Cost Comparison of Reservoir Heating Using Steam or Air
Authors: Wilson L.A. , Root P.J. 
Published: December 2007

Abstract
The relative costs of heating a reservoir by steam injection and by combustion have been examined. The comparison was based on a model similar to that proposed by Chu. The cost of boiler feed water, the price of fuel. pressure and plant capacity were parameters in determining the costs of air compression and steam generation. The analyses compare the cost of heating to the same radius by the two methods. Results suggest that the two primary factors for comparison are the price of fuel and the amount of crude burned during underground combustion. The cost of fuel has a greater effect on the cost of heat from steam than it does on its cost by combustion. As a result, analyses indicate that when the price of fuel is low, steam may be unequivocally cheaper than air. The influence of heat loss is such, however, that as the heated radius increases combustion becomes relatively more competitive depending upon the amount of crude burned. This implies that steam may be cheaper for small stimulation jobs (huff and puff) but combustion may be more economically attractive for heating large areas (flooding).
Introduction
Use of thermal methods of recovery is an accepted fact today. After an induction period of several years, processes are being widely used that involve reservoir heating to augment recovery. Of the several techniques, steam injection and forward combustion appear to be destined to dominate the field. Although the objectives of both are the same, the basic differences between generating heat in situ and injecting heat after surface generation influence the cost in different ways. This study compares the cost of heating a reservoir either by steam injection or by forward combustion. There has been no consideration of recovery. Presumably, recovery from the swept region would be high in either case. The sole consideration was the cost of heating to the same radial distance by either process.
PROCEDURE
THE MODEL
The basis for comparison was a mathematical model similar to that used by Chu for combustion. The model simulates a radial heat wave in two-dimensional cylindrical coordinates. It includes heat generation, conduction and convection within the reservoir and conduction in the bounding formations. Thus, heat losses from the formation are considered. Three significant modifications were made.
Equal logarithmic increments rather than equal increments were used for the mesh spacing in the r direction. By this technique large distances were simulated with relatively few mesh spaces. A backward difference approximation to the convection term was used to avoid troublesome oscillations which result from a central difference approximation when the convection term is large. The radial increments of the combustion zone motion were not necessarily uniquely related to the mesh configuration.
The cumbersome step function introduced by the heat of vaporization of steam was circumvented by assuming the enthalpy of the steam to be a linear function of temperature between reservoir temperature and steam temperature. This is equivalent to assuming an average heat capacity numerically equal to the difference between the enthalpy of saturated steam and the enthalpy of water at reservoir temperature divided by the difference between the two temperatures. Heat losses obtained by this model are in essential agreement with those obtained by the analytical solution of Rubenshtein. A detailed description of the mode presented in the Appendix. Using the model, the times required to heat to particular radial distances were obtained as a function of injection rate and other physical parameters. For the steam case, injected fluid was assumed to be saturated steam at pressures of either 500, 1,000 or 1,500 psia. The corresponding temperatures are 467, 544 and 596F, respectively. Thickness ranged from 10 to 50 ft and injection rate ranged from 100,000 to 1 million lb/D. Reservoir and overburden temperatures at the injection well were assumed to be that of saturated steam at the injection pressure. The effect of maintaining the overburden temperature at the well at a different temperature (initial reservoir temperature) was examined with no significant change in behavior. The influence of wellbore heat losses for the steam case was determined in the following manner. The rates of heat loss as a function of time were estimated using an approach similar to that suggested by Ramey. The data were based on injection through 2 1/2-in. tubing in 7-in. casing. Integration of these data over the entire injection period yielded the total heat loss. Total heat losses were then corrected to their equivalents in steam (this number resulted from dividing the total heat loss by the latent heat). This was considered additional steam required to accomplish the reservoir heating and the total cost was increased accordingly.
JPT
P. 233ˆ