A generalized formulation of the Buckley-Leverett displacement in naturally fractured porous media and an efficient solution by the method of differential quadrature and cubature for waterflooding are presented.
Waterflooding is one of the economically viable techniques for recovery of additional oil following the primary recovery. However, the applications to naturally fractured reservoirs have certain challenges that arise concerning the prediction of oil recovery. Waterflooding in clayey formations involves the adverse effects of formation damage which can reduce its efficiency. The characterization of naturally fractured porous formations still needs further research. The process of matrix-to-fracture transfer of oil by imbibition of water is not well understood. It is still not clear which modeling approach amongst the various alternatives would accurately describe the mechanism of oil recovery and flow of fluids in naturally fractured formations.
Numerous publications dealing with recovery of oil from reservoirs have appeared in the literature. By-and-large the modeling approaches proposed in most of these publications are highly computationally intensive or impractical for large field scale applications. Therefore, in search of a more practical approach, Kazemi et al have adopted the modeling approach by deSwaan and have demonstrated that the deSwaan approach provides certain advantages over the everpopular multiple porosity approaches reported in various publications. Basically, deSwaan's approach is a representative volume averaged description of the immiscible displacement process in fractured porous media. In this approach, deSwaan represented the matrix to fracture oil transport via a source term added to the conventional Buckley-Leverett equation by an empirical function given by Aronofsky, et al. Kazemi et al modified this function into a multi-parameter empirical function. Subsequently, Civan theoretically derived a similar function with only two parameters based on a hypothetical mechanism of oil transfer from matrix to fracture.
The primary advantage of Civan's theoretical model is the reduction of the number of empirical constants while providing insight into the mechanism of oil transfer from matrix to fracture by imbibition of water. The two constants in Civan's model are considered as being representative volumetric average parameters. The values of these parameters depend on various conditions including