We have developed a new constrained optimization approachto the coarsening of 3D reservoir models for flow simulation.The optimization maximally preserves a statistical measure ofthe heterogeneity of a fine scale model. Constraints arise fromthe reservoir fluids, well locations, pay/non-pay juxtaposition,and large scale reservoir structure and stratigraphy. Theapproach has been validated for a number of oil and gasprojects, where flow simulation through the coarsened modelis shown to provide an excellent approximation to highresolution calculations performed in the original model.The optimal layer coarsening is related to the analyses ofLi and Beckner (2000), Li, Cullick and Lake (1995), andTesterman (1962). It differs by utilizing a more accuratemeasure of reservoir heterogeneity and by being based onrecursive sequential coarsening, instead of sequentialrefinement. Recursive coarsening is shown to be significantlyfaster than refinement: the cost of the calculation scales as(NX·NY·NZ) instead of (NX·NY·NZ)2. The moreaccurate measure of reservoir heterogeneity is very important;it provides a more conservative estimate of the optimalnumber of layers than the analysis of Li et.al.. The latter isshown to be too aggressive and does not preserve importantaspects of the reservoir heterogeneity. Our approach alsodiffers from the global methods of Stern (1999) and Durlofsky(1994). It does not require the calculation of a global pressuresolution and it does not require the imposition of large scaleflow fields, which may bias the analysis, Fincham (2004).Instead, global flow calculations are retained only to validatethe reservoir coarsening.Our approach can generate highly unstructured, variableresolution, computational grids. The layering scheme for thesegrids follows from the statistical analysis of the reservoir heterogeneity. Locally variable resolution follows from theconstraints (reservoir structure, faults, well locations, fluids,pay/non-pay juxtaposition). Our reservoir simulator has beenmodified to allow a fine scale model to be initialized andfurther coarsened at run time. This has many advantages inthat it provides both simplified and powerful workflows,which allow engineers and geoscientists to work with identicalshared models.
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