Heat transfer analysis of a borehole heat exchanger array in a layered subsurface

Abstract

In the engineering design of borehole heat exchanger arrays, the subsurface is generally regarded as homogeneous, which leads to a large deviation in the prediction of actual performance. An analytical model with good flexibility describing the heat transfer behavior of BHE array in a layered subsurface is introduced using the Green’s function. The Green’s function which is the exact solutions to the temperature response of a ring coil heat source imbedded in a layered ground domain is obtained directly from the governing equations of the problem by the separation of variables techniques. Meanwhile, the nonuniformity of the heat flow rate along the borehole wall depth is addressed in the analytical layered model. Then, a numerical model of BHE array heat transfer in a layered subsurface is proposed based on the modified pipeline flow model. The numerical model is systematically verified with three experiment tests from the literatures and one test performed by the authors. The maximum RSM error and mean absolute percentage error for four test cases are 0.66 °C and 3.25%, showing a good agreement between the proposed numerical model and the measurements. Then, the accuracy of the analytical solution is validated with the existing simple homogeneous model and the proposed numerical model for multiple BHEs and multiple layers scenarios. The effects of the BHEs array and ground stratification on the temperature response are examined in details employing the analytical and numerical models, with the analytical model focusing on the thermal responses of the layered ground and the numerical model on the circulating fluid in the U-tubes. Results show that the presence of the BHE array increases the magnitude of the discrepancy in the temperature prediction between the layered and homogeneous model, particularly in the layers with low thermal diffusivities at large timescales. For the simulated case, the dimensionless temperature difference between the layered and homogeneous scenarios at the borehole wall in the BHE array is 0.35, while it is only 0.11 in a single BHE, resulting in an increase by 218%. Moreover, the ground stratification could affect the prediction of fluid temperature profile along the BHE depth, thus influencing the thermal circuiting between the two pipes of the U-tube. Compared with the homogeneous model, the coefficient of the thermal circuiting increases by up to 11.6% when the ground stratification is considered. Using the homogeneous model with equivalent thermal properties to design the ground source heat pump system in a layered subsurface would underestimate the short circuiting of the U-pipes and undersize the BHE system. The results of this study provide analytical formalism and numerical method to understand better how the design and operation of actual ground source heat pump is engineered.