# Sediment Transport in Sewage Pressure Pipes, Part I: Continuous Determination of Settling and Erosion Characteristics by In-Situ TSS Monitoring Inside a Pressure Pipe in Northern Germany

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## Abstract

**:**

## 1. Introduction

- Determine applicability and quality of an in-situ TSS-online measurement system inside a pressure pipe
- Characterize raw sewage erosion and sedimentation behavior under dry weather inflow continuously by TSS-online monitoring
- Identify mechanisms changing the transport behavior and characterize modified erosion and sedimentation

#### Literature Review

## 2. Materials and Methods

#### 2.1. Study Side

#### 2.2. In-Situ TSS Monitoring

^{−1}), pressure in DL2 directly after the pump (bar), flow in DL2 (Q

_{pipe}) (L/s).

#### 2.3. Sample-Specific Sensor Calibration

#### 2.4. Fit Calibration Function and Analysis of Sensor Data

- Fit calibration function (TSS to TSS) with errors in y and x direction using the total least-squares regression;
- Calculate function parameters uncertainties by Monte-Carlo simulation for 95% confidence level;
- Transform original sensor data TSS
_{sens}by the calibration function into calibrated sensor data TSS_{cal}; - Remove TSS
_{cal}values > 1.000 mg/L, based on local operators’ expertise; - Further error assessment by Walsh’s outlier test.

_{cal}(mg/L) from the original sensor data TSS

_{sens}(mg/L), see Equation (1).

_{sens}is transformed into calibrated sensor data TSS

_{cal}to obtain the estimated TSS values by Equation (1). Furthermore, the 95% confidence interval is calculated based on the function parameters uncertainties.

#### 2.5. Determination of Settling- and Erosion Data

_{0}(mg/L), a fixed value relating to the first TSS concentration in each single sedimentation event, C

_{rest}(mg/L), the final solids concentration at the end of each single setting event and the exponential decay rate α (1/s), which is the key parameter to describe the settling behavior.

_{0}settles to pipes invert, according to the decay rate α, which is received by solving the optimization problem in Equation (4). With n, the number of values in each settling sequence and TSS

_{cal}(mg/L), the measured and calibrated TSS concentration inside the pressure pipe.

_{a}(kg/(m s)) inside the pipe is calculated from the TSS concentration after pumps start (shown in Figure 3d), by Equation (5). With TSS

_{cal}

_{,i}− TSS

_{cal}

_{,i−1}(mg/L), the TSS difference between measurements, Δt (s), the time difference between measurements and A

_{s}(m

^{2}), the surface area of erosion (set to 1 m

^{2}for better comparability).

_{a}can be described as a function of the current bed shear stress, called erosion rate a (activation of sediments) (kg/(m s)), see Equation (6). With τ

_{pipe}(N/m

^{2}), the current bed shear stress, τ

_{crit}(N/m

^{2}), the critical bed shear stress where erosion starts and d (s), the erosion parameter, which describes the strength of the erosion (equal to slope of the first order polynomic function).

_{pipe}is calculated by Equation (7), based on the fluid density ρ = 1000 (kg/m

^{3}), the flow velocity v (m/s), and the friction factor λ (calculated after the Colebrook–White equation).

_{crit}depends on several parameters, as the formerly settling duration (higher τ

_{crit}values for longer settling duration) and the composition of the sewage (organic components raises τ

_{crit}due to biogenic changes). For a detailed description of τ

_{crit}see [1]. The erosion rate a is adjusted to the measured erosion rate e

_{a}by solving the optimization problem in Equation (8).

_{crit}is received.

## 3. Results and Discussion

#### 3.1. Sensor Calibration Results

^{2}value of 0.84 for TSS sensor PS Rostock-Schmarl and with a R

^{2}value of 0.85 for TSS sensor at the central wwtp Rostock. As found in literature, usual calibration functions used same functions with R

^{2}values between 0.83 and 0.92 [8] (calibration to turbidity) or, as already summarized in [15], between 0.80 and 0.95 [15] (calibration to turbidity). Reference [9] obtained a calibration function, for the same sensor used in this study, with a R

^{2}value of 0.94.

#### 3.2. Evaluation of the Erosion and Settling Approximation

_{a}are plotted versus all fitted erosion rates a(τ,w). A perfect fit is given by f(x) = x or a(τ,w) = e

_{a}. For the majority of erosion values, a(τ,w) follows the perfect fit course with deviations above and below. The fitting results are moderate. R

^{2}value of >=0.9 having 7.3% of the total approximations (n = 481 single events), 33.5% (n = 2100) were fitted with R

^{2}values of >=0.75, while R

^{2}values of >=0.5 having 54% (n = 3603). So the mathematical approximation by the erosion rate a(τ,w) is suitable to describe the real process of erosion. Because of the similar up- and downward deviation, a balance is assumed.

^{2}values of >=0.9 having 31% of the total approximations (n = 2084 single events), 58.4% (n = 3934) were fitted with R

^{2}values of >=0.75 and R

^{2}values of >=0.5 having 76% (n = 5161).

#### 3.3. Settling and Erosion Characteristics Inside the Pressure Pipe Under Dry Weather Inflow

_{inflow}and the resulting pump flow by Q

_{pipe}(right axes).

_{inflow}. Hence, there is a relationship between TSS and Q

_{inflow}. Low inflow results in low TSS values and vice versa. It results from the water usage and the hydraulic conditions in the upstream sewers. An increased solids amount reaching the PS by increased water consumption (stool, cooking, etc.). Furthermore, high water consumption raises the hydraulic performance in the upstream sewers and erodes deposits.

^{2}= 0.83). Similar to the smoother decline at the end of the erosion event, a more gradual increase is assumed for the beginning. The maximum erosion appears at ≈0.43 N/m² and so, before the maximum shear stress level of ≈0.5 N/m

^{2}is reached. A further increase of shear stress (feasible by parallel pumping of P1 and P2) would not result in further solids erosion, as the maximum erosion level is already reached and the decline remarks the emptying of the sediment layer.

#### 3.4. Comparison to Laboratory (Ex-Situ) Results

^{2}bed shear stress), is nearly equal to real world processes (duration ≈ 30 s). Thus, both methods (in-situ and ex-situ) are applicable to determine the erosion characteristics of raw sewage.

#### 3.5. Effect of Storm Water Inflow to Settling and Erosion Characteristics

_{inflow}, left axis). The TSS course (left axis) is separated into erosion (blue) and sedimentation sequences (red). The TSS concentration increases significantly up to ≈600 mg/L after the peak runoff reaches the pump sump. Figure 7b compares a dry weather inflow erosion rate (1b) with a storm water erosion rate (2b). The maximum erosion increases with the storm inflow almost by a factor of five. One reason is the storm runoff composition. Solids (sand, tire abrasion, etc.) are washed off from roads and entering the sewer. Furthermore, the increased discharge erodes pre-settled and consolidated deposits and spills a mixture of runoff solids and sewer solids to the PS.

_{0}) from ≈400 mg/L up to >600 mg/L. A better comparison of the settling processes is provided by the mean decrease, which is defined as the difference quotient in the interval [t

_{1};t

_{end}], see Equation (9).

#### 3.6. Comparison to Laboratory (Ex-Situ) Results

#### 3.7. Diurnal Variation Settling and Erosion

## 4. Conclusions

- The installed sensors are suitable for supervision of TSS fluxes inside sewage pressure pipes;
- Periodically calibration and maintenance of TSS sensors result in reliable data;
- TSS sensor data allow for a characterization of solids sedimentation and erosion behavior;
- Measured in-situ erosion and settling results are similar to ex-situ (laboratory) results;
- Settling accelerates with high inflow rates (storm water inflow, diurnal inflow peaks) and decelerates with low inflow (reduced TSS inflow in night phases);
- Erosion rate increases and decreases based on the available amount of solids, hence, with changing settling behavior;
- Solids are eroded before maximum shear stress level reached

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Visualization of the catchment area (18.9 km

^{2}) in Rostock (Germany) including a schematic view of the control and monitoring system during the study. The raw sewage inflow passes the rake and is collected inside the pump sump. Pumps P1 and P2 then conveying the raw sewage directly to the central wwtp in pressure pipe 2 (DL2). P1 and P2 are controlled over a variable-frequency drive (VFD) from a PC (connected over a serial port (SER) to the programmable logic controller (PLC)). The VFD adjusts pumps motor speed according to the control strategy [1,2,17]. All values from TSS sensors (TSS) and electromagnetic flowmeters (EMF) are stored in the PC.

**Figure 2.**TSS sensors for monitoring sediment flux in pressure pipes. (

**a**) TSS sensor in PS Rostock-Schmarl at the pressure side of the pump. (

**b**) TSS sensor in the central wwtp Rostock at the outflow side of the pressure pipe.

**Figure 3.**Data separation scheme: monitored TSS data (

**a**) is split into an erosion- (

**b**) and a sedimentation part (

**c**). Frequency data from both VFD (for P1 and P2) is used as decision criterion for data separation (if VFD1 and VFD2 = 0, then settling sequence, else erosion sequence). The separation into single erosion (

**d**) and sedimentation events (

**e**) is based on a time difference between each value. If the time difference is larger the logging interval of 5 s (see Table 1), a single event is detected and separated.

**Figure 4.**Calibration functions for calculating laboratory TSS values from in-situ measured sensor TSS values, including goodness of fit (R

^{2}) and 95% confidence interval. (

**a**) For TSS sensor in PS Rostock-Schmarl. (

**b**) For TSS sensor at the central wwtp Rostock.

**Figure 5.**Evaluation of the erosion and settling approximation. (

**a**) All measured erosion rates e

_{a}vs. all mathematical approximations by a(τ,w). (

**b**) All measured settling events inside the pipe vs. all mathematical approximations by C(t).

**Figure 6.**Monitored data in PS Rostock-Schmarl for day 328 (

**a**) including exemplary erosion and settling determination scheme (

**b**–

**e**). (

**a**) Q

_{inflow}and Q

_{pipe}(right axis) and TSS sensor data including 95% confidence levels (left axis). (

**b**) Settling event: TSS values (TSS

_{cal}) after pumps stop in the night. (

**c**) Erosion event: TSS values (TSS

_{cal}) after pumps start at night. (

**d**) Settling event determination: TSS values (TSS

_{cal}) and approximated settling rate C(t) including fit results. (

**e**) Erosion event determination: erosion rate e

_{a}and approximated erosion rate a(τ,w) including fit results.

**Figure 7.**Effect of storm water inflow to erosion and sedimentation. (

**a**) Q

_{inflow}and TSS data (both on left axis) during rainfall event from 06:00 p.m. to 08:00 p.m. with a peak of 4.9 mm/h (right axis). (

**b**) Erosion rate a(τ,w) during storm water inflow (2b) compared to dry weather inflow (1b). (

**c**) Settling rate C(t) during storm water inflow (2c) compared to dry weather inflow (1c) including mean decrease ∆C/∆t. The German Weather Service (DWD) provides the precipitation data.

**Figure 8.**Diurnal variation of the mean decrease ∆C/∆t (boxplots) including total mean decrease over 4250 single settling events (red line) and the average Q

_{inflow}for dry weather conditions (black line).

**Figure 9.**Diurnal variation of the max erosion (boxplots) including total average erosion over 3451 single erosion events (red line) and the average Q

_{inflow}for dry weather conditions (black line).

Sensor | Controller | Parameter | Measuring Range | Installed and Measured Duration | Interval | Service | Num. of Calibration Processes | Wiper Self-Cleaning Interval |
---|---|---|---|---|---|---|---|---|

Hach Lange Solitax inline Sc | Hach Sc 200 & Sc 1000 | Turbidity, TSS | 0.001–4000 FNU, 0.00–150.000 mg/L | 343 days installed; 292 days measured | 5 s | 1 per month | 5 processes with 73 samples | 15 min |

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**MDPI and ACS Style**

Rinas, M.; Tränckner, J.; Koegst, T. Sediment Transport in Sewage Pressure Pipes, Part I: Continuous Determination of Settling and Erosion Characteristics by In-Situ TSS Monitoring Inside a Pressure Pipe in Northern Germany. *Water* **2019**, *11*, 2125.
https://doi.org/10.3390/w11102125

**AMA Style**

Rinas M, Tränckner J, Koegst T. Sediment Transport in Sewage Pressure Pipes, Part I: Continuous Determination of Settling and Erosion Characteristics by In-Situ TSS Monitoring Inside a Pressure Pipe in Northern Germany. *Water*. 2019; 11(10):2125.
https://doi.org/10.3390/w11102125

**Chicago/Turabian Style**

Rinas, Martin, Jens Tränckner, and Thilo Koegst. 2019. "Sediment Transport in Sewage Pressure Pipes, Part I: Continuous Determination of Settling and Erosion Characteristics by In-Situ TSS Monitoring Inside a Pressure Pipe in Northern Germany" *Water* 11, no. 10: 2125.
https://doi.org/10.3390/w11102125