A Fast Analytical Method for the Dynamic Energy Simulation of Energy Piles With Short Time Resolution

This paper proposes an analytical method for the dynamic thermal simulation of energy piles with a short time resolution (e.g., tens of minutes) as an alternative to numerical approaches, which require relevant computational resources. The discussion is tailored to the implementation of analytical models in dynamic energy simulation software for buildings and HVAC systems. The main modeling challenges consist of accounting for the pile thermal capacity, configuration of pipes, and time-varying inlet temperature and flow rate values. The heat transfer process occurs in three characteristic periods, each of them characterized by a 2D or 3D geometry. The first period concerns the evolution of the fluid temperature and heat transfer over the length of the pipes, the second period concerns the thermal diffusion within the heat capacity of the foundation, and the third period is driven by pile geometry and ground source characteristics. For short time resolution analyses, we proposed a general linear set of equations based on the ε-NTU theory for heat exchangers, the infinite composite-medium line source solution, and the finite line source for the ground source. The proposed method is compared with a full transient 3D numerical simulation. The maximum deviation in terms of return temperature to the heat pump is 0.2 K. The general dimensionless form, the short time resolution, and the limited computational time makes the method suitable for building simulation software and optimization codes for thermal analysis and energy pile design.