Bioreactors yield coefficient

Where yield coefficients are constant for a particular cell cultivation system, knowledge of how one variable changes can be used to determine changes in the other. Such stoichiometric relationships can be useful in monitoring fermentations. For example, some product concentrations, such as CO2 leaving an aerobic bioreactor, are often the most convenient to measure in practice and give information on substrate consumption rates, biomass formation rates and product formation rates. 

Eqnations of this form can be written for each of the various products of the reaction, as well as for consnmption of the limiting substrate. Additional stoichiometric relations can also be developed for other species that are ntilized as nonlimiting substrates by the microorganism nndergoing fermentation. However, because the stoichiometry associated with the production of biomass is well established for only a very few simple fermentations, biochemists and others engaged in the design of bioreactors find it useful to employ the concept of yield coefficients in their efforts to analyze the performance of proposed bioreactors. In essence, these researchers determine the yield coefficients experimentally in a manner akin to the technique of eliminating time as a variable in considerations of competitive and consecutive reactions (see Chapter 9). 

Hence, to design a bioreactor when one knows the various yield coefficients, the other primary need for assessment of the selectivity of the biochemical transformation is a valid mathematical relation for the rate of consumption of the limiting substrate. 

An alternative approach to consideration of the multiple routes by which the limiting substrate is consumed in a bioreactor is to reexamine the pathways shown in Figure 13.3 and to write an expression for the rate of consumption of the limiting substrate when it proceeds via a particular pathway. The total rate at which substrate is consumed can then be written as the sum of the rates of consumption via the individual pathways. Thus, in terms of our formulation of the convention for yield coefficients for metabolism of cells that takes place in a constant-volume closed system, the rate of consumption of substrate can be expressed as a sum of terms associated with the rates at which biomass and other products of metabolic processes are formed plus a maintenance coefficient, m, that characterizes the rate at which a cell in a resting state must consume substrate for maintenance activities if it is to remain aUve ... 

These equations remain valid for bioreactors provided that one employs a suitable mathematical representation of the rate of disappearance of the substrate that is the limiting reagent. In Illustration 13.3 we employ an alternative form of the design equation to determine the holding time necessary to achieve a specified degree of conversion in a strictly batch bioreactor. This illustrative example also indicates how overall yield coefficients are employed as a vehicle for taking the stoichiometry of the reaction into account. Illustration 13.4 describes how one type of semibatch operation (the fed-batch mode) can be exploited to combine the potential advantages of batch and continuous flow operation of a stirred-tank reactor. 

Material balances on the substrate and the product species can be used with a rate expression and yield coefficients to specify completely the compositions of the remaining streams in Figure 13.8. For a generic biomass specific rate law and steady-state operation, a balance on the growth-limiting substrate around the combination of the mixing point and the bioreactor indicates that... 

Consider the growth of Sacchammyces cerevisiae in continuous culture under conditions at which the Monod parameters are Pj = 0.835 h" and = 0.025 g/L. The yield coefficient Tx/s 0.48 g dry biomass/g substrate. Prepare plots of the mass of biomass and substrate present in the bioreactor as functions of the dilution rate of the growth medium for feed concentrations of the limiting substrate equal to 20, 40, and 60 g/L. The feed is sterile (i.e., no microorganisms are present in the feed). 

The subscripts on the usual process parameters indicate the positions in the process to which these parameters refer. The kinetics of yeast growth can be described by a Monod rate expression with = 0.625 h and Kg = 2 g/L. Cell death and cell maintenance effects are negligible, as is formation of products other than yeast cells. The yield coefficient x/s is 0.44. The effluent from the bioreactor flows directly to a membrane filtration apparams. The membrane is completely permeable to the substrate, so the concentrations of the substrate in the CSTBR, the effluent from the bioreactor, and the permeate from the membrane and in the recycle stream are all identical. The membrane rejects a substantial proportion of the yeast cells so that the ratio of the concentration of yeast in the recycle stream is a factor of 4 larger than that in the effluent from the CSTBR. Volumetric expansion and contraction effects may be considered negligible. 

If 02 consumption were indeed zero order for a particular plant species, then it would appear that any phytoproduction process involving that species would require only that a minimum dissolved 02 concentration be maintained any concentration increase beyond that would be irrelevant. In the case of tobacco cells, any concentration greater than 15 % of air saturation would yield the same metabolic rate and, presumably, the same productivity of all metabolites. If, on the other hand, consumption is first order in the concentration range achievable in a practical bioreactor (equivalently, if Kf is comparable to working concentrations), then its concentration is an important control parameter in the bioreactor. However, Kobayashi et al. studied berberine production by suspended and immobilized cells of Thalictrum minus [50]. They assert that 02 uptake is a zero-order process but observed that berberine production depended on 02 availability. They controlled that availability by adjusting the speed of shaking of the culture flasks, thus varying the mass transfer coefficient for absorption of 02. 

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