A mathematical model of imbibition phenomenon in heterogeneous porous media during secondary oil recovery process

The present paper discuses the solution of one-dimensional mathematical model for counter-current water imbibition phenomenon occurring into an oil-saturated cylindrical heterogeneous porous matrix. During secondary oil recovery process when water is injected in oil formatted heterogeneous porous matrix then at common interface the counter current imbibition phenomenon occurs due to the difference of viscosity of water and oil which satisfies imbibition condition Vi=-VnVi=-Vn. The governing differential equation of this phenomenon is in the form of non-linear partial differential equation which has been converted into non-linear ordinary differential by using similarity transformation. The solution of this problem has been obtained in term of power series by using appropriate boundary condition at common interface. The graphical presentation is obtained by using MATLAB and final solution physically interpreted.

Graphical abstractSi(X,T)=f(0)+X2Tf′(0)+X28(T)2f″(0)+X348(T)3f′(0)+X4384(T)4fiv(0)+⋯Power series solution for non linear partial differential equation of counter-current imbibition phenomenon in heterogeneous porous media during secondary oil recovery process gives the saturation of injected fluid.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A mathematical model of counter-current imbibitions phenomenon in heterogeneous porous media is derived. ► A solution of non-linear partial differential equation for this phenomenon obtained in terms of power series. ► The solution described the saturation of injected fluid during secondary oil recovery process. ► The comparative study of this phenomenon in heterogeneous and homogeneous porous media is numerically explained. ► The results are extrapolated.