(453b) Global Minimization of Power Consumptions for Multicomponent Gas Membrane Cascades

Membrane gas separation has gained increasing attention in the chemical industry in the past decades. A few applications that have seen commercial success include acid gas removal from shale gas, distributed-scale nitrogen production from air, and hydrogen separation from steam methane reforming effluent stream. Many of these applications require the separation of a multi-component mixture into high recovery and purity products, which necessitates membrane systems that consist a series of membrane modules, referred to as a membrane cascade. However, multiple membrane cascade configurations exist for a given separation and the operating conditions of membranes in the cascade could also vary, leading to diverse energy consumptions and costs. It is hence critical to identify the optimal membrane cascade configuration and its corresponding operating conditions to achieve minimum power consumption of the system. Furthermore, calculation of the optimal power for a membrane process is essential for its proper evaluation vis-a-vis other separation processes. This information is also essential for the synthesis and design of hybrid membrane processes.

Although it has been suggested that one may use the local thermodynamic efficiency of permeation to analyze efficiency of membrane stages within a cascade to improve its power, a method is needed to identify an optimal membrane cascade with minimum power demand by drawing a suitable membrane cascade superstructure with all possible membrane cascade configuration embedded, and then formulate a Mixed Integer Nonlinear Program (MINLP) to identify the globally optimal configuration and its corresponding operating conditions. However, this optimization problem is challenging, due to the complicated membrane permeation phenomena and a large number of membrane cascade configurations to be evaluated. Most optimization studies on membrane cascades utilize either local optimization technique or meta-heuristics. These methods do not guarantee that the discovered cascades are globally optimal, or even close in energy consumption to an optimal cascade. A global optimization algorithm that guarantees the identification of globally optimum solution is therefore desired. Efforts towards this goal have been made by several researchers, but all of them are limited to binary cases, except for Taifan and Maravelias who recently published an optimization-based synthesis method for multi-component gas mixture separation [1]. In their model, they used a key insight from our current work to numerically integrate the membrane flux equation, leveraging previous conference presentations from our group [2].

Membranes have a wide range of real-life applications for multicomponent gas separations, such as H₂ separation from syngas, acid gas removal from shale gas, etc. which necessitate the development of global optimization framework for multicomponent membrane cascade. By a simple analogy with the rich search space of zeotropic distillation configurations, for the separation of an n-component mixture into n product streams, each enriched in one of the components, Agrawal suggested a systematic method to draw corresponding multicomponent membrane cascade schemes [3]. However, a method to optimize power of a multicomponent membrane cascade is lacking in the literature. In this article, we develop a mixed integer nonlinear programming (MINLP) model that, for a given multi-component feed, identifies the minimum power consumption and the corresponding optimal membrane cascade configuration. This MINLP formulation is significantly more advantageous than existing formulation in the sense that it can simultaneously guarantee global optimality and accuracy for up to 5-stage and up to 4-component membrane cascades.

Reference

[1] G. S. Taifan, C. T. Maravelias, Generalized optimization-based synthesis of membrane systems for multicomponent gas mixture separation, Chemical Engineering Science (2022) 117482.

[2] Z. Chen, R. T. Gooty, V. J. A. C. Velasco, Global optimization of multicomponent membrane cascade, in: AIChE Annual Meeting, 2020

[3] R. Agrawal, Membrane cascade schemes for multicomponent gas separation, Industrial & engineering chemistry research 35 (10) (1996) 3607–3617.