Analytical model for reactive solute transport in a channel-matrix system
-
摘要: 【目的】裂隙介质精确地定量刻画及其溶质运移理论研究已经成为裂隙含水层地下水污染防治的关键。目前裂隙含水层通常被概化为水平裂隙，而忽视管道裂隙几何特征以及基质扩散对溶质运移的影响。【方法】基于此，建立单裂隙管道-基质系统的溶质运移模型，并利用Laplace变换以及数值逆变换获得模型的半解析解，同时通过COMSOL Multiphysics软件建立数值模型进行验证。定量分析水动力弥散系数、迟滞因子等参数对溶质运移规律的影响，并计算溶质质量扩散通量以及存储量来反映溶质运移的时空规律。【结果和结论】研究结果表明： （1）管道裂隙水动力弥散系数越大，穿透曲线早期浓度越高而所达到的峰值越低，且裂隙中溶质浓度随着迟滞因子增大而降低。（2）扩散通量峰值随着裂隙弥散系数的增加而减小，并通过分析不同位置的穿透曲线以及扩散通量的空间分布曲线可得反向扩散是导致穿透曲线产生明显拖尾现象的主要原因。（3）脉冲注入条件下，裂隙作为主要的存储空间，其存储总量表现出快速增加后不断降低的趋势，而基质中存储量表现出不断增加的过程。总之，通过理论模型计算分析表明在管道裂隙-基质系统中，基质存储与反向扩散过程对裂隙系统中溶质运移规律的影响不容忽视。Abstract: [Objective] The accurate quantitative characterization of fractured media and the theoretical research on solute transport in fractured media have become the key to the prevention and control of groundwater contamination in fractured aquifers. Currently, fractured aquifers are generalized to horizontal fractures, ignoring the geometric characteristics of the open parts of fractures, called channels, and the impacts of matrix diffusion on solute transport. [Methods] A model for solute transport in a single channel-matrix system was established, obtaining the semi-analytical solutions using Laplace transform and numerical inverse transforms. The COMSOL Multiphysics software was employed to construct a numerical model for verification. Furthermore, the impacts of parameters like hydrodynamic dispersion coefficient and retardation factor on the solute transport pattern were quantitatively analyzed, and the spatio-temporal patterns of solute transport were revealed by calculating the solute diffusion flux and storage. [Results and conclusions] The results indicate that a higher hydrodynamic dispersion coefficient of the channel was associated with a higher early solute concentration and a lower peak concentration in the breakthrough curves. Moreover, the solute concentration in the fracture decreased with an increase in the retardation factor. The peak diffusion flux decreased with an increase in the dispersion coefficient in the fracture. By analyzing the breakthrough curves at different positions and the spatial distribution curves of diffusion flux, this study posits that back diffusion is the main cause of the significant tailing of the breakthrough curves. Under the boundary condition of pulsed injection, the total amount of solute stored in the fracture—the primary storage space—rapidly increased and then gradually decreased, while that in the matrix increased. Overall, the calculation and analysis of the theoretical model necessitate emphasizing the impacts of the solute storage capacity of the matrix and back diffusion on the solute transport patterns in the channel-matrix system.
-
Keywords:
- solute transport /
- channel /
- back diffusion /
- storage in matrix /
- semi-analytical solution
-
-
[1] WANG Junnan，WANG Lichun，DAI Junyi. The coupling effects of the matrix thickness and Peclet number on the late time transport tailing in the fracture-matrix systems[J]. Journal of Hydrology，2023，616：128829.
[2] NERETNIEKS I. Solute transport in fractured rock：Applications to radionuclide waste repositories[M]//Flow and Contaminant Transport in Fractured Rock. Amsterdam：Elsevier，1993：39-127.
[3] 齐跃明，周沛，周来，等. 考虑采动效应的闭坑矿井水硫酸盐污染规律[J]. 煤田地质与勘探，2024，52(4)：89-100. QI Yueming，ZHOU Pei，ZHOU Lai，et al. Sulphate contamination in an abandoned coal mine in light of mining effects[J]. Coal Geology & Exploration，2024，52(4)：89-100.
[4] 张丝诺. 面向修复的裂隙岩溶含水层溶质运移模拟[D]. 北京：中国地质大学(北京)，2021. ZHANG Sinuo. Simulation of solute transport in fractured Karst aquifer for restoration[D]. Beijing：China University of Geosciences (Beijing)，2021.
[5] 陈歌. 鄂尔多斯盆地东缘矿井水深部转移存储机理研究[D]. 徐州：中国矿业大学，2020. CHEN Ge. Study on transfer and storage mechanism of mine water depth in the eastern margin of Ordos Basin[D]. Xuzhou：China University of Mining and Technology，2020. [6] GYLLING B，MORENO L，NERETNIEKS I. The channel network model—a tool for transport simulations in fractured media[J]. Groundwater，1999，37(3)：367-375.
[7] 黄鸿蓝, 宋健, 杨蕴, 等. 三维裂隙网络中典型重金属污染物反应运移数值模拟[J/OL]. 地球科学, 2022: 1-16[2024-06-15]. https://kns.cnki.net/kcms/detail/42.1874.P.20220413.1809.008.html" target="_blank"> https://kns.cnki.net/kcms/detail/42.1874.P.20220413.1809.008.html HUANG Honglan, SONG Jian, YANG Yun, et al. Reactive transport numerical modeling of typical heavy metal pollutants in three-dimensional fracture networks[J/OL]. Earth Science, 2022: 1-16[2024-06-05]. https://kns.cnki.net/kcms/detail/42.1874.P.20220413.1809.008.html" target="_blank"> https://kns.cnki.net/kcms/detail/42.1874.P.20220413.1809.008.html. [8] 王礼恒，李国敏，董艳辉. 裂隙介质水流与溶质运移数值模拟研究综述[J]. 水利水电科技进展，2013，33(4)：84-88. WANG Liheng，LI Guomin，DONG Yanhui. Review of numerical simulation of flow and solute transport in fractured media[J]. Advances in Science and Technology of Water Resources，2013，33(4)：84-88.
[9] 郑志成，刘咏，王沐，等. 平行大理石板裂隙污染物运移实验与连续时间随机游走模拟[J]. 合肥工业大学学报(自然科学版)，2019，42(5)：677-682. ZHENG Zhicheng，LIU Yong，WANG Mu，et al. Experiments and model on contaminant transport in a single marble parallel plate fracture using continuous time random walk[J]. Journal of Hefei University of Technology (Natural Science)，2019，42(5)：677-682.
[10] 余成，雷文武. 粗糙单裂隙溶质运移优先通道的模拟研究[J]. 重庆交通大学学报(自然科学版)，2015，34(4)：91-94. YU Cheng，LEI Wenwu. Numerical modeling of preferential flow and transport channel between rough-walled fractures[J]. Journal of Chongqing Jiaotong University (Natural Science)，2015，34(4)：91-94.
[11] 严小三，钱家忠，陈冰宇，等. 大理石平板裂隙水运移实验与模拟研究[J]. 水动力学研究与进展A辑，2014，29(5)：524-529. YAN Xiaosan，QIAN Jiazhong，CHEN Bingyu，et al. Experimental and simulated study of water flow and transport in a single fracture of marble parallel plates[J]. Chinese Journal of Hydrodynamics，2014，29(5)：524-529.
[12] 朱汝雄. 裂隙岩体溶质运移模型实验及运移规律初步研究[D]. 南京：河海大学，2004. ZHU Ruxiong. Model experiment and preliminary study on solute transport law in fractured rock mass[D]. Nanjing：Hohai University，2004. [13] 朱永惠. 裂隙-基质系统溶质运移规律解析与数值模拟研究[D]. 武汉：中国地质大学，2020. ZHU Yonghui. Analysis and numerical simulation of solute transport law in fracture-matrix system[D]. Wuhan：China University of Geosciences，2020. [14] 黄勇，周志芳. 多尺度裂隙介质中溶质运移研究进展[J]. 河海大学学报(自然科学版)，2005，33(5)：500-504. HUANG Yong，ZHOU Zhifang. Advances in research on solute transport in multi-scale fractured media[J]. Journal of Hohai University (Natural Sciences)，2005，33(5)：500-504.
[15] CARDENAS M B，SLOTTKE D T，KETCHAM R A，et al. Navier-Stokes flow and transport simulations using real fractures shows heavy tailing due to eddies[J]. Geophysical Research Letters，2007，34(14)：176-192.
[16] MAHMOUDZADEH B，LIU Longcheng，MORENO L，et al. Solute transport in a single fracture involving an arbitrary length decay chain with rock matrix comprising different geological layers[J]. Journal of Contaminant Hydrology，2014，164：59-71.
[17] ZHU Yonghui，ZHAN Hongbin，JIN Menggui. Analytical solutions of solute transport in a fracture-matrix system with different reaction rates for fracture and matrix[J]. Journal of Hydrology，2016，539：447-456.
[18] SHARIFI HADDAD A，HASSANZADEH H，ABEDI J. Advective-diffusive mass transfer in fractured porous media with variable rock matrix block size[J]. Journal of Contaminant Hydrology，2012，133：94-107.
[19] MAHMOUDZADEH B，LIU Longcheng，MORENO L，et al. Solute transport through fractured rock：Radial diffusion into the rock matrix with several geological layers for an arbitrary length decay chain[J]. Journal of Hydrology，2016，536：133-146.
[20] NERETNIEKS I. Radionuclide transport in channel networks with radial diffusion in the porous rock matrix[J]. Nuclear Technology，2023，209(4)：604-621.
[21] KLEPIKOVA M V，LE BORGNE T，BOUR O，et al. Heat as a tracer of transport processes in fractured media：Theory and field assessment from multi-scale thermal push-pull tracer tests[J]. Water Resources Research，2016，52(7)：5442-5457.
[22] CIHAN A，TYNER J S. 2-D radial analytical solutions for solute transport in a dual-porosity medium[J]. Water Resources Research，2011，47(4)：W04507.
[23] ZHOU Renjie，ZHAN Hongbin. Reactive solute transport in an asymmetrical fracture-rock matrix system[J]. Advances in Water Resources，2018，112：224-234.
[24] VAN GENUCHTEN M T，TANG D H，GUENNELON R. Some exact solutions for solute transport through soils containing large cylindrical macropores[J]. Water Resources Research，1984，20(3)：335-346.
[25] RAHMAN M M，LIEDL R，GRATHWOHL P. Sorption kinetics during macropore transport of organic contaminants in soils：Laboratory experiments and analytical modeling[J]. Water Resources Research，2004，40(1)：W01503.
[26] DE HOOG F R，KNIGHT J H，STOKES A N. An improved method for numerical inversion of Laplace transforms[J]. SIAM Journal on Scientific and Statistical Computing，1982，3(3)：357-366.
[27] SHARIFI HADDAD A，HASSANZADEH H，ABEDI J，et al. Lumped mass transfer coefficient for divergent radial solute transport in fractured aquifers[J]. Journal of Hydrology，2013，495：113-120.
[28] TANG D H，FRIND E O，SUDICKY E A. Contaminant transport in fractured porous media：Analytical solution for a single fracture[J]. Water Resources Research，1981，17(3)：555-564.
计量
- 文章访问数: 32
- HTML全文浏览量: 3
- PDF下载量: 4
下载:
