Page 98 - Analysis and Design of Energy Geostructures

70 Analysis and Design of Energy Geostructures

Later, laminar and turbulent flows and the problem of seepage flow are addressed: the pur-
pose of this part is to expand on the regimes that govern mass transfer as well as on
the phenomenon of groundwater flow. Then, the mass conservation equation and the
associated initial and boundary conditions are presented: the goal of this digression is to
progress with the understanding and mathematical modelling of mass transfer. Next,
boundary layers in flow problems are discussed: the aim in this context is to characterise
the considered subjects in view of their influence on the operation of energy geostruc-
tures. Afterward, the momentum conservation equation is considered: the aim of this sec-
tion is to complete the mathematical description of mass transfer phenomena for

situations in which the equilibrium of the moving fluid is accounted for. Finally, ques-
tions and problems are proposed: the purpose of this part is to fix and test the under-
standing of the subjects covered in this chapter by addressing a number of exercises.

3.2 Idealisations and assumptions

Different materials characterise energy geostructure applications. These materials
include, for example (1) the soil or rock surrounding energy geostructures, (2) the
concrete constituting energy geostructures, (3) the steel reinforcing energy geostruc-
tures, (4) the plastic material constituting the pipes embedded in energy geostructures,
(5) the heat carrier fluid circulating in the pipes and (6) the air in a built environment
adjacent to energy geostructures.
In principle all of the aforementioned materials can be characterised by different
constituents and are heterogeneous at all scales, that is characterised by properties that
vary in space. Geomaterials such as soil, rock and concrete contain solid particles and
pores typically filled with water and air, with the solid particles consisting of different
solid components that may differ, for example in size, shape, mineralogy and behav-
iour. Reinforcing steel and plastic pipes are characterised by impurities in the form of
pores filled with air. The heat carrier fluid circulating in the pipes of energy geostruc-
tures and the air flowing in an adjacent built environment can be characterised by
impurities in the form of solid particles.
In practice, heterogeneous materials can be modelled via the continuum medium idea-
lisation as if they were homogeneous, that is characterised by properties that do not vary
in space. The main advantage of this approach is that governing equations and consti-
tutive equations can be applied to describe the behaviour and phenomena characteris-
ing such materials from a continuum perspective, with reference to an elementary
volume (see, e.g. Timoshenko and Goodier, 1951; Lai et al., 2009).
An approach for describing the behaviour and phenomena characterising materials
from a continuum perspective, without being influenced by their actual heterogene-

ities, relies on the concept and the definition of a so-called ‘Representative Elementary
Volume’ (REV). The REV concept, originally proposed by Lorentz (1952), is defined