Effect of the Pumping-injection flow rate on Heat 1 Transfer Characteristic of Borehole Heat 2 Exchangers for Coupling Ground-Source Heat 3 Pump System

: A coupling ground source heat pump system (CGSHP) is established in areas 9 where groundwater is shallow but the seepage velocity is weak, which sets up pumping and 10 injection wells on both sides of borehole heat exchangers (BHEs). A convection-dispersion 11 analytical model of excess temperature in aquifer that considers groundwater forced seepage 12 and axial effects and thermal dispersion effects is proposed. A controllable forced seepage 13 sandbox is built by equation analysis method and similarity criteria. Through indoor test and 14 the proposed analytical model, the correctness and accuracy of the numerical simulation 15 software FEFLOW7.1 is verified. The influence of different pumping-injection flow rate on 16 the heat transfer characteristic of BHEs is studied by numerical simulation. The results show 17 that the average heat efficiency coefficient of BHEs increases and the heat influence range of 18 downstream BHEs expands with the increasing of pumping-injection flow rate. The relation 19 curve between Pe and the increment of heat transfer rate per unit depth of BHEs (Δ  q ) is 20 distributed as Gaussian function. The pumping-injection flow rate that makes Darcy velocity 21 reaches 0.6×10 -6 ~1.4×10 -6 m∙s -1 in the aquifer is the best reference range for CGSHP s ystem ， so 22 400~600 m 3 ∙d -1 is taken as the best pumping-injection flow rate in this paper.


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The distribution area of shallow underground brackish water in China's Binhai plain of 134 Tianjin is 6,922 km 2 , of which the brackish water area with a mineralization content of 2-3 g·L -1 135 and 3-10 g·L -1 are 3,753 km 2 and 3169 km 2 respectively, accounting for more than 2/3 of the 136 city's total area (Zaiming 2012). Groundwater resources are rich in reserves and convenient for 137 exploitation, but the hydraulic gradient and the natural seepage generally range from 1.3×10 -2 138 m•a -1 to 12×10 -1 m•a -1 . Therefore, CGSHP system is suitable in Tianjin plain. The GSHP system that installed in Tianjin Binhai New Area, China, 2016 is taken as the 143 project prototype (Figure 2). The project has a research area of 150×120 m 2 and a vertical depth 144 of -83m that it is divided into 5 geotechnical layers. Among whole study area, the fine sand 145 layer has stronger permeability that is regarded as a well-developed confined aquifer, which geotechnical distribution and physical parameters are shown in Table 1. The project, which is mainly responsible for the energy supply of the adjacent school,  Table 2.

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In which, the conductive part of thermodispersion tensor Λ cond and the dispersive part of The problem for determining solution of seepage flow is associated with the problem of

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In the analytic model, ρece is the volumetric heat capacity of the porous medium (Eq.8).

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When the thermal conductivity in the aquifers is the same in each direction, the thermal 196 conductivity components of the Λ cond are determined by equation (9). λx and λy is the effective 197 longitudinal and transverse thermal conductivity coefficient, respectively, which are 198 determined by Eq.10 and Eq.11. r is the distance to the source located on the z-axis at the (x0, analysis model (Eq.6) and (Eq.7) can be simplified to Eq. 13 and Eq.14. 207 238 239 Table 3. Engineering prototype and experimental system design parameters            Table 1.  (Table 5). To divide one operation cycle (1 year) into four stages that are followed by summer 379 cooling stage (4 months), autumn intermittent stage 1 (2 months), winter heating stage (4 380 months) and spring intermittent stage 2 (2 months). The system runs five operation cycles 381 and BHEs operate continuously for 10 hours per day in both the cooling and heating stage.

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The inlet water temperature of BHEs during cooling/heating stage is constant at 31℃ /6℃ is 383 respectively.
the same aquifer since the total pumping-injection flow rate (∑G) is different (Figure 9). Darcy

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To describe accurately the evolution process of the aquifer's temperature field under 399 different operation modes, the calculation area with a temperature change of ±0.5 ℃ is defined as the coordinate distance between E (g) and the farthest acting position.

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When the pumping-injection flow rate is 0 m 3 •d -1 , there is only the heat conduction 403 between BHEs and the aquifer as well as between the aqueous medium units. The heat 404 transfer process is slow and the heat influence range is diffused symmetrically around BHEs.   downstream region and alleviating the thermal accumulation phenomenon of BHE. So, in order to obtain the difference between the temperature response ∆T disp with forced groundwater seepage and the temperature response ∆T cond without groundwater seepage at shown in Figure 11  further increases, not only the Δq decreases gradually, but also the energy consumption of 500 pumping and injection pumps increase that leads to the increase of operation cost of the 501 system. Furthermore, the change of aquifer spatial structure will be irreversible if the forced 502 seepage velocity is too high. Therefore, in order to obtain the best heat transfer enhancement 503 effect, system environment and economic benefits, the pumping-injection flow rate when

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In this paper, CGSHP system is proposed as the same as the effect of the flow rate of 508 pumping and injection wells on heat transfer characteristic of BHEs is studied for this system.

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The main conclusions of this study can be summarized as follows: