Uncertainty analysis of wireless temperature measurement (WTM) in borehole heat exchangers

Highlights

• Novel analysis of uncertainties related to wireless temperature measurement of vertical temperature profiles in borehole heat exchangers.

• Temperature profiles measured with the wireless probe show high reliability as a result of high precision (0.011 K) and accuracy (-0.11 K).

• Wireless probes are also suitable to correct systematic errors of common fiber optic measurements, which are up to -0.93 K in the present study.

• Future probes should have a slow descent velocity and a small thermal time constant toreduce the dynamic measurement error.

Abstract

The reliability of temperature measurements in open and closed geothermal systems is closely related to their design, quality control and performance evaluation. Thus, wireless and miniaturized probes, which provide highly resolved temperature profiles in borehole heat exchangers (BHEs), experience a growing interest in research. To ensure quality assurance and reliability of these emerging technologies, errors and uncertainties relating to wireless temperature measurements (WTMs) must be determined. Thus, we provide a laboratory analysis of random, systematic and dynamic measurement errors, which lead to the measurement uncertainties of WTMs. For the first time, we subsequently transfer the calculated uncertainties to temperature profiles of the undisturbed ground measured at a BHE site in Karlsruhe, Germany. The resulting precision of 0.011 K and accuracy of -0.11 K ensure a high reliability of the WTMs. The largest uncertainty is obtained within the first five meters of descent and results from the thermal time constant of 4 s. The fast and convenient measurement procedure results in substantial advantages over Distributed Temperature Sensing (DTS) measurements using fiber optics, whose recorded temperature profiles at the site serve as qualitative comparison. We additionally provide recommendations for technical implementations of future measurement probes. Our work will contribute to an improved understanding and further development of WTMs.

Introduction

Vertical borehole heat exchangers (BHEs) are the most common technology to extract thermal energy from the shallow underground. The standard BHE is a closed loop U-pipe system, where a circulating heat carrier fluid transports the thermal energy from the underground to the heat pump of a building (Florides and Kalogirou, 2007; Hähnlein et al., 2013; Lund et al., 2005; Rivera et al., 2017; Yang et al., 2010). The design of a BHE mainly follow standardized procedures using commercial software (Gaia Geothermal, 2009; Hellström and Sanner, 2000; Spitler, 2000), design tools (Chiasson, 2016; Kavanaugh, 2010), and national guidelines (SIA 384/6-C1:2010, 2010, SIA 384/6-C1:2010, 2010; Verein Deutscher Ingenieure, 2010). These different approaches all require the undisturbed ground temperature (UGT) as a design parameter. The UGT results from the thermal properties of the subsurface as well as the geothermal and surface heat flow and is defined as the ground temperature before the BHE operation (Nordell, 1993; Rees, 2016; Spitler and Bernier, 2016). Although the UGT directly influences the sizing and performance of a BHE, it is probably the most overlooked parameter in the planning and design of BHEs (Beier, 2011; Chiasson, 2016; Gwadera et al., 2017; Ouzzane et al., 2015; Radioti et al., 2017; Spitler and Gehlin, 2015). Various analytical approaches exist for estimating the UGT as a function of time and depth (Fluker, 1958; Givoni and Katz, 1985; Hillel, 1982; Kusuda and Archenbach, 1965; Wu and Nofziger, 1999). The quality of these models strongly depends on the reliability of the collected climate and geological data (Badache et al., 2016). However, temperature measurements at the proposed site with appropriate measurement technologies are not common.

The UGT is also an important parameter for the evaluation of thermal response tests (TRTs), which are essential for the design of large scale BHE fields (Acuña and Palm, 2013; Sanner et al., 2005; Gehlin, 2002; Spitler and Bernier, 2016). The measurement of the UGT is performed before the start of a TRT and directly effects its accuracy (Gehlin and Nordell, 2003). Claesson and Eskilson (1988) propose to measure the average UGT while circulating the heat-carrier fluid of the BHE without extraction or injection of heat. However, the pumping process significantly heats up the system resulting in an increased measured UGT (Gehlin and Nordell, 2003). Thus, measurements of vertical temperature profiles, also referred to as T-logs (Bayer et al., 2016), along the entire length of a borehole evolved as an increasing research focus in recent years. Meanwhile, the measurement of undisturbed and disturbed T-logs in BHEs is mostly carried out over the course of distributed and enhanced thermal response tests (DTRT/ETRT) (Wilke et al., 2019). This is based on distributed temperature sensing (DTS) using fiber optic and hybrid cables (Acuña et al., 2009; Cao et al., 2018; Fujii et al., 2009; Luo et al., 2015; Shim and Song, 2011; Soldo et al., 2016). Alternative devices to fiber optic cables are wired data loggers, which are either manually (Gehlin and Nordell, 2003) or automatically (Aranzabal et al., 2019a, 2020) lowered into a BHE. Raymond et al. (2016), for instance, manually lowered a wired data logger with a measurement frequency of 1 Hz into two BHEs to measure undisturbed T-logs at the site of Saint-Lazara, Canada. The measured T-logs allowed conclusions on the geothermal gradient and seasonal temperature variations at the site.

However, the small diameter of a BHE generally limits the selection of suitable measurement technologies for T-logs. Moreover, the measurement of T-logs, particularly when carried out with fiber optics, are time-consuming, cost-intensive, and require cumbersome handling, while wired data loggers unintentionally displace the fluid in the BHE (Raymond et al., 2016). In addition, strongly twisted or inclined BHEs can produce a discrepancy between the cable length of a wired logger and actual depth of the BHE (LQS-EWS, 2011). For this reason, different concepts of miniaturized wireless temperature probes were recently developed. Pioneers in the field of wireless temperature measurements (WTM) were Rohner et al. (2005), who developed a cylindrical probe, later called NIMO-T, with an adjustable weight depending on the actual requirements (Wagner and Rohner, 2008). This device records pressure and temperature at pre-selected time intervals during the descent. Bayer et al. (2016) used the NIMO-T for measurements in the urban environment of Zurich, showing a relation between the perturbation of the T-logs and the lifetime of buildings and asphalted streets. Martos et al. (2008) and Martos et al. (2011) introduced a spherical sensor system, containing a Pt100-sensor embedded in a polyoxymethylene (POM) shell, for T-log measurements over the course of a TRT. This probe has a density very close to the thermal fluid of a BHE and is therefore only suitable for measurements during a pumping process. Knowledge about flow rate and BHE diameter enables the calculation of the probe’s velocity indicating its position in the BHE. Due to the small density difference between BHE fluid and probe, this particular device is less suitable for measurements of the UGT. Aranzabal et al. (2019b) further developed this sensor system and compared it with various measurement technologies including wired data loggers, fiber optics, and GEOsniff®. The latter is a spherical sensor system, which is commercially available on the market and the further development of NIMO-T (Gottlieb et al., 2018).

Questions regarding errors and measurement uncertainties, which relate to WTMs have not yet been addressed and discussed. However, these investigations are essential for the suitability and development of this type of probe as well as the reliability of the recorded data. Thus, we analyze this by using the GS as a representative device for WTMs. In the following, we first describe the principle of WTMs and related basic equations. Then, we provide a quantitative analysis of statistic, random, and dynamic measurement errors by investigating their major causes under various boundary conditions. Based on this, we discuss the expanded measurement uncertainty U and evaluate its impact on the wirelessly measured UGT in BHEs. We compare them with T-logs measured with common stationary measurement technologies including fiber optics and punctual Pt100-sensors. This allows valuable conclusions on potential optimization needs and appropriate application fields of WTMs.