Solution by Group Invarient Method of Imbibition Phenomenon Arising in Fluid Flow Through Homogenos Porous Media

In this paper, primary counter-current imbibition in homogenous porous matrix is studied, where a wetting phase displaces non-wetting phase simultaneously, such that the non-wetting phase moves in the opposite direction to the wetting phase. In the present case the force mediating the displacement is only capillary pressure with wetting and non-wetting fluids flowing in opposite direction. Governing non-linear differential equation has been formulated and solved by using the group theoretic analysis method; an approximate expression for the wetting phase saturation has been obtained and also its graph has been obtained by using Matlab coding. Also saturation of injected fluid S_w increases at distance x increases for a fixed time t>0. It is concluded that after a long time t saturation of injected fluid will be closer to its minimum value.