Bioprocess mathematical model

There are several barriers to the successful control of bioprocesses due to particular circumstances that are related to their characteristics the complexities of microbial metabolisms, the nonlinearity of microbial reactions, the frequent use of batch and fed-batch operations, and the limited availability of sterihzable online sensors for important process variables such as cell and product concentrations. Furthermore, it is difficult to construct mathematical models that can predict the entire range of batch or fed-batch operations that many fermentation processes require. 

Sideman S, Pinczewski W (1975) Turbulent Heat and Mass Transfer at Interfaces Transport Models and Mechanisms. In Gutfinger C (ed) Topics in Transport Phenomena bioprocesses, mathematical treatment, mechanisms. Hemisphere, Washington... 

There is an increasing interest in technologies that maximize the production of various essential enzymes and therapeutic proteins based on E. coli cultivation. The costs of developing mathematical models for bioprocesses improvements are often too high and the benefits are too low. The main reason for this is related to the intrinsic complexity and non-linearity of biological systems. The important part of model building is the choice of a certain optimization procedure for parameter estimation. The estimation of model parameters with high parameter accuracy is essential for successful model development. 

Simutis,R., Dors, M., Lubbert, A., Increasing the efficiency of hybrid models in bioprocess supervision and control, in preparation). The simultaneous utilization of mathematical models, heuristic rule systems, and artificial neural networks has been referred to as a hybrid model. 

Figure 2.18. Procedure for constructing a formal kinetic mathematical model of a bioprocess (Moser, 1977c.) Explanation see text.

Figure 2.20. Overview of the five levels of process research and mathematical modeling of bioprocessing and bioreactor operation.

The diagram of the time dependence of the specific rate of a bioprocess is called the quantification diagram It gives the best insight into the process and is basic for designing mathematical models (cf. Sect. 2.4.2.1). 

Figure 5.48 summarizes practical situations in bioprocessing (A. Moser, 1981). Classification of situations can be achieved by distinction between sequential and simultaneous utilization, with a transition case of overlapping utilization. While sequential or consecutive consumption of substrates (Monod, 1942, 1949) can often be analyzed in two separate growth phases, the simultaneous utilization encountered in biological waste water treatment is more difficult for mathematical modeling. 

Pseudokinetic phenomena become evident only when process kinetic analysis is carried out with mathematical models. Most bioprocesses are basically heterogeneous systems. Generally, pseudohomogeneous rates measured in L phase analyses are used, because they are thought to reflect directly the intrinsic reaction rate of metabolism in the solid phase (biomass). Even under steady-state conditions, however, this assumption is not necessarily valid. 

Kornegay, B.H. (1975). Mathematical Modelling of Water Pollution Control Bioprocess, Keinath, T.M. and Wainielista, M. (eds.), Ann Arbor, Mich., Ann Arbor Science Publ. Inc. 

The main purpose of this chapter is to understand and discover, through examples, the importance of mathematical modeling and to start constructing simple mathematical models. The second purpose is introduce you to process and bioprocess simulation. Again, in the case of simulation, you have already been exposed to and practiced simulation through some exercises in previous chapters of the... 

Importance of Building Mathematical Models and Constructing Simple Models for Chemical and Bioprocess Engineering... 

In this section, we will attempt to develop mathematical models for different situations that you will face as a process or bioprocess engineer. Although these examples are limited and tailored to your mathematical background, it will be interesting and rewarding for you to discover that you can be involved with fascinating and ever-challenging examples. 

Another efficient way to study chemical and bioprocesses in microreactors is by means of mathematical models. Such studies can be coupled with experimental observations to give a better understanding of the reaction phenomena. The complexity of mathematical models grew simultaneously with the complexity of the reactive systems. 

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