A semi-analytical model for serpentine horizontal ground heat exchangers

This article focuses on a particular type of horizontal ground heat exchangers (HGHE) which can be used as a heat source (or heat sink) for geothermal heat pumps. It consists of a long pipe buried about 1 m below the ground surface and arranged in parallel regularly spaced sections, forming a serpentine. This article proposes a model for such a heat exchanger, where the serpentine is discretized axially and a three-step calculation procedure is performed on each node. The axial fluid temperature variation in the pipe is first computed by using an implicit numerical resolution scheme. Then, heat transfer in the ground surrounding the pipe is obtained by using the analytical cylindrical heat source solution. In the third step, used for mid- to long-term simulations, thermal interference between parallel pipe sections is taken into account using spatial superposition. Finally, these solutions are coupled iteratively to obtain the axial fluid and pipe temperatures at each time step. The model is then validated using a full-scale experimental facility located in Orléans, France. Following a brief description of the facility, validation results are reported. The main validation test consists of supplying the HGHE with a constant inlet fluid temperature (40°C [104°F]) for a 200-h period in soil at an initial temperature of 7.5°C (45.5°F). After an initial transient period, the recorded outlet fluid temperature matches the model prediction within 1°C (1.8°F).