Ozone Reaction Kinetics for Water and Wastewater Systems - Chapter 7 pps

7.1 RELATIVE IMPORTANCE OF THE DIRECT OZONE–B REACTION AND THE OZONE DECOMPOSITION REACTION *In Section 5.2 and Section 5.3, the kinetic regimes of the ozone decompositionreaction and an

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Reactions of Ozone

in Water

At pH lower than 12, the indirect reactions of ozone develop in the slow kinetic regime

of ozone absorption They are characterized by the presence of dissolved ozone andreaction factors and Hatta numbers lower than or close to unity and 0.3, respectively.Therefore, these reactions are typical of drinking water ozonation where the concen-trations of pollutants are very low (as high as part per million level but usually in thepart per billion level) Also, some wastewater ozonation can develop in this kineticregime as has been shown before — specifically, wastewater with low COD level(<200 mg/l) As presented in Section 7.1 in the slow kinetic regime, the two ways ofozone action — direct and indirect reactions (the latter through free radicals) — cancompete to remove any compound B present in the water Indirect reactions are due tothe ozone decomposition mechanism that can be initiated through the reaction of ozonewith the hydroxyl ion, which constituted the first and limiting step of the ozone mech-anism leading to hydroxyl radicals (see Section 2.5.1) Also, indirect reactions or thosedue to hydroxyl radicals can be favored through some other initiation reactions of ozonedecomposition (i.e., reactions of ozone with hydrogen peroxide, direct ozone photolysis,

or some catalytic-induced reaction) that constitute the so-called ozone-involvedadvanced oxidation processes (AOPs) as shown in the following chapters In this section,

as a first approximation to the AOPs, ozonation is considered as the ozone processcarried out in the absence of initiators such as hydrogen peroxide or UV radiation orsolid catalysts Also note that at pH < 12 the ozone decomposition reaction is slow sothat if the direct reactions are fast, the ozone decomposition will not take place

In the slow kinetic regime, since ozone can react directly with the compoundspresent in water or through free radicals, it is convenient to establish some guidelines

in order to know which of these reactions predominates This is useful for kineticstudy and modeling purposes because the equations used (the mass balance equations)can be simplified in their ozone absorption rate term Thus, a comparative studyabout the relative importance of the direct reactions of ozone and its decompositionreaction in water is first presented

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7.1 RELATIVE IMPORTANCE OF THE DIRECT OZONE–B REACTION AND THE OZONE DECOMPOSITION REACTION *

In Section 5.2 and Section 5.3, the kinetic regimes of the ozone decompositionreaction and any ozone–B direct reaction were treated together with the potentialconcentration profiles that ozone and B could have in the water phase It was seenthat the pH value was a crucial parameter for the kinetic regime of the ozonedecomposition reaction Thus, for pH lower than 12, this reaction is slow and itdevelops in the bulk water For the ozone–direct reactions, on the contrary, otherparameters such as the reaction rate constant and the concentration of the targetcompound B can also be fundamental to establish the kinetic regime Overall,however, when comparing the decomposition and some direct ozone reaction (when

B is a dissociating compound), pH is also fundamental because it affects the rateconstant value of the direct reaction Thus, significant variations of the second-orderrate constant of the reaction between ozone and compound B, k D, leads to drasticchanges of the kinetic regime of direct ozonation that can go from instantaneous toeven slow It is evident from these comments that for instantaneous, fast, and evenmoderate direct reactions, if ozone is consumed in the film layer, the ozone decom-position reaction can be neglected This conclusion is due to the absence of ozone

in the bulk water to decompose into free radicals The absence of dissolved ozoneduring fast direct reactions is, then, the main proof that confirms the lack of com-petition If there is no dissolved ozone in bulk water, there will be no ozonedecomposition reaction On the contrary, for pH > 12, the ozone decompositionreaction could be a moderate or even fast reaction and, then, this reaction willcompete with the fast direct reactions or it will be the only ozone-consuming reaction

in case the direct reactions are slow However, for pH < 12, if dissolved ozone isdetected, the ozone decomposition reaction could be the predominant reactionagainst other possible direct reactions — a situation usually encountered in drinkingwater ozonation Competition can be confirmed by calculating the Hatta numbers

of the ozone–B direct reaction, by knowing the pH of the water, or by checking thepresence of dissolved ozone.*

7.1.1 A PPLICATION OF D IFFUSION AND R EACTION T IME C ONCEPTS

Comparison between the ozone direct reaction and the ozone decomposition reactioncan also be made with the use of the diffusion and reaction time concepts, t D and

t R, defined in Section 4.2.4 The use of these parameters is based on the surfacerenewal theories1 (i.e., Danckwerts theory) Note that for a given ozonation contactorand hydrodynamic conditions, only tR depends on the chemical reaction rate of theozone reactions Thus, when comparing the ozone direct reaction and the ozonedecomposition reaction, t D is constant for both reactions

Two situations are presented according to the relative values of t D and t R foreach of the reactions considered These situations correspond to fast and slow kinetic

* Part of this section is printed with permission from Beltrán, F.J., Theoretical Aspects of the kinetics

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regimes (see Section 5.2 and Section 5.3) As it was shown in Section 5.2 for thecase of the ozone decomposition reaction, a plot of tR determined from the rateconstant of the reactions considered and the concentration of B as parameter can beprepared This will allow us to compare the relative importance between the directand decomposition reactions of ozone.2 Thus, Figure 7.1 taken from a previous work2

shows the conditions at which these reactions develop in the slow or fast kineticregimes Two values of the tD have been considered in Figure 7.1 that correspond

to typical values of the individual mass-transfer coefficient k L.3 According to Figure7.1, the ozone decomposition reaction will compete with any possible ozone–Bdirect reaction when both reactions simultaneously develop in the slow or fastreaction zones defined according to experimental conditions For example, for t D =3.2 s and a concentration of B of 10–6M, both reactions will compete if pH < 12and k D is about 5 × 105M–1s–1 or when pH > 11 and k D > 5 × 105M–1s–1

In another example, taken from,2 a similar plot can be prepared, but plotting, inthis case, t R against the pH This way of comparison could be useful for the case ofthe ozonation of dissociating compounds such as phenols where the apparent rateconstant, k D, varies with pH [see Equation (3.22) in Section 3.1] In Figure 7.2, thisplot has been prepared2 for the ozonation of o-chlorophenol (OCP) and atrazine(ATZ), two compounds of very different reactivity towards ozone Thus, for t D =3.2 s, the reaction ozone–ATZ would compete with the ozone decomposition reaction

at any pH values except at pH > 11 At these latter conditions, only the decomposition

of ozone will take place On the contrary, the reaction between ozone and OCP isthe only one to develop at pH between 2 and 11 Then, the reaction between thehydroxyl radical and OCP does not need to be considered in the correspondingkinetic study Not that in practical cases, the removal rate of B is the main objective.Thus, the reaction rate terms present in the mass balance of B correspond to theozone–B direct reaction and the hydroxyl radical–B reaction However, in order todecide if both reaction rate terms have to be considered, since the hydroxyl radical–Breaction depends on the development of the ozone decomposition reaction, the

constant Symbols in black correspond to the ozone decomposition reaction at different pH levels (From Beltrán, F.J., Theoretical Aspects of the kinetics of competitive ozone reactions

Associ-kD, M –1 s –1 (or k, s –1 )

10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 1 10 1 10 2 10 3 10 4 10 5 10 6 10 7

FAST REACTION ZONE

SLOW REACTION ZONE

10–1

10–2

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comparison between the latter reaction and the ozone–B reaction must be established.Also, not that in the case that both the hydroxyl radical–B and ozone–B directreactions compete, the importance of one of them could be negligible and, then, thecorresponding reaction rate term is also removed from the kinetic equation This isthe case of the direct reaction ozone–ATZ when pH > 7 Although in this case, thedirect reaction also develops (see Figure 7.2), its contribution to the removal of ATZcan be neglected against that of the hydroxyl radical reaction (see Section 7.2).Therefore, in the kinetic study, the reaction rate term due to the ATZ–ozone reactioncan be neglected.

7.2 RELATIVE RATES OF THE OXIDATION

OF A GIVEN COMPOUND*

A quantitative method to determine the relative importance of the direct ozonationand free radical oxidation of any given compound B during ozonation can be madethrough the determination of the ratio between both oxidation rates The procedure

is applied to the cases where ozone reactions develop in the slow kinetic regime,that is, the Hatta number of all ozone reactions is lower than 0.3 or the reaction time

is much higher than the diffusion time Whichever the ozone kinetic regime, theratio between the oxidation rates of B due to free radical oxidation and direct reactionwith ozone is:

(7.1)

The concentration of hydroxyl radicals C HO in Equation (7.1) is given by Equation (7.2):

-chlorophenol (OCP) and atrazine (ATZ) at different pH levels.(From Beltrán, F.J., Theoretical Aspects of the kinetics of competitive ozone reactions in water, Ozone Sci Eng., 17, 163–181,

* Part of this section is printed with permission from Beltrán, F.J., Estimation of the relative importance

FAST REACTION ZONE

SLOW REACTION ZONE

zk C R

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(7.2)

where the 2k i2C HO2C O3 represents the reaction rate of initiation of free radicals which,

in the case of ozonation, is a function of the concentrations of the ionic form ofhydrogen peroxide (generated through Reaction (2.18) in Table 2.4) and ozone Bysubstituting in Equation (7.1), the ratio of oxidation rates is attained as:

(7.3)

The problem with Equation (7.3) is that the concentration of hydrogen peroxide isunknown (notice that hydrogen peroxide is not added but generated) However, theinitiation rate term can be substituted, for practical purposes, with the rate of thereaction between ozone and the hydroxyl ion [Reaction (2.1) or Reaction (2.18)]that constitutes the first reaction in the ozone decomposition mechanism In thismethod, the concentration of hydrogen peroxide is not needed In fact, theozone–hydroxyl ion reaction has long been considered the initiation rate of the ozonedecomposition mechanism for yielding the superoxide ion and the hydroperoxideradicals [also Reaction (2.1)]:

(7.4)

Thus, if Reaction (7.4) is considered as the initiation reaction, the ratio between theoxidation rates in Equation (7.1) becomes a function of pH, rate constants andinhibiting character of the water, Σk s C s, that can be calculated as shown later (seealso Section 7.3.1.1):

k HO), the relative importance of the direct ozonation and free radical oxidation ratescan be estimated at different pH and inhibiting character of the water used In Figure7.3, this plot is presented for different pH values and at a given hydroxyl radical

C

k C HO

R D

k C

k C R

D

HO D

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inhibiting value kS s C s Examples for using Figure 7.3 are straightforward, but more

details are given on this procedure in a preceding work.4

7.3 KINETIC PARAMETERS

In the ozonation process of a given pollutant B, when the ozone reactions are in the

slow kinetic regime of absorption, the mass balance equation of B applied to a small

volume of reaction (which is perfectly mixed) in a semibatch system is as follows:

(7.7)

where the terms zk D C B C O3 and k HOB C HO C B represent the contributions of the direct

and hydroxyl radical reactions, respectively, to the disappearance of B In addition,

the mass balance of ozone in the water phase at the same conditions is

(7.8)

where the ozone decomposition rate r O3 has different contribution terms due to the

ozone reactions with target compound B, the hydroxyl ion, hydroperoxide ion, and

superoxide ion and hydroxyl radicals (see mechanism in Table 2.4 or Table 2.5):

micropol-lutants in water as a function of reaction rate constant ratio and different pH values in single

ozonation Conditions: 20ºC, Σ kHOSiCSi = 10 3 sec –1 (From Beltrán, F.J., Estimation of the

relative importance of free radical oxidation and direct ozonation/UV radiation rates of

Ozone Association With permission.)

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(7.9)

Not that because of the slow kinetic regime, the ozonation gas–liquid reaction is a

two-steps-in-series process, where the mass-transfer rate through the film layer is

equal to the ozone chemical reaction rate in the bulk water at steady state Comparing

the fast ozonation processes, from Equation (7.7) to Equation (7.9) it is evident that

some new unknown parameters appear These are the rate constant of the reaction

between the hydroxyl radical and B, k HOB, the rate constant of the decomposition

reaction, k d, and the concentration of hydroxyl radicals

Ozone is mainly consumed through reactions with the hydroxyl ion,

hydroper-oxide ion, hydroxyl radical (ozone acts as promoter of its own decomposition), the

superoxide ion radical, and through the direct reaction with B Rate constants of all

these reactions are known from literature or can be calculated as was shown for the

case of the rate constant of the direct reactions (see also Section 3.1 and Section

5.3).5–7 However, ozone is also consumed through other reactions that can have

significant importance such as the initiating reactions which are different from

Reaction (2.1) or Reaction (2.18) (see Reactions in Table 2.4 and Table 2.5) Thus,

the rate constants of these reactions must also be known In addition, because the

concentration of hydroxyl radicals is a function of the rate of inhibiting reactions

[the reaction between the hydroxyl radical and some scavenger species, denominator

of Equation (7.2)], the rate constants of these reactions are also needed Then, the

kinetic study of the ozone reactions in the slow kinetic regime will be addressed to

determine all these parameters

7.3.1 T HE O ZONE D ECOMPOSITION R ATE C ONSTANT

It is evident that for the determination of the apparent pseudo first-order rate constant

of the ozone decomposition, k app, the general Equation (7.9) used by Staehelin and

Hoigné8 through the mechanism of reactions given in Table 2.4 can be used Thus,

classical methods of homogeneous kinetics can be applied (see Section 3.1) Rate

constants of ozone reactions (with OH–, HO2–, HO•, and O2

–•) are common to anyozonation process and their values are already known (see Table 2.4 or Table 2.5)

However, some others such as those corresponding to Reaction (7.10) and Reaction

(7.11) below are unknown

(7.10)

(7.11)

Thus, k OHS and k i3 are system dependent and have to be determined for each case

In fact, reactions of ozone with initiating compounds [Reaction (7.10)] and those of

the hydroxyl radical with inhibiting compounds or scavengers [Reaction (7.11)] will

depend on the nature of the water treated Since in a real case the exact content of

the water is not known, a general procedure should be applied to determine these

rate constants as presented below

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Reaction (7.10) and Reaction (7.11) develop in surface waters where there can

be numerous substances that play the role of initiators and inhibiting species of theozone decomposition reaction However, these reactions are also present during theozonation of laboratory prepared waters as experimental results suggest For exam-ple, in a study on ozone decomposition with phosphate-buffered distilled water,2 theapparent rate constant of the ozone decomposition was found to be 8.3 × 10–5 and4.8 × 10–4 sec–1 at pH 2 and 7, respectively At the same conditions, however, therate constant of the first reaction of the mechanism [Reaction (2.1) or Reaction (7.4)]

is 7 × 10–11 and 7 × 10–6 sec–1, respectively The large difference among the valuesshown (for each pH) was due not to the other known reactions that initiate andpropagate the mechanism but to the presence of different substances In fact, thesesubstances are responsible for the differences observed in the apparent rate constantvalues of the ozone decomposition reaction when studied in different types of water.8

Due to the unknown nature of the initiating and inhibiting species present in

water, the true values of k i3 and k HOS, however, cannot be known, but the values oftheir products with the concentrations of these species could be expressed For thesake of simplicity, the concentrations of these substances are assumed to be constant

in the procedure that follows

From the basic mechanism of ozone decomposition (see Table 2.4 or Table 2.5)

by applying the pseudo steady-state conditions, the concentrations of hydroxyl andsuperoxide ion radicals can be expressed as follows:

(7.15)

In a homogeneous perfectly mixed batch reactor, the mass balance of ozone in water

is given by Equation (7.8) with the absorption rate term being removed and the ozonedecomposition rate term being given by Equation (7.15) The experimental concentra-tions of ozone at any time can then be fitted to Equation (7.15) to obtain the values of

the rate constants k A and k B and, hence, the values of k i3 and k t With these values, theinitiating and inhibiting character of the water regarding the ozone decomposition can

k HO

i pH

i O t

=(2 101 − 14+ )

3 3

k O

i pH

3 3 2

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be established Notice that k t involves all possible contributions of inhibiting stances

sub-7.3.1.1 Influence of Alkalinity

As observed before, the concentration of hydroxyl radicals will strongly depend on

the inhibiting character of the water treated (k t ) In many cases, carbonates are used

as scavenger substances of hydroxyl radical in ozonation studies9,10 to check theimportance of the free radical oxidation (indirect way of ozone action) In fact, thesesubstances are used because in the case of a natural (surface or ground water), theyare the main natural scavengers.8 The contributing term of these substances to theinhibiting character of the ozonated water is due to the following reactions11 (seealso Table 2.5):

(7.16)

(7.17)

The rate constants of these reactions are not very high when compared to otherhydroxyl radical reactions with organic pollutants.12 However, since the rate ofreaction is proportional to both the rate constant and concentration of reactants, thecarbonate–bicarbonate inhibiting effect is usually high as there is a concentration

of these ions in natural waters Thus, the k t term for carbonate–bicarbonate ions is

a function of pH and can be determined as follows:

(7.18)

where C HCO3t represents the total concentration of bicarbonates in water, with

(7.19)

and pK1 and pK2, the pK of equilibrium of carbonates in water Thus, at neutral pH

and 20ºC, k t is 1233 sec–1 that corresponds to an alkalinity of 10–4 M in total

carbonates This value is of the same order of magnitude as that from a given inhibitingpollutant at a concentration of 10–6 M whose reaction with the hydroxyl radical has

a rate constant value of 109 M–1sec–1 Rigorously, however, the inhibiting term due

to the alkalinity of water is not exactly that given by Equation (7.19) In fact, thecarbonate ion radical, CO3•–, generated in Reaction (7.16) and Reaction (7.17), reactswith hydrogen peroxide to regenerate the hydroperoxide radical or the superoxideion radical:13

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(7.21)

that in the presence of ozone eventually yields the hydroxyl radical (see Table 2.4).According to this, the carbonate–bicarbonate ions would not be absolute inhibitingspecies of the ozone decomposition in ozonation processes where hydrogen peroxide

is formed In addition, the carbonate ion radical also reacts with the organic matterpresent in water through selective reactions (similar to the case of the direct ozonereactions) and, in this way, terminates the radical chain.14–16 A compilation of rateconstant values of the reactions between the carbonate ion radical and differentsubstances can be seen elsewhere.17 From the above observation, it can be acceptedthat there is a fraction of carbonate-bicarbonate ions that, while reacting with thehydroxyl radical [Reaction (7.16) and Reaction (7.17)], eventually regenerates itthrough Reaction (7.20) and Reaction (7.21) Then, the fraction of carbonate ionradicals that reacts with hydrogen peroxide as compared to other reactions is:

(7.22)where

(7.23)

with C H2O2t and pK being the total concentration of hydrogen peroxide and pK value

of its equilibrium in water, and kCM the rate constant value of any reaction between

a given compound M present in water and the carbonate ion radical that terminatesthe radical chain

7.3.2 D ETERMINATION OF THE R ATE C ONSTANT OF THE OH-B R EACTION

The contribution of free radical reactions to the oxidation rate of pollutants (B) in

water during ozonation can be established if both the rate constant k OHB and theconcentration of the hydroxyl radical are known For the latter, in the absence of B,the appropriate expression is given in Equation (7.12) In the presence of B, depend-ing on the nature of the role of this substance on the ozone reaction mechanism, the

concentration of the hydroxyl radical will also depend on k HOB and C B (in the case

of B as inhibitor of ozone decomposition) The term k HOB C B will be part of theinhibiting character of the water given by Σk HOS C S Thus, the rate constant k HOB is

a crucial parameter to know Reactions of hydroxyl radicals are usually defined asnonselective, which could mean that the rate constant kHOB is always similar regard-

less of the nature of B, although this is not correct because k HOB can vary up to 3orders of magnitude For example, for an organochlorine compound such as

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trichloroethane, k HOB is 2 × 107 M–1sec–1 18 while for phenol it is about 1010 M–1sec–1.12

Then, k HOB must also be determined

The best way to determine k HOB is from data of the disappearance rate of B In

an ozonation system, the chemical disappearance rate of B is theoretically due tothe reaction with ozone (direct reaction) and with the hydroxyl radical In a semibatch

or batch well-agitated reactor, the accumulation rate of B is

(7.24)

The system is simplified if the direct reaction can be neglected, a situation that islikely to be present when the ozonation develops in the slow kinetic regime Then,the disappearance rate of B will be a function of the concentration of hydroxyl

radicals, C HO, that depends on the initiating and inhibiting character of the watersystem [see Equation (7.12)] It is evident from this information that the main

difficulty in determining determine k HOB is the unknown concentration of hydroxylradicals Two methods can be followed: the absolute and the competitive

7.3.2.1 The Absolute Method

This method leads to the direct determination of k HOB In fact, in a semibatch mixed ozonation system, by assuming the concentration of hydroxyl radical constant(as would correspond to a short live species), the integration of Equation (7.24),once the direct rate term has been neglected and variables have been separated,yields:

well-(7.25)

A plot of the left side of this equation against time should give a straight line of

slope k HOB C HO Then a value of C HO is needed to find k HOB According to Equation(7.12), the nature of the water used and the role of the substances (as initiators and/orinhibitors) present must be exactly known This is rather difficult because the ozonedecomposition is very sensitive to the action of substances present even at very lowconcentrations However, through a procedure similar to that shown before, values

of k i3 and k t that would correspond to the ozone–water system treated could bedetermined in the absence of B, and, consequently, the concentration of hydroxylradicals (see also Section 7.4) Two possible situations arise depending on theinhibiting or promoting nature of B If B promotes the ozone decomposition reaction,that is, B reacts with the hydroxyl radical to give the superoxide ion radical thateventually regenerates the hydroxyl radical (see mechanism in Table 2.4), the rate

constant k HOB would be

0

=

r HOB

t i

=

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