# Presentation: 239571

## Effects of scale, flow regime and transport model formulation on apparent transport and reaction rate coefficients 

**Effects of scale, flow regime and transport model formulation on apparent transport and reaction rate coefficients **

** ****Parameter Estimation**

- 	It is well known that hydrodynamic dispersion and physical mass transfer coefficients exhibit scale-dependence due to increases in fluid velocity variance that commonly occur with increased observation (averaging) scale. We hypothesize generally that reactive transport processes at different scales can be described by scale-independent mathematical formulations. More particularly, we hypothesize that kinetic coefficients for reactions occurring in heterogeneous media may exhibit scale-dependence due to smaller scale variability in fluid velocity, physical non-equilibrium limitations, reactive site densities and other media properties.
- Studies of reaction kinetics and transport have been performed at various scale on soils at the Oak Ridge FRC over a number of years undertaken through NABIR, EMSP and other programs. Experiments have involved Co-EDTA, Cd-EDTA, Cr and U reactions in batch systems, small disturbed cores, undisturbed cores of various sizes and field experiments. In this study, we focus on experiments involving Co(II/III)-EDTA as the data sets are more comprehensive and the reactions are fairly well-characterized. A conceptual model for Co(II)-EDTA and Co(III)-EDTA reactions with Oak Ridge soil material was developed that considers equilibrium/kinetic ion-exchange reactions, kinetic oxidation reaction of adsorbed Co(II), and kinetic mass transfer reactions. The conceptual model was implemented numerically using the code HYDROGEOCHEM 5.0, which was coupled with the inverse solution module PEST to allow estimation of unknown model parameters and their covariance by nonlinear regressions to experimental data.
- For the undisturbed columns, the estimated dispersivities increased in the order: large unsaturated dual-continuum (0.013 m) < small saturated dual-continuum (0.043 m) < large unsaturated mono-continuum (0.097 m) < small saturated mono-continuum (0.110 m). The mobile-immobile mass transfer coefficient was 6 times greater for unsaturated flow than for saturated flow, despite larger size of the former. However, reaction rate coefficients were consistent across all experiments. These results confirm scale-dependence of physical transport parameters, but indicate that apparent reaction coefficients remain consistent across scales and experimental conditions – which is very encouraging for the practical field applications of reactive transport models.

** ****Acknowledgements**

- This research was conducted at Oak Ridge National Laboratory (ORNL) with funding from the US Department of Energy. ORNL is managed by UT-Battelle LLC for the U.S. Department of Energy under contract DE-AC05-00OR22725.

**Fan Zhang****1*****, Jack Parker****1****, Phil Jardine****1****, Melanie Mayes****1****, Tonia Mehlhorn****1****, Jing-Ping Guo****2****, and Scott Cesar****1**** **
**1 ****Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831****, ****zhangf@ornl.gov**
**2 ****Department of Civil & Environmental Engineering, University of Maryland, Baltimore, MD 21250 **

** ****Saturated Undisturbed Column**

** ****Packed Column**

**Table 1. Geochemical Reactions**

| No. | Type | Reaction | Parameter |
| --- | --- | --- | --- |
| 1a | eq./ki. 
ion-exchange | 0.5Co(II)EDTA2-+X-Cl ↔ 
X-[Co(II)EDTA]0.5+Cl- | logKg1a = logKf1a-logKb1a |
| 1b | eq./ki. 
ion-exchange | Co(III)EDTA-+X-Cl ↔ 
X-Co(III)EDTA+Cl- | logKg1b =logKf1b-logKb1b |
| 2 | ki. oxidation | 2X-[Co(II)EDTA]0.5+0.5MnO2+2H++Cl- → 
X-Co(III)EDTA+X-Cl+0.5Mn2++H2O | logKf2 |

** ****Introduction**

** ****Unsaturated Undisturbed Column**

** ****Batch**

- Alternative modeling approaches are used for column simulation:
-  Mono-continuum model:  all the pore spaces are looked as mobile region.
-  Mobile-immobile dual-continuum model with first-order mass transfer: the pore spaces are considered to be partly mobile and partly immobile, which means θ = θm + θim. The chemical diffusion between the mobile and immobile regions are simulated using first order mass transfer of Cm  Cim with rate = _a_D*(Cm – Cim*θim/θm), in which Cm and Cim are mobile and immobile concentrations in unit of mol/L-mobile water; D* is free water diffusion coefficient that is different from species to species, and _a_ is a mass transfer factor.
- For column experiment modeling,  non-reactive Br breakthrough curve (BTC) simulation is first performed to  obtain estimation of dispersivity (1) using mono-continuum and estimation of dispersivity (2), mass transfer factor (_a_), and mobile region porosity (θm) using dual-continuum model. Basing on the parameters obtained in Br simulation, reactive CoEDTA transport is simulated to estimate oxidation reaction parameters.

- Fig. 3 Saturated Undisturbed Column BTC modeling
- Upper:  mono-continuum model;  Lower: dual-continuum model

**Table 2. Parameter Estimation Results**

- Fig. 1 Batch Co(II)EDTA Oxidation Modeling

- Fig. 2 Packed Column BTC Modeling

- Fig. 4 Unsaturated Undisturbed Column BTC modeling
- Upper:  mono-continuum model;  Lower: dual-continuum model

** ****References**

-   Jardine, P.M. and D.L. Taylor, 1995. Fate and transport of ethylenediaminetetraacetate chelated contaminants in subsurface environments. Geoderma 67: 125-140.
-   Mayes M.A., P.M. Jardine, I.L. Larsen, S.C. Brooks, and S.E. Fendorf, 2000. Multispecies transport of metal–EDTA complexes and chromate through undisturbed columns of weathered fractured saprolite. Journal of Contaminant Hydrology, 45: 243–265
-   Gwo, J. P.,  E. F. D’Azevedo, H. Frenzel, M. Mayes, G.-T. Yeh, P. M. Jardine, K.M. Salvage, F. M. Hoffman, 2001.HBGC123D: a high-performance computer model of coupled hydrogeological and biogeochemical processes. Computers & Geosciences, 27: 1231–1242.
-  Jardine, P. M., G. K. Jacobs, and J. D. O’Dell, 1993. Unsaturated Transport Processes in Undisturbed Heterogeneous Porous Media: II. Co-Contaminants. Soil Sci. Soc. Am. J., 57: 954-962.

- Co experiments in varying scales for soils that occur at the FRC include: 1) small batch samples, 2) small packed column (8.8 cm) subject to saturated flow, 3) small undisturbed column (14.5 cm) with saturated flow, and 4) large undisturbed column (40.0 cm) with unsaturated flow.  The reactive model includes Co(II)-EDTA2- adsorption (via ion exchange), oxidation of the adsorbed species to adsorbed Co(III)-EDTA-, and desorption of Co(III)-EDTA-.

| Experiment | Batch | Packed column | Small undisturbed column |  | Big undisturbed column |  |
| --- | --- | --- | --- | --- | --- | --- |
| Flow regime | Batch | saturated | saturated |  | unsaturated |  |
| Size (cm3) | 1.07 | 6.91 | 803 |  | 6158 |  |
| Structure | No | No | Yes |  | Yes |  |
| Model type  | Mono | Mono | Mono | Dual | Mono | Dual |
| Dispersivity 1 or 2 (m) | - | 0.00082 | 0.11 | 0.0435 | 0.0968 | 0.0129 |
| Mobile fraction θm/θ | - | - | - | 0.774 | - | 0.587 |
| Mass transfer factor a | - | - | - | 1.67 | - | 9.99 |
| Oxidation kinetics logKf2 (h-1) | 8.60 | 8.19 | 9.85 | 9.80 | 10.5 | 8.19 |