# Verification calculations

Several test cases were computed during the implementation of the conceptual smart K_{d}‑concept in the transport code r^{3}t. These test cases illustrated the extensions implemented in r^{3}t and verified that the implemented concepts basically work and produce plausible results. The retrieved smart K_{d}‑values show their highly nonlinear dependence on the environmental parameters and the concentration of the respective radionuclide.

In order to qualify the modified code r^{3}t and to verify the new methodology the previously implemented concept is compared via comparative calculations regarding simple and more complex systems. Here, results of simulations employing the code r^{3}t are compared to the results of simulations performed with the code PHAST, a program for simulating groundwater flow, solute transport and multicomponent geochemical reactions.

A simple box model is chosen for first simulations. Model variations account for different considerations of the model geometry, the model heterogeneity, the complexity of the flow and the variations in the geochemical environment. Model times and model dimensions are kept at a manageable extent.

A simple box model was chosen for the comparative calculations. It can be devided into two units (Fig. 1). At the left side of the model, an inflow is defined at two sections of the model boundary. This inflow may be varied in its flow velocity and geo-chemical conditions. The right side is open to flow and transport. The upper and lower model boundaries as well as parts of the left boundary are impermeable to flow and transport.

* Fig. 1: Geometry of the model with possible boundary conditions. Red: Inflow; Blue: Outflow; Black: Impermeable boundary*.

The following parameters are varied:

- Heterogeneity, e. g. via a variation of the mineralogical composition of the two units,
- Chemical environment, e. g. via a variation of the chemical composition of the in-flowing water,
- Complexity of the flow, e. g. via a variation of the inflow velocity at the two inflow locations at the left side of the model, and
- Model geometry, e. g. via using a more complex model geometry taking more hydrogeological units into account.