Dispersion effects on thermal convection in porous media

Kvernvold, Oddmund; Tyvand, Peder A.

doi:10.1017/s0022112080000821

Cited by 48 publications

(23 citation statements)

References 15 publications

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“…Note that the thermal diffusivity defined in Equation 7 is based on a mixture of fluid properties and porous medium properties. Katto and Masuqka [ 17] suggested that this is the appropriate thermal diffusivity to use, based on theory and experiments; their formulation was adopted by other researchers [18,6].…”

Section: Aspect Ratio Of Convection Cellsmentioning

confidence: 99%

“…K vemvold and Tyvand [18] studied theoretically the dispersion effects on thermal convection in a fluid-saturated porous layer bounded by two infinite horizontal planes at constant temperature. They considered incompressible flow (p = constant), for which the energy equation (Equation 3) can be simplified to give the following dimensionless form [ 11,18].…”

Section: Thermal Dispersion Effectsmentioning

confidence: 99%

“…) is a dimensionless number which can be I used to estimate the magnitude of the dispersion effects [18]. Dispersion effects increase with increasing Rayleigh number.…”

Section: The Dispersion Factor B (Equation 12mentioning

confidence: 99%

“…The simplest approach toward such an estimate is to use the simulated velocity patterns to estimate dispersive flux, based on the formulation given by Kvernvold and Tyvand [18]. Their expression for dispersive heat transfer was derived under the assumption of incompressible flow of a I fluid with small expansivity.…”

Section: The Dispersion Factor B (Equation 12mentioning

confidence: 99%

“…Transversal dispersion [18,6] Contours of (a) density (kg/m 3 ) and (b) internal energy (kJ/kg) for pure water in the critical region.…”

Section: The Dispersion Factor B (Equation 12mentioning

confidence: 99%

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Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Cox

Pruess

1990

Transp Porous Med

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Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374°C for pure water, higher for saline fluids) may ·be· encountered in deep zones of geothermal systems and above cooling intrusives. In the vicinity of the critical point the density and internal energy of fluids show very strong variations for small temperature and pressure changes. This suggests that convective heat transfer from thermal buoyancy flow would be strongly enhanced at near-critical conditions. This has been confirmed in laboratory experiments.We have developed special numerical techniques for modeling porous flow at nearcritical conditions, which can handle the extreme non-linearities in water properties near the critical point Our numerical simulations show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the simulations are considerably smaller than data reported from laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.

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Section: Aspect Ratio Of Convection Cellsmentioning

confidence: 99%

Section: Thermal Dispersion Effectsmentioning

confidence: 99%

“…) is a dimensionless number which can be I used to estimate the magnitude of the dispersion effects [18]. Dispersion effects increase with increasing Rayleigh number.…”

Section: The Dispersion Factor B (Equation 12mentioning

confidence: 99%

Section: The Dispersion Factor B (Equation 12mentioning

confidence: 99%

“…Transversal dispersion [18,6] Contours of (a) density (kg/m 3 ) and (b) internal energy (kJ/kg) for pure water in the critical region.…”

Section: The Dispersion Factor B (Equation 12mentioning

confidence: 99%

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Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Cox

Pruess

1990

Transp Porous Med

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CO₂ dissolution in the presence of background flow of deep saline aquifers

Emami-Meybodi

Ennis‐King

2015

Water Resources Research

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We study the effect of background flow on the dissolution and transport of carbon dioxide (CO 2 ) during geological storage in saline aquifers, and include the processes of diffusion, advection, and free convection. We develop a semianalytical model that captures the evolution of the dissolution in the absence of free convection. Using the semianalytical solution, we determine scaling relations for the steady rate of dissolution that follow either J st $ ffiffiffiffiffiffiffiffi Pe R p or J st $ Pe depending on the value of Pe/R, where R represents the ratio of the extent of CO 2 plume to the aquifer thickness and Pe is the Peclet number. Using direct numerical simulations, we provide detailed behavior of the convective mixing during the dissolution. We establish the criteria for forced and mixed (combined free and forced) convection in aquifers that is governed by the background flow. Accordingly, we provide the scaling relations J st $ ffiffiffiffiffiffiffiffi Pe R p and J st $ Ra R representing the forced and free convection asymptotes, respectively, where Ra is a Rayleigh number based on aquifer thickness. The results reveal that the background velocity can delay the onset of free convection and can alter the subsequent mixing. This phenomenon is more profound in the systems subject to strong background flows wherein horizontal component of the velocity field generated by background flow hinders the establishments of vertical component of the velocity field. Finally, by applying the proposed relations to several potential storage sites, we demonstrate the screening process in finding aquifers where the background flow exerts an important influence on the dissolution.

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The Henry problem: New semianalytical solution for velocity‐dependent dispersion

Fahs

Ataie-Ashtiani

Younès

et al. 2016

Water Resources Research

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A new semianalytical solution is developed for the velocity‐dependent dispersion Henry problem using the Fourier‐Galerkin method (FG). The integral arising from the velocity‐dependent dispersion term is evaluated numerically using an accurate technique based on an adaptive scheme. Numerical integration and nonlinear dependence of the dispersion on the velocity render the semianalytical solution impractical. To alleviate this issue and to obtain the solution at affordable computational cost, a robust implementation for solving the nonlinear system arising from the FG method is developed. It allows for reducing the number of attempts of the iterative procedure and the computational cost by iteration. The accuracy of the semianalytical solution is assessed in terms of the truncation orders of the Fourier series. An appropriate algorithm based on the sensitivity of the solution to the number of Fourier modes is used to obtain the required truncation levels. The resulting Fourier series are used to analytically evaluate the position of the principal isochlors and metrics characterizing the saltwater wedge. They are also used to calculate longitudinal and transverse dispersive fluxes and to provide physical insight into the dispersion mechanisms within the mixing zone. The developed semianalytical solutions are compared against numerical solutions obtained using an in house code based on variant techniques for both space and time discretization. The comparison provides better confidence on the accuracy of both numerical and semianalytical results. It shows that the new solutions are highly sensitive to the approximation techniques used in the numerical code which highlights their benefits for code benchmarking.

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Dispersion effects on thermal convection in porous media

Cited by 48 publications

References 15 publications

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

CO₂ dissolution in the presence of background flow of deep saline aquifers

The Henry problem: New semianalytical solution for velocity‐dependent dispersion

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Dispersion effects on thermal convection in porous media

Cited by 48 publications

References 15 publications

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

CO2 dissolution in the presence of background flow of deep saline aquifers

The Henry problem: New semianalytical solution for velocity‐dependent dispersion

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Product

Resources

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CO₂ dissolution in the presence of background flow of deep saline aquifers