A novel numerical approach for imposing a temperature boundary condition at the borehole wall in borehole fields

Abstract

The design of a borehole field should be based on a long-term simulation of its thermal response for the intended energy loads. A well-known method to evaluate the response is based on a pre-calculated dimensionless function, the g-function. When calculating g-functions, there are two commonly used approaches for treating the boundary condition at the borehole wall: a constant heat flux at every instant of time, or a uniform temperature at a constant total heat flow to the borehole field. This paper is focused on a new approach to model the thermal process of borehole fields; in particular with a precise representation of a uniform temperature boundary condition at the borehole wall. The main purpose of this model is to be used as a research tool to either generate g-functions for particular cases or handle situations that cannot be addressed by others methods. First, the almost constant temperature along the borehole heat exchanger in operation requires a boundary condition of essentially isothermal boreholes along the depth. In a common case, the borehole heat exchangers are connected in parallel, thus all boreholes should have the same temperature. Also, the total heat flow to the borehole field should be constant over time. For this purpose, a numerical model in which the boreholes are filled with a hypothetical highly conductive material has been built, reproducing the isothermal condition. By thermally interconnecting the boreholes, the equal temperature condition is satisfied. Finally, the specified total heat flow is fed into one spot at the highly conductive material. The model is validated by generating g-functions of some simple borehole field configurations. The g-functions present, in general, a good agreement with the existing solutions for a similar boundary condition. Moreover, the model is also tested against real experimental data from a 2 × 3 borehole field at an office building. The simulated daily fluid temperatures are compared with measured daily fluid temperatures for the sixth year of operation. The simulated values present, in general, a good agreement with the measured data. The results show that there are no significant differences with regard to the boundary conditions at the borehole wall, which for this specific case is due to the fact that the system is thermally balanced.