Effective computer simulation of equilibrium adsorption with limited solubility

Radioactive waste repositories are discussed to be built in compact granite rock massif somewhere in the Czech Republic. To support the decision-making, various computer simulations are performed. These simulations help to evaluate risks connected with potential isolation failures, followed by transport of released radionuclides in the groundwater. Transport of radionuclides is affected by many natural processes. In this paper we focus on two important processes: adsorption and limited solubility (surface precipitation) of radionuclides in groundwater. Presented approach is based on interpolation instead of time demanding solution of nonlinear equations arising from mathematical description of the problem. The effectiveness of the proposed approach consists in creation of an interpolation table of points lying on an isotherm and transformed to mass balance maintaining system of coordinates. This kind of table is used to project data from transport part of simulation on the isotherm. The interpolation table points are computed using free derivative, nonlinear equation solver which avoids some of numerical solution difficulties. Results achieved with the use of our approach are comparable to Newton-Raphson method achieved solutions, but the simulation times are shorter.