Estimating spatially variable representative elementary scales in fractured architecture using hydraulic head observations

Abstract

Water resources within large‐scale fractured aquifers are typically evaluated using continuum models. While any arbitrary scale of continuum can be imposed to represent fracture architecture, using the representative elementary volume eliminates errors that result from estimating network connectivity. In traditional theory, representative elementary scales (RES) are equal in magnitude and geometry throughout a domain and are normally determined using a structural indicator such as porosity or effective hydraulic conductivity. We present a fluid‐based methodology, analyzing scale‐dependent energy variation, to estimate RES using relatively low cost, readily available hydraulic head data. Hydraulic head predictions of RES (HYRES) reveal a spatial variation in elementary scale consistent with the flow field and fracture architecture. Porosity predictions of RES (PORRES) incorporate the structural effect of disconnected fracture regions but do not account for fluid behavior. RES estimated from hydraulic conductivity (KRES) are sensitive to fracture connectivity, which controls fluid movement, but are difficult to quantify because of scale and spatial variability. HYRES may be the superior approach for evaluating water resources because it is sensitive to fracture connectivity and avoids complications with scale and spatially dependent averaging. Our method is sensitive to fracture density, clustering, connectivity, and flow direction, but is insensitive to the magnitude of hydraulic gradient. HYRES is a novel approach to estimating spatially variable RES that improves water resource evaluation and flow characterization in fractured aquifers.