Field demonstration of a first constant-temperature thermal response test with both heat injection and extraction for ground source heat pump systems

Applied Energy 249 (2019) 79–86

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Field demonstration of a first constant-temperature thermal response test with both heat injection and extraction for ground source heat pump systems☆

T

Jie Jiaa, W.L. Leeb, , Yuanda Chenga ⁎

a b

Department of Built Environment and Energy Utilization Engineering, Taiyuan University of Technology, Taiyuan, China Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong

HIGHLIGHTS

thermal response test was proposed and demonstrated. • ATheconstant-temperature enables simultaneous heat injection and extraction tests. • A testnewdataconcept analysis method was developed based on the finite line source model. • Ground thermal was evaluated for both heat injection and extraction. • Convective effectconductivity enhanced ground heat transfer when heat injection was involved. • ARTICLE INFO

ABSTRACT

Keywords: Borehole heat exchanger Field demonstration Ground source heat pump Ground thermal conductivity Heat transfer Thermal response test

Getting an accurate estimate of site-specific ground thermal conductivity from thermal response tests (TRTs) is crucial to the efficient and sustainable use of ground source heat pump systems. In a conventional TRT, the ground thermal conductivity is estimated by perturbing the ground with a positive heat injection and the response is measured in time. Despite the simplicity, the conventional TRT does not take into account the ground thermal response to cooling pulses. This may lead to mode-biased estimation due to the presence of natural convective effect. To address the problem, a constant-temperature TRT that comprises simultaneous heat injection and extraction was proposed. A test data analysis method was developed based on the finite line-source model. On this basis, a very first field test was performed in Taiyuan, China, demonstrating the use of the proposed TRT concept with full-scale measurements. Results show that, in the case of this field test, the ground thermal conductivities derived separately from heat injection and heat extraction are 1.83 W/(m K) and 1.65 W/ (m K), respectively. The significant difference (10.9%) indicates that when heat injection is involved, the natural convective effect has enhanced ground heat transfer to increase the conductivity estimate. Thus, as compared to the conventional approach, the use of the proposed TRT can improve the characterization of the ground thermal response and conductivity. Relevant results and the test protocol reported in this study will be useful in providing the background information for this technology to be adopted in the ground source heat pump industry.

1. Introduction Ground source heat pumps (GSHPs) take advantage of the moderate temperature of the earth to provide efficient heating and cooling for buildings [1]. In a GSHP system, thermal energy is transferred from/to the ground by circulating a heat transfer fluid in borehole heat exchangers (BHEs). A BHE typically consists of a high-density

polyethylene U-tube buried vertically in a borehole of 20–300 m in depth backfilled with a grout mixture [2]. Site-specific ground thermal conductivity is among the key parameters that characterize the thermal performance of BHEs and thus is an essential basis for BHEs design [3]. Traditionally, its estimation is based on tabulated data or laboratory testing, but these methods disregard the site-specific conditions and effects such as ground water

The short version of the paper was presented at ICAE2018, Aug 22–25, Hong Kong. This paper is a substantial extension of the short version of the conference paper. ⁎ Corresponding author. E-mail address: [email protected] (W.L. Lee). ☆

https://doi.org/10.1016/j.apenergy.2019.04.145 Received 17 December 2018; Received in revised form 18 April 2019; Accepted 20 April 2019 Available online 03 May 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature cp g H k p q r R s t T V z

δ θ ρ σ φ

specific heat capacity (J/kg K) g-function borehole depth (m) thermal conductivity (W/m K) power in p-linear average heat transfer rate per unit depth of borehole (W/m) radial coordinate (m) thermal resistance (m K/W) variable of integration time (s) temperature (°C) volumetric flow rate (m3/s) axial coordinate (m)

Subscript 0 a b f g in out p s

Greek symbol α β γ

dimensionless parameter dimensionless parameter density (kg/m3) dimensionless parameter slope of the line obtained through linear fitting

initial/undisturbed average/mean borehole heat transfer fluid grout mixture borehole inlet borehole outlet p-linear average soil/ground

Superscript

thermal diffusivity (m2/s) dimensionless borehole radius Euler’s constant

*

influences. This leads to a crude design to require a more accurate method for estimation of the ground thermal conductivity. In-situ thermal response test (TRT), which automatically accounts for the total heat transport in the ground with actual borehole characteristics, is a reliable method for determining the ground thermal conductivity [4]. Conducting TRT test prior to the final design of a large installation has become a common practice in many countries [5]. Its popularity also leads to the publication of relevant guidelines on test procedures of a TRT, see References [6] and [7]. The idea of measuring the ground thermal response in-situ is first presented by Mogensen [8] and further developed by Eklöf and Gehlin [9]. Since then, little change has been made over the past decades on the field test methodology of TRT. In a conventional TRT, a heat transfer fluid flowing in a BHE is heated at a constant rate (usually by using electric resistance(s)) to provide a positive heating pulse to perturb the ground initially at equilibrium. The ground thermal response is evaluated by way of monitoring the mean temperature of the fluid at inlet and outlet of the BHE. The observed temperature data are then interpreted by analytical methods or inverse methods using numerical heat transfer models. For analytical methods, the line- [10] and cylindrical- [11] source models are commonly used. Both models are one-dimensional solutions to the heat conduction equation. For numerical methods, Shonder and Beck [12] developed a method using a one-dimensional finite difference model to simulate the ground temperature field. Yavuzturk et al. [13] reported another method utilizing a transient two-dimensional radialaxial finite volume model. More recently, Signorelli et al. [14], Bozzoli et al. [15] and Li et al. [16] developed more sophisticated three-dimensional models for TRT analysis. The advantage of numerical methods is able to provide detailed representation of the borehole geometry and characteristics [17]. However, they are more complex and time-consuming due to the amount of input data required, thus limiting their practical use [18]. Besides the above mentioned studies, relevant works have also been carried out on various aspects including: determination of proper test duration [19]; identification of test error [20]; modelling of heat transfer phenomenon [21]; and uncertainty [22] and sensitivity [23] analysis of derived estimates. Despite the research efforts, it is noted that, though GSHPs operate in both heat injection (in the summer) and extraction (in the winter) modes, previous works on TRTs typically consider only the ground thermal response to positive heating pulses [24]. The underlying

dimensionless

assumption is that the ground heat transfer is governed only by conduction, such that the conductivity estimates derived from heat injection and extraction tests are identical. However, this may not be true in practice. Witte [25] carried out a series of TRTs in Wales, UK, and found that, for the same borehole, the conductivity estimates resulting from heat injection are 10% to 15% higher than those from heat extraction. It is further found that heat injection during a TRT will create a temperature gradient in and around the borehole, leading to a densitydriven convective flow of ground moisture [26]. This convective effect enhances the ground heat transfer and thus increases conductivity estimates [27]. In this regard, conventional TRTs can be improved by including the evaluation of ground thermal response to cooling pulses to avoid mode-biased estimation. This concept also enables in-situ examination if a BHE is influenced by the convective effect. The presence of the convective flow makes it essential to find a proper heat injection rate for the implementation of conventional TRTs. This is because a higher or lower injection rate may correspondingly increase or decrease natural convection, resulting in inaccurate measurement of ground thermal conductivity. Thus the determination of the injection rate for a given application is always challenging [28]. Theoretically, the injection rate can be taken as the expected heating load on a single borehole. However, while the building load can readily be determined, the required number of boreholes for a given application depends on a detailed design of the borehole field, which in turn needs the site-specific ground thermal conductivity. For this reason, the injection rate is often chosen arbitrarily in practice within the range of 30–80 W/m of borehole depth as a rule-of-thumb [6]. This obviously brings uncertainty to the TRT estimates and impairs the effectiveness of conventional TRTs. In this context, a “constant-temperature” TRT that performs heat injection or extraction at fixed inlet temperatures (e.g. 35 °C) to represent the prevailing temperature when a GSHP is in operation may be preferred. Further, the proposed constant-temperature approach, which allows multi-level variable-rate heat injection, can account for the actual conditions where the heating/cooling load imposed on a borehole fluctuates according to the building load. Another limitation of conventional TRTs arises from using electric resistance(s) as the heating source where the power fluctuations in grid will lead to variation of heating pulse imposed on the borehole to affect the accuracy of the obtained ground thermal conductivity [29]. In this case, a power stabilizer can be used to help minimize the fluctuations in heat injection, although these fluctuations are rarely eliminated [30]. Another solution is to use the superposition principle to account for the 80

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effects of variable injection rates [31]. However, this method is rather complex and requires much computational effort, making it prohibitive for practical purposes. To overcome the limitations, this study proposed a constant-temperature TRT with both heat injection and extraction to determine the ground thermal conductivity and to examine the influence of natural convection on the borehole heat transport. A very first field test that comprises simultaneous heat injection and extraction tests on two boreholes both of 100 m depth is presented. The objective of this study is to demonstrate the use of the new TRT concept with full-scale field measurements. The results and the test protocol reported in this study will be useful in providing the background information for this technology to be adopted by the GSHP industry.

Tf , a (t ) = T0 +

(4)

2.2. Proposed TRT 2.2.1. Test rig configuration To allow both of the heat injection and extraction tests, a heat pump is used for providing simultaneous heating and cooling pulses to the ground. The schematic of the proposed test rig is shown in Fig. 2. It mainly consists of a water-to-water heat pump, two circulating pumps, two in-line electric resistances, and other auxiliary equipment. The heat pump comprises a variable speed compressor, an electronic expansion valve, and two tube-in-tube refrigerant-to-water heat exchangers acting as condenser and evaporator. A BHE is connected to each of the condenser and evaporator sides of the heat pump to perform the proposed TRT. Two purge tanks are used for purging the piping systems constituted by the test rig and the BHEs. The tanks are heavily insulated to avoid external heat transfer during tests. Water is circulated in the BHEs and is heated or cooled by the heat pump heat exchangers. Electric resistances are placed downstream of the heat exchangers to provide extra heating for maintaining constant inlet temperatures to the boreholes. This is realized with two PID controllers. They use real-time borehole inlet temperature as feedback, providing on-line adjustments to the heating output of the corresponding electric resistance. This active control also enables compensation for the power fluctuations in grid. Using heat pump in TRT test rigs has been reported in literatures, see Reference [33]. Witte et al. [25] proposed a test rig where an air-towater heat pump was used in conjunction with a purge tank and a three-way control valve to provide very uniform heat injection or extraction rate. The method, however, has intrinsic problems arising from

In this section, the proposed TRT is described in comparison with a conventional one in terms of test rig configuration, measurements, and data analysis method to highlight the differences between the two methodologies. 2.1. Conventional TRT A conventional TRT test rig typically consists of a circulating pump, purge valves, temperature sensors, a flow meter, an electric resistance as the heating source, and other auxiliary equipment (Fig. 1). During tests, heat is injected into the ground at a constant rate to perturb the ground temperature, while the fluid temperatures at inlet and outlet of the BHE as well as its flow rate are real-time monitored and recorded at less than 10 min intervals [7]. When analyzing the TRT data, the borehole is typically assumed an infinite line-source with uniform and constant heat generating rate embedded in a homogeneous and isotropic medium of infinite radial extent. With these assumptions, it is possible to obtain an analytical solution to the transient heat conduction problem. The solution is referred to as the Kelvin’s line-source model [32], which gives the ground temperature T around the borehole at time t and a radius r:

q r2 E1 4 ks 4 st

+ qRb

where Tf,a is the average fluid temperature (°C); rb is the borehole radius (m); Rb is the borehole thermal resistance (m K/W) that applies between the fluid in the BHE and the borehole wall. As indicated in Eq. (4), the ground thermal conductivity ks is inversely proportional to the slope of Tf,a when it is plotted against t on a logarithmic axis. This slope (i.e. q/4πks) can be obtained through linear fitting of measured Tf,a(t) versus ln(t), from which ks can be determined.

2. Test and analysis methodologies

T (r , t ) = T0 +

q 4 st ln 4 ks rb2

(1)

where T is the ground temperature (°C); r is the radial coordinate (m); t is the elapsed time from the start of the TRT (s); T0 is the initial (i.e. undisturbed) temperature of the ground (°C); q is the heat transfer rate per unit depth of borehole (W/m); ks is the ground thermal conductivity (W/m K); E1 denotes the exponential integral function; αs is the thermal diffusivity of the ground (m2/s). The specific heat transfer rate q can be determined from the measured temperatures by using:

q = cp, f

f

Vf (Tin

Tout )/ H

(2)

where cp,f is the specific heat capacity of the heat transfer fluid (J/kg K); ρf is the fluid density (kg/m3); Vf is the fluid volumetric flow rate (m3/ s); Tin and Tout are, respectively, the borehole inlet and outlet fluid temperatures (°C); H is the borehole depth (m). Eq. (1) can be simplified into the following form with an error within 2% when t is larger than 5r2/αs:

T (r , t ) = T0 +

q 4 st ln 4 ks r2

(3)

where γ is the Euler’s constant. By taking r in Eq. (3) as the borehole radius rb, and introducing a borehole thermal resistance Rb to describe the heat transfer within the borehole, the average fluid temperature circulating in the BHE can be given by:

Fig. 1. Schematic of the conventional test rig (FM: Flow meter; T: Temperature measurement). 81

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Fig. 2. Schematic of the proposed test rig (CHE: Condenser heat exchanger; EHE: Evaporator heat exchanger; EEV: Electronic expansion valve; FM: Flow meter; PID: PID controller; T: Temperature measurement).

the unstable behavior of the heat pump due to fluctuations in ambient temperature. Further, the test rig also has the limitation of not being able to conduct heat injection and extraction simultaneously, which may substantially increase the test duration of a TRT. The conventional TRT, together with the latest and the proposed TRT methodologies, are compared in Table 1. Their differences are highlighted. It is worth mentioning that the proposed TRT must be performed with an extra borehole, which is the main additional cost as compared to the conventional one. However, this additional cost will become negligible in the case when the boreholes under test can be included in the borehole field for use in the final GSHP system.

followed by integrating Eq. (5) along the borehole depth. The resulting expression for Tb(t) is rather complex, but can be simplified by using the “g-function” proposed by Eskilson [36], which gives a relation between the heat injected or extracted and the borehole wall temperature:

Tb (t ) = T0 +

q 4 ks

H 0

erfc(r +/ 4 s t ) r+

Rs =

r 2 + (z

s)2 , r =

r 2 + (z + s ) 2

g (t , ) 2 ks

(8)

Thermal resistance within the borehole (i.e. borehole thermal resistance, Rb) is a parameter that should be evaluated prior to the determination of the ground thermal conductivity. Rb applies between the fluid in the U-tube and the borehole wall. A range of methods have been proposed to evaluate Rb, from regression-based empirical models to analytical ones derived from heat transfer modelling. Among them, the multipole method proposed by Hellström [37] is a state-of-the-art method to compute Rb. It is derived from a two-dimensional analysis of the quasi-steady-state heat transfer within a borehole using a combination of line-sources and multipoles. Javed and Spitler [38] recently reviewed a number of methods for computing Rb and found that the multipole method yields the most accurate results under all investigated Table 1 Comparison of TRT methodologies.

Constant heating rate Constant inlet temperature Heat injection Heat extraction Heating/cooling source Test duration Data analysis method

erfc(r / 4 s t ) ds r (5)

r+ =

(7)

where g denotes the g-function that can be explicitly quantified with an analytical approach as detailed in Appendix A; t* is the dimensionless time given by 9αst/H2; β is the dimensionless borehole radius given by rb/H. Therefore, as indicated in Eq. (7), for a given g-function, the effective thermal resistance at the outside of the borehole Rs can be expressed as:

2.2.2. Test data analysis method Given that the conventional TRT data interpretation methods are developed based on a constant heat injection, they are not compatible with the newly proposed constant-temperature TRT concept. Accordingly, a new method is presented in this section for analyzing the TRT data. The infinite line-source model described in Section 2.1 is the most common model used to analyze TRTs because of its simplicity and convenience for application. However, it is important to note that the model is a one-dimensional (i.e. radial) solution to the transient heat transfer problem where the borehole was assumed to be an infinite linesource with uniform and constant heat generating rate. This one-dimensional nature renders it not capable of describing the axial variations in heat flow and temperature. In this regard, a more sophisticated two-dimensional model, referred to as the finite line-source model [34], was used in this study to evaluate the ground thermal response for more reliable TRT estimates. The model is adopted also because it is compatible with the assumption made by the “multipole method” for calculating the borehole thermal resistance as discussed below. According to Zeng et al. [35], the temperature distribution around a finite depth borehole can be expressed as a function of radial coordinate r, axial coordinate z and time t:

T (r , z , t ) = T0 +

q g (t , ) 2 ks

(6)

where erfc denotes the complementary error function. The above model covers a continuous and finite line-source. On this basis, the characteristic temperature of the borehole wall Tb(t) can be determined by taking the radial coordinate r as the borehole radius rb;

a b

82

Conventional TRT

TRT proposed by Witte [25]

TRT proposed in this study

√ ×

√ ×

× √

√ × Electric resistance (s) Short LSMa

√ √ Air-to-water heat pump Long LSM

√ √ Water-to-water heat pump Medium FLSMb

Kelvin’s line-source model. Finite line-source model.

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scenarios. Owing to its significantly better accuracy, the multipole method has been adopted by BHEs design program Earth Energy Designer [39]. The method is also used in this study, for which the zeroth-order analytical expression is given by:

Rb =

1 4 kg

+ ln

drilled at the field site in June 2016. The boreholes were dedicated for use in this field test and were 2 m apart to avoid thermal interference. A single U-shaped DN32 tube made of HDPE was buried in each borehole. Water was used as the heat transfer fluid in the U-tubes under a pressure of over 0.1 MPa. The space between the borehole wall and the outer tube surface was backfilled with a bentonite-sand grout mixture. The shank spacing (i.e. center-to-center distance between two legs of the U-tube) was kept constant along the borehole depth by using spacers.

2

2 1 (1

4 1 )

(9)

where kg is the thermal conductivity of the grout mixture (W/m K); δ, θ1, θ2 and σ are dimensionless parameters that can be found in the work by Javed and Spitler [38]. During TRTs, the ground temperature field initially at equilibrium is perturbed and the resulting response is represented by an average temperature of circulating fluid. A simple mean of the measured borehole inlet and outlet temperatures is commonly used in this case, but it has been shown that the approach tends to overestimate the average temperature and lead to biased TRT estimates [40]. This is because the simple mean method corresponds to a physically unrealistic hypothesis of constant heat rate along a borehole. In view of this fact, the “p-linear” average proposed by Marcotte and Pasquier [40] is used in this study as a better approximation:

| Tp| =

p (| Tin |p + 1 | Tout |p + 1 ) (1 + p)(| Tin |p | Tout |p )

3.2. Test rig and measuring instruments A field test was carried out using the test rig illustrated in Fig. 2. In the context of this study, a water-to-water heat pump with 5.6 kW nominal heating capacity and 4.5 kW nominal cooling capacity was used to provide heating and cooling pulses to the ground. The inverterdriven compressor of the heat pump was used to modulate the output capacity. Two pumps were used to circulate the heat transfer fluid (i.e. water) through the boreholes. The fluid flow rates were regulated by control valves. An electric resistance rated at 3 kW was installed downstream of each heat pump heat exchanger. Its heating output was continuously adjusted (between 0 and 3 kW) by a PID controller for maintaining a constant borehole inlet temperature. During tests, water pipes exposed to ambient and the purge tanks were heavily insulated to minimize disturbances caused by external heat transfer. Detailed specifications of the test rig are summarized in Table 2. The measuring instruments used in the field test and their accuracies are summarized in Table 3. The water temperatures inlet to and outlet from the boreholes were measured by high accuracy Pt100 RTDs immersed in pipelines. The water flow rates through the two boreholes were measured by variable area flow meters. To quantify the air temperature changes during tests, the ambient temperature was measured by thermocouples (Type K). The power consumptions of the electric resistances and the heat pump were separately measured by power quality testers. All the instruments used were connected to a data logger (Agilent 34970A), which allowed all measured data to be realtime monitored, recorded and processed.

(10)

where ΔTin and ΔTout are, respectively, the inlet and outlet fluid temperature increments with respect to the undisturbed ground temperature (°C). For typical TRT conditions, Eq. (10) gives the best approximation when p approaches −1 [40]. On the basis of the above analysis, and by assuming quasi-steadystate condition within the borehole, the heat transfer rate per unit depth of borehole q can be expressed as:

q=

2 ks Tp g + 2 ks Rb

(11)

where g is the analytical g-function. For a given g-function and Rb, Eq. (11) shows that q is linearly related to ΔTp. On this basis, a series of tests can be carried out with different ΔTp and q (both positive and negative) to constitute a complete TRT. Once the slope of the line φ obtained through linear fitting of scattered q against ΔTp, is determined, the ground thermal conductivity can be evaluated by:

ks =

4. Results and discussion The field test began two months after the backfilling was done in order to eliminate temperature disturbances caused by the drilling process. Prior to switching on the heat pump and the electric resistances, water was circulated in the two boreholes. Water temperatures at inlet and outlet of the two boreholes were measured at 10 s intervals until the observed temperatures reached a steady-state. In this field test, the temperatures were found to be stable after about 25 min, see Fig. 3. Accordingly, the average of the steady-state measurements (i.e. 16.1 °C) was taken as the undisturbed ground temperature. Once the undisturbed ground temperature was determined, the heat pump and the electric resistances were switched on to perform simultaneous heat injection and extraction tests. PID controllers were also activated to adjust the heating outputs of the resistances for

g 2 (1

Rb )

(12)

Note that the test data interpretation should be done with a method based on the same conceptual model to be used for BHEs design. This can mitigate the uncertainty brought by the assumptions of these models. For example, this study utilizes the finite line-source model, so one needs to make sure the same model is used in sizing of BHEs. 3. Field demonstration 3.1. Field site

Table 2 Specifications of the test rig used in this study.

The new concept TRT discussed in this study was demonstrated at the campus of the Taiyuan University of Technology (N37°44′, E112°42′) from August 6 to 12, 2016. Being the largest city in Shanxi Province, China, Taiyuan has a population of over 3.0 million. The city is located in a typical large-scale Cenozoic rift basin with an average ground elevation of approximately 800 m above the mean sea level. Bedrock in the basin mainly includes carbonate rocks, CarboniferousPermian coal-bearing strata and Triassic clastic rocks [41]. The ground elevation at the field site is approximately 816 m above the mean sea level, and the topographic slope is less than 1% southward. Two boreholes both of 200 mm diameter and 100 m depth were

Component

Parameter

Value

Water-to-water heat pump

Nominal heating capacity Nominal cooling capacity Working fluid Flow rate Power consumption Volume Heating output

5.6 kW 4.5 kW R22 30 L/min 90 W 85 L 3 kW (maximum)

Circulating pump Purge tank Electric resistance

83

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associated with q were evaluated using Kline and McClintock’s method. Results are summarized in Table 5. An additional fitting point is given as q = 0 when ΔTp = 0 (i.e. average fluid temperature = undisturbed ground temperature). A fairly straight trend is observed in the figure between the parameters, which is found consistent with the analysis in Section 2.2.2. On the basis of the above, the slope of the line (φ), resulting from linear fitting of scattered q against ΔTp, can be obtained, making it possible to evaluate ks by using Eq. (12). Regarding the g-function and the borehole thermal resistance (Rb), they were found to be 1.32 and 0.21 (m K)/W, respectively. Accordingly, ks derived from heat injection can be quantified through linear fitting of points shown graphically in Fig. 6 with q ≥ 0, yielding an estimate of 1.83 W/(m K). On the other hand, a fitting of the points with q ≤ 0 gives a ks of 1.65 W/(m K). A significant difference (10.9%) is therefore found between ks determined from heat injection and extraction, indicating a considerable natural convective effect that enhances ground heat transfer and increases estimated ks when heat injection is involved. It is worth mentioning that the estimated ks are effective ground thermal conductivities. The term “effective” is emphasized because the conductivity estimate is likely to vary with the ground temperature increments during tests. This reveals that the borehole inlet temperature in this proposed TRT should be chosen carefully to represent the prevailing temperature when a GSHP is in operation. Further, despite the field test was carried out in August, similar results are expected if the test is performed in other months (e.g. February). This is attributed to the active control of the electric resistances which enables compensation for changes in ambient temperature. In this case, the measured temperature response is determined only by site-specific ground properties. A global ks lumped for both heat injection and extraction can also be determined through linear fitting of all the points shown in Fig. 6, resulting in an estimate of 1.78 W/(m K). Table 6 summarizes the obtained φ and the corresponding estimates of ks when different fitting criteria are applied. The above analysis highlights the importance of including both heat injection and extraction in the same TRT to avoid mode-biased estimation and to improve the characterization of the ground thermal response and conductivity. It should be noted that the conductivity estimates derived from this proposed TRT may not be comparable with those from the conventional one. This is because the proposed TRT involves multi-level variable-rate heat injection, but the conventional TRT considers only the ground thermal response to a single constant heating pulse. However, the estimates are expected to become identical in the case when the influence of the natural convective effect is negligible.

Table 3 Summary of the measuring instruments and their accuracies. Instrument

Model

Range

Accuracy

Thermocouple Pt100 RTD Flow meter Power quality tester

OMEGA TT-K-24 OMEGA 1/10 DIN KROHNE H250 ISO-TECH IPM-3005

0–1250 °C −100 °C to 400 °C 0–32 L/min 0.01–9.999 kW

± 0.1 °C ± 0.1 °C ± 1.0% F.S. ± 20 W

Fig. 3. Measured temperatures for determining the undisturbed ground temperature.

maintaining constant borehole inlet temperatures. The field test demonstrated could therefore be divided into two stages. Each of the stages consisted of a heat injection test and a heat extraction test. The test procedures were similar for both stages. The only difference is that, in the first stage, the borehole inlet temperatures were set as 35 °C for heat injection and 6 °C for heat extraction, while in the second stage, borehole inlet temperatures were set as 30 °C and 8 °C, respectively. Note that there was a recovery period between the stages when all the components of the test rig were switched off to restore the ground back to the undisturbed state. The circulating water flow rate was maintained constant at 12.9 L/min for both tests of the two stages. This flow rate was large enough to generate a turbulent flow in the BHEs to minimize thermal resistance due to fluid advection. It also led to a temperature difference across the borehole of 3 °C to 5 °C that is similar to what is expected in practice. Figs. 4 and 5 illustrate the recorded borehole inlet and outlet water temperatures (Tin and Tout) at 1 min intervals and the resulting specific heat transfer rate (q) for the tests of the two stages. It can be seen in the figures that Tin increases/decreases dramatically with time at the beginning of each test and tend to become stable after about 1 h. It is further noted that even with external disturbances, steady-state Tin fluctuates around the pre-set temperature with an error within ± 0.2 °C. The evolution of Tout returns a similar trend where it increases/ decreases initially and becomes stable afterwards. The temperature difference between Tin and Tout is nearly constant after about 20 h, indicating that the heating/cooling output provided by the test rig has completely dispersed in the surrounding ground. The working condition of the heat pump was stable after achieving this steady-state, during which the heating outputs of the two electric resistances are summarized in Table 4. As explained in Section 2.2.2 and Eq. (11), the ground thermal conductivity (ks) can be estimated from the slope of scattered steadystate measurements of q when they are plotted against ΔTp. In the case of this field test, late measurements of the two parameters observed in heat injection/extraction tests are plotted in Fig. 6. The uncertainties

Fig. 4. Measured borehole inlet and outlet temperatures in the 1st stage (Heat injection Tin = 35 °C; Heat extraction Tin = 6 °C). 84

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Table 6 Estimated ground thermal conductivities.

Heat injection only Heat extraction only Heat injection + Heat extraction a

1st stage

2nd stage

1.16 0.51

0.60 0.36

Table 5 Relative uncertainties associated with measured q.

injection 1st stage extraction 1st stage injection 2nd stage extraction 2nd stage

3.08 2.97 3.05

1.83 1.65 1.78

+2.8% −7.3% 0%

Slope of the line resulting from linear fitting of q and ΔTp.

This study proposed a constant-temperature thermal response test (TRT) with both heat injection and extraction to determine the ground thermal conductivity and to examine the influence of natural convection on the borehole heat transport. A novel test rig configuration, associated with a new TRT data analysis method, was proposed in order to improve the characterization of the ground thermal response and conductivity. The test rig is featured by its ability to maintain a constant borehole inlet temperature and to enable conducting heat injection and extraction tests simultaneously. A field test was performed on two adjacent boreholes both of 100 m depth to demonstrate the use of the proposed TRT concept with full-scale measurements. The test was the very first demonstration of a constant-temperature TRT to assess the ground thermal conductivity with potential applications for the design of ground source heat pump systems. In the field test, a small capacity water-to-water heat pump was used for providing heating and cooling pulses. A linear heat source solution of finite length was adopted to evaluate the ground thermal response to heat injection and extraction. In the case of this field test, the undisturbed ground temperature and the borehole thermal resistance were determined to be 16.1 °C and 0.21 (m K)/W, respectively. A significant difference (10.9%) was found between ground thermal conductivities estimated from heat injection and extraction. For the boreholes under test, the conductivity estimate derived from heat injection was 1.83 W/(m K), and that from heat extraction was 1.65 W/(m K), thus confirming that density-driven convective effect caused by heat injection was considerable for the test site. As compared to the conventional TRT, the main advantage of the proposed TRT is to provide test data that better reflects the annual performance of borehole heat exchangers and enables a better characterization of site-specific ground thermal conductivity. Relevant results and the test protocol established in this study are useful in providing the background information for this technology to be adopted by the ground source heat pump industry.

Heating output (kW)

Fig. 6. Steady-state measurements of specific heat transfer rate and average fluid temperature (q > 0 denotes heat injection; q < 0 denotes heat extraction).

Heat Heat Heat Heat

% Difference

5. Conclusions

Table 4 Steady-state heating outputs of the electric resistances.

Heat injection Heat extraction

ks (W/(m K))

reliability and repeatability of in-situ tests. Second, the constant-temperature approach with multi-level variable-rate heat injection can account for the actual conditions where the heating/cooling load imposed on a borehole fluctuates according to the building load. Note that the proposed TRT method is compatible with the existing design procedures for GSHP systems. In practice, the estimated ks for heat injection and extraction can separately be used for computing the required borehole length for satisfying building cooling and heating loads [7]. The required total length can be taken as the longer of the two.

Fig. 5. Measured borehole inlet and outlet temperatures in the 2nd stage (Heat injection Tin = 30 °C; Heat extraction Tin = 8 °C).

Test

φa

Measured q (W/m)

Relative uncertainty (%)

50.8 −26.8 36.8 −21.5

3.5 5.4 4.3 6.4

Acknowledgement The authors appreciated the financial support from the National Natural Science Foundation of China (No. 51808372). The Opening Funds of State Key Laboratory of Building Safety and Built Environment and National Engineering Research Center of Building Technology (No. BSBE2018-02) was also acknowledged. The work was also supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 201802046) and Application Foundation Research Plan of Shanxi Province (No. 201801D221348).

Therefore, the proposed constant-temperature approach is superior to conventional TRTs performed with constant heat injection for the following two reasons. First, the proposed TRT can be performed in absence of a representative heat injection rate, which helps enhance the 85

Applied Energy 249 (2019) 79–86

J. Jia, et al.

Appendix A As indicated in Eq. (7), g-function is a dimensionless thermal response factor that characterizes the borehole wall temperature. It was originally computed numerically by Eskilson [36] using two-dimensional finite-difference equations on a radial-axial coordinate system, and tabulated values were given for various borehole field configurations. However, as the numerical approach is limited by a lack of flexibility, Lamarche and Beauchamp [42] recently proposed an analytical solution to the g-function, for which the mathematical expression is given by: 2

g (t , ) =

+1

erfc(µz ) z2

2

2

dz

2

+4

+1

erfc(µz ) z2

2

dz

DA

DB

(A.1) (A.2)

µ = 3/2 t *

where t is the dimensionless time; β is the dimensionless borehole radius; z is the axial coordinate; DA and DB are integrals of the complementary error function that can be found in the work by Lamarche and Beauchamp [42].

References [22]

[1] Yang H, Cui P, Fang Z. Vertical-borehole ground-coupled heat pumps: a review of models and systems. Appl Energy 2010;87:16–27. [2] Retkowski W, Ziefle G, Thöming J. Evaluation of different heat extraction strategies for shallow vertical ground-source heat pump systems. Appl Energy 2015;149:259–71. [3] Montagud C, Corberán JM, Ruiz-Calvo F. Experimental and modeling analysis of a ground source heat pump system. Appl Energy 2013;109:328–36. [4] Zhang CX, Guo ZJ, Liu YF, Cong XC, Peng DG. A review on thermal response test of ground-coupled heat pump systems. Renew Sustain Energy Rev 2014;40:851–67. [5] Zhang LF, Zhang Q, Huang GS, Du YX. A p(t)-linear average method to estimate the thermal parameters of the borehole heat exchangers for in situ thermal response test. Appl Energy 2014;131:211–21. [6] Sanner B, Hellström G, Spitler J, Gehlin S. Thermal response test—Current status and world-wide application. World geothermal congress. 2005. p. 24–9. [7] ASHRAE. ASHRAE handbook—HVAC applications. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers; 2015. [8] Mogensen P. Fluid to duct wall heat transfer in duct system heat storages. International conference on subsurface heat storage in theory and practice. 1983. p. 652–7. [9] Eklöf C, Gehlin S. TED—A mobile equipment for thermal response test. Luleå University of Technology; 1996. [10] Choi W, Ooka R. Interpretation of disturbed data in thermal response tests using the infinite line source model and numerical parameter estimation method. Appl Energy 2015;148:476–88. [11] Raymond J, Lamarche L. Simulation of thermal response tests in a layered subsurface. Appl Energy 2013;109:293–301. [12] Shonder JA, Beck JV. A new method to determine the thermal properties of soil formations from in situ field tests. Tennessee: Oak Ridge National Laboratory; 2000. [13] Yavuzturk C, Spitler JD, Rees SJ. A transient two-dimensional finite volume model for the simulation of vertical U-tube ground heat exchangers. ASHRAE Trans 1999;105:465–74. [14] Signorelli S, Bassetti S, Pahud D, Kohl T. Numerical evaluation of thermal response tests. Geothermics 2007;36:141–66. [15] Bozzoli F, Pagliarini G, Rainieri S, Schiavi L. Estimation of soil and grout thermal properties through a TSPEP (two-step parameter estimation procedure) applied to TRT (thermal response test) data. Energy 2011;36:839–46. [16] Li Y, Mao J, Geng S, Han X, Zhang H. Evaluation of thermal short-circuiting and influence on thermal response test for borehole heat exchanger. Geothermics 2014;50:136–47. [17] Li M, Lai ACK. Parameter estimation of in-situ thermal response tests for borehole ground heat exchangers. Int J Heat Mass Transf 2012;55:2615–24. [18] Choi W, Menberg K, Kikumoto H, Heo Y, Choudhary R, Ooka R. Bayesian inference of structural error in inverse models of thermal response tests. Appl Energy 2018;228:1473–85. [19] Beier RA, Smith MD. Minimum duration of in-situ tests on vertical boreholes. ASHRAE Trans 2003;109:475–86. [20] Witte HJL. Error analysis of thermal response tests. Appl Energy 2013;109:302–11. [21] Li M, Lai ACK. New temperature response functions (G functions) for pile and

[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

86

borehole ground heat exchangers based on composite-medium line-source theory. Energy 2012;38:255–63. Choi W, Kikumoto H, Choudhary R, Ooka R. Bayesian inference for thermal response test parameter estimation and uncertainty assessment. Appl Energy 2018;209:306–21. Wagner V, Bayer P, Kübert M, Blum P. Numerical sensitivity study of thermal response tests. Renew Energy 2012;41:245–53. Gehlin S. Thermal response test: method development and evaluation. Luleå Tekniska Universitet 2002. Witte HJL. Geothermal response tests with heat extraction and heat injection: examples of application in research and design of geothermal ground heat exchangers. Workshop geothermische response tests. 2001. p. 25–6. Witte HJL, Van Gelder GJ, Spitler JD. In situ measurement of ground thermal conductivity: a Dutch perspective. ASHRAE Trans 2002;108:263–72. Gustafsson AM, Westerlund L. Multi-injection rate thermal response test in groundwater filled borehole heat exchanger. Renew Energy 2010;35:1061–70. Witte HJL, Van Gelder AJ. Geothermal response tests using controlled multi-power level heating and cooling pulses (MPL-HCP): quantifying ground water effects on heat transport around a borehole heat exchanger. Ecostock 2006. Sharqawy MH, Mokheimer EM, Habib MA, Badr HM, Said SA, Al-Shayea NA. Energy, exergy and uncertainty analyses of the thermal response test for a ground heat exchanger. Int J Energy Res 2009;33:582–92. Raymond J, Therrien R, Gosselin L, Lefebvre R. A review of thermal response test analysis using pumping test concepts. Groundwater 2011;49:932–45. Hu PF, Meng QF, Sun QM, Zhu N, Guan CS. A method and case study of thermal response test with unstable heat rate. Energy Build 2012;48:199–205. Ingersoll LR, Plass HJ. Theory of the ground pipe heat source for the heat pump. ASHVE Trans 1948;54:339–48. Gustafsson AM, Westerlund L. Heat extraction thermal response test in groundwater-filled borehole heat exchanger—Investigation of the borehole thermal resistance. Renew Energy 2011;36:2388–94. Li M, Lai ACK. Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): a perspective of time and space scales. Appl Energy 2015;151:178–91. Zeng HY, Diao NR, Fang ZH. A finite line-source model for boreholes in geothermal heat exchangers. Heat Tran Asian Res 2002;31:558–67. Eskilson P. Thermal analysis of heat extraction boreholes. University of Lund; 1987. Hellström G. Ground heat storage—Thermal analyses of duct storage systems. University of Lund; 1991. Javed S, Spitler J. Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers. Appl Energy 2017;187:790–806. Hellström G, Sanner B, Klugescheid M, Gonka T, Mårtensson S. Experiences with the borehole heat exchanger software EED. Megastock 1997:247–52. Marcotte D, Pasquier P. On the estimation of thermal resistance in borehole thermal conductivity test. Renew Energy 2008;33:2407–15. Guo QH, Wang YX, Ma T, Ma R. Geochemical processes controlling the elevated fluoride concentrations in groundwaters of the Taiyuan Basin, Northern China. J Geochem Explor 2007;93:1–12. Lamarche L, Beauchamp B. A new contribution to the finite line-source model for geothermal boreholes. Energy Build 2007;39:188–98.