Deep bed and cake filtration of two-size particle suspension in porous media

Formation of low permeable external filter cake during drilling and water injection has been widely reported in the literature. It may cause significant decrease in well index. The process is very sensitive to size distribution of injected particles. We propose a new mathematical model for cake formation with deep bed filtration for two-particle-size injection. The basic equations account for three stages: formation of cake from large particles with simultaneous deep bed filtration of small particles; small particle capture in the cake with formation of the internal cake inside the external cake; build-up of the uniform cake from the mixture of two-size particles. The analytical model is derived for three stages. Two regimes of the cake formation are identified, which correspond to the high and low concentrations of injected small particles. The laboratory coreflood with two-particle-size suspension injection with monitoring the rate and pressure drop along the core is performed. The matched mathematical model shows good agreement with the laboratory data.