Abstract

Water and energy balances in water distribution networks (WDNs) are commonly used for managing water and energy losses, respectively. Recently, a new approach, the chlorine mass balance, has been proposed to assess chlorine losses within WDNs. However, previous research did not account for changes in chlorine masses in pipes and tanks within the networks (∆M_N). In this study, we introduce ∆M_N as a new component in the revised chlorine mass balance and assess its significance by utilizing a simple WDN model with a downstream tank. Our findings reveal that the hourly magnitude of ∆M_N can be comparable to the other two primary components: the chlorine mass delivered to users, and chlorine mass losses by reactions. This underscores the importance of ∆M_N for the short-term assessments, particularly in cases involving intermittent water supply and pressure-loss events. During non-supply periods, chlorine concentrations in stagnant water within pipes and tanks decrease due to reactions, resulting in negative ∆M_N. When water supply resumes, a portion of the input chlorine mass is used to restore chlorine levels in WDNs, resulting in positive ∆M_N. ∆M_N fluctuates between positive and negative values with an average value around zero in continuously operating general WDNs. Therefore, if the balance is assessed over a long period with many cycles of periodic patterns, ∆M_N becomes less significant.

1 Introduction

Disinfection is a crucial water treatment process designed to ensure the quality of drinking water by eradicating harmful microorganisms responsible for waterborne diseases. Among the various disinfection methods, chlorination stands out as the most widely applied due to its cost-effectiveness and the residual protection it offers in water distribution networks (WDNs) (e.g., Gibbs et al. 2006; Farooq et al. 2008; Tsitsifli and Kanakoudis 2018). However, as drinking water travels from its source to consumers, chlorine interacts with dissolved organic and inorganic compounds in the water (Ozdemir and Buyruk 2018; Zhong et al. 2021). It also reacts with certain pipe materials, biofilm, and loose deposits (Monteiro et al. 2020; Minaee et al. 2019). These chemical reactions result in the decay of free residual chlorine over time.

The World Health Organization (WHO 2011) has recommended a minimum chlorine concentration of 0.2 mg/l to deactivate bacteria and some viruses responsible for waterborne diseases, as well as to safeguard water against recontamination during storage. Conversely, the U.S. Environmental Protection Agency (USEPA 2012) has advised a maximum concentration of 4.0 mg/l to mitigate health risks, such as the formation of harmful disinfection by-products. Maintaining the required chlorine concentrations and controlling by-products poses a challenging task for waterworks (Li et al. 2019). This task becomes even more formidable in intermittent water supply systems, where water stagnation in pipes can deplete chlorine residuals, heightening the risk of microbial regrowth and contamination (Bivins et al. 2021; Preciado et al. 2021).

Water quality models for assessing drinking water can be broadly classified into data-driven and physics-based approaches. Mounce et al. (2015) exemplified a data-driven approach by using hydraulic parameters (flow or pressure) to identify significant turbidity changes in water distribution networks. Wang et al. (2023) further demonstrated the potential of data-driven methods by successfully approximating physics-based chlorine models using system identification algorithms without relying on network parameters. Chhipi-Shrestha et al. (2023) provided a comprehensive review of the broader landscape of artificial intelligence applications in drinking water quality assessment.

For physical-based models, computerized WDN models, combined with water quality analysis modules, have demonstrated the capability to accurately simulate chlorine distribution (Kowalska et al. 2018; Fisher et al. 2021). Consequently, numerous modeling studies have been dedicated to optimizing chlorine and by-product concentrations in WDNs (Fisher et al. 2018; Javadinejad et al. 2019; Monteiro et al. 2020; Sharif et al. 2017; Yoo et al. 2018; Abokifa et al. 2019; Onyutha and Kwio‑Tamale 2022). In a recent study, Kongbuchakiat et al. (2022) utilized such modeling techniques to evaluate operational performance from a water quality perspective, proposing a target chlorine resilience index.

Recently, many studies have combined two approaches to analyze water quality. For example, Rajakumar et al. (2019) demonstrated the application of real-time chlorine concentration modeling in WDNs using the ensemble Kalman filter (EnKF) for state and parameter estimation. The results indicate that the EnKF provides reliable and accurate estimates for both water quality parameters and system states, allowing for improved monitoring and management of WDNs. Pérez et al. (2022) investigated the supervision of chlorine concentration distribution throughout a full-scale WDN. They utilized on-line data from specific locations to dynamically calibrate the kinetic chlorine decay coefficient using principal component analysis. The calibrated coefficient was subsequently input into EPANET for network-wide supervision.

However, most modeling studies have not addressed how chlorine is lost within WDNs. In WDNs, water balance plays an essential role in assessing water losses (Alegre et al. 2016; AWWA 2016), and energy balance does a similar task for energy assessment (Cabrera et al. 2010; Lapprasert et al. 2018; Lipiwattanakarn et al. 2019; Lipiwattanakarn et al. 2021a). Lipiwattanakarn et al. (2021b) introduced the pioneering concept of the chlorine mass balance to evaluate chlorine losses in networks. This concept involves dividing the chlorine mass input from sources into three primary components: mass delivered to users, outgoing mass through water losses, and mass losses due to chemical reactions. Using a district metering area as an illustrative example, their concept could classify and quantify chlorine mass losses in detail. Importantly, their concept not only assesses how chlorine is lost, but can also be utilized to estimate by-product mass because by-products typically form as a result of chlorine decay processes (Li et al. 2019; Quintiliani et al. 2018). Most recently, Wongpeerak et al. (2023) introduced a novel theoretical framework for estimating chlorine balance components in WDNs using graph-based analysis. By analyzing simulated chlorine mass balance results from 20 real district metering areas, the authors proposed simplified equations that can estimate chlorine mass losses without the need for complex network simulations.

According to Cabrera et al. (2010), the variation in water volume and potential energy stored in downstream tanks over a given period, defined as net flow of water and energy compensation, respectively, must be considered in short-term water and energy balance assessments. This is because water and potential energy stored in the elevated water of the tank can offset the inflow and input energy required for the network. However, when integrated over a long enough period, the net flow and energy compensation by the tanks approach zero, thus negating their contribution to long-term analysis. Investigating Lipiwattanakarn et al.’s (2021b) chlorine balance in detail, we found that changes in chlorine masses in pipes and downstream tanks were not considered in their balance, along with chlorine mass losses due to reactions in tanks. Consequently, their concept was limited to long-term assessment without downstream tanks. In this study, we extend their concept by including the estimation of these components and present a short-term assessment of a simple WDN with a downstream tank.

2 Methodology

2.1 Revised free residual chlorine mass balance

Figure 1 presents a conceptual schematic illustrating the mass transport of free residual chlorine in a WDN with a downstream tank. The system input mass (M_IN) from the source enters the WDN and is stored in the pipes as M_N,P. During transport in the pipes, chemical reactions cause a reduction in mass, defined as M_RT,P. A portion of the remaining mass is delivered to users (M_U), while some may exit the WDN through leaks, designated as M_WL. In the presence of a downstream tank, there is an exchange of water and chlorine mass between the pipes and the tank. The tank receives and returns mass from the pipes, corresponding to its water inflow and outflow of the tank. Additionally, the mass in the tank (M_N,T) can be reduced by the chemical reactions in the tank (M_RT,T).

Figure 1 Conceptual schematic of free residual chlorine mass balance in water distribution network with downstream tank.

Table 1 shows the revised chlorine mass balance proposed in this study for short-term assessments. The previous chlorine mass balance by Lipiwattanakarn et al. (2021b) assumed the system input mass (M_IN) to be equal to the system output mass, divided into three components: M_U, M_WL, and M_RT. However, under the unsteady-state mass transport where the input mass does not equal the output mass, the change in mass in the network (control volume) must be accounted for. Therefore, we introduce ∆M_N, representing the chlorine mass changes for a defined time period. ∆M_N can be further broken down into the mass changes occurring in pipes (∆M_N,P) and tanks (∆M_N,T).

Table 1 Revised free residual chlorine mass balance and components by adding new components (shaded).

System input mass (MIN)	Mass delivered to users (MU)
	Outgoing mass through water losses (MWL)
	Mass losses by reactions (MRT)	Mass losses by reactions in pipes (MRT,P)
		Mass losses by reactions in tanks (MRT,T)
	Mass changes in networks (∆MN)	Mass changes in pipes (∆MN,P)
		Mass changes in tanks (∆MN,T)

A calibrated hydraulic simulation model is required to evaluate each component for a defined time period. Let t represent time. To perform the simulation over an extended period starting from the initial time (t_o) to the final time (t_f), the model must be stimulated in time intervals (Δt) to obtain dynamic results that reflect the time-dependent change within the system. Thus, the total number of time steps (n_t) will equal (t_f - t_o)/Δt+1).

The methods to calculate the components can be divided into three groups. The first group is the summation of the mass fluxes getting into or out of a WDN at each time step (i_t). These components are M_IN, M_U, and M_WL, which can be computed as follows:

(1)

(2)

(3)

Where:

C	=	chlorine concentration, and
Q	=	discharge at a node.

While i_t, i_IN, i_U, and i_WL are the indices of time and the locations of chlorine inputs, users and water losses, respectively, n_t, n_IN, n_U, and n_WL are the total numbers of them, respectively.

The second group is the summation of mass losses by reactions at each pipe and tank of a network. They are M_RT,P, M_RT,T, and M_RT, which can be written as follows:

(4)

(5)

(6)

Where:

R	=	decay rate of chlorine by chemical reactions, and
∀	=	water volume in each section of the pipe or tank.

While i_P and i_T are the indices of pipes and tanks, respectively, n_P and n_T are the total numbers of them, respectively.

Finally, the last and new group is the changes of chlorine mass in WDNs. The mass change calculation deviates from the first two groups. Instead of a summation across all time steps, it involves calculating the difference in mass within the network (control volume) between the initial time (t₀) and final time (t_f), in accordance with the concept of Reynolds Transport Theorem for a control volume. 

Let’s define the chlorine mass in networks at time t as M_N(t). As supplied water with chlorine mass can be stored in pipes and tanks, M_N(t) can be divided into M_N,P(t) and M_N,T(t) for pipes and tanks, respectively. These components can be computed as follows:

(7)

(8)

(9)

Where:

iP and iT	=	pipe and tank indices, respectively,
nP and nT	=	total number of pipe sections and tanks, respectively,
and	=	chlorine concentrations in pipe iP and tank iT, respectively, and
and	=	water volumes in pipe iP and tank iT, respectively.

Thus, the changes of chlorine mass (∆M_N, ∆M_N,P, and ∆M_N,T) between the initial and final times can be calculated as follows:

(10)

(11)

(12)

Where:

to and tf

=

initial and final times, respectively.

While positive values of ∆M_N, ∆M_N,P, and ∆M_N,T indicate increases in the chlorine mass in water volume, negative values imply decreases.

∆M_N,T is similar to the energy compensation of downstream tanks defined by Cabrera et al. (2010). However, they neglected the energy changes in pipes over a given period, akin to ∆M_N,P. This omission was possibly due to hydraulic modeling for a given period typically being a steady-state extended-period simulation. Thus, the simulated input and output energies balance each other without considering the energy changes in pipes due to the steady-state assumption. However, water quality modeling cannot rely on the steady-state assumption because of the chlorine mass transport in WDNs.

2.2 Water distribution system model

In this study, we employed the WNTR package in Python (Klise et al. 2020), which is compatible with the EPANET software (Rossman 2000), for both hydraulic and water quality modeling. Unlike the steady-state hydraulic solver, the water quality solver uses the principle of mass conservation coupled with reaction kinetics under unsteady transport conditions. For instance, the transport phenomena in pipes can be expressed using the advective transport equation as follows:

(13)

Where:

Ci	=	concentration (mass/volume) in pipe i as a function of distance x, and time t,
ui	=	flow velocity (length/time) in pipe i, and
r	=	rate of reaction (mass/volume/time) as a function of concentration.

While diffusion is a physical process that can influence water quality, it is often omitted or simplified in pipe network models due to the dominance of advection in most areas. However, in dead-end areas with low velocities, diffusion has a more significant impact on water quality concentrations (Tzatchkov et al. 2002; Shang et al. 2021).

Dynamic models for simulating pipe systems can be broadly categorized into Eulerian and Lagrangian approaches. Eulerian-based models divide pipes into equal segments. The concentration within each segment is then transferred to the next downstream segment. However, Eulerian methods have drawbacks, such as numerical diffusion and difficulty tracking sharp fronts. Rossman and Boulos (1996) compared four models, two Eulerian-based and two Lagrangian-based, finding that the time-driven Lagrangian method was the most efficient.

The EPANET’s water quality solver was developed by Rossman and Boulos (1996) drawing upon earlier work by Liou and Kroon (1987). It uses a Lagrangian time-based approach to track the fate of discrete segments of water as they move along pipes and mix at junctions between fixed-length time steps. However, this approach does not conserve constituent mass. Davis et al. (2018) showed that the EPANET’s water quality solver can experience mass imbalances during simulations, leading to errors in concentration estimates, especially when time steps are too long. They recommended that, to ensure mass balance, the water quality time steps should be shorter than the time required for a water parcel to move through the network pipe segment (link) with the shortest travel time for the simulation (the minimum residual time).

In this study, we use the EPANET’s example network 1 “Net1.inp”, included in the software installation (Rossman 2000), to demonstrate our chlorine mass balance concept with a time step of 1 min to ensure the conservation of chlorine mass because the minimum residual time in this network is found to be 2 mins. More details on the impact of different quality time steps on chlorine mass balance can be found in the supplementary material. The network configuration with its base demands and pipe diameters is shown in Figure 2. The network includes a source, a pump, a downstream tank and a network with demands at each junction. The base demand at each junction is between 100–200 gpm (379–757 lpm) shown in Figure 2A, and the diameter at each pipe is between 6–18 in (152–457 mm) in Figure 2B.

Figure 2 Network configuration with (A) base demands, and (B) pipe diameters.

3 Results and discussion

3.1 Temporal variations of flows, chlorine concentrations, and chlorine masses

The simulation runs for 96 hrs (4 days), with hourly results recorded. Figure 3 illustrates chlorine concentration distributions at two time points: the initial stage (Day 1, 12:00 AM), and the stage after the simulation for 72 hrs (Day 4, 12:00 AM). Initially, chlorine concentrations at all nodes are set to 0 mg/l to simulate the situation of very low concentration (Figure 3A), while the source provides water with a constant concentration of 1 mg/l. The network feathers no pressure-dependent flow (zero emitter coefficient), assuming no water loss, and, thus, node demands represent water delivered to users. A basic pump control system is applied in this study. The pump starts when the tank water level falls below 110 ft (33.53 m) and stops when the tank water level exceeds 140 ft (42.67 m). Consequently, the tank occasionally solely supplies water to the users. During that period, the network receives water with a lower concentration than the source, as depicted in Figure 3B. At Day 4, 12:00 AM, the pump stopped, and water was supplied by the tank. Chlorine concentrations range from 0.09 and 0.17 mg/l at junctions and pipes. The hourly results for a 96-hour duration are used for the analysis of the chlorine mass balance in the following section.

Figure 3 Free residual chlorine concentration distributions at (A) Day 1, 12:00 AM (initial conditions), and (B) Day 4, 12:00 AM (at 72 hr).

Figure 4 shows the flow patterns of the source, the tank, and the demand. Since the demand pattern is set to a 24-hour cycle, the patterns of both the source and the tank exhibit approximately 24-hour cycles as well. The source inflow, regulated by the pump, varies between 0 and 1,900 gpm. As described earlier, the pump stops when the tank water level reaches 140 ft; thus, the tank will solely feed the network demands until the tank water level drops below 110 ft. Meanwhile, the tank inflow fluctuates between -1,000 and 1,100 gpm, with negative values indicating tank replenishment. Notably, a gradual shift in pump start from prior to midnight to after midnight is due to the initial conditions, and it persists for several days before the results stabilize into a fully periodic 24-hour cycle. Throughout the simulation, the demand peaks at 1,760 gpm from 6:00 AM to 7:00 AM. It gradually decreases to a minimum of 440 gpm from 6:00 PM to 7:00 PM and subsequently rises back to its peak.

Figure 4 Time series of inflows from source and tank.

Figure 5 illustrates the variations in chlorine concentrations at the source, the tank and the critical chlorine point (CCP) during the simulation. The source maintains a constant chlorine concentration of 1 mg/l, while the tank and CCP concentrations are initially set to 0 mg/l. These results demonstrate how the system recovers from a complete absence of chlorine in the network, simulating a scenario where a failed system is rebooted. The extended-period simulation indicates that the system reaches a completely 24-hour periodic state after 10 days. However, the focus of our investigation will be on the initial 4 days, examining the system’s immediate response to this failure scenario. The tank’s concentration gradually increases over time as the tank is replenished with chlorinated water from the source. Notably, after reaching the completely periodic state, the tank's chlorine concentration fluctuates within a 24-hour period, ranging between 0.23 mg/l and 0.27 mg/l due to the balance between chlorine input and the decay reactions within the tank. However, the critical chlorine point exhibits a broader concentration range, spanning from 0.1 mg/l to 0.4 mg/l after reaching the completely periodic state. This variability is attributed to the fact that when the critical chlorine point receives water directly from the source, the chlorine concentration is notably high due to its short travel time from the source to the user. Conversely, when water is from the tank, users receive water with a lower chlorine concentration.

Figure 5 Time series of chlorine concentrations at source, tank, and critical point.

Figure 6 shows the hourly variations in each chlorine component, as outlined in the revised chlorine balance in Table 1. As previously mentioned, to assess the short-term chlorine mass balances, the changes in chlorine mass in the network (∆M_N) are crucial, where ∆M_N = M_IN - M_U - M_RT. The previous study (Lipiwattanakarn et al. 2021b) assumed that ∆M_N = 0, making their approach unsuitable for this case. In Figure 6A, we observe the primary input and output components (M_IN, M_U, M_RT and ∆M_N). Initially, M_IN supplies approximately 400 g/hr of chlorine mass flux from the source. When the pump stops as per the simple control system, the network ceases to receive water from the source, resulting in M_IN reaching zero. Instead, the network receives water from the tank, characterized by a low chlorine concentration. Consequently, ∆M_N undergoes an abrupt transition from a positive value to a significantly negative value as network concentrations experience a sudden and substantial drop. Additionally, both M_U and M_RT rapidly decrease. Conversely, when the pump restarts, and the network once again receives water with a high chlorine concentration from the source, ∆M_N undergoes an abrupt shift from a negative value to a substantial positive value. This shift is followed by a rapid increase in both M_U and M_RT. Thus, it becomes evident that the input chlorine mass from the source is primarily utilized to restore chlorine mass levels within the network, resulting in a notably positive ∆M_N before it is delivered to users as M_U. This phenomenon suggests that, particularly in cases of intermittent water supply and pressure-loss events, where network concentrations are low, a portion of the input chlorine mass is essential to replenish chlorine levels in water distribution networks before users can access it. Furthermore, as chlorine concentrations within the network increase, chlorine decay rates also rise, leading to an increase in M_RT. Additionally, the demand pattern depicted in Figure 4 influences the patterns of M_U and ∆M_N.

Figure 6B displays the output subcomponents (M_RT,P, M_RT,T, ∆M_N,P, and ∆M_N,T). These components are intricately tied to chlorine decay rates, which are, in turn, linked to concentration levels. M_RT,P is high when the source provides inflow with a high chlorine concentration, and it is low when the inflow is from the tank with a low chlorine concentration. Therefore, hourly M_RT,P ranges between 0 and 150 g/hr. In contrast, M_RT,T is influenced by the gradual increase in concentration within the tank, as shown in Figure 5. Notably, M_RT,P is found to be higher than M_RT,T because the average concentration in the pipes (0.45 mg/l) exceeds that of the tank (0.14 mg/l). Therefore, the overall chlorine decay rate in the pipes is well higher than that in the tank. ∆M_N,P and ∆M_N,T are computed as the differences of chlorine masses in pipes and tanks at the present time and the next time step, respectively. ∆M_N,P solely depends on the overall concentration change in the pipes because the water volume in the pipes does not change. The sudden decrease in ∆M_N,P occurs due to the shift from high-concentration water from the source to low-concentration water from the tank. Conversely, the abrupt increase in ∆M_N,P is caused by the reverse switch, where high-concentration water from the source again dominates the pipe network. However, ∆M_N,T depends on both concentration and water volume in the tank. When the network uses tank water, ∆M_N,T turns to be negative. On the other hand, ∆M_N,T is positive when water with chlorine fills the tank.

Figure 6 Time series of chlorine mass components, where (A) is main input and output components (M_IN, M_U, M_RT, and ∆M_N), and (B) is detailed output components (M_RT,P, M_RT,T, ∆M_N,P, and ∆M_N,T).

3.2 Free residual chlorine balance

Table 2 presents the simulation results of the chlorine mass balance for two days: (A) day 1, and (B) day 4. In this example, where no water loss is assumed, there is no outgoing chlorine mass through water loss (M_WL) as shown in Table 1. In the day 1 balance results (Table 2A), where the initial chlorine concentration is 0 mg/l, ∆M_N constitutes 18.1% of M_IN, indicating that a part of M_IN is used to restore the chlorine concentration within the network from its initial zero value. Moreover, ∆M_N is half the magnitude of both M_U and M_RT. While the hourly ∆M_N values in Table 2A demonstrate a similar magnitude to the hourly M_U and M_RT values, the daily ∆M_N magnitude is smaller. This discrepancy arises from the fact that hourly ∆M_N fluctuates between positive and negative values, while hourly M_U and M_RT consistently remain positive. Consequently, when these hourly values are summed, ∆M_N turns out to be smaller than M_U and M_RT.

In Table 2B, representing the day 4 balance, we observe a slight increase in M_IN due to a small rise in the inflow from the source. Similarly, M_U and M_RT increase, reflecting the higher chlorine concentration within the network compared to day 1. However, ∆M_N experiences a substantial decrease, constituting only 3.6% of M_IN. This decline can be attributed to the chlorine concentration within the network approaching a 24-hour periodic pattern, leading M_IN ≅ M_U + M_RT. Our findings underscore the significance of ∆M_N, particularly in cases where water quality simulations lack complete periodicity, such as intermittent water supply and pressure-loss events. In such cases, ∆M_N emerges as a crucial component that cannot be overlooked in the chlorine mass balance and assessment. Nevertheless, it is important to note that ∆M_N may not be necessary for the chlorine assessment when evaluated from a long-term perspective. Omitting ∆M_N in long-term assessments is akin to the negligible energy compensation in downstream tanks, as recommended by Cabrera (2010) in long-term energy assessments.

Table 2 Chlorine mass balance and components with downstream tanks for: (A) day 1, and (B) day 4.

(A) day 1

MIN 5.7 kg (100%)	MU 2.4 kg (42.4%)
	MRT  2.2 kg (37.3%)	MRT,P 2 kg (34.3%)
		MRT,T 0.2 kg (3.0%)
	∆MN  1.1 kg (18.1%)	∆MN,P 0.6 kg (10.2%)
		∆MN,T 0.5 kg (7.9%)

(B) day 4

MIN 6.1 kg (100%)	MU 2.8 kg (46.3%)
	MRT  3.1 kg (50.2%)	MRT,P 2.4 kg (38.3%)
		MRT,T  0.7 kg (11.8%)
	∆MN  0.23 kg (3.6%)	∆MN,P 0.03 kg (0.4%)
		∆MN,T 0.2 kg (3.2%)

4 Conclusions

This study presents a revised chlorine mass balance designed for short-term chlorine assessment in water distribution systems. This revised balance introduces a novel component, the chlorine mass changes in networks (∆M_N), which further breaks down into two subcomponents: the mass changes in pipes (∆M_N,P), and the mass changes in tanks (∆M_N,T). These terms become particularly significant when the simulation period lacks complete periodicity, as is often the case in scenarios such as intermittent water supply or pressure-loss events. During such periods, the chlorine concentration and mass in stagnant water stored in pipes and tanks can substantially decrease. When the system resumes operation, a notable portion of the chlorine mass input is allocated to restoring chlorine concentration and mass in pipes and tanks to their normal levels before reaching users. Furthermore, in the context of short-term energy balance and assessment, it becomes essential to consider energy changes in networks, mirroring the approach with ∆M_N. In conclusion, this revised chlorine mass balance presents accountable and efficient chlorine management in water distribution networks, allowing for precise quantification of each component of the chlorine mass input and output, even when assessed on an hourly timescale.

To enhance water quality management through effective chlorine use, chlorine mass balance can be a valuable tool in assessing the causes of chlorine loss across various processes and components. Future research should focus on further delineating the details of each process. For instance, the reaction component could be divided into decays due to bulk and wall processes, and the outgoing chlorine mass attributed to water losses could be classified into real and apparent losses. Consequently, water quality audits could become as well-established as water and energy audits, conducted annually.

Acknowledgments

This research is supported by the Metropolitan Waterworks Authority Thailand (MWAIT), grant number 32/2566. N. Charuwimolkul is supported by the Faculty of Engineering, Kasetsart University, grant number 65/04/WE/D.Eng.

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Supplementary material

Impact of different quality time steps on chlorine mass balance

Figure S1 demonstrates the impact of different quality time steps on temporal chlorine concentrations at the critical pressure point. In the cases of the quality time steps (1 min and 30 s) lower than the minimum residual time (2 mins in this study), the graph shows identical chlorine concentrations, indicating no error attributable to the quality time step length.

Table S1 presents the impact of different quality time steps on chlorine mass balance on day 1 of the simulation. In the case of the quality time step of 1 min, the balance shows no error. However, when the quality time step equals 20 mins, the error between the system input mass (M_IN) and the sum of the system output mass (M_U + M_RT + ∆M_N) is 0.3 kg (5.3%).

Figure S1 Time series of chlorine concentrations at the critical pressure point at different quality time steps.

Table S1 Chlorine mass balance and components with downstream tanks on day 1 at different quality time steps.

(A) time step = 1 min

MIN 5.7 kg (100%)	MU 2.4 kg (42.4%)
	MRT 2.2 kg (37.3%)	MRT,P 2 kg (34.3%)
		MRT,T 0.2 kg (3.0%)
	∆MN 1.1 kg (18.1%)	∆MN,P 0.6 kg (10.2%)
		∆MN,T 0.5 kg (7.9%)

(B) time step = 20 mins

MIN 5.7 kg (100%)	MU 2.3 kg (40.4%)
	MRT 2.1 kg (36.8%)	MRT,P 1.9 kg (33.3%)
		MRT,T 0.2 kg (3.5%)
	∆MN 1.0 kg (17.5%)	∆MN,P 0.6 kg (10.5%)
		∆MN,T 0.4 kg (7.0%)
	Error 0.3 kg (5.3%)