How to share underground reservoirs

Scientific Reports

Volumn 2, Issue , 2012, Pages

  Schrenk, K J ^a   Araujo N A M ^a   Herrmann, H J ^a,b  

^a ETH ZURICH   (Switzerland)

^b FEDERAL UNIVERSITY OF CEARÁ   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868271605     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep00751     Document Type: Article

References (35)

1. Hannesson, R. Extracting common oil: cooperation or competition? Energy J. 21, 105-120 (2000). (Pubitemid 34277939)
2. Christensen, J. R., Stenby, E. H. & Skauge, A. Review of WAG field experience. SPE Reserv. Eval. Eng. 4, 97-106 (2001). (Pubitemid 33817079)
3. Maugeri, L. Squeezing more oil from the ground. Sci. Am. 301, 56-63 (2009).
4. Yan, J., Zhao, B., Wang, L., Zelenetz, A. & Schwartz, L. H. Marker-controlled watershed for lymphoma segmentation in sequential CT images. Med. Phys. 33, 2452-2460 (2006). (Pubitemid 43967233)
5. Cieplak, M., Maritan, A. & Banavar, J. R. Optimal paths and domain walls in the strong disorder limit. Phys. Rev. Lett. 72, 2320-2323 (1994). (Pubitemid 24975152)
6. Fehr, E., Schrenk, K. J., Araújo, N. A. M., Kadau, D., Grassberger, P., Andrade Jr., J. S. & Herrmann, H. J. Corrections to scaling for watersheds, optimal path cracks, and bridge lines. Phys. Rev. E 86, 011117 (2012).
7. Herrmann, H. J., Hong, D. C. & Stanley, H. E. Backbone and elastic backbone of percolation clusters obtained by the new method of 'burning'. J. Phys. A: Math. Gen. 17, L261-L266 (1984).
8. Coniglio, A. Fractal structure of Ising and Potts clusters: exact results. Phys. Rev. Lett. 62, 3054-3057 (1989).
9. Lorenz, C. D. & Ziff, R. M. Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices. Phys. Rev. E 57, 230-236 (1998). (Pubitemid 128625721)
10. Ballesteros, H. G., Fernández, L. A., Mart́in-Mayor, V., Muñoz Sudupe, A., Parisi, G. & Ruiz-Lorenzo, J. J. Scaling corrections: site percolation and Ising model in three dimensions. J. Phys. A: Math. Gen. 32, 1-13 (1999).
11. Deng, Y. & Blöte, H. W. J. Monte Carlo study of the site-percolation model in two and three dimensions. Phys. Rev. E 72, 016126 (2005).
12. Stauffer, D. & Aharony, A. Introduction to Percolation Theory. Taylor & Francis, London, second edition, (1994).
13. Wettstein, S. J., Wittel, F. K., Araújo, N. A. M., Lanyon, B. & Herrmann, H. J. From invasion percolation to flow in rock fracture networks. Physica A 391, 264-277 (2012).
14. Isichenko, M. B. Percolation, statistical topography, and transport in random media. Rev. Mod. Phys. 64, 961-1043 (1992).
15. Sahimi, M. Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing. Rev. Mod. Phys. 65, 1393-1534 (1993).
16. Oliveira, E. A., Schrenk, K. J., Araújo, N. A. M., Herrmann, H. J. & Andrade Jr., J. S. Optimal-path cracks in correlated and uncorrelated lattices. Phys. Rev. E 83, 046113 (2011).
17. Fehr, E., Kadau, D., Araújo, N. A. M., Andrade Jr., J. S. & Herrmann, H. J. Scaling relations for watersheds. Phys. Rev. E 84, 036116 (2011).
18. Achlioptas, D., D'Souza, R. M. & Spencer, J. Explosive percolation in random networks. Science 323, 1453-1455 (2009).
19. Riordan, O. & Warnke, L. Explosive percolation is continuous. Science 333, 322-324 (2011).
20. Manna, S. S. & Chatterjee, A. A new route to explosive percolation. Physica A 390, 177-182 (2011).
21. Chen, W. & D'Souza, R. M. Explosive percolation with multiple giant components. Phys. Rev. Lett 106, 115701 (2011).
22. Nagler, J., Levina, A. & Timme, M. Impact of single links in competitive percolation. Nat. Phys. 7, 265-270 (2011).
23. Nagler, J., Tiessen, T. & Gutch, H. W. Continuous percolation with discontinuities. Phys. Rev. X 2, 031009 (2012).
24. Bizhani, G., Paczuski, M. & Grassberger, P. Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs. Phys. Rev. E 86, 011128 (2012).
25. Araújo, N. A. M. & Herrmann, H. J. Explosive percolation via control of the largest cluster. Phys. Rev. Lett 105, 035701 (2010).
26. Schrenk, K. J., Araújo, N. A. M. & Herrmann, H. J. Gaussian model of explosive percolation in three and higher dimensions. Phys. Rev. E 84, 041136 (2011).
27. Schrenk, K. J., Felder, A., Deflorin, S., Araújo, N. A. M., D'Souza, R. M. & Herrmann, H. J. Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition. Phys. Rev. E 85, 031103 (2012).
28. Ziff, R. M. Four-tap shift-register-sequence random-number generators. Comput. Phys 12, 385-392 (1998).
29. Newman, M. E. J. & Ziff, R. M. Efficient Monte Carlo algorithm and high-precision results for percolation. Phys. Rev. Lett. 85, 4104-4107 (2000). (Pubitemid 32020578)
30. Newman, M. E. J. & Ziff, R. M. Fast Monte Carlo algorithm for site or bond percolation. Phys. Rev. E 64, 016706 (2001).
31. Wilkinson, D. & Willemsen, J. F. Invasion percolation: a new form of percolation theory. J. Phys. A: Math. Gen. 16, 3365-3376 (1983).
32. Lenormand, R. Flow through porous media: limits of fractal patterns. Proc. R. Soc. Lond. A 423, 159-168 (1989).
33. Schrenk, K. J., Araújo, N. A. M., Andrade Jr., J. S. & Herrmann, H. J. Fracturing ranked surfaces. Sci. Rep. 2, 348 (2012).
34. Mandelbrot, B. B. The Fractal Geometry of Nature. Freeman, New York, (1983).
35. Tricot, C., Quiniou, J. F., Wehbi, D., Roques-Carmes, C. & Dubuc, B. Evaluation de la dimension fractale d'un graphe. Revue Phys. Appl. 23, 111-124 (1988).