Unsteady Energy Transfer in Vertical Geothermal Systems
A comprehensive energy analysis was performed on a unsteady strongly nonequilibrium thermodynamic system comprising the ground, a borehole heat exchanger (BHE), and a ground heat pump. The analysis was based on a theory of vertical geothermal systems (VGS) developed by the authors. The novelty of the proposed approach, in comparison to the conventional mathematical modeling of VGS, derives from the description of VGS as a unsteady single strongly nonequilibrium thermodynamic system consisting of soil (source of energy), borehole (energy well) and ground source heat pump (energy transducer), with continuity of energy flow conditions between its components. It was found that the system studied was characterized by two dimensionless parameters: the ratio of thermal conductivity and thermal diffusivity of the ground and the secondary fluid. Introduction of these parameters can significantly simplify the interpretation of results of theoretical and experimental studies using methods of the similarity theory. Furthermore, a definition of energy well debit was devised, the limiting stages of heat exchange in the conducting soil system were identified and a physical interpretation was made of the results obtained. The mathematical model developed was used for studying quantitative and qualitative characteristics of extractable energy. Finally, it was shown that the energy efficiency of each individual ground source heat pump (GSHP) system requires its own analysis and that the suggested approach can be used for optimization of GSHP systems in terms of their energy efficiency.