Development of Fractional Derivative-Based Mass and Heat Transport Model

Abstract

A numerical scheme to evaluate the effect of cold water injection in a geothermal reservoir has been proposed. The governing equations are derived based on non-Fickian mass transport model. We assume conduction into surrounding rocks using fractional derivative in time, as well as non-Fickian diffusion into the surrounding rocks has been derived. The constitutive parameters in the heat transfer model are capable to determine mechanisms of heat-fluid–rock interaction within the reservoir of a complex geological structure. Numerical investigations have shown that topography of a reservoir wall affects on tracer responses and temperature distributions. The long tails can be found in tracer response curves in a reservoir with rough surfaces. The permeability difference between a reservoir and surrounding rocks leads to retardation of tracer and thermal breakthrough.