Examination of Ambient Temperature Variations Effects on Predicted Fluid Temperatures in Vertical Boreholes
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A fully-coupled model of geothermal bore fields is presented, taking into account the axial variations of borehole wall temperatures and heat extraction rates along the borehole lengths, fluid temperature variations inside the U-tubes and depth-variation of ground temperature due to seasonal ambient temperature variations. The model incorporates an analytical finite line source model to calculate borehole wall temperatures. A steady-state analytical solution is used to calculate fluid temperatures from arbitrary borehole wall temperature profiles. Ground temperatures are calculated from a one-dimensional analytical solution to heat conduction in semi-infinite media with varying surface temperature. A system of equations is built and solved in the Laplace domain. The specific case of boreholes connected in series is discussed. Different assumptions for time- and depth-variation of ground temperatures are compared. Results show that time-varying uniform ground temperatures is accurate for simulations, with differences in predicted fluid temperatures within 1.5% of time-varying non-uniform ground temperatures.