An analytical solution of the problem of wall cake growth with washing-off

We obtain an analytical solution for the thickness of incompressible wall cake and pressure drop in the well bore zone in the case of single-phase filtration in a porous medium. We assume that the deposition of clay particles on the well wall is proportional to the flux through the wall. We describe filtration basing on Darcy's law. We obtain analytic formulas for the case of cake washing-off by the drilling fluid and clogging zone with parameters independent of time. We consider the cases of linear and radial filtration.