Macroscopic Model for Momentum Transport in Down-Flow Fluidization

Abstract

Down-flow fluidization is an attractive unit operation because it allows having a smooth circulation of the fluid and the solid support material as well as an uninterrupted and controlled operation of the fluid. In addition, since the solid support material is less dense than the fluid, the pump energy consumption required for bed expansion is smaller in comparison with upward fluidization. Momentum transport in fluidized beds is usually modeled by macroscopic models, which are expressed in terms of effective-medium coefficients, by making analogies with transport in porous media. In practice, it is desirable to derive these models and to predict the involved coefficients in a reliable manner. For this reason, in this work we derive a macroscopic model for the hydrodynamics of down-flow fluidization, using the method of volume averaging obtaining a model with the form of Darcy’s law with a correction in the relative velocity of the fluid to the solid. A salient feature of the model is that it allows predicting the apparent permeability coefficient in different geometries, and under different transport conditions. Also, the average model obtained can be used for both types of fluidization, because it is not restricted by the flow direction.