Feasibility of Using Adsorbent-Coated Microchannels for Pressure

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Feasibility of Using Adsorbent Coated Microchannels for Pressure Swing Adsorption: Parametric Studies on Depressurization Darshan Gopalrao Pahinkar, Srinivas Garimella, and Thomas R Robbins Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b01023 • Publication Date (Web): 17 Sep 2015 Downloaded from http://pubs.acs.org on October 7, 2015

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Industrial & Engineering Chemistry Research

Feasibility of Using Adsorbent Coated Microchannels for Pressure Swing Adsorption: Parametric Studies on Depressurization Darshan G. Pahinkar1, Srinivas Garimella*1, Thomas R. Robbins2 1

Sustainable Thermal Systems Laboratory, GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 2

UES, Inc., Laser-Hardened Materials Evaluation Laboratory Facility (RXAP), Dayton, OH, 45432

ABSTRACT

The feasibility of using adsorbent coated microchannels for a pressure swing adsorption process for carbon dioxide removal is investigated by analyzing the effectiveness of depressurization. As a result of large adsorbent particle size and the correspondingly large mass transfer resistances and a diffusion-based process design, the cycle times for conventional adsorbent-bed based PSA processes are long and gas removal capacities normalized with adsorbent mass are modest. However, this computational investigation of the depressurization stage that involves the pressure, temperature and adsorbent capacity response in a microchannel analogous to bed depressurization for Zeolite 5A, 13X and activated carbon shows that gas removal capacities

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during depressurization are greater than those for a conventional bed based PSA process under the same operating pressure limits, feed compositions and stage times. An activated carbon monolith yields the highest operating gas removal capacity during depressurization when compared to other adsorbents as a result of smaller selectivity of the activated carbon. A parametric study on the microchannel geometry shows that an increase in channel size aids in fast depressurization, due to reduced frictional resistance at the microchannel walls. It is found that the use of adsorbent microchannels in adsorption purification techniques can yield benefits through the reduction of total cycle time and overall plant capacity.

Keywords: Adsorbent-coated microchannel, pressure swing adsorption, depressurization. 1. INTRODUCTION Natural gas is becoming increasingly important as an energy source for automobiles and power generation. The raw natural gas stock typically contains contaminants such as N2, CO, CO2, and H2S in variable proportions from 10 to 30%. The acid gas contaminants (CO, CO2, and H2S) not only decrease the combustion potential of the fuel, but also pose expensive corrosion risks to machinery, and generate harmful environmental emissions1. Additionally, because CO2 has a relatively high freezing temperature, there is the possibility of freezing in natural gas pipelines, creating blocks of dry ice that clog pipelines and damage pumping equipment2. Removal of these acid gases is a high priority task in commercial applications3. Additionally, the power plant industry has also benefitted from the gas separation technologies for CO2 removal from post combustion flue gases4. Nearly 2.1 Gt gaseous CO2 is released due to fossil fuel combustion, contributing to global environmental concerns that have led to an increased attention to carbon


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capture and sequestration (CCS). For gas purification and CO2 removal applications, absorption, adsorption, and membrane separation technologies are in use or being investigated4-6. The absorption based gas separation method has been used traditionally for CO2 removal, wherein CO2 is absorbed in the solvent liquids such as MonoEthanolAmine (MEA) and the product gas (CH4 in case of CH4 purification, and N2 in case of flue gas CCS) is collected or released. Absorption systems are well understood and produce a high purity stream of product at high recovery rates. However they require high capital costs and large installation spaces7. Membrane gas separation is also used in off-shore locations where energy availability is an issue. Although, low cost and small space requirements are advantages of membrane separation, it suffers from drawbacks such as low durability, and inadequate chemical and thermal stability. However, continuous improvements in the membrane materials make the membrane process viable for gas separation applications2, 3. In adsorption-based gas separation technologies, pressure swing adsorption (PSA) has attracted increasing interest as compared to temperature swing adsorption (TSA)7, 8, because of its low energy requirements9 and capital costs, with its other major applications being air drying, and hydrogen purification . Generally, PSA processes employ an adsorbent bed with void spaces through which the high pressure feed gas is passed and gas separation is accomplished by selective adsorption of the impurities from the intended product. The adsorbent material is usually chosen in such a way that it accommodates the impurities with higher adsorption capacity and selectivity as compared to the product or the non-adsorbing gas10. The applicability of the PSA process utilized in gas separation has been investigated for adsorbents such as zeolite 13X11, 12, zeolite 5A13, molecular sieve carbon13, silicalite14, 15, silica molecular sieve16, LTAzeolites17, sepiolite18, activated carbon19, 20, and metal organic frameworks21-23 for the adsorption



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of CO2, CH4, N2, H2O. The selection of the appropriate adsorbent from these choices is driven by the gas mixture under investigation and the operating capacity of the adsorbent for each of these gases under a specified pressure swing. After the end of the feed stage, to aid the product recovery, a co-current or countercurrent purge step can help displace the product from the void spaces24. Once the product collection is stopped, the thermodynamic state of the adsorbent bed is altered by manipulating the pressure; hence, for regeneration of the adsorbent bed, the adsorbent bed pressure is reduced to low pressure conditions or near vacuum conditions in the case of vacuum pressure swing adsorption (VPSA)24, releasing the adsorbed impurities from the adsorbent crystals. The impurities are subsequently removed from the bed. The next purification cycle can start by pressurizing the bed with the feed gas or typically, the product gas, to improve the product purity, which brings the adsorbent back to the original thermodynamic state. Figure 1 represents the sequence of processes followed in a typical PSA process.

Figure 1: Basic stages of a pressure swing adsorption process cycle Kapoor and Yang 13 carried out an experimental and analytical investigation of a PSA cycle for CH4 – CO2 separation and used an adsorbent bed consisting of molecular sieve carbon (MSC) pellets as large as 3.18 mm. Their purification cycle consists of a sequence of feed pressurization, co-current purge for methane recovery, and depressurization followed by


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evacuation. This study involved an analysis of a kinetic separation of a CH4-CO2 mixture, where CO2 diffuses into the adsorbent crystals at a higher rate than CH4, while CH4 can be collected as product.

The adsorbent bed size was small (40 mm × 600 mm) compared to absorption

purification process installations and 0.56 kg of adsorbent particle mass was required to construct one adsorbent bed. For the kinetic PSA plant studied by Kapoor and Yang 13, the 60 s to 240 s long cycles generated product purities above 88% with a feed throughput capacity of up to 145 LSTP kg-ads-1 hr-1. They also conducted an equilibrium based separation study on zeolite 5A adsorbent for an equi-molar mixture of CH4-CO2 and reported feed throughput capacity of up to 120.75 LSTP kg-ads-1 hr-1 for a feed pressure of up to 472 kPa to a low-side pressure of absolute vacuum conditions. Cen, Chen and Yang 10 reported a study of a similar PSA process for ternary separation of CH4 – H2 – H2S using 0.41 kg of activated carbon with bed dimensions similar to those of Kapoor and Yang 13. For this cycle, the cycle time, which is dependent on the feed gas rate as well as the adsorbent capacity and selectivity, was 1350 s. In another investigation by Olajossy et al.24, CH4 separation from coal mine gas using the PSA process needed 1200 s for a 2.4-m long adsorbent bed with 3.9 kg activated carbon. Krishnamurthy et al.12 conducted an experimental investigation of a VPSA pilot plant involving removal of CO2 from flue gas with a composition of 85/15 (N2/CO2) using twin zeolite 13X adsorbent beds. Each of the adsorbent beds was 0.3 m × 0.87 m in size, packed with 42 kg of adsorbent with a void fraction of 0.43. The cycle times used for this study varied from 500 s to 560 s, with a total depressurization stage time consisting of blow down and evacuation of 460 s. For a feed pressure of 150 kPa and low-side pressure as low as 1 kPa, they reported a CO2 removal capacity normalized with adsorbent volume up to 1.4 ton CO2 m-3 ads day-1. It should be



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noted that the product from this CO2 removal process is collected during the blow down and evacuation stages of the process unlike during the feed stage for a purification process, when the impurities are adsorbed. Shen et al.20 investigated an activated carbon bed-based VPSA process that used a feed pressure range from 131 kPa to 324 kPa and a low-side pressure of 3 kPa. For a feed composition of 85/15 (N2/CO2), CO2 productivities ranged from 1.31 mol kg-ads-1 hr-1 to 2.42 mol kg-ads-1 hr-1. For a feed composition of 50/50 (N2/CO2), increased productivity of up to 5.56 mol kg-ads-1 hr-1 was observed. The total cycle time for this process ranged from 542 s to 934 s with a depressurization time of up to 420 s. For the 11 cases studied, they were able to achieve a CO2 purity of 93% and recovery of 96% in independent process runs. The total process performance, however, remained dependent on simultaneous variation of all the stage times and a clear trend of the process performance is difficult to discern. A clearer trend of productivity, purity and recovery was noticed with feed pressure and vacuum pressure, and favorable performance was observed as the difference between feed and vacuum pressure was increased. The adsorption stage time in some cases can be deliberately kept high under a reduced feed mass flow rate for increasing the sharpness of the adsorption wave front and product purity. However, such an adsorbent bed structure requires a longer time for regeneration and evacuation as a result of the increased time for the transmission of the pressure reduction to the void spaces, thus slowing the process down. Coarse-grained adsorbent particles in such beds offer large mass transfer resistances to the impurities to desorb. The time required for the desorption and regeneration of the bed increases accordingly. The large time scales associated with each of these stages, as well as the total cycle time for PSA processes also result in low product collection when normalized with time and adsorbent mass.


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The above discussion shows that PSA processes that utilize adsorbent beds require large cycle times and experience large mass transfer resistances for the adsorption and desorption of impurities. One of the potential solutions to these limitations is the use of adsorbent-coated microchannels for gas separation. The advantages of using microchannels instead of adsorbent beds in a PSA process are the extremely small mass of adsorbent that may be used in the microchannel compared with the mass of gas being purified and the extremely small mass transfer resistance offered to the adsorbing and desorbing gases. Additionally, because the process design is based on convection through the microchannel with a weaker dependence on diffusion through the adsorbent voids compared to the case with an adsorbent bed, quicker execution of the stages is possible with microchannels. The present study analyzes the use of adsorbent microchannels in a typical PSA process to reduce cycle time and improve process capacity by conducting parametric studies on depressurization. Adsorbent capacity and pressure responses for three adsorbents, zeolite 5A, activated carbon and zeolite 13X, are studied. A comparative assessment of the suitability of these adsorbent materials for depressurization is performed.

The effect of microchannel

dimensions on depressurization effectiveness is also investigated. Additionally, the process productivities, which can be characterized by CO2 removal capacities, are computed by simulating depressurization in adsorbent-coated microchannels for the process conditions used by Kapoor and Yang13 for the CH4-CO2 mixture, and by Shen et al.20 and Krishnamurthy et al.12 for the N2-CO2 mixture. The results are then compared with the process capacities reported in those studies to assess the viability of adsorbent microchannels in PSA based gas separation.



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2. MODELING METHODOLOGY The computational model of the depressurization stage involves analyses of the fluid dynamics (FD), heat transfer (HT), and mass transfer (MT) associated with the microchannel and the adsorbent layer. The modeled adsorbent material is assumed to be embedded in Polyetherimide (PEI) membrane to form a hollow adsorbent layer with voids. This polymer-adsorbent matrix design is based on the development of methods to fabricate the mixed matrix membranes by Lively et al.25. The polymer membrane serves as the continuous phase in the adsorbent layer, while the adsorbent particles form the discrete phase2. PEI is a glassy polymer, which does not offer resistance to gas flow due to its own polymeric linkages; hence, gas diffusion is governed by macroscopic diffusion equations. This adsorbent layer is attached to the monolith wall for additional support and to inhibit mass transfer beyond the adsorbent layer. The monolith wall material is modeled as fused silica, which provides support to the adsorbent layer. It has low thermal mass and minimizes dynamic heat losses during operation. It is also moderately flexible and can therefore provide a range of options to fabricate the monolith under consideration. Multiple adsorbent-coated microchannels can be stacked to form a monolith, a schematic of a section of which is shown in Figure 2.


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Figure 2: Schematic of the microchannel monolith showing characteristic dimensions for the baseline case. For the baseline case, the adsorbent-coated microchannel is assumed to have a characteristic dimension or hydraulic diameter, Dh, of 400 µm. The adsorbent layer thickness and monolith wall thickness are both assumed to be 50 µm for all the cases considered and remain constant, although Dh is varied for parametric studies. The monolith length is kept constant at 1 m.

Figure 3: Schematic of the microchannel cross section considered for FD/HT/MT modeling The FD/HT/MT models are developed and simulated in gPROMSTM Model Builder26, and the material properties of the system components are imported from the MultiflashTM property



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package. Table 1 shows a list of the numerical values of the parameters chosen for model simulation, while Figure 3 shows a schematic of the microchannel considered for simulation. Table 1: Numerical values of parameters used for simulation27 Parameter ε MF L T0 N ρFS kFS cP, FS eps kads cp,ads ρbinder kbinder cp,binder rcrystal

Value 0.55 1 1m 25°C 100 2200 kg m-3 1.3 W m-1 K-1 740 J kg-1 K-1 2 × 10-5 m 0.2 W m-1 K-1 800 J kg-1 K-1 1270 kg m-3 0.22 W m-1 K-1 1461 J kg-1 K-1 10-6 m

2.1 Governing equations The gases adsorbing into and desorbing out of the nanopores of the adsorbent crystals must overcome three mass transfer resistances: convection or film mass transfer resistance from the microchannel to the surface of the adsorbent layer; inter-crystalline diffusion resistance from the adsorbent layer surface to the polymer voids; and intra-crystalline diffusion resistance from the void space into the adsorbent pores. Accurate prediction of these mass transfer resistances is necessary to simulate the kinetics of the adsorption and desorption processes precisely. 2.1.1 Modeling assumptions • Radial variation of parameters in the adsorbent layer is neglected. A single axial node is assumed to represent the lateral cross section of the adsorbent layer. • Radial variation of velocity, concentration, and energy in the microchannel is neglected. The ratio of hydraulic diameter to the length of the microchannel under consideration is


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0.0004. As a result, the axial pressure gradient term is treated as being independent of any lateral dimension and varies only along the flow direction. Therefore, the gas flow in the microchannel is assumed to be nearly unidirectional. • The heat loss from the microchannel monolith wall to the surroundings is neglected. Several microchannels stacked together in parallel interact with each other thermally, and all are considered to demonstrate a similar thermal state at any instant of the process, which causes the heat loss from each microchannel to be absorbed by adjacent microchannels so that the net heat loss from the microchannels is considered negligible. 2.1.2 Mass and heat transfer resistances With the radial lumping of the adsorbent layer and gas channel domains, the conceptual

Figure 4: Idealized schematic of the microchannel cross section representation of the mass transfer resistance is shown in Figure 4. Heat and mass transfer resistances are estimated as follows. It is assumed that the adsorbent layer node is located at the midpoint of the adsorbent layer. The film mass and heat transfer coefficients, hT and hm, are calculated using the Churchill equations shown in Equation (1) and (2), where f is the friction factor calculated using Equation (3)28, 29.

11



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10

⎛ hT Dh ⎞ 10 10 ⎜⎜ ⎟⎟ = ( Nu ) = ( Nul ) + ⎝ k g ⎠ 2

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦

2 ⎡ ⎛ ⎞ ⎤ ⎢ ( 2200− Re) ⎜ ⎟ ⎥ ⎢ e 365 ⎜ ⎟ ⎥ 1 ⎢ + ⎜ ⎟ ⎥ 2 ⎢ ( Shl ) ⎜ Sh + 0.079 Re f Sc ⎟ ⎥ 56 ⎢ ⎥ ⎜ 0 (1 + Sc4 5 ) ⎟⎠ ⎥⎦ ⎢⎣ ⎝

−5

⎡ ⎛ ⎢ ( 2200− Re ) ⎜ ⎢ e 365 ⎜ 1 ⎢ + ⎜ 2 ⎢ ( Nul ) ⎜ Nu + 0.079 Re f Pr 56 ⎢ ⎜ 0 (1 + Pr 4 5 ) ⎢⎣ ⎝

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

−5

(1)

10

⎛ hm Dh ⎞ 10 10 ⎜ ⎟ = ( Sh ) = ( Shl ) + ⎝ DAB ⎠

(2)

⎛ 1 ⎞ ⎜ ⎟

⎛ ⎛ 8 ⎞12 ⎞⎝ 12 ⎠ ⎜ ⎜ ⎟ + ⎟ ⎜ ⎝ Re ⎠ ⎟ ⎜ ( −1.5) ⎟ 16 ⎤ ⎜ ⎡⎛ 37530 ⎞ ⎟ ⎥ ⎜ ⎢⎜⎝ Re ⎟⎠ + ⎟ ⎢ ⎥ ⎟ f = 8 ⋅ ⎜ 16 ⎥ ⎢ ⎜ ⎛ ⎟ ⎛ ⎡ 7 ⎤ 0.9 ⎞ ⎞ ⎥ ⎢ ⎜ ⎜ ⎟ ⎜ ⎢ ⎥ + ⎟ ⎟ ⎥ ⎢ ⎜ ⎜ ⎟ ⎜ ⎣ Re ⎦ ⎟ ⎟ ⎥ − 2.457 ⋅ ln ⎢ ⎜ ⎜ ⎟ ⎜ ⎟ ⎟ ⎥ eps ⎢ ⎜ ⎜ ⎟ ⎜⎜ 0.27 × ⎟⎟ ⎟⎟ ⎥ ⎜ ⎢⎜⎝ ⎟ Dh ⎠ ⎠ ⎦ ⎝ ⎝ ⎣ ⎠

(3)

In the above equations, Nul and Shl are assumed to be 4.01, which is the average of the laminar flow values for uniform wall flux and isothermal wall boundary conditions. The gas diffusion through the adsorbent layer can be either molecular diffusion or Knudsentype diffusion. A comparison of the mean free path and the void size is used to distinguish between the two gas diffusion types. The value of the mean free path, λ, which is dependent on system temperature and pressure, is determined from Equation (4) to be 4.16×10-8 m and 4.12×10-8 m for the CH4-CO2 mixture and the N2-CO2 mixture, respectively. The parameter values used in estimating the mean free paths of the gases at the specified pressure are listed in Table 2. 12


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Table 2: Parameters used for estimation of mean free path and diffusion coefficients for the mixture30. Parameter T P ΩCH4-CO2 Ω N2-CO2 dCH4 dCO2 dN2

MWCO2 MWCH4 MWN2 KB τ

Value 298 K 150 kPa 1.12 0.99 3.785 Å 3.941 Å 3.798 Å 44.01 g mol-1 16.04 g mol-1 28.01 g mol-1 1.380 × 10-23 J K-1 2

For adsorbent layer void sizes larger than 10-6 m, Knudsen-type diffusion is neglected because the void size becomes at least two orders of magnitude greater than the mean free path of the gases. For ordinary diffusion, the Chapman-Enskog theory-based calculation in Equation (5) is used to determine the binary diffusion coefficient of the mixture31. λ=

DAB

KB ⋅T 2π d 2 ⋅ P

1.858 ×10−27 ⋅ T 1.5 ⎛ 1 ⎞ = ∑i ⎜ MW ⎟ Pd 2Ω i ⎠ ⎝

(4) 0.5

(5)

The binary diffusion coefficient is independent of the adsorbent layer porosity and structure. The effective diffusivity is calculated using Equation (6), which accounts for the void fraction, ε, and tortuosity, τ 31. Deff = DAB ⋅

ε τ

(6)

The adsorbent layer demonstrates attributes that are a combination of adsorbent material and polymer membrane properties. The adsorbent volume fraction, density, specific heat, and 13



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thermal conductivity of the combined polymer-adsorbent matrix are calculated using Equations (7) through (10).

ω=

ρbinder ⋅ MFads ⋅ (1 − ε ) ( ρ ads + ρbinder ⋅ MFads )

ρm = ρads ⋅ ω + ρbinder ⋅ (1 − ω − ε )

CP ,m

⎡CP ,ads ⋅ ω ⋅ ρads + ⎤ ⎢ ⎥ ⎢CP ,binder ⋅ (1 − ω − ε ) ⋅ ρbinder ⎦⎥ ⎣ = ρm

km = kads ⋅ ω + kbinder ⋅ (1 − ω − ε )

(7) (8)

(9) (10)

With the calculation of required variables complete, the equivalent resistances for mass transfer and heat transfer can be found using Equations (11) and (12).

R e q , Mass

R e q , Heat

⎛ R ⎞ ln ⎜ w,mid ⎟ R 1 = + ⎝ h ⎠ hm ⋅ Peri 2π Deff

⎛ R ⎞ ln ⎜ w,mid ⎟ R 1 = + ⎝ h ⎠ hT ⋅ Peri 2π km

(11)

(12)

2.1.3 Adsorption equilibrium models In the present study, operating capacities of three different adsorbents subjected to depressurization are analyzed. For zeolite 5A, the Dual-Site Langmuir equation is used for calculating the competitive adsorption isotherms for N2, CH4 and CO2 in the zeolite 5A adsorbent crystals as shown in Equation (13) along with temperature dependence shown in Equation (14) through (17). Auxiliary parameters and coefficients used in the DSL equations are listed in Table 332. 14


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⎛

C A, Eq ,i = ρ ads ⎜ M B ,i

⎜⎜ ⎝

Bi ⋅ Pi 1 + ∑ Bi ⋅ Pi

+ M D ,i

i

⎞ Di ⋅ Pi ⎟ 1 + ∑ Di ⋅ Pi ⎟⎟ ⎠ i

(13)

⎛ −Q ⎞ Bi = b0i exp ⎜ B ,i ⎟ ⎝ RTw ⎠

(14)

⎛ −Q ⎞ Di = d0i exp ⎜ d ,i ⎟ ⎝ RTw ⎠

(15)

M B ,i = M D ,i =

A1,i Tw A3,i Tw

+ A2,i

(16)

+ A4,i

(17)

Table 3: Auxiliary parameters for competitive DSL equation used for estimation of zeolite 5A adsorbent capacity and intra-crystalline diffusion coefficient32 Factor 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

CH4 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

CO2 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

N2 605.423 -0.582 605.423 -0.582 3.73× 10-7 -7528.09 3.18× 10-7 -7941.248 5.2× 10-13 6275

To model the microporous diffusion and account for intra-crystalline diffusivity, the LDF constant shown in Equation (18) is used. Intra-crystalline diffusivity of the gases in the adsorbent is a function of activation energy and adsorbent layer temperature and can be determined using Equation (19). The constant, KLDF, is then used in Equation (20) to determine the instantaneous rate of adsorption. Heat of adsorption of component gases on zeolite 5A crystals is calculated using Equation (21)33. 15



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K LDF ,i =

15 ⋅ Dcrystal ,i

∂C A,i ∂t

(18)

r2

Dcrystal ,i = Do ,crystal ,i e

⎛ Ei ⎞ ⎜ − ⎟ ⎝ RTw ⎠

(19)

= K LDF ,i ⋅ ( C A, Eq ,i − C A,i ) −QB ,i ⋅ M B ,i ⋅ Bi ⋅ (1 + Di ⋅ Pi )

DH ads ,i =

(20) 2

−QD ,i ⋅ M D ,i ⋅ Di ⋅ (1 + Bi ⋅ Pi ) M B ,i ⋅ Bi ⋅ (1 + Di ⋅ Pi )

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2

2

(21)

+ M D ,i ⋅ Di ⋅ (1 + Bi ⋅ Pi )

For activated carbon, the temperature-dependent Sips model developed by Park et al.34 is used for the calculation of adsorbent capacities. Equation (22) shows the Sips equation, while the temperature dependence of the auxiliary parameters is shown in Equations (23) through (25). The intra-crystalline diffusivity for activated carbon is calculated using Equation (19)20. The numerical values of the parameters for activated carbon are shown in Table 4.

C A, Eq ,i

⎛ ⎞ ⎜ ⎟ ⎛ 1 ⎞ ⎜ ⎟ ⎜ ⎟ n B ⋅ P i ⎝ ⎠ ( i i) = ρ ads ⎜ qm ,i ⎟ ⎛ 1 ⎞ ⎜ ⎟ ⎟ ⎜ n ⎛ ⎞⎝ i ⎠ ⎜⎜ ⎟⎟ 1 + ⎜ ∑ Bi ⋅ Pi ⎟ ⎝ i ⎠ ⎠ ⎝

qm,i = K1,i + Bi = K 3,i e

K 2,i Tw

⎛ K 4,i ⎞ ⎜ ⎟ ⎝ Tw ⎠

ni = K5,i +

K6,i Tw

16


(22)

(23)

(24) (25)

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Table 4: Auxiliary parameters for competitive Sips equation used for estimation of activated carbon adsorbent capacity and intra-crystalline diffusion coefficient 20, 34. Factor K1, mol kg-1 K2, mol kg-1 K K3, kPa-1 K4, K K5 K6, K Do,crystal rc-1, s-1 E, J mol-1 ρads

CO2 14.12 -19.6× 10-3 0.79× 10-6 2494 0.764 160.8 12.995 18050

N2 9.947 -19.3× 10-4 22.3× 10-6 1070 0.508 176.6 9.492 12391 2100

For zeolite 13X, Equation (13) is used for calculation of adsorption capacity, while Equations (14) and (15) are used to calculate temperature dependence. Table 5 shows the parameters used in the DSL equation for zeolite 13X. It should be noted that zeolite 13X and activated carbon are used for analysis of only N2-CO2 mixture. Table 5:

Auxiliary parameters for competitive DSL equation used for estimation of zeolite 13X adsorbent capacity 35. Factor Mb, mol kg-1 Md, mol kg-1 b0, kPa-1 d0, kPa-1 Qb, J mol-1 Qd, J mol-1 E, J mol-1 ρads, kg m-3

N2 0 0 8× 10-7 3.93× 10-7 0 0 0

CO2 2.544 2.4185 8× 10-7 3.93× 10-7 -32725.1 -33048.1 36000 1600

2.1.4 Governing equations for the microchannel The governing equations for the gas channel involve the total mass balance, species balance, momentum balance, and energy balance for each node, and are shown in Table 6 along with the boundary conditions needed to obtain closure. 17



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2.1.5 Governing equations for the adsorbent layer The governing equations for the adsorbent layer involve the species and energy balance for each node, and are also shown in Table 6 with the boundary conditions. The source terms in the energy equation include the heat transfer from the microchannel to the adsorbent layer, heat transfer from the adsorbent layer to the fused silica wall and the volumetric rate of heat of adsorption for all component species. The resistance to heat transfer from the adsorbent layer to the fused silica is calculated using Equation (26), in which the conduction heat transfer resistance in the adsorbent layer and that in the fused silica are added.

Figure 5: gPROMS ModelBuilder architecture schematic showing the flow components used and their interconnections26

R e q , FS

⎛ R + th ⎞ ⎛ RFS ,mid ⎞ ln ⎜⎜ h ⎟⎟ ln ⎜ ⎟ Rw,mid ⎠ R + th ⎠ = ⎝ + ⎝ h 2π km 2π k FS

(26)

2.1.6 Governing equations for the fused silica The adsorbent layer considered in the present simulation is attached with the fused silica monolith wall. Although the fused silica wall is impermeable to species, the thermal mass of fused silica must be addressed for heat transfer from the adsorbent layer. The energy equation with the boundary conditions used for the fused silica wall is shown in Table 6, which is coupled with the energy equation for the adsorbent layer shown. 18


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In addition to the adsorbent layer and microchannel models, flow models for valves are also incorporated to represent realistic operation. Figure 5 shows the model architecture, where two simple gas valves with linear responses to pressure drop across them are connected to both the ends of the microchannels. Equation (27) is used to control the valve performance, and values chosen for the flow coefficient, Cv and time constant, CT are 10-5 kg s-1 kPa-1 and 0.5 s-1, respectively. These values are chosen such that the valves themselves do not impose a significant additional pressure drop on the flow, and the adsorbent layer response is analyzed primarily based on the feed and vacuum pressure constraints. •

mv = V p ,actual ⋅ Cv ⋅ ΔP dV p ,actual dt

(27)

= CT (V p ,assigned − V p ,actual )

The source and sink models, which simply list the feed and vacuum pressures, gas inlet and outlet temperatures, and feed composition are also incorporated and are connected with the valve models. Finally, the valve variables are coupled with the corresponding microchannel variables to attain model closure as shown in Equation (28).

yi , g hg

z =0

z =0

= yi ,v1,out

= hv1,out ,

•

•

m z =0 = m v1 yi , g hg •

z=L

z=L

= yi ,v 2,in

(28)

= hv 2,in , •

m z = L = mv 2 Table 6 also shows the initial conditions required at the start of the simulation for each of the governing equations. The model is simulated in two stages. First, the adsorbent layer is saturated by the feed mixture coming in from the source through the inlet valve for the adsorption time. 19



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This process represents the feed stage, although net product is not collected in this process. Both valves are fully open during this stage. As the adsorbent layer is saturated with the feed mixture, the inlet valve is closed and the adsorbent microchannel is allowed to reach the vacuum pressure by gas removal from the outlet valve, representing the depressurization stage of a typical PSA process. All the flow variables and adsorbent layer parameters discussed above are monitored during the entire process. For the parametric study on the channel response to depressurization, the feed pressure is 150 kPa and vacuum pressure is 2.5 kPa, unless stated otherwise. Additionally, the maximum grid Peclet number for the baseline case using this grid size is 0.28, which is well below the value of two required for computational stability of the stage model. The depressurization stage model is simulated with a second-order central-differencing scheme, with an implicit time step calculation in-built in gRPOMS ModelBuilder26.

20


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Table 6: Governing equations and their boundary and initial conditions Description Microchannel - Total Mass Balance

Microchannel - Species balance

Equations

C − C w ,i ∂ρ ∂ ( ρ u ) + = − ∑ g ,i ∂t ∂z i Acs ⋅ R e q , Mass BCs

ρ

Microchannel Momentum balance

Microchannel - Energy Balance

∂yg ,i

BCs

Monolith wall – Energy balance

∂z

− y g ,i ∑ i

Cg ,i − Cw,i Acs ⋅ R e q ,Mass

= DA

∂ ⎛ ∂Cg ,i ⎜ ∂z ⎝ ∂z

⎞ Cg ,i − Cw,i ⎟ + ⎠ Acs ⋅ R e q ,Mass

∂ ( ρ yi ) ∂ ( ρ yi ) = = 0 , IC yi , g = yi , feed ∂z z =0 ∂z z = L

P z =0 = Pv1,out , P z = L = Pv 2,in ,

; IC P = Pfeed − ( Pfeed − Pvacuum )

z L

∂ (U g ) ∂ (u ⋅ hg ) ∂ ⎛ ∂Tg ⎞ Tg − Tw + = ⎜ k g ⎟ − ∂t ∂z ∂z ⎝ ∂z ⎠ Acs ⋅ R e q, Heat ∂ ( hg ) ∂z

= z =0

∂ ( hg ) ∂z

= 0 , IC Tg = T0 z=L

∂Cw,i ⎞ Cg ,i − Cw,i ω ∂C A,i ∂ ⎛ = ⎜ Deff ⎟ + ∂t ε ∂t ∂z ⎝ ∂z ⎠ Aads ⋅ R e q , Mass ∂Cw,i ∂Cw,i BCs Deff = Deff = 0 , IC yi , w = yi , feed ∂z z =0 ∂z z = L Tg − Tw ∂C ∂Tw ∂ 2Tw T −T ρ mC p ,m = km 2 + + ∑ ω ⋅ hads ,i A,i − w FS ∂t ∂z Aads ⋅ R e q ,heat ∂t Aads ⋅ R e q , FS i ∂T ∂T BCs km w = km w = 0 , IC Tw = T0 ∂z z =0 ∂z z = L ∂TFS ∂ 2TFS T −T ρ FS C p , FS = k FS + w FS 2 ∂t ∂z AFS ⋅ R e q , FS ∂T ∂T BCs kFS FS = kFS FS = 0 , IC TFS = T0 ∂z z =0 ∂z z = L ∂Cw,i

Adsorbent layer – Energy balance

∂yg ,i

ΔP 2 Dh L ρf

C − C w ,i ∂u ∂u ∂P ∂ 2u ρu 2 + ρu − ∑ g ,i u=− +µ 2 − f ∂t ∂z ∂z ∂z 2 Dh i Acs ⋅ R e q , Mass

BCs

Adsorbent layer – Species balance

+ ρu

∂t

BCs

ρ

∂ ( ρu ) ∂ ( ρu ) = = 0 , IC u = ∂z z =0 ∂z z = L

+

21



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3. RESULTS AND DISCUSSION The pressure and adsorbent capacity response in a microchannel is first studied before the feasibility of the microchannel in an actual PSA depressurization is analyzed. Figure 6 shows the competitive adsorption isotherms for CO2 in an equi-molar mixture of CH4-CO2 for zeolite 5A, and in an equi-molar mixture of N2-CO2 for activated carbon and zeolite 13X at 25°C.

Figure 6: CO2 equilibrium concentration for an equi-molar mixture of CH4-CO2 for zeolite 5A and that of N2-CO2 for activated carbon and zeolite 13X at 25°C It can be seen that zeolites have greater affinity for CO2 as compared to activated carbon at the lower pressure range. It can also be seen that the slope of these curves for the zeolites change significantly only below 100 kPa at a constant temperature. There is a negligible change in zeolite adsorption capacity as the pressure exceeds atmospheric pressure. Hence, a PSA process design using zeolites with a very high feed pressure and atmospheric pressure as low-side pressure would not yield a desirable operating adsorbent capacity. However, the adsorption capacity of activated carbon, despite starting at a low value at low pressures, continues to rise across the entire pressure range under consideration. The CO2 selectivity for activated carbon, which is described by the slope of the equilibrium curve as pressure tends to 0 kPa, is smaller than that of the zeolites at a comparable adsorbent capacity. Hence, until the capacity curve 22


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saturates at very high pressures, PSA processes using activated carbon can benefit from large pressure changes for their operation10. For the present work, a parametric study on these adsorbents is conducted with a feed pressure of 150 kPa and vacuum pressure of 2.5 kPa on the adsorbent microchannel with the baseline case dimensions. The adsorption time and depressurization time are chosen to be 100 s and 150 s, respectively. A grid independence study is performed on the depressurization stage model to analyze the effect of axial grid density on the prediction of adsorbent capacity. Figure 7 shows the integrated adsorbed CO2 concentration curves on zeolite 5A for four different grid sizes with 50, 100, 200, and 500 calculation points, and simulated for the process conditions described earlier. It can be seen that all the curves are nearly identical, with a calculated maximum difference of 0.03% between the adsorbed concentration values for N = 50 and N=500. Based on these results, to maintain reasonable computational speeds, the analyses in this study are conducted using N = 100.

Figure 7: Grid independence study on adsorbed CO2 concentrations

23



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Figure 8 shows the transient variation of integrated CO2 adsorbed concentration for zeolite 5A, 13X and activated carbon. The integrated CO2 adsorbed concentration for each of the adsorbents reaches a constant value based on the capacities dictated by Figure 6. For zeolite 13X, 5A and activated carbon, these points are noted by A, C, and E, respectively in Figure 8. As the depressurization starts at 100 s, the response of the adsorbents is governed by the reduced equilibrium capacities at the reduced pressures. This process is also governed by the development of the local pressures and temperatures during depressurization. As the feed valve closes, the pressure in the microchannel starts to drop at all locations, but does not rapidly approach the low-side pressure. The local pressure attains a value that allows continuously diminishing flow through the microchannel by overcoming the frictional resistance at the microchannel walls as shown in Figure 9.

Figure 8: Transient variation of integrated CO2 adsorbed concentration for zeolite 5A, 13X and activated carbon for the baseline case

The mass flowrate decreases continuously as a result of falling driving pressure difference and density. The mass flow is sustained by slow desorption of gases from the adsorbent in the later stages of depressurization. For all the three adsorbents considered, the pressure profiles resemble 24


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those in Figure 9 for the entire duration of the depressurization stage for the baseline case. Thus, at the end of depressurization, the integrated CO2 adsorbed concentration drops to B, D and F, for zeolites 13X and 5A and activated carbon, respectively. Thus, the total operating CO2 removal capacities for each of these adsorbents are calculated as the vertical distances between A and B, C and D, and E and F, respectively and are used in process performance calculations in later sections.

Figure 9: Transient pressure variation for the upstream end, axial midpoint and downstream end of the microchannel for the baseline case The temperature decrease during depressurization plays an important role in desorption kinetics. Figure 10 shows a sample temperature variation at the axial midpoint of the microchannel during adsorption and depressurization stages for zeolite 5A, 13X and activated carbon. As pressure falls during depressurization, the temperature starts to drop at all axial locations. Additionally, when loss of partial pressure drives the desorption of adsorbed gases, the temperature drop is accelerated, because the desorption process is endothermic. As shown in Figure 10, the rate of desorption for activated carbon is the highest among the adsorbents considered; therefore, the cumulative temperature drop is the highest for activated carbon. As the stage progresses, the temperature profile at the axial midpoint recovers slowly due to gas flow 25



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from the upstream end. As expected, the rate of desorption at the upstream end is smaller than that at the downstream end, and the drop in temperature at that end is not pronounced. This in turn helps the adsorbent layer to return to the original temperature by convection.

Figure 10: Transient temperature variation at the axial midpoint of the adsorbent layer for zeolite 5A, 13X and activated carbon for the baseline case. More importantly, as the pressure falls, the adsorbent capacity decreases; however, as temperature drops following the pressure drop, the adsorbent capacity increases. This increase in adsorbent capacity stops further desorption from the adsorbent. It is interesting to note that in this kind of PSA process, where substantial temperature change is inherent; pressure swing and temperature swing are working against each other to readjust the adsorbent capacity at each time step. Such an interaction results in a sudden reduction of the slope of the adsorbed CO2 concentration curve in Figure 8 at about 40 s after the start of the depressurization. Further reduction in adsorbed concentration takes place due to the slow reduction of partial pressure of the component gases at a sustained diminishing mass flow out of the microchannel. For the baseline case, as seen in Figure 8, the pressure profile during depressurization evolves based on local friction resistance. Thus, the pressure at the microchannel upstream end does not decrease below 45 kPa, although the intended vacuum pressure, which the microchannel is expected to attain, is 2.5 kPa. This results in underutilization of the adsorbent layer, which is 26


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attributed to frictional pressure drop within the microchannel. Another parametric study is conducted to analyze the effect of varying microchannel diameters on depressurization effectiveness. Figure 11 shows the variation of integrated CO2 adsorbed concentration for Dh of 200 µm, 400 µm and 600 µm for zeolite 5A. As Dh is reduced to 200 µm, transmission of pressure upstream is further affected due to increase in friction at the microchannel walls and the depressurization process is strongly affected. However, as Dh is increased to 600 µm, friction at the walls decreases; thus the change in pressure is more effectively communicated to the upstream end. The upstream end pressure during depressurization, which is 45 kPa for the baseline case, decreases to 25 kPa, providing an additional pressure swing in the upstream region. It should be noted that for zeolites, a pressure swing of 20 kPa at sub-atmospheric pressures is substantial for enhancing the operating adsorbent capacity. The cumulative effect of reduced frictional pressure drop and increased mass flux at the outlet end can be seen in Figure 11, where the operating CO2 removal capacity increases by nearly 50% from the baseline value, as Dh is increased from 400 µm to 600 µm.

Figure 11: Transient variation of integrated CO2 adsorbed concentrations for zeolite 5A for different diameters.

27



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The depressurization model is also used for a parametric study on gas removal capacity under variable process conditions. The CO2 removal capacities, illustrated earlier as the difference between the adsorbed CO2 concentration at the start of depressurization and at the end of that stage achievable by using the adsorbent coated microchannels are compared with those of the PSA processes documented in the literature using the same adsorbent, depressurization stage time, feed mixture composition, feed pressure and vacuum pressure. Kapoor and Yang13 conducted experimental and computational analyses of kinetic separation of CH4-CO2 MSC adsorbent as well as an equilibrium based separation process using zeolite 5A. Due to very small size of the adsorbent assumed in the current work, the delay in intra-crystalline diffusion is small and hence, the process is representative of equilibrium based separation rather than a kinetic separation. The depressurization model in the present work is simulated for the process conditions shown in Table 7 (a) to (c) and the normalized CO2 removal capacities for Dh of 200 µm, 400 µm and 600 µm are compared with the corresponding feed throughputs reported by Kapoor and Yang. As the full VPSA process is not modeled in the present work, the purity and recovery factors cannot be used directly for a comprehensive comparison. Nevertheless, the CO2 removal capacity in the present work is a conservative process capacity estimate as compared to the feed capacity throughput. This is because the CO2 removed during depressurization must be added with the purified product collected during adsorption to calculate the total feed throughput. Hence the CO2 removal capacity shown in Table 7 is always smaller than the corresponding feed throughput.

28


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Table 7 (a): Comparison of depressurization capacities from the present study with equilibrium PSA process results of Kapoor and Yang13 using zeolite 5A (Feed pressure – 304 kPa, vacuum pressure – 34 kPa, feed composition 50/50 CH4/CO2, blowdown time 120 s)

Microchannel hydraulic diameter, Dh [µm]

Operating CO2 removal capacity [mol m-3]

Capacity Present work [LSTP-1 kg-1 cycle-1]

200

150

7.04

400

475

22.3

600

723

33.9

Cyclic capacity Kapoor and Yang [LSTP-1 kg1 cycle-1]

16.6

From Table 7(a) to (c), it can be seen that the CO2 removal capacity for zeolite 5A increases with an increase in Dh, analogous to the result shown in Figure 11. As the feed pressure is increased from 304 kPa to 464 kPa as shown in Table 7(b), the CO2 removal capacity slightly decreases for all diameters. The total CO2 swing capacity would have increased marginally with increase in feed pressure at a constant temperature as shown in Figure 6. However, the effect of the temperature drop on equilibrium concentration during depressurization is greater than the case with 304 kPa, which results in a very minor decrease in CO2 removal capacity. This result can be explained based on the counteracting effects of pressure and temperature swing described in the previous section. A decrease in vacuum pressure, however, has a significant effect on the CO2 removal capacity as a result of greater slope of CO2 adsorption isotherms at sub-atmospheric pressures. For the 600 µm microchannel, there is 97% increase in the CO2 removal capacity with decrease in vacuum pressure from 34 kPa to 1 kPa.

29



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Page 30 of 51

Table 7 (b): Comparison of depressurization capacities from the present study with equilibrium PSA process results of Kapoor and Yang13 using zeolite 5A (Feed pressure – 464 kPa, vacuum pressure – 34 kPa, feed composition 50/50 CH4/CO2, blowdown time 120 s) Microchannel hydraulic diameter, Dh [µm]



200

131

6.15

400

466

21.9

600

710

33.3

Cyclic capacity Kapoor and Yang [LSTP-1 kg1 cycle-1] 16.16

Additionally, except for the case with hydraulic diameter of 200 µm, the CO2 removal capacities for all the other cases shown in Table 7(a) to (c) are higher than those of Kapoor and Yang13 for similar process conditions. With Dh of 600 µm, the CO2 removal capacity is nearly twice the feed throughput documented by Kapoor and Yang13 for the first two cases shown in Table 7(a) and 7(b), and nearly four times as the vacuum pressure is decreased to 1 kPa. Table 7 (c): Comparison of depressurization capacities from the present study with equilibrium PSA process results of Kapoor and Yang13 using zeolite 5A (Feed pressure – 304 kPa, vacuum pressure – 1 kPa, feed composition 50/50 CH4/CO2, blowdown time 120 s) Microchannel Operating hydraulic CO2 diameter, Dh removal capacity [µm] [mol m-3]


400

787

36.0

600

1405

65.9

Cyclic capacity Kapoor and Yang [LSTP-1 kg1 cycle-1]

30


17.33

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Unlike the case with Kapoor and Yang13, the CO2 removal capacities from the present work can directly be compared with the productivity results reported by Shen et al.20 because they report CO2 captured during depressurization. The depressurization stage model developed in the present work is modified and used for their process conditions and a comparative assessment is shown in Table 8(a) to (c). Unlike zeolites, activated carbon has a nearly constant slope of the adsorption isotherm in the pressure range considered here, as shown in Figure 6; therefore, a steady increase in the feed pressure yields a corresponding increase in CO2 removal capacity. This trend is clearly observed in Tables 8(a) to (c). As an example, the capacity increases steadily by around 40% for a Dh of 600 µm when the feed pressure is increased from 131 kPa to 202 kPa and then from 202 kPa to 324 kPa. Table 8 (a): Comparison of depressurization capacities from the present study with PSA process results of Shen et al.20 using activated carbon (Feed pressure – 131 kPa, vacuum pressure – 10 kPa, feed composition 85/15 N2/CO2, blowdown time 135 s) Microchannel hydraulic diameter, Dh [µm]


Capacity Present work [mol kg-1 cycle-1]

200

100

0.14

400

636

0.94

600

881

1.31

Cyclic capacity Shen et al. [mol kg-1 cycle-1] 0.23

When compared with the results of Shen et al.20, the depressurization process in the present work captures 5.6, 3.9 and 4.9 times more moles of CO2 for a Dh of 600 µm. These results are based on the productivity in a single cycle; however, as a complete PSA cycle is not modeled here, comparison on a time basis cannot be made directly. Nevertheless, due to convection based faster dynamics, the feed and pressurization stages in the present work are not expected to be as 31



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long as the stage times listed by Shen et al.20 and the advantage in process performance of the present work is expected to be further amplified. Table 8 (b): Comparison of depressurization capacities from the present study with PSA process results of Shen et al.20 using activated carbon (Feed pressure – 202 kPa, vacuum pressure – 10 kPa, feed composition 85/15 N2/CO2, blowdown time 190 s) Microchannel hydraulic diameter, Dh [µm]



200

318

0.47

400 600

963 1229

1.43 1.83


In a similar fashion, the depressurization stage model is simulated for the process conditions utilized by Krishnamurthy et al.12 and a comparison is presented in Table 9. They used zeolite 13X for a binary mixture of N2-CO2, similar to the PSA studies of Shen et al.20 Apart from the expected trend of increase in CO2 removal capacity with microchannel size, the process performance in terms of CO2 removal from the present work exceeds that by Krishnamurthy et al.12 for all microchannel sizes considered with a 25 times CO2 removal capacity for the 600 µm microchannel size. It must be noted that the depressurization stage model is not simulated for the additional 310 s evacuation time that Krishnamurthy et al.12 considered for further removal of component gases from the system.

32


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Table 8 (c): Comparison of depressurization capacities from the present study with PSA process results of Shen et al.20 using activated carbon (Feed pressure – 324 kPa, vacuum pressure – 10 kPa, feed composition 85/15 N2/CO2, blowdown time 240 s) Microchannel hydraulic diameter, Dh [µm]



200

550

0.82

400

1377

2.05

600

1736

2.58


Thus, depressurization is proven to be effective, if the traditional adsorbent bed-based design is replaced by a microchannel monolith. Additionally, the favorable process performance prediction with microchannel mass exchangers during depressurization seen here warrants a comprehensive PSA process investigation in the future. Table 9: Comparison of depressurization capacities from the present study with PSA process results of Krishnamurthy et al.12 using zeolite 13X (Feed pressure – 150 kPa, vacuum pressure – 2.5 kPa, feed composition 85/15 N2/CO2, blowdown time 150 s Microchannel hydraulic diameter, Dh [µm]


Capacity Present work [kg m-3 cycle-1]

200

128

17.6

400

1026

141

600

1601

220

Cyclic capacity Shen et al. [kg m-3 cycle-1] 8.75

4. CONCLUSIONS The feasibility of using adsorbent-coated microchannels for a pressure swing adsorption process for CO2 removal is investigated by analyzing the effectiveness of depressurization. The pressure, temperature and adsorbent capacity responses for zeolite 5A, 13X and activated carbon 33



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are analyzed to understand critical factors affecting depressurization. The stage performance is compared with bed-based PSA process predictions from the literature to assess viability. It is found that PSA process designs using adsorbent beds as well as adsorbent-coated microchannels are greatly influenced by not only the range of pressure extremes, but also the independent feed and vacuum pressure values. Activated carbon is observed to show near constant operating capacity at all low as well as high pressures; however, for quick adsorbing zeolite adsorbents, very low pressures are required to effectively manipulate the thermodynamic conditions of the adsorbent. Quick depressurization in microchannels causes a pressure and temperature drop, with temperature and pressure changes affecting the process in opposite directions. For a depressurization applied to adsorbent-coated microchannels, frictional pressure drop plays an important role in deciding the adsorbent layer effectiveness and should be minimized by increasing the microchannel diameter. The depressurization in microchannels is found very effective when the stage performance is compared with the bed-based depressurization processes in the literature. Up to four times greater CO2 separation or removal capacities are obtained compared with CH4-CO2 separation studies by Kapoor and Yang13 using zeolite 5A. A similar performance is observed when microchannel depressurization is applied to N2-CO2 separation studied by Shen et al. using activated carbon. A performance comparison with the PSA process by Krishnamurthy et al.12 yields the highest gains from the approach used in the present study: up to 25 times CO2 can be removed with similar process conditions by using adsorbent-coated microchannels. These positive results for depressurization stage suggest the need for a further investigation of a full PSA process so that purity, recovery and energy efficiencies of the overall process can be 34


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assessed. It does appear, however, that the adsorbent-coated microchannels studied here are very effective in removing CO2 in natural gas purification as well as CCS applications compared to conventional bed-based designs. 5. AUTHOR CONTACT INFORMATION *Corresponding author Email: [email protected] Phone: 404-894-7479 6. ABBERVIATIONS Symbols A

Area [m2]

Å

angstrom [10-10 m]

A1.. DSL coefficients [mol kg-1 or mol kg-1 K] 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-1]

Cv

Valve flow coefficient [kg s-1 kPa-1]

d

Molecular size [Ǻ]

d,D DSL coefficients 35



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DA

Axial dispersion coefficient [m2 s-1]

DAB Binary diffusion coefficient [m2 s-1] Dcryst Intra-crystalline diffusion coefficient [m2 s-1] Deff Effective diffusion coefficient [m2 s-1] Dh Diameter [m] DH Heat of adsorption [J mol-1] E

Activation energy [J mol-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]

K1.. Sips equation constants KB

Boltzmann constant [J K-1]

KLDF Linear driving force constant [s-1] L

Length [m]

ṁ

Mass flowrate [kg s-1]

MF Adsorbent loading [kg kg-polymer-1] MW Molecular weight [kg kmole-1] n

Sips equation parameter [-]

N

Number of nodes [-] 36


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Nu Nusselt number [-] P

Pressure [Pa or bar]

Peri Channel perimeter [m] Pr

Prandtl number [-]

QB/D Heat of adsorption in DSL equation [J mol] r

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]

Sc

Schmidt number [-]

Sh

Sherwood number [-]

t

Time [s]

th

Adsorbent layer thickness [m]

T

Temperature [K]

u

Channel velocity [m s-1]

Vp

Valve position

y

Mass fraction [-]

z

Axial position [m]

Greek α

Void fraction [-]

Δ

Change or discrete step [-]

ε

Adsorbent matrix void fraction [m3 m-3]

λ

Mean free path [m] 37



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µ

Viscosity [kg m-1 s-1]

ρ

Density [kg m-3]

τ

Tortuosity factor [-]

ω

Adsorbent volume fraction [m3 m-3]

Ω

Collision integral [-]

Superscripts and Subscripts A

Axial dispersion

ads Adsorbent layer cs

Cross-sectional

Eq

Equivalent

FS

Fused silica

g

Microchannel

G

Gas phase

h

Hydraulic

Heat Related to heat transfer i

Assigned species

l

laminar

Mass Related to mass transfer m

Adsorbent-polymer matrix

mid Midpoint out Outlet v

Valve 38


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w

Adsorbent layer or wall

7. REFERENCES 1. Abatzoglou, N.; Boivin, S., A Review of Biogas Purification Processes. Biofuel. Bioprod. Bior. 2009, 3, 42-71. 2. Bernardo, P.; Drioli, E.; Golemme, G., Membrane Gas Separation: A Review/State of the Art. Ind. Eng. Chem. Res. 2009, 48, 4638-4663. 3. Baker, R. W., Future Directions of Membrane Gas Separation Technology. IInd. Eng. Chem. Res. 2002, 1393-1411. 4. Aaron, D.; Tsouris, C., Separation of CO2 from Flue Gas: A Review. Sep. Sci. Technol. 2005, 40, 321-348. 5. Meisen, A.; Shuai, X., Research and development issues in CO2 capture. Energ. Convers. Manage. 1997, 38, Supplement, S37-S42. 6. Moore, B. K. Gas-Liquid Flows in Adsorbent Microchannels. Georgia Institute of Technology Atlanta, 2012. 7. Yang, H.; Xu, Z.; Fan, M.; Gupta, R.; Slimane, R. B.; Bland, A. E.; Wright, I., Progress in carbon dioxide separation and capture: A review. J.Environ. Sci. 2008, 20, 14-27. 8. Riemer, P. W. F.; Webster, I. C.; Ormerod, W. G.; Audus, H., Results and full fuel cycle study plans from the IEA greenhouse gas research and development programme. Fuel 1994, 73, 1151-1158. 9. Göttlicher, G.; Pruschek, R., Comparison of CO2 removal systems for fossil-fuelled power plant processes. Energ. Convers. Manage. 1997, 38, Supplement, S173-S178. 10. Cen, P.-L.; Chen, W.-N.; Yang, R. T., Ternary Gas Mixture Separation by Pressure Swing Adsorption: A Combined Hydrogen-Methane Separation and Acid Gas Removal Process. Ind. Eng. Chem. Proc. Dd. 1985, 1201-1208. 11. Liang, Z.; Marshall, M.; Chaffee, A. L., Comparison of Cu-BTC and zeolite 13X for adsorbent based CO2 separation. Energ. Proc. 2009, 1, 1265-1271. 12. 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, 1830-1842. 13. Kapoor, A.; Yang, R. T., Kinetic separation of methane—carbon dioxide mixture by adsorption on molecular sieve carbon. Chem. Eng. Sci. 1989, 44, 1723-1733. 14. Lee, S. C., Prediction of permeation behavior of CO2 and CH4 through silicalite-1 membranes in single-component or binary mixture systems using occupancy-dependent Maxwell–Stefan diffusivities. J. Membrane Sci. 2007, 306, 267-276. 15. Delgado, J. A.; Uguina, M. A.; Sotelo, J. L.; Águeda, V. I.; García, A.; Roldán, A., Separation of ethanol–water liquid mixtures by adsorption on silicalite. Chem. Eng. J. 2012, 180, 137-144. 16. Morishige, K., Adsorption and Separation of CO2/CH4 on Amorphous Silica Molecular Sieve. J. Phys. Chem. C. 2011, 115, 9713-9718. 17. Palomino, M.; Corma, A.; Rey, F.; Valencia, S., New Insights on CO2−Methane Separation Using LTA Zeolites with Different Si/Al Ratios and a First Comparison with MOFs. Langmuir 2009, 26, 1910-1917. 39



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18. Delgado, J. A.; Uguina, M. A.; Sotelo, J. L.; Ruíz, B.; Rosário, M., Carbon Dioxide/Methane Separation by Adsorption on Sepiolite. J. Nat. Gas Chem. 2007, 16, 235-243. 19. Shao, X.; Feng, Z.; Xue, R.; Ma, C.; Wang, W.; Peng, X.; Cao, D., Adsorption of CO2, CH4, CO2/N2 and CO2/CH4 in novel activated carbon beads: Preparation, measurements and simulation. AIChE J. 2011, 57, 3042-3051. 20. Shen, C.; Yu, J.; Li, P.; Grande, C.; Rodrigues, A., Capture of CO2 from flue gas by vacuum pressure swing adsorption using activated carbon beads. Adsorption 2011, 17, 179-188. 21. Chowdhury, P.; Mekala, S.; Dreisbach, F.; Gumma, S., Adsorption of CO, CO2 and CH4 on Cu-BTC and MIL-101 metal organic frameworks: Effect of open metal sites and adsorbate polarity. Micropor. Mesopor. Mat. 2012, 152, 246-252. 22. Herm, Z. R.; Krishna, R.; Long, J. R., Reprint of: CO2/CH4, CH4/H2 and CO2/CH4/H2 separations at high pressures using Mg2(dobdc). Micropor. Mesopor. Mat. 2012, 157, 94-100. 23. Xiang, Z.; Peng, X.; Cheng, X.; Li, X.; Cao, D., CNT@Cu3(BTC)2 and Metal–Organic Frameworks for Separation of CO2/CH4 Mixture. J. Phys. Chem. C. 2011, 115, 19864-19871. 24. 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, 474-482. 25. 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, 7314-7324. 26. Process Systems Enterprise, I., gPROMS, www.psenterprise.com/gproms. In 1997-2015. 27. Mark, J. E., Polymer Data Handbook. In Oxford University Press Inc. : 1999. 28. Churchill, S. W., Comprehensive Correlating Equations for Heat, Mass and Momentum Transfer in Fully Developed Flow in Smooth Tubes. Ind. Eng. Chem. Fund. 1977, 16, 109-116. 29. Churchill, S. W., Friction-Factor Equations Spans All Fluid Flow Regimes. Chem. Eng.New York 1977, 84, 2. 30. Cussler, E. L., Chapter 2 - BINARY DIFFUSION. In Multicomponent Diffusion, Cussler, E. L., Ed. Elsevier: 1976; pp 5-27. 31. Hines, A.; Maddox, R., Mass Transfer Fundamentals and Applications. Prentice-Hall: Upper Saddle River, NJ, USA, 1985. 32. 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. 2009, 49, 838-846. 33. Gholami, M.; Talaie, M. R.; Roodpeyma, S., Mathematical modeling of gas dehydration using adsorption process. Chem. Eng. Sci. 2010, 65, 5942-5949. 34. Park, Y.; Moon, D.-K.; Kim, Y.-H.; Ahn, H.; Lee, C.-H., Adsorption isotherms of CO2, CO, N2, CH4, Ar and H2 on activated carbon and zeolite LiX up to 1.0 MPa. Adsorption 2014, 20, 631-647. 35. Determan, M. D.; Hoysall, D. C.; Garimella, S., Heat- and Mass-Transfer Kinetics of Carbon Dioxide Capture Using Sorbent-Loaded Hollow Fibers. Ind. Eng. Chem. Res. 2011, 51, 495-502.

40


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Figure 1: Basic stages of a pressure swing adsorption process cycle 347x230mm (96 x 96 DPI)



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Figure 2: Schematic of the microchannel monolith showing characteristic dimensions for the baseline case. 271x289mm (96 x 96 DPI)


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Figure 3: Schematic of the microchannel cross section considered for FD/HT/MT modeling 711x327mm (96 x 96 DPI)



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Figure 4: Idealized schematic of the microchannel cross section 303x144mm (96 x 96 DPI)


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Figure 5: gPROMS ModelBuilder architecture schematic showing the flow components used and their interconnections27 265x138mm (96 x 96 DPI)



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Figure 6: CO2 equilibrium concentration for an equi-molar mixture of CH4-CO2 for zeolite 5A and that of N2CO2 for activated carbon and zeolite 13X at 25°C 252x160mm (96 x 96 DPI)


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Figure 7: Grid independence study on adsorbed CO2 concentrations 252x160mm (96 x 96 DPI)



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Figure 8: Transient variation of integrated CO2 adsorbed concentration for zeolite 5A, 13X and activated carbon for the baseline case 252x160mm (96 x 96 DPI)


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Figure 9: Transient pressure variation for the upstream end, axial midpoint and downstream end of the microchannel for the baseline case 252x160mm (96 x 96 DPI)



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Figure 10: Transient temperature variation at the axial midpoint of the adsorbent layer for zeolite 5A, 13X and activated carbon for the baseline case. 252x154mm (96 x 96 DPI)


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Figure 11: Transient variation of integrated CO2 adsorbed concentrations for zeolite 5A for different diameters. 252x154mm (96 x 96 DPI)


Feasibility of Using Adsorbent-Coated Microchannels for Pressure

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