Exact solutions to the problem of deep-bed filtration with retardation of a jump in concentration within the framework of the nonlinear two-velocity model

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Abstract
Exact solutions with plane and cylindricalwaves are obtained for one-dimensional problems of injection of a suspension into a porous reservoir when lagging of the suspended particles behind the carrier fluid is taken into account in the case of large change in the porosity. It is shown that taking lagging of the particles behind the fluid into account can lead to slowing-down the motion of jump in concentration. This is in agreement with the results of a series of experiments. It is also noted that, in principle, models in which the particles pass in average ahead of the carrier fluid are possible in the problems of deep bed filtration.