MODELING THE FLOW OF POWER-LAW FLUIDS IN A PACKED-BED USING A VOLUME-AVERAGED EQUATION-OF-MOTION

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous micros tructure model based on a cell model is used. Numerical solution of th e resulting equation is effected using a penalty Galerkin finite eleme nt method. Experimental pressure drop values for dilute solutions of c arboxymethylcellulose flowing in narrow tubes packed with uniformly si zed spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model throu gh the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the be d pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.