Deduction of the Dimensionless Groups and Type Curves of Temperature Profiles in Two-Layer Soils with Water Flow at Depth

Iván Alhama, José Antonio Jiménez-Valera (), Manuel Cánovas and Francisco Alhama
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Iván Alhama: Mining and Civil Engineering Department, Technical University of Cartagena, Paseo Alfonso XIII, 30203 Cartagena, Spain
José Antonio Jiménez-Valera: Mining and Civil Engineering Department, Technical University of Cartagena, Paseo Alfonso XIII, 30203 Cartagena, Spain
Manuel Cánovas: Mining and Metallurgical Engineering Department, Universidad Católica del Norte, Antofagasta 1270709, Chile
Francisco Alhama: Applied Physics Department, Technical University of Cartagena, C/Doctor Fleming s/n., 30202 Cartagena, Spain

Mathematics, 2024, vol. 12, issue 2, 1-16

Abstract: In the common hydrogeologic scenarios of horizontal groundwater flow and a water table below the surface, the steady-state 2D thermal field resulting from the coupling between water flow and heat flow and transport gives rise to a vertical temperature profile that develops progressively over a finite extent of the domain. Beyond this region, the temperature profiles are linear and independent of horizontal position. Such profiles are related to the groundwater velocity so they can be usefully used to estimate this velocity in the form of an inverse problem. By non-dimensionalization of the governing equations and boundary conditions, this manuscript formally derives the precise dimensionless groups governing the main unknowns of the problem, namely, (i) extent of the profile development region, (ii) time required for the steady-state temperature profile solution to be reached and (iii) the temperature–depth profiles themselves at each horizontal position of the development region. After verifying the mathematical dependencies of these unknowns on the deduced dimensionless groups, and by means of a large number of accurate numerical simulations, the type curves related to the horizontal extension of the development of the steady-state profiles, the characteristic time to develop such profiles and the dimensionless vertical temperature profiles inside the characteristic region are derived. These universal graphs can be used for the estimation of groundwater horizontal velocities from temperature–depth measurements.

Keywords: non-dimensionalization; groundwater flow; heat transport; porous media; numerical modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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