Modeling the effect of permeability anisotropy on the steam-assisted gravity drainage (SAGD) process

The SAGD process utilizes horizontal wells hence permeability anisotropy can play a very strong role in recovery. In fact, it has been well documented that poor vertical permeability kills the SAGD process because the steam chamber will not grow properly. Several authors have attempted to model this phenomenom by using time-independent averaging (e.g. harmonic, geometric averaging etc.) methods only to discover the inadequacy of such an approach as several field implementations reveal a definite time component to this effect. Consequently most studies on the effect of anisotropy during SAGD have involved only commercial simulators. However, there exists a need to describe this phenomenon quantitatively prior to any numerical simulation and delineating conditions where it can be considered important or not. Isotropy of permeability can be geometrically represented as a sphere (or circle in 2D) where the permeability radii are the same in all directions. Anisotropy can be represented as an ellipsoid (or ellipse in 2D) with varying permeability radii in different directions and the principal axes representing principal permeability directions. In this work, we assume that the principal axes point in the vertical and horizontal directions. We will show that the SAGD process has a unique geometry that allows a meaningful mapping of the steam chamber wall to the coordinate frame of such an ellipsoid. We will then use this transformation to incorporate permeability anisotropy within the framework of Butler type models. This will be done in dimensionless space and the results obtained can be used as type curves for correcting any isotropic SAGD model for anisotropic effects. Our results show that the effect of anisotropy is time dependent (generally obeying a sigmoid function) and there exists a given time for a given set of reservoir and fluid properties, after the effect of anisotropy ceases to exist. This is remarkable because it suggests a way to improve modeling efficiency for reservoirs with strong anisotropic permeabilities. Our results also explain why most other static averaging methods fail. The analytical expression can be used as a fast SAGD predictive model suitable for history matching purposes.