Quantifying the physical and chemical mass transfer processes for the fate and transport of Co(II)EDTA in a partially-weathered limestone–shale saprolite

Journal of Contaminant Hydrology 90 (2007) 184 – 202 www.elsevier.com/locate/jconhyd

Quantifying the physical and chemical mass transfer processes for the fate and transport of Co(II)EDTA in a partially-weathered limestone–shale saprolite Jin-Ping Gwo a,⁎, Melanie A. Mayes b , Philip M. Jardine b a

University of Maryland, Baltimore County, Department of Civil and Environmental Engineering, 1000 Hilltop Circle, Maryland, MD 21250, United States b Oak Ridge National Laboratory, Environmental Sciences Division, P.O. Box 2008, Oak Ridge, TN 37831, United States

Received 25 April 2005; received in revised form 19 September 2006; accepted 22 September 2006 Available online 28 November 2006

Abstract The objective of the research is to quantify the relative contributions of physical and chemical mass transfer to the movement of Co(II/III)EDTA (chelates of Cobalt and Ethylene Diamine Tetraacetic Acid or EDTA) through a limestone–shale saprolite soil. Saprolite is a collective term referring to partially-weathered bedrock. It exists extensively in the subsurface. Because the parent bedding structures are maintained during the weathering process, saprolite soils are characterized by intensive fractures and secondary deposits of minerals such as Al-, Fe- and Mn-oxides on the fracture surfaces. Movement of reactive species through the soils may be influenced by diffusion into the rock matrix, a physical mass transfer (PMT) process, and interfacial chemical reactions, a chemical mass transfer (CMT) process. The PMT and CMT processes are phenomenologically similar but mechanistically different. In this research, previous laboratory observations from a Br and Co(II)EDTA tracer injection into an undisturbed saprolite soil column were used. Mechanistic reactive transport models were formulated to quantify the PMT and CMT processes. The PMT process was independently characterized by using the non-reactive tracer Br. Model parameters thus obtained were subsequently used as constraints to quantify the CMT processes involving Co(II)EDTA and its oxidation product Co(III)EDTA. Our calculations indicated that the PMT rates of the less reactive Co(III)EDTAwere comparable with their theoretical CMT rates. In contrast, for the more reactive species Co(II)EDTA, CMT rates are higher than PMT rates. Evaluations of alternative CMT process models further confirmed one of our hypotheses on the basis of previous experimental understandings. The hypothesis suggested that competition from Fe-oxide for Co(II)EDTA may account for the majority of the decrease of Co(III)EDTA effluent concentrations that resulted in the separation of total Co and ⁎ Corresponding author. Now at United States Nuclear Regulatory Commission, Washington, DC 20555. E-mail address: [email protected] (J.-P. Gwo). 0169-7722/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jconhyd.2006.09.013

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

185

Co(III)EDTA breakthrough curves. Because Co(III)EDTA is more mobile than Co(II)EDTA in the subsurface, the results of this research suggest independent quantifications of CoEDTA PMT and CMT processes if laboratory results are to be interpreted correctly and scaled up for field and predictive uses. © 2006 Elsevier B.V. All rights reserved. Keywords: Mass transfer; Reactive transport; Saprolite; CoEDTA; Interfacial reaction

1. Introduction Matrix diffusion, a diffusive mass transfer process that moves mass and solutes between primary and secondary porosities of structured soils and rocks, has been extensively studied and documented in the literature (e.g., Shuford et al., 1977; Tang et al., 1981; Frohne and Mercer, 1984; Seyfried and Rao, 1987; Jardine et al., 1988; Birgersson and Neretnieks, 1990; Abelin et al., 1991; Jardine et al., 1993; Wilson et al., 1993; McKay et al., 1993; Novakowski and Lapcevic, 1994; Vandergraaf et al., 1996; Holtta et al., 1996; Reedy et al., 1996; Selim and Ma, 1998; Jardine et al., 1999; Becker and Shapiro, 2000; Shapiro, 2001). The mechanism of matrix diffusion is fundamentally similar to free water diffusion in that mass and solutes move along the gradient of density and concentration. In the case of matrix diffusion, solutes may also move across the boundary of the primary soil aggregate/ rock matrix and the secondary macropores/fractures. Matrix diffusion is often revealed in the laboratory by the separation of tracer breakthrough curves (e.g., Hu and Brusseau, 1995; Mayes et al., 2003) and the decrease and recovery of solute concentrations during and immediately after flow interruptions (e.g., Reedy et al., 1996; Brusseau et al., 1997; Mayes et al., 2000). A flow interruption stops the injection of fluids and tracers, allowing more time for reactive tracers to interact with the solid phase and for all tracers to diffuse into or out of the matrix. As pointed out in previous investigations, matrix diffusion may be mathematically described, among others, by mobile–immobile models (e.g. van Genuchten and Wierenga, 1976; van Genuchten, 1981; Parker and Van Genuchten, 1984) and two-region models (e.g., Skopp et al., 1981). A two-site kinetic absorption model for reactive tracers is mathematically identical to that of a mobile–immobile model (e.g., see discussion in Parker and Van Genuchten, 1984). In the event that one is to determine mass transfer coefficients for reactive tracers by using the two-site model, it is not immediately unambiguous that model parameters obtained by curve-fitting should represent the matrix diffusion, the surficial absorption processes, or both. Thus, the fundamental questions in characterizing the fate and transport of reactive pollutants in structured soils are (1) the significance of the individual contributions of these two processes and (2) the approaches that might be taken to quantify them independently. In the last few decades, improved understanding of matrix diffusion, a physical mass transfer (PMT) process, has largely increased our confidence in characterizing and predicting the movement of conservative tracers in structured porous media (e.g., Jardine et al., 1988; Hu and Brusseau, 1995; Novakowski et al., 1995; Gwo et al., 1995; Reedy et al., 1996; Gwo et al., 1998; Selim and Ma, 1998; Jardine et al., 1999; Gwo et al., 2005a,b). Efforts in identifying the effects of interfacial reactions or chemical mass transfer (CMT) on the fate and transport of pollutants in the presence of PMT have also been reported in the literature (e.g., Jardine et al., 1993; Mayes et al., 2000; Jardine et al., 2002; Andersson et al., 2004). However, the relative contributions of PMT and CMT to the movement of reactive tracers remain difficult to quantify. This is particularly so for field studies that are complicated by large scale hydrogeological and geochemical heterogeneities (e.g., Jardine et al., 2002; Andersson et al., 2004). That reactive tracers may undergo interfacial

186

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

chemical transformation and producing new chemical species with different diffusion coefficients only further complicates the issue. Pollutants of differing diffusion coefficients may have different fate and transport behaviors in structured soils and rocks. For example, previous field-scale experimental and modeling studies reported in Jardine et al. (1999) and Gwo et al. (2005b) suggested that tracers with different diffusion coefficients may access or leach out of a rock matrix at different rates. Certain biogeochemical reactions are known to be influenced by the rates of electron donors and acceptors moving across the interface between the rock matrix and the preferential flow path, thereby influencing microbial biodegradation capacities (e.g., McMahon, 2001). Chemical transformation and field-scale hydrogeochemical heterogeneity have also resulted in differing opinions regarding the fate and transport of heavy metals in the subsurface (Zachara et al., 1995; Jardine et al., 2002). To improve our understanding of the mass transfer processes and to reduce uncertainty in waste site construction and remediation designs, it may be necessary that the PMT and CMT processes be separately characterized and their contributions be independently quantified. To this end, we believe that a better understanding may be gained and uncertainties may be reduced provided that, in addition to studies of model parameter uncertainties, alternative conceptual models of CMT and PMT may be formulated and rigorously tested (e.g., Jardine and Taylor, 1995; Gwo et al., 2005a). Laboratory experiments and their results may be used to evaluate against these models and to quantify their relative significance in effecting the CMT and PMT processes. One of the goals of this research is to identify these models and to test them against laboratory experimental observations. Details of the laboratory experiments and observations are described in Mayes et al. (2000) and summarized in the next section. We defer the objective statements of this research until the potential alternative conceptual models are identified in the next section. 2. Background A series of laboratory experiments were conducted to elucidate the effect of PMT and CMT on the fate and transport of metal and metal-EDTA chelates in a shale–limestone saprolite (Mayes et al., 2000). The experiment of particular interest to the current research is the injection of Co(II) EDTA into an undisturbed soil column. The soil column was extracted from the C-horizon of the Melton Branch Watershed Experimental Station on the US Department of Energy's Oak Ridge Reservation. The Reservation is located approximately 10 km southwest of Oak Ridge Tennessee, USA. The soils are acidic Inceptisols that have been weathered from interbedded shale–limestone sequences of the uppermost Conasauga Group of Cambrian age. Saprolite is a collective term referring to partially-weathered bedrocks with the primary deposits altered to clay minerals. It exists extensively on the land surface (e.g., Jardine et al., 1993; Pierson-Wickmann et al., 2002; Sequeira Braga et al., 2002; Turner et al., 2003; Mutakyahwa et al., 2003; Woodruff et al., 2004). For the saprolite used in this research, carbonate has been completely weathered and soil aggregate surface is coated with reactive, secondary deposits of Fe- and Mn-oxides and translocated clay minerals (Arnseth and Turner, 1988; Gwo and Jardine, 2005). The Fe-oxide mineralogy is primarily ferrihydrite and amorphous Fe(OH)3. The Mn-oxide mineralogy is primarily amorphous Mn(IV) oxides and the clay consists primarily of illite. The soil columns were extracted by hydraulically pressing an 8.4 cm diameter × 15 cm length stainless steel cylinder into an excavation pit to minimize sample disturbance. A cocktail of reactive and conservative tracers, including Br and Co(II)EDTA, were injected into the soil columns in the laboratory (Mayes et al., 2000). Two flow interruptions were performed for tracer injection into the soil column, one during the injection

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

187

and the other the elution phase of the experiment. Laboratory analyses of the effluent and analytical techniques were reported in Mayes et al. (2000) and are not repeated here. Shown in Fig. 1 are the measured concentrations of Br, total Co, Co(III)EDTA and Mn. Model predictions reported in Gwo et al. (2001) are also plotted. One surficial, Mn-oxide mediated oxidation reaction of Co(II)EDTA (reaction 1, Table 1) and three simple complexation reactions of CoEDTA and Mn to surface Fe-oxides (reactions 4–6, Table 1) were included in a suite of six heterogeneous geochemical reactions used by these authors (Table 1). Fast Br concentration recovery to previous level after the first flow interruption is characteristic of structured porous media (e.g., Hu and Brusseau, 1995; Reedy et al., 1996). It is clearly visible in the laboratory breakthrough curve (BTC) but not in the model prediction (Fig. 1a). The model used an equivalent porous medium conceptualization of the saprolite. It is essentially a single-domain model. It did not take into account the effects of pore structure and the PMT process. The majority of the CoEDTA, greater than 98%, was eluted as Co(III)EDTA according to model predictions. There was virtually no difference between the predicted BTC's of total Co and Co(III)EDTA (Fig. 2b). The decrease of model-calculated Co(III)EDTA and Mn concentrations during the first flow interruption were caused exclusively by CMT. The most noticeable difference between laboratory observation and model prediction is the decrease of the observed Co(III)EDTA concentrations and

Fig. 1. Laboratory observations (markers) and single-domain (equivalent porous medium) model predictions (lines) of (a) Br and (b) total Co, Co(III)EDTA and Mn2+ breakthrough concentrations. In (b), the predicted concentration curve of total Co overlaps with that of Co(III)EDTA. Reproduced with permission from (Gwo et al., 2001).

188

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

Table 1 Geochemical reactions of the laboratory soil column experiment Equation No. Reaction equation a

Rate coefficient/stability constant b, c

2− + 2Co(III)EDTA− + Mn2+ (aq) + 2H2O ⇔ 2Co(II)EDTA + 4H + MnO2 log kf = −25.36/−11.13 log kb = 6.72/4.54 H2O ⇔ H+ + OH− log K = − 14.00 −H+ + NSOH ⇔ NSO− log kf = −5.90/−6.95 log kb = −2.00/− 4.09 Co(III)EDTA− + Fe(OH)3(s) ⇔ Co(III)EDTA−(ads) log kf = −0.87/0.02 log kb = −1.96/− 0.47 log kf = 0.50/0.87 Co(II)EDTA2− + Fe(OH)3(s) ⇔ Co(II)EDTA2−(ads) log kb = −0.38/− 0.48 Mn2+(aq) + Fe(OH)3(s) ⇔ Mn2+(ads) log kf = 0.00/− 0.72 log kb = −2.00/− 3.21

1 2 3 4 5 6

NSOH represents the solid surface group with an associated OH− molecule. kf = forward reaction rate coefficient; kb = backward reaction rate coefficient; K = stability constant. c Values are shown as pairs obtained from single-/dual-domain models. The single-domain values are reproduced from Gwo et al., 2001. a

b

the subsequent separation of the Co(III)EDTA and total Co concentration curves after the first flow interruption. It was hypothesized in Mayes et al. (2000) that surficial reactions involving Fe-oxides and/or Mn-oxides were responsible for the separation of the concentration curves. Here, we also note that dissolution of Mn-oxides on fracture surface may increase the porosity, reduce tortuosity of the oxide coating, and modify the effective diffusion coefficient (product of molecular diffusion coefficient and tortuosity, e.g., Nguyen et al., 1982). Therefore, the following three alternative conceptual models of PMT and CMT are identified and formulated. 2.1. Alternative conceptual model 1 — effect of physical mass transfer The first model (Fig. 2) was formulated on the basis that fracture infilling and fracture surface mineral deposit are not unusual (e.g., Jardine et al., 1988; Weisbrod and Nativ, 2000; Whelan et al., 2002; McKay et al., 2005). The total extractable Mn of the saprolite soil was estimated to range from 0.4 to 0.9 g/kg (Arnseth and Turner, 1988). For this research, the total Mn2+ produced during the experiment is 5.76 mmol (Mayes et al., 2000). With a bulk density of 1.483 g/cm3 and a fracture porosity of 0.054 (Table 2) and assuming that the majority of the Mn-oxide was deposited on the fracture surface (Arnseth and Turner, 1988), the percentage of Mn-oxide dissolved during the experiment is about 4.8% to 10.9% of the extractable. After interfacial reactions of Co(II)EDTA, Mn-oxides may dissolve and the amount of surface Mn-oxide coating may be reduced. As a result, the differences in PMT coefficients of the reactive tracers may be magnified. This may lead to the separation of the BTC's of total Co and Co(III)EDTA. 2.2. Alternative conceptual model 2 — effect of Fe(OH)3(s) competition for Co(II)EDTA Previous studies suggested that surface-mediated dissociation of metal-EDTA involving Fe (III)-oxides may also occur (e.g., Szecsody et al., 1994; Nowack and Sigg, 1997; Szecsody et al., 1998a,b). In Mayes et al. (2000), the surface-mediated dissociation of Co(II)EDTA was suggested as one of the possible causes for the separation of Co BTC's after the first flow interruption. The

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

189

Fig. 2. Schematics of surface-mediated transformation of Co(II)EDTA and the three alternative physicochemical mechanisms: (1) physical mass transfer, thin line and box, (2) Fe-oxide competition for Co(II)EDTA, dark line and box, and (3) Mn-oxide surface passivation, dashed line and box.

following five additional reactions are thus added to the list in Table 1. They are used to model the surface-mediated dissociation of Co(II)EDTA and the subsequent release of Fe(III)EDTA (Eq. (1) and model 2 in Fig. 2), the adsorption of Co(II) thus released (Eq. (2)), the oxidation of Co(II) by surface Mn-oxide (Eq. (3)), the release and competition for aqueous EDTA of the surface oxidation product Co(III) or Eqs. (4) and (5), respectively: CoðIIÞEDTA2− þ FeðOHÞ3ðsÞ þ 3Hþ ⇔FeðIIIÞEDTA− þ CoðIIÞ2þ þ 3H2 O

ð1Þ

CoðIIÞ2þ þ FeðOHÞ3ðsÞ ⇔CoðIIÞðadÞ

ð2Þ

2þ þ 2H2 O 2CoðIIÞ2þ þ 3MnO2ðsÞ þ 4Hþ ⇔2CoðIIIÞMnO3þ 2 þ Mn

ð3Þ

2þ 2− CoðIIIÞMnO3þ þ CoðIIIÞEDTA− þ MnO2ðsÞ 2 þ CoðIIÞEDTA ⇔CoðIIÞ

ð4Þ

− 3þ CoðIIIÞMnO3þ þ CoðIIIÞEDTA− þ MnO2ðsÞ 2 þ FeðIIIÞEDTA ⇔Fe

ð5Þ

Reaction equations similar to Eqs. (1)–(5) were also used by the authors to model the reaction of CdEDTA2− with the same saprolite materials (Gwo and Jardine, 2005).

190

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

Table 2 Physical properties of the tracers and the undisturbed saprolite soil column, obtained from the literature, previous studies and model calibration in the current research Physical property

Fracture

Dispersivity (cm) Porosity Tortuosity Darcy velocity (cm/s) Flow rate (ml/s) Hydraulic conductivity (cm/s) Column length (cm) Column diameter (cm)

a

Matrix

4.0 × 10 0.054 0.78 2.32 × 10− 5 – – – –

Free water diffusion coefficient (cm2/s) Br− Co(III)EDTA− Co(II)EDTA2− Mn2+ H+ OH− Fe(III)EDTA− Fe(III) Co(II) O2(aq)

– – – – – – – – – –

−2

Solid phase concentration (g/l total soil volume) MnO2(s) 1.33 × 10− 2 Fe(OH)3(s) 7.29 × 10− 2 a b c d e f

a

All −4

4.0 × 10 0.374 0.37 1.84 × 10− 6 – – – – – – – – – – – – – –

b

3.5 0.428 b 0.1 c 2.50 × 10− 5 c 1.39 × 10− 3 c 8.9 × 10− 8 c 15 c 8.5 c

2.01 × 10− 5 3.72 × 10− 6 e 4.32 × 10− 6 d 6.88 × 10− 6 d 9.31 × 10− 5 d 5.27 × 10− 5 e 3.64 × 10− 6 d 6.07 × 10− 6 d 6.99 × 10− 6 f 2.10 × 10− 5 d

e

1.26 × 10− 6 1.39 × 10− 2

Obtained by a dual-domain, fracture-matrix model (Gwo et al., 1998). Obtained by a single-domain model (Gwo et al., 2001). Laboratory observations reported in Mayes et al. (2000). Millero, 2001. Estimated with the Hayduk and Laudie method (Tucker and Nelken, 1990). Cussler, 1984.

2.3. Alternative conceptual model 3 — effect of MnO2(s) surface passivation As suggested in Mayes et al. (2000), passivation of Mn-oxide surface as a result of oxygen consumption may lower the mineral surface reductive capacity. Earlier laboratory results using pyrolusite-coated silica suggested that the oxidation of Co(II)EDTA to Co(III)EDTA may uniformly transform the mineral surface from Mn(IV)- to Mn(III)-dominating Mn-oxide surface, largely reducing its reductive capacity or the so-called passivation (Jardine and Taylor, 1995). The hypothesis of these authors was later confirmed by spectroscopic analysis of the transformed Mn-oxide mineral surface (Fendorf et al., 1999). Their observations also suggested that Mn(II) released from the reduction of MnO2 was quickly absorbed to the oxide surface and no Mn2+ species were detected in the effluent. In contrast, a significant amount of free Mn(II) ions was detected in the effluent of the undisturbed saprolite soil column. It accounted for ∼ 90% of Mn liberated from the soil (Mayes et al., 2000). The breakthrough of Mn(II) is also consistent with those of the Co species in that it appears to be produced as a result of the reactive tracer injection. Nevertheless, we hypothesize that the passivation reaction may also occur directly on the oxide surface of the saprolite soil in the presence of dissolved O2.

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

191

According to the passivation mechanism suggested in Jardine and Taylor (1995), the aqueous phase Mn2+ released as a result of Co(II)EDTA oxidation may be oxidized by dissolved oxygen to form Mn2O3(s) on the MnO2(s) oxide surface, thereby blocking the stronger oxidant MnO2(s) from contacting with Co(II)EDTA in the solution (model 3 in Fig. 2). The Co(II)EDTA oxidation reaction in Table 1 is thus modified and two additional reactions (Eqs. (7) and (8)) as follows are added to the list: 2CoðIIIÞEDTA− þ Mn : MnO22þ þ 4H2 O⇔2CoðIIÞEDTA2− þ 8Hþ þ 2MnO2

ð6Þ

4Mn : MnO22þ þ O2 þ 4H2 O⇔2Mn2 O3 : MnO2 þ 8H þ þ 2MnO2

ð7Þ

2Mn2 O3 : MnO2 þ O2 ⇔6MnO2

ð8Þ

where reaction 1 in Table 1 is modified to account for the immediate adsorption of Mn(II) onto the MnO2(s) surface (the species Mn:MnO22+), or Eq. (6) above. Eqs. (7) and (8) represent the passivation reaction and the regeneration of MnO2 surface in the presence of dissolved oxygen, respectively (see Jardine and Taylor, 1995). The objective of this research is to quantify the relative contributions of PMT and CMT to the movement of Co(II/III)EDTA through a limestone–shale saprolite soil. Previous laboratory observations of Co(II)EDTA reactive transport through an undisturbed soil column (Mayes et al., 2000) are used. A dual-domain reactive transport model is formulated and evaluated against the laboratory observations to determine the rates of PMT and CMT of individual chemical species. A genetic-based search and optimization algorithm (e.g., Goldberg, 1989; Mahinthakumar et al., 1999; Gwo, 2001) and a nested Latin-hypercube search algorithm (e.g. Gwo et al., 2005a,b) are employed to calibrate the reactive transport model and to search for the near-optima of the relatively large number of model parameters. In the laboratory experiment reported in Mayes et al. (2000), the behaviors of non-reactive tracer (Bromide, Br) and reactive tracers (total Co and Co(III)EDTA) are noticeably different (Fig. 1). Concentrations of Co(III)EDTA effluent also deviate from those of total Co immediately after the flow interruption, which challenges previous conceptual understanding that the majority (greater than 98%) of the injected Co(II)EDTA is transformed to Co(III) EDTA by interfacial reactions with Mn-oxides (Jardine and Taylor, 1995). This prompted the authors to suggest that additional Fe- and/or Mn-oxide mediated surficial reactions may be responsible. In this manuscript, the above three alternative PMT and CMT mechanisms are evaluated to interpret the observed discrepancy. 3. Methodology It is well-documented in the literature that saprolite soils contain pore structures of various sizes and shapes (e.g., Wilson et al., 1992). We hypothesize here that water may move through two pore domains in the soil, the fracture and the matrix, because the bedding structure of the parent rock (e.g., bedding planes and fractures) remains well-preserved in the saprolite (Gwo, 2001). The PMT process may be independently quantified and characterized by using the BTC of the non-reactive tracer Br. Hydraulic, mass transfer and solute transport properties obtained from laboratory experiments (Mayes et al., 2000) and previous studies (Gwo et al., 1998,

192

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

2001) are used in the current study as constraints of model and model parameter optimization (Table 2). A dual-domain reactive transport model is used to interpret and predict the concentrations of chemical species observed in the above-mentioned experiment. Assuming no external source/sink of either fluid or chemical species and the pore fluid flow are in steady and equilibrium states, one may represent the reactive transport processes of an aqueous chemical species (subscript j ) in the fracture (subscript f ) and matrix (subscript m) as follows (Yeh et al., 1998):
 Acjf Acjf A Acjf hf hf Djf þ mf − ¼ hf rjf −ej ðcjf −cjm Þ At Az Az Az

ð9aÞ


 Acjm Acjm A Acjm hm Djm hm þ mm − ¼ hm rjm −ej ðcjm −cjf Þ At Az Az Az

ð9bÞ

where θ and v are water content and Darcy velocity, respectively; c, D and r, are the concentration, dispersion coefficient, and net production rate from aqueous and interfacial chemical transformation, respectively; t is time; z is vertical distance along the soil column; ε is the time-dependent, PMT coefficient between pore domains (see Eq. (10) next). In the lefthand-side of Eqs. (9a) and (9b), the first terms represent the storage of tracers in the soil and the second and third terms represent the advection and dispersion of the tracers. The first terms on the right-hand-side represent net production rate as results of CMT and the second terms are contributions to tracer storage from PMT. The dispersion coefficient may be represented as a function of fluid velocity, dispersivity, free water molecular diffusion coefficient, and tortuosity of a porous medium (e.g., Nguyen et al., 1982). The PMT coefficient is a time-dependent function of water content, effective diffusion coefficients, fracture characteristic width, and matrix block size distribution. The following PMT functional relationship, mathematically similar to that derived in Gwo et al. (1998), is used for the current study: ej ¼

hm Dm0; j ða−blnðtÞÞ lm2

ð10Þ

In Eq. (10), Dm0,j is the effective molecular diffusion coefficient of species j or the product of free water diffusion coefficient of species j with matrix domain tortuosity; lm is the characteristic block size of the matrix domain; and a and b are constants of the scaling function that depend on the mesoscale matrix block size distribution and other factors such as the thickness of fracture surface mineral coating (e.g., Gwo et al., 1998). Physically, a represents fast mass transfer contributed by the portion of matrix blocks that have relatively small sizes and b represents slow mass transfer as a result of matrix diffusion into larger matrix blocks that has a time scale close to or longer than solute transport through the soil column. Because the results of these authors were calibrated against previous observations from a saprolite soil column similar to that used in Mayes et al. (2000), they are used in this research to constrain model parameter search and optimization. Using the results of Gwo et al. (1998) for Br, or Dm0, j = Dm0,Br, we estimated the scaling function constants a and b to be 3.29 and 0.58, respectively. It is assumed that these constants and their values are independent of chemical species. They are calculated offline and are used without modification in the current research.

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

193

For adsorbed species in the solid phase, the mass balance equation of chemical species j may be represented as follows (Yeh et al., 1998): Aqbf sjf ¼ qbf rif At

ð11aÞ

Aqbm sjm ¼ qbm rim At

ð11bÞ

where ρb is the bulk density; sj and rj are the concentration of solid phase species j and its net production rate from interfacial chemical reactions. Given Nx heterogeneous and homogeneous chemical reaction equations of the following general form (Yeh et al., 1998): X

kf j

X

kbj

jaM

mjj gj ()

jaM

wjj gj ;

j a Nx for all pore domains

ð12Þ

the reaction rate terms in Eqs. (9a), (9b), (11a) and (11b) may be represented as follows (Yeh et al., 1998), X wjj−mjj rj ¼ Xj ; j a M: ð13Þ gj jaN x

In Eqs. (4) and (5), vκj and wκj are the stoichiometric coefficients of species j (with a formula of gj) in the reactant and product sides of the reaction equation κ, respectively; kfκ and kbκ are the forward and backward reaction rate coefficients, respectively; M is the total number of species in the system; γj is the activity coefficient; and Ωκ is the reaction rate of reaction κ. The reaction rate law, in general, could be prescribed. However, without supplemental information of reaction orders from laboratory experiments, the following theoretical reaction rate equation for reaction κ, as suggested by the collision theory, is used (Yeh et al., 1998): Xj ¼ kf j j ðgj xj Þmjj −kbj j ðgj xj Þwjj jaM

jaM

ð14Þ

where xj represents either cj or sj as in Eqs. (9a), (9b), (11a) and (11b), respectively. Note that we dropped the subscripts m and f off r in Eq. (13) as compared with Eqs. (9a) and (9b) because the same set of reaction rate equations and rate laws is prescribed for the fracture and matrix domains. For a particular reaction equation, identical rate coefficients are used for both pore domains. Eqs. (9a), (9b), (10), (11a), (11b), (12), (13), and (14) have been numerically implemented in the generic hydrobiogeochemistry simulator HBGC123D v.2 (v.1.1 is available at http://hbgc. esd.ornl.gov or see Gwo et al., 2001). A Lagrangian–Eulerian finite element method and a Newton–Ralphson method are used to solve the transport and geochemical reaction equations in HBGC123D, respectively. The two solution steps could be coordinated by using either a tight coupling or an operator splitting scheme (Yeh et al., 1998). In this research, small time step sizes are used in conjunction with the operator splitting scheme. A search procedure based on genetic algorithms (e.g., Gwo, 2001) is used to determine the fluid velocity, porosity and tortuosity of pore domains, using laboratory measured total flux rates and porosity as constraints. The PMT coefficients of aqueous chemical species are calculated according to Eq. (2) by using the free

194

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

water diffusion coefficients listed in Table 2. The free-water diffusion coefficients of metals and metal-chelates are obtained from the literature (e.g., Cussler, 1984; Millero, 2001) or estimated by using the Hayduk and Laudie method (Tucker and Nelken, 1990). Initial concentrations of Mn and Fe(III), in the solution and on the solid surface, are obtained from laboratory measurements (Mayes et al., 2000) and by assuming equilibrium between the solution and solid phases per the partitioning coefficient approach (Sheppard and Thibault, 1990). The initial concentrations of Feand Mn-oxides and the rate coefficients of interfacial reactions are determined by the genetic algorithm search procedure. The same suite of reaction equations as those used by Gwo et al. (2001) and shown in Table 1 are also used here. 4. Results and discussion 4.1. Dual-domain model predictions The results of the genetic algorithm search and the dual-domain model calibration are shown in Fig. 3a–c. The near-optimal reaction rate coefficients are listed in Table 1. The optimized solute

Fig. 3. Laboratory observations (markers) and calibration results of the dual-domain model (lines) of (a) Br, (b) Co(III) EDTA, and (c) total Co and Mn2+ breakthrough concentrations.

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

195

transport parameters, including dispersivities, porosities, tortuosities and Darcy velocities, are listed in Table 2. A fracture-matrix conceptual model of the saprolite soil appears to describe very well both the Br tracer recovery right after flow interruption and the long tailing that is absent in the prediction of the single-domain model (comparing Figs. 1a and 3a). The concave and convex shapes of Br concentration recovery during the first and second flow interruptions, respectively, are also reproduced very well in the model prediction (Fig. 3a). The decrease and increase of Br concentrations during the first and second flow interruption are unmistakably caused by the PMT process only. One notes the phenomenological similarity of the PMT effects on the predicted BTC of the conservative tracer Br (Fig. 3a) to the CMT effects on the predicted BTC's of the reactive tracers CoEDTA during the first flow interruption period (Fig. 1b). This in effect points to the difficulty in using BTC's of reactive tracers alone, with or without flow interruptions, to independently characterize the PMT and CMT processes. Previous investigations (e.g., Gwo et al., 1995, 1998) showed that, with a multiple-poredomain conceptual model, model fitted dispersivities are significantly smaller than those obtained under an equivalent porous medium or single-domain conceptual model. This is particularly so when mesoscale medium structures and hydrodynamics in the fractures are taken into account (e.g., Gwo et al., 1998). The dual-domain dispersivities, taken directly from a previous study of the same saprolite soil (Gwo et al., 1998), are two to four orders of magnitude smaller than the single-domain dispersivity (Table 2). Model fitted porosity of the fractures is around 12.62% of total porosity as compared to laboratory estimates of 5%–10% (Mayes, personal communication, 2005). These results suggest that the PMT and solute transport model parameters are relatively well calibrated to laboratory observations. With the dual-domain model, the Co(II)EDTA oxidation rate coefficient (kb of reaction 1 in Table 1) is about two orders of magnitude smaller than that obtained by the single-domain model. The adsorption and desorption rate coefficients of CoEDTA and Mn are comparable between the two models. This result indicates that, without considering the effect of PMT, a single-domain reactive transport model may overestimate the reaction rate coefficients of the CMT processes in structured soils. This result also directly correlates with our earlier observation that the singledomain, model-calculated decrease and recovery of reactive tracer concentrations during the flow interruption periods may be erroneously interpreted as solely caused by CMT processes. In essence, it may be advisable that one includes a non-reactive tracer in tracer injection studies and utilizes techniques such as flow interruption to separate the effects of the PMT processes from those of the CMT processes. The calculated PMT rate signatures of conservative and reactive tracers are also distinctively different. Shown in Fig. 4 are the model calculated PMT rates of Br (Fig. 4a) and those of Co(II) EDTA (Fig. 4b) along the length of the soil column. Before the tracer pulse is terminated, fracture is a source of Br to the rock matrix (times earlier than 30.5 days and curves with negative PMT rates). After the 30.5th day during the elution phase, the rock matrix is a source instead (positive PMT rates). For Co(II)EDTA, the rock matrix is mostly a source except near the injection end of the soil column during the first few hours of the elution phase (the BTC curve at 30.94th day, Fig. 4b). In the fracture, Co(II)EDTA is transformed in a much faster rate to Co(III)EDTA because of the much larger amount of Mn-oxide in the pore domain (Table 2). As a result, Co(II)EDTA moving through and into the rock matrix become a constant secondary source to the fracture. In contrast, the PMT rate signatures of Co(III)EDTA are similar to those of Br except that the rock matrix becomes a source slightly later than the 30.5th day, largely because of its reactive nature (data not shown). The calculated CMT rates of Co(II)EDTA and Co(III)EDTA are shown in Fig. 5a and b, respectively. Also shown in Fig. 5b are the calculated PMT rates of Co(III)EDTA. Comparison of

196

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

Fig. 4. Calculated physical mass transfer rates of (a) Br and (b) Co(II)EDTA along the length of the soil column at various times (indicated on the lines) of the tracer injection. The dashed lines use the left ordinate and the solid lines use the right ordinate so that the ranges of the mass transfer rates may be plotted together on one chart.

Figs. 4b and 5a suggests that Co(II)EDTA CMT rates are about one order of magnitude higher than its PMT rates. In contrast, the CMT and PMT rates of Co(III)EDTA fall approximately in the same ranges (Fig. 5b). These results indicate that (1) the movement of the less reactive Co(III)EDTA through the saprolite soil is relatively more influenced by PMT in comparison with the movement of the more reactive Co(II)EDTA and (2), for the more reactive Co(II)EDTA, CMT processes dominate the fate and transport in saprolite geological materials. Not withstanding the above conclusions, the predicted BTC's of Co(III)EDTA and total Co failed to separate after the first flow interruption (Fig. 3b). The predicted concentrations of Co (III)EDTA also rebound following the initial decrease after the tracer injection is re-initiated. In order to identify the causes of the BTC separation right after the first flow interruption, three alternative conceptual models, one related to the PMT and the other two to the CMT processes, were formulated and evaluated. The results are discussed next. Note that the aqueous and solid phase concentrations obtained during model calibration are used in the models without modification. However, because new chemical species are introduced, searches for the reaction rate coefficients of both the existing and additional reaction equations and for the initial concentrations of the new chemical species are necessary. We note that these searches in models 2 and 3 below are heuristics-based. A nested Latin-hypercube search algorithm (Gwo et al.,

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

197

Fig. 5. Model calculated interfacial reaction (chemical mass transfer) rates of (a) Co(II)EDTA and (b) Co(III)EDTA at various times of the tracer injection. Also shown in (b) are the physical mass transfer rates of Co(III)EDTA (dark lines).

2005a) was used to determine the most likely model parameters so that the best fits to laboratory curves may be obtained. No optimizations of model parameters were attempted. 4.2. Alternative conceptual model 1 — effect of physical mass transfer To simulate the effect of oxide dissolution on PMT rates, the mass transfer scaling factors in Eq. (10) were increased artificially by two folds right after the first flow interruption. The rest of the calibrated model and model parameters were not changed. We note that HBGC123D, the hydrobiogeochemical simulator used in this research, is not capable of modeling the effects of dissolution on the evolution of physical properties such as porosity, tortuosity and permeability. As stated earlier, one is more interested in the magnification of PMT coefficient differences than physical property evolution as a result of Mn-oxide dissolution. The resulting model predictions of Co(III)EDTA and total Co concentrations are shown in Fig. 6a (the thick solid and dashed lines for total Co and Co(III)EDTA, respectively). Further increasing of the scaling factors failed to separate the total Co and Co(III)EDTA BTC's after the first flow interruption, indicating the implausibility that PMT processes alone may cause the BTC separation under the laboratory experimental conditions.

198

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

Fig. 6. Laboratory observations and results of alternative conceptual models (dark lines): (a) increases in physical mass transfer rate coefficients, (b) Fe-oxide competition for Co(II)EDTA, and (c) Mn-oxide passivation. Also plotted on the figures are the results of model calibration (thin lines).

4.3. Alternative conceptual model 2 — effect of Fe(OH)3(s) competition for Co(II)EDTA The underlying hydrogeochemical model was recalibrated against laboratory observations. The prediction with the least curve-fitting error is presented here. The resulting forward reaction rate coefficients of Co(III)EDTA and Co(II)EDTA adsorption (reactions 4 and 5, respectively, in Table 1) are 37% and 45% smaller than those of the previously calibrated model, respectively.

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

199

Model predicted Co(III)EDTA and total Co breakthrough concentrations as a result of the revised reaction mechanism are shown in Fig. 6b (thick solid and dashed lines, respectively). The separation of total Co and Co(III)EDTA BTC's after the first flow interruption is well reproduced. In comparison with laboratory observations, the model suggests an earlier separation of the BTC's before the first flow-interruption is initiated. The free Co(II) ion in the model prediction consists of 14% of the total Co influent, comparing with 12% observed in the laboratory (Mayes et al., 2000). Model predicted amount of Co(II)EDTA in the effluent is less than 1% of the total Co influent. In the laboratory experiment, Co(II)EDTA was not detected in the effluent. These model predictions indicate that competition from the surface Fe-oxide for Co(II)EDTA may not be excluded as a possible interfacial reaction mechanism that may result in the separation of the total Co and Co(III)EDTA BTC's. 4.4. Alternative conceptual model 3 — effect of MnO2(s) surface passivation To evaluate this model, a dissolved oxygen concentration of 0.26 mM (Jardine and Taylor, 1995) was used for the model calculations. The prediction with the least curve-fitting error is presented here (Fig. 6c). The forward reaction rate coefficients of Co(III)EDTA and Co(II) EDTA adsorption (reactions 4 and 5, respectively, in Table 1) were 34% larger and 2 orders of magnitude smaller than those of the calibrated model reported earlier, respectively. The predicted, major Co(II) species in the effluent is Co(II)EDTA. Before the tracer pulse was terminated, the predicted aqueous Mn2+ concentrations were about one to two fold of the observed (data not shown). The relatively less evident separation of total Co and Co(III)EDTA BTCs (Fig. 6c) following the first flow interruption period, the increase of surface reactivity of the relatively more stable Co(III)EDTA, and the fact that Mn2+ was predicted in the effluent indicate that MnO2 surface passivation in the natural, undisturbed soil column may not be as pronounced as that in the laboratory prepared synthetic oxide columns (Jardine and Taylor, 1995; Fendorf et al., 1999). 5. Summary and conclusions A suite of dual-domain, fracture-matrix hydrogeochemical models was applied to a laboratory experiment of Br and Co(II)EDTA tracer injection through an undisturbed saprolite soil column. The PMT (physical mass transfer) and CMT (chemical mass transfer) processes were separately characterized. The solute transport and PMT model parameters of the nonreactive tracer, Br, were subsequently used as constraints to characterize the CMT processes and to determine the geochemical reaction rate coefficients of Co(II)EDTA and its oxidation product, Co(III)EDTA. As a result, the relative contributions of PMT and CMT to the fate and transport of Co(II)EDTA in the saprolite soil are independently quantified. Our results indicated that, for the more reactive Co(II)EDTA, CMT dominates the fate and transport processes. In contrast, the contributions of CMT and PMT to the fate and transport of the less reactive Co(III)EDTA were comparable. Further evaluation of alternative conceptual models suggested that Fe-oxide may compete with Mn-oxide for the aqueous Co(II)EDTA and may be more responsible for the laboratory-observed separation of total Co and Co(III)EDTA effluent concentration curves than Mn-oxide surface passivation. These conclusions pointed to the significance of characterizing independently the PMT and CMT processes in reducing prediction uncertainty of metal-EDTA chelate subsurface transport through structured, saprolite soils.

200

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

Acknowledgement This research is supported by the Environmental Management and Science Program (EMSP) and was supported by the Environmental Technology Partnership (ETP) program of the Office of Biological and Environmental Research, U.S. Department of Energy (US DOE). The authors would like to thank Mark Gilberson and Paul Bayer, contract officers for US DOE's EMSP and ETP programs, respectively, for financial support. References Abelin, H., Birgersson, L., Moreno, L., Wilden, H., Agren, T., Neretnieks, I., 1991. A large-scale flow and tracer experiment in granite, 2, results and interpretation. Water Resour. Res. 27, 3019–3135. Andersson, P., Byegård, J., Tullborg, E., Doe, T., Hermanson, J., Winberg, A., 2004. In situ tracer tests to determine retention properties of a block scale fracture network in granitic rock at the Äspö Hard Rock Laboratory, Sweden. J. Contam. Hydrol. 70, 271–298. Arnseth, R.W., Turner, R.S., 1988. Sequential extraction of iron, manganese, aluminum, and silicon in soils from two contrasting watersheds. Soil Sci. Soc. Am. J. 52, 1801–1807. Becker, M.W., Shapiro, A.M., 2000. Tracer transport in fractured crystalline rock: Evidence of non diffusive break through tailing. Water Resour. Res. 36, 1677–1686. Birgersson, L., Neretnieks, I., 1990. Diffusion in the matrix of granitic rock: Field test in the Stripa Mine. Water Resour. Res. 26, 2833–2842. Brusseau, M.L., Hu, Q., Srivastava, R., 1997. Using flow interruption to identify factors causing nonideal contaminant transport. J. Contam. Hydrol. 24 (3/4), 205–219. Cussler, E.L., 1984. Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press, New York. 525 pp. Fendorf, S., Jardine, P.M., Taylor, D.L., Brooks, S.C., Rochette, E.A., 1999. Auto-inhibition of oxide mineral reductive capacity toward Co(II)EDTA. In: Sparks, D.L., Grundl, T.J. (Eds.), Mineral-Water Interfacial Reactions, Kinetics and Mechanisms. ACS Symposium Series, vol. 715, pp. 358–371. Frohne, K.-H., Mercer, J.C., 1984. Fractured shale gas reservoir performance study — an offset well interference field test. J. Pet. Technol. 36, 291–300. Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Pub. Co., Reading, Mass. 412 pp. Gwo, J.P., 2001. In search of preferential flowpaths in structured porous media using a simple genetic algorithm. Water Resour. Res. 37 (6), 1589–1601. Gwo, J.P., Jardine, P.M., 2005. Determining adsorption–desorption kinetics of CdEDTA to a fractured saprolite soil. Soil Sci. 170, 325–339. Gwo, J.P., Jardine, P.M., Wilson, G.V., Yeh, G.-T., 1995. A multiple-pore-region concept to modeling mass transfer in subsurface media. J. Hydrol. 164, 217–237. Gwo, J.P., O'Brien, R., Jardine, P.M., 1998. Mass transfer in structured porous media: Embedding mesoscale structure and microscale hydrodynamics in a two-region model. J. Hydrol. 208, 204–222. Gwo, J.P., D'Azevedo, E.F., Frenzel, H., Mayes, M., Yeh, G.T., Jardine, P.M., Salvage, K.M., Hoffman, F.M., 2001. HBGC123D: A high performance computer model of coupled hydrogeological and biogeochemical processes. Comput. Geosci. 27, 1231–1242. Gwo, J.P., Jardine, P.M., Sanford, W.E., 2005a. Modeling field-scale multiple tracer injection at a low-level waste disposal site in fractured rocks: Effect of multiscale heterogeneity and source term uncertainty on conceptual understanding of mass transfer processes. J. Contam. Hydrol. 77 (1–2), 91–118. Gwo, J.P., Jardine, P.M., Sanford, W.E., 2005b. Effect of advective mass transfer on field scale fluid and solute movement: Field and modeling studies at a waste disposal site in fractured rock at Oak Ridge National Laboratory, Tennessee, USA. Hydrogeol. J. 13, 565–583. Holtta, P., Hakanen, M., Hautojarvi, A., Timonen, J., Vaatainen, K., 1996. The effect of matrix diffusion on radionuclide migration in rock column experiments. J. Contam. Hydrol. 21, 165–173. Hu, Q., Brusseau, M.L., 1995. Effect of solute size on transport in structured porous media. Water Resour. Res. 31, 1637–1646. Jardine, P.M., Taylor, D.L., 1995. Kinetics and mechanisms of Co(II)EDTA oxidation by pyrolusite. Geochim. Cosmochim. Acta 59, 4193–4203.

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

201

Jardine, P.M., Wilson, G.V., Luxmoore, R.J., 1988. Modeling the transport of inorganic ions through undisturbed soil columns from two contrasting watersheds. Soil Sci. Soc. Am. J. 52, 1252–1259. Jardine, P.M., Jacobs, G.K., Wilson, G.V., 1993. Unsaturated transport processes in undisturbed heterogeneous porous media. I. Inorganic contaminants. Soil Sci. Soc. Am. J. 57, 945–953. Jardine, P.M., Sanford, W.E., Gwo, J.-P., Reedy, O.C., Hicks, D.S., Riggs, J.S., Bailey, W.B., 1999. Quantifying diffusive mass transfer in fractured shale bedrock. Water Resour. Res. 35, 2015–2030. Jardine, P.M., Mehlhorn, T.L., Larsen, I.L., Bailey, W.B., Brooks, S.C., Roh, Y., Gwo, J.P., 2002. Influence of hydrological and geochemical processes on the transport of chelated metals and chromate in fractured shale bedrock. J. Contam. Hydrol. 55, 137–159. Mahinthakumar, G., Gwo, J.P., Moline, G.R., 1999. Subsurface biological activity zone detection using genetic algorithms. ASCE J. Environ. Eng. 125 (2), 1103–1112. Mayes, M.A., Jardine, P.M., Larsen, I.L., Brooks, S.C., Fendorf, S.E., 2000. Multispecies transport of metal-EDTA complexes and chromate through undisturbed columns of weathered fractured saprolite. J. Contam. Hydrol. 45, 243–265. Mayes, M.A., Jardine, P.M., Mehlhorn, T.L., Bjornstad, B.N., Ladd, J.L., Zachara, J.M., 2003. Transport of multiple tracers in variably saturated humid region structured soils and semi-arid region laminated sediments. J. Hydrol. 275, 141–161. McKay, L.D., Gillham, R.W., Cherry, J.A., 1993. Field experiments in a fractured clay till, 2, solute and colloid transport. Water Resour. Res. 29, 3879–3890. McKay, L.D., Driese, S.G., Smith, K.H., Vepraskas, M.J., 2005. Hydrogeology and pedology of saprolite formed from sedimentary rock, eastern Tennessee, USA. Geoderma 126, 27–45. McMahon, P.B., 2001. Aquifer/aquitard interfaces: Mixing zones that enhance biogeochemical reactions. Hydrogeol. J. 9, 34–43. Millero, F.J., 2001. Physical Chemistry of Natural Waters. Wiley, New York. 654 pp. Mutakyahwa, M.K.D., Ikingura, J.R., Mruma, A.H., 2003. Geology and geochemistry of bauxite deposits in Lushoto District, Usambara Mountains, Tanzania. J. Afr. Earth Sci. 36, 357–369. Nguyen, V.V., Gray, W.G., Pinder, G.F., Botha, J.F., Crerar, D.A., 1982. A theoretical investigation on the transport of chemicals in reactive porous media. Water Resour. Res. 18, 1149–1156. Novakowski, K.S., Lapcevic, P.A., 1994. Field measurement of radial solute transport in fractured rock. Water Resour. Res. 30, 37–44. Novakowski, K.S., Lapcevic, P.A., Voralek, J., Bickerton, G., 1995. Preliminary interpretation of tracer experiments conducted in a discrete rock fracture under conditions of natural flow. Geophys. Res. Lett. 22, 1417–1420. Nowack, B., Sigg, L., 1997. Dissolution of Fe(III) (hydr)oxides by metal-EDTA complexes. Geochim. Cosmochim. Acta 61, 951–963. Parker, J.C., Van Genuchten, M.Th., 1984. Determining transport parameters from laboratory and field tracer experiments. Bull., vol. 84–3. Virginia Agric. Exp. Stn., Blacksburg. Pierson-Wickmann, A.-C., Reisberg, L., France-Lanord, C., 2002. Behavior of Re and Os during low-temperature alteration: Results from Himalayan soils and altered black shales. Geochim. Cosmochim. Acta 66, 1539–1548. Reedy, O.C., Jardine, P.M., Selim, H.M., 1996. Quantifying diffusive mass transfer of non-reactive solutes in columns of fractured saprolite using flow interruption. Soil Sci. Soc. Am. J. 60, 1376–1384. Selim, H.M., Ma, L., 1998. Physical Nonequilibrium in Soils: Modeling and Application. Ann Arbor Press, Chelsea, Mich. 492 pp. Sequeira Braga, M.A., Paquet, H., Begonha, A., 2002. Weathering of granites in a temperate climate (NW Portugal): Granitic saprolites and arenization. Catena 49, 41–56. Seyfried, M.S., Rao, P.S.C., 1987. Solute transport in undisturbed columns of an aggregated tropical soil: preferential flow effects. Soil Sci. Soc. Am. J. 51, 1434–1444. Shapiro, A.M., 2001. Effective matrix diffusion in kilometer-scale transport in fractured crystalline rock. Water Resour. Res. 37, 507–522. Sheppard, M.I., Thibault, D.H., 1990. Default soil solid/liquid partition coefficients, Kds, for four major soil types: A compendium. Health Phys. 59, 471–482. Shuford, J.W., Fritton, D.D., Baker, D.E., 1977. Nitrate–nitrogen and chloride movement through undisturbed field soil. J. Environ. Qual. 6, 255–259. Skopp, J., Gardener, W.R., Tyler, E.J., 1981. Solute movement in structured soils: Two-region model with small interaction. Soil Sci. Soc. Am. J. 45, 837–842. Szecsody, J.E., Zachara, J.M., Bruckhart, P.L., 1994. Adsorption-dissolution reactions affecting the distribution and stability of Co(II)EDTA in iron-oxide coated sand. Environ. Sci. Technol. 28, 1706–1716.

202

J.-P. Gwo et al. / Journal of Contaminant Hydrology 90 (2007) 184–202

Szecsody, J.E., Zachara, J.M., Ashokkumar, C., Jardine, P.M., Ferrency, A.M., 1998a. Importance of flow and particlescale heterogeneity on CoII/IIIEDTA reactive transport. J. Hydrol. 209, 112–136. Szecsody, J.E., Ashokkumar, C., Zachara, J.M., Garvin, A.L., 1998b. Influence of iron oxide inclusion shape on CoII/IIIEDTA reactive transport through spatially heterogeneous sediment. Water Resour. Res. 34, 2501–2514. Tang, D.H., Frind, E.O., Sudicky, E.A., 1981. Contaminant transport in fractured porous media: Analytical solution for a single fracture. Water Resour. Res. 17 (3), 555–564. Tucker, W.A., Nelken, L.H., 1990. Diffusion coefficients in air and water. In: Lyman, et al. (Eds.), Handbook of Chemical Property Estimation Methods. American Chemical Society. Turner, B.F., Stallard, R.F., Brantley, S.L., 2003. Investigation of in situ weathering of quartz diorite bedrock in the Rio Icacos basin, Luquillo Experimental Forest, Puerto Rico. Chem. Geol. 202, 313–341. van Genuchten, M.Th., 1981. Non-equilibrium transport parameters from miscible displacement experiments. Research Report, vol. 119. U.S. Salinity Laboratory, Riverside, California. 88 pp. van Genuchten, M.Th., Wierenga, P.J., 1976. Mass transfer studies in sorbing porous media I. Analytical Solutions. Soil Sci. Soc. Am. J. 40, 473–480. Vandergraaf, T.T., Drew, D.J., Masuda, S., 1996. Radionuclide migration experiments in a natural fracture in a quarried block of granite. J. Contam. Hydrol. 21, 153–164. Weisbrod, N., Nativ, R., 2000. Salt accumulation and flushing in unsaturated fractures in an arid environment. Ground Water 38, 452–461. Whelan, J.F., Paces, J.B., Peterman, Z.E., 2002. Physical and stable-isotope evidence for formation of secondary calcite and silica in the unsaturated zone, Yucca Mountain, Nevada. Appl. Geochem. 17, 735–750. Wilson, G.V., Jardine, P.M., Gwo, J.P., 1992. Modeling the hydraulic properties of a multiregion soil. Soil Sci. Soc. Am. J. 56, 1731–1737. Wilson, G.V., Jardine, P.M., O'Dell, J.D., Collineau, M., 1993. Field-scale transport from a buried line source in variably saturated soil. J. Hydrol. 145, 83–109. Woodruff, L.G., Attig, J.W., Cannon, W.E., 2004. Geochemistry of glacial sediments in the area of the Bend massive sulfide deposit, north-central Wisconsin. J. Geochem. Explor. 82, 97–109. Yeh, G.-T., Salvage, K.M., Gwo, J.P., Zachara, J.M., Szecsody, J.E., 1998. HYDROBIOGEOCHEM: A Coupled Model of HYDROlogic Transport and Mixed BIOGEOCHEMical Kinetic/Equilibrium Reactions in Saturated–Unsaturated Media, ORNL/TM-13668. Oak Ridge National Laboratory. Zachara, J.M., Smith, S.C., Kuzel, L.S., 1995. Adsorption and dissociation of Co-EDTA complexes in Fe-oxide containing subsurface sands. Geochim. Cosmochim. Acta. 59, 4825–4844.