Mathematical modelling of membrane separation processes

This PhD thesis is dedicated to the modelling of membrane separation processes. During this research, models have been developed for the following processes: direct contact membrane distillation (DCMD), sweeping gas membrane distillation (SGMD) and anaerobic membrane bioreactors (AnMBRs) equipped with the magnetically induced membrane vibration (MMV) system. The proposed models for DCMD and SGMD are general predictive. In particular, these models allow simulating hollow fibre and flat sheet configurations under a wide range of process conditions with a minimum number of input data and without requiring empirical parameters or laboratory experiments. For this purpose, the momentum, as well as the mass and heat balances of the process are described by partial differential equations, algebraic and ordinary differential equations. The models were validated with experimental and literature data. The influence of operating conditions and membrane geometric characteristics on the process performance was investigated. A hydrodynamic model was developed for AnMBRs equipped with the MMV system. The model studies the effect of the membrane vibration on the hydrodynamics of the AnMBR tank. In particular, the proposed models was coupled with the biological AM2b model (B. Benyahia et al. / Chemical Engineering Journal 228 (2013) 1011-1022) to introduce mass balances of components and bacteria contained in the AnMBR tank. During the conducted parametric study, the effects of the vibration frequency and vibration amplitude on the fluid velocity, concentrations of influent components (organic matter, volatile fatty acids and soluble microbial products) and distribution of the bacteria in the AnMBR tank were studied. Despite the use of the large number of complex equations, the proposed models enable the broad evaluation of the key parameters together with the opportunity of the application for the multicomponent liquid solutions without the conduction of experiments. The conducted studies prove that all proposed models would be potentially applied for a pre-experimental study, optimization of process conditions, design of membrane modules, as well as for the further cost estimation of the processes.status: publishe