Physical Sciences and Mathematics Commons^™

Variation Of Constitutive Model Formulation On Analytical Cake Filtration Models, Scott A. Wells

Civil and Environmental Engineering Faculty Publications and Presentations

Constitutive properties are required to model porosity, effective stress, porewater pressure, or permeability during cake filtration. By using an analytical cake filtration model based on Tiller (1975) with various constitutive property formulations, predictions of effective stress, permeability, and porosity distributions in a filter cake can be made. This analytical approach was only valid when spatially average values of porosity and pressure differential were constant over time. Several different constitutive property formulations were compared to data of effective stress and permeability as a function of porosity for kaolin clay in water. Also the spatial distribution of porosity in a filter cake …

Analytical Modeling Of Cake Filtration, Scott A. Wells

Civil and Environmental Engineering Faculty Publications and Presentations

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 …

Gravity Drainage Prior To Cake Filtration, Scott A. Wells, Gregory K. Savage

Civil and Environmental Engineering Faculty Publications and Presentations

During the initial stages of a Buchner funnel or specific resistance test, gravity drainage occurs prior to application of the pressure differential. Some allow time for a small cake to form by gravity drainage. Filtrate data from the gravity drainage period can be used to determine constitutive properties of the cake under a hydrostatic pressure gradient. The constitutive properties that define the structure of the cake include the permeability and porosity as functions of the applied stress. Equations governing the drainage rate during a gravity filtration experiment assuming a constant and a non-constant average cake permeability and cake porosity were …