Simulation of solute transport through heterogeneous networks: analysis using the method of moments and the statistics of local transport characteristics

Min Li,Dong Wang,Jinzhou Zhao,Zheming Wang,Ying Wang,Tao Qi,Yves Bernabé

doi:10.1038/s41598-018-22224-w

Abstract

We used a time domain random walk approach to simulate passive solute transport in networks. In individual pores, solute transport was modeled as a combination of Poiseuille flow and Taylor dispersion. The solute plume data were interpreted via the method of moments. Analysis of the first and second moments showed that the longitudinal dispersivity increased with increasing coefficient of variation of the pore radii CV and decreasing pore coordination number Z. The third moment was negative and its magnitude grew linearly with time, meaning that the simulated dispersion was intrinsically non-Fickian. The statistics of the Eulerian mean fluid velocities {hat{{boldsymbol{u}}}}_{{boldsymbol{i}}}, the Taylor dispersion coefficients {hat{{boldsymbol{D}}}}_{{boldsymbol{i}}} and the transit times {hat{{boldsymbol{tau }}}}_{{boldsymbol{i}}} were very complex and strongly affected by CV and Z. In particular, the probability of occurrence of negative velocities grew with increasing CV and decreasing Z. Hence, backward and forward transit times had to be distinguished. The high-τ branch of the transit-times probability curves had a power law form associated to non-Fickian behavior. However, the exponent was insensitive to pore connectivity, although variations of Z affected the third moment growth. Thus, we conclude that both the low- and high-τ branches played a role in generating the observed non-Fickian behavior.

Highlights

We used a time domain random walk approach to simulate passive solute transport in networks
We considered ranges of the input parameters similar to those used in Bernabé et al.[35]: the network hydraulic radius R ranged from 20 to 100 × 10−6 m, the pore radii coefficient of variation CV varied from 0.05 to 1.05, the mean coordination number Z from 2.5 to 12 and the macro-scale fluid velocity U from 10−5 to 10−2 ms−1
We investigated ratios of pore length to hydraulic radius l/R between 5 and 10 and we used a single value for the coefficient of molecular diffusion (i.e., 10−10 m2 s−1)

Summary

Introduction

We used a time domain random walk approach to simulate passive solute transport in networks. Data recorded during tracer experiments often indicate that the dispersion tensor needed for ADE modeling varies with time or, equivalently, with traveled distance This type of behavior is expected during the transient (“pre-asymptotic”) regime preceding an eventual long-term Fickian regime. The probability P is generally assumed stationary in time and space and can be written P(s, τ), with s = x − x′ and τ = t − t′ This approach is well suited to interpret the results of random walk/particle tracking simulations[21,22,23,24,25,26,27,28]. Other mechanisms, such as those arising from, e.g., chemical interactions, may occur in real situations[11,19,20], but were not included here for the sake of simplicity

Methods

Results

Discussion

Conclusion