,
Supplementary Material
Implication of surface modified NZVI particle retention in the
porous media: assessment with the help of 1-D transport model
Trishikhi Raychoudhury1*, Vikranth Kumar Surasani2
1
Dr.Trishikhi Raychoudhury
Assistant Professor
Department of Civil and Environmental Engineering,
Indian Institute of Technology Patna
Bihta, Patna, Bihar 801103
*
Corresponding author: [email protected]
Phone no: 91-612-302-8179;
2
Dr. Vikranth Kumar Surasani
Assistant Professor
Department of Chemical Engineering,
Birla Institute of Technology and Science Pilani-Hyderabad Campus,
Hyderabad, Telangana, India-500078
Marquardt algorithm is used for least square error minimization and parameter
estimation. The details of the objective function are given below.
11
Objective:
Min  (Ci  Ci ,data ) 2  ( S i  S i ,data ) 2
S.1
i 1
Here, Ci,data and Ci are experimental and corresponding simulated normalized
concentration at the outlet. Si,data, and Si are the experimental and simulated solid phase
deposited mass along the column length.
Subjected to constrain:
Equation (1)-(5) given in the main paper
(1-D colloid transport model.)
Parameters to be estimated: β, kstr,i (i=1,2…7), Kdet,i (i=1,2,3,4), λ
Boundaries:  LB    UB
S.2
k str,i , LB  k str,i  k str,i ,UB
(i=1,2….7)
S.3
k det,i , LB  k det,i  k det,i ,UB
(i=1,2….4)
S.4
LB    UB
S.5
Here, βLB, βUB are the lower and upper bound of special distribution for straining
parameter β, kstr,i,LB , kstr,i,UB are the lower and upper bound for seven different straining
coefficient (based on sand size and particle size) kstr,i. kdet,i,LB , kdet,i,UB are the lower and
upper bound for four different (based four different sized sand) detachment coefficient
kdet,i.. Similarly, λLB and λUB are the lower and upper bound of λ, which is the ratio of
volume of particles per unit volume of particles deposited.
1
2
3
4
5
0.12
0.09
b)
0.03
0.06
775 m
510 m
250 m
150 m
Model fit: Raychoudhury_et al_2013
Model fit: This study
0.00
0.0
0
CMC-NZVI retention, S (mg/g)
1.0
0.6
0.4
At outlet
(L=9 cm)
0.2
C/C0
0.8
a)
1
2
3
5
6
7
8
4
5
0.5
0.4
d)
0.1
0.2
0.3
775 m
510 m
250 m
150 m
Model fit: Raychoudhury_et al_2013
Model fit: This study
1
2
3
4
5
6
7
8
Column length (cm)
0.8
1.2
1.6
e)
Raychoudhury_et_al_2013
This study
0.0
0.4
Kstr (min-1)
2.0
2.4
Pore volume (PV)
0.0
0.2
9
0.0
0.0
2
CMC-NZVI retention, S (mg/g)
1.0
0.6
0.4
At outlet
(L=9 cm)
0.2
C/C0
0.8
c)
1
4
Column length (cm)
Pore volume (PV)
0
3
0.4
0.6
0.8
1.0
1.2
1.4
-3
dp/dc(x10 )
Fig S1 Model fit and experimental data for (a) BTC and (b) retention profile of CMC-NZVI of C0
= 0.085 g/L, and (c) BTC and (d) retention profile of CMC-NZVI of C0=0.35 g/L. Here, constant
flow condition with similar condition as adopted in (Raychoudhury et al. 2014), (Table 1) is
considered. (e) Fitted value of straining rate coefficient with the function of dp/dc ratio.
9
3.0
1.5
2.0
2.5
dc=775 µm
dc=510 µm
dc=250 µm
dc=150 µm
1.0
Pore water velocity ( U/ )
a)
1
2
3
4
5
6
7
8
9
Column length (cm)
0
10 20 30 40 50 60 70 80 90 100
Distance (cm)
1.2
0.6
0.8
1.0
b)
0.4
T= 10 min (during injection)
T= 66 min (end of injection)
T= 110 min (with groundwater flow)
0.2
0.3
0.6
T= 10 min (during injection)
T= 66 min (end of injection)
T= 110 min (with groundwater flow)
Hydraulic
conductivity
(cm/min)
Permeability
)
(k per
0.9
1.2
1.5
a)
0.0
Deposited mass (S, mg/g)
1.8
Fig S2 Change in porewater velocity along the column length at the end of electrolyte flushing,
with C0 of 1.7 g/L.
0
10 20 30 40 50 60 70 80 90 100
Distance (cm)
Concentration (mg/L)
d)
T= 10 min (during injection)
T= 66 min (end of injection)
T= 110 min (with groundwater flow)
0
100 200 300 400 500 600
100 150 200 250 300
50
L =25cm
L= 50 cm
L = 100 cm
0
Concentration C (mg/L)
c)
0 10 20 30 40 50 60 70 80 90 100 110
Time (min)
0
10 20 30 40 50 60 70 80 90 100
Distance (cm)
Fig S3 Calculated (a) CMC-NZVI retention profile and (b) change in permeability along the
length of porous media at different time point, calculated for medium 3, with the specification
described in Table 1 and Figure 1 (c). Concentration vs time calculated for CMC-NZVI at three
different points. (d) Change in concentration with distance at three different time point.
References:
Raychoudhury T, Tufenkji N, Ghoshal S (2014) Significance of straining during
polyelectrolyte modified Iron nanoparticle transport in porous media Water
Research 50:80-89