A composite element solution of convection-conduction heat transfer in fractured rock mass

Abstract

A reliable and efficient numerical model is required for predictions of convection-conduction behavior in fractured rock mass to obtain a better understanding of heat transfer processes within it. This study presents a composite element formulation that addresses the problem of heat transfer via fluid flow in fractured rock mass. The three-dimensional convection-conduction equation is converted to an equivalent variational principle, and the governing equations of the rock sub-elements and fracture segments are subsequently deduced based on the composite element method (CEM). The developed CEM algorithm takes into account the heat transfer inside the fracture fluid and inside the rock matrix, respectively, as well as the heat exchange between the fracture fluid and the adjacent rock blocks. The CEM model allows for the simulation of the discontinuous characteristics of temperature across the fractures via a simplified computational mesh that is generated without restrictions, and the fractures are explicitly and automatically embedded into the mapped composite element via the CEM pre-process program. The composite element contains fracture segments exhibiting arbitrary shapes, the temperatures of fractures are interpolated from their corresponding mapped nodal temperatures of rock sub-elements delimited by the fractures, and, therefore, the temperature of the fracture is not necessarily continuous. The performance of the developed CEM algorithm is verified by comparisons with analytical solutions, a case study of lab experiments and numerical results, which demonstrate the validity and advantages of the composite element solution.