| Abstract |
The correct designing and sizing of geothermal heat exchangers plays a crucial role in the successful harnessing of geothermal energy for the energy-efficient heating and cooling of buildings. This designing and sizing is done during the building's design phase using theoretical models to analyze the thermal response of the geothermal heat exchanger during the whole lifespan of the building. Hence, the accuracy, flexibility, and speed of these models have a direct impact onto the analysis and its outcome. Most models in use nowadays exploit certain disparities in time and length scales of the problem to significantly reduce their mathematical complexity, allowing the aforementioned analysis to be performed in feasible amounts of time. Nevertheless, the most accurate and flexible ones (e.g. Superposition Borehole Model) still require several hours or days of computing time, while the faster ones (e.g. g-function model) introduce certain artificial simplifying assumptions that hinder their flexibility and accuracy. Since 2011, the author is pursuing a new modeling approach based on the use of asymptotic expansion techniques. These mathematical methods naturally exploit the large disparity in time and length scales, delivering analytical models without the need of artificially introduced simplifying assumptions. The resulting models present the accuracy and flexibility levels of the Superposition Borehole Model with a speed level more in line with the g-function model. A brief overview of the on-going work is given in the present paper, and a comparison with the state of the art is carried out to showcase the potential of the models under development. |