Analysis of forced periodic operations of continuous bioprocesses: multiple input variations

Continuous bioprocesses subject to time-invariant feed conditions are attra ctive due to ease of operation and control. Nonlinearities in kinetics of b ioprocesses provide an opportunity to possibly improve the time-average per formance of these by periodic forcing of feed conditions. This possibility is investigated in this article for cycling of dilution rare and feed conce ntration of the limiting substrate using the generalized pi-criterion. A un ified analysis of optimality of forced periodic operation of continuous cul tures producing a wide range of products and subject to periodic variation in either dilution rate or feed concentration of the limiting substrate has recently been reported (Parulekar, 1998, Chemical Engineering Science, 53, 2481-2502). The analysis is extended in this article, with the particular focus being the interaction effect due to simultaneous variations of the tw o input variables. Without placing any restrictions on the kinetics of the bioprocesses, it is established that subjecting a bioprocess to simultaneou s periodic variations in dilution rate and substrate feed concentration doe s always lead to improved performance, at least at high frequencies. Where appropriate, analytical expressions are obtained for optimum phase differen ce (between periodic variations in the two inputs) and optimum amplitude ra tio that lead to the maximum fractional improvement in the bioprocess perfo rmance (vis-a-vis operation at a steady state). Numerical illustrations per tain to bioprocesses generating many important metabolites. In each example , the two-dimensional control variable space is divided into appropriate re gions based on differences in the effects of periodic variations in either or both inputs on the bioprocess. The pi-criterion is also employed to inve stigate if forced periodic operation may enable cell retention in continuou s cultures under conditions where cell washout is the only admissible stead y state. (C) 1999 Elsevier Science Ltd. All rights reserved.