The Form of Waiting Time Distributions of Continuous Time Random Walk in Dead-End Pores

Abstract

Anomalous dispersion of solute in porous media can be explained by the power-law distribution of waiting time of solute particles. In this paper, we simulate the diffusion of nonreactive tracer in dead-end pores to explore the waiting time distributions. The distributions of waiting time in different dead-end pores show similar power-law decline at early time and transit to an exponential decline in the end. The transition time between these two decline modes increases with the lengths of dead-end pores. It is well known that power-law distributions of waiting time may lead to anomalous (non-Fickian) dispersion. Therefore, anomalous dispersion is highly dependent on the sizes of immobile zones. According to the power-law decline, we can directly get the power index from the structure of dead-end pores, which can be used to judge the anomalous degree of solute transport in advance.

Using a Pore-Scale Modelling Approach to Study Solute Dilution Process through Cemented Porous Media

“…The characteristics of the flow fields suggest that they are the bridges connecting the medium properties and the solute transport characteristics. It has been found that the mechanisms of many solute transport phenomena can be explained by analyzing the characteristics of the flow fields [38,39]. For example, previous studies have shown that the heterogeneity of a flow field has significant impacts on solute dilution.…”