = Fin parameter M = Mass [kg] ṁ = Mass flow rate [kg s−1] Ṁ = Mass collection rate [kg kg−1 h−1] MF = Adsorbent loading [kg kg-polymer−1] MW = Molecular weight [kg kmol−1] N = Number of nodes [−] P = Pressure [kPa] Pe = Peclet number [−] peri = Channel perimeter [m] QB/D = Heat of adsorption in DSL equation [J mol] R = Radius [m] rcrystal = Adsorbent crystal size [m] Re = Reynolds number [−] Req = Overall resistance [m−2 s or m-K W−1] Ru = Universal gas constant [J mol−1 K−1] t = Time [s] th = Adsorbent layer thickness [m] thFS = Monolith wall thickness [m] T = Temperature [K] u = Velocity [m s−1] V = Volume [m3] wL = HTF channel height [m] x = Mole fraction [−] y = Mass fraction [−] z = Axial position [m]

It is found that with the use of microchannels, the heat and mass transfer resistances, and the thermal mass of the system are reduced significantly, enhancing the stage-wise performance. The sharper adsorption wavefront at low system pressures, combined with a near constant operating CO2 adsorption capacity, results in collection of at least 10 times more product than that reported for the bed-based PSA processes and 40 times more product than that reported by Merel et al.16 for their TSA process, with competitive or higher purities. Additionally, small purge-to-feed ratios result in very high CH4 recovery factors. The total energy requirement for the process in the present study is competitive with the total energy requirement reported in the literature on bed-based processes. These energy requirement calculations are based on a 50 μm thick monolith wall. However, with the monolith wall as thin as 25 μm, the total energy required can be reduced to 60% of the values reported in Table 4, provided the structural rigidity of the monolith is maintained. For a cycle time of 138 s, if the monolith wall thickness is halved, the sensible heat required for the desorption stage shown in Table 4 decreases to 5.42 MJ h−1 kgads−1 from 10.3 MJ h−1 kg-ads−1. This is because the thermal mass in the system decreases. Therefore, the total energy required drops to 3.79 MJ h−1 kg-product−1. After modifying this value to account for the mass of CO2 removed, the CO2-specific energy requirement becomes 3.47 MJ kg-CO2−1 (0.96 kWh kgCO2−1) which is competitive even with the absorption systems using advanced MEA solvents, thereby giving the process analyzed in the present work an advantage in terms of process durability, capital cost, and process output over the absorption systems. Therefore, a TSA process using adsorbent-coated microchannels has been found feasible for natural gas purification, and warrants continued investigation for process output enhancement and energy requirement reduction.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Srinivas Garimella: 0000-0002-5697-4096 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to sincerely thank Mr. Tracy Fowler of ExxonMobil Upstream Research Company and Dr. Robert A. Johnson of ExxonMobil Research and Engineering Company for their valuable inputs throughout the course of this research. The authors also acknowledge financial support for this work from ExxonMobil Upstream Research Company.

■

Greek

Δ = Change or discrete step [−] ε = Adsorbent matrix void fraction [m3 m−3] η = Efficiency [−] μ = Viscosity [kg m−1 s−1] ρ = Density [kg m−3] τ = Tortuosity factor [−] ω = Adsorbent volume fraction [m3 m−3]

ABBREVIATIONS

Superscripts and Subscripts

Symbols 2

A = Area [m ] A1, A2... = DSL coefficients [mol kg−1 or mol kg−1 K] b,B = DSL coefficients C = Concentration [kg m−3] CA = Adsorbed concentration [mol m−3] CA,eq = Equilibrium concentration [mol m-3] cp = Heat capacity [J kg−1 K−1] CT = Valve time constant [s] Cv = Valve flow coefficient [kg s−1 kPa−1] d,D = DSL coefficients

A = Axial dispersion B = Base surface ads = Adsorption stage binder = Polymer, PEI com = Compressor CS = Cross-sectional deso = Desorption eq = Equilibrium f = Fin feed = Feed or adsorption L


Article


(20) Lee, T. S.; Cho, J. H.; Chi, S. H. Carbon Dioxide Removal using Carbon Monolith as Electric Swing Adsorption to Improve Indoor Air Quality. Build. Environ. 2015, 92, 209. (21) Pirngruber, G. D.; Guillou, F.; Gomez, A.; Clausse, M. A Theoretical Analysis of the Energy Consumption of Post-Combustion CO2 Capture Processes by Temperature Swing Adsorption Using Solid Sorbents. Int. J. Greenhouse Gas Control 2013, 14, 74. (22) Li, Z.; Xiao, G.; Yang, Q.; Xiao, Y.; Zhong, C. Computational Exploration of Metal−Organic Frameworks For CO2/CH4 Separation via Temperature Swing Adsorption. Chem. Eng. Sci. 2014, 120, 59. (23) Lively, R. P.; Chance, R. R.; Kelley, B. T.; Deckman, H. W.; Drese, J. H.; Jones, C. W.; Koros, W. J. Hollow Fiber Adsorbents for CO2 Removal from Flue Gas. Ind. Eng. Chem. Res. 2009, 48, 7314. (24) Lively, R. P.; Dose, M. E.; Xu, L.; Vaughn, J. T.; Johnson, J. R.; Thompson, J. A.; Zhang, K.; Lydon, M. E.; Lee, J.-S.; Liu, L.; Hu, Z.; Karvan, O.; Realff, M. J.; Koros, W. J. A High-Flux Polyimide Hollow Fiber Membrane to Minimize Footprint and Energy Penalty For CO2 Recovery from Flue Gas. J. Membr. Sci. 2012, 423−424, 302. (25) Determan, M. D.; Hoysall, D. C.; Garimella, S. Heat- and MassTransfer Kinetics of Carbon Dioxide Capture Using Sorbent-Loaded Hollow Fibers. Ind. Eng. Chem. Res. 2012, 51, 495. (26) Mark, J. E. Polymer Data Handbook; Oxford University Press Inc.: New York, 1999. (27) Pahinkar, D. G.; Garimella, S.; Robbins, T. R. Feasibility of Using Adsorbent Coated Microchannels for Pressure Swing Adsorption: Parametric Studies on Depressurization. Ind. Eng. Chem. Res. 2015, 54, 10103. (28) Gholami, M.; Talaie, M. R.; Roodpeyma, S. Mathematical Modeling of Gas Dehydration using Adsorption Process. Chem. Eng. Sci. 2010, 65, 5942. (29) Gholami, M.; Talaie, M. R. Investigation of Simplifying Assumptions in Mathematical Modeling of Natural Gas Dehydration Using Adsorption Process and Introduction of a New Accurate LDF Model. Ind. Eng. Chem. Res. 2010, 49, 838. (30) Hines, A.; Maddox, R. Mass Transfer Fundamentals and Applications; Prentice-Hall, Upper Saddle River, NJ, 1985. (31) Churchill, S. W. Comprehensive Correlating Equations for Heat, Mass and Momentum Transfer in Fully Developed Flow in Smooth Tubes. Ind. Eng. Chem. Fundam. 1977, 16, 109. (32) Churchill, S. W. Friction-Factor Equations Spans All Fluid Flow Regimes. Chem. Eng. (New York) 1977, 84, 91−92. (33) Engineering Equation Solver, http://www.fchart.com/ees/ (accessed October 2016). (34) gPROMS, https://www.psenterprise.com/products/gproms (accessed July 2016). (35) Cen, P.-L.; Chen, W.-N.; Yang, R. T. Ternary Gas Mixture Separation by Pressure Swing Adsorption: A Combined HydrogenMethane Separation and Acid Gas Removal Process. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1201. (36) Olajossy, A.; Gawdzik, A.; Budner, Z.; Dula, J. Methane Separation from Coal Mine Methane Gas by Vacuum Pressure Swing Adsorption. Chem. Eng. Res. Des. 2003, 81, 474. (37) Kapoor, A.; Yang, R. T. Kinetic Separation of MethaneCarbon Dioxide Mixture by Adsorption on Molecular Sieve Carbon. Chem. Eng. Sci. 1989, 44, 1723. (38) Clausse, M.; Merel, J.; Meunier, F. Numerical Parametric Study on CO2 Capture by Indirect Thermal Swing Adsorption. Int. J. Greenhouse Gas Control 2011, 5, 1206. (39) Kulkarni, A. R.; Sholl, D. S. Analysis of Equilibrium-Based TSA Processes for Direct Capture of CO2 from Air. Ind. Eng. Chem. Res. 2012, 51, 8631. (40) Krishnamurthy, S.; Rao, V. R.; Guntuka, S.; Sharratt, P.; Haghpanah, R.; Rajendran, A.; Amanullah, M.; Karimi, I. A.; Farooq, S. CO2 Capture from Dry Flue Gas by Vacuum Swing Adsorption: A Pilot Plant Study. AIChE J. 2014, 60, 1830. (41) Luis, P. Use of Monoethanolamine (MEA) For CO2 Capture In A Global Scenario: Consequences and Alternatives. Desalination 2016, 380, 93.

FS = Fused silica g = Microchannel h = Hydraulic heat = Related to heat transfer i = Assigned species (CH4, CO2, N2) in = Inlet L = HTF channel or liquid mass = Related to mass transfer mid = Midpoint out = Outlet sens = Sensible heat w = Adsorbent layer or wall

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Feasibility of Temperature Swing Adsorption in Adsorbent-Coated

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