Effects of non-darcy flow on heat-flow coupling process in complex fractured rock masses

Abstract

This paper presented a heat-flow coupling model for simulation of heat transfer process in complex fractured rock masses considering non-Darcy flow. Firstly, the Forchheimer equation and the Reynolds equation were coupled to obtain the governing equation to describe the non-Darcy flow behaviors. Then, combined with the heat transfer equation and considered the heat exchange process between fractures and rock matrix, the heat-flow coupling model was established. The model was solved by the finite element method. The calculation results of the non-Darcy flow model were compared with the fluid flow test results of crossed fracture and complex fracture network models and a good agreement was observed. The numerical simulation results of non-Darcy flow and heat transfer model were compared with analytical solution of flow-heat coupling in a single fracture, and the numerical solution and the analytical solution agreed well. Finally, a two-dimensional complex fracture network was generated for numerical experiments, and effects of equivalent hydraulic aperture df and hydraulic gradient J on the flow behaviors and the heat-transfer process in complex fractured rock masses were systematically discussed. Results showed that the proposed model can well describe the non-Darcy flow characteristics as well as the heat-flow coupling process in complex fracture networks. Considering the non-Darcy flow behaviors, the average temperature of the outlet dropped slower under non-Darcy than which under Darcy flow. It was also found that effects of non-Darcy flow on the heat transfer process will be more significant as the hydraulic gradient or the equivalent hydraulic aperture increases.