# SPE Reservoir Evaluation & Engineering Volume 8, Number 5, October 2005, pp. 372-376

SPE-86963-PA

### Mathematical Modeling of Steam-Assisted Gravity Drainage

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DOI  10.2118/86963-PA http://dx.doi.org/10.2118/86963-PA

### Citation

• Akin, S. 2005. Mathematical Modeling of Steam-Assisted Gravity Drainage. SPE Res Eval & Eng8 (5): 372-376. SPE-86963-PA.

### Summary

A mathematical model for gravity drainage in heavy-oil reservoirs and tar sands during steam injection in linear geometry is proposed. The mathematical model is based on the experimental observations that the steam-zone shape is an inverted triangle with the vertex fixed at the bottom production well. Both temperature and asphaltene content dependence on the viscosity of the drained heavy oil are considered. The developed model has been validated with experimental data presented in the literature. The heavy-oil production rate conforms well to previously published data covering a wide range of heavy oils and sands for gravity drainage.

### Introduction

Gravity drainage of heavy oils is of considerable interest to the oil industry. Because heavy oils are very viscous and, thus, almost immobile, a recovery mechanism is required that lowers the viscosity of the material to the point at which it can flow easily to a production well. Conventional thermal processes, such as cyclic steam injection and steam-assisted gravity drainage (SAGD), are based on thermal viscosity reduction. Cyclic steam injection incorporates a drive enhancement from thermal expansion. On the other hand, SAGD is based on horizontal wells and maximizing the use of gravity forces. In the ideal SAGD process, a growing steam chamber forms around the horizontal injector, and steam flows continuously to the perimeter of the chamber, where it condenses and heats the surrounding oil. Effective initial heating of the cold oil is important for the formation of the steam chamber in gravity-drainage processes. Heat is transferred by conduction, by convection, and by the latent heat of steam. The heated oil drains to a horizontal production well located at the base of the reservoir just below the injection well.

Based on the aforementioned concepts, Butler et al. derived Eq. 1 assuming that the steam pressure is constant in the steam chamber, that only steam flows in the steam chamber, that oil saturation is residual, and that heat transfer ahead of the steam chamber to cold oil is only by conduction. One physical analogy of this process is that of a reservoir in which an electric heating element is placed horizontally above a parallel horizontal producing well.

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### History

• Original manuscript received: 22 June 2004
• Revised manuscript received: 8 April 2005
• Manuscript approved: 25 June 2005
• Version of record: 15 October 2005