Planning the operation of large ground source heat pump (GSHP) systems requires accurate models of borehole heat exchangers (BHEs) that are not computationally intensive. In this paper, we propose parameter estimation using measured data as a method to improve the analytical models of BHE. The method was applied to a GSHP system operating for over 3 years. The deviation between modelled and measured load of the BHE reduced from 22% to 14%. Influence of the calibration data set was tested by changing time resolution and season of the calibration data. We concluded that the time resolution must be high enough to differentiate among the effects of different parameters and that different model parameters must be used for injection and extraction (seasons). The method was also applied to a GSHP that has been monitored for 10 years, which showed that accuracy of the model can be improved by annual updates of parameters.

ABSTRACT:With bore fields for energy extraction and injection, it is often necessary to predict the temperature response to heat loads for many years ahead. Mathematical methods, both analytical and numerical, with different degrees of sophistication, are employed. Often the g-function concept is used, in which the borehole wall is assumed to have a uniform temperature and the heat injected is constant over time. Due to the unavoidable thermal resistance between the borehole wall and the circulating fluid and with varying heat flux along the boreholes, the concept of uniform borehole wall temperature is violated, which distorts heat flow distribution between boreholes. This aspect has often been disregarded. This paper describes improvements applied to a previous numerical model approach. Improvements aim at taking into account the effect of thermal resistance between the fluid and the borehole wall. The model employs a highly conductive material (HCM) embedded in the boreholes and connected to an HCM bar above the ground surface. The small temperature difference occurring within the HCM allows the ground to naturally control the conditions at the wall of all boreholes and the heat flow distribution to the boreholes. The thermal resistance between the fluid and the borehole wall is taken into account in the model by inserting a thermally resistive layer at the borehole wall. Also, the borehole ends are given a hemispherical shape to reduce the fluctuations in the temperature gradients there. The improvements to the HCM model are reflected in a changed distribution of the heat flow to the different boreholes. Changes increase with the number of boreholes. The improvements to the HCM model are further illustrated by predicting fluid temperatures for measured variable daily loads of two monitored GCHP installations. Predictions deviate from measured values with a mean absolute error within 1.1 and 1.6 K.

Optimizing the operation of ground source heat pumps requires simulation of both short-term and long-term response of the borehole heat exchanger. However, the current physical and neural network based models are not suited to handle the large range of time scales, especially for large borehole fields. In this study, we present a hybrid model for long-term simulation of BHE with high resolution in time. The model uses an analytical model with low time resolution to guide an artificial neural network model with high time resolution. We trained, tuned, and tested the hybrid model using measured data from a ground source heat pump in real operation. The performance of the hybrid model is compared with an analytical model, a calibrated analytical model, and three different types of neural network models. The hybrid model has a relative RMSE of 6% for the testing period compared to 22%, 14%, and 12% respectively for the analytical model, the calibrated analytical model, and the best of the three investigated neural network models. The hybrid model also has a reasonable computational time and was also found to be robust with regard to the model parameters used by the analytical model.

Developing accurate models is necessary to optimize the operation of heating systems. A large number of field measurements from monitored heat pumps have made it possible to evaluate different heat pump models and improve their accuracy. This study used measured data from a heating system consisting of three heat pumps to compare five regression and two artificial neural network (ANN) models. The models’ performance was compared to determine which model was suitable during the design and operation stage by calibrating them using data provided by the manufacturer and the measured data. A method to refine the ANN model was also presented. The results indicate that simple regression models are more suitable when only manufacturers’ data are available, while ANN models are more suited to utilize a large amount of measured data. The method to refine the ANN model is effective at increasing the accuracy of the model. The refined models have a relative root mean square error (RMSE) of less than 5%.

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