Sensitivity and uncertainty analysis for geochemical models for repository safety assessment

A key component of safety assessment for radioactive waste repositories in deep geological formations is the simulation of potential radionuclide release scenarios and the transport of radionuclides through the repository system. The realistic modelling of (hydro-)geochemical processes is of high relevance for assessing the migration of radionuclides in groundwater systems. One important retardation process for radionuclides to be considered is sorption onto mineral surfaces of the host rock / sediments. Due to the heterogeneities of the natural system and the high complexity of the geochemical models with uncertain or varying input parameters, it is important to understand which of the input parameter uncertainties have considerable influences on the model output uncertainty. This in turn allows model reduction required to upscale from the molecular to the plug scale. Consequently, we performed sensitivity and uncertainty analysis (SA/UA) to investigate and understand our geochemical model.
For the quantification of the contaminant retention in groundwater, the solid/liquid distribution coefficients (Kd-values) calculated for a given groundwater/rock system are traditionally used. Most often conventional concepts with constant Kd values are applied in reactive transport simulations. Such an approach has the advantage to be simple and computationally fast but cannot reflect changes in geochemical conditions that will occur during the evolution of the repository system, e.g. due to climatic changes. Due to the German safety criteria with an assessment period of about 1 million years it is necessary to consider the impact of such geochemical changes on the radionuclide transport and retardation. For this, we developed a new approach, where the smart Kd concept (www.smartkd-concept.de) [1] is modified in complex geochemical models including mechanistic sorption models, and implemented it in reactive transport calculations [2, 3]. Possible migration scenarios for repository-relevant radionuclides (isotopes of Am, Cm, Cs, Ni, Np, Pu, Ra, Se, Th and U) through a typical sedimentary rock system covering potential repository host rocks, namely salt and clay formations in Northern Germany as natural geological barrier, were developed in the first stage.
Smart Kd-values and their associated sensitivities and uncertainties were computed for a wide range of important geochemical input parameters / boundary conditions such as pH value, ionic strength, concentration of competing cations and complexing ligands, e.g. dissolved inorganic carbon (DIC) and calcium (Ca2+). Our toolbox coupled the geochemical speciation code PHREEQC [4] with the numeric tool UCODE [5] and SimLab2.2/4 [6]. SimLab has the advantage to permit a simultaneous variation of all input parameters according to their probability density functions and mutual correlations. It provides (in contrast to UCODE, which also incorporates some simple SA/UA algorithms) methods for Global SA. Comparable SA/UA have been done with a new software package RepoSUN, which is based on SimLab4 [7]. For the varying parameters uncertainty intervals were defined from field investigations and log-uniform distributions were assumed for all parameters, except for the pH value, which was assumed to be uniformly distributed. The results, i. e. the smart Kd values, were analyzed in the following way:
o As the output distribution covers several orders of magnitude, a log-transformation was performed on the output data. Then the computed a-priory multidimensional smart Kd matrices (see for U(VI) in Fig. 1, left) are accessible for interpolations during subsequent transport simulations.
o A histogram of the model output visualizes the distribution (see for U(VI) in Fig. 1, right).
o Some statistical measures were calculated to characterize the distribution (minimum, maximum, mean, standard deviation).
o Sensitivity measures were calculated for each of the input parameters: the standardized regression coefficient (SRC), the standardized rank regression coefficient (SRRC) and the variance-based first-order sensitivity index (SI1).
On the basis of the results it could be shown that the smart Kd approach goes considerably beyond the conventional concepts. We could illustrate that constant Kd values (see for U(VI) in Fig. 1, right, green line) used in previous transport simulations [8] are a crude assumption, as in reality they rather range over several orders of magnitude. Moreover, with the results from the SA, the most important input parameters influencing the radionuclide retardation can be identified (key parameters of the model). The calculated sensitivity indices allowed us to assess the most and less sensitive parameters. From the visualized smart Kd matrix for U(VI) (Fig. 1, left) it is obvious that mainly the pH value and the DIC influences the sorption of U(VI) under the given conditions. SA is a useful means for reducing the complexity of a geochemical model by focusing on the most important input parameters.