Analytical solution for estimating transient vertical groundwater flux from temperature-depth profiles

Lin, Ying‐Fan; Chang, Chia‐Hao; Tsai, Jui-Pin

doi:10.1016/j.jhydrol.2022.127920

Cited by 10 publications

(9 citation statements)

References 53 publications

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“…A differential importance measure (DIM) method has also been proposed to classify the importance of the model parameters (Borgonovo & Apostolakis, 2001; Lin et al., 2022; Lin & Yeh, 2020b):

{\text{DIM}}_{k}\left(r,t;{P}_{k}\right)=\frac{\vert {X}_{k}\left(r,t;{P}_{k}\right)\vert }{\sum \vert {X}_{k}\left(r,t;{P}_{k}\right)\vert }

where DIM ∈ [0, 1]. Equation quantifies the contribution of a parameter's sensitivity to the sensitivities of all parameters in response to a phasor change.…”

Section: Methodsmentioning

confidence: 99%

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Advanced Analytical Model for Interpreting Oscillatory Pumping Tests With Wellbore Skin and Rate‐Dependent Skin Effects

Mahdavi,

Kurylyk,

Lin

2024

Water Resources Research

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Oscillatory pumping tests presents a potential advancement in aquifer testing as they minimize hydraulic perturbations and result in no net water abstraction or injection. However, aquifer property estimates can be less accurate if they are compromised by well head losses during the pumping test. Currently, oscillatory pumping test models ignore these losses. The objective of this study is to develop and evaluate an analytical solution that can interpret oscillatory pumping test data affected by rate‐dependent skin losses. Accordingly, the sensitivity of the drawdown response to small variations in aquifer and well parameters was analyzed. In addition, a previous field aquifer test was analyzed to evaluate the feasibility of the solution for aquifer parameter estimation. The results indicate that neglecting the rate‐dependent skin effect can lead to substantial errors in the determination of aquifer parameters such as transmissivity and storativity. Additionally, the proposed solution effectively reproduces the sharp groundwater level peaks observed in field data, whereas the solution that does not consider the rate‐dependent skin effect greatly underestimates the peak values.

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“…A differential importance measure (DIM) method has also been proposed to classify the importance of the model parameters (Borgonovo & Apostolakis, 2001; Lin et al., 2022; Lin & Yeh, 2020b):

{\text{DIM}}_{k}\left(r,t;{P}_{k}\right)=\frac{\vert {X}_{k}\left(r,t;{P}_{k}\right)\vert }{\sum \vert {X}_{k}\left(r,t;{P}_{k}\right)\vert }

where DIM ∈ [0, 1]. Equation quantifies the contribution of a parameter's sensitivity to the sensitivities of all parameters in response to a phasor change.…”

Section: Methodsmentioning

confidence: 99%

“…A differential importance measure (DIM) method has also been proposed to classify the importance of the model parameters (Borgonovo & Apostolakis, 2001;Lin et al, 2022;Lin & Yeh, 2020b):…”

Section: Sensitivity Analysismentioning

confidence: 99%

Advanced Analytical Model for Interpreting Oscillatory Pumping Tests With Wellbore Skin and Rate‐Dependent Skin Effects

Mahdavi,

Kurylyk,

Lin

2024

Water Resources Research

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“…Equations 1-5 compose the 2D heat transport model accounting for both conduction and advection with the arbitrary initial and upper boundary conditions in riparian zones, and the nonvertical flow is taken into account in this study. To date, many techniques could be used to derive analytical solutions of the advection-dispersion equation (ADE) such as the separation-of-variables method (Jiang et al, 2009(Jiang et al, , 2011, the integral transform techniques Guerrero et al, 2009;Y.-F. Lin et al, 2022), the Green's function method Leij et al, 2000), and etc. The integral transform technique involves using integral transforms such as Laplace or Fourier transforms to convert the ADE into an algebraic equation, which can be solved using inverse transforms (Cotta, 1993;Guerrero et al, 2009).…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The integral transform technique involves using integral transforms such as Laplace or Fourier transforms to convert the ADE into an algebraic equation, which can be solved using inverse transforms (Cotta, 1993;Guerrero et al, 2009). A variety of integral transforms have been obtained in many previous investigations, and this method has been successfully applied to many problems in hydrology and environmental science (Cotta, 1993;Guerrero et al, 2009;Y.-F. Lin et al, 2022;Mikhailov & Özişik, 1984;Wang et al, 2020;Zhu & Wen, 2019). For instance, Mikhailov and Özişik (1984) reviewed and classified the integral transform techniques for solving linear diffusion problems, and showed numerous applications in the field of heat and mass transfer.…”

Section: Mathematical Modelmentioning

confidence: 99%

A Two‐Dimensional Closed‐Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones

Shi

Zhan

Wang

et al. 2023

Water Resources Research

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Heat as a tracer has received increasing attention in recent decades and has become a popular and widely used tool for quantifying streambed fluxes, among many other applications. Nonvertical flow component is an important parameter for heat transport in riparian zones. However, previous investigations using heat as a tracer in the quantification of streambed fluxes frequently overlooked or simplified nonvertical flow component with erroneous presumptions. In this study, a novelty two‐dimensional closed‐form analytical solution for heat transport with vertical and nonvertical flow components and arbitrary initial and boundary conditions under losing conditions is presented for the first time using Green’s function method. The new model is tested by finite‐element solution and stochastic modeling. The capabilities of the new analytical solution are demonstrated using field data. Results show that the nonvertical flow component has a significant impact on heat transport in streambed. The temperature difference between the streambed and the surface water increases as the nonvertical flow component increases, and the amplitude of the temperature curves decreases with increasing horizontal distance from the center of stream at the same depth due to the influences of nonvertical flow. Stochastic modeling shows that an increasing nonuniform flow can result in overestimation of vertical and nonvertical flow components near the bank of stream, and the new analytical model works well in a heterogeneous streambed when the variance of natural logarithm of the streambed hydraulic conductivity is less than 0.10 (). The vertical and nonvertical flow components are more sensitive to temperature‐time data than the other parameters. The new analytical model is a significant advancement of the previous one‐dimensional analytical models which only considered vertical flow.This article is protected by copyright. All rights reserved.

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“…Groundwater temperature is also useful as an environmental tracer of groundwater processes (Anderson, 2005; Irvine et al, 2017; Kurylyk & Irvine, 2019; Rau et al, 2014). Multi‐depth groundwater temperature signals at diel and seasonal timescales have been used for estimating vertical groundwater fluxes in shallow aquifers (Taniguchi, 1993) as well as groundwater exchange fluxes in streambeds (Constantz, 2008; Irvine et al, 2017) and ocean sediment (Kurylyk et al, 2018; LeRoux et al, 2021; Deeper groundwater temperature profiles have been studied to investigate complex interrelationships between climate change, groundwater flow and deeper groundwater fluxes (Bense & Kurylyk, 2017; Chen & Bense, 2019; Li et al, 2019; Lin et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Shallow groundwater temperature patterns revealed through a regional monitoring well network

Smith,

O'Sullivan,

Kennedy

et al. 2023

Hydrological Processes

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Groundwater temperature is a critical control on groundwater quality, geothermal system efficiency and ecosystem dynamics in receiving surface waters. Despite the known importance of groundwater temperature, there is a lack of dedicated aquifer thermal monitoring across spatial and temporal scales. Pressure transducers and other sensors installed in groundwater monitoring well networks often record temperature as a secondary function, but these comprehensive groundwater temperature data sets are seldom analysed. In this study, we analysed seasonal, interannual and spatial patterns of shallow groundwater temperatures from a regional groundwater monitoring network in Nova Scotia, Canada and compared these subsurface temperature data to air temperature data from nearby climate stations using linear regressions and Fourier analysis. The results showed that seasonal groundwater temperatures were damped (with seasonal amplitudes 3.6%–42% of air temperature amplitudes) and lagged (phase shifted 43–145 days) compared to air temperature, with notable year‐to‐year variations in both damping and lagging. Results also highlighted the role of snowpack thickness on the lowest mean monthly groundwater temperatures. Given potential impacts of climate change, land cover change, urbanization and geothermal energy development on groundwater temperatures, we encourage water authorities and regulators to begin or enhance aquifer thermal monitoring and provide guidance for capitalizing on existing monitoring well infrastructure to track temperature dynamics and changes.

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Analytical solution for estimating transient vertical groundwater flux from temperature-depth profiles

Cited by 10 publications

References 53 publications

Advanced Analytical Model for Interpreting Oscillatory Pumping Tests With Wellbore Skin and Rate‐Dependent Skin Effects

Advanced Analytical Model for Interpreting Oscillatory Pumping Tests With Wellbore Skin and Rate‐Dependent Skin Effects

A Two‐Dimensional Closed‐Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones

Shallow groundwater temperature patterns revealed through a regional monitoring well network

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