Laminar and turbulent groundwater flows in confined two- and three-dimensional discrete fracture networks

Abstract

Using laminar or turbulent flow equations indiscriminately to describe groundwater flows in fracture networks may result in large errors. We propose a new method for simulating steady-state groundwater flows in two- and three-dimensional fracture networks by separating laminar flows and turbulent flows in individual fractures. Poiseuille's law is employed when the flow is laminar, while Swamee and Jain formula is utilized when the flow is turbulent. The model results are first compared to recently measured field groundwater flow data in a mining tunnel network. The effect of hydraulic gradient, aperture, fracture width in the third dimension, and fracture density is then examined. Using the laminar flow equation indiscriminately in all fractures overestimates groundwater flowrates, whereas using the turbulent flow equation underestimates them. The aperture contrast of large and small fractures has a significant impact on the potential errors of indiscriminately applying the laminar or turbulent flow equation and the flowrate difference between the three-dimensional and two-dimensional fracture networks. Total groundwater flowrates increase with fracture density in both three-dimensional and two-dimensional fracture networks, with the largest increase occurring when additional fractures are introduced parallel to the hydraulic gradient. The new approach may be utilized to estimate hydraulic head distribution and groundwater flowrate according to the crack patterns and geometric properties of the fractured rock.