Communications in Applied Mathematics and Computational Science

Nonlocal damage accumulation and fluid flow in diatomites

Grigory Barenblatt, Michiel Bertsch, and Carlo Nitsch

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Abstract

We investigate a new model for fluid flows in diatomite formations recently introduced by Barenblatt, Patzek, Prostokishin and Silin. We provide numerical evidences of the existence of a sharp front between the damaged and the undamaged rock, and we study the structure of this front. Finally, we simulate some infield operations and we set up a qualitative model control problem to maximize the profit during the oil extraction.

Article information

Source
Commun. Appl. Math. Comput. Sci., Volume 1, Number 1 (2006), 143-168.

Dates
Received: 28 September 2005
Accepted: 19 April 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.camcos/1513798508

Digital Object Identifier
doi:10.2140/camcos.2006.1.143

Mathematical Reviews number (MathSciNet)
MR2244273

Zentralblatt MATH identifier
1102.76070

Subjects
Primary: 76S05: Flows in porous media; filtration; seepage
Secondary: 74A45: Theories of fracture and damage 35K65: Degenerate parabolic equations

Keywords
flow in porous media oil engineering continuum damage mechanics degenerate parabolic system

Citation

Barenblatt, Grigory; Bertsch, Michiel; Nitsch, Carlo. Nonlocal damage accumulation and fluid flow in diatomites. Commun. Appl. Math. Comput. Sci. 1 (2006), no. 1, 143--168. doi:10.2140/camcos.2006.1.143. https://projecteuclid.org/euclid.camcos/1513798508


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References

  • G. I. Barenblatt, V. M. Entov, and R. V. M., Theory of fluid flows through natural rocks, Theory and applications of transport in porous media, vol. 3, Kluwer Academic Publishers, 1990.
  • G. I. Barenblatt, T. W. Patzek, V. M. Prostokishin, and D. B. Silin, SPE75230: Oil deposit in diatomites: A new challenge for subterranean mechanics, SPE/DOE Improved Oil Recovery Symposium, 2002.
  • J. Bear and Y. Bachmat, Introduction to modeling of transport phenomena in porous media, Kluwer Academic Publishers, 1991.
  • M. Bertsch and C. Nitsch, Traveling wave solutions of a nonlinear degenerate parabolic system from petroleum engineering, preprint, 2006.
  • M. Bertsch, R. Dal Passo, and C. Nitsch, A system of degenerate parabolic nonlinear PDE's: a new free boundary problem, Interfaces Free Bound. 7 (2005), no. 3, 255–276.