基于MINLP的气液混合膜级联最优设计
Optimal Design of Membrane Cascades for Gaseous and Liquid Mixtures via MINLP
摘要：
考虑到对减少CO2排放的日益关注，对于通过膜级联进行的给定分离，需要确定产生最低能耗的最佳设计。然而，设计膜级联是具有挑战性的，因为通常存在多个可行的配置，其在能量消耗和成本方面不同。在这项工作中，我们开发了一个混合非线性规划（MINLP），对于一个给定的二元分离，这可能是液体或气体，发现级联及其操作条件，最大限度地减少能源消耗。为了模拟级联中每个膜处的分离，我们利用从错流模型和溶解扩散理论导出的微分和代数方程的系统的解析解。我们提供的数值证据表明，我们的单级膜模型准确地预测实验数据。不幸的是，所得到的膜模型是非凸的，即使是最先进的求解器也很难证明级联和所确定的操作条件的全局最优性。在本文中，我们推导出各种削减，有助于放松质量，因此，加速收敛的分支定界求解器。更具体地说，我们证明了，在各种例子中，我们的削减帮助分支定界求解器收敛在5\%的最优差距在合理的时间内，这样的公差水平是没有达到一个简单的制定膜模型。所提出的最优化模型是一个易于使用的工具，为从业者和研究人员设计节能膜级联。
英文摘要：
Given the growing concern of reducing CO2 emissions, it is desirable to identify, for a given separation carried out through a membrane cascade, the optimum design that yields the lowest energy consumption. Nevertheless, designing a membrane cascade is challenging since, there are often multiple feasible configurations that differ in their energy consumption and cost. In this work, we develop a Mixed Integer Non-linear Program (MINLP) that, for a given binary separation, which may be either liquid or gaseous, finds the cascade and its operating conditions that minimize energy consumption. To model the separation at each membrane in the cascade, we utilize the analytical solution of a system of differential and algebraic equations derived from the crossflow model and the solution-diffusion theory. We provide numerical evidence which shows that our single-stage membrane model accurately predicts experimental data. Unfortunately, the resulting membrane model is non-convex and, even state-of-the-art solvers struggle to prove global optimality of the cascades and the operating conditions identified. In this paper, we derive various cuts that help with relaxation quality and, consequently, accelerate convergence of branch-and-bound based solvers. More specifically, we demonstrate, on various examples, that our cuts help branch-and-bound solvers converge within 5\% optimality gap in a reasonable amount of time and such a tolerance level was not achieved by a simple formulation of the membrane model. The proposed optimization model is an easy-to-use tool for practitioners and researchers to design energy efficient membrane cascades.
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