The investigation discussed in this paper was motivated by the need for model which is able to simulate both permeability reduction of hydrocarbon formations due to the mud-component invasion during over-balance drilling, casing/cementing, workover operations, and dynamics of permeability repairing during well cleanup. The paper focuses on development and validation of model to describe internal mud cake (IMC) dynamics, placing special emphasis on dynamics of the IMC removing during well cleanup procedure. Set of laboratory experiments with clay slurry injection and subsequent brine water backflow in samples of Bentheimer sandstone is discussed. The specific of these experiments is that backflow was carried out with alternating rates ("multirate" backflow). It is shown that the conventional deep-bed filtration model is not able to reproduce the dynamics of multirate backflow. The stochastic model we suggest takes into account pore size distribution and describes the mobilization of trapped particles within individual groups of pores within a "pore ensemble." We provide simulation results to show that the suggested model reasonably reproduces permeability dynamics during both clay slurry injection and brine water backflow stages.