Ind. Eng. Chem. Res. 1989,28, 1514-1520
1514
Critical Evaluations of Two Membrane Gas Permeator Designs: Continuous Membrane Column and Two Strippers in Series Yuen-Koh Kao,* Mei-Mei Qiu, and Sun-Tak Hwang Center of Excellence for Membrane Technology, Department of Chemical and Nuclear Engineering, University of Cincinnati, Cincinnati, Ohio 45221 Extensive calculation results of the performances of the continuous membrane column (CMC) and the two stripper in series permeator (TSSP)are presented in the form of their design surfaces. The results show that there exist two distinct regions in the design domain. In the region of lower stage cut and higher permeate enrichment, the CMC is the preferred design over the TSSP. The opposite is true for the region of higher stage cut and lower permeate enrichment. At any finite membrane area per unit feed rate, the permeate enrichment achievable by a TSSP has an upper limit, which is not so for a CMC. In terms of Rony’s separation index, the maximum separation achieved by the TSSP is always greater than that of the CMC with the same membrane area. The attainable enrichment of the TSSP is reduced significantly when a membrane of less permselectivity is used. The CMC, on the other hand, can produce a highly enriched product with membranes of any permselectivity. Selective permeation through a membrane is becoming increasingly attractive for gas separation. The advantages of membrane separation over conventional processes typically include reduced capital costs, compact and flexible modular design, simple operation, and low energy consumption. For many years, engineering approachesto the successful application of membranes for separation purposes have focused on the design of the permeator, which is the key equipment in a membrane system. Since the permeate enrichment in a single-state permeator is generally limited by the membrane selectivity and feed/permeate pressure ratio, multistage or cascading configurations are usually required in order to achieve the higher enrichment. Unfortunately, this is done at the expense of increased operating cost, especially for a low membrane-gas selectivity system. These conventional membrane permeators are being challenged by several noncascading alternatives. These include recycle permeators (Stern et al., 1984),two stripper in series permeators (TSSP) (Ohno et al., 1978), twomembrane permeators (Sirkar, 1980), etc. The recently developed continuous membrane column (CMC) exhibits the innovative aspects of an efficient and simplified membrane-separation system (Hwang and Thorman, 1980). As shown in Figure la, , the CMC is analogous to a distillation column in which the gas mixture is fed to the column in between the stripping and the enriching section. The more permeable gas gathers at the top of the enricher, and the less permeable gas gathers at the bottom of the stripper. Theoretically, the CMC can separate the feed mixture to a product of any degree of purity on a continuous basis with only one compressor. Although no explanation was given, the same arrangement as for the CMC was proposed in an earlier patent (Pfefferle, 1964). Several investigations, both theoretical and experimental, have been conducted to explore the continuous membrane column performance. Experiments were carried out for the binary gaseous systems C02/02, 0 2 / N 2 , and C02/N2 by Hwang et al. (1980). The results were analyzed by numerical simulation with the plug-flow model. Separation of methane from binary and ternary mixtures has been demonstrated by Hwang and Ghalchi (1982). The
* To whom correspondence
should be addressed.
0888-5885/89/2628-1514$01.50/0
orthogonal collocation method had been used as an alternative numerical method to simulate the continuous membrane column by Yoshisato and Hwang (1984). Recently, Chen et al. (1986) developed a new model for the continuous membrane column which includes the axial diffusion effect. This modification enables simulation of the cases in which the diffusion effect is important, thus eliminating the singularity encountered in the plug-flow model. Matson et al. (1983) compared the performance of the CMC enricher with the recycle permeator and two-unit series cell in terms of membrane and compression power requirements. Stern et al. (1984) reproduced the existence of the maximum permeate concentration of the more permeable gas in both the recycle permeator and the enricher section of a CMC operating at a fixed recycle ratio. They showed the possibility of separating a binary mixture in a CMC to almost any desired extent by operating this device at a sufficiently high reflux ratio and low stage cut. McCandless (1985) examined the performances of several permeator arrangements in terms of the enrichment, extent of separation, and membrane area requirement for different stage cuts and recycle ratios. However, no emphasis was focused on an accurate and comprehensive economic evaluation of each modular performance, and in most studies, these permeators were not compared with each other at their respective optimum operating conditions. The CMC configuration was examined parametrically and compared with several different recycle arrangements and multimembrane permeators (Yan and Kao, 1987; Kao et al., 1987a,b). Optimization calculations of the CMC enricher were performed by Hwang et al. (1980) for a system of given product purity and operating pressure ratio. Analytical solutions of two extreme cases (the low-pressure side is at vacuum and total reflux) were obtained. For general cases, a numerical trial-and-error method was applied. However, only the optimization of the compressor load was considered in his study. The two stripper in series permeater (TSSP)is studied and compared with the CMC in the present paper. In the TSSP configuration, as shown in Figure lb, the entire permeate stream of the second stripper is recycled and combined with the fresh feed and fed to the first stage. It was reported that the TSSP gives the best separation and requires the least membrane area at a high recycle ratio, 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1515
/L PERMEABLE GAS
-
L\
q lplt
q,,,r
Yir
t
q,xtd(q,x)
HIGH PRESSURE A ,I
I
I
1'
~
~
9tX
z
c d 2
0
,
I/
9
N
Figure 2. Material balance for a permeator. R = Recycle Stream STRIPPER
1
qr
qr
-
Feed 91
qr Yr
XI
qt00
Top Stream
Ytop
qtop YtCQ L p-
Stripper 2
Enricher
MEMBRANE
IA
LEAST PERMEABLE GAS
Pressure Ratio
lz2
p,
Stream
nPermeability
(a1 C M C
t
Ibl
Ratio
Lr-
TSS
02
Figure 1. Continuous membrane column (CMC) and two stripper in series (TSS) permeator.
as compared with several different recycle permeators (McCandless, 1985). In this paper, a critical evaluation of the TSSP and CMC covering the whole design domain will be presented for the separation of a binary gas mixture. Results from the computer simulation study will be presented in a series of design surfaces. The design surface presentation will provide a clear global view of the respective design. Comparisons of the two configurations are made in terms of product purity, stage cut, compressor load, extent of separation, and membrane area requirement. The optimal designs for the CMC and TSSP, based upon economic considerations, will be presented elsewhere.
Mathematical Model and Simulation Method Model Development. The essential part of a membrane separator using capillary membranes is a tubeand-shell heat-exchanger-like permeator module. In this study, a high-pressure feed stream is introduced to the tube side, while a low-pressure permeate stream is withdrawn from the shell side of the permeator. The governing equations describing the transport process in all permeator modules are the same except that a different set of boundary conditions must be provided to account for the particular configuration of each module. The plug-flow model of binary gas permeation in a capillary membrane (Thorman and Hwang, 1981) is adequate for most of the cases examined. In some extreme cases when the diffusion effect is significant, the diffusion-included model developed later by Kao et al. (1987a,b) was required for numerical convergence (Kao, 1988). The governing equations of the plug-flow model for a binary gas mixture include the overall and the component material balances over the shell side of a permeator: dqs _
Membrane Area Am
I 0 -
ik--
Bottom Stream qbot
a
Ybot
CMC
b
TSS
Figure 3. Important variables in the CMC and in the TSSP.
respectively, Q1 and Q2 are the permeability coefficients of the more permeable and less permeable components, respectively, Pt and P, are the total pressure at the tube and shell sides, respectively, q, is the shell-side flow, z is the axial coordinate, ro and ri are the outer and inner radii of the membrane capillary, and N is the number of the capillaries used in a permeator column. The tube-side composition and flow rate can be related to the shell-side counterparts by applying overall and component material balances, as shown in Figure 2, over both sides of the membrane: qt,h + qS = qS,OUt + qt
(3)
qt,inXin + QY = qs,outYout + qtX
(4)
The configuration of a continuous membrane column can be viewed as the combination of two permeator modules, arranged as a stripper and an enricher, as shown in Figure 3a with L1 and L2 denoting the lengths of the stripper and of the enricher, respectively. Proper boundary conditions are required to solve the above coupled nonlinear differential equations for each configuration. In the stripping section, the permeate flow rate is zero at the closed end of the low-pressure shell side, q,(z1=0) = 0
(5) In the enricher section, a portion of the permeate stream at the shell side is recycled to the tube side such that x(z,=L,) = y(z,=L2) (6) (7) qt(~Z=L2)= qS(z2=L2) - qtop A t the shell-side junction between the stripper and the enricher, both flow rate and composition are continuous:
where x and y are the concentrations of the more permeable component at the tube and shell side of the capillary,
4s(z2=0) = qs(zl=L1)
(8)
Y ( Z z = O ) = Y(Zl=Ll)
(9)
1516 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
At the feed location, the reject stream from the enricher is combined with the fresh stream and is fed to the stripper: qt(z1=L1) = qf + q,(z2=0)
(10)
q,(Zl=Ll)x(zl=Ll)= qfxf + q,(z2=0)x(z2=0) (11) The arrangement of the two stripper in series permeater is shown in Figure 3b. The inlet concentration to the primary (top) stripper is raised by mixing the feed and the permeate stream from the recycle (bottom) stripper. The mixing of the two streams provides the following junction conditions: qt(z2=L2)
= qs(z*=L1) + qf
(12)
~ t ( z z = L & ( ~ 2 = L 2=) Qs(Zi=Li)Y(zi=Li)+ qfxf (13) Here, the subscripts 1 and 2 denote the recycle (bottom) and the primary (top) strippers, respectively. At the junction of the two strippers both the flow rate and the composition are continuous: qt(z1=L1) = qt(z2'0)
(14)
x(z,=L,) = x(z,=O)
(15)
Similarly, at the closed end of the strippers, qs(z1=0) = 0
(16)
qs(z2=0) = 0
(17)
are also valid boundary conditions. The following dimensionless variables are defined 4s* = 4 s / f o
qt* = st/fo
z;* = Zi/Li
Li* = &/Lo
where fo is the maximum permeation rate across the membrane, i.e.,
and Lo is the length of the total column, Lo = L1 + L2. The dimensionless governing equations result as follows:
- Qt* + qs* - Qs*out = 0 + qe*Y - qt*x - qs*outYout = 0
qt*in qt*inXin
(21) (22)
where y = Q1/Q2is the permeability ratio of the more permeable component to the less permeable component or ideal separation factor; P, = P,/Pt, is the pressure ratio of the permeate side to the feed side. The orthogonal collocation method was used to solve the coupled nonlinear differential equations. Details on the numerical method can be found in earlier publications (Chen et al., 1986, Kao et al., 1987a). A typical CMC or TSS calculation is converged in less than 5 s of CPU time on a AMDAHL 470. Degree of Freedom. Since there are so many variables and parameters in the permeator design problem, it is worthwhile to consider first how much flexibility the designer has in specifying the operating conditions. As shown in Figure 3a, there are 12 variables encountered in determing the performance of an entire continuous mem-
brane column. These variables are (a) the compositions of the more permeable component at the feed, bottom reject outlet, as well as the top permeate outlet, namely, xf, xbt, and ybP, respectively; (b) the flow rates, qf, qbt, and qbP, of the feed, bottom, and top streams, respectively; (c) the permeability ratio, y; (d) the recycle ratio, defined as the ratio of the recycle flow rate to product flow rate, i.e., R = qr/qbp; (e) the pressures of the tube and the shell side, Pt and P,, respectively; (f) the membrane area, A,; and (g) the feed location or the length fraction of the stripping section, L1*. The governing equations will reduce the degree of freedom to eight. Additional design specifications will further reduce the degree of freedom. Normally the feed rate and concentration to the permeator are specified, as well as the operating pressure (Pt and P,) and the permselectivity of the membrane used (7). Therefore, the degree of freedom is reduced to three. The feed location of a CMC, represented by L1*,can be an independent design variable. However, in a design problem, this location should be chosen so that no mixing between the external feed steam and local stream takes place at the feed point (Kao et al., 1987a,b). This would require that the compositions for the following three streams, the bottom (reject) stream on the tube side of the enricher, the external feed stream, and the feed stream to the tube side of the stripper, be identical by specifying a particular recycle ratio. Adding this restriction to those conditions specified previously, the degree of freedom is reduced to two. Therefore, the design domain of a CMC with this optimal feed location specification is two-dimensional. Unlike the CMC, the recycle rate, qr, in a TSSP is not a controllable variable. Therefore, the number of degrees of freedom in the TSSP is one less than CMC's. The preceding no-mixing condition may also be applied to the TSS configuration. One may specify the length fraction of the recycle stripper so that the concentration of the recycle stream matches that of the feed stream to eliminate the mixing effect. However, as will be presented later in the text, this choice usually leads to a lower top product purity. Thus, in order to present a parallel parametric study with CMC, which has 2 degrees of freedom, the length fraction of the recycle or primary stripper is not restricted by the no-mixing condition. Variable Selection and Specification. The example chosen for this study is the separation of a binary gas mixture with a polymeric membrane with following parameters: feed concentration xf = 50% (mol %), pressure ratio P, = 0.1, and permeability ratio y = 5. The reference feed rate used in the comparative design study is the maximum permeation rate across 1m2 of the given membrane, i.e., qf = PtQl/(ro- r J . This feed rate selection allows for the generalization of the results of this study to a variety of membrane-gas systems. For example, the above case could be the separation of a 50% methane (l)/nitrogen (2) mixture using a phenylenesiliconerubber membrane (Hwang et al., 1974, Stern, 1966) with the following properties: total pressure at the tube side Pt = 10 atm; permeability of methane P C H , = 2.0 X lo-* (STP cm3)(cm)/(cm2)(s)(cmHg), 30 "C; membrane capillary dimensions, 0.610-mm o.d., 0.234-mm i.d. The design calculation will then be based on a feed rate of 3.63 X lod mol/s.
Discussion on Simulation Results The performances of the two designs obtained in this computer simulation will be presented in the form of various design surfaces. The domain of these design surfaces are the plane of product composition ( Ybp) and
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1517 1.o
- CMC
_..___ TSS
0.9
0.8 Ytop
0.7
0.0
"
0.5
0
0.6
0.5
1-
0.8
0.9
I.&
Ytop
0.5
,
I
I
Figure 4. Design surfaces of the stage cut for the CMC and TSS designs (y = 5).
the membrane area (A,) required for processing the specified amount of the feed mixture (3.63 X 10"' mol/$ The stage cut, 8, is selected as the primary surface variable. The remaining design variables, such as the feed location of a CMC, expressed as the length of its stripping section, L1*, or the length of the primary stripper of a TSSP, L2*, or any combination of these variables, e.g., the compressor load, is then represented as the design surface. These surfaces are constructed with values calculated with the mathematical model of the respective designs. The design surface presentation chosen for this study will give readers a better overall vista of the performance characteristics of either design, thus providing a useful guide in preliminary design and evaluation. Stage Cut. Figure 4 shows the design surfaces of the stage cut (e), defined as the ratio of the product rate to the feed flow rate (qb /qf) of both designs (solid lines for the CMC and dashed fine for the TSSP) over the domain of A , and ybp. For any given A,, the maximum stage cut is obtained when both designs are degenerated into a simple stripper. In this case, the top product concentration is at its lower limit as shown by the curve AB. Curve CB on the design domain marks the lower bound in the membrane area and the top product concentration, above which it is possible to find both a TSSP design and a CMC design with the optimal feed location restriction. Curve AB represents the simple stripper performance. The fact that a stripper with a smaller membrane area will obtain a higher product Concentration at a lower stage cut (see also Figure 5 ) provides the very basis upon which both designs built their enhanced separation performances. At a fixed total membrane area, both designs will produce a top product at a concentration higher than but at a stage cut lower than that of a simple stripper with the same membrane area. The design surface of a CMC ends at the boundary of ybp = 1and 8 = 0, which indicates that the CMC design can produce with any finite membrane area a top product of any desirable purity. A t the 8 = 0 limit, the column is operating at total reflux with the feed entering at the bottom of the column. This case is theoretically significant because it shows that a CMC can produce a nearly pure top product albeit at a very low cut. The TSS surface shown in the same figure has two boundaries represented by the curves A B and BD, respectively. The lower boundary, as might be expected, is the limiting case when the TSSP is degenerated into a single stripper; i.e., the recycle stripper is abandoned. The curve BD is the upper limit of yb,, at zero stage cut. This limiting case of no top product withdrawal was calculated by applying the wellmixed model proposed by Weller and Steiner (1950) on
the zero-area primary stripper. The feed to the primary stripper is the combined stream of the feed stream and the permeate stream from the recycle stripper. In comparison to a CMC with the same membrane area, the highest attainable top product concentration of the TSSP is always less than that of the CMC. As a matter of fact, the TSS design cannot obtain a nearly pure top product unless a very large membrane area is used. The CMC design, on the other hand, can obtain a nearly pure product with any given membrane area. Therefore, the CMC design can meet any ybp specification with any membrane area allotment. More top product, i.e., a larger stage cut, can always be recovered by increasing the membrane area requirement, A,. When the membrane area allotment is small, the top product purity increases rapidly, more so at a smaller membrane area, as the stage cut decreases. When a larger membrane area is used, the top product purity increases gradually with decreasing stage cut as long as the top product purity is less than a certain limit. When the top product purity exceeds this limit, the stage cut drops rapidly to zero. In principle, more top product at a specific purity can always be recovered by using a larger membrane area. The increase in membrane area for more recovery becomes very large when the top product purity specification is very high. The maximum ybp by the TSS design is limited by the total membrane area allotment. The top product recovery drops precipitously as its purity approaches the upper limit. In the region of lower top product purity, the TSS design can recover more top product than the CMC design with the same membrane area. The intercept of 8 surfaces of the CMC and the TSSP, curve EF,is the watershed in design selection. On the low yto side, TSSP is the better design and on the other side, 8MC is better. The difference between the two designs in terms of the product recovery and purity can be seen in a 2-D plot as shown in Figure 5 . In the region of small A , and high ybp (to the left of curve EF), the CMC appears to be the preferred design since it can achieve a higher 0 than the TSSP at the same ybp and A,. For instance, it is impossible to produce a top product of 90.5% CHI content with a TSSP when less than 1.6 m2 of the membrane area is used. In contrast, a CMC with the same membrane area can recover 21% of the feed as 90.5% CHI top product. On the other hand, in the region of large A , and low yb , the separation ability of the TSSP is higher than the CM& For instance, the cut attained by a TSSP is 0.644, larger
1518 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
..~... TSS ~
CMC
6.0
5.0 4.0 P
-83.0
0-
2.0 1 .o Ytop
Ytop
Figure 6. Optimal feed location surface of CMC (y = 5).
Figure 8. Comparison of compressor load surfaces of the CMC and TSS designs (y = 5).
/
/
A
A.-1 e
1 .o
0.8 0.6 N
f0.4 0.2 0.0 Ytop
Figure 7. Length fraction of the primary stripper surface of TSSP (Y
= 5).
than that of the CMC, which is 0.620, for the separation assignmentof 75% CHI purity with 3.5-m2membrane area. CMC Optimal Feed Location. The means by which a CMC attains the high top product purity can be explained by examining the surface of feed location, expressed as the length fraction of the stripping section, L1*, as shown in Figure 6. The curve AD is the special cases of L1*= 1, when the CMC is degenerated into a single stripper; namely, feed is introduced to the top of the entire column and without recycle. For a typical CMC column, L1*< 1. When the total membrane area is fixed, by reducing the length of the stripping section, one can obtain a more enriched permeate from the stripper (since a smaller area will produce a higher product purity albeit at a lower cut) at a rate comparable to the permeate of a simple stripper (because the actual feed to the stripping section will be higher than the case of a simple stripper due the addition of the recycle stream from the enricher to the feed). The permeate from the stripper is further enriched in the enriching section. Therefore, the enrichment in the top product stream can always be increased by moving the feed location downward in the column. The feed location will eventually reach the lower limit, L1* = 0. This is the limiting case mentioned earlier when the feed is introduced to the high-pressure side at the bottom of the stripping section of a CMC. Staging of TSSP. The way a TSSP achieves higher enrichment can be understood by examining the surface of the length fraction of the primary stripper, L2*, over the ytopand A , domain as shown in Figure 7 . At a fixed total membrane area, the reduction in the primary stripper size will increase the top product concentration but at a lower stage cut. In analogy to the optimal feed location of the CMC, the optimal length fractions of the primary stripper
may be chosen such that the compositions of the recycle and feed streams are identical. The TSS design under this restriction is represented by curve MN on the design surface and curve mn in the design domain. Clearly, the TSSP is less flexible than the CMC under this restriction. The top product concentration of a TSSP with a finite membrane area design under this no-mixing restriction is always lower than what is achievable with a hypothetical TSSP of zero membrane area. This result was calculated with the no-mixing model for both the primary and recycle strippers. What can be gained with this design restriction is that more top product is recovered at a lower top product purity so that less of the permeable species will be lost with the bottom reject stream. Without this no-mixing restriction, L2*varies from 1to 0 for any A,. The top product concentration, in the meantime, varies from the lower simple stripper limit (curve AB) to the upper limit (curve CD).The improvement in the top product purity results from both the recycling of the permeate at a composition higher than the feed from the recycle stripper and the smaller primary stripper membrane area. Compressor Load. It has been reported that the cost of operating a compressor is the prime component in the entire CMC operation cost (Yuen, 1980). Figure 8 shows the surface of the compressor load (qload), defined as the sum of the feed and the top recycle stream flow rates per unit feed rate, over the domain of ytopand A,,,. The lowest compressor load of both designs is obviously unity, corresponding to the case when both design are reduced to a single stripper. The upper limit of qload is a finite value corresponding to a CMC operating at total recycle and a TSSP with a zero-area primary stripper. In general, the compressor load required to operate a CMC is higher than what is required to operate a TSSP except in the range of very small membrane area requirement. The compressor load of the TSS design is larger than the CMC design in the higher y,,/smaller A , region. For example, when a top product of 75% CHI purity is to be recovered with 3.5-m2membrane area, the compressor load required by a TSSP is 17.6% less than CMC under the same circumstances. The fact that CMC design requires a larger compressor load more than any other factor leads to the high operating cost and, therefore, the slow acceptance by the industry of the CMC design. In the operation mode, it is more common to consider the recycle ratio in place of the compressor load. This can be readily obtained with the following equation:
R = -% a d 0
(23)
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1519 "O 0.8
1
-.....TSS
From tap Am =
- CMC
__.-..
,I
0.6
-
0.4
-
t
/
% .-_ _ - - --.. _ _-.
4.5, 3.5, 2.3, 2.0 1.6, 1.2, 0.9, 0.6 0.45, 0.35
. .
0.2 -
0.0
Y
0.0
I
I
0.2
I
1
I
0.6
0.4
0.8
Y
1 .o
0
Ytop
Figure 10. Comparison of design surfaces of the stage cut of the
Figure 9. Comparison of the extent of the separation surfaces of the CMC and TSS designs (y = 5).
CMC and TSS designs
(y
= 2).
A /
Separation Index. Rony (1972) proposed a more universal index for evaluating the separation performance of different separation processes. This is the extent of the separation, f , defined for a binary mixture, as the absolute value of the binary separation matrix written in terms of segregation fractions Yij: [ = abs det
y11
y12
where Yij = nij/nio,and nij is the molar rate of component i leaving a permeator module in flow region j and niois the molar rate of component i in the fresh feed to the permeator. The extent of the separation, {, can be expressed in terms of the feed composition and top product composition as follows (McCandless, 1985): { = 0
Ytop
- Xf
X f ( 1 - Xf)
A plot of { vs stage cut, 8, is shown in Figure 9. First to be noted here is that the value of { goes through a maximum only when A , is larger than a certain value. For example, for the CMC design, A , > 1.6. For the smaller values of A,, { increases with increasing stage cut, and a maximum is located at the single stripper boundary. For large A,, { maxima occur approximately at 0 = 0.5. This indicates that a CMC will reach its maximum separation ability when both the top and the bottom streams are viewed as the desired products. For a fixed feed composition and feed rate, an increase in the membrane area always leads to a higher extent of separation. The limit of { = 1could theoretically be approached by increasing A,. The performance of the TSS design measured with the separation index, {, follows a similar trend. Curve, EF, on which both the CMC and TSSP have the same value of f , defines the region of design choice. The existence of these two regions can also be identified by curve EF in Figure 4. In the region of stage cut less than EF, a CMC has a higher extent of separation than a TSSP of the same membrane area. The opposite is true for the high cut region. However, the maximal product separation with a fixed membrane area is always achieved by the TSS design. Effect of Permselectivity. The effect of membrane permselectivity on the performance of both designs is presented by their 0 surfaces in Figures 10 and 11, for the cases when the selectivity is higher (y = 10) and lower (y = 2) than the previous example, respectively. The feasible design domain of the TSSP reduces in size as the permselectivity decreases. One can see from Figures 10 that the
V Oh
UL'
nn V."
0.k
0.i
0.8
0.b
7 l.ia
YtOP
Figure 11. Comparison of design surfaces of the stage cut of the CMC and TSS designs (y = 10).
top product purity attainable by the TSS design reduces significantly when a less permselective membrane is used. In general, the TSS design region is restricted to the left of its upper bound curve BD, while the CMC design region extends all the way to ytop = 1. The CMC design can produce a high-purity top product but a significantly lower stage cut. The productivity can be increased by using a larger membrane area. On the other hand, Figure 11shows that the TSS design can produce high-purity product at a respectable production rate when a high selectivity membrane is available. In general, the CMC is a better design than the TSSP when a small membrane area or when a less selective membrane is used.
Conclusions The preceding discussion on the performances of CMC and TSS designs with respect to their design surface provides a guideline in determining whether the CMC or TSS configuration is to be selected for a particular separation problem. Both CMC and TSS designs have their own favorite regions such as indicated by curve EF in Figure 4. A preliminary selection of the permeator configuration may be conducted by locating these design conditions in the design domain. This information is summarized in Figure 1 2 for the three membrane permselectivities examined in this study. Curves EF, E%', and E '%" demarcate the design regions; within each region, one of the designs should be selected. If the design condition lies above these curves, the TSSP should be the design chosen to meet the separation requirement. According to the membrane area requirement, a CMC should be the design choice when the membrane area needs to be minimized due to the high membrane cost and
1520 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
2 = less permeable component f = feed stream
shell side tube side in = entrance out = exit bot = values at the bottom of the column top = values at the top of the column s = t=
Superscript * = dimensionless Greek Symbols y = 00
'
05
, 06
I
1
07
OB
I
I 09
lo
I
10
Ytop
Figure 12. Design regions of the CMC and TSSP.
when high product purity is the goal of the separation process. Otherwise, the TSS design will achieve the objective more economically. The compressor load is generally lower for the TSS design. If the maximum segregation in the product streams is desired, a TSSP will always outperform the CMC with the same membrane area. An accurate assessment on the merit of each design is not possible unless a comprehensive performance evaluation is made based on economic criteria. This subject will be addressed in a subsequent paper (Qiu et al., 1989).
Nomenclature A , = membrane area for processing 3.63 X lo4 mol/s of feed, m2 fo = maximum permation rate at a fixed feed pressure, mol/s Li = sectional length; for the CMC, i = 1, stripper, i = 2 , enricher;for the TSSP, i = 1,recycle stripper, i = 2, primary stripper Lo = length of the total column, m L1* = length fraction of the stripper in the CMC, the optimal feed location L2* = length fraction of the primary stripper in TSS design N = number of capillaries in a permeator column P = absolute pressure, Pa P, = pressure ratio across the membrane q = flow rate, mol/s = compressor load, defined as the sum of the feed and recycle stream rates, mol/s qr = recycle stream flow rate, mol/s Q = permeability, (mol.m)/(s.m2-Pa) ri = inner radius of the capillary, m ro = outer radius of the capillary, m R = recycle ratio x = mole fraction of the more permeable component in the tube (high pressure) side y = mole fraction of the more permeable component in the shell (low pressure) side z = axial coordinate along the permeator, m z, = axial coordinate from the exit of a permeator, m; for the CMC, i = 1,stripping section, i = 2, enriching section; for TSSP, i = 1, recycle stripper, i = 2, primary stripper Y,] = segregation fraction in eq 24 Subscripts
1 = more permeable component
separation factor
0 = stage cut E = extent of separation
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