• Ravi. Narayan Borana
• Vikas H. Pradhan
• Himanshu V. Chapani

During water flooding process, with the injection of water into the petroleum reservoir, oil is displaced in such a pattern that unstable fingers (water filled) rise, these fingers are unstable and consequently an important phenomenon viz. instability (fingering) arises. There is a two-phase immiscible flow, one phase being water and other being oil. This phenomenon is of a great practical importance and it has been extensively studied by the researchers and scientists working in the petroleum production industry especially during secondary oil recovery process, from different viewpoints in the recent past. In the present paper for a systematic study, this phenomenon is numerically discussed for the heterogeneous porous media. The heterogeneous porous medium is considered with a steady permeability, whereas porosity is assumed varying with the space co-ordinate. It makes possible to derive the non-linear governing equation for the Instability phenomenon in the heterogeneous porous medium. The governing equation is based on the mass conservation principle and important Darcy’s law. Under the specific standard relationships and basic assumptions considered, the numerical solution is obtained by using Crank-Nicolson finite difference scheme for the specified initial and boundary conditions. The numerical results are obtained by generating a MATLAB code. The oil recovery factor is shown in accordance with the standard relationship from the experimental results. The sensitivity of the basic parameters is studied to observe the corresponding effect on the obtained numerical solution for the saturation of water. The numerical results behave well with the physical phenomena and the basic properties of the parameters are preserved.

Darcy’s law, mass conservation principle, capillary pressure, heterogeneous porous medium, Crank-Nicolson finite difference method.

"Instability phenomenon in two phase heterogeneous porous medium and numerical solution of the governing equation ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 5, page no.198-205, June-2019, Available :http://www.jetir.org/papers/JETIR1905N32.pdf

"Instability phenomenon in two phase heterogeneous porous medium and numerical solution of the governing equation ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 5, page no. pp198-205, June-2019, Available at : http://www.jetir.org/papers/JETIR1905N32.pdf