Abstract
Summary An analytical heat transfer model is presented for the combined convection along a vertical fracture with conduction and convection in the reservoir. The model couples the energy (heat transfer) and fracture propagation equations resulting in a closed-form, dimensionless-temperature integral solution. Major model enhancements include incorporation of (1) a finite film coefficient, (2) time-dependent fracture temperature for calculating the instantaneous heat flux, (3) energy storage in the fracture, and (4) coupled energy and fracture propagation equations. The introduction of a power-law Nusselt number to determine the convection-film coefficient is also new and unique. The influence of fluid leakoff and a finite convection-film coefficient as heat-reduction mechanisms is discussed. The effect of energy storage and a time-dependent fracture temperature on the heat transfer rate is also illustrated. Finally, simulation studies illustrating the effect of heat transfer on fracture propagation characteristics are presented.
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