Tracer transport in fractured porous media: Distribution of tracer concentration within the rock matrix and the implementation of time domain random walk algorithm

In this work, a new Time Domain Random Walk (TDRW) algorithm is proposed to estimate the tracer distribution profile within the rock matrix. The development of the new algorithm stems from the statistical properties of the analytical solution to a single fracture-matrix system, in which the particle position at a certain time is calculated and recorded. With the position of each particle determined, the resulting distribution will then provide an estimate of the tracer distribution profile directly. In addition, the newly developed algorithm can readily be extended to a case of more complicated fracture-matrix system, in which an arbitrary injection boundary condition may also be used. To verify the accuracy and applicability of the new algorithm, three benchmark simulations are made, in which the results of different approaches are found to be identical. Nevertheless, the new algorithm has a higher computational efficiency, due to its lower calculation demand.