›› 2013, Vol. 34 ›› Issue (3): 685-695.

• Fundamental Theroy and Experimental Research • Previous Articles     Next Articles

A semi-analytical method for calculation of three-dimensional water flow and heat transfer in single-fracture rock with distributed heat sources

ZHANG Yong,XIANG Yan-yong   

  1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
  • Received:2012-02-16 Online:2013-03-11 Published:2013-03-20

Abstract: Taking the near field of nuclear waste repositories in fractured rocks as the subject of study, a simplified conceptual model for three-dimensional water flow and heat transfer in single-fracture rock is proposed. The mathematical model, taking into account of distributed heat source and saturated single-fracture rock of infinite extent, is formulated and solved by using a Green function approach, in which a fundamental solution of the governing differential equations after Laplace transform is employed. The fracture surface is discretized by rectangular elements. The singularities in the integral equation are handled through analytical integration in polar coordinates; and a numerical procedure is developed to solve the transient temperature distributions in fracture water and rock matrix. Two numerical examples with special flow field are provided for illustration of the proposed method with comparison of an analytical solution based on 1D rock thermal conduction; and other numerical examples with distributed heat sources are extended for characteristics of flow and heat transfer in single-fracture rock and the sensitivities to flow velocity, rock thermal conductivity and heat source intensity. The calculations show the following observations: Comparing with the direct Gaussian method, the proposed analytical approach to handling the singular integrals is more accurate. The temperature of water in the fracture calculated by using the semi-analytical method is lower in upstream and higher in downstream than the analytical solution, due to the fact that the former method takes into account 3D thermal conduction in the rock matrix, whereas the latter assumes 1D conduction. Without interior heat source, the greater the rock thermal conductivity, the lower the temperature of facture water, due to more heat exchange between fracture water and rock matrix. The larger the fracture water velocity, the more significant of the influence of the inlet fracture water temperature on the temperatures of fracture water and rock matrix. The effects of the distributed heat source on the temperatures of fracture water and rock are more sensitive in downstream as a result of the heat advection of fracture fluid flow.

Key words: nuclear waste repository, fractured rock, fracture water flow, 3D heat transfer, Green function, singular integral

CLC Number: 

  • TU 451
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