Flow rate influence on sediment depth estimation in sewers using temperature sensors

Sediment build-up in sewer systems not only poses environmental concerns but also leads to significant operational costs associated with maintenance and cleaning. Sewer inspection and cleaning efforts are scarce in most countries, leading to loss of hydraulic capacity, blockages and, consequently, an increased risk of flooding in urban areas. These tasks are often carried out periodically based on past experiences, but without using observation-based criteria. This strategy may lead to high costs if maintenance is not required as regularly. Some countries, such as Austria, rely on periodic maintenance based on image observations (Plihal et al. 2014), although these solutions are difficult to scale due to their cost. Improved monitoring approaches for measuring sediment build-up in pipeline networks will enable more effective cleaning strategies and enhance the understanding of sediment transport dynamics. Measuring sediment build-up across an entire sewer system presents significant difficulties, such as accessibility and equipment limitations (Bertrand-Krajewski et al. 2021). Previous attempts to monitor sediment build-up consisted mostly of single-pipe measurements that required a high cost of supervision and maintenance (e.g., Lepot et al. 2017).

This research uses temperature measurements as a proxy for estimating sediment depths in sewer systems. Temperature acts as a natural non-conservative tracer, providing very useful information in many applications such as sewer flow measurements or combined sewer overflow detections (e.g., Dürrenmatt et al. 2013; Montserrat et al. 2015). Recent studies advanced towards the detailed understanding of heat-transfer dynamics on the pipe network scale, especially the fluid–headspace–soil interaction (Abdel-Aal et al. 2021; Figueroa et al. 2021). In parallel, Regueiro-Picallo et al. (2023, 2024a) demonstrated that heat-transfer processes in urban drainage systems can be used as a method for monitoring sediment depths using temperature sensors. The methodology consists of dual temperature measurements in the fluid and sediment-bed layers to measure sediment build-up through changes in temperature dynamics. This approach was inspired by similar techniques used in river streambeds, which effectively identified accumulation and erosion processes by analysing daily temperature patterns (DeWeese et al. 2017; Sebok et al. 2017).

Temperature-based sediment monitoring systems assume that flow conditions do not affect heat-transfer processes between the water and sediment layer and therefore no hydraulic variables need to be measured. However, wastewater flows in sewers introduce forced convection at the water–sediment interface. This study examines the influence of convective processes on the estimation of sediment depths using temperature-based systems that ignored hydraulic variables. For this purpose, laboratory experiments in an annular flume were performed using various sediment depths, water temperature gradients, and flow rates. The main advantages of this type of facility were the steady flow conditions and the room-temperature control system (Tait et al. 2003). In addition, a numerical analysis was carried out to examine the heat transfer at the sediment–water interface. Finally, conclusions and recommendations are made for the design and implementation of low-cost, low-power, and low-computational sensor-based solutions to improve the understanding of sediment build-up processes and maintenance strategies for urban drainage systems.

The flume was equipped with 24 PT100 temperature sensors (RS Pro, UK) distributed in three cross-sections, covering the temperature measurements of the room, water, and sediment layer (see example in Figure 1 (right)). The data were controlled and collected in a laptop using temperature input modules at a frequency of 1 Hz (National Instruments – NI, UK). In addition, a water bath circulator (Julabo, UK) was installed on the bottom plate to simulate wastewater temperatures in sewers. To this end, a closed loop system was designed by connecting inlet and outlet hoses between the water bath and the annular flume.

The sediment bed consisted of a main layer of fine silica sand and a 10-mm top layer of coarse sand and gravel to avoid resuspension of fines and ensure a constant sediment depth during the experiments (no bed forms). The sediments were saturated before layering in the flume to prevent air voids. Furthermore, sub-samples were taken and analysed according to standardised methods to characterise the physical and thermal properties. Densities were determined from laboratory analysis while thermal properties (thermal conductivity and volumetric heat capacity) were measured by using a TP01 sensor (Hukseflux, The Netherlands).

The laboratory-scale experiments replicated water temperature fluctuations in sewer pipes during dry weather periods. These fluctuations show marked daily, cyclical patterns which can be characterised by a phase and an amplitude (Regueiro-Picallo et al. 2023). Experiments were carried out by establishing daily temperature patterns using the water bath circulator and flow conditions by setting top–bottom rotational velocities. In addition, the flume was filled with sediment layers, establishing three sediment depth conditions (⁠⁠: 60, 110, and 160 mm), and a layer of tap water was added on top. The objective was to measure the temperature time series in the system (water and sediment layers) and estimate the sediment depth by analysing the heat-transfer process.

An optimal ratio between top and bottom rotational velocities was used to establish the flow conditions while minimising the effect of lateral flow circulations (Cecchetto 2017). This ratio is influenced by the flume geometry (radius, width, and wall roughness), the water depth and viscosity, and the sediment roughness. Flume dimensions, water viscosity, and sediment roughness were assumed to be constant, while the water depth depended on the height of the water surface (constant) and the sediment depth. Therefore, a calibration of the optimal ratio was performed for each sediment depth condition.

Three flow velocities, expressed as a function of the rotational velocity and the mean radius of the flume (R = 1 m), ⁠, were tested in the annular flume. The bottom velocity, (m/s), was used as the characteristic velocity of the annular flume to set flow conditions of 0.1, 0.2, and 0.4 m/s (Booij 1994). Subsequently, top velocities, (m/s) were determined and set by applying the optimal ratio. In summary, 18 experiments were performed, combining three sediment depths (⁠⁠: 60, 110, and 160 mm), two temperature patterns (⁠⁠: 3.0 and 5.5 °C) and three flow conditions (⁠⁠: 0.1, 0.2, and 0.4 m/s).

In summary, two models differentiated by the top boundary condition (Dirichlet and Cauchy) were defined to evaluate the influence of flow velocity on heat-transfer processes in the water-sediment boundary and, consequently, on the sediment depth estimations. For this purpose, a numerical analysis was performed to compare both models by simulating the temperatures in the sediment layer under multiple flow velocity and sediment depth conditions. Moreover, experimental temperature measurements at the bottom of the sediment layer were compared with water temperatures to calculate harmonic characteristics and, subsequently, to estimate sediment depths in the experiments by applying the simplified surrogate model. The estimations were compared with reference depth measurements to evaluate the uncertainty of ignoring flow conditions in the surrogate model.

The physical and thermal properties of the sediments, i.e., fine and coarse sands, and gravels, were determined from laboratory analysis and sensor-based measurements, considering a composite sub-sample to analyse the thermal properties of coarse sands and gravels (Table 1). The effective thermal properties were calculated to describe the heat-transfer characteristics of a multi-layer system since the sediment bed consisted of various materials. The series model with horizontal layer distribution was used to calculate the effective thermal conductivity, ⁠, where and are the subscripts relative to the fine sand layer and to the composite layer of coarse sand and gravel, respectively (Radhakrishnan et al. 2010). Moreover, the volumetric heat capacity of a two-layer system was determined by the formula (Marín et al. 1996). As a result, a value of effective thermal conductivity and volumetric heat capacity was obtained for each sediment depth condition. Average effective thermal properties were assumed for the later heat-transfer analysis and sediment depth estimation, as the maximum relative deviations were less than 1% for both thermal conductivity and volumetric heat capacity. Measured sediment properties were similar to reference values for submerged and saturated sands (Abu-Hamdeh 2003; Nikiforova et al. 2013), and to sewer sediments with low organic matter content (Regueiro-Picallo et al. 2024a).

The water temperature fluctuations in the sediment layer were also numerically simulated with the two 1D heat diffusion models, i.e., with Dirichlet- and Cauchy-type top boundary conditions. In addition to the water temperature time series, the sediment thermal properties (⁠ and ⁠), the convective heat-transfer coefficient at the bottom boundary (h), the temperature outside the model ⁠, and the initial temperature of the sediment bottom were considered to simulate the temperatures at the bottom of the sediment layer. Moreover, the diffusion model with the Cauchy-type top boundary condition also considered the hydraulic conditions (⁠ and ⁠). Most of the above variables were measured (temperature, flow velocity, and flume geometry) or characterised by laboratory analysis (sediment thermal properties). The convective heat-transfer coefficient at the bottom boundary (h) was calibrated by fitting the experimental data and the simulated sediment temperatures using the heat diffusion models for large flow conditions, i.e., = 0.4 m/s, as large velocities barely influence the heat-transfer process at the water–sediment interface. The result of the calibration process was = 2.6 W/m²/°C. In addition, the mean room temperature was considered as the temperature outside the domain ⁠, which represents the soil temperature under actual conditions. Finally, the initial temperature of the sediment bottom was established by performing a 24-h warmup period of the model.

The Nash–Sutcliffe model efficiency coefficient (NSE) was used to compare the performance of the numerical models to simulate the sediment temperatures, taking the temperature measurements at the sediment bottom as reference observations (Figure 5). The NSE values ranged from 0.83 to 0.99 for the diffusion model with the Dirichlet-type top boundary condition, while for the model with the Cauchy-type top boundary condition, the NSE values ranged from 0.82 to 0.99. A strong fit between experimental and numerical temperatures was obtained (median NSE values were 0.98), which means that both models accurately reproduced the heat-transfer process in the sediment layer. No major differences between the NSE values were found and, consequently, both models can yield similar sediment depth estimations. The following section presents a numerical comparison between the 1D heat diffusion models to analyse the influence of the flow conditions on the top boundary of the sediment layer.

A fluid flowing over a surface generates a thermal boundary layer, which induces a convection process. In the present study, the wastewater flowing over the sediment bed induced a forced convection between both layers. The heat-transfer process at the sediment–water interface can be characterised by the convective heat-transfer coefficient, (Equation (7)), which is related to the Nusselt number, ⁠. High values indicate small thicknesses of the thermal boundary layer and, consequently, equal temperatures in the water layer and water-sediment contour. is expressed as a function of Reynolds and Prandtl numbers (Equation (8)), which relate inertial (hydraulic), thermal, and viscosity variables. Assuming that the water thermal properties and viscosity were constant in the experimental campaign, the convective heat-transfer coefficient between the water and sediment layers was only sensitive to the Reynolds number. Furthermore, can be assumed to be more sensitive to the flow velocity than to the characteristic length since the proportion to the latter is ⁠.

Temperatures at the bottom of the sediment layer were simulated with 1D heat-transfer models including Dirichlet- and Cauchy-type top boundary conditions to study the influence of flow conditions on heat-transfer processes and, consequently, on the sediment depth estimation. The simulated sediment temperatures were calculated using the following simplified input variables: (i) the mean water temperature time series of the experiments with a daily gradient of 5.5 °C; (ii) the effective thermal properties of the sediments; (iii) the heat loss condition at the bottom boundary, defined by = 2.6 W/m²/°C; and (iv) a range of sediment depths between 10 and 190 mm. Moreover, the flume length (⁠ = 6.28 m) was selected as the characteristic length, and Reynolds numbers ranging from 5 × 10⁵ to 5 × 10⁶, which were equivalent to bottom velocities of = [0.1, 0.8] m/s, were also considered for the simulations with the model that included the Cauchy-type top boundary condition.

The uncertainty of the sediment depth estimations for small temperature gradients (⁠ = 3.0 °C) was greater than for large gradients (⁠ = 5.5 °C). Consequently, the larger the daily temperature gradient the more precise estimations could be obtained. Moreover, the estimation uncertainty was not affected by the sediment depth, i.e., the precision was similar for the range of sediment depths tested (60, 110, and 160 mm). However, the precision will decrease for larger depths because the attenuation and time-shift of the temperature time series at the sediment bottom will be very large, particularly for organic sediments with low thermal diffusivities (Regueiro-Picallo et al. 2023). Furthermore, the sediment depth estimations generally decreased as the flow increased because of the convective heat-transfer process in the water-sediment interface (Figure 6). However, the deviations between the depth estimations considering the flow conditions did not exceed 10 mm, showing that the flow rate and, subsequently, the convective term had minimal impact on sediment depth estimations.

The performance of temperature-based systems for estimating sediment depths in sewers was evaluated considering different flow conditions and temperature daily patterns. Low flow velocities, = 0.1, 0.2, and 0.4 m/s, which are likely to sediment accumulation (Lange & Wichern 2013; Regueiro-Picallo et al. 2017), were tested. The bottom plate velocity was taken as a reference to establish the flow conditions as it is the characteristic velocity in annular flumes (Booij 1994). The results showed that the convective heat-transfer processes at the water–sediment interface due to the flow velocity could be neglected because they barely influenced the sediment depth estimation. Minimal deviations of the sediment depth estimations were obtained using the surrogate model, which excludes the convective heat-transfer coefficient in the top boundary ⁠. -values were very large for flow velocities higher than 0.1 m/s and therefore instantaneous heat transfer between the water and sediment layers can be assumed. Consequently, temperature-based systems can be used to monitor sediment accumulation in sewer systems without requiring the measurement of hydraulic variables, e.g., flow rates or water depths. Nevertheless, other variables, such as the sediment thermal properties and the convective heat-transfer coefficient at the sediment bottom, must also be considered to estimate sediment depths accurately.

Temperature fluctuations in urban drainage systems can be measured using the MONitoring Temperatures in SEdiments (MONTSE) device (Regueiro-Picallo et al. 2024a). MONTSE is comparable to distributed temperature sensing (DTS) devices, which are commonly deployed to detect illicit connections as well as infiltration and inflow into sewers (e.g., Vosse et al. 2013; Panasiuk et al. 2019). The vertical resolution of sensors of MONTSE permits the monitoring of temperature fluctuations by comparing measurements from sensors exposed to air, submerged in water, and buried in sediments. In addition, MONTSE includes a Dual-Probe Heat-Pulse (DPHP) module for in situ determination of sediment thermal properties, which consists of a heater cartridge that induces a heat pulse while a temperature sensor measures the response across the sediment bed (e.g., Ravazzani 2017; He et al. 2018). DPHP measurements are local, and, unlike sands and gravels, the thermal properties of organic sediments can oscillate both spatially and temporally due to biological processes, similar to the physicochemical properties of sewer sediments (Ristenpart 1995; Regueiro-Picallo et al. 2020). Small uncertainties can be assumed when using local measurements of thermal properties to estimate sediment depth (Regueiro-Picallo et al. 2024a). Furthermore, the convective heat transfer coefficient at the sediment bottom depends on the composition and thickness of the material in contact with the sediments (e.g., pipe), and can be assumed to be constant. The coefficient can be estimated with prior knowledge of the sewer system, although it is also possible to calibrate from reference sediment depth measurements, as for the experimental campaign.

The sediment depth estimations were computed using a simplified surrogate model, which was mainly based on the relationship with the harmonic characteristics of the water and sediment temperature time series as well as the sediment thermal properties and the convective heat-transfer coefficient at the sediment–pipe–soil boundary. A decomposition of the temperature fluctuations was performed to calculate the harmonic features (FFT algorithm). The annular flume was operated for a minimum period of 24 h prior to the start of each experiment with the aim of establishing the initial temperature conditions in the sediment layer and, consequently, minimise the oscillation of the harmonic features. Only the fundamental frequency (or first harmonic) was later considered as input to the surrogated model, although, as the time series shows two peaks during the day, the second harmonic could be added to the model to improve the depth estimations.

The 2D heat diffusion model of the sediment layer can be applied as an alternative method for estimating sediment depths, for example, by identifying the best fit between the simulated temperatures and the sensor measurements on the flume walls (Figure 1(b)). In the event of large sediment depths and significant convective heat transfer through the sediment–pipe–soil boundary, temperature fluctuations at the bottom of the sediment layer will be significantly attenuated in relation to water temperatures, leading to highly uncertain depth estimations. Under these conditions, the vertical sensor distribution on the wall will enable the identification of sensors buried in the sediment layer, as well as the estimation of the position of the sediment–water interface and, consequently, the sediment depth (e.g., Sebok et al. 2017). Only measurements from sensors located in the water layer and at the bottom of the sediment layer (centre of the flume base) were considered in this study because the temperature fluctuations at the bottom of the sediment layer were not fully attenuated for the worst conditions, = 160 mm, resulting in accurate depth estimations (±7 mm). The sediment depth estimation range can be approached using the diurnal damping depth (Luce et al. 2013), expressed as ⁠, where is the fundamental frequency (s⁻¹), or ⁠, where P is the period of the daily fluctuations (s), equal to 86,400 s. The diurnal damping depth relates time-, distance-scales and sediment thermal properties, and expresses the depth at which the amplitude of daily temperature fluctuations is of that at the surface, i.e., water-sediment boundary. A value of = 142 mm was obtained for the type of sediments that were tested in the experimental campaign. Organic sediments, such as sewer sediments, can show lower -values than sands and gravels and, consequently, lower sediment depth estimation ranges.

In concluding remarks, temperature-based systems could be low-cost and easy to scale and implement in sewer systems, leading to optimal inspection and cleaning strategies based on observations rather than periodic operations. This would reduce costs and the risk of combined sewer overflows (CSO) during rainfall events caused by sediment accumulation. Monitoring sediment build-up could also be used to develop accurate sediment transport models in sewer systems, resulting in optimal sewer system designs and the development of digital twin models. Future commercial and scientific perspectives include the installation of these systems to optimise the sediment management in sewer systems and other urban drainage infrastructures, such as sediment collectors.

Heat-transfer processes in sewers were investigated while considering the presence of sediment accumulation. The sediment layer provides a dampening effect on the temperature fluctuations of the wastewater, which follow a cyclical pattern under dry weather conditions. Temperature damping can be expressed by means of harmonic characteristics and is mainly affected by the sediment depth, as well as the sediment thermal properties, the heat loss at the boundaries and the flow velocity.

An experimental campaign was performed in an annular flume by reproducing heat-transfer processes in combined sewer systems under DWF conditions. This allows for the evaluation of the influence of hydraulic conditions and temperature patterns when estimating sediment depth using temperature-based systems. A numerical analysis of heat transfer models was carried out considering the influence of flow-forced convection at the water-sediment interface. Large values of the convective heat-transfer coefficient at the water–sediment interface were obtained, indicating that the temperature boundary layer above the interface was very small and, consequently, heat transfer occurred instantaneously for velocities greater than 0.1 m/s. Therefore, the hydraulic conditions in sewers hardly influenced the heat-transfer processes of sediment bed deposits. This allowed the use of simplified surrogate models based on the comparison of water and sediment-bed temperature measurements to estimate sediment depths, i.e., ignoring hydraulic variables.

Sediment depth estimations showed a low uncertainty and a high precision compared to the reference depth measurements when there was a large daily amplitude. In addition, deviations of the depth estimates were less than 10 mm considering the different flow velocity conditions established in the flume. These results confirmed that systems based on temperature measurements are a viable solution for sediment monitoring in combined sewer pipes without measuring hydraulic variables. Moreover, sediment thermal properties and convective heat transfer at the sediment–pipe–soil boundary must be determined. Effective thermal properties of the sediment were characterised in the experimental campaign using sub-samples, although heat-pulse methods can also be applied for in situ measurements. Knowing the sediment thermal properties, the depth estimation range can be also defined to establish an optimal vertical distribution of temperature sensors. In contrast, the convective heat-transfer coefficient at the sediment–pipe–soil boundary, which can be assumed to be constant, could be established using information of the sewer system. In summary, understanding heat-transfer processes in sewers, coupled with the measurement of thermal dynamics, will effectively monitor sediment build-up.

The authors are indebted to the User Group of the project CoUDlabs_TA_USFD_02_ANNULAR_Regueiro. Time series analysis of sewer temperatures in an annular flume to estimate sediment accumulation for their support in the experimental campaign. The User Group was composed of Manuel Regueiro-Picallo, Jeroen Langeveld, María Viklander, Mehwish Taneez, Petra van Daal-Rombouts and Jessica Thorsell.

The experimental campaign was funded by the EU under the Horizon 2020 INFRAIA program (Co-UDlabs project. GA No. 101008626). The work developed by Manuel Regueiro-Picallo was funded within the postdoctoral fellowship programme from the Xunta de Galicia (Consellería de Cultura, Educación e Universidade, ED481B-2021-082).

The data collected in the laboratory-scale experimental campaign is openly accessible in ZENODO and available in these in-text data citation reference: Regueiro-Picallo et al. (2024b), with a license Creative Commons Attribution 4.0 International (CC BY-NC 4.0). https://doi.org/10.5281/zenodo.10821837.

There are no conflicts of interest to declare.