Hydrogeology Journal

, 16:1239 | Cite as

Efficient upscaling of hydraulic conductivity in heterogeneous alluvial aquifers

  • Jan H. FleckensteinEmail author
  • Graham E. Fogg


An efficient method to upscale hydraulic conductivity (K) from detailed three-dimensional geostatistical models of hydrofacies heterogeneity to a coarser model grid is presented. Geologic heterogeneity of an alluvial fan system was characterized using transition-probability-based geostatistical simulations of hydrofacies distributions. For comparison of different hydrofacies architecture, two alternative models with different hydrofacies structures and geometries and a multi-Gaussian model, all with the same mean and variance in K, were created. Upscaling was performed on five realizations of each of the geostatistical models using the arithmetic and harmonic means of the K-values within vertical grid columns. The effects of upscaling on model domain equivalent K were investigated by means of steady-state flow simulations. A logarithmic increase in model domain equivalent K with increasing upscaling, was found for all fields. The shape of that upscaling function depended on the structure and geometry of the hydrofacies bodies. For different realizations of one geostatistical model, however, the upscaling function was the same. From the upscaling function a factor could be calculated to correct the upscaled K-fields for the local effects of upscaling.


Upscaling Hydraulic properties Heterogeneity Geostatistics Numerical modeling 

Upscaling efficace de la conductivité hydraulique dans les aquifères alluviaux hétérogènes


Une méthode efficace pour upscale la conductivité hydraulique (K) à partir de modèles géostatistiques 3D détaillés de l’hétérogénéité d’hydrofaciès vers un maillage de modèle plus grossier est présentée. L’hétérogénéité géologique d’un système de cône alluvial a été caractérisée en utilisant des simulations géostatistiques basées sur une probabilité d’évolution des distributions d’hydrofaciès. Pour comparer plusieurs compositions d’hydrofaciès deux modèles alternatifs avec des structures d’hydrofaciès et des géométries différentes et un modèle Gaussien multiple, tous avec la même moyenne et variance de K, ont été créés. L’upscaling a été réalisé sur cinq mises en œuvre de chacun des modèles géostatistiques en utilisant les moyennes arithmétiques et harmoniques des valeurs K au sein de colonnes verticales du maillage. Les effets de l’upscaling de l’équivalent K dans le domaine du modèle ont été étudiés au moyen de simulations en écoulement permanent. Un accroissement logarithmique de l’équivalent K dans le domaine du modèle avec un upscaling croissant, a été trouvé pour tous les domaines. La forme de cette fonction d’upscaling dépendait de la structure et de la géométrie des ensembles d’hydrofaciès. Pour différentes mises en œuvre d’un modèle géostatistique, toutefois, la fonction d’upscaling était la même. A partir de la fonction d’upscaling un facteur peut être calculé pour corriger les domaines de K upscaled des effets locaux de l’upscaling.

Sobre-escalado eficiente de la conductividad hidráulica en acuíferos aluviales heterogéneos


Se presenta un método eficiente para el sobre-escalado de la conductividad hidráulica (K) a partir de modelos geoestadísticos tridimensionales de heterogeneidades de hidrofacies a modelos con grillas de mayor escala. La heterogeneidad geológica de un abanico aluvial se caracterizó usando probabilidad de transición basada en simulaciones de la distribución de las hidrofacies. Para la comparación de la arquitectura de las distintas hidrofacies, se crearon dos modelos alternativos con diferentes estructuras y geometrías de las hidrofacies y un modelo multi-gaussiano, con la misma media y varianza de K. El sobre-escalado se logró con cinco realizaciones de cada modelo geoestadístico usando las medias aritmética y armónica de los valores de K en cada columna vertical de la grilla. Los efectos del sobre-escalado se investigaron con simulaciones del flujo en estado estacionario. Se halló que un incremento en el sobre-escalado produce un incremento logarítmico en el dominio del modelo con K equivalente. La forma de la función de sobre-escalado depende de la estructura y geometría de los cuerpos de hidrofacies. Sin embargo, para diferentes realizaciones de un dado modelo geoestadístico, la función de sobre-escalado fue la misma. Esa función de sobre-escalado permite calcular un factor que corrige los campos de K sobre-escalados por efectos locales del sobre-escalado.



The authors would like to thank CALFED for their funding through the California Bay-Delta Authority's Ecosystem Restoration Program: Grants ERP No. 99-NO6 and ERP No. 01-NO1. The helpful comments and suggestions from the managing editor, three anonymous reviewers and Christen Knudby were also greatly appreciated.


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of HydrologyUniversity of BayreuthBayreuthGermany
  2. 2.Department of Land, Air and Water Resources and Department of GeologyUniversity of California, DavisDavisUSA

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