Prediction of reinejction effects in fault-related subsidiary structures by using fractional derivative-based mathematical models for sustainable design of geothermal reservoirs

This study provides a method to evaluate the effects of cold-water injection into an advection-dominated geothermal reservoir. A fractional advection-dispersion equation (fADE) and a fractional heat transfer equation (fHTE) are applied to fault-related structures in geothermal areas where the fracture density is described by a power-law model. Synthetic production data generated by a numerical reservoir simulator reveal that the fADE and the fHTE are in reasonable agreement with the tracer responses and temperature change in a fault zone. Tracer analysis based on the fADE has potential to elucidate fault-related structures and to predict premature thermal breakthroughs quickly and efficiently.