非整数階微分を含む物質移動モデルを用いた坑井間距離の異なるトレーサー応答推定の検証

抄録

Use of fractional Advection-Dispersion Equation (fADE) has been proposed to describe mass transport in a fractured reservoir. In this study, a finite discrete method to solve the fADE is developed and its accuracy is tested against analytical solutions.
Tracer simulation is carried out using a 3D simulation code for flow analysis (FRACSIM-3D). The fADE mathematical model is applied to fit the numerical tracer results, which show highly anomalous behaviors such as a long tail. The solution to the fADE including a spatial fractional derivative is shown to be in reasonable agreement with the tracer response produced by FRACSIM-3D. The fitting parameters of the fADE equation obtained for well interval of 50 m are used to make predictions of tracer responses for well intervals of 100 m - 500 m. It has been shown that the tracer responses predicted by the fADE model are reasonable close to those obtained by FRACSIM-3D irrespective of the different well intervals. This study demonstrates that the fADE offers a method for predicting tracer responses in a fractured reservoir.