Gas Hold-up in a MWPB

In Fig. 4.16 the gas is shown to be the continuous phase of the MWPB. In this configuration, many direction changes in the flow of gas elements originate from the presence and moving of the packing spheres. If we consider that these changes take place randomly, then we can carry out the particularization of the stochastic flow description of the gas elements. This description has been successfully used for the case of gas-liquid flow in a fixed and in a mobile packed bed [4.28, 4.81]. 

The gas element evolves inside the MWPB in 3 states displacement in the +x direction with velocity +v displacement in the —x direction with velocity —v non-motion or displacement in the horizontal plane. The mathematical writing of the stochastic model is given by relations (4.182)-(4.187). In order to particularize this model to the case of gas element evolution inside the MWPB, we take into account the following considerations  

The sense of the x-axis is determined by the global gas flow direction and is inverse with respect to the liquid flow. 

It is difficult to select the values for the probabilities of passage between process states. 

The gas flowing element rapidly passes from one actual process state to another and tends to follow an elementary process type Istate. 

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