Analytical modeling of cake filtration

The specific resistance model of cake filtration is based on the assumption that the average cake resistance is constant over time. This implies also that the spatially average values of porosity and pressure differential are also constant over time since specific resistance is a function of both parameters. An analytical cake filtration model based on Tiller (1975) was derived using constitutive properties of kaolin suspensions in distilled water. Constitutive properties were determined by experiments performed using high-energy X-rays and porewater pressure probes to determine the spatial and temporal distributions of porosity and porewater pressure. Using these constitutive properties, predictions were made of porewater pressure and porosity distributions Using the analytical model. Porosity data were used to compare to the analytical-model prediction assuming that porosity and pressure were functions only of fractional cake position.