フラクチャーを有する媒体内の境界要素法による三次元熱伝導の解析

Abstract

Previously, the authors have developed a Three-dimensional numerical code by direct boundary element method for non-steady heat conduction. In order to confirm validity of the calculation system, at that time, they carried out both numerical calculation and analytical calculation for the model of infinite medium around a spherical cavity and compared numerical solution with strict solution. It was found from the comparison that precise solution can be given by using their numerical code. However, in the practical problems, thin fracture must be modeled in case as that artificial fracture produced by hydraulic fracturing is taken in. In addition to that, the detail of the procedure to calculate the influence coefficients related with the elements which consist of the fracture boundary should be explained. Therefore, in this paper, the authors describe the concrete procedure on calculation of the influence coefficients first and they carried out numerical calculations in which fracture boundary is taken next. As the numerical model, however, they dealt with non-steady heat conduction in infinite medium around a penny-shaped fracture in order to simplify the problem and to make explanation of the calculated result easier, because no strict solution can be given for any problem including fracture boundary. Furthermore, the time integral method was used as the calculation method and linear distributions of initial rock temperature was assumed in modeling. In such modeling, no volumetric integration is needed if the time integral method is adopted and, one can deals with the model where initial temperature distribution varies linearly as same as the model where it is constant.