Analytical solution for a radial advection-dispersion equation including both mechanical dispersion and molecular diffusion for a steady-state flow field in a horizontal aquifer caused by a constant rate injection from a well

IF 0.6 Q4 WATER RESOURCES Hydrological Research Letters Pub Date : 2018-01-01 DOI:10.3178/HRL.12.23

M. Aichi, Kento Akitaya

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引用次数: 4

Abstract

This study presents the analytical solution for a radial advection-dispersion equation for a steady-state flow field in a horizontal aquifer caused by a constant rate injection from a well, including the mechanical dispersion and molecular diffusion terms in addition to the retardation and first-order attenuation under a Robin-type boundary condition at the well. The derived analytical solutions were compared with finely-meshed finite difference solutions in steady-state and periodic steady-state problems with typical parameters. The results suggest that the analytical solution is exactly derived and ready for application. Comparisons with analytical solutions ignoring molecular diffusion suggest that the derived analytical solution should be used when the product of the decay constant and the retardation factor and the ratio of injection rate to diffusion coefficient are small. Comparisons with analytical solutions with Dirichlet-type boundary conditions confirmed that Robintype boundary conditions should be used to exactly evaluate the concentration profile.

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水平井等速注入引起的稳态流场径向平流-扩散方程的解析解，包括机械扩散和分子扩散

本文给出了水平井中恒定速率注入引起的稳态流场径向平流-弥散方程的解析解，包括机械弥散项和分子弥散项，以及井处robin型边界条件下的延迟和一阶衰减。将导出的解析解与具有典型参数的稳态和周期稳态问题的细网格有限差分解进行了比较。结果表明，解析解推导准确，可供实际应用。与忽略分子扩散的解析解的比较表明，当衰减常数与延迟系数的乘积和注入速率与扩散系数之比较小时，应采用导出的解析解。与dirichlet型边界条件下的解析解比较，证实了Robintype边界条件可以准确地评价浓度分布。

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来源期刊

Hydrological Research Letters WATER RESOURCES-

CiteScore

1.90

自引率

18.20%

发文量

审稿时长

10 weeks

期刊介绍： Hydrological Research Letters (HRL) is an international and trans-disciplinary electronic online journal published jointly by Japan Society of Hydrology and Water Resources (JSHWR), Japanese Association of Groundwater Hydrology (JAGH), Japanese Association of Hydrological Sciences (JAHS), and Japanese Society of Physical Hydrology (JSPH), aiming at rapid exchange and outgoing of information in these fields. The purpose is to disseminate original research findings and develop debates on a wide range of investigations on hydrology and water resources to researchers, students and the public. It also publishes reviews of various fields on hydrology and water resources and other information of interest to scientists to encourage communication and utilization of the published results. The editors welcome contributions from authors throughout the world. The decision on acceptance of a submitted manuscript is made by the journal editors on the basis of suitability of subject matter to the scope of the journal, originality of the contribution, potential impacts on societies and scientific merit. Manuscripts submitted to HRL may cover all aspects of hydrology and water resources, including research on physical and biological sciences, engineering, and social and political sciences from the aspects of hydrology and water resources.