Optimum synthesis of an electrodialysis framework with a background process—I: A novel electrodialysis model

Electrodialysis (ED) is a membrane process commonly employed for the desalination of brine or water contaminated by ionic components. The driving force for desalination is the potential difference between the contaminated and purified water. Despite its ability to produce ultra-pure products, the application of electrodialysis is exceeded by other treatment processes, due to its energy intensity. Energy consumption in ED is dependent on the physical characteristics of the unit. In this respect, it is possible to promote the use of electrodialysis by optimizing the process, making it more energy efficient. This can be done by developing an optimization framework for the process. Existing electrodialysis design models, based on current density, cater mainly for the desalination of brine. This paper presents a detailed derivation for a single stage electrodialysis design model, suitable for treating a binary mixture of simple salts. A simplified formulation is also presented, based on the assumption that the conductivity of the solution is constant over the entire unit. This simplifying assumption enables more versatile application of the ED design model with background processes. Using a pulp and paper case study, a comparison is done between the two models, indicating a deviation of less than 2% in all key variables. It is therefore possible to reliably use either of the models interchangeably, depending on the available information and the background process under consideration. Both models presented are mixed integer nonlinear programs (MINLP) solved using a combination of DICOPT and BARON solvers in GAMS®.