Skip to main content
Log in

Dogma: S-shaped

Ode to Ônibus 409

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. V. Azevedo, A. de Souza, F. Furtado, D. Marchesin, and B. Plohr (2010) “The solution by the wave curve method of three-phase flow in virgin reservoirs,” Transp. Porous Media 83: 99–125.

  2. S. E. Buckley and M. C. Leverett (1942) “Mechanism of fluid displacements in sands,” Transactions of the AIME 146: 107–116.

  3. J. Bruining (2007) Multiphase Flow in Porous Media. TU-Delft, Lecture notes. (94 pages.)

  4. P. Castañeda, F. Furtado, and D. Marchesin (2013) “The convex permeability three-phase flow in reservoirs.” IMPA Preprint Série E - 34: 1–35.

  5. P. Castañeda, E. Abreu, F. Furtado, and D. Marchesin “On a universal structure for immiscible three-phase flow in virgin reservoirs.” (Submitted.)

  6. O. A. Olei˘nik (1957) “Discontinuous solutions of non-linear differential equations,” Uspekhi Mat. Nauk 12: 3–73; English translation: AMS Transl. (1963) 26(2): 95–172.

  7. M. Shearer (1988) “Loss of strict hyperbolicity of the Buckley-Leverett equations in three-phase flow in a porous medium”, Numerical Simulation in Oil Recovery IMA Vol. Math. Appl. 11: 263–283.

  8. A. Spivak, H.S. Price, and A. Settari (1977) “Solution of the equations for multidimensional, two-phase, immiscible flow by variational methods,” Soc. Pet. Eng. J. 17: 27–41.

  9. H. Wahanik, A. A. Eftekhari, J. Bruining, D. Marchesin, and K. H. Wolf (2010) “Analytical solutions for mixed CO2-water injection in geothermal reservoirs,” CSUG/SPE 138154.

Download references

Acknowledgments

I thank Professor Furtado (University of Wyoming) and Marchesin (IMPA) for many enlightening conversations, their friendship, and the homework to do aboard the “4-O-9.” I am indebted to the reviewer for his fine comments and also to Gustavo Hime for his friendship. This work was supported by the Department of Mathematics at ITAM and by FAPERJ under Grant E-26/110.017/2014.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pablo Castañeda.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Castañeda, P. Dogma: S-shaped . Math Intelligencer 38, 10–13 (2016). https://doi.org/10.1007/s00283-015-9611-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-015-9611-4

Keywords

Navigation