Fractional Derivative Modeling on Solute Non-Fickian Transport in a Single Vertical Fracture

Chuantaidou Qiao,Hongguang Sun,Yongting Wu,Jiazhong Qian,Weidong Zhao,Yi Xu

doi:10.3389/fphy.2020.00378

Abstract

Solute transport in a single vertical fracture (SVF) cannot be reliably described by the classical advection-dispersion equation (ADE) model, due to the heterogeneity nature of fracture. This study conducted a group of experiments to investigate chloride ion transport in the SVFs under different rough-walled conditions, and then applied a time fractional advection-dispersion equation (F-ADE) model to offer an accurate description. A comparison between F-ADE model and a classical ADE model in describing experimental data, was also carried out. Results show that the FADE model is better than the ADE model in describing the breakthrough curve and heavy-tail phenomenon of solute transport in the fracture. Especially in the experiments with lower flow rate and higher roughness fracture, the FADE model can offer an accurate description, indicating that it is a promising tool for characterizing solute transport heterogeneous vertical fracture.

Highlights

Fracture water as part of underground water, is of great significance in water resources
The objective of this study is to conduct a group of experiments to investigate chloride ion transport in the single vertical fracture (SVF) under different rough-walled conditions, especially observe the non-Fickian transport phenomena, and to establish a time fractional advection-dispersion equation (F-advectiondispersion equation (ADE)) model to offer an effective description for the anomalous transport
According to the fitting results of breakthrough curves (BTCs) diagram and numerical analysis, it is clear that the heavy-tail phenomena of BTCs can be well-captured and described by the FADE model, while the ADE model can only roughly describe the peak value of BTCs

Summary

Introduction

Fracture water as part of underground water, is of great significance in water resources. It is closely related to the production and living activities of human beings and involves complex natural and human factors [1]. In heterogeneous media such as rock fractures, the assessment of solute transport in fractures can avoid overexploitation of groundwater resources and predict the diffusion of fluids and pollutants, which is one of the main tasks of hydrogeology [2, 3]. Quantifying pollutant transport in fractures has always been regarded as an important research topic [4, 5]. Researchers have developed several theoretical and empirical models to quantify solute transport in fractured media [7,8,9]. The breakthrough curves (BTCs) showed anomalous and trailing phenomena, indicating that the classic advectiondispersion equation (ADE) model based on the average transport could not accurately describe these phenomena [14,15,16,17]

Objectives

Methods

Conclusion