Abstract
Simulations of waterflooding in fractured media are based on the Warren and Root (WR) approach, which uses an empirical transfer function between the fracture and matrix block. Arbogast used homogenization to formulate an improved flow model in fractured media, leading to an integro-differential equation; also called the boundary condition (BC) approach. A wellposed numerical 3D model for the BC approach has been formulated. This paper derives this numerical model to solve full 3D integro-differential equations. The results of this model are compared with the ECLIPSE results. For the interpretation it is useful to define three dimensionless parameters, which characterize the oil production in fractured media. The most important of these parameters is a Peclet number defined as the ratio between the time required to imbibe water into the matrix block and the travel-time of water in the fracture system. The results of the WR approach and the BC approach are in good agreement when the travel-time is longer than the imbibition time. However, for times with the same order of magnitude and for the travel time shorter than the imbibition time, the approaches give different results. The BC approach allows the use of transfer functions based on fundamental principles, e.g., the use of a rate dependent capillary pressure function. When implemented, it can be used to improve recovery predictions for waterflooded fractured reservoirs.
