Solution of a Porous Medium Problem Using Laplace Transform

The present paper studies the flow of two immiscible fluids passed in a cylindrical porous medium. The porous medium is partially filled with oil and water is then passed through the medium. Due to the non-mixing nature of the fluids, the perturbations occur. The phenomenon of instabilities in the polyphasic flow through homogeneous porous medium is discussed under the assumption of mean capillary pressure. The resulting governing equation is a linear partial differential equation. The equation gives the saturation of water at any point in the cylinder at any time. In the present paper, the analytical solution has been obtained using the Laplace transform. Also the solution has been analysed graphically.