Numerical generation of the temperature response factors for Multiple BHE fields

Abstract

Ground Coupled Heat Pump (GCHP) systems connected to a set of vertical ground heat exchangers require short and long term dynamic analysis of the surrounding ground for an optimal operation. The thermal response of the ground for a multiple Borehole Heat Exchanger (BHE) field can be described by proper temperature response factors or “g-functions”. This concept was firstly introduced by Eskilson (1987). The g-functions are a family of solutions of the transient heat conduction equation and each of them refer to a given borehole field geometry. Furthermore the g-functions are the core of many algorithms for simulating the ground response to a GCHP system, including the well-known commercial software EED. Analytical approaches based on the Finite Line Source (FLS) model have been developed by Eskilson (1987), Zeng et al. (2002) and later by Lamarche (2007). Such solutions can be in principle applied together with space superposition to infer the thermal response for any BHE configuration. This study is a continuation of the previous work presented in Acuña et al. (2012), and a further investigation is devoted to optimize a numerical model of a squared configuration of 64 boreholes using the commercial software Comsol Multiphysics©. Symmetry conditions and different Fourier numbers have been applied and explored together with the effects related to the dimensions of the calculation domain with respect to the BHE depth and BHE field width. Furthermore, a parametric analysis is addressed to boundary conditions, which points out possible limits on the calculation domain extension. The results of the proposed numerical model are compared with the g-functions embedded within the EED software as well as those calculated by FLS method through the spatial superposition. In a closer approximation to reality, the numerical model is also studied accounting for an adiabatic part at the top of the BHE.