Proposal for a Method Predicting Suitable Areas for Installation of Ground-Source Heat Pump Systems Based on Response Surface Methodology
Abstract
:1. Introduction
2. Review of Hydrogeological Information and Numerical Simulation of the Study Area
3. Study Methods
3.1. Response Surface Methodology
3.2. Examination of the Average Method
3.2.1. Groundwater Flow Velocity
3.2.2. Subsurface Temperature
3.2.3. Thermal Conductivity
3.3. Creation of Estimation Formula for the HER
4. Application of the Estimation Formula for the HER to the Sendai Plain
5. Validation of the Estimation Formula by Constructing GHE Models
6. Discussion
7. Conclusions
- (1)
- It was found that the main factors affecting the HER were groundwater flow velocity (), subsurface temperature (), and thermal conductivity of solids ().
- (2)
- The average method in the vertical direction (GHE length) was evaluated. and can be calculated by arithmetic averaging. In contrast, has to be calculated as a combination of arithmetic and harmonic average.
- (3)
- The RSM was utilized to approximate the HER using the three parameters in the Sendai Plain. The estimated HER agreed well with the calculated one by the GHE models because the coefficient of determination and RMSE between the two HERs were 0.999 and 0.129, respectively.
- (4)
- The proposed method cannot only estimate the HER from hydrogeological parameters in an easy way but also highly increase the spatial resolution of a map by creating a GHE model without performing heat exchange simulations.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
3D | Three-dimensional |
GSHP | Ground source heat pump |
GHE | Ground heat exchanger |
HER | Heat exchange rate |
RSM | Response surface methodology |
3D | Three-dimensional |
Groundwater flow velocity | |
Subsurface temperature | |
Thermal conductivity of the solid | |
Heat exchange rate | |
to | Regression coefficients |
Average groundwater flow velocity | |
, | Parameters that vary with arithmetic average groundwater flow velocity |
Arithmetic average groundwater flow velocity | |
Harmonic average groundwater flow velocity |
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Layer | Formation (Thickness of the Formation (m)) | Horizontal Hydraulic Conductivity (m/Day) | Vertical Hydraulic Conductivity (m/Day) | Porosity (−) | Thermal Conductivity of Solids (W/m/K) |
---|---|---|---|---|---|
1–2 | Quaternary (<80 m) | 5.0 | 2.5 | 0.2 | 1.4 |
3–9 | Upper Neogene (540–620 m) | 0.4 | 0.2 | 0.1 | 1.5 |
10–17 | Lower Neogene (300 m) | 0.08 | 0.04 | 0.1 | 1.8 |
0 | 1 | 0 |
0.0011 | 0.98 | 0.02 |
0.0055 | 0.92 | 0.08 |
0.011 | 0.815 | 0.185 |
0.022 | 0.75 | 0.25 |
0.033 | 0.705 | 0.295 |
0.044 | 0.675 | 0.325 |
0.055 | 0.64 | 0.36 |
0.11 | 0.525 | 0.475 |
0.22 | 0.375 | 0.625 |
0.44 | 0.235 | 0.765 |
0.55 | 0.2 | 0.8 |
1.1 | 0.115 | 0.885 |
227.12 | 685.41 | −4.62 | −270.10 | −15143.42 | 0.02 | 77.18 | 71.44 | −476.98 | 3.77 |
No. | HER Estimate by RSM | HER Calculated by GHE Model | |||
---|---|---|---|---|---|
1 | 5.24 × 10−3 | 13.93 | 1.50 | 18.76 | 18.83 |
2 | 4.58 × 10−3 | 17.94 | 1.50 | 26.35 | 26.37 |
3 | 5.24 × 10−3 | 14.73 | 1.50 | 20.38 | 20.45 |
4 | 1.62 × 10−3 | 16.12 | 1.48 | 19.26 | 19.14 |
5 | 9.50 × 10−4 | 14.73 | 1.50 | 16.38 | 16.25 |
6 | 9.51 × 10−3 | 20.78 | 1.50 | 38.63 | 38.62 |
7 | 4.80 × 10−3 | 14.13 | 1.50 | 18.79 | 18.88 |
8 | 5.22 × 10−3 | 17.33 | 1.50 | 25.75 | 25.95 |
9 | 1.26 × 10−2 | 13.85 | 1.50 | 23.66 | 23.57 |
10 | 1.99 × 10−2 | 13.90 | 1.50 | 27.26 | 27.44 |
11 | 5.33 × 10−3 | 15.84 | 1.49 | 22.52 | 22.16 |
12 | 1.75 × 10−2 | 13.08 | 1.50 | 23.98 | 23.90 |
13 | 5.33 × 10−3 | 15.42 | 1.50 | 21.85 | 21.96 |
14 | 7.01 × 10−3 | 14.20 | 1.49 | 20.68 | 20.77 |
15 | 3.86 × 10−3 | 14.52 | 1.45 | 18.21 | 18.27 |
16 | 8.43 × 10−3 | 15.94 | 1.45 | 25.04 | 25.02 |
17 | 1.27 × 10−2 | 13.93 | 1.50 | 23.91 | 23.83 |
18 | 9.68 × 10−3 | 14.69 | 1.46 | 23.48 | 23.35 |
19 | 2.25 × 10−3 | 15.40 | 1.45 | 18.18 | 18.25 |
20 | 3.91 × 10−3 | 18.18 | 1.45 | 24.91 | 24.90 |
21 | 2.38 × 10−3 | 15.34 | 1.45 | 18.22 | 18.29 |
22 | 1.89 × 10−2 | 14.01 | 1.50 | 27.18 | 27.27 |
23 | 9.66 × 10−4 | 17.60 | 1.45 | 20.39 | 20.36 |
24 | 1.15 × 10−3 | 16.44 | 1.48 | 19.29 | 19.18 |
25 | 1.94 × 10−3 | 15.78 | 1.45 | 18.43 | 18.51 |
26 | 3.24 × 10−3 | 16.77 | 1.47 | 21.91 | 21.82 |
27 | 4.08 × 10−3 | 15.05 | 1.44 | 19.28 | 19.47 |
28 | 4.01 × 10−3 | 15.49 | 1.47 | 20.30 | 20.28 |
29 | 1.08 × 10−2 | 14.64 | 1.48 | 24.37 | 24.18 |
30 | 3.61 × 10−3 | 14.74 | 1.43 | 18.26 | 18.37 |
31 | 8.06 × 10−3 | 14.55 | 1.45 | 21.87 | 22.05 |
32 | 1.55 × 10−2 | 14.58 | 1.48 | 27.10 | 26.91 |
33 | 4.01 × 10−3 | 16.68 | 1.50 | 23.14 | 23.27 |
12.26 | −2903.62 | −20.39 | 228.72 | −146.16 | 0.95 | −48.30 | 187.32 | 444.94 | −5.89 |
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Kaneko, S.; Tomigashi, A.; Ishihara, T.; Shrestha, G.; Yoshioka, M.; Uchida, Y. Proposal for a Method Predicting Suitable Areas for Installation of Ground-Source Heat Pump Systems Based on Response Surface Methodology. Energies 2020, 13, 1872. https://doi.org/10.3390/en13081872
Kaneko S, Tomigashi A, Ishihara T, Shrestha G, Yoshioka M, Uchida Y. Proposal for a Method Predicting Suitable Areas for Installation of Ground-Source Heat Pump Systems Based on Response Surface Methodology. Energies. 2020; 13(8):1872. https://doi.org/10.3390/en13081872
Chicago/Turabian StyleKaneko, Shohei, Akira Tomigashi, Takeshi Ishihara, Gaurav Shrestha, Mayumi Yoshioka, and Youhei Uchida. 2020. "Proposal for a Method Predicting Suitable Areas for Installation of Ground-Source Heat Pump Systems Based on Response Surface Methodology" Energies 13, no. 8: 1872. https://doi.org/10.3390/en13081872