## 132 Trickle Bed Reactorspacked Column Reactors

A variety of packed columns are used either as trickle bed reactors (co-current downward flow of gas and liquid over catalyst pellets) or as column reactors (absorber/scrubbers or catalytic distillation towers, where gas and liquid phases flow counter-currently over a matrix of packings). Most conventional reaction engineering models assume drastically simplified flow patterns and are formulated as one-dimensional models. Recent experimental studies have shown the rich structure of multiphase flows through such equipment, which needs to be understood to develop reliable reactor engineering models. General volume-averaged conservation equations for multiphase flows are discussed in Chapter 4. These equations can also be applied to simulating gas-liquid flows through packed beds. It is, however, necessary to include appropriate closure models and models to account for bed heterogeneity in the overall computational model. Some recent approaches are briefly reviewed here.

Yin et al. (2000) developed a computational model to simulate flow and mass transfer in randomly packed distillation columns. It is necessary to develop appropriate models for interphase drag and dispersion coefficients. The general approach is to represent the overall pressure drop for gas-liquid flows in a packed column in two parts, namely wet and dry:

The dry pressure drop can be accounted for by volume-averaged governing equations using the representation shown in Eq. (13.2). Generally for packed bed operations, only the second term on the right-hand side of this equation (corresponding to turbulent contributions) is adequate to represent dry pressure drop. The parameter C2 appearing in this equation may be obtained by using available pressure drop correlations (Robins, 1991). Similar to gaseous flow through a fixed bed, the additional resistance offered by the bed is usually represented as an additional sink in the momentum equations (body force term). The presence of liquid phase in the packed bed reduces space for the gas phase and leads to higher pressure drop. Drag force exerted on the gas-liquid interface also contributes to the additional pressure drop. These two contributions (wet pressure drop) are usually modeled as interphase drag force. Available correlations of wet pressure drop (Robins, 1991) may be used to obtain expressions for a suitable interphase momentum exchange coefficient (refer Eq. (4.27)).

In addition to these pressure drop models, models to represent spreading of liquid in packed beds because of spatial variation in flow resistance are needed. In a randomly packed bed, the void fraction is not uniform. This implies that some flow channels formed within a packed bed offer less resistance to flow than other channels of equal cross-sectional area. Liquid will tend to move toward channels of lower resistance, leading to higher liquid hold-up in such channels. Thus, even if the initial liquid distribution is uniform, inherent random spatial variation of the bed leads to non-uniform liquid flow. Yin et al. (2000) assumed that the dispersion coefficient for liquid phase volume fraction is linearly proportional to the adverse gradient of the axial flow resistance (the higher the resistance, the lesser the tendency for liquid flow):

where Kc is a proportionality constant and can be determined by fitting experimental data. Rz is axial flow resistance and can be estimated by considering the inertial term of the Ergun equation. The dispersion coefficient can thus be written:

pU2 (1 - p)pU r = 1.75 Kc Iā;V p - 3.5 Kc --āā V U (13.6)

### Dpp2 Dp p

The first term on the right side of this equation represents the effect of bed structure (spatial variation of bed void fraction, p) on liquid spreading, and the second term implies that even for homogeneous packed beds, the liquid spreading will occur if the initial distribution of liquid is non-uniform. The turbulent dispersion coefficient is modeled conventionally using the turbulent viscosity and turbulent Prandtl number. Yin et al. (2000) used the value of turbulent Prandtl number as 0.01, which is much lower than the generally used value (nearly 1). In order to close the model equations, it is necessary to provide information about spatial variation of voidage in packed beds. Yin et al. (2000) carried out measurements of voidage distribution and used an empirical correlation based on their own measurements. With such a model, Yin et al. (2000) were able to simulate pressure drop and height equivalent to a theoretical plate for a column packed with Pall rings. Their simulation results were able to capture the influence of size of packings and gas flow rate on pressure drop adequately (Fig. 13.8). The CFD model was also able to adequately simulate HETP (height equivalent to a theoretical plate) values of Pall rings. These results are shown in Fig. 13.9. It can be seen that the improvement of separation efficiency with increase in pressure (lower HETP) was correctly captured by the CFD simulations. Thus, the computational models can be used to understand the influence of packings size, operating pressure and other design and operating issues on performance.

It must be noted that the porosity and its distribution in a packed bed are the key parameters in determining the flow distribution within the bed. In recent years, numerous attempts have been carried out to provide quantitative information about porosity distribution (Mueller, 1991; Borkink et al., 1992; Bey and Eigenberger, 1997). Mean porosity and its distribution are determined largely by particle size, shape, surface properties and method of packing. Generally, cross-sectional averaged porosity along the height of the bed is distributed randomly. The longitudinally averaged radial porosity profile exhibits a maximum near the wall. Recently, Jiang et al. (2000a, 2000b) considered such random distributions of porosity within the bed and developed a method to generate random distribution of bed porosity while satisfying the constraints on mean porosity and longitudinal averaged radial porosity profiles. A sample of random porosity distribution generated by their method is shown in Fig. 13.10. Such randomly distributed bed porosity may give more realistic results than assuming mean porosity all over the bed. It must be noted that the porosity distribution observed in a packed bed will be obviously dependent on scale of observation. It has been experimentally shown that at a scale of a cluster of particles, porosity has a Gaussian distribution (Jiang et al., 2000a) while at a much smaller scale, porosity has a bi-modal distribution (Jiang et al., 2001). This relationship between porosity

FIGURE 13.8 Comparison of predicted and experimental pressure drop for three Pall rings (from Yin et al., 2000).

FIGURE 13.8 Comparison of predicted and experimental pressure drop for three Pall rings (from Yin et al., 2000).

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