Characterization of Mass/Heat Transfer in Fractured Geothermal Reservoirs Using Mathematical Model of Complex Dynamical System

Abstract

A fractional advection–dispersion equation (fADE) offers a simple but effective tool for describing anomalous mass transport in a fractured reservoir. A diffusive analogy between mass and heat transfer is used to derive a new fractional heat transfer equation (fHTE) to analyze the thermal response within the reservoir. The fHTE derived here is used to model a reservoir around a fault zone with improved results over conventional models. The fracture density in the fault zone decays from the high permeability zone by a power-law. The fADE and the fHTE constitutional parameters are shown to correlate with the decay of fracture density. The fADE constitutional parameters, obtained by curve-fitting the tracer response, estimate the fHTE constitutional parameters to predict the thermal response to reinjection.