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

Kinetics of substrate utilization, metabolite and biomass production in cell cultures
Ideal reactors for studying cell growth kinetics
Continuous stirred-tank reactor (CSTR)

Fig. 7.3a illustrates the Main Components of a continuous stirred-tank Reactor (CSTR), while Fig. 7.3b shows the standard notation used in modeling and analyzing such reactors. When these reactors are used to study Cell culture growth, they are commonly referred to as chemostats. As shown in these diagrams, agitation is provided by an impeller, a stream of rising gas bubbles, or both. We assume that mixing in the CSTR is efficient enough to ensure complete homogeneity of the culture liquid, meaning that the concentrations of all components in each phase are uniform throughout the entire volume of the reactor. As indicated in the schematic, an important consequence of this is that the COMPOSITION OF THE effluent stream is identical to that of the reactor contents.

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FIG. 7.3. Continuous stirred-tank reactor (CSTR) designed for the CONTINUOUS CULTIVATION OF cell populations: (a) main components of a laboratory CSTR for studying a growing cell population; (b) notation commonly used in modeling and analyzing such reactors.

Complete mixing must also maintain a uniform dissolved oxygen concentration throughout the liquid phase. This is particularly important when analyzing aerated CSTRs, as it implies that in most cases we can study the processes occurring within the reactor independently of the specific aerator or impeller design. If the aeration system maintains a dissolved oxygen concentration that does not limit cell growth in the CSTR, the analysis of cell growth kinetics can be treated as an independent problem. Similar considerations apply to Heat transfer issues that may arise during Microbial growth. The system can be considered isothermal if the reactor is equipped with devices for complete mixing, efficient heat removal, and precise Temperature control; in this case, microbiological conversion processes can be studied under isothermal conditions. For the majority of the subsequent material, we will adopt all of these assumptions.

At steady state, when the concentrations of all components in the reactor remain constant over time, the following equation applies to any system component:

Designating the total culture volume in the reactor as V_R, as before, the steady-state equation can be written in the following form:

where F is the volumetric flow rate of the nutrient solution and the effluent stream, c_if is the molar concentration of component i in the feed stream, and c_i is the concentration of component i in the reaction mixture and the effluent stream.

By rearranging equation (7.5),

The rate of formation of component i can be easily determined by measuring its (steady-state) concentrations at the reactor inlet and outlet. The parameter D introduced in equation (7.6) is termed the dilution rate and is defined as

This parameter determines the residence time or Processing rate in the reactor and equals the number of reactor liquid-phase volumes passing through it per unit of time. The parameter D is the reciprocal of the mean residence time or mean holding time parameters more commonly used in chemical engineering. Here, however, we will use METABOLISM/2.html">THE CONCEPT OF dilution rate, which is standard in biochemical engineering literature.

A comparison of equations (7.3) and (7.6) reveals that process kinetics in a CSTR are simpler than in a batch reactor; indeed, there is no need to determine concentration-versus-time dependencies or to subsequently differentiate the experimental data. Studying cell population growth kinetics under these conditions offers the additional advantage that Cells can adapt to steady-state conditions in a CSTR, thereby transitioning into a state of balanced or nearly balanced growth. This creates a realistic opportunity to maintain a relatively defined, reproducible state of The Cell population—a task that is considerably more difficult in batch microbial processes. On the other hand, batch cell growth experiments can be carried out in small vessels placed on a thermostated shaker, whereas CSTR equipment is significantly more complex and expensive. Steady-state conditions in biological CSTRs can take several hours or even days to establish, which substantially increases the risk of contamination that could invalidate the experimental results. Finally, for large-scale production, batch processes may prove more practical in certain cases, characterized as they are by unsteady, unbalanced growth, as well as varying metabolic processes and activities at different Stages of the process; for such manufacturing operations, kinetic models based on CSTR steady-state conditions may prove entirely inapplicable. Consequently, the experimental study of microbial and higher Organism growth kinetics, along with The Development of corresponding mathematical expressions, must be preceded by a precise Definition of the intended scope of application for these expressions. This requirement forms the foundation for designing experimental and mathematical modeling programs.

In the next section, we will examine the simplest models of cell population growth. Our primary focus will be on cell growth kinetics in a CSTR, since the fundamental principles for formulating kinetic equations were established and most thoroughly developed through chemostat experiments.