HYDRODYNAMIC MODELING OF VERTICAL LIQUID SOLIDS FLOW

A one dimensional model for vertical non-accelerating liquid-solids flow in the steady state is formulated and experimentally verified. The theoretical basis of the model are the continuity and momentum equations for the fluid and particle phases of Nakamura and Capes, Can. J. Chem. Eng., 51 (1973) 39 and the authors' variational model for calculating fluid-particle interphase drag coefficients. The model gives the relationship between the fluid and particle flowrates, voidage and pressure gradient. Experiments were performed using water and spherical glass particles 1.20, 1.94 and 2.98 mm in diameter to obtain a correlation for the particle wall friction term and to verify the model. The loading ratio was varied from 0.048 to 1.25. For these ratios, the voidages ranged from 0.64 to 0.95, so that both dilute and dense phase transport were studied. The experimental data verifies the applicability of our variational model for the drag coefficient and the data of Kopko, Barton and McCormick, Ind. Eng. Chem. Process. Des. Dev., 14 (1975) 264, agree well with our model predictions. Two different flow regimes were identified and the choking criterion of Day, Littman and Morgan, Chem. Eng. Sci., 45 (1990) 355 for pneumatic transport was found to predict the regime transition.