Longitudinal dispersion of thermal energy through porous media with a flowing fluid

Green, D. W.; Perry, R. H.; Babcock, R. E.

doi:10.1002/aic.690100514

Cited by 47 publications

(22 citation statements)

References 24 publications

(8 reference statements)

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“…Interestingly, the results presented here show a more rapid increase in thermal dispersion with velocity (Figure 10) compared to Green et al 's [1964] results, possibly due to the larger thermal conductivity of the matrix as mentioned earlier. In a theoretical context, Yuan et al [1991] established a square relationship and concluded that the coefficient (in this case

β_{l, t})

is a function of porosity as well as fluid and solid thermal parameters.…”

Section: Discussionsupporting

confidence: 65%

“… Green et al [1964] conducted laboratory experiments in ideal porous media (glass spheres) with advective flow to derive the effective thermal conductivity. They suggested the following empirical relationship for the thermal dispersion coefficient

\frac{D_{l}^{t}}{D_{0}^{t}} = n \cdot {(\frac{v^{s} d_{50}}{D_{0}^{t}})}^{m} .

…”

Section: Methodsmentioning

confidence: 99%

“…This analysis highlights the well‐known fact that the solute Peclet number differs significantly from the thermal Peclet number for the same flow field conditions. The literature contains conflicting descriptions of the thermal dispersivity and the relationship between thermal dispersivity and fluid velocity with one group of authors suggesting a linear relationship [e.g., de Marsily , 1986; Anderson , 2005; Hatch et al , 2006; Keery et al , 2007; Vandenbohede et al , 2009; Vandenbohede and Lebbe , 2010; Rau et al , 2010], while others working in the chemical engineering area have identified the possibility of a nonlinear relationship [ Green et al , 1964]. To better understand the mechanics of the thermal dispersivity and to resolve this significant uncertainty concerning linearity, we describe the results of a detailed laboratory experiment that measures heat and solute transport separately, but under the same conditions, representative of naturally occurring groundwater flow systems ( Re < 3, according to Bear [1972]).…”

Section: Introductionmentioning

confidence: 99%

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Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments

Rau

Andersen

Acworth

2012

Water Resources Research

141

115

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[1] A review of heat and solute transport in sediments demonstrates that the use of heat as a tracer has not been experimentally evaluated under the same experimental conditions as those used for the evaluation of solute as a tracer. Furthermore, there appears to be disagreement in the earth science literature over the significance of the thermal dispersivity term. To help resolve this disagreement, detailed experimentation with typical groundwater flow velocities (Darcy range, Re < 2.5) was conducted in a specifically designed hydraulic tank containing well-sorted saturated sand. The experiment enabled, for the first time, the precise monitoring of heat and solute tracer movement from a point source in separate runs under identical solid matrix and steady state flow conditions. Experimental results demonstrate that heat transport with natural groundwater flow velocities can reach a transition zone between conduction and convection (0.5 < Pe t < 2.5). The thermal dispersion behavior can be described by using a thermal dispersivity coefficient and the square of the thermal front velocity. We propose an empirical formulation for thermal dispersion with Darcy flow in natural porous media and clarify the disagreement regarding its significance. Finally, it was observed that Darcy velocities independently derived from heat and solute experimentation show a systematic discrepancy of up to 20%, and that experimental thermal dispersion results contain significant scatter.Citation: Rau, G. C., M. S. Andersen, and R. I. Acworth (2012), Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments, Water Resour. Res., 48, W03511,

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β_{l, t})

is a function of porosity as well as fluid and solid thermal parameters.…”

Section: Discussionsupporting

confidence: 65%

\frac{D_{l}^{t}}{D_{0}^{t}} = n \cdot {(\frac{v^{s} d_{50}}{D_{0}^{t}})}^{m} .

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments

Rau

Andersen

Acworth

2012

Water Resources Research

141

115

View full text Add to dashboard Cite

show abstract

“…Heat transported by temperature gradients within the is also transported by the moving water itself and differential convection occurs due to the different flow pathways that are possible in porous media. These variations in magnitude and direction of the velocity field at the pore-scale create the so-called thermal dispersion (l d ) [15,16]. In addition, differential heat transport due to the heterogeneity of the permeability field at macroscopic scales also contributes to thermal dispersion [12,15,17e19].…”

Section: Thermal Dispersionmentioning

confidence: 99%

“…Then heat is transported by the moving water, and differential advection occurs due to the different flow pathways that are possible in porous media. This process is called thermal dispersion, and is generated by microscale mixing of the pore-scale interstitial water [15,16] as well as by differential transport in macroscale geological heterogeneities [12,17e19]. Usually, the dominant process is thermal diffusion [15].…”

Section: Introductionmentioning

confidence: 99%

Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions

Molina-Giraldo

Bayer

Blum

2011

International Journal of Thermal Sciences

146

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Influence of vertical and lateral heat transfer on permafrost thaw, peatland landscape transition, and groundwater flow

Kurylyk

Hayashi

Quinton

et al. 2016

Water Resources Research

126

133

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Recent climate change has reduced the spatial extent and thickness of permafrost in many discontinuous permafrost regions. Rapid permafrost thaw is producing distinct landscape changes in the Taiga Plains of the Northwest Territories, Canada. As permafrost bodies underlying forested peat plateaus shrink, the landscape slowly transitions into unforested wetlands. The expansion of wetlands has enhanced the hydrologic connectivity of many watersheds via new surface and near-surface flow paths, and increased streamflow has been observed. Furthermore, the decrease in forested peat plateaus results in a net loss of boreal forest and associated ecosystems. This study investigates fundamental processes that contribute to permafrost thaw by comparing observed and simulated thaw development and landscape transition of a peat plateau-wetland complex in the Northwest Territories, Canada from 1970 to 2012. Measured climate data are first used to drive surface energy balance simulations for the wetland and peat plateau. Nearsurface soil temperatures simulated in the surface energy balance model are then applied as the upper boundary condition to a three-dimensional model of subsurface water flow and coupled energy transport with freeze-thaw. Simulation results demonstrate that lateral heat transfer, which is not considered in many permafrost models, can influence permafrost thaw rates. Furthermore, the simulations indicate that landscape evolution arising from permafrost thaw acts as a positive feedback mechanism that increases the energy absorbed at the land surface and produces additional permafrost thaw. The modeling results also demonstrate that flow rates in local groundwater flow systems may be enhanced by the degradation of isolated permafrost bodies. Key Points:Observed permafrost thaw rates are compared to results from a 3-D groundwater flow and heat transfer model Lateral heat flow can accelerate discontinuous permafrost thaw and land cover change in peatlands Degradation of discontinuous permafrost enhances local groundwater flow Supporting Information:Supporting Information S1

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Longitudinal dispersion of thermal energy through porous media with a flowing fluid

Cited by 47 publications

References 24 publications

Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments

Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments

Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions

Influence of vertical and lateral heat transfer on permafrost thaw, peatland landscape transition, and groundwater flow

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