Formulation of a 1D finite element of heat exchanger for accurate modelling of the grouting behaviour: Application to cyclic thermal loading

Highlights

Formulation of a 1D pipe finite element for borehole heat exchanger modelling.

Assessment of the error due to the resolution scheme and the use of large time steps.

Focus on the grouting modelling.

Importance of the accurate modelling of daily variations of the power demand.

Limitations of the daily temperature variations to a near area around the borehole.

Abstract

This paper presents a comprehensive formulation of a finite element for the modelling of borehole heat exchangers. This work focuses on the accurate modelling of the grouting and the field of temperature near a single borehole. Therefore the grouting of the BHE is explicitly modelled. The purpose of this work is to provide tools necessary to the further modelling of thermo-mechanical couplings.

The finite element discretises the classical governing equation of advection-diffusion of heat within a 1D pipe connected to ground nodes. Petrov-Galerkin weighting functions are used to avoid numerical disturbances. The formulation is able to capture highly transient and steady-state phenomena.

The proposed finite element is validated with respect to analytical solutions. An example consisting of a 100 m depth U-pipe is finally simulated. A first continuous heating simulation highlights the non-symmetric distribution of temperature inside and near the borehole. An estimation of the error on the results as a function of the resolution parameters is also carried out. Finally simulations of cyclic thermal loading exhibit the need to take into account all daily variations if the grouting behaviour must be modelled. This is true especially in case of freeze-thaw damaging risk.

Keywords

  • Borehole heat exchanger;
  • Ground source heat pump;
  • Finite element;
  • Short-time step;
  • Numerical modelling

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