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 untilled 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 untilled fractures with a lognormal aperture (b, millimeters) distribution (mean In b --1.945 and øln 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. 1.

Evaluation of the representative elementary volume (REV) of a fractured geothermal sandstone reservoir

“…For such cases, the equivalent porous medium (EPM) approach is widely used (e.g. Long et al 1982;Khaleel 1989;Lee et al 1995;Min et al 2004;Blum et al 2005Blum et al , 2009). This conceptual model implies that fluid flow is similar to that through porous media having equivalent hydraulic properties as a given network with fractures explicitly represented.…”

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

“…To diminish the effect of random numbers, a large number of DFN realizations are required to determine the REV (Bear 1972;Oda 1988;Khaleel 1989;Kulatilake and Panda 2000;Brown et al 2000;Esmaieli et al 2010). When the REV does exist, it can be used to define the minimum volume of a sampling domain of a fracture network, beyond which the permeability of the sampling domain remains essentially constant (Long et al 1982;Zhou and Yu 1999;Chalhoub and Pouya 2008;Maghous et al 2008).…”

Flow and Transport in Fractured Rocks

“…The resulting S‐shaped breakthrough curve indicated the possibility of regarding this network as a single continuum. Hull and Clemo [1987] and Khaleel [1989] also studied the use of continua for fracture networks. Hsieh [1987] compared cross‐hole tests at two sites to examine the anisotropy in hydraulic conductivity.…”