Bioreactor Models

A number of examples from biochemical engineering are presented in this chapter. The mathematical models are either algebraic or differential and they cover a wide area of topics. These models are often employed in biochemical engineering for the development of bioreactor models for the production of bio-pharmaceuticals or in the environmental engineering field. In this chapter we have also included an example dealing with the determination of the average specific production rate from batch and continuous runs. 

J.L. Gouze and V. Lemesle. A bounded error observer with adjustable rate for a class of bioreactor models. In European Control Conference (ECC), Porto, Portugal, 2001. 

These are the equations which will be integrated below to come up with the basic overall bioreactor models. 

Resorting to an estimation approach, the monitoring problem is translated to the one of designing an estimator that, on the basis of the bioreactor model, and driven by a sequence of DD-measurements ys(to), ys(t-J,. ..,ys(tk) each sampling time instant (4) on-line yields estimates of the actual biomass iXPt)), substrate (S(tj)) and sulfide (P(ti)) concentrations. Besides, X and P measurement could be eliminated, meaning a cost reduction due to additional on-line laboratory analysis. 

Gemeiner et al. (1993) presented a similar method for the direct determination of catalytic properties of immobilized cells. Cephalosporin C transforming Trigonopsis variabilis were immobilized by three different methods, filled into a column and set into the ET. After thermal equilibration, Cephalosporin C solutions (0.1-50 mmol/1) were continously pumped through the ET until steady-state heat production was obtained. Again, the ET was shown to be suitable for a rapid and simple estimation of the kinetic properties of immobilized cells. Microkinetic factors such as mass transfer were taken into account (Stefuca et al. 1994). Thus, ET measurements allow us to obtain intrinsic data, even from immobilized cells. Moreover, the data can be applied to optimize biocatalyst design and bioreactor models (Gemeiner et al. 1996). 

Figure 1. Variables in the continuous bioreactor model. Biomass balance...

The application of interpretative models has been hampered by the technical challenges in collecting adequate data on-line, and as a result, to date bioreactor models have been of the predictive type. Some general conunents can be made about such models First, due to the heterogeneity of SSF systems, a spatial variable is often involved, which leads to partial differential equations and therefore makes solution of the equations more difficult than would occur in perfectly mixed systems. Second, the sophistication of the model and the detail with which it describes the system depend on the complexity of the system and the motivation behind the modeling work. 

In many bioreactor models intraparticle concentration gradients are ignored, and growth is modeled as depending only on the biomass concentration and temperature. In this case overall consmnption of oxygen, production of CO2, or consumption of nutrients can be calculated assuming that both growth-related and maintenance metabolism are involved ... 

Naessens, W., Maere, T., Nopens, L, Critical review of membrane bioreactor models—Rart 1 Biokinetic and filtration models. Bioresource Technology 2012, 122, 95-106. 

Csogor Z, Herrenbauer M, Schmidt K, Posten C Light distribution in a novel photo-bioreactor-modelling for optimization, J App/ Phycol 13 325—333, 2001. 

The process kinetic analysis is carried out in two different types of reactors. The so-called perfect bioreactor is used for obtaining true kinetic data. This laboratory reactor must therefore meet certain requirements with regard to all possible transport phenomena (see Sect. 4.2). A so-called bioreactor model is a scaled-down bioreactor with some geometrical similarity to the production unit. Here, significant transport phenomena (cf. Chap. 3) can be studied and quantified with a physical system in a first step. 

Bioreactor Models 125 BIOREACTOR MODELS FLOC REACTOR FILM REACTOR... 

A long-term preservation of metabolic functions of many cells requires their adhesion to suitable solid matrices and their culture at high cell density. These requirements make the diffusion of nutrients and of cell products a critical issue in culturing cells, especially in three-dimensional structures. Mathematical models are very useful to face these kinds of problems. In the following, the membrane bioreactor model for a bioartifidal liver is presented. 

A new bioreactor model, the wave-bioreactor, has been recently designed, in which the plant cells are introduced in a disposable plastic bag provided with all the probes (oxygen, pH, etc.) [22]. In this system, the disposable bag is placed over a rocker that moves the cells and the culture medium with wave-like motion, thus preventing the settling of the cells and creating a large turbulent surface for correct oxygen transfer (Fig. 89.13d). 

Large-Scale Industrial Fermentations Challenges for Bioreactor Modeling... 

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