The Transport of Heat by Flowing Groundwater in a Discrete Fracture
Abstract
In typical theoretical or experimental studies of heat migration in discrete fractures, conduction
and thermal dispersion are commonly neglected from the fracture heat transport equation,
assuming heat conduction into the matrix is predominant. In this study analytical and numerical
models are used to investigate the significance of conduction and thermal dispersion in the plane
of the fracture for a point and line sources geometries. The analytical models account for
advective, conductive and dispersive heat transport in both the longitudinal and transverse
directions in the fracture. The heat transport in the fracture is coupled with a matrix equation in
which heat is conducted in the direction perpendicular to the fracture. In the numerical model,
the governing heat transport processes are the same as the analytical models; however, the matrix
conduction is considered in both longitudinal and transverse directions. Firstly, we demonstrate
that longitudinal conduction and dispersion are critical processes that affect heat transport in
fractured rock environments, especially for small apertures (eg. 100 μm or less), high flow rate
conditions (eg. velocity greater than 50 m/day) and early time (eg. less than 10 days). Secondly,
transverse thermal dispersion in the fracture plane is also observed to be an important transport
process leading to retardation of the migrating heat front particularly at late time (eg. after 40
days of hot water injection). Solutions which neglect dispersion in the transverse direction
underestimate the locations of heat fronts at late time. Finally, this study also suggests that the
geometry of the heat sources has significant effects on the heat transport in the system. For
example, the effects of dispersion in the fracture are observed to decrease when the width of the
heat source expands.