Fractional derivative-based tracer analysis method for the characterization of mass transport in fractured geothermal reservoirs

The fractional advection-dispersion equation (fADE) has been proposed to describe mass transport in a fractured reservoir. This study develops a finite discrete method to solve the fADE and tests its accuracy against analytical solutions. Tracer simulation uses a three-dimensional simulation of flow analysis (FRACSIM-3D). The solution to the fADE incorporating a spatial fractional derivative shows reasonable agreement with the tracer response from FRACSIM-3D, which shows highly anomalous behaviors such as a long tail. The prediction by the fADE model is reasonably similar to those of FRACSIM-3D irrespective of differing well intervals.