ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 1015-1022
1015
Simulation of a Hollow-Fiber Gas Separator: The Effects of Process and Design Variables Rey. T. Chern,’ Wllllam J. Koros, and Peter S. Fedklw Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695
A model is developed for simulating the performance of an isothermal hollow-fiber gas separator. The model equations are solved numerically as a boundary-value problem. Permeate pressure buildup has been considered explicitly and concentration dependence of the permeabilities are taken into account by using the dual-mode sorption and transport models. The effects of possible penetrant competition according to the generalized dual-mode model are also examined. U t i l i of the computational results for separator module design is emphasized for various case studies by using “characteristic curves” which represent the relation between degree of separation and fast-gas recovery. The effects on separator performance caused by changes in fiber dimensions (inside diameter, outside diameter, and length), feed pressure, membrane area (number of fibers), feed composition, and feed flow rate are presented. A triple-separator arrangement for the separation of a 12% 188 % COp/CH, mixture is also discussed to illustrate how the results of single-stage studies can be readily extended to multistage design considerations.
Introduction and Background Successful application of membranes for separation purposes depends upon discovery of economically competitive membranes with high permselectivities and permeabilities. On the other hand, engineering considerations such as membrane configurations and flow patterns of the feed and permeate streams are also important in determining the performance of the final separator system. Recognition of this fact is reflected by the numerous modeling studies reported in the literature, by Weller and Steiner (1950),Naylor and Backer (1955),Oishi et al. (19611, Stern et al. (1965),Breuer and Kammermeyer (1967), Walawender and Stern (19721, Blaisdell and Kammermeyer (1973), Pan and Habgood (1974), Hwang and Kammermeyer (1975),Stern (1976),Antonson et al. (1977), Stern and Wang (1978), Pan and Habgood (1978), and Stern (1979). In most studies, however, emphasis has been focused primarily on the calculation techniques and comparison between different idealized flow patterns. The present paper will emphasize the effects of various design and process variables on separator performance and consider the implications for optimal hollow fiber separator design. Due to the large number of possible flow arrangements, the discussion in this paper will be confined to a countercurrent, shell-feed, hollow-fiber separator. However, the general approach can be applied, with slight modifications, to other situations including spiral-wound or flat-membrane systems. Hollow Fibers. The inside (i.d.) and outside (0.d.) diameters of typical fibers are in the ranges of 80-300 and 300-1000 pm, respectively, and the length has been reported to be up to 16 f t (Gerow, 1974, Klein et al., 1977). Due to the small cross section, a large number of fibers can be packed into separators with moderate diameters to provide a large membrane area per unit volume (>10000 m2/m3) (Gerow, 1974). In contrast to flat membranes, hollow fibers are self-supporting. The maximum external or internal pressures a t which they can be operated are determined by the modulus of the membrane material, the ratio of fiber 0.d. and i.d. and the detailed structure of the asymmetric membrane. An approximate analysis can be made by assuming the hollow fiber to be a homogeneous and isotropic elastic tube as suggested by Stern et al. (1977), Varga (1966), and Thorman et al. (1978). 0 196-43051851 1 124- 10 15$0 1.5010
The selective dense layer on the outside region of the hollow fiber is normally very thin (
flow= 13.250 SCFH
t
flow= 102,094 SCFH 0.0426
Yco-=
STRIPPIN6 SECTIOti
= 2 . 4 ~ 1 0SCFD ~
f l & = 24,280 SCFH
ENRICH1 NB SECTION p= 610 psia
f l w 12.983 SCFH
1.-
%=flow; 4.1'. 11,297 SCFH Permeate product
Figure 11. Example of a two-compression-stage separator system.
and thus decrease the loss of CHI to the permeate stream for a target residue purity. The feed pressures of the stripping stages are then determined by a balance between costs associated with membrane area, compression, and CHI losses. The two parallel modules in the feed stage are used to strip as much C02as possible while producing a permeate product of slightly more than 60 mol % C02. This target COz mole fraction is determined from the characteristic curve (curve 3) in Figure 7. Clearly, at the given conditions, a feed stream of a t least 60% COz is needed for producing a final permeate product of greater than 95 % COPfrom the second compression stage at a reasonably high COz recovery. On the other hand, no further compression is required in the stripping section where it is relatively easy to produce a residue product of greater than 98% CH,. Again we resort to the characteristic curves and choose the minimum COPrecovery to minimize CH, loss while keeping the residue purity above 98% CHI. In general, the feed stage in a cascade should be operated at maximum recovery of the most permeable component(s) while maintaining a high-enough purity such that few enriching stages will be required to satisfy the final permeate purity. This would maximize fast-gas production and minimize the waste of membrane area and recompression of the recycled permeate stream(s) in the stripping section. To ensure reasonable process flexibility for handling the feed rate and composition fluctuations, several optional designs may be included; for example, (A) feed pressures to the various stages may be allowed to change over a range of values, (B)part of the final permeate product may be recycled to the feed port of the last enriching stage to boost its feed concentration as reported by Pan and Habgood (1978) and Teslik and Sirkar (1981),and (C) some limited independent manipulation of the stage cut may be provided by using several parallel smaller modules in each
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24, No. 4, 1985
stage which can be turned on or off according to process requirements. The last option may not be very desirable because of increased module cost. Option B is a viable means of increasing the purity of the final permeate product, but it also causes significant reductions in the overall permeate production rate and increases in the compression load. Option A appears to be the most effective approach for providing process flexibility. However, a combination of these options may be needed if the feed rate and composition fluctuate significantly. Conclusions Treating the model equations as a boundary-value problem is shown to be an effective approach for membrane separator design calculations. Other than the obviously important variables such as the thickness of the selective layer and membrane permeability, fiber i.d., o.d., and length are shown to be very important in determining the performance of the final separator module. In particular, for a given fiber o.d., it is clear that a large fiber i.d. should be used in order to minimize the permeate pressure buildup which is deleterious in terms of both productivity and selectivity. The mechanical strength certainly must be considered as well, but even with moderately permeable membranes, an i.d. smaller than 100 pm can be undesirable. This consideration is even more important for membranes with higher permeabilities. Pressure and composition dependence of the penetrant permeabilities as described by the dual-mode transport model (eq 1and 2) has been included in the model equations. Under the same operation conditions, inclusion of the penetrant-competition (eq 2) results in roughly a 5-14% change in most of the dependent variables compared with the "no competition" case (eq 1)for the system examined. Finally, an example of a multiple-separator system is given to emphasize the importance of the single-stage analyses. Acknowledgment We gratefully acknowledge support of this work under ARO Grant DAAG29-81-K-0039. Nomenclature a = total membrane area in a seDarator module D,, ~ D A FA, , Cl,,, bA = dual-mode'parameters of A see Table I1 i.d., 0.d. = inside and outside diameter of the hollow fiber H ( z - z,) = the unit step function 1 = the "effective" thickness of the asymmetric fiber wall mfA,f= initial molar flow rate of A in the feed per fiber mpA= local molar flow rate of A in the fiber bore per fiber m = local total permeate molar flow rate per fiber RpA = local permeation flux of component A N F = total number of fibers in the module p 1 = local permeate total pressure in the fiber bore p I L = total permeate pressure at the open end of the fiber p 2 = feed-side total pressure R = universal gas constant T = temperature YIA = local mole fraction of A in the permate stream Y2A= local mole fraction of A in the shell stream (feed side) z = distance from the closed end of the fiber
z, = the effective length of the fiber ZL
= total length of the fiber
viscosity Subscript 0 = residue end of the module L = permeate exit end of the module 1 = permeate side 2 = shell side (feed side) A or B = component A or B Registry No. Coz, 124-38-9; CH4, 74-82-8. p =
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Received for review June 15, 1984 Accepted December 21, 1984
