Improved Prediction of Oil Recovery From Waterflooded Fractured Reservoirs Using Homogenization

Most 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. We use homogenization to obtain an improved flow model in fractured media, leading to an integro-differential equation; also called the boundary-condition (BC) approach. We formulate a well-posed numerical 3D model for the BC approach. This paper derives this numerical model to solve full 3D integro-differential equations in a field reservoir simulation. We compare the results of the upscaled model with ECLIPSE (TM) results. For the interpretation, it is useful to define three dimensionless parameters that 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 of the same order of magnitude as the imbibition time. However, if the travel time is shorter or longer 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.