Simple Bioprocess Models

Simple bioprocess models are typically based on batch fermentation processes where the change in cell concentration with respect to time is proportional to the current cell concentration. This first-order rate equation is mathematically described by 

Solving Eq. (5.23) during the exponential growth period reveals 

The exponential growth region can be described by a single relationship where the specific growth rate /r is a function of the substrate concentration C. Empirical evidence reveals that // is a maximum when is large, and n is linear with when Q is small. The specific function that describes the entire relationship including the two limiting extremes is called the Monod equation 

The Monod equation is not the only unstructured, nonsegregated empirical model of bioreactor cell growth. Others can be found in the summaries provided by Bellgardt (2000a), Dunn et al. (2003), or Nielsen et al. (2003). 

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To construct a simple unstructured model for bioprocesses, at least one of the reactions taking place in the culture must be specified in kinetic terms. Generally a complete set of constitutive equations for each of the N chemical reactions taking place in the culture can be written in the form of a sum or a matrix (Roels, 1980a Schubert and Hofmann, 1975). The net conversion rate of each of the components present follows with the aid of r — v -r. For a system in steady state, the net production rate is equal to minus the flow into the system, as is clear from Equ. 2.10. Furthermore, the elemental balance principle (according Equ. 2.11) specifies k relationships between the flows Fj... 

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... 

It is likely that most biomaterials possess non-linear elastic properties. However, in the absence of detailed measurements of the relevant properties it is not necessary to resort to complicated non-linear theories of viscoelasticity. A simple dashpot-and-spring Maxwell model of viscoelasticity will provide a good basis to consider the main features of the behaviour of the soft-solid walls of most biomaterials in the flow field of a typical bioprocess equipment. 

It is important that calibration models are rigorously validated and in the first instance that all variations are accounted for in the model using diverse samples that are expected to be observed in future bioprocess runs. Some investigators attempt to keep process conditions very reproducible but such conditions are uncommon in an industrial environment. In addition, multivariate calibration models will work well if identical media (composition) and process conditions are used on each successive run. Simple modifications such as use of a different media supplier can affect the spectral background. The predictive ability of the models will then be affected as they will be challenged with samples which they have not been trained to recognise [74]. 

Woll, J. M. Hatton, A. T. "A simple phenomenological thermodynamic model for protein partitioning in reversed micellar systems Bioprocess Eng. 1989,4, pp 193-199. 

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

Industrial processes cmivert low-value carbon into high value-added products. To be economically viable, the cost of the overall bioprocess must be significantly less than the selling price of the product. Many variables contribute to bioprocess costs, but for bulk biochemicals such as biofuels and industrial chemicals (which many isoprenoids are used for), the price of the feedstock is the primary cost driver (Rude and Schirmer 2009 WUlke and Vorlop 2008). Currently, carbohydrates from plant biomass are the most important carbon feedstock for fermentation. Plants accumulate simple sugars, cellulose or lipids, which bacteria can convert into energy, biomass and products. Popular model organisms exploited in industry (such as... 

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