Comparison of Numerical Methods to Solve Warren-Root PDE of Naturally Fractured Reservoirs

Based on Barren blatt et al. (1960) model on fluid flow in fractured media, Warren and Root (1963) introduced the double porosity concept into petroleum engineering [1, 2]. In their model, a fractured medium comprises of two overlapping media: matrix and fracture where the matrix has a low permeability and a high fluid storage and fracture has a high permeability with a low storage capacity [3]. In this study, Warren-Root PDE (Partial Differential Equation) is numerically modeled based on both finite difference and finite element approaches. The results have been verified with analytical solution obtained by Laplace transformation to examine that which method is more appropriate to model naturally fractured reservoir behavior. Based on comparison of numerical methods with exact solution, it has been concluded that finite element applied by COMSOL multi physics software provides exact results than finite difference method.

Keywords:

fractured reservoirs , boundary condition , Warren-Root PDE , finite element , finite difference , Laplace transformation