## The Basic Kinetic Expression

The various types of growth profiles that have been found in SSF systems were presented in Table 14.1. Section 14.3 pointed out that biomass profiles in SSF can be plotted on two different bases, referred to as relative biomass concentrations (kg-biomass kg-dry-solids-1) and absolute biomass concentrations (kg-dry-biomass kg-initial-dry-solids-1). It also argued that the basic kinetic profile should be plotted in terms of "absolute concentration", since various of the effects of growth on the environment will depend on the absolute and not the relative concentration. Assuming that this has in fact been done, the integrated form of the equation selected from Table 14.1 by regression analysis will be expressed in terms of absolute biomass concentration. The corresponding differential form of the equation will then be selected from Table 16.1, for incorporation into the kinetic sub-model of the bioreactor model. Note that, in order to describe the whole profile, it may be necessary to use several equations. Further, an integrated equation other than the four presented in Table 14.1 may have been used, in which case it will be necessary to differentiate the equation. Each of these equations has one or more parameters. It may be interesting to express some of these parameters as functions of key environmental variables such as the temperature and the water activity of the substrate. Experimental approaches to doing this are described later (Sect. 16.4).

However, even though it is desirable to determine the kinetic profile based on absolute biomass concentrations, the bioreactor model should be able to predict the relative biomass concentration, in order to allow comparison between the model predictions and experimental results obtained in the bioreactor, which are typically obtained in terms of relative biomass concentrations. In order to convert

Table 16.1. Differential forms of the equations that have been used to describe growth profiles or parts of growth profiles in SSF systems

Name Equationa Equation Parametersb number

Table 16.1. Differential forms of the equations that have been used to describe growth profiles or parts of growth profiles in SSF systems

Name Equationa Equation Parametersb number

 Linear dcxa dt = k