Transport model-based prediction of polymeric membrane filtration for water treatment

Abstract

Modelling is an integral part of the design, development, and scale-up of membrane-based separation processes. Among the different modelling approaches, transport phenomena-based models are thorough and versatile. This chapter focuses on various methodologies of transport phenomena-based models to quantify the mass transfer through the membranes. Typically, there are two flow domains in which the modelling is carried out: inside the flow channel and inside the membrane. These two domains are interconnected by the interface boundary condition at the membrane surface. The mass transfer problem in the flow channel can be solved by using numerical methods or semianalytical techniques, such as the similarity solution or approximate integral method. The governing equation for the solute and solvent transport within the membrane phase can be tailor-made depending on the nature of the membrane and solute. The solvent flux through the membrane is generally dictated by the osmotic pressure model. The solute flux through the membrane is governed by (1) the solution-diffusion model for a dense reverse osmosis membrane, (2) the extended Nernst Planck equation for the transport of ions through the charged pores of the membrane, and (3) merely the definition of real retention in the case of ultrafiltration membrane in which the size exclusion is the primary concern. However, these generalities will be modified to account for the physical nature of the membrane fouling, that is, whether the filtration is purely osmotic pressure controlling or purely gel polarization governed. The modelling of mixed matrix membrane is rather complicated, owing to solute adsorption in the membrane matrix. All these issues influence the modelling pathways and are discussed extensively in this chapter. In a nutshell, this chapter is a complete guide to understand the modelling of the membrane separation process validated by using synthetic as well as real solutions that include brackish water and textile and tannery effluent streams.