Fully heterogeneous three-dimensional SAGD simulation models are computationally expensive to evaluate, necessitating the need for simpler models that can capture the overall physics of the process while reducing computation time. This paper sheds some insights into the effect of permeability heterogeneity on SAGD performance, and presents both a physics-based upscaling technique that considers the unique geometry of the steam-plume during the SAGD process, as well as a statistical upscaling scheme based on variable selection and multivariate non-linear regression.
Full physics, two-dimensional SAGD simulations were performed using several stochastic shale models representing different proportions. Subsequently, the vertical variability in the models was averaged using a flow-based upscaling technique to obtain an effective anisotropic ratio. The performance of the upscaled models was assessed using full physics numerical simulation. It was observed that the upscaled anisotropic models gave different results compared to the fully heterogeneous models. The discrepancy between the heterogeneous and anisotropic models is largely due to upscaling. Two approaches were formulated to address this. The first approach iteratively adjusts the anisotropic permeability of the 2D model until a match to the 3D heterogeneous model was achieved. Then a non-linear regression model between the heterogeneous model parameters and the history-matched anisotropic permeability was formulated. In the second approach, an upscaling method considering the flux due to convergent flow towards a line sink was developed.
A key result presented in this paper is that heterogeneity plays a significant role in SAGD performance. Factors such as shale correlation length and proportion affect both the initial steam rise and the lateral spread of the chamber. Traditional upscaling techniques assuming power averages or flow-based assuming uniform flow over a plane are inadequate for approximating heterogeneous models. Statistical schemes such as the one presented in this paper perform much better in capturing the recovery characteristics of the SAGD process in heterogeneous media. Considerations such as optimum well pair spacing and optimal steam-oil ratio for maximizing bitumen recovery require quick evaluation of multiple scenarios and that may be possible using the approach presented in the paper.