Electrical Heating With Horizontal Wells, The Heat Transfer Problem
Authors: McGee Bruce C.W. , Vermeulen Frederick E. 
Published: December 2007

Abstract
It is desirable to introduce heat into the production system and reservoir of a horizontal well producing heavy oil. An increase in temperature around the wellbore can remove thermally alterable skin effects, increase the productive length of the well, improve pumping efficiency, and reduce the energy requirements to lift the oil to surface. One way to create the heat is to use electricity.
The heat transfer problem consists of solving several concurrent mechanisms. The horizontal well is constructed from commercial grade carbon steel pipe which is an electrically conducting ferromagnetic material. Therefore the heat losses within the horizontal well liner are generated by both ohmic, I2R and hysteresis effects. Heat is also electrically produced in the reservoir adjacent to the horizontal well by ohmic losses. To further complicate the heat transfer problem, heat is produced from the reservoir with the fluids and conducted from the well by the action of thermal conduction. In summary, the heat transfer problem consists of distributed heat sources in regions where there is current flow, convection, and conduction.
The objective of this paper is to present a semi-analytical model that can be used to calculate the temperature distribution along the length of a horizontal well that is being electrically heated. The analytical model can be used to determine a safe operating strategy based upon the resulting temperature distribution for a given operating current and fluid production rate. From the magnitude of the current, the size of the power supply system can be specified and the energy costs for electrically heating a horizontal well can be calculated.
It is found that for a long horizontal well, heat transfer to the adjacent reservoir by conduction is more significant than heat transfer by convection and electrical heating. It is also found that the safe operating magnitude of the current in the horizontal well, determined by the allowable temperature rise, is limited by the cooling effect of produced fluids. Also, the energy costs to heat the well are relatively small in comparison to other operating costs.

Introduction
A first order analytical model to determine the temperature distribution along the length of a horizontal well is presented in this paper. The mathematical procedure is new for solving electrical heating problems with multiple regions. The approach developed here is general and is useful for solving many types of boundary value problems. With little modification the model can be used for problems associated with heating a horizontal well using steam.
Horizontal Wells and Heavy Oil. Horizontal wells, typically 500 meters in length and longer, are becoming increasingly common in the exploitation of heavy oil reservoirs around the world. Horizontal wells offer prospects of improved performance over vertical wells, primarily due to the larger contact area between the formation and the wellbore. Also, the technology for drilling a horizontal well is as advanced as for drilling a vertical well.
There are production disadvantages and problems that are unique for a horizontal well producing heavy oil. The production rate declines very rapidly during the first several months of production. It is also possible that the entire length of the horizontal may not be productive. In some production systems, the limiting factor in producing the oil are the mechanical limitations of the pumping equipment, which are exceeded because of the very high viscosity of the oil. Finally, there may be skin effects, such as the visco-skin, that may further reduce the productivity of the well. This skin effect and other thermally alterable skin effects (for example, asphaltene precipitation), can effectively block flow into the well. Many of these production problems can be removed by the introduction of heat, such as electrical heating, into the production process.
Electrical Heating of a Horizontal Well. Electrical heating of vertical wells has been attempted on several occasions with encouraging results. There has been one electrical heating test using a plurality of vertical and horizontal wells. The test was conducted by Texaco Canada Petroleum Inc. and the Alberta Department of Energy Research and Development Division, formally known as AOSTRA.
Electrical heating is a thermal process which is used to introduce heat into the near wellbore region of a well. Features of the process are:
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