关键词: 壁面局部接触裂隙, Hele-Shaw模型, 水流-传热, 瞬时局部热平衡, 参数分析

Abstract: Water flow and heat transfer processes in fractured rocks may be encountered in several engineering disciplines, such as geological disposal of radioactive waste, geothermal development, petroleum exploration, etc. Currently existent theoretical models and calculation methods for water flow and heat transfer in fractured rocks are almost exclusively based on the assumption of parallel smooth fracture walls, without considering the effects of local fracture wall asperity contacts on water flow, water-rock heat exchange and heat transfer. The following studies are presented in this paper. Firstly, dealing with water flow in a fracture with rough walls, the Reynolds lubrication equation and the Hele-Shaw model of a fracture with local wall asperity contacts based on the Stokes equations are expounded; solutions are sought by using the PDE tool of the MATLAB software, and compared with the Walsh formula of the effective hydraulic aperture of a rough walled fracture. Secondly, the similarity between the water flow and heat transfer in a fractured rock with local fracture wall asperity contacts and the water flow and heat transfer in a fractured rock with fills is analyzed; the condition for applicability of the instantaneous local thermal equilibrium is proposed; and the time and its influencing parameters for local thermal equilibrium between the local fracture wall asperity contacts and the flowing water in the fracture are computationally analyzed under the premise that the Biot number condition can be satisfied by the local fracture wall asperity contacts. Lastly, assuming instantaneous local thermal equilibrium between the local fracture wall asperity contacts and the flowing water in the fracture, the distributions of temperatures in the flowing water and the rock matrix are calculated using an existing analytical solution for water flow and heat transfer in a fractured rock with fills, and the effects of the ratio of local asperity contact area, the fracture aperture and the averaged water velocity on the temperature distributions are analyzed, which indicate, under the prescribed conditions, (1) that due to the heat exchange between the local fracture wall asperity contacts and the flowing water in the fracture, the range of influence of the flowing water on the temperature of the rock matrix decreases with the increase of the ratio of local asperity contact area, whereas the degree of influence of the rock matrix on the temperature of the flowing water in the fracture increases as the ratio of local asperity contact area increases; (2) the influences of the fracture aperture and the water velocity on the temperatures of the rock matrix and the flowing water in the fracture are consistent in that the range of influence of the flowing water on the temperature of the rock matrix increases with the increases of the fracture aperture and the water velocity, whereas the degree of influence of the rock matrix on the temperature of the flowing water decreases as the fracture aperture and the water velocity increase.

Key words: fracture with local wall asperity contacts, Hele-Shaw model, water flow and heat transfer, instantaneous local thermal equilibrium, parametric analysis