Numerical simulation and optimization of multi-step batch membrane processes

A simple numerical technique is presented for batch membrane filtration design. The underlying model accounts for variable solute rejection coefficients, and it has a modular structure which permits to easily describe the batch process involving different arrangements of the three typical basic steps: pre-concentration, dilution mode and final concentration. The experimental design required to set up the model is discussed, together with the necessary sampling procedure. In order to validate the technique, multi-step nanofiltration experiments were carried out using a binary test solution containing organic and inorganic substances. The objective of the process is to remove the electrolyte from the solution and concentrate the organic component. The predictions for the multi-step process performances were found to be in good agreement with the experimental results. Finally, optimum-search techniques for the overall multi-step process are discussed, considering economical aspects and technological demands. The presented optimization procedure can be useful to find the optimum pre-concentration and dilution factors for a membrane plant with a defined module configuration and membrane area.