A MATHEMATICAL-MODEL FOR FLOW AND SOLUTE TRANSPORT IN NONHOMOGENEOUS ROCK FRACTURES

An analytical solution presented in a previous paper is incorporated into a numerical algorithm for determining water flow and solute transport in a single rectangular rock fracture with variable aperture and surface roughness. The flow is laminar and steady. Head and velocity are predicted analytically at each point in the fracture using the integral transform method. It is assumed that the solute is non-reactive and its transport is entirely advective. The method of characteristics is used to determine the trajectories of fluid particles in the flow field. It is shown that heterogeneities in the void space of a fracture and the associated channel flow create ''fingering'' of the solute and an apparent dispersion even if dispersion is not explicitly accounted for in the transport equation. Numerical examples are presented for flow and transport in fractures with rough surfaces having fractal dimensions ranging between 2.0 and 2.3. It is found that the flow rate passing through those fractures is about 65-95% of the flow rate that would pass if the fractures were modeled as two parallel plates with a uniform aperture equal to their average aperture and the cubic law was valid. Also, estimating the time of breakthrough for solute transport in rough fractures using their average apertures can be misleading. The actual time of breakthrough and the breakthrough curves can be determined using the technique presented herein which requires a detailed description of the fracture void space. Finally, it is shown that the conventional one-dimensional advection-dispersion model using a constant dispersion coefficient does not simulate accurately the apparent dispersion created by channel flow in fractures if their hydraulic or average apertures are used to compute the seepage velocity.