In the last years the interest in computer simulations of radioactive waste scenarios has increased. In this article we present numerical simulations with the software package TRAPRO. We consider a system of convection-diffusion-reaction-equations, that we coupled by their reaction terms. We present a new discretization method that improves the explicit discretization for the transport- and reaction-term. The method should replace the previous decoupled implicit method with an operator-splitting method by an explicit coupled method between transport and reaction. For analyzing the method we reduce our model to a simpler system of convection-reaction-equations. The numerical results will be compared with the exact solutions. With a test example we illustrate results of our recent research on this subject. Key words. radionuclide transport, sorption, numerical simulations AMS subject classifications. 76S05, 80A32, 65M60