A three-dimensional numerical model of borehole heat exchanger heat transfer and fluid flow

Common approaches to the simulation of borehole heat exchangers assume heat transfer within the circulating fluid and grout to be in a quasi-steady state and ignore axial conduction heat transfer. This paper presents a numerical model that is three-dimensional, includes explicit representations of the circulating fluid and other borehole components, and so allows calculation of dynamic behaviours over short and long timescales. The model is formulated using a finite volume approach using multi-block meshes to represent the ground, pipes, fluid and grout in a geometrically correct manner. Validation and verification exercises are presented that use both short timescale data to identify transport delay effects, and long timescale data to examine the modelling of seasonal heat transfer and show the model is capable of predicting outlet temperatures and heat transfer rates accurately. At long timescales borehole heat transfer seems well characterized by the mean fluid and borehole wall temperature if the fluid circulating velocity is reasonably high but at lower flow rates this is not the case. Study of the short timescale dynamics has shown that nonlinearities in the temperature and heat flux profiles are noticeable over the whole velocity range of practical interest. The importance of representing the thermal mass of the grout and the dynamic variations in temperature gradient as well as the fluid transport within the borehole has been highlighted. Implications for simplified modelling approaches are also discussed.