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

Transport Processes in Biotechnological Systems
Determination of Oxygen Transfer Rate
Determination of a$ Using Chemical Reactions between Gases and Liquids

Turning to the pathways of oxygen transfer shown in Fig. 8.1, it is easy to see that if oxygen is consumed at a sufficiently high rate in a chemical reaction occurring in the liquid phase, then c_l ≈ 0. In this case, by determining the liquid-phase chemical reaction rate as equal to k_la'c_l*, one can readily find the value of k_la'. In many early mass transfer studies, sodium sulfite was used as an O₂ scavenger; in the presence of catalysts (such as certain Metal Ions like Co²⁺), it is oxidized to sulfate:

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The kinetics of The oxidation of sulfite ion (in solution) to sulfate is quite complex. The reaction orders with respect to oxygen and sulfite depend on The Nature of the catalyst and its concentration, which points to the intricate Nature of the elementary steps leading to the overall simple result represented by equation (8.18). Regardless of the reaction order in the liquid film surrounding each gas bubble, the chemical reaction will proceed to a negligible extent (and, consequently, the situation will be close to the scheme shown in Fig. 8.1) only if the overall rate of reaction in the film is negligible compared to the mass transfer rate k_l(c* - с). If ζ is the thickness of the film involved in the mass transfer process, this criterion can be expressed mathematically as follows:

The reaction rate in the film will be lower than the rate corresponding to the sulfite concentration and the oxygen saturation level in the bulk liquid phase (c*, sulfite_liq); expressed in terms of the parameter (c*, sulfite_liq), which can be determined experimentally or by calculation, the condition for a low reaction rate in the film can be formulated as follows:

The mass transfer film "thickness" is equal to

Assuming that the reaction is of order a₁ with respect to oxygen and a₂ with respect to sulfite, we obtain the inequality

It follows that

In Danckwerts' experiment, a cobalt catalyst was used at a concentration of 10^-5 M (it is known that under these conditions a₁ = 2), while a sufficiently high sulfite concentration (e.g., 0.5 M) ensured that a₂ = 0. Then, when c ≪ c*, inequality (8.23) transforms into the expression

Assuming D_O2 = 1.6∙10^-5 cm²/s, k_r = 0.85∙10⁸ cm³/(g∙mol∙s) (for the cobalt catalyst), and c* = 1.35∙10^-7 g-mol/cm³, we obtain

k_l ≫ 0.01 cm/s

In the case of a less efficient catalyst (a smaller value of k_r), k_l will also decrease.

Later in this chapter, we will encounter certain equations showing that for large bubbles in Water, k_l ≈ 0.04 cm/s, and for small bubbles, k_l ≈ 0.01 cm/s. Therefore, this inequality establishes the minimum bubble size at which the above expressions remain valid. In the case of small and slowly rising gas bubbles, the reaction rate in the film surrounding these bubbles will reach significant values. Similarly, an increase in bubble diameter and an increase in medium viscosity (compared to water) will lead to a decrease in the mass transfer coefficient; the corresponding coefficient accounting for this film effect can be calculated if the reaction rate constant and its order are known [3–5].

The sulfite ion oxidation process also exhibits other interesting features. Specifically, the rate constant k_r depends, first, on the nature of the catalyst and its concentration; second, on the Ionic strength of the solution; third, on the presence of impurities affecting catalytic activity; and fourth, on the solution pH. For example, in the presence of cobalt salts at a concentration of 10^-5 M at 20 °C, increasing the pH from 7.50 to 8.50 is accompanied by a 10-fold increase in k_r. (H⁺ ions are generated in the reaction, so a base must be added to the mixture to maintain a constant pH.)

Despite all these complications, the literature describes Examples where the value of k_la' determined by the sulfite method for a given sparger, stirring speed, etc., agreed quite closely with The values of k_la' found in a specific microbiological process. (However, reverse cases are also known.) Assuming that the scheme shown in Fig. 8.1 reflects the biological process under study, virtually no O₂ absorption should take place in the liquid-side film surrounding the gas bubbles. Consequently, any chemical system that absorbs O₂ and is intended to simulate The behavior of a culture broth must satisfy the above fundamental inequality (8.19), In addition to other requirements. If growing Cells are concentrated in a thin liquid layer surrounding the gas bubbles, it may become necessary to use a different chemical model.

The rate of oxygen transfer can also be measured by other Methods. If the experimental system is a strictly batch culture, where neither liquid nor gaseous components are introduced into or removed from the system, can be found by determining The change in gas volume or pressure over time. In addition, as we will see in the next section, estimating c_l also AIDS in determining k_la'.

If gas is continuously introduced into and removed from the liquid phase, the following gaseous oxygen material balance equation can be used to determine :

Here, F_g is the volumetric gas flow rate, and p_O2 is the partial pressure of O₂. [Under what assumptions is equation (8.25) valid? Do these assumptions generally apply to biotechnological processes?]

As follows from equations (8.6) and (8.7) and the corresponding Structure/133.html">Discussion, the values of found in this manner can be used to determine k_la' only when the conditions throughout the entire volume of the Reactor are uniform and, therefore, the local oxygen utilization rates are equal to the corresponding average rate. Therefore, in Laboratory studies of mass transfer effects for the design of biological reactors, stirred-tank reactors are frequently used [Fig. 8.2, b (2)].

Once the issue of ensuring uniform conditions throughout the reactor volume has been resolved and both c_l* and c_l are known, equation (8.6) can be used to determine k_la'. The value of c_l* can be found in reference literature, such as Table 8.1, whereas direct Determination of C_l is now feasible (even in pure microbial cultures) using a sterilizable polarographic oxygen electrode. The operating principle of this current-generating electrode, whose output current is proportional to the local partial pressure of dissolved oxygen, is described in Chapter 10. The same chapter discusses an alternative METHOD FOR DETERMINING k_la' based on monitoring changes in O₂ concentration using an oxygen electrode.

In various reactors and natural processes, the local oxygen transfer rate may vary depending on the spatial coordinates of a given point. If such variations are characteristic of the reactor where mass transfer rates are being measured, the resulting volume-averaged value of _klа' can no longer be directly applied in scale-up operations, where laboratory-scale findings are translated to significantly larger industrial equipment. Scale-up methods will be discussed later in this chapter. Variations in dissolved O₂ concentration within the "homogeneous" phase (liquid phase, mold pellet, microbial biofilm, etc.) were measured using miniature oxygen probes with a sensor tip diameter of approximately 10 µm. This device has been used, in particular, to investigate local oxygen concentration profiles within mold pellets and to determine diffusion coefficients in microbial aggregates.