Quantifying Groundwater Infiltration into Sewers with Chemical Markers Measurements and Bayesian Chemical Mass Balance Model: Methodology and Verification

Abstract

Urban sewer conditions assessment is important for the proper conveyance of sanitary water to wastewater treatment plants prior to environmental discharge. An effective approach to address this important process needs to be developed. This paper presents a data-driven methodology for sewer condition assessment with gridding-based chemical markers measurement in combination with a Bayesian chemical mass balance (CMB) model. A field study was performed in an urban sewer in Nanjing, China, to test the robustness of the developed methodology. In this site, data library of chemical markers (total nitrogen, phosphate, chloride, and total hardness) for source flows, including domestic wastewater, commercial wastewater and groundwater, was established. Meanwhile, a gridding-based measurement of these chemical markers in sewer flows was performed along the assessed sewer. Then, the CMB model with Bayesian inference and parallel Markov Chain Monte Carlo simulations was developed to quantify source contributions in sewer flows based on the chemical markers data of source and sewer flows. Accordingly, the proportion of clean water infiltration into the sewer and associated sewer defect level can be assessed. The Bayesian CMB model presented that groundwater contributed 11~14% of the sewer flow, indicating a neglectable sewer defect condition. The sewer assessment result was further verified by on-site physical inspection with distributed temperature sensing of in-sewer flows, proving the reliability of the developed methodology. Using this data-driven approach, a preliminary screening of the high-risk sub-catchments with severe sewer defect levels can be made for the following targeted sewer defects locations, optimizing the labor-intensive, system-wide physical inspections. Therefore, the proposed approach offers a cost-effective solution for system-wide sewer inspections.

1. Introduction

Underground sewer systems are one of the largest infrastructures in cities, which convey foul sewage to wastewater treatment plants (WWTPs) for contaminant removal. The widespread use of sewer systems is rooted in their crucial role in our lives as it protects both our health and the water environment. Meanwhile, the growing use and aging of sewer networks bring huge challenges for management and maintenance. For example, the total length of underground sewer systems in China reaches 900,000 km, approximately half of which is over 10 years [1]. The potential problems with deteriorated or malfunctioning sewer systems, such as pipe defects and associated clean water infiltrations in the areas where the sewer invert lies below the groundwater table, are commonly linked to insufficient sewer flow-carrying capacities and associated sewer overflows and flooding [2,3,4,5,6]. Facing the huge underground asset, low-cost techniques for assessing the performance of sewer networks are highly valued in finding a solution to these problems.

Currently, sewer condition assessment is predominantly conducted by visual inspection methods, with the most commonly used being closed-circuit television (CCTV) examination [7,8,9,10]. However, CCTV examination is often labor-intensive and expensive, due to the cumbersome procedures of sewer blocking, draining, and sediments dredging in sequence before each inspection [11,12,13,14]. In particular, blocking municipal trunk sewers for CCTV examination is challenging as it disrupts normal sewage conveyance. Additionally, CCTV examination cannot offer quantitative assessment of infiltrated clean water flows based on the acquired in-sewer videos and images.

To optimize the use of physical inspections for large-scale sewer network assessment, recent advances make use of the measurement of sewer flows and chemical markers as an alternative to visual inspection methods [15,16,17,18,19,20,21,22]. These approaches can provide a preliminary evaluation of system-wide sewer conditions. Sewer flow measurement relies on a volume balance approach, where clean water flow is estimated as the deficit between in-sewer flow and consumer sewage discharge. However, obtaining accurate sewage discharge data for all consumers is challenging, introducing uncertainty in clean water flow estimation. Alternatively, with measured chemical marker concentrations for sewer flows and their contributing sources (e.g., sewage and clean water), a source apportionment modeling can be established to quantify the fractional contributions of each source, while acquiring comprehensive sewage discharge data is not required.

In practice, for the investigation of sewer catchment, there are usually many sewage sources and extraneous flows connecting to the urban sewers, and the source concentrations vary on spatial and temporal scales. It is impossible to measure every source input and then establish an entry–exit mass balance equation. From this perspective, the efficient determination of the flow fractions of different contributing sources based on the well-designed measurement of marker concentrations of in-sewer and source flows needs to be addressed.

Recently, the Bayesian chemical mass balance (CMB) model was demonstrated as a flexible approach to infer the contributions of various sources by employing limited measurements of the sources and environment recipient, as demonstrated in other fields of water pollution control [23,24,25,26,27,28,29]. However, no literature was found concerning the use of Bayesian CMB model in assessing the source flow contributions into urban sewers and the associated sewer performance. Confronting the high-dimensional problem characterized by the complicated source inputs, a mathematical model offering reliable output for the quantification of diverse source flows is also left to be developed and verified.

Motivated by the above challenges, the objective of this paper is to present a data-driven methodology for cost-effective sewer condition assessment, by combining gridding-based chemical markers measurement with a Bayesian mathematical model. The developed methodology was tested in an actual sewer and then verified by the refined in-sewer inspections using distributed temperature sensing (DTS).

2. Materials and Methods

2.1. Study Site Description

An on-site study was performed in one urban sewer in Nanjing, China (Figure 1), where high-density polyethylene sewer pipes were constructed. The investigated sewer reach is 400 m long, and has a circular profile with a diameter of 400 mm. As seen in Figure 1, this investigated sewer pipe connects an upstream sewer of 300 mm diameter and also receives sewage of nearby living communities and social units through two branch sewers of 400 mm diameter.

As the investigated sewer is located in downtown area of Nanjing City with heavy traffic, it is anticipated that a low-cost sewer condition assessment without disturbance to sewer flow conveyance could be performed, so as to offer effective strategies for the following pipe maintenance. Specifically, on the condition that the investigated sewer is assessed to be malfunctioned, the pipe repair needs to be made. However, there is also the case that the investigated sewer is assessed to be well-functioning. In this case, sewer pipe repair would not be a mandatory task. Given the groundwater table at this site is above the sewer invert due to abundant rainfall, quantification of groundwater infiltration into sewers can serve as a reliable proxy for potential sewer defects, supporting decision-making for the necessity of sewer pipe repair.

2.2. Workflow of the Study

A schematic diagram to illustrate workflow of this study is illustrated in Figure 2. As seen in this figure, this study introduces a data-driven model for sewer defects assessment with quantified groundwater fraction as a proxy. The accomplishment of this model includes (1) a robust Bayesian CMB model to estimate proportions of sewage and groundwater within the sewer flows, and (2) measurements of chemical markers for both the contributing sources and in-sewer flows.

The developed model is verified with in-sewer physical detection with DTS measurement. Specifically, DTS approach includes the procedures of (1) collecting in-sewer temperature data using DTS, (2) analyzing the thermal behavior of sewer flows to find the potential problematic points, and (3) quantifying the groundwater flows at the problematic points for model verification.

2.3. Model Development

2.3.1. The Bayesian CMB Model

The concentration of a marker in the sewer flows can be reproduced by linear combinations of several known sources, which can be written in a matrix form as

$$\mathrm{AX}=\mathrm{C}$$

(1)

where $\mathrm{A} = {\left[{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right]}_{\mathrm{m}\times \mathrm{n}}$ is the source profile matrix, containing the concentration of marker $\mathrm{i}$ in source $\mathrm{j}$; $\mathrm{X} ={ \left[{\mathrm{x}}_{\mathrm{j}}\right]}_{\mathrm{n}\times 1}$ is the source contribution vector, representing the fractional contributions of each source (residential wastewater, commercial wastewater, and infiltrated groundwater in this case) into the sewer manhole sample; $\mathrm{C} = {\left[{\mathrm{c}}_{\mathrm{i}}\right]}_{\mathrm{m}\times 1}$ is the measured concentration of each selected marker in sewer manhole flows; m and n are the numbers of chemical markers and contributing sources, respectively. On the condition that the number of selected chemical markers is equal to that of contributing sources, the source profile matrix $\mathrm{A}$ is then squared.

Considering $\mathrm{X}$ is defined as the fractional contribution of sources, the sum of its elements should be unity

$$\sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{j}}=1$$

(2)

Because of heterogeneities in the elemental composition of source samples, the exact values of the source profile matrix $\mathrm{A}$ are very hard to obtain. For example, it is impossible to monitor all the scattered sources in the sewer catchment and obtain the exact flow-weighted average marker concentration of each source type. Facing this uncertainty, the goal of this study is to infer the posterior probability distribution of $\mathrm{X}$ based on measured marker concentrations of sources and sewer samples. Considering the uncertainty of source profiles, the posterior probability includes both $\mathrm{X}$ and $\mathrm{A}$ using Bayesian inference, which can be expressed as

$$\mathrm{p}\left(\mathrm{X},\mathrm{A}|\tilde{\mathrm{C}}\right)={\displaystyle \frac{\mathrm{p}\left(\mathrm{X}\right)\mathrm{p}\left(\mathrm{A}\right)\mathrm{p}\left(\tilde{\mathrm{C}}|\mathrm{X},\mathrm{A}\right)}{\mathrm{p}\left(\tilde{\mathrm{C}}\right)}}\propto \mathrm{p}\left(\mathrm{X}\right)\mathrm{p}\left(\mathrm{A}\right)\mathrm{L}\left(\tilde{\mathrm{C}}|\mathrm{X},\mathrm{A}\right)$$

(3)

where $\mathrm{p}\left(\mathrm{X}\right)$ is the prior distributions for $\mathrm{X}$,$\mathrm{p}\left(\mathrm{X}\right)={\prod }_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)$; $\mathrm{p}\left(\mathrm{A}\right)$ are the prior distributions for $\mathrm{A}$, $\mathrm{p}\left(\mathrm{A}\right)={\prod }_{\mathrm{i},\mathrm{j}=1}^{\mathrm{n}}\mathrm{p}\left({\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)$; $\mathrm{p}\left(\tilde{\mathrm{C}}|\mathrm{X},\mathrm{A}\right)$ is the likelihood function; $\mathrm{p}\left(\tilde{\mathrm{C}}\right)$ is the normalization factor; $\mathrm{L}\left(\tilde{\mathrm{C}}|\mathrm{X},\mathrm{A}\right)$ is the normalized likelihood function.

Usually, it can be assumed that the recipient profiles $\tilde{\mathrm{C}}$ is lognormally distributed with known variances, and that their elements are independent of each other. Therefore, a posterior distribution can be presented with the following form:

$$\mathrm{p}\left(\mathrm{X},\mathrm{A}|\tilde{\mathrm{C}}\right)=\prod _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)\prod _{\mathrm{i},\mathrm{j}=1}^{\mathrm{n}}\mathrm{p}\left({\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)\left[-{\displaystyle \frac{\mathrm{n}}{2}}\log \left(2\mathsf{\pi }\right)-\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[\log \left({\mathsf{\sigma }}_{\mathrm{i}}\right)-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{\sum {\mathrm{a}}_{\mathrm{i}\mathrm{j}}{\mathrm{x}}_{\mathrm{j}}-\widetilde{{\mathrm{c}}_{\mathrm{i}}}}{{\mathsf{\sigma }}_{\mathrm{i}}}}\right)}^2\right]\right]$$

(4)

where ${\mathsf{\sigma }}_{\mathrm{i}}$ is the variance of the measured concentration of marker $\mathrm{i}$ within the sewer.

In Equation (4), the prior distribution of $\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)$ is considered a flat distribution (e.g., uniform distribution between 0 and 1) with parameters all equal to one and therefore satisfying constraints set by Equation (2). The prior distribution of $\mathrm{p}\left({\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)$ is assumed to be a normal distribution by analyzing the measured source data from multiple samples. Therefore, Equation (4) can be used to calculate the posterior probability distributions of various parameters including $\mathrm{n}$ source contributions and $\mathrm{n}\times \mathrm{n}$ source marker composition, as well as the credible intervals through integration.

Equation (4) is characterized as a high-dimensional problem that is not suitable for conventional numerical integration. Typically, the Markov Chain Monte Carlo (MCMC) method provides a practical way to sample from a high-dimensional probability density function. MCMC generates random walks through the search space and constantly tries to move from the current state to a new one during the sampling process. The traditional MCMC approach is a random walk metropolis (RWM) algorithm, which may be inefficient and unreliable when applied to complex posterior distributions with long tails and multiple regions of attraction. Under this scenario, the RWM algorithm may fall into the local optimal area, resulting in the Markov chain being stuck in place even after millions of iterations and misleading solutions [30].

To avoid premature convergence in high-dimensional problems, we introduce an improved Bayesian–MCMC model with parallel multi-chain samplings, which can lower the possibility of premature convergence by setting different initial points to explore the posterior target distribution. In this way, the use of multiple chains could improve the diversity of the early Markov chains and the adaptability of the global searching. Additionally, differential evolution adaptive metropolis with self-adaptive randomized subspace sampling was employed to choose an appropriate orientation for the target distribution [30,31,32]. Correction of outlier chains based on interquartile range (IQR) was also conducted to speed up the convergence to the target distribution. The $\widehat{\mathrm{R}}$-statistic for each estimation parameter was calculated to determine whether or not the sampled chains have converged [32]. The technical route for the improved Bayesian CMB approach with parallel MCMC simulations is provided in Figure 3.

2.3.2. Design of Chemical Markers Measurement

Determination of sampling sites. As mentioned above, the exact values of the source profile matrix $\mathrm{A}$ are practically very hard to obtain. In a sewer catchment, it is difficult to collect samples from every sewage source in a big catchment and establish a data library for chemical markers. The necessary simplification is to conduct water quality samplings in several typical living communities and other units and then establish a probability data library to represent the most likely range of chemical marker concentrations in the whole catchment. In the following, Bayesian inference can be utilized to estimate the posterior probability distribution of the unknown information about the fractional contributions of each source based on measured marker concentrations of sources and sewer samples, as described above.

Determination of sampling duration. Practically, it is impossible to identify the location and timing of each source input, bringing about uncertainty for CMB modeling. This uncertainty, however, can be reduced by defining relatively long-time intervals for source apportionment. If the time interval for marker fluxes (for example, daily marker fluxes) is significantly longer than the maximum source residence time of the study site, the influent mass tends to balance the effluent mass, thus rendering different marker residence times insignificant. From this perspective, the sampling activity should usually last continuously for 24 h or a longer time period. Accordingly, $\mathrm{C}$ in Equation (1) is defined as daily averaged instead of transient concentration.

Determination of sampling number. It is important to determine the number of observations needed for each source category in order to build a useful data library for Bayesian CMB modeling. China’s technical specification for investigation and elimination of illicit discharges of municipal drainage pipes states that the water quality survey should continue for over 24 h with a sampling time interval of less than 4 h, generating at least 6 samples for each source and sewer manhole [33]. The US technical guide suggested at least 10 samples to generate a confidence interval of the mean plus and minus its 25 percent [34]. Accordingly, the sampling activity in this case continued for 48 h with a fixed time interval of 4 h and accordingly generated 12 samples for each sampling site. More specifically, one way is to perform continued 48 h monitoring on working days for every site, and another way is to conduct continued 48 h monitoring on both working days and weekends for each site.

2.3.3. On-Site Data Acquisition of Chemical Markers

Multiple samples were taken at each sampling site including both the sewage sources and sewer manholes. Input data for shallow groundwater was directly obtained from local geological survey.

Samples of sewage sources were collected in three living communities and two commercial units in the whole catchment (Figure 2). For each sampling site, the collection of wastewater samples continued for 48 h with a fixed time interval of 4 h. For the five sampling sites, the sampling activities were conducted within the periods of 19–21 December 2020 (Saturday to Monday). These sewage samples were kept at approximately 4 °C, using ice packs, and transported back to the laboratory every day for immediate processing.

As seen in Figure 1, samples of sewer flow were collected in five manholes along the investigated sewer pipe. Considering this study focused on quantifying groundwater infiltration into the sewer, sampling activity was implemented within two days from 11 to 13 September 2020 (Friday to Sunday), when a 48 h antecedent dry period was observed prior to the fieldwork to exclude in-sewer concentration change due to potential stormwater runoff inflow into the sewer. During the sample collection, a bucket that could be laid horizontally into a shallow flow was used to collect water from the manholes for a timed interval. Water samples were collected every 4 h, resulting in 12 samples for each investigated manhole. The sewage samples were kept and pre-processed as mentioned above.

All of the collected samples were analyzed for total nitrogen (TN), total phosphorus (TP), chloride, and total hardness (sum of calcium and magnesium). Among these markers, TN, TP, and chloride are indicators of sanitary wastewater, the production and secretion of which are controlled by the metabolic activities of human bodies and usually follow regular daily patterns. Total hardness is an indicator of groundwater, since their compounds in the aquifer are likely to be dissolved by percolating rainwater made acidic by carbon dioxide. Chloride and hardness are less likely to undergo physical and chemical reactions within the sewer. For TN and TP in domestic sewage, it is mainly composed of ammonia nitrogen, nitrate, and phosphate featuring non-particulate forms, which are less likely to settle down at the sewer bottom and resulting in chemical mass loss within the sewers, compared to the organic indicators of chemical oxygen demand (COD) and biological oxygen demand (BOD). Therefore, TN and TP are more conservative than COD and BOD when employed as chemical markers for mass balance analysis.

Analysis for TN was based on the alkaline potassium persulfate digestion ultraviolet spectrophotometric method (China’s HJ 636-2012) [35]. TP was measured based on the ammonium molybdate spectrophotometric method (China’s GB/T 11893-1989) [36]. Chloride was analyzed based on the silver nitrate titration method (China’s GB/T 11896-1989) [37], and total hardness was measured using the edetate disodium titration method (China’s GB/T 5750.4-2006) [38].

2.4. Model Verification

The reliability of the developed model can be verified by on-site physical inspection. Specifically, it can be validated with DTS, an equipment for measuring real-time, in-sewer water temperature on a spatial and temporal scale [12,14,39]. The in-sewer setup of the DTS is provided in Supporting Information Figure S1.

Benefiting from the high-resolution water temperature measurement by DTS, the occurrence of clean water inflow or infiltration into the sewer can be detected and quantified by analyzing temperature variations caused by extraneous water, which typically differs in temperature from the upstream flow. The details are provided in Supporting Information Section S1.

3. Results and Discussion

3.1. Data Library of the Measured Chemical Markers

A summary of measured marker concentrations for residential wastewater and commercial wastewater is presented in Figure 4, along with the concentration profile for local shallow groundwater acquired from the local water affairs municipality. Measured marker concentration profiles of the in-sewer water at the investigated manholes are summarized in Figure 5.

Figure 4 shows that among the selected markers, TN, TP, and chloride exhibit significantly higher concentrations in sanitary sewage (residential and commercial wastewater) than in shallow groundwater. By contrast, hardness exhibits a higher concentration in groundwater than in sanitary sources, demonstrating its indication of clean water. The difference in chemical marker concentrations between residential wastewater and commercial wastewater is not obvious. Generally, TN and TP show higher concentrations in residential wastewater than in commercial wastewater, which may be associated with an increased proportion of greywater in the commercial units. The higher concentration of chloride in commercial wastewater than in residential wastewater could be explained by the fact that commercial activities (e.g., the use of detergents for washing) result in more consumption of inorganic substances. Additionally, marker concentrations in commercial wastewater exhibit a wider range than in residential wastewater due to a variety of activities in the former case. Figure 5 demonstrates decreased marker concentrations of TN, TP, and chloride in sewer flows as compared to those in sanitary sources, indicating the entry of clean water into the investigated sewer pipe.

3.2. Assessed Sewer Conditions Based on Bayesian CMB Model

With determined marker concentrations (Figure 3 and Figure 4), the Bayesian CMB method described was applied to quantify source contributions for a general sewer condition assessment. In this case, the sources contributing to sewer flows include residential wastewater, commercial wastewater, and infiltrated groundwater. Accordingly, three markers would be adequate to form a square source profile matrix (see Equation (1)) for modeling performance. Specifically, two chemical marker combination scenarios were implemented in modeling. One was based on TN, TP, and hardness, and the other was based on TN, chloride, and hardness.

For each scenario, twelve parameters were included in the Bayesian inference concerned, including the fractional contributions of three sources (${\mathrm{x}}_{\mathrm{j},}\mathrm{j}=1,2,3$) and nine source marker profiles (${\mathrm{a}}_{\mathrm{i}\mathrm{j}},\mathrm{i},\mathrm{j}=1,2,3$). A list of the twelve parameters is shown in Supporting Information Table S1. The prior distributions of the three source contributions were assumed as an even distribution between 0 and 1 (${\mathrm{x}}_{\mathrm{j}},~\mathrm{U}(0,1))$, because no additional information about the contributions were presented. The prior distributions of the nine marker concentrations were designated as a normal distribution (${\mathrm{a}}_{\mathrm{i}\mathrm{j}}~\mathrm{N}(\mathsf{\mu },{\mathsf{\sigma }}^2)$), where the mean value $\mathsf{\mu }$ and standard deviation $\mathsf{\sigma }$ were determined according to the investigated data from multiple samples (see Figure 3).

At each investigated sewer manhole, the improved Bayesian–MCMC method with parallel multiple Markov chains was employed to provide estimations of high-dimensional parameters (see Figure 2). The number of Markov chains in the parallel computation was 10 (N = 10), and the pre-set number of iterations was 50,000. The ${\mathsf{\sigma }}_{\mathrm{i}}$ of each marker in the likelihood function (see Equation (4)) was set according to the standard deviation of measured concentrations of multiple samples from each manhole, and the observation $\widetilde{{\mathrm{c}}_{\mathrm{i}}}$ of each marker was determined based on the averaged concentration of multiple samples from each manhole. During the MCMC simulation process, the $\widehat{\mathrm{R}}$-statistic for each estimation parameter was calculated to determine whether or not the sampled chains have converged. Typically, the multi-chains will achieve convergence when the values of ${\widehat{\mathrm{R}}}^{\mathrm{i}}$ are less than 1.2 for each parameter, i $\in \left\{1,2,\dots ,12\right\}$. In this case, the $\widehat{\mathrm{R}}$ for all of the twelve parameters became less than 1.2 when iterating to about 10,000 times (see Supporting Information Figures S3 and S4). Accordingly, the resulting posterior distribution and maximum posterior estimation (MAP, as indicated with red and blue cross) of each source contribution are provided in Figure 6. Specifically, MAP is a statistical parameter used to estimate the most probable value of an unknown parameter by combining prior knowledge with the observed data (see Equation (3)). In this study, the MAP values represent the most probable flow fractions for each source type across all simulations (50,000 simulations in this case) with the Bayesian CMB model. The correlation information of all twelve parameters (data set plots and histogram plots) is also presented in Supporting Information Figures S5 and S6.

As shown in all cases in Figure 6, the MAP values (i.e., Bayesian CMB-inferred source contributions) based on scenario I (TN, TP, and hardness) are almost the same as those based on scenario II (TN, chloride, and hardness). The slight difference in the proportions of source flows between the two scenarios indicates the robustness of the developed CMB approach with the improved Bayesian–MCMC simulation. Such an approach can adequately provide source contribution estimations through the exploration of the full parameter space. For all the five manholes, sanitary wastewater (including residential and commercial wastewater) is the major contributor to sewer flows, accounting for 86~89% of the total sewer flow. Considering both residential and commercial sewage are domestic wastewater collected by municipal sewer systems, and this study focused on quantifying clean water infiltration into urban sewers, we did not conduct further analysis on the proportion of residential versus commercial wastewater and their discharge sources.

Compared to the sanitary wastewater, groundwater had the lowest contributions among the five manholes, accounting for only 11~14% of the total flow within the investigated sewer. No obvious difference in groundwater flow fractions were found along the investigated sewer, which can be explained by the fact that side inflows (including both sewage connection and infiltrated groundwater from manhole 1 to manhole 5) were significantly lower than the upstream inflow. From another perspective, it also indicated small amounts of groundwater infiltrated into the investigated sewer.

The estimated flow fraction of groundwater is also an indication of the severity of sewer defects. Specifically, this severity can be assessed by using [6,40]

$$\mathsf{\epsilon }=\mathsf{\delta }/{\mathsf{\delta }}_0$$

(5)

where $\mathsf{\epsilon }$ is sewer defect index; $\mathsf{\delta }$ is the actual groundwater infiltration flow; ${\mathsf{\delta }}_0$ is the allowable groundwater infiltration flow in the sewer, which is usually set as 15~20% of the dry-weather flow according to China’s National Code for Design of Outdoor Wastewater Engineering [37]. Usually, $\mathsf{\epsilon }$ ≤ 1, $1<\mathsf{\epsilon }2$, and $\mathsf{\epsilon }>2$ categorize the severity of sewer defects from low- to high-risk levels into neglectable, slight, and severe grades, respectively.

Given that groundwater infiltration represents just 11~14% of the total flow in this investigated sewer, the calculated ε falls below 1 $(\mathsf{\epsilon }$ < 1), indicating negligible sewer defects. The model inferred sewer condition was further verified by DTS inspections in the following section.

3.3. Verification of the Sewer Assessment Results with Physical Inspection

The sewer assessment results were validated with the DTS approach stated in Section 2.4. A thermal image for the obtained DTS data from the investigated sewer is presented in Figure 7, where over 6,386,000 water temperature records were included during the period from 11 September, 19:00 to 23 September, 18:00 in the year of 2020. It was found that clean water infiltration or inflow into the investigated sewer led to local water temperature change neighboring the sewer problematic points. The problematic points were identified as groundwater infiltration at position 40 m and clean water inflow at 301 m according to an on-site survey.

Specifically, at sewer location 40 m, the average water temperature before and after groundwater infiltration was 26.25 °C and 26.2 °C, respectively, with infiltrated groundwater measured at 24.2 °C. This corresponded to a 2.4% clean water contribution to the sewer flow (see Supporting Information Section S4). Similarly, at sewer position 301 m, water temperatures declined from 25.94 °C (before clean water inflow) to 25.86 °C (after clean water inflow), quantifying a 5.5% surface water contribution (see Supporting Information Section S4). It can be found that no significant groundwater inflows were detected along the investigated sewer.

It is necessary to note that besides the temperature variations observed at 40 m and 301 m, the DTS also detected subtle thermal anomalies at approximately 10 m, 110 m, 140 m, and 210 m along the pipeline, which were close to the DTS resolution limit of ±0.01 °C. Specifically, slight temperature change at 201 m was associated with branch sewer connection at manhole 3. The minor variations at 10 m, 110 m, and 140 m likely represented negligible clean water infiltration events, as their magnitude approximated the DTS detection limit and therefore had minimal impact on the in-sewer flow.

Therefore, the detection of sewer problematic points and associated clean water flow quantification using DTS, further confirming that the assessed sewer pipe was under a neglectable sewer defect condition. The in-sewer physical inspection using DTS proved the reliability of the assessed sewer conditions using our developed approach.

3.4. Implications for Large Sewer Network Inspection

As a non-intrusive approach, the developed methodology shows promise for cost-effective assessment of sewer defects. In this case, direct CCTV inspection of the investigated sewer, including cumbersome procedures of pipe blocking, pipe draining, in-pipe sediments dredging, CCTV operation, and in-pipe image analysis, would cost 40,000 RMB. By contrast, the estimated cost for chemical markers measurement was about 21,000 RMB, which was approximately 50% of the direct CCTV inspection. When scaling this methodology to a large sewer system, the economic benefit would be more effective. For the use of this approach in a large sewer catchment, its implementation involves the procedures below.

Firstly, the whole sewer system can be divided into several sub-catchments or grids based on key mid-way locations within the sewer network (e.g., locations connecting branch sewer with trunk sewer, mid-way sewage lifting pump stations).

Secondly, gridding-based in-sewer water quality measurement is performed to quantify clean water contribution into the sewer flow in combination with a Bayesian CMB model. Concurrently, on-site sampling is required to establish a site-specific source database. Regarding scaling of this methodology to a larger urban sewer network, such implementations typically require (1) expanded on-site sampling to establish a comprehensive chemical marker database covering all potential sources such as domestic sewage as well as industrial wastewater discharge of different trades, and (2) increased gridding-based in-sewer sampling given the increased spatial complexity of larger sewer system. Screening more conservative chemical markers that characterize diverse source inflows can also aid in expanding the model’s applicability. Through this process, the sub-catchments will be systematically ranked (from low to high risk) according to the quantified groundwater contributions to the sewer flows.

Thirdly, for the identified high-risk sewer sub-catchments, refined sewer detection with physical instruments such as CCTV or DTS is employed to locate the sewer problematic points for following pipe repairs.

Using this methodology, the severe sewer defects that contribute significant clean water inflow or infiltration into the sewer system can be located through progressive, preliminary high-risk area screening and the following targeted problem points detection, avoiding the need for labor-intensive, system-wide physical inspections.

However, it is necessary to note that groundwater infiltration only occurs where the groundwater water table is above the pipe inverts. In practice, sewer invert elevations vary significantly over the large sewer network, indicating some sub-catchments may not meet the hydraulic condition of groundwater infiltration. To address this limitation, it is necessary to acquire the data of groundwater level and sewer network elevation surveys for a screening of the sub-catchments where the groundwater table exceeds sewer inverts prior to the use of the developed methodology. From this perspective, the method’s applicability to large sewer networks also depends on the availability of the fundamental data of groundwater table and sewer network from local authorities.

4. Conclusions and Perspectives

This study presented a data-driven methodology for assessing urban sewer conditions by integrating gridding-based chemical markers measurement with a Bayesian CMB model. The approach was applied to an actual urban sewer in a downtown area, demonstrating its effectiveness in quantifying source contributions and evaluating sewer defect levels with clean water infiltration as a proxy.

With the well-designed measurements of chemical markers for contributing sources and in-sewer flows, the developed Bayesian CMB model, enhanced with parallel MCMC simulations, can effectively address the high-dimensional problem of source apportionment. In this case, with a site-specific data library, the model quantified the contributions of domestic sewage (including residential and commercial wastewater, 86–89%) and groundwater infiltration (11–14%) to sewer flows, with consistent results across different chemical marker combinations (TN–TP–hardness and TN–chloride–hardness). The quantified groundwater flow proportion in the investigated sewer indicated a neglectable sewer defect condition, which was further validated by on-site physical inspection using DTS.

The proposed methodology can offer a cost-effective solution for large-scale sewer inspections compared to direct use of physical instruments. By dividing sewer networks into sub-catchments and employing gridding-based water quality measurements, high-risk grids can be preliminarily screened. Physical inspections (e.g., CCTV or DTS) can then be focused on these grids, significantly reducing time and resource expenditures.

Finally, the methodology can be tested on a larger sewer network by integrating DTS detections for further validating model-inferred high-risk sewer pipes, so as to prove it can catch more diverse infiltrations. Meanwhile, a definite cost comparison between this method and conventional CCTV inspections can be compared to further test the cost-effectiveness of this method for a large sewer system. Further research could also explore the integration of real-time water quality monitoring and the Bayesian CMB model to enhance the use of this data-driven approach in smart water system management for both dry-weather and wet-weather days (e.g., potential stormwater inflow into sewers). With the support of smart technologies (e.g., real-time acquisition of consumer water use data), sewer flow measurements can also be incorporated with the developed approach to strengthen data-driven sewer system inspection and maintenance from the perspectives of both water flow and water quality.