Dynamic Modeling and Control of Distributed Heat Transfer Mechanisms: Application to a Membrane Distillation Module

Abstract

Sustainable desalination technologies are the smart solution for producing fresh water and preserve the environment and energy by using sustainable renewable energy sources. Membrane distillation (MD) is an emerging technology which can be driven by renewable energy. It is an innovative method for desalinating seawater and brackish water with high quality production, and the gratitude is to its interesting potentials. MD includes a transfer of water vapor from a feed solution to a permeate solution through a micro-porous hydrophobic membrane, rejecting other non-volatile constituents present in the influent water. The process is driven by the temperature difference along the membrane boundaries. Different control applications and supervision techniques would improve the performance and the efficiency of the MD process, however controlling the MD process requires comprehensive mathematical model for the distributed heat transfer mechanisms inside the process. Our objective is to propose a dynamic mathematical model that accounts for the time evolution of the involved heat transfer mechanisms in the process, and to be capable of hosting intermittent energy supplies, besides managing the production rate of the process, and optimizing its energy consumption. Therefore, we propose the 2D Advection-Diffusion Equation model to account for the heat diffusion and the heat convection mechanisms inside the process. Furthermore, experimental validations have proved high agreement between model simulations and experiments with less than 5% relative error. Enhancing the MD production is an anticipated goal, therefore, two main control strategies are proposed. Consequently, we propose a nonlinear controller for a semi-discretized version of the dynamic model to achieve an asymptotic tracking for a desired temperature difference. Similarly, an observer-based feedback control is used to track sufficient temperature difference for better productivity. The second control strategy seeks for optimizing the trade-o between the maximum permeate flux production for a given set of inlet temperatures of the feed and the permeate solutions, and the minimum of the energy consumed by the pump ow rates of the feed and the permeate solutions. Accordingly, Extremum Seeking Control is proposed for this optimization, where the pump flow rates of the feed and the permeate solutions are the manipulated control input.