Numerical Simulation Of In-Situ Electrical Heating To Increase Oil Mobility
Authors: Todd J.C. , Howell E.P. 
Published: March 2010

Abstract
The in-situ electrical heating of oil reservoirs has been modeled in a two-part numerical simulation. The first part consists of a radial electrothermic model to calculate the currents resulting from the near-wellbore effects of high current densities. The radial model sequentially solves the electrical potential distribution, resulting power terms foreach cell, the temperature distribution, heat flow produced by the electrical energy and the single-phase flow of fluid due to the thermal expansion of the fluids. The use of the radial model to examine the effects of resistivity, wellbore size and well cooling temperature is shown. The second part of the simulation scheme uses the radial model currents and heat removal rates to establish the electrical energy level in the three-dimensional electrothermic model. The 3-D model solves voltage, heat and pressure equations sequentially, with the restriction that the maximum current per foot of electrode must not exceed the radial model current per foot. Radial resistance equations are calculated between the electrode node and the adjacent node to use in the simulation of the large energy dissipation near the electrode. The effects of electrode radius and well spacing on the flow potential are shown for the electrode placed near an underburden high-resistivity member. The combined use of the radial model currents with the three-dimensional electrothermic model establishes a useful tool to evaluate and optimize the in-situ electrical heating of oil-bearingformations.

Introduction
The largest occurrences of hydrocarbons exist as very viscous material. In-situ electrical heating of these heavy oil reservoirs has been proposed(1) as a means to mobilize "the oil for recovery by the application of a driving medium. The flow of electrical current between electrode wells drilled into the oil sand permits the in-situ generation of heat within the reservoir in proportion to the resistance of the stratum. The electrical heating obtained heats the oilsand to reduce the viscosity, permitting more fluid oil to be driven to a producing well. The singular advantage of electrical heating lies in the ability to heat the reservoir to mobilize the oil without the flow of fluids or heat flow. Thus, electrical heating can mobilize heavy oil where other means have not been successful. The distribution of electrical heat and its effects on the fluidity of the oil have been modeled by using the currents, from a radial model of the near-wellbore effect, which are inserted in a three-dimensional model of the well pattern. The 3-D model has radial terms inserted in the Cartesian grid to improve the simulation. A description of the radial and three-dimensional electrothermic models is given. Modeling results of electrical heating are shown with respect to several factors influencing the successful formation heating.

Theory
The electrothermic (coined word for this type of model) models consist of successive steady-state solutions of the electrical potential, temperature distribution and pressure distribution. The electrical potential distribution is used to calculate the resulting current flow and energy dissipatedin each of the network cells.