Global parametric sensitivity analysis of a model for dead-end microfiltration of bacterial suspensions

One of the central problems in membrane implementation is that foulants deposit on surfaces of microfilters employed for water and wastewater treatment and reuse, reducing their productivity. In an effort to remove as much of the deposited materials as possible and maintain the flux, the direction of flow across these membranes is regularly and frequently reversed. However, backwashing only removes the loosely or reversibly bound materials necessitating the entire system to be taken off-line for chemical cleaning when fouling increases beyond a threshold value. We recently presented a mathematically rigorous methodology to determine timing and duration of backwashes so as to delay membrane chemical cleaning and reduce associated operational complexity and costs. By considering an optimal control formulation, using the flow direction as the control variable, the optimal timing and maximum volume of water that can be microfiltered in a given time period were predicted during dead-end filtration of bacterial suspensions. The value of these predictions depend on our ability to accurately and precisely estimate input parameters such as the clean membrane resistance, influent water quality estimates, and biofilm and exo-polymeric substance formation rates and effects. These estimates are inherently uncertain leading to uncertainty in the predictions, which can be rigorously quantified using Sobol indices. These provide a global method for assessing the sensitivity of model predictions (e.g. optimal timing and volume filtered) with respect to variations in the inputs.