Page 107 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 79

anddesignofenergygeostructures.Inadditiontothe previous variables, a
dependence of thermal conductivity of soil, rock and concrete on time (through
the so-called phenomenon of ageing) and temperature can be highlighted. In fact
a variation of these variables leads to a change in the size of the material pores
(via, e.g. cementation and thermal expansion of the solid grains because of the
former and latter variable, respectively), which can modify the effective value of
thermal conductivity of the material. In principle the thermal conductivity of soils
canincreaseasaconsequenceofageing(Brandon and Mitchell, 1989)and an
increase in temperature (Hiraiwa and Kasubuchi, 2000), whereas that of concrete
does not sensibly vary (Kim et al., 2003) or decreases (Shin et al., 2002)asacon-
sequence of ageing and an increase in temperature, respectively. In practice the
effect of ageing can be significant only in specific applications and the effect of
temperature can be significant for temperature variations that do not characterise

energy geostructure applications (e.g. greater than 80 C 100 C). Based on the
previous comments, the influence of ageing and temperature on the variation of
the thermal conductivity of geomaterials may be neglected for the analysis and
design of energy geostructures.
Typical values of thermal conductivity for relevant materials are reported in
Table 3.4. The thermal conductivity of soils typically varies between 0.2 and 3 W/

(m C) and can achieve values of 3.5 W/(m C). The thermal conductivity of rocks
can achieve values greater than 5 W/(m C). Steel has a much greater thermal con-

ductivity than soils, rocks and concrete, while the polyethylene characterising the pipes
embedded in energy geostructures usually has a lower thermal conductivity than the
previous materials.
In many instances, the effective thermal conductivity of porous materials, such as
soils, rocks and concrete, assumed to be isotropic and with pores fully filled with a
fluid, can be evaluated as

λ 5 λ f n 1 λ s ð1 2 nÞ ð3:4Þ
where λ f is the thermal conductivity of the general fluid filling the pores of the mate-
rial and λ s is the thermal conductivity of the solid particles. For materials with pores
fully saturated with water, λ f is replaced by the thermal conductivity of the water λ w .
The same approach may be applied to materials with pores fully saturated with air by
using the thermal conductivity of the air λ a . When a dry material is however charac-
terised by relatively low values of porosity, for example n # 0.2, the contribution of
the thermal conductivity of air in the calculation of the effective thermal conductivity
is often neglected because it plays a limited role in the final result. A number of math-
ematical expressions for the estimation of the effective thermal conductivity of geoma-
terials are reported in Table 3.5.