Elfeki, A.M., Bruining, J., Dekking, F.M., Kraaikamp, C. and Uffink, G. (2002). Modeling Adsorption Kinetics of Chemically Interactive Porous Sediments by a Two-State Random Walk Particle Method. Poster Presentation on the third meeting on DIOC “Water” mini-symposium on 7th November, 2002..Faculty of Civil Engineering and Geosciences, TU Delft, The Netherlands.

1. Modelling Adsorption Kinetics of Chemically
Interactive Porous Sediments by a Two-State
Random Walk Particle Method
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A
B
C
D
E
F
.
00.1110
0 50 100 150 200 250
Time (days)
0
20
40
60
80
100
Centroriddisplacement(m)
The off-diagonal elements of the Chain
a=1.0,b=0.0
a=0.5,b=0.5
a=0.1,b=0.1
a=0.1,b=0.9
a=0.9,b=0.1
a=0.9,b=0.9
0 50 100 150 200 250Time (days)
0.0
0.4
0.8
1.2
1.6
LateralVariance(m^2)
The off-diagonal elements of the Chain
a=1.0,b=0.0
a=0.5,b=0.5
a=0.1,b=0.1
a=0.1,b=0.9
a=0.9,b=0.1
a=0.9,b=0.9
0 50 100 150 200 250Time (days)
0
40
80
120
160
200
LongitudinalVariance(m^2)
The off-diagonal elements of the Chain
a=1.0,b=0.0
a=0.5,b=0.5
a=0.1,b=0.1
a=0.1,b=0.9
a=0.9,b=0.1
a=0.9,b=0.9
Introduction: Field observations of
contaminant plumes show very ragged plumes
(See Cape Cod site, Figure 1, from LeBlanc et
al., 1991). This is believed to be due to effects
of physical heterogeneity of the medium,
reactivity between solid matrix and solutes and
transient conditions of the flow system. In this
research we focus on reactivity. Other aspects
will be addressed in the future.
Elfeki, A.M., Bruining, J., Dekking, F.M., Kraaikamp, C. and Uffink, G.
TU-Delft (CiTG, ITS) and RIVM.
Figure 1 Cape Cod Site
Approach: In this research, we focus
on the interaction between the solid matrix
and the chemicals under steady
groundwater flow. We present a stochastic
approach to address linear and non-linear
adsorption mechanisms using a two-state
particle tracking random walk theory. The
particles are assigned two states: either
mobile (free) or immobile (adsorbed). The
kinetics between particles are modelled
with a transition probability matrix [see
matrix form]. Various transition probability
matrices are investigated to describe
various adsorption mechanisms (slow and
fast reaction rates). Both linear and non-
linear adsorption are addressed. However,
the presentation in this research addresses
only the linear case. Analytical model of the
linear adsorption process is also developed
and comparison is foreseen.
Simulation: Table 1 shows six
cases. The simulations parameters
are displayed in Table 2. Case A is a
reference case with no adsorption.
The rest are cases with different
degree of adsorption reactions
described in the table by a and b, the
off-diagonal elements of the matrix.
Figure 3 describes plume spatial
moments of the mobile phases. When
a and b are high this leads to slower
kinetics (long plumes see case D)
while when they are low one obtains
fast kinetics (see case F) .
Table 1
Figure 2 Simulations with different a and b
After 150 days since release.
Figure 3 Plume Spatial
Moments
Conclusions: A model is
developed to address the kinetics in
adsorption process. The model is
capable of handling linear and non-
linear adsorption behaviour. Only the
linear case is presented here.
1
1
lk
i m
i a a
p
m b b
 
   
Table 2
Case a b
A 1.0 0.0
B 0.1 0.9
C 0.5 0.5
D 0.1 0.1
E 0.9 0.1
F 0.9 0.9
Parameter Numerical
Value
Time Step 3 [days]
Longitudinal
Dispersivity
0.1 [m]
Lateral
Dispersivity
0.01[m]
Effective
Porosity
0.3 [-]
Injected Mass 100 [grams]
Gradient 0.01 [-]
No. of
Particles
5000
[particles]
K 10. [m/day]