Direct simulation of non-additive properties on unstructured grids

Pauline Mourlanette,Pierre Biver,Philippe Renard,Benoît Nœtinger,Guillaume Caumon,Yassine Alexandre Perrier

doi:10.1016/j.advwatres.2020.103665

Abstract

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 paper 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.The method is illustrated on a synthetic case. 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 computational cost is much lower than the conventional approach based on a pressure-solver upscaling.

Highlights

Subsurface phenomena cannot be observed directly due to scale issues and inaccessibility
This paper focuses on the spatial modeling of permeability fields
Several points are randomly placed inside each cell and, for every realization, the permeability is simulated on these points using the Spectral Turning Bands (STB) approach (Fig. 1c.)

Summary

Introduction

Subsurface phenomena cannot be observed directly due to scale issues and inaccessibility. The high spatial variability of rock types and the associated permeability field as well as the high spatial and temporal variability of fluid types and displacements is a main source of uncertainties. Estimating these uncertainties is important in a context of engineering design and decision making. Similar uncertainty issues coupled with decision-making are encountered in other applied geoscience engineering, such as oil and gas industry (Preux, 2016), CO2 storage in aquifers (Michael et al, 2010; Akhurst et al, 2015), or geothermal energy production (Vogt et al, 2010; Quinlivan et al, 2015; Witter et al, 2019). To assess the uncertainty related to this problem, one can employ geostatistical simulation methods (Deutsch and Journel, 1992; Goovaerts, 1997; Chilès and Delfiner, 2012)

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Conclusion