Dynamic liquid holdup, averaging

The averaging of the dynamic liquid holdup is achieved in a similar way by introducing Eq.2 and 9 into Eq.7. 

Various methods for estimating KLs are described by Satterfield.150 The most conservative estimate of KLS is obtained as KI S = D/<5,, where D is the molecular diffusivity of the reactant in the liquid phase and <5L the average thickness of liquid film surrounding the particles. This estimation assumes no turbulence in the liquid film. The average thickness of the liquid film can be obtained from a knowledge of the dynamic liquid holdup and the outside area of catalyst particles per unit volume of the reactor, os. For example, if the dynamic liquid holdup is 50 percent of the void volume e, then <5L = e/2as. Various methods for estimating fcL and Ks under trickle-flow conditions are described in Chap. 6. 

Figure 7-12 Dynamic and total liquid holdup as a function of average gas interparticle pore velocity in a 10.2-cm-i.d. column packed with 1.9-cm x 1.9-cm ceramic cylinders.22...

Residence time distribution measurements, together with a theoretical model, provide a method to calculate the rate of mass transfer between the liquid flowing through the column, the dynamic holdup, and the stagnant pockets of liquid in between the particles. We have chosen the cross flow model (10). It has to be noted that the model starts from the assumption that the flow pattern has a steady-state character, which is in conflict with reality. Nevertheless, average values of the number of mass transfer units can be calculated as well as the part of the liquid being in the stagnant situation. 

In this dynamic situation the volume of the dispersed phase held up in the liquid pool is also variable, depending on the rate of rise of the bubbles and the volumetric feed rate. Statistical averages are used to characterize the system, since the holdup, interfacial area, and bubble diameter vary with time and with position in the vessel. 

The dynamic holdup depends mainly on the particle size and the flow rate and physical properties of the liquid. For laminar flow, the average film thickness is predicted to vary with, as in flow down a wetted-wall column or an inclined plane. In experiments with water in a string-of-spheres column, where the entire surface was wetted, the holdup did agree with theory [28]. For randomly packed beds, the dynamic holdup usually varies with a fractional power of the flow rate, but the reported exponents range from 0.3 to 0.8, and occasionally agreement with the 1/3 power predicted by theory may be fortuitous. 

Liquid was delivered into the packed bed with a needle. The gas feed line was connected to the feed section with a T-junction therefore, the gas flowed through the annular area between the liquid feed line and the outer pipe. When the gas and liquid flows were stopped, the liquid entirely remained in the micro-structured bed. Thus, the bed has zero dynamic holdup and only static holdup. The static holdup (gj.) is expressed as the fraction of the space between the particles that is, on average, filled with liquid ... 

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