Mathematical Geosciences

, Volume 45, Issue 3, pp 321–340 | Cite as

Rock Type Connectivity Estimation Using Percolation Theory

  • Saeid Sadeghnejad
  • Mohsen MasihiEmail author
  • Mahmoudreza Pishvaie
  • Peter R. King


Complicated sedimentary processes control the spatial distribution of geological heterogeneities. This serves to make the nature of the fluid flow in the hydrocarbon reservoirs immensely complex. Proper modeling of these heterogeneities and evaluation of their connectivity are crucial and affects all aspects of fluid flow. Since the natural variability of heterogeneity occurs in a myriad of length scales, accurate modeling of the rock type connectivity requires a very fine scheme, which is computationally very expensive. Hence, this makes other alternative methods such as the percolation approach attractive and necessary. The percolation approach considers the hypothesis that a reservoir can be split into either permeable (sand/fracture) or impermeable rocks (shale/matrix). In this approach, the connectivity of the permeable fraction governs the flow. This method links the global properties of the system to the density of the permeable objects distributed randomly in the system. Moreover, this approach reduces many results to some simple master curves from which all-possible outcomes can be predicted by simple algebraic transformations. The current study contributes to extending the applicability of the methodology to anisotropic systems as well as using the complicated and more realistic sandbody shapes (for example, ellipsoids). This enables us to attain a better assessment of the connectivity and its associated uncertainty of the complicated rock types. Furthermore, to validate the approach, the Burgan reservoir dataset of the Norouz offshore oil field in the south of Iran was used. The findings are in conformity with the percolation approach predictions.


Percolation theory Rock type Connectivity Ellipsoid sandbodies Anisotropy Validation 



The authors would like to acknowledge useful conversations with Dr Tavakoli. In addition, we are grateful to the editor and reviewers who provided many useful suggestions.


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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  • Saeid Sadeghnejad
    • 1
  • Mohsen Masihi
    • 2
    Email author
  • Mahmoudreza Pishvaie
    • 2
  • Peter R. King
    • 3
  1. 1.Department of Chemical EngineeringTarbiat Modares UniversityTehranIran
  2. 2.Department of Chemical and Petroleum EngineeringSharif University of TechnologyTehranIran
  3. 3.Earth Science & Engineering DepartmentImperial CollegeLondonUK

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