# Modeling the Chlorine Series from the Treatment Plant of Drinking Water in Constanta, Romania

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

^{2}= 0.98). Gómez-Coronel et al. [17] reported satisfactory results in the chlorine concentration at the input of a water distribution system simulated in EPANET, with a genetic algorithm implemented in MATLAB. The EPANET MSX software was used to model chlorine decay in Algarve’s drinking water supply systems [18]. García-Ávila et al. [19] employed the same tool with a built-in first-order equation for modeling chlorine decay for a case study from Ecuador. Nejjari et al. [20] proposed a methodology for efficiently calibrating the free chlorine decay models tested on the Barcelona water transport network. Zhang et al. [21] elaborated a model for integrating water quality and operation for forecasting water production (using a genetic algorithm-enhanced artificial neural network). In contrast, other authors focused on optimizing the chlorine dosing [22,23].

## 2. Materials and Methods

#### 2.1. Data Series and Statistical Analysis

^{3}/h. Cișmea II has 12 wells with depths between 90 and 150 m and a pumping capacity of 1940 m

^{3}/h. The Galeșu surface water source, with 13,050 m

^{3}/h catching capacity, is situated along the banks of Poarta Alba–Midia (on the Channel Danube–Black Sea). It has five intakes equipped with metal sieves for retaining the suspended particles.

^{3}per day.

^{3}, one of 6.000 m

^{3}, and another of 10,000 m

^{3}. The Caragea Dermen groundwater source can also be accessed. It is formed by 18 wells with depths between 35 and 90 m and has a supply capacity of 3.549 m

^{3}/h. The water from different sources undergoes different chlorination processes. Only after chlorination are the streams of water mixed and introduced into the distribution network. The studied data series (Figure 2) is formed of the monthly free chlorine residual concentration collected at the outlet of PCTP during January 2013–December 2018.

#### 2.2. Statistical Analysis

#### 2.3. Mathematical Modeling

- Determine the trend using the linear trend computed via Sen’s method;
- Calculate the detrended series by subtracting the trend from the data series;
- Determine the seasonal component;
- Determine the remainder (random or residual component) as the difference between the detrended series and the seasonal component.

## 3. Results and Discussion

#### 3.1. Results of the Statistical Analysis

#### 3.2. Models

_{12}type. For its validation, the residuals’ series analysis was performed. The Shapiro–Wilk test indicates that the hypothesis that the series in Gaussian cannot be rejected (p-value > 0.100 > 0.05; Figure 10a), the correlogram (Figure 10b) indicates the correlation absence, and the Levene test (Figure 10c) rejected the heteroskedasticity hypothesis. The p-value associated with the Box–Ljung test is p = 0.1137, indicating that the hypothesis of residuals’ series independence cannot be rejected. Moreover, MAD = 0.0695, MSD = 0.00868, and MAPE = 16.5426, showing that the SARIMA performs best among all the proposed models.

_{12}.

## 4. Conclusions

_{12}model is more complex since it involves the first-order differentiation of the series and its seasonal components (to reach its stationarity), and considering the innovation process (by the presence of the moving average, one for both series and seasonality). While the last methodology provides the most accurate results, all the others may be used for modeling and forecast given the easiness and availability of their implementation in MINITAB and R.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Time series decomposition plot for the studied series. DECA; (

**b**) the Q-Q plot of the random component. Mean is the average of the residual component’s values, StDev is the standard deviation of the residual component’s values, N is the number of the values, AD is the value of the Anderson–Darling statistics from the Anderson–Darling applied to the residual component, and P-value is the p-value computed in the Anderson–Darling test on the residual component.

**Figure 4.**DECA: (

**a**) Seasonal indices (1 corresponds to January and 12 to December); (

**b**) Detrended data by season; (

**c**) Percent variation by season; (

**d**) Residuals by season.

**Figure 5.**DECM: (

**a**) Original Data, (

**b**) Detrended series, (

**c**) Seasonally adjusted series, (

**d**) Seasonally adjusted and detrended series (residual component).

**Figure 6.**MAA12: (

**a**) The initial series. (Observed is the default name given to it by the software); (

**b**) Trend; (

**c**) Seasonal component; (

**d**) Random component.

**Figure 7.**The random component’s correlogram in MAA12. The blue dotted line represents the limits of the confidence interval at a 95% confidence level.

**Figure 8.**(

**a**) Holt–Winters multiplicative model; (

**b**) Residuals’ histogram; (

**c**) Residuals correlogram.

**Figure 9.**Forecast with the MHW model. The black curve is the series, the blue one is the forecast and the grey backgrounds are the confidence intervals at 95% and 99%, respectively.

**Figure 10.**SARIMA model. Residual series analysis (

**a**) Results of the Shapiro–Wilk test; (

**b**) Correlogram; (

**c**) Results of the Levene test.

**Figure 11.**Forecast based on the SARIMA model. The black curve is the series, the blue one is the forecast and the grey backgrounds are the confidence intervals at 95% and 99%, respectively.

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**MDPI and ACS Style**

Bărbulescu, A.; Barbeș, L.
Modeling the Chlorine Series from the Treatment Plant of Drinking Water in Constanta, Romania. *Toxics* **2023**, *11*, 699.
https://doi.org/10.3390/toxics11080699

**AMA Style**

Bărbulescu A, Barbeș L.
Modeling the Chlorine Series from the Treatment Plant of Drinking Water in Constanta, Romania. *Toxics*. 2023; 11(8):699.
https://doi.org/10.3390/toxics11080699

**Chicago/Turabian Style**

Bărbulescu, Alina, and Lucica Barbeș.
2023. "Modeling the Chlorine Series from the Treatment Plant of Drinking Water in Constanta, Romania" *Toxics* 11, no. 8: 699.
https://doi.org/10.3390/toxics11080699