Geoscience Reference
In-Depth Information
ensures their separation. In rocks, similar processes take place when geological fluids move
through the pores of a sediment during diagenesis or through rock layers during metamor-
phism: because of the large volumes of fluid involved and because of the broad range of
reactivity from one element to another, considerable chemical separation in the fluid and
strong mineralogical and geochemical modifications of the rock matrix are commonplace.
In a two-phase flow, such as water percolating along an aquifer through a porous soil
or a magmatic liquid in a molten rock matrix, or of particles sedimenting in the ocean,
the processes are both more complicated and more diverse. The constitutive equations
of chromatography are difficult to establish because, besides continuity and conservation
equations for each species in each phase (e.g. solid and liquid), we have to add a condition
describing transfers between phases, such as phase-change kinetics (melting, dissolution,
or crystallization) and chemical fractionation. The concentration of an element
i
in the
interstitial mobile phase (liquid) can generally be described by a balance statement of
the type:
d
C
liquid
d
t
=
diffusion
+
advection
+
phase changes
(5.18)
To illustrate the concepts in the simplest way, let us ignore the diffusive term and the
term related to transfer during phase change. The advective effect is then dominant. Let
us denote
i
v
liquid
the velocity at which the liquid moves relative to the solid matrix and
v
i
the mean velocity at which element
i
moves (
<v
liquid
). The theory of chromatography
is quite heavy-going, but we can try to find a way around the worst difficulties by writing
that the material flux of
i
moving with the velocity
v
v
liquid
must be the sum of the fluxes of
v
liquid
C
i
i
moving with the element velocity
in both the solid and in the liquid:
ϕv
liquid
C
liquid
≈
ϕv
i
C
liquid
+
(
i
C
solid
1
−
ϕ) v
(5.19)
(note that the fluxes have to be weighted by the porosity
ϕ
for the liquid and by the fraction
1-
ϕ
for the matrix). This equation can be rearranged as:
ϕ
i
v
≈
C
liquid
v
liquid
(5.20)
C
solid
/
ϕ
+
(
−
ϕ)
1
Let us define in the usual way the partition coefficient
C
solid
/
C
liquid
as
D
i
. Ions that migrate
with the water of an aquifer without interacting with the impregnated rock (
D
i
0) will
therefore move faster than the ions that readily exchange between rock and water (
D
i
≈
0)
and spend a large part of their time of transit in the solid rock. For instance, chlorine ions
have no affinity for minerals and, like a dying substance, move at the same speed as the
water. Ions such as Zn
2
+
or Pb
2
+
are readily absorbed by the surface of the minerals. They
are very much delayed by this reactivity. This is the principle behind the purification of nat-
ural water in the ground. The containment within nuclear-waste repositories of radioactive
actinides, which normally have mineral/water
D
i
0, also relies heavily on this property.
Let us now consider the situation where the ratio
C
solid
/
C
liquid
and, therefore, the veloc-
ity of
i
in the interstitial mobile phase, depends on its concentration. One more time, we
will draw on a real-life analogy now taken from the experience of driving on highways at
rush hour (
Fig. 5.7
). We assume that the highway has only one lane and that passing is not
