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1987 | Buch

Thermal Flows in Porous Media

verfasst von: Horia I. Ene, Dan Poliševski

Verlag: Springer Netherlands

Buchreihe : Theory and Applications of Transport in Porous Media

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SUCHEN

Über dieses Buch

The transport of heat through a porous medium in the presence of exterior forces, generally produced by the Earth's gravitational field and/or a pressure gradient, is called conduction when the Darcean fluid is static (motionless), and convection when the Darcean fluid is in motion. It is customary to use the term convection also to describe the motion which arises from the density differences due to temperature gradients within the Darcean fluid. We think that because this last phenomenon is more general it should be given a specific name; here we call it thermal flow. In the sense of the above definitions, convection and thermal flow are two distinct phenomena (they occur together, in underground combustion for instance), and the convective motion which arises when a Darcean l'luid is in contact with a source of heat is a particular case of thermal flow. Thermal flow occurs naturally and is important in many geophysical and industrial problems, particularly in oil exploration, and in the petroleum, chemical and nuclear industries (for instance, in the evaluation of capability of heat-removal from a hypothetical accident in a nuclear reactor). It can play a part in the transfer of heat from the deep interior of the Earth to a shallow depth in the geothermal regions. However, in the field of energy conversion little attention has yet been paid to the insulating characteristics of the saturated porous materials introduced in some enclosures (storage tanks) to decrease the convective and radiative transfer of heat.

Inhaltsverzeichnis

Frontmatter

Single-Phase Flow

Frontmatter
Chapter 1. The Homogenization Method for the Study of Fluid Flow in Porous Media
Abstract
The homogenization method is a mathematical method used for the study of the initial-value and boundary-value problems in domains with a periodic structure. If the dimensions of a period are small compared to the size of the whole domain, it is natural to define a small parameter ε as the ratio between those dimensions. The study of the initial-value and boundary-value problems is associated with this small parameter. The asymptotic process ε → 0 represents the transition from microscopic to macroscopic phenomena.
Horia I. Ene, Dan Poliševski
Chapter 2. Natural Convection in Bounded Domains
Abstract
In a rigid, porous medium, gravitational forces and density differences due to temperature gradients can set a viscous fluid in motion. Attempts to describe this motion have always met serious difficulties. Supposing that the skeleton is fixed, we can accept that the velocity of the fluid is far lower than the acoustic velocity, and thus that the motion has little effect on the pressure; therefore we neglect variations of the thermodynamic quantities resulting from pressure changes. Moreover, we assume that the temperature differences are small enough to use the Boussinesq approximation; that the density of the gravitational force varies affinely with the temperature. We adopt the model proposed in Chapter 1, which was obtained by a homogenization process for which we have proved the convergence; we refer to it sometimes as the Darcy-Boussinesq system.
Horia I. Ene, Dan Poliševski
Chapter 3. Natural Convection in Unbounded Domains
Abstract
If the porous medium is not bounded, no analysis is possible without information on the behaviour of the solution at infinity. From this aspect arise some peculiarities which prevent one from using any result obtained for the bounded case without first carefully checking its validity.
Horia I. Ene, Dan Poliševski

Multiphase Flow

Frontmatter
Chapter 4. Macroscopic Equations
Abstract
Multiphase flow in porous media occurs in many branches of engineering; an example is the exploitation of oil fields by in situ combustion. In such problems, increasingly complex phenomena develop during the flow: diffusion in the various phases, exchange of components between the phases, heat transfer and chemical reactions. The equations used in the mathematical formulation of the laws governing these flows must account for all such phenomena.
Horia I. Ene, Dan Poliševski
Chapter 5. Underground Combustion
Abstract
The general equations obtained in the previous chapter may be simplified to give the equations for underground combustion. For this we consider only four phases: gas, oil, water and coke. The total number of components is n, and they will be present in any fluid phase. Note that coke is a solid phase.
Horia I. Ene, Dan Poliševski
Backmatter
Metadaten
Titel
Thermal Flows in Porous Media
verfasst von
Horia I. Ene
Dan Poliševski
Copyright-Jahr
1987
Verlag
Springer Netherlands
Electronic ISBN
978-94-009-3717-8
Print ISBN
978-94-010-8164-1
DOI
https://doi.org/10.1007/978-94-009-3717-8