1250
Ind. Eng. Chem. Res. 1994,33, 1250-1258
Simulation of a Four-Bed Pressure Swing Adsorption Process for Oxygen Enrichment Cheng-tung Chou' and Wen-Chun Huang Department of Chemical Engineering, National Central University, Chung-Li 32054, Taiwan, R.O.C.
Dynamic simulation with the valve equation approach of a four-bed pressure swing adsorption (PSA) process for oxygen enrichment over zeolite 5A was performed. Product pressurization, feed pressurization, production, blowdown, purge, and pressure equalization are included in this process. The numerical results were compared to the experimental results of Chiang et al. (1994) and gave reasonable agreements. The effects of production rate and purge rate on the purity and recovery were also explored by simulation. When breakthrough did not occur for the depressurizing bed during the pressure equalization step, operation at the minimum purge rate gave a relatively high recovery for producing a product of purity more than 95% oxygen. When breakthrough occurred, the theoretical results show that, for a fixed production rate, there is a purge rate giving the maximum recovery and a different purge rate giving the highest purity.
Introduction Pressure swing adsorption (PSA) is a cyclic process for gas purification and separation. More and more commercial separation processes employing PSA technology have been developed since the first patent of a PSA process in the United States (Skarstrom, 1960)was described. This separation technology needs lower energy and is less costly than the conventional separation processes like absorption and distillation, and it can provide a very efficient and flexible means of gas separation. The Skarstrom process operates with two beds, and it includes four operation steps: feed pressurization, production, blowdown (countercurrent depressurization),and purge. For improving the performance of this basic PSA process, more operation steps were developed, such as pressure equalization, product pressurization, and cocurrent depressurization. Besides the operation steps, the number of adsorption beds was modified to achieve the optimal operation of a PSA process and multibed (more than two beds) processes are now commonly used commercially. Although multiple adsorption beds are usually involved in the applications of PSA processes in industry, the detailed operation information is usually retained by each company and seldom revealed. Most of the published studies, therefore, are limited to the processes of singleand dual-bed systems. The study of Tomita et al. (1986) is one of the few literature references discussing multibed processes and is an experimental study of a four-bed PSA process for hydrogen purification to discuss the effects of feed rate, cycle time, and bed length on the product purityrecovery relation. Some of the modeling studies in dual-bed PSA processes, such as Farooq et al. (1988),Farooq and Ruthven (1990), and Ackley and Yang (1990),assume that bed pressure is constant during the production step and the solid phase is frozen during the pressurization and blowdown steps. Farooq et al. (1986) also used a linear pressure change assumption for the pressurization and blowdown steps. Doong and Yang (1986) and Kapor and Yang (1986) used the measured pressure history as input into the simulation program to deal with the pressure change during the pressure-changing steps. In the present study a simulator for the modeling of multibed and multistep PSA processes
* TOwhom correspondence should be addressed.
E-mail address:
[email protected].
Internet
with the incorporation of a valve equation is provided. The history of bed pressure is predictable from the valve equation approach. The difference among the three approaches of valve equation, frozen solid, and linear pressure change was compared in Chou and Huang (1994). The accuracy of the valve equation approach was tested for breakthrough curves and a dual-bed PSA process of air system and gave a good representation of the experimental pressure and concentration profiles (Chou et al., 1992). The predicted flow rates also agreed reasonably with the experimental data. In the present study a more complex four-bed PSA process is simulated with the valve equation approach. In this process the steps of product pressurization, feed pressurization, production, blowdown, purge, and pressure equalization are included in a cycle. The objectives of this theoretical study are, first, to prove that the modeling is appropriate for the four-bed PSA process by comparing the simulation results with the experimental data of Chiang et al. (19941, and, second, to obtain the optimal purge rates for this PSA process at different production rates. When comparing simulation results with the experimental data of Chiang et al., there are reasonable agreements. For the study of the optimal purge rate, two situations for obtaining the optimal purge are presented depending on whether breakthrough occurs in the depressurizing bed during the pressure equalization step. Explanations for the existence of the optimal purge rate are also given.
Process Description A four-bed PSA process producing enriched oxygen continuously over 5A zeolite was studied. In this process pressure equalization and product pressurization are accommodated in addition to the basic four steps of feed pressurization, production, blowdown, and purge. The cycle time is 200 a. Figure 1shows the first 50 s of a whole cycle, which represents the period of producing product from bed A. Each flow rate is controlled by the opening of a manipulated valve. The valves 1,2,5, and 6 control the flow rates of feed, purge, pressure equalization, and product pressurization, respectively. The flow rate through valve 3 is the sum of production and purge rates. Valve 4 controls the outlet flow rate during the blowdown and purge steps. The feed air pressure and purge gas pressure are kept at preset values by pressure regulators. The actual outlet flow rate from the bed during the production step
0888-5885/94/2633-1250$04.5010 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1251
vLml$ PROD CRON
PRESSURE EqUALlZAnON
T
PURCE
PRESSURE EQUAUZAmN
0
20 40
60 80 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0
Time (sec) Figure 2. Pressure history of a bed for a typical experimental run. Seven time intervals are indicated: production (I), pressure equalization for depressurization(II),blowdown (III),purge (IV),pressure equalization for pressurization (V),product pressurization (VI),and feed pressurization (VII).
8
VALVE 1
5
6.0 VALVE 4
VALVE 1
p V E 4
1
m D A O N P m s ~ k i L m N P m E
Bw&m
Figure 1. First 50 s of the operation schedule of the four-bed process with a 200-6 cycle.
includes the production rate and the purge rate, and the flow rate for pressurizing another bed is added in if the product pressurization step exists. At the start of a cycle, feed air is fed to bed A from one end and a product of enriched oxygen is drawn from the other end at a high bed pressure, and then some product is used to purge bed C. At the same time, beds B and D are connected to equalize the pressure of the two beds. This operation step lasts 20 s. For the next 20 s bed A keeps being fed with air, producing product and purging bed C, and at the same time, bed B is pressurized by the product from bed A. At this step bed D is depressurized by blowdown. For the next 10 s, bed A keeps producing product and purging bed C, bed B is pressurized with feed air, and bed D is at blowdown. The first 50 s are the period of producing product from bed A. Then the product is produced from bed B during the second 50 s with a phase change. The roles of beds B, C, D, and A at the second 50 s replace those of beds A, B, C, and D a t the first 50 s, respectively. After this phase change beds C and D are used to produce enriched oxygen during the third and fourth 50-5 periods, respectively, and the overall cycle is completed. The experimental measures of bed pressure, feed rate, production rate, and purge rate were done by Chiang et al. (1994). The typical pressure history of a bed during a cycle is shown in Figure 2. A cycle is divided into seven time intervals, and the pressure equalization includes interval I1 (depressurizing) and interval V (pressurizing). The feed rate and production rate varied continuously within a cycle due to the change of the pressure of the beds being fed by air or producing enriched oxygen. Figure 3 shows the histories of feed rate, purge rate, and production rate during a cycle for an experimental run. A pattern repeats four times, and each represents the flow rate of a bed.
Mathematical Model The theoretical model contains the following assumptions:
r
7
80
3 5.5 -
I 2 2 I
rn
v v) o) cl
p:
8
3
s e
&
h
5.0 -
h
e
.-E
'2 \
E 60
z
6;
4.5 - 2 4.0 -
3.5 -
.e I
-6
rn
40
v
Y u
3 20
p:
5 :
d
2.5 -
3.0
2.0
L
90
$
a
-20 4
0
50
100
150
200
Time (sec)
Figure 3. Feed rates, purge rates, and production rates for a typical experimental run.
(1)Flow is described by the axial dispersed plug flow model. (2) The equilibrium relation for oxygen is a Langmuir isotherm, and that for nitrogen is Sips equation. (3) The axial pressure drop is negligible. (4) The ideal gas law is applicable. (5) The local equilibrium model which neglects masstransfer resistance is assumed. (6) The solid and gas phases reach thermal equilibrium instantaneously. (7)The radial temperature and concentration gradients are negligible. Subject to these assumptions, the following set of equations describes the system: overall material balance
mass balance for component a
1252 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 Table 1. Constants for the Extended Langmuir-Sips Eauations.
energy balance
gas
a
02
1.9391 X 10-'
b
3.4442 X
N2 6.1746 X 10-' 1.2129 X 10-1 At 297.15 K,Miller et al. (1987).
The adsorbate concentrations in the solid phase, na and nb, are equal to those at equilibrium, na* and nb*, owing to the local equilibrium approximation. From the extended Langmuir-Sips isotherm the equilibrium adsorption concentrations could be expressed as na* =
+
1 blPy
alPY + b p ( 1 -yId
The isotherm constants are functions of temperature and expressed as the following: al = a: exp(H,lRT); a, = a t exp(H,,/RT)
(5)
b, = b: exp(H,lRT); b, = b t exp(H,,/RT) (6) Within this four-bed PSA process, flow streams (such as feed flow and product flow) are built through the manipulated valves and the valve equation is used to calculate flow rates at the ends of beds in the theoretical calculation unless otherwise specified. The flow formula for gases recommended by Fluid Controls Institute Inc. was the valve equation used to calculate the flow rates at both ends of a bed:
for P2> 0.53P1
Q = 77.01~~
(7)
or
mT] for
Q = 65.31cp1[ 1
1/2
P, I0.53P, (critical flow) (8)
where Q = flow rate in L/s (1atm, 273 K) c, = valve flow coefficient
SG = specific gravity of gas (air at 1atm and 294.4 K = 1)
T = absolute temperature of flowing gas (K) P, = upstream pressure (atm)
P2= downstream pressure (atm) The associated boundary conditions are (1)
at bed inlet, y = yin,T = Tin
(2)
at bed outlet, aylaz = 0, aT/az = 0
boundary condition for flow rate is calculated from the valve equation Initial conditions for the start-up of the cyclic operation (3)
d
0.8260
with saturated beds are y(z,t=O) = 0.22, P(t=O) = 1atm, na(Z,t=O) = n,*, and nb(Z,t=O) = nb*. Since the adsorption equilibrium of argon is about the same as that of oxygen, oxygen and argon were taken as one component in the simulation to simplify calculations. For the results shown in this study, we have adjusted the calculated data to present the purity of oxygen only. Most of the calculations were done with the method of lines combined with the cubic spline approximation. When a high-purity product was obtained, usually at a low production rate, upwind finite difference was used to replace the cubic spline approximation to deal with the sharp concentration wave front. With the method of lines, the PDEs (partial differential equations) of eqs 1-3 were discretized into a set of ODES (ordinary differential equations) with respect to time and the program LSODE in the package of ODEPACK (Hindmarsh, 1983)was used to do the integrations. Besides, adaptive grid points controlled by judging the magnitudes of the second spatial derivatives of concentration and temperature were used to ensure that there were enough grid points around shock waves (Hu and Schiesser, 1981). The detailed calculating scheme was shown in Chou et al. (1992). Estimation of Parameters
In this study 5A zeolite was used to separate air for producing enriched oxygen by a PSA process. The quantity of argon contained in air is small, and the argon adsorption is essentially identical to that of oxygen in the pressure range of operating. The 02-Ar pair was therefore treated as a single component in the theoretical model to simplify the modeling, and binary Langmuir-Sips equations were used to represent the equilibrium relation between the solid and gas phases. The isotherm constants and heats of adsorption used were taken from the experimental data of Miller et al. (1987). The adsorption constants are shown in Table 1. Two heat-transfer resistances are involved in the calculation of the overall heat transfer-coefficient h. One is the heat transfer from fluid to wall, and the equation from Beek (1962)was used. The other is the heat transfer from wall to the ambient, which is assumed to be free convection, and the heat-transfer coefficient was taken from Minkowycz and Sparrow (1974). The axial dispersion coefficient D, could be expressed as 0.75D~+ (0.5dpa)/(1 + 0.95Dd/ndP) (Wen and Fan, 1975). The molecular diffusivity DM should be proportional to F . 6 p - l (Bird et al., 1960). In the simulation, since the variation of temperature was small, it is assumed that DMis proportional to (TIP)to simplify calculations. D,, therefore, could be expressed as D,O(PO/P)(T/P), where d ~ ) ,= Duo = 0.75D~O+ (0.5dptio)/(l + 0 . 9 5 D ~ ~ / Z i ~ii/tio (PO/P)(T / P ) , and PO and P are the reference pressure (1 atm) and temperature (273.14 K), respectively. The velocityiio (at PO and P )based on the average feed velocity of the experimental results was used to calculate Duo. The effective thermal conductivity h was estimated from Yagi et al. (1960),and the solid heat capacity was estimated
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1253 20
80
-j
I
I
I
I
I
300
1.2
--_
PE (depressurizing)
-
8
-
40-
4
%
3
k
J
' 1 2 1-( + a
I
20 2o 10 10
- Exp. - - Simu.
01
3
m
0.6
2 :
I
I
I
1
I
50
100
150
200
!% E
8
250
Figure 4. Comparison between experimental data and simulation results for run 11. Table 2. Parameters Used in Calculation
(c,)
200
150
0.0
Time (sec)
(c
-
Pressure
0
feed gas composition column length column diameter bed voidage (6) adsorbent particle size particle density (p,) bed density dispersion coefficient (&O) overall heat transfer coefficient (h) average thermal conductivity (h) solid heat capacity ) heat capacity of 02 heat capacity of N2 (cpb) adsorption heat of 02 (Ha) adsorption heat of NZ(Hb)
M
-
0)
E
h
PD
air (22%02 and Ar, 78% N2) 8.00 x 10-1 m 1.023 X 10-l m 3.40 X 10-1 Linde 5A Zeolite 1/16-in. pellets 1.21 X 103 kg/m3 8.00 x 102 kg/m3 2.00 X lo-' m2/s (at STP) 2.50 J/K-mz.s 3.90 X 10-1J/K.m.s 8.10 X 102 J/kg.K 2.94 X 10IJ/mol.K 2.91 X 10IJ/mol.K 1.51 X l(r J/mol 2.26 X l(r J/mol
from Breck (1974). Parameters used in calculations are shown in Table 2.
Results and Discussion Comparisonwith ExperimentalData. To verify the applicability of the theoretical model, the simulation results were compared to the experimental data of Chiang et al. (1994). For the convenience of comparison, the experimental measured feed flow rate and purge flow rate were input into the simulationprogram, and the production rate was calculated from the valve equation. Table 3 shows the comparison between the results of theoretical calculations and the experimental data. The simulation results gave good agreements with the experimental data in the yield, purity, and recovery. In addition, the dynamic data during a whole cycle were compared. Figure 4 shows the comparison of bed pressure, production rate, and product concentration of oxygen for run 11. The simulated pressure history was very similar to the experimental values. The production rate was slightly different from that of the experimental data. For the pressure history, the bed pressure changed continuously during the whole cycle except at most of the blowdown and purge steps. The pressure variation of the bed during the production step brought about the fluctuation of production rate. With the introduction of the valve equation into the theoretical model, the pressure history and production rate history could be predicted well. The product concentration had a greater undulation for simulation than that of the experimental data, and the average product purity was slightly different. The smaller undulation of the experimental results may be caused by the dispersion effect of
100
0.0
0.2
0.4
0.6
0.8
1.0
Dimensionless Axial Position Figure 5. Concentrationand temperature profiles at the end of the production (PD) and pressure equalization (PE) steps for run 3.
h
PE (depressurizing)
R LI
e
I
0.0
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1
100
Dimensionless Axial Position Figure 6. Concentrationand temperature profiles at the end of the production (PD) and pressure equalization (PE) steps for run 12.
the sampling product in the piping before it reached the oxygen analyzer. Figures 5 and 6 show the calculated concentration and temperature profiles at the end of the production and pressure equalization steps (for the depressurizing bed). The position of the temperature wave front coincided with that of concentration wave front. For the process producing the lower concentration product (Figure 61, the concentration wave front of the depressurizing bed was pushed through the bed during the pressure equalization step, but for the process producing the higher concentration (Figure 5), this phenomenon did not occur. If a higher product purity is desired, the concentration wave front must be kept in the depressurizing bed during the pressure equalization step. Numerical Regression for Simulation with High Production Rates. In order to study the influence of production rate and purge rate on production, calculations were performed for PSA operations at a feed pressure of 4.25 atm and a blowdown pressure of 1 atm. Multiple simulations runs were carried out for the production rate referred to as the "high in the range 5.5-10 L/min (STP), production rate" in this paper, and for the purge rate in the range 3-24 L/min (STF'),and each run was operated at a fixed production rate and a fixed purge rate. The other flow rates were controlled by preset valve Coefficients, and the valve coefficients were 1.4 X l@l, 6.5 X 1k1,2.0
1254 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 Table 3. Comparison between Experimental Data of Chiang et al. and Theoretical Calculations yield (L/mina) purity ( % ) run no. feed (L/mino)purge (L/mina) expt aim expt sim
9.24 8.84 8.60 7.74 2.40 6.43 5.03 4.00 11.32 10.12 7.54 5.16
56.95 56.33 57.00 55.04 52.00 54.49 51.59 51.24 61.36 59.80 57.30 55.19
1 2 3 4 5 6 7 8 9 10 11 12 a Average
1.85 2.26 3.05 3.86 9.02 2.05 2.47 3.66 3.91 4.78 7.56 9.65
1.85 2.26 3.04 3.88 9.11 2.05 2.48 3.66 3.92 4.81 7.57 9.66
94.50 91.40 89.08 84.80 48.67 91.25 88.58 82.44 87.10 83.77 63.29 51.49
loo
u
1
70
-
60
-
50
-
I
/.
h
5
5
a
92.04 93.29 90.74 91.61 51.20 87.09 86.14 82.70 92.83 87.84 65.84 51.67
14.57 17.40 22.69 28.33 40.22 16.41 20.24 28.01 26.41 31.85 39.79 42.86
14.18 17.70 22.97 30.63 42.56 15.59 19.79 28.05 28.20 33.58 41.32 42.53
flow rate at STP. 100
ON
recovery ( % ) expt aim
Production Rate o 6
I
I
I
5
10
15
20
25
40 0
50
9 (STP liter/min)
v I
40
I
Purge Rate
r,
0 6 0 15 v 21
(STP liter/min) (STP liter/min) (STP liter/min)
1
-
-
4
30
I
t
(STP liter/min)
I
I
" i
6
8
10
12
Production Rate (STP liter/min) Figure 9. Effects of production rate on purity.
Purge Rate (STP liter/min) Figure 7. Effects for purge rate on purity.
45
ho 40 ON U
F P 0
2
35
/
Production Rate (STP liter/min) 0 8 (STP liter/min) v 9 (STP liter/min) 0 6
0
I
I
1
I
1
5
10
15
20
25
30 30
4
6
Purge Rate 0 6 (STP liter/min) 0 15 (STP liter/min)
v 21 (STP liter/min)
8
10
12
Purge Rate (STP liter/min) Figure 8. Effects of purge rate on recovery.
Production Rate (STP liter/min) Figure 10. Effects of production rate on recovery.
X lO-l, and 8.6 X for valves 1,4,5,and 6, respectively. Figures 7 and 8show the effects of purge rate on the purity and recovery at a fixed production rate. Figures 9 and 10 show the effects of production rate on the purity and recovery at a constant purge rate. We performed the numerical regressions (the solid line) for these simulation results, and it was found that the cubic polynomials gave good fitting for the data in Figures 7-10. Therefore, the dependence of product purity and recovery on the production rate and purge rate could be described by the cubic-polynomial expressions and the following form is used
Y(or 0) = (A,
+ AID + A P 2 + A @ ) ( l +
B,R
+ B2R2+
B a 3 ) (9) where Y, 0,D, and R stand for purity (% 1, recovery ( % 1, production rate (STPL/min), and purge rate (STPL/min), respectively, and Ai, Bi are regression constants. Table 4 shows the coefficients,which were obtained from regression with the production rate of 5.5-10 L/min (STP) and the purge rate of 3-24 L/min (STP).The simulation results and regression curves are shown in Figure 11 by plotting the purity versus the recovery. The solid lines in this figure are the regression curves for two production rates.
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1255 Table 4. Regression Coefficients'
Y 0 a
Ao 1.503 X 102 5.050 X 10'
Ai
A2
-2.224 X 10' -5.191 X 100
1.350 X 100 6.251 X 10-l
Bi 3.437 x 10-2 7.233 X 10-3
A3
-2.086 x 10-2 -1.837 X le2
B2
B3
5.995 X lo-' -2.043 X lo-'
-6.133 X 106 -1.598 X 106
The coefficienta were determined from eq 9 with Y and 0 in % and D and R in STP L/min. 0.9
loo
I
I
1
I
I
I
1
0.8
0
2
.-
0.7
v
ON 0.6 u 0
24 STP liter/min 18 STP liter/min 12 STP liter/min 6 STP liter/min 3 STP liter/min
0.5 .r(
c,
2 &
Production rate
0,
g
d
6 (STP liter/min)
40 30
--
0.4
/
0.3
9 (STp liter/min)
35
40
0.2
45
I
Recovery of 0, (%)
0.1 1 0.0
Figure 11. Relation between purge and recovery for different purge rates at fixed production rates.
For a fixed production rate there was a purge rate giving the maximum recovery and a different purge rate giving the highest purity. The recovery of the highest-purity operation was only slightly less than the maximum recovery. Therefore, operation at the highest-purity condition seems very plausible. When the purge rate decreased from the maximum-recovery condition, the purity dropped very quickly although the recovery only decreased slightly. When the purge rate increased from the maximum-recoverycondition,the purity first increased slightly and then decreased slightly,and the corresponding recovery decreased gradually. Reason for Maxima of Purity and Recovery. To study the reason for the existence of the maxima of purity and recovery with respect to the purge rate, the concentration profiles within a bed were plotted during each step of a cycle. By observing the movement of concentration wave front in the adsorber during a whole cycle, the reason for maximum of purity came out naturally. The concentration profiles at the end of production step are shown in Figure 12. Each line in this figure represents a purge and 24 L/min (STP), and the production rate of 3,6,12,18, rate is 8 L/min. As seen from this figure the position of the concentrationwave front was essentially identicalwhen the purge rate increased from 3 to 18 L/min. After the production step, the pressure equalization for depressurizing, blowdown, and purge steps proceeded according to the schedule. Figure 13 shows the concentration profiles at the end of purge, and the higher purge rate would obtain a more complete regeneration of the bed. Then at the pressure equalization step for pressurizing, the lowconcentration gas stream from the depressurizing bed would penetrate into this bed. The deeper penetration of the low-concentrationgas stream will reduce the product purity at the production step after this bed passing the product pressurization and feed pressurizationsteps. From Figure 14,the run with a purge rate of 18 L/min got the least amount of penetration because of the best regeneration obtained when the purge rate increased from 3 to 18 L/min, and certainly, this run achieved the highest product purity. The greater amount of nitrogen adsorbed
I I
I
I
I
0.2
0.4
0.6
0.8
1 .o
Dimensionless Axial Distance Figure 12. Concentration profiles at the end of the production step; production rate = 8 L/min (STP). 1 .o
R
Purge Rate 24 STP liter/min 0.8 : 18 STP liter/min 0
Y
ON o 0.6
-
(LI
6 STP lite 3 STP lite
8
3 u
ct:' si
0.4
Q)
r.
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1 .o
Dimensionless Axial Distance Figure 13. Concentration profiles at the end of purge step; production rate = 8 L/min (STP). during the pressure equalization step for pressurizing for the bed of less complete purge would increasethe quantity of low-concentrationgas stream entering this bed. When the purge rate exceeded 18Llmin, the purity waa reduced, as shown in Figure 7. This decline was caused by the advancement of the concentration wave front at the end of the product step for the purge rate of 24 L/min over the wave fronts of the other purge rates, as shown in Figure 12. This advancement caused the low-concentration gas stream to penetrate more deeply into the bed with the purge rate of 24 L/min than with the purge rate of 18 L/min, as shown in Figure 14. Therefore, for a production rate of 8 L/min, there existed a maximum purity at a purge rate around 18 L/min.
1256 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1.2 I
1
I
I
I
1
~
1 .o
0.8
0
h
n
ho
be
v
W
0 " ( I
0.8 c 0
0.6
0
g
."4
.r(
4
E
*
.
30 STP liter/min 24 STP liter/min 6 STP liter/min
STP liter/mon
2
0.6
0
2
0.4
E4
E4
0.4
0)
0)
ii
4
0.2
0.2
-
6 STP liter/min 0.0 I 0.0
Dimensionless Axial Distance
1.2
c ON 0
1 .o
30
ho
t
W
89
0 "
0
*
n
45
40 35
I
0.8
I
-m-.-.-.-.-.
6e
I
0.6
1 .o
Figure 16. Concentration profiles at the end of production step; production rate = 4 L/min (STP).
60
v
I
0.4
Dimensionless Axial Distance
Figure 14. Concentration profiles of the pressurizing bed at the end of the pressure equahation step; production rate = 8 L/min (STP).
-
1
0.2
0.8
.
I
I
I
0.6
0.8
Purge Rate 30 STP liter/min 24 STP liter/min 6 STP liter/min 3 STP liter/min
c 0
-
0.6 .r(
4
u
25 20
6 Ll
-
0.4
Q, *
15 101
1 I
0
1
I
I
I
I
I
5
10
15
20
25
30
I 50
s
0.2
35
Purge Rate (STP liter/min) Figure 15. Effects of purge rate on purity and recovery: production rate = 4 L/min (STP).
In this process the outlet gas during the blowdown and purge steps is pushed into the surroundings and discarded. When the purge rate increased at a fixed production rate, the ratio of waste gas to feed also increased, and the ratio of product to feed decreased correspondingly. At the same time, as seen from Figure 12, the product purity increased with the increase of purgerate until reaching the maximum purity condition. When the purge rate increased from a small value, the increase of product purity overcame the small reduction in the ratio of product to feed, hence the recovery increased. Then the increased rate of product purity was gradually offset by the reduction in the rate of product-to-feed ratio and was finally overcome by it, and hence the recovery decreased. Therefore there existed a maximum recovery when the purge rate increased a t a fixed production rate. Theoretical Results for Simulation with Low Production Rate. Figure 15 shows the effects of purge rate on the purity and recovery for the runs with a production rate of 4 L/min (STP),referred to as the "low production rate". As seen from this figure, products with a purity of more than 95% oxygen were obtained when the purge rate was between 6 and 24 L/min. The recovery decreased
0.0 0.0
0.2
0.4
1 .o
Dimensionless Axial Distance Figure 17. Concentration profiles at the end of purge step; production rate = 4 L/min (STP). with the increase of purge rate, and the purity decreased drastically when the purge rate was over 24 L/min. Matz and Knaebel(1988) studied a typical four-stepPSA process for splitting oxygen from air with high-purity product as the purging gas and the gas for pressurizing the adsorption bed from the product end. Their experiments generated products with purity of more than 98% oxygen and argon and yielded nearly double the recovery of oxygen for minimal purge compared with that availablewith complete purge. They also showed that incomplete purge gives a greater recovery than complete purge does when the pressure ratio is specified. For those runs in Figure 15, we have results similar to what was mentioned above: the recovery decreases with the increase of the purge rate, though the four-bed process discussed here is different from the single-bed process of Matz and Knaebel(1988). Figures 16 and 17 show the concentration profiles for four different purge rates of 2,6,24, and 30 Llmin at the end of the production and purge steps, respectively. The smallest purge rate of 2 L/min gave the highest recovery.
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1267 isjust for the convenience of calculations. In the simulator the flow rates of all gas streams controlled by manipulated valves can be calculated by the valve equation. Besides, the simulator is very flexible and the process parameters are read from the input files. The process parameters include bed numbers, how the process units are connected at each step, cycle time, the opening of valves,the isotherm data, and the physical data. The CPU time for the computation of a cycle is about 2-6 min in VAX 9320and it usually takes 80-120 cycles to reach the cyclic steady
1 .o
R
0.8
0 " c 0
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0.6
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State.
4
0
0.4 0)
0
d
.
0.2
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0.0 0.0
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Purge Rate 30 STP liter/min 2 4 STP liter/min 6 STP liter/min 2 STP literjmin
I
1
I
I
0.2
0.4
0.6
0.8
1 1 .o
Dimensionless Axial Distance Figure 18. Concentration profiles of the pressuring bed at the end of the pressure equalization step; production rate = 4 L/min (STP).
The drastic reduction in purity after the purge rate of 24 L/min in Figure 15 is because the wave front of the depressurizing bed was pushed out of the bed during the pressure equalization step, as seen in comparing Figures 16 and 18,and the low-concentration stream was pushed into the other pressurizing bed during the pressure equalization step, as shown in Figure 18. Figure 18 shows the concentration profiles of the pressurizing bed at the end of pressure equalization. For the run with a purge rate of 30 L/min, the low-concentration gas at the product end (dimensionless axial distance equal to 1.0)was pushed out as product during the production step, and therefore a drastic reduction of purity occurred. For the runs with a production rate of 4 L/min, we faced a numerical stability difficulty for the calculations with the cubic spline approximation due to the stiffness of the high-purity product system. To solve this numerical stability difficulty, the upwind finite difference was used to carry out the calculations for the runs with a production rate of 4 L/min. Other Discussion. As seen from the simulation results for the runs with "high production rates" (production rate = 6,8,and 9 L/min) and the runs with the "low production rate" (4L/min), the main difference between them is that, during the production step, breakthrough of the concentration wave front occurs for the runs with high production rates, but the wave front is still inside the bed for the runs with the low production rate. Therefore, very high purity products could be obtained with the low production rate. If a high-purity product is required, operation at the low production rate and a small purge rate such as 6 L/min is suggested. If only a moderate-purity product is needed, operation with high production rate is suggested. From the regression equation, eq 9,the optimal condition-the maximum purity condition for the runs with high production rates-can be predicted. In Table 3, the simulation results used to compare with the experimental data were obtained with the input of experimental feed and purge rates into the simulator. The theoretical results used to explore the effects of purge rate and production rate on the purity and recovery were obtained with the input of fixed production and purge rates into the simulator for each run. The reason why these flow rates were not calculated by the valve equation
As seen from Table 3 and Figure 15,the simulation results in Figure 15 have higher product purity than the experimental data in Table 3 for the runs with nearly the same production rate. For the experimental data of runs 4 and 9 in Table 3, the production rates are all about 4 L/min, and the purge rates are about 8 and 11 L/min, respectively. The experimental and simulation results of Table 3 have lower product purity and about the same recovery compared to the simulation results of Figure 15. The lower purity in the experimental results of Table 3 is because of the nonuniform operation of the four beds. From Figure 3, the four split peaks of feed rate are not uniform and one of the peaks is lower than the others. That means that the flow resistance of the four beds is not exactly the same. As mentioned in the above paragraph the simulation results in Table 3 used to compare with the experimental data were obtained with the input of experimental feed and purge rates into the calculations, and therefore agree reasonably with the experimental data. That is for the check of the accuracy of the simulation method. However, for studying the effects of purge rate and production rate on the purity and recovery, the input of fixed production and purge rates was used instead. The simulation results in Figure 15 were obtained with such input. Therefore, the lower purity in the experimental and simulation results of Table 3 compared to the simulation results of Figure 15 can be explained by the fact that a uniform four-bed process produces a higher purity product than a nonuniform four-bed process does. In this study, we just explored the optimal purge rates for different production rates. For this complex multibed process, the other process variables could also be studied to improve the performance. The scheduling of cycle time, the pressure ratio (PH/PL),and the incorporation of the other process step, such as cocurrent blowdown, could be the material for future study. Conclusions A simulator suited for the modeling of multibed and multistep PSA processes was provided. This simulator includes the valve equation and provides a flexible way to predict the pressure change and flow rates during a whole cycle. The simulator with a local equilibrium approximation and an extended Langmuir-Sips isotherm was used to dynamically simulate a four-bed PSA process producing oxygen over zeolite 5A and gave a good representation of the experimental data of Chiang et al. (1994). In the process, feed pressurization, product pressurization, pressure equalization, blowdown, purge, and production steps are included. The simulator was also used to explore the effects of purge rate and production rate on the purity and recovery. Whether breakthrough occurs for the depressurizating bed and whether the low-concentration stream is pushed into the pressurizing bed during the pressure equalization step are important factors affecting the product purity. For the runs with the "low production rate" (4L/min), in order
1258 Ind. Eng. Chem. Res., Vol. 33, No. 5,1994
to obtain a product of purity more than 95% oxygen, a purge rate greater than a minimum value and less than a maximum value was needed. A purge rate less than a maxmium rate was to ensure that the low-concentration stream was not pushed into the pressurizing bed during the pressure equalization step. The operation at the minimum purge rate gave a relatively high recovery. For the runs with high production rates, in which the low-concentration stream was pushed into the pressurizing bed during the pressure equalization step, the simulation showed that for a fixed production rate there were a purge rate giving the maximum recovery and a different purge rate giving the highest purity. The recovery of the highestpurity operation was only slightly less than the maximum recovery. Therefore, operation at the highest purity condition seems very plausible. For these runs, the product purity and recovery could be expressed as cubic polynomials of the production rate and purge rate and the resulting regression equation could be used to predict the optimal condition-the maximum-purity condition.
Acknowledgment The authors wish to thank the National Science Council of the Republic of China for financial support under Project NO. NSC82-0402-E008-041. Nomenclature a1 = isotherm constant for oxygen, kmoVatmm3 solid a2 = isotherm constant for nitrogen, kmol/atmoJ3~.m3solid bl = isotherm constant for oxygen, atm-l b2 = isotherm constant for nitrogen, atm4.826 C = total adsorbate concentration in gas phase, kmol/m3 C, = average heat capacity of 0 2 and Nz, J/mol.K C,i = heat capacity for component i, J/mol.K C,, = solid heat capacity, J/kg.K d = 0.826, isotherm constant for nitrogen, dimensionless d, = diameter of catalyst particle, m D, = axial dispersion coefficient, m2/s D M = molecular diffusivity, m2/s h = overall heat-transfer coefficient, J/m2.K-s Hi = adsorption heat for component i, J/mol k = average thermal conductivity,J/mK.s L = length of adsorption bed, m ni = adsorbate concentration in solid phase for component i, km0i/m3 P = total pressure of a bed, atm r = adsorber radius, m R = ideal gas constant atmm~/kmol.K t = time, s T = temperature, K T, = ambient temperature, K u = interstitial flow velocity of gas, m/s y = mole fraction of oxygen, dimensionless z = axial distance coordinate, m Greek Letters e = void fraction of the packed bed, dimensionless ps
Subscripts
a = component 02 b = component NZ
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Superscripts 0 = the gas reference state at 0
*
'
Received for review August 25, 1993 Revised manuscript received January 10, 1994 Accepted January 25, 1994.
= particle density, kg/m3
O C and 1 atm, or the preexponential constants defined in eqs 5-6 = the quantity at equilibrium state
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Matz, M. J.; Knaebel, K. S.Pressure Swing Adsorption: Effects of Incomplete Purge. AIChE J. 1988,34, 1486. Minkowycz, W. J.; Sparrow, E. M. Local Nonsimilar Solutions for Natural Convection on a Vertical Cylinder. J. Heat Tramjer, TRANS. ASME., 1974,96,173. Skaratrom, C. W. U.S. Patent 2,944,627, to Esso Research and Engineering Company, 1960. Tomita, T.; Sakamoto, T.; Ohkamo,U.; Suzuki, M. The Effects of Variables in Four-Bed Pressure Swing Adsorption for Hydrogen Purification. In Fundamentals of Adsorption; Athanasios, I. L., Eds.; Engineering Foundation: New York, 1986; pp 569-578. Wen, C. Y.; Fan, L. T. Models for Flow Systems and Chemical Reactor, Dekker: New York, 1975, pp 169-171. Yagi, S.; Kunii, D.; Wakao, N. Studies on Axial Effective Thermal Conductivities in Packed Beds. AIChE J. 1960, 6, 543.
Abstract published in Advance ACS Abstracts, March 15, 1994.
