Study area
4.5 Geochemical modeling (PHREEQC)
output. The coefficient of determination, r2, to test the best-fitting of the kinetic model to the experimental data was calculated using the Eq:
∑ ∑ ̅̅̅ ∑ ̅̅̅ (4.7)
where is the amount of As ion on adsorbed on the surface of the sediment at any time, t, (µg/mg) obtained from the second-order kinetic model , is the amount of As ion on adsorbed on the surface of the sediment at any time t, (µg/mg) obtained from experiment, and
̅ is the average of qt (µg/mg).
4.5.1 Inverse geochemical model
The geochemical code PHREEQC (Parkhurst and Appelo, 1999) was used for inverse modeling. This model was used to calculate the water quality changes when the river water located near to the drilling Site_1 was considered to be recharging the groundwater. Since groundwater move along its flow paths below the ground surface it dissolves many chemical species (Appelo and Postma, 2005). Therefore, the chemical composition of groundwater reveals its evolution from the geological minerals interaction in the aquifers. Inverse modeling was carried out with a known initial solution concentration of the river water flowing near the Site_1. The potential mineral phases for the model input were selected from the XRD, SEM and chemical analysis of the sediment samples. These phases were constrained (precipitation/dissolution) using a conceptual model of general trends in chemical data and saturation indices ( ( )where is ion activity product and Ks is the solubility product constant), the over-saturated phases from the groundwater data were allowed to precipitate.
The inverse model in PHREEQC allows uncertainty limits that are constrained to satisfy the mole balance for each element and valence state, as well as charge balance for each solution within the simulation. The inverse model simulations were constrained within the specified uncertainty limit, which was taken as 7% in the model run. The models were first run using the “minimal” identifier. After checking for adequacy and geochemical consistency, the models were rerun using “Multiple Precision Solver” (default tolerance 1E-12) without
“minimal” identifier for details. A set of uncertainty terms was generated for each inverse model by the PHREEQC program to account for uncertainties in the model simulation:
1. The sum of residuals is the sum of the uncertainty of the unknowns weighted by the inverse of the uncertainty limit (for this application <8).
2. The sum of delta/uncertainty is the sum of the adjustments to each element concentration weighted by the inverse of the uncertainty limit (for this application
<8).
3. Maximum fractional error in element concentration is the adjustment to any element concentration in any solution (<0.07).
If no adjustments are made, all the three quantities would be zero.
4.5.2 Surface Complexation Model (SCM)
The equilibrium surface complexation model (SCM) of PHREEQC – version 2.17.01 (Parkhurst and Appelo, 1999) was used to simulate the sorbed As on hydroferric oxides (Hfo) phases, derived from the selective sequential extraction (SSE) data and then comparing the model output with the observed data. The modeling is confined to the use of diffuse layer model (DLM) (Dzombak and Morrel, 1990) mathematical formulation contained in PHREEQC. The SCM developed assumes that the major anion competing with As for sorption sites are carbonates, phosphates, silicates and sulfates. The sorption of common cations which were found in the study viz. Ca2+, Mg2+ were included in the model.
The model was assumed to be in chemical equilibrium and steady state conditions. The main factors controlling As partitioning in SCM under these assumptions were surface site densities, pH and competing ions (Miller, 2001; Robinson et al., 2011; Sharif et al., 2011).
The biotransformation, kinetically limited reactions and sorption by organic matter are assumed to be secondary effects. The assumptions made may not be valid for all systems, but may apply to many. The transferability of laboratory surface complexation modeling to the fields is assumed to be limited to the primary factors, due to simplification of modeling system.
The modeled sorbent were selected as ferrihydrite (Hfo_s and Hfo_w) and goethite (Goe_).
Using the surface complexation approach the adsorption of As species to Hfo were described by equilibrium mass action equations. Ligand sorption was considered to occur at two sorption sites on ferrihydrite with a sorption density of 0.005 mol/mol Fe for strong site which was denoted as Hfo_s, and 0.2 mol/mol Fe for weak site which was denoted as Hfo_w (Dzombak and Morrel, 1990). Ligand sorption for goethite was considered to occur at only one sorption site with a density of 0.00000384 mol sites/m2 (Manning and Goldberg, 1996).
From Dzombak and Morrel (1990), the specific surface was used as 600 m2/g for ferrihydrite (Hfo_s and Hfo_w) and, 43.7 m2/g for goethite (Goe_) (Manning and Goldberg, 1996).
Published physical and chemical properties of surface complex parameters are presented including As(III) and As(V) in Table 4.4-4.5. The surface reaction considered and thermodynamic constants used for ferrihydrite (Hfo_s and Hfo_w) and goethite (Goe_) are shown in Table 4.4-4.5.
Table 4.4 Surface reactions and thermodynamic constants for PHREEQC surface complexation model with strong (Hfo_s) and weak (Hfo_w) adsorption sites.
Adsorption reaction Log K Reference
Hfo_sOH + H+ = Hfo_sOH2+ 7.29 Allison et al. (1990)
Hfo_wOH + H+ = Hfo_wOH2+ 7.29
Hfo_sOH = Hfo_sO- + H+ -8.93
Hfo_wOH = Hfo_wO- + H+ -8.93
Arsenite
Hfo_sOH + H3AsO3 = Hfo_sH2AsO3 + H2O 5.41 Allison et al. (1990) Hfo_wOH + H3AsO3= Hfo_wH2AsO3 + H2O 5.41
Arsenate
Hfo_sOH + H3AsO4 = Hfo_sH2AsO4 + H2O 8.61 Hfo_wOH + H3AsO4= Hfo_wH2AsO4 + H2O 8.61 Hfo_sOH + H3AsO4 = Hfo_sH2AsO4- + H2O +
H+
2.81 Hfo_wOH + H3AsO4= Hfo_wH2AsO4-
+ H2O + H+
2.81 Hfo_sOH + H3AsO4 = Hfo_sOHAsO43-
+ 3H+ -10.12 Hfo_wOH + H3AsO4= Hfo_wOHAsO43-
+ 3H+ -10.12 Phosphate
Hfo_sOH + PO4-3
+ 3H+ = Hfo_sH2PO4 + H2O 31.29 Allison et al. (1990) Hfo_wOH + PO4-3
+ 3H+ = Hfo_wH2PO4 + H2O 31.29 Hfo_sOH + PO4-3
+ 2H+ = Hfo_sHPO4-
+ H2O 25.39 Hfo_wOH + PO4-3
+ 2H+ = Hfo_wHPO4-
+ H2O 25.39 Hfo_sOH + PO4-3
+ H+ = Hfo_sPO42-
+ H2O 17.72 Hfo_wOH + PO4-3
+ H+ = Hfo_wPO42-
+ H2O 17.72 Carbonate
Hfo_wOH+ CO32-
+ H+=Hfo_wCO3-
+ H2O 12.56 van Geen et al. (1994) Hfo_wOH+ CO32-
+2H+=Hfo_wHCO3+ H2O 20.62 Silica
Hfo_sOH + H4SiO4= Hfo_sH3SiO4 + H2O 4.28 Swedlund and Webster Hfo_wOH + H4SiO4= Hfo_wH3SiO4 + H2O 4.28 (1999)
Hfo_sOH + H4SiO4= Hfo_sH2SiO4-
+ H2O + H+ -3.22 Hfo_wOH + H4SiO4= Hfo_wH2SiO4-
+ H2O + H+ -3.22 Hfo_sOH + H4SiO4= Hfo_sHSiO42-
+ H2O + 2H+ -11.69 Hfo_wOH + H4SiO4= Hfo_wHSiO42-
+ H2O + 2H+
-11.69 Calcium
Hfo_sOH + Ca2+= Hfo_sOHCa2+ 4.97 Allison et al. (1990) Hfo_wOH + Ca2+= Hfo_wOCa+ + H+ -5.85
Table 4.5 Surface reactions and thermodynamic constants for PHREEQC surface complexation model with goethite (Goe_) adsorption sites.
Surface reaction Log K Reference
Goethite
Goe_OH + H+ = Goe_OH2+ 7.52 Dixit and Hering (2003)
Goe_OH = Goe_O + H+ -10.6
Phosphate
Goe_OH + H3PO4 = Goe_H2PO4 + H2O 8.05 Sigg (1979) Goe_OH + H3PO4 = Goe_HPO4-
+ H2O + H+ 3.40 Goe_OH + H3PO4 = Goe_PO42-
+ H2O + 2H+ -2.20 Arsenate
Goe_OH + AsO4-3 + 3H+ = Goe_H2AsO4 + H2O 30.94 Dixit and Hering (2003) Goe_OH + AsO4-3 + 2H+ = Goe_HAsO4- + H2O 26.75
Goe_OH + AsO4-3
+ H+ = Goe_H2AsO42-
+ H2O 20.16 Arsenite
Goe_OH + AsO3-3 + 3H+= Goe_H2AsO3 + H2O 39.87 Goe_OH + AsO3-3 + 2H+= Goe_HAsO3- + H2O 32.34 Silicate
Goe_OH + H4SiO4 = Goe_H3SiO4 + H2O 4.35 Sigg (1979) Goe_OH + H4SiO4 = Goe_H2SiO4-
+ H2O + H+ -3.04 Carbonates
Goe_OH + 2H++ CO32- = Goe_HCO3 + H2O 20.78 van Geen et al. (1994) Goe_OH + H++ CO32- = Goe_CO3- + H2O 12.71
Goe_OH + CO32-
= Goe_OHCO32-
3.56 Appelo et al. (2002) Flouride
Goe_OH + F- = Geo_F + OH- -4.54 Sigg (1979)
Sulfate
Goe_OH + SO42- + 2H+ = Geo_ HSO4 + H2O 13.61 Ali and Dzombak (1996) Goe_OH + SO42-
+ H+ = Geo_ SO4-
+ H2O 8.19 Goe_OH + SO42-
= Geo_ OSO43-
+ H+ -6.26
Goe_OH + SO42-+ Cu2+ = Geo_ OHCuSO4 + H+ 9.46 Ferrous
Geo_OH + Fe2+ + H2O = Goe_OFeOH+ + 2H+ -10.95 Dixit and Hering (2006) Geo_OH + Fe2+ = Goe_OFe+ + H+ -0.60
Calcium
Geo_OH + Ca2+ = Goe_OCa+ + H+ -7.18 Ali and Dzombak (1996) Magnesium
Geo_OH + Mg2+ = Goe_OMg+ + H+ -5.94 Sigg (1979)
The Component Additivity (CA) approach was used in the SCM. It assumed that one mineral phase dominates adsorption, which facilitate a straight forward equilibrium calculation if the exposed surface area and surface-site density of that mineral phase in the soil or sediment can be quantified (Davis et al., 1998; Miller, 2001; Robinson et al, 2011; Sharif et al., 2011). The surface complexation model assumed that amorphous Fe-oxides are the dominant mineral adsorbent phase compared with amorphous Mn(IV) and Al(III) oxides and any crystalline and clay minerals. The sorbent phases ferrihydrite (Hfo_w and Hfo_s) and goethite (Goe_) were quantified from the selective sequential extraction (SSE) which is operationally defined.
The surface composition of the sediments was kept in equilibrium with the mean groundwater quality of the tubwell-1 (T-1) and tubwell-2 (T-2) of the Site_1. The PHREEQC input data sets were prepared as explained i.e. groundwater composition, the sorbent phase (Hfo_w and Hfo_s or Goe_) were instructed to interact using the given thermodynamic data sets tabulate (Table 4.4-4.5). The water-mineral ratio for PHREEQC was calculated by assuming the porosity 30% and density of 2.5 g/cm3. The difference between the modeled As and the actual extracted As was expressed as percentage difference (%) between extracted As and modeled As.