Mathematical modeling and periodical heat extraction analysis of deep coaxial borehole heat exchanger for space heating

•The transient numerical model of coaxial borehole heat exchanger is developed.•Verification of the proposed model using the operating data from the literature.•Comparison of the periodical heat extraction and power under 4 operating modes.•Analysis of the underground temperature distribution transients within 30 days.•Long-term operation performance of the borehole heat exchanger within 20 years. The geothermal energy is considered as one of the most promising renewable techniques for district heating. The deep coaxial borehole heat exchanger (BHE) is an economic and efficient measure for extracting the geothermal energy from underground, which attracts numerous attentions recently. However, the researches on the influences of the operation modes on the periodical heat extraction performances of the deep coaxial BHE are rare. In this paper, an unsteady numerical model of the dynamic operation of the coaxial borehole heat exchanger is established, based on the principles of energy conservation and mass conservation. The proposed model is verified using the operating data from the literature. Space heating of a school building (located at Tianjin, China) is taken as a scenario, and different operation modes during the heating period are simulated and analyzed. Comparisons were carried out on four operating modes: the continuous operation mode, “16+8 mode” (run for 16 h and stop for 8 h), “12+12 mode” and “8+16 mode”. The recovery of underground temperature distribution during the winter holiday was studied. Results show that, except for the continuous operation mode, the differences between the other three modes on the total extracted heat throughout the whole year and during the 24 h within the 90th day are unobvious. Under the “12+12 mode”, when the BHE reaches the stable level, the heat extraction power can be maintained at 301.6–528.1 kW in the first year, and the decline rate lower than 15% during the 20-year operation period. In addition, at 1 m from the center of the tube and at depths of 500 m, 1000 m, 1500 m, and 2000 m, the recovery rates of the underground temperature distribution relative to the initial temperature during the winter vacation are 7.35%, 13.78%, 16.57%, and 17.74%, respectively.