Analytical modeling and validation of the thermal behavior of seasonal storage tanks for solar district heating

Abstract

In the context of the complex worldwide energy crisis, the solar district heating and the embedded seasonal storage tanks can contribute to the increase of energy efficiency in district heating systems. The analytical investigation of the thermal behavior of the storage tanks allows the evaluation of the reduction in energy consumption, that can be achieved, and the correct sizing of both solar fields and storage tanks.The study presents complete analytical models for fully mixed and stratified seasonal storage tanks, integrated in solar district heating systems. The provided validation of both models was realized by comparison with results available in the literature. Three and five comparisons were conducted for the fully mixed model and for the stratified model, respectively.The Mean Deviation (MD), Mean Bias Error (MBE) and Root Mean Square Error (RMSE) were used in the validation process. For the fully mixed model, in all the comparisons, the differences between the storage tank temperature provided by the model and the corresponding temperature from the reference are lower than 16.7 °C (occasionally). MD is lower than 2.9 °C, while MBE is lower than 5.9 % and RMSE is lower than 9.9 %. For the stratified model, in all the comparisons the differences between the storage tank temperatures provided by the model and the similar temperature from the references are lower than 2.35 °C. MD is lower than 0.5 °C, while MBE and RMSE are lower than 1.55 % for all the comparisons. The reasonable differences between the model and the reference, in the case of the fully mixed tank and the neglectable differences in the case of the stratified tank, validated both analytical models, that can be further used with high confidence, in investigations related to the thermal behavior of solar district heating systems with seasonal thermal storage.