# Parametric Study for Evaluation of Design Parameters of Standing Column Well

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1 Proceedings World Geothermal Congress Bali, Indonesia, 5-9 April Parametric Study for Evaluation of Design Parameters of Standing Column Well Dong-Yeop Kwak 1, Duhee Park 1, Jae-Hoon Chang 1, Sang-Min Na, and Sisam Park 1. Rm 53 Jaesung Civil Eng. Bldg., Hanyang University, Haengdang-dong, Sungdong-gu, Seoul, Korea. GS E&C Research Institute, 17-1 Deoksung-ri, Lidong-myun, Cheoin-gu, Yongin, Kyeongki-do, Korea Keywords: Standing column well, numerical model, heat transfer, design parameters, parametric study ABSTRACT While the standing column wells are widely used in practice for its efficiency, the design parameters of the wells are difficult to select. In order to determine the design parameters of standing column well in Korea, parametric study was performed using a numerical model. The properties representative of Korea, including geothermal gradient, hydraulic conductivity, and thermal conductivity were selected and applied in the analyses. The results show that the numerical model can be successfully used in selection process of important design parameters. The development of a new numerical model can be very useful. Rees et al. () performed a comprehensive parametric study using a numerical SCW model and evaluated the design parameters of the SCW. However, development of a numerical code requires extensive amount of time and expertise. Instead of developing a dedicated software for modeling the SCW in Korea, this paper used a commercial finite-volume analysis code to numerically simulate the SCW and to perform the parametric study. 1. INTRODUCTION The ground heat source heat pump system have become popular in Korea as a green energy source for heating / cooling of residential and office buildings. Vertical closedloop heat exchanger is the most widely used geothermal heat pump system, whereas standing column well (SCW) is being newly introduced and applied in Korea. SCW pumps water from the bottom of a borehole and returns it to the same well after heat extraction and/or rejection. The pumping induces radial groundwater flow into and out of the well, as well as flow within the borehole. The heat is transferred in complex mechanisms involving convection, advection, and conduction. SCW is known to be more efficient than a closed-loop pump since the groundwater is used directly for heat transfer. However, the complex hydro-thermal coupled behavior of the SCW makes it difficult to accurately predict the performance of a SCW. For a wider application of the SCW in Korea, it is important to understand the influence of various parameters on the performance of a SCW and to develop a design guideline considering the local site conditions. This paper performed parametric study to evaluate the influence of selected parameters using a D numerical model. The effects of each variable were discussed and compared in the following.. NUMERICAL MODEL OF SCW Various numerical models have been developed and studied in the past (Braud et al., 193; Deng, ; Mikler, 1993; Oliver and Braud, 191; Yuill and Mikler, 1995). Deng () developed two-dimensional (D) hydro-thermal coupled model to simulate the heat transfer within the standing well. It was shown that the numerical model can accurately model the temperature changes within the well. In addition, one-dimensional model was developed to increase the numerical effectiveness. It was demonstrated that the simplified model was also quite accurate for selected case studies. Figure 1: Material properties and boundary conditions used to model a SCW system. 1

2 The program used in this study was FLUENT (Fluent Inc., ), which is a commercial computer program for modeling fluid flow and heat transfer. FLUENT uses the finite-volume method to solve the governing equations for the fluid flow and heat transfer. The material and boundary conditions used in the SCW model are shown in Figure 1. It is possible to perform threedimensional (3D) analysis with FLUENT. However, D axi-symmetric analysis was performed to reduce the computational cost. 3D analysis is planned to evaluate the effect of the spacing of the SCW. The flow in the SCW and the ground is initiated by prescribing a flow rate to the suction pipe inlet and discharge pipe outlet. In order to determine the optimum time increment for the parametric study, a sensitive analysis was performed. Figure 3 shows the calculated temperatures in the borehole for 1,, 1,, sec time increments, respectively. The calculated peak temperatures for sec and sec time steps show significant discrepancy compared to the 1 sec interval. Comparisons show that using 1 sec time increment is acceptable and the discrepancy between 1 sec time step result is within tolerable level. In the parametric study, 1 sec time increment was used. The borehole, located at the center of the numerical domain, is composed of the well boundary, suction pipe inlet, discharge pipe outlet, suction and discharge pipes. The ground is modeled as a porous medium. The lateral, upper, and lower boundaries of the ground were set to pressure inlet boundaries, at which the total heads were set to zero. Constant temperatures were applied at the boundaries. Input properties for the ground included hydraulic conductivity, thermal conductivity, density, and specific heat. In addition to the properties of the ground, the thermal properties of the pipes were specified. The accuracy of the numerical model of the SCW was thoroughly validated through actual measurements. More details on the numerical model is discussed in the companion paper (Park et al., 9). 3. PARAMETRIC STUDY In this paper, a parametric study was performed to evaluate the effect of various parameters on the performance of the SCW system in Korea using the numerical model described in the previous section. The base case of the parametric study was slightly modified from a SCW installed at Euryeong Sports Complex, Korea. The dimensions of the borehole, suction and discharge pipes, and the numerical domain, and the mesh are shown in Figure. The input properties for the base case are summarized in Table 1. The domain radius and depth were set to 1 m and 35 m. The depth of the ground below the bottom of the borehole was 5 m, which was the minimum depth recommended to model water flow and thermal conduction in the aquifer without being influenced by the boundary (Deng, ). The suction and discharge pipes were made of HDPE. The density, specific heat, wall thickness, and thermal conductivity of the pipes selected in this study were 95 kg/m 3, 17 J/kg- C, 5.5mm,. W/m- C, respectively. The density of soil layer was assumed to be 7 kg/m 3. In the numerical simulation, the water that is returned to the well was used as the input. The resulting change in the temperature of the borehole was simulated and the calculated water temperature pumped from the well is compared with the measured data. The SCW was numerically operated for one day, and the difference between the input (water returned to the well) and output (water pumped from the well) temperatures were compared. To compare of the degree of influence of each parameter, the temperature of the input was set constant throughout the duration of the numerical simulation to 3 C for summer season (cooling mode) and 5 C for the winter season (heating mode). It is of course not realistic that the temperature of the water returned to the well is constant, but it was considered appropriate for the purpose of this study. A short time increment can improve the accuracy of the analysis, but at the cost of the increased computational cost. Figure : Mesh and numerical dimension of the base case of the parametric study. Temperature ( C) 1 1 1sec sec 1sec sec sec Time of operation (min) Figure 3: Sensitivity analysis to determine the optimum time step.

3 Table 1: Property values used in the parametric study. Parameter Units Case Base case Porosity Hydraulic conductivity -5 m/sec Thermal conductivity W/m- C Specific heat capacity J/kg- C Geothermal gradient C/m depth depth depth Flow rate kg/sec Borehole depth m Borehole diameter mm Suction pipe diameter mm Bleeding rate % Variables for Parametric Study The variables for the parametric study can be classified into two groups, which are a) site dependent variables and b) design variables. A total of five site dependent variables were included in this study, which were the porosity, rock hydraulic conductivity, rock thermal conductivity, rock specific heat capacity, and geothermal gradient. The ranges of the hydraulic and thermal properties of the rock were based on the data of Choi (), Deng (), Hellstrom (1991), Kwon et al. (), and Shin and Kim (1993). Design variables are parameters that the designer of the SCW needs to select considering local geological/hydrological conditions and engineering judgment. A total of five variables were used, which were flow rate, borehole depth, borehole diameter, suction pipe diameter, and bleeding rate. As with the site dependent variables, the variables were varied from the base case. Table 1 summarizes the cases performed in the parametric study. In each case, only one parameter is changed from the base case. The only exception was the bleeding rate. To clearly demonstrate the effect of the bleeding, the hydraulic conductivity of the ground was increased five times to 5-5 m/sec. 3. Results of Parametric Study The results of each case in the parametric study are shown in Figure ~ Figure 13. The results are shown in terms of the absolute temperature difference between input temperature (water returned to the well) and calculated temperature (water pumped from the well). If the absolute temperature difference increases, it means that the performance and the effective of the SCW are increasing. The calculated absolute output temperature difference of the base case was 1.9 C for the cooling mode and 3.3 C for the heating mode Site Dependent Variables The site dependent variables considered in this study are porosity, hydraulic conductivity, thermal conductivity, specific heat capacity, and geothermal gradient. The porosity (Figure ) and specific heat capacity (Figure 5) have negligible influence on the performance of the SCW. Hydraulic conductivity has the most critical influence on the performance, as shown in Figure. It is estimated that as the hydraulic conductivity increases, the heat transfer through both advection and convection increases. Another 3 important variable is the thermal conductivity. Increasing thermal conductivity results in enhanced performance. However, the relationship between thermal conductivity and performance is nonlinear. The effect on the temperature difference decreases at thermal conductivities higher than.5 W/m- C, as shown in Figure 7. Figure shows the influence of the geothermal gradient on the SCW system. The temperature difference becomes higher with increasing the geothermal gradient in the heating mode, but shows opposite trend in the cooling mode. It indicates that when the geothermal gradient increases, the temperature at the bottom of the well increases accordingly, causing the water pumped at the bottom to be higher Porosity Figure : Temperature difference after 1 day operation due to the variation in the porosity Specific heat capacity (J/kg- C) Figure 5: Temperature difference after 1 day operation due to the variation in the specific heat capacity

4 1 Hydraulic Conductivity (x -5 m/sec) Figure : Temperature difference after 1 day operation due to the variation in the hydraulic conductivity Thermal Conductivity (W/m- C) Figure 7: Temperature difference after 1 day operation due to the variation in the thermal conductivity Geothermal gradient ( C/m) Figure : Temperature difference after 1 day operation due to the variation in the geothermal gradient. 3.. Design Parameters The SCW system has only a few design parameters, which are the flow rate of the system, borehole depth and diameter, pipe diameter, and bleeding rate. Effects of all design parameters were studied in this paper. Figure 9 shows that decreasing the flow rate increased the efficiency of the SCW system in both the cooling and heating modes. As the flow rate decreases, the water velocity in the borehole becomes slower, and therefore has more time to transfer heat with the borehole wall. If the flow rate increases, the input water from the heat pump is mixed quickly within the borehole, the time for heat transfer is reduced. The simulation demonstrates that the flow rate in the SCW system is important and that it has to be determined considering the efficiency of the SCW and the demand of the building. The borehole depth also has an important effect on the performance of the SCW system. The effect of borehole depth is shown in Figure. Due to the geothermal gradient, the water temperature increases along with the depth of borehole. As the borehole depth increases, the total flow path becomes longer, thereby maximizing the heat transfer with the borehole wall. In addition, the higher temperature at deeper locations allows warmer water to be pumped into the suction inlet. Both mechanisms contribute to the enhanced performance of the SCW in the heating mode for higher borehole depths. In the case of cooling mode, the amount of performance enhancement is less than in the heating mode. The reason for the difference is that as the higher temperature of the water has negative effect on the performance of the heat pump in the cooling mode Flow rate (kg/sec) Figure 9: Temperature difference after 1 day operation due to the variation in the flow rate Borehole depth (m) Figure : Temperature difference after 1 day operation due to the variation in the borehole depth. The variation of borehole diameter and suction pipe diameter have limited influence on the performance, as shown in Figure 11 and Figure Borehole diameter (mm) Figure 11: Temperature difference after 1 day operation due to the variation in the borehole diameter.

5 Suction pipe diameter (mm) Figure 1: Temperature difference after 1 day operation due to the variation in the suction pipe diameter. The effect of the bleeding rate is shown in Figure 13. The bleeding had a pronounced influence on the output temperature for both the heating and cooling modes. As the bleeding rate increased, the heat transfer between the ground and the input water increased, and hence improved the performance of the well. However, the effect of bleeding was influenced by the hydraulic conductivity of the ground. If the permeability of the ground was smaller, the influence of the bleed would have decreased accordingly Bleeding rate (%) Figure 13: Temperature difference after 1 day operation due to the variation in the bleeding rate.. CONCLUSION A parametric study was performed using a numerical model to evaluate the degree of influence of five site dependent variables and five design variables. The numerical simulation of the SCW was performed using a commercial finite-volume analysis software. The ground water flow and heat transfer were modeled through coupled hydro-thermal analysis. The base case of the parametric study was modified from a SCW installed at Euryeong, Korea. The properties of the borehole, pipes, and the rock of the base case were used as a reference, and the variables were varied to investigate the influence of each parameter. The SCW was numerically operated for a duration of one day, and the difference between the input (water returned to the well) and output (water pumped from the well) were compared for both cooling and heating modes. The results of parametric study showed that among the site dependent variables, the hydraulic conductivity and thermal conductivity of the rock had the most important effect on the SCW system installed at Euryeong. The geothermal gradient also had non-negligible influence. Porosity and specific heat capacity had secondary influences on the performance of the SCW. Among the design variables, flow rate, borehole depth, and bleeding had important influence on the performance. The bleeding had the most critical influence on the performance, but only for the case in which the hydraulic conductivity is sufficient to allow abundant radial flow. REFERENCES Braud, H.J., Klimkowski, H., and Oliver, J.: Earth-source heat exchanger for heat pumps, Transactions of the ASAE,, (193), Choi, B.-Y.: The problem and solution about heat pump supply, Engineering Workshop of SAREK, (), Deng, Z.: Modeling of standing column wells in ground source heat pump systems, Oklahoma State University, (). Hellstrom, G.: Ground heat storage thermal analyses of duct storage systems, Dep. of Mathematical Physics, Lund Univ., (1991). Inc., F.: Fluent.3 User's Guide, Lebanon, New Hampshire, (). Kwon, O.-I., Baek, Y., Seo, Y.-S., and Yim, S.-B.: A study on inference of deterioration depth of Rock according to temperature distribution and rock type in Korea, Korean Geo-Environmental Conference, Wonju, (). Mikler, V.: A theoretical and experimental study of the "energy well" performance, Masters thesis, The Pennsylvania State University, (1993). Oliver, J., and Braud, H.: Thermal exchange to earth with concentric well pipes, Transactions of ASAE,, (191), 9-9. Park, D., Kwak, D.-Y., Kim, K.-K., Park, S., Na, S-M: Numerical simulation of standing column well, submitted to World Geothermaal Congress, Bali, Indonesia, (9). Rees, S.J., Spitler, J.D., Deng, Z., Orio, C.D., and Johnson, C.N.: A study of geothermal heat pump and standing column well performance, ASHRAE TRANSACTIONS, 1, (), Shin, Y.-K., and Kim, Y.-D.: A study on the relationships between the quartz content, and the specific heat and density of rocks in Dogae colliery, The Korean Society for Geosystem Engineering, 3, (1993), -5. Yuill, G.K., and Mikler, V.: Analysis of the effect of induced groundwater flow on heat transfer from a vertical open-hole concentric-tube thermal well, ASHRAE TRANSACTIONS, 1, (1995),

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