Heat and Mass Transport in Steam-Drive Processes
Authors: Mandl G. , Volek C.W. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
Steam-injection tests in the field have shown that heat transport in the oil/water region, ahead of the steam zone, may play a significant part in the production process. Since earlier theoretical work on steam drive neglects heat flow from steam zone into the oil/water region, a re-examination and an extension of that theory are presented.
It is found that the "old" theory ceases to be consistent with the physical model of the process at a certain critical time tc, which depends on injection rate, temperature, and quality of the steam. The critical time marks an important change in the heat flow across the condensation front: the heat flow, which is purely conductive during 0 less than t less than t, becomes predominantly convective at t = t. Accordingly, at t = t. the equation which governs expansion of the steam zone changes.
On the basis of the new equation, an approximate description for the steam-zone growth during t less than t is developed by making use of upper and lower bounds for the exact solution of the problem. The boundary conditions for heat and mass flow inside the oil/water region are established and, in particular, a simple method is presented of determining the saturation at the downstream side of the condensation front.
Experimental results show that the theory gives an accurate description of steam zone expansion before the critical time. At times relatively near critical time and also after critical time experimental data show theoretical steam zone volumes to be somewhat high. Even so, the accuracy of the calculated steam zone volumes is sufficient for practical purposes.

I. THEORY OF STEAM-ZONE GROWTH

Introduction
The engineering evaluation of steam-drive processes is mainly based on a mathematical description of the steam-zone growth presented several years ago by Marx and Langenheim). In that theory, the flow of heat from the steam zone into the liquid zone ahead of the condensation front (fig. 1) was neglected. Since we must expect, however, that heat transport into and inside the liquid region (i.e. the region between condensation front and production wells) will effect both the water/oil flow and the growth of the steam zone, it seems reasonable to re-examine and to generalize the "old" theory. Observations made in several field tests emphasize the need to study the heat flow across the condensation front (CF). It was found on several occasions that heat was transported in the liquid zone far ahead of the advancing CF, resulting in an early breakthrough of warm water. This' seems to occur especially when high injection pressures are applied, when "wet" steam is injected, or when a pronounced "gravity-tongue" of steam is formed.