Three different methods, the discrete fracture, dual and single continuum approaches, are currently used for simulation of naturally fractured reservoirs. A dual porosity or dual permeability approach is applied in simulation when fractures are well developed to form a flow network. On the other hand, the single continuum model, 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 addresses several issues for characterizing naturally fractured reservoirs: an effective approach to determine equivalent or effective permeability tensors, the representative elementary volume (REV) for effective permeability determination, and applications of the permeability tensor to flow simulation.
The complex variable boundary element method is used to compute potential field and streamlines in two-dimensional fracture systems under the periodic boundary conditions. The complex potential at a point is expressed as summation of potentials for matrix, fractures, and fracture intersections. The fracture system is assumed to comprise infinitely thin fractures of infinite conductivity, and allowed to include discrete or intersected fractures.
Effective permeabilities calculated for stochastic fracture distributions are correlated with the fracture geometric parameters: the total length, the mean length, and the mean orientation angle. Effects of length and orientation variations are minor, and can be ignored. Non-parametric regression shows roughly equal levels of influence of the geometric parameters on both diagonal and off-diagonal elements of the permeability tensors. A REV study for stochastic distributions demonstrates behavior of effective permeability depending upon the area of the effective permeability calculations. Effective permeabilities estimated for regional fracture type systems show a strong effect of the fracture intersections of which flow potential reduces the diagonal elements of the effective permeability tensors. Finally, the effective permeabilities are applied to a simulation model to calculate tracer propagation.