Method for estimating the depth of circulation of thermal and non-thermal waters in the upper crust

Abstract

In this work we consider model formulations that allow better understandings of the relations between Darcy velocity and temperatures in coupled two-dimensional systems. The revised theoretical formulations are capable of accounting for the effects of heat transfer by fluid movements in horizontal and vertical directions. The models have been found useful in estimating the maximum and minimum depths of thermal and non-thermal waters in several geological units in Brazil. The best fitting values encountered are 1.8 to 2.7 km for the Paraná basin, 2.0 to 2.8 km for the Parnaiba basin, 1.6 to 2.3 km for the Amazon basins, 2.0 to 2.7 km for the San Francisco Province, 1.9 to 2.4 km for the Sergipe-Alagoas basins and 2.0 to 2.8 km for the Borborema Province. The models have also allowed estimation the average values of Péclet number and Darcy velocity for groundwater flows in these units. Note that higher horizontal velocities are associated with smaller depths of circulation. This is a natural consequence of the fact that in systems where horizontal velocities are high the quantities of vertical flows are less intense.

A Two‐Dimensional Closed‐Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones

“…As far as we know, some analytical models, such as those proposed by Alexandrino et al. (2021), Lu and Ge (1996), and Pasquale et al. (2010), discussed 2D geothermal transport considering both vertical and horizontal flow, but they did not solve the 2D initial boundary value problem (IBVP) exactly.…”

“…As far as we know, some analytical models, such as those proposed by Alexandrino et al (2021), Lu and Ge (1996), and Pasquale et al (2010), discussed 2D geothermal transport considering both vertical and horizontal flow, but 10.1029/2022WR034059 3 of 20 they did not solve the 2D initial boundary value problem (IBVP) exactly. Instead, they added the horizontal flow as a sink and source term into the 1D vertical transport governing equation, and by doing so, they made an erroneous assumption that horizontal flux gradient was constant.…”