# Calculation of Dry Weather Flows in Pumping Stations to Identify Inflow and Infiltration in Urban Drainage Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Inventory and Configuration Phase

_{p}pumps, a total of${\mathrm{N}}_{\mathrm{SC}}{=2}^{{\mathrm{N}}_{\mathrm{p}}}$ potential pump status combinations (SC) can be defined. These are all the theoretical combinations of the different pumps being idle or active. The total number of transitions from one status combination to another, further called pump status combination changes (SCC), equals ${\mathrm{N}}_{\mathrm{SCC}}{=\mathrm{N}}_{\mathrm{SC}}^{2}$. These SCs and SCCs can be grouped in operational regimes and regime changes: e.g., all SCs that contain a single active pump can be grouped into a regime “single pump use”; all SCs that contain two active pumps can be grouped into a regime “double pump use”, etc. Possible regime changes are then, e.g., the switch from “single pump use” to “double pump use” or vice versa. Appendix A gives an elaborated example of the operational regimes and regime changes for a typical “2 + 1” pump configuration (2 active pumps + 1 spare).

#### 2.2. Data Preprocessing Phase

#### 2.3. Flow Calculation Phase (Cycle Based)

^{3});

_{in}(t): the flow entering the pumping station (m

^{3}/s);

_{out}(t): the flow pumped out from the pumping station (m

^{3}/s).

_{DWF}: the control volume between the dry weather switch-on and switch-off level (m

^{3}) (see Figure 2);

^{3}/s);

^{3}/s);

^{3}/s);

_{fill}: the duration of the filling cycle (s);

_{empt}: the duration of the emptying cycle (s).

_{DWF}is assumed to be constant. However, in reality, settings of switch levels can change over time, meaning that during the processing of longer data sets, V

_{DWF}can vary throughout the data set. This has to be handled during the data preprocessing phase, resulting in a list of V

_{DWF}values per cycle.

_{DWF}for the shortened cycles must be calculated by using the interpolated level at the moment of forced switch-on.

#### 2.4. Linearising the Cycle-Averaged Flows

_{in,2avg}for cycle 2 is transformed into a time-dependent flow varying linearly between Q

_{in,2,1}at time t

_{2,1}, the start of the cycle, and Q

_{in,2,2}at time t

_{2,2}, the end of the cycle. The gradient of this linear variation during the cycle is found by averaging the gradients of the lines that connect the average flows of the successive filling cycles at their respective midpoints. After this linearisation of the filling flows, the flows during the emptying cycles are calculated as linearly varying flows by connecting the end and start values of the linearised flows of the surrounding filling cycles.

#### 2.5. Correction for Phase-Out Time of Pump Flows

_{ph}). In some cases, this can cause the water level in the wet well to continue dropping down after the pump has switched off. A similar phenomenon occurs at the switch-on of pumps: because the pump has a delay time to reach its full capacity, the water level can initially continue to rise above the switch level. However, this delayed start does not affect cycle-based calculations and therefore will not be considered further here.

_{ph}is not known, it must be derived from the observed time at which the level reaches the switch-off level again after the initial dropdown. This is further indicated as the zero-level recovery time, or Δt

_{0}(see Figure 5). In many cases, it will not be possible to derive Δt

_{0}from the available level records. Either the time during which the level drops down below the switch-off level can be shorter than the time interval of the available level data series, or the combination of the incoming flow and pump flow can be such that the water level does not initially drop down at all. In such cases, Δt

_{ph}is set to 0.

_{1}and zero flow at the (still unknown) time t

_{ph}(=t

_{1}+ Δt

_{ph}) and (ii) a linear variation of the incoming flow between Q

_{in,1}, at switch-off time t

_{1}, and Q

_{in,2}, at switch-on time t

_{2}, with the cycle duration ∆t

_{c}= t

_{2}− t

_{1}, Δt

_{0}can be calculated as:

_{0}≤ ∆t

_{ph}(Equation (4)) and ∆t

_{0}≥ ∆t

_{ph}(Equation (5)).

_{ph}from the observed ∆t

_{0}, which yields Equation (6) for ∆t

_{0}≤ ∆t

_{ph}:

_{0}≥ ∆t

_{ph}:

_{ph}can now be consolidated into a single median value per pump $\tilde{\Delta {\mathrm{t}}_{\mathrm{ph},\mathrm{p}}}$(p = 1…N

_{P}). The limitation of this procedure is the assumption that no more than 1 pump is active during dry weather emptying cycles.

#### 2.6. Further Iterative Calculation of Pump Flows and Incoming Flows

## 3. Results

#### 3.1. Results of the Flow Calculation Phase

_{DWF}(see further, Section 3.2).

#### 3.2. Estimation of the Uncertainty of the Results

_{DWF}, and the relative error on the calculated flows δQ equals the sum of the relative errors of the control volume and the cycle duration (δV

_{DWF}+ δ (Δt

_{c})). From these two parameters, the control volume is the one with the highest uncertainty. Even if detailed information to calculate this volume is available, it remains very difficult to account for space taken up by objects such as pump bodies, lifting chains, rising mains and valves, ladders, and benchings. Therefore relative errors of >10% on V

_{DWF}are not unusual. If the control volume extends well into the incoming pipes, this error may be even higher, as explained in Appendix D.

_{DWF}.

_{DWF}and hence of the calculated flows can be reduced if independent flow measurements are available. Because the incoming flows and the pump flows are linked by the continuity equation, it takes only one reference flow, either the incoming flow or the pump flows, to correct both calculations.

_{vol}can be determined from the comparison between reference and calculated flows, e.g., based on daily volumes or averages. Because of the linear relationship, as expressed in Equations (2) and (3), the calculated flows simply need to be multiplied by this correction factor. This is illustrated in Figure 9, where reference pump flows are available from electromagnetic flow meters at the rising mains. The remaining deviations between the calculated and measured pump flows per emptying cycle after correction are due to (i) the differences between the fixed time interval of the measurements (1 min) and the instantaneous registration of the switch times (resolution 1 sec) and (ii) the variability of the pumped flows over the duration of the cycle as a result of the pumps being variable-frequency-driven.

_{DWF}varies over time due to varying switch-on/-off levels or forced switch-on, multiple correction factors have to be determined for different periods. Moreover, when the flow dependency of the in-pipe control volume would have a significant impact on the calculated flows, a simple linear correction may not be sufficient to bring the calculated flows in accordance with reference flows. This is explained in more detail in Appendix D. More investigation is needed to assess what accuracy can be obtained in such cases.

#### 3.3. Identifying the Presence of Inflow and Infiltration

## 4. Discussion

- Pumping stations that have at least one pump permanently active during periods of minimum dry weather flow. This means that in such cases, there are no filling cycles without active pumps, for which the incoming flow is only a function of the control volume and the cycle duration.
- Pumping stations with only one set of switch levels that make it harder to distinguish between dry weather and non-dry weather cycles, especially for periods of light rain.
- Pumping stations with extremely low switch frequencies, where the low number of cycles per day does not allow the reliable linearisation of the calculated average cycle flows.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{P}= 3;

_{SC}= 8;

_{SCC}= 64.

- “zero” (no pumps working);
- “single” (1 pump working);
- “double” (2 pumps working in parallel).

Status Comb n° | Pump1 | Pump2 | Pump3 | Regime |
---|---|---|---|---|

1 | 0 | 0 | 0 | Zero |

2 | 0 | 0 | 1 | Single |

3 | 0 | 1 | 0 | Single |

4 | 0 | 1 | 1 | Double |

5 | 1 | 0 | 0 | Single |

6 | 1 | 0 | 1 | Double |

7 | 1 | 1 | 0 | Double |

8 | 1 | 1 | 1 | - |

- “single on” (S1) (transition from “zero” to “single” regime);
- “single off” (S0) (transition from “single” to “zero” regime);
- “double on” (D1) (transition from “single” to “double” regime);
- “double off” (D0) (transition from “double” to “single” regime);
- “single change” (Sx) (transition between “single” regimes with different status combinations);
- “double change” (Dx) (transition between “double” regimes with different status combinations).

To Stat Comb | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|---|

From Stat Comb | |||||||||

1 | - | S1 | S1 | - | S1 | - | - | - | |

2 | S0 | - | Sx | D1 | Sx | D1 | - | - | |

3 | S0 | Sx | - | D1 | Sx | - | D1 | - | |

4 | - | D0 | D0 | - | - | Dx | Dx | - | |

5 | S0 | Sx | Sx | - | - | D1 | D1 | - | |

6 | - | D0 | - | Dx | D0 | - | Dx | ||

7 | - | - | D0 | Dx | D0 | Dx | - | - | |

8 | - | - | - | - | - | - | - | - |

## Appendix B

_{sw}situated between h

_{sw,forw}(i.e., the switch level calculated by forward extrapolation) and h

_{sw,backw}(i.e., the switch level calculated by backward extrapolation). For every such value, one can calculate the gradients of the level curves between h

_{prec}and h

_{sw}, on one hand (S

_{prec}), and between h

_{sw}and h

_{succ}, on the other hand (S

_{succ}). In this, h

_{prec}represents the last level record before the switch and h

_{succ}is the first level record after the switch. These gradients can then be compared with the gradients of the level curves that are used for the forward and backward extrapolation (S

_{forw}and S

_{backw}). The optimal value of h

_{sw}can be defined as the value that yields the minimum value of δ

_{S}(the average relative difference with the extrapolation gradients) (Equation (A1)).

## Appendix C

Pumping Station | Drainage Area | Nr. Pumps Configuration | Nominal Pump Capacities (Single Use) | Nr. PE Connected | Impervious Area Connected |
---|---|---|---|---|---|

Wauberg | Peer | 3 pumps (2 + 1) | P1 and P2: 18 L/s P3: 27 L/s | 982 | 11 ha |

Wijgmaalsesteenweg | Leuven | 3 pumps (2 + 1) | 69 L/s | 4857 | 48 ha |

Vuntlaan | Leuven | 3 pumps (2 + 1) | 198 L/s | 22,484 | 183 ha |

Zuidstraat | Leuven | 2 pumps (1 + 1) | 31 L/s | 1254 | 13 ha |

#### Appendix C.1. Inventory and Configuration Phase

- Pump configuration and operational regimes/regime changes including the history of switch-on/-off levels;
- Indication of which regimes are considered dry weather regimes;
- Storage geometry (pump well and incoming pipes);
- Assumed nominal pump capacities per pump and per regime;
- (History of) conversion parameters between locally measured levels and national reference levels (TAW);
- Indication of potential cycle duration limits.

#### Appendix C.2. Data Preprocessing Phase

^{3}instead of 3.4 m

^{3}).

## Appendix D

**Figure A6.**(

**a**) Static storage-based delineation (left); (

**b**,

**c**) backwater curve-based delineation (right top and right bottom). The dark blue volumes are considered dead storage; the light blue ones are active storage.

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**Figure 6.**Example of individual cycles’ flows: (

**a**) pumped flows per cycle per pump (top); (

**b**) average incoming flows for filling and emptying cycles and linearised flows for all cycles (bottom) (PS Zuidstraat).

**Figure 7.**Example of calculated pump flows with pumps of different nominal capacities: (

**a**) pumped flows per cycle per pump (top); (

**b**) average incoming flows for filling and emptying cycles and linearised flows for all cycles (bottom) (PS Wauberg).

**Figure 8.**Effect of missing pump loggings on the calculated cycle flows: (

**a**) pumped flows per cycle per pump (top); (

**b**) average incoming flows for filling and emptying cycles and linearised flows for all cycles (bottom) (PS Wijgmaalsesteenweg).

**Figure 9.**Calculated vs. measured pump flows before (

**a**) and after (

**b**) control volume correction (PS Vuntlaan).

**Figure 10.**Overview of daily incoming volumes: (

**a**) only dry weather days (top); (

**b**) all days including rainfall for the selected period (bottom) (PS Zuidstraat).

**Figure 11.**Calculated incoming flows at the start and end of a dry period with high initial infiltration (PS Zuidstraat).

**Figure 12.**Example of the impact of a construction site’s pumped groundwater drainage. The inflow period extends from 22 June 2022 to 22 July 2022. (PS Wauberg).

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**MDPI and ACS Style**

Van Assel, J.; Kroll, S.; Delgado, R.
Calculation of Dry Weather Flows in Pumping Stations to Identify Inflow and Infiltration in Urban Drainage Systems. *Water* **2023**, *15*, 864.
https://doi.org/10.3390/w15050864

**AMA Style**

Van Assel J, Kroll S, Delgado R.
Calculation of Dry Weather Flows in Pumping Stations to Identify Inflow and Infiltration in Urban Drainage Systems. *Water*. 2023; 15(5):864.
https://doi.org/10.3390/w15050864

**Chicago/Turabian Style**

Van Assel, Johan, Stefan Kroll, and Rosalia Delgado.
2023. "Calculation of Dry Weather Flows in Pumping Stations to Identify Inflow and Infiltration in Urban Drainage Systems" *Water* 15, no. 5: 864.
https://doi.org/10.3390/w15050864