Biomedical Engineering Reference
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64
64
64
C/Co
0.8
0.6
0.4
0.2
0
48
48
48
32
32
32
16
16
16
0
0
0
0
16
x
32
0
16
32
0
16
32
x
x
t =
120
t =
2880
t =
49800
FIGURE 7.7
SPH simulation of reactive transport and precipitation in a porous medium
with a microfracture. The Damkohler number was
Da
=2
.
548 and the Peclet
numbers before precipitation were
Pe
m
=0
.
082 for the matrix and
Pe
f
=22
.
82
for the fracture. The light gray particles represent mineral grains, and the
black particles represent precipitated mineral. The gray scale denotes the
dimensionless concentration,
C/C
0
. A solution with a solute concentration
of (
C
0
=4
C
eq
) was injected via the upper boundary, located at
y
= 64, into
the fractured porous medium, which was initially filled with a solution hav-
ing a solute concentration of
C
eq
[(Tartakovsky et al. 2007a,b) (Tartakovsky,
A.M., Meakin, P., Scheibe, T., and Wood, B.,
Water Res. Res.,
3, 2007,
doi:10.1029/2005WR004770. Copyright 2007 American Geophysical Union.
Reproduced/modified by permission of American Geophysical Union.)
reaction
A+B
↔
C
(7.35)
precipitated on the soil grains once the product concentration,
C,
exceeded
the equilibrium concentration,
C
eq
. The simulations showed that the precip-
itate formed a thin layer in the mixing zone, and that the precipitate layer
significantly reduced the mixing between the two reactants, A and B. To pre-
vent dissolution due to reduced mixing, the injected solutions contained the
reaction product,
C
, with a concentration of
C
eq
. The rate of precipitation
increases with increasing Peclet number, and the width of the precipitation
zone decreases with increasing Damkohler number.
Because the precipitate separating the two solutions has a width on the
order of the grain diameter, continuum scale simulations would provide mis-
leading results (the amount of precipitation would be seriously overestimated).
On the other hand, pore scale simulations cannot be used to simulate large-
scale processes. In this case, a multiscale multiresolution model that uses small
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