Numerical modelling of groundwater flow in heat extraction from the subsoil

Low-temperature geothermal resources have become very competitive thanks to their considerable environmental benefits, including the reduction in CO2 emissions and other greenhouse gases. Geothermal systems for heating or cooling of buildings use heat available in the upper part of the subsurface; this is often done via Ground Soil Heat Pump systems that can be generally closed or open. The former are considered in this study. Closed systems are commonly known as Ground-Coupled Heat Pumps (GCHPs). In a GCHP system, heat is extracted from or rejected to the ground via an external closed circuit constituting the ground heat exchanger (GHE) through which pure water or antifreeze fluid circulates. The GHEs commonly used consist of high-density polyethylene pipes (HDPE) installed in either vertical boreholes or in horizontal trenches. This paper deals with heat exchangers installed inside foundation piles; heat extraction from the subsoil is investigated in the case of clay and dry sand and in saturated sand where groundwater flow occurs. Moreover, in examining the role of groundwater flow in the performance of GHEs, the paper investigates to what extent taking into account the right velocity field for seepage around the pile instead of using a schematic uniform value affects the results. A mathematical model in 2D space is introduced, comprising a pair of parabolic and elliptic partial differential equations for soil temperature and the groundwater velocity field, respectively. The equations are solved numerically by means of the Finite Difference Method and Finite Element Method, respectively. The numerical model is validated by comparing the results of the conduction equation with the solutions of cylindrical and infinite line source (CILS and ILS) and those of the advection-diffusion equation with a moving infinite line source (MILS) model. The results show that groundwater flow is able to restore the initial undisturbed temperature in the subsoil very quickly and it is essential to take into account the correct seepage field around the GHEs to estimate system efficiency correctly for high values of velocity (> 2∙10-5 m/s)