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Predicting oil recovery using percolation

Author

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  • King, Peter R.
  • Jr., José S.Andrade
  • Buldyrev, Sergey V.
  • Dokholyan, Nikolay
  • Lee, Youngki
  • Havlin, Shlomo
  • Stanley, H.Eugene

Abstract

One particular practical problem in oil recovery is to predict the time to breakthrough of a fluid injected in one well and the subsequent decay in the production rate of oil at another well. Because we only have a stochastic view of the distribution of rock properties we need to predict the uncertainty in the breakthrough time and post-breakthrough behaviour in order to calculate the economic risk. In this paper we use percolation theory to predict (i) the distribution of the chemical path (shortest path) between two points (representing well pairs) at a given Euclidean separation and present a scaling hypothesis for this distribution which is confirmed by numerical simulation, (ii) the distribution of breakthrough times which can be calculated algebraically rather than by very time consuming direct numerical simulation of large numbers of realisations.

Suggested Citation

  • King, Peter R. & Jr., José S.Andrade & Buldyrev, Sergey V. & Dokholyan, Nikolay & Lee, Youngki & Havlin, Shlomo & Stanley, H.Eugene, 1999. "Predicting oil recovery using percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 107-114.
    • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:107-114
    DOI: 10.1016/S0378-4371(98)00583-4
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    Cited by:

    1. Koohi Lai, Z. & Jafari, G.R., 2013. "Non-Gaussianity effects in petrophysical quantities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5132-5137.
    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. Duccio Piovani & Carlos Molinero & Alan Wilson, 2017. "Urban retail location: Insights from percolation theory and spatial interaction modeling," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-13, October.
    4. Stanley, H.Eugene & Andrade, José S, 2001. "Physics of the cigarette filter: fluid flow through structures with randomly-placed obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 17-30.
    5. Sadeghnejad, S. & Masihi, M. & King, P.R., 2013. "Dependency of percolation critical exponents on the exponent of power law size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6189-6197.
    6. Manwart, C. & Hilfer, R., 2002. "Numerical simulation of creeping fluid flow in reconstruction models of porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 706-713.
    7. Stalgorova, Ekaterina & Babadagli, Tayfun, 2014. "Scaling of production data obtained from Random Walk Particle Tracking simulations in highly fractured porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 181-192.
    8. Najafi, M.N. & Ghaedi, M., 2015. "Geometrical clusters of Darcy’s reservoir model and Ising universality class," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 82-91.

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