![]()
In the modeling of any system, one is always faced with the dilemma of choosing the level of complexity that correctly predicts the response of interest. In the case of modeling the electrical heating of wells and reservoirs for heavy or extra-heavy oil at low frequencies (below the microwave range) and considering only one liquid phase and no gas phases, the systems of equations shown in this article are considered sufficient. The problem is still unsolved for the case of microwave heating of reservoirs, in which a complete model, which correctly takes into account the electric losses of a system of solid grains, liquids with dissolved gases and salts (with the corresponding complex geometrical, scaling, and electrochemical properties in the presence of electrical diffusion currents and space charges), is not yet available. For the case of concentrated heating (either resistive or inductive) and distributed heating in the reservoir and surrounding regions (at frequencies below the microwave range) or distributed heating in the metal elements (at any frequency) the equations given next (in a cylindrical coordinate system) are deemed sufficient. The third term on the left, the product of temperature multiplied by the divergence of the velocity, has been neglected in many models of heating of reservoirs (it is strictly zero only for incompressible fluids.).
Site News