Abstract: Amathematical model for Non-Darcy flow of two-phase fluid through anisotropic double-porosity media with a vertically fractured well working is established. Numerical solution to the model is presented by using finite difference method. An example is given and discussed. Distribution of water saturation in the direction of radius, maximum permeability and minimum permeability and changeof iso-saturation level with time are obtained. Results show that: (1) the iso-saturation level moves faster and water breaks through the well sooner in the directionof the larger permeability than in that of the smaller; (2) the imbibition makes velocity of the level movement become smaller and time of water breakthrough get larger; (3) the level moves and water breaks through the well faster in Non-Darcy flow than that in Darcy flow; and (4) the larger the injection rate is, the faster the level moves and the sooner water breaks through the well. The injection rate mustn’t be too large before
water breaks through the well so that the imbibition can play an important role in water-flooding development of the low-permeability double-porosity reservoir. And the injection rate should be raised appropriately after water breaks through the well in order to weaken the influence of Non-Darcy flow on the development.

Key words: anisotropy, doubl media, vertically fracture well, two-phase fluid, Non-Darcy flow