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

José Antonio Jiménez-Valera and Francisco Alhama
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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

Mathematics, 2022, vol. 10, issue 15, 1-19

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.

Keywords: nondimensionalization; inverse problem; analytical solutions; numerical modeling; groundwater flow (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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