留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

井筒混合效应和表皮效应对注水井溶质径向弥散的影响

马科 马冲 詹红兵 刘洋

马科, 马冲, 詹红兵, 刘洋. 井筒混合效应和表皮效应对注水井溶质径向弥散的影响[J]. 地质科技通报, 2023, 42(4): 130-137. doi: 10.19509/j.cnki.dzkq.tb20220616
引用本文: 马科, 马冲, 詹红兵, 刘洋. 井筒混合效应和表皮效应对注水井溶质径向弥散的影响[J]. 地质科技通报, 2023, 42(4): 130-137. doi: 10.19509/j.cnki.dzkq.tb20220616
Ma Ke, Ma Chong, Zhan Hongbin, Liu Yang. Mixing effect and skin effect on radical solute transport around an injection well[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 130-137. doi: 10.19509/j.cnki.dzkq.tb20220616
Citation: Ma Ke, Ma Chong, Zhan Hongbin, Liu Yang. Mixing effect and skin effect on radical solute transport around an injection well[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 130-137. doi: 10.19509/j.cnki.dzkq.tb20220616

井筒混合效应和表皮效应对注水井溶质径向弥散的影响

doi: 10.19509/j.cnki.dzkq.tb20220616
基金项目: 

国家自然科学基金项目 42272296

详细信息
    作者简介:

    马科(1979—), 男, 副教授, 主要从事多场物理耦合理论方面的研究工作。E-mail: 263205863@qq.com

    通讯作者:

    詹红兵(1966—), 男, 教授, 主要从事溶质运移、地热、地下水方面的研究工作。E-mail: zhan@geos.tamu.edu

  • 中图分类号: P641

Mixing effect and skin effect on radical solute transport around an injection well

  • 摘要:

    注水井理论模型研究一直是水文地质学领域的热点问题。充分考虑含水层的非均质性,利用两区MIM(Mobile-Immobile)对流扩散模型来描述溶质在含水层中的运移过程,同时考虑表皮效应和井筒混合效应,建立一种描述注入井附近含水层溶质径向运移的动力学模型。并采用Laplace变换、Stehfest数值逆变换得到了该动力学模型的半解析解。然后改变表皮区的有效孔隙度和径向弥散度以及井筒的半径,来分析固定观测点的溶质穿透曲线和溶质浓度分布曲线的变化规律。研究表明,井筒混合效应和表皮效应对穿透曲线、溶质径向运移过程和影响区域均有着非常显著的影响。在考虑井筒混合效应时,井筒半径越大,井筒效应越明显。而表皮区域有效孔隙度越大,溶质的迁移扩展速率越小;径向弥散度越大,观测点的溶质浓度曲线越陡峭,表明该点的溶质浓度变化速率较快,且能更早达到稳定值。与前人研究相比,本研究模型能更好地描述注水井中的溶质径向弥散过程。

     

  • 图 1  注水井溶质径向迁移概念模型

    B为承压层厚度;Q为注入量;γw为注入井半径;r1为表皮区+注入井半径;r为离井筒中心的径向距离

    Figure 1.  Conceptual model of radial solute transport in a single push well

    图 2  不同观测点AB的穿透曲线半解析解和数值解对比结果

    Figure 2.  Comparison of the semianalytical solution and numerical solution of BTCs at observation points A and B

    图 3  不同表皮区有效孔隙度(θ1m)时观测点A的穿透曲线(a)及溶质浓度径向分布曲线(b)

    Figure 3.  Breakthrough curves of observation point A (a) and concentration distribution curves (b) for different effective porosities (θ1m) in the skin zone

    图 4  不同表皮区径向弥散度(α1)时观测点A的穿透曲线(a)及溶质浓度径向分布曲线(b)

    Figure 4.  Breakthrough curves of observation point A (a), and concentration distribution curves (b) for different radical dispersivities (α1) in the skin zone

    图 5  不同注入井半径(rw)时观测点A的穿透曲线

    Figure 5.  Breakthrough curves of observation point A for different wellbore radii (rw)

    图 6  t=5 h时(a)和t=30 h时(b)不同注入井半径(rw)的溶质浓度径向分布曲线

    Figure 6.  Concentration distribution curves for different well radii (rw) of wellbore when t=5 h (a) and t=30 h (b)

    图 7  观测点A的BTCs半解析解与文献[25]研究结果对比图

    Figure 7.  Comparison of the semianalytic solution of this paper with the results of reference [25] at observation point A

    表  1  无量纲参数定义

    Table  1.   Definitions of dimensionless variables

    $ r_{\mathrm{D}}=\frac{r}{\alpha_2}$ $ t_{\mathrm{D}}=\frac{Q t}{2 \pi B \alpha_2^2 \theta_{2 \mathrm{~m}} R_{2 \mathrm{~m}}}$
    $ C_{1 \mathrm{mD}}=\frac{C_{1 \mathrm{~m}}}{C_0}$ $ C_{1 \mathrm{imD}}=\frac{C_{1 \mathrm{im}}}{C_0}$
    $ C_{2 \mathrm{mD}}=\frac{C_{2 \mathrm{mD}}}{C_0}$ $ C_{2 \mathrm{imD}}=\frac{C_{2 \mathrm{im}}}{C_0}$
    $ \lambda_{1 \mathrm{mD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{1 \mathrm{~m}}$ $ \lambda_{2 \mathrm{mD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{2 \mathrm{~m}}$
    $ \beta_2=\frac{\theta_{2 \mathrm{im}}}{\theta_{2 \mathrm{~m}}}$ $ \beta_1=\frac{\theta_{1 \mathrm{im}}}{\theta_{1 \mathrm{~m}}}$
    $ \varepsilon_1=\frac{R_{1 \mathrm{~m}}}{R_{2 \mathrm{~m}}}$ $ \varepsilon_2=\frac{R_{1 \mathrm{im}}}{R_{2 \mathrm{~m}}}$
    $ \varepsilon_3=\frac{R_{2 \mathrm{im}}}{R_{2 \mathrm{~m}}}$ $ \beta=\frac{V_{\mathrm{w}}}{2 \pi B \theta_{2 \mathrm{~m}} R_{2 \mathrm{~m}} \alpha_2^2}$
    $ k_1=\frac{\alpha_1}{\alpha_2}$ $ k_2=\frac{\theta_{2 \mathrm{~m}}}{\theta_{1 \mathrm{~m}}}$
    $ \omega_{1 \mathrm{D}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q \theta_{1 \mathrm{im}}} \omega_1$ $ \omega_{2 \mathrm{D}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q \theta_{2 \mathrm{im}}} \omega_2$
    $ \lambda_{1 \mathrm{imD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{1 \mathrm{im}}$ $ \lambda_{2 \mathrm{imD}}=\frac{2 \pi B \theta_{2 \mathrm{~m}} \alpha_2^2}{Q} \lambda_{2 \mathrm{im}}$
    下载: 导出CSV

    表  2  模型参数默认取值

    Table  2.   Default parameter values used in this study

    参数 参数
    Q/(m3·h-1) 2.5 B/m 5
    rw/m 0.1 r1/m 0.8
    θ1m 0.15 θ2m 0.15
    θ1im 0.1 θ2im 0.1
    ω1/(1·h-1) 0.05 ω2/(1·h-1) 0.05
    α1/m 0.5 α2/m 0.5
    下载: 导出CSV
  • [1] Wang Y, Zheng C, Ma R. Safe and sustainable groundwater supply in China[J]. Hydrogeology Journal, 2018, 26(5): 1301-1324. doi: 10.1007/s10040-018-1795-1
    [2] 王攀, 靳孟贵, 路东臣, 等. 永城市浅层地下水污染分布特征及来源识别[J]. 地质科技通报, 2022, 41(1): 260-268. doi: 10.19509/j.cnki.dzkq.2021.0136

    Wang P, Jin M G, Lu D C, et al. Distribution characteristics and source idenfication of shallow groundwater pollution in Yongcheng City[J]. Bulletin of Geological Science and Technology, 2022, 41(1): 260-268(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2021.0136
    [3] 肖骢. 变渗透性黏性土弱透水层中砷的迁移转化机制: 以江汉平原为例[D]. 武汉: 中国地质大学(武汉), 2019.

    Xiao C. Migration and transformation mechanism of arsenic in variable-permeability clayey aquitard at Jianghan Plain[D]. Wuhan: China University of Geosciences(Wuhan), 2019(in chinese with English abstract).
    [4] 江欣悦, 李静, 郭林, 等. 豫北平原浅层地下水化学特征与成因机制[J]. 地质科技通报, 2021, 40(5): 290-300. doi: 10.19509/j.cnki.dzkq.2021.0511

    Jiang X Y, Li J, Guo L, et al. Chemical characteristics and formation mechanism of shallow groundwater in the northern Henan Plain[J]. Bulletin of Geological Science and Technology, 2021, 40(5): 290-300(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2021.0511
    [5] Hebig K H, Zeilfelder S, Ito N, et al. Study of the effects of the chaser in push-pull tracer tests by using temporal moment analysis[J]. Geothermics, 2015, 54: 43-53. doi: 10.1016/j.geothermics.2014.11.004
    [6] 文章, 李旭. 考虑表皮效应的径向溶质迁移模型以及半解析解[J]. 地质科技通报, 2020, 39(1): 60-66. doi: 10.19509/j.cnki.dzkq.2020.0107

    Wen Z, Li X. Semi-analytical solution for radial solute transport model with skin effect[J]. Bulletin of Geological Science and Technology, 2020, 39(1): 60-66(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2020.0107
    [7] Yeh H D, Chen Y J. Determination of skin and aquifer parameters for a slug test with wellbore-skin effect[J]. Journal of Hydrology, 2007, 342(3/4): 283-294.
    [8] 肖勋, 施文光, 王全荣. 井内混合效应与尺度效应对注入井附近溶质径向弥散过程的影响[J]. 地球科学, 2020, 45(4): 1439-1446. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202004025.htm

    Xiao X, Shi W G, Wang Q R. Effect of mixing effect and scale-dependent dispersion for radial solute transport near the injection well[J]. Earth Science, 2020, 45(4): 1439-1446(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202004025.htm
    [9] Huang J, Christ J A, Goltz M N. Analytical solutions for efficient interpretation of single-well push-pull tracer tests[J]. Water Resources Research, 2010, 46(8): LU08538.
    [10] Wang Q, Shi W, Zhan H, et al. Models of single-well push-pull test with mixing effect in the wellbore[J]. Water Resources Research, 2018, 54(12): 10155-160171.
    [11] De Hoog F R, Knight J, Stokes A. An improved method for numerical inversion of Laplace transforms[J]. SIAM Journal on Scientific and Statistical Computing, 1982, 3(3): 357-366. doi: 10.1137/0903022
    [12] Schroth M H, Istok J D. Approximate solution for solute transport during spherical-flow push-pull tests[J]. Groundwater, 2005, 43(2): 280-284. doi: 10.1111/j.1745-6584.2005.0002.x
    [13] Chen K, Zhan H, Yang Q. Fractional models simulating non-Fickian behavior in four-stage single-well push-pull tests[J]. Water Resources Research, 2017, 53(11): 9528-9545. doi: 10.1002/2017WR021411
    [14] Leij F J, Toride N, Field M S, et al. Solute transport in dual-permeability porous media[J]. Water Resources Research, 2012, 48(4): W04523.
    [15] 王宝辉, 董荟思, 徐兆明, 等. 多孔介质中污染物溶质迁移模型研究进展[J]. 化工进展, 2010, 29(7): 1338-1368. https://www.cnki.com.cn/Article/CJFDTOTAL-HGJZ201007033.htm

    Wang B H, Dong H S, Xu Z M, et al. Research development in migration model of pollutant solute in porous media[J]. Chemical Industry and Engineering Progress, 2010, 29(7): 1338-1368(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-HGJZ201007033.htm
    [16] Van Genuchten M T, Wierenga P. Mass transfer studies in sorbing porous media I: Analytical solutions[J]. Soil Science Society of America Journal, 1976, 40(4): 473-480.
    [17] 高光耀, 冯绍元, 黄冠华. 饱和非均质土壤中溶质大尺度运移的两区模型模拟[J]. 土壤学报, 2008, 45(3): 398-404. https://www.cnki.com.cn/Article/CJFDTOTAL-TRXB200803002.htm

    Gao G Y, Feng S Y, Huang G H. Simulation of solute transport at large scale in saturated heterogeneous soil with two-region model[J]. Acta Pedologica Sinica, 2008, 45(3): 398-404(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-TRXB200803002.htm
    [18] Gao G, Zhan H, Feng S, et al. A new mobile-immobile model for reactive solute transport with scale-dependent dispersion[J]. Water Resources Research, 2010, 46(8): W08533.
    [19] Zhou R, Zhan H, Chen K. Reactive solute transport in a filled single fracture-matrix system under unilateral and radial flows[J]. Advances in Water Resources, 2017, 104: 183-194.
    [20] Li N, Wen Z, Zhan H, et al. The single-well test dilemma: The skin effect and variable-rate pumping perspective[J]. Hydrogeology Journal, 2018, 26(7): 2521-2529.
    [21] Chen Y J, Yeh H D, Chang K J. A mathematical solution and analysis of contaminant transport in a radial two-zone confined aquifer[J]. Journal of Contaminant Hydrology, 2012, 138: 75-82.
    [22] 高光耀, 冯绍元, 马英, 等. 考虑弥散尺度效应的一维反应性溶质运移两区模型及应用[J]. 水利学报, 2011, 42(6): 631-640. https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB201106004.htm

    Gao G Y, Feng S Y, Ma Y, et al. One-dimensional two-region model for reactive solute transport with scale-dependent dispersion and its application[J]. Journal of Hydraulic Engineering, 2011, 42(6): 631-640(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB201106004.htm
    [23] Akter A. Rainwater harvesting: Building a water smart city[M]. Cham, Switzerland: Springer, 2022.
    [24] Wang Q, Wang J, Zhan H, et al. New model of reactive transport in a single-well push-pull test with aquitard effect and wellbore storage[J]. Hydrology and Earth System Sciences, 2020, 24(8): 3983-4000.
    [25] Li X, Wen Z, Zhu Q, et al. Numerical simulation of single-well push-pull tests in a radial two-zone confined aquifer[J]. Hydrogeology Journal, 2019, 27(7): 2645-2658.
  • 加载中
图(7) / 表(2)
计量
  • 文章访问数:  484
  • PDF下载量:  25
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-11-02
  • 录用日期:  2023-04-13
  • 修回日期:  2023-04-13

目录

    /

    返回文章
    返回