Onset of convective stability in a fluid-saturated porous layer subjected to time-dependent heating

Kim, Min Chan; Kim, Sin

doi:10.1016/j.icheatmasstransfer.2004.06.002

Cited by 23 publications

(29 citation statements)

References 12 publications

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“…In the following, we follow previous works of Foster, 3,6 Kim and Kim, 27 Ennis-King and Paterson, 28 and Hassanzadeh et al 33 to perform a linear stability analysis for this new problem of transient concentration field in the presence of background flow.…”

Section: The Physical Problemmentioning

confidence: 99%

“…By making use of the Galerkin technique, the amplitude functions are represented by a system of linearly independent functions satisfying the boundary conditions 3,6,[27][28][29]32,33 :…”

Section: Stability Analysismentioning

confidence: 99%

“…As suggested by Kim and Kim, 27 two criteria have been chosen for determining the onset of instability. The first criterion is the critical time when the amplification factor is at a minimum, designated as the intrinsic instability time, and is represented by qc/qt D 5 0.…”

Section: Choice Of Criteria For the Onset Of Instabilitymentioning

confidence: 99%

“…3,6,20 Kaviany 20 investigated the onset of thermal convection in a porous medium both theoretically and experimentally. Kim et al, 25 Kim et al, 26 and Kim and Kim 27 studied the onset of buoyancy-driven flow in a porous medium without basic flow. Ennis-King and Paterson 28 Ennis-King et al 29 and Hong and Kim 30 performed a linear stability analysis to investigate the role of permeability anisotropy on the onset of convection.…”

Section: Introductionmentioning

confidence: 99%

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The effect of natural flow of aquifers and associated dispersion on the onset of buoyancy‐driven convection in a saturated porous medium

2008

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in Wiley InterScience (www.interscience.wiley.com).Carbon dioxide injection into deep saline aquifers is an important option for managing CO 2 emissions. Injected CO 2 dissolves into formation brines from above, increasing brine density and creating an unstable hydrodynamic state favorable for natural convection. Long-term buoyancy-driven flow of high-density CO 2 -saturated brine leads to faster trapping through improved dissolution and can reduce the risk of CO 2 leakage from storage sites. We investigate the role of natural flow of aquifers and associated dispersion on the onset of convection. A linear stability analysis of a transient concentration field in a laterally infinite, horizontal, and saturated porous layer with steady horizontal flow is presented. The layer is subjected to a sudden rise in CO 2 concentration from the top and is closed from the bottom. Solution of the stability equations is obtained using a Galerkin technique and the resulting equations are integrated numerically. We found simple scaling relationships that follow t Dc ;60(1 1 Pe T )Ra -2 for the onset time of convection and a;0.05Ra/(1 1 Pe T ) for the wavenumber of the initial instabilities. Results reveal that transverse dispersion increases the time to onset of convection for the entire range of Ra. Furthermore, transverse dispersion decreases the critical wavenumber of the instabilities. These results facilitate screening candidate sites for geological CO 2 storage.

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Section: The Physical Problemmentioning

confidence: 99%

“…By making use of the Galerkin technique, the amplitude functions are represented by a system of linearly independent functions satisfying the boundary conditions 3,6,[27][28][29]32,33 :…”

Section: Stability Analysismentioning

confidence: 99%

Section: Choice Of Criteria For the Onset Of Instabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effect of natural flow of aquifers and associated dispersion on the onset of buoyancy‐driven convection in a saturated porous medium

2008

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“…They found the critical Rayleigh number to be 4π 2 for constant temperature boundaries. Foster (1965a) and Kim and Kim (2005) used amplification theory for predicting the instability time. This method gives the critical time of instability and the initial wavelength of instabilities.…”

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confidence: 99%

Linear Stability Analysis of Double-Diffusive Convection in Porous Media, with Application to Geological Storage of CO2

2009

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Onset of double-diffusive buoyancy-driven flow resulted from vertical temperature and concentration gradients in a horizontal layer of a saturated and homogenous porous medium is investigated using amplification factor theory. After injection of CO 2 into a deep saline aquifer, the density of the brine saturated with CO 2 increases slightly. This increase in density induces natural convection. The effect of geothermal gradient is also considered in this work as a second incentive for convection and the double-diffusion convection was studied. Linear stability analysis is used to predict the inception of instabilities and initial wavelength of the convective instabilities. The analysis presented is applied to acid gas injection (as an analogue for CO 2 storage) into saline aquifers in the Alberta basin. It is found that the geothermal gradient does not have significant effect on the onset of convection for these aquifers. It is shown that the geothermal effects on the onset of natural convection are negligible as compared to the solutal effects induced by dissolution and diffusion of CO 2 in deep saline aquifers. Therefore, the linear stability analysis and the long-term numerical simulation of CO 2 sequestration into such saline aquifers may be assumed to be isothermal in terms of natural convection occurrence. List of SymbolsA Time components of the perturbed velocity amplitude function a Dimensionless wave number B Time components of the perturbed concentration amplitude function C Concentration (kg/m 3 ) 123 442 M. Javaheri et al.D Molecular diffusion (m 2 /s) D Derivative operator E Time components of the perturbed temperature amplitude function d Derivative g Gravitational acceleration (m/s 2 ) H Porous layer thickness (m) i Imaginary number K Thermal conductivity (W/m K) k Permeability (m 2 ) Le Lewis number (dimensionless) p Pressure (kg/m s 2 ) Ra Rayleigh number (dimensionless) T Temperature (K) T 1 Temperature of the bottom layer (K) t Time (s) u Velocity in x-direction (m/s) V Volume (m 3 ) v Velocity in y-direction (m/s) v Vector of Darcy velocity (m/s) w Velocity in z-direction (m/s) w Amplification factor (dimensionless) x Coordinate direction (m) y Coordinate direction (m) z Vertical coordinate direction (m) α Thermal diffusivity (m 2 /s) β C Coefficient of density increase by concentration (m 3 /kg) β T Coefficient of thermal expansion (K −1 ) φ Porosity (dimensionless) ρ Density (kg/m 3 ) μ Viscosity (kg/m s) ρ Density difference (kg/m 3 ) σ Matrix to fluid specific heat capacity (dimensionless) ∇ 2 Laplacian operator ∇ 2 H ∂ 2 /∂ x 2 D + ∂ 2 /∂ y 2 D

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Stability of gravitationally unstable double diffusive transient boundary layers with variable viscosity in porous media

Sabet

Abedi

2017

AIChE Journal

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We study the double diffusive convection (DDC) in porous media through linear stability analysis (LSA) and direct numerical simulations (DNS). Unlike the previous studies that assume static solutal or thermal fields, the developed model is able to capture the transient behavior of both fields. We show that under the assumption of static field, the role of Lewis number cannot be distinguished. Under transient fields, we conclude that higher Lewis numbers result in earlier instability of the boundary layers. Moreover, the effect of viscosity contrast is explained in terms of the mobility of the boundary layer. The DNS results confirm the validity of LSA predictions. We also obtain the critical Rayleigh number and show that in the presence of viscosity contrast, it can be much smaller than the conventional limit of 4π2. This study provides a better understanding of the transient nature of DDC in the presence of viscosity variations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2471–2482, 2017

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Onset of convective stability in a fluid-saturated porous layer subjected to time-dependent heating

Cited by 23 publications

References 12 publications

The effect of natural flow of aquifers and associated dispersion on the onset of buoyancy‐driven convection in a saturated porous medium

The effect of natural flow of aquifers and associated dispersion on the onset of buoyancy‐driven convection in a saturated porous medium

Linear Stability Analysis of Double-Diffusive Convection in Porous Media, with Application to Geological Storage of CO2

Stability of gravitationally unstable double diffusive transient boundary layers with variable viscosity in porous media

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