# Effect of Depth-Dependent Hydraulic Conductivity and Anisotropy on Transit Time Distributions

V.G. Rumynin, P.G. Leskova, L.N. Sindalovskiy, A.M. Nikulenkov

Research output

### Abstract

The paper presents exact closed-form analytical solutions describing a two-dimensional profile confined groundwater flow induced by areal recharge in a laterally bounded aquifer with anisotropic permeability, which decreases with depth. The mathematical formulation of the problem for a rectangular flow domain in terms of hydraulic head and stream function are free of the limitation of the Dupuit–Forchheimer assumption. Two different types of outflow boundary conditions associated with the aquifer discharge area, Dirichlet and Neumann, are explored. Analytical solutions with respect to stream function allow examining the distribution of recharge over depth (between contouring streamlines) for a variety of flow parameter combinations. The solutions are extended to allow the groundwater transit time distribution (TTD) to be calculated. It was found that the dependence of the transit time function on hydraulic conductivity anisotropy and depth-decay coefficients may exhibit non-monotonic behavior. The mathematical models introduced in the article are accompanied by computational simulations.
Original language English 124161 Journal of Hydrology 579 20 Sep 2019 https://doi.org/10.1016/j.jhydrol.2019.124161 Published - Dec 2019

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hydraulic conductivity
anisotropy
recharge
aquifer
groundwater flow
boundary condition
outflow
permeability
groundwater
simulation
distribution
effect
parameter

### Cite this

@article{d938bc4cb90948c49aa22a719d4e1fe6,
title = "Effect of Depth-Dependent Hydraulic Conductivity and Anisotropy on Transit Time Distributions",
abstract = "The paper presents exact closed-form analytical solutions describing a two-dimensional profile confined groundwater flow induced by areal recharge in a laterally bounded aquifer with anisotropic permeability, which decreases with depth. The mathematical formulation of the problem for a rectangular flow domain in terms of hydraulic head and stream function are free of the limitation of the Dupuit–Forchheimer assumption. Two different types of outflow boundary conditions associated with the aquifer discharge area, Dirichlet and Neumann, are explored. Analytical solutions with respect to stream function allow examining the distribution of recharge over depth (between contouring streamlines) for a variety of flow parameter combinations. The solutions are extended to allow the groundwater transit time distribution (TTD) to be calculated. It was found that the dependence of the transit time function on hydraulic conductivity anisotropy and depth-decay coefficients may exhibit non-monotonic behavior. The mathematical models introduced in the article are accompanied by computational simulations.",
author = "V.G. Rumynin and P.G. Leskova and L.N. Sindalovskiy and A.M. Nikulenkov",
year = "2019",
month = "12",
doi = "10.1016/j.jhydrol.2019.124161",
language = "English",
volume = "579",
journal = "Journal of Hydrology",
issn = "0022-1694",
publisher = "Elsevier",

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TY - JOUR

T1 - Effect of Depth-Dependent Hydraulic Conductivity and Anisotropy on Transit Time Distributions

AU - Rumynin, V.G.

AU - Leskova, P.G.

AU - Sindalovskiy, L.N.

AU - Nikulenkov, A.M.

PY - 2019/12

Y1 - 2019/12

N2 - The paper presents exact closed-form analytical solutions describing a two-dimensional profile confined groundwater flow induced by areal recharge in a laterally bounded aquifer with anisotropic permeability, which decreases with depth. The mathematical formulation of the problem for a rectangular flow domain in terms of hydraulic head and stream function are free of the limitation of the Dupuit–Forchheimer assumption. Two different types of outflow boundary conditions associated with the aquifer discharge area, Dirichlet and Neumann, are explored. Analytical solutions with respect to stream function allow examining the distribution of recharge over depth (between contouring streamlines) for a variety of flow parameter combinations. The solutions are extended to allow the groundwater transit time distribution (TTD) to be calculated. It was found that the dependence of the transit time function on hydraulic conductivity anisotropy and depth-decay coefficients may exhibit non-monotonic behavior. The mathematical models introduced in the article are accompanied by computational simulations.

AB - The paper presents exact closed-form analytical solutions describing a two-dimensional profile confined groundwater flow induced by areal recharge in a laterally bounded aquifer with anisotropic permeability, which decreases with depth. The mathematical formulation of the problem for a rectangular flow domain in terms of hydraulic head and stream function are free of the limitation of the Dupuit–Forchheimer assumption. Two different types of outflow boundary conditions associated with the aquifer discharge area, Dirichlet and Neumann, are explored. Analytical solutions with respect to stream function allow examining the distribution of recharge over depth (between contouring streamlines) for a variety of flow parameter combinations. The solutions are extended to allow the groundwater transit time distribution (TTD) to be calculated. It was found that the dependence of the transit time function on hydraulic conductivity anisotropy and depth-decay coefficients may exhibit non-monotonic behavior. The mathematical models introduced in the article are accompanied by computational simulations.

UR - https://www.sciencedirect.com/science/article/pii/S0022169419308960

U2 - 10.1016/j.jhydrol.2019.124161

DO - 10.1016/j.jhydrol.2019.124161

M3 - Article

VL - 579

JO - Journal of Hydrology

JF - Journal of Hydrology

SN - 0022-1694

M1 - 124161

ER -