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Upscaling and Optimal Coarse Grid Generation for the Numerical Simulation of Two-Phase Flow in Porous Media Hassan Mahani Centre for Petroleum Studies Department of Earth Science and Engineering, Imperial College London, London SW7 2AZ, UK Abstract: Flow in porous media is affected by properties and processes that occur on all scales such as reservoir heterogeneity. Numerical models are often used to predict the behavior of flow in these systems. However such models cannot represent explicitly processes/properties on all scales and the level of details that can be incorporated in a simulation model is constrained by the computational capacity and resources available. “Upscaling’ of small scale properties/processes is used to transfer information from scale of measurement(small) to a larger scale to study the physical impact of subgrid scale properties sand process on the scale that governing equations are explicitly expressed. Although there is an extensive literature demonstrating that the large grid flow equations may not be the same as those on the small scale, the most commonly applied methods assume that form of flow equations doesn’t change with change of scale and involve the use of an effective permeability and modified relative permeabilities often combined with specialized gridding techniques. Indeed careful coarse grid generation can improve performance of upscaling and remove the requirement to upscaling multi-phase flow properties. In essence all these methods attempt to minimize differences between fine and coarse grid simulations by optimizing the location of coarse grid block boundaries. Permeability-based techniques preserve the variation of permeability within the coarse grid resulting in finer gridding around regions of extreme permeability, while flow-based techniques refine the grid in areas of high flow-rate. In this thesis a novel grid coarsening technique has been developed that is based upon conserving vorticity in the flows through heterogeneous porous media while scale of simulation changes. We optimize location of coarse grid boundaries by firstly recognizing areas of high and low vorticity from single-phase flow simulation. We then generate simulation models which are more refined in the areas of high vorticity intensity and coarser in low vorticity. We finally demonstrate the successful application of the method to two-phase simulations in a range of heterogeneous models. This robust technique provides an insight into the success of the existing flow-based and permeability-based griddings and essentially incorporates both flow effects and geology complexity in gridding.
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