Modeling of breakpoint reaction in drinking water distribution pipes

Environment International, Vol. 19, pp. 543-560, 1993 0160-4120/93 $6.00 +.00 Printed in the U.S.A. All rights reserved. Copyright @1993 Pergamon Press Ltd.

MODELING OF BREAKPOINT REACTION IN DRINKING WATER DISTRIBUTION PIPES

Chungsying Lu Department of Environmental Engineering, National Chung Hsing University, Taichung, Taiwan 40227, R.O.C.

Pratim Biswas Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, OH 45221, U.S.A.

Robert M. Clark Drinking Water Research Division, U.S. Environmental Protection Agency, Cincinnati, OH 45268, U.S.A.

El 9302-113M (Received 15 February 1993; accepted 20 June 1993)

A mathematical model accounting for concurrent mass transfer and a series of chemical reactions under the breakpoint chlorination is developed to predict disinfectant concentration profiles in the drinking water distribution pipe. The model is validated by comparing its numerical solutions to experimental data in the literature. The impact of important parameters on the model perfor- mance is examined by a sensitivity analysis. Practical applications of the model to minimize water quality deterioration in the distribution system are discussed in view of the results. This work can provide insight into the factors that influence all of the fundamental reactions and disinfectant transport of the breakpoint reaction. Operational criteria for the chlorination of distributed water are derived.

INTRODUCTION

There are two commonly encountered problems with regard to water quality control in the drinking water distribution system. The first problem is that of taste, odor, and contaminants in water. The other is deterioration of bacteriological quality (White 1986). To effectively control these problems, it is imperative to maintain a disinfectant residual in distributed water.

Chlorine is the most widely employed disinfectant in the United States (McGuire and Meadows 1987). A drinking water utility must be able to predict the

location at which the chlorine concentration drops below a certain minimum desired level to ensure low bacterial concentrations in distributed water. Once this location is determined, chlorine may be rein- jected or a higher dosage of chlorine added at the treatment plant to satisfy the chlorine demand in the entire network. As a result, the chlorine residual is an excellent parameter for studying water quality in the drinking water distribution system.

If finished water that leaves the treatment plant does not contain nitrogenous compounds, the chlorination of distributed water would be relatively simple. A first order decay rate constant, k, is sufficiently

543

544 C. Lu et al

NOMENCLATURE

C Molar concentration of free chlorine, mol L "x

Ct Initial concentration of free chlorine, mg L "x

Co Initial molar concentration of free chlorine, reel L "1

Ct.G Molar concentration of HOCI, NHa, NH2CI, NHCI2, NCI3, and I, respectively, reel L "=

C .... The cup mixing average molar concentration of species, reel L "t

D3.~ Effective diffusivity of NH2CI, NHCI2. NCI~, and I, respectively, cm 2 s "x

De Effective diffusivity of free chlorine, cm 2 s "~

DN Effective diffusivity of total ammonia, cmz s "t

f(r) Flow parameter, plug flow:f(r)=l, laminar flow:f(r)=2[1-(r/R) 2]

I Intermediates species (ammoniacal nitrogen)

k Rate constant (see Table 1)

K, Equilibrium constant of HOCI, reel L "~

Kb Equilibrium constant of NH4 ÷, reel L "~

N Molar concentration of total ammonia, mol L "~

Nt Initial concentration of total ammonia, mg L ~

No Initial molar concentration of total ammonia, reel L "t

P Sum of the endproducts such as N2, HCI, H20

R Pipe radius, cm

r Radial distance from the center of the pipe, cm

T Water temperature, *K

U,, Average flow velocity in the pipe, cm s "~

Vdj Wall consumption rate, cm s "~

z Axial distance from the inlet along the pipe, cm

Ar Grid size in the radial direction, cm

Az Grid size in the axial direction, cm

employed to describe the reactivity of chlorine with organic or inorganic compounds in the distributed bulk water (Lu 1991; Biswas et al. 1993). However, this is not the case. Nitrogenous substances appear in most treatment plant effluents as either organic or inorganic nitrogen. Van der Wende et al. (1989) reported that the ammonia and nitrate concentrations in a typical treatment plant effluent are 0.1 and 0.2 mg L -1 as nitrogen, respectively. Haas and Karra (1984) showed that the rate of chlorine demand exertion appears to be much slower than the rate of conversion of free to combined chlorine. Therefore, if chlorine is added to distributed water which con- tains ammonia nitrogen, it will rapidly be converted to combined chlorine. In this case, the first order decay rate constant, k, is not adequate in describing these complex reactions between chlorine and ammonia.

In most situations for chlorination of distributed water, the breakpoint phenomenon (where the chlorine to ammonia nitrogen molar ratio exceeds 1.5) is predominant. This is due to the fact that concentration of ammonia nitrogen present in finished water is always low enough to induce the breakpoint reaction. Hence, an understanding of the detailed chemistry of the chlorine-ammonia system as well as the dynamics of breakpoint reaction in the pipe is necessary for minimizing water quality deterioration in the distribution system.

The breakpoint phenomenon has been extensively studied in the water and wastewater treatment plants (Morris and Wei 1969; Pressley et al. 1972; Wei 1972; Saunier and Selleck 1979). However, the kinetics of the breakpoint reaction has been neglected for studying water quality in the drinking water distribution system. This work attempts to study the detailed chemistry of the breakpoint phenomenon and transport of free and combined chlorine residuals in the pipe. The impact of important parameters on water quality is also investigated so that the practical application of chlorination to distributed water can be better understood and analyzed.

THEORY

There are eight chemical reactions relating to the formation and hydrolysis of the chlorinated deriva- tive of ammonia (Morris and Issac 1981). This study employs these chemical reactions and incorporates redox reactions proposed by Morris and Wei (1969) to describe the physicochemical phenomena of the breakpoint reaction in the drinking water distribution pipe. Figure 1 shows a schematic diagram of this process in a plug flow system.

Modeling of breakpoint reaction in water pipes 545

A x n n ~ o ~ ~ ., w

H0Cl + NH3: NH2Cl + H20 H0Cl + NH2Cl : NHCl 2 + H20 H0Cl + NHCI 2 : NCl 3 + H20 NH2CI + NH2Cl = NHCl 2 + NH 3

Redox Reactions ()

Fig. 1, Schematic diagram of breakpoint chlorination in a plug flow reactor.

Basic assumptions

The following assumptions are made in examining the formation of free and combined chlorine by the breakpoint reaction and the transport of these species in pipes:

1. The activity coefficient of chemical species is unity, a reasonable assumption in a dilute liquid.

2. Molecules are the major reactants and products for the formation of chloramines (Wei and Morris 1949). The effect of ion transport is neglected.

3. The effective diffusivity of each species remains constant throughout the pipe.

4. The nitrate end product is negligible compared to nitrogen gas (Pressley et al. 1972).

5. The water temperature and pH value do not change in the pipe, which is valid for chemical reactions in a dilute liquid.

6. Chlorine and ammonia concentration profiles are well mixed at inlet of the pipe.

7. The chemical mixtures are either in a plug flow or in a fully developed laminar flow.

8. The axial diffusion term is neglected compared to the axial convection term.

9. Chloride is not considered because chloride does not react with many species in water.

Chemistry When chlorine is dispersed in pure water as either

a gas or in solution, it rapidly hydrolyzes to HOCI and HCI.

During breakpoint reaction, the HOCI and added NH4+ undergo partial dissociation. The equilibrium chemical reactions and constant expressions are:

HOCI (-~ H + + OCl" Ka = [H+] [OC1-] (2)

[HOC1]

NH4 + <----> H + + NH3 Kb - [H +] [NH3] (3)

[NH4 +]

The temperature dependance of the pKa and pKb values have been established by Morris (1966) and Emerson et al. (1975), respectively

3000.00_ 10.0686 + 0.0253T (4) pK~= T

2729.92+ 0.09018 (5) p K b - T

where T is temperature in °K. Let C and N denote the concentrat ion of free

chlorine and total NH3. Then,

C = [HOCI] + [OCl] (6)

N = [NH4 +] + [NH3] (7)

The effect of temperature and pH value on the distribution of HOC1 in water can be determined by combining equations (2), (4) and (6); while the distribution of NH3 is determined using equations (3), (5) and (7). Therefore,

[HOCI] = c (8)

I + Ka/[H +]

[NH3] - N (9)

C12 + H20 ~-~ OCl + H + + CI" (I) I + [H+]/Kb

546 C. Lu et al,

The following sequence of chemical reactions between HOCI and NH3 is known to form inorganic chloramines in a series of bimolecular reactions (Morris and Issac 1981):

NH 3 + HOCI k f!

NH2CI + H 2 0 km

(10)

kt2 NH2CI + HOCI ~ NHCI2 + H20 (11)

kh2

k f3 NHC12 + HOCI ~ NCI 3 + H20 (12)

k~

As the molar ratio of chlorine to ammonia exceeds 1.5, the disproportionation of NH2CI takes place according to (Morris and Issac 1981)

kind 2 NH2CI ~- NHCI2 + NH3 (13)

kam

The decomposition of NHCI2 in an aqueous system might slowly produce the intermediate reactive species I (ammoniaeal nitrogen) and P (the sum of the end products such as N2, HCI, H20) (Morris and Wei 1969):

km NHCI2 + H20 --," I + P (14)

Assuming that nitrogen gas is the only end product of the ammonia nitrogen oxidation, the intermediate species, I, further reacts rapidly by two competing reactions (White 1986; Morris and Wei 1969):

kd2 I +NH2CI ~ N2 + P (15)

kd3 I + NHCI 2 ~ N2 + P (16)

Previous studies (Morris and Issac 1981; Leao 1981; Leao and Selleck 1981) of the kinetics reactions between aqueous chlorine and ammonia reported rate constants and expressions for the formation of chloramines and nitrogen gas. These are summarized in Table 1.

Mass balance equations

Consider chemical species j with an average flow velocity Uav entering a long circular pipe in a steady state condition. The transport process is described by

0 cj D_t 0 Uav f (r) = Oz r 0-r (r o r ) (17)

where Cj is the concentration of the species j; Dj is the effective diffusivity of species j; f(r) is the flow parameter term depending on the flow pattern (for laminar flow:f(r)=2[1-(r/R)2], for plug flow:f(r)=l); R is the pipe radius; r is the radial position in the pipe; and z is the axial distance along the pipe. As a series of chemical reactions occur, equation (17) is rewritten for each constituent accounting for these reactions. The mass balance equation of each constituent inside the pipe thus becomes

Free chlorine (C) mass balance:

Uavf(r) OC Dc 0 "~r 0z - r 0r (r )-kflCIC2+khlC3

-kf2 CI C3 + kh2 C4 - kf3 C1 C4 + kh3 C5 - kl C

(18)

Total NH3 (N) mass balance:

Uav f (r) O N Oz

DN 0 ON r Dr (r~j-kftClC2+khtC3--'

- kdra C2 C4 + kind C3 C3 - k2 N

NH2CI (C3) mass balance: (19)

Uav f (r) 0 C3 D3 0 ~ r 3 0z - r 0r (r )+kftCIC2-khlC3

- kf2 C1 C3 + kh2 C4 + kdm C2 C4 - kmd C3 C3

- kd2 C3 C6 - k3 C3 (20)

NHC12 (C4) mass balance:

Uavf(r) 0C4 _ D4 0 0z r Or

( r~ C4) + kf2C1 C3 - k h 2 C 4

- kf3 CI C4 + kh3 C5 - kdm C2 C4 + kind C3 C3 - kd I C4

- kd3 C4 C6 - k4 C4 (21)


Table 1. Summary of rate constants and expressions for aqueous ammonia-chlorine system.

Rate Constant Arrhenius Expression Rate Constant at 25"C Rate Expression References

kn, M "~ s" 6.60xl0~exp(-1510/T) 4.20x106 kn[NHa][HOCI ] (M&I)

khl, S" 1.38x10Sexp(-8800/T) 2.10xlO "s kht[NH2C! ] (M&I)

ku, M "t s "1 3.00xl0Sexp(-2010/T) 3.50xi02 kn[NH2CI][HOCI ] (M&I)

kh2, S 1 7.60X10 "7 kh2[NHCI2] (M&I)

kf3, M "~ s t 2.00x10Sexp(-3420/T) 2.1 ks[NHCI2][HOC1] (M&I)

ks, s "t '5.10xl03 exp(-5530/T) 4.50x10 "5 kh3[NCl3] (M&I)

k~d, M "l s "1 8.00xl01exp(-2160/T) 5.60x10 "2 kmd[NH2CI][NH2C1] (M&I)

kdm, M "1 s "l 24.0 kd,[NHCI2][NHa] (M&I)

kd l, M "l s "1 2.77x102 kdI[NHCI2][OH'] (L&S)

kd2, M "~ s "~ 8.33x103 kd2[I][NH2CI ] (L&S)

kd3, M "1 s "1 2.78x104 ka3[I][NHCI2] (L&S)

M&I (Morris and Issac 1981); L&S (Leao and Selleck 1981)

NCI3 (C5) mass balance:

Uav f (r) 0 C5 D._.55 ~__ 0C5. 0z = r Dr (r---~-r) + kf3 Cl C4

- kh3 C5 - ks C5 (22)

I (C6) mass balance:

Uavf(r) OC60z - D 6 ~ r ( r - ~ r 6 ) + k d l C 4 - k d 2 C 3 C 6 r

- kd3 C4 C6 - k6 C6 (23)

where C1 and C2 denote the molar concentration of HOC1 and NH3; and kj (j = 1, 2, • • .,6) represent the first order decay rate of C, N and C3-6, respectively, with organic compounds or microorganisms in the bulk water. The boundary conditions are

z = 0 , C = C o , N = N o , C3-6=0 a t 0 < r < R

r = 0, 0C/0r = 0N/Dr = 0C3-6/0r = 0 at 0 < z

r = R, DcOC/0r = -VdlC, DN 0 N/0r = -Vd2N,

Dj 0 Cj/0r = -Vdj Cj (j=3,4,5,6) at 0 < z

(24)

where Co and No depict the molar concentration of free chlorine and total NH3 at inlet of the pipe; and Vdj are the wall consumption rate of C, N, and C3-6, which are proportional to the degree of absorptivity of the pipe surface (Lu 1991; Biswas et al. 1993). The consumption process at the pipe wall can be viewed conceptually by analogy to the transfer of mass or heat flow from the bulk liquid phase to the pipe surface. Three different wall conditions may be used depending on the wall characteristics:

548 C. Lu et al.

(a) perfect sink (Vdj----~ oo or C = N = C3-6 = 0), (b) no consumption (Vdj = 0 or OC/3r = 0N/0r

= 0C3-6/0r = 0), (c) partial consumption (Vdj is some finite value).

Equations (18) to (23) along with the appropriate boundary conditions form a set of coupled partial differential equations (PDE) that describes disinfectant transport under breakpoint reaction in the pipe. Using an explicit finite-difference scheme at P radial points across the pipe, the six PDE's are transformed to 6xP ordinary differential equations (ODE). These are then solved by a stiff ordinary differential equation solver, DIVPAG (IMSL 1987). The cup mixing average concentration (Cavcm) in the pipe at any location z is obtained by

Ca.cm(Z) =

R f~0 C (r, z) Uav f (r) r dr

~Uav f (r) r d r

(25)

RESULTS AND DISCUSSION

Model verification

Model parameters were chosen based on the experimental system for a plug flow reactor (PFR) reported by Saunier and Selleck (1979). The PFR consisted of a 13 200 cm long, 1.9 cm diameter PVC pipe. The inlet flow rate was 120 cm 3 s 1 which provided an inlet veloci ty of 42.3 cm s "l and a Reynolds number of 8380.

As indicated, the flow conditions in the pipe are turbulent. The eddy diffusivity has to be used as it is typically some orders of magnitude larger than the molecular diffusivity. An approximated est imate

of the eddy dif fus ivi ty provided by Edwards et al. (1979) was used to compute the effective diffusivity (Deddy = 1.233 x 10 -2 Uav R = 0.495 cm 2 s-l). Reac- tivity of chlorine species with organic compounds or microorganisms in the bulk water can also be neglected (kj = 0) compared to rate constants of the breakpoint reaction. Since the experiment was based on a laboratory-scale PVC pipe which is resistant to corrosion of chlorine residual, it is reasonable to neglect consumption of these chlorine species at the pipe walls (Vdj = 0). The rate constants of kh2, kdm, kdl, kd2 and kd3 described in Table 1 were measured at 298°K values, and a common formula stating rate constants are doubled for every 10°K increase in temperature (Montgomery 1985) is used in this work.

On solving the model equations with the literature values listed in Table 1, discrepancies are observed between model simulations and experimental data for chloramines. These may be due to: (1) the rate constant of kdl was measured in the presence of excess ammonia (C0/N0< 1.5), an area which has been essentially ignored in recent years (Saunier and Selleck 1979), (2) the formation of NC13 occurs only at very low pH values (<4.4) or at high C0/N0 (<1.5) (Wolfe et al. 1984). All the experimental data of kf3 in the literature were measured below pH 4.6 due to the instability of NHC12 in the presence of excess HOCI (Morris and Issac 1981). Therefore, errors are ex- pected if these rate constants are employed in the simulation of breakpoint reaction. Better agreement with experimental data is obtained if the value of kdl about 2 to 3 orders of magnitude (see Table 2) larger than that listed in Table 1 is used. This range of kdl is consistent with that reported by Wei (1972). The reported value of kf3 in Table 1 was replaced by a value determined by trial and error leading to the best fit of simulated NC13 to experimental data.

Table 2. Simulation conditions for the breakpoint reaction in the pipe.

Figure No. pH T,°K Nt,mg/L Co/N o kal,M-'s "1 ko,M'ls -1

2 7.20 288.3 0.95 1.97 4.0 x 104 20

3 7.60 288.5 1.02 2.77 5.5 x 104 40

4 8.10 288.4 0.98 1.94 2.0 x 104 100

Model ing of breakpoint react ion in water pipes 549

Three different process conditions were selected as case studies. Table 2 lists the system parameters and the respective values of kdl and kf3 used for the simulation of breakpoint reaction. The disinfectant concentration profiles along the pipe are shown in Figs. 2, 3 and 4. As can be seen, the simulated concentration profiles match the experimental data well.

It is seen from Table 2 that the value of kdt is in proportion to the value of C0/No. This agrees with the statements of White (1986), who reported that the decomposition of NHC12 is enhanced as the value of Co/No increases. On the other hand, the value of kf3 is proportional to pH value. The pH value ranges analyzed here has not been studied in the literature to confirm this observation.

Sensitivity analysis The pH value, water temperature, initial reactant

concentration, and molar ratio of chlorine to ammonia nitrogen are well known factors that influence the disinfectant concentration profiles under the breakpoint reaction. Another factors that may affect disinfectant concentrat ion profi les are the numerical technique, the inlet flow rate, and the uncertain parameters kdl and kf3. The system parameters of Fig. 3 were chosen as the base case (no symbol lines) to be used in the sensitivity analysis. Trials are con-

ducted at above (squares) and below (circles) the base case by certain factors.

The stability of the numerical scheme as a function of the grid size (Ar, Az) was determined. Trials with points of 40 and 10 in the radial direction using perfect sink wall condition (Cj = 0 at r = R) yield concentration profiles nearly identical to that of 20 points used in the base case. It is also found that varying Az from 10 "1 to 10 -3 cm produces essentially identical solutions. These imply that the numerical scheme used in this study is reliable and stable.

The impact of water temperature on free chlorine and NH2CI is shown in Fig. 5a; while the impact of water temperature on total chlorine, NHCI2 and NC13 is shown in Fig. 5b. As indicated, free chlorine is insensitive to varying water temperature, on the other hand, total chlorine, NH2C1 and NHCI2 are lower at high water temperatures. The temperature ef fec t on total chlorine is in accord with the experimental results (Wei and Morris 1974), which demonstrated that the rate of decrease in total chlorine is reduced as temperature is decreased. The rate of increase in NCI3 is slower for a higher temperature water.

The effect of varying pH values from 6.6 to 8.6 on free chlorine and chloramines is shown in Fig. 6. It is seen from Fig. 6a that a higher pH value results in higher free chlorine and NH2C1. This is because at a

S ' "

o ~ a

"5

=:1 O -1 0

._o

e¢.

o

:~1 O -=

_ [ ] • ,

T o t a l C h l o r i n e & A

Free C h l o r i n e A J - - ~ N H ~ C l A - ~ \ -~

\ . \ , , I , = , = , ! , I - I , , , , , , , !

~ 2 5

0 ~ 10 5 10 + Axial D is tance, z (crn)

Fig. 2. Breakpoint chlorination kinetics of tap water in a plug flow reactor (pH = 7.2, T = 288.3°K, Ni = 0.95 mg L "= and CJN° = 1.97).

Lines = s imula t ion results; symbols = exper imenta l data (Saunier and Sel leck 1979).

550 C. Lu et al,

• 2

0 0

1 • o

5

.

<

"6 2.

o 1 0 -1.

0 s o _ToLal _Chlorine w ~ • \

n~ ~ Free Chlorine \ 131 ;, N H.,Cl \ \ A A ~

: ~ 1 0 - = , , , , , , , , , ,, 2 5 2 5

0 ~ 10 4 10 ~ Axiol Dis tonce, z (c rn)

Fig. 3. Breakpoint chlorination kinetics of tap water in a plug flow reactor (pH = 7.6, T = 288.5°K, Ni = 1.02 mg L" and Co/N, = 2.77).


5 -

c:

2 =

Z 1 ":

.

0 5 - E E <

~ 1 0 -1 _ o

. i .a

o s . ~ 4.4 o

cJ o ~ 1 0 -2

• • • •

@ •

~, Free Chlorine ,-~ a NH=Cl " \

2 5 10 4

Axial Distance, z ( c m )

o O 1 i

A z~

Fig. 4. Breakpoint chlorination kinetics of tap water in a plug flow reactor (pH = 8.1, T = 288.4°K, N, = 0.98 mg L", and CJNo = 1.94).



e-

o

Z 5

t- O E E

<

~ 1 0 -I _ c "

o 4 - . '

o ° - - =t .J

o h -

i... - -

o

:~10 -=

.... G

,El , , \ \ \

0 3 Axial

F r e e C h l o r i n e - - - - N H = C l

\ \ \

\ \ \

\ \ \

\ \ \

\ \ \

, ~ , , , , ' b

10 4 Distance, z (cm)

(o)

c- G) ~a 0

Z

o - - c- o

E E

<C

"5

10

T o t a l C h l o r i n e - - - - NHCI=

° - -

- - "1:1 , , \ (g. o10 -1 . ~ \ \ \

- \ \ \

o , e t ~ " % - - - > : ' - . . . - < " \ \

" 5 1 0 - 2 ~ . . . . . . ~ ,.., , , ' ' ' ' ' I ' ' ' 2 5 2

10 ~ 10 + Axial Distance, z (cm)

(b) Fig. 5. Effect of water temperature on the disinfectant concentration profiles:

(a) free chlorine and NH2C1, (b) total chlorine, NHCIffi and NCI~.

O = 278°K, 1"7= 298°K, no symbol lines = 288.5°K.

.552 C, Lu o t a l

2

L ° -

Z

.2 c- O

E E =

<

o ~ 1 0 -1 _ E

0

o n,"

2- t

o 0

"~10 -2

10 3

---. - - 0 0 0

\ \ \ "Q \ \

\ \ \ \ \

\ \

"o\ \ \ Free Chlorine \

_ _ N H = C l \ \ \

R\ \ \

\ \

I I ~ . . . . I ~

10 4 Axial Distance, z (cm)

(0)

\ \

.~ . . '1

C "" v

m \

\ ! !

10 I= (D 5

0

Z 2

o

c 1 o

E E

<

o

"E

o 1 0 -I

o o ~ 4 , J

o n~

L . 1J 2

o

:~10 -=

Total Chlorine _ _ NHCI= . . . . . NCI=

10 10 ~ Axial Distance, z (cm)

Cb) Fig. 6. Effect of pH value on the d is infectant concentra t ion profi les:

(a) free chlor ine and NH=C1, (b) total ~hlorine, NHCI= and NCl=.

O = 6.6, [ ] = 8.6, no symbol l ines = 7.6.


higher pH value, the distribution of HOCI is lower leading to a lower free chlorine consumption rate. The distribution of NH3 is enhanced at a higher pH value leading to a higher NH2C1 formation rate. As the pH of the water decreases, the ammonia molecule becomes more chlorinated (Wolfe et al. 1984), that is NH3 --> NH2C1 ---> NHCI2 ---> NC13. Therefore, Fig. 6b shows higher total chlorine, NHC12 and NCI3 at a lower pH value.

A sensitivity analysis of initial total NH3 (Ni) and initial molar ratio of free chlorine to total NH3 (Co/No) is depicted in Figs. 7, 8, and 9. Figure 7 shows the result for C0/N0 of 2.77 at three different Ni values: 0.51, 1.02, and 2.04 mg L "I. Figures 8 and 9 present the results for Ni of 1.02 mg L 1 and for initial chlorine concentration (Ci) of 14.3 mg L 1 , respectively, at three different Co/N0 values: 1.77, 2.77, and 3.77. For a given Co/N0, an increase of Ni yields lower free chlorine and NH2CI (Fig. 7a). This is because the formation of NH2CI and NHCI2 is a second-order reaction while their decomposition is a first-order reaction. Therefore, the rate of decrease in both free chlorine and NH2CI increases for a higher Ni. On the other hand, an increase of Co/No produces a higher free chlorine and a lower NH2CI at a given Ni (Fig. 8a). This is because, as the chlorine dose is increased beyond s toichiometr ic values (Co/No = 1.5), the free chlorine residual increases in an amount equal to the increase in the dosage (White 1986). The lower NH2CI is the result of the spon- taneous formation of NHCI2 and NH3 from NH2C1 in the presence of excess free chlorine. A lower Co/No provides a higher NH3 for a given Ci, consequently resulting in a higher NH2CI from the direct reaction of HOC1 and NH3, and from a shift in the disproportionation reaction. Lower free chlorine is formed since more HOCI have been reacted by NH3 (Fig. 9a). The NHC12 is higher initially, but a faster decay rate is observed at later times for the condition of higher Ni and C0/No. This agrees with experimental results of Wei and Morris (1974). As Ni and Co/N0 increase, a higher NCI3 exists in the solution. The total chlorine is higher at a higher Co/No but lower at a higher Ni (Figs. 7b, 8b, and 9b).

The influence of various inlet flow rates of 30, 120, 240 cm 3 s 1 is shown in Fig. 10. A flow rate of 30 cm 3 s "t (Reynolds number = 2095) is considered as a laminar flow reactor. In this case, molecular diffusivity is used instead of eddy diffusivity. The estimates of molecular diffusivity are available in the previous study (Lu 1991). As can be seen in Fig. 10, the plug flow reactor results in higher total chlorine, free chlorine, NH2CI and NHCI2 than the laminar

flow reactor. This is because a shorter residence time is obtained for a plug flow reactor. The NCI3 is lower in a reactor with a higher inlet flow rate.

There are two uncertain rate constants, kf3 and kdl, in the study of breakpoint react ion in the distr ibution pipes. Their effects on free chlorine and chloramines are shown in Fig. 11. Circles indicate literature values listed in Table 1, while no symbol lines imply best fit values of experimental data reported in Table 2. Discrepancies would exist between model simulations and experimental data if literature values are used. Higher kf3 and kdl produce lower chloramines and total chlorine but a higher free chlorine.

Practical application

When a breakpoint phenomenon occurs in the drinking water distribution system, the physicochemical properties of each disinfectant must be considered as they influence distributed water quality. As indicated by Montgomery (1985) and White (1986), NHCI2 and NCI3 are re la t ively ineffec t ive ger- micides. In addition, they produce object ionable tastes and foul odors when present in distributed water. Therefore, it is essential to minimize these compounds at the consumer's tap. On the other hand, both free chlorine and NH2CI may produce beneficial as well as adverse effects on public health (Lu 1991). Thus, the development of disinfection methodology, which takes into account the simultaneous transport of optimal free chlorine and chloramines throughout the distribution system, is important for the control of distributed water quality. According to the sensitivity analysis, the operational criteria for the breakpoint chlorinat ion in the dis tr ibut ion system are discussed.

Water temperature. The effect of water temperature on free chlorine is not significant, while some varia- tions take place for the combined chlorine residual. As indicated in Fig. 5, a high temperature water leads to a lower combined chlorine residual and may sub- sequently cause the proliferation of microorganisms at the pipe walls of distribution systems. This is consistent with Plowman and Rademacher's (1958) statement that during the summer, there is a rapid loss of combined chlorine residual. In addition, the chloroform yield and water corrosion rate increase with rising water temperature (Montgomery 1985). To prevent these adverse effects at high water temperatures, a lower Co/N0 may be used to provide combined chlorine residual. The problems of chloroform yield and water corrosion can be minimized by adjusting the pH of the water.

554 C. Lu et al

c. I o L )-- -..

i "" " Z s k ~ "~

. - -

o ~ E \~, \ E 2 \ < \ \

.:E_-I 0 -' [] t - - - - \ o \

,.1_#

o . - -

o 13::

2 L. o -6 : ~ 1 0 -2

0 ~ Axial

10

c (9

o t _

Z

o

~" 1 -- o E ' E s:

<

i o

c

o 1 0 -1

. 0 5 -

o

"° -2 [ ~ 1 0 ,

i . , _ j , _ j ~

\ \

\ \

\ \

\ b \

\ \ \ \

\ \

~ , I , , i

1 0 ' Distance, z (cm)

(a)

Free Chlor ine - - - - NH2Cl

\ \ ®

\ \ q

I ~ I I 2

Total Ch lor ine - - - - NHCl2 . . . . . NCla

,

..... .,--,'-,----------------- . . . . . . . \ \ ~ . . . . . . . . . . . . . . . . . .

. '"'" c~.-'"'" \~ \ O)n-'O--O-O--

i i ~ I i I I i j L . I ~ / I I 2 5 2

10 3 1 0 " Axial Distance, z (cm)

(b) Fig. 7. Effect of initial ammonia nitrogen dose on the disinfectant concentration profiles:

(a) free chlorine and NH2CI, (b) total chlorine, NHCI2 and NCI,.

O = 0.51 mg L "I, [] = 2.04 mg L "I, no symbol lines = 1.02 mg L "I.


o~ o

z 1 t- O E E

,_o

' - 1 0 -1 _ o

.9 o I'Y

L o o

: ~ 1 0 -2

D ,. .7. -.7. o - o 0 . ' 7 . ~

\ \

\ \ 0 \ N \

- - Free Chlorine ~ \ Q - - - - NHaCI \ \ \

\ \ O, \ \

\ \ ®

10 = 10 ~ Axial Distance, z (cm)

(o)

1 0

c a o~ o k =

Z 2

E° 11~

.

~ 2 E

o 1 0 - ' -

.9 s5 o r~

L . o 2 -

0

~ 1 0 -=

Total Chlorine - - NHCl2

I . . . . . NC6

~ . . . ~ . . ~ . . ~ . . ~ . , ~ , = i . ~ l _ l

X \

=_...-...'", o...---??,, ._, g , , 2 5 2

10 ~ 10 4 Axiol Distance, z (cm)

(b)

Fig. B. Effect of initial molar ratio of chlorine to ammonia nitrogen (with Nt = 1.02 mg L") on the disinfectant concentration profiles:

(a) free chlorine and NH,Cl, (b) total chlorine, NHCI= and NCI~.

O = 1.77. [ ] = 3.77. no symbol lines = 2.77.

555

556 C. Lu et al

( -

o

i L.

z 1

o ,I E E "~x <

o ° ~

c - - 1 0 -1 _ 0

o s , ~

o n," I . . 2

o o

" ~ 1 0 -=

a ,

Free Chlorine - - - - NH=Cl

X X \ X

\ \ \

"q, \ \ \ ®

\ \ \

\ \ 'b, N \ \

\ \

' ' ~ . . . . ' l '

1 0 4 A x i a l D i s t a n c e , z ( c m )

(0)

10 c ~ Total Chlor ine

s - - - - NHCI= o ~ ] ~ . . . . . NCI~

"~, 1

< : : -6

oi0 -' I . . . ~ - - ~ - - - G .... G--G-~ o ' ~ .. \~>..___~ ................. ~-~ =~ .........--"..... .......... 9\ \ \ "o\ b -6 _, ~.-"" ..- '"" ~,.~..~,..~---~,-~-o- : ~ 1 0 ~e j , , .~ . . . . , j , ,

1 0 ~ 1 0 " A x i a l D i s t a n c e , z ( c r n )

(b) Fig. 9. Effect of initial molar ratio of chlorine to ammonia ni trogen (with Ci = 14.3 mg L "~) on the disinfectant concentrat ion profiles:

(a) free chlorine and NH=CI. (b) total chlorine, NHCI, and NCh.

0 = 1.77, [ ] = 3.77, no symbol lines = 2.77.

Modeling of breakpoint react ion in water pipes 557

2-

¢- q~

0 L .

z 5~ u

"E 0 E E =

<

o 72_1 0 -1 _ r-

o • , ~ 5 -

.9 u

2 t

o

:~1 0 -~ -

=.=

"o \ \ \ \

® \

b \ \

i •

\

Axial

" - O " C C - ~ "

\

Free Chlorine - - - - NHaCI

\

\ \ \ \

\ \ \ \

\

(~ \ \~

i I%J | | | I I 5

1 0 4 D i s t a n c e , z ( c m )

- I i -

10 r -

Q } 5

o~ o I . _

Z t

E} ° - -

c 1 o E E 5

<

o10-1 :

.o_ 5- o

r~

o 2

o

:~10 -a

. Total Chlorine - - - - NHCI= . . . . . NCI~

\ \ \

\ X ..~ . . . . . . -~-== . . . . ~ - . - . - . l ~ - - - ~ - ~ l a . . . . . . . . . a . . . . . . . . . ~ . . . . . %

2 a t

10 10 ~ Axial Distance, z (cm)

(b) Fig. 1O. Effec t of inlet f low rate on the d is infec tant concent ra t ion profi les:

(a) free chlor ine and NHsCI, (b) total chlorine, NHCI=, and NCI,.

O = 30 c m ' s "I, E l = 240 cm ~ s", no symbol l ines = 120 c m ' s",

558 C. Lu et al.

c-

O

Z

10 ;

2

1

o ° ~

¢'* 2 - o

EF10 -~ - < s:

"EIO -~ "

o s"

0 2-

10

o

: ~ 1 0 ~

10 ~

\ a ,

- Free C h l o r i n e _ _ NH~CI

~,, , ,

Axiol

13 D

\ " a ,

\ \ \

lg \

h J = = J ' l

1 0 ' D i s t a n c e . z ( c m )

(o)

\

\ \

\ 'o

10 - 6 -

z

° ~ 2 -

~ - ~ . . . = .-..-.

~ _ _ e - - - - -e - - e - - o - - o - - o - e e

~- ~ . . . . - ~ To to l Ch lo r i ne " " -.. _ _ _ _ NHCI=

0 "~ . . . . . NClz - I ' ~. '~

< ~ . . . . . . . . . . . . _ ~ _ ~ _e_ - ~ . . . . . . . . . . . . . ,, ~ . ~ -

._o . > ' ~ _ . . . . . . . . . . . . ~ . . . . . . . ~ . . . . ~ - - ~ - - ~ - ~ - a ~

S. i * " Q,, \ t.- o \

: ~ 1 0 "~ " ~ , , ~ - ~ , , , , ~, '~ ,

10 ~ 1 0 ' A x i a l D i s t e n c e , z ( c m )

(b)

!

Fig. I t . Effect of k , and k,, on the d is infec tant concent ra t ion profi les:

(a) free chlor ine and NHjC], (b) total chlorine, NHCIffi and NCh.

O: k~, = 2.1 M "~ s", k,,= 2.77 x 10 = M" s';; [~] : k~,= I00 M'; s", k,, = 5.5 x 10' M" s"; no symbol lines: kts = 40 M" s "~, k°, = 5.5 x 10" M "~ s "~.


The pH value. The pH value of the water is an important water quality factor affecting disinfectant transport in the drinking water distribution system. As shown in Fig. 6, a higher pH water leads to presence of both free chlorine and NH2CI residuals many times longer than a lower pH water without producing chlorinous taste and odor problems. Fur- thermore, corrosion of the iron pipe may decrease at a higher pH level (Montgomery 1985). The disad- vantages of a higher pH water include an increase of THM formation and a decrease of germicidal efficiency (White 1986). Due to the multifarious effects of pH value on quality of distributed water, the selection of an optimal pH value in distributed water must be based on the environmental problems present in the distribution system.

Initial ammonia nitrogen dose. As depicted in Fig. 7, the initial total NH3 (Ni) produces a weak influence on free chlorine, but results in a pronounced effect on combined chlorine residual. For a higher Ni water, a higher amount of end products such as nitrogen gas and NCI~ are formed, consequently reducing the germicidal efficiency. These results indicate that a higher Ni water must be prohibited in the practical waterworks.

Initial molar ratio of chlorine to ammonia nitrogen. As presented in Figs. 8 and 9, the initial molar ratio of free chlorine to total NH3 (C0/N0) has a strong effect on the free and combined chlorine residuals. Decreasing the molar ratio below 1.77 decreases free chlorine drastically, but increases NH2C1. The lower values of Co/No can be considered as a means of controlling biofilm regrowth at the pipe wall. On the other hand, the higher values of Co/N0 can be used for inactivation of suspended bacteria. Selection of the optimal C0/N0, which maintains sufficient free chlorine and NH2CI throughout the distribution system, is imperative to prevent the deterioration of distributed water.

Flow rate. As indicated in Fig. 10, when inlet flow rates are low, which is the case in certain segments of the network (dead-end or off the main branch), the disinfectant concentration profiles along axial distance are relatively small. Furthermore, the low inlet flow rate of the water is insufficient to remove par- ticulates from the pipe wall surface so that deposits formed on the wall can yield sheltered regions which promote the biofilm regrowth rate (Lu 1991). Hence special environmental concerns must be considered under slow flow conditions.

CONCLUSIONS

A mathematical model accounting for mass transfer and the chemistry of the breakpoint reaction in the distribution pipe was developed. The model simulation was verified by comparing its solution to experimental data in the literature. The impact of important parameters on the disinfectant transport were then determined by a series of sensitivity analyses. The following scenarios to maintain distributed water of a high quality under breakpoint chlorination are suggested:

1. At higher water temperatures, use a lower C0/No to provide combined chlorine residuals.

2. Select an optimal pH water according to water quality in a distribution system, basic waters are highly recommended.

3. Prevent a high Ni in distributed water.

4. Adopt an optimal Co/N0 based on the environmental problems of the distribution system.

5. Implement a flushing program in the dead-end, off branch pipes or after a long-term stagnation.

6. The appropriate injection locations can be easily decided from the this study.

Ultimately, it must be recognized that rate constants ofkdl and k s , and the kinetic studies of chlorine residual with pipe wall would require extensive em- pirical supports. In addition, the information of some rate constants (kh2, kdm, kdl, kd2 and kd3) other than 25°C value is needed in an effective modelling.

A c k n o w l e d g m e n t - - This work was supported by the USEPA. The conclusions represent the views of the authors and do not necessarily represent the opinions, policies, or recommendations of the USEPA.

REFERENCES

Biswas, P.; Lu, C.S.; Clark, R.M. A model for chlorine concentration decay in drinking water distribution pipes. Water Res.; 1993. (In press)

Edwards, D.K.; Denny V.E.; Mills, A.F. Transfer processes: an introduction to diffusion, convection and radiation. New York, NY: McGraw-Hill Inc.; 1979.

Emerson, K.; Russo, R.C.; Lund, R.E.; Thurston, R.V. Aqueous ammonia equilibrium calculations: effect of pH and temperature. J. Fish. Res. Bd. Can. 32: 2379; 1975.

Haas, C.N.; Karra, S.B. Kinetics of wastewater chlorine demand exertion. J. Water Pollut. Control Fed. 56:170 ;1984.

IMSL (International Mathematics and Statistical Libraries). Con- tents Document, Vol. 2, Version 1.0, Houston, Texas; 1987.

560 C. Lu et al

Leao, S.F. Chemistry of combined chlorine: reactions of sub- stitution and redox. Ph.D. Thesis, University of California, Berkeley, CA; 1981.

Leao, S.F.; Selleck, R.E. Chemistry of combined residual chlorination. In: Jolly, R.L. et al. Water chlorination, environmental impact and health effects, Vol. 4, Chap. 9. Ann Arbor, MI: Ann Arbor Science; 1981.

Lu, C.S. Theoretical study of particle, chemical and microbial transport in drinking water distribution systems. Ph.D. Thesis, University of Cincinnati, Cincinnati, OH; 1991.

McGuire, M.; Meadows R. A progress report of American Water Works Association, Research Foundation Trihalomethane Sur- vey Report. Presented at conference on current research in drinking water treatment, Cincinnati, OH; 1987. Available from: AWWARF, Cincinnati, OH.

Montgomery, J.M. Water treatment principles and design. New York, NY: Wiley-Interscience Publication; 1985.

Morris, J.C.; Wei, I. Chlorine-ammonia breakpoint reactions: model mechanisms and computer simulation. Presented at annual meet- ing, Am. Chem. Soc., Minneapolis, MN; 1969. Available from: American Chemical Society, Columbus, OH.

Morris, J.C. The acid ionization constant of HOC1 from 5°C to 35°C. J. Phys. Chem. 70: 3798-3805; 1966.

Morris, J.C.; Isaac, R.A. A critical review of kinetic and ther- modynamic constants for the aqueous chlorine-ammonia system. In: Jolley, R.L. et al., eds. Water chlorination, environ-

mental impact and health effects, Vol. 4, Chap. 2. Ann Arbor, MI: Ann Arbor Science; 1981.

Plowman, H.L.; Rademacher, J.M. Persistence of combined available chlorine residual in Gray-Hobart distribution system. J. Am. Water Works Assoc. 50: 1250; 1958.

Pressley, T.A.; Dolloff, F.B.; Roan, S.G. Ammonia-nitrogen removal by breakpoint chlorination. Envir. Sci. Technol. 6: 622-628; 1972.

Saunier B.M.; Selleck, R.E. Kinetics of breakpoint chlorination in continuous flow systems. J. Am. Water Works Assoc. 71: 164- 172; 1979.

Van der Wende, E.; Characklis, W.G.; Smith, D.B. Biofilm and bacterial drinking water quality. Wat. Res. 23: 1313; 1989.

Wei I.; Morris, J.C. Kinetic studies on the chloramines. I: the rates of formation of monochloramine, N-chlormethylamine and N- chlordimethylamine. J. Am. Chem. Soc. 71: 1664-1671; 1949.

Wei, I.W. Chlorine-ammonia breakpoint reactions: kinetics and mechanism. Ph.D. Thesis, Harvard University, Cambridge, MA; 1972.

Wei, I.W.; Morris, J.C. Dynamics of breakpoint chlorination. In: Rubin, A.J., ed. Chemistry of water supply, treatment and distribution. Ann Arbor, MI: Ann Arbor Science; 1974.

White, G.C. Handbook of chlorination. New York, NY: Van Nostrand Reinhold Co., 1986.

Wolfe, R.L.; Ward, N.R.; Olson, B.H. Inorganic chloramines as drinking water disinfectants: a review. J. Am. Water Works Assoc. 76: 74-88; 1984.

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Modeling of breakpoint reaction in drinking water distribution pipes