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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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