Numerical solution of the Rapoport–Leas equation using the method-of-lines and the DASSL code

We consider the problem of the one dimensional oil displacement by injection of water in a laboratory experiments in a porous media. Under the assumptions of incompressibility of the fluids in the porous media and the mass conservation of the phases, the fractional flow theory leads to the Rapoport–Leas equation. The continuity of the pressure in the borders of the sample provides the boundary conditions for this parabolic semi-linear problem. The method-of-lines and DASSL code algorithm is propose, as a good alternative to the classical numerical techniques.