Modeling and Optimal Design of Spiral-Wound Membrane Systems for Gas Separations.

Abstract

Membrane system economics can be significantly affected by process modeling and design. Available spiral-wound permeator models are difficult to use for process design because of their mathematical complexity and high computational demands. Existing sequential design methods yield suboptimal flowsheets when multiple permeation stages are required. In this dissertation, more effective modeling and design techniques for spiral-wound systems separating binary and multicomponent gas mixtures are developed. An approximate modeling approach based on the assumption that the residue flow rate is constant in the direction of bulk permeate flow is proposed. This assumption allows a significant simplification of basic transport models which are derived from material balances and permeation relations. The approach reduces the solution of mixed-boundary nonlinear differential equations to a more computationally tractable problem involving a small number of nonlinear algebraic equations. Approximate models for both binary and multicomponent mixtures are developed. Case studies for separating CO2 from natural gas mixtures show that the approximate models yield accurate predictions over a wide range of operating conditions with considerably less computing time than the basic transport models. An estimation technique for determining uncertain/unknown model parameters from experimental data also is proposed. A nonlinear programming (NLP) design technique is proposed for optimizing operating conditions and analyzing parameter sensitivities for prespecified permeator configurations. The NLP method is extended to develop a mixed-integer nonlinear programming (MINLP) strategy which utilizes a permeator system superstructure to simultaneously optimize the permeator configuration and operating conditions which minimize the total process cost. Case studies for CO2/CH 4 separations in natural gas treatment and enhanced oil recovery demonstrate that the design methodologies are sufficiently robust to handle gas separations with very demanding requirements. Optimal designs are derived for different number of separation stages for both continuous and discrete membrane areas. The proposed approach provides an efficient tool for preliminary design of multi-stage membrane systems for binary and multicomponent gas separations.