A mathematical model for spontaneous imbibition as a recovery mechanism

Abstract

Spontaneous imbibition is a process where the wetting fluid displaces the non-wetting fluid in a porous medium by means of capillary forces. Spontaneous imbibition plays a significant role in the recovery of hydrocarbons, especially from fractured reservoirs and particularly where the matrix has low permeability. An increasing portion of remaining reserves in both oil and gas reservoirs are retained in low permebility rocks and in these reservoirs spontaneous imbibition is the key recovery mechanism. In this study we have derived an analytical solution of a model that describes counter-current imbibition, in terms of a non-linear diffusion equation, based on ideas presented in a paper by Tavassoli, Zimmerman and Blunt [19]. We have also considered a discrete scheme for the equation which allowed us to compute a numerical solution of the model. We have then used the solutions to gain insight into which parameters that control the oil recovery by spontaneous imbibition. A comparison of the numerical and the analytical solution have been made to test the validity of the analytical solution.