Table 2 Assumed parameters used in the case study

Average trace length L_i (m)

3 (Wang 2011)

Fracture density in vertical direction K

15 (Zhou et al. 2017; Wen et al. 2017)

Viscosity coefficient of groundwater ν (m²/s)

1.003 × 10^–6(Xu and Yu 2022)

The fracture water head gradient J

0.001 (Huang et al. 2020)

The inner diameter of U-bend loop d (m)

0.026 (Ou 2011)

The borehole diameter (m)

0.15

The borehole depth l_i (m)

150

The average temperature difference between fracture flow and borehole in winter Δt_w-p (^oC)

10

The fracture water velocity is assumed to be high u (m/s)

3 × 10^–4

The fracture water velocity is assumed to be medium u (m/s)

7 × 10^–4

The fracture water velocity is assumed to be low u (m/s)

1.1 × 10^–3

The specific heat capacity of carbonate rock kJ/(kg ^oC)

0.58

The porosity of carbonate rock

5%

Saturation of pore waster

3%