Dynamics of Heat Transport from a Reservoir to the Adjoining Formation in a Thermal Flood

Heat transfer from a petroleum reservoir to adjoining rocks is detrimental to thermal floods. While such thermal losses are inevitable, understanding the timescales of these heat exchanges would improve the design and management of thermal floods. Employing lumped-parameter system analysis and assuming series flow, this paper presents transfer functions that characterize response times of a reservoir and its surroundings to changes in temperature of the heat source. The reservoir-surrounding system is modelled as individual thermal capacitors and resistors. The transfer functions, solved for a step disturbance, describe the limiting case of negligible interaction between these subsystems. For a step-change in temperature of the heat source, responses of the reservoir and surroundings are simulated for some combinations of their properties. Simulation results explain time-delay between reservoir and surrounding temperatures. The time-delay is controlled by four distinct parameters vis-à-vis surroundings time constant (τr), reservoir time constant (τa), ratio of thermal resistances (R) as well as the ratio of conductive to convective heat flow (βr). These parameters are governed by petrophysical, transport and thermophysical properties of the heating medium, reservoir, and surrounding formation. It is shown that lag-time in thermal responses of reservoir and surroundings can range from few weeks to several years. For practical applications and analyses, these results provide insights into conditions under which a thermal flood may be approximated as adiabatic vs. non-adiabatic.