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Dimensionless Characterization to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in Aquifers

Author

Listed:
  • José Antonio Jiménez-Valera

    (Mining and Civil Engineering Department, Technical University of Cartagena, 30203 Cartagena, Spain)

  • Francisco Alhama

    (Applied Physics Department, Technical University of Cartagena, 30203 Cartagena, Spain)

Abstract

The outcome of a dimensionless characterization study in a two-dimensional porous media domain in which groundwater flows at a constant horizontal velocity is presented in this report. Using spatial discrimination, the dimensionless groups that govern the solution patterns are determined from dimensionless governing equations. As a boundary condition on the surface, the case of constant temperature is studied. From the mathematical deduction of the groups, a characteristic horizontal length emerges. This length determines the region in which temperature–depth profiles are affected by flow. Existing analytical solutions have been shown to be invalid due to the severe assumption that the horizontal thermal gradient has a constant value. Therefore, universal solutions based on pi theorem have been obtained for the characteristic horizontal length, temperature field, temperature–depth profiles and horizontal temperature profiles. Dependencies between dimensionless groups have been depicted by universal curves, abacuses and surfaces. These graphical solutions are used in an easy way to estimate groundwater velocity from experimental temperature measurements in the form of an inverse problem. In addition, an easy and fast protocol for estimating fluid flow velocity and groundwater inlet temperature from temperature profile measurements is proposed. This protocol is applied in a scenario of groundwater discharge from a quaternary aquifer to a salty lagoon located in the southeast of Spain.

Suggested Citation

  • José Antonio Jiménez-Valera & Francisco Alhama, 2022. "Dimensionless Characterization to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in Aquifers," Mathematics, MDPI, vol. 10(15), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2717-:d:877823
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    References listed on IDEAS

    as
    1. J F Sánchez Pérez & M Conesa & I Alhama & F Alhama & M Cánovas, 2017. "Searching fundamental information in ordinary differential equations. Nondimensionalization technique," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-20, October.
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    Cited by:

    1. Encarnación Martínez-Moreno & Gonzalo García-Ros & Iván Alhama & Francisco Alhama, 2023. "Characterization of Flow under Impervious Dams: Dimensionless Groups and Universal Solutions," Mathematics, MDPI, vol. 11(3), pages 1-22, January.
    2. Iván Alhama & José Antonio Jiménez-Valera & Manuel Cánovas & Francisco Alhama, 2024. "Deduction of the Dimensionless Groups and Type Curves of Temperature Profiles in Two-Layer Soils with Water Flow at Depth," Mathematics, MDPI, vol. 12(2), pages 1-16, January.

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