This paper focuses on the compound phenomenon of Instability and Imbibition called Fingero-Imbibition phenomenon arising in two immiscible phase (oil and water) flow through homogeneous porous media in vertical downward direction. Mathematical formulation leads to non linear partial differential equation. The analytical solution is obtained by using generalised separable method in terms of quadratic polynomial by using appropriate boundary conditions and its physical interpretation is given with numerical tabulated values and graphical presentation.
Present study explores the Fingering (Instability) phenomenon's mathematical model that ensues during the process of secondary oil recovery where two not miscible fluids (water and oil) flow within a heterogeneous porous medium as water is injected vertically downwards. Variational iteration method with proper initial and boundary conditions is being used to determine approximate analytic solution for governing nonlinear second order partial differential equation. Whereas MATLAB is applied to acquire the solution's numerical findings and graphical representations.
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