Mathematical Geosciences

, Volume 48, Issue 5, pp 511–535 | Cite as

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

  • Xiaoying Zhang
  • Chongxuan Liu
  • Bill X. Hu
  • Qinhong Hu


The additivity model assumed that field-scale reaction properties in a sediment including surface area, reactive site concentration, and reaction rate can be predicted from field-scale grain-size distribution by linearly adding reaction properties estimated in laboratory for individual grain-size fractions. This study evaluated the additivity model in scaling mass transfer-limited, multi-rate uranyl (U(VI)) surface complexation reactions in a contaminated sediment. Experimental data of rate-limited U(VI) desorption in a stirred flow-cell reactor were used to estimate the statistical properties of the rate constants for individual grain-size fractions, which were then used to predict rate-limited U(VI) desorption in the composite sediment. The result indicated that the additivity model with respect to the rate of U(VI) desorption provided a good prediction of U(VI) desorption in the composite sediment. However, the rate constants were not directly scalable using 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 to 8 mm), which is often ignored in modeling U(VI) sorption and desorption, is statistically significant to the U(VI) desorption in the sediment.


Scaling Additivity model Uranium surface complexation Multi-rate mass transfer Statistical analysis 



This research is supported by the US DOE, Office of Science, Biological and Environmental Research (BER), as part of the Subsurface Biogeochemical Research (SBR) Program through Pacific Northwest National Laboratory (PNNL) SBR Science Focus Area (SFA) Research Project. QH thanks the financial support of the Subsurface Biogeochemical Research Program #DE-SC0005394, Office of Biological and Environmental Research, US Department of Energy, for Project ER65073. The authors thank the anonymous reviewers for their helpful and constructive comments.


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Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  • Xiaoying Zhang
    • 1
    • 2
  • Chongxuan Liu
    • 3
  • Bill X. Hu
    • 1
  • Qinhong Hu
    • 4
  1. 1.Department of Earth, Ocean and Atmospheric ScienceFlorida State UniversityTallahasseeUSA
  2. 2.College of Life Science and TechnologyJinan UniversityGuangzhouChina
  3. 3.Pacific Northwest National LaboratoryRichlandUSA
  4. 4.The University of Texas at ArlingtonArlingtonUSA

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