A version of WHAM by Lofts (2005) was used which enabled me to call WHAM VI in EXCEL spreadsheet. It includes a dynamic link library (DLL) file and the VBA code. In EXCEL, the VBA functions were programmed to call WHAM VI to execute specific calculations and then return Cu partition coefficients. Detailed
instructions and programs on how to call WHAM VI in EXCEL spreadsheet can be found in the Appendix C. The model parameters are desorption rate coefficient kd, which kept constant for all conditions, and the fraction of active organic matter (f) for each soil.
Ideally, WHAM VI can be used to calculate a partition coefficient at each time step during the numerical calculations. This will require a lot of time to conduct all calculations, especially when using SOLVER to do a global fitting. My
preliminary tests demonstrated that reducing the times to call WHAM will not
significantly affect the model performance. Thus I chose to call WHAM VI every five time steps. Between the WHAM VI calculation, partition coefficient kept constant as the previous WHAM VI calculation. This simplification significantly reduced the total calculation time.
The WHAM VI input parameters included the solution chemistry composition, including pH, [Ca2+], [NO3-], {Fe3+}, {Al3+}, and [Cu2+], and SOM, including the particulate [HA] and [FA]. Ponizovsky et al. (2006) have demonstrated that inorganic components (metal oxides and clay fraction) are not important for Cu binding using WHAM VI calculations. In my experimental conditions and for the soils I used, I did not expect significant contributions of inorganic components to Cu binding. Then only SOM was considered. For the solution species, the concentrations were input as exactly used in the experiments. Free Fe3+ and Al3+ activities were calculated using Eq. (6.25). From the values summarized by Stumm and Morgan
which is similar to the values used by Tipping et al., 2003. For the SOM, only the active fraction was used in WHAM VI calculations and the active fraction consists of 84% HA and 16% FA (Tipping et al., 2003). Table 6.2 gave WHAM input parameters for the three soils at pH 5.5. At different pH, the difference of input parameters are free Fe3+ and Al3+ activities, which can be calculated by Eq (6.25). In Table 6.2, the concentrations of HA and FA were automatically recalculated based on the fraction of active organic matter, which was optimized by model fitting. The total Cu
concentration was input into WHAM VI at each time step when calling WHAM VI through the user built function. Table 6.3 lists the fitted model parameters.
Figures 6.5 - 6.10 presented the modeling results and WHAM VI predicted partition coefficients for each experiment. Generally, WHAM VI based kinetics model gave relatively good fits for all experimental data.
Table 6.2 WHAM input parameters at pH 5.5
Parameter pH [Ca2+] [NO3-] {Fe3+} {Al3+} [HA] [FA]
Specie Fixed Total Total Activity Activity Total Total
Unit M M M M g/L g/L
Matapeake 5.5 0.003 0.006 3.16E-14 1.00E-08 7.55E-01 1.44E-01 Boonton
Bergen 5.5 0.003 0.006 3.16E-14 1.00E-08 8.05E-01 1.53E-01 Boonton
Union
5.5 0.003 0.006 3.16E-14 1.00E-08 1.39E00 2.64E-01
Table 6.3 Model fitting parameters for WHAM VI based kinetics model Kinetics parameter Fraction of active organic matter (f)
kd (1/min) Matapeake Boonton Bergen Boonton Union
2.3E-2 0.46 0.33 0.27
0 200 400 600 800 1000 1200
0 100 200 300 400 500
Data Model
E ff luent Cu conc e n tr at ion ( à g/L)
time (min)
(a)
Figure 6.5 Kinetics of Cu sorption and desorption on the Matapeake soils at pH 5.5. (influent [Cu] = 1.7 mg/L): (a) Effluent Cu concentration vs.
time; (b) WHAM VI predicted partition coefficient vs. time.
0.1 1 10 100
0 100 200 300 400 500
K p (L /g )
time (min)
(b)
Figure 6.5 Continued.
0 100 200 300 400 500
0 100 200 300 400 500
Data Model
E ff luent Cu c onc e n tr ati on ( à g/ L )
time (min)
(a)
Figure 6.6 Kinetics of Cu sorption and desorption on the Matapeake soils at pH 6.0. (influent [Cu] = 1.4 mg/L): (a) Effluent Cu concentration vs.
time; (b) WHAM VI predicted partition coefficient vs. time.
0.1 1 10 100 1000
0 100 200 300 400 500
K p (L /g )
time (min)
(b)
Figure 6.6 Continued.
0 50 100 150 200 250
0 100 200 300 400 500
Data Model
E ff luent Cu c onc e n tr ati on ( à g/ L )
time (min)
(a)
Figure 6.7 Kinetics of Cu sorption and desorption on the Matapeake soils at pH 6.5 (Influent [Cu] = 1.5 mg/L): (a) Effluent Cu concentration vs.
time; (b) WHAM VI predicted partition coefficient vs. time.
0.1 1 10 100 1000
0 100 200 300 400 500
K p (L /g )
time (min)
(b)
Figure 6.7 Continued.
0 100 200 300 400 500
0 100 200 300 400 500
Data Model
E ff luent Cu c onc e n tr ati on ( à g/ L )
time (min)
(a)
Figure 6.8 Kinetics of Cu sorption and desorption on the Matapeake soils at pH 5.5 with influent [Cu] = 0.85 mg/L: (a) Effluent Cu
concentration vs. time; (b) WHAM VI predicted partition coefficient vs. time.
0.1 1 10 100
0 100 200 300 400 500
K p (L /g )
time (min)
(b)
Figure 6.8 Continued.
0 200 400 600 800 1000
0 100 200 300 400 500
Data Model
E ff luent Cu c onc e n tr ati on ( à g/ L )
time (min)
(a)
Figure 6.9 Kinetics of Cu sorption and desorption on the Boonton Bergen soil at pH 5.5 (influent [Cu] = 1.6 mg/L; [SOC] = 3.43%): (a) Effluent Cu concentration vs. time; (b) WHAM VI predicted partition coefficient vs. time.
0.1 1 10 100
0 100 200 300 400 500
K p (L /g )
time (min)
(b)
Figure 6.9 Continued.
0 100 200 300 400 500 600 700 800
0 100 200 300 400 500
Data Model
E ff luent Cu c onc e n tr ati on ( à g/ L )
time (min)
(a)
Figure 6.10 Kinetics of Cu sorption and desorption on the Boonton Union soil at pH 5.5 (influent [Cu] = 1.7 mg/L; [SOC] = 7.15%): (a) Effluent Cu concentration vs. time; (b) WHAM VI predicted partition
coefficient vs. time.
0.1 1 10 100
0 100 200 300 400 500
K p (L /g )
time (min)
(b)
Figure 6.10 Continued.
The WHAM predicted Kp can handle the variation of solution chemistry and soil compositions. The value of Kp increased dramatically with pH due to more strong binding sites at higher pH, e.g. phenolic function groups in SOM. With increase of Cu loading in soils, the value of Kp decreased quickly, which corresponds to more Cu binding to carboxylic groups.
It is interesting that the fraction of active organic matter decreased with increase of SOC concentrations (Figure 6.11(a)). It means with higher SOC
concentration, more SOM is inactive. The total mass concentrations of active organic matter increased with SOC concentrations, indicating more reaction sites for higher SOC concentration soils (Figure 6.11(b)). With only three soils, it is premature to make any mechanism conclusion. More research is needed to quantitatively
characterize the active organic matter. Gustafsson et al. (2003) applied the SHM to model the partition of trace metals between soils and solutions by optimizing the active humic substance (and Al) in their model. But they did not find any clear relationship between the active humic substance with SOM or other extraction methods. The active organic matter obtained by Tipping et al. (2003) also did not show any dependence on the organic carbon in the soils.
0.25 0.3 0.35 0.4 0.45 0.5
0.02 0.03 0.04 0.05 0.06 0.07 0.08
Ac tiv e O C / S O C
SOC (g OC/g)
(a)
Figure 6.11 The active organic matter vs. SOC concentration: (a) percentage plot; (b) mass concentration plot.
0 0.005 0.01 0.015 0.02 0.025 0.03
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Ac ti v e or ga ni c car bon (g O C /g)
SOC (g OC/g)
(b)
Figure 6.11 Continued.
The Cu desorption coefficient obtained is 2.31×10-2 1/min which is quite close to the value obtained from the kinetics model based on the Freundlich equation.
These two independent kinetics models gave similar Cu desorption rate coefficient may indicate (i) these two approaches predicted the Cu nonlinear binding behavior in the similar way or (ii) the kinetics parameter is the real constant in the conditions my experiments covered.