Development of a Pressure Swing Adsorption Cycle for Producing

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

pubs.acs.org/IECR

Development of a Pressure Swing Adsorption Cycle for Producing High Purity CO2 from Dilute Feed Streams. Part I: Feasibility Study Hanife Erden, Armin D. Ebner, and James A. Ritter* Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208, United States S Supporting Information *

ABSTRACT: Simulations of a 3-bed 9-step pressure swing adsorption (PSA) cycle were carried out to study the enrichment and recovery of 0.4 vol % CO2 from dry air using 13X zeolite with the feed pressure and flow rate fixed at 1 atm and 570 SLPM. The goal was to produce 97 vol % CO2 at greater than 62% CO2 recovery, less than 1 kW vacuum pump power, and small volume. The PSA cycle step sequence consisted of feed (F), idle (I), heavy reflux (HR), cocurrent equalization down (EqD), forced cocurrent depressurization (CoD), countercurrent depressurization (CnD), light reflux (LR), countercurrent equalization up (EqU), and light product pressurization (LPP). A parametric study revealed the following effects on the PSA process performance. Increases in the HR = LR = F step time (thus cycle time) caused significant increases in the CO2 purity and vacuum pump power, while the CO2 recovery exhibited a modest maximum. Increases in the LR ratio caused significant increases in both the CO2 recovery and power but only a modest increase in the CO2 purity. Increases in the CnD end pressure caused only slight changes in all three parameters, with the CO2 purity increasing and CO2 recovery and power decreasing. Increases in the LR pressure caused significant decreases in both the CO2 recovery and power, with only a slight decrease in CO2 purity. Increases in the CoD end pressure caused a significant decrease in the CO2 purity, a modest increase in the CO2 recovery, and only a slight decrease in power. The best PSA process performance produced a CO2 purity of 96.3 vol % at a CO2 recovery of 87.8% and a feed throughput of 1264 L(STP)/h/kg, while consuming 572 W. This new PSA cycle was very effective at concentrating CO2 (over 242 times) because of a forced CoD step and a very long HR = LR step time relative to the other cycle steps, where the source of the HR was exclusively from the LR step. The LR step dominated the power requirement, so much that the power required by the CnD step and especially the forced CoD step were both insignificant in comparison.

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system.8 Two of the beds remove H2O vapor via TSA using silica gel and 13X zeolite in a layered bed, while the other two beds remove CO2 via TSA/PSA using 5A zeolite. Because of dusting issues with the 5A zeolite, possibly caused by the TSA cycle, there was an incentive to investigate just PSA for the purpose of removing metabolic CO2 from dry spacecraft cabin air. Therefore, the objective of this feasibility study was to develop a PSA cycle that could be used for enriching and recovering metabolic CO2 from spacecraft cabin air. The goal was to enrich a dilute feed stream containing 0.4 vol % CO2 in dry air to around 97 vol % at high recovery, low vacuum pump power, and small volume. Four, 3-bed PSA cycle schedules were devised with 13X zeolite and systematically studied via simulation using the dynamic adsorption process simulator (DAPS). The most complex one, i.e., a 3-bed 9-step PSA cycle schedule, was the only one that provided the required separation and met the constraints. A parametric study was carried out with this unique PSA cycle schedule using DAPS. The results are reported here.

INTRODUCTION Carbon dioxide (CO2) is produced by any type of combustion process and is the product of many chemical processes.1,2 More recently, the CO2 released from these industrial processes and also transportation and especially the electric power industry has been widely accepted as being the cause of climate change. This has kept the gas separations community busy, with the largest effort perhaps being associated with the removal of CO2 from the flue gas of coal fired power plants. Adsorption technology, especially pressure swing adsorption (PSA) processes, has been proposed and studied extensively for this purpose.1,3−5 The gas separations community has also been investigating the capture and concentration of CO2 from air, mainly but not exclusively by adsorption technology.6 A similar effort to capturing CO2 from air has, in fact, been underway since the launch of human space flight. With the average adult human producing about 1 kg/day of metabolic CO2,7 it easily builds up to unsafe levels in small, completely closed spaces, like spacecraft cabins. As a result, a considerable effort has been put forth by NASA to remove metabolic CO2 from spacecraft cabin air using adsorption technology.8 The current system being tested on the international space station (ISS) for long-term space travel is a 4-bed temperature swing adsorption/pressure swing adsorption (TSA/PSA) © XXXX American Chemical Society

Received: December 5, 2017 Revised: May 16, 2018 Accepted: May 17, 2018

A

DOI: 10.1021/acs.iecr.7b05024 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Four alternative 3-bed PSA cycle schedules devised for concentrating dilute CO2 from spacecraft cabin air, with their complexity systematically increasing from (a) to (d). The corresponding cycle step sequences are (a) 3-bed 5-step: F-HR-I-CnD-LPP; (b) 3-bed 5-step: F-HR-CnD-LR-LPP, (c) 3-bed 7-step: F-HR-EqD-CnD-LR-EqU-LPP, and (d) 3-bed 9-step: F-I-HR-EqD-CoD-CnD-LR-EqU-LPP. F: feed; I: idle; HR: heavy reflux; EqD: equalization down; CoD: cocurrent depressurization; CnD: countercurrent depressurization; LR: light reflux; EqU: equalization up; LPP: light product pressurization.

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PSA CYCLE DESCRIPTIONS This feasibility study was being done to show whether a PSA process could replace the TSA/PSA process on the international space station (ISS). Thus, there were many constraints that had to be met. The CO2 in the feed was fixed at 4000 ppm (0.4 vol %), i.e., the steady-state level allowed on the ISS. The CO2 purity had to be around 97 vol % CO2, while the CO2 recovery had to be high enough to remove the metabolic CO2 produced by four astronauts, which is about 1.0 kg/person/day. The feed flow rate was also fixed at 570 SLPM because of the upstream TSA process that removed H2O vapor prior to CO2 removal. On the basis of this feed flow rate, CO2 feed concentration, and CO2 removal rate, the CO2 recovery had to be >62.0%. Finally, a minimum number of beds had to be used to minimize the volume occupied by the PSA unit, while ensuring a continuous feed PSA cycle that consumed less than about 1 kW of power. The following thought processes and systematic procedure were utilized to develop a PSA cycle that could concentrate a dilute CO2 stream to nearly pure CO2. It was clear at the outset that a HR step had to be included in this continuous feed PSA cycle schedule to enrich such a dilute feed stream. Since it is not possible to construct a continuous feed PSA cycle schedule with a HR step using only two beds, a 3-bed PSA cycle schedule was necessarily required. In a preliminary study, four continuous feed 3-bed PSA cycle schedules were devised with a HR step and evaluated with DAPS. These schedules are shown in Figure 1. The 3-bed 5-step PSA cycle schedule in Figure 1a was too restrictive because the source of the HR gas and the CO2 enriched HP both had to come from the countercurrent depressurization (CnD) step. This severely limited the enriching capability of the cycle. To relax this limitation, a light reflux (LR) step was added to this schedule to provide an alternative source of the HR gas, namely, from the LR step. This 3-bed 5-step PSA cycle schedule shown in Figure 1b also allowed the HP to be produced from the CnD and/or LR step. The enrichment obtained from this PSA cycle was better but not good enough. A bed-to-bed equalization step was added to this schedule to cocurrently flush the air from the void space in the bed and fill it with desorbed CO2 gas before any countercurrent

step took place. This 3-bed 7-step PSA cycle schedule shown in Figure 1c improved the enrichment considerably, but it was still not good enough to satisfy the purity constraint on the CO2 in the HP. Since adding another equalization step would necessarily require adding an additional bed,9 making it an undesirable 4-bed PSA process, a forced cocurrent depressurization (CoD) step assisted with a vacuum pump was added instead. This 3-bed 9-step PSA cycle schedule shown in Figure 1d proved to be the only one of the four that was capable of enriching 0.4 vol % CO2 to nearly 97 vol %. Hence, it is described in detail below, with results only from this cycle reported on later. The same 3-bed 9-step PSA cycle schedule is shown again in Figure 2, along with the corresponding PSA cycle step sequence interbed connection diagram and the first unit block of it with the cycle step times indicated. The cycle step sequence consisted of feed (F), idle (I), heavy reflux (HR), cocurrent equalization down (EqD), forced cocurrent depressurization (CoD), countercurrent depressurization (CnD), light reflux (LR), countercurrent equalization up (EqU), and light product pressurization (LPP). The cycle step times for the I, EqD, CoD, CnD, EqU, and LPP steps were always fixed at the values shown, whereas the HR, LR, and F step times varied according to the value of x, as explained and discussed later. The cycle step sequence interbed connection diagram is used to explain each cycle step. The PSA cycle step sequence begins with the F step, where a bed is fed with 0.4 vol % CO2 in dry air at atmospheric pressure PH. During this step, a light product (LP) is produced from the light end of the bed containing much less CO2 than in the feed stream. The next step is the I step, where a bed has both of its ends closed, thereby remaining at PH and thus not performing any gas separation function; nevertheless, an I step is necessary to maintain alignment of coupled steps in the cycle schedule, e.g., the HR and LR steps in this case. The HR step follows the I step, where a bed receives gas in its heavy end at PH from a bed undergoing the LR step at PLR via a vacuum pump. The gas leaving the light end of the bed is taken as LP, and it may contain some CO2. The EqD step is the next step, where a bed equalizes in pressure to PEq with a bed undergoing the EqU step through their light ends. A unique forced CoD step follows the EqD step. This step is unique because it utilizes a vacuum B


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Figure 2. (a) Complete 3-bed 9-step PSA cycle schedule selected for further study, (b) corresponding cycle step sequence and interbed connection diagram, and (c) corresponding first unit block of the 3-bed 9-step PSA cycle schedule in (a) showing step times (ts) and x = 0, 250, 500, or 750. F: feed; I: idle; HR: heavy reflux; EqD: equalization down; CoD: cocurrent depressurization; CnD: countercurrent depressurization; LR: light reflux; EqU: equalization up; LPP: light product pressurization.

equal to that in the interparticle void spaces (εb); axial pressure drop along the column is described by the Ergun equation, and the mass transfer between the gas and solid phases is described by a modified linear driving force (LDF) approximation for macropore limited diffusion. For an N-component system, the overall and component mole balances over a differential volume element, respectively, yield

pump to decrease the pressure of a bed to an intermediate pressure PCoD by removing gas from its light end with its heavy end closed. The gas leaving the light end of the bed is also taken as LP and again may contain some CO2. The CnD step follows the CoD step, where a vacuum pump is again utilized to decrease the pressure of a bed to PL through its heavy end with its light end closed. The gas leaving the heavy end of the bed is taken as heavy product (HP). This is the only step that produces HP and is thus the step that produces the enriched CO2 stream. The LR step follows the CnD step and continues to remove gas from its heavy end via the vacuum pump while receiving gas as LR in its light end from the bed undergoing the F step. The gas leaving the heavy end of the bed is provided to the bed undergoing the HR step as HR. During this step, the bed undergoing the LR step may increase slightly in pressure to PLR due to the LR gas entering the light end of the bed. The EqU step is next, where a bed equalizes in pressure to PEq with the bed undergoing the EqD step through their light ends. The final step is the LPP step, where a bed is pressurized back to PH by receiving gas in its light end from a bed undergoing the F step with its heavy end closed. With the F step following LPP, this PSA cycle step sequence repeats indefinitely. Mathematical Model. The performance of the 3-bed 9-step PSA cycle schedule shown in Figure 2 was evaluated via simulation using DAPS.10 DAPS is written in FORTRAN and uses finite differences along with the time adaptive DAE solver called DASPK.11 The following assumptions are imposed in DAPS: ideal gas, 1-D plug flow (i.e., no radial concentration or thermal gradients), no heat transfer resistance between the gas and solid phases, no column wall thermal capacitance, no axial dispersion, and no axial thermal conduction. In addition, the gas phase concentration in the intraparticle void spaces (εP) is

⎛ 1 ∂P ∂vC T 1 ∂T ⎞⎟ (εb + (1 − εb)εP)C T⎜ − + εb + ⎝ P ∂t T ∂t ⎠ ∂z

N

∑ Sj = 0 j=1

(1)

(εb + (1 − εb)εP)C T

∂yi ∂t

+ εbC Tv

∂yi ∂z

N

− yi ∑ Sj + Si = 0 j=1

(2a)

i = 1to N − 1 N

∑

yi +

yj = 1.0

j = 1, j ≠ i

i=N (2b)

where

CT =

P RT

Si = (1 − εb)ρp

(3)

∂qi ∂t

(4)

εp and ρp are the pellet porosity and density, εb is the bed porosity, v is the interstitial velocity, yi is the mole fraction of component i in the gas phase, T is the temperature of both the C


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heat of adsorption of component i, hw is the heat transfer coefficient at the inside wall of the column, and rb,i is the internal radius of the column. The axial pressure drop along the column is evaluated via the Ergun equation according to

gas and solid phases, P is the pressure, and qi is adsorbed phase loading of component i. The mass transfer rate of component i between the gas and adsorbed phases is described by a modified linear driving force (LDF) expression for macropore limited diffusion, which is given by12 ∂qi ∂t

= kM, i(qi* − qi)

i = 1to N

⎛ 1 − ε ⎞2 1 − εb ∂P b⎟ v + 1.75 × 10−3C TMg v| v| = 0 + 1.5 × 10−1μg ⎜⎜ ⎟ 2rpεb ∂z ⎝ 2rpεb ⎠

(5)

(13)

with 1

kM, i = 1+

⎛ RTρp ⎞ ∂qi* ⎜ ⎟ ⎝ εp ⎠ ∂Pi

where μp and Mg are the viscosity and average molecular weight of the gas phase and rp is the effective radius of the pellet. For an N-component system, there are 2N + 3 variables and equations that must be solved at each node. The initial conditions of any cycle step correspond to the prevailing conditions at the end of the previous cycle step. The initial and boundary conditions are summarized in Tables S1 and S2. These represent the equations used in the first (z/L = 0) and last (z/L = 1) nodes of the bed with L being the bed length. At given boundaries, the molar flow rate Ḟ through a valve is described by the valve equation according to c vvsign Ḟ = min(49.08 |P −2 − P+2|0.5 , 41.63P −) SgT − (14)

ki (6)

where kM,i is the effective macropore mass transfer coefficient of species i, q*i is the equilibrium loading of component i given by the three process Langmuir (TPL) isotherm model,

∂qi* ∂Pi

is the

slope of the isotherm of species i, and ki is the mass transfer coefficient representing the diffusion of species i in the macropores. The equilibrium loading qi*of component i is calculated from the multicomponent form of the TPL model in the perfect positive formulation13,14 according to qi* = q1,s i + q3,s i

b1, iPyi

N ⎡ ⎤ ⎣1 + ∑ j = 1 b1, jPyj ⎦

+ q2,s i

b2, iPyi

N ⎡ ⎤ ⎣1 + ∑ j = 1 b2, jPyj ⎦

where cv is the valve coefficient, vsign is the velocity with the sign being + for cocurrent flows and − for countercurrent flows, Sg is the molecular weight ratio between the gas and air at 1 atm and 21.45 °C, P− and T− are the pressure and temperature upstream of the valve, and P+ is the pressure downstream of the valve. The comma is there to identify choking (left term) from nonchoking (right term) conditions. In eq 14, the molar flow rate is in SLPM and cv is dimensionless; T is in Kelvin, and P is in kPa. When the flow exits the bed, P− and T− are the pressure and temperature of the bed at the end closest to the valve, and P+ is the pressure outside the bed. When the flow enters the bed, P− and T− are the pressure and temperature outside the bed, and P+ is the pressure of the bed at the end closest to the valve. When concentrations, flow rates, temperatures, and valve equations are not specified or required, consistency at the boundary is maintained by utilizing the corresponding balances identified in eqs 1 to 4, 11, and 12. PSA Process Performance Indicators. The process performance indicators for this PSA cycle are evaluated in terms of the CO2 purity in the heavy product (HP), the CO2 recovery in the HP, and the feed throughput, respectively, defined as

b3, iPyi

N ⎡ ⎤ ⎣1 + ∑ j = 1 b3, jPyj ⎦

(7)

where the temperature dependences of parameters b1,i, b2,i, and b3,i are given by ⎛ B1, i ⎞ b1, i = b1,0 i exp⎜ ⎟ ⎝T ⎠

(8)

⎛ B2, i ⎞ b2, i = b2,0 i exp⎜ ⎟ ⎝ T ⎠

(9)

⎛ B3, i ⎞ b3, i = b3,0 i exp⎜ ⎟ ⎝ T ⎠

(10)

qsj,i

is the saturation capacity for component i on site j and bj,i is the affinity parameter for component i on site j. Bj,i and b0j,i are the adsorption energy of the component i on site j and the preexponential factor for component i on site j, respectively. The energy balance is expressed as

yCO ,HP =

⎛ ∂T ∂P ⎞⎟ ∂T + ((1 − εb)ρP Cpp) (εb + (1 − εb)εP)⎜Cpg C T − ⎝ ∂t ∂t ⎠ ∂t n ⎛ ∂q ⎞ ∂T ∂T + ΔHi i ⎟ + (1 − εb)ρP ∑ ⎜Cpa, j qj + εbCpg C Tv ∂t ∂t ⎠ ∂z j=1 ⎝ +

2 hw (T − T0) = 0 rb,i

2

(15)

R CO2,HP =

∑ (yj Cpg,j) j=1

molesof CO2 productproduced duringCnD molesof CO2 fed tothebed duringF (16)

⎛ L(STP) ⎞ gasfed toone bed duringFinonecycle θF⎜ ⎟= massof adsorbent inonebed × total cycletime ⎝ hkg ⎠ (17)

(11)

n

Cpg =

molesof CO2 productproduced duringCnD total molesof productproduced duringCnD

(12)

In addition to CO2 recovery, CO2 purity, and feed throughput, the power (PP) required by the vacuum pump during the CnD, LR, and CoD steps was calculated using the following equations:

Cpg,i and Cpa,j are, respectively, the molar heat capacities of component i in the gas and adsorbed phases (assumed to be equal), Cpp is the heat capacity of the pellet, ΔHi is the isosteric D


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Industrial & Engineering Chemistry Research s

E=

∑∫ i

γ−1 ⎤ ⎡ γ ⎥1 γ ⎞ ⎢⎛⎜ PH ⎞⎟ − 1⎥ nstep ̇ (t )dt ⎟RT ⎢⎜ ⎜ ⎟ δ ⎝ γ − 1 ⎠ ⎢⎝ Pstep(t ) ⎠ ⎦⎥ ⎣

to the TPL isotherm model (eqs 7 to 10 in single component form) simultaneously at all three of the available temperatures. The resulting TPL model parameters are given in Table 2.

tstep ⎛

t=0

(18)

nstep ̇ (t ) =

Table 2. TPL and Toth Isotherm Parameters, and Macropore Mass Transfer Coefficients for CO2, N2, and O2 in 13X Zeolite

Pstep(t )vstep(t )Aεb RT (t )

(19)

E PP = tc/Nb

CO2

N2

O2

TPL Parameters15

(20)

where E is the energy consumed by the vacuum pump, tstep is the duration of a certain step, PH is the F or HR step pressure and also the pump discharge pressure, PL is the suction pressure of the vacuum pump, γ is the isentropic constant (equal to 1.4), δ is the vacuum pump efficiency (assumed to be 0.8), ṅstep(t) is the molar flow rate leaving a bed during a certain step at time t, Pstep(t) is the pressure during a certain step, vstep(t) is the interstitial velocity at the end of a bed corresponding to ṅstep(t) during a certain step, A is the cross-sectional area of the bed, tc is the cycle time, and Nb is the number of beds. The other process parameter of interest was the light reflux ratio (LRR). LRR is defined as the ratio of the number of moles fed to a bed undergoing the LR step to the total number of moles leaving a bed undergoing the F step. All the gas leaving a bed undergoing the LR step was sent to a bed undergoing the HR step. So, in this case, the heavy reflux ratio was tied directly to the LRR and not independently varied. Bed, Adsorbent, and Process Characteristics. The bed, adsorbent, and process characteristics used in DAPS are listed in Table 1. The final bed size was based on processing a feed

adsorbent pellet radius, m pellet density, kg/m3 pellet porosity pellet heat capacity, kJ kg−1 K−1 Process Characteristics

13X Zeolite 0.0015 1100 0.45 1.1

feed mole fraction for CO2, N2, O2 feed temperature, K outside wall temperature, K high pressure, kPa feed flow rate, SLPM feed throughput, L(STP) h−1 kg−1 vacuum pump efficiency

0.438

0.149

2.238

0.733

0.248

qs3,i, mol kg−1

1.853

0.607

b01,i, 10−8 kPa−1

2.4417

75.95

408.33

b02,i, 10−8 kPa−1

4.5204

75.95

408.33

b03,i, 10−8 kPa−1

1.3737

75.95

408.33

0.206

B1,i, K

5757.03

2370.32

1833.21

B2,i, K

4606.08

2370.32

1833.21

B3,i, K

4224.86 2370.32 Toth Parameters

1833.21

b0i , 10−8 kPa−1 ni

6.571

12.717

4.420

36.819

11.708

41.082

0.3612

ΔHi, kJ mol−1

0.5437

−39.33 −19.54 Macropore Mass Transfer Coefficient12

ki, s−1

47

70

0.4902 −15.33 70

The corresponding experimental data and TPL model fits are shown in Figure 3. Details about the experiments and fitting procedure are given elsewhere.15 The TPL model inherently has an isosteric heat of adsorption that depends on the adsorbed phase loading.14 Because the version of DAPS used in this work does not account for a loading-dependent isosteric heat of adsorption, ΔHi in eq 11 was obtained from the Toth equilibrium adsorption isotherm model according to

Bed Characteristics 0.1143 (4.5 in.) 0.3048 (12 in.) 0.3403 725.7 8000 0.006 0.01

1.338

qsi , mol kg−1

Table 1. PSA Bed, Adsorbent, and Process Characteristics bed radius, m bed length, m bed porosity bulk density, kg m−3 wall density, kg m−3 wall thickness, m heat transfer coefficient, kW m−2 K−1 Adsorbent Characteristics

qs1,i, mol kg−1 qs2,i, mol kg−1

qi* = qis

biPyi 1

[1 + (bjPyj )ni ]ni

⎛ ΔHi ⎞ ⎟ bi = bi0exp⎜ − ⎝ RT ⎠

(21)

(22)

qsi

where and bi are the saturation capacity and affinity parameters for component i, respectively. ni is the parameter that indicates the heterogeneity of the adsorbent for component i. ΔHi and b0i are the adsorption energy of component i and the pre-exponential factor of component i, respectively. The same equilibrium adsorption isotherm data provided elsewhere15 were fitted to eqs 21 and 22 simultaneously at all three of the available temperatures to obtain ΔHi. The Toth model parameters are also given in Table 2. kM,i values for CO2, N2, and O2 were obtained experimentally from a unique open system, macroscopic, pressure swing, frequency response technique.12 The apparatus and procedure are provided elsewhere.12 The values of kM,i for each gas are also listed in Table 2.

0.004, 0.79, 0.206 294.25 294.25 101.325 570 1264 0.8

flow rate of 570 SLPM. As an aside, this final bed size also met the volume constraint imposed by NASA. As mentioned earlier, this flow rate was set by the upstream H2O vapor removal system. A relatively small value for the heat transfer coefficient was also chosen so the bed operated closer to the adiabatic condition. Equilibrium adsorption isotherms for CO2, N2, and O2 adsorbed by 13X zeolite were measured in-house,15 with the results fitted

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RESULTS AND DISCUSSION A parametric study was conducted using DAPS to investigate the effects of five PSA process parameters on the PSA process performance in terms of the CO2 purity and CO2 recovery in the heavy product and the vacuum pump power requirement. E


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Figure 3. CO2, N2, and O2 equilibrium adsorption isotherms on 13X zeolite at three temperatures12 in linear−linear and log−log scales: experimental data (symbols) and DPL model (lines). Symbols: T = 25 °C (Δ), 50 °C (◊), and 75 °C (□).

provided to a bed from a bed producing an enriched CO2 stream during the LR step, the more CO2 became adsorbed resulting in an even more enriched CO2 stream (HP) from the bed undergoing the CnD step. This increase in the adsorbed phase loading of CO2 in the bed with increasing x is depicted in Figure 5a, which shows the corresponding periodic state adsorbed phase bed profiles for CO2 at the end of the HR step (feed or heavy end located at the left side of the figure). The large adsorbed phase loading front clearly changed its penetration into the bed from about 25% to about 50% with increasing x. It is noteworthy that the sharp increases in the small adsorbed phase loadings observed below 10% penetration into the bed were due to decreases in the bed temperature caused by a trailing, cooler thermal front in the bed, as shown in Figure 5b. This trailing thermal front was due to the temperature boundary condition being fixed at TF at z = 0, even during the HR step (see Table S1). In fact, Figure 5a shows three adsorbed phase loading fronts in the bed. From right to left, the first one was due to the feed step, where it is apparent that breakthrough of CO2 into the light product had occurred; the second one, around the middle of the bed, was due to the HR step, but in the warmer region of the bed with the temperature increase

The parameters included the HR = LR = F step time (cycle time), LR ratio (LRR), CnD end pressure (PL), LR pressure (PLR), and CoD end pressure (PCoD). The ranges of these parameters are summarized in Table 3 for 13 runs carried out with DAPS. The variable x in Table 3 extended the duration of the HR = LR = F step time and thus the cycle time, as shown in Figure 2c. The resulting periodic state PSA process performances for the 13 runs are also summarized in Table 3. The periodic state was established in DAPS when the material balance of each species individually closed to within 0.2%. Effect of Heavy Reflux/Light Reflux/Feed (HR = LR = F) Step Time. Figure 4 shows the effect of the duration of the HR = LR = F step time on the performance of the 3-bed 9-step PSA cycle. To do this, four values of x were studied (i.e., x = 0, 250, 500, and 750 s, as shown in Table 3). These x values were added to the base case step time of 700 s (Figure 2), and they also correspondingly increased the total cycle time tc. The rest of the parameters, i.e., LRR, PCnD, PLR, and PCoD, were, respectively, fixed at 0.1, 1 kPa, 5, and 1 kPa. This study corresponds to Runs 1 to 4 in Table 3. Figure 4a shows that the CO2 purity in the heavy product (HP) increased with increasing values of x. The longer HR was F


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Industrial & Engineering Chemistry Research Table 3. PSA Process Performance of the 3-Bed 9-Step PSA Cycle Schedule in Figure 2ca power (W) run

a

x (s)

tc (s)

LRR

1 2 3 4

0 250 500 750

3000 3750 4500 5250

0.10 0.10 0.10 0.10

5 3 6 7

500 500 500 500

4500 4500 4500 4500

0.08 0.10 0.12 0.14

8 3 9

500 500 500

4500 4500 4500

0.10 0.10 0.10

3 10 11

500 500 500

4500 4500 4500

0.10 0.10 0.10

12 3 13

500 500 500

4500 4500 4500

0.10 0.10 0.10

PCnD (kPa)

PLR (kPa)

PCoD (kPa)

yCO2,HP (%)

RCO2,HP (%)

Heavy Reflux/Light Reflux/Feed (HR = LR = F) Step Time, i.e., x 1.0 5.0 5.00 92.13 74.83 1.0 5.0 5.0 94.32 76.94 1.0 5.0 5.0 95.75 77.01 1.0 5.0 5.0 96.75 76.06 Light Reflux Ratio (LRR) 1.0 5.0 5.0 94.77 70.41 1.0 5.0 5.0 95.75 77.01 1.0 5.0 5.0 96.18 81.20 1.0 5.0 5.0 96.47 83.85 CnD End Pressure (PL) 0.8 5.0 5.0 95.30 77.40 1.0 5.0 5.0 95.75 77.01 1.2 5.0 5.0 96.12 76.66 LR Pressure (PLR) 5.0 5.0 95.75 77.01 1.0 4.0 5.0 96.21 82.74 1.0 3.0 5.0 96.26 87.76 1.0 CoD End Pressure (PCoD) 4.0 96.79 76.25 1.0 5.0 5.0 95.75 77.01 1.0 5.0 7.0 93.24 77.15 1.0 5.0

CoD

CnD

LR

total

6.6 5.0 3.9 3.2

31.4 31.0 30.2 29.2

435.1 470.5 493.9 510.7

473.0 506.5 528.1 543.1

4.1 3.9 3.8 3.7

27.9 30.2 31.9 33.0

397.1 493.9 590.3 686.3

429.0 528.1 626.0 723.1

4.0 3.9 3.9

33.7 30.2 28.7

491.6 493.9 495.8

529.4 528.1 528.3

3.8 3.8 3.9

33.4 31.9 30.2

630.3 551.3 493.9

667.5 587.1 528.1

4.3 3.9 3.5

30.1 30.2 30.5

494.6 493.9 493.7

529.0 528.1 527.6

Run 3 is the base case; the varied process parameter is underlined, and the best run is Run 11.

Figure 4. Effect of the heavy reflux/light reflux/feed (HR = LR = F) step time by increasing x on the periodic state PSA process performance for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 1−4 in Table 3).

Figure 5. Effect of the heavy reflux/light reflux/feed (HR = LR = F) step time by increasing x (a) on the periodic state adsorbed phase bed profiles for CO2 and (b) corresponding temperature bed profile at the end of the HR step for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 1−4 in Table 3).

caused by the high CO2 concentration in the gas being fed to the bed undergoing the HR step (Figure 5b); the third one near the heavy end of the bed was also due to the HR step, but in the cooler region of the bed due to the TF boundary condition as noted above (Figure 5b). In contrast to the CO2 purity in the HP, Figure 4a also shows that the CO2 recovery in the HP exhibited a maximum

somewhere between x = 250 s and x = 500 s. In a PSA cycle schedule where the duration of the LR step is identical to that of the F step, the recovery of the heavy gas (in this case CO2) always decreases with increasing cycle time. This was not the case for this 3-bed 9-step PSA cycle schedule because the G


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noteworthy that the CO2 purities achieved in all cases did not vary significantly, indicating that the amount of CO2 in the bed at any of these operating conditions was already enough to overwhelm the concentration of air during the production of heavy product in the CnD step. In contrast, Figure 6a also shows there was a significant impact of the LRR on the recovery of CO2. In going from an LRR = 0.08 to 0.14, the recovery of CO2 improved from 70.4% to around 83.9%. These results revealed the importance of the LR step in bed regeneration, even though all the gas leaving the LR step went into the bed undergoing the HR step to enrich the adsorbed phase loading (Figure 7). The sensitivity of the CO2 recovery to changes in

duration of the LR step was always shorter than the duration of the F step, with both increasing proportionally with increasing x. This caused more regeneration and thus CO2 recovery with increasing tc for the smaller values of x. The results were as expected for the larger values of x (500 and 750 s); i.e., the CO2 recovery decreased with increasing tc. Figure 4b shows the effect of increasing x on the total vacuum pump power consumption, as well as on that consumed by each of the three individual steps involved in energy consumption, namely, CnD, CoD, and LR. The results showed that the CoD and CnD steps did not contribute significantly to the total power consumption and that their respective contribution only decreased slightly with increasing values of x. The results also showed the LR step consumed, by far, the most power, causing the power consumption to increase with increasing values of x. This result was expected because of the extremely long duration of the LR step. It is noteworthy that approximately 50 W of additional power was required with every additional 250 s of LR step duration. This incremental addition of power with increasing x corresponded to about twice the power consumed by both the CoD and CnD steps when added together. Effect of Light Reflux Ratio (LRR). Figure 6 shows the effect of the duration of the LRR on the performance of the

Figure 7. Effect of the light reflux ratio (LRR) on the periodic state adsorbed phase bed profiles for CO2 at the end of the HR step for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3 and 5−7 in Table 3).

the LR step further explained the maximum observed in the CO2 recovery that resulted from increasing the LR step duration (Figure 4a). Figure 6b shows the effect of increasing the LRR on the total vacuum pump power consumption, as well as on that consumed by each of the three individual steps involved in energy consumption, namely, CnD, CoD, and LR. As with the HR = LR = F step time, the LR step overwhelmingly dominated the total power consumption compared to that of the CoD and CnD steps when added together. It also shows that LRR had no effect on the power consumption of both the CoD and CnD steps, while a consistent linear increase of around 100 W in total power consumption resulted when incrementally increasing LRR by 0.02, essentially due to the LR step. Effect of Countercurrent Depressurization End Pressure (PCoD). Figure 8 shows the effect of the PCnD on the performance of the 3-bed 9-step PSA cycle. To do this, three values of PCnD were studied (i.e., PCnD = 0.8, 1.0, and 1.2 kPa, as shown in Table 3). The rest of the parameters, i.e., x, LRR, PLR, and PCoD were, respectively, held at 500 s, 0.1, 5, and 1 kPa. This study corresponds to Runs 3, 8, and 9 in Table 3. Figure 8a shows that the CO2 purity increased while the CO2 recovery decreased with increasing values of PCnD. The CO2 purity going down with lower values of PCnD was due to the beds being regenerated better, which was indicated by the corresponding CO2 recovery increasing. The fact that the beds were loaded with less CO2 before the CnD took place is clearly depicted in Figure 9, which shows the locations of the corresponding periodic state adsorbed phase bed profiles for CO2 at the end of the HR step. The CO2 fronts were closer to the feed end of the bed, indicating the bed was loaded with less CO2 and regenerated better with decreasing values of PCnD. These CO2 fronts were also very close to each other, with almost perfect

Figure 6. Effect of light reflux ratio (LRR) on the periodic state PSA process performance for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3 and 5−7 in Table 3).

3-bed 9-step PSA cycle. The LRR is a fraction and defined as the amount of gas fed to a bed undergoing the LR step divided by the amount of gas leaving a bed undergoing the F step, both through their light ends. To do this, four values of LRR were studied (i.e., LRR = 0.08, 0.10, 0.12, and 0.14, as shown in Table 3). The rest of the parameters, i.e., x, PCnD, PLR, and PCoD, were, respectively, fixed at 500 s, 1 kPa, 5, and 1 kPa. This study corresponds to Runs 3, 5, 6, and 7 in Table 3. Figure 6a shows that the CO2 purity increased with increasing values of LRR. This result was confirmed by the locations of the corresponding periodic state adsorbed phase bed profiles for CO2 at the end of the HR step shown in Figure 7. It is H


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Figure 10. Effect of the light reflux pressure (PLR) on the periodic state PSA process performance for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3, 10, and 11 in Table 3).

Figure 8. Effect of the countercurrent depressurization end pressure (PCnD) on the periodic state PSA process performance for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3, 8, and 9 in Table 3).

at 500 s, 0.1, 1.0 kPa, and 1.0 kPa. This study corresponds to Runs 3, 10, and 11 in Table 3. Figure 10a shows both the CO2 purity and the CO2 recovery increased with decreasing values of PLR. The effect of PLR on the CO2 recovery was significant, while its effect on the CO2 purity was only minimal. Figure 11, which shows the locations of the

Figure 9. Effect of the countercurrent depressurization end pressure (PCnD) on the periodic state adsorbed phase bed profiles for CO2 at the end of the HR step for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3, 8, and 9 in Table 3).

overlap of the CO2 concentrations located downstream past z/L = 0.5. This explained why the changes of both the CO2 purity and the CO2 recovery did not vary much with changes in PCnD. Figure 8b shows the effect of increasing PCnD on the total vacuum pump power consumption, as well as on that consumed by each of the three individual steps involved in energy consumption, namely, CnD, CoD, and LR. Again, the LR step overwhelmingly dominated the total power consumption compared to that of the CoD and CnD steps when added together. It also shows that increases in PCnD had no effect on the power consumption of the CoD step, while that for the CnD step decreased and that for the LR step increased but both only slightly. The net effect on the total power consumption was essentially independent of PCnD. Effect of Light Reflux Pressure (PLR). Figure 10 shows the effect of the PLR on the performance of the 3-bed 9-step PSA cycle. To do this, three values of PLR were studied (i.e., PLR = 3.0, 4.0, and 5.0 kPa, as shown in Table 3). The rest of the parameters, i.e., x, LRR, PCnD, and PCoD, were respectively, fixed

Figure 11. Effect of the light reflux pressure (PLR) on the periodic state adsorbed phase bed profiles for CO2 at the end of the HR step for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3, 10, and 11 in Table 3).

corresponding periodic state adsorbed phase bed profiles for CO2 at the end of the HR step, explained the small influence of PLR on the CO2 purity. There was a significant redistribution of the CO2 bed profiles at the end of the HR step, where lower values of PLR caused the CO2 loadings to increase slightly in the first 40% of the bed and vice versa in the remaining 60% of the bed. The lower CO2 loadings closer to the light end of the bed (i.e., the air-rich side), exhibited with lower PLR, revealed the ability of this parameter to regenerate the bed, with its concomitant influence on the CO2 recovery. Figure 10b shows the effect of increasing PLR on the total vacuum pump power consumption, as well as on that consumed I


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vacuum pump is required with proper valving and piping. This interesting fact was due to none of the vacuum-requiring cycle steps overlapping with each other in this 3-bed 9-step PSA cycle schedule (Figure 2).

by each of the three individual steps involved in energy consumption, namely, CnD, CoD, and LR. The total power consumption increased significantly with decreasing values of PLR, causing a net change of 60 to 70 W per 1 kPa reduction in PLR. Again, the power consumed during the LR step dominated. The power consumed during the CoD and CnD steps minimally changed, with a slight decrease exhibited by the CnD step with increasing PLR. Effect of Cocurrent Depressurization End Pressure (PCoD). Figure 12 shows the effect of the PCoD on the performance of

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CONCLUSIONS The dynamic adsorption process simulator (DAPS) was used to carry out simulations of continuous feed, unequal step time, pressure swing adsorption (PSA) cycles to study the enrichment, and recovery of 0.4 vol % CO2 from dry air using 13X zeolite with the feed pressure and flow rate fixed at 1 atm and 570 SLPM. The goal was to produce 97 vol % CO2 at a CO2 recovery greater than 62%, low vacuum pump power (less than 100 kW), and small volume. After devising and evaluating four 3-bed PSA cycle schedules with an HR step, the best one was a 3-bed 9-step PSA cycle schedule. It consisted of the following steps: feed (F), idle (I), heavy reflux (HR), cocurrent equalization down (EqD), cocurrent depressurization (CoD), countercurrent depressurization (CnD), light reflux (LR), countercurrent equalization up (EqU), and light product pressurization (LPP). A parametric study revealed the following effects of five PSA process parameters on the PSA process performance. Increases in the HR = LR = F step time (thus cycle time) caused significant increases in the CO2 purity and vacuum pump power, while the CO2 recovery exhibited a modest maximum. Increases in the LR ratio caused significant increases in both the CO2 recovery and power but only a modest increase in the CO2 purity. Increases in the CnD end pressure caused only slight changes in all three parameters, with the CO2 purity increasing and CO2 recovery and power decreasing. Increases in the LR pressure caused significant decreases in both the CO2 recovery and power, with only a slight decrease in CO2 purity. Increases in the CoD end pressure caused a significant decrease in the CO2 purity, a modest increase in the CO2 recovery, and only a slight decrease in power. Even though the trends associated with each of these five PSA process parameters were as expected, the PSA process performance of this 3-bed 9-step PSA cycle surpassed expectations, especially the CO2 enrichment in the heavy product. The best performance obtained with this new 3-bed 9-step PSA cycle produced a CO2 purity of 96.3 vol % at a CO2 recovery of 87.8% and feed throughput of 1264 L(STP)/h/kg, while consuming only 572 W of vacuum pump power. The corresponding conditions were 4500 s cycle time, HR = LR step time of 1200 s, LR ratio = 0.1, PCnD = 1 kPa, PLR = 3 kPa, and PCoD = 5 kPa. This new PSA cycle was very effective at concentrating CO2 (over 242 times) because of a forced CoD step combined with a very long HR = LR step time relative to the other cycle steps, where the source of the HR gas was exclusively from the LR step. The LR step dominated the power requirement, so much that the power required by the CnD step and especially the forced CoD step was insignificant in comparison. Moreover, because none of the cycle steps requiring vacuum overlapped with each other in this 3-bed 9-step PSA cycle schedule, only one vacuum pump was required.

Figure 12. Effect of the cocurrent depressurization end pressure (PCoD) on the periodic state PSA process performance for the 3-bed 9-step PSA cycle schedule in Figure 2 (Runs 3, 12, and 13 in Table 3).

the 3-bed 9-step PSA cycle. To do this, three values of PCoD were studied (i.e., PCoD = 4.0, 5.0, and 7.0 kPa, as shown in Table 3). The rest of the parameters, i.e., x, LRR, PCnD, and PLR were, respectively, fixed at 500 s, 0.1, 1.0, and 5.0 kPa. This study corresponds to Runs 3, 12, and 13 in Table 3. Figure 12a shows the CO2 purity dramatically increased while the CO2 recovery decreased minimally with decreasing values of PCoD. This result clearly revealed the effectiveness of the forced CoD step in removing air from the light of the bed prior to bed regeneration through the heavy end with minimal impact on CO2 recovery. In fact, no perceivable amount of CO2 was removed from the light of the bed during this step. Figure 12b shows the effect of increasing PCoD on the total vacuum pump power consumption, as well as on that consumed by each of the three individual steps involved in energy consumption, namely, CnD, CoD, and LR. The effect of PCoD on the power consumption of any of these energy consuming steps was insignificant. The power consumption during the LR and CnD steps remained essentially constant, while that for the CoD step was so small that its reduction with increasing PCoD values played no role in the total power consumption. The power consumption during the LR step overwhelmed the other steps, as before. This significant result provided another good reason to implement the forced CoD step for enriching CO2. Not only does it not require much power, but also only one

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b05024. Tables summarizing the initial and boundary conditions used in the mathematical model (PDF) J


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AUTHOR INFORMATION

PL = pressure at the end of the CnD step, kPa PLR = pressure at the end of the LR step, kPa Pstep = pressure during a certain step, kPa PP = vacuum pump power, W P(t) = suction pressure of the vacuum pump, kPa qi = adsorbed phase loading of component i, mol kg−1 qi* = adsorbed phase equilibrium loading of component i, mol kg−1 qsi = Toth model parameter for component i, mol kg−1 qs1,i = three process Langmuir model parameter for component i, mol kg−1 qs2,i = three process Langmuir model parameter for component i, mol kg−1 qs3,i = three process Langmuir model parameter for component i, mol kg−1 R = universal gas constant, kPa m3 mol−1 K−1 RCO2,HP = recovery of CO2 in the heavy product rb,i = column internal radius, m rp = adsorbent particle radius, m Sg = molecular weight ratio between gas and air at 1 atm and 21.45 °C t = time, s tc = cycle time, s tstep = duration of a certain step, s ts = step time, s T = temperature, K T0 = ambient temperature, K v = interstitial velocity, m s−1 vstep = interstitial velocity during a certain step, m s−1 x = HR = LR = F cycle step time extension, s yi = mole fraction of component i yCO2,HP = mole fraction of CO2 in the heavy product defined z = column axial coordinate, m

Corresponding Author

*E-mail: [email protected]. ORCID

James A. Ritter: 0000-0003-2656-9812 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Continued financial support provided over many years by the NASA Marshall Space Flight Center is greatly appreciated. NOMENCLATURE A = cross-sectional area of the bed, m2 bi = Toth model parameter for component i, kPa−1 b0i = Toth model parameter for component i, kPa−1 B1,i = three process Langmuir model parameter for component i, K−1 B2,i = three process Langmuir model parameter for component i, K−1 B3,i = three process Langmuir model parameter for component i, K−1 b1,i = three process Langmuir model parameter for component i, kPa−1 b2,i = three process Langmuir model parameter for component i, kPa−1 b3,i = three process Langmuir model parameter for component i, kPa−1 b01,i = three process Langmuir model parameter for component i, kPa−1 b02,i = three process Langmuir model parameter for component i, kPa−1 b03,i = three process Langmuir model parameter for component i, kPa−1 Cpg,i = gas phase heat capacity of component i, kJ mol−1 K−1 Cpa,i = adsorbed phase heat capacity of component i, kJ mol−1 K−1 Cpg = gas phase heat capacity, kJ mol−1 K−1 Cpp = adsorbent particle heat capacity, kJ mol−1 K−1 CT = total molar concentration, mol m−3 cv = valve coefficient, dimensionless E = energy defined, kJ/mol CO2 Ḟ = molar flow rate through the valve, L(STP)/min hw = overall heat transfer coefficient, kW m−2 K−1 ΔHi = Toth isosteric heat of adsorption of component i, kJ mol−1 ki = mass transfer coefficient of component i, s−1 kM,i = is the effective macropore mass transfer coefficient of component i L = column length, m Mg = gas phase average molecular weight, kg mol−1 ni = Toth model parameter for component i ṅstep = molar flow rate, mol s−1 N = number of components Nb = number of beds P = pressure, kPa PCoD = pressure at the end of the CoD step, kPa PEq = pressure at the end of the eq step, kPa PH = highest feed or HR step pressure and vacuum pump discharge pressure, kPa Pi = partial pressure of component i, kPa PI = pressure during the idle (I) and HR steps (=PH), kPa

Greek Symbols

γ = isentropic constant δ = vacuum pump efficiency εb = column porosity εp = adsorbent particle porosity ρp = adsorbent particle density, kg m−3 μg = gas phase viscosity, Pa s θF = feed throughput, L(STP) h−1 kg−1

Cycle Step Acronyms

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CnD = countercurrent depressurization CoD = cocurrent depressurization Eq = equalization EqD = equalization down EqU = equalization up F = feed HE = heavy end HR = heavy reflux HP = heavy product I = idle LE = light end LP = light product LPP = light product pressurization LR = light reflux

REFERENCES

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Industrial & Engineering Chemistry Research (3) Samanta, A.; Zhao, A.; Shimizu, G. K. H.; Sarkar, P.; Gupta, R. Post-Combustion CO2 Capture Using Solid Sorbents: A Review. Ind. Eng. Chem. Res. 2012, 51, 1438. (4) Lee, S.-Y.; Park, S.-J. A Review on Solid Adsorbents for Carbon Dioxide Capture. J. Ind. Eng. Chem. 2015, 23, 1. (5) Riboldi, L.; Bolland, O. Overview on Pressure Swing Adsorption (PSA) as CO2 Capture Technology: State-of-the-Art, Limits and Potentials. Energy Procedia 2017, 114, 2390. (6) Sanz-Perez, E. S.; Murdock, C. R.; Didas, S. A.; Jones, C. W. Direct Capture of CO2 from Ambient Air. Chem. Rev. 2016, 116, 11840. (7) Fenske, J. D.; Paulson, S. E. Human Breath Emissions of VOCs. J. Air Waste Manage. Assoc. 1999, 49, 594. (8) Knox, J. C.; Campbell, M.; Murdoch, K.; Miller, L. A.; Sverdrup, J. E.; Jeng, F. Integrated Test and Evaluation of a 4-Bed Molecular Sieve (4BMS) Carbon Dioxide Removal System (CDRA), Mechanical Compressor Engineering Development Unit (EDU), and Sabatier Engineering Development Unit (EDU), International Conference on Environmental Systems, Rome, Italy, July 11−14, 2005; https://ntrs. nasa.gov/search.jsp?R=20050206339. (9) Ebner, A. D.; Mehrotra, A.; Ritter, J. A. Graphical Unit Block Approach for Complex PSA Cycle Scheduling of Parallel Interacting Trains of Columns and Tanks. Adsorption 2015, 21, 229. (10) Mohammadi, N.; Hossain, M. I.; Ebner, A. D.; Ritter, J. A. New PSA Cycle Schedules for Producing High Purity Oxygen Using Carbon Molecular Sieve. Ind. Eng. Chem. Res. 2016, 55, 10758. (11) Brown, P. N.; Hindmarsh, A. C.; Petzold, L. R. Using Krylov Methods in the Solution of Large Scale Differential-Algebraic Systems. SIAM J. Stat. Comp. 1994, 15, 1467. (12) Rahman, A. N.; Ebner, A. D.; Ritter, J. A. Open System Macroscopic Pressure Swing Frequency Response Technique for Measuring Adsorbate-Adsorbent Mass Transfer Coefficients, unpublished work. (13) Ritter, J. A.; Bhadra, S. J.; Ebner, A. D. On the Use of the Dual Process Langmuir Model for Correlating Unary and Predicting Mixed Gas Adsorption Equilibria. Langmuir 2011, 27, 4700. (14) Bhadra, S. J.; Ebner, A. D.; Ritter, J. A. On the Use of the Dual Process Langmuir Model for Predicting Unary and Binary Isosteric Heats of Adsorption. Langmuir 2012, 28, 6935. (15) Mohammadi, N., Erden, L.; Rahman, A. N.; Ebner, A. D.; Ritter, J. A. Adsorption Equilibria of Nitrogen, Oxygen, Argon, Carbon Dioxide, Carbon Monoxide, Methane, Ethane, Ethylene, Propane and Propylene on 13X Zeolite, unpublished work.

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Development of a Pressure Swing Adsorption Cycle for Producing

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