# Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments

## Abstract

This study statistically analyzed a grain-size based additivity model that has been proposed to scale reaction rates and parameters from laboratory to field. The additivity model assumed that reaction properties in a sediment including surface area, reactive site concentration, reaction rate, and extent can be predicted from field-scale grain size distribution by linearly adding reaction properties for individual grain size fractions. This study focused on the statistical analysis of the additivity model with respect to reaction rate constants using multi-rate uranyl (U(VI)) surface complexation reactions in a contaminated sediment as an example. Experimental data of rate-limited U(VI) desorption in a stirred flow-cell reactor were used to estimate the statistical properties of multi-rate parameters for individual grain size fractions. The statistical properties of the rate constants for the individual grain size fractions were then used to analyze the statistical properties of the additivity model to predict rate-limited U(VI) desorption in the composite sediment, and to evaluate the relative importance of individual grain size fractions to the overall U(VI) desorption. The result indicated that the additivity model provided a good prediction of the U(VI) desorption in the composite sediment. However, the rate constants were not directly scalable using the additivity model, andmore »

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)

- OSTI Identifier:
- 1324913

- Report Number(s):
- PNNL-SA-103689

Journal ID: ISSN 1874-8961; KP1702030

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- Mathematical Geosciences

- Additional Journal Information:
- Journal Volume: 48; Journal Issue: 5; Journal ID: ISSN 1874-8961

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Zhang, Xiaoying, Liu, Chongxuan, Hu, Bill X., and Hu, Qinhong.
```*Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments*. United States: N. p., 2015.
Web. doi:10.1007/s11004-015-9620-z.

```
Zhang, Xiaoying, Liu, Chongxuan, Hu, Bill X., & Hu, Qinhong.
```*Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments*. United States. doi:10.1007/s11004-015-9620-z.

```
Zhang, Xiaoying, Liu, Chongxuan, Hu, Bill X., and Hu, Qinhong. Mon .
"Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments". United States. doi:10.1007/s11004-015-9620-z.
```

```
@article{osti_1324913,
```

title = {Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments},

author = {Zhang, Xiaoying and Liu, Chongxuan and Hu, Bill X. and Hu, Qinhong},

abstractNote = {This study statistically analyzed a grain-size based additivity model that has been proposed to scale reaction rates and parameters from laboratory to field. The additivity model assumed that reaction properties in a sediment including surface area, reactive site concentration, reaction rate, and extent can be predicted from field-scale grain size distribution by linearly adding reaction properties for individual grain size fractions. This study focused on the statistical analysis of the additivity model with respect to reaction rate constants using multi-rate uranyl (U(VI)) surface complexation reactions in a contaminated sediment as an example. Experimental data of rate-limited U(VI) desorption in a stirred flow-cell reactor were used to estimate the statistical properties of multi-rate parameters for individual grain size fractions. The statistical properties of the rate constants for the individual grain size fractions were then used to analyze the statistical properties of the additivity model to predict rate-limited U(VI) desorption in the composite sediment, and to evaluate the relative importance of individual grain size fractions to the overall U(VI) desorption. The result indicated that the additivity model provided a good prediction of the U(VI) desorption in the composite sediment. However, the rate constants were not directly scalable using the additivity model, and U(VI) desorption in individual grain size fractions have to be simulated in order to apply the additivity model. An approximate additivity model for directly scaling rate constants was subsequently proposed and evaluated. The result found that the approximate model provided a good prediction of the experimental results within statistical uncertainty. This study also found that a gravel size fraction (2-8mm), which is often ignored in modeling U(VI) sorption and desorption, is statistically significant to the U(VI) desorption in the sediment.},

doi = {10.1007/s11004-015-9620-z},

journal = {Mathematical Geosciences},

issn = {1874-8961},

number = 5,

volume = 48,

place = {United States},

year = {2015},

month = {9}

}