Efficiency, wetting

If the dry efficiency at this point in the column is 90%, the wet efficiency is calculated by means of Equation 291 ... 

This fraction could be viewed as a fixed-bed wetting efficiency. If he t = s and hyt= 1, the bed is completely filled with fluid (fully wetted). The term is analogous to the catalyst wetting efficiency/w for trickle beds (Section 3.7.3). However, this equality is valid solely in fixed beds where a single fluid flows through. The active volume of the solid, which is occupied by the fluid, amounts to the fixed-bed volume occupied by the fluid minus the volume occupied by fluid ... 

In a reactor completely filled with liquid, the wetting efficiency is 100% or, in other words, the external wetting of the catalyst is complete (Burghardt et al., 1995). While it is true that when a fixed bed is completely filled with liquid wetting is complete (wetting efficiency is unity), the opposite is not true in a trickle bed, a portion of the bed voids will be always occupied by the gas phase. Thus, while in a well-operated trickle bed the wetting efficiency could be unity, its total liquid holdup based on the void volume is always lower than the bed voidage, i.e. the bed is never completely filled with liquid. 

The catalyst wetting efficiency of the external catalyst surface can be calculated at atmospheric pressure using the correlation of El-Hisnawi et al. (1981 Wu, 1996) ... 

In Figure 3.48, the effect of particle size, liquid density, and liquid dynamic viscosity on wetting efficiency is presented. It is evident that by increasing particle size and liquid density, and decreasing liquid dynamic viscosity, the wetting efficiency is decreased. 

Figure 3.48 The effect of particle size, liquid density, and liquid dynamic viscosity on wetting efficiency.

In Figure 3.49, the minimum liquid superficial velocity versus particle size in order to have a wetting efficiency higher than 90% for water as liquid phase at 25 °C is presented. 

For the typical case of water systems used in environmental applications, e.g. removal of S02 from gas streams, the minimum superficial velocity of water for a wetting efficiency higher than 90% v.s. can be correlated to particle size as follows ... 

The Reynolds number is based on superficial velocity. This equation is proposed for applications with organic liquids such as n-hcxane, light petroleum fractions, and similar species. In the trickle flow regime, the increase in the gas flow rate leads to a decrease in the wetting efficiency (Burghardt et al., 1995). 

The importance of the wetting efficiency results mainly from the fact that it is closely related to the reaction yield, and more specifically to the catalyst effectiveness factor (Burghardt et al., 1995). The reaction rate over incompletely covered catalytic particles can be smaller or greater than the rate observed on completely wetted packing, depending on whether the limiting reactant is present only in the liquid-phase or in both gas and liquid-phases. 

First, we have to check the wetting efficiency of the bed because the simple trickle-bed model assumes complete wetting and thus it is not applicable otherwise. By using the El-Hisnawi et al. correlation, the wetting efficiency can be estimated (eq. (3.411)). To do that, we need the Galileo number and the Reynolds number. The liquid superficial velocity can be evaluated as follows ... 

It is evident that the model predictions are veiy close to the experimental values for a high wetting efficiency, while the model predicts higher conversions for lower wetting efficiencies. This is expected as the simple model assumes complete wetting, i.e. better performance of the reactor. 

Die difference from the real value (lm) is mainly due to the approximation made about the mass transfer coefficient as well as the complete wetting of the catalyst, as the actual wetting efficiency is 88%. Furthermore, the problem is more complicated because under incomplete wetting, the gas reactant reaches the catalyst surface more easily than the unwetted part, as Horowitz et al. found out experimentally. 

The aim of this example is to demonstrate the use of the simplified model for reactions other than first order with respect to the gas reactant and zero order to the liquid one, and more specifically to demonstrate the case of first order with respect to the gas reactant and half order to the liquid one, which may have, under specific operating conditions, an analytic solution. For example, if the liquid mass superficial velocity was higher, say 10 kg/m2 s, the wetting efficiency is 1 and the mass transfer contribution lower than 4.07%. At the same time, there is no contribution of the unwetted part of the catalyst. Under these conditions, the approximate model is expected to exhibit a better performance. The same result can be achieved for smaller particles. 

According to the experimental results of Medeiros et al. (2001), the wetting efficiency is 100% and plug flow is assumed for liquid flow rates in the vicinity of 14 x 10 5 m3/s, which is the case in this example. 

The conditions (a), (b), (c), and (d) are met since we have the experimental value of the gas-liquid mass transfer coefficient, the wetting efficiency is given to be 100%, plug-flow condition is assumed in the original study, and the expansion factor is zero as the oxygen concentration has been taken as constant. 

Wetting efficiency Tlie Reynolds and Galileo numbers are 13.18 and 1.88 x 105. Using die correlation of El-Hisnawi (eq. (3.411)), the wetting efficiency is 0.99, satisfying condition (b). 

Due to the relatively high pressure, the wetting efficiency is evaluated from the correlation of Al-Dahhan et al. (eq. (3.414)) ... 

Failing to identify the limiting reactant can lead to failure in the scale-up of trickle-bed reactors (Dudukovic, 1999). Gas-limited reactions occur when the gaseous reactant is slightly soluble in the liquid and at moderate operating pressures. For liquid-limited reactions, concurrent upflow is preferred (packed bubble columns) as it provides for complete catalyst wetting and thus enhances the mass transfer from the liquid phase to the catalyst. On the other hand, for gas reactions, concurrent downflow operation (trickle-bed reactors), especially at partially wetted conditions, is preferred as it facilitates the mass transfer from the gas phase to the catalyst. The differences between upflow and downflow conditions disappear by the addition of fines (see Section 3.7.3, Wetting efficiency in trickle-bed reactors). 

Fig. 31. (a) Dynamic liquid hold-up, and (b) wetting efficiency as a function of liquid superficial velocity for 1.5- and 3-mm cylinders. Gas fiow rate was constant at 31.3mms . The line shows the best fit of the data to the percolation model of Crine et al. (104). Reprinted from reference (103) with permission from Elsevier, Copyright (2003). 

Recently Iliuta and Larachi [44] developed a generalized slit model for the prediction of frictional two-phase pressure-drop, liquid hold-up, and wetting efficiency in TBR operated under partially-and fully wetted conditions. This proposed model mimicked the actual bed void by two geometrically identical inclined slits, a wet slit and a dry slit (see Figure 5.2-14). 

In the first slit, the liquid wets the wall with a film of uniform thickness the gas being in the central core (wet slit). The second slit is visited exclusively by the gas (dry slit). The high-pressure-and high-temperature-wetting efficiency, liquid hold-up and pressure-drop data reported in the literature for TBR in the trickle-flow regime were successfully forecasted by the model. 

I. Iliuta and F. Larachi, The generalized slit model pressure gradient, liquid hold-up and wetting efficiency in gas-liquid trickle flow, Chem. Engng. Science, 54 (1999) 5039-5045. 

Hydrodynamic parameters that are required for trickle bed design and analysis include bed void fraction, phase holdups (gas, liquid, and solid), wetting efficiency (fraction of catalyst wetted by liquid), volumetric gas-liquid mass-transfer coefficient, liquid-solid mass-transfer coefficient (for the wetted part of the catalyst particle surface), gas-solid... 

Xs.—The wetting efficiency is obtained by calculating the fraction of the pixels identifying the surface of the packing that are in contact with liquid during gas-liquid flow. Liquid-containing voxels adjacent to the wall of the column, and the internal surface of the porous packing elements are not considered in the analysis. 

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