Effect of nonlinear seepage on flow and heat transfer process of fractured rocks

A numerical model for nonlinear flow and heat transfer in a fractured rock mass is proposed. First, the Forchheimer equation and the Reynolds equation are coupled to obtain the nonlinear seepage control equation, then combined with the heat transfer control equation, considering the heat exchange between the fracture and the rock matrix, the effect of nonlinear seepage on the flow and heat transfer process of fractured rock mass is studied. The effectiveness of the nonlinear seepage model for fractured rock mass is verified by comparing the experimental data of nonlinear seepage in fracture network. Finally, the nonlinear seepage heat transfer analysis is carried out by two-dimensional single-fracture and three-dimensional fracture network models.The result shows that the model can accurately describe the nonlinear seepage characteristics of fractured rock masses. As the fracture aperture d_f increases, the nonlinear effects of fluids continue to strengthen, and the deviation between the nonlinear conditions and the seepage heat transfer results under linear conditions is greater. The critical hydraulic gradient J_cis determined by the normalized hydraulic conductivity coefficient T/T₀. It is found that the fracture aperture plays a dominant role in the critical hydraulic gradient J_c, and the critical hydraulic gradient J_c and the fracture aperture d_f satisfy the power function decreasing relationship. The normalized thermal breakthrough time t/t₀≥1, and the stability period under nonlinear conditions is longer than the stable period under linear conditions and increases with the increase of the fracture aperture and the number of fractures.