Refinement of Ground-Source Heat Pump Installation Area Prediction Method Using Response Surface Methodology

1. IAH 46th @Malaga Development of the method predicting suitable area for installation of ground-source heat pump system using response surface methodology Shohei Kaneko1), Youhei Uchida1), Akira Tomigashi, Mayumi Yoshioka1), Gaurav Shrestha1) and Takeshi Ishihara1) 1) National Institute of Advanced Industrial Science and Technology (AIST)

2. Introduction Background Evaluation of installation potential of ground-source heat pump (GSHP) system is conducted to spread the system. Problem 1) It takes time to make the map by conventional method ⇒Can HER be estimated by hydrogeological condition ? 2) Average method when inputting 3D hydrogeological information affecting HER into 2D map Created by spatial interpolation of the simulation results by GHE model GHE Location Purpose of this study 1) To create estimation formula for heat exchange rate (HER) to obtain a solution equivalent to the numerical analysis result 2) To consider average method of 3D hydrogeological parameters Aiming to create estimation formula for HER in an easy way

3. Method of creating conventional potential map [Step1] Groundwater flow and heat transport simulation in the study area [Step3] Potential map was created by spatial interpolation of GHE model results Kaneko etal.,2018 Extracting hydrogeological parameters at GHE Loc. ※hydraulic conductivity (K), groundwater flow velocity (v), Subsurface temperature (T), thermal conductivity (λ), volumetric heat capacity(ρc), porosity (n) …etc. GHE Location [Step2] Heat exchange rate simulation by GHE model at the GHE Location Visualization based on the estimated heat exchange rate

4. Ground Heat Exchanger (GHE;100-m depth) model GSHP system settings for HER Operation scenario: 120 days of space heating per year from Dec to Mar(24-h operation) Inlet temperature: 5°C Flow rate of circulation fluid: 20 L/min The same hydrogeological parameters from the same locations of GHE in the regional model were used. Constructed GHE models. Locations of GHE models.

5. Proposed method for refinement of potential map (1) [Step1] Estimation formula for HER was created using response surface methodology※1 ：HER ※2：①v(Groundwater flow velocity) ②T(Subsurface temperature) ③λ(Thermal conductivity) ※2Average value from top to 100m depth ：Regression coefficient ※1based on Tomigashi et al. (2013) GHE model： ①v, ②T, ③λ R2 = 0.95 HER Simulation Applying to Estimation formula RMSE 0.943(W/m) Calculated HER (Conventional) Estimated HER Comparison of Calculated HER and Estimated one. GHE model

6. Proposed method for refinement of potential map (2) [Step2] HER was estimated by extracting hydrogeological parameters (v, T, λ) from regional model using the estimation formula BHE Length :100 m Formation A Need to average to obtain parameters in case of ununiform layer Formation B 1 mesh of the regional model Vertical model mesh Horizontal model mesh of regional model 3 parameters (v, T, λ) can be obtained at each mesh HER can be estimated at each mesh by using estimation formula Examine average method of these parameters

7. Influence of temperature profile on HER Hydrogeological settings: ・v：1e-6 m/day ・λ：1.5 W/(m・K) ・Simple average T：15℃ (Pattern of the profile was changed) Result: Pattern of temperature profile have little effect on HER. （depends on Simple average T） Reference Scenario 1 Scenario 2 Scenario 3 Scenario 4 HER （W/m） 15.10 (99.9%) 15.09 (99.9%) 15.11 15.13 (100.1%) 15.12 (100.1%) Pattern of temperature profile to the model and its HER

8. Influence of average thermal conductivity on HER Hydrogeological settings: ・v：1e-6 m/day ・Simple average λ：1.5 W/(m・K) ・T：15℃ Result: HER almost depends on Simple average λ λ of unconsolidated formation: 1.0 - 2.0 W/(mㆍK) Ref. Scen. 1 Scen. 2 Scen. 3 Scen. 4 Ref. HER （W/m） 15.11 14.89 (98.4%) 15.06 (99.7%) 15.11 (100.0%) 15.01 (99.3%) 14.91 Pattern of thermal conductivity to the model and its HER

9. HER in 2-layer (ununiform) and uniform model Result: ・HER was different in having same simple average v ・Difference of HER increases with v in ununiform and uniform model. →average method is needed to consider Scen. 1 Scen. 2 Inlet T Outlet T Grout T 0.3 0.4 v1 m/day v2 m/day 0.22 0.14 0.04 62.36 ≡ v: 0.2 m/day at uniform v 56.27 ≡ v: 0.13 m/day at uniform v HER （W/m） 63.27

10. Influence of groundwater flow velocity on HER Result: HER increases with v, and the relationship between the two showed non-linear. Scen. 1 Scen. 2 v m/day Relationship between v and HER

11. Proposed average method of v at 2-layer model ：simple average ：harmonic average Parameters α and β which change with v Relationship between v and HER

12. Refinement of the potential (HER) map Area A Refined Conventional L L L L H H A A Distribution of v Area B L L H H Distribut-ion of T B B C This method can reflect hydrogeological condition (v, T, λ) ⇒High Resolution C

13. Conclusions 1）It was found that the main factors affecting HER were groundwater flow velocity; v, subsurface temperature; T and thermal conductivity; λ. 2）Average method in vertical direction (BHE length) was evaluated. T and λ can be calculated by simple average. On the other hand, v have to be calculated as a combination of simple and harmonic average. 3）This proposed method improved spatial resolution of the potential map as well as created estimation formula for HER in an easy way. Further Study Universal estimation formula for HER will be created. Leading to potential map of GSHP system in all parts of Japan