Sensitivity and Uncertainty Analysis Applied to Radionuclide Sorption onto Single Minerals and Sediments

Sorption is one of the key retardation processes considered in safety assessment of radioactive waste repositories. Whereas most often conventional distribution coefficients (KD values) are utilized, additionally taking credit from mechanistic sorption models (Surface Complexation Models, SCM) helps to increase confidence both in the underlying basic chemical processes and in their numerical representation. Quality-assurance of long-term safety assessment studies requires the identification of the most sensitive geochemical and thermodynamic model input parameters [1] by means of sensitivity analysis (SA) and uncertainty analysis (UA). Such an approach is tested here rigorously for a variety of test cases: Se(IV/VI) sorption onto goethite, Np(V) sorbed onto hematite, and U(VI) sorption onto a simplified aquifer material resembling the overburden of a salt-rock repository.

In each case KD computations were based on a 1-site, 2pK Diffuse Double Layer Model. A component-additivity approach was used for the simplified aquifer. The mineral characterization comprised selected values for the specific surface area (SSA, typically following a log-normal error distribution function − EDF) and the surface site protolysis constants pK1 and pK2. The data selection was based on the mineral-specific sorption database RES³T [2] as were the decisions about the most relevant surface species and their formation constants. All surface reaction constants were assumed to be Gaussian distributed and were normalized to a reference site density of 2.31 sites/nm². The aqueous speciation of selenate and selenite (basically the hydrolysis steps of H2SeO4 and H2SeO3) as well as the more complex aqueous speciation for Np and U was based on the respective NEA TDB reviews [3,4].

Computations for the single-mineral systems were performed with the code FITEQL [5] as the innermost routine for calculating the speciation and subsequently deriving KD values. The outermost shell was a specially programmed tool to generate the necessary parameter variations and to derive statistical evaluations, namely variances as a function of the input parameter set, from the associated Kd distribution. There is also an option available to introduce correlated variables in the form of a correlation matrix. The coupling between these two codes is performed by UCODE [6]. The simplified aquifer was analysed by a combination of PhreeqC [7] for the geochemical speciation, interfaced by UCODE with the SimLab package [8] for SA/UA.

The SCM for the case of Se sorption onto goethite used an of 44.0 ± 2.8 m²/g, pK1 = 7.04 ± 0.15 and pK2 = 9.41 ± 0.24. Based on the available literature, for both Se oxidation states a protonated and an unprotonated inner-sphere surface complex was selected as most probable species: »Fe SeO3 , »Fe HSeO3, »Fe SeO4 , and »Fe HSeO4 with the following respective formation constants log K: 13.79 ± 0.40, 20.36 ± 0.24, 7.69 ± 0.39, and 14.36 ± 0.60. SA and UA were performed on six different pH levels (4 – 9), for two total selenium concentrations (10-4 M and 10-7 M), and for two redox scenarios (+300 mV and +800 mV), the solid-liquid ratio was set to 10 g/L, and atmospheric carbonate was excluded. Sensitivity analysis of its sorption onto goethite revealed that namely the uncertainty of the unprotonated inner-sphere surface complexes affects the overall uncertainty of the distribution coefficient KD, independent from the redox state. Moreover, the uncertainty of the computed KD values is in the order of about 5-30 %.

The system Np(V)-hematite was investigated based on the following parametrization: SSA = 22.5 ± 1.9 m²/g, pK values of 7.23 ± 0.40 and 9.49 ± 0.44 for the 1st and 2nd surface protolysis steps, and complex formation constants of -2.61 ± 0.21, -4.57 ± 0.18, 3.64 ± 0.28, and -10.53 ± 0.9 for the surface species »Fe–O–NpO2, »Fe–O–COO−, »Fe–O–COOH, and »Fe–O–NpO2(HCO3)22−, respectively. Total Np(V) concentration was set to 10−7 M and the geochemical environment characterized as oxidizing with ambient air and temperature, with a pH stepping from 4 to 9. It turned out that log K for the formation of the ternary surface complex »Fe O NpO2 is the input parameter influencing strongest the overall KD values in this system.

Concerning the most complex case, the aquifer model (composition: 85% quartz, 10% feldspar, 0.5% muscovite, 0.5% gibbsite, 0.5% goethite, 2% calcite, and 1.5% kaolinite) the varied input factors for the KD computations were solely geochemical parameters (contrary to the above cases), namely the pH value, the carbonate content, the ionic strength, the total concentrations of calcium, aluminium, and of uranium. Whereas the first two parameters followed a trigonal EDF, the latter four were log-trigonal distributed (all based on geochemical analyses of more than hundred samples). The most influential factors were identified to be the pH, the Ca content, and the carbonate content.

Based on these examples and further test cases, a generalization of application areas and limits for SA and UA applied to sorption phenomena will be discussed, considering both thermodynamic and environmental parameters.

[1] Ochs, M., Payne, T.E., Brendler, V. (2011). Thermodynamic Sorption Modeling in Support of Radioactive Waste Disposal Safety Cases, NEA Report, Paris.
[2] Brendler, V., Vahle, A. Arnold, T. Bernhard, G. and Fanghänel, T. (2002). „RES³T - Rossendorf Expert System for Surface and Sorption Thermodynamics“, J. Contam. Hydrol. 61, 281-291.
[3] Olin, Å., Noläng, B. Öhman, L.-O. Osadchii, E., Rosén, E., (2005). Chemical thermodynamics of selenium. Chemical Thermodynamics Vol. 7 (OECD NEA ed.), Elsevier, Amsterdam.
[4] Guillaumont, R., Fanghänel, T., Fuger, J., Grenthe, I., Neck, V., Palmer, D.A., Rand, M.H (2003). Update on the chemical thermodynamics of uranium, neptunium, plutonium, americium and technetium. Chemical Thermodynamics Vol. 5 (OECD NEA ed.), Elsevier, Amsterdam.
[5] Herbelin, A. L. et al. (1999). FITEQL 4.0 Report 99-01, Dept. Chemistry, Oregon State University, Corvallis.
[6] Poeter, E.P.; Hill, M.C. (1998). Documentation of UCODE, a computer code for universal inverse modeling: U.S.G.S. Water-Resources Investigations Report 98-4080, 122 p.
[7] Parkhurst, D.L.; Appelo, C.A.J. (1999). User’s guide to PHREEQC (Version 2) - A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations: U.S.G.S. Water-Resources Investigations Report 99-4259, 312 p.
[8] Saltelli, A., Tarantola, S. SimLab, http://simlab.jrc.ec.europa.eu/

Financial support through the NEA Sorption Project Phase III and the German Federal Ministry of Economics (Contract 02 E 10528) is gratefully acknowledged.