Geoscience Reference
In-Depth Information
n
C
a
C
b
K
sp
R ¼
sK
r
1
;
ð
11
:
10
Þ
where K
r
is a kinetic rate coefficient, K
sp
is the solubility product of the solid ab ,
and n is an empirical reaction order. The rate of change of porosity can be derived
from the sink term by dimensional analysis. As R is defined as the number of
moles precipitated per unit time per unit volume of fluid, multiplying by both
porosity and molar volume (M
v
) yields the volumetric rate of change of precipi-
tated material per unit volume of bulk matrix:
o
/
ot
¼ /M
v
R
:
ð
11
:
11
Þ
Equation (
11.10
) is valid for near-equilibrium systems, so that it can be applied to
mass-transfer-limited processes, that is, systems in which the large-scale rate of
change of porosity is limited by the solute flux rather than the reaction kinetics.
Application of this model showed that the complete reduction in porosity near
the inlet does not lead to clogging of a system: nonsupersaturated fluids are able to
flow around closed regions and into more permeable areas where mixing and
subsequent deposition can occur. Thus, mixing-induced precipitation is expected
to reduce porosity in concentrated regions rather than lead to evenly precipitated
material throughout the porous domain.
11.4 Transport of Immiscible Liquids
Petroleum products, synthetic organic solvents, and other toxic organic com-
pounds dissolved in organic solvents, generally referred to as nonaqueous phase
liquids (NAPLs), are a key class of contaminants in the subsurface. These com-
pounds are generally insoluble or only slightly soluble in water. As a consequence,
NAPLs remain as distinct liquid phases as they are transported downward from
land surface to the water table; this migration is governed mostly by the density
and viscosity of the NAPL. Specific contaminants often are classified as dense
NAPLs (DNAPLs), such as trichloroethylene and carbon tetrachloride, or as light
NAPLs (LNAPLs), such as oil and gasoline, according to their density relative to
water. DNAPLs sink through the water table region, downward through the fully
saturated zone, while LNAPLs remain in the capillary fringe, ''floating'' on the
surface of the free water. A schematic illustration of LNAPL and DNAPL trans-
port from land surface is shown in Fig.
11.1
.
Figure
11.1
provides only a coarse-level picture of NAPL migration. Depending
on the viscosity and density ratios, between the NAPL and the resident water, as well
as the properties (physical and chemical) of the porous medium, a variety of
(unstable) fingering and (stable) fronts can develop with depth. More specifically,
the degree of fingering in the displacement and the actual rate of downward (and
