Effective Permeability Calculation Using Boundary Element Method in Naturally Fractured Reservoirs

Abstract

A model is presented to calculate the effective permeability tensor in naturally fractured reservoirs using Boundary Element Methods (BEM). Arbitrary fractures of different scales based on their length are considered. Interface boundary condition is used to model the short fractures as an enhancement of matrix permeability. Long fractures, on the other hand are treated as source/sink in the corresponding blocks. Periodic boundary condition is applied to the grid-block boundaries to calculate the elements of effective permeability tensor. Darcy's law and Navier-stoke's equation are applied to fluid flow in rock matrix and fractures, respectively. An important feature of this approach is that the fluid flow in matrix-fracture interface is coupled by Poisson's equation and fluid flow in the rest of the matrix is formulated by Laplace's equation. This paper also presents an innovative approach to optimization and parallelization of the model by High Performance Computing (HPC) techniques. The model has been validated against analytical results and applied to a typical case where arbitrary fractures of different sizes are assumed within the grid blocks. The effective block permeability tensors can be implemented into a reservoir simulator to calculate fluid flow through the naturally fractured reservoirs.