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

Transport Phenomena in Biotechnological Systems
Gas-Liquid Mass Transfer in Cellular Systems
Oxygen Uptake Rate in Cellular Metabolism Processes

When designing aerobic bioreactors, we often use mathematical expressions that describe The system of interest with varying degrees of approximation to determine whether oxygen transfer (or another growth-limiting nutrient) or cellular uptake is the rate-limiting step of the process. The maximum possible mass-transfer rate is determined by simply substituting c_l = 0 into the aforementioned equations, under which condition all oxygen entering the solution is rapidly consumed by the Cells. In the previous chapter, we established that the maximum oxygen uptake rate is xμ_mах/Y_O2, where x is The Cell culture density and Y_O2 is The ratio of the number of gram-atoms of carbon in the resulting carbon-containing cellular compounds to the number of moles of oxygen assimilated.

If k_la'c_l* significantly exceeds xμ_mах/Y_O2, it is evident that the primary barrier to further increasing the oxygen uptake rate is microbial METABOLISM, meaning the process rate is limited by biochemical factors. In the opposite extreme case, when k_la'c_l* ≪ xμ_max/Y_O2, the apparent value of cl approaches zero, and the process rate in the Reactor must be governed by transport phenomena.

In reality, the situation is somewhat more complex. At steady state, the rates of oxygen uptake and absorption must be equal

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If the dependence of μ on c_l is known, equation (8.14) can be used to determine c_l and, consequently, the oxygen uptake rate.

In the general case, there exists a critical dissolved oxygen concentration at which all cells are saturated with O₂ and its amount exceeds the minimum required for the immediate capture of all electron pairs participating in the Respiratory Chain reactions; under this condition, therefore, the process rate will be limited by some other biochemical mechanism (Chap. 5). For example, if the dependence of the specific Cell Growth Rate μ on the oxygen concentration obeys the Monod equation, then

A general solution for equations of this type was provided in Section 4.4.1, but here, for clarity, we will assume that c_l is significantly smaller than c_l*. Such a situation is quite common for bioreactors. If c_l ≪ c_l*, then c_l can be expressed as follows:

If the value of c_l found in this manner exceeds the critical value ccr (approximately 3K_O2), the microbial oxygen uptake rate is limited by some other factor, such as a low concentration of another substrate, even if the average dissolved oxygen concentration in the liquid phase is well below the saturation level. Critical oxygen concentrations for various organisms range from 0.003 to 0.05 mmol/L (Table 8.2), or from 0.1 to 10% of the maximum O₂ solubility (Table 8.1), or from 0.5 to 50% of air-saturation concentration. Clearly, oxygen mass transfer is especially critical for organisms characterized by high critical oxygen concentrations, such as Penicillium Molds.

Table 8.2. Typical values of c_O2,с_r in the presence of substratea

^а From: Finn R. К., p. 81 in Biochemical and Biological Engineering Science, Blakebrough N. (ed.), vol. 1, Academic Press, Inc., New York, 1967.

Various factors can influence the total microbial oxygen demand xμ/Y_O2, which in turn determines the minimum k_la' values required in design calculations [Equation (8.14)]. The most important factors of this type include the cell species, culture growth phase, carbon sources, medium pH, and the type of microbiological process under study; the latter factor encompasses parameters of substrate utilization, biomass production, or metabolic product yield (Chap. 7).

FIG. 8.5. Oxygen uptake rate by a batch culture of Myrothecium verrucaria. [Reproduced from: Darby R. Т., Goddard D. R., Аm. J. Bot., 37, 379 (1950).]

As seen in the batch oxygen uptake results presented in Fig. 8.5, the specific O₂ demand reaches a maximum at the beginning of the exponential phase, while x continues to increase during later growth stages. The product xμ, and consequently the total oxygen demand, reach a maximum at the end of the exponential phase and the very beginning of the stationary phase; thus, the oxygen uptake rate peaks later than the specific growth rate.

The oxygen uptake rate is strongly influenced by The Nature of the carbon-containing nutrient. Glucose, for instance, is generally metabolized faster than other CARBOHYDRATES. The maximum oxygen consumption rates of Penicillium have been found to be 4.9, 6.7, and 13.4 mol/(L·h) when growing on lactose, sucrose, and glucose, respectively [2].

The total cellular oxygen demand is composed of requirements for cell maintenance, respiratory oxidation reactions (utilized for cell growth and Biosynthesis), and The oxidation of substrates into corresponding metabolic end products. In studying metabolic stoichiometry (Chap. 5), we observed that the oxygen uptake rate dedicated to cell growth is usually directly related to The amount of carbon source substrate consumed. Furthermore, more reduced substrates, such as methane and higher Hydrocarbons, require enhanced cellular oxygen uptake compared to substrates like glucose, in which the degree of reduction of carbon atoms is approximately the same as in cellular components. Thus, the ratios Y_O2/с [i.e., the ratio of the number of moles of oxygen consumed to the number of moles of substrate metabolized (per carbon atom)] are 1.34, 1.0, and 0.4 for typical microorganisms growing on methane, paraffin hydrocarbons, and carbohydrates, respectively.

Oxygen can also act as a reactant participating in biotransformations. In The production of 5-ketogluconic acid from glucose, for example, during the initial stage of batch Acetobacter growth, part of the glucose in the medium is oxidized to gluconic acid; in this process, O₂ is utilized for both cell growth and metabolic product synthesis. After glucose depletion, cell growth ceases, and gluconic acid is converted into 5-ketogluconic acid According to the following reaction equation:

С₆Н₁₂О₇ + ¹/₂O₂ → С₆Н₁₀О₇ + Н₂О      (8.17)

In The final stage of the process, only this specified reaction takes place, and oxygen consumption is associated with The formation of the metabolic product in accordance with the stoichiometry of Equation (8.17).