A temporally relaxed theory of physically or chemically non-equilibrium solute transport in heterogeneous porous media

Lin, Ying‐Fan; Huang, Junqi; Carr, Elliot J.; Hsieh, Tung-Chou; Zhan, Hongbin; Yu, Hwa‐Lung

doi:10.1016/j.jhydrol.2023.129432

Cited by 5 publications

(1 citation statement)

References 57 publications

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“…If denoting β = θ m /θ as the partition parameter of the mobile water zone, there is 1 − β = θ im /θ. Furthermore, considering linear adsorption, first-order degeneration and zero-production reactions in the process, and a mobile-immobile solute transport model with sources is given as (see [16,17,23,28], for instance)…”

Section: Introductionmentioning

confidence: 99%

Determination of space-time-dependent source terms in the integer-fractional mobile-immobile solute transport system

Yu,

Liu,

2023

Preprint

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We consider a numerical inversion problem of determining two space-time-dependent source terms in the integer-fractional mobile-immobile solute transport model by using the Dirichlet-Neumann boundary data. The unique existence of a solution to the forward problem is obtained by the inverse Laplace transform, and a dynamical system connecting the known data with the unknown sources is established by the variational method and boundary homogenization. The dynamical system is discretized to a linear system at given time in the homogenized polynomial space, and the source functions can be reconstructed by the alternative iteration and Tikhonov regularization. Two examples are presented to illustrate the validness of the inversion algorithm. MSC(2010) 35R11; 35R30; 65N21

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Section: Introductionmentioning

confidence: 99%

Determination of space-time-dependent source terms in the integer-fractional mobile-immobile solute transport system

Yu,

Liu,

2023

Preprint

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Integrated hydrological and hydraulic modeling for predicting sediment transport in hydraulic road structure design: the case of oued ait ourir, high atlas, Morocco

Messaoudi,

Wafik,

Najine

et al. 2024

Model. Earth Syst. Environ.

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Using Rainfall‐Induced Groundwater Temperature Response to Estimate Lateral Flow Velocity

Chen,

Guo,

Yin

et al. 2024

Water Resources Research

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This study introduces a novel heat tracing method for estimating lateral groundwater flow velocity induced and sustained by heavy rainfall events in lowland areas, leveraging the distinct temperature difference between rainfall and groundwater. The method is motivated by the observation that the rainfall‐induced groundwater temperature signal dissipates along the flow path. To explain the observed temperature anomaly and then estimate the lateral flow velocity, we develop a semi‐analytical model for heat transport in the aquifer, accounting for conduction losses to adjacent layers. Our findings reveal that interactions between the aquifer, vadose zone, and bedrock significantly influence the temperature signal, thereby affecting velocity estimation. Inaccuracies in measured aquifer properties, such as thickness, porosity, and thermal conductivity of surrounding layers, increase the uncertainty of velocity estimates. However, variations in aquifer thermal conductivity have a minimal effect on the method's overall accuracy. When estimating multiple parameters, velocity estimates tend to be less reliable, especially if aquifer porosity remains uncertain. This is due to the challenges of simultaneously inverting both velocity and porosity. Overall, this work underscores the potential of using heat as a tracer for assessing lateral groundwater flow following rainfall, offering a practical, low‐cost solution applicable in a wide range of settings.

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A temporally relaxed theory of physically or chemically non-equilibrium solute transport in heterogeneous porous media

Cited by 5 publications

References 57 publications

Determination of space-time-dependent source terms in the integer-fractional mobile-immobile solute transport system

Determination of space-time-dependent source terms in the integer-fractional mobile-immobile solute transport system

Integrated hydrological and hydraulic modeling for predicting sediment transport in hydraulic road structure design: the case of oued ait ourir, high atlas, Morocco

Using Rainfall‐Induced Groundwater Temperature Response to Estimate Lateral Flow Velocity

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