Onset of convection in a layered porous medium heated from below

1980 ◽  
Vol 96 (2) ◽  
pp. 375-393 ◽  
Author(s):  
R. Mckibbin ◽  
M. J. O'Sullivan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Homogeneous System ◽  
Onset Of Convection

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.

scholarly journals Linear Stability Effect of Densely Distributed Porous Medium and Coriolis Force on Soret Driven Ferrothermohaline Convection

2018 ◽  
Vol 23 (4) ◽  
pp. 911-928
Author(s):  
R. Sekar ◽  
D. Murugan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Normal Mode ◽  
Coriolis Force ◽  
Linear Stability Analysis ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Stability Effect ◽  
Mode Technique

Abstract The effect of Coriolis force on the Soret driven ferrothermohaline convection in a densely packed porous medium has been studied. A linear stability analysis is carried out using normal mode technique. It is found that stationary convection is favorable for the Darcy model, therefore oscillatory instability is studied. A small thermal perturbation is applied to the basic state and linear stability analysis is used for which the normal mode technique is applied. It is found that the presence of a porous medium favours the onset of convection. The porous medium is assumed to be variable and the effect of the permeable parameter is to destabilize the system. The present work has been carried out both for oscillatory as well as stationary instabilities. The results are depicted graphically.

scholarly journals On the porosity influence on stability of flow over porous medium

2020 ◽  
Vol 30 (1) ◽  
pp. 134-144
Author(s):  
K.B. Tsiberkin
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Short Wave ◽  
Wave Instability ◽  
Plane Parallel ◽  
Long Wave ◽  
The Stability ◽  
Critical Wavenumber

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

Stability of Piston-Like Displacements of Water by Steam and Nitrogen in Porous Media

1982 ◽  
Vol 22 (05) ◽  
pp. 625-634 ◽  
Author(s):  
David A. Krueger
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Gravitational Force ◽  
Absolute Permeability ◽  
Water Steam ◽  
The Stability ◽  
Condensation Front

Abstract Downhole steam generation leads to consideration of reservoir fluid displacement by a mixture of steam and nitrogen. The linear stability analysis of the steam condensation front has been generalized to include a noncondensing gas. Roughly speaking, the addition of nitrogen increases the likelihood of having fingers, but, compared with the no-nitrogen case, the fingers will grow more slowly. Introduction The theory of the stability of flows through porous media has been a subject of interest for more than 25 years, dating back to the pioneering work of Dietz, Chuoke et al., and Saffman and Taylor. They considered injecting one fluid (e.g., water) to force a second fluid (e.g., oil) out of a porous medium. The primary result was that instabilities (fingering) occurred when the driving fluid was more mobile than the driven fluid. Hagoort included multiple fluid phases. Miller generalized the original work to include steam driving water (liquid). He showed that the thermodynamic phase transition (steam to water) introduces two stabilizing effects. The first effect introduces a water/steam velocity ratio as a multiplier of the mobility ratio. This factor is less than one because of the volume change upon condensation. The second effect is the cooling of incipient steam fingers by the surrounding water, which retards their growth. Baker anticipated these effects in a qualitative way to explain his experiments, which showed a more stable displacement by steam than was expected on the basis of mobility ratios alone. Armento and Miller also have considered the stability of the in-situ combustion front in porous media. Their work deals with a region where steam is generated. This paper reformulates Miller's results for a condensation front in a more useful form including general numerical results and extends the theory to include injection of a noncondensing gas (e.g., nitrogen) together with the steam. Depending on the particular situation, the presence of nitrogen can be either stabilizing or destabilizing. The motivation for the generalization comes from enhanced oil recovery projects where the exhaust gases from the steam generator are injected into the reservoir along with the steam. This paper considers perturbations on a flat condensation front that is perpendicular to its velocity. The gravitational force along this velocity is included, but the component of the gravitational force perpendicular to the velocity is not. Thus we include the effect of gravity on fingering, but we do not discuss the gravity override problem. In Stability Analysis we present two steps:determination of the motion of a flat condensation front (details are in the Appendix) andevaluation of the characteristic time for growth or decay of a perturbation of that front. In Results wegive the results for a specific reservoir;discuss the sensitivity of these results to the important reservoir parameters (flow velocities and absolute permeabilities),show that, if surface tension and gravitation are unimportant, the stability condition is independent of the absolute permeability and absolute flow rates, anddiscuss the longest wavelength for a stable perturbation. In the final section we discuss the main conclusions. Stability Analysis We consider a homogeneous porous medium with fluids in two regions as illustrated in Fig. 1. A steam/nitrogen mixture is injected at the left, and water (liquid) and nitrogen are produced at the fight. The linear stability analysis proceeds in two main stages and follows the general methods as discussed by Chandrasekhar and the specific application of Miller. First, we assume that the condensation front is flat, moves with constant velocity, v, and has properties that vary with z alone. SPEJ P. 625^

Sign in / Sign up

Export Citation Format

Share Document