Transport of particle suspensions in oil reservoirs is an essential phenomenon in many oil industry processes. Solid and liquid particles dispersed in the drilling fluid (mud) are trapped by the rock (porous medium) and permeability decline takes place during drilling fluid invasion into reservoir resulting in formation damage. The formation damage due to mud filtration is explained by erosion of external filter cake. Nevertheless, the stabilization is observed in core floods, which demonstrates internal erosion. A new mathematical model for detachment of particles is based on mechanical equilibrium of a particle positioned on the internal cake or matrix surface in the pore space. In the current work the analytical solution obtained to mud filtration with one particle capture mechanism with damage stabilization. The particle torque equilibrium is determined by the dimensionless ratio between the drag and normal forces acting on the particle. The maximum retention function of the dimensionless ratio closes system of governing equations for colloid transport through porous medium.
 A. C. Payatakes, et al., “Application of Porous Medium Models to the Study of Deep Bed Filtration,” The Canadian Journal of Chemical Engineering, Vol. 52, No. 6, 1974, pp. 722-731. doi:10.1002/cjce.5450520605
 D. Jiao and M. M. Sharma, “Mechanism of Cake Buildup in Crossflow Filtration of Colloidal Suspensions,” Journal of Colloidal and Interfacial Science, Vol. 162, No. 2, 1994, pp. 454-462. doi:10.1006/jcis.1994.1060