A Nuclide Transport Model in the Fractured Rock Medium Using a Continuous Time Markov Process

A stochastic way using continuous time Markov process is presented to model the one-dimensional nuclide transport in fractured rock matrix as an extended study for previous work ［1］. A nuclide migration model by the continuous time Markov process for single planar fractured rock matrix, which is considered as a transient system where a process by which the nuclide is diffused into the rock matrix from the fracture may be no more time homogeneous, is compared with a conventional deterministic analytical solution. The primary desired quantities from a stochastic model are the expected values and variance of the state variables as a function of time. The time-dependent probability distributions of nuclides are presented for each discretized compartment of the medium given intensities of transition. Since this model is discrete in medium space, parameters which affect nuclide transport could be easily incorporated for such heterogeneous media as the fractured rock matrix and the layered porous media. Even though the model developed in this study was shown to be sensitive to the number of discretized compartment showing numerical dispersion as the number of compartments are decreased, with small compensating of dispersion coefficient, the model agrees well to analytical solution.