A New Approach to the Analytical Treatment of Steam-Assisted Gravity Drainage: A Prescribed Interface Model

The majority of the models in the literature for the steam-assisted-gravity-drainage (SAGD) process solve the problem of conductive heat transfer ahead of a moving hot interface using a quasisteady-state assumption and extend the solution to the base of the steam chamber where the interface is not moving. This approach, as discussed by Butler (1985) and Reis (1992), results in inaccurate or sometimes infeasible estimations of the oil-production rate, steam/oil ratio (SOR), and steam-chamber shape. In this work, a new approach for the analytical treatment of SAGD is proposed in which the problem of heat transfer is directly solved for a stationary source of heat at the base of the steam chamber, where the oil production occurs. The distribution of heat along the interface is then estimated depending on the geometry of the steam chamber. This methodology is more representative of the heat-transfer characteristics of SAGD and resolves the challenges of those earlier models. In addition, it allows for the extension of the formulations to the early stages of the process when the side interfaces of the chamber are almost stationary, without loss of the solution continuity. The model requires the overall shape of the steam chamber as an input. It then estimates the movement of chamber interfaces using the movement of the uppermost interface point and by satisfying the global material-balance requirements. Oil-production rate and steam demand are estimated by Darcy's law and energy-balance calculations, respectively. The result is a model that is applicable to the entire lifetime of a typical SAGD project and provides morerepresentative estimations of in-situ heat distribution, bitumen-production rate, and SOR. With the improved knowledge obtained on the fundamentals of heat transfer in SAGD, the reason for the discrepancies between the various earlier models will he clarified. Results of the analytical models developed in this work show reasonable agreement with finescale numerical simulation, which indicates that the primary physics are properly captured. In the final section of the paper, the application of the developed models to two field case studies will be demonstrated.