8084
Ind. Eng. Chem. Res. 2005, 44, 8084-8094
Optimization of Pressure Swing Adsorption and Fractionated Vacuum Pressure Swing Adsorption Processes for CO2 Capture Daeho Ko,† Ranjani Siriwardane,‡ and Lorenz T. Biegler*,† Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, and National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia 26507
This work focuses on the optimization of cyclic adsorption processes to improve the performance of CO2 capture from flue gas, consisting of nitrogen and carbon dioxide. The adopted processes are the PSA (pressure swing adsorption) process and the FVPSA (fractionated vacuum pressure swing adsorption) process, modified from the FVSA (fractionated vacuum swing adsorption) process developed by Air Products and Chemicals, Inc. The system models are currently bench scale and adopt zeolite13X as an adsorbent. The high-temperature PSA is better for high purity of product (CO2), and the high-temperature FVPSA is much better than the normal-temperature PSA processes. The main goal of this study is to improve the purity and recovery of carbon dioxide. The Langmuir isotherm parameters were calculated from experimental data taken at National Energy Technology Laboratory (Siriwardane, R.; NETL, DOE, 2004). Moreover, efficient optimization strategies are essential to compare these processes. To perform optimization work more efficiently, we modified the previous optimization method by Ko et al. (Ind. Eng. Chem. Res. 2003, 42, 339-348) in a manner similar to that by Jiang et al. (AIChE J. 2003, 49, 11401157). This allows us to obtain optimization results with more accurate cyclic steady states (CSSs), better convergence, and faster computation. As a result, optimal conditions at CSS are found for these systems. 1. Introduction As discussed in the report of Kessel et al.,5 almost 42% of industrial CO2 emissions are from energy conversion. Because the CO2 accumulation of greenhouse gases may seriously affect the global climate, efficient capture of carbon dioxide is very important. One way to mitigate CO2 accumulation in the air is to capture CO2 from the emission sources and inject it into the ocean.6 Gas absorption has been used to recover CO2; however, this process is energy-consuming for the regeneration of solvent and has corrosion problems.7 On the other hand, gas-solid adsorption processes may be applicable for the removal of CO2 from power plant flue gas. A few cyclic adsorption processes are used commercially for the regeneration of CO2.8 In pressure swing adsorption (PSA) and vacuum pressure swing adsorption (VPSA), the adsorbent is regenerated by decreasing the total or partial pressure. Thermal (or temperature) swing adsorption (TSA) regenerates the sorbent by increasing temperature. PSA processes have been suggested as an energy-saving process and as an alternative to traditional separations, distillation, and absorption3 for bulk gas separations such as CO2 capture. To dispose of CO2 to the ocean or depleted oil fields, CO2 needs to be highly concentrated.7 In this sense, PSA or VPSA processes may be useful. PSA operation has initially adopted the steps of the classical Skarstrom cycle:9 pressurization with feed, adsorption with high pressure, depressurization, and purge. In the 1960s, a pressure equalization step was suggested to save repressurization energy after the purge step.10-12 Since the 1980s, VSA has also been * Corresponding author. Tel.: (412) 268-2232. Fax: (412) 268-7139. E-mail:
[email protected]. † Carnegie Mellon University. ‡ National Energy Technology Laboratory.
attractive in enhancing regeneration efficiency.13-15 Among the many applications of PSA processes, the production of top-product- and bottom-product-enriched gases from feed gas is very important, but almost all the PSA processes produce only top-product- or bottomproduct-enriched gases. This characteristic is based on the following reasons.16 First, the gas-phase bed concentration of the strong adsorbate is not high. Instead, the strong species lie in the void space of the adsorbent, and thus, the released vent gas also has a high concentration of weak adsorbate, which is discarded. Consequently, in these PSA processes, only one productenriched stream is produced at the feeding step. Air Products solved this problem by using a vacuum swing adsorption (VSA) process. The key technology of the VSA in air separation is to introduce a nitrogen-rinse step after the air-adsorption step.17 Moreover, in the 1990s, a fractionated vacuum swing adsorption (FVSA) process was developed by Air Products, which simultaneously produces a 98+% nitrogen-enriched gas and an 80-90% oxygen-enriched gas from ambient air.16,18 The FVSA process studied is a dual-bed, four-step process which simultaneously produces concentrated oxygen and nitrogen with ambient air as the feed.16,18 Our previous work3 treated the optimization of PSA to remove CO2 to obtain high N2 purity. However, the previous model needs to be updated because its CO2 purity and recovery were not high. So the current work adopts new isotherm data ranging from 303.15 K to 390.15 K and optimizes three types of adsorption processes: a normal-temperature PSA, a high-temperature PSA, and a modified fractionated vacuum pressure swing adsorption (FVPSA) process, based on the FVSA concept, to improve the CO2 purity as well as the N2 purity. The PSA operation adopts a Skarstrom cycle and the modified FVPSA operation consists of four steps: pressurization, adsorption, cocurrent blowdown,
10.1021/ie050012z CCC: $30.25 © 2005 American Chemical Society Published on Web 09/13/2005
Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005 8085 Table 1. Parameters for Adsorption Models parameters
values
bed radius (Rbed) pore diameter (Dpore) particle radius (Rparticle) particle tortuosity (τparticle) particle porosity (DM) diffusion volume (Dv) bed density (Fbed) wall density (Fwall) bed void (bed) particle density (FDM) R heat capacity of solid (Cps)
1.1 × 10-2 m 1.0 × 10-9 m 1.0 × 10-3 m 4.5 0.38 26.9 (CO2); 18.5 (N2) 1.06 × 103 kg/m3 7.8 × 103 kg/m3 0.348 1.87 × 103 kg/m3 8.314 J/mol/K 504 J/kg/K
and countercurrent regeneration. In FVPSA, nitrogen is produced at the top of the bed during the adsorption and cocurrent blowdown steps, and carbon dioxide is obtained at the bottom of the bed during the countercurrent regeneration step. To calculate the gas velocity of the boundary during the pressure-change step, valve equations are used.19 This study presents an updated PSA optimization method from the previous study3 and performs optimizations of the PSA and FVPSA processes. The next section describes the operating procedures of the target processes and model equations. Section 3 then introduces the updated optimization strategy and compares the previous optimization method with the new one. Section 4 presents the optimization results, while Section 5 summarizes and concludes this study. 2. Operations of Target Processes and the Model Equations 2.1. Target Processes. The target processes are PSA and FVPSA, currently at bench scale as in our previous work.2,3 The FVPSA cycle is modified from FVSA from Air Products. The adsorbent is zeolite13X, and the feed gas consists of 85% nitrogen and 15% carbon dioxide. The parameters for the adsorption model are shown in Table 1. The operation steps of the cyclic processes are shown in Figure 1. The previous work2,3 explains the PSA operation adopted in this study: (1) pressurization step with feed gas at high pressure, (2) adsorption step with feed gas producing N2-rich product at the top of the bed, (3) depressurization step to atmospheric pressure (∼1 atm) with CO2-rich exhaust exiting at the bottom of the bed, and (4) purge step with the carrier gas (pure N2) at atmospheric pressure (∼1 atm) regenerating CO2-rich exhaust from the adsorbent. The FVPSA operation also consists of four steps: (1) pressurization step with feed at high pressure, (2) adsorption step with feed at high pressure producing
Figure 1. Four-step operation of PSA and FVPSA processes.
Table 2. Values of Parameters of the Dual-Site Langmuir Isotherm k1,i(1) k2,i(1) k3,i(1) k4,i(1) k1,i(2) k2,i(2) k3,i(2) k4,i(2)
CO2 (i ) 1)
N2 (i ) 2)
units
2.817 269 -3.5 × 10-4 2.83 × 10-9 2 598.203 3.970 888 -4.95× 10-3 4.411× 10-9 3 594.071
1.889 581 045 -22 462 × 10-4 1.163 388 × 10-9 1 944.605 788 1.889 581 045 -2.246 2× 10-4 1.163 388× 10-9 1 944.605 788
mol/kg 1/K 1/Pa K mol/kg 1/K 1/Pa K
N2, (3) cocurrent blowdown step (blowdown effluent step) to intermediate pressure (∼1 atm) exhausting the top product (N2), and (4) countercurrent blowdown step (countercurrent regeneration step) at low pressure (∼0.1-0.7 atm) obtaining product (CO2) at the bottom of the bed. 2.2. Model Equations. The following model assumptions and equations are adopted in this study. The current assumptions 1-5 are the same as the previous work,2,3 and assumptions 6-9 are different. 1. The gas phase follows ideal gas law. 2. Radial variation of temperature, pressure, and concentration is neglected. 3. Competitive adsorption behaviors are described by the Langmuir equation for the mixture gas. 4. The adsorption rate is approximated by the linear driving force (LDF) expression. 5. The physical properties of the bed are independent of the temperature. 6. The axial diffusion coefficient is affected by temperature. 7. Pressure drop along the bed is calculated by the Ergun equation. 8. The superficial velocity along the bed is calculated by nonisothermal overall mass balance equations. 9. During the pressure-change step (pressurization and depressurization of PSA; pressurization, cocurrent blowdown, and regeneration steps of FVPSA), the superficial velocity profile is linear along the bed and affected by the valve equation. From additional numerical experiments, we found this assumption to be reasonable. The following dual-site Langmuir isotherm describes the adsorption equilibrium.
q/i )
qmi(1)bi(1)Pi
+
qmi(2)bi(2)Pi
n
1+
bi(1)Pi ∑ i)1
n
1+
(1)
bi(2)Pi ∑ i)1
The isotherm parameters are calculated by the following equations (eqs 2a-2d) depending on the temperature, with a range from 303.15 to 393.15 K.
qmi(1) ) k1,i(1) + k2,i(1)T
(2a)
bi(1) ) k3,i(1) exp(k4,i(1)/T)
(2b)
qmi(2) ) k1,i(2) + k2,i(2)T
(2c)
bi(2) ) k3,i(2) exp(k4,i(2)/T)
(2d)
The isotherm parameter values, which are shown in Table 2, were obtained from experimental data taken at National Energy Technology Laboratory (NETL). The isotherm parameter values calculated by using a non-
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Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005
Table 3. Model Equations of PSA and FVPSA Processes component mass balance
-Dx
[
∂2yi ∂z2
+ 2T
∂yi
( ){ ( )} ( )( )( )]
∂u ∂z
+
u ∂P P ∂z
∂ 1
∂z
∂z T
∂yi
+u
∂t overall mass balance
∂yi
() ()
∂ 1
+ uT
+T
∂z T
FparticleRT 1 - bed P pressure drop: Ergun eq
-
P
∂z
+
∂z
(
)
n ∂q ∂qi i RT 1 - bed Fparticle )0 - yi P bed ∂t i)1 ∂t
+
∂z
(3)
1 ∂yi ∂P
+2
∂ 1
n
∂2 1
+
∂z2 T
1 ∂2P P ∂z2
( )( )( ( ))]
+2
T ∂P
∂ 1
P
∂z T
∂z
+
(4)
∂qi
i)1
(1 - bed)2
2 particle
P ∂t
[ ()
- Dx T
∑ ∂t ) 0
bed
∂P µu ) 150 ∂z 4R
1 ∂P
+
∂t T
∑
bed
3
(1 - bed) + 1.75 u|u|Fgas 2Rparticlebed3
(5)
linear driving force model
∂qi 15De,i ) (q/i - qi) ∂t (R )2
(6)
diffusion coefficients
particle DKDM De ) τparticle DK + DM
(7a)
particle
DK ) 48.5Dpore
100T1.75 DM ) energy balance of gas w/in the bed
x
x
P(DvN2
1/3
MwN2MwCO2 + DvCO21/3)2 ∂T
∂t ∂qi
n
∑∆H
i
i)1
isosteric heat of adsorption
-∆H ) R
[
d ln P d(1/T)
valve eq
R u ) Cv πRb2
R
u ) Cv πRb2
where
(7c)
MwN2 + MwCO2
(tFgasCpg + FbedCps) Fbed
(7b)
T Mw
x x
]
+ FgasCpgbedu +
∂t
∂T ∂z
- KL
∂2T
-
(8)
∂z2
2hi
(T - Twall) ) 0 Rbed (9)
q
T
1.179
n
∑y M i
wi
x
Phigh2 - Plow2 , P2
if Plow > 0.53Phigh
i)1
T n
∑y M i
Phigh , P
(10)
if Plow e 0.53Phigh
wi
i)1
Phigh g Plow P ) Phigh if the gas stream is leaving the bed P ) Plow if the gas stream is entering the bed
linear regression method agree well with the experimental data, as shown in Figure 2. For the whole temperature range (303.15-393.15 K), the selectivity of CO2 over N2 is very high, as shown in Figure 2. Tables 3 and 4 list the model equations and mole flux variables to calculate the performances (purities and recoveries), respectively. The mass balance equations are also derived in the Appendix. The boundary conditions for each operating step are shown in Table 5.
Here, the LDF model is used with the mass transfer coefficients defined in eqs 6 and 7. For this study, these coefficients, described in ref 14, only represent an approximation. We note that more accurate models have been proposed in ref 15; they can be applied here as well with the same optimization approaches. The valve equations of Table 3 are used to calculate the gas velocity during the pressure-change steps, i.e., pressurization and depressurization steps for the PSA, and
Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005 8087
Figure 2. Adsorption isotherms at different temperatures (303.15-393.15 K) on zeolite13X. Table 4. a. Mole Flux Variables at Each Operating Step of PSA [3] pressurization
adsorption
depressurization
purge
∂(feedi)/∂t ) uPi/RT|z)0 ∂(producti)/∂t ) 0 ∂(exhausti)/∂t ) 0 ∂(purge feedi)/∂t ) 0
∂(feedi)/∂t ) uPi/RT|z)0 ∂(producti)/∂t ) uPi/RT|z)L ∂(exhausti)/∂t ) 0 ∂(purge feedi)/∂t ) 0
∂(feed)/∂t ) 0 ∂(producti)/∂t ) 0 ∂(exhaust)/∂t ) -uPi/RT|z)0 ∂(purge feedi)/∂t ) 0
∂(feed)/∂t ) 0 ∂(producti)/∂t ) 0 ∂(exhaust)/∂t ) -uPi/RT|z)0 ∂(purge feedi)/∂t ) -uPi/RT|z)L
b. Mole Flux Variables at Each Operating Step of FVPSA pressurization
adsorption
cocurrent blowdown
countercurrent regeneration
∂(feedi)/∂t ) uPi/RT|z )0 ∂(producti)/∂t ) 0 ∂(exhausti)/∂t ) 0 ∂(purge feedi)/∂t ) 0
∂(feedi)/∂t ) uPi/RT|z )0 ∂(producti)/∂t ) uPi/RT|z)L ∂(exhausti)/∂t ) 0 ∂(purge feedi)/∂t ) 0
∂(feed)/∂t ) 0 ∂(producti)/∂t ) uPi/RT|z)L ∂(exhausti)/∂t ) 0 ∂(purge feedi)/∂t ) 0
∂(feed)/∂t ) 0 ∂(producti)/∂t ) 0 ∂(exhaust)/∂t ) -uPi/RT|z)0 ∂(purge feedi)/∂t ) 0
are calculated by
Table 5. a. Boundary Conditions of PSA Operation pressurization
adsorption
depressurization
regeneration
yi|z)0 ) yf,i ∂yi/∂z|z)L ) 0
yi|z)0 ) yf,i ∂yi/∂z|z)L ) 0
∂yi/∂z|z)0 ) 0 ∂yi/∂z|z)L ) 0
T|z)0 ) Tfeed ∂T/∂z|z)L ) 0 u|z)0 W eq 10 u|z)L ) 0
T|z)0 ) Tfeed ∂T/∂z|z)L ) 0 u|z)0 ) ufeed u|z)L W eq 4
∂T/∂z|z)0 ) 0 ∂T/∂z|z)L ) 0 u|z)0 W eq 10 u|z)L ) 0
yi/∂z|z)0 ) 0 yCO2|z)L ) 0; yN2|z)L ) 1 ∂T/∂z|z)0 ) 0 T|z)L ) Tpurge u|z)0 W eq 4 u|z)L ) upurge
purityCO2,ave )
pressurization
adsorption
yi|z)0 ) yf,i ∂yi/∂z|z)L ) 0 T|z)0 ) Tfeed ∂T/∂z|z)L ) 0 u|z ) 0 W eq 10 u|z)L ) 0
yi|z)0 ) yf,i ∂yi/∂z|z)L ) 0 T|z)0 ) Tfeed ∂T/∂z|z)L ) 0 u|z ) 0 ) ufeed u|z)L W eq 4
∂yi/∂z|z)0 ) 0 ∂yi/∂z|z)L ) 0 ∂T/∂z|z)0 ) 0 ∂T/∂z|z)L ) 0 u|z ) 0 ) 0 u|z)L W eq 8
countercurrent regeneration ∂yi/∂z|z)0 ) 0 ∂yi/∂z|z)L ) 0 ∂T/∂z|z)0 ) 0 ∂T/∂z|z)L ) 0 u|z)0 W eq 10 u|z)L ) 0
pressurization, cocurrent blowdown, and countercurrent regeneration steps for FVPSA. On the basis of the mole flux variables of Table 4, the purities and recoveries of CO2 (i ) 1) and N2 (i ) 2)
2
2
(11)
∫(∑exhausti) dt|exhaust step i)1
purityN2,ave )
b. Boundary Conditions of FVPSA Operation cocurrent blowdown
∫(exhaustCO ) dt|exhaust step
∫(productN ) dt|product step 2
2
(12)
∫(∑producti) dt|product step i)1
∫exhaustCO dt|exhaust step ∫feedCO dt|feed step
(13)
∫productN |product step - ∫purgeN |purge step ∫feedN |feed step
(14)
recoveryCO2,ave )
2
2
recoveryN2,ave ) 2
2
2
where feed step of PSA and FVPSA ) pressurization
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and adsorption steps; product step of PSA ) adsorption step for PSA; product step of FVPSA ) adsorption and cocurrent blowdown steps; exhaust step of PSA ) depressurization and regeneration steps; and exhaust step of FVPSA ) regeneration step. In the PSA process, the work to compress the feed gas is given by
power ) Pfeed γ RTfeed γ-1 Patm
[( )
(γ-1)/γ
]
Pfeed - 1 u(0)π(Rbed)2 (15) RTfeed
∫0
tP+tA
powerave )
(power) dt (16)
tP + tA
On the other hand, the work for the VPSA process is given by
power1 ) Pfeed γ RTfeed γ-1 Patm
[( )
power2 ) Patm γ RTreg γ-1 Preg
[( )
powerave )
∫0t
P
(γ-1)/γ
+ tA
(γ-1)/γ
]
Pfeed - 1 u(0,t)π(Rbed)2 RTfeed (17a)
]
Preg - 1 u(0,t)π(Rbed) (17b) RTreg
conditions determined by this CSS definition are given by
φ(z,t)|t)0 ) φ(z,t)|t)tcycle
tA + tP
+
∫0t
R
(power2) dt tR
(18)
The average specific power is the work per mole of CO2 capture; for both processes, it is defined by
powerave (exhaustCO2,ave)
(20)
CSS constraints need to be enforced for the optimization of cyclic adsorption processes. With our previous approach in ref 3, we used the tailored single discretization (TSD) and employed the following type of function to define the initial condition profile:
φ|t)0 ) f(z), here f(z) ) ka +
kb
(
)
z - kc 1 + exp kd
2
(power1) dt
specific powerave )
Figure 3. H2/CO2 gas separation PSA process.
The function type (f(z)) may be changed depending on the CSS shape and the function (eq 21) with initial values of the optimization variables ka, kb, kc, and kd that were obtained from a nonlinear regression based on successive substitution (SS) from the first cycle to the CSS cycle (∼500th cycle or 1,000th cycle). The final variable values for ka, kb, kc, and kd at CSS are determined from the optimization to satisfy the following modified CSS conditions (either eq 22a or eq 22b) instead of eq 203.
∫|φ(t)0)(z) - φ(t)t )(z)| dz eδ ∫|φ(t)0)(z)| dz
(22a)
∫|φ(t)0)(z) - φ(t)t
(22b)
cycle
where exhaustCO2,ave ) (
∫ ExhaustCO
2
dt|exhaust step)π(Rbed)2 tR
(19)
The term power1 refers to the pressurization and adsorption steps for the PSA and FVPSA cycles. The term power2 refers only to the vacuum step (regeneration step) in FVPSA; it is set to zero for the PSA cycle. The resulting mathematical model consists of a set of partial differential and algebraic equations that is solved using the gPROMS modeling tool.20,21 The centered finite difference method (CFDM) is used to discretize the spatial domain into n discretization points, and the method of lines (MOL) is used to solve the resulting system of differential-algebraic equations (DAE). DASOLV, the DAE solver and direct sensitivity code in gPROMS, is used to simulate the cycle, and the reduced space SQP (SRQPD) algorithm in gPROMS is adopted to solve the nonlinear programming (NLP) problem for the optimization. 3. Optimization Strategies 3.1. Cyclic Steady State (CSS). CSS requires that the bed profiles at the beginning of the cycle are the same as those at the end of the cycle. So the initial
(21)
cycle)
(z)| dz e δ
where δ is a small positive constant. In ref 22, we used the method of lines to discretize z to zi, i ) 1, ..., n, and defined eq 20 as φ(zi,0) ) φ(zi,tcycle) for i ) 1, ..., n, with φ(zi,0) ) [yN2,i, yCO2,i, qN2,i, qCO2,iTi]T as variables in the optimization problem. Similarly, we now consider the uTSD (updated TSD) approach, where we also use eq 20 along with the method of lines discretization to determine CSS, as in ref 22. As a safeguard in the CSS computation, we also add an additional variable, , and define the following,
- e φ(zi,0) - φ(zi,tcycle) e , i ) 1, ..., n
(23)
where is a nonnegative variable which forms an L∞ penalty term in the objective function, shown below. Consequently, with ) 0, CSS is satisfied at each spatial discretization point. In the TSD and uTSD methods, the CSS condition is enforced by the optimization in gPROMS. The TSD method obtains the CSS by using the CSS constraint (eq 22a) with the small CSS tolerance (δ), while the uTSD method determines this by minimizing a penalty
Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005 8089 Table 6. Optimization Results of the Previous TSD and Updated TSDa
a
optimization algorithm
previous TSD
updated TSD
total CPU time for optimization (s) no. of NLP iterations (SRQPD) no. of function evaluations purityH2 (%) power (W) CSS accuracy ((∫L0 |q1,t)0 - q1,t)tcycle| dz)/(∫L0 |q1,t)0| dz)) CSS accuracy ((∫L0 |q2,t)0 - q2,t)tcycle| dz)/(∫L0 |q2,t)0| dz)) CSS accuracy ((∫L0 |y1,t)0 - y1,t)tcycle| dz)/(∫L0 |y1,t)0| dz)) objective function value
1 667.03 66 145 95.169 4 6.138 34 0.029 95 0.026 01 0.030 12 0.045 149 4
628.265 32 34 95.145 8 2.928 3 5.193 91 × 10-8 1.338 13 × 10-8 1.027 31 × 10-7 0.021 543 8
Here, the optimal value of in uTSD is 1.298 58
×
10-24.
function with the nonnegative CSS variable () along with the CSS constraint (eq 23). 3.2. Optimization Algorithms. We briefly compare the uTSD method with the TSD method developed in refs 2, 3, and 4. Like TSD, uTSD also uses binary variables in gPROMS to express the changing operating conditions and update the optimization procedure. The tailored single discretization (TSD) optimization strategy is summarized below:2-4 (1) Formulate the bed models in Table 3 using the method of lines (MOL) as the spatial discretization; (2) Express changes in boundary conditions for operating steps by using binary variables in gPROMS and obtain the initial CSS profile using successive substitution (SS) to CSS (this requires at least 500 cycles); (3) Using nonlinear regression, find variable values for ka, kb, kc, and kd in eq 21 that match the initial CSS profile; (4) Choose additional variables for optimization such as cycle time, feed and purge velocities, feed pressure, and bed length and add CSS constraints (eq 22) to the optimization model with a small positive tolerance (δ). Choose an objective function Φ based on the terms in eqs 11-19, i.e., recovery, purity, and/or power. (5) Solve the following optimization of the PSA model: Min Φ, s.t. eq 22, as well as constraints on power, recovery, and purity and bounds on the optimization variables. Though TSD worked well in our previous study, it has two shortcomings. First, the CSS condition (eq 22) is only approximate. It is obtained by setting the small tolerance, δ. However, setting δ too small makes it difficult to converge to the optimal point or requires a long computation time for the optimization. Second, a nonlinear regression step is required to get the proper function in eq 21 to describe the CSS profile accurately. However, the regression may sometimes be impossible or inaccurate when the real CSS shape is not predictable by any function type. Moreover, the nonlinearity of the CSS condition (eq 22) makes the optimization more expensive. To eliminate the above problems as well as maintain the merits of TSD, the uTSD approach removes the regression step from the optimization procedure of TSD and determines the CSS profiles by minimizing the variable from eq 23. This approach is summarized below: (1) Formulate the bed models in Table 3 using the method of lines (MOL) as the spatial discretization; (2) Express changes in boundary conditions for operating steps by using binary variables in gPROMS; (3) Initialize the cycle at CSS and set decision variable values for φ(zi,0); (4) Choose additional variables for optimization such as cycle time, feed and purge velocities, feed pressure,
Figure 4. CSS profiles obtained from the optimizations.
and bed length and add CSS constraints (eq 23) to the optimization model with the nonnegative variable (). Choose an objective function Φ based on the terms in eqs 11-19, i.e., recovery, purity, and/or power; (5) Solve the following optimization of the PSA model: Min Φ + M, s.t. eq 23, as well as constraints on power, recovery, and purity and bounds on the optimization variables. Here, the penalty constant M is a large value (∼105). In the optimization models of this work (Sections 4.2 and 4.3), the time horizon is ∼90-330 s for PSA and 85-410 s for FVPSA. The degrees of freedom consists of 15 decision variables plus the initial conditions, φ(zi,0), as discussed next.
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Table 7. Constraints of Optimization Case A variable
LB
tP tA tDP tR L Pfeed Pinitial, Ppurge ∂P/∂t|step1 ∂P/∂t|step2, ∂P/∂t|step4 ∂P/∂t|step3 Tfeed,Tpurge uads,t)0 ∂uads/∂t|step1 ∂uads/∂t|step2, ∂uads/∂t|step3 ∂uads/∂t|step4
UB
10 35 10 35 0.25 170 90 5 -10-10 -50 295 0 10-5 -0.1 0
unit
50 115 60 105 2 2000 110 50 10-10 -2 323.15 0 0.1 10-5 0
variable
s s s s m kPa kPa kPa/s Pa/s kPa/s K m/s m/s2 m/s2 m/s2
ureg,t)0 ∂ureg/∂t|step1 ∂ureg/∂t|step2, ∂ureg/∂t|step3 ∂ureg/∂t|step4 φz|t)0 φz|t)0 - φz|t)tcycle Cv1L Cv3L powerave purityN2,ave recoveryCO2,ave purityCO2,ave
LB
UB
-0.2 10-5 0 -0.0261 φz|LB 0 - 3 × 10-9 5 × 10-9 0 90% 90% 45% eqs 1-19, 23
unit
-10-5 0.051 0 -10-10 φz|UB 10-3 5 × 10-3 5 × 10-2 105 100% 100% 100%
m/s m/s2 m/s2 m/s2
m‚sxmol‚K m‚sxmol‚K J/s
Table 8. Optimization Results for PSA at Normal Temperature and High Temperature variables
results of Case A
results of Case B
bed length (L) (m) feed pressure (Pfeed) (kPa) purge pressure (Ppurge) (kPa) initial pressure within the bed (Pinitial) (kPa) feed temperature (Tfeed) (K) purge temperature (Tpurge) (K) input velocity at adsorption step (ufeed) linear change of velocity at feed end (m/s) input velocity at purge step (upurge): linear change of velocity at product end (m/s) pressurization time (tP) (s) adsorption time (tA) (s) depressurization time (tDP) (s) regeneration time (tR) (s) valve coefficient at step 1 (Cv1L) (m ‚s xmol‚K) valve coefficient at step 3 (Cv3L) (m ‚s xmol‚K) CSS tolerance () average CO2 purity (purityCO2,ave) (%) average CO2 recovery (recoveryCO2,ave) (%) average N2 purity (purityN2,ave) (%) average N2 recovery (recoveryN2,ave) (%) average power (powerave) (W) average CO2 product (productCO2ave) (mol/s) average specific power (specific powerave ) powerave/productCO2,ave) (J/mol CO2) objective function (%) total CPU time on Pentium 4 with 1.8 GHz machine (s) no. of NLP iterations (SRQPD) no. of function evaluations optimization tolerance of NLP solver (SRQPD)
1.483 49 1 428.03 90.0 90.0 323.15 323.15 0.136 725 ∼ 0.138 111 -3.66093 × 10-18 ∼ -0.2 50 69.321 7 60 105 4.983 97 × 10-7 5 × 10-9 0 56.414 6 97.515 6 99.496 9 86.704 7 182.699 0.102 3 1 786.55 -153.709 3 018.48 80 92 0.002
1.648 37 1 352.77 90.0 90.0 370.15 370.15 0.201832 ∼0.203 094 -4.701 75 × 10-7 ∼ -0.131 863 46.021 3 63.078 8 60 105 1.788 12 × 10-7 5 × 10-9 0 71.936 2 94.432 1 98.9860 93.498 8 240.318 0.095 8 2 508.98 -166.246 5 866.42 155 184 0.002
Table 9. Constraints of Optimization Cases C1 and C2 variable tP tA tDP tR L Pfeed Ppro Preg, Pinitial ∂P/∂t|step1 ∂P/∂t|step3 ∂P/∂t|step4 Tfeed uads,t)0 ∂uads/∂t|step1 ∂uads/∂t|step2
LB 10 35 10 30 0.25 170 70 9.9 5 -50 -9 275 0 10-5 -0.1
UB 55 150 55 150 2 2000 130 70 50 -2 -0.1 370 0 0.1 3 × 10-3
unit s s s s m kPa kPa kPa kPa/s Pa/s kPa/s K m/s m/s2 m/s2
variable ∂uads/∂t|step3 ∂uads/∂t|step4 φz|t)0 φz|t)0 - φz|t)tcycle Cv1L Cv3U Cv4L purityN2,ave recoveryCO2,ave powerave purityCO2,ave (Case C1) purityCO2,ave (Case C2)
4. Optimization Results 4.1. Comparison of the new TSD (uTSD) with the TSD. To demonstrate that the new method (uTSD) is better than TSD, this study first considers a simplified PSA process. The model is not as detailed as
LB -0.1 0 φz|LB 0 - 5 × 10-9 5 × 10-9 5 × 10-9 90 90 0 80 90 eqs 1-19, 23
UB
unit
10-5
m/s2
0 φz|UB 10-3 5 × 10-4 9 × 10-4 5 × 10-4 100 100 5 × 105 100 100
m/s2
m‚s xmol‚K m‚s xmol‚K m‚s xmol‚K % % J/s % %
the current target processes (normal temperature PSA, high temperature PSA, and FVPSA of this work), but it allows us to compare the methods easily and quickly. The operation is the Skarstrom cycle shown in Figure 3.
Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005 8091 Table 10. Optimization Results for FVPSA at High Temperature variables
results of Case C1
results of Case C2
bed length (L) (m) feed pressure (Pfeed) (kPa) cocurrent blowdown product pressure (Ppro) (kPa) countercurrent regeneration pressure (Preg) (kPa) initial pressure within the bed (Pinitial) (kPa) feed temperature (Tfeed) (K) input velocity at adsorption step (ufeed) linear change of velocity at the feed end (m/s) pressurization time (tP) (s) adsorption time (tA) (s) cocurrent blowdown time (tPRO) (s) regeneration time (tR) (s) valve coefficient at step 1 (Cv1L) (m‚s xmol‚K) valve coefficient at step 3 (Cv3U) (m‚s xmol‚K) valve coefficient at step 4 (Cv4L) (m‚s xmol‚K) CSS tolerance () average CO2 purity (purityCO2,ave) (%) average CO2 recovery (recoveryCO2,ave) (%) average N2 purity (purityN2,ave) (%) average N2 recovery (recoveryN2,ave) (%) average power (powerave) (W) average CO2 product (productCO2,ave) (mol/s) average specific power (specific powerave ) powerave/productCO2,ave) (J/mol CO2) objective function (%) total CPU time on Pentium 4 with 1.8 GHz machine (s) no. of NLP iterations (SRQPD) no. of function evaluations optimization tolerance of NLP solver (SRQPD)
0.25 652.053 70.0 11.800 2 11.800 2 370 3.057 15 × 10-2 ∼0.135 572 34.065 5 35 20.447 7 150 4.939 2 × 10-4 5 × 10-9 5 × 10-4 5.143 96 × 10-18 88.942 3 96.904 7 99.445 97.873 9 112 228 16.954 6 6 619.34 -185.847 1 886.97 46 46 0.002
0.25 682.015 70.00 14.657 14.657 370 2.294 87 × 10-2 ∼0.127 803 39.951 3 35 21.689 6 150 4.674 53 × 10-4 6.81735′× 10-4 5 × 10-4 1.539 2 × 10-18 90.00 93.807 5 98.899 98.160 5 106 838 17.886 5 5 973.08 -183.808 2 685.17 63 66 0.002
0.3 m e L e 3 m
(25a)
3 atm e Pfeed e 20 atm
(25b)
1 s e tP, tDP e 50 s
(25c)
80 s e tA, tR e 950 s
(25d)
0.004 m/s e ufeed|z)0 e 0.1 m/s
(25e)
-0.2 m/s e upurge|z)0 e -4 × 10-5 m/s
(25f)
90% e purityH2 e 100%
(25g)
The constraints are listed in Table 7. The decision variables of the PSA optimization are the following: step times, bed length, initial bed pressure, feed pressure, pressure change rate with respect to time during pressurization and depressurization steps, purge pressure, temperatures, input feed gas velocity during the adsorption step, input purge gas velocity during the purge step, CSS variable (), and valve coefficients during pressurization and depressurization. Table 8 lists the optimization results. Note that since CO2 recovery and purity are maximized, the purity and recovery constraints are inactive. 4.3. PSA Optimization at High Temperature: Case B. We now consider the optimization model for CO2 capture using PSA at high temperatures. The optimization models and the decision variables are the same as the models in Section 4.2, except for the following differences in temperature and product specification:
power e 40 J/s
(25h)
Subject to
The optimization formulation is
Min power/purityH2 for TSD
(24a)
Min power/purityH2 + M for uTSD
(24b)
s.t.
eq 22a as CSS condition (δ ≈ 0.03) 24
general PSA model equations
Judging from the optimization results in Table 6, the updated tailored single discretization (uTSD) has the following advantages over the tailored single discretization (TSD): fewer iterations, faster calculation, more accurate CSS ( ≈ 0), and better results. Figure 4 compares the accuracy of CSS in TSD and uTSD methods. 4.2. PSA Optimization at Normal Temperature: Case A. In this section, we consider the following optimization model for CO2 capture using PSA at normal temperatures.
Min objective ) -purityCO2 - recoveryCO2 + M (26)
350 K e Tfeed, Tpurge e 370.15 K
(27a)
purityCO2,ave g 64%
(27b)
Table 8 summarizes the optimization results. Again, note that since CO2 recovery and purity are maximized, the purity and recovery constraints are inactive. 4.4. FVPSA Optimization at High Temperature: Cases C1 and C2. To improve the purities over PSA, two FVPSA models are optimized. The objective function is given by eq 26, and Table 9 lists the constraints. Note that Case C2 has tighter bounds on CO2 purity than Case C1. The optimization results are listed in Table 10. The decision variables of the FVPSA optimizations are the following: step times; bed length; initial bed pressure; feed pressure; product purge pressure; regeneration pressure; pressure change rate according to the
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time during the pressurization, product purge, and regeneration steps; temperatures; input feed gas velocity during the adsorption step; the CSS variable (); and valve coefficients during the pressurization, product purge, and regeneration steps. Table 10 lists the optimization results. Note that Cases C1 and C2 show the tradeoff between high purity and high recovery. In Case C2, we see that CO2 purity increases by just over 1% but with a >3% loss in CO2 recovery. Finally, note that the average power requirement in Table 10 is significantly larger than that in Table 8, because of a much higher velocity in the feed pressurization step. In Table 10, the valve coefficient in step 1 (Cv1L) is 3 orders of magnitude higher than that in Table 8. This also leads to a much higher feed introduced at this step, and consequently, the specific power in Table 10 is higher.
Similarly, the specific power (the average power per mole of CO2 recovered (J/mol)) values of FVPSA are larger than those of the PSA cases. Acknowledgment This research was funded by the Department of Energy through the National Energy Technology Laboratory (NETL). Appendix. Derivation of Component and Overall Mass Balance Equations In the axial dispersed plug flow model, a mass balance for component i is15
5. Conclusions An improved optimization algorithm is described for cyclic adsorption processes in gPROMS. The updated optimization method shows the following advantages over the previous method:.2-4 faster calculation, more robust convergence, and more accurate CSS solutions. With the new optimization procedure, we performed simulations and optimizations of normal temperature PSA, high-temperature PSA, and FVPSA processes at bench scale to get high CO2 purity and recovery from the mixture gas (85% N2 and 15% CO2). The process models are formulated by using partial differential algebraic equations (PDAEs) that describe the dynamic behaviors and spatial distribution of the variables within the bed. The centered finite difference method (CFDM) is used for the discretization of the spatial domain, and a reduced space SQP algorithm is adopted for the optimizations. The optimization results lead to the following observations: (1) The optimal feed pressure of high-temperature PSA is lower than that of normal-temperature PSA. The optimal feed pressure of high-temperature FVPSA is much lower than those of PSA cases. In high-temperature FVPSA, higher feed pressure is required to get higher CO2 purity. (2) The optimal purge and blowdown pressures are almost at the lower bounds of the optimization constraints. This means that the regeneration of CO2 can be improved by reducing the pressure at the regeneration (purge) step. The cocurrent blowdown step of FVPSA to evacuate the N2 within the bed also requires a low pressure (lower bound) (3) In PSA, the optimized depressurization and regeneration times are the upper bounds of optimization constraints to obtain the required CO2 purity. In FVPSA, the optimal regeneration time also hits the upper bound to get the high CO2 purity. In summary, we can conclude the following: (1) The high-temperature FVPSA is much better than PSA in obtaining high purity of CO2 (∼90%) while maintaining high values of other performance measures (recoveries of both components and N2 purity). In other words, the FVPSA shows good performance to get high purities and recoveries of both components. This is mainly because of the characteristic of zeolite 13X and the operating conditions. (2) The average power (watts) for FVPSA operation is considerably larger than that for PSA operation because of a high velocity (and valve coefficient) in the feed pressurization and countercurrent blowdown steps.
∂2Ci
- Dx
∂z
2
∂(uCi) ∂Ci 1 - ∂qi + + Fp ) 0 (A1) ∂z ∂t ∂t
+
The overall mass balance is
- Dx
∂2C
+
∂(uC)
∂z2
+
∂z
∂C ∂t
+ Fp
1-
n
∑ i)1
∂qi
)0
(A2)
∂t
If the ideal gas law is applied, the first three terms of eq A2 are expressed by
- Dx
∂2C ∂ ∂ P ) - Dx ) 2 ∂z ∂z RT ∂z Dx ∂ ∂ 1 1 ∂ P + (P) R ∂z ∂z T T ∂z
( )
( () ) (A3) D ∂ 1 ) - (P ( ) + 2(∂P∂z )(∂z∂ (T1)) + T1 ∂∂zP) R ∂z T 2
x
2
2
2
∂(uC) 1 ∂ 1 u ∂P P ∂u ∂ uP ) uP + ) + ∂z ∂z RT R ∂z T T ∂z T ∂z
( ) ( () ) ∂C 1 ∂ 1 1 ∂P ∂ P ) ( ) ) (P ( ) + ∂t ∂t RT R ∂t T T ∂t )
(A4) (A5)
Therefore, the overall mass balance with the ideal gas law is
-
( ( ) ( )( ( )) ) ( () ) ( () )
Dx
∂2 1
∂z2 T ∂ 1
+2
∂P
∂ 1
+
1 ∂2P
+ T ∂z2 1 u ∂P P ∂u 1 ∂ 1 1 ∂P uP + + P + + + R ∂z T T ∂z T ∂z R ∂t T T ∂t 1 - n ∂qi ) 0 (A6) Fp i ) 1 ∂t R
P
∂z ∂z T
∑
Equation A6 is the same as the overall mass balance equation (eq 4). The component mass balance can be obtained from eqs A1 and A2:
- Dx
[
∂2Ci ∂z2 ∂Ci
[
∂t
- yi - yi
][ ] [
∂2 C ∂z2
+
∂(uCi) ∂z
- yi
]
∂(uC) ∂z
+
]
n ∂q 1 - ∂qi i + Fp ) 0 (A7) - yi ∂t ∂t i)1 ∂t
∂C
∑
Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005 8093
In the first parenthesis of the left-hand side (LHS) in eq A7, 2
∂ Ci ∂z
2
)
( ) (
) ( ) ( ) ( )( )
∂yi ∂C ∂ ∂(yiC) ∂ +C ) yi ) ∂z ∂z ∂z ∂z ∂z
∂yi ∂ ∂ ∂C y + C ∂z i ∂z ∂z ∂z
)
( )( )
∂2yi ∂yi ∂C ∂2 C ∂C ∂yi + yi 2 + +C 2 ∂z ∂z ∂z ∂z ∂z ∂z
(A8)
( )( )
∂2yi ∂yi ∂C ∂2C )2 + yi 2 + C 2 × ∂z ∂z ∂z ∂z
[
∂2Ci ∂z2
- yi
] ( )( )
∂2yi ∂yi ∂C ∂2 C ) 2 + C ∂z ∂z ∂z2 ∂z2
(A9)
The following is calculated by applying the ideal gas law to eq A9,
[
] ( )( ( ))
∂2Ci
2 ∂yi ∂ P P ∂ yi ∂2C - yi 2 ) 2 + ∂z ∂z RT RT ∂z2 ∂z2 ∂z
)
( )( ( )
)
2 2 ∂yi ∂ 1 1 ∂P P ∂ yi P + + R ∂z ∂z T T ∂z RT ∂z2 (A10)
In the second parenthesis of the LHS in eq A7,
( )
∂(uCi) ∂ uyiP ) ) ∂z ∂z RT uyi ∂P uP ∂yi yiP ∂u 1 ∂ 1 + + uyiP + (A11) R ∂z T T ∂z T ∂z T ∂z
[
yi
]
()
yi ∂(uC) ∂ uP ∂ 1 u ∂P P ∂u ) yi + ) uP + ∂z ∂z RT R ∂z T T ∂z T ∂z (A12)
( ) [
]
()
Therefore,
[
]
∂(uCi) ∂(uC) uP ∂yi - yi ) ∂z ∂z RT ∂z
(A13)
In the third parenthesis of the LHS in eq A7,
( )
( ) [ ()
∂Ci 1 ∂ yiP ∂ yiP ) ) ) ∂t ∂t RT R ∂t T yi ∂P P ∂yi 1 ∂ 1 yiP + (A14) + R ∂t T T ∂t T ∂t yi
]
yi ∂ 1 1 ∂P ∂C ∂ P ) P + ) yi ∂t ∂t RT R ∂t T T ∂t
( ) [ ()
]
(A15)
Therefore,
[
]
∂Ci ∂C P ∂yi - yi ) ∂t ∂t RT ∂t
(A16)
If we substitute the first three terms in eq A7 by eqs A10, A13, and A16, the following component mass balance equation is obtained.
- Dx
[ ( )( ( ) 2 ∂yi
R ∂z
P
∂ 1
∂z T
+
)
1 ∂P T ∂z
[
+
]
2 P ∂ yi
RT ∂z2
+
]
uP ∂yi
+
RT ∂z
n ∂q 1 - ∂qi i ) 0 (A17) + Fp - yi RT ∂t ∂t i)1 ∂t
P ∂yi
∑
This equation (eq A17) is the same as the component mass balance equation (eq 3). Nomenclature qmi ) Langmuir constant (mole/kg) as a function of temperature bi ) Langmuir constant (1/Pa) as a function of temperature k1,i ) Langmuir isotherm parameter (mole/kg) k2,i ) Langmuir isotherm parameter (1/K) k3,i ) Langmuir isotherm parameter (1/Pa) k4,i ) Langmuir isotherm parameter (K) ka ) parameter to predict CSS profile of TSD method kb ) parameter to predict CSS profile of TSD method kc ) parameter to predict CSS profile of TSD method kd ) parameter to predict CSS profile of TSD method Cpg ) heat capacity of gas (J/kg/K) Cps ) heat capacity of adsorbent (J/kg/K) Cv1L ) valve coefficient at the feed end of the bed during the first step Cv3L ) valve coefficient at the feed end of the bed during the third step in PSA Cv3U ) valve coefficient at the product end of the bed during the third step in FVPSA Cv4L ) valve coefficient at the feed end of the bed during the fourth step in FVPSA De ) effective diffusivity (m2/sec) DK ) Knudsen diffusion (m2/sec) DM ) molecular diffusion (m2/sec) Dparticle ) particle diameter (m) Dv ) diffusion volume Dx ) dispersion coefficient (m2/sec) hi ) heat transfer coefficient (J/m2/sec/K) -∆H ) isosteric heat of adsorption (J/mole) i ) a component identifier (“i ) 1” denotes CO2, “i ) 2” is N2) KL ) effective axial thermal conductivity (J/m/sec/K) L ) bed length (m) Mw ) molecular weight n ) number of elements for finite difference method P ) total pressure (Pa) PSTP ) pressure at standard condition (105 Pa) (Pa) Pfeed ) feed pressure (Pa) Pi ) partial pressure (Pa) Ppurge ) purge pressure (Pa) in PSA Ppro ) cocurrent blowdown product pressure (Pa) in FVPSA Preg ) countercurrent regeneration pressure (Pa) in FVPSA Pinitial ) initial pressure within the bed (Pa) qi ) solid-phase concentration (mol/kg) qi* ) amount of adsorption of component i in equilibrium state of mixture R ) universal gas constant (J/mol/K) q ) state variable Rbed ) bed radius (m) Rparticle ) particle radius (m) t ) time (sec) tcycle ) cycle time (sec) tP ) pressurization time (sec) tA ) adsorption time (sec) tDP ) depressurization time (sec) in PSA tPRO ) cocurrent blowdown product time (sec) in FVPSA tR ) purge time in PSA and regeneration time (sec) in FVPSA
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Ind. Eng. Chem. Res., Vol. 44, No. 21, 2005
T ) gas temperature within the bed (K) Twall ) column wall temperature (K) TSTP ) temperature at standard condition (298.15 K) (K) Tfeed ) feed temperature (K) u ) superficial gas velocity (m/sec) uads ) inlet feed gas velocity at the feed end of the bed during the adsorption step (m/sec) ufeed ) inlet feed gas velocity at the feed end of the bed during the adsorption step (m/sec) upurge ) inlet purge gas velocity at the product end of the bed during the purge step (m/sec) ureg ) inlet purge gas velocity at the product end of the bed during the purge step (m/sec) w ) constraints yf ) feed mole fraction yi ) mole fraction of component i z ) the axial position (m) or state variable Greek Letters ) CSS tolerance which is a very small value µ ) gas viscosity (kg/m/sec) Fbed ) bed density (kg/m3) bed ) bed void particle ) particle porosity t ) total void fraction Fgas ) gas density (kg/m3) ∆Hi ) isosteric heat of adsorption (J/mol) of the component i Fparticle ) particle density (kg/m3) Fwall ) wall density (kg/m3) φ ) representative of mole fraction (y), adsorption amount (q), and temperature (T) Φ ) objective function
Literature Cited (1) Siriwardane, R. N2/CO2 isotherm data; Technical Report; National Energy Technology Laboratory, U.S. Department of Energy: Morgantown, WV, 2004. (2) Ko, D.; Siriwardane, R.; Biegler, L. T. Optimization of PSA using Zeolite 13X for CO2 Sequestration. Presented at 2002 AIChE Annual Meeting, Indianapolis, IN, Nov. 6, 2002. (3) Ko, D.; Siriwardane, R.; Biegler, L. T. Optimization of a pressure-swing adsorption process using zeolite13X for CO2 sequestration. Ind. Eng. Chem. Res. 2003, 42, 339-348. (4) Ko, D.; Siriwardane, R.; Biegler, L. T. Simulation and Optimization of FVPSA for CO2 Recovery. Presented at 2004 CAPD Annual Review Meeting, Carnegie Mellon University, Pittsburgh, PA, Mar. 8, 2004. (5) Kessel, L. B. M.; Saeijs, I. C. P. L.; Lalbahadoersing, V.; Arendsen, A. R. J.; Stavenga, M.; Heesink, A. B. M.; Temmink,
H. M. G. IGCC power plant: CO2 removal with moderate temperature adsorbents, final report. TNO report R98/135; 2002. (6) PICHTR. CO2 ocean sequestration: Field experiment. http:// www.co2experiment.org (accessed 2001). (7) Park, J.-H.; Beum, H.-T.; Kim, J.-N.; Cho, S.-H. Numerical analysis on the power consumption of the PSA process for recovering CO2 from flue gas. Ind. Eng. Chem. Res. 2002, 41, 4122-4131. (8) IEA Greenhouse R&D program. Carbon dioxide capture from power stations. http://www.ieagreen.org.uk/capt5.htm (accessed 1994). (9) Skarstrom, C. W. Method and apparatus for fractionating gaseous mixtures by adsorption. U.S. Patent No. 2944627, 1960. (10) Marsh, W. D.; Pramuk, F. S.; Hoke, R. C.; Skarstrom, C. W. Pressure equalization depressurizing in heatless adsorption. U.S. Patent No. 3,142,547, 1964. (11) Berlin, N. H. Method for providing an oxygen-enriched environment. U.S. Patent No. 3,280,536, 1966. (12) Wagner, J. L. Selective adsorption process. U.S. Patent No. 3,430,418, 1984. (13) Ruthven, D. M. Principles of adsorption and adsorption processes; Wiley: New York, 1984. (14) Yang, R. T. Gas separation by adsorption processes; Butterworth: Boston, MA, 1987. (15) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure swing adsorption; VCH Publishers: New York, 1994. (16) Chou, C.-T.; Ju, D.-M.; Chang S.-C. Simulation of a fractionated vacuum swing adsorption process for air separation. Sep. Sci. Technol. 1998, 33 (13), 2059-2073. (17) Sircar, S.: Zondlo, J. W. U.S. Patent 4,013,429, 1997. (18) Sircar, S.; Hanley, B. F. Fractionated vacuum swing adsorption process for air separation. Sep. Sci. Technol. 1993, 28 (17 and 18), 2553-2566. (19) Chou, C.-T.; Huang, W.-C. Incorporation of a valve equation into the simulation of a pressure swing adsorption process. Chem. Eng. Sci. 1994, 49 (1), 75-84. (20) gPROMS introductory user’s guide, release 2.3.1; Process Systems Enterprise Ltd.: London, U.K, 2004. (21) gPROMS advanced user guide, release 2.3; Process Systems Enterprise Ltd.: London, U.K., 2004. (22) Jiang, L.; Biegler, L. T.; Fox, V. G. Simulation and optimization of pressure-swing adsorption systems for air separation. AIChE J. 2003, 49 (5), 1140-1157. (23) Nilchan, S. The optimisation of periodic adsorption processes. Ph.D. Thesis, University of London, U.K., 1997. (24) Kim, W.-G.; Yang, J.; Han, S.; Cho, C.; Lee, C.-H.; Lee, H. Experimental and theoretical study on H2/CO2 separation by a fivestep one-column PSA process. Korean J. Chem. Eng. 1995, 12 (5), 503-511.
Received for review January 4, 2005 Revised manuscript received July 28, 2005 Accepted August 5, 2005 IE050012Z
