Analytical solutions of solute transport in a fracture-matrix system with different reaction rates for fracture and matrix
Analytical solutions of solute transport in a fracture-matrix system with different reaction rates for fracture and matrix
复制标题
具有不同裂缝和基质反应速率的裂缝-基质系统中溶质输运的解析解
DOI：
10.1016/j.jhydrol.2016.05.056
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发表时间：
2016
影响因子：
6.4
通讯作者：
Jin Menggui
中科院分区：
文献类型：
--
作者：
Zhu Yonghui;Zhan Hongbin;Jin Menggui
本文采用解析和数值模拟的方法研究了裂缝-基质系统中溶质的反应输运问题。假定裂缝内地下水流速足够高（不小于0.1 m/d），以保证裂缝内以平流为主的输送。该问题包括沿断口的平流、基质中的横向扩散、线性吸附以及在断口和基质中同时发生的一级反应。考虑了裂隙中的等浓度边界条件和衰减源边界条件。在恒定浓度源下，我们得到了考虑无反应输运的封闭解析解以及两种介质中具有不同一级反应的稳态解。在有衰减源的情况下，得到了半解析解。解析解和半解析解与COMSOL Multiphysics的数值模拟结果吻合良好。通过敏感性分析来评估基质扩散系数、裂缝孔径和基质孔隙度的相对重要性。结果表明，一级反应和基质在裂隙中的扩散会降低溶质峰浓度，缩短溶质穿透裂隙的距离。这些解决方案可以用于评估裂缝和基质中浓度的时空分布，以及评估岩石基质中储存的污染物质量。所有这些都有助于设计受污染裂缝岩石的修复方案或对受污染裂缝基质系统进行风险评估。
This study deals with the problem of reactive solute transport in a fracture–matrix system using both analytical and numerical modeling methods. The groundwater flow velocity in the fracture is assumed to be high enough (no less than 0.1 m/day) to ensure the advection-dominant transport in the fracture. The problem includes advection along the fracture, transverse diffusion in the matrix, with linear sorption as well as first-order reactions operative in both the fracture and the matrix. A constant-concentration boundary condition and a decay source boundary condition in the fracture are considered. With a constant-concentration source, we obtain closed-form analytical solutions that account for the transport without reaction as well as steady-state solutions with different first-order reactions in the two media. With a decay source, a semi-analytical solution is obtained. The analytical and semi-analytical solutions are in excellent agreement with the numerical simulation results obtained using COMSOL Multiphysics. Sensitivity analysis is conducted to assess the relative importance of matrix diffusion coefficient, fracture aperture, and matrix porosity. We conclude that the first-order reaction as well as the matrix diffusion in the fractured rock would decrease the solute peak concentration and shorten the penetration distance into the fracture. The solutions can be applied to assess the spatial–temporal distribution of concentrations in the fracture and the matrix as well as to assess the contaminant mass stored in the rock matrix. All of these are useful for designing remediation plans for contaminated fractured rocks or for risk assessment of contaminated fracture–matrix systems.