## Mass Transfer Rate Measurements

Methods for the determination of kLa in a reactor can be grossly classified as steady-state and nonsteady-state methods. In the steady-state methods, the rates of oxygen uptake in steady-state operation are evaluated, either by measurement of inlet and outlet rates of oxygen or by di i as rect analysis of a compound that reacts with the oxygen, as in the case of the sulfite method. One of the problems associated with these procedures is that the changes in oxygen concentration in the gas streams are usually small, and the errors of measurement thus have a substantial influence. When a chemical is added to the system, there is the question of whether the addition has provoked changes in the physicochemical properties, which thus become different from the properties of the original system.

Transient methods may be applied to follow the response of the dissolved oxygen concentration in the system after a step-change of oxygen concentration in the inlet gas stream. These methods have the advantage that addition of an alien material is not required and that a single concentration is measured. The correct use of this method has been analyzed in depth by Linek et al. (137).

One important point to take into account is the dynamics of the oxygen electrode. The lag in the response of the oxygen electrode makes it necessary to discern between the electrode response and the real oxygen concentration, especially when close to a sharp change in concentration. A correct analysis should also include the model of the dynamic behavior of the electrode. In order to simplify these procedures, approximations based on truncation of parts of the response curve have been proposed (133,138). These methods are based on truncating the first part of the electrode response obtained in a transient experiment. Once the error included in the value of kLa is set, the extent of truncation is fixed, allowing simplification of the analysis of the remainder of the curve. It should be kept in mind that this simplification implies the loss of part of the information, and due care should be given to statistical analysis of the results.

Variations of the method have been proposed to minimize disturbances in the system by introduction of step variations of agitation or pressure (137,139). In this way, the method can be applied to bioreactors during real operation of the system.

One problem that may appear in the measurement of mass transfer rates, especially when viscous liquids are used, is related to the presence of very small bubbles that are depleted of oxygen very rapidly but do not disengage in the gas separator, thus constituting an inert volume of gas in the reactor (134). Kawase and Moo-Young (140) analyzed the use of transient absorption of CO2 for the determination of kLa and concluded that the error due to small bubble retention was much smaller than that in the case of O2.

Whatever the method used for the determination of kLa, the process of data elaboration is basically the same as is shown schematically in Figure 27 (141). The measured variable (usually oxygen concentration) is compared to the value predicted by a mathematical model of the process. The model includes kLa as a parameter, and the value of kLa that gives the best fit is chosen. It is thus obvious that the choice of the model is very important, and poor assumptions on flow characteristics of gas or liquid phases may lead to errors and deviations from the true values (142). All the models are a simplified (amenable to mathematical treatment) description of the system. It should be kept in mind, therefore, that kLa is not a property of the

Response

Compare and choose the kLa that gives the best fit

Response

Compare and choose the kLa that gives the best fit

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