Generalizing time domain random walk algorithms to account for transient flow and geochemistry

In the study of radionuclide transport through sparsely fractured rock, time domain random walk algorithms are often used due to their low numerical dispersion and reduced computational cost. However, a limitation of these algorithms is that steady flow and geochemical conditions are often assumed, or rough approximations are used to simulate transient conditions. In this work, we show how a time domain random walk method that simulates transport through a fracture-matrix system can be extended to account for transient flow magnitude and transient geochemistry. The method is based on approximating those transient conditions using piecewise constant conditions, with sudden stepwise changes. Then, the effect of these stepwise changes can be simulated by interrupting the algorithm at the time of each change and sampling the current location of the particle. The changes in the flow and geochemistry can then be applied, and the algorithm can be resumed. The method has been implemented in the code Migration Analysis of Radionuclides in the Far Field (MARFA) for the case of transport through a fracture system with diffusion into a rock matrix of infinite extent. A few tests are simulated, and the obtained breakthrough curves are compared against a semi-analytical solution that we derive, as well as against equivalent models simulated using the PFLOTRAN code. Results show that the new generalization is a reliable approach to simulate solute transport under a wide range of flow and geochemistry conditions.