High Resolution Geostatistics on Coarse Unstructured Flow Grids

Caumon, Guillaume; Grosse, Olivier; Mallet, Jean-Laurent

doi:10.1007/978-1-4020-3610-1_71

Cited by 1 publication

(2 citation statements)

References 15 publications

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“…if its inner vertices all have the same number of neighbours (e.g. Hirasaki and O'Dell, 1970;Caumon et al, 2005) (Fig. 2.1 and Fig.…”

Section: Structured Gridsmentioning

confidence: 99%

“…2.5b). The values of the large cells are computed by upscaling, analytically or numerically, the values of the fine cells contained within the larger unstructured grid cells (e.g., He et al, 2002;Caumon et al, 2005;Durlofsky, 2005). Such a method to honor support effect is illustrated in Gross and Boucher (2015) for an arbitrary variable (Fig.…”

Section: Use Of a Fine Gridmentioning

confidence: 99%

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Direct simulation of non-additive variables on unstructured grids : the case of permeability

Mourlanette¹

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Uncertainties related to permeability heterogeneity can be estimated using geostatistical simulation methods. Usually, these methods are applied on regular grids with cells of constant size, whereas unstructured grids are more flexible to honor geological structures and offer local refinements for fluid-flow simulations. However, cells of different sizes require to account for the support dependency of permeability statistics (support effect). This work presents a novel workflow based on the power averaging technique. The averaging exponent ω is estimated using a response surface calibrated from numerical upscaling experiments. Using spectral turning bands, permeability is simulated on points in each unstructured cell, and later averaged with a local value of ω that depends on the cell size and shape, but also on the proportion of each facies inside the cell. The method is first illustrated on a synthetic case, with a single facies. The simulation of a tracer experiment is used to compare this novel geostatistical simulation method with a conventional approach based on a fine scale Cartesian grid. The results show the consistency of both the simulated permeability fields and the tracer breakthrough curves. The application to an industrial case with two facies is then presented and shows both consistent permeability fields and computational costs acceptable for the industry. Indeed, the computational cost for several realizations is much lower than the conventional approach based on a pressure-solver upscaling. The method works for the presented cases, but its theoretical ro-bustness can still be improved. A discussion on pressure solver upscal-ing parameters selection and power averaging limits is available in the conclusion, as well as a few research perspectives on multiple facies and non stationary proportions inclusion, the management of anisotropy and the extension to multiphase flow.

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“…if its inner vertices all have the same number of neighbours (e.g. Hirasaki and O'Dell, 1970;Caumon et al, 2005) (Fig. 2.1 and Fig.…”

Section: Structured Gridsmentioning

confidence: 99%

Section: Use Of a Fine Gridmentioning

confidence: 99%