In this article a system of equation to describe the steady state external filter cake thickness profile along the cuboid crossflow filtration setup geometry as well as the well bore geometry are introduced. The first equation is obtained from the analysis of forces acting on a deposited particle at the outermost limit of the external cake. The second equation is obtained from the volume conversation of the transporting fluid in the given geometry. Coupling the two equations yields an implicit solution of the cake profile. Boundary conditions are required as well as the quantification of an empirical factor that can be quantified experimentally.
Experiments conducted were analysed and the empirical friction coefficient was quantified and presented. Simulations based on the developed solution are also presented.