Search

Because there is no general design method for depth filters, especially for layered configurations, we here address this methodological gap. 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, we present a computational strategy 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. This article is protected by copyright. All rights reserved.

Depth filters are often used in biotechnology processes to remove cell debris from cell culture solutions. A model of filter plugging was developed to allow predictions of required filter area from limited amounts of initial data. The filter microstructure was idealized as an assembly of randomly oriented, straight, cylindrical fibers. It was assumed that filters plug as solids coat the surfaces of fibers, making them thicker and reducing filter porosity and permeability. The Carman-Kozeny equation was used to allow calculation of filter permeability as a function of filter fiber radius, filter solid fraction, and volume filtered. An explicit equation for filtrate volume as a function of time during constant pressure operation was derived, and an explicit equation for pressure as a function of time during constant flow rate operation was derived. A second model that accounted for the combined effects of fiber coating and surface caking was also derived. The models were tested on data from a replica cell culture fluid filtered through a glass fiber based depth filter and data from E. coli lysate filtered through glass fiber and diatomaceous earth based depth filters. The fiber coating model provided good fits of the volume vs. time data and good predictions of filter capacity from limited initial data. The combined cake-fiber coating model provided improved performance over the fiber coating model. The models are useful tools for sizing of depth filters for fermentation and cell culture applications and may be useful for other liquid and gas filter applications.