At the Moment Fast Solving Models Are Useful

The previous sections have pointed out that at present many simplifications are made, in both the kinetic and the balance/transport sub-models of a bioreactor model, in order to arrive at a fast-solving model. The question arises as to whether such fast-solving models are useful tools in bioreactor design, or whether we need to develop more sophisticated models before we can use them fruitfully.

Table 13.1 compares the characteristics of a fast-solving model with a model that attempts to describe as many phenomena as possible in a "fully-mechanistic"

manner. Such a fully-mechanistic model has not yet been developed for an SSF bioreactor, although various of the models that have been proposed within the SSF literature have incorporated one or more of the characteristics listed for it. These two model types represent two extremes. Most of the presently available bioreac-tor models lie on a continuum between them, although, on the whole, they lie closer to the fast-solving model than they do to the fully-mechanistic model.

A fully-mechanistic model would be more likely than a fast-solving model to describe the performance of a bioreactor under a wide range of operating conditions. It would also give a much better insight into which phenomena were most responsible for limiting growth in different systems, under different operating conditions and at different times during the process. However, the amount of work necessary to establish a fully-mechanistic model seems prohibitive, at least to the present moment, as shown by the fact that such a model has not yet been developed! Further, even if such a model were developed, the description of both mac-roscale and microscale heterogeneity would lead to solution times of hours to days, even on a supercomputer. In contrast, the current fast-solving models can typically be solved on personal computers in less than a minute.

Will fast-solving models enable us to fulfill our objectives in modeling a bioreactor? Various objectives that we might have include:

1. To use models to contribute to decisions about which type of bioreactor to use;

2. To use the model that describes the selected bioreactor to contribute to decisions on the design parameters, such as how large the bioreactor should be and what geometric aspect it should have;

3. To use the model to help in the sizing of auxiliary equipment, such as the specifications of the blower, in terms of air flow rates and pressures;

4. To incorporate the model into process control strategies.

Certainly current fast-solving models are able to make worthwhile contributions to our attainment of all of these objectives, as will be demonstrated by the modeling case studies in Chaps. 22 to 25 and the process control case study in Chap. 28. Further, it is important to note that if a model is to be incorporated into a control system, it needs to be able to be solved reasonably rapidly, otherwise the control action will be unduly delayed.

Of course, in accepting the use of a fast-solving model, we must also accept its limitations. A fast-solving model will subsume many fundamental phenomena within simplified equations. As a result, the model will not be very flexible. As an example, a simple empirical kinetic equation such as the logistic equation might be used to describe growth. It may fit the growth data well, but it hides the inter-particle phenomena that combine to cause the biomass profile to appear as a logistic curve. With a simple change from one substrate to another, there is no guarantee that the logistic equation will still describe the biomass profile adequately. Even if it does, it will be necessary to re-determine the parameters of the equation.

Table 13.1. Two extremes of approaches to modeling SSF bioreactors

Characteristic

A simple fast-solving model

A fully-mechanistic model

What is the general aim?

How are the growth kinetics described?

How is the stoichiometry of growth described?

How is the bed treated?

Is the bioreactor wall recognized as a separate system?

If the bed is mixed, how is mixing modelled?

If the bed is static, are gradients recognized?

To concentrate on the processes in Fig. 2.6(a), simplifying as much as possible the processes in Fig. 2.6(b)

• An empirical equation, not involving nutrient or 02 concentrations, is used

• Average biomass concentrations are used

Experimentally determined overall growth yields are used. Elemental balances are not done.

As a single pseudo-homogeneous phase with the average properties of the solid and gas phases in equilibrium

No. Transfer across the wall is subsumed in a global equation describing transfer from bed to surroundings

Perfect mixing is assumed

Macroscale temperature and moisture gradients are described

Are pressure drops described? No

To describe as many of the processes in Fig. 2.6 as possible

• Intra-particle diffusion of nutrients and 02 are described and the growth equation parameters depend on the local values of these variables

• Spatial distribution of the biomass is described

The growth reaction is described by a stoichiometric equation that balances the various elements (C, N, S, P etc.)

The solids and inter-particle gas phase are treated as different sub-systems and equations are written for heat and mass transfer between them

Yes. Conduction across the wall is described as well as conduction within the wall from hotter to colder regions

Real mixing patterns are described

Macroscale temperature and moisture gradients are described

Yes. The effect of the growth of the biomass on the pressure drop through the bed is described

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