Numerical Solution and Sensitivity Analysis of Pore Liquid Pressure and Cake Porosity to Model Parameters

Abstract

Filter cake formation is important in groundwater and oil wells where drilling contains suspended mud particles. The accumulation of these mud particles on the borehole wall creates a pressure drop in the well. Furthermore, the migration of colloidal particles into adjacent porous rock could damage the formation and cause productivity decline. In this study, numerical solutions for pore liquid pressure variation across the cake with variable total stress and associated porosity variation are obtained. Mass equations for captured and suspended particles are averaged along the mud cake thickness, taking into account conditions on the cake surface and at the filter septum. The variability of total stress in soil consolidation’s problem is considered to determine the pore liquid pressure along the mud cake thickness. Then, the relation between porosity and pressure is studied to determine the mud cake porosity. Experimental data obtained by various researchers is used to compare and test the validity of numerical solutions to develop guidelines for model applications. Results show that the pore liquid pressure increases with the decrease of membrane impedance value (i.e. less pervious membrane). Also, the pressure profile has a cubic function of dimensionless cake thickness. The conclusions from the sensitivity analysis conducted in this study agree with earlier conclusions.