Modeling steam assisted gravity drainage in heterogeneous reservoirs using different upscaling techniques
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This thesis presents different methods that improve the ability to relate the flow properties of heterogeneous reservoirs to equivalent anisotropic flow properties in order to predict the performance of the Steam Assisted Gravity Drainage (SAGD) process. Process simulation using full scale heterogeneous reservoirs are inefficient and so the need arises to develop equivalent anisotropic reservoirs that can capture the effect of reservoir heterogeneity. Since SAGD is highly governed by permeability in the reservoir, effective permeability values were determined using different upscaling techniques. First, a flow-based upscaling technique was employed and a semi-analytical model, derived by Azom and Srinivasan, was used to determine the accuracy of the upscaling. The results indicated inadequacy of flow-based upscaling schemes to derive effective direction permeabilities consistent with the unique flow geometry during the SAGD process. Subsequently, statistical upscaling was employed using full 3D models to determine relationships between the heterogeneity variables: k[subscript italic v]⁄k[subscript italic h] , correlation length and shale proportion. An iterative procedure coupled with an optimization algorithm was deployed to determine optimal k[subscript italic v] and k[subscript italic k] values. Further regression analysis was performed to explore the relationship between the variables of shale heterogeneity in a reservoir and the corresponding effective properties. It was observed that increased correlation lengths and shale proportions both decrease the dimensionless flow rates at given dimensionless times and that the semi-analytical model was more accurate for cases that contained lower shale proportions. Upscaled heterogeneous values inputted into the semi-analytical model resulted in underestimation of oil flow rate due to the inability to fully account for the impact of reservoir barriers and the configuration of flow streamlines during the SAGD process. Statistical upscaling using geometric averaging as the initial guess was used as the basis for developing a relationship between correlation length, shale proportion and k[subscript italic v]⁄k[subscript italic h]. The initial regression models did not accurately predict the anisotropic ratio because of insufficient data points along the regression surface. Subsequently a non-linear regression model that was 2nd order in both length and shale proportion was calibrated by executing more cases with varying levels of heterogeneity and the regression model revealed excellent matches to heterogeneous models for the prediction cases.