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Geofluids
Volume 2018 (2018), Article ID 8329406, 6 pages
https://doi.org/10.1155/2018/8329406
Research Article

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

School of Earth Sciences and Engineering, Nanjing University, Nanjing, China

Correspondence should be addressed to Jianguo Jiang; nc.ude.ujn@gnaij.ougnaij

Received 22 July 2017; Revised 16 November 2017; Accepted 12 December 2017; Published 8 January 2018

Academic Editor: Dan Lu

Copyright © 2018 Yusong Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.