Analytical Model for Heat Transfer in a Discrete Parallel Fracture–Rock Matrix System

Abstract

Mass transport and heat transfer in the single fracture situated in the rock matrix have been investigated extensively in the past decades. Extended from the single fracture, the model of parallel fractures in the rock matrix considers the interactions of multiple fractures and the ambient rock matrix. Heat transfer in such discrete fractures is important to understand thermal energy transfer in the fractured porous media. In this study, an analytical solution is developed for transient heat transfer in discrete parallel fractures in the rock matrix. The newly proposed model accounts for thermal convection, conduction, and dispersion in the fractures, transverse thermal conduction in the rock matrix, and the interactions between parallel fractures. The analytical solutions of the spatiotemporal temperature distributions in the fractures and rock matrix are derived in the Laplace domain and verified with the previous study. The results illustrate that: (1) the fracture aperture and spacing are important to the temperature evolutions in the system. Heat transfers faster when discrete parallel fractures are wide and closely spaced; (2) different roles of longitudinal thermal conduction are observed at high and low flow velocities in the fractures; (3) thermal dispersivity in the fractures is important for temperature evolution and should not be ignored; (4) when the fractures are closely spaced, transverse thermal conduction in the rock matrix has minor influence on fracture temperature. It becomes important when the fractures are sparsely distributed; and (5) the sensitivity analysis indicates that the parallel fracture-rock matrix is most sensitive to fracture thermal dispersivity.

An Analytical Solution for Variable Viscosity Flow in Fractured Media: Development and Comparative Analysis With Numerical Simulations

“…Previous analytical solutions typically concentrated on specific fracture setups. For instance, Zhang and Ayala (2019) developed solutions for a single fracture with changing viscosity, while solutions for flow through parallel fractures were addressed by Zhou and Wang (2023), and Toller (2022) focused on intersecting fractures.…”

Effects of Soil Type and Thermal Boundary on Predicting Temperature Profiles and Groundwater Fluxes

“…The subsurface heat transfer induced by groundwater flow is frequently modeled by a one‐dimensional (1D) heat conduction‐advection equation, which is solved by numerical approaches (Voytek et al 2014; Koch et al 2016; Li et al 2019) or analytical methods (Reiter 2001; Weir 2009; Zhou and Wang 2022). The numerical approaches include finite‐difference, finite‐element, finite‐volume, and other schemes.…”