Ind. Eng. Chem. Res. 2007, 46, 4595-4605
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Biogas to Fuel by Vacuum Pressure Swing Adsorption I. Behavior of Equilibrium and Kinetic-Based Adsorbents Carlos A. Grande* and Alı´rio E. Rodrigues Laboratory of Separation and Reaction Engineering (LSRE), Associate Laboratory, Department of Chemical Engineering, Faculty of Engineering, UniVersity of Porto, Rua Dr. Roberto Frias, s/n 4200-465, Porto, Portugal
Purification of biogas by vacuum pressure swing adsorption was evaluated to produce fuel grade methane (FGM). Two different adsorbents were employed to evaluate the process performance with equilibrium- and kinetic-based adsorbents. Carbon molecular sieve 3K was employed as the example of a kinetic adsorbent because methane diffusion is extremely small. A five-step cycle configuration (feed, intermediate depressurization, blowdown, purge, and pressurization) was employed to compare with results obtained with a fourstep cycle without intermediate depressurization. The effect of different operating variables like step times and pressure conditions of the cycle was analyzed. We have employed zeolite 13X as the equilibrium-based adsorbent (much higher capacity for CO2 with fast diffusion of both gases). Different operating conditions as well as a new cycle configuration were evaluated. Methane with purity over 98% was obtained with both adsorbents. The CMS 3K adsorbent showed much higher methane recovery (close to 80%) compared to those obtained with zeolite 13X (close to 60%) because of low adsorption in the pressurization step and because the stream exiting the intermediate depressurization step can be considered as being a product. 1. Introduction Methane is the most important non-CO2 greenhouse gas (GHG), accounting for 10% of total GHG emissions in developed countries and almost 20% in developing countries.1 The greenhouse warming potential (GWP) of this gas is 21 times higher than that of carbon dioxide. Also, the life of methane molecules in the atmosphere is 10 times smaller than carbon dioxide, so any reduction in methane emissions is much more important in the short- and medium-term atmosphere reconstruction. In Portugal, methane emissions constitute 10.2% of total GHG. Almost 40% of total methane emissions come from anaerobic fermentation of municipal solid waste, whereas 50% comes from agriculture including manure fermentation.2 This means that almost 90% of all methane released to atmosphere comes as biogas. By biogas, we mean the gaseous mixture produced by anaerobic fermentation of organic matter (animal manure, solid waste, and others) by methanogenic bacteria in the absence of oxygen. Biogas is a multicomponent mixture containing mainly methane and carbon dioxide, whereas many other gases (contaminants) are almost always below 4% and saturated with water. The molar fraction of methane in biogas is between 0.45-0.65 balanced by carbon dioxide and contaminants. The amount and nature of these contaminants (sulfurbearing, aromatic, and chlorinated compounds) depend strongly on the biogas source. Since the establishment of the Kyoto protocol, the combination of tighter environmental controls together with requirements of smaller costs in contaminant treatment have merged into new efficient processes for recovery of methane from biogas streams. In Portugal and many other European countries, which have to import natural gas (NG) and other fossil fuels, biogas can be treated as an important national resource of fuel. Methane is the smaller hydrocarbon molecule with a lower heating value of 50 MJ/kg (35.7 MJ/Nm3). When compared with other carbon* To whom correspondence should be addressed. Tel.: 351 22 508 1618. Fax: 351 22 508 1674. E-mail:
[email protected].
based fuels, methane presents the lower emission factor: 57.3 tons of CO2 per TJ of energy. A low emission factor combined with the renewable origin of the fuel is beneficial from many points of view. Accordingly, to present alternatives, there are several paths to recover energy from biogas:3 heat recovery from actual flares, energy and/or combined heat and power (CHP) applications, purification for further incorporation in methane pipeline network, and reaction to produce chemical feedstock (i.e., methanol and diesel fuel). In several countries, there is specific legislation in the use of renewable energy for production of fuels in order to promote this industry. Actually, several countries (United States, Sweden, France, Germany, Denmark, and The Netherlands) produce methane with fuel grade from biogas. The CO2 removal from these plants is carried out by amine scrubbing, membrane-based processes, physical absorption with water, chemical absorption with polyglycol ether (Selexol), and pressure swing adsorption.4,5 Pressure swing adsorption (PSA) is one of the most known industrial processes for gas separation.6 Adsorption processes for removal of CO2 from NG streams are based on materials with selective adsorption to CO2 by different equilibrium capacities7 or by differences in uptake rates.8 In this work, we have studied the feasibility of employing a vacuum pressure swing adsorption (VPSA) process to produce purified methane that meets fuel grade specifications: minimum methane purity of 98%. Starting from the biogas mixture, we have assumed that water and contaminants were previously removed and we have focused in the CH4-CO2 separation process according to a process block diagram previously proposed for this purpose.9 We have employed existing data of adsorption equilibrium and kinetics of two different adsorbents to compare VPSA behavior for kinetic- and equilibrium-based separation. Carbon molecular sieve 3K (Takeda) and zeolite 13X (CECA) were the adsorbents employed in this study. On the basis of previously published data on adsorption properties of pure gases and benchmark VPSA experiments,10,11 we have simulated VPSA cycles comprising five steps: pressurization,
10.1021/ie061341+ CCC: $37.00 © 2007 American Chemical Society Published on Web 05/23/2007
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feed, intermediate co-current depressurization, counter-current blowdown, and counter-current purge with product. As an example of application of VPSA technology, we focused in the production of fuel-grade methane from a biogas feed of 1000 Nm3/h (P ) 1 atm; T ) 298K) with a methane content of 55% balanced by carbon dioxide. Several operating conditions were evaluated and different cycle configurations were also studied for the equilibrium-based adsorbent. 2. Modeling and Simulations The simulations of CH4-CO2 separation by VPSA process rely on a mathematical model previously tested for binary separations12 and specifically for this separation.11 Adsorption equilibrium of methane and carbon dioxide on carbon molecular sieve 3K from Takeda Corp. and on zeolite 13X from CECA was also previously published.10,11 The multicomponent extension of the multisite Langmuir model was employed for description of single-component data and used to predict multicomponent adsorption equilibrium. To describe the adsorption kinetics of CH4 and CO2 in both adsorbents, we have employed a bidisperse model in which macropores and micropores resistances are separately incorporated. To reduce the computational time required to make the simulations, we have employed a bi-LDF (linear driving force) model approximation for both resistances. The LDF constants for micropore diffusion in the CMS 3K adsorbent were calculated by combining the micropore resistance and surface barrier at the mouth of the micropores13 in a single parameter (Kµ,i). Macropore diffusion constant (Kp,i) was calculated using the Bosanquet equation (molecular + Knudsen diffusion) assuming a tortuosity factor of 2.2 for CMS 3K. Diffusion of either CH4 or CO2 into the zeolite 13X extrudates was very fast. In zeolite 13X, crystal diffusivity coefficients at infinite dilution used in the model were obtained from literature.14,15 The micropore diffusivity coefficients have an exponential dependence with temperature. To calculate the relative importance of macro and micropore resistances, the γ parameter was employed.16-18 This parameter is defined as
Dc,i γ)
rc2 pDp,i
(1)
(p + (1 - p)∂Cc/∂Cg)Rp2 where Cc is the micropore concentration and Cp is the macropore concentration. If γ is much smaller than one, the controlling resistance is in the micropores, whereas for values much larger than one, the control for diffusion is in the macropores. The macropore diffusivity is calculated by the Bosanquet equation as described in Table 3. To calculate the γ parameter, we have assumed a tortuosity factor of 2.0. With the parameters of the adsorbent given in Table 7, we find a value of γ > 1000, indicating that macropore resistance is controlling the diffusion process. This fact is a combination of the small crystal diameter of zeolite 13X extrudates employed and the large macropores of the extrudates. Adsorption equilibrium and kinetic parameters for pure methane and carbon dioxide in carbon molecular sieve 3K (Takeda Corp.) and zeolite 13X (CECA) are shown in Table 1. Adsorption equilibrium isotherms of CH4 and CO2 at 308 K on these adsorbents are shown in Figure 1 together with the fitting of the multisite Langmuir model. The adsorption equilibrium parameters reported in Table 1 are merely fitting parameters
Figure 1. Adsorption equilibrium of CH4 and CO2 at 308 K on (a) Takeda CMS 3K11 and (b) zeolite 13X CECA10.
and no physical meaning was attributed to them. These parameters were previously employed in the description of binary breakthrough curves, validating the prediction of multicomponent separation in VPSA process.11,20 The performance of the VPSA process was evaluated according to three different parameters: purity of the CH4-rich stream, product recovery defined as the amount of feed obtained with fuel grade, and the unit productivity. The definition of these parameters is dependent on the cycle configuration employed. In this case, we are evaluating two different adsorbents operating in kinetic and equilibrium-control, which is the reason why two configurations were employed. The purity, recovery, and productivity for both cycles are defined in Table 2. For the calculation of VPSA productivity, we have considered that the process is composed by two columns (n ) 2). The equations of the mathematical model employed in this work are shown in Table 3. Boundary and initial conditions for all the steps employed are also shown in Table 4. Numerical simulations were carried out using gPROMS (PSE Enterprise, UK). The orthogonal collocation method on finite elements (OCFE) was used with 35 finite elements and two interior collocation points in each element of the adsorption bed for the kinetic-based adsorbent, whereas 50 finite elements were employed for the zeolite 13X. 3. Kinetic-Controlled VPSA Process: CMS-3K The target of the VPSA process proposed is to reach fuelgrade methane (FGM), maximizing the recovery of methane. In this work, FGM is defined as a stream of methane with purity higher than 98%, where the 2% remaining should be CO2. It is assumed that water and sulfur compounds present in biogas are removed in prior separation stages. It is important to point out that the cycle scheme presented in this work assumes that all the biogas available will be converted to FGM. Other cycle
Ind. Eng. Chem. Res., Vol. 46, No. 13, 2007 4597
schemes can be employed depending on other requirements, i.e., combination of fuel-grade methane production and electricity generation. We have employed a kinetic adsorbent, carbon molecular sieve 3K (Takeda Corp., Japan), that allows carbon dioxide to diffuse within the micropore network, whereas methane molecules have a strong resistance in the bottlenecked micropores of the adsorbent,13 taking 3 days to reach adsorption equilibrium.11 Also, the adsorption capacity of CO2 is higher than that of CH4, which enhances the overall adsorbent selectivity: for the same contact time, many more molecules of CO2 are adsorbed than CH4 molecules. The step configuration of an appropriate VPSA cycle has to take into account several considerations related to the adsorption equilibrium and kinetic properties of the gases in the adsorbent. Some of the considerations for the system employed in this work are presented below: (a) According to the shape of the isotherms of CO2, it is necessary to apply a vacuum to desorb this gas with high unit productivity. This has the disadvantage of increasing the power consumption of the process. (b) In the time of a VPSA cycle (less than 1000 s), CH4 cannot be adsorbed in the micropores. For the definition of the cycle configuration, it can be assumed that CH4 is not adsorbed. (c) As CH4 can be considered as being not adsorbed, pressurization time can be directly calculated, no matter if pressurization is with feed or with product streams. (d) Purge step time should not be very long, because CH4 cannot penetrate the micropores and displace CO2. Methane employed in the purge stream will not displace the CO2 adsorbed in the adsorbent but will reduce its molar fraction in the gas phase. Initial benchmark CH4-CO2 separation studies using a VPSA (vacuum pressure swing adsorption) process showed that highpurity CH4 could be produced employing this adsorbent.11 The main problem observed was that the recovery of methane was around 60%, which is a very small value to make it worth extending this concept and applying it on an industrial scale. The process performance obtained with a four-step cycle was also confirmed by other researchers.19 To improve this behavior, in this work, we have employed a different cycle configuration to a five-step process, which comprises the following: (1) Feed: the step in which CO2 is preferentially retained in the fixed-bed column, whereas CH4 is released in the top at high pressure (CH4 production step). (2) Intermediate depressurization: the column inlet (z ) 0) is closed and a fast depressurization to an intermediate pressure, Pinter, occurs. The exit stream is also considered to be a product, because it can be employed for pressure equalization to reduce energy for pressurization. This action has positive impacts in the product recovery of the system, as can be seen in Table 2 by increasing the value of the first term in the recovery equation. (3) Counter-current blowdown: the column is evacuated until the low pressure, Pblow, is reached. This step produces a CO2rich stream and partially regenerates the adsorbent. (4) Counter-current purge with product: in this step, part of the product (CH4-rich stream) is employed to displace the CO2 to the feed end, avoiding product contamination in the following cycles. As CH4 cannot penetrate the microporous structure, the step should not last much more than the space time. This step is also performed at low pressure (Pblow).
Figure 2. VPSA cycle scheme used for CH4-CO2 separation with CMS3K (Takeda): (1) counter-current pressurization with product; (2) feed; (3) intermediate depressurisation; (4) counter-current blowdown; (5) countercurrent purge with product.
(5) Counter-current pressurization: the column is pressurized from the low pressure to the final pressure employed in the feed step, Pfeed. Some of the product stream is used in this step. The scheme of the cycle configuration of the VPSA process is shown in Figure 2. The most important modification introduced to previously existing data is that an intermediate depressurization step was added before the blowdown step. This step is extremely important for improving methane recovery; if depressurization is fast, most of the CH4 of the gas phase and from the macropore structure of the adsorbent will exit the column, whereas CO2 from the adsorbed phase will start its desorption without leaving the column. In a previous study,11 we verified no significant impacts in purity and recovery of CH4, whether co-current or counter-current pressurization are employed. In this new cycle including intermediate depressurization, a pressure equalization step will exist and then counter-current partial pressurization will happen, which is why we have decided to completely pressurize the product. On the basis of benchmark results using a four-step cycle configuration,11 a preliminary scale-up of the process was performed. The scale-up considered the ratio of feed flowrate and the mass of adsorbent in the column to be constant. We have assumed that a stream of 16 667 SLPM (standard liters per minute at 1 atm and 25 °C) of biogas are available for purification. This flowrate is equivalent to 1000 m3/hour of biogas, available for example, from a municipal landfill station. The properties of the column and the adsorbent employed in the simulations of the VPSA process are detailed in Table 5. For the design of the column, we have employed LC/Dw ) 5. With a fixed flowrate and bed volume, we have evaluated the performance of the process for different step times and pressure conditions. Adsorption equilibrium and kinetic parameters of CO2 and CH4 in CMS-3K (Takeda Corp.) were also reported previously.11 Another aspect to take into account in these scaleup simulations is the adiabatic behavior of the VPSA columns. The simulated performance of the VPSA process for biogas purification to FGM using CMS-3K for different operating conditions is reported in Table 6. Initially, the reference case (run A in Table 6) was a standard Skarstrom-type cycle with counter-current pressurization. A high purity of methane was obtained, but recovery was not higher than 60%. Low methane recovery was due to large losses of methane in the blowdown step: large Phigh/Plow ratio between feed and blowdown steps. A solution for reduceing the Phigh/Plow ratio is to reduce the amount of CH4 in the column before the blowdown step. It was
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Figure 3. Simulations of VPSA cycles without (left) and with (right) intermediate depressurisation. (a, b) CO 2 concentration; (c, d) CO2 adsorbed phase concentration; (e, f) molar flow of single gases at the end of the column; (g, h) temperature histories for cyclic steady state in different locations of the column (1, 2, 3, and 4 m from feed inlet). Experimental conditions are detailed in Table 2 (runs A and 1). Numbers in (a, c) correspond to 1, pressurization; 2, feed; 3, blowdown; 4, purge. Numbers in (b, d) correspond to 1, pressurization; 2, feed; 3, intermediate depressurization; 4, blowdown; 5, purge.
observed that when an intermediate depressurization step is introduced, the recovery of methane increases drastically with small effects on purity. This is because the diffusivity of CO2 is not very high and if the intermediate depressurization is short (fast depressurization), there is no time for its desorption. This is shown in Figure 3, where simulations A and 1 (with and without intermediate depressurization) are compared. The results are presented for the cyclic steady state (CSS), which was normally reached after more than 150 cycles of operation. In the unsteady-state operation, the purity was always higher than the values reported in Table 6, whereas CH4 recovery was lower.
No significant variations are observed in the amount of CO2 adsorbed between the end of the feed step and the end of the depressurization step (marked with numbers 2 and 3 in Figure 3d). In either the plots of concentration or adsorbed phase (Figure 3a-d), the kinetic nature of the process can be observed: only a small portion of the total capacity of the adsorbent is employed, and the mass-transfer profiles are broad. This corresponds to the observed thermal responses: the bulk CO2 adsorption takes place in only the first portion of the column, where large temperature peaks are observed (see z ) 1 m from feed inlet in panels g and h in Figure 3). Also, the
Ind. Eng. Chem. Res., Vol. 46, No. 13, 2007 4599 Table 1. Adsorption Equilibrium and Kinetic Parameters of CH4 and CO2 Adsorption in Zeolite 13X (CECA)10 and CMS 3K (Takeda)11 Zeolite 13X CECA, France gas
qmax,i (mol/kg)
K0i (kPa-1)
ai
-∆Hi (kJ/mol)
Dp,i/Rp2 (s-1)
Dµ,i (m2/s)
CH4
28.871
4.34 × 10-1
8.136
15.675
1.47 × 10-2 (301 K) 1.64 × 10-2 (323 K) 1.23 × 10-2 (301 K) 1.35 × 10-2 (323 K)
3.00 × 10-8 (301 K) 3.30 × 10-8 (323 K) 3.92 × 10-9 (301 K) 5.35 × 10-9 (323 K)
CO2
17.901
3.20 × 10-5
13.120
54.729
CMS 3K Takeda Corp., Japan K0i (kPa-1)
qmax,i (mol/kg)
gas CO2 CH4
10-8
1.73 × 2.48 × 10-10
8.974 11.797
ai
-∆Hi (kJ/mol)
Dp,io/Rp2 (s-1)
8.287 6.303
38.947 33.674
3.45 3.11
Table 2. Process Performance Parameters (CH4 Purity and Recovery and Unit Productivity) Defined for Kinetic Adsorbents and Equilibrium-Based Adsorbents Kinetic-Based Adsorbent (cycle scheme shown in Figure 2): CMS 3K
∫
tfeed+tdepres
CCH4u
0
PURITY )
(∫
tfeed+tdepres
0
RECOVERY )
∫
tfeed+tdepres
0
|
CCH4u
CCH4u
z)LC dt
∫
tpurge
-
z)LC dt
|
0
∫
tfeed
0
PRODUCTIVITY )
∫
+
|
z)LC dt
tfeed+tdepres
0
CCH4u
CCH4u
|
|
z ) LC dt
CCO2u
-
∫
| ) |
tpress
0
dt
z)LC
CCH4u
z)LC dt
z)0 dt
yCH4,feedn˘ feed Recovery nωadsorbentPurity
Equilibrium-Based Adsorbent (cycle scheme shown in Figure 4): Zeolite 13X
∫
tfeed
0
PURITY )
(∫
tfeed
0
CCH4u
∫
tfeed
0
RECOVERY )
|
z)LC dt
|
CCH4u
∫
+
|
z)LC dt
∫
z)LC dt
tpress+tfeed
0
PRODUCTIVITY )
CCH4u
tfeed
CCO2u
0
-
∫
tpurge
0
CCH4u
|
| ) | z)LC dt
CCH4u
z)LC dt
z)0 dt
yCH4,feedn˘ feedRecovery nωadsorbentPurity
low effectiveness of the purge in removing adsorbed CO2 can be observed in both cycles with or without intermediate depressurization (see panels c and d in Figure 3). Other important operating conditions are the feed and intermediate pressures employed in the cycle. In this study, we have kept the blowdown and purge pressures constant at a value small enough to desorb substantial amounts of CO2 and not optimize the power consumption of the system that will be greatly influenced by the Pblow value. It was verified that when feed pressure increases, the performance of the process is improved. It was also observed that increasing the intermediate pressure from 200 to 250 kPa purity close to 98% was achieved with more than 80% methane recovery. In simulations 1-4 (see Table 6), it could be noticed that purity is very close to 98%, although in all cases, it is lower than the prefixed value. The only way to increase product purity is to reduce the number of moles of CO2 in each cycle. To compare the performance of the unit with previous experiments, we have reduced the inlet flowrate of biogas entering the feed step. With a small reduction
Dµ,io/rc2 (s-1)
Ea,i (kJ/mol)
22.12 25.551 2.33 × 10-6 (Dµ,i/rc2 at 308 K)
kb,io, (s-1)
Eb,i (kJ/mol)
1.0 × 10-4 (kb,i at 308 K)
to 16 000 SLPM (instead of the 16 667 used in other simulations), we have obtained a purity of 98.1% with a recovery close to 80%. We could observe that it was necessary to reduce the feed flowrate in almost 5% compared to the scale-up performed with previous benchmark experiments. There are two factors that contribute to this reduction. The first one is the displacement of the CO2 (to the product end) because of the depressurization step, and the second and most important one is the adiabatic behavior of the column (negligible heat transfer between the column and the surroundings of the VPSA unit). If the column operates adiabatically, more heat of adsorption is accumulated in the bed, reducing the total bed capacity, resulting in a smaller feed step compared with non-adiabatic behavior. Application of this VPSA process has two main problems: the first one is the small diffusivity of CO2 in the adsorbent that results in dispersive concentration profiles inside the column, employing only a small amount of the adsorbent equilibrium capacity (see Figure 3d). We obtained a much smaller productivity than the one calculated only on the basis of equilibrium theory, requiring a much larger unit to process a desired flowrate. It can be observed that the only simulation that produced methane with greater than 98% purity (simulation 5 in Table 6) has a productivity of 3.83 mol CH4/kg.h. Another area for improvement in this process is the requirement of a very low pressure for blowdown in order to remove substantial amounts of CO2. This problem could be partially surveyed with a more intensive degree of integration of the VPSA process in the biogas plant (together with production of electricity). The results obtained in this work show that it is possible to produce FGM from biogas employing carbon molecular sieve 3K as a kinetic adsorbent obtaining a recovery of methane close to 80%. In present days, with increased concerns about greenhouse gas emissions, this process may represent an alternative solution to obtaining new fuels with small emissions of CO2 (methane is the lower hydrocarbon with higher H/C ratio). 4. Equilibrium-Controlled VPSA Process: Zeolite 13X One of the weakest points of the kinetic adsorbents in this separation is that only a small portion of the equilibrium capacity is effectively employed, reducing the productivity of the process. A possibility for increasing the amount of CO2 removed per cycle is to have an adsorbent with fast kinetics and large differences in adsorption equilibrium. To compare the kinetic adsorbent with one material with high equilibrium selectivity toward carbon dioxide, we have employed zeolite 13X. The properties of the column and adsorbent extrudates are shown in Table 7. The same column size and adsorbent weight were employed in these simulations, but the properties of the
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Table 3. Mathematical Model Used in VPSA Modeling for Separation of CH4/CO2 with Zeolite 13X and CMS 3K component mass balance
(
)
∂Ci ∂yi ∂(uiCi) a′kfi ∂ ) c DaxCT - (1 - c) (C - ci) c ∂t ∂z ∂t ∂z Bii + 1 i
LDF equation for the macropores
∂ci ∂〈qi〉 Bii 8Dp,i + Fp ) pKp,i (C - ci); Kp,i ) ∂t ∂t Bii + 1 i R2
p
p
LDF equation for the micropores
∂〈qi〉 15Dµ,i ) Kµ,i(q/i - 〈qi〉); Kµ,i ) ∂t r2
energy balance in the gas phase
∂Tg ∂ ∂ ∂Tg ∂Ct ) + cRgTg cCtC ˜v λ - u i Ct C ˜p ∂t ∂z ∂z ∂z ∂t
c
( )
(1 - c)a′hf (Tg - Ts) energy balance in the solid phase
(1 - )[ ∑ c
p
n i)1
ci C ˜ Vi + Fpwc
∑
n i)1
〈qi〉 C ˜ v,ads,i + FpC ˜ ps
2hw (T - Tw) Rw g ∂Ts
] ∂t )
(1 - ) R T ∂c∂T + F ∑ (-∆H ) ∂〈q∂t 〉 + (1 - )a′h (T - T ) i
c
p g s
i
n i)1
b
i
c
f
g
s
∂Tw ) Rwhw(Tg - Tw) - RwlU(Tw - T∞) ∂t Dw 1 Rw ) ;R ) Dw + e e(Dw + e) wl (Dw + e) ln Dw
FwC ˜ pw wall energy balance
Ergun equation
(
150µg(1 - c) 1.75(1 - c)Fg ∂P )ui + |ui|ui 3 2 ∂z d 3d
( ) [ ∑( )] c
adsorption equilibrium model
q/i
qmax,i
macropore diffusion calculations
)
2
p
q/i
) KiPyi 1 -
i
(
)
qmax,i
c
; Ki ) K0i exp(-∆Hi/RgTs)
1 1 1 ) τp + ; Dk ) 9700rp Dp,i Dm,i Dk,i
adsorbent are somewhat different (particularly adsorbent density). This adsorbent presents large differences in adsorption equilibrium of CO2 (more adsorbed gas) and CH4 as showed in Figure 1, whereas diffusion of both gases is fast. Adsorption equilibrium and kinetic parameters were also previously reported10,20 and parameters obtained from independent measurements of equilibrium and kinetic determination were employed in the modeling of the VPSA process studied in this work. The five-step cycle proposed was also employed to determine the behavior of the zeolite 13X adsorbent with the performance parameters employed for kinetic adsorbents, where the stream exiting the depressurization step was considered to be a product that can be employed in counter-current purge or pressurization steps. As a direct basis of comparison with the kinetic adsorbent, we have employed the cycle depicted in Figure 2. As explained before, the stream exiting the co-current depressurization stream can be recycled to the column at z ) LC (as a pressure equalization step), which is why it was considered to be a product. With equilibrium-based adsorbents, the diffusion of CO2 within the adsorbent is very fast and when the intermediate depressurization is performed, some CO2 rapidly desorbs and exits the column. For this reason, the stream exiting the depressurization step cannot be recycled to z ) LC. The only way to employ this stream in a pressure equalization step is by recycling it to z ) 0: this step should be performed to avoid low recovery of methane. In this way, some CO2 will be used in a “cleaned” column, reducing the capacity of the column to treat fresh feed. This will result in a decrease in unit productivity.
p
ai
x
T Mw
For this reason, in the simulations performed with zeolite 13X, the stream exiting the depressurization step cannot be considered to be product (see Table 2). The scheme of the VPSA cycle configuration employed for simulations of biogas separation with zeolite 13X is shown in Figure 4. Another cycle modification is that the pressurization is done with the feed stream and not with product. As diffusion of both gases is very fast, methane adsorption in the pressurization step was considerable, enhancing the amount of product employed in this step. The amount of gas to be recycled to the column in this co-current pressure equalization step corresponds to 12% of the feed (342.7 mol of CH4 and 168.2 mol of CO2 for a total feed of 3726.3 mol of feed per cycle). The values can be calculated from integration of the values showed in Figure 5e marked as “depressurization release”. The results obtained in the different simulations employing the cycle scheme depicted in Figure 4 are summarized in Table 8. In this table, the initial results with the counter-current pressurization with product are also shown (runs 2-4). It can be observed that when the same cycle configuration is used as with the CMS sample, the recovery of methane is very low. Another negative aspect of the cycle employed for kinetic adsorbents is that in the initial cycles, the amount of methane produced is smaller than the amount required for pressurization and purge, which is why recovery is negative in the first cycles. This means that an additional source of previously purified methane is required or the VPSA cycle has to be operated so as to employ larger adsorption steps in the initial stages, which complicates control of the unit.
Ind. Eng. Chem. Res., Vol. 46, No. 13, 2007 4601 Table 4. Boundary and Initial Conditions of VPSA Process for Fuel Production from Biogas Employing Zeolite 13X and CMS-3K Counter-Current Pressurization with Methane P(LC) ) Pinlet
u(0) ) 0
∂y(i,0)
|
∂z
z-
- y(i,LC)|z- +
y(i,LC)|z+ ) 0 )0
z-
λ
u(0)C(i,0)|z+ ) u(0)C(i,0)|z-
|
Dax ∂y(i,0)
z+
∂z
u(0)
- y(i,0)|z+ +
|
∂Tg(LC) ˜ pTg(LC)|z- + - - uCC ∂z z uCC ˜ pTg(LC)|z+ ) 0
Feed Step P(LC) ) Pexit
|
∂Tg(0)
z+
∂z
- uCC ˜ pTg(0)|z+
|
z-
)0
|
z-
)0
∂y(i,LC) ∂z
y(i,0)|z- ) 0 λ
∂z
u(LC)
|
∂Tg(0) ∂z
|
Dax ∂y(i,LC)
)0
z-
∂Tg(LC) ∂z
Figure 4. VPSA cycle scheme used for CH4-CO2 separation with zeolite 13X (CECA): (1) co-current pressurization with feed; (2) feed; (3) intermediate depressurisation; (4) counter-current blowdown; (5) countercurrent purge with product.
uCC ˜ pTg(0)|z- ) 0 Counter-Current Blowdown P(0) ) (Pfeed - Pblow) × u(LC) ) 0 exp(-0.1t - (N - 1)ttotal (tpress + tfeed)) + Pblow
| |
∂y(i,0) ∂z
z-
)0
z+
)0
∂Tg(0) ∂z
∂z
P(0) ) Pexit
∂y(i,0)
|
z-
∂z
)0
| |
∂y(i,LC) ∂z ∂Tg(LC)
z-
)0
z-
)0
Counter-Current Purge with Methane u(LC)C(i,LC)|z+ ) u(LC)C(i,LC)|z-
|
Dax ∂y(i,LC) u(LC)
∂z
z-
- y(i,LC)|z- +
y(i,LC)|z+ ) 0
|
∂Tg(0) ∂z
z-
)0
λ
|
∂Tg(LC) ∂z
z-
- uCC ˜ pTg(LC)|z- +
uCC ˜ pTg(LC)|z+ ) 0 Initial Conditions of the VPSA Column q(i,z) ) 0 Tg(z) ) Ts(z) ) Tw(z) ) 301 K P(z) ) 120 kPa y(CH4,z) ) y(CO2,z) ) y(N2,z) ) 0 ; y(He,z) ) 1
It can be observed in Table 8 that when methane purity is higher than 98%, the product recovery is small (less than 50%). One of the reasons for this low recovery is that the adsorption equilibrium isotherm of CO2 at temperatures around the ambient temperature is very steep. The difficulty in desorbing the CO2, associated with a large heat of adsorption, decreases the capacity of the bed severely. In the feed step, the temperature increases around 70 K in the initial cycles (fresh adsorbent) and around 30 K in the adsorption zone when CSS is achieved. The behavior of the VPSA process for run 3 (see Table 8) is shown in Figure 5. It can be observed that the amount of CO2 adsorbed at the end of the feed step is clearly displaced during the intermediate depressurization step (shaded area in Figure 5d). As a consequence of this displacement, a peak of CO2 is observed in the molar flowrate exiting the column, which indicates that is impossible to employ this stream as product. Another interesting feature presented when using this adsorbent is the heat effects also shown in Figure 5f. Oscillations at temperatures higher than 30 K are observed in practically the entire column. This temperature increase is detrimental in terms of bed capacity:
during the adsorption step, the temperature increases, reducing the capacity of the bed, and starts to decrease in the desorption steps (blowdown and purge), increasing the CO2 capacity in steps for which CO2 is to be desorbed from the column. On the other side, the increase in temperature facilitates the CO2 desorption in the blowdown step. If the column loses part of the heat generated in the adsorption (feed) step, the blowdown step may reach temperatures lower than the feed temperature, where the isotherm of CO2 is much steeper. On the other side, in the blowdown step, the temperature decreases, increasing CO2 capacity and isotherm steepness and reducing its desorption and thus the overall bed capacity. A technological alternative to the observed heat effects can be solved by using PSA columns with intensive heat transfer, like a heat exchanger. As an example of the possibility of process improvement that can be reached with enhanced heat transfer, we have made simulations on a system in which the columns are composed of 20 equal and smaller columns that have the same total adsorbent volume, as in the previous example, and that process the same step flowrates. The columns have also the same spatial properties (like porosity, bed length, bed density, etc.) in both examples. The same mathematical model was applied just by changing the column diameter and step flowrates of each column to obtain the same gas velocity. The comparison is shown in Table 8 (simulation 3 and simulation 4, where the column is divided into 20 subcolumns). The recovery increases to 40% starting from 22%, although this value is still small. This small recovery is due to the large amount of methane required to pressurize the bed (almost 1 mol/kg) being adsorbed from the low pressure till feed pressure. The only solution to this problem is to modify the cycle and employ methane from the feed and adsorb CO2 in the pressurization step (cycle scheme shown in Figure 4). Simulations 5 and 6 were performed using this strategy. It can be observed that recovery of CH4 is higher than 58% in both runs, although in this case, purity is not above 98%. This solution of subdividing the column into smaller units for thr enhancement of heat transfer will not be a very interesting solution for the case of kinetic adsorbents: the temperature profile only advances in less than 40% of the column (see Figure 3h), whereas in the case of equilibrium adsorbents, temperature increase is observed in almost the whole length of the column. The preliminary results of biogas separation using zeolite 13X are not as good as expected. There are several ways to improve the behavior of this adsorbent for biogas separation, most of them applicable to small- and medium-sized units. One of them is to reduce the blowdown pressure, even though power
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Figure 5. Simulations of VPSA cycle employing zeolite 13X as selective adsorbent with cycle scheme showed in Figure 2. Gas-phase concentration of (a) CH4 and (b) CO2, amount adsorbed of (c) CH4 and (d) CO2; (e) molar flowrate at the exit of the column, (f) temperature histories for cyclic steady state in different locations of the column (1, 2, 3, and 4 m from feed inlet). Experimental conditions are detailed in Table 8 (run 3). Numbers in (a-d) correspond to 1,pressurization; 2, feed; 3, intermediate depressurization; 4, blowdown; 5, purge. Table 5. VPSA Parameters Employed in the Simulation of Biogas Purification to Obtain Fuel-Grade Methane Using CMS-3K Adsorbent param column length (m) column radius (m) column porosity column density (kg/m3) feed flowrate (SLPM) pressurization flowrate (SLPM) purge flowrate (SLPM)
value
param
value
4.667 0.4667 0.33 715.43 16666.7 10000 500
(kg/m3)
1060 0.46 9 × 10-4 3 880 25 10
pellet density pellet porosity extrudate radius (m) macropore radius (µm) adsorbent specific heat (J kg-1 K-1) overall heat transfer (W m-2 K-1) blowdown pressure (kPa)
consumption may be high, which is a penalty in overall biogas recovery, considering that power should be produced from biogas. Another possibility is to increase the heat exchange in the columns. This may reduce the temperature oscillations in the cycle approaching the isothermal behavior.
the energy requirements of the VPSA unit. As a first approximation, we have calculated the power requirements by adiabatic compression with the following equation
5. Power Consumption of the VPSA Process
where γ ) Cp/Cv (equal to 3/2 for ideal gases), Rg is the universal gsd constant, Phigh is the discharge pressure, Plow is the suction or blowdown pressure, B˙ is the molar flowrate to be compressed, and η is the mechanical efficiency, which typically assumes a value of 0.8. For the compression of methane from 800 to 20 000 kPa, γ ) 1.31was employed.
For the removal of CO2 for biogas upgrade, the biogas stream was compressed up to 800 kPa. The CH4 obtained as product stream from the VPSA process should be further compressed for use in cylinders as fuel. In this work, we will evaluate the required energy for compression of the different streams and
Power )
( ) [( ) Phigh γ RgTfeed γ-1 Plow
γ-1/γ
-1
]
B˙ 1000η
(2)
Ind. Eng. Chem. Res., Vol. 46, No. 13, 2007 4603 Table 6. Simulation Results for Methane Purification from Biogas Using CMS-3K for Different Step Times and Pressure Conditions at 306 Ka run
Qfeed (SLPM)
tfeed (s)
tdepres (s)
tblow (s)
Pfeed (kPa)
Pinter (kPa)
purity (CH4%)
recovery (CH4%)
productivity (mol of CH4 h-1 kg-1)
A 1 2 3 4 5
16666.7 16666.7 16666.7 16666.7 16666.7 16000
135 135 135 135 130 130
0 10 10 10 10 10
160 160 160 160 140 140
600 600 800 800 800 800
200 200 200 250 250 250
99.1 97.2 97.3 97.8 97.9 98.1
53.1 85.7 85.6 81.5 80.8 79.7
2.63 4.33 4.32 4.09 4.05 3.83
a
Pressurization time ) 70; surge step ) 50 s. All other parameters are detailed in Table 1.
Table 7. VPSA Parameters Employed in the Simulation of Biogas Purification to Obtain Fuel-Grade Methane Using Zeolite 13X (CECA) Adsorbent param
value
param
value
column length (m) column radius (m) column porosity column density (kg/m3) pellet density (kg/m3) purge flowrate (SLPM)
4.667 0.4667 0.33 756.46 1130 500
pellet porosity extrudate radius m macropore radius µm adsorbent specific heat (J kg-1 K-1) overall heat transfer (W/ m-2 K-1) blowdown pressure (kPa)
0.54 8 × 10-4 1.6 920 25 10
Table 8. Simulation Results for Methane Purification from Biogas Using Zeolite 13X for Different Step Times and Pressure Conditions at 306 Ka run
Qfeed (SLPM)
tfeed (s)
tdepres (s)
tblow (s)
Pfeed (kPa)
Pinter (kPa)
purity (CH4%)
recovery (CH4%)
productivity (mol of CH4 h-1 kg-1)
2,1b 3b 4b,c 5d 6d
25 000 25 000 25 000 25 000 23 000
200 220 220 120 120
10 10 10 10 10
140 140 140 140 140
800 800 800 800 800
250 250 250 250 250
97.1 99.4 98.6 92.8 95.0
60.7 22.3 41.2 60.5 58.3
4.35 1.56 2.91 4.54 4.27
a Pressurization time ) 70 s; purge step-time ) 50 s. All other parameters are detailed in Table 3. b Counter-current pressurization with product. Pressurization flowrate ) 23 000 SLPM; pressurization time ) 70 s. c Overall heat-transfer coefficient ) 50 W m-2 K-1; hw ) 100 W m-2 K-1 instead of 30. d Purge flowrate ) 5000 SLPM; purge step-time ) 50 s.
Table 9. Energy Requirements for VPSA Process for CO2 Removal from Biogas Using CMS-3K and Zeolite 13X (for experimental conditions, see Tables 6 and 8) energy requirements
CMS-3K, run 5
Zeolite 13X, run 1
compression to 800 kPa (kW) compression to 20 000 kPa (kW) power for purge step (kW) blowdown step (kW) total power (kW) consumption per mol (kW/mol)
57.7 73.2 28.1 129.8 288.8 0.27
90.2 87.6 62.5 282.5 522.8 0.41
To calculate the total power consumption of the whole system, we have assumed that the biogas is available at 200 kPa. For a continuous process, the whole stream will be compressed up to 800 kPa, where the removal of CO2 takes place. The purified CH4 (VPSA product) will be further compressed to 20 000 kPa. Additional energy consumption is caused by the vacuum pump of the VPSA unit performing the blowdown and purge steps. The blowdown energetic consumption is from decompression from the intermediate pressure (250 kPa) to the final blowdown pressure (10 kPa), whereas for the purge, the product is available at 800 kPa and is employed at 10 kPa. The power consumption of both processes was estimated using adiabatic compression, and the results for both processes are detailed in Table 9. Note that the amount of power consumed by both processes does not correspond to the same flowrate (16 000 SLPM for CMS-3K and 25000 SLPM for zeolite 13X). To normalize, we have divided the total power requirements by the number of moles obtained as product. It can be observed that in the cases studied, the power requirements obtained for CMS-3K are much smaller than the ones obtained for zeolite 13X. However, it should be noted that the power requirements for the process may be far from ideal because this was not considered initially as a parameter to be optimized and the values
given in this work represent only an indicative value of energy consumption for biogas upgrading. 6. Conclusions Purification of biogas to obtain fuel-grade methane was studied employing a vacuum pressure swing adsorption (VPSA) process. Two different cases were evaluated: equilibrium- and kinetic-based separation employing zeolite 13X and carbon molecular sieve 3K, respectively. For the kinetic adsorbent CMS-3K, a five-step cycle configuration (feed, intermediate depressurization, blowdown, purge, and pressurization) was employed. When comparing a cycle with and without intermediate depressurization, the addition of this step in the process produced an immediate increase in product recovery to almost 80% without significant reduction in methane purity. The same cycle steps were employed in the case of equilibrium-based adsorbent zeolite 13X, although the cycle configuration was somewhat different: the stream exiting the depressurization step has to be recycled as feed and pressurization is done with the feed stream. Unit productivities obtained employing the CMS 3K adsorbent were much higher that those obtained with zeolite 13X. Several process innovations should be introduced if zeolite 13X is to be employed as adsorbent in order to overcome some problems with this adsorbent: a very low pressure is required in blowdown because of isotherm steepness and large heat effects within one cycle. Power consumption for both examples was calculated. In the conditions employed, the consumption using CMS-3K adsorbent was 0.27 kW/mol of product, whereas for zeolite 13X, the power consumption was 0.41 kW/mol of product.
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Acknowledgment The authors thank the Foundation for Science and Technology (FCT) for the financial support through Projects POCI/EQU/ 59330/2004 and POCI/N001/2005. Notation a′ ) area to volume ratio (m-1) ai ) number of neighboring sites occupied by a molecule of component i Bii ) Biot number of component i ci ) averaged concentration in the macropores for component i (mol/m3) Ci ) concentration of component i in the gas phase (mol/m3) C ˜ p ) molar constant pressure specific heat of the gas mixture (J/molK) C ˜ ps constant pressure specific heat of the adsorbent (J kg-1 K-1) C ˜ pw ) specific heat of the column wall (J kg-1 K-1) C ˜ vi ) molar constant volumetric specific heat of component i (J mol-1 K-1) C ˜ v,ads,ii ) molar constant volumetric specific heat of component i adsorbed (J mol-1 K-1) CT ) total gas concentration (mol/m3) dp ) pellet diameter (m) Dax ) axial dispersion coefficient (m2/s) Dp,i ) macropore diffusivity of component i (m2/s) Dm,i ) molecular diffusivity of component i (m2/s) Dk,i ) Knudsen diffusivity of component i (m2/s) Dw ) internal diameter of the column (m) Dµ,i ) micropore diffusivity of component i (m2/s) o ) limiting diffusivity at infinite temperatures for compoDµ,i nent i (m2/s) e ) column wall thickness (m) Ea,i ) activation energy of micropore diffusion for component i (kJ/mol) Eb,i ) micropore surface barrier activation energy for component i (kJ/mol) hf ) film heat-transfer coefficient between the gas and the solid phase (W m-2 K-1) hw ) film heat-transfer coefficient between the gas phase and the column wall (W m-2 K-1) kfi ) film mass-transfer coefficient (m/s) Ki ) adsorption equilibrium constant of component i (kPa-1) Koi adsorption equilibrium constant at the limit T f ∞ of component i (kPa-1) Kµ,i ) LDF constant for mass transfer in the micropores for component i (m/s) Kp,i ) LDF constant for mass transfer in the macropores for component i (m/s) LC ) column length (m) n ) number of columns in the PSA unit N ) cycle number n˘ feed ) moles of biogas available per unit of time (mol/s) P ) total pressure (kPa-1) Pblow ) total pressure (kPa-1) Pfeed ) feed pressure (kPa--) Pinter ) intermediate pressure (kPa-1) qi ) adsorbed phase concentration of component i (mol/kg) q/i ) adsorbed gas-phase concentration in the equilibrium state of component i (mol/kg) 〈qi〉 ) extrudate averaged adsorbed phase concentration of component i (mol/kg) qmax,i ) maximum amount adsorbed of component i according to the multisite Langmuir model (mol/kg)
Qfeed ) feed flowrate (min-1) Qpress ) pressurization flowrate (min-1) Qpurge ) purge flowrate (min-1) rc ) radius of the zeolite crystal (m) Rc ) radius of the PSA column (m) Rp ) radius of the adsorbent extrudate (m) Rg ) universal gas constant (J/molK) Rw ) radius of the column wall (m) tblow ) counter-current blowdown step time (s) tdepress ) intermediate depressurization step time (s) tfeed ) feed step time (s) tpress ) pressurization step time (s) tpurge ) purge step time (s) Tg ) temperature of the gas phase (K) Ts temperature of the solid phase (K) Tw ) temperature of the column wall (K) T∞ ) temperature outside the column (considered constant over each run) (K) u ) superficial velocity of component i (m/s) U ) global external heat-transfer coefficient (W m-2 K-1) yi ) molar fraction of component i yCH4,feed ) molar fraction of methane in the feed Greek Letters Rw ) ratio of the internal surface area to the volume of the column wall (m-1) Rwl ) ratio of the logarithmic mean surface area of the column shell to the volume of the column wall (m-1) Fb ) bulk density of the column (kg/m3) Fg ) gas density (kg/m3) Fp ) adsorbent (particle) density (kg/m3) Fw ) column wall density (kg/m3) λ ) axial heat dispersion (W m-2 K-1) -∆Hi ) isosteric heat of adsorption of component i (kJ/mol) c ) porosity of the column p ) porosity of the extrudate τp ) extrudate tortuosity ωads ) weight of adsorbent loaded in each PSA column µg ) gas viscosity (Pa s) Literature Cited (1) Key GHG Data; United Nations Framework Convention on Climate Change: Bonn, Germany, 2005; http://unfccc.int/essential_background/ background_publications_htmlpdf/items/3604.php (accessed February 2007). (2) Relato´ rio do Estado do Ambiente 2003; Instituto do Ambiente, Ministerio do Ambiente e do Ordenamento do Territo´rio: Amadora, Portugal, 2005. (3) Goossens, M. A. Landfill Gas Power Plants. Renewable Energy 1996, 9, 1015. (4) Hagen, M.; Polman, E.; Jensen, J. K.; Myken, A.; Jo¨nsson, O.; Dahl, A. Adding gas from biomass to the gas grid. Report SGC 118, Contract XVII/4.1030/Z/99-412; Swedish Gas Centre: Malmo¨, Sweden, 2001. (5) Franklin County Sanitary LandfillsLandfill Gas (LFG) to Liquefied Natural Gas (LNG)sProject; National Renewable Energy Laboratory: Golden, CO, 2005; http://www.eere.energy.gov/afdc/pdfs/landfillreportfinal.pdf (accessed February 2007). (6) Sircar, S. Pressure Swing Adsorption. Ind. Eng. Chem. Res. 2002, 41, 1389. (7) Sircar, S. High Efficiency Separation of Methane and Carbon Dioxide Mixtures by Adsorption. Adsorpt. Ion Exch. AIChE Symp. Ser. 1988, 84, 70. (8) Daiminger, U.; Lind, W. Adsorption Processes for Natural Gas Treatment, A Technology Update; Engelhard: Iselin, NJ; http:/http:// www.engelhard.com/documents/Adsorption %20Process%20for%20Natural% 20Gas%20Treatment%20paper.pdf (accessed December 2006). (9) Knaebel, K. S.; Reinhold, H. E. Landfill Gas: From Rubbish to Resource. Adsorption 2003, 9, 87.
Ind. Eng. Chem. Res., Vol. 46, No. 13, 2007 4605 (10) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Adsorption Equilibrium of Methane, Carbon Dioxide and Nitrogen on Zeolite 13X at High Pressures. J. Chem. Eng. Data. 2004, 49, 1095. (11) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Upgrade of Methane from Landfill Gas by Pressure Swing Adsorption. Energy Fuels 2005, 19, 2545. (12) Da Silva, F. A. Cyclic Adsorption Processes: Application to Propane/Propylene Separation. Ph.D. Dissertation, University of Porto, Portugal, 1999. (13) Srinivasan, R.; Auvil, S. R.; Schork, J. M. Mass transfer in carbon molecular sievessan interpretation of Langmuir kinetics. Chem. Eng. J. 1995, 57, 137. (14) Caro, J.; Bulow, M.; Karger, J. Comment on hydrocarbon diffusivity in zeolites. Chem. Eng. Sci. 1985, 40, 2169. (15) Bar, N. K.; McDaniel, P. L.; Coe, C. G.; Seiffert, G.; Karger, J. Measurement of intracrystalline diffusion of nitrogen in zeolites NaX and NaCaA using pulsed field gradient NMR. Zeolites 1997, 18, 71. (16) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984.
(17) Silva, J. A. C.; Rodrigues, A. E. Analysis of ZLC Technique for Diffusivity Measurements in Bidisperse Porous Adsorbent Pellets. Gas Sep. Purif. 1996, 10, 207. (18) Ahn, H.; Moon, J.-H.; Hyun, S.-H.; Lee, C.-H. Diffusion Mechanism of Carbon Dioxide in Zeolite 4A and CaX Pellets. Adsorption 2004, 10, 111. (19) Kim, M.-B.; Bae, Y.-S.; Choi, D. K.; Lee, C.-H. Kinetic Separation of Landfill Gas by a Two Bed Pressure Swing Adsorption Process Packed with Carbon Molecular Sieve: Nonisothermal Operation. Ind. Eng. Chem. Res. 2006, 45, 5050. (20) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Separation of CH4/ CO2/N2 Mixtures by Layered Pressure Swing Adsorption for Upgrade of Natural Gas. Chem. Eng. Sci. 2006, 61, 3893.
ReceiVed for reView October 18, 2006 ReVised manuscript receiVed February 24, 2007 Accepted April 16, 2007 IE061341+
