Znd. Eng. Chem. Res. 1991,30, 1981-1989 from conical mass flow hoppers. Chem. Eng. Sci. 1977,32,241.
Zenz,F. A.; Othmer, D. F . Fluidization and Fluid-Particle Systems;
Reinhold: New York, 1960. Zhang, J.-Y.; Rudolph, V.;Leung, L. S. Non-fluidized flow of gassolids in standpipes under negative pressure gradient. In Fluidization VI; Grace, J. R., et al., Eds.; Engineering Foundation: New York, 1989a; p 154. Zhang, J.-Y.;Rudolph, V.; Leung, L. S. Standpipe flow against a
1981
negative pressure gradient. Proceedings of the Seventeenth Australasian Chemical Engineering Conference,CHEMECA 89, Aug 23-25; 1989b; p 882. Zhang, J.-Y. Non-fluidized standpipe flow under negative pressure gradient. PbD. Thesis, University of Queensland, Australia, 1990.
Receiued for review January 8, 1991 Accepted April 8, 1991
Simultaneous S02/N0, Removal and SO2 Recovery from Flue Gas by Pressure Swing Adsorption Eustathios S. Kikkinides and Ralph T. Yang* Department of Chemical Engineering, State University of New York at Buffalo, Buffalo,New York 14260
The feasibility of employing pressure swing adsorption (PSA) for simultaneous SOz/NO, removal from flue gas and concentrating the SO2 in the desorption stream (expressed as enrichment ratio) is established by model simulation. A weak-base macroreticular resin is used as the sorbent. Concentrating the adsorptive is a new and promising application for PSA. This work also delineates the underlying principles for concentrating the adsorptive. The purge/feed ratio is a key parameter for the adsorptive enrichment ratio, which reaches a peak value a t a certain purge/feed ratio. Effects of the other PSA cycle parameters on the enrichment ratio are also illustrated. For a simulated power-plant flue gas containing 0.5% SOz, 0.13% NO2,and 18% COz, a simple Skarstrom cycle can produce a purified stream with 0.035% SO2,and 0.069% NO2,while the desorption stream contains 7% SOz. Further improvement can be obtained by employing a more complex PSA cycle by which a purified stream with 0.064% SO2, and 0.055% NO2, and a desorption stream with 9% SOz can be produced. The desorption stream can be readily converted t o elemental sulfur by commercial processes. Preliminary experiments performed in this laboratory using polymeric sorbents instead of macroreticular resins suggest the validity of this work and indicate that the results of the present work can be further improved by using these polymeric sorbents.
Introduction The pressure swing adsorption (PSA)process, first developed by Skarstrom (1959), has been employed in a broad range of industrial applications such as drying, air separation, hydrogen purification, normal paraffin and isoparaffin separation, etc. (Yang, 1987). In the PSA process the adsorbent is rapidly regenerated by reducing the partial pressure of the adsorbed component and/or purging at a low pressure. This results in short cycle times (minutes) together with a requirement for a minimal energy input, which gives rise to a much higher feed throughput (sorbent productivity) compared to all other cyclic processes. A variation of PSA is vacuum swing adsorption, in which a subatmospheric pressure is used in desorption (Sircar and Zondlo, 19771, also a commercialized process. In the present study PSA is considered for the first time for SOz/NO, removal and sulfur recovery, for flue gas applications. Postcombustion desulfurization and denitrification systems must be efficient, of low cost, mechanically simple, and with no serious maintenance requirements. Fixed bed adsorbers have the potential for providing desulfurization systems with the desired characteristics. However, successful practical application depends on the availability of a proper adsorbent. Macroreticular resins, which are basic polymeric sorbents, have found commercial and commercially promising applications for water conditioning and aqueous separations (Kuo et al., 1987; Garcia and King, 1989). A unique sorbent property of the resins is that some resins exhibit low selectivity toward both water and carbon dioxide. This
* Author to whom correspondence should be addressed
property has prompted research in the past two decades into their sorption properties for SOz and NO, for consideration of pollution control (Chen and Pinto (1990) and the literature cited therein). Chen and Pinto (1990) have recently reported reversible adsorption capacities of a weak-base resin, Dowex MWA-1, for SOz, NOz, and COz at two temperatures. On the basis of these data, they have suggested thermal swing adsorption for flue gas cleanup. The data reported by Chen and Pinto were based on moisture-free conditions. In contrast to the inorganic sorbents (zeolites, carbon, silica gel, and alumina) the presence of moisture usually does not decrease the resin’s capacity for acidic gases (such as SO2) and sometimes increases it (Belyakova et al., 1975). However, weak-base resins exhibit a serious limitation on the rates of sorption. Layton and Youngquist (1969) observed an attainment of 50-60% of the equilibrium capacity of SOz on Amberlyst A-21 in approximately one-half hour, followed by a very slow approach to equilibrium over a week or more. Similar behavior has been observed for the sorption of all three gases, SOz, NOz,and COz, in Dowex MWA-1, by Chen and Pinto. The data reported in the latter work reflected the useful capacity of the resin and corresponded roughly to the amount sorbed during the first 30 to 60 min. In the present work, preliminary experiments have been undertaken in our laboratory which indicated that there exist polymeric sorbents which are hydrophobic and can exhibit high selectivity of SOz over COz with much higher rates of adsorption compared to the ones reported on ion-exchange resins. The first objective of this research was to study the feasibility of simultaneous SOZ/NO2removal as well as the enrichment of SO2 in the desorption product to a con-
0888-5885/91/2630-1981$02.50/00 1991 American Chemical Society
1982 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991
centration high enough for sulfur recovery by the Claus process. The degree of enrichment in the desorbed stream is not of interest in all previous studies of PSA (except that of Ritter and Yang (1991)) because this stream is not considered as a product. The second objective of this work was to establish the underlying principles for enrichment and recovery of the desorbed product. The tool of the study is a theoretical model that has proven abilities for predicting PSA performance.
Table I. LRC Parameters for Adsorntion Isotherms Sulfur nitrogen carbon dioxide dioxide dioxide 35 "C 50 "C 35 "C 50 " C 35 "C 50 "C 103q,, 15.6 15.6 35.5 35.5 37.0 37.0 L(STP)/g 102B,kPa-"" 2.04 1.10 0.453 0.256 2.7 X 2.2 X
Experimental Section The thermogravimetric analysis (TGA) technique, employing a Cahn system 113 recording microbalance with programmed temperature control, was used to measure uptake curves as well as equilibrium isotherms. Highpurity helium was used as the inert carrier gas and the gas for regeneration. A polymeric sorbent, XUS-40323, as well as the macroreticular resin Dowex MWA-l, both supplied by Dow Chemical Company, were used to measure SOz and COP rates of adsorption and equilibrium isotherms. XUS-40323 is a macroporous styrenic adsorbent. Its adsorptive properties come from its lack of functional groups, high surface area (650 m2/g) and small pores in its structure (the mean pore diameter is 100 A). Furthermore, it is hydrophobic, which is a desirable property for flue gas cleanup, superior to the Dowex MWA-1 resin.
sorbent is used, one can obtain the equilibrium amount of SO, adsorbed on Dowex MWA-1 in less than a minute, while keeping the COz equilibrium amount adsorbed at the same low level as with the Dowex MWA-1 resin. Thus the equilibrium model is justified depending on the sorbents. Other assumptions in the model are ideal gas behavior, negligible axial dispersion, negligible radial variations in concentration, and negligible bed pressure drop. The total mass balance in the bed can be written as
Process Description In the present study the Skarstrom PSA cycle (using two beds) is considered for the majority of the simulations. A multibed five-step process has also been employed in order to show the effect of the additional cocurrent depressurization step on the PSA performance. During the Skarstrom cycle, each bed undergoes the following cycle steps: (I) feed repressurization (i.e., repressurization with feed), (11) high-pressure feed (adsorption), (111) countercurrent blowdown (or evacuation), and (IV) countercurrent purge with product (at low pressure). Previous investigators have used either pure light component (Kapoor and Yang, 1989; Cen and Yang, 1985; Doong and Yang, 1986) or the volume-averaged effluents from the one bed during step I1 (Doong and Yang, 1987a; Suh and Wankat, 1989) to purge the other bed. However both approximations are not accurate in a multicomponent system when one or more species breaks through the bed during step 11. Therefore in the present study the instantaneous effluent composition from one bed during step I1 is used to purge the other bed as it would occur in a real process. The PSA flue gas cleanup process performance is judged by the following factors: (1) step I1 product purity and recovery, (2) desorption product (SO,) purity and recovery, and (3) feed throughput. The desorption product purity will be expressed as the enrichment ratio, Le., the SO2 concentration ratio of exhaust to feed. Mathematical Model Both isothermal and adiabatic models are used in this study. Due to the dilute concentrations of SOz and NOz, which are the strongly adsorbed components, the adiabatic model results show a thermal wave of +0.5 "C during adsorption and -0.5 "C during desorption. Therefore the results are based on the isothermal model. In addition, the equilibrium model is used. The equilibrium assumption seems to be in contradiction with the slow sorption rates described in introduction. However, preliminary experimental results on XUS-40323 indicated that if this
10-4
n
1.0
1.0
1.0
1.0
0.38
10-4
0.38
Similarly, the mass balance equations for each of the species are ac, auc, - + - + pB =0 i = 1, 2 , ..., N (2) at az where Ci = P y i / R T and q = Cqi. If the resistance to mass transfer is negligible (equilibrium model), we have (3)
where qi* is the equilibrium amount adsorbed. The equilibrium mixture adsorption can be calculated by the the loading ratio correlation (LRC) (Yang, 1987):
A typical flue gas contains N,, CO,, SO2,NO2,and water. The reversible sorption data of Chen and Pinto (1990) on a weak-base macroreticular resin Dowex MWA-1 are used in the PSA simulation model. The resin's capacity for nitrogen was assumed to be negligible in comparison with the acidic gases. Furthermore, the effect of moisture on the adsorption capacity was not considered, since the LRC coefficients were obtained under dry conditions. As mentioned, Belyakova et al. (1975) has found that the adsorptive power of weak-base macroporous resins with respect to adsorbable acidic gases not only does not decrease, but can even slightly increase in some cases when water is present. Thus the approximation introduced by neglecting the presence of water in the model is expected not to affect significantly the PSA performance. The model parameters for the LRC equation for CO,, SOz, and NOz, are given in Table I for two different temperatures, 35 and 50 "C, and the corresponding single isotherms for each species are shown in Figure 1. A note needs to be made on the NOz. Due to the complex heterogeneous reactions in the flue gas, oxides of nitrogen are represented by NO,. Since only NO2 data are available, and the difference between NO and NOz sorption is not expected to be large, we use NOz in this study. The LRC equation predicts the following selectivity sequence for the resin: SOz > NOz > C02. This is a desirable sequence if the main objective is flue gas desulfurization. However, at high concentrations of COP,the adsorption capacity of the resin for both SO2and NO, can
Ind. Eng. Chem. Res., Vol. 30, No. 8,1991 1983 be significantly decreased. The following simulated flue gas composition (molar) is considered in this study: Nz (and Ar) = 81.37%, COz = 18%, SOz = 0.5%, and NOz = 0.13%. Initial and Boundary Conditions. Two different initial conditions for the startup of the cyclic operation have been used: 1. Both beds are assumed to be initially clean containing only pure Nz. fori = Nz at t = 0 and 0 < z < L , yi = x i = 1 at t = 0 and 0 < z < L, for i = COz, SOz, NOz yi = x i = 0 at t = 0 and 0 < z < L, P = PH where x i = qi/q. 2. Both beds are initially saturated with feed gas at high pressure (PH). a t t = O a n d O < z < L , y i = y f , i f o r i = 1 , 2 , ...,N at t = 0 and 0 < z < L , x i = ribti) for i = 1, 2, at t = 0 and 0
< z < L, P
u = Uf P = PH step 111. countercurrent blowdown at z = L , ayi/az = o
I
I
E
30
60
90
120
150
I
I
1
I
I
90
120
150
10
3
0
& d
0 40 I
I
I*
TISOT
W
o 0
30
d
X
Q
f0 @
20
: 6
u=o
P = P(t)
0
step IV. countercurrent purge at z = L , Y i = Yp,i(t) at z = L ,
u = Upurge P = PL where ~ , , ~ (ist the ) instantaneous effluent mole fraction of species i, during step 11. step I. pressurization with feed at z = 0, Y i = Yf,i at z = L ,
I
20
n
at z = 0,
I
30
0
= PH
1
IA
..., N
The boundary conditions for the ensuing cycles are step 11. high-pressure adsorption at z = 0, Yi = Y f j
at z = L ,
40 1
u=o
P = P(t) The initial conditions for each step are the conditions at the end of the preceding step. Note that the pressure history is an input in PSA and is represented usually by a quadratic form: P ( t ) = a0 a,t a# (5)
+
+
In the present study a2 = 0, resulting in a linear dependence of pressure with time. The adsorber characteristics together with the operating conditions for the standard case are listed in Table 11. In all Skarstrom cycle PSA model simulations performed, it was assumed that the duration of cycle steps I and I11 was very short compared to the cycle time; therefore the length of cycle steps I and I1 and that for cycle steps I11 and IV were combined where equal lengths of time were alloted for each set. A 9-min cycle was used in the simulations
0 0
30
60
P (kPa) Figure 1. Single-component isotherms for SOz,NOz,and C02at (A) T = 35 O C and (B)T = 50 O C . Table 11. Adsorption Bed Characteristicsand Operating Conditions for the standard simulation resin bed bed length 500 cm bed diameter: 100 cm void fraction (e): 0.43 resin density: 0.64 g/cm3 bed density: 0.37g/cm3 operating conditions feed composition, 70: N2/COz/NOZ/SO2= 81.37/18.00/0.13/0.50 feed rate: 8.395 X IO5 L(STP)/h purge/feed = 0.02 PH = 1.2 atm PL = 0.03 atm total cycle time: 9 min ambient temperature, T = 308 K
with the following distribution: step I, 0.5 min; step 11, 4.0 min; step 111, 0.5 min; step IV, 4.0 min. Numerical Solution of the Model. The implicit backward finite difference scheme, used previously in this laboratory for PSA model simulations, was employed in the present work to solve eqs 1 and 2 combined with eqs 3 and 4. In the previous works the computation was initiated by assuming a set of values for yi. Equation 4 was
1984 Ind. Eng. Chem. Res., Vol. 30, No. 8,1991
then used to calculate qi. Then eqs 1and 2 were solved for u and yi, respectively, and the new values of yi were compared to the assumed ones. The iteration scheme was continued until yi was within lo* of the assumed value. However this scheme was found to converge very slowly (Cen and Yang, 1985). Therefore in the present work Newton's method is used to solve the set of nonlinear equations for yi that results after the discretization in time and space. Although this modification introduces slightly more complexity to the numerical scheme, it achieves rapid convergence and thus requires less computationaltime for the numerical simulation. Furthermore, in step I a shooting method is used to solve for u and yi, since yi at z = 0 is known whereas the only information for u is at z = L. In a typical computation, 200 space and lo00 time steps were used for each PSA cycle. The model was always stable and convergent at least in the range of conditions used in this study. All computations were performed in a VAX-780 computer. It took approximately 15 min of CPU time for each cycle, and it generally took four to six cycles to reach cyclic steady state. Results and Discussion The main objective of this study was to examine if and under what conditions it is possible to concentrate SOz in the exhaust stream while keeping the SO2 and NOz amounts in the product sufficiently low. The concentration of SOz in the desorption product should be 5% or more for elemental sulfur recovery by the Claus process. The aspect of applying PSA for concentrating in addition to purifying has not been systematically studied before. An additional objective of this study was to optimize the various PSA variables in order to achieve maximum SOz enrichment in the desorption stream together with sufficiently high SO2recovery and to achieve a sufficiently low amount of SO2 and NOz in the product stream. The SOz enrichment will be taken as the volume-averaged value of the effluent from steps I11 and IV, divided by the feed concentration of SOz. The SOz recovery is calculated by SO2 recovery = amount of SOz from steps I11 and IV amount of SOz in the feed used in steps I and I1 (6) Finally the results using a Skarstrom (two-bed) cycle are compared to the results using a multibed five-step process in order to examine the effect of the additional step of cocurrent depressurization on the PSA process performance. Experimental Results on Polymeric Adsorbent. Preliminary experiments on XUS-40323 performed in our laboratory have shown that SOz can reach an adsorption capacity similar to the one obtained on Dowex MWA-1 in less than a minute. A typical uptake curve that corresponds to a step change in the SO2partial pressure from 0 to 1atm is shown in Figure 2. The solid curve in the same figure corresponds to the theoretical solution of the diffusion equation. For the case of COz the equilibrium isotherms on both XUS-40323 and Dowex MWA-1 at room temperature are shown in Figure 3. It can be seen that the amount of C 0 2 adsorbed is almost the same for a partial pressure of COB less than 0.15 atm, and then becomes much higher on Dowex MWA-1 as the pressure increases from 0.15 to 1 atm. The results from these preliminary experiments justify the use of the equilibrium model in the mathematical simulation of the PSA process. Furthermore the PSA model simulation results presented in this work represent
120 n
M
2 E
v
c1
w Q
2
60
[r)
n a b
2 3
:
30
6
H
i
Y
SORBENT: X U S - 4 0 3 2 3
5
0
25
20
15
10 TIME
(min)
Figure 2. Uptake curve of SO2on polymeric mrbent XUS-40323 at 1 atm and 35 "C. 30
I
A
n
M
I
I
I
I
I
l
l
DOWEX MWA--1. T z 2 5 - C XUS-40323, T=25'C
2 E
v
n
20
/
w Q
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n a b 2 3
10
0
E
6
0.0
0.2
0.4
pco,
0.6 (atm)
0.8
1.0
Figure 3. Singlecomponent isotherms for COSon Dowex MWA-1 and on XUS-40323 at 25 "C.
a conservative feasibility of the process. Transient PSA Process Behavior. As has been pointed out elsewhere (Doong and Yang, 1986), the major difference between the results on once-through adsorption breakthrough curves and the PSA behavior is due to the adsorbed amount that is accumulated in the bed at a cyclic steady state. In all simulations performed in this work, it was observed that the initially sharp SOzwave front during the first cycle became increasingly diffusive as the number of cycles increased. This was generally due to the large amount of SOz introduced to the bed by feed repressurization (Doong and Yang, 1987b). It is interesting to notice that there was a critical value of y, y being the ratio of purge to feed velocity, below which a peak wm obaerved in the SOz bed concentration profile. At y = ycr this peak smoothed out to a plateau, and for y > ya the peak or the plateau no longer existed. This behavior was probably due to the residual amount of SO2 left in the bed during the
Ind. Eng. Chem. Res., Vol. 30,No. 8, 1991 1985
...
..... ,
CYCLE 1 CYCLE 2 CYCLL 3
.._. CYCLC
,006
I
4 I
I
A
Table 111. Effect of Purge/Feed on PSA Performance for PL = 0.03 atm (Feed SO, = 0.5%, NO2 = 0.13%,and COS = 18%) volume-averaged effluent concn, % product an stream desorption stream recovery, O"2
,
.004
,002
.ooo 0.0 ,006 I
0.2
0.4
I
1
0.0
0.8
I
I
IB
1.0 1
P/F
SO2
NO,
0.010 0.015 0.020 0.025 0.030 0.040 0.050 0.060
0.238 0.142 0.068 0.035 0.029 0.029 0.029 0.029
0.072 0.068 0.069 0.069 0.069 0.069 0.069 0.069
NO?
CO,
1.21 1.16 1.06 0.98 0.92 0.82 0.74 0.68
29.82 28.30 27.15 26.34 25.73 24.76 23.99 23.37
% 55.91 74.18 88.27 94.56 95.80 95.87 95.91 95.94
Table IV. Effect of Purge/Feed on PSA Performance for PL = 0.04 atm (Feed SO, = 0.5%, NO, = 0.13%,and C 0 2 = 18%) volume-averaged effluent concn, % product so2 stream desorption stream recovery, SO2 NO2 SO2 NO2 COP % P/F 0.010 0.015 0.020 0.025 0.030 0.040 0.050 0.060
.004
SO, 5.38 6.43 6.99 6.92 6.54 5.79 5.18 4.70
0.303 0.229 0.158 0.093 0.051 0.029 0.029 0.029
0.085 0.070 0.069 0.069 0.069 0.069 0.069 0.069
4.24 5.09 5.73 6.17 6.25 6.28 5.78 4.69
0.99 1.14 1.07 0.99 0.92 0.81 0.74 0.67
30.32 28.77 27.57 26.60 25.84 24.79 24.02 23.39
43.22 57.62 71.13 83.29 91.37 95.48 95.59 95.59
.002
.ooo 0.0 ,006 I
0.2
0.4
0.6
0.8
1.0
I
4
I
I
1
Table V. Effect of Purge/Feed on PSA Performance for PL = 0.05 atm (Feed SO, = 0.5%, NO, = 0.13%,and C 0 2 = 18%) volume-averaged effluent concn, % product SO2 recovery, stream desorption stream P/F SO, NO, SO, NO, CO, % 0.020 0.025 0.030 0.035 0.040 0.050 0.060
IC
z/L Figure 4. Transient and steady-state SOz concentration profiles in the bed, at three different times during the adsorption step, for (A) P / F = 0.025, (B)P / F = 0.020, and (C)P/F = 0.015. All the other parameters correspond to the standard run and are given in Table 11.
purge step and consequently readsorbed during the feed repressurization and the adsorption step. Thus if the purge velocity is not high enough to sufficiently clean the bed, an appreciable amount of SO2 can remain in the bed as a rolling wave during the subsequent steps. Similar types of wave fronts have been also observed by Cen and Yang (1985) and Doong and Yang (198713). Typical examples
0.224 0.168 0.113 0.069 0.043 0.029 0.029
0.070 0.069 0.070 0.070 0.070 0.070 0.070
4.78 5.20 5.53 5.69 5.64 5.18 4.69
1.06 1.00 0.93 0.86 0.81 0.73 0.67
27.90 26.91 26.08 25.40 24.86 24.04 23.41
58.46 69.22 79.44 87.77 92.74 95.33 95.41
of SO2 breakthrough curves during the adsorption and desorption steps for these three cases are presented in Figures 4 and 5. As mentioned earlier, simulations were performed starting from two different initial conditions. In all simulations only one cyclic steady state was observed. The concentration profiles for the two cases were found to move in opposite directions, converging to the same final steady state. This result was expected, since the model considered in this work was isothermal and the isotherms were mostly within their linear regions under the examined pressure range, and therefore there are no apparent reasons for multiple steady states (for the nonisothermal case see the in-depth discussion by LeVan (1990);for the case of nonlinear isotherms see Ritter and Yang (1991)).Furthermore the uniqueness of the cyclic steady state assures the accuracy of the numerical scheme. Effect of Purge/Feed Ratio. The molar purge/feed ratio, P/F, was varied by decreasing the purge flow rate. Three different sets of results for three different values of purge pressure, PL,were calculated. The results of adsorption and desorption product volume-averaged concentrations and SO2recoveries for PL = 0.03,0.04, and 0.05 atm are summarized in Tables 111, IV, and V, respectively.
1986 Ind. Eng. Chem. Res., Vol. 30,No. 8, 1991 0
0
I
A ,A
+ ,0
,
PL = 0.03 atm PL = 0.04 atm P = 0 . 0 5 atm
I SO
,120
-
90
,090 01
0
-
,060
80
z
M
n 0
,030
.ooo
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,
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0.6
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1
- ENRICHMENT _ - _R E C O V E R Y 5 0.00
0"
>."
I
I
0.02
I
I
0.04
I
1
50
0.06
P/F .OB0
Figure 6. Effect of purge/feed (P/F)ratio on SOz enrichment and
.os0
recovery, for three different values of the purge pressure. The feed concentration of SOz is 0.5%. All the other parameters are for the standard run given in Table 11.
.030
,000
0.0 ,180
I
0.2
0.4
0.6
0.8
1.0
0 2
0 4
0 6
0 8
1 0
P
so
. I20 ,090
,060
,030
OGO 0 0
z/L Figure 5. SOzconcentration profiles in the bed at cyclic steady state during the countercurrent blow down and purge steps for (A) P/F = 0.025, (B)P/F = 0.020, and (C) P/F = 0.015. All the other parameters correspond to the standard run and are given in Table 11.
In addition, the SO2 enrichment ratio and recovery are plotted against the purge/feed ratio for the three different PL values in Figure 6. Notice again that the desorption volume-averaged effluent concentrations are from both steps I11 and IV. In all three cases the SO2 enrichment ratio exhibits a maximum, which varies with the value of Pb This is an important result and it is in contrast to the results pertaining to the purified product (from the adsorption step). The product purity from the adsorption step increases
monotonically with P / F and levels off (Yang, 1987). The results of this work showed that there exists an optimum P / F value, where SO2enrichment becomes maximum. An intuitive interpretation of this phenomenon is given as follows. A certain amount of purge is needed in order to strip and elute the SO2 from the bed. However, further increasing the purge amount will dilute the SO2 product, thereby decreasing the SO2enrichment. Using the results from the three sets, one can calculate the optimum P / F value for each value of Pb It is interesting to notice that for all three cases the calculated value of y is almost identical, and it is close to the critical value for which a rolling front is observed in the SO2 wave fronts. The SO2and NO2 concentrations in the product stream are plotted against the purge/feed ratio for the three different pressures in Figure 7. In all three cases the SO2 and NOz concentrations decrease with P / F and level off. The corresponding NO2 effluent amounts do not change significantly as the values of P / F or PL change and are about 690-700 ppm in the product stream and about 0.8-1.0% in the desorption (exhaust) stream. This is probably because NOz is weakly adsorbed compared to SO2 and thus is already breaking through the bed at the end of the adsorption step. The SOz recovery follows an expected pattern; i.e., as the value of P / F increases, SO2 recovery increases and eventually it approaches a constant value as P / F further increases. It is interesting to point out that, in the range of P / F where the volume-averaged concentrations of the various components in the adsorption product are maintained almost constant, the volume-averaged concentrations of these components in the purge product will be very close to their values calculated by a simple overall mass balance. Notice though that this result cannot be seen from Tables III-V since the volume-averaged concentrations of the various gases in the desorption product correspond to the effluents obtained from both the countercurrent blowdown and purge steps. In order to illustrate the above statement,
Ind. Eng. Chem. Res., Vol. 30,No. 8,1991 1987 0
I
A
I I
4800 I
I
0 0
I
PL = 0.03 a t m P = 0.04 a t m P: = 0 . 0 5 a t m I
I
Table VII. Effect of Limiting Pressures on PSA Performance (Feed SOz = 0.5%, NO, = 0.13%,and COS = 18%) volume-averaged effluent concn,
I
%
product desorption SO2 stream stream recovery, P ~ , a t m P ~ , a t m SO2 NO2 SO2 NO2 COP % 0.03 1.2 0.068 0.069 6.99 1.06 27.15 88.27 0.06 2.4 0.089 0.073 5.40 0.81 41.49 84.75
3600
Table VIII. Effect of Bed Utilization Factor on PSA Performance (Feed: SO2 = 0.5%, NO, = 0.13%,and CO, = 18%1 volume-averaged effluent concn, % product SO2 stream desorption stream recovery, u,t,/L SO2 NO2 SO2 NO2 COZ % 0.98 0.068 0.069 6.99 1.06 27.15 88.27 0.78 0.054 0.052 6.26 1.14 28.06 91.46
2400
1200
1
0.00
I
0.02
I
I
0.04
1
I
0.06
P/F Figure 7. Effect of purge/feed (P/F) ratio on SO2 and NOz concentrations in the product stream, for three different values of the purge pressure. The feed concentrations of SOz and NO2 are 0.5% and 0.13%, respectively. Standard run conditions.
Table VI. Effect of Purge/Feed on Volume-Averaged Effluent Concentrations from Purge Step for PL= 0.03 atm (Feed SOz = O.S%, NO, = 0.13%,and CO, = 18%) volume-averaged effluent concn from purge step, % results from overall simuln results mass balance P/F SO2 NO2 SOP NO2 0.030 1.50 12.2 12.2 1.50 0.040 9.4 1.16 9.2 1.13 0.050 7.7 0.97 7.3 0.90 0.060 6.5 0.83 6.1 0.75
the effluent volume-averaged concentrations of SOz and NOz in the purge step obtained by the simulation model for PL = 0.03 atm, as well as the ones obtained by an overall mass balance, are compared in Table VI. For the calculations based on the overall mass balance the volume-averaged concentrations at P / F = 0.03 were used as the reference. The results from Table VI support the above statement and verify the validity of the numerical scheme. Similar results can be obtained for PL = 0.04 and PL = 0.05 atm. Effect of High to Low Pressure Ratio. The results in Figure 6 also show that for the same value of P/F, as PL increases both SOz enrichment and recovery decrease. Hence as PL increases, the maximum value of SOz enrichment drops and the correspondingoptimum P / F value is shifted to higher values. For P/F I0.05 there is no significant difference in both SOzenrichment and recovery for all three different values of PL,i.e., no PL effect. From Figure 7 it follows that both SOz and NOz concentrations in the product stream are increasing as PLincreases. Again for P / F L 0.05 there is no significant PL effect. The feed pressure PH is not amenable to changes, since, as can be seen in Figure 1, a small increase in that value will increase the partial pressure of COz to the sharply
increasing region of ita isotherm, and COPwill become a dominant adsorbate. In order to see the effect of the absolute pressure range, a simulation was performed for P / F = 0.02and PH/PL = 40 except that the feed and purge pressures were doubled to 2.4 and 0.06 atm, respectively. Since the feed pressure was doubled, the molar flow rate was also doubled, for the same feed velocity. Table VI1 shows that a more contaminated product effluent resulted in this case. In addition, both SO, concentration and recovery in the desorption product were decreased. This is due to the peculiar behavior of the COPisotherm. Thus while at PH = 1.2 atm the partial pressure of COz lies in the flat region of the isotherm where a very small amount of COPis adsorbed, when PHis doubled, the amount of COzadsorbed is sharply increased. In the latter case COz becomes a significant competitor of SOz. Effect of the Bed Utilization Factor. The bed utilization factor is defined as bed utilization factor = u,t,/L (7) where u, is the wave-front velocity, t , is the time of the adsorption step, and L is the length of the bed. This factor is an indicator of the extent of utilization of the bed capacity. Under isothermal conditions and with constant interstitial velocity, u, the wave-front velocity is given by
[ T
uc=u/ l+-
€(
z)]
-
(8)
In general dq*/dC can vary with space and time, but one can assume linear isotherms to obtain an asymptotic value for u, so that one can estimate the magnitude of the bed utilization factor. With the use of the standard input values from Tables I and 11, the bed utilization factor for SOz was approximately 0.98. This result indicates that an appreciable amount of SOz had broken through the bed at the end of the adsorption step. An additional simulation run was made in which 80% of the feed flow rate was used, resulting in a utilization factor of 0.78. The results were compared to the standard case and were summarized on Table VIII. When the bed utilization factor was lowered, the effluent concentration of SOz was lowered too in both the adsorption and the desorption streams. In contrast, the SOz recovery was increasing. Finally it is interesting to notice that, in the case of the lower utilization factor, six cycles were required
1988 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 .010
Table I X . Effect of Ambient Temperature on PSA Performance (Feed: SO2 = 0.570, NO2 = 0.13%, and COZ = 18%) volume-averaged effluent concn,
T,K
u,t,/L
308 323 323
0.98 1.77 0.98
0.068 0.244 0.077
0.069 0.096 0.067
4801
I
I
\
j
.008
%
product stream Sop NO1
I
\\
400
desorption stream SO2 NO2 Cog 6.99 4.71 5.01
1.06 0.70 0.81
27.15 26.46 28.06
SO2 recovery,
\
70
88.27 55.01 87.56
to reach cyclic steady state whereas in the standard case only four cycles were required. Effect of the Ambient Temperature. The simulation results for the standard run for two different ambient temperatures are summarized in Table IX. The higher ambient temperature resulted in an earlier breakthrough of SO2during step 11, compared to the standard case. Thus the product was contaminated with an appreciable amount of SOz, while on the other hand the SO2enrichment in the desorption stream was significantly lower than that from the standard case. Finally the SO2 recovery is reduced from nearly 90% for the standard case to about 55% for the case of T = 50 "C. Therefore increasing the ambient temperature while keeping the other parameters the same resulted in less favorable results for both pollution control and SO2 enrichment. An additional simulation was performed with T = 50 "C, but with the same bed utilization factor maintained so a fair comparison could be made. The results are also shown in Table IX. It is interesting to notice that, although the values of the average effluent SO2 in the product stream and SO2recovery were very similar to those in the standard case, the SO2enrichment was still significantly lower than the one from the standard case. The conclusion is that even if the throughput was decreased in order to obtain a similarly pure product with the standard case, the SO2 enrichment remained much lower than the one from the standard case, due to the reduced sorbent capacity at the higher temperatures. Comparison with the Five-Step Process. The multibed PSA processes have replaced the Skarstrom cycle for bulk gas separation. A major difference between the Skarstrom process and the multibed process is that the latter involves the additional step of cocurrent depressurization in the PSA cycle for internal product recovery. In this work the five-step process was considered, in which the additional cocurrent depressurization (CD) step was introduced after the adsorption and before the countercurrent blowdown step. To incorporate this step into the Skarstrom cycle, the adsorption step is cut short before the break point; the concentration front was kept far from reaching the exit of the bed. The major function of the cocurrent depressurization step is to increase the concentration of the strong adsorptive in the bed. This is done by lowering the pressure in the voids, which enhances the concentration of the strong adsorptive in both phases (Yang, 1987). The net result of the incorporation of the CD step in the Skarstrom cycle is the product purity enhancement of the strong adsorptive, which in turn increases the product recovery of the weak adsorptive. In this work the effect of the CD step was considered by performing a simulation of the five-step process. Each step was 4 min long, resulting in a total cycle time of 20 min. A bed utilization factor of 0.78 for the case of SO2 was used so that this component would not break through the bed during the adsorption step. The pressure during the CD step was considered to decrease linearly with time,
.006
0"
+
.004
.002
,000 0.0
0.2
0.8
0.6
0.4
1.0
Z/L
Figure 8. SO2 concentration profiles during the adsorption and cocurrent depressurization steps, in the five-step process at cyclic steady state. The bed utilization factor is 0.78. All the other operating conditions correspond to the standard run and are given in Table 11.
.150
,120
P
>
K----' '\ -
\ \
\
y20
\
\ \
\SO0
\
II
-
.090
.060
0.0
0.2
0.4 0.6 z/L
0.8
1.0
Figure 9. S O p concentration profiles during the countercurrent blowdown and purge steps, in the five-step process at cyclic steady state. The bed utilization factor is 0.78. All the other operating conditions correspond to the standard run and are given in Table 11.
from 1.2 atm at the beginning to 0.06 atm at the end of this step. The results are shown in Table X. As can be seen, a significant increase in the SO2enrichment was achieved using the five-step process compared to the corresponding cases using the Skarstrom cycle. This result was solely due to the additional CD step. To visualize the effect of this step on the SO2enrichment, the SO2 concentration fronts for both the adsorption and the CD steps are presented in Figure 8 at the cyclic steady state. In Figure 9 the SO2 concentration fronts at the subsequent countercurrent blowdown and purge steps are also presented. Hence by using a more complex process, higher SO2 enrichment can be obtained without significantly lowering
Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1989 Table X. Comparison between the Skarstrom and the Five-step Cycles (Feed SOt = 0.5%, NO, = 0.13%. and COS 18%) volume-averaged effluent concn, % product desorption SOP stream stream recovery, % process u,t,/L SOz NOz SOz NOp COz 88.27 Skarstrom 0.98 0.068 0.069 6.99 1.06 27.15 Skarstrom 0.78 0.054 0.052 6.26 1.14 28.06 91.46 five-step 0.78 0.064 0.055 9.02 1.60 30.04 87.69
the purity of the product stream. Nevertheless, unless there is a superseding need for higher SO2enrichment, the simple two-bed Skarstrom cycle is considered efficient for both S02/N0, removal and SO2 recovery.
Acknowledgment This work was supported by NSF under Grant CTS8914754. We appreciate helpful discussions with Dr. H.
Robert Goltz of Dow Chemical Company.
Nomenclature B = Langmuir constant, kPa-', kPa-'/" in eq 4 C = concentration in bulk flow, mol/cm3 d = diameter of the bed, cm L = length of the bed, cm N = total number of components in the mixture n = exponent in eq 4 P = pressure, kPa or atm q = moles adsorbed per gram of solid, mol/g qa = saturated amount adsorbed, mol/g or L(STP)/g R = gas constant T = ambient temperature, K t = time, s u = superficial velocity, cm/s u, = wave-front velocity, cm/s u = interstitial velocity, cm/s x = mole fraction in the adsorbed phase y = mole fraction in the gas phase z = axial position in the bed, cm Greek Letters y = volumetric purge to feed ratio
= fractional void in the bed = density of the bed, g/cm3 pI = density of the sorbent, g/cm3 c
pB
Subscripts
a = adsorption B = bed
f = feed H = high i = species i j = species j L = low p = product Superscript * = equilibrium
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Received for reuiew December 26, 1990 Revised manuscript received April 22, 1991 Accepted May 8,1991
