A Fractional Differential Model for Elastoviscoplastic Filtration of Liquids in Porous Media

In this work, the problem of anomalous filtration of liquid in a porous medium is studied, taking into account the threshold pressure gradient (TPG). The flow of a homogeneous liquid in a porous medium was modeled by a differential equation with fractional derivatives. Fractional derivatives are defined in the Caputo sense. The problem was solved numerically by the finite difference scheme method. The pressure gradient and filtration velocity were calculated with known values of the TPG. The profiles of pressure and filtration velocity are determined for different values of the orders of fractional derivatives α and β, with respect to the filtration velocity and pressure gradient, respectively. An increase in TPG leads to a decrease in the filtration velocity. Moreover, this decrease is greater as the time increases t. Simultaneously with the decrease in g 0 , the zone of distribution of the filtration velocity decreases, which means an increase in the size of the zone with stationary liquid.