Evaluation of Singular Value Decomposition (SVD) Enhanced Upscaling in Reservoir Simulation

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Abstract Reservoir upscaling is an important step in reservoir modeling for converting highly detailed geological models to simulation grids. It substitutes a heterogeneous model that consists of high-resolution fine grid cells with a lower resolution reduced-dimension homogeneous model using averaging schemes. Its objective is to use a coarse grid model to represent a fine grid model, thus to reduce simulation time. The benefit of upscaling in reservoir simulation is that it efficiently saves simulation time, and effectively preserves key features of data for flow simulation. Singular Vector Decomposition (SVD) is a matrix decomposition method. It has been used for image processing and compressing. It has been proved to be capable of providing a good compression ratio, and effectively saves digital image storage space. SVD also has been used in noise suppression and signal enhancement. It has been shown to be effective in reducing noise components arising from both the sound sampling and delivery system. This study evaluates the effect of SVD in parameterization and upscaling for reservoir simulation. A two-phase flow reservoir model was created using data from the SPE tenth comparative solution project [1]. Simulation results show that SVD is valid in the parameterization of permeability values. The reconstructed permeability matrices using certain amount of singular values are good approximations of the original permeability values. Simulation results from SVD processed permeability values are similar to that using the original values. SVD is then applied on the upscaled permeability value to evaluate the effectiveness on upscaling. Simulation results were compared between the base case, upscaled case, and SVD upscaled case. The simulation results did not show a significant improvement in the accuracy of predicting oil production by applying SVD on the upscaled permeability values. It could be because the reconstructed permeability matrix has the same dimension before and after the SVD processing, thus the model accuracy and efficiency are not significantly improved. Future work includes adding more cases to further explore the effect of SVD on upscaling. The number of grid blocks may be increased, and more layers can be added to investigate whether SVD enhance upscaling for larger scale reservoir simulation models.