Some model of a suspension filtration in a porous media that accounts for the two-zone and multistage character of deposition kinetics

The problem of suspension filtration in a porous medium consisting of active and passive zones is posed and numerically solved in the case of a multistage kinetics of particle deposition. Some mathematical model of the process is proposed that is based on the general conservation laws and additional phenomenological assumptions. The influence of the multistage kinetics of particle deposition on the filtration characteristics is considered. We establish that, as the parameter characterizing the duration of the stage of formation of the irreversible deposition increases, a region with complete saturation of the passive zone capacity appears near the filter inlet. No further increase of the deposition concentration in the passive zone is observed, while the process of particles movement in suspension and deposition of them in the active zone continues.