In this appendix we shall show how the methods studied in the main part of the book can be used to resolve far-from-trivial engineering or physical problems. All purely technical details will be omitted, although references to the corresponding sections of the main text will be provided.

Heat loss in injection of heat into oil stratum [67]

The injection of heat into oil strata is one of the tertiary methods of oil recovery, and has been extensively discussed in the technological literature. Although the most effective method of thermally influencing oil production seems to be the injection of superheated steam into production wells, the injection of a hot incompressible liquid is discussed in the literature primarily because it is much more amenable to analysis than steam injection, which involves consideration of the very complicated phenomenon of phase transition in porous media. Analysis of the injection of a hot incompressible liquid is incomparably easier, and provides useful information from the engineering point of view.

One of the basic problems in analyzing the process of heat injection is determining the ratio of the amount of heat used efficiently to improve oil recovery to the heat lost due to the unavoidable heat exchange between the productive stratum and surrounding unproductive rocks. In order to calculate this ratio, one need not know the spatial distribution of temperature within the productive stratum but only the overall effect of the temperature distribution.