Utilizing the finite line source solution for evaluating heat loss and heat storage rates in borehole thermal energy storage systems

Abstract

This study employs the finite line source (FLS) method, a fully analytical model, to evaluate thermal interactions, heat loss, and heat storage rates of borehole thermal energy storage (BTES) systems. The proposed model provides rapid and accurate simulations, in contrast with existing methodologies that rely on time-consuming numerical models. The model first assesses the temperature distribution within and around the boundaries of the BTES. Using the determined temperatures, Fourier's law is applied to calculate heat losses, and the principle of energy conservation is used to determine the thermal energy stored within the BTES. To account for variations in heat exchange rates among boreholes and over time, the FLS solution is superposed both spatially and temporally, and a specific load aggregation technique is employed to reduce computational cost. Further computational efficiency is achieved by approximating the error function required for the FLS solution with a Gaussian Q-function and by using hierarchical agglomerative clustering to categorize boreholes with similar temperatures and heat exchange rates. The proposed method is validated through several case scenarios of increasing complexity and compared against the publicly known duct ground storage (DST) model and simulations conducted using COMSOL software. The results demonstrate the effectiveness of the FLS method in assessing thermal interactions, heat loss, and heat storage rates of different BTES configurations with regular or irregular borehole arrangements, as well as various series-parallel connections. It is also observed that approximating the FLS solution and categorizing boreholes into groups can significantly reduce calculation time, depending on the size and complexity of the problem. An application of the proposed method is also presented, wherein the borehole spacing and length of a BTES are optimized to minimize heat losses and maximize heat storage over time. A grid independence analysis revealed that most inaccuracies of the proposed method occur during the early operational stages, particularly in the evaluation of heat storage rates. These inaccuracies can be mitigated by increasing the radial, axial, and angular segments around boreholes and refining time intervals. Alternatively, inaccuracies can be reduced by evaluating heat storage rates by subtracting heat loss rates from heat exchange rates, similar to the approach used in the DST model. © 2025