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

Abstract
This paper presents a new model for oil production during steam assisted gravity drainage (SAGD) in tar sands in radial geometry e.g., around vertical wells. The model assumes that the steam zone is an inverted cone, the temperature profile in the oil declines exponentially with distance away from me steam/oil interface, and the viscosity depends on the temperature through a power law. An energy balance is used to determine the latent heat injection fate for steam to expand the steam zone and balance eat losses. The energy balance and oil production fate equations are combined to estimate the steam-oil ratio for this process. Results obtained with this model suggest that SAGD in radial geometry is a promising recovery process. Additional studies of the process are recommended.

Introduction
One of the few successful oil recovery methods for tar sands is steam injection. The high temperature of the steam lowers the itumen viscosity allowing it to flow toward production wells. During steam injection, the density difference between the injected steam vapor and the oil induces gravity segregation of the phases in the reservoir. The steam vapor rises to the top of the formation, while the heated oil drains to the lower parts of the reservoir. Steam Assisted Gravity Drainage (SAGD) in linear geometry along horizontal wells has received considerable attention and a number of models for this process have been developed(1–5).
SAGD in radial geometry around a single, vertical well has not received as much study, but may also become an important recovery process. During this process, steam is injected into the reservoir through a vertical well and fluids are produced from the bottom of the formation. Experimental studies of the SAGD process in radial geometry have shown that the steam zone shape around the injection well is roughly an inverted cone with the vertex at the bottom of the well. In this paper, a conic steam zone shape will be used in developing a model for the SAGO process in radial geometry. A conic steam zone shape has also been used in modeling team injection in lower-viscosity, heavy-oil reservoirs(6–7).
One proposed application of the SAGD process in radial geometry is the Single-Well Injection/Production Steamflood (SWIPS) or vertical HASDrive process(8–9). SAGD in radial geometry is also expected to be important around a vertical injection, while in the horizontal well HASDrive process(10), In the SWIPS process the vertical well can be dually completed as an injector at the top and a producer at the bottom, while in the horizontal well HASDrive process, the fluids are pushed from the vertical injection well along a heated horizontal well at the bottom of the formation to a separate production well.

Model Derivation
The oil flow rate in the bitumen along the steam zone interface from gravity drainage can be found using Darcy's Law. If qo is the oil drainage rate at a given height, the oil flow rate can be expressed as
Equation (1) Available In Full Paper
where is the hydrostatic potential difference between the steam and oil along the steam zone interface,