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

• Fractional advection-dispersion predicts 3D mass transport in fractured reservoir.
• Finite discrete fADE method is tested against analytical solutions.
• Numerical tracer results are highly anomalous, including a long tail.
• fADE incorporating spatial fractional derivative agrees with FRACSIM-3D.
• fADE predicts similar tracer responses to FRACSIM-3D irrespective of well spacing.

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.