均质砂箱含水层多级水流系统溶质运移的非费克现象

高一攀; 孙蓉琳; 何世伟; 王润

doi:10.19509/j.cnki.dzkq.tb20250044

均质砂箱含水层多级水流系统溶质运移的非费克现象

doi: 10.19509/j.cnki.dzkq.tb20250044

1.
中国地质大学（武汉）环境学院，武汉 430078
2.
湖北省地质局水文地质工程地质大队，湖北荆州 434020

基金项目: 国家自然科学基金项目(42172286)

详细信息

作者简介:
高一攀：E-mail：gaoyipan86@163.com

通讯作者:
E-mail：sunronglin@cug.edu.cn

中图分类号: P641.2；P641.69
计量
- 文章访问数: 39
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2025-01-24
- 录用日期: 2025-06-24
- 修回日期: 2025-06-20
- 网络出版日期: 2025-06-24

Non-Fickian phenomenon of solute transport in hierarchical groundwater flow systems of homogeneous sandbox aquifer

1.
School of Environmental Studies, China University of Geosciences (Wuhan), Wuhan 430078, China
2.
Hydrogeology and Engineering Geology Brigade, Hubei Provincial Bureau of Geology, Jingzhou Hubei 434020, China

More Information

Author Bio:
E-mail：gaoyipan86@163.com

Corresponding author: E-mail：sunronglin@cug.edu.cn

摘要

摘要:
探讨均质砂箱含水层多级水流系统排泄点及内部溶质运移的非费克现象与关键影响因素，明晰该模式下非费克现象的表现规律，为复杂嵌套式盆地地下水污染防控与治理提供实验和理论依据。基于室内砂箱实验与 COMSOL Multiphysics 数值模拟，通过改变降雨入渗强度，构建单一区域、局部 + 区域二级、局部+中间+区域3级3种水流系统模式，开展溶质运移动态监测与穿透曲线分析。溶质运移穿透曲线分析显示：同一水流模式中，非费克现象显著程度为区域水流系统>中间水流系统>局部水流系统；不同水流模式中，非费克现象显著程度为单一区域水流系统>局部+区域二级水流系统>局部+中间+区域三级水流系统；砂箱河谷排泄点与含水层内部监测点均呈现明显的早到、拖尾非费克运移特征。该非费克现象受地下水流速、溶质运移路径和降雨入渗强度共同影响，浅部受流速影响更大，深部受运移路径影响更显著；降雨入渗强度与深部非费克现象呈明显负相关，对浅部则无明显相关性。研究成果丰富了均质含水层多级水流系统溶质运移理论，为实际盆地地下水污染评价与修复提供了科学参考。
- 均质含水层 /
- 多级水流系统 /
- 降雨入渗强度 /
- 溶质运移 /
- 非费克现象 /
- 砂箱实验
Abstract:
Objective
Groundwater solute transport is a core research content in hydrogeology, and the non-Fickian phenomenon widely existing in the transport process is the key to revealing the intrinsic mechanisms of solute migration. Traditional studies have mostly focused on the non-Fickian phenomenon caused by the heterogeneity of aquifer media, while the research on solute transport in homogeneous aquifers under the hierarchical groundwater flow system model remains relatively limited. This study aims to investigate the non-Fickian phenomenon of solute transport at the discharge points and inside the homogeneous sandbox aquifer with hierarchical groundwater flow systems, as well as its key influencing factors. It is also intended to clarify the manifestation patterns and dominant controlling factors of the non-Fickian phenomenon under the hierarchical flow system model in homogeneous aquifers, and to provide experimental and theoretical basis for the prevention, control, and treatment of groundwater pollution in complex nested basins.
Methods
Based on the combination of laboratory sandbox physical experiments and COMSOL Multiphysics numerical simulation, three different groundwater flow patterns were constructed in the aquifer by adjusting the rainfall infiltration intensity: single regional flow system, local + regional two-level flow system, and local + intermediate + regional three-level flow system. The dynamic monitoring of solute transport at river valley discharge points and internal monitoring points of the aquifer was carried out, and the non-Fickian characteristics of solute transport were systematically analyzed by using the breakthrough curve of solute transport as the core analysis index.
Results
The analysis of solute transport breakthrough curves showed that in the same flow pattern, the significance degree of the non-Fickian phenomenon in different hierarchical flow systems followed the order of regional flow system > intermediate flow system > local flow system. Among different groundwater flow patterns, the significance degree of the non-Fickian phenomenon was ranked as single regional flow system > local + regional two-level flow system > local + intermediate + regional three-level flow system. Distinct non-Fickian transport characteristics of early arrival and tailing were observed at both the river valley discharge points of the physical sandbox and the internal monitoring points of the numerical sandbox, directly reflecting the non-Fickian phenomenon in the hierarchical flow system of the homogeneous aquifer.
Conclusions
The non-Fickian phenomenon of solute transport in the hierarchical groundwater flow systems of the sandbox aquifer is jointly affected by groundwater flow velocity, solute transport path, and rainfall infiltration intensity, with notable differences in the dominant influencing factors of aquifers at different depths. The non-Fickian phenomenon in the shallow aquifer is more significantly affected by groundwater flow velocity, while that in the deep aquifer is mainly controlled by the solute transport path, with a longer path leading to a more obvious non-Fickian tailing phenomenon. There is a significant negative correlation between rainfall infiltration intensity and the non-Fickian phenomenon in the deep aquifer, meaning the smaller the rainfall intensity, the more prominent the non-Fickian tailing phenomenon in the deep part, while rainfall infiltration intensity shows no obvious correlation with the non-Fickian phenomenon in the shallow aquifer. This study enriches the theoretical system of solute transport in hierarchical groundwater flow systems of homogeneous aquifers, and provides important scientific reference for the practical evaluation and remediation of groundwater pollution in nested basins.
- homogeneous aquifer /
- hierarchical groundwater flow systems /
- rainfall infiltration intensity /
- solute transport /
- non-Fickian phenomenon /
- sandbox experiment

HTML全文

图 1 砂箱装置示意图

Figure 1. Schematic diagram of sandbox device

下载: 全尺寸图片幻灯片

图 2 数值模拟砂箱内部浓度监测点位置图

Figure 2. Location of concentration monitoring points inside numerical sandbox

下载: 全尺寸图片幻灯片

图 3 不同水流系统模式的溶质运移等时点图(a1～c1)和流速分布(a2～c2)图

Figure 3. Solute transport isotime point diagrams (a1−c1) and flow velocity distribution diagrams (a2−c2) under different groundwater flow system patterns

下载: 全尺寸图片幻灯片

图 4 不同水流系统模式的排泄点处单位浓度增量随时间变化散点图（t_0.5r. 浓度上升至1/2峰值浓度的时间；下同）

Figure 4. Scatter plots of unit concentration increment over time at discharge points under different groundwater flow system patterns

下载: 全尺寸图片幻灯片

图 5 同一水流模式排泄点处穿透曲线图（t_p. 浓度达到稳定的时间；C_max. 浓度最大值；下同）

Figure 5. Breakthrough curves at discharge points under same groundwater flow pattern

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图 6 模拟水位和实测水位拟合散点图

Figure 6. Scatter plots of fitting between simulated and observed water levels

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图 7 排泄点处溶质模拟浓度和实测浓度拟合曲线图

Figure 7. Fitting curves of simulated and observed solute concentrations at discharge points

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图 8 Case C（局部+中间+区域三级水流系统）流速分布(a)及稳定浓度分布(b)图

Figure 8. Flow velocity distribution (a) and stable concentration distribution (b) of local + intermediate + regional three-level groundwater flow system in Case C

下载: 全尺寸图片幻灯片

图 9 Case C（局部+中间+区域三级水流）内部监测点溶质运移穿透曲线图

Figure 9. Solute transport breakthrough curves at internal monitoring points of local + intermediate + regional three-level groundwater flow system in Case C

下载: 全尺寸图片幻灯片

图 10 砂箱内部9个浓度监测点的lg(t_p-t_0.5r)与降雨强度的相关散点图

Figure 10. Scatter plots of correlation between lg(t_p-t_0.5r) and rainfall intensity of nine concentration monitoring points inside sandbox

下载: 全尺寸图片幻灯片

表 1 砂箱溶质运移实验方案

Table 1. Experimental cases for solute transport in sandbox

方案	水流模式	降雨强度/(m·d⁻¹)			上游降雨盐水浓度/(mg·L⁻¹)
方案	水流模式	上游	中游	下游	上游降雨盐水浓度/(mg·L⁻¹)
Case A（R）	单一区域水流系统	1.102	1.046	1.048	1704
Case B（L+R）	局部+区域2级水流系统	3.274	3.656	3.362	1699
Case C（L+I+R）	局部+中间+区域3级水流系统	8.323	4.353	8.384	1688

下载: 导出CSV

参考文献(42)

[1]	TÓTH J. Cross-formational gravity-flow of groundwater: A mechanism of the transport and accumulation of petroleum (The generalized hydraulic theory of petroleum migration)[J]. Problems of Petroleum Migration, 1980, 10: 121-128.
[2]	TÓTH J. A theoretical analysis of groundwater flow in small drainage basins[J]. Journal of Geophysical Research, 1963, 68(16): 4795-4812.
[3]	梁杏, 张人权, 靳孟贵. 地下水流系统: 理论应用调查[M]. 北京: 地质出版社, 2015. LIANG X, ZHANG R Q, JIN M G. Grounduater flow systems: Theory, application, and regulation: Theory, application and regulation[M]. Beijing: Geological Publishing House, 2015.
[4]	ZHAO K Y, JIANG X W, WANG X S, et al. An analytical study on nested flow systems in a Tóthian Basin with a periodically changing water table[J]. Journal of Hydrology, 2018, 556: 813-823. doi: 10.1016/j.jhydrol.2016.09.051
[5]	韩汝杰, 李静, 李晓波. 莱州湾滨海平原沉积环境对古卤水盐分迁移能力的影响[J]. 地质科技通报, 2024, 43(5): 259-271. doi: 10.19509/j.cnki.dzkq.tb20230307 HAN R J, LI J, LI X B. Influence of the sedimentary environment on the salt migration ability of ancient brine in the coastal plain of Laizhou Bay[J]. Bulletin of Geological Science and Technology, 2024, 43(5): 259-271. (in Chinese with English abstract doi: 10.19509/j.cnki.dzkq.tb20230307
[6]	DAI X, XIE Y Q, SIMMONS C T, et al. Understanding topography-driven groundwater flow using fully-coupled surface-water and groundwater modeling[J]. Journal of Hydrology, 2021, 594: 125950. doi: 10.1016/j.jhydrol.2020.125950
[7]	SHI J X, JIANG X W, ZHANG Z Y, et al. Interaction of focused recharge and deep groundwater discharge near a wetland: A study in the Ordos Basin, China[J]. Journal of Hydrology, 2023, 626: 130361. doi: 10.1016/j.jhydrol.2023.130361
[8]	SUN R L, XIAO W, JIANG L Q, et al. Laboratory studies of the temporal evolution process of the riparian groundwater flow system related to rainfall[J]. Journal of Hydrology, 2023, 625: 130086. doi: 10.1016/j.jhydrol.2023.130086
[9]	张人权, 梁杏, 靳孟贵, 等. 当代水文地质学发展趋势与对策[J]. 水文地质工程地质, 2005, 32(1): 51-56. doi: 10.3969/j.issn.1672-562X.2018.01.036 ZHANG R Q, LIANG X, JIN M G, et al. The trends in contemporary hydrogeology[J]. Hydrogeology and Engineering Geology, 2005, 32(1): 51-56. (in Chinese with English abstract doi: 10.3969/j.issn.1672-562X.2018.01.036
[10]	党婧萱, 田涛, 李闯, 等. 基于机器学习与多源数据融合的江苏省潜水位空间分布估计[J]. 地质科技通报, 2026, 45(2): 351-360. doi: 10.19509/j.cnki.dzkq.tb20240228 DANG JINGXUAN, TIAN TAO, LI CHUANG, et al. Exploration of groundwater table spatial estimation in Jiangsu Province based on machine learning and multi-source data fusion[J]. Bulletin of Geological Science and Technology, 2026, 45(2): 351-360. (in Chinese with English abstract doi: 10.19509/j.cnki.dzkq.tb20240228
[11]	张萧琅, 焦赳赳. 非稳态地下水流系统响应降雨变化的数值模型研究[J]. 地质科技通报, 2023, 42(4): 154-161. ZHANG X L, JIAO J J. Numerical modelling study on non-steady-state groundwater flow systems in response to changing rainfall[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 154-161. (in Chinese with English abstract
[12]	梁杏, 牛宏, 张人权, 等. 盆地地下水流模式及其转化与控制因素[J]. 地球科学, 2012, 37(2): 269-275. doi: 10.3799/dqkx.2012.028 LIANG X, NIU H, ZHANG R Q, et al. Basinal groundwater flow patterns and their transformation and dominant factors[J]. Earth Science, 2012, 37(2): 269-275. (in Chinese with English abstract doi: 10.3799/dqkx.2012.028
[13]	ZHANG X L, LI H L, JIAO J J, et al. Fractal behaviors of hydraulic head and surface runoff of the nested groundwater flow systems in response to rainfall fluctuations[J]. Geophysical Research Letters, 2022, 49(2): e2021GL093784. doi: 10.1029/2021GL093784
[14]	JIANG X W, WANG X S, WAN L, et al. An analytical study on stagnation points in nested flow systems in basins with depth-decaying hydraulic conductivity[J]. Water Resources Research, 2011, 47(1): 2010WR009346. doi: 10.1029/2010WR009346
[15]	LIANG X, LIU Y, JIN M G, et al. Direct observation of complex Tóthian groundwater flow systems in the laboratory[J]. Hydrological Processes, 2010, 24(24): 3568-3573. doi: 10.1002/hyp.7758
[16]	GUPTA I, WILSON A M, ROSTRON B J. Groundwater age, brine migration, and large-scale solute transport in the Alberta Basin, Canada[J]. Geofluids, 2015, 15(4): 608-620.
[17]	ZHANG X L, JIAO J J, LI H L, et al. Effects of downward intrusion of saline water on nested groundwater flow systems[J]. Water Resources Research, 2020, 56(10): e2020WR028377. doi: 10.1029/2020WR028377
[18]	NIU H, WANG J Z, NI S N, et al. Laboratory observations of solute transport in groundwater basins[J]. Journal of Cleaner Production, 2023, 423: 138832. doi: 10.1016/j.jclepro.2023.138832
[19]	黄康乐. 多孔介质水动力弥散尺度效应研究: 现状与展望[J]. 水文地质工程地质., 1991, 18(3): 25-26. doi: 10.16030/j.cnki.issn.1000-3665.1991.04.011 HUANG K L. Study on the hydrodynamic dispersion scale effect of porous media: Current status and prospects[J]. Hydrogeology and Engineering Geology, 1991, 18(3): 25-26 (in Chinese with English abstract doi: 10.16030/j.cnki.issn.1000-3665.1991.04.011
[20]	BERKOWITZ B, EMMANUEL S, SCHER H. Non-Fickian transport and multiple-rate mass transfer in porous media[J]. Water Resources Research, 2008, 44(3): 2007WR005906.
[21]	董贵明, 常大海, 田娟, 等. 弥散尺度效应的试验研究进展及展望[J]. 水文, 2017, 37(2): 8-13. doi: 10.3969/j.issn.1000-0852.2017.02.002 DONG G M, CHANG D H, TIAN J, et al. Research progress and prospects of dispersion scale effect test[J]. Journal of China Hydrology, 2017, 37(2): 8-13. (in Chinese with English abstract doi: 10.3969/j.issn.1000-0852.2017.02.002
[22]	宫玥, 张敏, 任宇, 等. 砂箱弥散试验尺寸效应及弥散度尺度效应[J]. 地球科学与环境学报, 2019, 41(6): 748-756. GONG Y, ZHANG M, REN Y, et al. Inherent size effect in sand-box dispersion experiments and scale effect of dispersivity[J]. Journal of Earch Sciences and Environment, 2019, 41(6): 748-756. (in Chinese with English abstract
[23]	BRADLEY J, SINGH K, WANG L C. Intrapore geometry and flow rate controls on the transition of non-fickian to fickian dispersion[J]. Water Resources Research, 2023, 59(1): e2022WR032833. doi: 10.1029/2022WR032833
[24]	XIONG Y W, HUANG G H, HUANG Q Z. Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk[J]. Journal of Contaminant Hydrology, 2006, 86(3/4): 163-175. doi: 10.1016/j.jconhyd.2006.03.001
[25]	SHARMA P K, ABGAZE T A. Solute transport through porous media using asymptotic dispersivity[J]. Sadhana, 2015, 40(5): 1595-1609. doi: 10.1007/s12046-015-0382-6
[26]	LI Y H, BIAN J M, WANG Q, et al. Experiment and simulation of non-reactive solute transport in porous media[J]. Groundwater, 2022, 60(3): 330-343. doi: 10.1111/gwat.13153
[27]	FAROUGHI S A, SOLTANMOHAMMADI R, DATTA P, et al. Physics-informed neural networks with periodic activation functions for solute transport in heterogeneous porous media[J]. Mathematics, 2024, 12(1): 63. doi: 10.3390/math12010063
[28]	JAISWAL S, CHOPRA M, DAS S. Numerical solution of two-dimensional solute transport system using operational matrices[J]. Transport in Porous Media, 2018, 122(1): 1-23. doi: 10.1007/s11242-017-0986-x
[29]	QIAN J Z, WANG Z K, GARRARD R M, et al. Non-invasive image processing method to map the spatiotemporal evolution of solute concentration in two-dimensional porous media[J]. Journal of Hydrodynamics, 2018, 30(4): 758-761. doi: 10.1007/s42241-018-0077-7
[30]	WANG L C, CARDENAS M B. Non-Fickian transport through two-dimensional rough fractures: Assessment and prediction[J]. Water Resources Research, 2014, 50(2): 871-884. doi: 10.1002/2013WR014459
[31]	WANG L C, CARDENAS M B, ZHOU J Q, et al. The complexity of nonlinear flow and non-fickian transport in fractures driven by three-dimensional recirculation zones[J]. Journal of Geophysical Research: Solid Earth, 2020, 125(9): e2020JB020028. doi: 10.1029/2020JB020028
[32]	刘咏, 张琪, 钱家忠, 等. 基于图像法的多孔介质双分子反应溶质运移模拟[J]. 地学前缘, 2022, 29(3): 248-255. doi: 10.13745/j.esf.sf.2022.1.28 LIU Y, ZHANG Q, QIAN J Z, et al. Simulation of bimolecular reactive solute transport in porous media via image analysis[J]. Earth Science Frontiers, 2022, 29(3): 248-255. (in Chinese with English abstract doi: 10.13745/j.esf.sf.2022.1.28
[33]	宋羿, 严小三, 骆乾坤, 等. 采用图像法实时监测二维多孔介质溶质运移实验与模拟研究[J]. 合肥工业大学学报(自然科学版), 2018, 41(12): 1690-1694. doi: 10.3969/j.issn.1003-5060.2018.12.019 SONG Y, YAN X S, LUO Q K, et al. Experimental and simulation study on real-time monitoring of solute transport in two-dimensional porous media using image method[J]. Journal of Hefei University of Technology (Natural Science), 2018, 41(12): 1690-1694. (in Chinese with English abstract doi: 10.3969/j.issn.1003-5060.2018.12.019
[34]	王泽坤, 严小三, 宋羿, 等. 含透镜体多孔介质中溶质二维运移实验与模拟研究[J]. 合肥工业大学学报(自然科学版), 2018, 41(7): 968-972. doi: 10.3969/j.issn.1003-5060.2018.07.019 WANG Z K, YAN X S, SONG Y, et al. Numerical simulation study on bimodal migration of heterogeneous radial solute anomaly in porous media[J]. Journal of Hefei University of Technology (Natural Science), 2018, 41(7): 968-972. (in Chinese with English abstract doi: 10.3969/j.issn.1003-5060.2018.07.019
[35]	郭芷琳, 马瑞, 张勇, 等. 地下水污染物在高度非均质介质中的迁移过程: 机理与数值模拟综述[J]. 中国科学: 地球科学, 2021, 51(11): 1817-1836. GUO Z L, MA R, ZHANG Y, et al. Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion[J]. Scientia Sinica (Terrae), 2021, 51(11): 1817-1836. (in Chinese with English abstract
[36]	SU D Y, XIE M L, MAYER K U, et al. Simulation of diffusive solute transport in heterogeneous porous media with dipping anisotropy[J]. Frontiers in Water, 2022, 4: 974145. doi: 10.3389/frwa.2022.974145
[37]	PEREZ L J, BEBIS G, MCKENNA S A, et al. Solute transport prediction in heterogeneous porous media using random walks and machine learning[J]. GEM - International Journal on Geomathematics, 2023, 14(1): 30. doi: 10.1007/s13137-023-00240-x
[38]	钱家忠, 王永媛, 刘雅静, 等. 分段非均质多孔介质中双分子反应性溶质运移实验与模拟研究[J]. 环境科学学报, 2023, 43(10): 123-132. QIAN J Z, WANG Y Y, LIU Y J, et al. Experimental and simulation study on bimolecular reactive solute transport in segmented heterogeneous porous media[J]. Acta Scientiae Circumstantiae, 2023, 43(10): 123-132. (in Chinese with English abstract
[39]	左孔辉, 李旭, 朱棋, 等. 非均质孔隙介质径向溶质双峰反常运移数值模拟研究[J]. 安全与环境工程, 2024, 31(3): 225-234. doi: 10.13578/j.cnki.issn.1671-1556.20230097 ZUO K H, LI X, ZHU Q, et al. Numerical simulation study on bimodal migration of heterogeneous radial solute anomaly in porous media[J]. Safety and Environmental Engineering, 2024, 31(3): 225-234. (in Chinese with English abstract doi: 10.13578/j.cnki.issn.1671-1556.20230097
[40]	王培源, 童曼, 张鹏. 地下水位波动驱动的沉积物充放电规律与机制[J]. 地质科技通报, 2026, 45(2): 240-248. doi: 10.19509/j.cnki.dzkq.tb20240788 WANG PEIYUAN, TONG MAN, ZHANG PENG. Patterns and mechanisms of sediment charging and discharging driven by groundwater level fluctuations[J]. Bulletin of Geological Science and Technology, 2026, 45(2): 240-248. (in Chinese with English abstract doi: 10.19509/j.cnki.dzkq.tb20240788
[41]	易磊, 漆继红, 许模, 等. 基于砂槽模型研究不同水流密度下盆地地下水流系统[J]. 水文地质工程地质, 2019, 46(3): 40-46. doi: 10.16030/j.cnki.issn.1000-3665.2019.03.06 YI L, QI J H, XU M, et al. A study of the characteristics of groundwater flow system of a basin under variable density condition based on a physical sand box model[J]. Hydrogeology & Engineering Geology, 2019, 46(3): 40-46. (in Chinese with English abstract doi: 10.16030/j.cnki.issn.1000-3665.2019.03.06
[42]	GELHAR L W, WELTY C, REHFELDT K R. A critical review of data on field-scale dispersion in aquifers[J]. Water Resources Research, 1992, 28(7): 1955-1974. doi: 10.1029/92WR00607