Rigorous Modelling of Fractures in a Porous Medium

Abstract

While fractured formations are possibly the most important contributors to the oil production world-wide, modelling fractured formations with rigorous treatments has eluded reservoir engineers in the past. To-date, one of the most commonly used fractured reservoir model remains the one that was suggested by Warren and Root more than three decades ago. In this paper, a new model for fractures embedded in a porous medium is proposed. The model considers the Navier Stokes equation in the fracture (channel flow) while using Brinkman equation for the porous medium. Unlike the previous approach, the proposed model does not require the assumption of orthogonality of the fractures (sugar cube assumption) nor does it impose incorrect boundary conditions for the interface between the fracture and the porous medium. The proposed model is derived through a series of finite element modelling runs for various cases using Navier Stokes equation in the channel while maintaining Brinkman equation in the porous medium. Various cases studied include different fracture orientations, fracture frequencies, fracture width, and the permeability of the porous medium. Finally, a series of numerical runs also provided validity of the proposed model for the cases for which thermal and solutal effects are important. Such a study of double diffusive phenomena in the context of fractured formations has not been reported before.