An Improved Reservoir Conduction Heating Model

Steam injection into petroleum reservoirs has become a common method of increasing producing rates and ultimate recovery. In producing rates and ultimate recovery. In addition, hot fluids are being studied for producing shale oil utilizing conduction producing shale oil utilizing conduction heating. This is a study of the temperature distributions resulting from heat conduction. When steam enters an oil reservoir or shale-oil bed through a single high-permeability channel or fracture, conduction may be a principal heating mechanism. Under certain principal heating mechanism. Under certain assumptions this can be likened to the conduction heating of an infinite body from a disk source. This problem of reservoir or rock heating has been treated by Boberg, Satter, Thomas, Marx-Langenheim and others. Satter and Thomas proposed conduction models for reservoir problems. In reviewing these two models it was problems. In reviewing these two models it was found that both assumed vertical linear heating above and below substantially disk sources. It was suspected that the above models would lead to very optimistic heating as each lacked terms providing for radial or horizontal conduction. providing for radial or horizontal conduction. The radial-horizontal heat conduction terms have now been added, and it was found that the Thomas model forecast an optimistic heated zone. A Thomas isotherm may be 50 percent farther out than the same isotherm in percent farther out than the same isotherm in the new model incorporating radial heat conduction terms. Briefly, the radial term withdraws heat from the region above and below the source, thereby lowering the magnitude of the isotherms. Satter's model is similar to Thomas' model, and it, too, gave optimistic answers by about 25 percent or more. In the new model, superposition of heating rates was used to evaluate temperature distributions for varying heat rates. Assuming that production can be simulated using negative conduction heating rates, temperature distributions through multiple injection-soak-production cycles were studied. Using this model, it was found that, after steam injection, the temperature distribution is characterized by nearly horizontal isotherms. For injection periods and rates normally used in petroleum reservoirs, the vertical penetration of the isotherms is much less than penetration of the isotherms is much less than their radial spread for the initial injection period. During soaking, little radial spread period. During soaking, little radial spread of the isotherms occurs, but more vertical penetration occurs. Production of fluids results penetration occurs. Production of fluids results in a removal of heat from above and below the initial heat source. During any production period, a maximum of approximately 36 percent period, a maximum of approximately 36 percent of the injected heat can be removed in practical times. As a result, heat buildup occurs during successive cycles and both radial and vertical spread of the heated zone occurs.