## 1 Introduction  
For the safe storage of especially highly radioactive waste, emplacement in deep subsurface geological repositories is favoured worldwide to ensure the protection of human and nature from the potential radiation exposure of the waste packages for periods of up to one million years [1]. Claystones are among potential host rocks due to their low permeability. Hence, diffusion is the primary transport process in intact formations [2, 3, 4]. Another important and positive aspect of claystones with regard to the storage of nuclear waste is the high sorption capacity retarding the potential migration of radionuclides. The diffusive transport through the host rock is quantified with numerical simulations usually using [PERSON]'s law [2]. According to this method, only one diffusion coefficient is used for all species, major and minor ions as well as all radionuclides, in the same way. A more advanced approach is the multi-component (MC) diffusion, where each species in the system is assigned its own diffusion coefficient and transport is calculated separately for the diffuse double layer (DDL) and the free porewater [5, 6]. The surfaces of clay minerals are charged due to their internal structure and contact to the external porewater. Dependent on pH of the solution and the hydroxyl groups on the mineral surface the DDLforms, compensating the net surface charge by attraction of counter-ions and repulsion of co-ions [7]. Enhanced transport of counter-ions as well as decreased transport of co-ions occurs in the DDL [2,5]. As a consequence, anionic, cationic and neutral species show different diffusive migration pattern in clay formations [6,8]. The Swiss Opalinus Clay is a potential host rock for the storage of nuclear waste [2]. The formation has been investigated for the last 25 years in the underground research laboratory Mont Terri and hence offers a comprehensive database [9]. Furthermore, the MC diffusion approach has already been successfully applied to the Opalinus Clay to model diffusion experiments, for instance with caesium, sodium, chloride and tritium [6]. The Opalinus Clay is subdivided into shaly, sandy and carbonate-rich facies [10], which differ in their mineralogical composition. As a result of the water rock interaction, the geochemical conditions in the porewaters of the facies vary and impact on sorption and transport of radionuclides [11]. Uranium is one of the main components in spent fuel [12], for which we apply diffusion simulations for the far-field (\(>\)50 m) of a potential host rock to assess its migration behaviour. Uranium is redox sensitive and its speciation between U(IV) and U(VI) is controlled by the porewater composition. In the geochemical system of the Opalinus Clay, uranium is mainly present as anionic as well as neutral, ternary uranyl complex bound to calcium and carbonate. In a previous study, the migration of uranium in the Opalinus Clay was assessed in one-dimensional diffusion simulations using Fick's laws as a function of different partial pressures of carbon dioxide (pCO\({}_{2}\)) covering the range of measured values for the formation and depending on the mineralogical heterogeneity in the facies [11]. The various facies govern the geochemistry of the system, especially via the pCO\({}_{2}\) and thus by the carbonate and calcium concentrations as well as the resulting pH through which the anionic, ternary uranyl complex \(CaUO_{2}(CO_{3})_{3}^{2-}\) is the predominant species in the system [11]. Based on their results, [PERSON] et al. [11] prioritized the governing parameters for the sorption of uranium in the Opalinus Clay as follows: pCO\({}_{2}\), Ca\({}^{2+}\) concentration, pH, pe and clay mineral quantity. Furthermore, the effect of anion exclusion on the migration lengths was estimated by an adapted porewater diffusion coefficient, what reduced uranium migration by 30%. The work presented here thus aims to extend the findings of [PERSON] et al. [11] by means of the MC approach.