Abstract
A mathematical model is proposed for approximating the distribution of resistance heating in a process that employs an alternating electric current to heat an oil reservoir. The model assumes radial flow both of fluid and of current.
Introduction
We have been investigating the feasibility of an oil recovery technique that would employ an alternating electric current to heat an oil reservoir. The process should improve the mobility ratio at the displacement front, since the viscosity of most oils is more temperature-sensitive than the viscosity of water. Thermal expansion of heated oil also may make some contribution to oil recovery. The selective electric reservoir heating (SERH) process would employ electrodes installed in water injection wells, and high-salinity water would be injected during heating. This low-resistivity fluid would reduce heating in the portion of the reservoir that has been invaded by this fluid. It also would cool the electrode sufficiently so that boiling (which would break the electric circuit) would not occur, and it would displace some of the heated oil to production wells where it can be recovered.
Model for Resistive Adjacent Beds
A relatively simple model of the heating process can be developed if we consider a homogeneous, horizontal, isotropic reservoir that is uniform in thickness and bounded above and below by highly resistive formations. For this system we assume that the flows both of injected water and of electricity are radial near the injection well (Fig. 1). The region invaded by injected water is a cylinder with radius r and an average resistivity of R. The outer boundary of the model used to represent the system is a cylinder with a radius of r, which is half the distance between adjacent electrode wells in a pattern flood. The average resistivity of the portion of the reservoir that has not yet been contacted by injected water is R. Since we have assumed that R and R are not functions of r, and since the same current flows in the invaded and uninvaded zones, we can show by integration of Ohm's law that
percent heating (1) percent heating (1) where Eq. 1 gives the percentage of heating that occurs in the uninvaded portion of the reservoir (where heating is desired) when the radius of the invaded portion of the reservoir is r. The percentage of heating that occurs in the uninvaded zone is equal to the percentage of the voltage drop that occurs in this zone. Resistivities in Eq. 1 may be estimated.
(2)
(3)
These resistivities are functions of time, since water resistivity decreases with an increase in temperature, and since water saturations may change during the recovery process. process. If we consider the case of a constant injection rate, with injected water displacing the formation water, the radius of the invaded zone is given by
(4)
SPEJ
P. 750