The Effect of Permeability Contrast in Percolation Reservoir Models on the Breakthrough Time Distribution

Document Type : Research Paper

Authors

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

Abstract

In waterflooding process, the time for breakthrough of injecting fluid into a production well is of great importance. Predicting this time helps in designing reservoir development plan. Due to uncertainties in reservoir characterization, estimating the breakthrough is not easy, so alternative methods to estimate quickly the breakthrough time is useful. The percolation method uses limited available reservoir data to predict the breakthrough time distribution, and it may be used for engineering applications. However, implementation of this to real reservoirs requires some adjustments. The aim of this study is to show how percolation approach can be used to real problems. In particular, the effects of permeability contrast between the reservoir and non-reservoir parts in the model are investigated. In order to use the breakthrough scaling function to more realistic reservoir models, a dimensionless breakthrough time was used. The analysis of the breakthrough time of models with zero permeability background (tk=0) and such time for the case of non-zero permeability background (tk=αk) shows a linear dependency which can be used to find breakthrough time distribution. Hence, this correction extends the applicability of the percolation method for predicting breakthrough time when permeability of the system background is not zero.

Keywords


  1. Sahimi M (1994) Applications of percolation theory, 1st Edition, CRC Press, London, 1-276. ##
  2. Stauffer D, Aharony A (1994) Introduction to percolation theory, 2nd Edition, Taylor and Francis, London, 1- 192. ##
  3. King P, Masihi M (2018) Percolation theory in reservoir engineering, World Scientific, 300: 978-1-78634-523-3. ##
  4. Flory P J (1941) Molecular size distribution in three dimensinal polymerrs, Journal of the American Chemical Society, 63, 11: 3083-3090. ##
  5. Broadbent S R, Hammersley J M (1957) Percolation processess, Mathematical Proceedings of the Cambridge Philosophical Society, 629-641. ##
  6. Selyakov V I, Kadet V V (1996) Percolation models for transport in porous media with applications to reservoir engineering, Springer, 1-243. ##
  7. King P R, Buldyrev S V, Dokholyan N V, Havlin S, Lopez E, Paul G, Stanley H E (2002) Percolation theory, London petrophysical society. ##
  8. Chandler R, Koplik J, Lerman K, Willemsen J F (1982) Capillary displacement and percolation in porous media, Journal of Fluid Mechanics, 119: 249-267. ##
  9. Lenormand R, S Bories (1980) Description d’un mécanisme de connexion de liaison destiné à l’étudedu drainageavec piégeage en milieu poreux, Comptes Rendus Hebdomadaires des Séances de ‘L’académie des Sciences, 279-291. ##
  10. Wilkinson D, Willemsen J F (1983) Invasion percolation: a new form of percolation theory, Journal of Physics A: Mathematical and General, 16: 3365-3376. ##
  11. Chayes J T, Chayes L, Newman C M (1985) The stochastic geometry of invasion percolation, Communications in mathematical physics, 101: 383-407. ##
  12. Dhar D (2017) Self-tuning to the critical point: invasion percolation, Journal of Physics A: Mathematical and Theoretical. ##
  13. Rui G, Xin W, Mingguang C, Bo C, Chunming H (2017) The fractures optimization method with the threshold Pressure of multistage fracturing in tight oil reservoir, In SPE Reservoir Characterisation and Simulation Conference and Exhibition. OnePetro. ##
  14. Blunt M J (2017) Multiphase flow in permeable media, 1st edition, Cambridge University Press, 02-16, Cambridge, United Kingdom|New York. ##
  15. Ghanbarian B (2022) Estimating the scale dependence of permeability at pore and core scales: Incorporating effects of porosity and finite size, Advances in Water Resources, 161: 104123. ##
  16. Ghanbarian B (2022) Scale dependence of tortuosity and diffusion: Finite-size scaling analysis, Journal of Contaminant Hydrology, 245: 103953. ##
  17. Sahimi M (2022) Universal frequency-dependent permeability of heterogeneous porous media: effective–medium approximation and critical-path analysis, Transport in Porous Media, 1-15. ##
  18. Soltani A, Sadeghnejad S (2018) Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations, Physica A: Statistical Mechanics and its Applications 508: 376-389. ##
  19. Hamzehpour H, Pazoki S, Khazaei M, Sahimi M (2021) Dependence of percolation and flow properties of fracture networks on the morphology, Physica A: Statistical Mechanics and its Applications 584: 126361. ##
  20. Sadeghnejad S, Masihi M, Shojaei A, Pishvaie M R, King PR (2012) Field scale characterization of geological formations using percolation theory, Transport in Porous Media, 92: 357–372. ##
  21. Sadeghnejad S, Masihi M (2011) Water flooding performance evaluation using percolation theory, Journal of Petroleum Science and Technology, 1, 2: 19-23. ##
  22. Andrade J S, Buldyrev S V, Dokholyan N V, Havlin S, King P R, Lee Y, Paul G, Stanley H E (2000) Flow between two sites on a percolation cluster, Physical Review E, 62, 6: 1-31. ##
  23. King P R, Buldyrev S V, Dokholyan N V, Havlin S, Lopez E, Paul G, Stanley H E (2002) Using percolation theory to predict oil field performance, Statistical Mechanics and its Applications, 314, 1-4: 103-108. ##
  24. Dokholyan N V, Lee Y, Buldyrev S V, Havlin S, King P R, Stanley H E (1999) Scaling of the distribution of shortest paths in percolation, Journal of Statistical physics, 93, 3: 603-613. ##
  25. Shokrollahzadeh S, Masihi M, Ghazanfari M H, King P (2019) Effect of characteristic time on scaling of breakthrough time distribution for two-phase displacement in percolation porous media, Transport in Porous Media, 130, 3: 889-902. ##
  26. Oliveira C L N, Araújo A D, Lucena L S, Almeida M P, Andrade Jr. JS (2012) Post-breakthrough scaling in reservoir field simulation, Physica A: Statistical Mechanics and its Applications, 391, 11: 3219-3226. ##