Thermal Dispersivity Research Articles

Parameter estimation based on vertical heat transport in the surficial zone

Measured groundwater temperatures in the surficial zone are dependent on the properties of porous media and vertical flow velocity. Sensitivity analyses, collinear diagnostics and an inverse numerical solution to the one-dimensional heat-transport equation are used to determine which parameters can be estimated from temperature measurements in the surficial zone. This is done for heat transport in the saturated zone considering a constant vertical flow velocity. The use of temperature profiles, temperature time-series and temperature envelopes are considered. There is an important difference between a conduction and a convection dominated system. Sensitivity analysis shows that temperature measurements are sensitive to effective thermal conductivity and heat capacity and are insensitive to effective porosity and thermal dispersivity. In a conduction dominated system, temperature is also insensitive for vertical velocity. Collinear diagnostics show that in a conduction dominated system, only the combination of heat capacity and effective thermal conductivity, the thermal diffusivity, can be derived. In a convection dominated system, both the vertical velocity and the effective thermal conductivity can, theoretically, be derived.

Analysis of thermal dispersion in an array of parallel plates with fully-developed laminar flow

The effect of thermal dispersion upon heat transfer across a periodic array of parallel plates is studied. Three basic heat transfer problems are addressed, each for steady, fully-developed, laminar fluid flow: (a) transient heat transfer due to an arbitrary initial temperature distribution within the fluid, (b) steady heat transfer with constant heat flux on all plate surfaces, and (c) steady heat transfer with constant wall temperatures. For problems (a) and (b), the effective thermal dispersivity scales with the Peclet number Pe according to 1 + CPe 2 , where the coefficient C is independent of Pe . For problem (c) the coefficient C is a function of Pe .

Open-loop groundwater heat pumps development for large buildings: A case study

A study of the feasibility of providing the heating and cooling needs of the new, large commercial building near Turin, Italy, by means of an open-loop indirect groundwater heat pump (GWHP) system is described. A finite element subsurface flow and transport simulator (FEFLOW) was used to investigate possible configurations of extraction and injection wells for five different scenarios. Modelling results confirmed the hydrogeological capacity of the site to provide the necessary amount of groundwater and associated energy with limited environmental impact. Injection of warmer (or cooler) water in the aquifer creates a thermal plume whose dimensions and geometry depend on the properties of the subsurface formations, particularly their thermal dispersivity values. The study suggests that there are several possible well configurations that could support the GWHP system without adversely affecting the aquifer.

Conservative Solute Versus Heat Transport in Porous Media During Push-pull Tests

Both heat and solute transport in porous media are described by partial differential equations of similar form. Nevertheless, observing these phenomena in the field on the scale of well tests clearly indicates dissimilar behaviour. This article studies the aforementioned transport processes by interpreting two push-pull tests of different duration. In both tests, chloride is applied as a conservative tracer and lower temperature water is injected in higher temperature pristine water at different flow rates. Simulation and interpretation of the tests are performed by means of ReacTrans, a two-dimensional, axially symmetric, finite-difference, solute and heat transport model. Since conflicting views exist in literature on the relation between solute and thermal dispersivity, analysis of field observations focuses on parameters which describe aquifer characteristics affecting these processes. Parameter estimation is conducted through sensitivity analysis and collinear diagnosis in order to identify derivable parameters. It is concluded that longitudinal solute dispersivity and thermal diffusivity could be inferred accurately from chloride and temperature data sampled from the injection/extraction well respectively. Involving supplementary data sampled from an observation well enables derivation of effective porosity from chloride data and thermal retardation from temperature data. Moreover, it is inferred that longitudinal solute dispersivity is scale dependent. Thermal diffusivity, however, seems not to be. This points to dissimilar development of transition zones during solute and heat transport. It is concluded that conductive transport of heat is much more important than effects of velocity variations through the pore space.

Controlling reverse-flow reactors via multiscale transient thermal dispersion

Since the chemical reactor is the heart of any chemical processing plant, there exist significant opportunities to increase industrial profits and minimize ecological impacts. One such opportunity is improving thermal stability in packed bed reverse-flow reactors. A fundamental study of the effect of multiscale, transient, thermal dispersion within packed bed reactors is undertaken here to evaluate its utility to improve thermal stability and satisfy economic and environmental goals. A new reactor configuration is investigated, where a regular pattern of cylindrical rods is inserted into the packed bed using a multiscale approach. These rods can increase the effective thermal dispersivity in the bed over thermal conduction by up to 2-orders of magnitude. It is found that the magnitude of the dispersion can be tuned by adjusting the key operating parameter, the reversal time, such that the reactor can stay ignited without the need for external fuel supply during extended lean conditions while remaining thermally stable during extended rich conditions. The ensuing multiscale thermal dispersion, in concert with a simple control strategy, allows for indefinite reactor operation without runaway or extinction, as predicted by simple, generalized analytical models for any chemical reaction and illustrated with numerical simulations. Some added benefits of this study are that the tight controllability of these reactors may allow for increased reaction selectivity, energy efficiency, and reduced pollution levels.

Indirect estimation of soil thermal properties and water flux using heat pulse probe measurements: Geometry and dispersion effects

Traditionally, analytical solutions for heat transport in soils have been used in combination with heat pulse probe (HPP) measurements to estimate soil thermal properties. Although the analytical method has resulted in accurate estimation of soil thermal properties, we suggest that parameter estimation using inverse modeling (IM) provides new and unique opportunities for soil thermal characterization. Moreover, we show that the IM approach provides accurate estimation of soil water flux density in both unsaturated and saturated soil conditions for a wider range of water velocities than originally thought possible. Specifically, we show that accurate soil water velocity is obtained, simultaneously with soil thermal properties, if heat dispersion is included in the heat transport equation. The requirement for including heat dispersivity depends on the value of the newly defined dimensionless Keith Jirka Jan (KJJ) number, which is equal to the ratio of thermal dispersion to thermal conductivity. For example, when KJJ > 1, ignoring thermal dispersivity leads to errors in the water flux density which can exceed 10%. By including thermal dispersivity, water flow velocities were accurately determined for water flux densities ranging from 1.0 to >10 m d−1. We also demonstrate the general application of inverse modeling to estimate soil thermal properties and their functional dependence on volumetric water content in a separate numerical experiment. We suggest that inverse modeling of HPP temperature data may allow simultaneous estimation of soil water retention (when combined with matric potential measurements) and unsaturated hydraulic conductivity (through water flux estimation) from simple laboratory experiments.

Internal energy transport in adiabatic systems: Thermal taylor dispersion phenomena

This paper outlines a general theory of thermal convective-conductive Taylor dispersion phenomena applicable to all adiabatic systems, both continuous and spatially periodic. General expressions are obtained for the macroscale thermal propagation velocity vector U ∗ and effective thermal dispersivity dyadic α ∗ in terms of the prescribed thermophysical microscale data. By way of example, we address the problem of heat conduction in a composite medium. As a specific illustration, we show that although a composite medium may be composed of two separately homogeneous materials possessing identical (isotropic) thermal diffusivities α, the effective thermal dispersivity α ∗ of the composite medium may nevertheless differ by many orders of magnitude from the constant diffusivity α characterizing the individual phases; moreover, in contrast to the scalar, isotropic nature of the microscale diffusivity α, the effective macroscale dispersivity α ∗ will generally be anisotropic, depending upon which (if either) of the two homogeneous phases is continuous and which discontinuous! Detailed calculations are also presented for the effective thermal dispersivity dyadic for Darcy flow through the interstices of a two-dimensional packed bed composed of insulated circular cylinders in various spatial configurations. Results are given for the effective thermal dispersivities in terms of the Peclet number and bed porosities. While most of the numerical data were obtained for the Stokes flow case, Re = 0 (Re = Reynolds number), a few isolated calculations were also performed at Reynolds numbers up to about 100.

THERMAL TAYLOR DISPERSION PHENOMENA IN NONADIABATIC SYSTEMS

Abstract This paper outlines or general 'one-dimensional’ theory of convective-conductive internal energy transport phenomena in complex, multidimensional, nonadiabatic systems whose rate of heat loss to their surroundings is characterized by a 'Newton's law of cooling’ heat transfer coefficient h. Taylor dispersion theory is used to effect the coarse-graining ofthe microscale thermal problem, therby producing an effective-medium theory of the mean thermal transport process. Both ducts ('continuous’ systems) and model packed beds (spatially periodic systems) are analyzed. Expressions are derived for the macroscale thermal propagation velocity vector U¯∗ and effective thermal dispersivity dyadic α¯∗ in terms of the prescribed microscale data. Additionally, an expression is obtained for a third macrotransport coefficient, H¯∗, representing the effective or overall macroscale heat transfer coefficient, and distinct from the microscale heat transfer coefficient h. (This is the same type of quantity as arises ...

Thermal Taylor dispersion in an insulated circular cylinder—II. Applications

The thermal dispersion theory derived in Part I is here applied to convective heat transfer in an externally insulated tube possessing a finite wall thickness. Expressions are derived for the mean axial thermal propagation velocity UU★ and thermal dispersivity \\ ̄ ga★ of the composite system for both laminar and turbulent flows. For each, the effect of the nonzero wall thickness is such that UU★ is always less than the average fluid velocity V . In a laminar flow system, \\ ̄ ga★ can either be larger or smaller than the fluid diffusivity α f , depending upon the thermal properties of the fluid and wall, as well as upon the magnitude of the Peclet number. For turbulent flows, \\ ̄ ga★ can be either larger or smaller than both α f and the zero wall thickness effective thermal dispersivity, \\ ̄ ga★ 0 , although now it further depends upon the Prandtl number.

Thermal Taylor dispersion in an insulated circular cylinder—I. Theory

Taylor-Aris dispersion techniques are used in this paper to address a broad class of convective and diffusive internal energy transport phenomena in an externally insulated circular cylinder. Expressions are derived for the mean axial thermal propagation velocity U ̄ ★ and thermal dispersivity \\ ̄ ga★ . In general, these quantities may differ respectively from the average fluid velocity V ̄ and the fluid thermal diffusivity α f . These generic results apply equally to laminar and turbulent flow systems.

Thermal dispersion in a porous medium

The thermal dispersion conductivity tensor for convection in a porous medium is derived based on the method of volume averaging of the velocity and temperature deviations in the pores. The velocity and temperature deviations are obtained based on flow over a dilute array of spheres, incorporated with a scale analysis. A multiplying constant (i.e. the thermal dispersivity tensor) is introduced to account for the interaction of spheres. Separate considerations are given to the creeping flow at low Reynolds numbers, as well as boundary layer flow and wakes at high Reynolds numbers. It is found that the velocity and porosity dependencies in the thermal dispersion conductivity tensor are different for high Reynolds number and low Reynolds number porous media flows. The value of the transverse thermal dispersivity for a nearly parallel flow at high Reynolds numbers is determined by comparing the predicted heat transfer characteristics with existing experimental results for forced convection of water and air through heated packed channels and cylindrical packed tubes.