Comprehensive Study of the Energy Consumption of Membranes and Distillation

Molecular separations are essential in the production of many chemicals and purified products. Of all the available separation technologies, distillation, which is a thermally driven process, has been and continues to be one of the most utilized separation methods in chemical and petrochemical plants. Although distillation and other commercial technologies fulfilled most of the current separation needs, the energy-intensive nature of many molecular separations and the growing concern of reducing CO2emissions has led to intense research to seek for more energy-efficient separation processes. Among the emerging separation technologies alternative to distillation, there is special attention on non-thermally driven methods, such as membranes. The growing interest in non-thermal methods, and particularly in the use of membranes, has been influenced significantly from the widespread perception that they have a potential to be markedly less energy-intensive than thermal methods such as distillation. Even though many publications claim that membranes are more energy-efficient than distillation, except for water desalination, the relative energy intensity between these processes in the separation of chemical mixtures has not been deeply studied in the literature. One of the objectives of this work focuses on introducing a framework for comparative analysis of the energy intensity of membranes and distillation. A complication generally encountered when comparing the energy consumption of membranes against an alternative process is that often the purity and recovery that can be achieved through a single membrane stage is limited. While using a multi-stage membrane process is a plausible solution to achieve both high purity and recovery, even for a simple binary separation, finding the most suitable multistage membrane process is a difficult task. This is because, for a given separation, there exists multiple cascades that fulfill the separation requirements but consume different amounts of energy. Moreover, the energy requirement of each cascade depends on the operating conditions. The first part of this work is dedicated to the development of a Mixed Integer Non-linear Program (MINLP) which allows for a given gaseous or liquid binary separation, finding the most energy-efficient membrane cascade. The permeator model, which is derived from a combination of the cross-flow model and the solution diffusion theory, and is originally expressed as a differential-algebraic equation (DAE) system, was integrated analytically before being incorporated in the optimization framework. This is in contrast to the common practice in the literature, where the DAE system is solved using various discretization techniques. Since many of the constraints have a non-convex nature, local solvers could get trapped in higher energy suboptimal solutions. While an option to overcome this limitation is to use a global solver such as BARON, it fails to solve the MINLP to the desired optimality in a reasonable amount of time for most of the cases. For this reason, we derive additional cuts to the problem by exploiting the mathematical properties of the governing equations and from physical insights. Through numerical examples, we demonstrate that the additional cuts aid BARON in expediting the convergence of branch-and-bound and solve the MINLP within 5%-optimality in all the cases tested in this work