Variability of residual chlorine in swimming pool water and determination of chlorine consumption for maintaining hygienic safety of bathers with a simple mass balance model

Trial-and-error chlorination as a conventional practice for swimming pool water disinfection may fail to consistently maintain the pool’s residual chlorine within regulatory limits. This study explored the variability of residual chlorine and other common water quality parameters of two sample swimming pools and examined the potential of using a mass balance model for proactive determination of chlorine consumption to better secure the hygienic safety of bathers. A lightly loaded Pool 1 with a normalized bather load of 0.038 bather/m/day and a heavily loaded Pool 2 with a normalized bather load of 0.36 bather/m/day showed great variances in residual free and combined chlorine control by trial-and-error methods due to dynamic pool uses. A mass balance model based on chemical and physical chlorine consumption mechanisms was found to be statistically valid using field data obtained from Pool 1. The chlorine consumption per capita coefficient was determined to be 4120 mg/bather. The predictive method based on chlorine demand has a potential to be used as a complementary approach to the existing trial-and-error chlorination practices for swimming pool water disinfection. The research is useful for pool maintenance to proactively determine the required chlorine dosage for compliance of pool regulations. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/wh.2018.217 ://iwaponline.com/jwh/article-pdf/17/2/227/845998/jwh0170227.pdf Alvyn P. Berg Ting-An Fang Hao L. Tang (corresponding author) Environmental Engineering Program, Indiana University of Pennsylvania, Indiana, Pennsylvania 15705, USA E-mail: htang@iup.edu This article has been made Open Access thanks to the generous support of a global network of libraries as part of the Knowledge Unlatched Select initiative.

In addition, NSPF defines an ideal free chlorine range of 2-4 mg/L. It is important to note that these guidelines on residual chlorine are routinely exceeded in pools (Bradford ). According to CDC, approximately 1 in 10 (10. Operation of swimming pools generally involves constant recirculation of water (at an elevated temperature for heated pools) and unavoidable continual loading of anthropogenic organics from bathers. It is common for many pools to be used for several years before a total water replacement is conducted (Afifi & Blatchley III ). Thus, significant chlorine consumption arises from the reactions between chlorine and the bather load, which include sweat, urine, skin particles, hair, microorganisms, cosmetics, and other personal care products (Judd & Bullock ). Additionally, chlorine consumption could be promoted by UV exposure for outdoor pools, elevated temperature, and water agitation induced volatilization through an air-water interface (Weng & Blatchley III ; Weng et al. ; Chowdhurry et al. ). Therefore, the residual chlorine maintaining practice needs to consider the chlorine consumption mechanisms. This is important for compliance of pool regulations, reduction of disinfection byproducts formation, and economization of free chlorine usage.
The current residual chlorine maintaining practices can be classified into manual and automatic chlorine dosing, both of which are based on trial-and-error methods.
Manual chlorine dosing is a conventional method for maintaining residual chlorine in small pools such as pools in private residential homes. The amounts of dosed tablet chlorine (i.e. Ca(ClO) 2 ) are empirically determined and the pool can be easily overdosed or insufficiently dosed.
Automatic dosing reduces manpower and is more applicable to larger pools. It may use an oxidation-reduction potential (ORP) controller or a digital timer to turn on/off the chlorine dosing pumps. The ORP controller functions by measuring the ORP of the water, comparing it to a manually maintained set point, and adding chlorine if the measured ORP falls below the set point. An ORP controller may cease to control the residual chlorine if an undesirable reaction couple dominates the ORP of the water (Bradford ).
Automatic feeding of chlorine on a digital timer may also fail during certain periods when the timer is not properly programmed to match the dynamic pool uses. Since the use of trial-and-error methods for residual chlorine control is reactive, it would be desirable to have an unconventional method that can proactively determine the chlorine con-

Swimming pools under investigation
Two sample swimming pools in Indiana, Pennsylvania were selected for the investigation. Both pools were indoor heated pools and similar water temperatures (28.6 C for Pool 1 and 29.8 C for Pool 2 on average) were maintained throughout the experimental period. In addition, they had similar water ages, since the total water replacement had not been conducted for approximately one year. The notable differences of the two pools were the size, bather load and the chlorine dosing method. A description of the two pools is summarized in Table 1  To compensate for the water loss during the pools' operation, make-up water was added to both pools periodically at 1.9 and 1.7% (estimations on daily basis), respectively. Pool 1 used tablet chlorine which was initially dissolved by the recirculating pool water with an Accu-Tab chlorination system (Axiall Corporation, Georgia, USA). The chlorine tablets, weighing 330 g each, were commercially available Accu-Tab blue calcium hypochlorite tablets with minimum 65% available chlorine. The application of ORP controller resulted in a tablet consumption rate of 36 tablets per month. The controller also regulated the dosing of CO 2 for pH control with a pH sensor, which depleted a 22.7 kg CO 2 gas cylinder every week. The set points of the controller were 7.5 pH and 650 mV ORP. Pool 2 used liquid chlorine at a NaClO con-  (1)) that was used to describe the presence of chlorine in pool water: The statistical modeling process examined the p-value of any not-yet-determined coefficient to test the hypothesis that the model coefficient was significantly different from zero, and the null hypothesis can be rejected if the p-value was less than 0.05. The Durbin-Watson statistic, a measure of serial correlation between the residuals, was used to test residuals for their independence of each other. If the residuals were not correlated when the independent variable was time, and the deviation between the observation and the regression line at one time were not related to the deviation at the previous time, the Durbin-Watson statistic would be 2.
In addition, constant variance tests were performed by computing the Spearman rank correlation between the absolute values of the residuals and the observed value of the dependent variable. When this correlation was significant, the constant variance assumption may be violated, indicating a different model (i.e. one that more closely follows the pattern of the data) may be used, or a transformation of one or more of the independent variables may be used to stabilize the variance. Furthermore, the coefficient of determination (R 2 ) was used to measure how well the model described the data. An R 2 of one indicates that all the variability of dependent variables is addressed. The closer R 2 is to one, the better the model predicts the dependent variable.

RESULTS AND DISCUSSION
Variability of water quality in the lightly loaded Pool 1 with ORP controlled chlorine dosing The number of daily admitted bathers in Pool 1 ranged from 0 to 350 with an arithmetic mean of 34 and a standard deviation of 58 (Figure 2(a)).  Figure 2(b). Note that a pH below 7.2 may cause damage to the filtration components and pool surface as well as bather discomfort due to corrosive water, while a pH above 7.8 may cause cloudy water, inefficient use of sanitizer, bather discomfort, and scaling on the pool surface, pipes, and filtration components. In addition, the correlation between pH and disinfection by-products formation  ), we used k × n to describe the overall free chlorine consumption by the second and third processes, where k was the per capita free chlorine consumption rate constant in mg Cl 2 /bather and n was the number of bathers on any given day. Additionally, the term 'Chlorine Out' was neglected, considering there were no apparent water discharges from the pools. Therefore, Equation (1) became: where ΔCl 2 was the change in free chlorine amount in mg Cl 2 and a was the added free chlorine amount in mg Cl 2 .
The free chlorine change (ΔCl 2 ) was determined by the difference in residual free chlorine between any two closest sampling events. The chlorine addition (