A p(t)-linear average method to estimate the thermal parameters of the borehole heat exchangers for in situ thermal response test

The p-linear average method has been developed to estimate the ground thermal parameters for the design of a Ground-Coupled Heat Pump (GCHP) system, including the ground thermal conductivity, the ground thermal diffusivity and the borehole thermal resistance. Conventionally, the parameter p is considered as a constant, although essentially its value varies with time. To deal with the variation of the p value, this paper proposes a new approach, titled as p(t)-linear average method, to estimate the ground thermal parameters as well as the p values at the different sampling times. The proposed method has been evaluated using the data collected from an in situ thermal response test (TRT). It is found that the proposed method leads to a 6.31% reduction of the borehole thermal resistance when compared to the conventional arithmetic mean temperature method (the p-linear average model with p=1). Besides, compared to the theoretical results, the maximum relative error in the borehole thermal resistance for the conventional arithmetic mean temperature method is as high as 40.69%. In contrast, the maximum relative error for the p(t)-linear average method is less than 3% for all the typical practical cases. Therefore, the proposed p(t)-linear average method is more accurate to be used to estimate the ground thermal parameters for the design of a GCHP system.