In recent years, three simple tracers (conductivity, turbidity and temperature) have shown their advantages to many other tracers for tracing and assessment of extraneous water (or inflow and infiltration, I/I) into sewer systems due to low detection cost and high monitoring frequency. A better understanding of the error and uncertainty of the three simple tracers on the quantification of I/I will help to improve the reliability and reduce the cost of actual projects. A large-scale experimental model simulating a 36 m long sewer was constructed for conducting extraneous water flow tests including groundwater infiltration, wastewater inflow and hot water inflow under different I/I flow rates and concentrations. The accuracy and uncertainty of the three tracers were estimated, and their correlation with tracer concentration difference before and after extraneous inflow was also analyzed. Experimental results provide guidance for the practical applicability of the three tracers under different I/I conditions.

  • Large-scale experimental tests were conducted to evaluate three simple tracers for I/I assessment.

  • The accuracy and uncertainty of three simple tracers were evaluated.

  • The suitable conditions for each of the three tracers were illustrated.

     
  • QSW

    sanitary wastewater flow rate, m3/h

  •  
  • QI/I

    extraneous water flow rate, m3/h

  •  
  • QWW

    total wastewater flow rate in sewer, m3/h

  •  
  • CSW

    concentration of the tracer in sanitary wastewater

  •  
  • CI/I

    concentration of the tracer in extraneous water

  •  
  • CWW

    concentration of the tracer in total wastewater

  •  
  • RQ-M

    measured I/I ratio, %

  •  
  • RQ-C

    calculated I/I ratio, %

  •  
  • RQ-Ci

    calculated I/I ratio at the i-th time point, %

  •  
  • RC

    concentration ratio of the extraneous water and sanitary wastewater

  •  
  • APE

    absolute percent error, %

  •  
  • MAPE

    mean absolute percent error, %

  •  
  • n

    total number of data during the relatively steady period

  •  
  • detection uncertainty

  •  
  • relative uncertainty of calculated I/I ratio, %

In recent years, with the aging and deterioration of underground sewer pipes, the control of extraneous water (or inflow and infiltration, I/I) into sewer systems has become a critical and urgent task of municipal assets management, especially in many developing countries such as China (Staufer et al. 2012; Guo et al. 2016, 2020). Therefore, many proposed methods in the literature have been tried and applied in practice to detect and quantify the extraneous water in local sewer systems, including the flow-based method (Weiss et al. 2002; De Bénédittis & Bertrand-Krajewski 2005a), the stable isotope method (Houhou et al. 2010; De Bondt et al. 2018), and chemical tracer methods (Kracht & Gujer 2005; Shelton et al. 2011; Bareš et al. 2012). However, many of these methods are very expensive due to the high equipment cost or complex applying conditions (Zhao et al. 2020). Therefore, some simple water quality tracers such as conductivity (Zhang et al. 2018), turbidity (Aumond & Joannis 2008), and temperature (Beheshti & Sægrov 2019; Panasiuk et al. 2019) have received significant attention due to their low detection cost and high monitoring frequency.

Aumond & Joannis (2008) compared the conductivity and turbidity tracers for an I/I dilution model, and found that conductivity is more suitable for the model than turbidity. Bareš et al. (2009) conducted I/I analysis based on COD and the total suspended solids (TSS), and results showed that TSS was more biased due to uncertainties such as sedimentation phenomenon. Zhang et al. (2018) investigated four chemical tracers for assessing the rain induced inflow and infiltration (RDII) in Wuxi City in China. Their study concluded that conductivity has the best sensitivity for RDII simulation compared with other three chemical tracers including COD, NH4+-N, PO43−-P. Hoes et al. (2009) and Panasiuk et al. (2019) verified the effectiveness of the method of monitoring the in-sewer temperature based on the distributed temperature sensor (DTS) for locating and quantifying the I/I.

However, previous researches on the three tracers are usually based on field survey and data analysis, and are subjected to considerable uncertainties due to their underlying assumptions and general principles which are not estimated (De Bénédittis & Bertrand-Krajewski 2005a). In order to investigate the variability and associated uncertainties in I/I estimation of the three tracers, a large-scale experimental setup with 36 meters of DN 300 sewer pipes was constructed to compare the sensitivity and accuracy of each tracer under different I/I situations. The absolute percent error (APE) and the relative uncertainty of I/I analysis were calculated and major influencing factors were investigated. The reliability of the three tracers under different I/I conditions were compared and presented.

Experimental setup

The experimental setup is shown in Figure 1. It was composed of water supply part and sewer part. For the water supply part, there were two sets of water sources and pipelines, which represent the main sewer flow and the extraneous water inflow respectively. Both of them were equipped with a water tank for storing and supplying test water, a pump and an electromagnetic flowmeter for reading the inflow. For the sewer part, it consisted of 36 m DN 300 HDPE pipe with the slope range from 1.25‰ to 5.00‰ and all pipelines were installed at least 1.05 m above the ground. There were five inspection wells (MH 1–MH 5) along the sewer pipe for inner observation and sampling. The main sewer flow started from the bottom of MH 1 into the pipeline in order to reduce the turbulence, and the simulated extraneous water was pumped and mixed with main flow in MH 2.

Figure 1

Experimental setup.

Figure 1

Experimental setup.

Close modal

I/I quantitative model and experimental conditions

Generally, I/I quantitative model based on mass conservation principle can be expressed as follows:
formula
(1)
formula
(2)
formula
(3)

With QWW = total wastewater flow rate in sewer, QSW = sanitary wastewater flow rate, QI/I = extraneous water flow rate, CWW = concentration of the tracer in total wastewater, CSW = concentration of the tracer in sanitary wastewater, CI/I = concentration of the tracer in extraneous water, RQ-C = calculated I/I ratio. The experimental water with different conductivity and turbidity was prepared by dissolving sodium chloride and kaolin powder in tap water with normal temperature of 24 °C–25 °C stored in water tanks. The measured conductivity of tap water was 122–125 μS/cm, and the measured turbidity was less than 0.10 NTU.

In order to explore influences of the flow rate and the pollution concentration of the extraneous water, two independent variables RQ-M and RC were defined by Equations (4) and (5) respectively. RQ-M is the measured I/I ratio read by the two flowmeters. By fixing QSW and changing QI/I, different RQ-M can be set to investigate influences of the inflow rate of the extraneous water on the wastewater flow. RC is the concentration ratio of the extraneous water and the sanitary wastewater. By changing CI/I and CSW, different RC can be set to investigate the influences of the pollution concentration of the extraneous water on the wastewater flow. Table 1 gives the experimental test conditions in this study.

Table 1

Test conditions for three tracers

Test no.RCCSWCI/IRQ-MQI/IQSW
uS/cmuS/cm%m3/hm3/h
A-1 0.24 512 122 4.41, 27.34, 52.18,77.70 0.16, 1.30, 3.76, 12.16 3.45 
A-2 0.12 1,026 122 13.78, 34.72, 46.72, 79.69 0.55, 1.81, 2.98, 13.74 3.44 
A-3 0.08 1,565 122 11.34, 19.98, 44.08, 79.98 0.43. 0.87, 2.72, 13.78 3.45 
A-4 0.06 1,979 122 13.10, 23.55, 43.43, 79.00 0.51, 1.06, 2.65, 12.79 3.43 
CSWCI/IRQ-MQI/IQSW
Test no.RCNTUNTU%m3/hm3/h
A-5 0.00 25.41 0.00 14.72, 21.69, 42.36, 74.47 0.57, 0.91, 2.39, 9.63 3.29 
A-6 0.00 45.27 0.00 12.03, 31.48, 53.89, 75.92 0.44, 1.49, 3.73, 10.40 3.24 
A-7 0.00 63.14 0.00 6.85, 21.34, 42.91, 62.42 0.24, 0.84, 2.33, 5.15 3.14 
A-8 0.00 83.24 0.00 14.59, 33.14, 45.25, 68.38 0.50,1.59, 2.56, 6.70 3.08 
RCCI/ICSWRQ-MQI/IQSW
Test no.µS/cmµS/cm%m3/hm3/h
B-1 0.22, 0.36, 0.55, 0.72, 0.83 366, 601, 922, 1,180, 1,349 1,656 11.76 0.46 3.48 
B-2 0.19, 0.39, 0.55, 0.72,0.88 309, 627, 884, 1,169, 1,454 1,624 35.24 1.88 3.45 
B-3 0.21, 0.36, 0.55, 0.70, 0.85 343, 590, 900, 1,126, 1,367 1,633 60.76 5.35 3.45 
CI/ICSWRQ-MQI/IQSW
Test no.RCNTUNTU%m3/hm3/h
B-4 0.23, 0.39, 0.57, 0.69, 0.79 14.67, 25.54, 39.56, 46.34, 52.56 66.60 11.76 0.46 3.48 
B-5 0.19, 0.34, 0.54, 0.69, 0.85 12.35, 22.48, 34.66, 44.44, 56.89 65.04 35.24 1.88 3.45 
B-6 0.25, 0.33, 0.58, 0.65, 0.86 15.73, 20.93, 36.32, 45.08, 60.18 65.75 60.76 5.35 3.45 
TSWTI/IRQ-MQSWQI/I
Test no.RC°C°C%m3/hm3/h
C-1 1.61 24.9 40.0 15.67 2.25 0.42 
C-2 1.75 22.9 40.0 24.08 2.88 0.91 
C-3 1.63 25.0 40.8 36.49 2.14 1.23 
C-4 1.83 24.0 43.8 60.74 2.13 3.30 
Test no.RCCSWCI/IRQ-MQI/IQSW
uS/cmuS/cm%m3/hm3/h
A-1 0.24 512 122 4.41, 27.34, 52.18,77.70 0.16, 1.30, 3.76, 12.16 3.45 
A-2 0.12 1,026 122 13.78, 34.72, 46.72, 79.69 0.55, 1.81, 2.98, 13.74 3.44 
A-3 0.08 1,565 122 11.34, 19.98, 44.08, 79.98 0.43. 0.87, 2.72, 13.78 3.45 
A-4 0.06 1,979 122 13.10, 23.55, 43.43, 79.00 0.51, 1.06, 2.65, 12.79 3.43 
CSWCI/IRQ-MQI/IQSW
Test no.RCNTUNTU%m3/hm3/h
A-5 0.00 25.41 0.00 14.72, 21.69, 42.36, 74.47 0.57, 0.91, 2.39, 9.63 3.29 
A-6 0.00 45.27 0.00 12.03, 31.48, 53.89, 75.92 0.44, 1.49, 3.73, 10.40 3.24 
A-7 0.00 63.14 0.00 6.85, 21.34, 42.91, 62.42 0.24, 0.84, 2.33, 5.15 3.14 
A-8 0.00 83.24 0.00 14.59, 33.14, 45.25, 68.38 0.50,1.59, 2.56, 6.70 3.08 
RCCI/ICSWRQ-MQI/IQSW
Test no.µS/cmµS/cm%m3/hm3/h
B-1 0.22, 0.36, 0.55, 0.72, 0.83 366, 601, 922, 1,180, 1,349 1,656 11.76 0.46 3.48 
B-2 0.19, 0.39, 0.55, 0.72,0.88 309, 627, 884, 1,169, 1,454 1,624 35.24 1.88 3.45 
B-3 0.21, 0.36, 0.55, 0.70, 0.85 343, 590, 900, 1,126, 1,367 1,633 60.76 5.35 3.45 
CI/ICSWRQ-MQI/IQSW
Test no.RCNTUNTU%m3/hm3/h
B-4 0.23, 0.39, 0.57, 0.69, 0.79 14.67, 25.54, 39.56, 46.34, 52.56 66.60 11.76 0.46 3.48 
B-5 0.19, 0.34, 0.54, 0.69, 0.85 12.35, 22.48, 34.66, 44.44, 56.89 65.04 35.24 1.88 3.45 
B-6 0.25, 0.33, 0.58, 0.65, 0.86 15.73, 20.93, 36.32, 45.08, 60.18 65.75 60.76 5.35 3.45 
TSWTI/IRQ-MQSWQI/I
Test no.RC°C°C%m3/hm3/h
C-1 1.61 24.9 40.0 15.67 2.25 0.42 
C-2 1.75 22.9 40.0 24.08 2.88 0.91 
C-3 1.63 25.0 40.8 36.49 2.14 1.23 
C-4 1.83 24.0 43.8 60.74 2.13 3.30 
The total 66 tests can be divided into three series (Series A, B, C) to verify the performance of tracers under different I/I scenarios. Test series A was used to simulate groundwater infiltration: A-1 to A-4 using conductivity as the tracer, and A-5 to A-8 using turbidity as the tracer. The extraneous water used was tap water without any materials added (122 μS/cm, 0 NTU), and the value range of RC was relatively small (RC = 0–0.24). Test series B was used to simulate wastewater inflow with different tracer concentrations, so the value range of RC was larger (RC = 0.19–0.88). Test series C was used to simulate hot water inflow (CI/I > CSW), so RC was greater than 1:
formula
(4)
formula
(5)

Sample collection and detection

Locations of water quality sampling and online monitoring points are shown in Figure 1(a). For the conductivity and turbidity conditions, CSW and CI/I were measured from the two water tanks respectively. CWW was obtained by sampling at the downstream three sampling points (SP-1–SP-3). The conductivity detector (KEDIDA, CT-3031, Shenzhen) used had a range of 0–1,999 μS/cm and accuracy of ±2% FS, the turbidity detector (YUEFENG, SGZ-400B, Shanghai) had a range of 0–400 NTU and the accuracy was ±6% FS.

For the temperature conditions, five temperature sensors with accuracy ±1% FS deployed at different locations along the sewer were used to monitor and record the in-sewer temperature data online. The first temperature monitoring point MP-S was set at the 0.2 m upstream of MH 2 for recording the sanitary wastewater temperature, and the second sensor was installed at MP-E in MH 2 to monitor the temperature of the inflow water. For monitoring the total wastewater after inflow, three real-time temperature sensors (MP-1–MP-3) were set at 1 m, 12 m and 24 m downstream of MH 2, respectively, to observe the time–space changing of the temperature along the sewer.

Data uncertainty analysis

The APE was used as the statistical metrics to evaluate the I/I quantitative accuracy of three tracers under each test condition, which represents the relative difference between the measured RQ-M and calculated RQ-C. In addition, in the hot water inflow test, data collected at MP-1 to MP-3 were used to calculate the mean absolute percent error (MAPE). The calculation formulas are given as follows:
formula
(6)
formula
(7)
where n is the total number of data during the relatively steady period; RQ-Ci is the I/I calculation ratio at the i-th time point during the steady temperature period in hot water inflow test.
According to the uncertainty propagation law, when the three water quality components were measured by using sensors with the same uncertainty, i.e., , the uncertainty of the results caused by the detection uncertainty can be expressed as the following formula (De Bénédittis & Bertrand-Krajewski 2005b):
formula
(8)

By comparing the relative uncertainty of the output results, the applicability of each tracer method can be evaluated, for example, if , then the method is not valid.

Uncertainty analysis of conductivity tracer tests

Figure 2 shows the APE and the relative uncertainty of the conductivity tracer under groundwater infiltration tests, and Figure 3 shows results under wastewater inflow tests. In groundwater infiltration tests as shown in Figure 2, the overall APE range of the conductivity tracer tests is 3.50%–50.44%. It was found that as RQ-M increased from 10% to be more than 55%, the APE reduced from being more than 20% to be less than 10%. Therefore, there exists a negative correlation between APE and RQ-M. However, in both of groundwater infiltration tests and wastewater inflow tests, no obvious trend was found between APE and RC.

Figure 2

APE and relative uncertainty of groundwater infiltration tests of the conductivity tracer (QSW = 3.42–3.45 m3/h). (a) Test no. A-1: CSW = 512 μS/cm, Rc = 0.24. (b) Test no. A-2: CSW = 1,026 μS/cm, Rc = 0.12. (c) Test no. A-3: CSW = 1,565 μS/cm, Rc = 0.08. (d) Test no. A-4: CSW = 1,979 μS/cm, Rc = 0.06.

Figure 2

APE and relative uncertainty of groundwater infiltration tests of the conductivity tracer (QSW = 3.42–3.45 m3/h). (a) Test no. A-1: CSW = 512 μS/cm, Rc = 0.24. (b) Test no. A-2: CSW = 1,026 μS/cm, Rc = 0.12. (c) Test no. A-3: CSW = 1,565 μS/cm, Rc = 0.08. (d) Test no. A-4: CSW = 1,979 μS/cm, Rc = 0.06.

Close modal
Figure 3

APE and relative uncertainty of wastewater inflow tests of the conductivity tracer (QSW = 3.45–3.48 m3/h). (a) Test no. B-1: RQ-M = 11.76%, CSW = 1,656 μS/cm. (b) Test no. B-2: RQ-M = 35.24%, CSW = 1,624 μS/cm. (c) Test no. B-3: RQ-M = 60.76%, CSW = 1,633 μS/cm.

Figure 3

APE and relative uncertainty of wastewater inflow tests of the conductivity tracer (QSW = 3.45–3.48 m3/h). (a) Test no. B-1: RQ-M = 11.76%, CSW = 1,656 μS/cm. (b) Test no. B-2: RQ-M = 35.24%, CSW = 1,624 μS/cm. (c) Test no. B-3: RQ-M = 60.76%, CSW = 1,633 μS/cm.

Close modal

The relative uncertainty of each test was calculated and inserted in Figures 2 and 3. Firstly, it was found that the relative uncertainties of the conductivity tracer tests were all less than 1, indicating the conductivity tracer had good applicability for both groundwater infiltration and wastewater inflow conditions. Secondly, in the groundwater infiltration tests, as shown in Figure 2, it was found that as RQ-M increased, basically decreased. For example, in Test no. A-1, when RQ-M increased from 4.41% to 77.90%, of SP-1 decreased from 0.32 to 0.03, which was consistent with the change trend between RQ-M and APE. However, in wastewater inflow tests, as shown in Figure 3, an obvious positive relationship exists between RC and , which differs from the results between APE and RC. For example, in Test no. B-1, when RC increased from 0.22 to 0.83, d(RQ-C)/RQ-C of SP-1 increased from 0.03 to 0.08. This is because only represents the uncertainty caused by detection error, but APE also includes other test uncertainty factors, such as accidental errors during experiments.

Based on tests results of the conductivity tracer, it was concluded that the conductivity tracer performed better for detecting and quantifying I/I under higher RQ-M conditions, implying that the amount of the extraneous water is the main factor affecting the I/I quantitative accuracy.

Uncertainty analysis of turbidity tracer tests

Figure 4 shows the APE and the relative uncertainty of the turbidity tracer under groundwater infiltration tests, and Figure 5 shows results under wastewater inflow tests. In groundwater infiltration tests as shown in Figure 4, the overall APE range of the turbidity tracer tests is 0.06%–47.47%. It was found that as RQ-M increased from 15% to be more than 55%, the APE reduced from being more than 30% to be less than 15%. Therefore, as with the results of conductivity tracer shown in Figure 2, there is also a negative correlation between APE and RQ-M for the turbidity tracer. However, according to the wastewater inflow tests results in Figure 5, it was found that there was an obvious positive correlation between RC and APE, which was different from results of the conductivity tracer shown in Figure 3. Further, the APE-RQ-M and APE-RC curves of the turbidity tracer at different sampling points (SP-1 to SP-3) have shown more deviations than those of the conductivity tracer, which indicated that the stability of turbidity tracer performed worse than the conductivity tracer. This is probably caused by depositions of some of the insoluble turbidity materials when transporting along the pipe (Schilperoort et al. 2006).

Figure 4

APE and relative uncertainty of groundwater infiltration tests of the turbidity tracer (QSW = 3.08–3.29 m3/h). (a) Test no. A-5: CSW = 25.41 NTU, Rc = 0. (b) Test no. A-6: CSW = 45.27 NTU, Rc = 0. (c) Test no. A-7: CSW = 63.14 NTU, Rc = 0. (d) Test no. A-8: CSW = 83.24 NTU, Rc = 0.

Figure 4

APE and relative uncertainty of groundwater infiltration tests of the turbidity tracer (QSW = 3.08–3.29 m3/h). (a) Test no. A-5: CSW = 25.41 NTU, Rc = 0. (b) Test no. A-6: CSW = 45.27 NTU, Rc = 0. (c) Test no. A-7: CSW = 63.14 NTU, Rc = 0. (d) Test no. A-8: CSW = 83.24 NTU, Rc = 0.

Close modal
Figure 5

APE and relative uncertainty of wastewater inflow tests of the turbidity tracer (QSW = 3.45–3.48 m3/h). (a) Test no. B-4: RQ-M = 11.76%, CSW = 66.60 NTU. (b) Test no. B-5: RQ-M = 35.24%, CSW = 65.04 NTU. (c) Test no. B-6: RQ-M = 60.76%, CSW = 65.75 NTU.

Figure 5

APE and relative uncertainty of wastewater inflow tests of the turbidity tracer (QSW = 3.45–3.48 m3/h). (a) Test no. B-4: RQ-M = 11.76%, CSW = 66.60 NTU. (b) Test no. B-5: RQ-M = 35.24%, CSW = 65.04 NTU. (c) Test no. B-6: RQ-M = 60.76%, CSW = 65.75 NTU.

Close modal

As for the relative uncertainty , the change trend between with RQ-M and RC was consistent with that of the conductivity tracer. However, of the turbidity tracer was greater than 1 in many test conditions, which indicates that the method is not suitable in these conditions. For example, in Test no. A-5, when RQ-M increased from 14.72% to 74.47%, of SP-1 decreased from 4.61 to 1.37.

Based on tests results of the turbidity tracer, it is concluded that the turbidity tracer performed better under higher RQ-M and lower RC conditions. Compared to the conductivity tracer, the turbidity tracer had smaller RQ-M and RC ranges for effectively quantifying I/I.

Uncertainty analysis of temperature tracer tests

In order to study the I/I quantitative accuracy of the temperature tracer, artificial hot water inflow tests were conducted to simulate the scene of extraneous water with abnormal thermal behavior into the sewer system. The temperature of sanitary wastewater TSW (tap water) was 24.0 °C–25.0 °C (George et al. 2003), and the temperature of extraneous water TI/I (hot water) was kept at 40.0 °C–43.8 °C.

The time-space changes of the in-sewer temperature along the pipeline are shown in Figure 6. The time resolution of the temperature sequence is 30 seconds. When the extraneous inflow starts, the in-sewer temperature measured at the three monitoring points successively increased from the upstream to the downstream; when the inflow stops, it decreased gradually to the normal values. Besides, there was a temperature difference between MP-1 and MP-3 due to the heat loss and the temperature decay rates of four test conditions under stable temperature state were −0.02, −0.09, −0.10, −0.08 °C/m, respectively. In this study, the pipeline was exposed to the atmosphere and therefore there was lack of thermal protection from the surrounding soil, therefore, the temperature decay rate was larger than the measured value of 0.1 °C per kilometer of the actual sewer wastewater (Schilperoort & Clemens 2009).

Figure 6

In-sewer temperature variation (left), corresponding RQ-C and I/I uncertainty (right) under four conditions. (a) Test no. C-1: RQ-M = 15.67%, TSW = 24.9 °C, TI/I = 40.0 °C. (b) Test no. C-2: RQ-M = 24.08%, TSW = 22.9 °C, TI/I = 40.0 °C. (c) Test no. C-3: RQ-M = 36.49%, TSW = 25.0 °C, TI/I = 40.8 °C. (d) Test no. C-4: RQ-M = 60.74%, TSW = 24.0 °C, TI/I = 43.8 °C.

Figure 6

In-sewer temperature variation (left), corresponding RQ-C and I/I uncertainty (right) under four conditions. (a) Test no. C-1: RQ-M = 15.67%, TSW = 24.9 °C, TI/I = 40.0 °C. (b) Test no. C-2: RQ-M = 24.08%, TSW = 22.9 °C, TI/I = 40.0 °C. (c) Test no. C-3: RQ-M = 36.49%, TSW = 25.0 °C, TI/I = 40.8 °C. (d) Test no. C-4: RQ-M = 60.74%, TSW = 24.0 °C, TI/I = 43.8 °C.

Close modal

The analytical RQ-C values of MP-1–MP-3 are shown in the right column of Figure 6. The MAPE and the average relative uncertainty were calculated at each monitoring point according to the measured data obtained during the steady state. The overall MAPE range was 2.81%–45.86%, and that for was 0.25–1.17. Firstly, due to the heat loss along the sewer, the MAPE and of the downstream monitoring points were larger. For example, when RQ-M = 15.67%, the value of MP-3 exceeded 1, indicating that the monitoring result at this 24 m downstream point was not valid anymore. Besides, there was also a negative correlation between MAPE and RQ-M as well as between and RQ-M, which is consistent with the conductivity and turbidity tracers. Therefore, when the amount of extraneous inflow accounts for an obvious part of the sewer flow, the reliability of the temperature tracer becomes higher.

Influences of tracers' relative concentration differences

In order to further analyze influences of RQ-M, RC and the monitoring distance on APE, the correlation between the relative concentration difference (defined as (CI/I-CWW)/CI/I when CI/I > CSW > CWW and (CSW-CWW)/CSW when CSW > CI/I > CWW) and APE was studied and plotted, as shown in Figure S1. In addition, Pearson's coefficients of the three tracers were calculated and shown in Table 2.

Table 2

Correlation between relative concentration difference of three sampling points and APE under different test conditions

Test no.Tracer-test conditionPearson's coefficients (p-value)
SP-1SP-2SP-3
A-1 to A-4 Conductivity-groundwater infiltration −0.83 (<0.05) −0.82 (<0.05) −0.85 (<0.05) 
B-1 to B-3 Conductivity-wastewater inflow −0.75 (<0.05) −0.67 (<0.05) −0.73 (<0.05) 
A-5 to A-8 Turbidity- groundwater infiltration −0.89 (<0.05) −0.83 (<0.05) −0.79 (<0.05) 
B-4 to B-6 Turbidity-wastewater inflow −0.82 (<0.05) −0.83 (<0.05) −0.87 (<0.05) 
Test no. Tracer-test condition MP-1 MP-2 MP-3 
C-1 Temperature-hot water inflow RQ-M = 15.67% −0.77 (<0.05) −0.60 (0.05) −0.14 (0.68) 
C-2 Temperature-hot water inflow RQ-M = 24.08% −0.78 (<0.05) −0.11 (0.72) 0.87 (<0.05) 
C-3 Temperature-hot water inflow RQ-M = 36.49% −0.55 (0.054) 0.80 (<0.05) 0.88 (<0.05) 
C-4 Temperature-hot water inflow RQ-M = 60.74% −0.98 (<0.05) 0.99 (<0.05) 0.99 (<0.05) 
Test no.Tracer-test conditionPearson's coefficients (p-value)
SP-1SP-2SP-3
A-1 to A-4 Conductivity-groundwater infiltration −0.83 (<0.05) −0.82 (<0.05) −0.85 (<0.05) 
B-1 to B-3 Conductivity-wastewater inflow −0.75 (<0.05) −0.67 (<0.05) −0.73 (<0.05) 
A-5 to A-8 Turbidity- groundwater infiltration −0.89 (<0.05) −0.83 (<0.05) −0.79 (<0.05) 
B-4 to B-6 Turbidity-wastewater inflow −0.82 (<0.05) −0.83 (<0.05) −0.87 (<0.05) 
Test no. Tracer-test condition MP-1 MP-2 MP-3 
C-1 Temperature-hot water inflow RQ-M = 15.67% −0.77 (<0.05) −0.60 (0.05) −0.14 (0.68) 
C-2 Temperature-hot water inflow RQ-M = 24.08% −0.78 (<0.05) −0.11 (0.72) 0.87 (<0.05) 
C-3 Temperature-hot water inflow RQ-M = 36.49% −0.55 (0.054) 0.80 (<0.05) 0.88 (<0.05) 
C-4 Temperature-hot water inflow RQ-M = 60.74% −0.98 (<0.05) 0.99 (<0.05) 0.99 (<0.05) 

Through the two-tailed significance test, the APE was significantly correlated with the relative concentration difference under most test conditions at the 95% confidence level (p-value < 0.05), as shown in Table 2. Firstly, there was a negative correlation between APE and the relative concentration for conductivity and turbidity tracers. The Pearson correlation coefficient of the conductivity tracer is −0.67 to −0.85, while that of turbidity tracer is −0.79 to −0.89, which indicates that the turbidity tracer is more sensitive to the relative concentration difference than the conductivity tracer. Therefore, the turbidity tracer is more suitable for cases with large relative concentration differences.

In addition, for conductivity and turbidity, the Pearson coefficient at different monitoring points had little difference under each test condition; however, it is interesting to find that, for the temperature, the Pearson coefficient fluctuated greatly among three monitoring points. For the first monitoring point MP-1 which was nearest to the I/I location, it retained a negative correlation with APE. This is consistent with the conductivity and turbidity tracer. However, for the downstream monitoring points MP-2 and MP-3, their relative temperature difference and APE evolved from a weak negative correlation to a strong positive correlation from Test no. C-1 to no. C-4. The temperature differences at different monitoring points due to the heat loss rate and monitoring distance determined the accuracy and reliability of the I/I quantitative results.

Based on the large-scale experimental setup, three I/I scenarios including groundwater infiltration, wastewater inflow, and hot water inflow were simulated by artificially preparing the flow and concentration of the wastewater. I/I quantitative reliability of the three simple tracers was verified, which provides guidance for their practical application. The APE ranges of the three tracers rank as turbidity (0.06%–55.54%) > conductivity (3.50%–50.44%) > temperature (2.81%–45.86%), and the relative uncertainty ranges rank as turbidity (0.35–12.45) > temperature (0.25–1.17) > conductivity (0.01–0.34). The accuracy and stability of the conductivity tracer and the temperature tracer were better than that of turbidity. The temperature tracer has disadvantages in terms of temporal and spatial variability, which has been rarely reported in previous publications. Experimental findings in this work provide useful guidance for using these tracers for quantifying and locating I/I in sewer systems. However, considering complex conditions in real sewer systems, more investigations including field experiments will be needed before wide engineering applications are applied.

This work was supported by the National Science Foundation of Anhui Province (grant number:1908085QE211), Key Research and Development Program in Anhui Province (grant number: 202104i07020012) and the Ningbo University SUD Laboratory Open Fund.

All relevant data are included in the paper or its Supplementary Information.

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Supplementary data