MEMBRANE  SYSTEMS MODELING AND DESIGN Gas separation membranes have emerged as a viable alternative to more mature technologies such as chemical absorption and cryogenic distillation. The economics of membrane separation processes depend critically on process design. Multiple separation stages and recycle are required for demanding applications such as the separation of methane/carbon dioxide mixtures in natural gas treatment and enhanced oil recovery. The design of a membrane system involves the determination of: (i) the configuration of the permeator network; and (ii) the operating conditions of the individual permeators. Membrane systems currently are designed via a suboptimal procedure in which the permeator configuration is chosen by process heuristics and the operating conditions are determined using some type of optimization procedure. We have developed approximate modeling and optimal process design techniques for membrane separation systems comprised of spiral-wound gas permeators. This research has been supported by NSF and Praxair. The lack of suitable permeator models is a major obstruction to effective simulation and design of spiral-wound membrane processes. Basic transport models consist of nonlinear  differential-algebraic-integral equations with mixed boundary conditions. We have derived approximate models which provide a more reasonable compromise between prediction accuracy and computational efficiency by assuming the residue flow rate is constant in the direction of bulk permeate flow. This assumption yields nonlinear alge braic equation models which can be solved very efficiently and reliably. The accuracy of the approximate models compares favorably with the basic transport models for gas mixtures containing as many as eight components. On the other hand, the approximate models can be solved with less than 1% of the computing effort. We have used the approximate models to develop a nonlinear programming framework for estimating unknown model  parameters from experimental data. We have developed an optimal design strategy for spiral-wound membrane systems based on the approximate permeator models and rigorous mathematical programming. A permeator system superstructure is used to efficiently represent a very large number of possible system configurations. The superstructure is formulated as a mixed-integer nonlinear programming (MINLP) problem and solved using standard optimization tools to yield the system configuration and operating conditions which minimize the annual process cost. The optimal design methodology has been evaluated for the separation of methane/carbon dioxide mixtures in natural gas treatment and enhanced oil recovery. Permeator configurations have been derived for different number of separation stages under a wide range of operating conditions. The results demonstrate that the proposed approach provides an efficient methodology for preliminary design of multi-stage membrane separation systems for multicomponent gas mixtures. References Qi, R. and M. A. Henson, ``Approximate Modeling of Spiral-Wound Gas Permeators,'' J. Membrane Science, 121, 11-24 (1996). Qi, R. and M. A. Henson, ``Modeling of Spiral-Wound Permeators for Multicomponent Gas Separations,'' Ind. Eng. Chem. Res., 36, 2320-2331 (1997). Qi, R. and M. A. Henson, ``Design of Membrane Gas Separation Systems via Nonlinear Programming,'' AIChE Annual Mtg., Los Angeles, CA, November 1997. R. Qi and M. A. Henson, "Optimal Design of Spiral-Wound Membrane Networks for Gas Separations", J. Membrane Sci., 148, 71-89 (1998).  [Abstract] R. Qi and M. A. Henson, "Optimization-based Design of Spiral-Wound Membrane Systems for CO2/CH4 Separations", Sep. Purif. Technol., 13, 209-225 (1998). [Abstract]