Effective Permeability Estimation for Simulation of Naturally Fractured Reservoirs

Abstract

Abstract Appropriate modeling of naturally fractured reservoirs is one of the most important and challenging issues in reservoir characterization. In simulation, a double porosity or dual permeability model is applied when fractures are well developed to form a fracture network. On the other hand, the single-continuum approach, where the fracture system is represented by effective permeability, is commonly used if fractures are discrete or disconnected. Focusing on the latter case, this paper proposes a semi-analytical technique to evaluate effective permeability for periodically or randomly fractured media including infinitely thin, infinite-conductivity fractures. The complex variable boundary element method is used to compute potential and stream functions in the two-dimensional space for discretely distributed fracture system under the periodic boundary conditions. Effective permeability is evaluated first for discrete fracture systems of regular patterns as well as a single inclined fracture to demonstrate the validity of the method. 500 distributions of stochastic fractures are next generated to establish correlation between effective permeability and the fracture statistics, i.e., total length L, mean length m, and standard deviation of fracture length σ. Sensitivity to the parameters shows that the incremental gain of effective permeability is proportional to L, that the larger m, the larger effective permeability, and that non-zero σ increases effective permeability. The effective permeability tensors are also determined for oriented fractures. Analyses by non-parametric regression show that the diagonal elements, kxx and kyy are highly affected by the angle between the oriented fractures and the pressure gradient, while the off-diagonal elements kxy and kyx are strongly affected by both the total length and the angle.