Improving the design of depth filters: A model-based method using optimal control theory

Because there is no general design method for depth filters, especially for layered configurations, this methodological gap is addressed here. Using optimal control theory, paths of the filter coefficient, a measure for local filtration performance, are determined along the filter depth. An analytical optimal control solution is derived and used to validate the numerical algorithm. Two optimal control scenarios are solved numerically: In the first scenario, the goal of constant deposition along the filter depth is addressed. The second scenario aims at maximizing the time until some maximal pressure drop is reached. Furthermore, a computational strategy is presented to derive discrete layers suitable for practical design from the continuous optimal control solutions. All optimized scenarios are compared to one-layered filter designs and significant improvements are found. As this work is based on strongly validated and widely used filtration models, the presented methods are expected to have broad applicability.