Statistical behavior of fingering in a displacement process in heterogeneous porous medium with capillary pressure

1969 ◽  
Vol 47 (3) ◽  
pp. 319-324 ◽  
Author(s):  
A. P. Verma
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Capillary Pressure ◽  
Equation Of Motion ◽  
Perturbation Solution ◽  
Heterogeneous Porous Medium ◽  
Water Displacement ◽  
Statistical Behavior ◽  
Oil Water ◽  
Special Case

The stabilization of fingers in a specific oil–water displacement process with capillary pressure has been statistically discussed for a given heterogeneous porous medium. The equation of motion has been solved by a perturbation method. It is shown that the perturbation solution does produce "stable" fingers in one special case corresponding to the investigated problem.

Nonlinear behavior of instabilities in diphasic flow in a heterogeneous porous medium

1980 ◽  
Vol 58 (12) ◽  
pp. 1729-1733
Author(s):  
D. S. Pal
Keyword(s):  
Porous Medium ◽  
Statistical Model ◽  
Capillary Pressure ◽  
Nonlinear Behavior ◽  
Heterogeneous Porous Medium ◽  
Water Displacement ◽  
Oil Water ◽  
Statistical Viewpoint

The nonlinear behavior of instabilities (fingers) in a specific oil–water displacement process, which includes the effects of capillary pressure in a heterogeneous porous medium, has been analysed from a statistical viewpoint. It is shown that, based on theories available for capillary pressure, the statistical model does not lead to any stabilization of the fingers.

Imbibition in a cracked porous medium

1969 ◽  
Vol 47 (22) ◽  
pp. 2519-2524 ◽  
Author(s):  
A. P. Verma
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Viscosity Ratio ◽  
Perturbation Technique ◽  
Water Imbibition ◽  
Phase Saturation ◽  
Water Viscosity ◽  
Oil Water ◽  
The Relationship ◽  
Special Case

In this paper, one special case of oil–water imbibition phenomena in a cracked porous medium of a finite length is analytically discussed. The equation for the linear countercurrent imbibition is a nonlinear differential equation whose solution has been obtained by a perturbation technique. For definiteness, specific results have been used for the relationship between relative permeability and phase saturation) impregnation function, oil–water viscosity ratio, and capillary pressure dependence on phase saturation due to Jones, Bokserman et al., Evgen'ev, and Oroveanu, respectively. An expression for the wetting phase saturation has been derived.

Thermodynamic Analysis of the Darcy Law

1961 ◽  
Vol 28 (2) ◽  
pp. 208-212 ◽  
Author(s):  
R. G. Mokadam
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Gravitational Force ◽  
Equation Of Motion ◽  
Darcy Law ◽  
Navier Stokes ◽  
Proportionality Factor ◽  
Navier Stokes Equation ◽  
Special Case

The Darcy law is used extensively to describe the flow of fluids through porous media. According to this law the fluid flow is linearly dependent upon the pressure gradient and the gravitational force. The proportionality factor is generally known as the permeability of the porous medium. The Darcy law cannot be derived from the Navier-Stokes equation since this equation includes terms which characterize the fluid only. With the help of nonreversible thermodynamics it is possible to develop a general equation of motion of a fluid through a porous body, and obtain the Darcy law as a special case of such an equation.

scholarly journals Generalization of hyperbolic perturbation solution for heteroclinic orbits of strongly nonlinear self-excited oscillator

2015 ◽  
Vol 23 (19) ◽  
pp. 3071-3091 ◽  
Author(s):  
Yang-Yang Chen ◽  
Le-Wei Yan ◽  
Ray Kai-Leung Su ◽  
Bo Liu
Keyword(s):  
Perturbation Method ◽  
Present Method ◽  
Perturbation Solution ◽  
Heteroclinic Orbits ◽  
Heteroclinic Solutions ◽  
Strongly Nonlinear ◽  
Excited Oscillator ◽  
Special Case ◽  
Perturbation Solutions

A generalized hyperbolic perturbation method for heteroclinic solutions is presented for strongly nonlinear self-excited oscillators in the more general form of [Formula: see text]. The advantage of this work is that heteroclinic solutions for more complicated and strong nonlinearities can be analytically derived, and the previous hyperbolic perturbation solutions for Duffing type oscillator can be just regarded as a special case of the present method. The applications to cases with quadratic-cubic nonlinearities and with quintic-septic nonlinearities are presented. Comparisons with other methods are performed to assess the effectiveness of the present method.

Homotopy Perturbation Method for General Form of Porous Medium Equation

2009 ◽  
Vol 12 (11) ◽  
pp. 1121-1127 ◽  
Author(s):  
Jafar Biazar ◽  
Zainab Ayati ◽  
Hamideh Ebrahimi
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Porous Medium Equation ◽  
Homotopy Perturbation ◽  
Medium Equation

Analysis of two-dimensional solute transport through heterogeneous porous medium

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Atul Kumar ◽  
◽  
Lav Kush Kumar ◽  
Shireen Shireen ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

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