Abstract: A mathematical model for two-phase flow through dual porosity media with imbibition is an integral and differential e-quation with initial and boundary conditions. Such a model is difficult to obtain accurate andlytical solutions. A new concept of taking drainage front as moving outer boundary is proposed so that numerical solution to the model can be found by using a fi-nite difference approach and extrapolation method. Relative permeability curve in fracture system without simplifying assumption is adopted in the model. Results show that imbibition has greater effects on distribution of water saturation and that moving velocity of the water-oil displacement front has nothing to do with intensity of imbibition. This conclusion is in good agreement with that obtained by Chen-LiuTs assumption about relative permeability in fracture system and from characteristic method. The method pro-posed in this paper is much better solving nonlinear problems.

Key words: dual porosity media, imbibition, percolation, finite difference method, extrapolation method