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Point-to-point connectivity prediction in porous media using percolation theory

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  • Tavagh-Mohammadi, Behnam
  • Masihi, Mohsen
  • Ganjeh-Ghazvini, Mostafa

Abstract

The connectivity between two points in porous media is important for evaluating hydrocarbon recovery in underground reservoirs or toxic migration in waste disposal. For example, the connectivity between a producer and an injector in a hydrocarbon reservoir impact the fluid dispersion throughout the system. The conventional approach, flow simulation, is computationally very expensive and time consuming. Alternative method employs percolation theory. Classical percolation approach investigates the connectivity between two lines (representing the wells) in 2D cross sectional models whereas we look for the connectivity between two points (representing the wells) in 2D aerial models. In this study, site percolation is used to determine the fraction of permeable regions connected between two cells at various occupancy probabilities and system sizes. The master curves of mean connectivity and its uncertainty are then generated by finite size scaling. The results help to predict well-to-well connectivity without need to any further simulation.

Suggested Citation

  • Tavagh-Mohammadi, Behnam & Masihi, Mohsen & Ganjeh-Ghazvini, Mostafa, 2016. "Point-to-point connectivity prediction in porous media using percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 304-313.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:304-313
    DOI: 10.1016/j.physa.2016.05.011
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    References listed on IDEAS

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    1. da Silva, Luciano R & Paul, Gerald & Havlin, Shlomo & Baker, Don R & Stanley, H.Eugene, 2002. "Distribution of backbone mass between non-parallel lines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 140-145.
    2. Ganjeh-Ghazvini, Mostafa & Masihi, Mohsen & Ghaedi, Mojtaba, 2014. "Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 214-221.
    3. da Silva, Luciano R. & Paul, Gerald & Havlin, Shlomo & Baker, Don R. & Stanley, H.Eugene, 2003. "Scaling of cluster mass between two lines in 3d percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 307-318.
    4. Oliveira, C.L.N. & Araújo, A.D. & Lucena, L.S. & Almeida, M.P. & Andrade, J.S., 2012. "Post-breakthrough scaling in reservoir field simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3219-3226.
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    Cited by:

    1. Soltani, Ali & Sadeghnejad, Saeid, 2018. "Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 376-389.
    2. Huang, Xudong & Yang, Dong & Kang, Zhiqin, 2021. "Impact of pore distribution characteristics on percolation threshold based on site percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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