## 94 Example 3 Bubble Column Reactor

Bubble column reactors, in which sparged gas provides the necessary mixing, offer an attractive way to carry out gas-liquid processes. Because of their simple construction and operation, bubble columns are widely used in process industries. However, the simple construction also has the drawback of having fewer degrees of freedom available to a reactor engineer to tailor performance. The performance of bubble columns is controlled by several physical and chemical phenomena with different spatial and temporal scales. Gas-liquid fluid dynamics is determined by local gas volume fraction (hold-up) but extends over the whole reactor. Gas-liquid mass transfer and chemical reactions depend on local concentrations and on local gas-liquid interfacial areas. Interfacial area depend on local gas hold-up and bubble size distribution. Bubble size distribution depends on a variety of parameters, including type and location of sparger, local and global mean and turbulence fields properties of liquid phase and so on. Although much progress has been made in gaining a better understanding of each of the phenomena mentioned, a comprehensive computational model, which is able to simulate all of the above interactions simultaneously, is still too difficult to develop and use for industrial applications. As mentioned in the case of the polymerization reactor, uncertainties in estimating the parameters of sub-models describing various phenomena make the task of developing a comprehensive model less justifiable. On the other hand, conventional reaction engineering models, which include detailed descriptions of reaction and mass transfer from bubbles, normally consider ideally mixed systems or one-dimensional models (see for example, Fleischer et al, 1995). Both the assumptions often do not hold true for bubble column reactors. Under these circumstances, it may be more efficient and may be necessary to use a multilayer or multiscale modeling strategy. Recently Bauer and Eigenberger (1999) proposed such a multiscale modeling strategy based on the fact that the influence of mass transfer and reaction on fluid dynamics can be represented by three variables:

• interphase drag coefficient or interphase momentum exchange terms;

• interfacial area; and

• local gas flux due to mass transfer and reaction from gas bubbles.

If the values of local mean bubble diameter and local gas flux are available, a fluid dynamic model can estimate the required influence of mass transfer and reactions on the fluid dynamics of bubble columns. Fortunately, for most reactions, conversion and selectivity do not depend on details of the inherently unsteady fluid dynamics of bubble column reactors. Despite the complex, unsteady fluid dynamics, conversion and selectivity attain sufficiently constant steady state values in most industrial operations of bubble column reactors. Accurate knowledge of fluid dynamics, which controls the local as well as global mixing, is however, essential to predict reactor performance with a sufficient degree of accuracy. Based on this, Bauer and Eigenberger (1999) proposed a multiscale approach, which is shown schematically in Fig. 9.13.

Detailed hydrodynamics

Detailed hydrodynamics

Simplified reactor model

Number density function for bubble size

Simplified reactor model or

Mass transfer and reaction models

Population balances for bubble size and bubble concentration

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