New model of chlorine-wall reaction for simulating chlorine concentration in drinking water distribution systems

Accepted Manuscript New model of chlorine-wall reaction for simulating chlorine concentration in drinking water distribution systems Ian Fisher, George Kastl, Arumugam Sathasivan PII:

S0043-1354(17)30730-3

DOI:

10.1016/j.watres.2017.08.066

Reference:

WR 13189

To appear in:

Water Research

Received Date: 17 April 2017 Revised Date:

14 July 2017

Accepted Date: 29 August 2017

Please cite this article as: Fisher, I., Kastl, G., Sathasivan, A., New model of chlorine-wall reaction for simulating chlorine concentration in drinking water distribution systems, Water Research (2017), doi: 10.1016/j.watres.2017.08.066. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Processes affecting chlorine bulk-decay and wall-reaction

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ACCEPTED MANUSCRIPT NEW MODEL OF CHLORINE-WALL REACTION FOR SIMULATING

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CHLORINE CONCENTRATION IN DRINKING WATER DISTRIBUTION

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SYSTEMS

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Ian Fishera, George Kastlb and Arumugam Sathasivanb

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a

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email: [email protected]

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b

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Bag 1797, Penrith NSW 2791, Australia

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ABSTRACT

Corresponding Author, Watervale Systems, PO Box 318, Potts Point NSW 1335, Australia;

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School of Computing, Engineering and Mathematics, Western Sydney University, Locked

Accurate modelling of chlorine concentrations throughout a drinking water system needs

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sound mathematical descriptions of decay mechanisms in bulk water and at pipe walls. Wall-

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reaction rates along pipelines in three different systems were calculated from differences

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between field chlorine profiles and accurately modelled bulk decay. Lined pipes with

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sufficiently large diameters (>500mm) and higher chlorine concentrations (>0.5mg/L) had

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negligible wall-decay rates, compared with bulk-decay rates. Further downstream, wall-

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reaction rate consistently increased (peaking around 0.15 mg/dm2/h) as chlorine

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concentration decreased, until mass-transport to the wall was controlling wall reaction. These

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results contradict wall-reaction models, including those incorporated in the EPANET

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software, which assume wall decay is of either zero-order (constant decay rate) or first-order

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(wall-decay rate reduces with chlorine concentration). Instead, results are consistent with

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facilitation of the wall reaction by biofilm activity, rather than surficial chemical reactions. A

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new model of wall reaction combines the effect of biofilm activity moderated by chlorine

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concentration and mass-transport limitation. This wall reaction model, with an accurate bulk

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chlorine decay model, is essential for sufficiently accurate prediction of chlorine residuals

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ACCEPTED MANUSCRIPT towards the end of distribution systems and therefore control of microbial contamination.

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Implementing this model in EPANET-MSX (or similar) software enables the accurate

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chlorine modelling required for improving disinfection strategies in drinking water networks.

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New insight into the effect of chlorine on biofilm can also assist in controlling biofilm to

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maintain chlorine residuals.

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Keywords: chlorine decay model, wall-reaction rate, bulk decay, system model, biofilm,

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mass-transport

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Nomenclature

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A, B

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amplification factor (dm/h) and rate-coefficient (L/mg) for effect of chlorine on BioF

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BioF

biofilm activity (dm/h)

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CCl,

chlorine concentration (mg/L)

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CR, Cf, Cs

total, fast and slow reactants (mgCl-equiv/L)

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D

pipe diameter (mm or dm)

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Deq

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kb1

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kR, kf, ks

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km

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kwi

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Rb, Rw

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rw

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t

time (h)

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2RA

augmented two-reactant [decay model]

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AOC

assimilable organic carbon

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AQUASIM

system modelling and parameter optimisation package

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wall-reaction equivalent pipe diameter (dm)

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first-order bulk decay rate-coefficient total, fast and slow reaction coefficients (L/mg/h)

mass-transport coefficient (dm/h) wall-reaction coefficient of order i (i=0,1,2) volumetric bulk- and wall-decay rates (mg/L/h) surficial wall-decay rate (mg/dm2/h)

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ACCEPTED MANUSCRIPT DBP

disinfection by-product

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DOC

dissolved organic carbon

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EPANET

USEPA distribution system modelling software

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EXPBIO

new biofilm-mediated wall-decay model

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FO

first-order

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GAC

granulated activated carbon

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ICC

initial chlorine concentration

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QL

quantification limit

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SO

second-order

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WDR

wall-decay rate (mg/dm2/h)

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ZO

zero-order

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1. INTRODUCTION

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1.1 Limitations of chlorine decay models for distribution system simulation

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System models that can simulate chlorine profiles are critical to controlling water quality

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delivered to consumers, by improving disinfection strategies in chlorinated distribution

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systems. The aim of chlorine control is to provide sufficient disinfection at system extremities

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while simultaneously keeping disinfection by-products (DBPs) below regulated limits. Such

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system models have been available since 1994, to predict chlorine decay and hence the

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residuals occurring system-wide (e.g. the original EPANET software of Rossman, 1994).

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Even then, reactions in bulk water – “bulk decay” – were characterised separately from

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reactions of chlorine with pipe walls and the biofilm/chemical-deposit matrix adhering to

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them – “wall decay”. Bulk-decay models have been developed since the 1950s, including an

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extensive comparison by Powell et al. (2000). Figure 1 shows the key processes involved. It

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is crucial to accurately model both these components of chlorine loss.

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ACCEPTED MANUSCRIPT A major conceptual problem is that bulk decay cannot be measured directly in the system

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because the chlorine dosed upstream simultaneously interacts with substances in bulk water

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and those adhering to the walls (as well as the wall surface itself), to an extent dependent on

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the location sampled and the variable flow regime. The decay coefficients derived from

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laboratory decay-tests on such samples are therefore inherently randomly variable. For

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example, the “combined approach” of Courtis et al. (2009) may characterise low-level

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chlorine concentrations in a closely monitored system, but it does not enable the

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characterisation of bulk decay that is a pre-requisite to accurately quantifying wall decay

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throughout a system. To efficiently and accurately characterise bulk decay as a property only

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of the source water, bulk decay parameters must be derived from decay-tests on water

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sampled post-treatment and before secondary chlorination. Otherwise, the model parameters

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derived cannot properly represent the decay that occurs following different initial chlorine

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doses.

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The difference between chlorine concentrations measured at any two connected points in a

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distribution system is the sum of bulk and wall decay (Hallam et al., 2002). Wall decay is

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therefore quantified as the difference between this measured sum and the bulk decay

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calculated by the selected bulk-decay model. Any error in the bulk-decay prediction will

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result in an error of equal magnitude (but opposite sign) in the derived wall decay (as

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illustrated in Figure S1 in Supplementary Material.). Consequently, the estimate of wall

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decay will differ from the “true” wall decay by the same amount. When such estimates are

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used to calibrate the wall-decay coefficients in a system model such as EPANET, the

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coefficients derived will reflect the same errors; that is, they will compensate for the errors in

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the bulk-decay model, rather than giving a true estimate of wall decay. Consequently, the

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common practice of using wall-decay parameters in EPANET and its commercial derivatives

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as calibration coefficients (e.g. Georgescu and Georgescu, 2012) may result in false estimates

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ACCEPTED MANUSCRIPT of wall decay within a distribution system. The practice may simply be compensating for an

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inadequate representation of bulk decay. The use of a single value for wall-decay coefficient

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across a system (e.g. Pirozzi et al., 2002; Monteiro et al., 2014) may lead to similar error in

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some parts of a system. These issues become important when actions to increase chlorine

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residuals are selected on the basis of the relative magnitude of wall and bulk decay obtained

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from system model predictions.

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Fisher et al. (2011) suggested this problem could be overcome by using a bulk-decay model

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with only a single set of parameter values to accurately describe chlorine decay over the full

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range of system operating conditions. Any model of sufficient accuracy could be used for the

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purpose of investigating wall decay, but using a single parameter-set is required for

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efficiency. The augmented two-reactant (2RA) model is used in this paper because it is the

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simplest model with the required capability, for combinations of initial dose, temperature and

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booster doses in single waters, and also in blended waters (Fisher et al., 2012, 2015, 2016)

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and Liu et al. (2014) extended it to simultaneously account for the effect of pH variation. The

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variable rate-coefficient (VRC) model of Jonkergouw et al. (2009) and its modification to

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represent bulk decay over a wide range of temperature (Hua et al., 2015) may provide an

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alternative of similar complexity and accuracy to the 2RA model. However, this has not yet

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been established across a similar wide range of waters, operating conditions or pH.

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It has long been recognised that chlorine decay in unlined iron pipes can be much greater than

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that in bulk water due to corrosion (e.g. Kiené et al., 1998). However, in pipes lined with (or

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composed of) less reactive material, bulk-decay rates can be greater than wall-decay rates,

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especially at higher chlorine concentrations and larger-diameter pipes. The relative

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importance of bulk decay also increases with pipe diameter due to the corresponding decrease

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in surface-to-volume ratio. Consequently, an accurate bulk-decay model might be expected to

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ACCEPTED MANUSCRIPT predict chlorine concentration accurately along a pipe of sufficiently large diameter, when the

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reduction due to wall decay is less than the accuracy of measurement of the total decay.

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Zhang et al. (1992) fitted an accurate, two-phase FO model to bulk decay-tests run

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simultaneously during system measurements in three independent large-diameter pipes

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(asbestos cement or steel, 250-800mm), so that the same conditions of initial chlorine

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concentration (ICC) and temperature prevailed for bulk and system decay in each case. They

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concluded that there was a negligible difference between the bulk and (measured) in-pipe

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decay rates in each case; i.e. they found wall decay was negligible compared with bulk decay

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in these large-diameter pipes. However, the bulk decay coefficient exceeded the total in-pipe

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coefficient by more than the error they estimated. This indicates some inaccuracy in

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prediction of bulk decay.

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Fitting an accurate bulk-decay model to decay-test data generated independently of any

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system measurements is a more effective general alternative to conducting bulk-decay

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experiments simultaneously with in-system measurements. Its proposed use raises the

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following questions. Can such a bulk model accurately predict chlorine levels in single, lined

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or non-ferrous pipes of sufficiently large diameter; i.e. allowing no effect of wall demand? If

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so, can it also make accurate predictions along a continuous pipe “run” (comprising several

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such pipe lengths of sufficiently large, but decreasing diameter) and in any associated well-

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mixed tanks, as wall decay should be negligible compared with bulk decay in both cases?

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These questions can only be addressed, now that bulk-decay models are sufficiently general

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and accurate.

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1.2 Wall-decay mechanisms

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As travel time increases and pipe diameter and bulk reaction rate decrease down a

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distribution system, wall decay should eventually become a quantifiable component of the

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ACCEPTED MANUSCRIPT overall chlorine decay. Corrosion reactions in unlined iron pipes may be quantifiable in pipes

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immediately downstream of a treatment plant. In addition, other chemical and biological

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mechanisms can result in increasing chlorine-decay rate with travel time, due to chemical

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deposition (including catalytic agents) or biofilm formation on the pipe walls (Figure 1).

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These mechanisms are detailed in Section S1 of the Supplementary Material.

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To determine a chemical mechanism for a wall-decay model, it is necessary to know whether

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the reactions with chlorine that occur at the wall are the same as those that occur in bulk

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water; i.e., whether they involve the same metallic or dissolved organic carbon (DOC)

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compounds and reaction sites. If these molecules are adsorbed on the ferric hydroxide surface

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described in Section S1 in higher concentrations than in bulk water, they can react faster with

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chlorine than they would in the bulk reaction. This may simply accelerate the same reaction

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occurring in bulk water or it may enable reaction on additional sites of the DOC molecules,

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due to the heterogeneous catalytic effect on the surface (Ramseier et al., 2011).

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In addition to chemical reactions with chlorine, there are also reactions possible with

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biological material on the pipe wall. Such biofilm is present even in the presence of

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substantial chlorine residual. Admittedly, the higher concentration of chlorine limits biofilm

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growth and activity (Kiené et al., 1998). However, chlorine produces assimilable organic

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carbon (AOC) from DOC (van der Kooij 1987), which stimulates biofilm growth as chlorine

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concentration subsides (van der Wande and Characklis, 1990). Biofilm produces organic

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metabolites which may readily react with and reduce chlorine. It is reasonable to assume that

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enzymatic processes in biofilm (similar to that observed by Bal Krishna et al., 2012), as well

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as the reaction with extracellular polymeric substances, could be responsible for chlorine

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reduction.

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1.3 Wall-decay quantification

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ACCEPTED MANUSCRIPT There are two types of test-rig that have been used to quantify wall-decay rates – pipe-

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reactors and pipe-loops. Pipe-reactors recirculate water through a bench-scale annulus, one

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surface of which is test-pipe material of uniform diameter (e.g. DiGiano and Zhang, 2005)

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while the remainder of the apparatus is comprised of inert material. Pipe-loops recirculate

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water around a much longer, full-scale, single-diameter pipe circuit (of order 100m length –

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Clark and Haught, 2005; Rossman, 2006; Douterelo et al. 2013; Jamwal and Kumar, 2016).

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After these rigs are filled with chlorinated water, they are generally closed off and the water

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is recirculated for a considerable period while the chlorine decays to low levels. The water is

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at a similar concentration anywhere in the rig at a given time. In contrast, in a real pipeline

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(of order 1-10km), a given small length of pipe experiences a similar chlorine concentration

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over the whole of a test period. Consequently, quite different mechanisms may be dominant

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at pipe locations experiencing markedly different chlorine concentrations. In particular, test-

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rig results are unlikely to represent the biofilm development in a real pipeline because the

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relatively high initial chlorine concentrations used in such tests are likely to inactivate/inhibit

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the organisms in the biofilm. Furthermore, the surface density of biofilm developed during

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short quiescent pre-test periods is likely to be much lower than that developed at the

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downstream end of a pipeline with a similar low level of chlorine over extended periods.

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Finally, the chemical substances required for either chemical deposition or biofilm formation

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are continually replenished in a real pipeline, but are not in a test-rig. Consequently, any

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conclusions reached on the basis of test-rig results, and particularly those related to biofilms,

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need to be confirmed in real distribution systems, which is a focus of this paper.

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At a sufficiently long travel time down a distribution system, wall decay will become a

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quantifiable component of the overall chlorine decay. To characterise the consequent

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longitudinal variation along a pipe run to points of low chlorine concentration, differences in

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chlorine concentration must be measured across at least three contiguous pipes. In real

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ACCEPTED MANUSCRIPT systems, pipe-diameter and flow commonly decrease downstream, so that each pipe-length

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along the run needs to be of uniform diameter and material; otherwise, quantification of wall-

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decay rates becomes inherently uncertain. This approach also enables resolution of whether a

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quantifiable increase in wall-decay rate downstream is due only to the increase in surface-to-

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volume ratio, or is also due to an increase in surficial wall-decay rate.

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Hallam et al. (2002) conducted detailed field measurements to quantify wall-decay rates in

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single pipes. These included a run of four pipes in their study of pipes in a UK distribution

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system, but three were cast iron (i.e. unlined). Ten of their eleven pipes were ≤200mm in

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diameter and turbulence of all flows was in the transition zone. Furthermore, the initial

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chlorine level in each pipe length was less than 0.35 mg/L, which does not provide the

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appropriate range for pipe-run analysis.

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Several system studies have quantified wall-decay rates by minimising the sum of differences

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between measured chlorine concentrations at key locations and corresponding concentrations

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predicted by bulk- and wall-decay models, within modelling packages such as EPANET.

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These system studies have characterised one or, at best, two groups of pipes with different

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wall-decay rate coefficients and included limitation of mass-transport (e.g. Vasconcelos et al.,

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1997; Georgescu and Georgescu, 2012; Monteiro et al., 2014). Such estimates do not provide

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an adequate basis for examining variation in wall-decay rates along the system.

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1.4 Wall-decay characterisation

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In system studies, wall decay has been described as either a zero-order (ZO) or FO process

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with respect to chlorine (e.g. Vasconcelos et al., 1997, Hallam et al., 2002; Brown et al.,

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2011). DiGiano and Zhang (2005) characterised their results from unlined and lined pipe-

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section reactors similarly. These processes constitute two limiting cases:

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ACCEPTED MANUSCRIPT 219

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Zero order – the decay is controlled by the catalyst or organic concentrations, which

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are approximately constant at the pipe wall (due to the surface saturation governed,

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for example, by a Langmuir adsorption isotherm)

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First order – the reaction rate is proportional to chlorine concentration at the pipe wall

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surface and that concentration is proportional to chlorine in the bulk water.

Fisher et al. (1996) represented wall-decay rate as an acceleration of the bulk-decay rate. This

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representation is effectively second-order (SO), because their bulk-decay (2RA) model was

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FO with respect to both chlorine and its reactants. Both the FO and SO concepts imply that

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“surficial” chlorine reaction rate at the wall [mg/dm2/h] decreases with the chlorine

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concentration in bulk water, whereas this rate is independent of chlorine concentration under

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the ZO assumption. However, if wall-decay rate is not quantifiable in large upstream pipes,

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and wall-decay rate increases downstream, then there must be an inverse relationship of wall-

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decay rate with chlorine concentration, as the latter decreases downstream. The rates of

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chemical reactions between compounds on the wall and chlorine are most unlikely to be

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inversely related to their concentrations. Consequently, the cause is likely to be biofilm

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formation and activity.

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The order of wall-decay reaction rate in real systems therefore needs to be reconsidered,

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firstly to remove error arising from the bulk-decay estimates and secondly to make its

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characterisation downstream as accurate and simple as possible. This can be achieved with a

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single parameter, the “apparent surficial wall-reaction rate” [mg/dm2/h], as developed in

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Section 2. This parameter includes the effect of a possible limitation due to lateral mass-

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transport of chlorine to the wall, rather than treating it as a separate process. Clark and

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Haught (2005) showed such limitation is significant in low flows (limited mass-transport) in

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an unlined iron pipe-loop (fast wall-decay reaction). The studies considered here are confined

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ACCEPTED MANUSCRIPT to lined or non-ferrous pipes, which are increasingly used worldwide. The significance of

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mass-transport limitation is yet to be established under the varied flow regimes encountered

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in these real systems.

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In smaller-diameter lined pipes, overall decay is likely to be mainly due to interaction of

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chlorine with the biofilm/chemical layer adhering to the pipe wall. It is therefore possible

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that there are seasonal changes in apparent wall reactivities. These would probably be due to

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growth and sloughing of this layer, possibly involving large differences in flow rate and

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chlorine penetration. The data collection and quantification of wall-reaction rates therefore

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needs to be repeated several times over the year to determine whether this is a significant

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effect.

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1.5 Aims

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The general aim of this paper is to address four key issues identified above:

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1. To determine whether the 2RA bulk-decay model derived from laboratory decay tests

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accurately predicts chlorine concentrations in tanks and the upstream (large-diameter)

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pipes of a pipe run; i.e. whether wall decay is negligible in comparison.

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2. To quantify chlorine wall-decay rates along a pipe run, once total in-pipe decay (bulk+wall) exceeds accurately modelled bulk decay, under various operating

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conditions (such as source water, flow rate and temperature).

3. To derive limits of quantification for wall-decay rates, based upon chlorine measurement error.

4. To develop a model describing wall-decay rate along a pipe run, including limitation of lateral mass-transport, which is useable in system-wide chlorine modelling. 2. WALL REACTION RATE – CONCEPT DEVELOPMENT

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ACCEPTED MANUSCRIPT In volumetric terms, wall-decay rate [Rw mg/L/h] is the apparent “volumetric” rate at which

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free chlorine [CCl mg/L] is consumed as a bulk-water parcel travels along a pipe, over and

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above the rate [Rb mg/L/h] at which it is consumed by the reactants in that parcel. For a pipe

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of diameter D [dm], the surface-to-volume ratio of the water parcel is 4/D, so that:

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-dCCl/dt = Rb+Rw = Rb+(4/D)rw

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where rw [mg/dm2/h] is the apparent wall-surface decay rate. Length units of decimetres [dm]

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are used to maintain compatibility between volumetric entities such as concentrations [mg/L]

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and surficial entities such as wall-reaction rate coefficient [mg/dm2/h]. All equations have

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been written so that variables and coefficients have non-negative values.

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2.1 Previously assumed forms for wall-decay rate in a single pipe

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The functional forms previously assumed for wall decay and embedded within the EPANET

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package (Rossman, 1994), and their combination with FO bulk-decay models, are developed

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and discussed in Section 1.2 of the Supplementary Material.

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The 2RA model assumes that

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-dCCl/dt=kf×Cf×CCl+ks×Cs×CCl

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-dCf/dt=kf×Cf×CCl

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-dCs/dt=ks×Cs×CCl

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where Cf and Cs are respectively the fast- and slow-reactant concentrations [mgCl-equiv/L]

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and kf and ks are the corresponding SO decay-rate coefficients [L/mgCl/h]. The latter two

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coefficients vary with temperature according to an Arrhenius function (Fisher et al., 2012)

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characterised by a single parameter E/R [K], where E is the activation energy [J/mol] and R

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the universal gas constant [J/K/mol].

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(4) (5) (6)

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ACCEPTED MANUSCRIPT Fisher et al. (1996) proposed the concept of “equivalent diameter”, Deq [dm]. (This is not

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related to the hydraulic concept of equivalent diameter. It therefore has no effect on any

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hydraulic entity such as flow or mass-transport rates.) It is the diameter of a pipe having the

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same wall-reaction rate as the physical pipe of interest (diameter D dm), in which wall decay

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per unit length is equal to bulk decay in the associated volume (π/4×Deq2 [dm3]); i.e.,

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-dCCl/dt=Rb[1+Deq/D] =Rb+(4/D)Rb×Deq/4

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(7)

i.e. rw=Rb×Deq/4

(8)

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Effectively, the wall-decay rate here is SO because Rb is SO, and therefore Deq/4 [dm] is a SO

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wall-reaction rate coefficient. It does not account for mass-transport limitation.

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2.2 Implied variation of wall-decay rate in a single pipe

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Consider a pipe of uniform diameter and ZO wall-decay rate (constant kw0), with a constant

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flow entering at concentration CCli (Figure 2). Mass-transport to the wall must be limited as

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CCl approaches zero, as it is proportional to CCl (Eq. S3). It therefore increases linearly from

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zero to a value calculable from Eqs. S3-S5 for that flow (line OA, Figure 2). However, rw

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increases with CCl along this line only until CClz (point B) is reached, and then follows line

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BC (rw=kw0). That is, rw is a piecewise-linear function of chlorine (lines OBC).

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Assuming FO wall-decay rate (with constant kw1) implies a linear decrease in rw over the full

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range of chlorine concentration. However, this decrease is slower than that of the mass-

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transport limited rate (line OA) because rw decreases linearly at the rate defined by Eq. S9

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(line OD). The slope of this line is always ≤km, the mass-transport coefficient, because

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kw1×km/(kw1+km) asymptotes to km as kw1 is increased.

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2.3 An alternative model of wall-decay rate in a single pipe (EXPBIO)

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ACCEPTED MANUSCRIPT If biofilm activity becomes sufficiently great in downstream pipes, an inverse relationship

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must exist between wall-decay rate and chlorine concentration (Section 1). Hallam et al.

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(2001) found that biofilm activity (BioF) decreased exponentially as bulk chlorine increased

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from zero in a full-scale distribution system; i.e.;

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BioF=A×exp(-B×CCl)

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where A is an amplification factor [dm/h] and B is the rate-coefficient [L/mg] for the effect of

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chlorine. If the wall-reaction rate is FO with respect to both biofilm activity and wall

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concentration, then:

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rw=A×exp(-B×CCl)×Cw

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This must balance the mass flux to the wall (as in Eq. S7); i.e.,

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km(CCl-Cw)=A×exp(-B×CCl)×Cw

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Transposing gives

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Cw=CCl/(1+A×exp(-B×CCl)/km)

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Combining Eqs. 11 and 12 gives the final model of wall-decay rate (termed EXPBIO),

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including mass-transport limitation, which is illustrated in Figure 2 for comparison with the

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previously assumed models of Section 2.2; i.e.,

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rw=A×exp(-B×CCl)× CCl/(1+A×exp(-B×CCl)/km)

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2.4 Wall-decay rate in several contiguous uniform-diameter pipes

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Now consider several contiguous pipes, each of uniform diameter, which decreases with

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distance downstream. Even assuming ZO wall-decay rate, Rw would increase downstream

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inversely with diameter (Eq. 1). However, this may be offset by the changes to mass-

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transport due to changes in both D and the flow, which is usually reduced by diversion at

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(12)

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(13)

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ACCEPTED MANUSCRIPT each change in diameter. Consequently, to account for these effects, specific systems must be

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modelled, explicitly including mass-transport and wall-decay rate coefficients, while

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simulating flow and chlorine concentration.

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3. METHODOLOGY

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3.1 System Selection and Definition

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Three Australian distribution systems were chosen to provide the range of flows, source

339

waters, treatment levels, chlorine levels and seasons summarised in Table 1. A pipe run was

340

selected from each system, which met the minimum requirement of providing three

341

contiguous estimates of pipe-wall decay coefficient for evaluation of its longitudinal

342

variation. These included three pipes and a reservoir in the Greenvale-Sydenham case (Figure

343

3) and four pipes in the Mirrabooka and North Richmond cases (Figures 4 and S8).

344

Recording chlorine analysers and flow-meters were installed at appropriate points along the

345

selected pipe runs (at each end of the pipes listed in Table 2, except at the end of the Yuroke

346

branch, and also on Sydenham Reservoir outlet). They recorded data continuously for 1-2

347

weeks at a time, from which stable diurnal patterns of flow and chlorine concentration were

348

extracted for comparison with predicted chlorine concentrations at the same points. Grab

349

samples were also taken periodically during these recording periods, to ensure that the

350

analyser data was accurate (and for recalibrating analysers). In the Greenvale-Sydenham

351

system, the simple diurnal flow regime (pumps_on and pumps_off) provided near-steady

352

conditions in Dec99 for quantifying wall decay along a run of large pipes (Section S2). Data

353

were collected four times over a year in the Mirrabooka system (Section S3) and the North

354

Richmond system (Section S4) to determine whether wall-decay rates also varied over time.

355

3.2 Derivation of Bulk Decay Models

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ACCEPTED MANUSCRIPT Using AQUASIM modelling software (Reichert, 1998), the 2RA model was fitted to data

357

from laboratory decay tests conducted on bulk water samples taken from each source water

358

immediately before final chlorination at the head of each system. These tests were conducted

359

at various combinations of initial and booster free-chlorine doses, and temperature. The

360

procedure was described in detail by Fisher et al (2012) for initial dose and temperature. For

361

Greenvale Reservoir water, the set of 2RA parameter values adopted (Table 3) were based on

362

those previously found to accurately describe bulk decay over all combinations of initial and

363

booster doses, temperature and time (Fisher et al., 2016), as discussed in Section S2.

364

For Mirrabooka water, the 2RA parameter values were derived from samples taken after the

365

two source waters were mixed, as these were the only data available from tests conducted at

366

more than one temperature. Decay tests were conducted, at several different ICCs and

367

temperatures, on samples taken from the High-Level tank in each measurement period. The

368

low value obtained for E/R was due to using low initial concentrations (~0.5mg/L) and

369

relatively small temperature differences (4°C). This does not adversely affect the system

370

simulations as annual system temperature variation was smaller. Decay was much lower in

371

the Jun03 sample because a different bore was supplying the treatment plant in that period.

372

A single 2RA model parameter-set was derived for North Richmond water (Table 3), as

373

described for Greenvale water. No modification of the laboratory-derived parameter values

374

was required for either Mirrabooka or North Richmond water.

375

3.3 System Modelling Approach

376

Models of average flows through the pipe runs (and diversions from them) were constructed

377

within the AQUASIM modelling software (Reichert, 1998) for Greenvale-Sydenham and

378

Mirrabooka systems.

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ACCEPTED MANUSCRIPT Chlorine concentrations were computed in the Greenvale-Sydenham system model by

380

assuming each pipe was an advective reactor, in which the 2RA bulk-decay reactions, defined

381

in Eqs. 4-6, were simulated in water parcels moving along the pipe run, at the average flows

382

previously determined, until diurnal steady-state was reached at each station. The same bulk

383

decay equations were applied within each fully-mixed tank.

384

For the Mirrabooka system model (Figure 4), flows generated at each station (S1-S5) from a

385

detailed EPANET model were averaged over each of the four designated periods. Differences

386

between these average flows at adjacent sites were used to derive average diversions (away

387

from the pipe run) at each site in each period. The average inflow at S1 varied from 2.5ML/d

388

in Jun03 to 9ML/day in Feb04.

389

To examine longitudinal variation, a (different) constant value of wall-decay rate coefficient

390

(kw0) was assumed within each pipe along the run, in both system models. The 2RA bulk

391

model was therefore combined with the ZO wall-decay model defined by Eq. S2, to form the

392

2RA-ZO representation of chlorine decay overall within each pipe; i.e.

393

-dCCl/dt = [kf×Cf×CCl+ks×Cs×CCl+(4/D)×kw0]

394

coupled with Eqs. 5-6 to describe simultaneous decay of the reactants.

395

The parameter values in the 2RA bulk-decay models were derived from the laboratory decay-

396

test data (Section 3.2). Wall-reaction rate coefficients (constant within each pipe) were then

397

optimised simultaneously to produce the best fit of the 2RA-Z0 model to the measured

398

chlorine concentrations at each location along the pipe run. Measured concentrations were

399

averaged over the same period as the flows. The period was chosen to ensure stability of

400

flows and concentrations. The optimised kw0 were then examined for a higher-order

401

relationship with chlorine concentration.

(14)

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ACCEPTED MANUSCRIPT A more complex hydraulic model (Section S3) was previously constructed for Mirrabooka

403

within DSMtool (Fisher et al., 2004). This version of EPANET2 was designed to simulate

404

chlorine concentrations using the 2RA bulk-decay model and the “equivalent diameter”

405

representation of wall decay (Eq. 7). Results from the AQUASIM and DSMtool models were

406

compared for differences in their longitudinal variation of wall decay. Finally, a DSMtool

407

model was constructed for the more complex North Richmond system (Figure S8), to show

408

whether wall decay could be similarly represented there.

409

3.4 Limit (threshold) of quantification of wall-decay rates

410

A limit of quantification for each pipe was estimated by first recognising that the accuracy of

411

chlorine measurement is better than ±0.05 mg/L at 1mg/L free chlorine (Harp, 2002). As wall

412

decay can only reduce measured chlorine below that due to bulk decay, then wall decay is

413

only quantifiable if it produces a reduction of at least 0.05 mg/L free chlorine below that

414

predicted by the bulk-decay model. The kw0 value that resulted in this reduction in a given

415

pipe was estimated by varying only its value during multiple runs of the previously calibrated

416

2RA-ZO model.

417

3.5 Impact of lateral mass-transport

418

The mass-transport formulation of Eqs. S3-S5 assumes that chlorine flux to the wall is

419

proportional to bulk chlorine concentration. Consequently, as chlorine decreases towards

420

zero, then so should mass-transport of chlorine to the pipe wall. In each measurement period,

421

mass-transport in each pipe along the Mirrabooka pipe run was calculated from Eqs. S3-S5

422

for comparison with the corresponding quantified wall-decay rate.

423

4. RESULTS AND DISCUSSION

424

4.1 Does the bulk-decay model accurately predict chlorine in large pipes?

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ACCEPTED MANUSCRIPT Chlorine concentrations were derived from the Greenvale-Sydenham AQUASIM model for

426

all sites in Figure 3, assuming that only bulk decay was occurring. These predictions are

427

shown in Figure S3B for comparison with field data in Figure S3A. The model successfully

428

predicted chlorine concentrations within ±0.08 mg/L of measured values at S1E, S3E and S4

429

during pumps_on and pumps_off periods, (see Table S1). The larger differences were at S3E,

430

but maximum and minimum values of predicted and measured values in Table S1 were each

431

still 0.61 mg/L. Considering chlorine measurement error is typically ±0.05 mg/L, assuming

432

only bulk decay in pipes 1, 2 and 3 gave excellent predictions of chlorine residual at S3E and

433

S4 . It was concluded that negligible wall decay was occurring in these lined large-diameter

434

pipes.

435

4.2 How far downstream can wall decay first be quantified?

436

Bulk chlorine concentrations were computed by the Mirrabooka AQUASIM model. These

437

concentrations were then compared with the corresponding average measured chlorine

438

concentration at each site, to determine the distance downstream at which wall decay could

439

first be quantified. In all four periods, no wall decay could be quantified in the first pipe

440

(770mm diameter). In two periods of high flows, the same was found for the first two pipes

441

and, in the highest-flow period, for all four pipes. That is, the 2RA bulk-decay model, with

442

parameters derived solely from laboratory decay-tests, predicted chlorine concentrations in

443

those pipes and periods within experimental error (±0.05mg/L). At stations downstream,

444

chlorine concentrations were increasingly over-predicted by the bulk-decay model alone (as

445

in Figure 5).

446

The single kw0 value associated with each pipe in the 2RA-ZO model (Eq. 14) was then

447

simultaneously optimised along the full pipe run in each period. Optimised kw0 values (Figure

448

6) were zero in the same pipes/periods identified in the previous paragraph as having

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ACCEPTED MANUSCRIPT negligible wall decay. The bulk+wall decay predictions obtained (from Eq. 14) were identical

450

to the average measured chlorine concentrations (e.g. those in Figure 5).

451

4.3 Limit (threshold) of quantification of wall-decay rate

452

Even though wall-decay rate was not quantifiable in the Greenvale-Sydenham system, it was

453

still possible to estimate the quantification limit (QL) for each pipe. A kw0 value of only 0.007

454

mg/dm2/h was needed in pipe2 to reduce total chlorine by 0.05 mg/L at S2E during

455

pumps_on. This kw0 value is small, but even so, it could still not be quantified in the

456

Greenvale case because the bulk decay model predicted a marginally lower chlorine level

457

than measured. In contrast, higher kw0 values of 0.79 and 0.35 mg/dm2/h were required in

458

pipes 1 and 3 respectively, as they are so much shorter. Again, the very small differences

459

between bulk model predictions and measured chlorine drop over each pipe (within

460

measurement error) precluded quantification of any wall decay.

461

The QL for wall-decay rate in each pipe of the Mirrabooka system at each time was similarly

462

determined. Results (Figure 6) show that, in every case, positive estimates of kw0 were all

463

greater than the corresponding QLs. The latter were about 0.04 mg/dm2/h all year, except in

464

Jun04 when they were about 0.02 mg/dm2/h. This is probably due to the flows in Jun04 being

465

less than half those at other times, so that smaller kw0 values could achieve the standardised

466

0.05 mg/L drop in chlorine. In contrast, pipes for which zero kw0 was estimated had higher

467

QLs (0.04-0.09 mg/dm2/h) because these were the largest-diameter pipes.

468

4.4 What is the functional form of wall-decay rate along a pipe run?

469

The optimised value of kw0 for each pipe length of the Mirrabooka pipe run in each period is

470

plotted against travel time in Figure 7. Of the seven non-zero differences between adjacent

471

pipes, six were positive (i.e. kw0 increased with distance downstream). The single negative

472

difference is probably due to the almost-zero chlorine level in the last pipe in Mar03; that is,

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ACCEPTED MANUSCRIPT the corresponding kw0 was transport-limited by the low chlorine concentration in the bulk

474

water, rather than any inherently lower demand at the wall. No wall decay could be

475

quantified in any period until travel time exceeded 4h. The “onset” of quantifiable wall-

476

reaction rate at the same travel time (and hence at different distances downstream) in each

477

period suggests that it occurs at some minimum velocity. It does not appear to be positively

478

related to chlorine concentration, as that concentration is markedly higher in Jun03 than in

479

any other period.

480

As travel-time increased further, kw0 increased linearly at the same rate in all periods except

481

Jun03, when it increased much more slowly. In contrast, measured and predicted chlorine

482

concentrations decreased monotonically downstream (e.g. Figure 5), strongly suggesting that

483

rw is inversely, rather than directly related to chlorine concentration as implied by the FO

484

assumption. Neither is it constant, as implied by the ZO assumption (Figure 2). This was

485

corroborated by plotting the quantified wall-decay rates against bulk chlorine concentrations,

486

for each period (Figure 6). That is, wall-decay rate was not a ZO or FO process in this

487

system, as has been previously universally assumed. In contrast, the inverse relationship is

488

well explained by the biofilm-mediated wall-decay model EXPBIO (Eq. 13 developed in

489

section 2.3), as shown by its close approximation (Figure 8) to the quantified wall-decay rates

490

for all non-Jun03 periods, using a single set of parameter values. A similar result was

491

obtained for Jun03 (Figure 6A) using a different parameter-set to account for the different

492

source-water.

493

Making different assumptions regarding the relationship between wall-decay rates and

494

chlorine leads to substantial differences in predictions of longitudinal chlorine concentrations.

495

These are illustrated in Figure 9 for Mirrabooka water. Assuming FO or ZO (Figure 2) can

496

only result in concave-downwards longitudinal chlorine profiles, which leads to considerable

497

error in the upstream region compared with the near-zero difference from bulk decay

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ACCEPTED MANUSCRIPT obtained from the EXPBIO model. In the downstream region, only the EXPBIO model can

499

predict accelerating wall decay with decreasing chlorine concentration, due to the real inverse

500

relationship between wall-decay rate and chlorine concentration.

501

4.5 Mass-transport limitation

502

Overall wall-decay rate rw is controlled by two processes in series – mass-transport and wall-

503

reaction – so it cannot increase indefinitely with decrease in chlorine concentration. As

504

discussed in section 2.2, wall-decay rate will eventually become transport-limited with

505

decreasing chlorine concentration, even in turbulent flow, because it is proportional to

506

chlorine concentration (Eq. S3).

507

During the pumps_on period in the Greenvale-Sydenham system, the flow was approaching

508

full turbulence from Greenvale to Sydenham Reservoir inlet (1.0×106
509

assuming the usual hydraulic roughness for an asphalted lining. Although unlikely at such

510

high Re and relatively high chlorine concentrations (>0.4mg/L), limitation of chlorine

511

transport to the wall could not be evaluated because the quantified wall-reaction rate was zero

512

along this entire pipe run.

513

In the Mirrabooka pipe run, flows were also near fully-turbulent (0.3×105
514

considering the greater hydraulic roughness of cement lining. Eq. S3 implies that the

515

quantified wall-decay rates (rw) should not exceed the calculated mass-transport rate

516

(km×CCl). The rw results generally supported this theory, although three somewhat higher rw

517

values were obtained from the lower pipes (Figure 6).

518

On a plot of rw against chlorine, the limit to mass-transport for a given flow regime is a

519

straight line from one of the calculated points to the origin (Section 2.2), as chlorine

520

concentration decreases down the pipe (due to bulk and wall decay). These limits are shown

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ACCEPTED MANUSCRIPT as dotted lines for each measurement period in Figure 6. The effect of mass-transport

522

limitation is to reduce wall-decay rate sharply as chlorine concentration approaches zero.

523

4.6 Combined functional form for wall-decay rate

524

The functional form for wall-decay rate under a given flow regime is therefore a combination

525

of a linear increase with chlorine concentration (from the origin), to represent the transport-

526

limited component, followed by an intersecting negative exponential curve to represent the

527

rate when limited by the intrinsic wall decay.

528

These combined functions had similar shape in each of the three measurement periods in

529

which rw was positively quantified (Figure 6). However, the maximum rw differed by a factor

530

of three. This could be due to generally lower levels in Jun03 resulting from lower biological

531

growth on pipe walls due to supply of better quality source water. It may be due to greater

532

inhibition of biofilm growth by higher chlorine concentration along the pipe run. Lower

533

temperature in June is an unlikely cause, as all kw0 were standardised to 20°C using an

534

Arrhenius function of temperature, which was derived for the bulk-decay coefficients defined

535

in Eq. 4.

536

The proposed wall-reaction rate profile supports the hypothesis that chlorine consumption on

537

the wall is facilitated by biofilm and increases as chlorine concentration in bulk water

538

diminishes below 0.5 mg/L. This provides a basis for detailed mapping of biofilm

539

development under diminishing chlorine concentration and the possibility of controlling

540

biofilm and therefore also chlorine decay.

541

The reaction of chlorine with DOC in water leads predominantly to partial oxidation of DOC

542

and part chlorination to form chlorinated and brominated organic compounds. Ramseier et

543

al. (2011) recognised that pre-oxidation with ozone or permanganate increases AOC, but

544

chlorine has limited impact. Whether DOC metabolites formed after chlorination can promote

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24

ACCEPTED MANUSCRIPT biofilm growth and consequently accelerate chlorine decay needs verification in full-scale

546

systems, as this would have major implications for optimisation of water treatment. Liu et al.

547

(2002) measured AOC using a technique based on van der Kooij et al. (1987) at three WTPs

548

and two sites along each corresponding downstream pipe, after secondary disinfection with

549

chlorine. They concluded that AOC along distribution pipes was a balance between increase

550

due to oxidation followed by decrease due to biofilm, which varied with season and system-

551

specifics such as flow. However, no flow modelling and only the broad range of disinfectant

552

doses were presented. It is therefore not possible to relate these findings to chlorine

553

concentration.

554

4.6 Corroboration of wall-decay rate function in dynamic (DSMtool) models

555

Results from the dynamic network models set up in DSMtool are given in Sections S3 and S4

556

for Mirrabooka and North Richmond respectively. In each period, the optimised Deq was zero

557

in the same upstream pipes as those for which optimised kw0 values were zero; i.e. wall-decay

558

rate was also not quantifiable in the same pipes in the dynamic model. Deq then subsequently

559

increased downstream in both systems (Figure S7), just as kw0 did in the constant-flow

560

models for Mirrabooka. That is, the same behaviour of increasing surficial wall-decay rate

561

with decreasing chlorine concentration was evident under dynamic flow conditions after

562

rechlorination.

563

Better understanding of wall-decay mechanisms enables implementation of new strategies to

564

control disinfection throughout distribution systems. For example, it is possible that biofilm

565

density and therefore chlorine stability will be influenced by initial condition of the system. A

566

clean system may have good penetration of chlorine and inhibition of biofilm growth, but

567

resilient biofilm may form over time which accelerates chlorine decay. Such a system may

568

exhibit significant hysteresis, depending on whether it starts from a dense-biofilm or no-

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25

ACCEPTED MANUSCRIPT biofilm state. Additionally, it may be feasible to periodically increase chlorine residuals to

570

burn biofilm, so that wall decay remains suppressed for an extended time, even when chlorine

571

dose is returned to the pre-cleaned level.

572

5. CONCLUSIONS

573

Major advances were made in measuring and modelling distribution-system chlorine

574

concentrations, from post-filtration dose to system extremities. In scientific terms:•

Bulk decay was first rigorously separated from wall decay, by subtracting bulk decay

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569

generated from a decay model derived only from laboratory decay-tests on post-

577

filtered water (not on any samples from the distribution system). The 2RA model, or

578

possibly the VRC model, is sufficiently accurate for this purpose, while also enabling

579

efficient representation of a wide range of system operating conditions.

580

•

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Surficial wall-decay rates (WDRs) were then accurately quantified along a series of contiguous pipes, from high to low chlorine concentrations, so that a functional

582

relationship with chlorine could be developed. •

586 587 588

•

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exceeded that possibly arising from chlorine measurement error.

584 585

A method was developed to estimate the quantification limit, to show whether a WDR

Results from three disparate systems consistently showed WDR increased to a maximum (of approximately 0.15 mg/dm2/h) as chlorine concentration decreased

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from high levels, then decreased as chlorine concentration approached zero. The WDR increase contradicts all wall-decay models provided within EPANET, the most

589

widely-known system modelling package, and its commercial derivatives. The WDR

590

decrease was due to limitation of chlorine transport to the wall, arising from low

591

concentration (driving force) rather than lack of hydraulic transport.

26

ACCEPTED MANUSCRIPT 592 593

•

A new model (EXPBIO) was developed to adequately describe all these effects on WDR and which is suitable for system-wide modelling.

The scientific advances also provide a sound basis for advances in professional practice of

595

system modellers and managers. The EXPBIO model can be built into the EPANET-MSX

596

(Multi-Species Extension) package by users themselves, just as the 2RA bulk model has

597

been. It can therefore be applied to any system represented within the EPANET package. The

598

EXPBIO parameters can be efficiently estimated for such a system, after fitting an accurate

599

bulk-decay model to decay-tests on post-filtered water, by utilising in-system chlorine

600

measurements in the 0.1-0.5mg/L range. The quantification limit can also be estimated to

601

check whether WDRs exceed that possibly due to chlorine measurement error. This

602

procedure mostly improves the accuracy of predicting low chlorine levels near system

603

extremities, where bacterial regrowth is highest and risk of failing bacterial indicators is

604

greatest. False conclusions regarding the cause of low chlorine levels (bulk or wall decay)

605

may also be avoided. It also provides a rigorous basis for exploring whether seasonal/event

606

variations in treated water quality affect either bulk- or wall-decay rates. Additionally, it

607

provides a better basis for prediction of DBP formation, using the well-documented link

608

between this formation and chlorine reacted. Consequently, more appropriate system

609

disinfection strategies can be devised using the EPANET-MSX model to ensure that adequate

610

disinfection can be maintained to system extremities, while DBP formation is kept below

611

regulated limits.

612

6. ACKNOWLEDGEMENTS

613

The authors were responsible for the field and laboratory data collection. This and

614

developing/running the EPANET/DSMtool system models were contributions to the research

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ACCEPTED MANUSCRIPT program of the Australian Cooperative Research Centre for Water Quality and Treatment by

616

Melbourne, Sydney and Western Australia Water Corporations.

617

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ACCEPTED MANUSCRIPT Table 1 Characteristics of three systems selected for range of conditions of interest Source water

Greenvale- Raw Sydenham (27,000 ML Melbourne reservoir) Mirrabooka Perth

Treated1 groundwater/ artesian blend

Pipe dia./ lining Large (1700 mm max) Bitumen Medium (300770mm) Cement

Tanks (on pipe run) 2

0

Flows Pumps on 5h Pumps off 19h Daily averages/ full extended period (EP) simulation Full (EP) simulation

Free Cl (mg/L) 1.6-0.4

0.6<0.1

Season Summer

Summer Autumn Winter Summer

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North Treated2 river Small (200 2 0.75Winter Richmond water mm min) rechlor0.1 Spring Sydney Cement inated Summer 1 Aeration followed by conventional coagulation/sedimentation and filtration 2 Conventional coagulation/sedimentation and filtration followed by GAC adsorption.

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3

4

1350 2220 -

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System Greenvale-Sydenham Diameter (mm) 1700 1150 900 Length (m) 600 21420 1360 Mirrabooka Diameter (mm) 767 675 457 294 Length (m) 839 717 988 871 North Richmond Diameter (mm) 615 455 254 194 Length (m) 1840 1800 2550 4060

Yuroke branch

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Pipe

ACCEPTED MANUSCRIPT Table 3. Parameter values for bulk decay models derived from laboratory decay tests and modifications made to represent bulk decay in Greenvale and Mirrabooka systems. Cf0 [mg/L]

Cs0 [mg/L]

kf [L/mg/h]

ks [L/mg/h]

E/R [K]

0.50

2.65

5.0

0.0073

9050

Mirrabooka Jan03, Jun03, Feb04 Jun03

4.1 -

49.9 22.9

0.0054 -

0.0017 0.0017

1300 1300

North Richmond

0.535

20.7

0.0215

8.47e-5

19100

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Parameter Model Greenvale

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Figure 1. Processes affecting bulk and wall decay in a pipe. Wall decay decreases chlorine concentration in laminar sub-layer (dotted). Mass transport limits decrease to zero concentration at wall (full line).

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Figure 2. Theoretical zero-order (ZO), first-order (FO) and EXPBIO wall decay rates as functions of chlorine in a uniform-diameter pipe, including lateral mass-transfer limitation.

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Cl dose

Q1

S1

Yuroke Tank

S1E S2

Yuroke Q2 Zone S2E S3

S3E

S4

Sydenham Qout Tank

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Figure 3. AQUASIM model of Greenvale Reservoir-Sydenham Tank system. Sn (n=1,2…) are upstream pipe ends. Label SnE refers to the downstream end of the nth pipe. Chlorine measurement sites are S1, S1E, S3E and S4. Qn are discharges.

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S2E S3

S3E S4

S5 Q5

Qin Q1

Q2

Q3

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High Level Tank

S1E S2

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Figure 4. AQUASIM model of Mirrabooka pipe run abstracted from Mirrabooka High Level system model (shown in Figure S2). Sn (n=1,2…) are chlorine measurement sites. Label SnE refers to the downstream end of the nth pipe. Qn are discharges.

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Figure 5. Measured and predicted free chlorine in Mirrabooka system in Jan03.

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Figure 6. Mirrabooka wall-reaction (kw0) and mass-transfer (mt) rates as functions of chlorine concentration in A) Jun03, B) Jan03, and C) Mar03 and Feb04. Quantification limit (QL) is defined in text. Dotted lines show implied transfer-limited rates for lowest chlorine concentrations. EXPBIO_jun are model predictions of wall reaction rate for Jun03 (parameter values: A=4, B=9, km=0.4).

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Figure 7. Mirrabooka wall-reaction rate (kw0) as a function of travel time at different times of year.

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Figure 8. Quantified wall-reaction rates (kw0) along Mirrabooka pipe run compared with EXPBIO model predictions (parameter values: A=1000, B=26, km=0.8). Figure 6A shows Jun03 predictions.

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Figure 9. Chlorine concentration in Mirrabooka water flowing along a single pipe undergoing bulk decay, different assumed relationships of wall-decay rate with chlorine concentration, and masstransport (m/t) limitation (ltd). Bulk only – no wall reaction, ZO wall – zero-order wall reaction, FO – first-order wall reaction, EXPBIO – new wall reaction model.

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Figure 10. Comparison of wall decay rate (rw) calculated from Mirrabooka data with corresponding mass-transport limited values (km*CCl).

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Wall decay is measured as chlorine loss in-pipe minus modelled loss from bulk water Wall decay rates were not quantifiable in large pipes even when chlorine >0.5mg/L Wall decay rates increased as chlorine concentration decreased below 0.5mg/L These relationships are consistent with biofilm activity at lower chlorine levels A new model was proposed to describe this behaviour and mass-transport limitation

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