Ind. Eng. Chem. Res. 1994,33,1600-1605
1600
Pressure Swing Adsorption Process: Performance Optimum and Adsorbent Selection Ravi Kumar Air Products and Chemicals, Znc., 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195-1501
Simulation results for an adsorptive gas separation process are presented. A feed gas mixture containing 25% methane and 75% hydrogen at a pressure of 20 atm is separated by a four-bed, nine-step pressure swing adsorption process to produce high purity hydrogen. The optimum operating conditions for producing maximum net product are identified. I t is shown that improving masstransfer characteristics of the adsorbent is helpful, but only up to a limit, after which it does not help to further reduce the mass-transfer resistance. It is also shown that the best adsorbent cannot be chosen by considering only the selectivity or working capacity. A combination of both of these properties is important. On the other hand, higher saturation capacity improves the performance of the simulated process.
Introduction Adsorptive gas separation processes are important unit operations in the industrial gas business. Small tonnage, medium purity nitrogen (-98+ % ) and oxygen (-go+ % ) markets are overwhelmed by this technology. Production of high purity hydrogen and the removal of trace impurities from air prior to cryogenic distillation are almost exclusively carried out by adsorption (Kumar, 1993). There are processes available for the production of carbon dioxide and methane (Kumar and Van Sloun, 1989), and a new process has been recently introduced in the market place for the production of high purity carbon monoxide using adsorption (Kumar et al., 1993). In most instances, the choice of the best material or directions for the future development of the adsorbents is usually done by empirical techniques such as carrying out experiments on process development units. However, as the understanding of adsorption has improved and sophisticated mathematical models have been developed, it is now possible to screen materials efficiently and effectively by a priori simulating these processes on highspeed computers. Equilibrium and kinetics are the two basic properties of adsorbents which affect their performance in a process. In the present study, effects of changing these properties on the performance of a pressure swing adsorption process are analyzed by a mathematical model. Also, the model is used to develop an understanding of this process and identify conditions for the optimum performance.
Further assuming that the gas and solid phases are in thermal equilibrium and neglecting axial conduction of heat, the overall energy balance is given by
The temperature dependence and composition dependence of constant-volume and constant-pressure heat capacities of the gas phase are taken into account. The temperature dependence of the solid phase heat capacity is expressed by a quadratic equation. The steady state momentum balance is given by Ergun's equation:
The equilibrium isotherms are assumed to be described by the Langmuir model: mbiPyi ni = 1+ biPyi
bi = bio exp(qilRT) (6) The mass transfer is described by the linear driving force model: ani -at_ - ki(ni*- ni)
Mathematical Model Details of the mathematical model and results from an experimental validation study were previously published (Kumar et al., 1994). In summary, the component (i) mass balance in a bulk system, neglecting axial dispersion is given by
The overall mass balance is given by
(7)
The governing partial differential equations were discretized in space and the resulting system of ordinary differential equations was solved using the LSODE integrator from Lawrence Livermore Laboratory. An HP 735 workstation was used for simulations. In the present study, the total 20-ft length of the column was divided into forty special nodes. The first 10 f t of the column from the feed end had 10 nodes, the next 5 f t also had 10 nodes, and the last 5 f t had 20 nodes. This node division was chosen to minimize computational time while maximizing the accuracy of the product purity.
Process Cycle The gas phase is assumed to be ideal, and the bulk density of the solid phase is assumed to be constant. 0888-5885/94/2633-1600$04.50/0
A nine-step, four-bed process cycle to produce high purity hydrogen from a feed mixture containing 25% 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 6,1994 1601 Table 1. Simulation Parameters adsorbent Ca-exchangedA zeolite particle diameter bulk density heat capacity at 70 OF feed gas H? CH4 temperature column inside diameter column length adsorbent void fraction interstid void fraction gas to wall heabtransfer meff
1/16-in. pelleta 0.0053 ft
46.21 lb/fts, as packed 0.22 Btu/(lb°F) 75% 25% 25 'C
0.93 in. 20 ft 0.100
0.380 0.005 Btu/(h.ftP.'F)
Table 2. Equilibrium Parameters (Adsorbent: Ca-Exebaneed Zeolite A) adsorbate
H.
CH. P R
0 D R
i
m, mmol/g bo, atm-I (eq 6)
9.38 X 1V
4.cal/g-mol
5341
1.51
4.68 X lo-' 2069
repressurization step 10 (Figure 2), used the gas stream stored in step 2 as the influent. The initial conditions in the bed at the start of the next cycle were assumed to be the same as the final conditions in the bed at the end of the previous cycle, step 10 (Figure 2). The process was assumed to have reached cyclic steady state when there was no change in the bed inventory at a fixed time in the cycle.
Results and Discussion The simulation parameters used in this study are summarized in Table 1. A gas mixture containing 25% methane and 75% hydrogen was fed to a 20-ft-long, 0.93in. internal diameter bed packed with a typical Ca-A zeolite. The gas to wall heat-transfer coefficient, hw, was assumed to be low (0.005 Btu/(h.fWF)) in order to simulate adiabatic operating conditions. Feed pressure was21 atmandfeedtemperaturewas25OC.Thepressures and 9) at the end of the blowdown and purge steps (PEL were about 1.35 atm. Product hydrogen contained a few parts per million of methane. The equilibrium isotherms for this adsorbate-adsorbent system were fitted by the Langmuir model, eq 5, and the corresponding parameters are summarized in Table 2. Effectof the MassTransferCoefficient. Thelinear driving force model, eq 7, is used to describe the rate of mass transfer in this study. Since mass transfer in these systems is primarily controlled by macropore diffusion, which in turn is dominated by molecular diffusion, it is further assumed that the mass-transfer coefficient is inversely proportional to the operating pressure (Ruthven, 1984):
ki = PFACi/P
(8)
For the typical commercial Ca-A pellets used in this study, pore size distribution data gave the average size and the fraction of the large macropores in the pellet, dl = 3400 A and tl = 0.22 cm3/gand, of the small macropores in the pellet, ds= 1700A and = 0.04cm3/g. This resulted in a mass-transfer coefficient of 0.24 s-l for methane and 9.7 s-l for hydrogen at 20 atm and 25 OC (Wakao and Smith, 1962) for the 25% CHd, 75% Hz gas mixture used in this study. This in turn gave PFACCH,= 4.8 atm/s and PFACH, = 194 atm/s.
1602 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1.00
I I
0.90 0.80
1
I
I
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I
1
I
I
1
I
1.00
0.70
I
"'"1
tI
1 FEEDIPROD. 2 FEEDIPROD. & REPRES. 3 FIRST COC. D.P. 4 SECOND COC. D.P. 15 THIRD COC. D.P.
I
I
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1
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I
0.90
6 BLOWDOWN 7 HYDROGENPURGE
0.60
-
Ycn4
-
0.40
0.30
\3
0.30
-
-
0.20 0.10 -
0.00
0
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2
4
6
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10 12 14 COLUMN HEIGHT (FT) 8
16
18
20
Figure 3. Mole fraction of methane in the gas phase for the first five steps, case no. 1-7.
2
0
4
6 8 10 12 14 COLUMN HEIGHT (FT)
16
18
20
Figure 4. Mole fraction of methane in the gas phase for the last five steps, case no. 1-7.
Table 3. Effect of Mass-Transfer Coefficient on Process Performance (&A,O = 0.938 X atm-I, m = 1.51 mmol/p;) caseno.
PFACCH,
PFACH,
QF
QP
1-1 1-2 1-3 1-4
15 8 4.8 1
353 185 194 25
1.02 1.02 1 0.91
1.02 1.02 1 0.88
RH* 85.6 85.6 85.3 82.5
Table 3 summarizes the simulation results for various cases with different mass-transfer coefficients. Relative quantity of net product, Qp, and hydrogen recovery, RH*, decreased as mass-transfer coefficient was decreased. However, as methane mass-transfer coefficient decreased up to -0.24 s-l (PFAC = 4.8 atm/s),the loss in the process performance was minimal. Further decreasing the methane mass-transfer coefficient to 0.05 s-l (PFAC = 1atm/ s), case no. 1-4, Table 3, reduced the process performance significantly. This implies that a restricted pore structure, i.e., slow mass transfer, is detrimental to the process performance. On the other hand, opening the macropore structure to increase the mass-transfer coefficient will result in reducing the bulk density of the adsorbent. This in turn will reduce the volumetric production from the process. The increase in the mass-transfer coefficient, as demonstrated by cases nos. 1-1, 1-2, and 1-3 in Table 3, resulted only in a minimal increase in the mass productivity; therefore, a balance between the process performance increase due to the increased mass-transfer coefficient and the process performance decrease due to the reduced bulk density of the adsorbent has to be maintained and opening the pore structure to increase the mass-transfer coefficient beyond a certain limit may not be advantageous. The remaining cases in this study was simulated with PFACCH,atm/s = 4.8 and PFACH, = 194 atm/s. Effect of the Purge Gas Quantity. This process utilizes an internal gas stream to purge the contaminated adsorbent. As shown in Figure 2, the second cocurrently depressurized gas stream (CoCDP2) from step 4 was used to purge the bed at low pressure in the countercurrent direction (CCC purge) in step 7 . This step on the one hand has the advantage of cleaning the bed by countercurrent purge, but on the other hand has the disadvantage of contaminating the product end of the bed in step 4. This is more clearly demonstrated by the impurity (methane) composition profiles in the bed at the end of each step in Figures 3 and 4 for case no. 1-7 (Table 4). A t the end of the feed step, methane concentration front is at location 2 in the bed as shown in Figure 3. As the bed is depressurized in the cocurrent direction, methane desorbs from the adsorbent, increasing methane concentration along the column length and moving the methane
I
I
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1
1.o
0.5
1.5
Q PU
Figure 5. Relative process performance as a function of relative purge gas quantity, case no. 1. Table 4. Effect of Purge Gas Quantity on Process Performance (&H,O = 0.938 X lo4 atm-l, S = 50.5, m = 1.51 mmol/g) Caseno.
Qpu
p*
PBL
1-5 1-3 1-6 1-7 1-8 1-9
0.26 0.56 0.91 1 1.24 1.53
11.2 9 6.5 6.1 4.5 3.4
5.8 4.7 3.6 3.4 2.7 2.2
QF
QP
0.79 0.91 0.97 1 0.98 0.97
0.80 0.92 0.98 1 0.97 0.93
RH* ykL
Y:,,
84 85 85 85 83 80
74.3 61.7 54.1 52.1 47.4 43.1
39.9 43.9 50 51.6 58.1 64
concentration front toward the product end. This is depicted by locations 3 , 4 , and 5 in Figure 3 for the first, second, and third cocurrent depressurization steps, respectively. Hydrogen desorbed during the second cocurrent depressurization step, Le., between locations 3 and 4 in Figure 3, is used for purging the bed in countercurrent direction. This gas moves methan towards the feed end from location 6 to 7 as shown in Figure 4. Therefore, higher quantity of the purge gas will move the methane front farther back toward the feed end, location 7 in Figure 4, but at the same time it will cause more contamination of the product end, location 4 in Figure 3, in the bed providing the internal purge gas stream. These two opposing factors result in an optimum for the purge gas quantity. Table 4 summarizes the effect of the purge gas quantity on the process performance. As the purge gas quantity, Qpu, is increased, the quantity of net product, Qp, the quantity of fresh feed, QF,and hydrogen recovery, RH^, first increase and then decrease. As shown in Figure 5 , the maximum in the net product and the fresh feed gas
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1603
2'o 1.5
r---l -
2-
/
Q NET -"D O, ,
I
I
0
1
3
2
4
5
P (atm)
Figure 7. Pure methane equilibrium isotherms for the four cases with different bCHl0 at 25 "c: 1, bcb0 = 0.94 X 1 w atm/s; 2, bCbO = 9.38 X lo"' atm/s; 3, bcb" = 2.81 X l eatm/s; and 4, bcbO = 0.31 X lo"' atm/s. Table 5. Effect of Isotherm Shape on Process Performance: ~CH: Variation (m= 1.51 mmol/g) case no.
QPU
2-1 2-2 2-3
0.84 1 1.20
3-1 3-2 3-3 4-1 4-2 4-3
QF QP RH, &I, bcbO= 9.38 X l eatm-l, S = 505.2
0.98 0.99 73 38.8 1 1 72 42.5 1.02 0.98 69 48.0 bcb0 = 2.81 X le atm-I, S = 151.4 0.86 0.99 0.99 82 46.3 1 1 82 50.7 1 1.10 1 0.99 81 52 bcbo = 0.31 X lo"' atm-I, S = 16.7 0.52 0.91 0.90 80 40.8 1 1 1 80 45.8 1.47 1 0.96 77 52.3
44.5 41.9 39.1 52.8 50.2 48.5 55.3 45.6 35.4
lower q results in improved performance due to the adiabatic nature of the process. Figure 7 shows the methane isotherms with different bo values. Table 5 and Figure 6 summarize thesimulationresults. As noted above, optimum in the process performance was observed at yLL = y:,. As bo changes, the following two key parameters are affected binary selectivity:
=--nCH, YH, SCHdHz YeH, nH,
and isothermal working capacity: anise CH, = ncH4(5atm) - ncH4(1.35atm) Table 6 summarizes the four optimum cases, from Table 5 and Figure 6, for each of the isotherm shapes of Figure 7. I t is observed that as bo decreases (column 2, Table 6), selectivity decreases (column 3, Table 6) and working capacity increases (column 4, Table 6). The best process performance, i.e., the maximum net product, Qp, is obtained for the methane isotherm with binary selectivity -50, case no. 1-7, Table 6. In order to understand the reasons for the optimum in bo, three more simulations were carried out. In these simulations, the adsorbent bed was assumed to be saturated with the feed gas mixture at the feed pressure and temperature. The bed was then depressurized to -1.35 atm and then was purged with pure hydrogen at the same flow rate for all the four cases.
1604 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 Table 6. Optimum Performance for Different Isotherms: h ~ .Variation " (m= 1.51 mmol/g) case no. 2-2 3-2 1-7 4-2 201
I
20
ScH,/nPat 25 "C
atm-I 9.38 X lo4 2.81 X lo4 0.94 X 1 W 0.31 X lo4
bCH:,
I
16
I
I
12
I
I
I
8
I
4
Ank& at 25 "C 0.095 0.255 0.430 0.460
505.2 151.4 50.5 16.7 I l l
I
I
I
40
0
I
80
I
I
I
I
1 1
120 160 2 0 0
+ P(atm) t (s) Figure 8. Quantity of methane desorbed in blowdown and purge steps for various equilibrium isotherm cases.
Table 7. Optimum Performance for Different Isotherms: m Variation (ha: = 0.94 X lo-' atm-I, SCHJH~ = 50.5) case no. 1-7 5-1
m,mmol/g 1.51 2.27
QF
QP
RH.
1 1.24
1 1.28
85 88
The last three columns of Table 6 and Figure 8 summarize the results of these simulations. These show the quantity of methane rejected during the blowdown, and purge, @&,O, steps. Higher total rejected methane, C 2 k 4 O , translates into higher processing capability of the adsorbent and therefore better performance. It is observed that the quantity of methane rejected during the blowdown step (column 6, Table 6 and left-hand portion of Figure 8)increases as working capacity, due to decreasing bo, increases. However, the quantity of methane rejected during the purge step (column 7, Table 6) shows an optimum as selectivity, due to decreasing bo, decreases. This behavior results in a maximum for the total quantity of methane rejected (last column, Table 6 and right-hand portion of Figure 8) with bo and therefore an optimum in the process performance. Several conclusions can be made based upon these observations. First, if this process does not include a purge step, the fourth adsorbent (case no. 4-2, Table 6) with the highest working capacity and the lowest bo will outperform the other adsorbents. Second, for a process such as described in this study and including both the blowdown and purge steps, highest selectivity or maximum working capacity alone cannot be chosen as criteria for adsorbent selection. It is the combination of these two quantities which leads to the best adsorbent. Third, in the given scenerio, if working capacity can be increased without affecting the selectivity, a better adsorbent will be achieved. This was attempted by arbitrarily increasing the saturation capacity (m)of the adsorbent with optimum bCHlo (=0.94 X lo4 atm-l; case no. 1-7, Table 6) by 50%. Results are summarized in Table 7. It is observed that increasing the saturation capacity by 50 % increases hydrogen recovery by 3 percentage points and net productivity by -28%.
+
-
QP
QEi.
QZ,"
QEiy"
0.49 0.82 1 0.80
5.3 7.0 8.6 9.1
7.3 9.5 10.3 8.4
12.6 16.5 18.9 17.5
Conclusions Simulations for a typical Hz PSA process reveal the following: 1. The optimum process performance is expected for the purge flow quantity such that yLL = yiu, 2. Increasing the mass-transfer coefficient by opening the macropore structure is helpful but only up to a certain limit, after which it may result in reduced volumetric performance due to reduction in the bulk density of the adsorbent. In addition, one should be careful about the reduced physical strength of the adsorbent as the macropore structure is opened. 3. Highest selectivity or maximum working capacity alone cannot be chosen as the criterion for adsorbent selection. It is the combination of these two quantities which leads to the best adsorbent. 4. Increasing the saturation capacity while keeping the same selectivity leads to a better adsorbent. One method to achieve this is to use binderless materials. Acknowledgment The author is thankful to Air Products and Chemicals, Inc., for their permission to publish this work and members of our Hydrogen PSA team, especially Mr. W. E. Waldron and Mr. W. C. Kratz for many interesting discussions. Nomenclature b = Langmuir parameter
bo = preexponential parameter in the Langmuir model, eq 6 Cp, = cCpgi(T')yi,heat capacity of the gas phase at constant pressure Cw = adsorbent heat capacity C,, = cC,,;(T)yi, heat capacity of the gas phase at constant volume dl = average diameter of the large macropores d, = average diameter of the small macropores d, = particle diameter D = column diameter t = total bed voidage ti = interstitial void fraction €1 = pellet void fraction of the large macropores e, = pellet void fraction of the small macropores hw = bed to wall heat-transfer coefficient K = Henry's law constant k = mass-transfer coefficient m = saturation capacity of the adsorbate n = solid-phase loading P = total pressure P* = pressure at the end of the second cocurrent depressurization (provide purge) step, atm PBL= pressure at the end of the blowdown step, atm PFAC = proportionality parameter for mass-transfer coefficient PgL = pressure at the start of the blowdown step, atm P p = pressure at the end of the purge step, atm = mlb-mol of impurity, methane in the blowdown effluent per pound of the adsorbent
QEk4
Ind. Eng. Chem. Res., Vol. 33, No. 6,1994 1605 = mlb-mol of impurity, methane in the purge effluent per pound of the adsorbent QF = relative fresh feed processed Qp = relative net product produced Qpu = relative purge gas quantity q = isosteric heat of adsorption R = gas constant RH*= hydrogen recovery S = binary selectivity p = gas-phase mass density pb = bulk density of the adsorbent pg = gas-phase molar density t = time variable T = system temperature T , = wall temperature p = viscosity v = superficial linear velocity x = distance variable yiL = impurity, methane concentration in the effluent gas at the start of the blowdown step, ppm ybu = impurity, methane concentration in the effluent gas at the end of the purge step, ppm y = gas-phase mole fraction i = component Subscript
i = component
Superscript
* = corresponding equilibrium concentration Literature Cited Batta, L. B. Selective Adsorption Process. U.S.Patent 3,564,816, 1971. Kumar, R. Adsorptive Gas Separations: An Introduction. Presented at the AIChE Summer National Meeting, Aug 19,1991,Pittsburgh, PA. Kumar, R.; VanSloun, J. K. Purification by Adsorptive Separation. Chem. Eng. Prog. 1989,1,34-40. Kumar. R.: Kratz. W. C.: Guro. D. E.: Golden. T. C. A New Process for the Production of High Purity Carbon Monoxideand Hydrogen. Proceedings ojthe Thirdlnternationul Symposium on Separation Technology, Antwerp, Belgium, Aug 22-27,1993;Process Technologies Proceedings 11; Elsevier: Amsterdam, 1994. Kumar, R.; F0x.V. G.; Hartzog, D. G.; Larson, R. E.; Chen, Y. C.; Houghton, P. A.; Naheiri, T. A Versatile Process Simulator for Adsorptive Separations. Chem. Eng. Sci. 1994,in press. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984;133-135. Wakao, N.; Smith, J. M. Diffusion in Catalyst Pellets. Chem. Eng. Sci. 1962,17,825-834.
Received for review August 23, 1993 Revised manuscript received March 2, 1994 Accepted March 24, 1994'
Abstract published in Advance ACSAbstracts, May 1,1994.
