The effects of borehole thermal resistances and fluid flow rate on the g-functions of geothermal bore fields

A model to calculate g-functions accounting for the axial variation of borehole wall temperatures and heat extraction rates due to thermal interaction between the fluid and the borehole wall is presented. Boreholes are divided into segments, with each borehole segment modeled as a finite line source. Borehole wall temperatures are calculated from the spatial and temporal superposition of the finite line source solution. A delta-circuit of thermal resistances is used to consider the heat transfer between the fluid and the borehole wall. A system of equations is built in the Laplace domain and solved for an equal inlet fluid temperature for all boreholes in the bore field. The values of the g-function tend toward the g-function obtained using a uniform heat extraction rate boundary condition as the borehole thermal resistance increases and tend toward the g-function obtained using a uniform temperature boundary condition as the borehole thermal resistance decreases. It is shown that modeling the thermal interaction between the fluid and the borehole wall is required to accurately predict the g-function. (C) 2015 Elsevier Ltd. All rights reserved.