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 paper a novel model has been developed to describe the steady state external filter cake thickness profile along the well-bore.A set of equations are derived from the force balance for a deposited particle on the cake surface and the volume conservation of the fluid in the well-bore. These equations are combined with the Darcy's law in radial geometry and the equation of flow in the well-bore, and solved numerically to obtain the cake thickness and fluid velocity profiles along the well-bore.

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