Effect of size on ground-coupled heat pump performance

Here we document and explain interactions between two thermodynamic trends that determine the optimum performance of refrigeration and heat pump systems. We show analytically why the performance of the system must increase with the size of the installation. The second law efficiency of heat pump systems must increase with their size. We also show that the power requirement for a specific ground-coupled heat pump system must decrease as the size of the ground heat exchanger increases. From these two trends emerges the tradeoff between the size of the heat pump and the size of the ground heat exchanger. The challenge is to find the optimum size of the ground-coupled heat pump. We show numerically the optimum heat pump size and the ground heat exchanger size that correspond to minimum total power requirement subject to a cost constraint.