Modification of Butler's Unsteady-State SAGD Theory to Include the Vertical Growth of Steam Chamber

Abstract Steam-Assisted Gravity Drainage (SAGD) is a widely used thermal recovery technique in western Canada. Use of numerical simulators, although successful in history-matching and performance prediction of the process, is extremely time consuming for field-scale optimization purposes. Therefore, analytical and semi-analytical models are desirable tools for quick field-wide performance forecast. The first theoretical study of SAGD was conducted by Butler et al. (1981). An elegant analytical model was developed to estimate the oil production rate of a laterally spreading steam chamber, assuming a steady-state mode of thermal conduction beyond the advancing steam front. This model has been the basis for all other SAGD analytical/semi-analytical studies. The model was later modified by Butler and Stephens (1981) and Butler (1985) to overcome the shortcomings of the steady-state heat transfer assumption. The majority of the analytical models of SAGD to date, assume that steam chamber has reached the over-burden from the start of the process and that it can only grow sideways. In real applications, however, steam chamber will rise vertically during its early stages of development. Therefore, these models are not capable of capturing the physics of the vertical growth phase adequately and their estimations of the oil production rate and steam oil ratio (SOR) may be questionable. A uniform steam chamber development during the vertical growth is crucial to an efficient SAGD process during the rest of the project's lifetime. Therefore, it is important to have a reliable estimation of the performance of this phase. In this work, the unsteady-state SAGD model of Butler (1985) has been modified to include the vertical growth phase. Darcy's law and material balance were combined to estimate the oil production rate and steam chamber growth. Energy balance was then used to estimate SOR. Validation of the estimations for oil production rate, steam chamber shape and SOR from this new model against the results of fine-scale numerical simulation indicates that the model has successfully captured the primary physics of the vertical growth phase. The model also predicts a more accurate in-situ distribution of thermal energy and SOR compared to the original model of Butler (1985). A closed form solution is possible for oil production rate, chamber height and SOR under some simplifying assumptions during the vertical growth phase; however, a numerical approach is required beyond this phase. The mathematics are simple enough to allow coding with simple computer programs to yield quick realistic field-scale performance predictions.

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