Porous media equivalents for networks of discontinuous fractures

TLDR

The study uses flow theory in fractured rock and anisotropic porous media to define when a fractured rock can be treated as a continuum, requiring negligible permeability change with volume and a predictive permeability tensor. A realistic two‑dimensional fracture system model was built, assigning fracture shape, size, orientation, and location as random variables based on field data, and then subjected to simulated flow tests. Flow‑test simulations produced permeability ellipses that reveal fractured rock does not always act as a homogeneous anisotropic medium, but behaves more like a porous medium when fracture density is high, apertures are uniform, orientations are varied, and larger samples are used, suggesting the new tool will improve field‑data analysis.

Abstract

The theory of flow through fractured rock and homogeneous anisotropic porous media is used to determine when a fractured rock behaves as a continuum. A fractured rock can be said to behave like an equivalent porous medium when (1) there is an insignificant change in the value of the equivalent permeability with a small addition or subtraction to the test volume and (2) an equivalent permeability tensor exists which predicts the correct flux when the direction of a constant gradient is changed. Field studies of fracture geometry are reviewed and a realistic, two‐dimensional fracture system model is developed. The shape, size, orientation, and location of fractures in an impermeable matrix are random variables in the model. These variables are randomly distributed according to field data currently available in the literature. The fracture system models are subjected to simulated flow tests. The results of the flow tests are plotted as permeability ‘ellipses.’ The size and shape of these permeability ellipses show that fractured rock does not always behave as a homogeneous, anisotropic porous medium with a symmetric permeability tensor. Fracture systems behave more like porous media when (1) fracture density is increased, (2) apertures are constant rather than distributed, (3) orientations are distributed rather than constant, and (4) larger sample sizes are tested. Preliminary results indicate the use of this new tool, when perfected, will greatly enhance our ability to analyze field data on fractured rock systems. The tool can be used to distinguish between fractured systems which can be treated as porous media and fractured systems which must be treated as a collection of discrete fracture flow paths.