LAUSR

Abstract The approximate solution of fingero imbibition phenomena governed by a nonlinear partial differential equation is discussed in the present paper. The primary oil recovery process was due to natural soil pressure, but in the secondary oil recovery process water flooding plays an important role. When water is injected through the injection well for recovering the reaming oil after primary oil recovery process, it comes to contact with the native oil and at that time the fingero imbibition phenomena occur due to different viscosity. For the mathematical modeling, we consider the homogeneous inclined porous medium and comparative study of without inclination and with inclination has been done, and also optimal homotopy analysis method has been used to solve the partial differential equation governed by the mathematical modeling. The graphical representation of the solution is given by MATHEMATICA and physically interpreted.