Simplified Heat Calculations for Steamfloods
Authors: Vogel J.V. 
Published: December 2007

Summary
The heat requirements for many steam floods can be estimated more accurately by using the equations for linear heat flow from an infinite plane rather than the equations derived for vertical front steam chest expansion. The linear equations are simple enough to be suitable for rapid desk-type calculations. Calculation results agree with recommendations of some that a steam flood should begin with high injection rates that are later reduced. The suggested equations provide a rational basis for designing such a provide a rational basis for designing such a variable-injection-rate steam flood. In addition, they are a useful surveillance tool to monitor the flood performance where unforeseen conditions cause significant performance where unforeseen conditions cause significant deviation from design assumptions. They then can be used to calculate necessary adjustments in injection rates. Heat needs predicted by the equations are conservative; they are the maximum required to heat a given reservoir to a given temperature. Steam usage beyond this usually indicates vertical leakage to nonoil producing zones or lateral leakage beyond the desired flood producing zones or lateral leakage beyond the desired flood area. Finally, the equations were developed from an assumption that steam overlay would occur quite rapidly and thus the time required for its occurrence could be neglected. Consequently, the equations would overestimate heat consumption for this early period while overlay is being established. They should not be used to estimate heat required for steam breakthrough into producing wells.

Introduction
Frontal Displacement Concept. Most mathematical models for making steam drive calculations are based on the frontal displacement of oil by steam over the full thickness of an oil sand (Fig. 1). Solutions have usually been displayed as curves that relate the percentage of total heat retained in the oil zone to a dimensionless time. Fig. 2 is an example of such a solution by Prats. Throughout this paper, "total heat" means the total net heat injected into the formation and excludes head produced back with the produced fluids. Proper allowance produced back with the produced fluids. Proper allowance for surface heat losses, wellbore losses, and reproduced heat is assumed. In 1978, Myhill and Stegemeier examined the accuracy of heat calculations made with a frontal displacement model. They compared the ultimate oil/steam ratios (OSR's) predicted by such calculations to those that were actually measured in seven laboratory model studies and 11 actual steam drives. As shown in their comparisons (Figs. 3 and 4), the correlation was quite good. The measured OSR's were generally less than but within 70% of the predicted ratios. Among other factors causing the actual OSR's to be somewhat less than those calculated, Myhill and Stegemeier cited extreme steam overlays, which were not treated by the simple vertical front displacement models. Examples of such overlays in the cases they studied are shown in Figs. 5 through 8. According to published reports of steam drive field projects, steam overlay is a very common phenomenon. projects, steam overlay is a very common phenomenon. Almost all reports either mention an overlay directly or report steam breakthroughs into producing wells within 1 or 2 months after beginning injection-an effect that would be expected with steam overlay.
Descending Steam Chest Models. To provide a mathematical treatment for steam overlay effects, Doscher and Ghassemi and Neuman proposed models in which the principal direction of steam frontal movement is vertically downward. It is assumed in these models that all the injected steam goes immediately to the top of the zone and both the downward growth and areal spread of the steam zone vs. time then are calculated. A constant injection rate is assumed. Fig. 9 is a simplified illustration of the concept. One difference between these two proposed models involves calculation of heat requirements. Both agree on the methods of calculating heat stored in the steam chest; they also agree on heat flow into the overburden. However, they differ about the heat flow from the descending steam chest into the underlying formation. Doscher and Ghassemi's calculations provide for downward heat flow by conduction only. Neuman, on the other hand, presents equations to support a position that if both conduction and convection are considered, me heat flow downward is a mirror image of the heat flow upward (except for differences in the thermal properties). As seen in Fig. 10, the Neuman approach yields properties). As seen in Fig. 10, the Neuman approach yields a simpler equation identical to that for heat flow from a stationary plane. A comparison of the cumulative heat flows resulting from the two different assumptions is shown also in Fig. 10.
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