An analytical model for transient heat transfer in ground-coupled heat exchangers of closed-loop geothermal systems

Abstract

Vertical borehole heat exchangers are widely used as sustainable and reliable tools to effectively extract thermal energy from the ground. For an effectual design and implementation of these borehole heat exchangers, it is essential to have an in-depth understanding of heat transfer within the boreholes and the geothermal reservoir. While in situ tests and numerical heat transfer analyses are proven to provide reliable results, they usually need highly compatible hardware along with expensive software and expertise acquisition. The present study presents a ‘one-dimensional’ analytical heat transfer representation of borehole geothermal heat exchangers which can amenably predict the performance of these systems. For validation of the proposed model, several grid sizes are selected to represent a wide range of typical application scenarios. Selected scenarios are run to test the capability of the proposed analytical model versus its numerical counterpart. These scenarios are examined under two distinct test cases. In the first case, the proposed analytical solution is tested in estimating the borehole wall temperatures of single and multiple borehole arrangements in a time scale ranging from hours to years. The results obtained in this case are validated with two-dimensional numerical models with a constant flux boundary condition on the borehole wall. On the other hand, a second round of tests are focused on estimating the fluid outlet temperatures by introducing an actual fluid flow in the proposed three-dimensional, U-tube, ground-coupled heat exchanger scenarios within similar transient time-scale. In this sense, single borehole, double borehole, quadruple borehole and ‘N × N’ borehole scenarios; the latter representing very large grids, are numerically modeled and compared with the proposed analytical model. This comparison study shows the amenability of the proposed analytical model in predicting system performance with high precision. Numerical validations conducted with both two-dimensional and three-dimensional transient models have shown that the proposed unidimensional analytical solution is capable to estimate system performance in an effective manner. Overall, the proposed analytical solution is proven to provide robust results in prediction of transient heat transfer in single and multiple ground-coupled heat exchangers both in short and long term with high accuracy.