A Steam-Assisted Gravity Drainage Model For Tar Sands: Linear Geometry
Authors: Reis John C. 
Published: March 2010

Abstract
This paper presents a new predictive model for gravity drainage in tar sands during steam injection in linear geometry, e.g. along horizontal wells. The model has been validated against published experimental data. The model assumes that the steam Zone shape is an inverted triangle with the lower vertex fixed at the production well. The temperature profile in the oil is assumed to decline exponentially with distance away from the steam/oil interface, but unlike previously published models, the temperature decline is independent of position on the interface. An energy balance is used to determine the latent heat injection rate for steam to expand the steam zone, preheat the formation ahead of the steam zone, and balance heat losses to the overburden. The energy balance and oil production rate equations are combined to yield the steam-oil ratio for this process.

Introduction
Oil recovery from tar sands is limited to the very high viscosity of the oil (bitumen). Injecting steam to lower the viscosity is one of the few in situ methods for recovering this resource. The most widely used process is cyclic steam injection, but because this process can only contact a small fraction of a reservoir, the amount of oil it can recover is limited. Steam drive is a proven recovery method for reservoirs having a lower oil viscosity, but is unreliable In tar sands because the high bitumen viscosity inhibits communication between the injection and production wells.
Recent developments in horizontal well technology now make new methods to recover oil from tar sands feasible. One promising new process is the Steam-assisted Gravity Drainage (SAGO) process. [0 this process, steam is injected into the formation through a horizontal well and oil drains into a separate, parallel, horizontal well located below the injection well. A variation on this recovery process is to inject steam into vel1.ical wells and drain the oil to a lower horizontal well.
The driving force for oil production in the SAGO process is the density difference between the steam vapour and the bitumen. Two now regimes for gravity drainage are possible, depending on how the steam is injected: (I) where the steam fingers upward into a cold reservoir and oil flows downward in counter current flow (1–3), and (2) where oil drains downward along the interface or a laterally expanding steam zone(4–6). This paper presents a new model for the latter process.

Steam Zone Model
During steam injection, the steam zone will grow laterally as oil drains along the steam/oil interface to the production well. The steam zone near the overburden will widen, while near the bottom it will remain essentially fixed at the production well. The resulting steam zone cross section will be roughly an inverted triangle, as shown in Figure l.
For this configuration, assume a coordinate system fixed to the moving steam/oil interface, with coordinates εand η, perpendicular and parallel to the interface, respectively. Oil will drain along the interface, with the drainage rate (velocity) being dependent upon the local viscosity (temperature), which in turn is dependent upon the distance from the interface.