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In-situ measurement of borehole thermal properties in Melbourne
Applied Thermal Engineering 73 (2014) 285e293
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
In-situ measurement of borehole thermal properties in Melbourne Tshewang Lhendup, Lu Aye*, Robert James Fuller Renewable Energy and Energy Efficiency Group, Department of Infrastructure Engineering, Melbourne School of Engineering, The University of Melbourne, Victoria 3010, Australia
h i g h l i g h t s In-situ thermal response of borehole heat exchangers in Melbourne were analysed. Slope determination, two variable parameter fitting and the GPM model were applied. Three thermal conductivity values obtained were applied in TRNSYS simulations. The GPM model provides better agreement with measured temperatures from boreholes.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 March 2014 Accepted 21 July 2014 Available online 31 July 2014
The ability to quantify the ground thermal properties of a site is important for the appropriate sizing of ground heat exchangers. This paper presents the results of in-situ measurements of the thermal properties of two 40 m deep borehole thermal storage systems in Melbourne. The measurements from the tests were analysed using three methods: conventional slope determination, two variable parameter fitting technique and using Geothermal Properties Measurement (GPM) model. The values of effective thermal conductivities obtained from the three methods were applied in 12 TRNSYS simulations. The value from the GPM model was found to give relatively less error when the measured and simulated outlet temperatures were compared. Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved.
Keywords: Thermal response test Ground thermal conductivity Borehole thermal resistance Inter-seasonal thermal storage
1. Introduction The effective thermal conductivity of the soil and borehole thermal resistance are important parameters for sizing the borehole heat exchanger (BHE) of an inter-seasonal thermal storage system or a ground-coupled heat pump. These properties vary with the type of soil, local soil moisture content and particle size and hence are site-specific. Moreover, soil type variation within a borehole depth may also exist. It is therefore necessary to determine the thermal properties of the ground at each specific installation site. The effective ground thermal conductivity and effective borehole thermal resistance can be determined either by referring to existing literature relevant to the type of soil, conducting heat probe tests on soil samples or by performing an in-situ test [1e3]. For an estimation of the soil thermal conductivity based on the literature, the task is to identify the type of soil and its moisture content and refer to the existing data. As the soil type may vary
* Corresponding author. E-mail address: [email protected] (L. Aye). http://dx.doi.org/10.1016/j.applthermaleng.2014.07.058 1359-4311/Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved.
along the length of the borehole, this estimate may not necessarily represent the true value as the estimate is confined to only one type of soil layer. The data on soil thermal conductivity is available for a range of soil types in the literature as shown in Table 1 [1,2,4e6]. Similarly, the volumetric heat capacity of the soil is also determined based on the type of soil. Another method to determine the soil thermal conductivity is by a heat probe test [7e9]. The test is performed on a soil sample in a laboratory [1]. In this method, constant heat is supplied to the soil and the corresponding change in soil temperature is observed over a given time period. Based on the temperature change of the soil, the thermal conductivity can be determined by a parametric estimation. Because only a small sample of soil is tested, the value obtained may not be considered to be representative for the entire depth of the borehole. Since the borehole may have different types of soil along its length with different thermal properties, estimates from this method may also not be representative of the entire length of the borehole. The third method of determining ground thermal properties is by an in-situ thermal response test (TRT) combined with a parametric estimation algorithm [2,3,10,11]. This method is a mimic of the BHE system. It was first proposed by Mogensen [12] and further
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Table 1 Thermal conductivity and volumetric heat capacity. Material
Thermal conductivity (W m1 K1)
Volumetric heat capacity (kJ m3 K1)
Gravel Sand Silt Clay Clay stone Sandstone
2.0e3.3 1.5e2.5 1.4e2.0 0.9e1.8 2.6e3.1 3.1e4.3
2200e2700 2500e3000 2500e3100 2200e3200 2340e2350 2190e2200
studied and developed by Austin [3], Austin, Yavuzturk and Spitler [13] and Gehlin [14]. Since then several researchers [1,10,15e19] have used the TRT method to determine the BHE thermal conductivity based on the methodology described by the above authors. The principle of the TRT is based on constant heat injection from a source for 50e60 h by using the BHE. Austin [3] found that by conducting the test for a minimum of 50 h, the BHE thermal conductivity obtained would be within 2% of the value that would be obtained had the test been conducted for a longer duration. As the performance of the system is not only affected by the soil thermal properties but also by the properties of the grout, U-tube pipe and heat transfer fluid, the thermal conductivity obtained by this method is the effective thermal conductivity of the ground considering the BHE characteristics. The value of measured effective thermal conductivity from the TRT is influenced by the duration of the test. The heat transfer during the initial few hours of the test is dominated by transient effects. Therefore, it is recommended to disregard the measured data during the initial 10e15 h [14]. This is mainly to avoid transient temperature gradients and using data which is significantly influenced by the grout thermal properties. Austin [3] found that best estimates were obtained when 12 h of initial data were disregarded and Gehlin [20] suggests discarding 12e20 h initial data when processing the experimental data. The number of hours to discard depends on when the temperature reaches a steady state. A further study conducted by Yu et al. [21] found that after 35 h of testing, the value of measured effective thermal conductivity became relatively constant. The inconsistency in the value of soil thermal conductivity resulting from the different methods was reported by Witte, Gelder and Spitler [1]. They compared the values of soil thermal parameters by several methods. The types of soil while drilling a 35 m borehole were identified. The borehole comprised of 11 different soil types. Based on these, Witte, Gelder and Spitler [1] obtained the soil thermal conductivity for each layer from the literature. They estimated soil thermal conductivity for the borehole to vary from 1.2 to 3.4 W m1 K1 with weighted average of 1.90 W m1 K1. Next they determined soil thermal conductivity by performing the heat probe test on nine samples from different layers of soil from the same borehole. The measured thermal conductivity varied from 1.09 to 2.87 W m1 K1 with a weighted average of 2.09 W m1 K1. Finally, the effective soil thermal conductivity was determined by conducting an in-situ test on the same borehole. From the test they estimated the average effective soil thermal conductivity to be 2.10 W m1 K1. While these estimates show that the soil thermal conductivity obtained by the laboratory and in-situ test are almost equal, the results may have been different had the laboratory test been conducted on only one soil sample. Similar results were obtained in another test conducted by Witte [5] in Netherlands. The researcher estimated soil thermal conductivity to be 1.83 W m1 K1 from the literature, 2.10 W m1 K1 from a laboratory test and 2.13 from in-situ test. In both the studies, the authors observed that the average soil thermal
conductivity estimate based on reference tables to be the lowest, followed by the laboratory test and the in-situ test. These comparisons suggest that the value obtained for the thermal conductivity of the soil varies with the method used to determine it. Furthermore, the literature also suggests that the most common and accepted method is the TRT. Since an estimation of effective thermal conductivity of soil of the borehole on site is essential, the TRT method was used to determine the effective soil thermal conductivity and borehole effective thermal resistance of boreholes to be used for an inter-seasonal underground thermal storage system which is located at the Burnley campus of the University of Melbourne. Thus, the aim of this paper is to determine the thermal conductivity and resistance of the boreholes used for inter-seasonal heat and coolth storage in Melbourne. The measurements from the tests were analysed using three methods: conventional slope determination, two variable parameter fitting technique and using Geothermal Properties Measurement (GPM) model. 2. TRT set up Fig. 1 illustrates the TRT set up schematically. The TRT was performed on two 40 m deep boreholes, i.e. heat storage borehole (HSB) and coolth storage borehole (CSB), each borehole having two U-tubes. The two boreholes are 8 m apart centre-to-centre. The TRT set up consists of a 0.125 m3 electric hot water tank rated at 4.8 kW, 0.2 m3 buffer tank, water pump, flow meter, high density polyethylene (HDPE) pipes and temperature sensors. These pipes form the piping network from the tanks to the borehole heat exchanger headers. All the surface pipes and the water tank were insulated at the system, which detailed descriptions can be found in Lhendup, Aye and Fuller [22]. Fig. 2 illustrates the geometry and layout of the TRT boreholes. Additionally, there are temperature sensors inserted at 2, 21 and 40 m depths to monitor the temperature of the fluid along the borehole heat exchanger. Soil around the borehole was assumed to be homogeneous with a constant infinite line source at the centre of the borehole. A total of four TRTs, two on each
Fig. 1. Schematic of the TRT set-up.
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287
Fig. 2. Layout and geometry of TRT boreholes.
borehole were performed. The tests were performed for a period of 96.5 h. Heat was injected into the borehole using an electric hot water heater by maintaining a flow approximately 840 kg h1 loop1 throughout the experiment. The inlet and outlet temperatures were recorded using a data logger (DataTaker® DT600) every two minutes during the tests. Table 2 summarises the TRT set up parameters.
Fig. 3. Monthly average of daily ambient and ground temperature at 2, 21 and 40 m deep from Feb 2012 to Feb 2013.
4. Response analysis 3. Undisturbed ground temperature The main advantage of using a ground coupled heat pump (GCHP) is that the ground temperature is nearly constant throughout the year. The undisturbed ground temperature indicates the temperature of the ground under the normal conditions. Prior to the TRT, the undisturbed ground temperature was determined by two methods. The detailed procedure and results can be found in Lhendup, Aye and Fuller [22]. The undisturbed ground temperature was also measured directly from the borehole (MB2) located at two metres from the centre of the HSB (Fig. 2). There are three thermistors installed at 2, 21 and 40 m depths. The borehole was filled with same type of grout as the other boreholes discussed in the preceding sections. Temperature recording was started 45 days after the borehole was grouted and continued for next 20 months. Fig. 3 shows the monthly average of daily ground temperatures measured at those depths. At 2 m, the ground temperature follows the trend of the ambient temperature and there is a time shift of 60 days. Thus, the maximum and minimum temperatures at 2 m depth occur 60 days later than the corresponding values of the ambient temperature. The amplitude of temperature fluctuation decreases with the depth. At 21 m depth, the ground temperature was observed to be 17.2 C while at 40 m depth, it was 17.4 C. In both cases the ground temperature is within the range of measurement uncertainties.
Table 2 TRT parameters. Parameter Borehole Depth Diameter Back fill Heat exchanger (U-tube) Material Type Outer diameter Inner diameter Conductivity Shank spacing Heat carrier fluid Type Conductivity Specific heat capacity Density Flow rate Test duration
Unit
Value
m 40 mm 115 Cement with 15% bentonite Polyethylene Double U-tube mm mm W m1 K1 mm
25 21.32 0.4 70
Water W m1 K1 kJ kg1 K1 Kg m3 kg h1 loop1 h
0.6 4.18 1000 @ 25 C 840 96
The two most-commonly used analytical models for computing the effective thermal conductivity are cylindrical source and line source models. Several researchers [1,10,15e17,23,24] used the line source model to determine the effective thermal conductivity from TRT data. The line source model is widely used due to its simplicity and relatively better accuracy [10,14]. Furthermore, Gehlin [14] found that temperature response from the line source model and measured data showed closer agreement than the other models. In this study the line source model (Equation (1)) [3,14] was used to determine the effective thermal conductivity from the experimental data. Equation (1) was derived based on the assumptions of negligible axial temperature gradient, infinite length of the borehole and a constant heat source.
(
Qinj lnðtÞ þ 4plg D !)
Tfm ¼
þ Tug Tfm ¼
Tin þ Tout 2
Qinj D
for t
5rb2 a
1 4plg
ln
! ! ! 4a g þ R b rb2 (1)
(2)
where Tfm is the mean temperature of water circulating through the BHE (K) defined in Equation (2), Qinj the heat injected to the ground (W), lg is the effective thermal conductivity of the BHE (W m1 K1), D is borehole depth (m), t is the elapsed time from the beginning of test, a is the thermal diffusivity (m2 s1), rb is the radius of borehole (m), g is the Eulers's constant (0.5772), Rb is the effective borehole thermal resistance of BHE (mK W1), Tug is the undisturbed ground temperature (K), Tin is the BHE inlet water temperature (K) and Tout is the BHE outlet water temperature (K). In Equation (1), only the first term is variable and the other terms on the right hand side are constant. Therefore Equation (1) is further simplified to Equation (3).
Tfm ¼
Qinj lnðtÞ þ b which can be generalised as y ¼ ax þ b 4plg D (3)
where b is a constant and the term a ¼ Qinj/4plgD is the slope of the curve determined from the plot of Tfm and the natural logarithm of time in seconds after discarding the initial few hours of data. Thus the soil thermal conductivity lg can be calculated from Equation (4).
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Fig. 4. Temperature response and power input during TRT on Loop-1 of heat storage borehole (HSB_L1).
Fig. 6. Temperature response and power input during TRT on Loop-1 of coolth storage borehole (CSB_L1).
4.1. Discard time
lg ¼
Qinj 1 4pD a
(4)
The effective soil thermal resistance Rb can be determined by Equation (5).
b Tug 1 Rb ¼ 4plg Qinj D
! ! 4a ln 2 g rb
(5)
The following assumptions were made when determining the effective ground thermal conductivity and resistance from the test data: (i) no ground water flow across the borehole; (ii) the contact thermal resistance between the pipe and the grout, and that of grout and the soil are negligible; (iii) the effect of heat transfer from horizontal ground surface to the borehole is negligible. Water was initially heated to 60 C. Once the water attained this temperature, the pump was run to circulate the water for four days. Figs. 4e7 shows the detailed temperature response and power input during the four TRTs. The figures indicate that the mean temperature response during the various TRTs is not smooth but varies with time. It was observed that the temperature fluctuation is not due to ambient coupling but due to the variation of input power to the water heater which fluctuated depending on the time of the day and day of the week. The inlet and outlet temperatures of the circulating water increases rapidly in the beginning. This is due to transient heat transfer during the initial period. After about 20 h since the start of the test the rate of heat transfer stabilises.
Fig. 5. Temperature response and power input during TRT on Loop-2 of heat storage borehole (HSB_L2).
As suggested by several researchers in the past it is advisable to discard the initial few hours of data as the heat transfer in the initial hours take place in the grout of the borehole instead of the ground [3,14,20,21]. Apparently a different discard time could lead to different slopes and this in turn could result in different values of soil thermal conductivity and resistance. To assess how the discard time affects the thermal conductivity and resistance of the soil, a series of evaluations were performed with different discard times. Figs. 8 and 9 shows variation of soil thermal conductivity and resistance with different discard times. Thus, as pointed out by several researchers in the past, it is important to discard the correct initial time period while using the conventional slope determination method so that the soil thermal properties are reasonably acceptable and representative. In order to determine the initial time period to be discarded, soil thermal conductivity was plotted with respect to the time elapsed. The initial discarded time period was based on the period after which the calculated soil thermal conductivity is relatively steady with respect to the experiment time elapsed. As shown in Fig. 10, the soil thermal conductivity is relatively varying within the first 20 h due to capacitance effect of the borehole and the grout. Therefore, first 20 h data was discarded in the analysis in Section 4.3. 4.2. Test duration According to Austin [3] and Yavuzturk [25], the test duration should be more than 50 h including the discard time, otherwise the
Fig. 7. Temperature response and power input during TRT on Loop-2 of coolth storage borehole (CSB_L2).
T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293
Fig. 8. Ground thermal conductivity with varying discard times.
uncertainty in estimated thermal conductivity and borehole resistance is likely to be significant. Austin [3] also found that after a 50 h test, the thermal conductivity is within 2% of a longer test. In this paper the TRT was performed until the change in ground thermal conductivity and resistivity is not significant. From the results, it was found that after 70 h the thermal conductivity and resistivity is relatively constant as illustrated in Figs. 10 and 11. 4.3. Slope determination method The ground thermal conductivity and resistance were determined using Equations (3) and (4). Figs. 12e15 shows the plot of mean fluid temperature versus natural logarithm of the time in seconds. The resulting effective thermal conductivity and thermal resistance of the soil is shown in Table 3. Ideally the thermal conductivity determined from the two TRTs conducted on the same borehole should be equal for the same test parameters. However, this was not the case as shown in Table 3. There was a variation of 0.2 and 0.4 W m1 K1for two different loops of HSB and CSB respectively. The difference in effective thermal conductivities and effective thermal resistance between the two loops in the same borehole may be attributed to two reasons. The first reason is due to uneven twisting of the loops while inserting into the borehole. This could result in an uneven distance between the borehole and the U-tubes. The other reason is due to the fact the second TRT was conducted on disturbed ground. The temperatures of the ground surrounding the boreholes have changed at the end of the first TRT. This is evident from the monitoring borehole temperatures recorded at one metre distance from the centre of borehole and at 21 m deep as shown in Fig. 16. It should be noted that the tests were conducted for one loop of the
Fig. 9. Ground thermal resistance with varying discard times.
289
Fig. 10. Thermal conductivity for different test duration.
double-u heat exchanger since our immediate interest was in using one loop for follow-on thermal storage experiments. ON/OFF in Fig. 16 indicates the time at which TRT was started and stopped in each loop of the boreholes. At the end of the first TRT the ground temperature has increased by 2 C. The temperature gradient will induce natural convection in the ground water and enhance heat transfer in and around the borehole heat exchanger. Due to this the heat transfer per unit length in the second TRT on the same borehole is higher than that of the first TRT (Table 3). Moreover, the power supply voltage at the site was fluctuating during the day and night, and on week-days and weekends. Thus the input heat to the BHE was not maintained constant over the test period. Therefore the slope determination method of finding thermal conductivity may not provide a representative value of the effective thermal conductivity, as Equation (1) was based on the assumption of constant heat input. In order to understand the variation of thermal conductivity due to a non-constant heat input, the calculated effective thermal conductivity of the ground was compared to the values derived from a two parameter curve fitting method and a geothermal properties measurement (GPM) computer program [26].
4.4. Two parameter curve-fitting The thermal properties of the BHE were estimated using the two parameter curve fitting method based on Equation (1). Curvefitting was done using SigmaPlot. The only parameters that were allowed to vary are the borehole effective thermal conductivity and effective thermal resistance. The SigmaPlot curve fitter is based on the MarquardteLevenberg algorithm. It finds the parameters (lg & Rb) by an iterative process that gives the best fit between the
Fig. 11. Thermal resistance for different test duration.
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Fig. 14. Logarithmic time plot of mean fluid temperature (CSB_L1). Fig. 12. Logarithmic time plot of mean fluid temperature (HSB_L1).
The slope determination method based on the line source model needs constant heat input to the BHE, otherwise it affects the accurate determination of the thermal properties of the BHE. Shonder and Beck [26] presented a new method to determine thermal properties from a TRT using a parameter estimation technique and developed a computer program, GPM model. The model is based on parameter estimation using the numerical solution of heat conduction. It minimises the sum of squares of errors between measured and calculated mean fluid temperature with respect to the parameters sought. In this method, the soil and grout volumetric heat capacity should be known to determine the BHE thermal properties. The grout volumetric heat capacity was determined using C-Therm TCi Thermal Conductivity Analyser [27] on two grout samples prepared during the borehole grouting. The value was found to be 1521 kJ kg1 K1. The type of soil on the site is clay. Therefore volumetric heat capacity was assumed to be 1300 kJ kg1 K1 [1]. It should be noted that the thermal conductivity estimates by GPM method is relatively insensitive to the value of the volumetric heat capacity [26]. Unlike the slope determination method which uses average heat input in determining the
thermal properties, GPM uses field-measured heat input which makes it suitable for a non-constant heat input to the BHE. The developers validated GPM with experimental data and the results were found reliable and accurate even for a short test period and also with varying input power. Thus whenever a constant power input could not be maintained, researchers in the past used the GPM method to determine the thermal conductivity from TRT [28]. Saljnikov et al. [29], Roth et al. [10] and Georgiev, Busso and Roth [16] compared borehole thermal conductivity and resistance using slope determination method, two parameter curve fitting and the GPM model. From the slope determination method and two parameter curve fitting method, the thermal conductivity was nearly equal but it was almost 30% higher from the GPM model. Tables 4 and 5 shows a comparison of the thermal conductivity and resistance determined by the conventional slope determination method, curve fitting and GPM model. The results obtained from GPM model and curve fitting methods were found to agree, which is not the case for the conventional slope determination method. The conventional slope determination method varies by 2% to 37% compared with the other two methods. This could be attributed to the assumption in the heat transfer equation that the heat input in the conventional slope determination method is constant throughout the experiment which is not true in this experiment. As a result, slope of the curve in the case of the conventional slope determination method may not be a true representation of the actual slope had the heat input been constant. This explains the difference between the conventional slope determination method and the other two methods. In the case of a constant heat transfer rate, the slope determination method and parameter estimation were found to give similar values [1] which is not so in this case as the heat transfer rate is not constant. Based on the four TRTs conducted on the two boreholes and their corresponding results from the three methods, it is reaffirmed
Fig. 13. Logarithmic time plot of mean fluid temperature (HSB_L2).
Fig. 15. Logarithmic time plot of mean fluid temperature (CSB_L2).
equation and the measured data by minimising the sum of the squares of the difference between each pair of measured and the simulated values (Equation (6)). The process continues until the differences between the measured and simulated values converge.
SD ¼
n X
ðTmea Tsim Þ2
(6)
i¼1
4.5. Geothermal properties measurement (GPM) model
T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293 Table 3 Effective ground thermal conductivity and borehole thermal resistance from slope determination method. Loops HSB_L1 HSB_L2 CSB_L1 CSB_L2
Heat transfer rate (W m1)
Slope
86.91 89.44 99.25 103.29
3.92 4.41 2.95 3.61
Constant 6.55 0.82 14.70 8.82
Conductivity (W m1 K1)
Resistance (mK W1)
1.76 1.61 2.68 2.28
0.21 0.18 0.18 0.17
that the conventional slope determination method using the line source model may not represent the true effective thermal conductivity and borehole effective thermal resistance when the heat input to the BHE is variable. During each test the input power varied up to 10% which is more than the uncertainty of the power measurement. The effective thermal conductivity and resistance determined by the GPM model were considered to be the most representative of this BHE. The effect of ground water has not been evaluated in this paper. 5. TRNSYS simulations The TRT were also studied by means of TRNSYS simulations. The BHE was represented by a Type 257, a modified version of TEES Type 557 [30]. The measured time series borehole inlet and the ambient temperatures, and flow rates were used as inputs to the model. In order to further analyse the effect of the different methods of analysing the TRT data, the simulation was performed for different values of effective thermal conductivity shown in Table 4. A total of 12 simulations were performed. The measured and simulated borehole outlet temperatures were compared. From the results, root mean square error (RMSE) and mean bias error (MBE) of the outlet water temperatures were determined (Figs. 17 and 18). Both RMSE and MBE were found to be the lowest for the thermal conductivity corresponding to the value determined by the GPM model except in case of HSB-L1. For HSB_L1, the slope determination method gives the minimum RMSE and MBE. This finding reinforces the fact that the GPM model gives relatively appropriate values when the input power during the TRT is not constant. The above comparison is only true for the assumed constant grout thermal conductivity. From the TRNSYS simulations, it was found that the simulated and the measured mean outlet water temperatures agreed well. The effective thermal conductivity obtained from the GPM model
Fig. 16. Monitoring borehole temperature at 21 m depth and 1 m from the centre of BHE during TRT (L1: Loop-1, L2: Loop-2).
291
Table 4 Comparison of effective thermal conductivity (W m1 K1) using different evaluation methods. Evaluation method
HSB_L1
HSB_L2
CSB_L1
CSB_L2
Slope determination Curve-fitting GPM model Test date
1.76 2.43 2.22 8e12 March 2012
1.61 2.08 1.95 28 Marche 1 April 2012
2.68 2.28 2.21 2e6 March 2012
2.28 2.24 2.08 14e18 March 2012
Table 5 Comparison of borehole effective thermal resistance (mK W1) using different evaluation methods. Evaluation method
HSB_L1
HSB_L2
CSB_L1
CSB_L2
Slope determination Curve fitting GPM model
0.19 0.27 0.16
0.18 0.23 0.17
0.19 0.17 0.13
0.20 0.17 0.13
gives a lower deviation than the slope determination and the curve fitting methods.
6. Energy balance It is important to account for the heat exchange in the ground, losses in the pipes and buffer tank and heat input to the electrical heater and the pump. This is because energy injected into the ground is being used to determine the ground thermal properties. Fig. 19 shows energy model of the TRT circuit. Based on the First Law of Thermodynamics, the total energy in the TRT loop can be expressed as: heater input þ pump input ¼ heat injected þ loss in the pipes from heater to the BHE þ loss in the pipes from BHE to the buffer tank þ losses from buffer tank to the heater (Equations (7) and (8)).
Qt ¼ Qinj þ Qloss
(7)
QHT þ QP ¼ Qinj þ QPL1 þ QPL2 þ QHTL
(8)
_ p;wat ðTin Tout Þ Qinj ¼ mC
(9)
_ p;wat ðTho Tin Þ QPL1 ¼ mC
(10)
Fig. 17. Plot of RMSE and effective thermal conductivity of BHE.
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Fig. 20. Fraction of heat injected and lost during TRT on HSB. Fig. 18. Plot of MBE and effective thermal conductivity of BHE.
%Qinj ¼ _ p;wat ðTout Tbi Þ QPL2 ¼ mC
_ p;wat ðTin Tout Þ mC ðQHT þ QP Þ
(11) %Qloss ¼
_ p;wat ðTho Tbo Þ QHTL ¼ QHT þ QP mC
(13)
(12)
where Qt is the total heat input during the TRT (W), Qinj is the heat injected to the ground (W) defined in Equation (9); Qloss is the total heat loss (W); QHT and QP are the electricity input to the heater and the pump (W); QPL1 is the heat loss in the pipe between the heater and the BHE (W) defined in Equation (10); QPL2 is the heat loss in the pipe between the BHE and the buffer tank (W) defined in Equation (11); QHTL is the heat loss between the buffer tank and heater including the pump and the heater (W) defined in Equation (12); m_ mass flow rate (kg s1), Cp,wat is the specific heat capacity of water (kJ kg1 K1), Tin and Tout are the ground inlet and outlet temperatures ( C); Tho is the heater outlet temperature ( C), Tbi and Tbo are the buffer tank inlet and outlet temperatures ( C). The percentage heat injected and lost can be expressed as a percentage of total heat input to the system and were determined using Equations (13) and (14) respectively.
ðQPL1 þ QPL2 þ QHTL Þ ðQHT þ QP Þ
(14)
The summation of the fractions for heat inputs, heat injected to the ground and the heat losses should be equal to 1. Figs. 20 and 21 shows the fraction of heat injected and lost with respect to the heat input. In the HSB, the average heat loss is about 30% while the average heat injected into the ground is 70%. In the CSB, the average heat loss is 17% while the average heat injected is 81%. The summation of heat transfer in HSB is 100% while it is about 98% in the CSB. The difference could be attributed to the uncertainties in the temperature sensors and the measuring instruments. In all the loops there is some energy unaccounted for as shown in Table 6. The unaccounted energy is within the measurement uncertainties. Therefore, Qinj, calculated using Equation (8), is a true representative of the energy injected into the ground.
7. Conclusions In-situ thermal response tests have been conducted on two boreholes with a view to use for inter-seasonal heat and coolth storage in Melbourne. A total of four TRT (two on each borehole) were performed on the two 40 m deep boreholes. From the four TRT, it can be concluded that it is important to maintain constant power input during the in-situ tests. If not the effective thermal
Fig. 19. TRT energy model.
Fig. 21. Fraction of heat injected and lost during TRT on CSB.
T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293 Table 6 Average energy balance. QHT þ QP (MJ)
HSB_L1 HSB_L2 CSB_L1 CSB_L2
17.60 17.51 17.48 17.50
Qinj (MJ)
12.31 12.75 14.21 14.89
Qloss (MJ)
5.21 4.55 2.87 2.08
Unaccounted (MJ)
(%)
0.08 0.20 0.39 0.52
0.5 1.1 2.2 3.0
conductivity obtained from the TRT will not be a true representative of the reality. Since the heat input during the TRT in this study was varying, the effective thermal conductivity and borehole effective thermal resistance were compared using three methods: slope determination, curve fitting and GPM model. Results from the GPM model and two parameters curve fitting methods agree well. The slope determination method results in inconsistent thermal conductivity and resistance for the same borehole due to the unstable heat input to the TRT system. The thermal conductivities evaluated by the three methods were used for TRNSYS simulations. Among the three methods, GPM model was found to have lowest RMSE and MBE when compared to the simulated values for borehole outlet water temperatures. The effective thermal conductivity determined from the second TRT on the same borehole was found to be lower than that of the first TRT. This is because the second TRT was conducted few days away from the first one on the disturbed ground. A lesson learned is that it is necessary to have enough time lag, before another insitu TRT, to allow the ground temperature return back to its initial value.
References [1] H.J.L. Witte, G.J.V. Gelder, J.D. Spitler, In-situ measurement of ground thermal conductivity: a Dutch perspective, ASHRAE Trans. 108 (2002) 268e272. [2] D. Banks, An Introduction to Thermogeology: Ground-source Heating and Cooling, Blackwell Publishing, Oxford, 2008. [3] W.A. Austin, Development of an In-situ System for Measuring Ground Thermal Properties (Master Thesis), Oklahoma State University, Stillwater, Oklahoma, 1998. [4] ASHRAE, ASHRAE Handbook, Heating, Ventilating, and Air-conditioning Applications, American Society of Heating and Refrigeration and AirConditioning Engineers Inc., Atlanta, 1999. [5] H.J.L. Witte, Geothermal response tests with heat extraction and heat injection: examples of application in research and design of geothermal ground €ischer workshop über Geothermische Response heat exchangers, in: Europa Tests, EPFL, Lausanne, 2001. [6] L. Jun, Z. Xu, G. Jun, Y. Jie, Evaluation of heat exchange rate of GHE in geothermal heat pump systems, Renew. Energy 34 (2009) 2898e2904. [7] O.K. Nusier, N.H. Abu-Hamdeh, Laboratory techniques to evaluate thermal conductivity for some soils, Heat Mass Transf. 39 (2003) 119e123. [8] K.L. Bristow, R.D. White, G.J. Kluitenberg, Comparison of single and dual probes for measuring soil thermal properties with transient heating, Aust. J. Soil Res. 32 (1994) 447e464.
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[9] N.H. Abu-Hamdeh, R.C. Reeder, Soil thermal conductivity: effects of density, moisture, salt concentration, and organic matter, Am. J. Soil. Sci. Soc. 64 (2000) 1285e1290. [10] P. Roth, A. Georgiev, A. Busso, E. Barraza, First in situ determination of ground and borehole thermal properties in Latin America, Renew. Energy 29 (2004) 1947e1963. [11] G. Florides, S. Kalogirou, First in situ determination of the thermal performance of a U-pipe borehole heat exchanger, in Cyprus, Appl. Therm. Eng. 28 (2008) 157e163. [12] P. Mogensen, Fluid to duct wall heat transfer in duct system heat storages, in: International Conference on Subsurface Heat Storage in Theory and Practice, Stockholm, Sweden, 1983, pp. 652e657. [13] W.A. Austin, C. Yavuzturk, J.D. Spitler, Development of an in-situ system for measuring ground thermal properties, ASHRAE Trans. 106 (2000) 365e379. [14] S. Gehlin, Thermal Response Test: Method Development and Evaluation (PhD Thesis), Division of Water Resources Engineering, Department of Environmental Engineering, Lulea University of Technology, Lulea, 2002, p. 191. [15] S. Hwang, R. Ooka, Y. Nam, Evaluation of estimation method of ground properties for the ground source heat pump system, Renew. Energy 35 (2010) 2123e2130. [16] A. Georgiev, A. Busso, P. Roth, Shallow borehole heat exchanger: response test and charging-discharging test with solar collectors, Renew. Energy 31 (2006) 971e985. [17] H. Esen, M. Inalli, In-situ thermal response test for ground source heat pump system in Elazig, Turkey, Energy Build. 41 (2009) 395e401. [18] S. Signorelli, S. Bassetti, D. Pahud, T. Kohl, Numerical evaluation of thermal response tests, Geothermics 36 (2007) 141e166. [19] H. Wang, C. Qi, H. Du, J. Gu, Improved method and case study of thermal response test for borehole heat exchangers of ground source heat pump system, Renew. Energy 35 (2010) 727e733. [20] S. Gehlin, Thermal Response Test-in-situ Measurements of Thermal Properties in Hard Rock (Licentiate Thesis), Division of Water Resources Engineering, Department of Environmental Engineering, Lulea University of Technology, Lulea, 1998, p. 73. [21] M.Z. Yu, X.F. Peng, X.D. Li, Z.H. Fang, A simplified model for measuring thermal properties of deep ground soil, J. Exp. Heat Transf. 17 (2004) 119e130. [22] T. Lhendup, L. Aye, R.J. Fuller, Experimental study of coolth charging of an inter-seasonal underground thermal storage system, in: Solar 2012, 50th Annual AuSES Conference, Swinburne University of Technology, Hawthorn Campus, Melbourne, Australia, 2012. [23] M.H. Sharqawy, S.A. Said, E.M. Mokheimer, M.A. Habib, H.M. Badr, N.A. AlShayea, First in situ determination of the ground thermal conductivity for borehole heat exchanger applications in Saudi Arabia, Renew. Energy 34 (2009) 2218e2223. [24] M.H. Sharqawy, E.M. Mokheimer, H.M. Badr, Effective pipe-to-borehole thermal resistance for vertical ground heat exchangers, Geothermics 38 (2009) 271e277. [25] C. Yavuzturk, Modelling of Vertical Ground Loop Heat Exchangers for Ground Source Heat Pump Systems (PhD Thesis), Mechanical Engineering, Oklahoma State University, 1999, p. 251. [26] J.A. Shonder, J.V. Beck, A New Method to Determine the Thermal Properties of Soil Formations from In-situ Field Tests, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 2000. [27] C-Therm TCi Operator Manual, C-Therm Technologies Ltd., 921 College Hill Road Fredericton, New Brunswick, Canada. [28] D. Banks, J. Withers, R. Freeborn, An overview of the results of in-situ thermal response testing in the UK, in: 11th International Conference on Thermal Energy Storage; Effstock 2009, Stockholm, Sweden, 2009. [29] A. Saljnikov, D. Goricanec, D. Kozic, J. Krope, R. Stipic, Borehole and aquifer thermal energy storage and choice of thermal response test method, in: 4th WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment, Elounda, Greece, 2006. [30] S. Chapuis, Stockage thermique saisonnier dans un champ de puits geothermiques verticaux en boucle fermee (Master Thesis), Department of Mechanical Engineering, Polytechnic School of Montreal, Montreal, 2009.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
In-situ measurement of borehole thermal properties in Melbourne Tshewang Lhendup, Lu Aye*, Robert James Fuller Renewable Energy and Energy Efficiency Group, Department of Infrastructure Engineering, Melbourne School of Engineering, The University of Melbourne, Victoria 3010, Australia
h i g h l i g h t s In-situ thermal response of borehole heat exchangers in Melbourne were analysed. Slope determination, two variable parameter fitting and the GPM model were applied. Three thermal conductivity values obtained were applied in TRNSYS simulations. The GPM model provides better agreement with measured temperatures from boreholes.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 March 2014 Accepted 21 July 2014 Available online 31 July 2014
The ability to quantify the ground thermal properties of a site is important for the appropriate sizing of ground heat exchangers. This paper presents the results of in-situ measurements of the thermal properties of two 40 m deep borehole thermal storage systems in Melbourne. The measurements from the tests were analysed using three methods: conventional slope determination, two variable parameter fitting technique and using Geothermal Properties Measurement (GPM) model. The values of effective thermal conductivities obtained from the three methods were applied in 12 TRNSYS simulations. The value from the GPM model was found to give relatively less error when the measured and simulated outlet temperatures were compared. Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved.
Keywords: Thermal response test Ground thermal conductivity Borehole thermal resistance Inter-seasonal thermal storage
1. Introduction The effective thermal conductivity of the soil and borehole thermal resistance are important parameters for sizing the borehole heat exchanger (BHE) of an inter-seasonal thermal storage system or a ground-coupled heat pump. These properties vary with the type of soil, local soil moisture content and particle size and hence are site-specific. Moreover, soil type variation within a borehole depth may also exist. It is therefore necessary to determine the thermal properties of the ground at each specific installation site. The effective ground thermal conductivity and effective borehole thermal resistance can be determined either by referring to existing literature relevant to the type of soil, conducting heat probe tests on soil samples or by performing an in-situ test [1e3]. For an estimation of the soil thermal conductivity based on the literature, the task is to identify the type of soil and its moisture content and refer to the existing data. As the soil type may vary
* Corresponding author. E-mail address: [email protected] (L. Aye). http://dx.doi.org/10.1016/j.applthermaleng.2014.07.058 1359-4311/Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved.
along the length of the borehole, this estimate may not necessarily represent the true value as the estimate is confined to only one type of soil layer. The data on soil thermal conductivity is available for a range of soil types in the literature as shown in Table 1 [1,2,4e6]. Similarly, the volumetric heat capacity of the soil is also determined based on the type of soil. Another method to determine the soil thermal conductivity is by a heat probe test [7e9]. The test is performed on a soil sample in a laboratory [1]. In this method, constant heat is supplied to the soil and the corresponding change in soil temperature is observed over a given time period. Based on the temperature change of the soil, the thermal conductivity can be determined by a parametric estimation. Because only a small sample of soil is tested, the value obtained may not be considered to be representative for the entire depth of the borehole. Since the borehole may have different types of soil along its length with different thermal properties, estimates from this method may also not be representative of the entire length of the borehole. The third method of determining ground thermal properties is by an in-situ thermal response test (TRT) combined with a parametric estimation algorithm [2,3,10,11]. This method is a mimic of the BHE system. It was first proposed by Mogensen [12] and further
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Table 1 Thermal conductivity and volumetric heat capacity. Material
Thermal conductivity (W m1 K1)
Volumetric heat capacity (kJ m3 K1)
Gravel Sand Silt Clay Clay stone Sandstone
2.0e3.3 1.5e2.5 1.4e2.0 0.9e1.8 2.6e3.1 3.1e4.3
2200e2700 2500e3000 2500e3100 2200e3200 2340e2350 2190e2200
studied and developed by Austin [3], Austin, Yavuzturk and Spitler [13] and Gehlin [14]. Since then several researchers [1,10,15e19] have used the TRT method to determine the BHE thermal conductivity based on the methodology described by the above authors. The principle of the TRT is based on constant heat injection from a source for 50e60 h by using the BHE. Austin [3] found that by conducting the test for a minimum of 50 h, the BHE thermal conductivity obtained would be within 2% of the value that would be obtained had the test been conducted for a longer duration. As the performance of the system is not only affected by the soil thermal properties but also by the properties of the grout, U-tube pipe and heat transfer fluid, the thermal conductivity obtained by this method is the effective thermal conductivity of the ground considering the BHE characteristics. The value of measured effective thermal conductivity from the TRT is influenced by the duration of the test. The heat transfer during the initial few hours of the test is dominated by transient effects. Therefore, it is recommended to disregard the measured data during the initial 10e15 h [14]. This is mainly to avoid transient temperature gradients and using data which is significantly influenced by the grout thermal properties. Austin [3] found that best estimates were obtained when 12 h of initial data were disregarded and Gehlin [20] suggests discarding 12e20 h initial data when processing the experimental data. The number of hours to discard depends on when the temperature reaches a steady state. A further study conducted by Yu et al. [21] found that after 35 h of testing, the value of measured effective thermal conductivity became relatively constant. The inconsistency in the value of soil thermal conductivity resulting from the different methods was reported by Witte, Gelder and Spitler [1]. They compared the values of soil thermal parameters by several methods. The types of soil while drilling a 35 m borehole were identified. The borehole comprised of 11 different soil types. Based on these, Witte, Gelder and Spitler [1] obtained the soil thermal conductivity for each layer from the literature. They estimated soil thermal conductivity for the borehole to vary from 1.2 to 3.4 W m1 K1 with weighted average of 1.90 W m1 K1. Next they determined soil thermal conductivity by performing the heat probe test on nine samples from different layers of soil from the same borehole. The measured thermal conductivity varied from 1.09 to 2.87 W m1 K1 with a weighted average of 2.09 W m1 K1. Finally, the effective soil thermal conductivity was determined by conducting an in-situ test on the same borehole. From the test they estimated the average effective soil thermal conductivity to be 2.10 W m1 K1. While these estimates show that the soil thermal conductivity obtained by the laboratory and in-situ test are almost equal, the results may have been different had the laboratory test been conducted on only one soil sample. Similar results were obtained in another test conducted by Witte [5] in Netherlands. The researcher estimated soil thermal conductivity to be 1.83 W m1 K1 from the literature, 2.10 W m1 K1 from a laboratory test and 2.13 from in-situ test. In both the studies, the authors observed that the average soil thermal
conductivity estimate based on reference tables to be the lowest, followed by the laboratory test and the in-situ test. These comparisons suggest that the value obtained for the thermal conductivity of the soil varies with the method used to determine it. Furthermore, the literature also suggests that the most common and accepted method is the TRT. Since an estimation of effective thermal conductivity of soil of the borehole on site is essential, the TRT method was used to determine the effective soil thermal conductivity and borehole effective thermal resistance of boreholes to be used for an inter-seasonal underground thermal storage system which is located at the Burnley campus of the University of Melbourne. Thus, the aim of this paper is to determine the thermal conductivity and resistance of the boreholes used for inter-seasonal heat and coolth storage in Melbourne. The measurements from the tests were analysed using three methods: conventional slope determination, two variable parameter fitting technique and using Geothermal Properties Measurement (GPM) model. 2. TRT set up Fig. 1 illustrates the TRT set up schematically. The TRT was performed on two 40 m deep boreholes, i.e. heat storage borehole (HSB) and coolth storage borehole (CSB), each borehole having two U-tubes. The two boreholes are 8 m apart centre-to-centre. The TRT set up consists of a 0.125 m3 electric hot water tank rated at 4.8 kW, 0.2 m3 buffer tank, water pump, flow meter, high density polyethylene (HDPE) pipes and temperature sensors. These pipes form the piping network from the tanks to the borehole heat exchanger headers. All the surface pipes and the water tank were insulated at the system, which detailed descriptions can be found in Lhendup, Aye and Fuller [22]. Fig. 2 illustrates the geometry and layout of the TRT boreholes. Additionally, there are temperature sensors inserted at 2, 21 and 40 m depths to monitor the temperature of the fluid along the borehole heat exchanger. Soil around the borehole was assumed to be homogeneous with a constant infinite line source at the centre of the borehole. A total of four TRTs, two on each
Fig. 1. Schematic of the TRT set-up.
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287
Fig. 2. Layout and geometry of TRT boreholes.
borehole were performed. The tests were performed for a period of 96.5 h. Heat was injected into the borehole using an electric hot water heater by maintaining a flow approximately 840 kg h1 loop1 throughout the experiment. The inlet and outlet temperatures were recorded using a data logger (DataTaker® DT600) every two minutes during the tests. Table 2 summarises the TRT set up parameters.
Fig. 3. Monthly average of daily ambient and ground temperature at 2, 21 and 40 m deep from Feb 2012 to Feb 2013.
4. Response analysis 3. Undisturbed ground temperature The main advantage of using a ground coupled heat pump (GCHP) is that the ground temperature is nearly constant throughout the year. The undisturbed ground temperature indicates the temperature of the ground under the normal conditions. Prior to the TRT, the undisturbed ground temperature was determined by two methods. The detailed procedure and results can be found in Lhendup, Aye and Fuller [22]. The undisturbed ground temperature was also measured directly from the borehole (MB2) located at two metres from the centre of the HSB (Fig. 2). There are three thermistors installed at 2, 21 and 40 m depths. The borehole was filled with same type of grout as the other boreholes discussed in the preceding sections. Temperature recording was started 45 days after the borehole was grouted and continued for next 20 months. Fig. 3 shows the monthly average of daily ground temperatures measured at those depths. At 2 m, the ground temperature follows the trend of the ambient temperature and there is a time shift of 60 days. Thus, the maximum and minimum temperatures at 2 m depth occur 60 days later than the corresponding values of the ambient temperature. The amplitude of temperature fluctuation decreases with the depth. At 21 m depth, the ground temperature was observed to be 17.2 C while at 40 m depth, it was 17.4 C. In both cases the ground temperature is within the range of measurement uncertainties.
Table 2 TRT parameters. Parameter Borehole Depth Diameter Back fill Heat exchanger (U-tube) Material Type Outer diameter Inner diameter Conductivity Shank spacing Heat carrier fluid Type Conductivity Specific heat capacity Density Flow rate Test duration
Unit
Value
m 40 mm 115 Cement with 15% bentonite Polyethylene Double U-tube mm mm W m1 K1 mm
25 21.32 0.4 70
Water W m1 K1 kJ kg1 K1 Kg m3 kg h1 loop1 h
0.6 4.18 1000 @ 25 C 840 96
The two most-commonly used analytical models for computing the effective thermal conductivity are cylindrical source and line source models. Several researchers [1,10,15e17,23,24] used the line source model to determine the effective thermal conductivity from TRT data. The line source model is widely used due to its simplicity and relatively better accuracy [10,14]. Furthermore, Gehlin [14] found that temperature response from the line source model and measured data showed closer agreement than the other models. In this study the line source model (Equation (1)) [3,14] was used to determine the effective thermal conductivity from the experimental data. Equation (1) was derived based on the assumptions of negligible axial temperature gradient, infinite length of the borehole and a constant heat source.
(
Qinj lnðtÞ þ 4plg D !)
Tfm ¼
þ Tug Tfm ¼
Tin þ Tout 2
Qinj D
for t
5rb2 a
1 4plg
ln
! ! ! 4a g þ R b rb2 (1)
(2)
where Tfm is the mean temperature of water circulating through the BHE (K) defined in Equation (2), Qinj the heat injected to the ground (W), lg is the effective thermal conductivity of the BHE (W m1 K1), D is borehole depth (m), t is the elapsed time from the beginning of test, a is the thermal diffusivity (m2 s1), rb is the radius of borehole (m), g is the Eulers's constant (0.5772), Rb is the effective borehole thermal resistance of BHE (mK W1), Tug is the undisturbed ground temperature (K), Tin is the BHE inlet water temperature (K) and Tout is the BHE outlet water temperature (K). In Equation (1), only the first term is variable and the other terms on the right hand side are constant. Therefore Equation (1) is further simplified to Equation (3).
Tfm ¼
Qinj lnðtÞ þ b which can be generalised as y ¼ ax þ b 4plg D (3)
where b is a constant and the term a ¼ Qinj/4plgD is the slope of the curve determined from the plot of Tfm and the natural logarithm of time in seconds after discarding the initial few hours of data. Thus the soil thermal conductivity lg can be calculated from Equation (4).
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Fig. 4. Temperature response and power input during TRT on Loop-1 of heat storage borehole (HSB_L1).
Fig. 6. Temperature response and power input during TRT on Loop-1 of coolth storage borehole (CSB_L1).
4.1. Discard time
lg ¼
Qinj 1 4pD a
(4)
The effective soil thermal resistance Rb can be determined by Equation (5).
b Tug 1 Rb ¼ 4plg Qinj D
! ! 4a ln 2 g rb
(5)
The following assumptions were made when determining the effective ground thermal conductivity and resistance from the test data: (i) no ground water flow across the borehole; (ii) the contact thermal resistance between the pipe and the grout, and that of grout and the soil are negligible; (iii) the effect of heat transfer from horizontal ground surface to the borehole is negligible. Water was initially heated to 60 C. Once the water attained this temperature, the pump was run to circulate the water for four days. Figs. 4e7 shows the detailed temperature response and power input during the four TRTs. The figures indicate that the mean temperature response during the various TRTs is not smooth but varies with time. It was observed that the temperature fluctuation is not due to ambient coupling but due to the variation of input power to the water heater which fluctuated depending on the time of the day and day of the week. The inlet and outlet temperatures of the circulating water increases rapidly in the beginning. This is due to transient heat transfer during the initial period. After about 20 h since the start of the test the rate of heat transfer stabilises.
Fig. 5. Temperature response and power input during TRT on Loop-2 of heat storage borehole (HSB_L2).
As suggested by several researchers in the past it is advisable to discard the initial few hours of data as the heat transfer in the initial hours take place in the grout of the borehole instead of the ground [3,14,20,21]. Apparently a different discard time could lead to different slopes and this in turn could result in different values of soil thermal conductivity and resistance. To assess how the discard time affects the thermal conductivity and resistance of the soil, a series of evaluations were performed with different discard times. Figs. 8 and 9 shows variation of soil thermal conductivity and resistance with different discard times. Thus, as pointed out by several researchers in the past, it is important to discard the correct initial time period while using the conventional slope determination method so that the soil thermal properties are reasonably acceptable and representative. In order to determine the initial time period to be discarded, soil thermal conductivity was plotted with respect to the time elapsed. The initial discarded time period was based on the period after which the calculated soil thermal conductivity is relatively steady with respect to the experiment time elapsed. As shown in Fig. 10, the soil thermal conductivity is relatively varying within the first 20 h due to capacitance effect of the borehole and the grout. Therefore, first 20 h data was discarded in the analysis in Section 4.3. 4.2. Test duration According to Austin [3] and Yavuzturk [25], the test duration should be more than 50 h including the discard time, otherwise the
Fig. 7. Temperature response and power input during TRT on Loop-2 of coolth storage borehole (CSB_L2).
T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293
Fig. 8. Ground thermal conductivity with varying discard times.
uncertainty in estimated thermal conductivity and borehole resistance is likely to be significant. Austin [3] also found that after a 50 h test, the thermal conductivity is within 2% of a longer test. In this paper the TRT was performed until the change in ground thermal conductivity and resistivity is not significant. From the results, it was found that after 70 h the thermal conductivity and resistivity is relatively constant as illustrated in Figs. 10 and 11. 4.3. Slope determination method The ground thermal conductivity and resistance were determined using Equations (3) and (4). Figs. 12e15 shows the plot of mean fluid temperature versus natural logarithm of the time in seconds. The resulting effective thermal conductivity and thermal resistance of the soil is shown in Table 3. Ideally the thermal conductivity determined from the two TRTs conducted on the same borehole should be equal for the same test parameters. However, this was not the case as shown in Table 3. There was a variation of 0.2 and 0.4 W m1 K1for two different loops of HSB and CSB respectively. The difference in effective thermal conductivities and effective thermal resistance between the two loops in the same borehole may be attributed to two reasons. The first reason is due to uneven twisting of the loops while inserting into the borehole. This could result in an uneven distance between the borehole and the U-tubes. The other reason is due to the fact the second TRT was conducted on disturbed ground. The temperatures of the ground surrounding the boreholes have changed at the end of the first TRT. This is evident from the monitoring borehole temperatures recorded at one metre distance from the centre of borehole and at 21 m deep as shown in Fig. 16. It should be noted that the tests were conducted for one loop of the
Fig. 9. Ground thermal resistance with varying discard times.
289
Fig. 10. Thermal conductivity for different test duration.
double-u heat exchanger since our immediate interest was in using one loop for follow-on thermal storage experiments. ON/OFF in Fig. 16 indicates the time at which TRT was started and stopped in each loop of the boreholes. At the end of the first TRT the ground temperature has increased by 2 C. The temperature gradient will induce natural convection in the ground water and enhance heat transfer in and around the borehole heat exchanger. Due to this the heat transfer per unit length in the second TRT on the same borehole is higher than that of the first TRT (Table 3). Moreover, the power supply voltage at the site was fluctuating during the day and night, and on week-days and weekends. Thus the input heat to the BHE was not maintained constant over the test period. Therefore the slope determination method of finding thermal conductivity may not provide a representative value of the effective thermal conductivity, as Equation (1) was based on the assumption of constant heat input. In order to understand the variation of thermal conductivity due to a non-constant heat input, the calculated effective thermal conductivity of the ground was compared to the values derived from a two parameter curve fitting method and a geothermal properties measurement (GPM) computer program [26].
4.4. Two parameter curve-fitting The thermal properties of the BHE were estimated using the two parameter curve fitting method based on Equation (1). Curvefitting was done using SigmaPlot. The only parameters that were allowed to vary are the borehole effective thermal conductivity and effective thermal resistance. The SigmaPlot curve fitter is based on the MarquardteLevenberg algorithm. It finds the parameters (lg & Rb) by an iterative process that gives the best fit between the
Fig. 11. Thermal resistance for different test duration.
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Fig. 14. Logarithmic time plot of mean fluid temperature (CSB_L1). Fig. 12. Logarithmic time plot of mean fluid temperature (HSB_L1).
The slope determination method based on the line source model needs constant heat input to the BHE, otherwise it affects the accurate determination of the thermal properties of the BHE. Shonder and Beck [26] presented a new method to determine thermal properties from a TRT using a parameter estimation technique and developed a computer program, GPM model. The model is based on parameter estimation using the numerical solution of heat conduction. It minimises the sum of squares of errors between measured and calculated mean fluid temperature with respect to the parameters sought. In this method, the soil and grout volumetric heat capacity should be known to determine the BHE thermal properties. The grout volumetric heat capacity was determined using C-Therm TCi Thermal Conductivity Analyser [27] on two grout samples prepared during the borehole grouting. The value was found to be 1521 kJ kg1 K1. The type of soil on the site is clay. Therefore volumetric heat capacity was assumed to be 1300 kJ kg1 K1 [1]. It should be noted that the thermal conductivity estimates by GPM method is relatively insensitive to the value of the volumetric heat capacity [26]. Unlike the slope determination method which uses average heat input in determining the
thermal properties, GPM uses field-measured heat input which makes it suitable for a non-constant heat input to the BHE. The developers validated GPM with experimental data and the results were found reliable and accurate even for a short test period and also with varying input power. Thus whenever a constant power input could not be maintained, researchers in the past used the GPM method to determine the thermal conductivity from TRT [28]. Saljnikov et al. [29], Roth et al. [10] and Georgiev, Busso and Roth [16] compared borehole thermal conductivity and resistance using slope determination method, two parameter curve fitting and the GPM model. From the slope determination method and two parameter curve fitting method, the thermal conductivity was nearly equal but it was almost 30% higher from the GPM model. Tables 4 and 5 shows a comparison of the thermal conductivity and resistance determined by the conventional slope determination method, curve fitting and GPM model. The results obtained from GPM model and curve fitting methods were found to agree, which is not the case for the conventional slope determination method. The conventional slope determination method varies by 2% to 37% compared with the other two methods. This could be attributed to the assumption in the heat transfer equation that the heat input in the conventional slope determination method is constant throughout the experiment which is not true in this experiment. As a result, slope of the curve in the case of the conventional slope determination method may not be a true representation of the actual slope had the heat input been constant. This explains the difference between the conventional slope determination method and the other two methods. In the case of a constant heat transfer rate, the slope determination method and parameter estimation were found to give similar values [1] which is not so in this case as the heat transfer rate is not constant. Based on the four TRTs conducted on the two boreholes and their corresponding results from the three methods, it is reaffirmed
Fig. 13. Logarithmic time plot of mean fluid temperature (HSB_L2).
Fig. 15. Logarithmic time plot of mean fluid temperature (CSB_L2).
equation and the measured data by minimising the sum of the squares of the difference between each pair of measured and the simulated values (Equation (6)). The process continues until the differences between the measured and simulated values converge.
SD ¼
n X
ðTmea Tsim Þ2
(6)
i¼1
4.5. Geothermal properties measurement (GPM) model
T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293 Table 3 Effective ground thermal conductivity and borehole thermal resistance from slope determination method. Loops HSB_L1 HSB_L2 CSB_L1 CSB_L2
Heat transfer rate (W m1)
Slope
86.91 89.44 99.25 103.29
3.92 4.41 2.95 3.61
Constant 6.55 0.82 14.70 8.82
Conductivity (W m1 K1)
Resistance (mK W1)
1.76 1.61 2.68 2.28
0.21 0.18 0.18 0.17
that the conventional slope determination method using the line source model may not represent the true effective thermal conductivity and borehole effective thermal resistance when the heat input to the BHE is variable. During each test the input power varied up to 10% which is more than the uncertainty of the power measurement. The effective thermal conductivity and resistance determined by the GPM model were considered to be the most representative of this BHE. The effect of ground water has not been evaluated in this paper. 5. TRNSYS simulations The TRT were also studied by means of TRNSYS simulations. The BHE was represented by a Type 257, a modified version of TEES Type 557 [30]. The measured time series borehole inlet and the ambient temperatures, and flow rates were used as inputs to the model. In order to further analyse the effect of the different methods of analysing the TRT data, the simulation was performed for different values of effective thermal conductivity shown in Table 4. A total of 12 simulations were performed. The measured and simulated borehole outlet temperatures were compared. From the results, root mean square error (RMSE) and mean bias error (MBE) of the outlet water temperatures were determined (Figs. 17 and 18). Both RMSE and MBE were found to be the lowest for the thermal conductivity corresponding to the value determined by the GPM model except in case of HSB-L1. For HSB_L1, the slope determination method gives the minimum RMSE and MBE. This finding reinforces the fact that the GPM model gives relatively appropriate values when the input power during the TRT is not constant. The above comparison is only true for the assumed constant grout thermal conductivity. From the TRNSYS simulations, it was found that the simulated and the measured mean outlet water temperatures agreed well. The effective thermal conductivity obtained from the GPM model
Fig. 16. Monitoring borehole temperature at 21 m depth and 1 m from the centre of BHE during TRT (L1: Loop-1, L2: Loop-2).
291
Table 4 Comparison of effective thermal conductivity (W m1 K1) using different evaluation methods. Evaluation method
HSB_L1
HSB_L2
CSB_L1
CSB_L2
Slope determination Curve-fitting GPM model Test date
1.76 2.43 2.22 8e12 March 2012
1.61 2.08 1.95 28 Marche 1 April 2012
2.68 2.28 2.21 2e6 March 2012
2.28 2.24 2.08 14e18 March 2012
Table 5 Comparison of borehole effective thermal resistance (mK W1) using different evaluation methods. Evaluation method
HSB_L1
HSB_L2
CSB_L1
CSB_L2
Slope determination Curve fitting GPM model
0.19 0.27 0.16
0.18 0.23 0.17
0.19 0.17 0.13
0.20 0.17 0.13
gives a lower deviation than the slope determination and the curve fitting methods.
6. Energy balance It is important to account for the heat exchange in the ground, losses in the pipes and buffer tank and heat input to the electrical heater and the pump. This is because energy injected into the ground is being used to determine the ground thermal properties. Fig. 19 shows energy model of the TRT circuit. Based on the First Law of Thermodynamics, the total energy in the TRT loop can be expressed as: heater input þ pump input ¼ heat injected þ loss in the pipes from heater to the BHE þ loss in the pipes from BHE to the buffer tank þ losses from buffer tank to the heater (Equations (7) and (8)).
Qt ¼ Qinj þ Qloss
(7)
QHT þ QP ¼ Qinj þ QPL1 þ QPL2 þ QHTL
(8)
_ p;wat ðTin Tout Þ Qinj ¼ mC
(9)
_ p;wat ðTho Tin Þ QPL1 ¼ mC
(10)
Fig. 17. Plot of RMSE and effective thermal conductivity of BHE.
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T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293
Fig. 20. Fraction of heat injected and lost during TRT on HSB. Fig. 18. Plot of MBE and effective thermal conductivity of BHE.
%Qinj ¼ _ p;wat ðTout Tbi Þ QPL2 ¼ mC
_ p;wat ðTin Tout Þ mC ðQHT þ QP Þ
(11) %Qloss ¼
_ p;wat ðTho Tbo Þ QHTL ¼ QHT þ QP mC
(13)
(12)
where Qt is the total heat input during the TRT (W), Qinj is the heat injected to the ground (W) defined in Equation (9); Qloss is the total heat loss (W); QHT and QP are the electricity input to the heater and the pump (W); QPL1 is the heat loss in the pipe between the heater and the BHE (W) defined in Equation (10); QPL2 is the heat loss in the pipe between the BHE and the buffer tank (W) defined in Equation (11); QHTL is the heat loss between the buffer tank and heater including the pump and the heater (W) defined in Equation (12); m_ mass flow rate (kg s1), Cp,wat is the specific heat capacity of water (kJ kg1 K1), Tin and Tout are the ground inlet and outlet temperatures ( C); Tho is the heater outlet temperature ( C), Tbi and Tbo are the buffer tank inlet and outlet temperatures ( C). The percentage heat injected and lost can be expressed as a percentage of total heat input to the system and were determined using Equations (13) and (14) respectively.
ðQPL1 þ QPL2 þ QHTL Þ ðQHT þ QP Þ
(14)
The summation of the fractions for heat inputs, heat injected to the ground and the heat losses should be equal to 1. Figs. 20 and 21 shows the fraction of heat injected and lost with respect to the heat input. In the HSB, the average heat loss is about 30% while the average heat injected into the ground is 70%. In the CSB, the average heat loss is 17% while the average heat injected is 81%. The summation of heat transfer in HSB is 100% while it is about 98% in the CSB. The difference could be attributed to the uncertainties in the temperature sensors and the measuring instruments. In all the loops there is some energy unaccounted for as shown in Table 6. The unaccounted energy is within the measurement uncertainties. Therefore, Qinj, calculated using Equation (8), is a true representative of the energy injected into the ground.
7. Conclusions In-situ thermal response tests have been conducted on two boreholes with a view to use for inter-seasonal heat and coolth storage in Melbourne. A total of four TRT (two on each borehole) were performed on the two 40 m deep boreholes. From the four TRT, it can be concluded that it is important to maintain constant power input during the in-situ tests. If not the effective thermal
Fig. 19. TRT energy model.
Fig. 21. Fraction of heat injected and lost during TRT on CSB.
T. Lhendup et al. / Applied Thermal Engineering 73 (2014) 285e293 Table 6 Average energy balance. QHT þ QP (MJ)
HSB_L1 HSB_L2 CSB_L1 CSB_L2
17.60 17.51 17.48 17.50
Qinj (MJ)
12.31 12.75 14.21 14.89
Qloss (MJ)
5.21 4.55 2.87 2.08
Unaccounted (MJ)
(%)
0.08 0.20 0.39 0.52
0.5 1.1 2.2 3.0
conductivity obtained from the TRT will not be a true representative of the reality. Since the heat input during the TRT in this study was varying, the effective thermal conductivity and borehole effective thermal resistance were compared using three methods: slope determination, curve fitting and GPM model. Results from the GPM model and two parameters curve fitting methods agree well. The slope determination method results in inconsistent thermal conductivity and resistance for the same borehole due to the unstable heat input to the TRT system. The thermal conductivities evaluated by the three methods were used for TRNSYS simulations. Among the three methods, GPM model was found to have lowest RMSE and MBE when compared to the simulated values for borehole outlet water temperatures. The effective thermal conductivity determined from the second TRT on the same borehole was found to be lower than that of the first TRT. This is because the second TRT was conducted few days away from the first one on the disturbed ground. A lesson learned is that it is necessary to have enough time lag, before another insitu TRT, to allow the ground temperature return back to its initial value.
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