Multidimensional matrices

One feature of the approach is that all smart K_d-values are pre-calculated by the geochemical code PHREEQC for the defined range of environmental parameters and can be accessed from a multidimensional matrix. As an example a 3-D subset from the pre-calculated multidimensional matrix is shown in Fig. 1. The dependence of the smart K_d-value on pH, ionic strength (IS) and Ca-concentration for Np(V) and U(VI) obious and realized with random sampling (sampling size = 10,000). Clearly, the pH is the main influencer concerning the sorption of both radionuclides. For Np the K_d will be higher with increasing pH up to maximum uptake between pH 8-9 before it lowers in the more alkaline conditions. For U maximum uptake occurs in the near neutral pH range and as for Np the K_d will lower with increasing pH.

Furthermore, combined effects are visible depending on the Ca contents and the IS. The flow and transport code d³f++ interpolates the appropriate value from this matrix for the specific environmental parameter values that are calculated at each time step and for each point of the model area.

Fig. 1: Multidimensional K_d-matrix for for Np(V) (left) and U(VI) (right) sorption in the upper aquifer as a function of pH, ionic strength IS, and Ca-concentration (K_d in m³ kg^-1, logarithmic scale).