Page 52 - Physical Principles of Sedimentary Basin Analysis

34 Properties of porous media

◦
halves when the temperature increases from 0 Cto T = 1/c 0 . Table 2.3 shows examples
C
of the coefficient c 0 for various rocks. For example c 0 = 5 · 10 −4◦ −1 gives a reduction
◦
of 7% when the temperature increases from 0 C to 150 C. The temperature dependence
◦
is therefore negligible in the basin sediments and also to some degree in the crust, because
of the uncertainty with respect to rock types and the value of λ 0 .
Increasing pressure leads to increasing heat conductivity for rocks and minerals. The
increase is expressed by adding a factor 1 + α 0 p to the temperature-dependent heat
conductivity. The relationship (2.104) therefore generalizes to

1 + α 0 p

λ(p, T ) = λ 0 . (2.105)
1 + c 0 T
Both pressure and temperature increase with depth, and their effect on the heat conduc-
tivity are in opposite directions. The coefficient α 0 has been measured in the range 0.05
to 0.2GPa −1 for crystalline rocks by Seipold (1995). If we estimate the pressure at 4 km
depth to be 0.1 GPa we get that the heat conductivity increases by 2% by using the upper
bound for α 0 . The effect is therefore negligible in sedimentary basins.
Most rocks have an anisotropic heat conductivity because of anisotropy in the mineral
texture, like for instance foliation. The anisotropy is often measured with the ratio of the
heat conductivities parallel to the layering and normal to the layering, when isotropy is
assumed in the bedding plane. The anisotropy ratio has been measured to be in the range
1.1to1.5 for clay and claystones and mudstones from the UK (Midttømme et al., 1998).
Even stronger anisotropy might appear on the formation scale because of interlayering of
sandstones and shales.
The heat conductivity is in general a tensor quantity

⎛ ⎞
λ xx λ xy λ xz
λ = ⎝ λ yx λ yy λ yz ⎠ (2.106)
λ zx λ zy λ zz
which is symmetric, just like the permeability. Exactly the same results apply for the heat
conductivity tensor as for the permeability tensor, for instance rotation, principal values,
directional heat conductivity and averaging.
The heat conductivity appears quite often in the heat equation as thermal diffusivity,
κ = λ/ c, which is the heat conductivity (λ) divided by the density ( ) and the specific heat
capacity (c). Table 2.5 shows the density, specific heat capacity and the thermal diffusivity
2 −1
for several common minerals. Except for quartz the thermal diffusivity is ∼10 −6 m s .
A sediment matrix (skeleton) is a mixture of several minerals and we are normally inter-
ested in the average density and the average specific heat capacity for the solid. The average
density of a mineral ensemble, where mineral i has mass m i and volume V i ,issimply

m i m i V i
= (2.107)
av =
V i V i V tot