Geoscience Reference
In-Depth Information
or temperatures are mixed, resulting in a new solution that is oversaturated. While
widely discussed in the geochemical literature, only limited reference to mixing-
induced precipitation has been made in hydrological studies.
In addition to considering the mode by which supersaturation is reached, the
physical changes in the rock resulting from precipitation also crucially affect the
dynamics of precipitation. Porosity can be reduced by crystal growth, and this can
have an effect on additional physical parameters in the porous matrix, such as the
specific surface area. Both porosity and specific surface area are important
parameters in subsurface systems, as they determine to a large extent both the
permeability of the rock and the chemical kinetics of mineral precipitation.
Therefore, both porosity and specific surface area must be incorporated into mass
conservation and transport equations. Changes in porosity can be related to the
volumetric changes in the amount of mineral precipitated in a relatively
straightforward manner, but changes in specific surface area are more difficult to
quantify.
One approach to quantitatively relate changes in porosity to changes in specific
surface area is to assume that the porous medium is composed of spherical grains.
The resulting specific surface area per unit volume of rock s, is related to the
porosity, /, by the relationship (Lichtner
1988
)
2
=
3
1
/
1
/
o
;
ð
11
:
8
Þ
s ¼ s
o
where s
o
is the specific surface area of the rock at a porosity of /
o
. Alternatively, if
it is assumed that the pores can be approximated by spheres, the specific surface
area can be expressed by Kieffer et al. (
1999
)
2
=
3
/
/
o
s ¼ s
o
:
ð
11
:
9
Þ
Therefore, in the first model, the specific surface area increases with decreasing
porosity, while in the second, the opposite relationship is specified. While some
attempts have been made to experimentally verify these models in individual rock
types (Kieffer et al.
1999
; Jové Colon et al.
2004
), the data concerning a wide
range of rocks and precipitation-dissolution reactions remain limited.
Emmanuel and Berkowitz (
2005
) examined the dynamics and patterns of
changing porosity during mixing-induced precipitation, using a two-dimensional
numerical model that simulates mixing-induced precipitation in both homoge-
neous and heterogeneous porous media. The role of specific surface area also was
explored. The precipitation of a and b in equimolar amounts to form a solid ab was
considered, a scenario that ensures that R
a
= R
b
. The sink term can then be
assumed to have the generic form often valid for near-equilibrium conditions
(Morse and Arvidson
2002
):
