Multidimensional matrices

One feature of the approach is that all smart Kd-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 Kd-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 Kd 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 Kd 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 Kd-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 (Kd in m³ kg-1, logarithmic scale).