A mathematical model of multicomponent permeation systems with high-flux, asymmetric hollow-fiber membranes is presented. The model takes into account the permeate pressure variation inside the fiber. In the special case of negligible permeate pressure drop, the model yields a simple analytical solution for membrane area calculation that eliminates the numerical integration step required in existing methods. Laboratory multicomponent permeation experiments have verified the mathematical model and have demonstrated the technical feasibility of using the high-flux asymmetric cellulose acetate hollow fiber for H, , CO,, and H, S separation. It is shown that the selectivity of the cellulose acetate membrane is ideally suited to the recovery of hydrogen from the purge gas of reactor recycle loops. For the separation of high-concentration CO, or H,S, the test data show that the permeabilities of the individual components in mixed gas permeation are significantly different from those of pure gases.

The permeation behavior of the high-flux asymmetric membrane differs from that of the conventional symmetric membrane. A calculation method for predicting the gas separation performance of a permeator with asymmetric membrane is presented. The model takes into account the permeate pressure drop and is applicable to both hollow-fiber and spiral-wound modules. The effect of permeate-feed flow pattern on module performance is analyzed. It is shown that for the high-flux asymmetric membrane, the countercurrent flow pattern is not necessarily always the preferred operating mode. The mathematical model is verified by large-scale field pilot-plant experiments for helium recovery from natural gas using large hollow-fiber modules (220 m2/unit). C. Y. PANAlberta Research Council Edmonton, Alberta, Canada SCOPEThe conventional symmetric membrane has a homogeneous structure with uniform permeation properties across its thickness. This type of membrane has not been widely used for gas separation mainly due to low rates of permeation imposed by the membrane thickness required for maintaining membrane integrity and strength. Recent development of asymmetric membranes, however, has made membrane permeation an important unit operation for gas separation. The membrane consists of an ultrathin skin and a porous supporting layer with negligible resistance to gas flow. The skin, which acts as the separation barrier, is highly permeable due to its thinness. This permits the use of highly selective polymers with inherently poor permeability for specific gas separation. The presence of the porous supporting layer, howeve:, renders the permeatiop behavior of the asymmetric membrane somewhat different from that of the familiar symmetric membrane. A calculation method for predicting the performance of a permeator with the high-flux asymmetric membrane is presented. Both hollow-fiber and spiral-wound modules are considered. The effect of flow pattern on the performance of the asymmetric membrane is found to be significantly different from that of the symmetric membrane. Laboratory and pilot-plant data are presented to substantiate the mathematical model. CONCLUSIONS AND SIGNIFICANCEThe porous supporting layer of the asymmetric membrane prevents the mixing of permeate fluxes of varying compositions on the membrane skin surface. Consequently, the asymmetric membrane always gives rise to cross-flow type of permeation regardless of the flow pattern and direction of the bulk permeate stream flowing outside the porous layer. It is this characteristic that sets the permeation behavior of the asymmetric membrane apart from the conventional symmetric membrane.It is shown that, for the asymmetric membrane with narrow permeate flow path such as hollow fibers, the permeate pressure build-up is strongly dependent on the feed-permeate (the bulk stream) flow pattern. The countercurrent mode has the lowest permeate pressure build-up but the feed flow is in the undesirable direction in relation to the permeate pressure build-up. The cocurrent pattern, on th...

A theoretical analysis of the single-stage permeation process is presented. A unified mathematical formulation and calculation methods are given for various feed-permeate flow patterns (countercurrent, cocurrent, cross flow) with two permeable components Including the case with a nonpermeable fraction in the feed and a purge stream in the permeate. It is confirmed that the countercurrent flow pattern is always the best and that the cross-flow pattern is always intermediate with respect to membrane area, enrichment, or recovery. It is shown that the permeate/feed concentration ratio cannot be larger than the smallest of the permeability ratio, the feed/permeate pressure ratio, or the reciprocal of the feed concentration. For a given recovery of the more permeable component, the required membrane area decreases with Increasing permeabilities of both components. Purging on the permeate side of the membrane with a small gas stream can, in some cases, greatly reduce the membrane area requirement without diluting the permeate stream significantly. The effectiveness of purging generally increases with decreasing feed concentration and with Increasing membrane selectivity relative to the feed/permeate pressure ratio.

Calculation methods for determining pure gas permeabilities and gas separation performance of hollow fiber modules with significant permeate pressure drop inside the fiber are presented. A sequential optimization method for determining the near‐optimum permeate pressures in cascade operation is developed. It is shown that the performance of narrow hollow fiber modules can be significantly affected by the permeate pressure build‐up inside the narrow fiber. For a given module and given recovery there exists an optimum permeate outlet pressure which minimizes the membrane and permeate compression costs. Examples given relate to the recovery of helium from natural gas.

Calculation methods for single-and multi-stage permeation of a multi-component mixture are presented. The use of the local permeate concentration in the formulation results in a relatively simple form of solution for the binary system in the