This article studies the development of asymptotic and approximate solutions for the growth of the steam zone in steam injection processes in one-dimensional reservoirs at constant injection rates. These solutions are generally derived by using integral balances which include heat losses to the surroundings and the hot liquid zone. In this way, the effects of preheating, caused by heat transport in the hot liquid zone ahead of the steam front are fully accounted.

At the beginning of injection the advance of the front is well described by the Marx-Langenheim model, provided that the injection rates are sufficiently high. At longer times deviations occur and a criterion is developed, in terms of a single heat transfer dimensionless parameter R, that defines the time interval of applicability of the Marx-Langenheim model. The asymptotic behavior at large times depends solely on a dimensionless parameter A, defined as the ratio of the latent to the total heat injected. It is shown that the final dimensionless expression does not depend on R (i.e., on the injection rates), although the time taken to reach the asymptotic state is significantly influenced by R.

An approximate analytical solution that reduces to the respective asymptotic expressions at small and large times is obtained under conditions of high injection rates (R ≫ 1). The solution is shown to give a better approximation to the steam zone rate of growth for intermediate and large times than the approximate expressions developed by Marx and Langenheim3 , Mandl and Volek4 , and Myhill and Stegemeier5 . For a wider range of operating conditions (including low injection rates), i.e., for R between 1 and ∞, an approximate numerical solution based on a quasi-steady state approximation is presented. The proposed solution requiring very modest computation is expected to give reliable results under a variety of operating conditions.

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