Smart Kd-concept as efficient approach to improve geochemistry in reactive transport modelling for repository safety assessment

A key component of performance assessment (PA) for radioactive waste repositories in deep geological formations is the forecast of potential radionuclide transport through the repository system. Understanding and appropriate modelling of all relevant (hydro-)geochemical processes is essential for predicting the migration of radionuclides. One important retardation process is sorption on mineral surfaces of the host rock or sedimentary overburden. For the quantification of the radionuclide retention the solid/liquid distribution coefficients (Kd-values) calculated for a given groundwater/rock system are traditionally used in reactive transport modelling (RTM) and most often considered as a constant value due to the large temporal and spatial scales considered in PA. Such a conventional concept has the advantage to be simple and computationally fast but cannot reflect changes in geochemical conditions that are expected during the evolution of the repository system caused by climatic or geological changes. Due to the German safety criteria with an assessment period of one million years it is necessary to consider the impact of such hydrogeological and geochemical changes on the radionuclide transport and retardation. The challenge for large-scale RTM is the integration of important geochemical parameters and processes at affordable computational costs into the codes. Most often a full direct coupling of a transport code with a geochemical speciation code, however, leads to unacceptably long computational times for PA relevant systems.
As an effective way to integrate variable geochemistry in RTM, we developed the smart Kd-concept (www.smartkd-concept.de), a mechanistic approach mainly based on surface complexation models and implemented it into a transport code [1], [2]. The philosophy behind this approach is to compute a-priori multidimensional look-up tables with distribution coefficients (referred to as smart Kd-values as they are based on mechanistic sorption models) for a wide range of important environmental input parameters. Such parameters are typically pH, ionic strength, concentration of competing cations and complexing ligands such as calcium (Ca) and dissolved inorganic carbon (DIC). These smart Kd-values can be accessed during each transport simulation step. Equations describing pH and concentrations of ions as a function of mineral phases are implemented into the transport code, and the resulting values are used to obtain the corresponding smart Kd-values from the look-up table. The smart Kd values are calculated using the geochemical code PHREEQC [3] with a bottom-up approach, i.e. the mineral-specific sorption of dissolved species on each single mineral phase contributes to the distribution coefficient for the whole sediment. Parameter variation was performed with the numeric tool UCODE [4].
The capability of this approach is demonstrated for the sorption of repository-relevant radionuclides (isotopes of Am, Cm, Cs, Ni, Np, Pu, Ra, Th and U) and possible migration scenarios through a typical sedimentary rock system covering potential repository host rocks, namely salt and clay formations in Northern Germany as natural geological barrier for a deep geological repository site. This serves as a comprehensive proof-of-concept and demonstrates the capability to describe the sorption behaviour in dependence of changing geochemical conditions quite well. As a side-effect, the large Kd-matrices that were computed can be further analysed by sensitivity and uncertainty analysis (SA/UA) as provided by SimLab2.2/4 [5], [6].
Results of this case study showed that the smart Kd approach goes considerably beyond the conventional concepts. We can illustrate that constant Kd values previously used in transport simulations, here exemplarily shown for uranium U(VI) (Figure 1, right, green line [7]), are a rough approximation, as in reality they rather range over several orders of magnitude. Moreover, with the results from SA, those input parameters influencing strongest the radionuclide retardation variation can be identified (key parameters of the model). The calculated sensitivity indices allowed us to rank all parameters with respect to sensitivity on Kd. From the visualized smart Kd matrix for U(VI) (Figure 1, left) it is obvious that mainly the pH value and the DIC determine 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.