Hydrothermal Modeling of Pile Heat Exchangers in the Unsaturated Zone
Résumé
Pile heat exchangers (PHE) are an attractive way to exchange thermal energy with shallow underground since they combine the structural role of geostructures with ground heat exchangers, making it possible to mutualize both investments. PHE are typically 5 to 20 m deep and can be partially located in the unsaturated (vadose) zone. Thermal properties of soil depend on water content, which is heterogeneous in the unsaturated zone. The presented study investigates the influence of groundwater table depth upon the amount of heat transferred by the PHE. It is a part of a research project ‘‘GECKO’’ (geo-structures and hybrid solar panel coupling for optimized energy storage) which is supported by a grant from the French National Research Agency (ANR). The authors focused on deriving an effective thermal conductivity of the ground, denoted ¯(λ_m ), as this value is essential to a consistent PHE sizing. A three-dimensional finite elements (FE) model developed in COMSOL-Multiphysics ® of a 10 m deep PHE has been set up. The geometry of the pipes, pile concrete and surrounding ground is discretized. Stationary distribution of matric potential is determined by solving the Richards equation while the resolution of the heat equation leads to the temperature evolution in the heat-carrier fluid, the concrete and the surrounding ground. Several cases were modelled for ground water table depths ranging from 0.5 m to 9.5 m (cf. Figure 1). The two mentioned bounds respectively correspond to situation where the PHE stands in almost saturated or unsaturated soil. The considered soil, a homogenous Fontainebleau sand, is subject to large water content variations which lead to large thermal conductivity variations: The estimated thermal conductivity is 3.01 W.K-1.m-1 at saturation, i.e. matric potential ψ = 0 m, and
0.46 W.K-1.m-1 for ψ = -10 m. Other soils ranging from clay to sandy loam exhibit a smaller influence of moisture content and matric potential upon thermal conductivity. To determine an effective thermal conductivity of the ground ¯(λ_m ) the PHE was subject to a thermal response test (TRT) – i.e. a constant power given to the heat-carrier fluid. ¯(λ_m ) was estimated based on the evolution of fluid temperature, according to state-of-the-art procedures for TRT interpretations. The analytical model used for the interpretation considers that the pile behaves as an infinite line emitting a constant heat flow in a homogenous media. ¯(λ_m ) is tuned so that the evolutions of inlet/outlet averaged fluid temperatures computed by both models (FE and analytical) match. As a result, ¯(λ_m ) ranges from 3.01 ± 0.01 W.K-1.m-1 for a groundwater level depth of 0.5 m to 1.33 ± 0.04 W.K-1.m-1 for a groundwater level depth of 9.5 m. The effective thermal conductivity ¯(λ_m ) is almost identical to the ground conductivity averaged over the PHE height. These preliminary results suggest that for a single PHE standing in an unsaturated soil the temperature evolution of the heat-carrier fluid can correctly be described by an analytical model considering a homogenous media whose thermal conductivity is equal to the averaged ground conductivity. Further development should focus on similar study for a group of PHE.
Domaines
Sciences de la Terre
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