• MANSI K DESAI
• DR. SHAILESH S. PATEL

In this present paper, The approximate solution of imbibition phenomenon governed by linear and non-linear partial differential equation is discussed. When water is injected in 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 imbibition phenomenon occurs due to different viscosity. The Saturation of injected water is calculated by homotopy perturbation method for Linear and Non linear differential equation of Imbibition phenomena under assumption that Saturation is decomposed in to saturation of different levels. The obtained results as compared with previous works are highly accurate. For the mathematical modeling, we consider the homogeneous porous medium and homotopy preturbation method has been used to solve the partial differential equation governed by it. The graphical representation of the solution is given by Met lab and physically interpreted.

Imbibition Phenomenon, Linear equation, Non-linear diffusion equation, Homotopy Perturbation method.

" A STUDY OF LINEAR AND NON LINEAR DIFFUSION EQUATIONS ARISING IN FLUID FLOW THROUGH POROUS MEDIA BY HOMOTOPY PERTURBATION METHOD", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 12, page no.650-659, December-2018, Available :http://www.jetir.org/papers/JETIR1812393.pdf

" A STUDY OF LINEAR AND NON LINEAR DIFFUSION EQUATIONS ARISING IN FLUID FLOW THROUGH POROUS MEDIA BY HOMOTOPY PERTURBATION METHOD", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 12, page no. pp650-659, December-2018, Available at : http://www.jetir.org/papers/JETIR1812393.pdf