Vol. 1, No. 1, 2006

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Nonlocal damage accumulation and fluid flow in diatomites

Grigory Isaakovich Barenblatt, Michiel Bertsch and Carlo Nitsch

Vol. 1 (2006), No. 1, 143–168
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.

Keywords
flow in porous media, oil engineering, continuum damage mechanics, degenerate parabolic system
Mathematical Subject Classification 2000
Primary: 76S05
Secondary: 74A45, 35K65
Milestones
Received: 28 September 2005
Accepted: 19 April 2006
Published: 9 May 2007
Authors
Grigory Isaakovich Barenblatt
Department of Mathematics
University of California
Berkeley CA 94720
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Mail Stop 50A/1148
Berkeley, CA 94720
United States
http://math.lbl.gov/barenblatt/barenblatt.html
Michiel Bertsch
Istituto per le Applicazioni del Calcolo “Mauro Picone”
Consiglio Nazionale delle Ricerche
Viale del Policlinico, 137
I-00161 Roma
Italy
Dipartimento di Matematica
Universitá degli Studi di Roma “Tor Vergata”
Via della Ricerca Scientifica
I-00133 Roma
Italy
Carlo Nitsch
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”
Universitá degli Studi di Napoli “Federico II”
Via Cintia, Monte S. Angelo
I-80126 Napoli
Italy
http://wpage.unina.it/c.nitsch/