Self-similar motions of a thin slug of a neutral admixture in a two-phase flow in a porous medium (Q1115766)

Exact solutions are obtained for the self-similar problems relating to motion of a thin slug of a neutral admixture in a porous medium with allowance for two-phase flow and diffusion. With radial flow in a porous medium the regime with constant rate of injection is self-similar. Self- similar motion in plane-parallel flow in a porous medium corresponds to prescription on the injection gallery of a flow rate inversely proportional to the square root of the time. Cases are analyzed involving various different initial values of the water saturation of the bed. Laws of motion are derived, together with variations in time of the value of the peak concentration. Another topic studied is the dependences of the dynamics of the slug on the coefficient of diffusion, the ratio of viscosities of the phases, the initial water saturation, and the rate flow in a porous medium.