12. Kolloquium Bauen in Boden und Fels - Januar 2020 211 Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model Matin Liaghi, M.Sc. Universität Stuttgart, Institut für Geotechnik, Stuttgart, Deutschland Prof. Dr.-Ing. Bernhard Westrich Universität Stuttgart, Institut für Geotechnik, Stuttgart, Deutschland Univ.-Prof. Dr.-Ing. habil. Christian Moormann Universität Stuttgart, Institut für Geotechnik, Stuttgart, Deutschland Abstract Detailed knowledge of subsurface thermal properties is a key factor for an efficient and optimum design of a Borehole Heat Exchanger (BHE). Thermal response test (TRT) is the commonly used method for a reliable determination of the heat transport parameters of the underground. In this method heat transport mechanism is considered to be pure conduction. This assumption is considered as the main limitation of this approach, which might lead to deviations. Consequently, applying this method the determination of subsurface thermal properties under groundwater advection is related to some difficulties. In this paper, parameter sensitivity analysis has been performed by assist of a three dimensional thermo-hydro coupled model. The thermal properties of the subsurface is evaluated with comparison to the TRT test results in a BHE which is installed in different geological layers under high groundwater advection effect. After validation of the numerical model, it has been used to perform a parameter study on different influential parameters on TRT results. The magnitude of influence for each parameter is quantified and discussed in this study. 1. Introduction The rising cost of fossil and fuels and their global negative impacts on the climate of the planet leads to increase the importance of utilization of shallow geothermal energy systems [1, 2].Ground source heat pump (GSHP) systems are considered as supplies of the energy to diminish the primary energy use in commercial and residential buildings for space heating and cooling. Several studies are performed in this field, which considering a GSHP in cold climate region [3] as well as a mild climate region [4]. Providing an efficient and optimized design of BHE for a specific site location strongly depends on the level of the detailed information about the underground thermal properties. The most commonly used method to assist the design of Borehole Heat Exchangers (BHE) is the thermal response test (TRT), which is used to assess the thermal properties of the subsurface. The exact evaluation of a TRT, especially in complex conditions concerning geology and groundwater flow is highly important for designing a BHE. A TRT is performed on a heat exchanger probe, by injecting a constant amount of energy into [5] or extracted from the ground [6] by circulating fluid with a defined heat input using heat pump over a period of time. The inlet and outlet water temperature along with water flow rate are measured continuously being later used to analyse the reaction of the subsurface to the temperature. By using TRT, it is possible to evaluate the effective thermal conductivity, which is a combination of subsurface and filling material thermal conductivity. The effective thermal conductivity resulting from TRT considers all the heat transport in the subsurface including both conduction and convection (in the presence of groundwater). Based on [7] the theoretical basis of TRT and its further interpretation has been studied in many investigations since 1990th such as [8], [9] and many others. The line source theory is known as the most popular method to evaluate a thermal response test. This theory is based on Kelvin line source equation [10]. In this model, the subsurface is considered as a homogeneous and isotropic medium with a uniform initial temperature field, which the BHE is implemented inside that as an infinite 212 12. Kolloquium Bauen in Boden und Fels - Januar 2020 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel line source with radially purely conductive heat flux per unit length. Another approach to analyze the heat transfer between the BHE and its surrounding domain is the cylindrical heat source approach. In this method, the BHE with a specific diameter is considered to be placed in an infinite homogeneous domain. This approach considers a constant initial temperature for the whole domain and a definite heat flux per unit surface from the cylinder to the adjacent medium. These TRT interpretation methods depict some deficiencies due to different reasons as following: 1. Ignoring the heterogeneity of the subsurface. 2. Assuming a constant initial temperature for the whole domain and neglecting the natural geothermal temperature gradient of the earth [11]. 3. Neglecting the axial heat flux especially at the surface of the ground due to the ambient temperature fluctuations. 4. Purely conductive heat transport and ignoring convective heat transport due to groundwater flow [12]. A numerical simulation can assist the investigation to overcome the limitations and improve the accuracy of TRT interpretation. 2. Hans-Rehn-Stift case study The Institute of Geotechnical engineering (IGS) at University of Stuttgart has been working on a geothermal project of Hans-Rehn-Stift since 2017. The Hans-Rehn- Stift is a residential facility for elderly people, which is placed in the city of Stuttgart. Its evaluation is part of the ´GeoSpeicher´-project in Baden Württemberg state of Germany. 2.1 Project conditions The heat supply of the facility is ensured by various types of heat supply such as a combined heat and power plant, solar thermal energy and an air heat pump. In addition, the base load of the heat demand is covered by a geothermal probe field, consisting of 21 (double U-pipe) geothermal probes. 20 of these BHEs have the depth of about 90 m and one of them is extended up to 190 m and used for thermal response test and studying the geology and hydrology properties of the field and later operated as a part of the system for energy production. The underground along the BHEs is formed mainly by 2 layers of limestone and sandstone and a thin layer of claystone. The thermal properties of the soil layers were chosen from VDI-RICHTLINIEN (VDI 4640) (2015) and are shown in Table 1. Table 1 Soil layers thermal properties Figure 1. Geological stratification of subsurface and different underground zones Noteworthy to mention that above thermal properties belong to the saturated soil and not dry soil. 2.2 TRT condition To obtain the natural undisturbed temperature profile of the subsurface before any TRT operation, the temperature of the fluid inside the pipe through the 190 depth of the BHE was measured. To ensure an undisturbed temperature profile along the depth of the ground, it was waited long enough after installation of the BHE that the whole system reached the steady state condition. This phase of study is called initial state. Afterwards, the TRT test has been performed for the Hans-Rehn-Stift. Most important information for the TRT test is documented in Table 2. Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model 12. Kolloquium Bauen in Boden und Fels - Januar 2020 213 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel Table 2 Details information of TRT test After completion of the TRT, two measurements were carried out: first one after 2 h and the second one after 26 h. As it is explained above, these measurements were performed inside the inlet pipe of the probe through the whole depth using ´NIMO-T´ temperature device. The TRT results are interpreted using line source theory obtaining an effective thermal conductivity of 8.7 W/ m · K. It is concluded that this significantly high thermal conductivity is due to groundwater flow. A groundwater velocity of 1.2 m/ d was estimated for this field. However, groundwater flow makes it difficult to interpret the thermal response test with regard to the absolute value of the heat conductivity, since the convective portion of the heat transport is not taken into account in the evaluation model. Therefore, the importance of the numerical investigation to assist the interpretation of the TRT becomes more significant. The numerical model can provide a better possibility to quantify more accurately the effective thermal conductivity of the subsurface under the effect of high convection groundwater flow. Furthermore, it can provide a better estimation of groundwater velocity. In this paper, a numerical simulation has been used to study the thermal response test for the Hans-Rehn-Stift to propose a better estimation for subsurface thermal properties as well as groundwater velocity using parameter study. 3. Numerical model A numerical thermal-hydraulically coupled model was developed in the software environment COMSOL Multiphysics version (5.3). Figure 2. Numerical model domain geometry and boundaries. 3.1 Basic approach The model geometry as shown in Figure 2 includes a calculation section with 200 m depth, 10 m length, and 7 m width. Within the three-dimensional calculation domain, a geothermal probe (BHE) with 190 m depth and 20 cm diameter was implemented in the coordinates of , . The dimension was chosen so that the temperature distribution of the BHE is not influenced by the model boundaries. The groundwater flow into the model domain is applied using the difference hydraulic head on the two sides of the domain (h1, inlet boundary) and (h2, outlet boundary) based on Darcy’s law (Eq.1) to generate the target filter velocity of 1.2 in the high convection zone. No flow condition (-n · ρu = 0) is set for the remaining boundaries of the domain. In the numerical model, the heat transfer in the porous medium is coupled with the groundwater flow (Eq. 2), assuming equilibrium temperature between the porous medium and water. The temperature of the groundwater flow is applied as a constant temperature boundary of 11 °C at the inflow. Based on the field measurements at the initial state before Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model 214 12. Kolloquium Bauen in Boden und Fels - Januar 2020 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel performing any TRT test, 11 °C is considered as the initial temperature of the domain in the groundwater zones (5 - 80 m) and top section (0 - 5) of the model (Fig. 3). For the depth from 80 m up to 200 m, the natural temperature gradient of the subsurface in this region is applied using Eq. 3. Where H is the depth in each specific location in the subsurface. The effect of the ambient temperature on the near surface depth is considered into the model by applying a heat flux boundary temperature, which contains temperature, air pressure and wind velocity based on recorded data of the nearest weather station to the project site (Leinfelden-Echterdingen). At the bottom of the model, based on the natural temperature gradient computation a constant temperature boundary of 17°C has been defined. Thermal insulation boundary is set for the remaining surfaces as (-n · q = 0). For conducting the mesh structure of the numerical model, the top surface of the model is discretized by means of free triangle mesh and then it is swept down to the bottom of the domain, generating 292,210 prism elements. Based on the fact, that temperature gradient in the radial direction is significantly higher than the vertical gradient, accordingly the mesh distribution is also much finer in radial direction in comparison to the axial direction. To prove the property of the discretization, the final mesh structure has been chosen according to the convergence of the outlet temperature within 0. 7%. 3.2 Initial state Based on a geo-hydrological report for this project the groundwater velocity of 1.2 m/ d was assumed for the numerical model by means of constant potential heads. To model the initial state the simulation was carried out as a transient problem with a simulation duration of 5 months. For this phase of the study, there is no fluid circulation in the pipes of the BHE, therefore the temperature profile within the pipes should be representative of the initial temperature profile in the subsurface before TRT test. Figure 3 shows the comparison between the measured temperature profile in the field and the calculated temperature profile within the geothermal probe pipe before the start of the TRT test. Figure 3. Initial temperature profile of the subsurface before the start of the TRT. Figure 3 depicts a good agreement between the numerical results and field measurements. The influence of the groundwater flow can be seen in depth from 6 m up to 80 m, causing a constant temperature of 11 °C in this section. The lower section from 80 m until 190 m, where located in the conduction zone without any groundwater effects, the natural geothermal temperature gradient is formed. Furthermore, the numerical model was successful to capture the influence of the ambient temperature which leads to temperature anomaly up to 6 m depths near the surface. The Temperature profile according to Figure 3 was then taken as initial temperature for the TRT phase. 3.3 TRT state Considering TRT operation in the field, the numerical model was conducted to simulate the exact same conditions as in the field. 162 h circulation of the fluid and 10,000 W energy input in each time step were implemented into the numerical model. For comparison between the numerical model and the TRT test, two measurements were used, one after 2 h and the second one after 26 h after the end of the heat supply. The results of the measurements and the simulation are shown in Figure 4. Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model 12. Kolloquium Bauen in Boden und Fels - Januar 2020 215 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel As can be seen in Figure 4, there is a better agreement between the simulation and field measurement after 26 h (b) than after 2 h (a). The reason is that, as the more time passes after the stop of the test, the system is getting more close to the steady state situation especially due to the high convection effect (39 m - 80 m), which transports the excess heat around the BHE due to the TRT test to downstream. The stepwise reduction of the temperature from 6 m to 18 m and from 18 m to 39 m is due to different hydraulic conductivity values and accordingly different groundwater velocities. The wavy shape of the TRT temperature profile at the surface could be due to mixing of the fluid inside the pipe during the measurement. Difference between the exact time of the measurement in the field and extracting the results from the numerical model especially after 2 h, could mention as another source of the deviation. During this time the system exposed to the fast transition to the steady condition. Figure 4. Comparison of TRT field measurements vs. numerical simulation: (a) after 2 h and (b) after 26 h. On the other hand, it seems that 2 h was not enough time for the simulation to reduce the temperature of the fluid inside the pipe. Therefore, a parameter study was conducted to investigate the influence of some parameters, i.e. inflow rate inside the pipes, pipe cover thickness, thermal conductivity and groundwater velocity. The parameter study was focused on the situation 2 h after TRT because of the fact that the heat transfer between BHE and ambient soil is much higher than after 26 h and hence more suitable to detect the sensitivity of the thermodynamics parameters which are to be separately quantified. 3.3.1 Inlet flow rate inside the pipes As it is discussed, numerical results show a higher temperature in the system especially 2 h after TRT. Circulation inlet flow rate inside the BHE can be considered as a potential reason for this phenomenon. Lower inlet flow rate leads to lower energy input to the system and consequently lower temperature in the subsurface due to TRT test. Therefore, lower flow rates range of 1 m3 up to 1.3 m3 have been considered for a parameter study. Figure 5 shows the average temperature value over the total length of the inlet pipe due to different circulation flow rate. Figure 5. Parameter study on inlet flow rate effect (2 h after TRT). Figure 5 shows that 23 % reduction of circulation flow in the BHE lead to a negligible reduction (0.09 °C) of average temperature through the length of the inlet pipe of the BHE. This can be explained by the fact that the flow inside the pipes is turbulent for this range of the inlet flows. Due to the turbulent flow inside the pipes there is the maximum heat transfer from the running flow inside the pipes to the its adjacent domain. Therefore, changing the inlet flow magnitude could not make a significant change in the final results. 3.3.2 Pipe cover thickness In a BHE, U-shape pipes are installed inside a cylindrical frame filled with the grout material. The thickness of the concrete over the pipes has a direct effect on thermal resistance and accordingly on heat transfer through the pipes to the adjacent domain and the other way around. As there is no information about the pipe cover thickness for the BHEs in Hans-Rehn-Stift project, the typical cover of 15 mm was chosen for the numerical calculations. A parameter study is performed to evaluate the influence of the cover thickness with the range of 5 mm up to 40 mm on the average temperature along the inlet pipe (Fig 6). Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model 216 12. Kolloquium Bauen in Boden und Fels - Januar 2020 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel Figure 6. Parameter study on pipe cover thickness effect (2 h after TRT). There is a linear relation between the pipe cover thickness and average temperature through the pipe. It can be figured out each 5 mm more grout cover leads to about 0.2°C increase of the average temperature. By increasing pipes cover they are less exposed to the high convection effect due to groundwater flow in the soil domain around the BHE, thus, the temperature in the pipe shows slightly higher values. Long depth of BHEs pipes could lead to some deformation of the pipe inside the grout body and accordingly different heat transfer rate which is not possible to take into account in the numerical model and ends up to some deviation between numerical calculation and recording results. 3.3.3 Thermal conductivity As shown in Figure 1, the thickness of the claystone layer in comparison to the entire domain is relatively small and accordingly its effect is negligible. Therefore in the numerical simulation, just the main layers of limestone and sandstone were considered. Based on VDI criteria (Table 1) the proposed saturated thermal conductivity mean values for these soils are 2.70 and 2.80 W/ m · K. Therefore the value of 2.70 W/ m · K was considered as the thermal conductivity value for the entire domain. For the parameter study, the thermal conductivity is varied in a range from 2.4 W/ m · K up to 3.6 W/ m · Kfor these type of soils based on VDI table. The results of the parameter study for the relevant situation (2 h after TRT) are shown in Figure 7. Based on Figure 7, the influence of thermal conductivity is limited in the special case of the Hans-Rehn-Stift due to the leading convection effect in the zone with high groundwater flow and therefore the influence of thermal conductivity is negligible. Figure 7 (a) shows the nonlinear relation between the thermal conductivity and the temperature inside the pipe of the BHE. 50 % increase in thermal conductivity value leads to only 2.2 % changes in temperature values. On the other hand, results show almost a linear relation between the thermal conductivity and the temperature change inside the pipe in the conduction zone. Fig. 7(b) illustrates 7.4 % changes in the temperature inside the pipe due to a 50 % change in thermal conductivity values. Correspondingly, the higher influence of thermal conductivity in the low convection zone due to lower groundwater velocity can be explained. Figure 7. Parameter study on thermal conductivity effect (2 h after TRT). 3.3.4 Groundwater velocity To investigate the influence of the groundwater velocity on the TRT, the range of the velocity between 1.2 m/ d up to 2 m/ d in high convection zone was studied by adjusting different hydraulic head and the results are shown in Figure 8. Despite the thermal conductivity, Figure 8 shows the influence of groundwater velocity in the entire domain, especially in convection zones. 33 percent increase in groundwater velocity from 1.2 m/ d to 1.6 m/ d leads to 3.7 % and 2.3 % decrease in temperature in high convection and conduction zones respectively. Furthermore, this effect is even more significant in the low convection zone between the depths 21 m and 40 m, where the influence reaches up to 4.4 %. The reason is that in the lower convection zone the groundwater velocity is small and therefore there is a low convective transport effect. Consequently, the system is further from the steady condition and has more potential for the change due to higher groundwater velocity. Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model 12. Kolloquium Bauen in Boden und Fels - Januar 2020 217 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel Figure 8. Parameter study on groundwater velocity effect (2 h after TRT). This proves the importance of the right estimation of groundwater velocity due to its significant impact on the heat transport process and accordingly on designing ground heat exchangers. At the end, by considering the parameter study using a numerical model, the values of 3.3 W/ m · K and 1.7 m/ d have been chosen for the thermal conductivity and groundwater velocity respectively. Figure 9 shows the final results and improvement of the numerical simulation especially for the relevant situation of 2 h after TRT (Figure 9a). Figure 9. Comparison between numerical simulation final results and TRT test: (a) after 2 and (b) after 26 . 4. Conclusion A numerical model approach was developed to simulate the heat transport due to a thermal response test (TRT) in a borehole heat exchanger (BH) under high groundwater flow velocity. The numerical model was successfully compared with the recorded temperature data of a TRT test in Hans-Rehn-Stift project. The model was used for further investigation on this case study, where the line source assumptions illustrate several shortages in case of interpretation of the TRT. The influence of different parameters on the TRT under high advection effect due to high groundwater velocity has been investigated using the parameter study. It is shown that in the case of turbulent flow the magnitude of inflow rate in the pipes does not make any significant difference in the final results and it is negligible. Pipe cover added thickness has bigger effects than inlet flow on the TRT results. Investigations in this study show that the extra cover of 5 mm leads to about 0.2 °C difference in the average temperature of the results. Therefore, a better estimation of the pipe cover thickness leads to a more reliable investigation of TRT tests using a numerical model. The parameter study shows that in the absence of groundwater flow or low convection effect, thermal conductivity plays a primary role in heat transport and should be taken into account as a decisive parameter. On the other hand, its influence is negligible under high groundwater flow advection. Despite the thermal conductivity, groundwater velocity must be considered as a decisive parameter in both convection and conduction zones. Numerical simulations show that the filter velocity is the only parameter with significant effect in high groundwater convection effect situation. Based on the numerical simulations a value of 1.7 m/ d has been estimated for the groundwater velocity in Hans- Rehn-Stift project considered in the case study investigated. References [1] Blum, P.; Campillo, G.; Münch, W.; Kölbel, T.: CO2 savings of ground source heat pump systems a regional analysis, Renewable Energy 35: 122e7, 2010 [2] Florides, G.; Kalogirou S.: Ground heat exchangers, a review of the systems, models and applications, Renewable Energy 32, 2461, 2007 [3] Bakirci, K.: Evaluation of the performance of a ground-source heat-pump system with series GHE (ground heat exchanger) in the cold climate region, Energy 35, pp. 3088-3096, 2010 [4] Pulat, E.; Coskun, S.; Unlu, K.; Yamankaradeniz, N.: Experimental study of horizontal ground source heat pump performance for mild climate in Turkey, Energy 34, pp. 1284-1295, 2009 [5] Gehlin, S.: Thermal response test: in situ measurements of thermal properties in hard rock, Licential thesis, Sweden, Lulea University of technology, 1998 [6] Witte, H.J.L.; van Gelder, G.J.; Spitler, J.D.: In-situ measurements of ground thermal conductivity: the Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model 218 12. Kolloquium Bauen in Boden und Fels - Januar 2020 Parametersensitivityanalysisonthermalresponsetests(TRT)undercomplexconditionofhighgroundwaterflowusingthermo-hydrocouplednumericalmodel Dutch perspective, ASHRAE Transactions: Research; 108(1): 263e72, 2002 [7] Sanner, B.; Hellström, G.; Spitler, J.; Gehlin, S.: Thermal Response Test - Current Status and World- Wide Application. Proceedings World Geothermal Congress, Tukey, 2005 [8] Hellström, G.: Ground heat storage, thermal analysis of duct storage systems, I. Theory. 262 p., LTH, 1991 [9] Claesson, J.; and Eskilson, P.: Conductive heat extraction to a deep borehole, thermal analysis and dimensioning rules. Energy 13/ 6, pp. 509-527, 1988 [10] Carslaw, H.S.; Jaeger, J. C.: Conduction of heat in solids. Second edition, Oxford University Press, Oxford, 1959 [11] Signorelli, S.: Geoscientific investigations for the use of shallow low-enthalpy systems, Doctoral thesis, ETH Zürich, 2004 [12] Signorelli, S.; Bassetti, S.; Pahud, D.; Kohl, T.: Numerical evaluation of thermal response test. Geothermics, Vol. 36, pp. 141-166, 2007 [13] VDI-RICHTLINIEN, Thermal use of the underground - Ground source heat pump systems. VDI 4640, Blatt 2, 2019 Parameter sensitivity analysis on thermal response tests (TRT) under complex condition of high groundwater flow using thermo-hydro coupled numerical model