Modeling of External Filter Cake Build-up in Radial Geometry

The problem of formation damage (i.e., permeability reduction due to injection of particulates), is a matter of interest in several engineering fields. In the previous attempts to model the external cake formation, cake thickness has been considered to be only dependent on time; even though in practical applications, the dependency of the cake profile on space can be important. In this article, a novel model has been developed to describe the steady state external filter cake thickness profile along the wellbore. A set of equations is derived from the force balance for a deposited particle on the cake surface and the volume conservation of the fluid in the wellbore. These equations are combined with Darcy's law in radial geometry and the equation of flow in the wellbore, and solved numerically to obtain the cake thickness and fluid velocity profiles along the wellbore.