Geodesic
An analytical solution of the problem of wall cake growth with washing-off
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 14-21

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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.
Keywords: well bore zone, wall cake, drilling fluid filtration. 
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     author = {O. B. Bocharov and D. Yu. Kushnir},
     title = {An analytical solution of the problem of wall cake growth with washing-off},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {14--21},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a1/}
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O. B. Bocharov; D. Yu. Kushnir. An analytical solution of the problem of wall cake growth with washing-off. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 14-21. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a1/