Incompressible Cake Filtration of a Yield Stress Fluid

Filtration of Non-Newtonian fluid occurs frequently in industry. A correlation is developed by introducing the Yield Stress model in place of the Newtonian model used in the Ergun equation. The resulting model has three parameters that are functions of the geometry and roughness of the particle surfaces. Two of the parameters can be deduced in the limit as the yield stress becomes negligible and the model reduces to the Ergun equation for Newtonian fluids. The third model parameter is determined from experimental data. The correlation relates a defined friction factor to the dimensionless Reynolds and Hedstrom numbers that can be used to predict pressure drop for flow of a yield stress fluid through a packed bed of spherical particles. This model is applied to predict incompressible cake filtration performance of a yield stress fluid. Modeling results show that for a constant pressure filtration the cake growth rate and filtrate flow rate for the incompressible filter cake are similar to that for a Newtonian fluid, until the flow rate decreases to the level that the shear stress is not sufficient to maintain the flow. At this point the friction factor increases more rapidly than that for the Newtonian fluid, and the flow rate and cake growth rates decrease rapidly. For a given material and pressure drop the transition between Newtonian-like flow and the yield stress flow can be predicted as a function of cake height.