Abstract
Our work is focused on certain theoretical aspects of non-linear non-Darcy flows in porous media, and their application in reservoir and hydraulic engineering. The goal of this paper is to develop a mathematically rigorous framework to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. Using fundamental geometric methods, we have proved the existence of a nonlinear scaling operator which relates constant mean curvature surfaces and time invariant pressure distribution graphs constrained by the Darcy-Forchheimer law. The hereby obtained properties of fast flows and their geometric interpretation can be used as analytical tools to evaluate important technological parameters in reservoir engineering.
Original language | English |
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Pages (from-to) | 1734-1751 |
Number of pages | 18 |
Journal | Nonlinear Analysis: Real World Applications |
Volume | 11 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2010 |
Keywords
- CMC surface
- Nonlinear Forchheimer flow
- Porous media
- Productivity index