A method for determining the optimal back-washing frequency and duration for dead-end microfiltration

• Analysis of a theoretical model.
• Comparison with experimental data.
• Novel prediction obtained from the model.
• Forward filtration and backwashing.

Microfiltration is used in a variety of industrial and municipal water purification settings where one of the main concerns is fouling from the particulate matter that is removed from the water. Our focus has been on developing a unified model that captures fouling behavior in a consolidated manner rather than describing individual blocking regimes using power law models. The unified model provides greater insights into fouling mechanisms so that a deeper understanding of flux decline can be obtained. Moreover, by characterizing both forwards and backwashing behavior together, mathematical theory is available to develop strategies that increase the effectiveness of microfiltration in conjunction with backwashing used to regenerate the filter. We present a very simplified model that was developed to provide details regarding the mathematical analysis and how optimal control theory can be used to predict the timing and duration of backwashing that will optimize the overall water flow through the membrane. We use optimal control theory to derive an analytic solution to the optimal problem and develop a strategy to implement the solution. The model estimates of forward operation are compared with experimental data for constant pressure filtration and indicate that the model is able to capture the basic processes. More interestingly, the optimal control solution and proposed implementation strategy are consistent with empirical demonstrations but provide mathematical evidence that the flux may be increased dramatically by precise timing of the forward and backwashing cycles. Model predictions can be evaluated during pilot-testing that often precedes microfilter regulatory approval and plant design.