Summary
This paper focuses on techniques for quantifying accelerated-production rates achieved by installing wellbore heaters in heavy-oil-producer wells. The uniform injection of heat into the wellbore of heavy-oil producers reduces local near-well fluid viscosity, lowers dynamic pressure, and results in increased production rates. Wellbore heat penetrates into the surrounding reservoir through conduction. Because of the exponential dependence of heavy-oil viscosity on temperature, small changes in temperature can substantially reduce near-wellbore oil viscosity. Conduction-heat transfer into the formation is balanced by convection back into the wellbore by the inflowing produced fluids. The higher the flow rate, the lower the heat-penetration depth is for a fixed heater-injection rate.
Schild (1957) presented a steady-state model that deploys boundary condition at an infinite radial location, resulting in the prediction of an infinite-influence region for the temperature when the Péclet number is smaller than unity. Production-improvement factor (PIF) on the order of 100 is reported and will be shown to be overoptimistic when the transient nature is properly represented. In this paper, a transient model is presented dependent on the boundary conditions at a finite radial distance from the wellbore. Predictions of the PIF suggest values on the order of three at small Péclet numbers. Influence of the formation thermal conductivity and permeability can be lumped into a defined Péclet number. The developed correlation is demonstrated to cover the effect of this Péclet number, together with the viscosity ratio, on the PIF.