No abstract

Gray box models combine the short deuelopment time of data-driven black box mod-

In the serial gray box modeling strategy, generally available knowledge, represented in the macroscopic balance, is combined naturally with neural networks, which are powerful and convenient tools to model the inaccurately known terms in the macroscopic balance. This article shows, for a typical biochemical conversion, that in the serial gray box modeling strategy the identification data only have to cover the input‐output space of the inaccurately known term in the macroscopic balances and that the accurately known terms can be used to achieve reliable extrapolation. The strategy is demonstrated successfully on the modeling of the enzymatic (repeated) batch conversion of penicillin G, for which real‐time results are presented. Compared with a more data‐driven black box strategy, the serial gray box strategy leads to models with reliable extrapolation properties, so that with the same number of identification experiments the model can be applied to a much wider range of different conditions. Compared to a more knowledge‐driven white box strategy, the serial gray box model structure is only based on readily available or easily obtainable knowledge, so that the development time of serial gray box models still may be short in a situation where there is no detailed knowledge of the system available. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 549–566, 1997.

A new bioreactor, in which a series of air-lift reactors with an internal loop is incorporated into one vessel, is introduced. With this multiple air-lift loop reactor (MAL) and approximation of an aerated plug-flow fermentor is strived for. Mixing, liquid velocity, and gas hold-up were measured as a function of the gas flow rate in this new internal-loop reactor geometry. As a reference, hydrodynamics were also investigated in a conventional internal-loop reactor. A model description of the hydrodynamics in the second compartment of the MAL is given. This model is based on a two-phase, drift-flux model and a friction coefficient. Frictional losses were independent of the reactor bottom geometry, and were observed to increase with the gas flow rate as a result of the presence of stationary gas bubbles in the downcomer. The hydrodynamics and mixing of the second MAL compartment were comparable with those of conventional internal-loop reactors.