Modeling the formation of disinfection byproducts in chlorinated swimming pool water: Role of body fluid analog Open Access

Pollutants from pool users are introduced into swimming pool water in the form of body fluids, such as sweat, urea, saliva, and/or suspended particles, such as hair and skin cells, as well as certain synthetic chemicals originating from sunscreen or deodorants (Keuten et al. 2012, 2014; Virkutyte et al. 2012). The initial input of anthropogenic pollutants can be substantially decreased by thorough pre-swim showering, whereas the continuous input of post-shower pollutants cannot be avoided (Yeh et al. 2014). Because of the recirculation of swimming pool water and inefficient conventional pool water treatment, pollutants accumulate and remain in the pool water before the pool is emptied and renovated (Barbot & Moulin 2008; Yeh et al. 2014). Seawater or disinfected distributed drinking water is used to refill or partially replace pool water, which is referred to as filling water. Although filling water can dilute the anthropogenic pollutant content, it also introduces natural organic matter (NOM) that remains in freshwater after treatment, and inorganic matter such as bromide, into the swimming pool water (Kanan & Karanfil 2011; Manasfi et al. 2016). Chlorine is an input substance that inactivates microorganisms and ensures microbiological safety of swimming pool water. However, chlorine reacts with inorganic matter and NOM originating from swimmers and from filling water, leading to the formation of potentially harmful disinfection byproducts (DBPs) (Zwiener et al. 2007; Richardson et al. 2010; Chowdhury et al. 2014). The exposure risk assessment illustrated that swimming pool water could be more genotoxic than chlorinated tap water, emphasizing the importance of controlling DBPs concentrations in swimming pool water (Plewa et al. 2008; Liviac et al. 2010).

Among the commonly detected and regulated DBPs, trihalomethanes (THMs) are the predominant species, and one has been studied most intensively. Trichloromethane (TCM) is the main THM compound formed in fresh chlorinated swimming pools, ahead of dibromochloromethane, bromodichloromethane, and tribromomethane (Chu & Nieuwenhuijsen 2002; Chowdhury et al. 2014), whereas brominated THMs are important in saline water pools or bromine-disinfected pools (Lourencetti et al. 2012). A better understanding of the kinetics of chlorine consumption and THM formation in swimming pool water is helpful for guaranteeing a healthy pool environment. Therefore, a so-called body fluid analog (BFA) was proposed as a surrogate for the chemical composition of micropollutants introduced into swimming pools, which facilitates the following investigation.

The BFA contains several constituents, including urea, uric acid, amino acids, and ammonia chloride, which are mixed at typical ratios to represent the pollutants introduced by pool users (Borgmann-Strahsen 2003; Judd & Bullock 2003; Goeres et al. 2004). Efforts have been made to understand the chemistry of the reactions between chlorine and individual BFA constituents, such as urea (Blatchley & Cheng 2010; De Laat et al. 2011), uric acid (Lian et al. 2014), and organic nitrogen DBP precursors such as creatinine and L-histidine (Li & Blatchley 2007). However, less attention has been paid to the time-course contribution of an individual constituent to chlorine consumption and THM formation in the BFA mixture. Moreover, the results of previous investigations are rarely related to the prediction of chlorine consumption and DBP formation in swimming pool water, particularly when compared with the model simulation for disinfected drinking water.

The formation of THM can be simulated using multiple regression or reaction kinetic approaches. The former was developed using multiple regression analysis of THM concentration, water quality parameters such as total organic carbon (TOC) or dissolved organic carbon (DOC), and operational parameters. However, the application of the multivariate approach may be limited to simulating the dynamic variation in the THM concentration in swimming pool water. This is because the observed fluctuations in THM concentration lag NOM concentration by several days (Peng et al. 2016). In other words, the responses of THM formation to the variation of precursors are not simultaneous, as the precursors with low reactivity require a longer reaction time with chlorine. Unlike the multiple regression approach, the kinetic approach is based on a reaction theory that considers the quantity and properties of reactants and has been widely used in the simulation of drinking water quality (Fisher et al. 2012, 2021). Therefore, it is reasonable to consider the reactivity of organic THM-precursors in swimming pool water. Currently, the THM species formation model was reported based on the concept that THM-productive chlorine consumption was linearly related to the formation of THM or individual THM species (Sathasivan et al. 2020). However, the residual chlorine in swimming pool water is relatively stable while the composition and concentration of precursors are variable depending on the number of swimmers. Therefore, the development of THM formation model for swimming pool water should focus on the reactivity and concentration of reactants.

Consequently, to optimize chlorine dosage and minimize DBPs, the objective of this study was to develop kinetic models for chlorine consumption and THM formation in swimming pool water. The BFA was applied as a surrogate for the micropollutants released by pool users, while humic acid (HA) was used to represent the NOM introduced by the filling water. The BFA and HA mixture was treated as synthetic swimming pool water. The detailed aims were to: (i) determine the specific chlorine demand and specific trihalomethane formation potential (THMFP) of each BFA constituent and HA; (ii) evaluate the time-course contributions of the individual constituents to the chlorine consumption and THM formation of synthetic swimming pool water; (iii) determine the reaction rate coefficients of chlorine consumption and TCM formation for each BFA constituent and HA; and (iv) simulate the kinetics of chlorine consumption and THM formation for the BFA mixture and the BFA and HA mixture based on the proposed models.

All reactants were reagent grade chemicals and used without further purification. BFA organic stock solutions were prepared by gravimetrically adding known constituents into purified water and dissolving at pH 12 (NaOH, 2 mol/L) according to the method described by Judd & Bullock (2003), the pH of which was then adjusted to neutral using 1 mol/L sulfuric acid. The composition of the stock BFA solution and the percentages of carbon and nitrogen contributed by individual BFA constituents are listed in Table 1. The HA stock solution was prepared by dissolving sodium salt (Sigma-Aldrich, MO, USA) at pH 12 (NaOH, 2 mol/L) and stirring at 20 °C for ca. 30 h. The solution was adjusted to neutral pH and then filtered through a 0.45 μm polycarbonate filter (Nuclepore Track-Etch Membrane, Whatman, Germany) to remove suspended solids. Dilution of BFA and HA to target aqueous-phase concentrations was accomplished with distilled deionized water (18.2 MΩ•cm at 25 °C; Direct-Q system, Merck Millipore, MA, USA). The BFA and HA mixture, which surrogated the swimming pool water, was labeled as BFA + HA and prepared by mixing and diluting BFA and HA stock solutions to the target concentration. All the solutions were freshly prepared before the chlorination experiments, and the final non-purgeable organic carbon (NPOC) concentrations were measured. A chlorine stock solution (≈15.5 mM) was prepared from a commercial sodium hypochlorite solution (14% active chlorine; VWR, PA, USA). Phosphate buffer (10 mM) was prepared. The chlorine stock and buffer solutions were refrigerated at 4 °C.

The NPOC concentration of organic samples was fixed at 2 mg/L to study the specific chlorine demand and specific THMFP of the individual BFA constituents and HA. Chlorination was performed using 300 mL brown glass bottles. The glassware was pre-soaked in a dilute chlorine bath (≈2 mM) for at least 15 h and then rinsed with purified water before the chlorination experiments (De Laat et al. 2011). All samples were maintained at pH 7.2 with phosphate buffer before chlorination. To allow the chlorine reaction to approach completion, an appropriate volume of chlorine stock solution was spiked into individual samples to achieve an initial chlorine concentration (ICC) of 50 mg/L. It should be illustrated that the chlorine concentration of swimming pool water is adjusted and maintained at an adequate level ranging from 0.3 to 2.0 mg/L in different countries and regions, which are dependent upon several factors such as pool type, the number of people in the pool, temperature, and pH (Barbot & Moulin 2008; Long et al. 2019). The chlorine in the gas or liquid form is continuously added to the swimming pool to guarantee enough chlorine residual, thus, it has difficulty conducting re-chlorination under laboratory conditions. To make sure the chlorine concentration is not a limitation for reaction, i.e., enough chlorine remains in the water sample at the end of maximum reaction time, a high initial dosage of 50 mg/L was applied. The chlorinated samples were then immediately hermetically closed and incubated in head-space free glass bottles at 28 ± 1 °C. After 168 h, the residual chlorine was measured, and the remaining sample was quenched by the addition of sodium thiosulfate solution for further TCM measurements.

Two independent experiments were conducted to study the kinetics of chlorine decay and THM formation. Experiment series were performed to investigate the time-course contribution of individual BFA constituents to chlorine consumption and THM formation of BFA. Therefore, the NPOC of BFA was initially set at 3 mg/L, and the theoretical values of NPOC, nitrogen, and solution concentrations of each BFA constituent were calculated according to the receipt (Table 1). In other words, the NPOC concentration of BFA is a summation of the carbon contributed by the individual BFA constituents. Chlorination of each BFA constituent and BFA was conducted according to their respective NPOC concentrations, as shown in experiment series I (Table 2). Similar experiments were performed using the same procedures as those for the chlorine demand and TCM formation potential tests, however, the reaction times were 4, 24, 72, 120, and 168 h.

Experiment series II was conducted to determine the reaction rate coefficients of individual BFA constituents and HA. Therefore, all organic substances were designed to have an identical NPOC at 2 mg/L, as shown in experiment series II (Table 1). Chlorination experiments were conducted using the same procedures as those used for experiment series I. Eventually, the chlorine consumption and THM formation dataset of synthetic swimming pool water was obtained, including the mixture of BFA and HA at different mixing ratios. An ICC of 50 mg/L was selected for the chlorination experiments. The pH was fixed at 7.2 ± 0.1, and the temperature was maintained at 28 ± 1 °C.

The free chlorine concentration was determined according to the N, N-diethyl-p-Phenylenediamine (DPD) Standard Colorimetric Method 4500-Cl G (APHA 2005). The chlorine stock solution was periodically standardized using the DPD method. The NPOC concentration was measured using a TOC-VCPH (Shimazu, Kyoto, Japan). A pH meter 340i (Wissenschaftlich-Technische-Werkstätten, Weilheim, Germany) was used to measure pH. THM concentrations were determined using a membrane inlet mass spectrometer (MIMS) 2000 (Mikrolab Aarhus, Højbjerg, Denmark), which comprised a Prisma QME 220 PT mass spectrometer (Pfeiffer Vacuum, Asslar, Germany) equipped with electron ionization. THM standards were purchased from Sigma-Aldrich. Before measurement, THM without purification was diluted with ultrapure water to the target solution concentrations and measured for MIMS calibration. Water samples were first analyzed in the mass spectrum scan mode (49-m/z-215). Then, the THM concentration was quantified using selected ion monitoring. Because all the synthesized samples were prepared with ultrapure water, which does not contain bromide, only TCM was detected in all the THM species. Ions at m/z 83 were chosen to quantify TCM, with a quantification limit of 2.5 μg/L. More detailed operation conditions for the MIMS can be found in the literature (Shang & Blatchley 1999; Yang et al. 2012).

The underlying assumption is that the reaction rate coefficient is not a constant but varies with the reaction progress owing to the different phases of the reaction; thus, the decay model is referred to as a VRRC, where α [L/mg/h] and β [dimensionless] are the model parameters for ⁠; [mg/L] is the chlorine concentration; [mg/L] is the reactant concentration at time t; is the maximum chlorine demand, that is, ⁠. is the consumed reactant concentration at time t; thus, ⁠. Based on the principle of mass conservation and the hypothesis that the stoichiometric coefficient for chlorine and the reactant is equal to one, the consumed reactant is equal to based on the Euler method. Finally, the ⁠.

Data obtained from experiment series II were used to determine the best-fit parameters of α [L/mg/h] and β toward chlorine decay, as well as γ [L/μmol/h] and θ toward TCM formation for each substance. Excel Solver, which uses the generalized reduced-gradient algorithm, was used to solve Equations (1) and (3) to obtain the model parameters for each substance. They were calculated numerically with a 0.5 h time interval by minimizing the sum of the squared errors between the experimentally determined chlorine or TCM concentrations and simulations at corresponding times. Once the best-fit parameters were determined, the rate coefficients of the mixtures were calculated using Equations (5) and (6). Furthermore, the kinetics of chlorine decay and TCM formation with respect to the mixtures were predicted using Equations (7) and (8) with a 0.5 h time interval.

The accuracy of the model simulation was evaluated using the coefficient of determination (R²) and root-mean-square error (RMSE). These methods are frequently used as measures of model adequacy and describe the difference between the predicted data and those obtained experimentally (Piñeiro et al. 2008). The RMSE evaluates the prediction capability of the model, with a smaller RMSE value indicating a greater predictive capability. The obtained RMSE is also expected to be of a similar magnitude as the measurement error, which indicates a reasonable fit.

A chlorine demand test was performed to evaluate the reactivity of the investigated substances toward chlorine consumption. Experiment datasets were interpreted in the form of the DOC-related specific chlorine demand (mg Cl₂/mg C) and the solution concentration-related chlorine demand (mol Cl₂/mol BFA component).

The concentration-related chlorine demand is shown in Figure 1(b). The horizontal axis shows the ratios of ICC to the initial solution concentration of the individual BFA components, which are referred to as the specific chlorine doses (ICC/solution concentration, mol Cl₂/mol BFA component). This shows that the specific chlorine demand plateaued at chlorine doses > 20 mol Cl₂/mol BFA. The highest specific chlorine demand was observed for L-histidine, which reached 14 mol Cl₂/mol histidine, followed by uric acid with 10.5 mol Cl₂/mol, and creatinine with 7.5 mol Cl₂/mol. These results can be explained by the structure of the compounds, that is, the more electron-donating functional groups (-NH₂ and -OH) and double bonds in the structure, the higher the chlorine demand (Hong et al. 2009). Specifically, L-histidine and creatinine, which contain an aromatic ring and functional group of -NH₂, showed a higher specific chlorine demand than that of hippuric acid, which has no functional groups on its ring and therefore has the lowest demand. The demand for urea was 3.3 mol Cl₂/mol urea, which falls within the theoretical chlorine demand that ranges between 3 and 8 mol Cl₂/mol of urea (De Laat et al. 2011).

The data shown in Figure 1(c) are the DOC-related specific chlorine demands of ∑₇BFA and HA. ∑₇BFA reached the highest plateau level of 14 mg Cl₂/mg C. However, HA was exhibited at 3 mg Cl₂/mg C, which was nearly five times lower than that of BFA. This result agrees with the conclusions reported by Kanan & Karanfil (2011) that BFA is more reactive than HA toward chlorine consumption.

The chlorine consumption of urea plateaued at 24 h, whereas the consumption of L-histidine increased with increasing reaction time and plateaued at 120 h. These results indicate that individual substances show different reactivity to chlorine and therefore play different roles in the kinetic chlorine consumption of the mixture. For a clearer illustration, time-course contribution percentages were calculated, that is, the chlorine consumption of individual substances divided by the summation of all substance consumption (total consumption) at the corresponding time, as shown in Figure 2(b).

Urea contributed 78.9% to the total consumption at 4 h, while it was 70.4% at 168 h. Uric acid also showed slight decreasing percentages, that is, from 4.5% at 4 h to 4.3% at 168 h. The decreasing percentages may indicate that urea and uric acid were responsible for the total chlorine consumption in the early phase of the reaction. Conversely, the total chlorine consumption contributed by creatinine, HA, and L-histidine increased until 72 h and remained fairly stable until 168 h, indicating that they were responsible for the total chlorine consumption in the later reaction phase. Therefore, the reactivity of chlorine with creatinine, HA, and L-histidine may be slower than that with urea. These hypotheses are further discussed in Section 3.1.3 by deriving their respective reaction rate coefficients.

To determine the chlorine decay reaction rate coefficient for each substance, the proposed model (Equation (1)) was applied individually to the decay dataset obtained from experiment series II. The chlorine demand of i^th reactant, as required by Equation (2), was calculated as the DOC concentration of an individual substance (DOC = 2 mg/L, experiment series II) multiplied by their corresponding specific chlorine demand (Figure 1(b)). The best-fit parameters of and for each substance were obtained by curve fitting. The variable reaction rate coefficient of chlorine with respect to the ith reactant was calculated using Equation (2). The values of the best-fit parameters and ⁠, chlorine demand and rate coefficient are listed in Table 3.

Table 3

Best-fit model parameters α and β, overall reaction rate coefficient of chlorine decay, chlorine demand, and corresponding R² and RMSE with respect to individual substances and substance mixture

.	.	.	.	.	.	RMSE .
Substance (⁠⁠) .	L/mg/h .	.	L/mg/h .	mg/L .	R2 .	mg/L .
Uric acid	2.81 × 10−2	3.85	2.81E-2–6.06 × 10−4	24.50	0.983	0.501
Urea	6.73 × 10−3	0.14	6.73E-3–5.85 × 10−3	39.00	0.994	0.576
L-histidine	4.22 × 10−3	0.32	4.22E-3–3.07 × 10−3	27.48	0.966	1.074
Creatinine	2.85 × 10−3	0.59	2.85E-3–1.58 × 10−3	22.79	0.990	0.856
Humic acid	2.81 × 10−3	0.97	2.81E-3–1.07 × 10−3	2.98	0.992	0.080
Hippuric acid	1.39 × 10−3	2.30	1.39E-3–2.57 × 10−4	2.34	0.874	0.345
Citric acid	4.25 × 10−4	0.41	4.25E-4–2.87 × 10−4	9.25	0.979	0.481
Ammonia	7.10 × 10−3	3.67	7.10E-3–1.94 × 10−4	3.30	0.964	0.123
Mixture					R2	RMSE
	L/mg/h		L/mg/h	mg/L		mg/L
BFA	–	–	6.52E-3–2.88 × 10−4	42.20	0.994	1.122
BFA + HA	–	–	6.30E-3–9.20 × 10−4	47.35	0.994	1.155

.	.	.	.	.	.	RMSE .
Substance (⁠⁠) .	L/mg/h .	.	L/mg/h .	mg/L .	R2 .	mg/L .
Uric acid	2.81 × 10−2	3.85	2.81E-2–6.06 × 10−4	24.50	0.983	0.501
Urea	6.73 × 10−3	0.14	6.73E-3–5.85 × 10−3	39.00	0.994	0.576
L-histidine	4.22 × 10−3	0.32	4.22E-3–3.07 × 10−3	27.48	0.966	1.074
Creatinine	2.85 × 10−3	0.59	2.85E-3–1.58 × 10−3	22.79	0.990	0.856
Humic acid	2.81 × 10−3	0.97	2.81E-3–1.07 × 10−3	2.98	0.992	0.080
Hippuric acid	1.39 × 10−3	2.30	1.39E-3–2.57 × 10−4	2.34	0.874	0.345
Citric acid	4.25 × 10−4	0.41	4.25E-4–2.87 × 10−4	9.25	0.979	0.481
Ammonia	7.10 × 10−3	3.67	7.10E-3–1.94 × 10−4	3.30	0.964	0.123
Mixture					R2	RMSE
	L/mg/h		L/mg/h	mg/L		mg/L
BFA	–	–	6.52E-3–2.88 × 10−4	42.20	0.994	1.122
BFA + HA	–	–	6.30E-3–9.20 × 10−4	47.35	0.994	1.155

Note: the range of indicates the changes of rate coefficient from t= 0 h to t= 240 h; DOC of individual substance and HA were 2 and 1 mg/L, respectively; DOC of BFA (∑₇BFA) was 3 mg/L while it of BFA + HA was 4 mg/L.

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Based on Equation (2), is equal to the initial ⁠, indicating reflects the initial reaction rate when ⁠. Uric acid exhibited the highest ⁠, which is consistent with the conclusions in the literature that uric acid appears to consume free chlorine faster than most other organic-N precursors (Li & Blatchley 2007; Lian et al. 2014). Ammonium chloride and urea showed the second and third highest values of ⁠, respectively, which were an order of magnitude lower than ⁠. The calculated confirmed the assumption derived from the results of experiment series I, that is, the reactivity of chlorine with urea may be faster than that of creatinine, HA, and L-histidine. α values of hippuric acid and citric acid showed the lowest reactivity toward chlorine consumption compared with that of the other BFA components.

As all the synthesized samples were prepared with ultrapure water, which does not contain bromide, only TCM was detected in all the THM species. Specific TCMFP was calculated as TCMFP divided by the corresponding DOC concentration (μmol TCM/mg C). Citric acid exhibited considerably higher specific TCMFP at 10.6 μmol/mg C than that of all the other individual BFA components despite its low chlorine consumption. HA showed the second-highest value of specific TCMFP at 0.82 μmol/mg C, which was approximately 2.5 times higher than that of BFA at 0.45μmol/mg C. This indicates that HA resulted in more TCM formation than BFA did. Therefore, controlling the organic precursor in the filling water is helpful in decreasing TCM formation in pool water.

Although citric acid contributed the least to chlorine consumption, over 50% of the total TCM was formed due to the presence of citric acid. Approximately 90% of total TCM formation was attributed to the presence of citric acid and HA. Urea, hippuric acid, and creatinine were responsible for 64% of the total DOC of BFA + HA whereas <10% of TCM formation was caused by these components. Moreover, the time-course contribution of HA and citric acid to total TCM formation showed an adverse trend. Specifically, the contribution percentage of HA decreased, while that of citric acid increased with increasing reaction time. This suggests that HA may be responsible for total TCM formation in the early phase of the reaction. This hypothesis was further confirmed by deriving reaction rate coefficients.

The proposed model (Equation (3)) was applied to each TCM formation dataset of an individual substance obtained from experiment series II. The best-fit parameters of γ [L/μmol/h] and θ were determined by curve fitting, as shown in Figure 3. The of individual substance i was experimentally determined. The variable reaction rate coefficient of TCM formation was calculated by applying the best-fit parameters to Equation (4). The values of the best-fit parameters, and are shown in Table 4.

Table 4

Best-fit model parameters and θ, reaction rate coefficient of TCM formation, TCM formation potential, and corresponding R² and RMSE with respect to individual substances and mixture

.	.	.	.	.	.	RMSE .
Substance (⁠⁠) .	L/μmol/h .	.	L/μmol/h .	μmol .	R2 .	μmol/L .
Uric acid	7.83 × 10−5	0.95	7.83E-5–3.11 × 10−5	0.06	0.964	0.004
Urea	1.69 × 10−4	1.53	1.69E-4–4.18 × 10−5	0.05	0.902	0.005
L-histidine	3.92 × 10−5	0.00	3.92E-5–3.92 × 10−5	0.39	0.896	0.050
Creatinine	2.88 × 10−5	0.35	2.88E-5–2.10 × 10−5	0.07	0.956	0.005
Humic acid	1.33 × 10−4	1.70	1.33E-4–2.44 × 10−5	0.82	0.997	0.010
Hippuric acid	3.73 × 10−5	1.33	3.73E-5–1.11 × 10−5	0.05	0.947	0.004
Citric acid	5.72 × 10−5	0.00	5.32E-5–5.32 × 10−5	19.70	0.948	0.176
mixture					R2	RMSE
	L/μmol/h		L/μmol/h	μmol		μmol/L
BFA	–	–	5.55E-5–4.89 × 10−5	1.72	0.981	0.069
BFA + HA	–	–	8.36E-5–6.95 × 10−5	2.54	0.959	0.124

.	.	.	.	.	.	RMSE .
Substance (⁠⁠) .	L/μmol/h .	.	L/μmol/h .	μmol .	R2 .	μmol/L .
Uric acid	7.83 × 10−5	0.95	7.83E-5–3.11 × 10−5	0.06	0.964	0.004
Urea	1.69 × 10−4	1.53	1.69E-4–4.18 × 10−5	0.05	0.902	0.005
L-histidine	3.92 × 10−5	0.00	3.92E-5–3.92 × 10−5	0.39	0.896	0.050
Creatinine	2.88 × 10−5	0.35	2.88E-5–2.10 × 10−5	0.07	0.956	0.005
Humic acid	1.33 × 10−4	1.70	1.33E-4–2.44 × 10−5	0.82	0.997	0.010
Hippuric acid	3.73 × 10−5	1.33	3.73E-5–1.11 × 10−5	0.05	0.947	0.004
Citric acid	5.72 × 10−5	0.00	5.32E-5–5.32 × 10−5	19.70	0.948	0.176
mixture					R2	RMSE
	L/μmol/h		L/μmol/h	μmol		μmol/L
BFA	–	–	5.55E-5–4.89 × 10−5	1.72	0.981	0.069
BFA + HA	–	–	8.36E-5–6.95 × 10−5	2.54	0.959	0.124

Note: the range and indicate the changes of rate coefficient from t= 0 h to t= 240 h; the and for substance mixture are calculated.

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As shown, γ is equal to the initial ⁠, which indicates that γ reflects the initial rate coefficient at t= 0. Urea showed the highest initial rate coefficient, followed by HA, which was an order of magnitude higher than those of the other BFA components. Moreover, the initial γ_HA was higher than that of citric acid, which agrees with the observations and assumptions obtained from experiment series I (Section 3.2.2), that is, HA may have a higher reactivity toward TCM formation than citric acid does. Although citric acid exhibited the highest specific TCMFP, its rate coefficient was not the highest. This implies that citric acid may be responsible for TCM formation at the slow phase when the circulation time of swimming pool water is long. Moreover, citric acid and histidine show the rate constant (θ = 0), while HA shows the higher θ value indicating the HA rate coefficient varied with reaction time. This may be due to the heterogeneous characteristics of HA. HA contains different reactive sites compared with citric acid and histidine.

The goodness of curve fitting is shown in Figure 4 for the TCM formation of all substances. Graphically, the model accurately describes the experimental data. The values of R² ranged from 0.89 to 0.99, indicating a moderate to good simulation (Table 4). The RMSE was observed to range from 0.004 to 0.17 μmol/L. These results indicated that the model successfully simulated the experimental datasets.

As the model parameters and for individual substances are determined, the reaction rate coefficients for substance mixture can be calculated according to Equation (6). Then, the kinetics of TCM formation with respect to BFA and BFA + HA can be predicted by applying Equation (8). The TCMFP used for model prediction is shown in Table 4.

Figure 4(b) shows the experimental and predicted TCM formation results for BFA and BFA + HA as a function of time. The TCM formation profiles are characterized by an initial fast consumption stage and a later slower formation stage. A good to moderate agreement of TCM concentration was found between experimental data and model predictions for BFA and BFA + HA with R² values of 0.98 and 0.95, respectively. Although the RMSE ranged from 0.07 to 0.12 μmol/L, it falls in typical precision with 5% error. Thus, graphical and quantitative analyses confirmed an accurate fit to the experimental data.

This study investigated the reactivity of substances remaining in swimming pool waters toward chlorine consumption and TCM formation. Kinetic experiments were conducted to derive the rate coefficients of individual substances. Based on the obtained individual rate coefficients, the proposed models were used to simulate the chlorine consumption and TCM formation of substance mixtures, that is, BFA (mixture) and a BFA and HA mixture (BFA + HA).

The results showed that urea exhibited the highest DOC-related specific chlorine demand, which is attributed to its higher nitrogen concentration than other BFA components. BFA was more reactive than HA toward chlorine consumption. However, the specific TCMFP of HA was approximately 2.5 times higher than that of BFA, indicating that HA is more reactive toward TCM formation. Citric acid showed a considerably higher specific TCMFP than other BFA components. Uric acid exhibited the fastest initial rate coefficient of chlorine decay, which was an order of magnitude higher than those of hippuric and citric acids. Regarding TCM formation, urea and HA were attributed to the fast-reacting TCM formation precursors, which were a magnitude higher than that of citric acid.

For substance mixtures, a hypothesis was proposed to calculate the (overall) rate coefficient, that is, the rate coefficients of the mixture depend on the rate coefficient of the individual substance and the concentration of the substance remaining in the water. This hypothesis and the obtained rate coefficient of the individual substances were validated by simulating the kinetics of chlorine consumption and TCM formation with respect to BFA and BFA + HA. It was found that the model provided excellent simulation results.

The work was jointly supported by the National Natural Science Foundation of China (Grant No.: 22006041); Guangdong Basic and Applied Basic Research Foundation (Grant No.: c212019102500000020, 2020A1515111128) and Guangzhou Basic and Applied Basic Research Foundation (Grant No.: 202002030169). Part of the experimental work was conducted in Dresden University of Technology, the first author thanks the support.

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

The authors declare there is no conflict.