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

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.

A Universal Graphical Solution to Calculating Seepage in Excavation of Anisotropic Soils and Non-Limited Scenarios

“…Dimensionless groups were assembled using discriminated non-dimensionalization, a technique that has been applied in anisotropic scenarios involving hydraulic conductivity (with k x and k y ) to solve problems of soil consolidation, seepage under dams and heat transport in aquifers [22][23][24]. This technique has allowed us to determine the parameters according to the two dimensions of the problem (x, y), that is, k x , L * and c (in the x direction) and k y , b , a and T * (in the y direction), so every monomial respects the basic rule of including only parameters defined in the selected direction.…”

Inverse Problem Protocol to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in a 2D Aquifer

“…T (x,y,t=0) = T ini (5) According to [10], the horizontal extent of the development of temperature profiles is…”

“…The horizontal groundwater flow with a constant temperature coming from an inlet border, in an extended aquifer whose surface and bottom are subjected to isothermal (Diritlech) conditions, gives rise to a temperature field within the aquifer that depends on both the depth and the horizontal location. The extension of the region in which the temperature field is developed has been recently studied and characterized dimensionally [10]. These authors provide expressions for the width of the developed region as a function of the depth of the aquifer, groundwater velocity and thermal diffusivity of the porous media, and the latter combines the thermal conductivity of the soil-fluid matrix and the specific heat of the fluid.…”

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

“…In relation to horizontal flow, it is worth mentioning the work of Lu and Ge [15] on shallow semi-confined aquifers assuming the existence of a horizontal thermal gradient throughout the domain, a severe assumption since this gradient is caused by the heat balance between water transport and thermal conditions at the boundaries. Regarding the investigation of universal solutions, Jiménez-Valera and Alhama [16] have recently presented a study based on the dimensionless characterization that derives the dimensionless groups of this problem but referring to single-layer scenarios with horizontal flow and a water table at the surface. In this scenario of a dry soil layer superimposed on a saturated soil layer, the existence of three boundary temperatures-at the top, at the bottom and that of the inlet water-together with the geometric and thermal characteristics of the scenario, plus the groundwater velocity itself, mean that the overall number of parameters influencing the solution of the problem is certainly high.…”

“…Once the dimensional variables of the governing equation have been replaced by their corresponding dimensionless variables, and the terms of the equation have been simplified (eliminating the derivative factors of these terms), the dimensionless groups as independent quotients between each pair of terms can immediately by obtained. To these dimensionless groups, the form factors derived from the equations defining the boundary conditions must be added [16,17]. According to the pi theorem, such zero-dimensional groups, and not the individual parameters of the problem of non-zero dimension in general, are the only ones that govern or determine the solution of the problem [18].…”