Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Kinetics of substrate utilization, metabolic product formation, and biomass growth in cell cultures
Ideal reactors for studying cell growth kinetics
Ideal batch reactor

It is practically impossible to obtain useful information on microbial population growth kinetics if conditions vary across different Regions of the Reactor volume. Therefore, it is preferable to study kinetics exclusively in completely mixed bioreactors. Here, we will examine batch and continuous stirred-tank reactors. Other reactor types, including fed-batch reactors and partially mixed systems, will be discussed in Chapter 9.

The foundation of many biochemical processes is batch Cell growth, in which—following the inoculation of viable Cells into a liquid medium—nothing is added to or withdrawn from the system throughout the entire growth period (with the exception, perhaps, of certain gases). Typically, in such a reactor, the concentrations of nutrients, cells, and metabolic products change continuously as the population grows.

The material balance for component i indicates that The rate of its accumulation, expressed as the time derivative of the total amount of component i, must equal the rate of its formation resulting from Chemical Reactions within the reactor. Thus,

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or

where V_R is the culture volume; c_i is the number of moles of i per unit volume of the culture; r_fi is the number of moles of i formed by the reaction per unit volume of the culture per unit time.

If no liquid feeds or withdrawals are applied to the reactor, and if liquid loss via the gas stream is negligible, then V_R remains constant and equation (7.2) simplifies to:

It should be noted that similar equations can express not only Changes in the number of moles, but also in mass or concentration (density) of a component. Furthermore, if component i is part of the gas stream entering or leaving the reactor, the aforementioned equations must be supplemented with terms accounting for the net mass transfer rate of component i via the gas phase.

It follows from equation (7.3) that determining the rate of change in the concentration of component i allows for the direct Determination of the overall rate of formation of i in reactions (including intracellular ones) occurring within a batch reactor. In the general case, the formation rate r_fi depends on the state of The Cell population (composition, Morphology, age distribution, etc.) and all environmental parameters that affect reaction rates within the cells and the medium. At the same time, as we mentioned in the Introduction to this chapter, cell growth kinetics are typically described in a simplified manner by taking into account only the most critical parameters. In the subsequent sections, we will see how reaction stoichiometry and rates are related to the rate of formation of cell metabolites.