For any rate of heat injection into a reservoir, the fraction of the heatremaining in it is independent of the recovery process, be it steam, hot water, or combustion.
Most of the information available on the heat efficiency of hot fluidinjection processes, both water and steam, has been obtained from calculatedtemperature distributions in the pay zone and adjacent formations. The usualapproach has been to write the heat balance equations in terms of thetemperatures, and then to introduce whatever simplifications are necessary tohelp obtain an analytical or a numerical solution.
In either case, the assumption has often been made that the vertical thermalconductivity in the flooded interval is infinite, so that the temperatureswithin the flooded interval are then independent of vertical position. Becauseit was first made by Lauwerier, position. Because it was first made byLauwerier, and has been used extensively since, this assumption will bereferred to as the Lauwerier assumption.
Excellent reviews of the literature on the heat efficiency of hot fluidinjection processes have been given by Spillette, Flock et al., and Ramey. Ofcourse, the most significant contributions take into account the effect of afinite vertical thermal conductivity on the vertical temperature profile.
The most general analytic expression for the heat efficiency of a hot fluidinjection process is that of Antimirov who considers injection of a heatedincompressible fluid into a reservoir through an arbitrary number of wells. Therate of heat injection into the reservoir, as well as the injectiontemperature, is an arbitrary function of time. The geometry of the horizontalflow is arbitrary, although the reservoir is considered to be of uniformthickness and properties and to be of infinite areal extent. Heat transferwithin the reservoir is by horizontal convection and conduction, and byvertical conduction. In the formations adjacent to the flooded interval, heattransfer is by conduction in any direction. Thus, the available expression forthe heat efficiency due to hot water injection has been developed for rathergeneral conditions.
This degree of applicability has not been obtained for other thermalrecovery processes. By making the Lauwerier assumption we have been able toobtain expressions for the heat efficiency that are essentially independent ofthe thermal recovery process, be it steam, hot-water, or undergroundcombustion. Clearly, then, the approach followed here is more restrictive thanthat of Antimirov in that it uses the Lauwerier assumption. At the same timeless restrictive assumptions are made about the horizontal heat transfermechanisms, either in the flooded interval or in the formations adjacent toit.
The main difference between our approach and that of other investigators isthat the heat balance in the pay zone is expressed for the pay zone as a wholerather than for a volume element within it. The Lauwerier assumption isintroduced after the problem is developed along these lines as far as possible.problem is developed along these lines as far as possible. The details of thedevelopment of the heat efficiency are given in the Appendix, while the mainfeatures of the model are discussed in the next section. Results and theirimplications are discussed later in a separate section.