Quad-Tree decomposition method for areal upscaling of heterogeneous reservoirs: Application to arbitrary shaped reservoirs

In this paper, Quad-Tree decomposition method is applied for areal upscaling of irregular shaped petroleum reservoirs. Quad-Tree decomposition is a recursive data structuring technique which generates an upscaled model with non-uniform (unstructured) gridblocks. This type of coarsening reduces the number of gridblocks, but preserves the main heterogeneity features of the original fine model. Because of the quadruplet nature of the Quad-Tree decomposition, this method cannot be used for upscaling of irregular-shaped models, directly. In this study, by circumscribing a square to the irregular-shaped reservoirs, a temporary model is obtained which can be upscaled by Quad-Tree decomposition. After upscaling, the extra gridblocks outside of the real reservoir are removed to give the final upscaled model. The proposed algorithm is used for simulation of oil and water two-phase flow in two different case studies. The simulation results demonstrate that the resulted upscaled model can give accurate results compared to the original fine model, but is 13.5 times faster than the original fine model.