New Approach for Simulating Groundwater Flow in Discrete Fracture Network

Abstract

In this study, a new approach is developed to compute groundwater flow rate and hydraulic head distribution in a two-dimensional discrete fracture network (DFN) in which both laminar and inertial flows coexist in individual fractures. The potential errors in both flow rate and hydraulic head, from the approach based on uniform flow assumption in relation to DFN and flow characteristics, are examined. The cubic law is used to calculate hydraulic head distribution and flow behaviors in fractures in which flow is laminar, whereas Forchheimer’s law is used to quantify inertial flow behaviors. The Reynolds number is used to distinguish flow characteristics in individual fractures. The combination of linear and nonlinear equations is solved iteratively to determine flow rates in all fractures and hydraulic heads at all intersections. Applying the cubic law in all fractures regardless of actual flow conditions overestimates the flow rate when inertial flow may exist whereas applying Forchheimer’s law indiscriminately underestimates the flow rate in the network. The contrast of apertures of large and small fractures in the DFN has significant influence on the potential error of using only the cubic law or Forchheimer’s law. Both the cubic law and Forchheimer’s law simulate similar hydraulic head distributions, as the main difference between these two approaches lies in predicting different flow rates. Fracture irregularity does not significantly affect the potential errors from using only the cubic law or Forchheimer’s law if the network configuration remains similar. The relative density of fractures does not significantly affect the relative performance of the cubic law or Forchheimer’s law.