Improved VRC-3R⁻ model for bulk water residual chlorine decay in the UV/Cl₂ process for a water distribution network

Abstract

The combination of UV irradiation and chlorine (UV/Cl₂), as a new and efficient process, has been widely applied in drinking water disinfection. In this study, an improved VRC-3R⁻ (variable rate coefficient – 3 reactants minus other reactants) residual chlorine decay model was proposed in the UV/Cl₂ process in a water distribution network. Firstly, the single-factor experimental method was employed to assess the effects of initial residual chlorine concentration in the UV disinfection stage (C₀₁) and pipe network decay stage (C₀₂), UV intensity (F), inorganic nitrogen ([NO₂⁻]), ammonia nitrogen ([NH₄⁺]), and total organic carbon (TOC) on residual chlorine decay during the UV disinfection stage and pipe network decay stage. Next, the response surface method (RSM) was used to establish multivariate functions among the decay coefficients in the UV disinfection stage (k) and pipe network decay stage (K), C₀₁, C₀₂, temperature (T), and pH as correction coefficients. Finally, the model was calibrated using EPANET 2.0. In conclusion, (1) the optimal residual chlorine concentration and UV dose were 7.75 mg L⁻¹ and 50.1 mJ cm⁻², respectively; the pipe network disinfection by-product safety was confirmed. (2) The longest hydraulic retention time (HRT) in the pipe network was 5.12 h before the secondary chlorination. (3) The additional decay model by UV irradiation was established by subtracting the residual chlorine decay function with and without UV irradiation using the RSM's fitting results. (4) The calibration function value of the new model for two cases reached δ_1win (C) = 0.18, δ_1sum (C) = 0.16, δ_2win (C) = 0.16 and δ_2sum (C) = 0.14 in summer & autumn and spring & winter, respectively, which were less than the minimum (0.33) and standard values (0.25). (5) The residual chlorine concentration at the end of the water distribution network was less than 0.1 mg L⁻¹ in summer & autumn, exhibiting the importance of secondary chlorination to provide a reference for this process's application in water distribution networks.

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Water impact

Optimal parameters for the UV/Cl₂ process were determined: 6 W UV lamp and 7.75 mg-Cl₂ per L NaClO ensured 30 min contact time, enabling treated water's residual chlorine concentration of more than 0.03 mg L⁻¹; the minimum UV dose was 50.1 mJ cm⁻² by calculation and the maximum HRT was 5.12 h entering the water distribution network. This information was useful for the UV/Cl₂ process's control.

1. Introduction

Chlorine disinfection is widely used to disinfect drinking water. However, it is easy to form chlorine-containing disinfection by-products (DBPs) that reduce the chlorine-resistant microorganisms' inactivation rate. To reduce health risks, UV (ultraviolet)/Cl₂ has become one of the most popular advanced oxidation processes (AOPs) and disinfection processes.¹ UV/Cl₂ is divided into two categories: (1) chlorination followed by UV irradiation that is commonly used; (2) UV irradiation followed by chlorination to improve the disinfection capacity with a large amount of active free radical production and less power consumption.² Although the latter has many problems, such as more DBP production and higher cost which restrict its application, it is still attractive for two reasons. Firstly, the UV/Cl₂ process does not require additional chlorine to quench the residual H₂O₂; secondly, the HOCl and OCl˙ radical generation has higher reaction coefficients, quantum yields and lower energy demands than residual H₂O₂ under irradiation via 254 nm UV lamps. Therefore, it has an excellent energy-saving effect.³

The residual chlorine decay during chlorine disinfection has always been the interest of researchers and has been studied since the 1950s, focusing on the temperature effect.⁴ Then, other factors' effects, including total organic carbon (TOC), pH and initial residual chlorine concentrations, were summarised in the 1990s.⁵ In China, the residual chlorine decay theoretical system was first systematically described in 1998.^6,7 Since then, its related theories have been continuously improved. Recently, the development of computer technology and mathematical tools significantly advanced the residual chlorine decay model's specificity and accuracy. In 2009, the variable rate coefficient model (VRC) was proposed, highlighting the key effect of different reaction rates between various in-water substances and residual chlorine species on residual chlorine decay.⁸ In 2011, the 2R (2 reactants) model was proposed, considering the difference in the reaction rates between different chlorine-reactive species and substances in water, causing the decay rate divergence.⁹ In 2015, the TOC effect on variable reaction rates was explained, showing that booming new models would further discuss the factors and their mechanisms.¹⁰

In recent years, significant progress has been made in studying residual chlorine decay. In 2016, the basic process, using single-factor experiments to determine the different factors' influence on the residual chlorine decay mechanisms, the correction coefficient equation was formulated and proposed.¹¹ Then, the RSM (response surface method) was raised in 2018 to integrate the effects of TOC, initial residual chlorine concentration (C₀, including C₀₁ and C₀₂), and pH to further improve the correction coefficient's accuracy.¹² Additionally, the influences of secondary chlorine,¹³ the hydraulic model¹⁴ and the wall decay coefficient¹⁵ on residual chlorine decay have attracted much attention recently. Therefore, both the theoretical system and engineering application have been becoming increasingly robust.

Although most studies on the UV/Cl₂ process have focused on water treatment, recent studies on residual chlorine decay in the UV/Cl₂ process have also been reported. In 2007, the UV disinfection effect on residual chlorine decay in tanks was first proposed.¹⁶ In 2016, the UV/Cl₂ process was studied in secondary disinfection by monitoring and evaluating the residual chlorine concentration.¹⁷ In 2020, the relationship between the residual chlorine decay coefficient and UV dose was proposed, initially revealing the UV dose mechanism on residual chlorine decay.¹⁸ However, a proper discussion regarding the correction coefficient mechanism was needed. Excluding the transformation of ClO⁻ to ClO₂⁻, the mechanism was discussed corresponding to different halogen elements, and the proportion of various active species was revealed at different pH values in 2017 and 2020.^19,20 However, the photochemical reaction analysis between UV and residual chlorine was still lacking in the residual chlorine decay model, negatively affecting the model's accuracy.

In this study, by mixing the VRC and 2R model, an improved VRC-3R⁻ (variable rate coefficient – 3 reactants minus other reactants) bulk residual chlorine decay model in the UV/Cl₂ process was established by analysing the photochemical reaction among radicals produced by UV, water molecules and residual chlorine.¹³ Firstly, the Dahuofang reservoir water was taken as the water sample, and the relationship between additional residual chlorine decay and UV intensity was derived by analysing the photochemical reaction and products mentioned above. Simultaneously, the disinfection by-product safety effects at the optimal residual chlorine concentration, UV dose and hydraulic residence time (HRT) were also evaluated. Secondly, the single-factor experiment and RSM were used to fit the correction coefficient model to provide a reference for the process's efficient use in drinking water disinfection. Finally, the calibration function was constructed for a virtual case and an actual case each. Through field experiments and laboratory experiments, EPANET 2.0 software was used for modelling, simulation, and ultimately verifying the model's accuracy.

2. Model establishment

2.1 The bulk water residual chlorine decay model on UV irradiation

After using the UV/Cl₂ process, active free radicals played an important role in degradation and disinfection by water ionization, chlorine hydrolysis and UV irradiation.²² The species of Cl˙, ClO˙, and Cl₂˙ were commonly referred to as reactive chlorine species (RCS), represented by the C_RCS.²³ Similarly, OH˙, O₂˙, and any other non-chlorine radicals were called reactive oxide species (ROS), represented by C_ROS.²⁴ The theoretical diagram was shown in Fig. 1.

Fig. 1 Schematic diagram of the residual chlorine decay principle under UV irradiation.

The RCS had a clear reaction with soluble organic impurities more quickly, while non-radical free chlorines (ClO⁻, HClO, ClO₂⁻, ClO₃⁻, etc., called NRFC) reacted more slowly.²⁵ Meanwhile, the NRFC was also divided into faster and slower parts. The presence of multiple free radicals in the reaction system caused variations in different types of RCS and ROS reaction rate constants. Therefore, simply describing the residual chlorine decay with the 2R model would be biased. Therefore, the VRC model was introduced to describe the residual chlorine decay process, further improving the 2R model.⁸ The residual chlorine total amount was expressed as the sum of NRFC and RCS, and residual chlorine decay should be included in the process effect because RCS played a more dominant role in microbial inactivation and pollutant degradation in the UV/Cl₂ process than NRFC.¹ Moreover, the previous experiments above demonstrated that the residual chlorine decay on UV irradiation was significantly faster than that without irradiation, thus, the effects of RCS and ROS should not be ignored.

The reaction rate constant should be decomposed and extended to construct the 3R (3 reactants) model. Additionally, the chlorine reactants reduced by ROS equivalent were corrected, and the temperature factor was considered in the experiment design and data fitting. Thus, the model was eventually called the VRC-3R⁻ model.¹³ It was worth mentioning that if the relative proportions of RCS and ROS changed over time, the decay coefficients in the UV disinfection stage (k) and pipe network decay stage (K) would not be constant. However, the radical types and their proportions varied with external conditions, such as the initial residual chlorine concentration in the UV disinfection stage (C₀₁) and pipe network decay stage (C₀₂), pH and temperature (T). The RSM can be used to describe the interrelationship between k, K, pH, C₀₁, C₀₂, and T. k is a multifactorial variable, and external conditions affected k by affecting the proportion of RCS and ROS. Because ROS bore the impurities that the effective chlorine (RCS and NRFC) should bear to be degraded, the impurity concentration that reacted with the available chlorine, as well as the reaction rate between the effective chlorine and impurities, was reduced, resulting in the residual chlorine decay coefficient reduction.²⁶ Hence, the kinetic equations of the residual chlorine and impurity reaction minus the one for the ROS and impurity reaction explained the reduction of the residual chlorine decay coefficient under ROS pressure.

In summary, the VRC-3R⁻ model was represented as follows:

i.e. κ_1f = κ₁ × C_f1, κ_2s = κ₂ × C_s1, κ_3s = κ₃ × C_s2, and κ_2f = κ₄ × C_f2, which were the products of the corresponding partial reaction coefficient and reactant concentration; κ_1f was the decay coefficient of RCS, which was the first part that reacted with organic matter more quickly, min⁻¹; κ_2s was the decay coefficient of the NRFC which reacted with organic matter more quickly, min⁻¹; κ_3s was the decay coefficient of the NRFC which reacted with organic matter more slowly, min⁻¹; κ_2f was the decay coefficient of ROS, which was the second part that reacted with organic matter more quickly, min⁻¹; κ₁ was the rate constant of the RCS that reacted with organic matter, L mg⁻¹ min⁻¹; C_RCS was the concentration of RCS, mg L⁻¹; C_f1 was the concentration of organic matter that reacted with RCS in water, which was the first part having a faster reaction rate, mg L⁻¹; κ₂ was the rate constant of NRFC and organic matter which reacted more quickly, though more slowly than with RCS, L mg⁻¹ min⁻¹; C_NRFC was the concentration of NRFC, mg L⁻¹; C_s1 was the concentration of organic matter which reacted more quickly with NRFC in water, mg L⁻¹; κ₃ was the rate constant of NRFC and organic matter which reacted more slowly, L mg⁻¹ min⁻¹; C_s2 was the concentration of organic matter which reacted more slowly with NRFC in water, mg L⁻¹; κ₄ was the rate constant of the ROS reacted with organic matter, L mg⁻¹ min⁻¹; C_ROS was the concentration of ROS, mg L⁻¹; C_f2 was the rate constant of the ROS reacted with organic matter, mg L⁻¹; C_R was the total concentration of the organic matter reacted with residual chlorine at moment t, mg L⁻¹. κ_j was the rate constant of the organic matter reacted with the j type of disinfection effective substance (RCS, faster and slower NRFC and ROS, therefore j = 1, 2, 3, 4), L mg⁻¹ min⁻¹); κ_j,i was the rate constant of the j type of disinfection effective substance reacted with the i type of organic matter, L mg⁻¹ min⁻¹; C_tj,i was the concentration of the i type of organic matter at moment t (i = 1, 2, …, n), when the rate constant of the j type of disinfection effective substance reacted with the i type of reactant, mg L⁻¹.

All free radicals' reaction coefficients were indicated by eqn (3) to consider the self-quenching influence between conspecific free radicals. The indirect or direct reactions between heterologous free radicals were also considered.¹⁹

k_overall = k_direct + k_indirect − k_reformation (3)

where k_direct was the free radical rate constant generation by direct photohydrolysis, L mg⁻¹ min⁻¹; k_indirect was the contribution rate constants of OH˙ and Cl˙ indirect photolysis, L mg⁻¹min⁻¹; k_reformation was the contribution rate constants in the radical generation after quenching, L mg⁻¹ min⁻¹.

2.2 Establishment and simplification of the bulk residual chlorine decay model in the UV disinfection stage in the UV/Cl₂ process

The total reaction rate increased even if C_ROS objectively reduced the residual chlorine decay rate, and this change was caused by UV irradiation. The residual chlorine decay rate constant in the UV/Cl₂ process minus the one of the chlorine disinfection process was the total effect of UV on residual chlorine decay, which was explained by eqn (4):

κ_1f × C_RCS + (κ_2s + κ_3s) × C_NRFC − κ_4s × C_ROS = (k_bulk + k_RCS − k_ROS)[Cl₂] (4)

i.e. k_UV = k_RCS − k_ROS

where k_UV was the residual chlorine decay coefficient's net value related to UV intensity, L mg⁻¹ min⁻¹; k_bulk was the bulk residual chlorine decay coefficient without UV irradiation, L mg⁻¹ min⁻¹; k_RCS was the increasing residual chlorine decay coefficient's added value in the presence of RCS, L mg⁻¹ min⁻¹; k_ROS was the residual chlorine decay coefficient's discount value due to the ROS calculation for organic matter, L mg⁻¹ min⁻¹.

Therefore, the simplified and modified residual chlorine decay model was shown as eqn (5):

k_bulk is expressed as eqn (6):

k_bulk = k_self + k_TOC + k_NO2⁻ + k_NH4⁺ (6)

where k_self, k_TOC, k_NO2⁻ and k_NH4⁺ represent the residual chlorine decay coefficient of self-decomposition, TOC, reductive ions (mainly NO₂⁻) and ammonia nitrogen (mainly NH₄⁺), min⁻¹, respectively. k_self = 0.0013 h⁻¹.¹¹

Eqn (7) and (8) defined the UV dose as the product of UV intensity and time,²⁷i.e.

I = Ft (7)

k_UV = f(I) = C₀e^−f(I) (8)

where I was the UV dose, mJ cm⁻²; F was the UV intensity, mW cm⁻²; t was the irradiation time, min.

In conclusion, the residual chlorine decay model was simplified as eqn (9)

C_t = C₀₁ × e^−kt₁ (9)

where C_t was the residual chlorine concentration at moment t; C₀₁ was the initial residual chlorine concentration under UV irradiation, mg L⁻¹; t₁ was the UV irradiation time, min. Generally, the maximum of t₁, called t_1max, was equal to 30 min to achieve the necessary contact period.²¹

k was the total decay coefficient expression in the UV disinfection stage, h⁻¹, which was expressed as eqn (10):

k = (θ_T × θ_pH × θ_C01) × [k_self + k_TOC + k_NO2⁻ + k_NH4⁺ + k_UV] (10)

where θ_T, θ_pH and θ_C01 were the correction coefficients of T, pH and C₀₁.

The RSM was used to fit the multivariate relationship of k and three factors: T, C₀₁ and pH, to obtain more accurate results shown as eqn (11):

k = θ(T, pH, C₀₁) × k_bulk (11)

which was the residual chlorine decay correction coefficient of the UV disinfection stage in the whole UV/Cl₂ process.¹²θ(T, pH, C₀₁) is the multivariate correction coefficients of T, pH and C₀₁.

The mechanistic model above defined the UV effect as a correction factor expressed by (k_RCS–k_ROS). The method mentioned above could adjust the parameters more accurately than the single-factor model without affecting the whole model. In addition, the parameter regulation's independence and various factors' theoretical relevance were reflected. Particularly, the correction coefficients in the model were separated into UV and non-UV factor correction coefficients, making finding problems in the experiments and process easy and resolvable within the time frame.

2.3 Establishment and simplification of the bulk residual chlorine decay model in the pipe network decay stage in the UV/Cl₂ process

Since the presence of UV led to the reaction of active free radicals with organic matter, microorganisms and other substances in water, the specific indicators of organic matter and disinfection by-product composition were changed. Then the results of the chlorine disinfection in the water distribution network analysed by the bulk residual chlorine decay model would be different.

Similarly, the bulk residual chlorine decay was indicated by eqn (12):

C_t = C₀₂e^−Kt₂ (12)

where C₀₂ was the treated water's initial residual chlorine concentration, mg L⁻¹, as indicated by eqn (13):

C₀₂ = C₀₁e^−kt_1max (13)

K was the total residual chlorine decay coefficient in the water distribution network, h⁻¹, expressed by eqn (14):

K = (Θ_T × Θ_pH × Θ_C02) × (K_self + K_TOC + K_NO2⁻ + K_NH4⁺) (14)

i.e. K_bulk = K_self + K_TOC + K_NO2⁻ + K_NH4⁺

where K_bulk was the bulk chlorine decay coefficient, h⁻¹; K_self, K_TOC, K_NO2⁻ and K_NH4⁺ represented the residual chlorine decay coefficient of self-decomposition consumption, TOC, reductive ions and ammonia nitrogen, h⁻¹, respectively. t₂ was the residual chlorine decay time without irradiation in the pipe network decay stage, h.

It was also checked that K_bulk = k_bulk = 0.0013 h⁻¹.¹¹Θ_T, Θ_pH and Θ_C02 were the correction coefficients of T, pH, and C₀₂ on residual chlorine decay in the pipe network decay stage, respectively. Similar to section 2.2, to consider the interaction influence between multiple factors, the RSM was used for fitting the multivariate relationship between k and three factors: T, C₀₂ and pH, to obtain more precise results,¹²i.e.

K = Θ(T, pH, C₀₂) × K_bulk (15)

which was the residual chlorine decay correction coefficient expression in the pipe network decay stage. Θ(T, pH, C₀₂) was the multivariate correction coefficients of T, pH and C₀₂.

3. Experiment materials and methods

3.1 Experiment purpose

Firstly, in the UV disinfection and pipe network decay stages of the UV/Cl₂ process, the correction coefficient of UV intensity (F), the initial residual chlorine concentration (C₀₁ & C₀₂) in the two stages, NO₂⁻, NH₄⁺ and TOC to residual chlorine decay was determined; secondly, the model's accuracy was further corrected using the RSM. Finally, the experimental results established a more accurate residual chlorine decay model.

3.2 Experiment materials

1 bottle of 1500 g norm NaClO (analytically pure), 1 pack of residual chlorine A reagent and residual chlorine B reagent each, and Milli-Q ultrapure water as the solvent were purchased from Qiwei Instrument and Technology Corporation in Zhejiang. The residual chlorine content was measured using standard methods. One bottle of 100 g norm KH₂PO₄, 1 bottle of 200 g norm NaOH, 1 bottle of 100 g norm NaNO₂ and NH₄Cl each, 100 mL of configured humic acid solution and 1000 mL HCl solution. All reagents above, which were analytically pure, were purchased from Shanghai Sinopharm Reagent Corporation.

3.3 Experiment devices and instruments

Since the objective was bulk residual chlorine decay, it was not necessary to consider the residual decay loss from the pipe wall. Therefore, the beaker experiment's sealing process in the reactor was used to measure the bulk residual chlorine decay.

The reactor was a UV irradiation reactor made of cardboard: (1) a large, enclosed cardboard container; (2) 6 W, 12 W, 16 W, 20 W and 25 W low-pressure mercury lamps each, producing 254 nm UV light; (3) thermostatic magnetic stirrers.

The device is shown in Fig. 2 below.

Fig. 2 Plan view of the reactor.

The UV lamp was assembled to the center of the cardboard reactor's four sides. Each specific lamp was selected for the experiment, pulled back down, replaced with a new one and so on.¹ The different lamps' UV intensities were measured using KI/KIO₃ photometry in the reactor. Each lamp was measured using 9.96 g KI, 2.14 g KIO₃ and 0.381 g Na₂B₄O₇. It was configured as 1 L solution for photolysis experiments to measure the UV intensity and dose in a fixed volume reactor at different UV lamp powers.^28–30

This experiment device used the instrument protocol for the UV/ chlorine-free process in 2021.³ Meanwhile, the UV intensity and dose were measured and calculated by the principle modelling scheme.²⁹ Furthermore, the measured UV intensities were corrected using the correction method proposed, and all UV lights were equipped with gratings to improve the illumination uniformity. Besides, the Petri coefficient was increased to 1 to improve the measurement's accuracy.³⁰

3.4 Measurement index

The indicators to be measured in the experiment are shown in Table 1.

Table 1 List of the main monitoring methods and indicators

Index	Unit	Analytical technique	Detectability
pH	—	Portable pH measuring meter	0.01
Dimness	NTU	Portable turbidity measuring meter	0.01
Chrominance	Degree	Colorimeter	5
NH4^+	mgN L^−1	Naer reagent color method	0.025
NO2^−	mgN L^−1	N-(1-Naphthyl)-ethylenediamine photometry	0.025
NO3^−	mgN L^−1	UV spectrophotometry	0.01
CODMn	mg L^−1	Acid process	0.01
TOC	mg L^−1	Total organic carbon analyzer	0.05
UV254	AU cm^−1	UV spectrophotometry	0.002
Residual chlorine	mg-Cl2 per L	Portable residual chlorine tester	0.01
T	°C	Mercury thermometer	0.1
TP	mg L^−1	Total phosphorus tester	0.01–0.6
TN	mg L^−1	Total nitrogen tester	0.05–0.2

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The water samples for the experiment were taken from Dahuofang reservoir. The measured water quality indicators are shown in Table 2.

Table 2 Measured water quality indicators

Index	Filtered water	UV/Cl2-treated water
pH	7.5	7.7
Dimness	0.31–0.65	0.10–0.25
TP	0.02–0.04	0.01–0.02
TN	1.8–2.0	1.0–1.4
Chrominance	3–5 degrees	1–3 degrees
NH4^+	0.07–0.17	0.02–0.05
NO3^−	1.24–1.4	0.5–0.8
NO2^−	0.12–0.15	0.03–0.06
CODMn	2.64–2.95	2.20–2.32
TOC	2.34–2.58	0.3–0.6
Residual chlorine	0	0.4–0.7
T	25 °C	25 °C

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3.5 Experiment procedures

Before performing the residual chlorine decay experiments, a 1000 ml beaker was filled with 10 mg-Cl₂ per L sodium hypochlorite solution. After 24 hours of placement, it was thoroughly washed with Milli-Q ultrapure water to meet the chlorine-free requirement.³¹

The UV power was determined to be 16 W. A sample of 3.5 mg-Cl₂ per L and two samples of 1000 mL norm were prepared for residual chlorine decay experiments with UV irradiation and without UV irradiation, both in 30 min. To investigate the effect of three factors on k, NO₂⁻, NH₄⁺ and TOC concentrations in the other samples were adjusted from 0.01 to 0.05 mg L⁻¹, 0 to 3.5 mg L⁻¹ and 0.2 to 1 mg L⁻¹, respectively. The interval was set to ensure that the decrease in residual chlorine concentration among the measurements did not exceed 10%. According to the method above, the residual chlorine concentration was measured at regular intervals to determine the optimal residual chlorine concentration and UV dose. Then the single-factor relationship among k & K, NO₂⁻, NH₄⁺ and TOC, as well as the multifactorial relationship between k & K, pH, C₀₁ & C₀₂ and T, was investigated in the UV disinfection stage and pipe network decay stage to plot the fit curves and response surfaces, respectively. The duration of UV irradiation was 30 min. After the removal, UV irradiation was set for 2 h, and the measurement method remained unchanged.

The following methods controlled each factor: different amounts of NaClO were added to the other samples to simulate the different C₀₁ in the water distribution network from 2.5 to 4.5 mg L⁻¹; the pH was adjusted from 6.5 to 8.5 by mixing NaOH solution with HCl solution; meanwhile, the pH remained constant using the KH₂PO₄–NaOH buffer solution; the sample solution was adjusted in the incubator from 25 to 35 °C, ensuring that T was constant during the whole decay process; the NaNO₂ and NH₄Cl solutions were used to adjust the [NO₂⁻] and [NH₄⁺], ranging from 0 to 0.05 mg L⁻¹ and 0 to 3.5 mg L⁻¹, respectively; at the same time, a humic acid solution was used to simulate TOC in the samples from 0.2 to 1 mg L⁻¹. When each factor was studied, all others were controlled and unchanged.

The Origin software was not only used to fit the residual chlorine decay curve and correction coefficient but also determined the relationship between each factor and residual chlorine decay coefficient, which was the function between the correction coefficient and each factor. Ultimately, the RSM experiments were designed by DesignExpert software, and then the updated expression of k and K was further obtained by fitting the response surface in two stages. All experimental data were the results after averaging over three times measurements.

4. Results and discussion

4.1 Effect of UV dose

According to the experiment conditions, the UV doses corresponding to each residual chlorine concentration were calculated.

The curve of UV dose and residual chlorine concentration was measured. According to the experiment fitting results, the transient residual chlorine concentration after UV irradiation showed the obvious exponential function relationship, which was as follows (eqn (16)):

C₁(I) = 3.54e^−0.03I (16)

The fitted curves and their experimental data are shown in Fig. 3-a, respectively. In eqn (16), C₁ (I) indicated the initial residual chlorine concentration after the removal of UV irradiation, which was also known as the initial residual chlorine in the pipe network decay stage, mg L⁻¹.

Fig. 3 The relationship between different UV doses and residual chlorine concentrations in residual chlorine decay. (a) UV irradiation experiment. (b) Blank experiment.

By turning off the UV lamp, a blank experiment was conducted on the residual chlorine decay. The residual chlorine decay expression with C₀₁ = 3.5 mg L⁻¹ obtained under the blank experiment was shown as eqn (17):

C₂(t) = 3.488e^−0.003t (17)

where C₂ (t) is regarded as the residual chlorine concentration in the pipe network decay stage, mg L⁻¹. The results are shown in Fig. 3-b.

According to the figure above, the basic form of eqn (16) and Fig. 3-a was consistent with the previous results.¹⁸ The experimental data showed that the residual chlorine drops quickly before about 7 mJ cm⁻² but slowly after about 25 mJ cm⁻².

4.2 Optimum initial residual chlorine concentration (C₀₁) and UV dose

To solve the problem of low residual chlorine in the treated water due to fast residual chlorine decay and obtain the amount of NaClO which met the treated water residual chlorine specification, the residual chlorine decay equation was transformed as:where t_0.3 was the time that the residual chlorine concentration decayed to 0.3 mg L⁻¹ after affiliating NaClO, min.³²

When C_t = 0.3 mg L⁻¹ and the UV power was 16 W, eqn (18) obtained the time required for residual chlorine decaying to C_t = 0.3 mg L⁻¹ with the various initial concentrations of residual chlorine solution irradiated by UV, as shown in Table 3 and Fig. 4.

Table 3 The time at which the residual chlorine decays to 0.3 mg L⁻¹ under different initial residual chlorine concentrations

C 01/(mg L^−1)	t 0.3/(min)
2.5	12.327
3	13.387
3.5	14.283
4	15.060
4.5	15.744

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Fig. 4 Fitting result of the relationship between C₀₁ and t_0.3.

After fitting, the relationship between t_0.3 and C₀₁ was:

t_0.3 = 1.701C₀₁ + 8.205, R² = 0.996 (19)

When the contact time reached 30 min, the critical value method was used to determine the C₀₁ specified.

When t_0.3 = 30 min, C₀₁ = 12.8 mg L⁻¹ was obtained. This meant that when the UV power was 16 W, the residual chlorine C₀₁ = 12.8 mg L⁻¹ should be added to ensure that the treated water residual chlorine met the specifications, and there was also enough contact time to kill E. coli and other microorganisms. However, more disinfection by-products were generated due to a large amount of chlorine. In addition, the UV dose was calculated to be I = 126 mJ cm⁻², much higher than the previously determined doses of 20 mJ cm⁻² and 80 mJ cm⁻².²¹ Therefore, the supplementary experiment was conducted: if the initial residual chlorine concentration was set at 12.8, 10.8, 8.8, 6.8 and 4.8 mg L⁻¹, 6 W and 12 W UV lamps would be used for the irradiation experiment in 30 min to determine the residual chlorine decay coefficient and fit the decay coefficient's change rule varied with UV intensity and residual chlorine concentration. The experimental results are shown in Fig. 5 and 6 and Table 4.

Fig. 5 Experiment results of different initial residual chlorine concentrations at 6 W & 12 W UV power. (a) 6 W. (b) 12 W.

Fig. 6 Fitting results of different initial residual chlorine concentrations at 6 W & 12 W UV power.

Table 4 The fitting results of different initial residual chlorine concentrations at 6 W & 12 W UV power

6 W			12 W
C 0	k	R ^2	C 0	k	R ^2
12.8	0.061	0.998	12.8	0.068	0.999
10.8	0.08	0.990	10.8	0.092	0.995
8.8	0.091	0.997	8.8	0.106	0.999
6.8	0.12	0.986	6.8	0.132	0.995
4.8	0.138	0.984	4.8	0.151	0.994

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Therefore, the relationships between the residual chlorine decay coefficient and initial residual chlorine concentration under UV irradiation were proposed by eqn (20) and (21):

k_6w = 0.1844 − 0.0098C₀₁, R² = 0.992 (20)

k_12w = 0.1982 − 0.0101C₀₁, R² = 0.998 (21)

where k_6w and k_12w are the residual chlorine decay coefficients under 6 W and 12 W UV light irradiation, respectively, min⁻¹.

By respectively substituting C_t = 0.3 mg L⁻¹ and eqn (20) and (21) into the residual chlorine decay equation, the following eqn (22) and (23) were obtained as follows:

0.3 = C₀₁₋₁e^{−(0.1844−0.0098C₀₁₋₁)t_1max}, t_1max = 30 min, P = 6 W (22)

0.3 = C₀₁₋₂e^{−(0.1982−0.0101C₀₁₋₂)t_1max}, t_1max = 30 min, P = 12 W (23)

where C_01–1 = 7.75 mg L⁻¹ and C_01–2 = 8.56 mg L⁻¹, regarded as the initial residual chlorine concentrations under 6 W and 12 W UV light irradiation, respectively.

In conclusion, the following two process parameters met the specifications:

(1) When the UV power was 6 W, the minimum NaClO of 7.75 mg-Cl₂ per L met the specifications, and the calculated UV dose was 50.1 mJ cm⁻².

(2) When the UV power was 12 W, the minimum NaClO of 8.56 mg-Cl₂ per L met the specifications, and the calculated UV dose was 100.2 mJ cm⁻².

The optimal parameter was clearly scheme 1. It was measured that the process parameters mentioned above decreased the E. coli inactivation rate to 7.0 and reduced the coliform value below 3 CFU L⁻¹.³² Simultaneously, all detection indices during UV disinfection, such as the initial residual chlorine (7.5 mg L⁻¹), UV intensity (5.7–10 mW cm⁻²), and ammonia nitrogen (1.5 mg L⁻¹), were much lower than the national standard value especially since the ammonia nitrogen concentration in this study was much lower than previous studies.³³ Therefore, the content of treated water disinfection by-products, including THMs (trihalomethanes) and HAAs (haloacetic acids), was safe. In addition, according to the disinfection by-products mentioned, the UV/Cl₂ process pipe network decay stage was generally monotonous and decreasing, further ensuring the safety of water quality.¹⁸ More importantly, In scheme 1, the UV dose was 50.1 mJ cm⁻² < 80 mJ cm⁻², thus reducing power consumption. Although the residual chlorine concentration was 7.75 mg L⁻¹ > 3 mg L⁻¹, less UV dose allowed more residual chlorine to disinfect. So this parameter was considered positive in improving UV utilization.²¹

4.3 Inorganic nitrogen ([NO₂⁻])

According to the experiment conditions above, the experiment results were fitted to obtain the relationship between k & K and [NO₂⁻].

The images and experimental data were shown in Fig. 7 and Table 5.

Fig. 7 The fitting result of the residual chlorine decay concentration and decay coefficient in two stages under different [NO₂⁻]. (a) Changes in residual chlorine decay concentration under different [NO₂⁻] in the UV disinfection stage. (b) Changes in the residual chlorine decay coefficient under different [NO₂⁻] in the UV disinfection stage. (c) Changes in residual chlorine decay concentration under different [NO₂⁻] in the pipe network decay stage. (d) Changes in residual chlorine decay coefficient under different [NO₂⁻] in the pipe network decay stage.

Table 5 The fitting results of the residual chlorine decay coefficient under different [NO₂⁻]

k (min^−1)	[NO2^−]/(mg L^−1)	R ^2	k = f([NO2^−])	K (h^−1)	[NO2^−]/(mg L^−1)	R ^2	K = f([NO2^−])
0.131	0	0.987	k 1 = 5.47[NO2^−] + 0.113	0.241	0	0.993	K = 0.261 + 82.569[NO2^−]^1.828
0.159	0.01	0.989	R 1 ^2 = 0.980	0.279	0.01	0.989	R ^2 = 0.999
0.216	0.02	0.984	k 2 = 0.18e^[NO2−] + 0.052	0.327	0.02	0.984
0.258	0.03	0.975	R 2 ^2 = 0.998	0.392	0.03	0.985
0.33	0.04	0.965		0.495	0.04	0.985
0.403	0.05	0.946		0.605	0.05	0.987

---

There were two fitting results as follows (eqn (24) and (25)) in the UV disinfection stage:

k′ = 5.47[NO₂⁻] + 0.113 (24)

k′′ = 0.181e^{18.514[NO₂−]} + 0.052 (25)

where [NO₂⁻] was the concentration of NO₂⁻, mg L⁻¹; k′ and k′′ were the linear and curve fitting results of rate constants, respectively, min⁻¹. Comparing the value size of R², it was more appropriate to determine the corresponding curve of k′′, but a linear model of k′ also satisfied the fitting requirements. Therefore, when the accuracy requirement was not high, k′ was also used as the correction coefficient of the residual chlorine decay model. However, in the pipe network decay stage, the fitting result of K expressed by eqn (26) was clear that the curve was more appropriate:

K = 0.261 + 82.569[NO₂]^1.828 (26)

Nevertheless, k′, k′′ and K were not the residual chlorine decay model's correction coefficient. Because NO₂⁻ reacted with chloramine (NH₂Cl) in water, a few NO˙ radicals as well as NO₃⁻ were produced under UV irradiation.^9,34,35

The kinetic model was established as shown in eqn (27):

where k_NH2Cl was the rate constant of organic matter and NH₂Cl in the UV disinfection stage, min⁻¹; k_NO2⁻ was the rate constant of organic matter and NO₂⁻ in the UV disinfection stage, min⁻¹; [NH₂Cl] and [NO˙] were the concentration of NH₂Cl and NO˙, respectively, mg L⁻¹.

In the case of the blank experiments,

(NO₂⁻) = 0 (28)

The decay coefficient was shown in eqn (29) and (30):

k_NH2Cl = k_x1[X] (29)

k_NO2⁻ = k_x2[NO₂⁻] (30)

where k_x1 and k_x2 were the reaction coefficients of organic matter with NH₂Cl and NO₂⁻, respectively, min⁻¹; [X] was the concentration of organic matter, mg L⁻¹.

According to k_NH2Cl = 0.131 min⁻¹, therefore:

k_NO2⁻ = k − k_NH2Cl = 5.74[NO₂⁻] − 0.018 (31)

which was the correction coefficient of [NO₂⁻] for the residual decay coefficient in the UV disinfection stage.

Similarly

K = K_NH2Cl + K_NO2⁻ (32)

where K_NH2Cl was the rate constant of organic matter and NH₂Cl in the pipe network decay stage, h⁻¹; K_NO2⁻ was the rate constant of organic matter and NO˙ in the pipe network decay stage, h⁻¹; K_NH2Cl = 0.241 h⁻¹, i.e.

K_NO2⁻ = K − K_NH2Cl = 0.02 + 82.569[NO₂]^1.828 (33)

which was the correction coefficient of [NO₂⁻] for the residual decay coefficient in the pipe network decay stage.

4.4 Ammonia nitrogen

The ammonia nitrogen existed as ammonium ions and free ammonia in water, and there was a chemical balance relationship between them. The pH at equilibrium was found to be 9.25. When the pH was below 9.25, the reaction was spontaneously directed in the direction of NH₄⁺ generation process.^29,36,37 Additionally, the ammonia nitrogen in the water also formed chloramine with HClO, and NO˙ free radicals were also generated to participate in the reaction under ultraviolet irradiation, which also affected the residual chlorine decay rate. In contrast, NO₂⁻ also reacted with chloramine and NO˙ radicals, thus, using only NO₂⁻ to indirectly study the ammonia effects, nitrogen was no longer precise. Therefore, [NH₄⁺] was used as the dominant ammonia nitrogen condition for a more comprehensive study.

In spite of experimental conditions, the residual chlorine decay experimental results and fitting curves in the UV disinfection stage and pipe network decay stage were obtained, and the relationships between k & K and [NH₄⁺] were further fitted to obtain the results shown in Fig. 8 and Table 6.

Fig. 8 The fitting result of the residual chlorine decay concentration and coefficient in two stages under different [NH₄⁺] concentrations. (a) Changes in residual chlorine decay concentration under different [NH₄⁺] in the UV disinfection stage. (b) Changes in residual chlorine decay coefficient under different [NH₄⁺] in the UV disinfection stage. (c) Changes in residual chlorine decay concentration under different [NH₄⁺] in the pipe network decay stage. (d) Changes in residual chlorine decay coefficient under different [NH₄⁺] in the pipe network decay stage.

Table 6 The fitting results of the residual chlorine decay coefficient under different [NH₄⁺]

k/(min^−1)	NH4^+/(mg L^−1)	R ^2	k = f([NH4^+])	K/(h^−1)	NH4^+/(mg L^−1)	R ^2	K = f([NH4^+])
0.131	0	0.987	k = 0.053[NH4^+] + 0.126	0.241	0	0.993	K = 0.126[NH4^+] + 0.225
0.160	0.5	0.993	R ^2 = 0.998	0.304	0.5	0.985	R ^2 = 0.978
0.192	1	0.988		0.378	1	0.991
0.218	1.5	0.984		0.464	1.5	0.990
0.265	2.5	0.979		0.528	2.5	0.992
0.318	3.5	0.974		0.696	3.5	0.995

---

The linear function satisfied the accuracy requirement. The two stages' equations obtained from the fitting were shown as eqn (34) and (35):

k = 0.053[NH₄⁺] + 0.126 (34)

K = 0.126[NH₄⁺] + 0.225 (35)

where [NH₄⁻] was the concentration of NH₄⁺, mg L⁻¹.

Similar to section 4.3, ammonia nitrogen was replaced by chlorine to produce NH₂Cl, which had a weak ability for disinfection. Inadequate disinfection capacity meant less HClO produced, causing various degrees of reduced residual chlorine concentrations.

In addition, in the UV disinfection stage, chloramine and ammonia nitrogen produced NO˙ radicals under UV irradiation. These radicals weakened the disinfectants' degradation ability and were easily oxidized, making it more difficult to compete with residual chlorine and further increasing the residual chlorine decay rate.³⁴ Therefore, the residual chlorine decay coefficients, k & K, fitted in this experimental step, included the residual chlorine decay decreasing value contributed by the reaction between organic matter and chloramine. Hence, the residual chlorine decays coefficient caused by the reaction between NH₂Cl and organics should be subtracted, similar to eqn (31) and (32), the relationship between the residual chlorine decay coefficient and [NH₄⁺] was expressed by eqn (36) and (37), i.e.:

k_NH4⁺ = k − k_NH2Cl = 0.053[NH₄⁺] − 0.005 (36)

K_NH4⁺ = K − K_NH2Cl = 0.126[NH₄⁺] − 0.016 (37)

where k_NH4⁺ and K_NH4⁺ were the correction coefficient of NH₄⁺ in the UV disinfection stage and pipe network decay stage. It was the ammonia nitrogen correction coefficient to the bulk residual chlorine decay model in the UV disinfection stage and pipe network decay stage, respectively.

4.5 TOC

Organic matter in water is one of the most important factors affecting residual chlorine decay in the UV disinfection and pipe network decay stages. The residual chlorine decay experimental data and the relationships between k & K and TOC under the specified experimental conditions were measured and fitted. The results were shown in Fig. 9 and Table 7.

Fig. 9 The fitting result of the residual chlorine decay concentration and coefficient in two stages under different TOC. (a) Changes in residual chlorine decay concentration under different TOC in the UV disinfection stage. (b) Changes in residual chlorine decay coefficient under different TOC in the UV disinfection stage. (c) Changes in residual chlorine decay concentration under different TOC in the pipe network decay stage. (d) Changes in residual chlorine decay coefficient under different TOC in the pipe network decay stage.

Table 7 The fitting results of the residual chlorine decay coefficient under different TOC

k (min^−1)	TOC/(mg L^−1)	R ^2	k = f(TOC)	K (h^−1)	TOC/(mg L^−1)	R ^2	K = f(TOC)
0.124	0.2	0.997	k = 0.123 + 0.083TOC^2.245	0.319	0.2	0.937	K 1 = 0.119 + 0.856TOC
0.138	0.4	0.997	R ^2 = 0.992	0.440	0.4	0.956	R 1 ^2 = 0.980
0.146	0.6	0.995		0.613	0.6	0.988	K 2 = 0.241 + 0.759TOC^1.430
0.175	0.8	0.989		0.790	0.8	0.990	R 1 ^2 = 0.998
0.206	1	0.982		1	1	0.996

---

Therefore, the residual chlorine decay correction coefficient obtained in the two stages was shown as eqn (38)–(40):

k = 0.123 + 0.083TOC^2.245 (38)

K′ = 0.856TOC + 0.119 (39)

K′′ = 0.241 + 0.759TOC^1.430 (40)

where TOC was the concentration of TOC measured, mg L⁻¹. There were two forms of expression for the decay coefficient in the pipe network decay stage. Comparing the value size of R², nonlinear fitting was more suitable in the pipe network decay stage. However, the linear fit also met the requirements when the accuracy specification was not high.

Since the TOC concentration in the water was low in most cases, the decay rule could be expressed by the expression above. However, if the sudden water pollution led to high TOC in the water, especially with TOC concentration increasing to more than 1 mg L⁻¹, the residual chlorine decay coefficient's upper appreciation would decline, and even the slope would decline by nearly 20 times.¹¹ In addition, the high TOC produced many disinfection by-products, which would become a major hidden danger affecting human health. Therefore, plenty of research is still required during the safety evaluations of disinfection by-products produced by high TOC.

5. Model establishment by the RSM

According to the residual chlorine decay model's basic form, the residual chlorine decay correction coefficients for the three factors, C₀, pH and temperature (T), were connected by multiplier numbers, and there was an apparent mutual correlation between each factor. Therefore, C₀, pH and T were selected for the RSM experimental design to determine the interactive relationship between the three factors and the bulk residual chlorine decay coefficient.

For the UV disinfection and pipe network decay stages, the experimental design was performed by the Box–Behnken surface response design using DesignExpert software.¹² The 3 factors' interaction test was designed, taking three levels for each factor. Because the number of factors was 3, 12 + 3 = 15 trials were performed to obtain the RSM image and fitting results which would be directly substituted as correction coefficients. Then the additional decay model by UV was to be further derived.³⁸

5.1 The correction coefficients by the interaction of C₀₁, pH and T

5.1.1 Experimental design of the RSM in the UV disinfection stage. The experiment parameters are shown in Table 8.

Table 8 The list of experimental design and data

Experiment data
Std	Run	C 01	pH	T/°C	k	Predicted value
2	1	4.5	6.5	32.5	0.348	0.3516
7	2	2.5	7.5	45	0.662	0.6705
14	3	3.5	7.5	32.5	0.226	0.226
8	4	4.5	7.5	45	0.508	0.4988
12	5	3.5	8.5	45	0.452	0.4471
4	6	4.5	8.5	32.5	0.162	0.1761
10	7	3.5	8.5	20	0.068	0.0624
6	8	4.5	7.5	20	0.112	0.1035
5	9	2.5	7.5	20	0.187	0.1963
1	10	2.5	6.5	32.5	0.559	0.5449
15	11	3.5	7.5	32.5	0.226	0.226
3	12	2.5	8.5	32.5	0.251	0.2474
9	13	3.5	6.5	20	0.244	0.2489
13	14	3.5	7.5	32.5	0.226	0.226
11	15	3.5	6.5	45	0.728	0.7336

---

The correction coefficient expression was obtained by fitting the data above as follows (eqn (41)):

k = 5.2238 − 0.5874C₀₁ − 0.983125pH − 0.000404T + 0.0305C₀₁ × pH − 0.00158C₀₁ × T − 0.002pH × T + 0.049125C₀₁² + 0.054875pH² + 0.00059T², AdjR² = 0.996, PreR² = 0.977 (41)

where T is the temperature, K.

The ANOVA (analysis of variance) table is shown in Table 9.

Table 9 Variance analysis

Source	Sum of squares	df	Mean square	F-Value	p-Value
Model	0.578	9	0.0642	377.02	<0.0001	Significant
A–C01	0.035	1	0.035	205.34	<0.0001
B–pH	0.1119	1	0.1119	656.67	<0.0001
C–T	0.378	1	0.378	2219.05	<0.0001
AB	0.0037	1	0.0037	21.84	0.0055
AC	0.0016	1	0.0016	9.16	0.0292
BC	0.0025	1	0.0025	14.68	0.0122
A^2	0.0089	1	0.0089	52.31	0.0008
B^2	0.0111	1	0.0111	65.27	0.0005
C^2	0.0313	1	0.0313	183.95	<0.0001
Residual	0.0009	5	0.0002
Lack of fit	0.0009	3	0.0003
Pure error	0	2	0
Cor total	0.5789	14

---

According to the ANOVA, the imputed item was not significant. Moreover, AdjR² = 0.996 and PreR² = 0.977, so the model fits well and could be used to analyze and predict the residual chlorine concentration.

Next, the response surfaces under the effect of T, pH, and C₀₁ are plotted in Fig. 10, respectively.

Fig. 10 The response surfaces of three factors. (a) pH–C₀₁. (b) pH–T. (c) C₀₁–T.

Observing the response surface, it was concluded that all pairwise factor interactions were relatively significant, and the contour distribution was dense and uniform. It was also found that the influence of pH and T on the surface was relatively curly, showing that the effect of pH and T on the residual chlorine decay was nonlinear; the increase of T greatly improved the degradation rate at different C₀₁ and pH values as well, which needs to be noted in practical application. The present results also supported the previous experiments' findings.¹² At the same time, the increasing pH hindered the residual chlorine decay process caused by the temperature increase and reduced the declining decay rate value caused by the C₀₁ increase. The reason was that when the C₀₁ and even pH increase led to faster decomposition, plenty of residual chlorine was retained to ensure normal disinfection and degradation capacity. Moreover, free radicals were produced in the UV disinfection stage, and a large number of OH˙ free radicals produced under alkaline conditions shared the pollutant degradation pressure with residual chlorine, so the residual chlorine decay rate was also slowed down.³⁹ Additionally, the increase of C₀₁ significantly reduced the negative impact of temperature on the residual chlorine decay. Hence, in the high-water temperature area, the chlorine addition amount should be appropriately increased according to the model prediction results to ensure the appropriate residual chlorine concentration at the end of the water distribution network, especially since the decay rate is significantly faster in the UV/Cl₂ process.⁴⁰

5.1.2 Experiment design of the RSM in the pipe network decay stage. The experiment parameters are shown in Table 10.

Table 10 The list of experimental design and data

Experiment data
Std	Run	C 02	pH	T/°C	K	Predicted value
3	1	0.2	8.5	32.5	0.204	0.1891
10	2	0.4	8.5	20	0.135	0.146
14	3	0.4	7.5	32.5	0.205	0.203
4	4	0.6	8.5	32.5	0.149	0.1446
6	5	0.6	7.5	20	0.163	0.1564
11	6	0.4	6.5	45	0.678	0.667
15	7	0.4	7.5	32.5	0.202	0.203
13	8	0.4	7.5	32.5	0.202	0.203
12	9	0.4	8.5	45	0.525	0.5333
5	10	0.2	7.5	20	0.278	0.2819
8	11	0.6	7.5	45	0.472	0.4681
7	12	0.2	7.5	45	0.703	0.7096
9	13	0.4	6.5	20	0.323	0.3148
1	14	0.2	6.5	32.5	0.475	0.4794
2	15	0.6	6.5	32.5	0.142	0.1569

---

From the data, the correction coefficient expression was obtained as follows (eqn (42)):

K = 5.224 − 0.5874C₀₂ − 0.9831pH − 0.0004T + 0.0305C₀₂ × pH − 0.002C₀₂ × T − 0.002pH × T + 0.0491C₀₂² + 0.0549pH² + 0.0006T², AdjR² = 0.995, PreR² = 0.971 (42)

The ANOVA table is shown in Table 11.

Table 11 Variance analysis

Source	Sum of squares	df	Mean square	F-Value	p-Value
Model	0.5389	9	0.0599	304.65	<0.0001	Significant
AC02	0.0673	1	0.0673	342.63	<0.0001
BpH	0.0458	1	0.0458	232.78	<0.0001
C–T	0.2734	1	0.2734	1391.15	<0.0001
AB	0.0193	1	0.0193	98.3	0.0002
AC	0.0034	1	0.0034	17.12	0.009
BC	0.0003	1	0.0003	1.56	0.2672
A^2	0.0007	1	0.0007	3.75	0.1106
B^2	0.0024	1	0.0024	12.1	0.0177
C^2	0.1289	1	0.1289	656.04	<0.0001
Residual	0.001	5	0.0002
Lack of fit	0.001	3	0.0003	108.53	0.0091	Significant
Pure error	6.00 × 10^−6	2	3.00 × 10^−6
Cor total	0.5399	14

---

According to the ANOVA, the imputed item wasn't significant. Moreover, because AdjR² = 0.995 and PreR² = 0.971, the model fits well and could be used to analyze and predict the residual chlorine decay. The misfit term was 0.0091 < 0.01, which had good significance and could be used as the residual chlorine decay model correction coefficient.

Next, the response surfaces under the effect of T, pH, and C₀₂ were plotted, respectively, as shown in Fig. 11.

Fig. 11 The response surfaces of three factors. (a) pH–C₀₂. (b) pH–T. (c) C₀₂–T.

By observation, a similar trend to the UV disinfection stage was obtained. Firstly, the increasing C₀₂ offsets the pH effect on residual chlorine decay, but without the OH˙ radical assistance, the response surface eased a lot. As the pH decreased, the decline of C₀₂ also enhanced the residual chlorine decay coefficient. Secondly, as T increased, the pH effect on the residual chlorine decay decreased, and the K increase was not apparent in the UV disinfection stage. Similarly, when the pH and C₀₂ decreased, the improved K value was limited to some extent. Finally, the temperature still weakened different C₀₂ decay.

Notably, in the pipe network decay stage, when C₀₂ was higher (4–4.5 mg L⁻¹) and T was lower (20–25 °C), the curve appeared that the residual chlorine decay coefficient increased with pH. But it did not occur during the UV disinfection stage. The reason may be that in the UV disinfection stage, the pollutants in the water have been oxidized by free radicals into substances more likely to react with the residual chlorine, accelerating the residual chlorine decay rate;⁴¹ as C₀₂ increased, the reaction rate accelerated, partly offsetting the effect of the decreasing residual chlorine decay rate caused by increasing pH. This revealed a greater risk of secondary contamination from the disinfection by-products generated in the UV/Cl₂ process. Additionally, economic and safety concerns also arose at low temperatures, high initial residual chlorine concentration, and high pH, which were also worth further exploration.

5.2 Correction coefficient superposition of [NO₂⁻], [NH₄⁺], and TOC

In the previously established model, it was found that the correction coefficients of the three factors, inorganic nitrogen, ammonia nitrogen and organic matter, were connected with plus signs.

Adding the self-decomposition rate together:

k_self = K_self = 0.0013 h⁻¹ = 0.078 min⁻¹

According to eqn (22) and (29):

k_bulk = k_self + k_TOC + k_NO2⁻ + k_NH4⁺

K_bulk = K_self + K_TOC + K_NO2⁻ + K_NH4⁺

Each correction coefficient's result was obtained as eqn (43) and (44)

k_bulk = 0.078 + 0.113 + 5.47[NO₂⁻] + 0.053[NH₄⁺] + 0.126 + 0.123 + 0.083TOC^2.245 (43)

K_bulk = 0.013 + 0.02 + 82.569[NO₂⁻]^1.828 + 0.126[NH₄⁺] − 0.016 + 0.241 + 0.759TOC^1.430 (44)

which were the residual chlorine decay correction coefficient model of the two stages under the combined influence of inorganic nitrogen, ammonia nitrogen, and organic matter, respectively.

5.3 The model's experiment results

The experimental fitting results above were added to eqn (10) and (14) from section 2, and then the final residual chlorine decay correction coefficient model was obtained:

1) In the UV disinfection stage:

k = (5.2238 − 0.5874C₀₁ − 0.9831pH − 0.000404T + 0.0305C₀₁ × pH − 0.00158C₀₁ × T − 0.002pH × T + 0.049125C₀₁² + 0.054875pH² + 0.00059T²)[0.078 + 0.113 + 5.47[NO₂⁻]^1.828 + 0.053[NH₄]⁺ + 0.126 + 0.123 + 0.083TOC^2.245 + 0.034F − 0.06] (45)

2) In the pipe network decay stage:

K = (5.224 − 0.587C₀₂ − 0.983pH − 0.0004T + 0.031C₀₂ × pH − 0.002C₀₂ × T − 0.002pH × T + 0.049C₀₂² + 0.055pH² + 0.0006T²)[0.0013 + 0.02 + 82.569[NO₂⁻]^1.828 + 0.126[NH₄⁺] − 0.016 + 0.241 + 0.759TOC^1.430] (46)

As a previous result, the bulk water residual chlorine decay correction coefficient model was obtained in the chlorine disinfection process as follows (eqn (47)):where the residual chlorine decay model in the chlorine disinfection process was subtracted by the one in the UV/Cl₂ process to obtain the additional residual chlorine decay equation by UV:

1) In the UV disinfection stage:

C_t = C₀₁ × (e^−k_bulkt − e^−kt), t ≤ t_1max (48)

2) In the pipe network decay stage:

C_t = C₀₁e^−k_bulkt − C₀₂e^{−K(t−t_1max)}, t ≥ t_1max (49)

where C₀₂ is 0.6, 0.5, 0.4, 0.3 and 0.2 mg L⁻¹ in the experiment. k and K are controlled by eqn (45) and (46). The theoretical diagram is shown in Fig. 12.

Fig. 12 The function graph of the additional decay effect of UV irradiation on the residual chlorine.

Based on the model above, C_t = 0.05 mg L⁻¹, C₀ = 0.3 mg L⁻¹ and the treated water index measured in Table 2 was brought into the residual chlorine decay model, and the longest HRT was obtained to be 5.12 h.

6. Model operation and validation

6.1 Calibration model establishment

In general, the residual chlorine reaction rate constant with wall attachments was recorded as k_w, and the transmission rate constant between substances was recorded as k_f. A lot of experimental data were used to summarize the standard of three rate constants: k_b was 0.03/h, k_w was 10⁻⁶ m s⁻¹ and k_f was 10⁻⁷ m s⁻¹.⁴²Eqn (45) and (46) were used as the bulk decay coefficient k_b & K_b expression.⁴³

Since the wall residual chlorine decay didn't involve UV irradiation, the wall residual chlorine decay coefficient K_wall was expressed as eqn (50):⁴⁴

K_wall = 133.2962 × e^{1.805 log Re} × C_t1^0.24531 × pH^−4.89502 × k₀ (50)

where R_e is the hydraulic radius; k₀ is the wall residual chlorine decay coefficient, and C_t1 is the treated water's initial residual chlorine concentration.

The pump water from S city's booster pump station was selected as the water quality monitoring point. The measured water quality data are shown in Table 12.

Table 12 Water quality data of some monitoring points in different seasons

Seasons	UV dose/(mJ cm^−2)	Average T/°C	Average TOC/(mg L^−1)	Average pH	Average [NH4^+]/(mg L^−1)	Average [NO2^−]/(mg L^−1)	Residual chlorine pumped out/(mg L^−1)	Bulk residual chlorine decay coefficient/h^−1
Spring & winter	50.1	13	0.05	7.7	0.025	0.025	0.5	0.003
Summer & autumn	50.1	22	0.07	7.3	0.028	0.027	0.55	0.009

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Moreover, k_w was mainly limited by the biofilm attached to the pipe wall, and the biofilm formation was related to the pipe's material and age. Therefore, the initial k_w value was set according to the different kinds of pipe materials and age, and then the water quality model was corrected by comparing the simulated value with the measured value in the later period to meet the water quality model's accuracy requirements. The author also sorted out the wall initial residual chlorine decay coefficient from the different types of pipe walls. The detailed data are shown in Table 13:

Table 13 Different types of the wall initial residual chlorine decay coefficient

Types	The wall initial residual chlorine decay coefficient/(m d^−1)
DN200 ductile iron pipe	0.024
DN300 ductile iron pipe	0.022
DN350 ductile iron pipe	0.021
DN400 ductile iron pipe	0.020

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The water quality model calibration's purpose was to adjust the error as low as possible to ensure high model accuracy. It required solving the reaction coefficients to construct the following objective functions as eqn (51):

where C_nip indicates the residual chlorine simulation value at monitoring point i under working conditions n at p time; C^s_nip is the measured residual chlorine value at monitoring point i under the working conditions n at p time; G_H (H, Q) is the hydraulic leveling process and G_Q (Q, C) is the residual chlorine decay kinetic equation. In eqn (51), both G_H (H, Q) and G_Q (Q, C) are equal to 0.⁴⁴ Q, C and H were flow, residual chlorine concentration and hydraulic pressure, respectively.

Python IDE available in Chinese Python Net (https://www.cnpython.com/pypi/epanet2/) was used to enter the restriction parameter conditions and solve the function. Then the residual chlorine decay coefficient was fed into the water quality model, and the residual chlorine was calculated and analyzed.

It was proposed that the residual chlorine model's calibration accuracy (δ) was less than 50% as the calibration standard value, which was defined as eqn (52):

where x is the simulation value, X is the measured value and λ is the initial residual chlorine concentration of treated water.

Meanwhile, combined with the minimum sum of square calibration function (min f(C)), which was as follows (eqn (53)):

where C_i and C_i⁰ were the simulation value and measured value of the residual chlorine concentration, respectively, mg L⁻¹. n was the number of nodes.

The following accuracy function of the minimum sum of square calibration (min δ(C)) was derived as eqn (54):

where λ was 0.5 mg L⁻¹, and δ_win (C) and δ_sum (C) were the calibration function values of spring & winter and summer & autumn, respectively.^45,46 Ultimately, in order to calibrate the water quality model to obtain a more definite conclusion, a certain area of S city supplied by Dahuofang reservoir and the example pipe network given in the EPANET 2.0 manual instruction were chosen as the actual case and the virtual case, respectively.

6.2 Simulation and calibration results

6.2.1 Case 1. Case 1 was a residential community's water distribution network located in a district of S city, using the UV/Cl₂ process for water distribution. The pipes were made of ductile iron. The site's map is shown in Fig. 13. The water distribution network in this area was modelled using EPANET 2.0. According to the parameters in part 1.1, this case's residual chlorine concentrations in winter & spring and summer & autumn were simulated. The field measured experimental values and simulation values by the previous model were compared with the model's simulation values in section 6.1. The results are shown in Fig. 14 and 15.

Fig. 13 Case 1, actual site's map.

Fig. 14 Case 1: simulation results. (a) Case 1: spring & winter (new model). (b) Case 1: spring & winter (previous model). (c) Case 1: summer & autumn (new model). (d) Case 1: summer & autumn (previous model).

Fig. 15 Comparison of the actual residual chlorine value, the new model and previous model's simulation in case 1. (a) Case 1: spring & winter. (b) Case 1: summer & autumn.

6.2.2 Case 2 (virtual case). Similar to section 6.2.1, the example water distribution network in the EPANET 2.0 software description manual was used as a virtual case, and the experiment device was constructed, as shown in Fig. 16.

Fig. 16 Experiment device.

The pipes were made of ductile iron, the same as case 1. After setting the water quality conditions shown in Tables S12 and S13,† the water distribution network in this area was modelled using EPANET 2.0 as well. According to the parameters in section 6.1, the residual chlorine concentrations in winter & spring and summer & autumn were simulated. The field measured experimental values and the previous model's simulation values were compared with the new model's simulation values in section 6.1, which are shown in Fig. 17 and 18.

Fig. 17 Case 2: simulation results. (a) Case 2: spring & winter (new model). (b) Case 2: spring & winter (previous model). (c) Case 2: summer & autumn (new model). (d) Case 2: summer & autumn (previous model).

Fig. 18 Comparison of the actual residual chlorine value, the new model and previous model's simulation result in case 2. (a) Case 2: spring & winter. (b) Case 2: summer & autumn.

6.3 Simulation conclusion

Based on the comprehensive analysis and comparison results of the two cases above, the conclusions were as follows:

(1) The new model's calibration function reached δ_1win(C) = 0.18, δ_1sum(C) = 0.16, δ_2win(C) = 0.16 and δ_2sum(C) = 0.14 in the summer & autumn and spring & winter, respectively, which were less than the minimum value of the previous model equivalent to 0.33 and the standard value equivalent to 0.25. So, the water quality model's accuracy met the requirements.

(2) Because the direct and secondary effects of UV on residual chlorine decay were not considered and TOC was high in summer & autumn, the disinfection by-products further accelerated the residual chlorine decay, causing the old model's data to be too large. When using the UV/Cl₂ process, the new model's prediction results confirmed that the residual chlorine concentration was less than 0.1 mg L⁻¹ at the distal end of the water distribution network in summer & autumn, so secondary chlorination measures should be taken in certain seasons.

(3) The new model's accuracy was greater in summer & autumn than in spring & winter. The reason was that the organic matter, as well as the temperature, was low in spring & winter, hence, decreasing the reaction rate. Ice in some regions led to uneven concentration distributions and reaction rate differences. In addition, the actual water consumption in the region was small in winter & spring, and the model experiment of water consumption distribution equilibrium was different from the actual working conditions, but each point's error between the simulated values and measured experimental values could be controlled within 0.25.

(4) Case 1 was an actual water distribution network with a large scale but with a larger error, while case 2 was a virtual water distribution network with a small scale and a smaller error. Therefore, in addition to the water distribution network's scale that might affect the prediction accuracy, laboratory studies with small errors might also deviate from the actual situation. In all, it is still necessary to promote and apply the UV/Cl₂ process to practical engineering and large-scale water distribution networks to acquire more accurate conclusions through further research.

7. Final conclusion

Through the residual chlorine decay model establishment above under the UV/Cl₂ process, the conclusions were as follows:

1. Through analysing the UV/Cl₂ process's reaction mechanism, an improved VRC-3R⁻ model of residual chlorine decay was constructed. In theoretical derivation, the three correction coefficients T, C₀, and pH were multiplied, and five correction coefficients F, [NO₂⁻], [NH₄⁺], TOC and self-decomposing were added.

2. The residual chlorine decay model applying the UV factor was successfully constructed by fitting the experimental data. In addition, a segment function of the additional decay effect of ultraviolet light on the residual chlorine was derived.

3. A 6 W UV lamp with at least 7.75 mg-Cl₂ per L NaClO met the specification of 30 min contact time to keep the treated water's residual chlorine concentration more than 0.03 mg L⁻¹; after calculation, the UV dose was 50.1 mJ cm⁻²; the longest HRT under the conditions above was 5.12 h entering the pipe network. The disinfection by-products met the safety specifications as well.

4. Through the RSM, the functions among the k & K, T, pH and C₀₁ & C₀₂ were fitted in two stages with R² > 0.97, all of which met the accuracy requirements.

5. The new model's calibration function reached δ_1win(C) = 0.18, δ_1sum(C) = 0.16, δ_2win(C) = 0.16 and δ_2sum(C) = 0.14 in summer & autumn and spring & winter, respectively, which were less than the previous and standard values. This predicted that the residual chlorine concentration at the distal end of the water distribution network was less than 0.1 mg L⁻¹, revealing the necessity for secondary chlorination.

6. The network's scale and laboratory environment might affect the simulation prediction's accuracy, which required further experiments and numerical simulations in different regions & water quality and extensive networks to reveal more practical conclusions. The Dahuofang reservoir's water quality in northeast China, as the subject of research, provided a technical basis for the operation and design of the water distribution network in the area.

Author contributions

In this research work, Haipei Wang was involved in the conceptualization, methodology, software, formal analysis, and validation under the joint supervision of Bing Wang and John C. Crittenden; Haifeng Pan and Lixin Wang wrote and translated the paper, respectively. All authors approved the paper's final version.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This study was supported by the Liaoning Provincial Department of Education (No. lnqn202011).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ew00647b

‡ First author.

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