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Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling

  • Tawfik RajehEmail author
  • Rachid Ababou
  • Manuel Marcoux
  • Israel Cañamon
Article
  • 27 Downloads

Abstract

A fast upscaling procedure for determining the equivalent hydraulic conductivity of a three-dimensional fractured rock is presented in this paper. A modified semi-analytical superposition method is developed to take into account, at the same time, the hydraulic conductivity of the porous matrix (KM) and the fractures (KF). The connectivity of the conductive fracture network is also taken into account. The upscaling approach has been validated by comparison with the hydraulic conductivity of synthetic samples calculated with full numerical procedures (flow simulations and averaging). The extended superposition approach is in good agreement with numerical results for infinite size fractures. For finite size fractures, an improved model that takes into account the connectivity of the fracture network through multiplicative connectivity indexes determined empirically is proposed. This improved model is also in good agreement with the numerical results obtained for different configurations of fracture networks.

Keywords

Fractured porous medium Three-dimensional upscaling Equivalent hydraulic conductivity Numerical simulations Darcy Random fracture sets Network connectivity 

Notes

Acknowledgements

The first three authors wish to acknowledge the financial support of ADEME (France) in the framework of the GeotRef project “Géothermie haute énergie en Reservoirs fracturés” (www.geotref.org). We thank the anonymous reviewers for their careful reading of the manuscript and for their insightful comments and suggestions.

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Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  1. 1.Institut de Mécanique des Fluides de Toulouse (IMFT)CNRS and Université de ToulouseToulouseFrance
  2. 2.ETSI de Minas y Energía, Departamento de Ingeniería Geológica y MineraUniversidad Politécnica de MadridMadridSpain

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