# Chlorine Concentration Modelling and Supervision in Water Distribution Systems

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{b}is a constant that contains the different parameters and physicochemical phenomena that may affect chlorine decay, such as natural organic matter, inorganic compounds, or temperature [6]. More sophisticated models have also been studied, including second-order models [11].

## 2. Materials and Methods

#### 2.1. Case Study Network

_{1}and T

_{2}) equipped with sensors for chlorine concentration (input of T

_{1}(Cl

_{1}) and output of T

_{2}(Cl

_{2})), flowmeters (outflows from the tanks, Q

_{1}and Q

_{2}), and water level (H

_{1}and H

_{2}). Water flows from T

_{1}to T

_{2}through a 6859 m main. T

_{2}is a boosting station with known sodium hypochlorite (Apliclor Water Solutions S.L., Sant Martí Sesgueioles, Spain) addition. The geometry of the tanks (volume) and pipes (length and diameter) are known. Water from T

_{2}is distributed to the rest of the network (through Q

_{2}) of the DMA.

_{2}in Figure 2) and the two sampling points are highlighted (S

_{1}and S

_{2}).

#### 2.2. On-Line Calibration

_{2}.

_{2}) at the outflow of T

_{2}depends on the input chlorine concentration (Cl

_{1}) and the residence time in the system (t). The solution of Equation (1) is as follows:

_{b}is the decay constant and α is considered as 1.

_{b}, which was calibrated on-line using the measurements available so that it was adapted throughout the year to the different water characteristics and environmental conditions. Estimations were performed on a weekly basis, since some information was only available at this frequency (chlorine dosing in T

_{2}).

_{1}was calculated from the hydraulic information available using (3). The weekly mean residence time at tank T

_{1}and the pipe was calculated using the flowmeter data (Q

_{1}) and the volume of this subsystem.

_{1}, the level data of the tank (H

_{1}) and the geometric information was used. The residence time in T

_{2}was calculated using the mean values of the volume obtained from the level data (H

_{2}) and the mean values of the tank effluent (Q

_{2}), as shown in (4):

_{b}constant was calculated which explained the chlorine concentration ${\overline{Cl}}_{2}$ at the outflow of T

_{2}given the residence time calculated using (6)

_{b}calibration is shown in the Supplementary Material (Section S2).

#### 2.3. Chlorine Decay Calibration and Validation

_{1}and 11 samples in S

_{2}. Thus, the first 21 samples in S

_{1}were used for the training and the remaining ones for the validation. The algorithm used for this calibration is shown in the Supplementary Material (Section S3).

#### 2.4. Parametrised Chlorine Decay Model

_{b}obtained from the on-line calibration using the least square error fitting method implemented in the “Solver” function in Excel.

_{power}, a, and A are constants, E

_{a}is the activation energy (Jmol

^{−1}), R is the universal gas constant, and T is the temperature. Finally, the parametrized chlorine decay model was compared with that obtained in the on-line calibration to assess its coherence throughout the year.

## 3. Results and Discussion

#### 3.1. On-Line Calibration

_{b}obtained are presented in Figure 4. In the upper graphic, the weekly evolution between February 2017 and April 2018, can be observed. A different icon was used for the data of each trimester to clearly identify the season of the year. In the lower graphic obtained, K

_{b}are grouped by month to observe how this parameter evolves throughout the year (some months include estimations of both years). It seems clear that there may be a seasonal variation related to temperature.

#### 3.2. Chlorine Decay Validation

_{2}due to the rechlorination and mixing effect. The dataset used in this validation was not used for the estimation. The dataset for calibration consisted of the mean values corresponding to the stationary state. Figure 5 shows the chlorine concentration data and the model prediction. It can be observed how this high-frequency dynamic is adjusted with the model obtained with the mean values. For this prediction, K

_{b}evolves weekly.

_{b}, estimated by on-line calibration, with the distribution K

_{b}

^{*}was obtained by adjusting the concentration in the training set of chlorine sampling. This relation was applied to the entire period and the predicted concentration was compared with the measurements for the validation set of samples. A total of 40 days were simulated. The decay constant for both the bulk and wall were fitted using the first 21 samples of the chlorine concentration in S1. These are the first samples of upper graphic in Figure 6.

_{b}obtained in the transport system was divided by 2, as if the calibrated effect was distributed in the two phenomena (K

^{*}

_{b,bulk}= K

^{*}

_{b,wall}= K

_{b}/2). The results obtained are compared with the available experimental data in Figure 6. The mean absolute percentage error was 16% for S

_{1}(including calibration and validation samples) while it was 17% using only validation samples. Therefore, not significantly different deviations were obtained for the calibration and the validation steps. Graphically, the fit may seem poor; however, the concentration is lower in S

_{2}than in S

_{1}both in prediction and measurements, and the mean values in both sampling points are coherent between the prediction and measurements. One aspect that may justify part of the mismatching is that the exact hour of the day of the manual measurements was not available and, therefore, each experimental data may not be in its exact position. This difficulty could be overcome with on-line chlorine sensors instead of manual analysis. Figure 7 presents the measured chlorine concentration at the source (T

_{2}) and the chlorine prediction in the two sampling points (S

_{1}and S

_{2}). The chlorine concentration decreases with the residence time, since the concentration in S

_{2}is lower than in S

_{1}, and both are lower than in T

_{2}.

_{b}obtained with the on-line calibration were used to calibrate the parameters of the two equations, an Arrhenius model (8) and a power model (9), to predict the temperature effect on the decay constant. The following Equations (10) and (11) show the results obtained.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Up: Mean K

_{b}calculated weekly indicating the season of the year (by trimester). Down: Data of mean K

_{b}grouped by month.

**Figure 5.**Chlorine decay model validation at the output of T

_{2}. Up: data from January 2017. Down: data from March 2017. Due to high frequency of sampling measurement, data appears like a thick line.

**Figure 6.**Simulation results for the two sampling points (

**S**and

_{1}**S**) compared with experimental samplings.

_{2}**Figure 7.**Measured chlorine concentration at the source (T

_{2}) and prediction at the two sampling points (S

_{1}and S

_{2}).

**Figure 8.**Distribution of network nodes with low concentration (<0.4 ppm, green), acceptable concentration (0.4 ppm > chlorine < 1 ppm, black), and excessive concentration (>1 ppm, red).

**Figure 10.**Contribution of variables to dimension 5. Variables with contributions below the dotted line are considered not significant for that dimension.

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**MDPI and ACS Style**

Pérez, R.; Martínez-Torrents, A.; Martínez, M.; Grau, S.; Vinardell, L.; Tomàs, R.; Martínez-Lladó, X.; Jubany, I.
Chlorine Concentration Modelling and Supervision in Water Distribution Systems. *Sensors* **2022**, *22*, 5578.
https://doi.org/10.3390/s22155578

**AMA Style**

Pérez R, Martínez-Torrents A, Martínez M, Grau S, Vinardell L, Tomàs R, Martínez-Lladó X, Jubany I.
Chlorine Concentration Modelling and Supervision in Water Distribution Systems. *Sensors*. 2022; 22(15):5578.
https://doi.org/10.3390/s22155578

**Chicago/Turabian Style**

Pérez, Ramon, Albert Martínez-Torrents, Manuel Martínez, Sergi Grau, Laura Vinardell, Ricard Tomàs, Xavier Martínez-Lladó, and Irene Jubany.
2022. "Chlorine Concentration Modelling and Supervision in Water Distribution Systems" *Sensors* 22, no. 15: 5578.
https://doi.org/10.3390/s22155578