THE TRANSPORT OF HEAT BY FLOWING GROUNDWATER IN A DISCRETE FRACTURE

Coupled thermal-hydrological processes in fractured rock are of primary importance to nuclear waste repository safety assessments and thermal remediation methods. In typical theoretical or experimental studies of heat migration in discrete fractures, conduction and thermal dispersion are commonly neglected from the heat transport equation for the fracture, assuming heat conduction into the matrix is predominant. In this study existing one-dimensional and two-dimensional analytical solutions of the heat transport equation are modified to investigate the significance of conduction and thermal dispersion in the plane of the fracture. Natural flow conditions are considered with fracture aperture ranging from 100 µm to 1000 µm and flow velocity ranging from 1 m/day to 50 m/day. Thermal dispersion is assumed to increase linearly with flow velocity. In general, we demonstrate that longitudinal conduction and dispersion within the fracture plane are critical processes which significantly affect the position of the heat front in the fracture and should not be ignored. The one-dimensional analysis shows more than 20 % relative error in the position of the heat front could result by neglecting longitudinal dispersion in the fracture heat transport equation under many common flow conditions. In the two-dimensional analysis, dispersion in the transverse direction significantly retards the movement of the heat front. Neglecting dispersion could overestimate the position of the heat front by more than 40 % at late time. We also found that longitudinal conduction can only be ignored for conditions with large aperture and high flow velocity.