A unified framework for the construction of short- and long-term g-functions for parallel-connected ground heat exchangers

The construction of g-functions is central to the design of ground-source heat pump systems. However, most formulations rely on simplified boundary conditions (BC) and subsurface assumptions, while neglecting short-term effects due to borehole thermal capacity and fluid flow rate. G-functions constructed under BC-I and BC-II assume depth-invariant heat fluxes, whereas BC-III enforces a uniform borehole wall temperature, providing only an approximate representation of parallel-connected ground heat exchangers. This study introduces a method for constructing both short- and long-term BC-IV g-functions that inherently account for variations in heat flux and wall temperature along and between boreholes. The approach combines numerically simulated thermal interactions, measured at the borehole outlet, between pairs of borehole with a block matrix algorithm that enforces uniform inlet fluid temperatures across the ground heat exchanger. The framework accommodates complex subsurface conditions, including geological heterogeneities, groundwater flow, and short-term effects. Verifications against g-functions obtained with a reference 3D numerical model show strong agreement across four scenarios involving homogeneous and heterogeneous porous media, layered groundwater flow, and various ground heat exchanger layouts.