Study of the combined effect of temperature and free chlorine concentration on the chlorine bulk decay coefficient in water supply systems

Water quality standards and regulations are established to safeguard public health and the environment. Networks must comply with these standards, and regular monitoring is essential to ensure that water quality meets the required criteria. Disinfection of water with chlorine is a common and effective method to kill or inactivate harmful microorganisms, such as bacteria and viruses, and to prevent the spread of waterborne diseases. Chlorination is widely used in water treatment processes to ensure safe drinking water quality in both urban and rural water distribution networks (de Souza et al. 2024). After the initial disinfection, a certain amount of chlorine is often left in the water as residual chlorine. This residual chlorine helps maintain the water quality as it travels through the distribution system, preventing the regrowth of microorganisms. However, during its transit through water distribution systems, chlorine residual undergoes decay influenced by several factors, including temperature (Komala et al. 2024), pipe material (Maleki et al. 2023), pH levels (Komala et al. 2024), as well as its role in the inactivation of microorganisms present in the water, among others. Therefore, monitoring these factors and adjusting chlorine dosages are essential steps in effectively managing water distribution systems.

Mathematical modeling of water networks is essential for understanding the system, efficient design and planning, resource optimization, predictive analysis, water quality management, leak detection, climate change adaptation, operational decision support, emergency response, and regulatory compliance. Furthermore, it enhances the overall resilience and sustainability of water distribution systems. For effective water quality monitoring in a water distribution system, particularly regarding chlorine concentration, mathematical models, e.g., EPANET (Rossman 2000), EPANET–MATLAB^® programming software (Zaghini et al. 2024), and computation fluid dynamics simulations, require data on chlorine bulk and wall decay coefficients (Hallam et al. 2002; Maphanga et al. 2024). These coefficients serve as crucial parameters for modeling the dynamics of residual chlorine within drinking water systems. Several researchers have developed models to describe the bulk decay of chlorine in drinking water (Vasconcelos et al. 1997; Maleki et al. 2023).

Among the various factors that influence the decay rate of bulk chlorine in drinking water supply systems, temperature has been reported as a primary factor significantly influencing k_b values in drinking water distribution networks (Kahil 2016). García-Ávila et al. (2020) conducted experiments for estimating k_b. Their experimental study involved the analysis of water samples at hourly intervals to measure free residual chlorine. The experimental findings revealed an average mass decomposition rate of 0.15 h⁻¹. Furthermore, their results demonstrated that temperature has a notable impact on the reaction rate of chlorine in water, with k_b increasing as temperature rises. Hua et al. (1999) conducted a comprehensive study examining how water quality parameters affect the chlorine bulk-decay coefficient (k_b) of free chlorine across various water samples, with an empirical focus on the initial chlorine concentration (C₀) and its relation to k_b. Using a mixed first/second-order model, they analyzed chlorine decay at temperatures ranging from 6 to 20 °C, using samples from a water treatment plant (WTP) and tap water connected to the same facility. Intraclass correlation coefficients for WTP and tap water were measured at under 0.2 and 0.4 mg/L, respectively, values considered insufficient to represent typical distribution systems, where intraclass correlation coefficients can reach up to 5mg/L. The decay tests carried out over several weeks with samples reflecting varying water quality revealed that first-order decay coefficients for both sample groups did not exhibit temperature-dependent variations by the Arrhenius relationship.

Jadas-Hecart et al. (1992) categorized the decay of chlorine into two distinct phases. The initial phase involves immediate consumption within the first 4 h, while the second phase represents a slower consumption occurring after the initial 4-h period. This subsequent phase is commonly referred to as the long-term chlorine demand. Fisher et al. (2011) demonstrated that the two-reactant model proposed by Kastl et al. (1999) stands out as the most straightforward model capable of depicting the chlorine bulk-decay coefficient. This decay initiates from any initial chlorine concentration (ICC) within the 1–6 mg/L range. This model demonstrated its effectiveness in addressing a fundamental disinfection concern within the system, specifically in determining the ICC necessary to achieve desired chlorine concentrations at all endpoints throughout the system under specified temperature conditions. Kiéné et al. (1998) established a correlation involving the first-order chlorine decay coefficient (k, min⁻¹), total organic carbon (TOC) within the range of 1–3 mg L⁻¹, and temperature (5–25 °C) based on the analysis of 21 water samples with undisclosed origins. In a study by Saidan et al. (2017), the first-order chlorine decay rate coefficient is defined as the decay attributed to the inherent quality of the water, specifically termed the bulk-decay coefficient k_b. The water's temperature influences the k_b value (Hua et al. 1999) as well as the concentration of TOC.

In summary, several authors have emphasized the significance of temperature as a primary factor influencing the chlorine bulk-decay rate coefficient (Kahil 2016; Monteiro et al. 2017; Kulkarni et al. 2018). However, initial chlorine concentration has also emerged as a critical parameter affecting residual chlorine decay within water distribution systems (Tiruneh et al. 2019; Onyutha 2024). To the best of our knowledge from the literature, there are no previous studies specifically focused on determining the combined impact of temperature and initial chlorine concentration on the k_b value. Therefore, this study aims to elucidate the influence of the combined effect of the initial chlorine concentration and temperature on the k_b value, contributing to the planning and management of water quality in water supply systems.

The experimental design to study the simultaneous effect of the initial chlorine concentration and temperature on k_b value was carried out in three steps: (1) Experimental study to obtain the k_b value. (2) Application of surface response methodology through a central composite design (CCD) to evaluate the effect of chlorine concentration and temperature on the k_b value. (3) Validation of the statistical model.

In the experiments, each scenario involved the collection of samples from the 3.5 L crystal bottle, thus preventing any adverse reactions with materials. Before experimentation, the bottle was thoroughly cleaned with a concentrated calcium hypochlorite solution at 10 mg/L. Subsequently, it was rinsed with distilled water and allowed to dry. The taps were run for approximately three minutes before water collection to avoid collecting stagnant water. In every scenario, an extra dose of chlorine was added to the tap-collected water to achieve the desired concentration specified for that particular scenario. An HI 83099 chemical oxygen demand (COD) and multiparameter photometer from Hanna Instruments, utilizing the N,N-diethyl-p-phenylenediamine (DPD) method, was employed to determine chlorine concentration in the water samples. This method involved adding DPD chemical powder to the water sample. Hypochlorous acid (free chlorine) in the sample promptly reacted with the DPD indicator, resulting in a pink color proportional to the chlorine concentration. The process entailed adding a reagent to a 10 mL water sample, and all spot samples were taken in duplicate to enhance measurement accuracy and serve as a quality control measure.

This study selected a temperature range of 22.93 to 37 °C to analyze chlorine decay in potable water, reflecting both current standards and expected temperature increases in urban water distribution systems. In some countries, maintaining drinking water below 25 °C is crucial to prevent health risks, including Legionella growth (Agudelo-Vera et al. 2020). However, with the effects of climate change and urbanization, urban subsurface temperatures are expected to increase, leading to more frequent exceedances of this 25 °C threshold (Agudelo-Vera et al. 2020). In Mexico City, where this study was conducted, water extracted from some wells can reach temperatures above 40 °C (CONAGUA 2024) due to geothermal influences in deep aquifers. This temperature range enables a thorough analysis of chlorine decay under current and future conditions, offering insights to maintain safe chlorine levels as urban water temperatures rise.

Chlorine concentrations ranged from 0.38 to 4.62 mg/L. In long-distance pipelines, higher initial concentrations are often applied to offset chlorine loss due to reactions with organic and inorganic matter, thereby minimizing the need for reinjection points. Operators may dose up to 3 mg/L or higher at the treatment site to ensure that residual chlorine levels remain within the acceptable range (typically 0.5–1.5 mg/L) by the time the water reaches the end user. Some countries, like Brazil, permit a broader range from 0.2 to 5 mg/L to ensure public health safety standards (de Souza Batista et al. 2024).

The CCD is an experimental method used to build second-order (quadratic) models in response surface studies. Its implementation involves a fractional factorial design that establishes the basic levels of the factors, central points that help evaluate the variability and improve the accuracy of the model, and finally star (axial) points that allow for the estimation of quadratic terms. This method is efficient in estimating quadratic terms, flexible for various problems with multiple factors, and provides additional information about the curvature of the response and the interactions between factors. CCD is currently employed in various scientific fields, such as improving the liquid–solid technique for curcumin solubility (Aghajanpour et al. 2024), optimizing the development of pharmaceutical formulations (Somadasan et al. 2024), among others (Arhamnamazi et al. 2024; Gupta et al. 2024; Satkın & Aktas 2024).

In this study, a CCD was employed to analyze the combined effect of chlorine concentration (mg L⁻¹) and temperature (°C) on the k_b value. The CCD consisted of four factorial, four axial, and two central points, totaling 10 experimental runs. For greater precision, treatments were evaluated in triplicate. The CCD response variable was the logarithm base 10 of k_b (Log₁₀k_b). The CCD matrix used is presented in Table 1.

The quadratic statistical model, derived through multiple regression from the CCD, was validated by comparing the k_b values predicted by the model with those obtained experimentally under specified chlorine concentration (mg L⁻¹) and temperature (°C) conditions.

Experimental studies were conducted to determine k_b values. The measured chlorine concentrations were plotted against time, and an exponential adjustment was applied to obtain k_b for each scenario. The behavior was observed to adjust to first-order kinetics (with a minimal R² = 0.93), as shown in Table 2.

Results concerning the effect of temperature and initial chlorine concentration on k_b are analyzed in this section. The bulk coefficients vary from 0.048 to 0.48 h⁻¹. The lower k_b value (0.048 h⁻¹) was obtained in scenario 2, corresponding to an initial chlorine concentration of 4 mg/L and a temperature of 25 °C. On the other hand, the highest value (0.48 h⁻¹) was recorded in scenario 5, where the initial data included a chlorine concentration of 0.38 mg/L and a temperature of 30 °C.

Some authors have suggested that temperature plays a crucial role in the k_b value, which agrees with the obtained results in the present investigation. The scenarios 7, 8, and 9, where the initial chlorine concentration equaled 2.5 mg/L, k_b values would be similar if the temperature did not exert an impact. Contrarily, variations in k_b values were observed throughout these experiments, indicating that temperature contributes to the variations in k_b values. For instance, three distinct k_b values were determined in these scenarios based on temperature variations. The highest value was recorded in scenario 8 (k_b = 0.096 h⁻¹) at the highest temperature (37.07 °C), followed by scenario 9 (k_b = 0.056 h⁻¹) and scenario 7 (k_b = 0.049 h⁻¹), associated with temperatures of 30 and 22.93 °C, respectively. Table 2 shows that all scenarios' determination coefficient (R²) values were close to 1, indicating a well-fitted model. Finally, scenario 6 was executed with the highest initial chlorine concentration (4.62 mg/L) at a temperature of 30 °C. The corresponding k_b value was 0.068 h⁻¹, and R² was 0.96, denoting a highly accurate and well-fitted model. Finally, the k_b values obtained from scenarios 3 and 5 in this study, corresponding to chlorine concentrations of 1 and 0.38 mg/L and temperatures of 35 and 30 °C, exhibited higher values of 0.164 and 0.48 h⁻¹, respectively.

The initial chlorine concentration significantly influences the k_b value. Observing scenarios 1 and 2, conducted at a temperature of 25 °C, it becomes apparent that the initial chlorine concentrations of 1 and 4 mg/L had a distinct impact on the resulting k_b values. In the first scenario, where the initial chlorine concentration was 1 mg/L, the k_b value equaled 0.072 h⁻¹, and the model demonstrated an adequate degree of fit with an R² of 0.94. In scenario 2, the k_b value was 0.048 h⁻¹, and the R² was 0.94, similar to the observation in scenario 1. In comparing both scenarios, the chlorine decay was faster in scenario 1, resulting in a higher k_b value. Similar trends were observed in other scenarios; for example, the maximum k_b value of 0.48 h⁻¹ occurred in scenario 5, aligning with the fastest chlorine decay. The second-highest k_b value was recorded in scenario 3. In summary, the results of these scenarios demonstrated that a lower initial chlorine concentration leads to a shorter decay time and a higher k_b value. Results of these scenarios showed that as the temperature increases, k_b values also increase. The same trends were observed in a study conducted by García-Ávila et al. (2020), in which temperatures ranged from 15.7 to 19.4 °C; initial chlorine concentration ranged from 0.7 to 1.80 mg/L. Their findings revealed a positive correlation between temperature and k_b values. However, it was noted that the k_b values (0.124; 0.163; 0.128; 0.133; 0.192; 0.163 h⁻¹) obtained in their study are higher than most k_b values obtained in this study. This difference may be attributed to a lower range of initial chlorine concentration used in their study.

Saidan et al. (2017) conducted experimental studies in which the concentrations of Cl₂ were determined at the following values: 1.2, 1.75, and 2.88 mg/L. The decay rate constant was calculated to be 0.0221 h⁻¹, which is lower than the k_b value obtained in this study. This difference may be attributed to variations in the initial chlorine concentration.

An examination of the kinetics of chlorine decay revealed that, for each initial chlorine concentration, the sample with a higher initial chlorine dose might exhibit a lower decay rate in most cases. This finding aligns with the observations from scenario 2 of our study, where the lowest decay rate coefficients were identified at an initial chlorine concentration of 4 mg/L. However, results from scenario 6 indicate that different k_b values may arise with varying temperatures, even with the same initial chlorine concentration. Changes in temperature, whether increasing or decreasing, can extend or shorten the chlorine decay process, thereby impacting the k_b values. Consequently, the decay pattern may also vary.

The CCD matrix is shown in Table 3.

An analysis of variance (ANOVA) was applied to the CCD to determine the parameters that significantly affect the value of k_b with a confidence level of 95% (Table 4). The linear factors (chlorine concentration and temperature) significantly affected the value of k_b, as did the quadratic term of chlorine concentration (p-value < 0.05). However, the interaction term of chlorine concentration–temperature and the quadratic term of temperature were found to have no significant effect on the k_b value (p-value > 0.05), so the quadratic model was discarded. Considering only the factors with a significant effect on k_b, it can be seen that the linear effect of chlorine concentration (50.635%) and its quadratic term (28.806%) explained approximately 79.441% of the variability in the average value of k_b. In comparison, the temperature term explained only 6.180% of the variability in the value of k_b.

The negative sign of the linear chlorine coefficient confirms the antagonistic (negative) effect of chlorine concentration on the k_b value; as the chlorine concentration increases, the k_b value will decrease. In contrast, the positive signs of the linear temperature coefficient and the quadratic chlorine coefficient indicate the synergistic (positive) effect of temperature and squared chlorine on the k_b value; as the temperature and squared chlorine concentration increase, the k_b value will increase. The model's intercept constant value (−0.661615) indicates the average value of Log₁₀ (k_b), independent of the chlorine and temperature concentrations tested in the CCD.

The data predicted for Log₁₀ (k_b) by the quadratic model was similar to the experimentally obtained data (Table 3). The goodness of fit of the quadratic model with the experimental data showed acceptable values. The high values of the coefficient of determination (R²) and the adjusted coefficient of determination (R_adj²) indicate a high dependance and correlation between the experimentally observed data and those predicted by the model. The R² was 85.6217%, while the was 83.963%, indicating that the proposed quadratic model explains 83.963% of the observed variability in the value of k_b; a second-order response surface model is useful for prediction purposes when ⁠. Relatively lower values of standard error of estimation (0.097) and mean absolute error of estimation (0.091) were computed, indicating that there exists a good fit of the quadratic model to the experimental data.

This response surface was obtained from the quadratic model predicting k_b (Equation (3)). From this graph, three conclusions can be drawn: (1) increasing the temperature will cause a linear increase in k_b value. However, this increase in the k_b value will be slight, within the same order of magnitude; (2) increasing the chlorine concentration will result in a sharp, quadratic decrease in the k_b value. This decrease in the k_b value can be up to an order of magnitude; (3) in the experimental zone tested, there is a combined effect of chlorine concentration (3.332 mg/L) and temperature (23°C) where a minimum k_b value (0.0347 h⁻¹) was observed. The equivalent of Log₁₀ (k_b) equal to −1.459. Considering a confidence level of 95%, there is certainty that the prediction confidence interval of the average Log₁₀ (k_b) value predicted by the quadratic model, under these conditions, will be between −1.775 and −1.144 (0.0168 ≤ k_b ≤ 0.0718).

Finally, a new experiment was conducted using the same initial chlorine concentration (3.33 mg/L) and temperature (22.3 °C) conditions under which the minimum k_b value was predicted.

This study investigated the combined effect of temperature and free chlorine concentration on k_b using a CCD. Ten scenarios were conducted, varying chlorine concentration (0.38–4.62 mg/L) and temperature (22.93–37.07 °C). The chlorine bulk-decay coefficients (k_b) were determined through exponential adjustments of measured chlorine concentrations over time. Statistical analysis using ANOVA from CCD highlighted that both the chlorine concentration and temperature affect the k_b values (p-value < 0.05). However, the chlorine concentration is the factor that most affects the k_b values, explaining 50.635% of the variability of k_b, while temperature only explains 6.18% of the variability of k_b. The quadratic term of chlorine concentration is responsible for explaining 28.81% of the variability of k_b. The quadratic model from multiple regression analysis could explicate 83.963% of the observed variability in the value of k_b, which makes it valid for prediction purposes. In light of our results, this work is the only one where a CCD was used to explain the combined effect of chlorine concentration and temperature on k_b and is capable of accurately reproducing results from other researchers.

Given that chlorine concentration has a significant impact on bulk chlorine decay coefficient (k_b), operators should carefully adjust initial dosing. In warmer temperatures, where chlorine decay accelerates, slightly higher initial doses may be necessary to maintain effective residual levels, especially in long-distance pipelines. Additionally, routine monitoring of chlorine residuals along different points of the distribution system is essential. Adjust chlorine levels proactively based on temperature changes to avoid under-dosing, which could lead to microbial contamination, or over-dosing, which may cause taste and odor issues. Predictive models, such as the quadratic model developed in this study, anticipate k_b values under various temperature and concentration scenarios. Implementing tools and systems that incorporate CCD-based models can enhance operators' ability to predict and manage chlorine decay effectively. This approach will support proactive water quality management and maintain chlorine levels within regulatory standards, thus protecting public health.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.