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Published in Petroleum Transactions, AIME, Volume 204, 1955, pages 205–212. Abstract A design is presented for an electrical analog computer which can solve non-steady state heat transfer problems in an extensive radial formation containing a moving cylindrical source. The computer is used to simulate a simplified thermal oil recovery process in which heat transfer from a moving, constant temperature source takes place radially by conduction only. Temperature distribution curves are shown for several different assumed modes of travel for the heat source. The data are used to estimate the residual fuel requirements necessary to maintain a self-propagating isothermal front for the particular system being studied. Although the computer is designed to represent an unique system, conversion factors can be adjusted to show the effects of changing the assumed values of system constants, such as thermal conductivity of the formation and temperature of the source isotherm. Examples are given to illustrate the relative influence the assumed values of these variables will have upon the quantity of fuel required to maintain the source. The maximum effect of heat transfer by the flowing air stream is estimated mathematically, and full requirements for this system are shown to be markedly reduced. Inasmuch as the examples discussed refer to a simplified process, the results are not directly applicable to a practical field operation. It is believed, however, that the data illustrate some general trends which are important in thermal recovery processes. Data from laboratory and field experimentation can be used to modify the computer to take into account the influence of heat transfer by various mechanisms, for example, by injected air and by fluids ahead of the hot zone. With such refinements it would be possible to estimate more accurately the limiting values for the rate of travel of the high temperature front and for the required air injection rates. Use of this computer should aid in evaluating the economic feasibility of oil recovery by various thermal processes. It is hoped this paper will stimulate further work by others to help accomplish this objective.

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