Quantitative Characterization of Heat Transport in Fractured Rock

Abstract

The quantitative characterization of heat transport in fractured rock is a crucial yet challenging task due to the complexity of the heat exchange between the fluid and solid phases and the specific applications of interest. The aim of this study was to identify the key variables controlling the complex thermohydrological processes and to estimate the temperature variances fully accounting for the properties of heat source, groundwater influx, and rock matrix. The study involved sensitivity analyses using a proposed implementation scheme based on Latin-hypercube-one-at-a-time (LH-OAT) method using numerical simulation. The numerical model was developed with a domain of 100 × 50 × 25 m including a top fractured rock layer (15 m), a bedrock layer beneath (10 m), and a heating area. Further heat dissipation study was conducted using a detailed hydrogeological data set from a well-characterized field site. In addition, a 2-D semi-analytical solution was derived to estimate the fracture or rock matrix temperatures. The sensitivity analyses using the modified LH-OAT method successfully ranked the variables based on their significance on matrix temperature variances: heat source > groundwater influx > rock matrix. The heat source scaling was demonstrated to have a decisive impact on temperature variance in the input variability space, yet it appears to have strong correlations with other factors. A correlation between the heat dissipation effect in the heating zone and the transmissivity of fractured rock was also identified based on the case study by numerical modeling. A mathematical relationship between groundwater influx, heat source, and temperature variance was described using the derived semianalytical solution that fully coupled the advective and conductive heat transport in the fracture fluid and heat conduction in the rock matrix. The generality of the solution greatly facilitates the definitions of the heat source dimensions and the energy delivery strength. The transient temperature analyses highlight the significance of a heat source in the rock matrix and imply that the spatial temperature variation is strongly associated with heat delivery strength. The early time temperature variances can be attributed to the heat source configuration and the later time temperature is mainly controlled by the amount of delivered energy.