Innovative Methodology to Compute the Temperature Evolution of Pile Heat Exchangers

Abstract

Energy geostructures such as heat exchanger piles couple the structural role of geostructures with heat and cold supply via shallow geothermal energy. This combination makes it possible to cut down the investment costs of ground heat exchangers. A thermal dynamic simulation is often necessary to optimize the energetic system made of ground heat exchangers, heat pump and building. To do so it appears mandatory to rely on numerical models of pile heat exchangers that run over a reasonable amount of time. The resolution of the heat and mass balance equations with numerical techniques such as the finite element (FE) method allows to account for complex geometry of the ground heat exchangers and spatial heterogeneities of the underground properties (e.g. thermal and hydraulic conductivities). However, this often leads to computation times that are not compatible with engineering practices. Analytical solutions are an alternative, but the range of these solutions is limited due to the fact that the geometry of the pile tends to be oversimplified and that the thermal capacity of the concrete is neglected. Moreover, known solutions may overestimate the heat transfer by convection since they do not account for the fact that the pile is an obstacle to the underground flow. This paper focuses on overcoming hurdles mentioned above. First, a resistive-capacitive (RC) circuit have been developed to account for the thermal inertia of the pile. In this model a pile section is divided into as many zones as they are circulation pipes in the pile. Combining thermal capacities and resistances enables an accurate description of the transient heat transfer in the concrete. Values of the circuit components are determined by comparison with FE simulations for simple boundary conditions. Second, the coupled equations accounting for heat diffusion and flow in saturated porous media (i.e. Darcy’s law) have been normalized, so that the temperature evolution at the pile wall depends on only two numbers: the number of Fourier Fo, i.e. the ratio of thermal conduction over thermal inertia, and the number of Peclet Pe, i.e. the ratio of heat transferred by convection over the heat transferred by thermal conduction. The temperature evolution has been solved with a FE model under a constant heat flux condition. Correlations have been established over the computed wall pile temperature, referred to as the ‘step response’. These correlations are valid over durations ranging between a few minutes and a few years. Third, the RC circuit has been combined to a heat balance over the heat carrier fluid and to the correlations for step response. The following algorithm is used to solve temperatures in the fluid, pile and surrounding ground: Temperatures at the nodes of the RC circuit are solved with an implicit Euler method, while the evolution of pile wall temperature is computed by discretizing the convolution of time-variable flux with the step response. Finally, the paper exhibits a few application cases for this innovative methodology.