TY - JOUR
T1 - Analysis of generalized Forchheimer flows of compressible fluids in porous media
AU - Aulisa, Eugenio
AU - Bloshanskaya, Lidia
AU - Hoang, Luan
AU - Ibragimov, Akif
N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - This work is focused on the analysis of nonlinear flows of slightly compressible fluids in porous media not adequately described by Darcy's law. We study a class of generalized nonlinear momentum equations which covers all three well-known Forchheimer equations, the so-called two-term, power, and three-term laws. The generalized Forchheimer equation is inverted to a nonlinear Darcy equation with implicit permeability tensor depending on the pressure gradient. This results in a degenerate parabolic equation for the pressure. Two classes of boundary conditions are considered, given pressure and given total flux. In both cases they are allowed to be unbounded in time. The uniqueness, Lyapunov and asymptotic stabilities, and other long-time dynamical features of the corresponding initial boundary value problems are analyzed. The results obtained in this paper have clear hydrodynamic interpretations and can be used for quantitative evaluation of engineering parameters. Some numerical simulations are also included.
AB - This work is focused on the analysis of nonlinear flows of slightly compressible fluids in porous media not adequately described by Darcy's law. We study a class of generalized nonlinear momentum equations which covers all three well-known Forchheimer equations, the so-called two-term, power, and three-term laws. The generalized Forchheimer equation is inverted to a nonlinear Darcy equation with implicit permeability tensor depending on the pressure gradient. This results in a degenerate parabolic equation for the pressure. Two classes of boundary conditions are considered, given pressure and given total flux. In both cases they are allowed to be unbounded in time. The uniqueness, Lyapunov and asymptotic stabilities, and other long-time dynamical features of the corresponding initial boundary value problems are analyzed. The results obtained in this paper have clear hydrodynamic interpretations and can be used for quantitative evaluation of engineering parameters. Some numerical simulations are also included.
UR - http://www.scopus.com/inward/record.url?scp=70350728162&partnerID=8YFLogxK
U2 - 10.1063/1.3204977
DO - 10.1063/1.3204977
M3 - Article
AN - SCOPUS:70350728162
VL - 50
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 10
M1 - 103102
ER -