Analytical and Numerical Modelling of Thermal Conductive Heating in Fractured Rock

Abstract

Analytical and numerical modelling studies were conducted to assess the performance of thermal conductive heating (TCH) systems for the purpose of contaminated site remediation. Modelling was conducted in a fractured bedrock environment containing a system of parallel, equally-spaced horizontal fractures.

A semi-analytical solution to the two-dimensional heat conduction equation was developed and used to study temperature distributions between two thermal wells. A sensitivity analysis was conducted to assess the relative importance of hydrogeological parameters (hydraulic gradient, fracture aperture, fracture spacing) and rock material properties (density, thermal conductivity, heat capacity). Hydrogeological parameters were far more important than rock material properties in determining treatment zone temperature distributions. Knowledge of the bulk groundwater influx may be sufficient to predict the temperature within the treatment zone for low to moderate values of influx.

To further the analysis, numerical modelling was employed. A three-dimensional domain was constructed, representing a symmetrical portion of a heater well cluster. Simulations were run for different combinations of bulk permeability, fracture spacing, matrix permeability, and matrix porosity. Flow concentration in fractures had a significant effect on treatment zone temperature distributions when bulk permeability was high. For low values of bulk permeability, the minimum treatment zone temperature changed by less then 7% when modelling the fractured medium as an equivalent homogeneous porous medium.

Fracture spacing significantly influenced the time needed reach complete steam saturation, even in cases where it did not affect temperature distributions. A pressure rise may occur in the matrix as water expands thermally, elevating the boiling point of water. The magnitude of the pressure rise is affected by the distance to the nearest fracture, as well as the matrix permeability and porosity. For a given bulk permeability, the time needed to reach complete steam saturation will be lengthened by an increase in fracture spacing, an increase in matrix porosity, or a decrease in matrix permeability. Of these parameters, the matrix permeability is the most significant.

The time needed to reach complete steam saturation in the matrix cannot be predicted if the fracture spacing, matrix permeability, and porosity are not known. Further, a clear temperature plateau is not observed during boiling in the matrix, posing a difficulty in monitoring thermal treatment, where temperature measurements may be the only information available.