# Towards a Predictive Model for Initial Chlorine Dose in Humanitarian Emergencies

^{*}

## Abstract

**:**

_{254}and 30-min chlorine demand). With these relationships, the two chlorine decay models can be calibrated quickly and frequently in the field, allowing effective determination of initial chlorine dose. These two models calibrated based on the suggested water parameters from the study could predict chlorine decay in water having a main chlorine demand-inducing constituents as natural organic matter. However, they underpredicted chlorine decay in surface water with additional chlorine reactants. Further research on additional chlorine decay mechanisms is needed to expand the applicability of the models.

## 1. Introduction

## 2. Background

#### 2.1. Two-Phase Chlorine Decay Behavior

#### 2.2. Temperature

#### 2.3. Decay Kinetic Models

## 3. Materials and Methods

_{254})), temperature, and 30-min chlorine demand. A total of 64 chlorine decay tests, in both 125-mL glass brown bottles (Fisher Scientific, Canada) and 20-L plastic jerrycans (ULINE, Seattle, WA, USA) were conducted from August 2019 to January 2020.

#### 3.1. Apparatus Preparation

#### 3.2. Synthetic Water Preparation

_{254}, representing the amount of natural organic content in the water. This relationship was determined and used for the stock humid acid in the Public Health and Environmental Engineering (PH2E) laboratory at the University of Victoria (Victoria, Canada). The prepared water was then distributed into three 2-L Erlenmeyer flasks for temperature adjustments.

_{254}value measured in cm

^{−1}, and $X$ is the concentration of humic Acid measured in mg/L.

#### 3.3. Temperature Control

#### 3.4. Chlorine Stock Solution Preparation

#### 3.5. Matrix for Test Conditions

_{254}settings, the selections were based on several studies, which determined the UVA

_{254}value of numerous water sources (e.g., river and reservoir) ranging from 0.0 to 0.8 cm

^{−1}[30,31,32], with the value for most cases found below 0.3 cm

^{−1}. Therefore, the selected values of 0.05, 0.10, 0.20, 0.30 cm

^{−1}represented most cases studied.

#### 3.6. Natural Water Samples Preparation

_{254}, and ammonia concentration. The water was then incubated and tested at 30 °C for chlorine decay. All the water quality parameters were tested again before chlorine dosing.

#### 3.7. Data Analysis

## 4. Results

^{2}distribution from data fitting for all five models are demonstrated in the box and whisker plot (Figure 3). Figure 4 shows three randomly selected representative tests from the experiments and the regression curves from the five models to demonstrate their fitness. As shown in the results, the different available chlorine decay models in literature, except for first order model, can describe chlorine decay behavior very well, with 100% of the regression achieved an R

^{2}value above 0.9. The selection of models should be based primarily on model simplicity and the difficulty in model parameters calibration.

#### 4.1. Correlation and Mathematical Relations

_{254}and 30-min chlorine demand of water appear to have significant impacts on chlorine decay rates. Feben and Taras’s empirical model and first order model were selected for further analysis because of their simplicity and the higher correlation values obtained between their $k$ values and the water parameters. Due to the structures of these two models, water chemistry directly and solely impacts the $k$ value in the equation, leading to high correlations between $k$ and water parameters. For the rest of the models, the impacts from additional model parameters (i.e., $n$ in power models, $w$ in parallel models) likely lower the correlations between k and water parameters.

_{254}value and the temperature (Figure 5). The decay constants for Feben and Taras’s empirical model and first order model increased linearly and exponentially with the increase in UVA

_{254}, respectively (Figure 6). Both models’ decay constants followed Arrhenius relationship with the water temperature, specifically, the linear relationship between the natural log of decay constant and the reciprocal of water temperature in Kelvin (Figure 6). When the water parameters were determined in the field, the ‘$k$’ value could be estimated based on the identified relations.

#### 4.2. Decay Kinetics and Water Chlorine Demand

#### 4.3. Quality Control

#### 4.4. Verification

_{254}and 30-min chlorine demand.

## 5. Discussion

_{254}and temperature) or using the 30-min chlorine demand, which is a proxy for the chlorine decay property of the water. This process substantially reduces the calibration requirement of the models, allowing the application of the chlorine decay models in humanitarian treatment contexts. The proposed model calibration methods also serve humanitarian field staff involved in water supply interventions by addressing the inadequacies and inconsistencies of current “rule-of-thumb” for chlorine dosing.

#### 5.1. Model Calibration Using Impacting Factors and Their Mathematical Relations

^{2}value decreased from 0.988 to 0.960. The decay constant term was found linearly related to the change in water’s organic content under all doses and temperature conditions but with different slope. The $\mathrm{ln}(k$) over $1/T$ plot (Figure 6, plot c) showed linear relations between natural log of decay constant and the reciprocal of temperature in Kelvin. This verified the Arrhenius-type relationship. The slopes of the lines were very similar for all doses and organic content combinations with an average value of 1397$K$. Based on this result, the decay constant at a certain temperature from 10 °C to 30 °C can be estimated according to Equation (3) when the decay constant is known for the same water at any known temperature from 10 to 30 °C.

_{254}value and the decay constant under all three initial dosages conditions and all temperature settings were exponential. The four points for an initial dose of 1 mg/L in water with 0.2 and 0.3 cm

^{−1}for the 20- and 30-degree curves in Figure 6 (plot b) did not follow the exponential trend, because the chlorine residual was completely reacted before 24 h, and the decay kinetics for the entire period was not able to be calculated. This also meant that the initial chlorine was not sufficient to maintain a chlorine residual of greater than 0.2 mg/L for 24 h for the tested conditions. Otherwise, all chlorine decay kinetics increased exponentially with the increase in water organics content. For impacts from temperature, the $\mathrm{ln}(k$) over $1/T$ plot (Figure 6, plot d) showed similar slopes of the regression lines for all doses and organic content combinations with an average value of 4818$K$. The values of the slope were less consistent in the case of first order model compared to those of Feben and Taras’s empirical model. Equation (4) can be used to adjust the k value for first order model based on the water’s temperature.

#### 5.2. Model Calibration Using 30-min Chlorine Demand

#### 5.3. Discussion on Discovered Relations

_{254}in the water. Humic acids mostly contain organics with aromatic compounds, and the dominate reactions between chlorine and the aromatic compounds are electrophilic substitution followed by stepwise substitutions [33]. An increase in humic acid concentration increases the available sites for the reactions. A linear increase in the UVA

_{254}of water leads to linear increase in chlorine consumption demonstrated by the consumption term $k{t}^{n}$, in Feben and Taras’s empirical model.

_{254}values. However, the turbidity of all test water was below 10 NTU. This again suggested that turbidity was indeed not an adequate indicator for chlorine decay in test water in the study.

#### 5.4. Impacts from Storage Container

#### 5.5. Additional Chlorine Reduction Mechanisms

#### 5.6. Outlook

## 6. Conclusions

_{254}, temperature, and 30-min chlorine demand) in the field, and this strategy satisfies the need for a practice-oriented, emergency-adapted dose prediction approach. With the discovered relations between chlorine decay model parameters and water parameters, humanitarian field staff can determine the appropriate initial chlorine dose for achieving FCR objectives by measuring several obtainable field water quality parameters.

_{254}and temperature on chlorine decay kinetics. The exact values of the parameters were not required to be determined. Only 30-min chlorine demand is needed to evaluate if the initial doses were feasible for the test water in field.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental setup for chlorine decay tests in bulk “brown bottles” tests (

**left**) and in jerrycans (

**right**).

**Figure 3.**R

^{2}from model fitting on all 64 chlorine decay tests using the five models. From top to bottom of each box are the maximum value, third quartile, median, first quartile, and minimum value of R

^{2}for the specific model it represents.

**Figure 5.**The combined impacts on chlorine decay constant in Feben and Taras’s empirical model and first order model from temperature and natural organic matter (NOM) (all initial dose cases).

**Figure 6.**(

**a**) Decay constants from Feben and Taras’s empirical model versus NOM of the test water. (

**b**) Decay constants from first order model versus NOM of the test water. (

**c**) $\mathrm{ln}\left(k\right)$ versus $1/T$ for all cases– Feben and Taras’s empirical model. (

**d**) $\mathrm{ln}\left(k\right)$ versus $1/T$ for all cases—first order model. (Details can be found in Supplementary Material File S1).

**Figure 7.**Mathematical relationship between decay constant and 30-min chlorine demand of test water. Figure (

**a**) is for decay constant in Feben and Taras’s empirical model. Figure (

**b**) is for decay constant in first order model.

**Figure 8.**Predictions of chlorine decay in (

**a**) well water, (

**b**) reservoir water, and (

**c**) pond water using the three developed models, and their comparisons with the measured values.

Guidelines/Studies | Chlorine Dose Recommendations | References |
---|---|---|

Descriptive Based | ||

CDC | 1/8 teaspoon (8 drops) of bleach (5–6% or 8%) for each gallon of clear water; Double value for cloudy water | [14] |

US EPA | 2 drops to ½ teaspoon of bleach (6% or 8.25%) to certain amount of water (1 L to 8 gallons) | [15] |

Empirical Based | ||

WHO | Find the dose to reach at least 0.5 mg/L free chlorine at 30 min after dosing | [6] |

Exact Values | ||

Lantagne | 1.875 mg/L free chlorine for water with turbidity <10 NTU 3.75 mg/L free chlorine for water with turbidity 10–100 NTU | [9] |

JHU and IFRC | 2.50 mg/L free chlorine, verify that there is at least 1.00 mg/L free chlorine residual at 30 min after dosing | [16] |

FMH | 2.00 mg/L free chlorine and aim to reach 0.50 mg/L free chlorine residual | [17] |

**Table 2.**Five Models evaluated by Wu (2020) [24] and their empirical solutions.

Model | Equation ^{1} | Data Modification OR Model Restrictions | References |
---|---|---|---|

Feben and Taras’s empirical model | $C={C}_{0}-k{t}^{n}$ | Optionally fix n value based on regression results | [25] |

First order model | $C={C}_{0}\times {e}^{-kt}$ | Exclude data prior to 30 min reaction time | [26] |

Power model | $C={(kt\times \left(n-1\right)+{\left(\frac{1}{{C}_{0}}\right)}^{\left(n-1\right)})}^{(\frac{-1}{n-1})}$ | Optionally fix n value based on regression results | [26] |

Parallel first order model | $C=w\times {C}_{0}\times {e}^{-{k}_{1}t}+\left(1-w\right)\times {C}_{0}\times {e}^{-{k}_{2}t}$ | N/A | [26] |

Limited parallel power model | $C={C}^{*}+{({k}_{1}t\times \left({n}_{1}-1\right)+{\left(\frac{1}{\left(w\right)\left({C}_{0}-{C}^{*}\right)}\right)}^{\left({n}_{1}-1\right)})}^{(\frac{-1}{{n}_{1}-1})}$ $+{({k}_{2}t\times \left({n}_{2}-1\right)+{\left(\frac{1}{\left(1-w\right)\left({C}_{0}-{C}^{*}\right)}\right)}^{\left({n}_{2}-1\right)})}^{(\frac{-1}{{n}_{2}-1})}$ | N/A | [27] |

^{1}For the listed equations, $C$ is the chlorine residual measured at time $t$, ${C}_{0}$ is the initial chlorine dose, ${C}^{*}$ is the stable component of chlorine added, $k$ is the decay constant term, $n$ is the power term, and $w$ is the ratio term.

Models | Parameters | UVA_{254} | Temperature | 30-min Chlorine Demand |
---|---|---|---|---|

Feben and Taras’s empirical model | $k$ | 0.86 | 0.18 | 0.78 |

First order model | $k$ | 0.67 | 0.24 | 0.77 |

Power model | $k$ | 0.35 | 0.09 | 0.51 |

Parallel first order model | ${k}_{1}$ | −0.32 | −0.19 | −0.28 |

Parallel first order model | ${k}_{2}$ | 0.43 | 0.10 | 0.38 |

Limited parallel power model | ${k}_{1}$ | 0.26 | −0.06 | 0.30 |

Limited parallel power model | ${k}_{2}$ | 0.00 | −0.22 | −0.04 |

Water ID | Turbidity (NTU) | pH | UVA_{254} (cm^{−1}) | Ammonia (mg/L) | 30-min Chlorine Demand (mg/L) |
---|---|---|---|---|---|

Well Water | 12.6 | 7.52 | 0.009 | 0.01 | 0.11 |

Reservoir Water | 0.43 | 7.27 | 0.05 | 0.04 | 0.52 |

Pond Water | 9.67 | 6.3 | 0.212 | 0.43 | 3.12 |

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**MDPI and ACS Style**

Wu, H.; C. Dorea, C.
Towards a Predictive Model for Initial Chlorine Dose in Humanitarian Emergencies. *Water* **2020**, *12*, 1506.
https://doi.org/10.3390/w12051506

**AMA Style**

Wu H, C. Dorea C.
Towards a Predictive Model for Initial Chlorine Dose in Humanitarian Emergencies. *Water*. 2020; 12(5):1506.
https://doi.org/10.3390/w12051506

**Chicago/Turabian Style**

Wu, Hongjian, and Caetano C. Dorea.
2020. "Towards a Predictive Model for Initial Chlorine Dose in Humanitarian Emergencies" *Water* 12, no. 5: 1506.
https://doi.org/10.3390/w12051506