Ind. Eng. Chem. Res. 1990,29, 2167-2170
2167
Comparison of Countercurrent Recycle Cascades with Continuous Membrane Columns for Gas Separations The performance of ideal countercurrent recycle cascades (CCRCs) are compared with continuous membrane columns (CMCs) using ideal “plug flow” models. The calculations show that CCRCs require much smaller total membrane area and much lower compressor duty than CMCs for the same overall cut and enrichment, especially a t higher enrichments and stage cuts. The basic reasons for the greater efficiency of CCRC are explored.
Introduction and Background The continuous membrane column (CMC) was introduced by Hwang and Thorman in 1980, claiming it to be a revolutionary separation technique because it is capable of achieving high product purity without cascading. The degree of enrichment is theoretically unlimited (Hwang and Thorman, 1980; Yoshisato and Hwang, 1984). In a more recent theoretical study, it was shown that the CMC can produce highly enriched products with membranes of any perselectivity and that they can obtain a nearly pure product with any given membrane area (Kao et al., 1989). The CMC is thought of as a continuous reflux cascade with an infinite number of stages (Yoshisato and Hwang, 1984; Rautenbach and Dahm, 1987). In spite of its claimed theoretical promise, the CMC has not found practical applications because of high area and compressor duty requirements (Kao et al., 1989; Rautenbach and Dahm, 1987). Several studies have compared the CMC with other one and two compressor membrane modules (Kao et al., 1989; Rautenbach and Dahm, 1987; McCandless, 1985; Matson et al., 1983). However, apparently no one has made calculations for multistage cascade performance for comparison with the CMC, probably because the CMC is viewed as a cascade with an infinite number of stages. This paper makes that comparison using ideal countercurrent “plug flow” models for both the CMC and the countercurrent recycle cascade (CCRC). It also explores the basic reasons for the difference in efficiency of the two designs. Membrane Cascades There are probably many possible cascade configurations that could be considered for comparison with the CMC, but a very effective cascade design is the simple countercurrent recycle cascade, which in some ways is similar to a continuous distillation column (Benedict et al., 1981). This cascade is shown schematically in Figure 1 together with a diagram for a continuous membrane column. It utilizes a series of N countercurrent recycle permeators where the feed to a given stage (except for the two end stages) consists of a reject stream from the next lowest numbered stage and a permeate (recycle) stream for the next highest numbered stage. The recycle must be compressed before it is mixed with the high-pressure reject stream. Several variations of the basic design are possible, but only an “ideal” cascade will be considered in this study. In an ideal cascade, the compositions of permeate and reject streams that make up the feed to the interior stages are the same composition; that is, there is no mixing of streams of different compositions between stages. In addition, the feed is introduced within the cascade where the high-pressure-side composition is the same as the feed. Model Equations and Calculation Methods Stern and Wang (1978) and Blaisdel and Kammermeyer (1973) have developed the differential equations necessary to model ideal countercurrent plug flow permeator be0SSS-5SS5/90/2629-2167$02.50/0
havior. In general, the model equations for each stage consist of coupled, nonlinear, ordinary differential equations that relate stream composition and their flow rates to the membrane area. Those equations, together with appropriate boundary conditions for each stage, are applied successively to model each permeator in the CCRC or each section in the CMC. These equations are solved simultaneously by using numerical methods. A trial-and-error procedure is used, using backward integration starting at the high-pressure product (reject) end. Values for X O ( N ) are assumed, and the integration is carried out for each stage to stage 1where material balances are checked. The assumed X O ( N ) is correct when all material balances are satisfied within a specified tolerance. The model equations were solved on a digital computer by using a fourth-order Runge-Kutta numerical integration routine. A Wegstein convergence routine was used to estimate new values of X O ( N ) to try in the calculations, and convergence was usually obtained in a few cycles. For this study, a comparison of enrichment, required area, and compressor duty when producing a specified amount of permeate product was desired. For the CMC, the main (design) variable is the recycle ratio, while the important variable in the CCRC is the number of stages, with the recycle ratios to the various stages being set by the no-mix criteria. The recycle ratio is defined as RR = rate of permeate recycle/permeate product rate. In the CCRC, the cut in stage N must also be specified and was chosen to be consistent with the theory of ideal cascades developed by Benedict et al. (1981). In this study, it varied from about 0.3 to 0.5 depending on a* and the number of stages in the cascade. This value of 6 ( N )must be chosen so that all material balances in stages N - 1to 1 are satisfied. Membrane properties and operating prameters were assumed to be XIF = 0.2, LLO(1) = 20 cm3 (STP)/s, OP = 0.2 and 0.025, PH = 760 cmHg, PL = 760 cmHg, PA = 2.5 X lo-@cm3 (STP) cm/(s cm2cmHg) a* = 5.0 and 1.05, and 6 = 2.54 X cm. The above parameters were arbitrarily fixed but were the same for both the CMC and CCRC, so a valid comparison could be made. The listed permeability is about one-half that of O2 in silicone rubber. With a feed composition of 0.20, the system could represent the separation of O2 from the air when a* = 5.0 (Ward et al., 1976), while it might represent the separation of the boron isotopes in BF, when a* = 1.05 (Herbst, 1989).
Results and Discussion The results of the calculation are presented in the Table I, which compares enrichment, required area, and compressor duty for the CMC and CCRC for the several cases investigated. The compressor duty is the total volume of gas that must be compressed, both feed and recycle, and is a direct measure of the energy required for the separation. The number of compressors also includes both feed and recycle, N for the CCRC and 2 for the CMC. Two cases were considered: case one with overall cut = 0.2 = 0 1990 American Chemical Society
2168 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
-1
S TR/PP/NG SEC T/ON
ENR/CH/NG SECTION
LHO(N-2) iL H I ( N - I )-LLO(N) /XO(N-Z)=YOIN)
LHIF XIF
REJECT W
I
C
T
* LHO(N);(I-Bp)LHIF
* N L
*
FEE0 SWGE LA
-
PERMEATE PRODUCT
IDEAL
COUN rERcuR,?mr
RECYCLE CASCADE
LHIF
L H I ( I)=(RA)(LLO) ENRICHING
sEcr/oN
LLO=(Bp)LHIF YO
CONT/NUOUS MEMBRAN€ COLUMN Figure 1. Schematic diagrams for an ideal countercurrent recycle cascade and a continuous membrane column. Table I. Comparison of the CCRC and CMC"
case
system
1
CMC (RR = 15) CCRC CMC(RR=
1 1
no. of compressors
enrichment YO a* = 5.0 2 0.761
compressor duty, area, cm2 cm3/s 18600
400
3 2
0.778 0.950
10500 360000
195 10100
CCRC CCRC CMC(RR= 100) CCRC CCRC
6 8
0.945 0.980 0.957
24600 33700 71000
336 430 2800
0.968
13600 19500
1020 1190
CMC(RR= 1 x 106) CMC(RR= 500) CCRC CCRC CMC(RR= 1 x 106) CMC(RR= 500) CCRC CCRC CRCC CRCC
2
0.285
2.9 x 109
2.0 x
2
0.234
1.5 X lo6
10100
22
0.301 0.238 0.300
0.6 X lo6
8 2
99400 2.9 x 109
4560 742 2.0 x 107
2
0.238
1.5 X lo6
10100
20
0.320 0.250 0.946 0.946
7.1 X 2.0 x 4.6 X 1.7 x
5610 2120 3.1 X lo5 1.2 x 105
500) 1 1
2 2 2
2
3 4
0.985 01
1 1 1 1
2 2 2 2 1
2
8
230 140
= 1.05
lo5 105 10' 107
io7
"Case 1: 8, = 0.2, LHIF = 100, LLO = 20. Case 2: 8, = 0.025, LHIF = 800. LLO = 20.
XIF, which would result in a maximum extent of separation (McCandless, 1985); and case two with low cut = 0.025. This was included since the CMC is reported to perform better at low cuts (Kao et al., 1989). In both cases, the feed rate was adjusted to produce a permeate product rate of 20 cm3 (STP)/s and so LHIF = 100 and 800 cm3/s for cases 1 and 2, respectively. a* = 5.0. For case 1, the CMC would produce an enrichment of about 76% when the permeator is designed
for a recycle ratio of 15. This would require an area of about 18600 cm2and a compressor duty of 400 cm3/s. The CCRC designed for three stages could produce about 78% enriched product and would require only about 56% of the area and 49% of the compressor duty of the CMC. The CMC would require a recycle ratio of 500 to produce 95% enriched product and would require a total area of about 360000 cm2with a compressor duty of 10 100 cm3/s. Six stages would be required for the CCRC to produce about the same enrichment, but the CCRC would require only about 7% of the area and 3% percent of the compressor duty of the CMC to make about the same separation. Enrichment in the CCRC could be increased to 98% using eight stages. For case 2, the CMC would produce about 96% enriched product with a recycle ratio of 100. Area and compressor duty requirements would be about 71 000 cm2 and 2800 cm3/s,respectively. However, the CCRC with three stages would produce about 97% product with only about 19% of the area and 36% of the compressor duty of the CMC for the same feed rate and cut. Enrichment would be increased to about 99% using a four-stage CCRC. a* = 1.05. With a* = 1.05, case 1,a recycle ratio of 1 X lo6 in the CMC would result in an enrichment only to about 29% and would require a huge area and compressor duty. A recycle ratio of 500 would result in an enriched product of only 23%. For comparable enrichments, CCRC would require 22 and 8 stages, respectively, but would require only about 0.03% and 7% of the area and compressor duty of the CMC, respectively. A similar trend is observed for case 2. From this, it is obvious that the CMC cannot practically produce a highly enriched product when a membrane of low permselectivity is used; however, as shown by the last two rows in Table I, the CCRC design can produce a highly enriched product if enough stages are used. It would take about 230 and 140 stages to produce about 95% product when a* = 1.05 for cases 1 and 2, respectively. Although total area and compressor duty requirements are high, the CCRC might be practical for high-valued products.
'h
"olG
Ind. Eng. Chem. Res., Vol. 29,No. 10,1990 2169 FLOW I N CCRC, ALPHA=5 FLOW I N CMC,ALPHA=5
2b.00
i o . 00
s'0.00
60.00
AREA (SQUARE CM X 10-3)
ib0.00
?k
0
1'
N=7
RR=100
ENRICHMENT I N CCRC,
ALPHA=5
N=7
RR=100
E N R I C H M E N T I N CMC, ALPHA=5
SECT ION
*-I
+
t
---__
0
!' -ENRICHING
o 0 00.00 '
2b.00
SECTION-[ io.00
s'0.00
\ '*
0
0.00
5.00
10.00
15. 00
20.00
25.00
30.00
AREA (SQUARE CM X 10-3)
\
s'0.00
---.
0
1bo.00
AREA (SQUARE CM X 10-3)
Figure 2. Flow rates and enrichment in the CMC as a function of area for case 1.
General Discussion In the CMC design, high enrichment is only achieved with high recycle ratios, approaching pure product when the permeator is designed and operated with infinite recycle. As a result, the claims of Kao et al. (nearly pure product with membranes of any permselectivity and any given membrane area) cannot be true if a finite product rate is to be realized, since area is required to produce the recycle. The CMC design requires more area and compressor duty than the CCRC for the same overall cut and enrichment for all cases investigated. The difference is especially great for high enrichment and extent of separation. With membranes of low permselectivity, the CMC can produce only moderate enrichment even with very high recycle ratios, while the CCRC can produce high enrichment provided enough stages are used. Area and compressor duty for the individual stages in the CCRC are reasonable. The basic reasons for the difference in efficiency between the CMC and CCRC designs can be traced to the way the recycle is produced and utilized to effect the separation. In the CMC, all of the permeate product plus recycle is enriched up to the final permeate product composition.
Figure 3. Flow rates and enrichment in the CCRC as a function of area for case 1.
At the high recycle ratio required for enrichment, most of the permeate leaving the enriching section is recycle. This recycle must be compressed and repermeated. Thus, much of the area in the enriching section is used to permeate the enriched recycle and contributes little to the actual separation. On the other hand, in the CCRC, the recycle is produced and utilized throughout the separation sequence. In it, the flux of the more permeable species going from the stripping section through the enriching section is just enough to produce the enriched product, which is the entire permeate from stage 1. These differences are compared and contrasted in Figures 2 and 3 for N = 7 in the CCRC and RR = 100 in the CMC for a* = 5 , case 1. In these figures, the flow rates and composition in the CCRC and CMC are plotted as a function of membrane area and show how the separation develops as the high-pressure stream (LH) travels from left to right and the low-pressure stream (LL) goes from right to left. Figure 2 shows flow and concentration in a CMC. LL is higher than LH in the enriching section and differs by an amount equal to the permeate product rate everywhere in the enriching section, while LH is higher and differs from LL by an amount equal to the reject product rate everywhere in the stripping section. Enrichment increases in the LL and reject composition decreases in the LH
2170
Ind. Eng. Chem. R e s . 1990,29, 2170-2172
monotonically. In much of the enriching section, there is very little difference between y and x , and the incremental increase in enrichment with area is very small in most of the enriching section. A very large area is required to enrich all of the permeate product plus recycle up to the final enrichment. Figure 3 presents the same information for the CCRC. In the flow versus area plot, the vertical lines indicate where recycle and feed are added, while the slopping lines (LH decreases and LL increases) indicate permeation. In the concentration versus area plot, the vertical lines represent the difference between the permeate composition leaving stage n and the composition of the permeate in stage n + 1,at the reject end of that stage. As can be seen, in the CCRC, the more permeable species is stripped from the high-pressure stream by permeation and is “pumped up” to higher concentrations as the permeate is produced and recycled to the next stage in the separation train. The basic reason the CCRC is more efficient than the CMC can be explored by thermodynamic analysis. The CCRC is probably more efficient because the overall process is less irreversible than the CMC and hence produces less entropy increase for the same separation. The entropy increase is a measure of the excess work required to make a separation over the thermodynamic minimum. Although beyond the scope of the present study, a thermodynamic analysis of ideal permeator performance for various designs will be the topic of a future study. Conclusion It is concluded that a countercurrent recycle cascade is theoretically more efficient than a continuous membrane column. Nomenclature F = stage where feed is introduced into the cascade LH = local molar rate on high-pressure side LHIF = molar rate of fresh feed LHI(n = molar rate of feed to the Zth stage LHO(I) = molar rate of reject from the Zth stage LL = local molar rate on low-pressure side LLO(I) = molar rate of permeate product from the Ith stage N = end stage in cascade that produces reject product; number of permeators in a cascade PH = pressure on high-pressure side of membrane PL = pressure on low-pressure side of membrane PA = permeability of most permeable species in membrane
RR = recycle ratio = rate of recycle/permeate product rate X = local high-pressure concentration XIF = composition of fresh feed XI(0 = composition of high pressure stream entering the Zth stage X O ( I ) = composition of reject stream f r o m the Zth stage Y O ( I ) = composition of permeate stream from the Zth stage Y = local low-pressure concentration Greek L e t t e r s CY* = ideal separation factor = PA/PB 6 = membrane thickness Op = overall cut = LLO(I)/LHIF O(N) = cut in the Nth stage
Literature Cited Benedict, M.; Pigford, T. H.; Levi, H. W. Nuclear Chemical Engineering, 2nd ed.; McGraw-Hill: New York, 1981;p 685. Blaisdel, C. T.; Kammermeyer, K. Countercurrent and Co-current Gas Separation. Chem. Eng. Sci. 1973,28, 1249-1255. Herbst, R. S. Separation of Boron Isotopes by Gas Phase Permeation of BF,. M.S. Thesis in Chemical Engineering, Montana State University, Bozeman, 1989. Hwang, S.-T.; Thorman, J. M. The Continuous Membrane Column: AZCHE J . 1980, 26 (4),558-566. Kao, Y.-K.; Qui, M.-M; Hwang, S.-T. “Critical Evaluations of Two Membrane Gas Permeator Designs; Continuous Membrane Column and Two Strippers in Series. Znd. Eng. Chem. Res. 1989,28, 1514-1520. Matson, S. L.; Lopez, J.; Quinn, J. A. Separation of Gases with Synthetic Membranes. Chem. Eng. Sci. 1983, 38 (4),503-524. McCandless, F.P. A Comparison of Some Recycle Permeators for Gas Separations. J. Membr. Sci. 1985,24, 15-28. Rautenbach, R.; Dahm, W. Oxygen and Methane Enrichment-A Comparison of Module Arrangements in Gas Permeation. Chem. Eng. Technol. 1987, I O , 256-261. Stern, S.A.; Wang, S.-C. Countercurrent and Co-current Gas Separation in a Permeation Stage; Comparison of Computation Methods. J . Membr. Sci. 1978, 4, 141-148. Ward, W.J., 111; Browall, W. R.; Salemme, R. M. Ultrathin Silicone/Polycarbonate Membrane for Gas Separation Process. J. Membr. Sci. 1976, I , 99-108. Yoshisato, R. A.; Hwang, S.-T. Computer Simulation of a Continuous Membrane Column. J. Membr. Sci. 1984, 18, 241-250.
F.P . McCandless Department of Chemical Engineering Montana State University Bozeman, Montana 5971 7 Received for review April 3, 1990
Accepted July 9,1990
ADDITIONS AND CORRECTIONS Comments on “Model for Hold-Up Measurements in Liquid Dispersions Using an Ultrasonic Technique” Sir: In a paper published by our group (Yi and Tavlarides, 1990),a model for hold-up measurements in liquid dispersions is discussed. Continuing our research efforts in the same area, we realized that even though the model can predict the dispersed-phase holdup of liquid dispersions within 7 % relative error (see Tables IV and V of the cited article), still there are some aspects that need further 0888-5885/90/2629-2170$02.50/0
clarification. In the cited paper, sound-wave refraction and reflection phenomena were considered in order to estimate the path length of sound in the dispersed phase as
L&,i = L&?gd,i
i = 1, 2
(1)
(see &O eq 12 of the cited article), where L is the distance
0 1990 American Chemical Society
