Abstract
As operational scientists the authors know well from experience that apparently well-run treatment works can have the occasional coliform failure but all the resamples are compliant.
This paper explores why, in the authors’ opinion, this is a consequence of the underpinning disinfection kinetics and two major operational factors, pH and actual retention times.
In most cases, drinking water disinfection kinetics are first order and take the form . The key point is that such equations are asymptotic towards zero, that is they get closer and closer to zero but never reach it. This means that we can never be sure that all coliforms and E. col have been removed by the disinfection process.
The Chick-Watson equation expands on this to include the effect of chlorine concentration and the effect of water quality and is expressed as N_{t} = N_{0 }e^{(-λct)}. This introduces the idea that disinfection is dependent on both chlorine concentration, c, and contact time, t..
The water industry uses CT values as a measure of disinfection effectiveness, where C is the free chlorine residual in mg/l, T the contact time in minutes and the CT value is the product of the two.
The calculated value is compared against standard values for each water type (surface water and different qualities of ground water) such as those discussed in TWORT^{[1]}. The comparison helps a practitioner form a judgement on the effectiveness of the disinfection process.
The simpler version, which the author uses when introducing the subject to non-scientific staff, is that the chlorine residual must be “strong enough for long enough”, the phrase making the point that the disinfection process is not instantaneous but requires sufficient time to work in addition to the necessary level of chlorine.
The implication is that satisfactory disinfection can be achieved by a higher chlorine residual for a shorter time or a lower chlorine residual for a longer time. The choice is often decided by local factors such as flow rates and tanks sizes.
The aim of this paper is to help non-scientific operational staff understand the theory behind CT values, the factors that can significantly compromise the disinfection process, and how these might be managed in a practical operational manner to minimise the likelihood of bacteriological failures at treatment works.
The main considerations are that:
- 100% removal of Escherichia coli, also known as E. coli and coliforms in the disinfection process is not possible but understanding and managing the effect of pH and retention time on the disinfection process can reduce the likelihood of a bacteriological compliance failure.
- Many current measurement methods do not distinguish between the more powerful disinfectant, hypochlorous acid, and 80% less effective disinfectant, the hypochlorite ion. This can result in the C value being overestimated by up to 75%
- Not accounting for streamlining, that is water taking the easiest path, in contact tanks can cause CT values to be overestimated by up to 75%.
In an extreme case, a poorly baffled tank at pH 9.0, failing to account for the effect of pH and streamlining on retention times can reduce actual CT value to around less than 1% of the nominal CT value. Even at pH 7.5 in a moderately well baffled tank the actual CT value is about still only around 26% of the nominal CT value.
In both cases the disinfection efficiency is significantly compromised, making occasional compliance failures more likely. The paper discusses how these factors might be managed in a practical operational manner to minimise such occurrences.
Introduction
The authors, who have both been operational scientists at some time in their careers, know from experience that apparently well-run treatment works can have the occasional coliform failure but then all the resamples are compliant.
This not common but not unknown. DWI data^{[2]} shows that in the first quarter of 2020 there were no E. coli failures and seven coliform failures from the 44,805 samples taken. This is a failure rate of less than 0.02%.
While reducing the coliform failure rate further is likely to be an industry aspiration, this paper looks at why a very low background level of bacteriological failures is to be expected and two factors, pH and actual retention times, make bacteriological failures more likely if not properly accounted for and managed.
After a discussion on why 100% bacteriological compliance is not theoretically possible, the paper focuses on the effect of pH and streamlining on CT values and why the current operational way of determining these significantly overestimates such values, making bacteriological failures more likely.
Finally, the paper makes recommendations on how these factors can be managed operationally in a practical way to minimise random failures further.
Disinfection Kinetics and the Chick-Watson equation
In the majority of everyday situations, disinfection follows first order kinetics: N_{t}=N_{0}e^{-kt} where N_{t} is the number of surviving organisms, N_{0} is the original number of organisms, e is a mathematical constant sometimes referred to as Euler’s number^{[3]}, k is a constant and t is the time in seconds.
The key point is that such equations are asymptotic towards zero, that is the value of N_{t} gets closer and closer to zero, but never reaches it. It reinforces the idea that even a high reduction in bacteria numbers, say 10-log, does not guarantee a zero coliform final treated water.
While this theory may be familiar to scientific staff, non-scientific staff will probably have experienced it when a treatment works has a low-level bacteriological failure which is not evident in resamples.
In 1908, Watson^{[4]} proposed the addition of an additional factor, λ, and the chlorine concentration, c, to the simple first order kinetics equation proposed by Chick^{[5]} earlier that year, to take into account the effect of water types and the resistance of different organisms to disinfection. This gives what is referred to today as the Chick-Watson equation: ln(N_{t}/N_{o})= -λc^{-nt} Where
ln = natural logarithm
N_{t} = number of microbial organisms at time t, in coliform forming units/ml (CFU/ml)
N_{0} = number of viable organisms at time 0, in CFU/ml
λ = coefficient of lethality, specific to each organism and water type
c = concentration of disinfectant in mg/l
n = coefficient of media attributes (e.g., dilution, pH), generally taken a 1
t = contact time in seconds
Taking n=1 rearranging and taking antilogs gives N_{t}= N_{0}e^{-λct} . This equation is a variation of the simple first order kinetics equation discussed above and introduces the idea that disinfection relies on both the concentration of the disinfectant and the contact time.
In the water industry this concept is expressed numerically using CT values, where C is the free chlorine residual in mg/l, T the contact time in minutes and the CT value is the product of the two
Effect of pH on disinfecting power – Henderson HasselbaLch
With CT values being widely used in potable water treatment as a measure of disinfection effectiveness, it is important that the methods for determining C and T are giving realistic estimates of the true values. Therefore, it is important to understand the different disinfecting power of aqueous chlorine species and which species the measurement method is responding to.
Chlorine dissolves in water to form aqueous chlorine, (Cl_{2}(aq)), hypochlorous acid (HOCL) and the hypochlorite ion (OCl^{–}). The ratio of these species is strongly dependent on pH, a lower pH favouring the formation of aqueous chlorine and hypochlorous acid while a higher pH favours the formation of the hypochlorite ion.
This is important because sources indicate that Hypochlorous acid is between 80^{[6]} and 100^{[7]} times more powerful as a disinfectant that the hypochlorite ion. TWORT^{[8]} similarly states “hypochlorous acid is a far more powerful bactericide than the hypochlorite ion”.
This effect is marked. Calculations using the Henderson Hasselbalch equation show that increasing the pH from 7.0 to 8.0 reduces the proportion of hypochlorous acid from 77% to 26%.
If this is not considered, calculated CT values will be significantly above the real CT value.
Determining hypochlorous acid concentration directly is difficult because N,N’ Diethyl-1,4 Phenylenediamine (DPD) reacts with both hypochlorous acid and the hypochlorite ion under standard test conditions^{[9]},^{[10]} due to the inclusion of a slightly acidic phosphate buffer^{[11]}. The same is true of some potentiometric methods^{[12]}
This can be addressed using Henderson-Hasselbalch formula^{[13]} to calculate the hypochlorous acid concentration at a given pH. The general form of the Henderson-Hasselbalch equation is pH = pK_{a)} + log_{10}([Conjugate Base]/[Acid]) where:
- pH is the solution pH
- pK_{a} is the acid dissociation constant
- [Conjugate Base] is the molar concentration of the conjugate base
- [Acid] is the molar concentration of the acid
Calculating chlorine species concentrations
The proportion of hypochlorous acid at a given pH is given by the equation \frac{[HOCl]}{[HOCl]+[OCl^-]} . To convert these to quantities that are known or can be measured, the following steps are required:
Step 1: Divide the top and bottom of the above equation by [HOCL] to give \frac{[HOCl]/[HOCl]}{[HOCl/[HOCl]]+[OCl^-]/[HOCL}
This simplifies to \frac{1}{1+\frac{[OCl^-]}{[HOCL}}
Step 2: Rearrange the acid dissociation equation k_a=\frac{[H^+][OCL^-]}{[HOCL]} to give \frac{k_a}{[h^+]}=\frac{[OCL^-]}{[HOCl]}
Step 3: Substitute \frac{k_a}{[h^+]} for \frac{[OCl^-]}{HOCL]} in \frac{1}{1+\frac{[OCl^-]}{[HOCL}} to give \frac{1}{1+\frac{k_a}{[h^+]}} .
This equation, which is identical to the one given in White’s Handbook of Disinfection, p75, can be used in a spreadsheet to calculate and graph %[HOCL] vs pH. This, and similar calculations for [Cl_{2}(aq)] vs pH and [OCL^{–}} vs pH, are shown in Figure 1
Figure 1: Chlorine Species vs pH
A copy of the spreadsheets used in this paper can be requested from the lead author on the understanding that they have been developed as teaching tools and must be validated by the user for operational decision-making purposes.
Taking a factor of 80 for the relative disinfecting power of hypochlorous acid and the hypochlorite ion, and applying this to a mass balance equation gives C_{e} = [HOCL]+[OCl^{–}]×0.0125 where
C_{e} = Effective free chlorine concentration
[HOCL] = Calculated hypochlorous acid concentration
[OCL^{–}] = Calculated hypochlorite ion concentration
While this can readily be done using a spreadsheet, a more practical option may be to create a look-up table give the percentage of hypochlorous acid for a given pH and have it available as a laminated pocket card. An example is shown in Table 1.
Such a card would enable non-scientific staff to readily assess hypochlorous acid concentrations in the field and avoids the possibility of calculation errors.
This shows that at pH 7.0, the effective free chlorine concentration, C_{e}, is 77.8% of the nominal free chlorine concentration as determined by DPD or some potentiometric methods, but between pH. 7.5 and pH 8.0 it drops from around 52.7% to 26.5%.
The 77.8% value is likely to be acceptable in practice, but values of 52.7% and 25% value are much less likely to be so and makes bacteriological failures more likely.
The effect of streamlining on Retention times
The time element of the CT calculation relies on having an accurate assessment of the time taken for water to pass through a tank. Relying on hydraulic retention times (HRT), that is the tank volume/flow rate, will always give an unduly optimistic CT calculation.
One approach is to apply a Baffling Factor (BF) to the HRT to give a realistic estimate of the actual retention time for most of the water passing through a given tank.
The Water Security Agency^{[14]} uses Baffling Factors (BFs) to measure the actual retention time. BFs are expressed as T_{10}/T, where T_{10} refers to the effective contact time, which is the time it takes 10% of the volume of a unit to pass through that unit and T is referred as theoretical detection time.
The Agency has a table off typical BF values for use when experimentally determined baffle factors are not available. This is shown in Table 2
Baffling Conditions | Baffling Factor |
---|---|
No contact time: Atmospheric or Hydropneumatic tank with a single combined inlet/outlet | 0 |
Unbaffled : No intrabasin baffles, mixed flow, agitated basin, very low length to width ratio, high inlet and outlet flow velocities | 0.1 |
Poor: Single or multiple unbaffled inlets and outlets, no intrabasin baffles | 0.3 |
Average: Baffled inlet or outlet with at least 2 or more intrabasin baffles | 0.5 |
Superior: Perforated inlet baffle with at least 2 or more serpentine or perforated intrabasin baffles. An outlet weir or perforated launders | 0.7 |
Near –Plugflow: High length to width ration of 5:1 or greater pipeline flow | 0.9 |
Plug flow: very high length to width ratio of 40:1 or greater pipeline flow | 1.0 |
Two values of interest for potable water disinfection from this table are for tank arrangements described as “Poor: Single or multiple unbaffled inlets and outlets, no intra-basin baffles” and “Average: Baffled inlet or outlet with at least 2 or more intra-basin baffles”.
These correspond to the commonly used unbaffled and baffled contact tanks, and the BFs are 0.3 and 0.5 respectively. This suggests that relying on HRTs for CT calculations risks overstating the actual retention time by between half and three quarters.
This has signification implications for CT calculations and the consequent risk of bacteriological failure but can be readily addressed by applying table BFs to calculated HRTs to give an Effective Retention Time, (ERT).
A better solution is to determine the ERT for individual tanks experimentally. Tracer studies are a well-known and effective way of doing this but are time-consuming and perhaps best kept for high risk situations.
Implications for CT calculations
Using the effective free chlorine residual and the ERT rather than nominal values in CT will highlight any instances of marginal CT values. This knowledge will enable an organisation to produce a prioritised action plan to address such issues.
Table 3 gives a ready reckoner based on C_{e} values derived from the Henderson-Hasselbalch equation and ERT values taken from the baffling factors in Table 2. Applying the appropriate factor in the table to the nominal CT value gives the Effective CT value (CT_{e}).
Taking a base case of 100% hypochlorous acid concentration and perfect plug flow as having a value of 1, values that would be given by a DPD test and simple retention time calculation respectively, Table 3 shows the CTe value for various combinations of pH and BF.
This shows that at pH 7.0, normally a reasonable pH for maintaining hypochlorous acid concentrations, in a baffled contact tank the CT_{e} is less than 40% of the nominal CT value. This is the light red value in Table 3
Similarly, even with perfect plug flow, which is unachievable in practice, at pH 8.0 the CT_{e} is just over 25% of the nominal CT value. This is the dark red value in Table 3. Both effects increase the likelihood of bacteriological sample failures.
pH | |||||||||
BF | 5.0 | 5.5 | 6.0 | 6.5 | 7.0 | 7.5 | 8.0 | 8.5 | 9.0 |
1 | 0.988 | 0.988 | 0.971 | 0.916 | 0.775 | 0.52 | 0.256 |
0.098 |
0.033 |
0.9 |
0.889 |
0.889 |
0.874 |
0.824 |
0.697 |
0.469 |
0.231 |
0.088 |
0.030 |
0.8 | 0.790 | 0.790 | 0.777 | 0.732 | 0.620 | 0.417 | 0.205 | 0.079 | 0.027 |
0.7 | 0.691 | 0.692 | 0.680 | 0.641 | 0.542 | 0.365 | 0.179 | 0.069 | 0.023 |
0.6 | 0.593 | 0.593 | 0.582 | 0.549 | 0.465 | 0.313 | 0.154 | 0.059 | 0.020 |
0.5 | 0.494 | 0.494 | 0.485 | 0.458 | 0.387 | 0.261 | 0.128 | 0.049 | 0.017 |
0.4 | 0.395 | 0.395 | 0.388 | 0.366 | 0.310 | 0.209 | 0.102 | 0.039 | 0.013 |
0.3 | 0.296 | 0.296 | 0.291 | 0.275 | 0.232 | 0.156 | 0.077 | 0.029 | 0.010 |
0.2 | 0.198 | 0.198 | 0.194 | 0.183 | 0.155 | 0.104 | 0.051 | 0.020 | 0.007 |
0.1 | 0.099 | 0.099 | 0.097 | 0.092 | 0.077 | 0.052 | 0.026 | 0.010 | 0.003 |
Other considerations – Temperature
Data from Twort^{[15]} shows that the effect of temperature on hypochlorous acid concentration is small, around 5%, compare to the 50% plus of pH changes this is shown in Figure 2. It is the authors’ opinion that that the focus should be on pH and retention time rather than temperature.
Figure 2: Hypochlorous Acid concentration vs pH and Temperature
other considerations – Carbon Blinding
Carbon blinding refers to bacteria trapped in carbon fines from granular activated carbon (GAC) filters being protected from attack by chlorine and hypochlorous acid. This has the effect of reducing the effective chlorine concentration, C_{e}, further.
Data is not readily available to quantify this effect, so it must be assumed that calculated C_{e} values are the best possible case when GAC filters are used pre-disinfection.
Operational implications
The low bacteriological failure rates for final treated waters shows ineffective final water disinfection is not a major issue for UK water companies. However, companies and water treatment practitioners need to be aware of these effects, especially when investigating bacteriological failures from treatment work.
It is suggested that pH effects and baffling factors be included in
- Drinking Water Safety Plan (DWSP) reviews
- Reviews of bacteriological failure reviews at treatment works
- Training for operational managers, scientists, and treatment technicians
- Designs for new treatment works and upgrading treatment works
Authors
Bob Windmill, MSc, MBA, CSci
Academic Director, British Water Engineering College, bob@bwec.org.uk
Lee Dark, MSc, CSci
Principal Monitoring Scientist with Southern Water, lee.dark@southernwater.co.uk
Acknowledgements
Thank you to Anthony Lucio, a post doctorate researcher at Warwick University, for his help with turning the Henderson-Hasselbalch equations into workable spreadsheet equations.
refrerences
- TWORT, Twort’s Water Supply, 6^{th} ed. pp428-430 ↑
- Drinking water 2020 Quarter 1 p3. Online at <URL> http://www.dwi.gov.uk/about/annual-report/2020/CIR_Q1_2020.pdf. Accessed 09/09/202 ↑
- Wkepedia, e (mathermatical constant) [Online]. <URL> https://en.wikipedia.org/wiki/E_(mathematical_constant) [Accessed 16/10/2020} ↑
- USBR, Appendix 11. A primer in disinfection characterization [Online] <URL> https://www.usbr.gov/gp/dkao/biota_transfer/app11.pdf [Accessed] 09/09/2020 ↑
- TU Delft, Disinfection, [Online} <URL> https://ocw.tudelft.nl/wp-content/uploads/Disinfection-1.pdf {Accessed] 09/08/2020 ↑
- Hydro Instruments, Basic Chemistry of Chlorination [Online], <URL> http://www.hydroinstruments.com/files/Basic%20Chemistry%20of%20Chlorination.pdf p2 [Accessed] 09/09/2020 ↑
- Aquaox, Hypochlorous Efficacy [Online] <URL> https://www.aquaox.com/wp-content/uploads/2016/05/HOCL-Efficacy.pdf p4 [Accessed] 09/09/2020] ↑
- TWORT, Twort’s Water Supply, 6^{th} ed. P427 ↑
- Harp, L. D., Current technology of chlorine analysis for water and wastewater, [Online] <URL> https://www.hach.com/cms-portals/hach_com/cms/documents/pdf/LIT/L7019-ChlorineAnalysis.pdf p3 {Accessed] 10/09/2020 ↑
- Palintest, Free and combined chlorine – understand the difference. [Online] <URL> https://www.palintest.com/content-hub/free-and-combined-chlorine-understand-the-difference [Accessed] 10/09/2020 ↑
- Google Patents, Liquid DPD reagent, method for measuring concentration of residual chlorine, and phosphate buffer solution [Online] <URL> https://patents.google.com/patent/JP2004003880A/en [Accessed] 10/09/2020 ↑
- Sensorex, Free chlorine aperometric 4020mA sensors p1 [Online] <URL> https://www.sensorex.com/docs/instructions/InstrFCL2.pdf [Accessed] 10/09/2020 ↑
- Wikipedia. Henderson-Hasselbalch equation. [Online] <URL> https://en.wikipedia.org/wiki/Henderson%E2%80%93Hasselbalch_equation [Accessed] 07/09/2020 ↑
- The Water Security Agency, WSA 510 Contact Time (CT) Calculation p1, [Online] <URL> http://www.saskh20.ca/pdf/Contact_Time_Calculation.pdf [Accessed] 10/09/2020 ↑
- TWORT, Twort’s Water Supply, 6th ed. P 426 ↑