Numerical Evaluation of Effective Unsaturated Hydraulic Properties of Fractured Rocks using a Stochastic Continuum Approach

Abstract

This study builds on past studies that have investigated the effective properties of unsaturated porous media and merges stochastic continuum concepts to develop a numerical procedure for estimating the effective flow parameters that are independent of pressure head or saturation. The procedure involves the development of a numerical permeameter based on randomly generated, spatially correlated fields of fundamental fracture properties such as spacing and aperture. Local values of hydraulic conductivity, and the van Genuchten fitting parameters α and n in this random field are computed from local values of mechanical aperture and spacing based on the cubic law and relationships established from pore‐scale fracture simulations. By considering multiple realizations of these spatially correlated fields and by running the numerical permeameter over a range of effective saturations and flow rates, outputs are generated that can be fit with the standard van Genuchten model to estimate block effective values of saturated hydraulic conductivity and the van Genuchten unsaturated hydraulic parameters of a fracture continuum at the field scale. These parameters can then be incorporated to conventional numerical simulators originally developed for porous media. The study shows that reasonable approximations to the results obtained through computationally demanding stochastic simulations can be developed based on estimates of the mean fracture spacing and aperture. Although the example application assumes the presence of an impermeable rock matrix, the hydraulic properties estimated for the fracture continuum with this methodology can be combined with those measured or similarly estimated for a matrix continuum in dual‐permeability continuum models.