Scale dependence of continuum models for fractured basalts

Abstract

Numerical simulations are carried out to determine the scale above which an equivalent porous medium (EPM) model can be used to represent flow through the dense interiors of fractured basalts. Steady laminar flow is assumed to occur through the interconnected network of conduits formed by the intersecting column‐defining fracture patterns of the basalt dense interiors. The basalt rock matrix is considered to be impermeable. A porous medium equivalence is established in terms of fluid (Darcian) fluxes. A polar plot for the equivalent hydraulic conductivity is used to test whether a given fractured basalt system can be approximated as an EPM. For interconnected colonnade network models of filled or unfilled fractures with uniform apertures and a column diameter of 1 m, EPM models are appropriate at a length scale of approximately 6 times the column diameter. For network models of filled or unfilled fractures with a lognormal aperture (b, millimeters) distribution (mean In b=−1.945 and σln b=0.896), EPM models can be justified at length scales of approximately 22 and 27 times the column diameter, respectively. The computed equivalent K values for clay‐filled fractures compare favorably with the field‐measured data. This suggests that a model comprised of an interconnected network of filled fractures may not be an unlikely representation of flow through the dense interiors at the small scales considered in this study. Several limitations of the study are noted.