The effect of fracture aperture and matrix permeability on suitability of the equivalent porous medium model for steady-state flow in fractured porous media

Abstract

The equivalent porous medium (EPM) method is an efficient approximate processing method for calculating groundwater yield taking into account the equivalent permeability coefficient of a fractured geological medium. The EPM method finds wide application in addressing various hydrogeological problems ranging from local to regional scales; however, the adequacy of the EPM model for evaluating water head and velocity distributions has not been comprehensively assessed. This study quantitatively investigated the influence of fracture and matrix permeability on the EPM model’s suitability, defined by a 15% threshold for hydraulic-head prediction error, via numerical simulations. A fractured porous media system (fracture-matrix system) was considered as the prototype, and the EPM model simulation results were compared with those obtained using the discrete fracture-matrix (DFM) model. Results indicate a decrease in EPM suitability with larger fracture apertures. With a constant fracture aperture, the suitability of the EPM model increases as the matrix permeability increases. The size of the fracture aperture significantly affects the suitability of the EPM model, and it determines the point at which its suitability begins to increase and eventually stabilize. The fitted curve depicting the influence of matrix permeability on the suitability of the EPM model conforms to the Boltzmann formula, and the fracture aperture is linearly related to the parameter x₀ in the formula. The derived empirical formula enables quantitative assessment of the impact of fracture and matrix permeabilities on the suitability of the EPM model in fractured porous media.