Page 137 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 109

3.11.2 Typical values of hydraulic conductivity and forced convection
coefficient

The hydraulic conductivity of materials depends on the characteristics of the medium
across which the fluid flows as well as on the physical properties of the flowing fluid
itself. For soils this parameter depends on (1) granulometry, (2) soil fabric, (3) dry den-
sity and (4) temperature (Vulliet et al., 2016). For rock masses hydraulic conductivity
depends on the characteristics of the fractures network (Vulliet et al., 2016).
The hydraulic conductivity is the variable characterised by the largest range of vari-
ation in energy geostructure applications. Typical values of hydraulic conductivity are
reported in Table 3.11.
The dependence of the hydraulic conductivity on granulometry, soil fabric, dry
density (i.e. aspects (1) (3)) for soils and on the characteristics of the fractures network
for rocks can be considered via a number of mathematical expressions. A usual refer-
ence for the derivation of such expressions is the Poiseuille’s law (Poiseuille, 1844) for
flow through a round capillary, which gives the mean flow velocity
2
v rw;i 52 krh 52 gD p ð3:38Þ
32η rh
f
where D p is the effective hydraulic diameter and η is the kinematic viscosity of the
f
fluid. For soils the effective diameter may be chosen depending on the material grada-
tion and compaction state. For rocks the effective diameter corresponds to a represen-
tative dimension of the problem, for example the effective diameter of the pores and
joints in the rock mass. Table 3.12 summarises a number of mathematical expressions
for the estimation of the hydraulic conductivity of soils and rocks.
The dependence of the hydraulic conductivity on temperature (i.e. aspect (4)) can
be appreciated by expressing this variable as

i
i
k ρ g k g
k 5 f 5 ð3:39Þ
μ η
f f
where k is the intrinsic (or geometric) permeability, that is a property of the
i
porous material only (not of the fluid). The term η summarises the dependence
f
of the hydraulic conductivity on the fluid type. Because the viscosity and density
of fluids depend on temperature, the hydraulic conductivity also depends on
temperature.
For water the dependency of the dynamic viscosity on temperature can be consid-
ered via the expression (Thomas and King, 1994):

21:562
ð
μ 5 0:6612 T 2229Þ ð3:40Þ
w