M. R. Azad; A. Kamkar Rouhani; B. Tokhmechi; M. Arashi
Abstract
Upscaling based on the bandwidth of the kernel function is a flexible approach to upscale the data because the cells will be coarse-based on variability. The intensity of the coarsening of cells in this method can be controlled with bandwidth. In a smooth variability region, a large number of cells will ...
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Upscaling based on the bandwidth of the kernel function is a flexible approach to upscale the data because the cells will be coarse-based on variability. The intensity of the coarsening of cells in this method can be controlled with bandwidth. In a smooth variability region, a large number of cells will be merged, and vice versa, they will remain fine with severe variability. Bandwidth variation can be effective in upscaling results. Therefore, determining the optimal bandwidth in this method is essential. For each bandwidth, the upscaled model has a number of upscaled blocks and an upscaling error. Obviously, higher thresholds or bandwidths cause a lower number of upscaled blocks and a higher sum of squares error (SSE). On the other hand, using the smallest bandwidth, the upscaled model will remain in a fine scale, and there will be practically no upscaling. In this work, different approaches are used to determine the optimal bandwidth or threshold for upscaling. Investigation of SSE changes, the intersection of two charts, namely SSE and the number of upscaled block charts, and the changes of SSE values versus bandwidths, are among these approaches. In this particular case, if the goal of upscaling is to minimize the upscaling error, the intersection method will obtain a better result. Conversely, if the purpose of upscaling is computational cost reduction, the SSE variation approach will be more appropriate for the threshold setting.
B. Tokhmechi; M. Rabiei; H. Azizi; V. Rasouli
Abstract
A complete and accurate analysis of the complex spatial structure of heterogeneous hydrocarbon reservoirs requires detailed geological models, i.e. fine resolution models. Due to the high computational cost of simulating such models, single resolution up-scaling techniques are commonly used to reduce ...
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A complete and accurate analysis of the complex spatial structure of heterogeneous hydrocarbon reservoirs requires detailed geological models, i.e. fine resolution models. Due to the high computational cost of simulating such models, single resolution up-scaling techniques are commonly used to reduce the volume of the simulated models at the expense of losing the precision. Several multi-scale techniques have also been developed for simulating heterogeneous reservoirs including those in which a limited number of blocks down-scale, i.e. splitting coarse blocks into fine cells around the well-zones in the case of simulation of hydraulic fracturing. In these cases, locally computed basis functions are employed to construct a global solver at a coarse-scale such as wavelet- and kernel-based up-scaling techniques. In this paper, a novel/robust 2D block-ordering system is presented, which enables solving multi-resolution up-scaling fluid flow simulations. The results will be described for a simple model, and fluid flow equations will be developed in order to show the structure of transmissibility matrix. It is confirmed that with a developed block-ordering system not only the accuracy of history match increases but also the CPU time decreases.
