Environmental Engineering Reference
In-Depth Information
are referred to as mechanistic or structured models. In such models, rate expressions are
proposed that attempt to describe the mechanistic role of each enzyme in the metabolic
pathway. A fundamental structured model also includes information about characteristic
microbial cell dimensions and effects of rate-limiting mass transfer across cell walls.
In a structured model, the limiting substrate participates in the first reaction pathway; the
product of this reaction participates as a reactant in the next pathway, and so on to capture the
full cascade of transformations as well as regulatory feedback reactions. Certain structured
models have been successful in predicting important effects, such as the differential uptake of
two separate substrates. This confirms the value of such models when they can be properly
validated [14]. Currently, however, the use of structured models is limited by the lack of
rigorous verification, which in turn results from the considerable experimental challenges
involved in determining numerous enzymatic parameter values. Accordingly, utilization of
such models for design purposes is restricted to the range of parameters that can be validated
by experimental data [15].
The second, probably most widely-used set of kinetics models comprises those that
assume the presence of a single growth-limiting substrate. Among these so-called black-box
models, the most prominent is the Monod equation, in which the biomass specific growth
rate, μ, is related to the substrate concentration, S, in a nonlinear form (Equation 1). The
parameters KS and ìmax, describing the half-saturation constant and maximum specific
growth rate, respectively, are determined experimentally [16].
(Equation 1)
Extensions of the Monod equation to capture effects of metabolite repression and other
inhibitory and/or limiting effects are available. Black-box models can be extremely useful in
their estimations of overall fermentation behavior in early stages of process design. At the
same time, they lack the level of detail often necessary for precise optimization of bioreactor
function [15].
Another class of black-box models comprises those based on artificial neural networks
(ANNs). ANNs structure is characterized by the total number of nodes, responsiveness of
each node to an average input, and the response function for each node [17].
Model parameters for ANNs are termed weights, and the process of determining weights
from experimental data is called the training procedure. While utility of these models is again
restricted to the region over which experimental data are available, they offer the valuable
ability to accommodate increased metabolic complexity compared to limiting-substrate
models [18].
Finally, so-called gray-box modeling is also applied to bioreactor design, referring to
strategies that attempt to combine both fundamental knowledge and empirical data to obtain
models of moderate complexity with qualitative behavior in reasonable agreement with
experimental data. This class of models is best represented, both conceptually and
industrially, in the form of fuzzy-rule systems. Fuzzy-rule theory was developed by Zadeh
[19, 20] and has become increasingly important in practical process modeling and control.
Relationships between fuzzy variables are, in turn, formulated using fuzzy logic operators to
