(d)

w

Fig. 14.5. Various types of kinetic profiles that have been found in SSF. The arrows indicate the parts of the profile that correspond to the kinetic type. (a) linear; (b) logistic; (c) exponential; (d) deceleration parameters of the kinetic equation, at least for the conditions under which the experiment was done. Note that, as will be discussed in Chap. 16, the parameters will typically not appear in the final kinetic equation as constants, but rather as functions of key environmental variables.

The logistic equation fits reasonably well to around 75% of the literature profiles obtained in SSF systems (Viccini et al. 2001). The other 25% of profiles are described acceptably by one of the other three equations. Note that many of the experimental growth profiles obtained in the past were not done with kinetic analysis in mind. As a consequence, often there are relatively few data points during the period of rapid growth. This can lead to a situation in which several of the equations can adjust reasonably to the data, it not being possible to determine which gives the best fit. Chapter 15 gives some advice about how to plan experiments to avoid such problems.

Other important issues related to the kinetic analysis that you would need to do for your own system are presented in the following paragraphs.

Use absolute concentrations. As noted in Sect. 14.3.4, it is advisable to undertake the experiments in such a manner as to be able to plot the data in terms of absolute concentrations and to fit an equation to this absolute concentration data.

Table 14.1. Equations that have been used to describe growth profiles or parts of growth profiles in SSF systems3

Name Equation Equation Parameters to be number found by regression

Table 14.1. Equations that have been used to describe growth profiles or parts of growth profiles in SSF systems3

number found by regression

Linear |
C = |
C„ + |
kt |

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