Development and Experimental Validation of the Model of a

Feb 24, 2004 - The only possible criticisms of this paper may be as follows. ...... Beltran et al.3 reported the value of kL to be 3.1 × 10-4m s-1 fo...
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Ind. Eng. Chem. Res. 2004, 43, 1418-1429

Development and Experimental Validation of the Model of a Continuous-Flow Countercurrent Ozone Contactor Raman Kumar and Purnendu Bose* Environmental Engineering and Management Program, Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

The objective of the research described in this paper was the development of a fully mechanistic model for ozone mass transfer from the gaseous to aqueous phase and aqueous ozone self-decomposition in a continuous-flow countercurrent ozone contactor. The developed model incorporated concepts describing the rate and extent of ozone mass transfer from gaseous phase to aqueous phase and comprehensive consideration of ozone decomposition reactions in the aqueous phase. Simulation of the effects of changes in the influent gaseous ozone concentration, aqueous-phase pH, and scavenger concentration on the ozone mass transfer and decomposition was accompanied by an explanation of the simulation results based on the current understanding of ozone mass transfer and aqueous ozone chemistry. Experimental work included fabrication and operation of a laboratory-scale continuous-flow countercurrent ozone contactor. Experimental data concerning the steady-state aqueous ozone concentration in the reactor and the effluent gaseous ozone concentration from the reactor were obtained at various influent gaseous ozone concentrations, aqueous-phase pHs, and aqueous scavenger concentrations. The experimental data were then compared with the results obtained from simulation runs conducted under similar conditions. A comparison of experimental data and model simulation results under similar conditions showed an adequate positive correlation. The discrepancy between some experimental data and simulation results was discussed in terms of the sensitivity of the ozone mass transfer and aqueous-phase self-decomposition to changes in the temperature and ionic strength of the aqueous medium. Introduction Bubble-type ozone contactors are the most popular devices used for application of ozone to water and wastewater for achieving various treatment objectives. Hence, comprehensive mathematical modeling of such systems is required for the design of efficient contactors for various water and wastewater treatment objectives. Modeling of ozone contactors involves providing a mathematical description of the system, including specification of the reactor type (i.e., semibatch or continuous flow), reactor dimensions, mode of contact of liquid and gaseous phases (i.e., cocurrent or countercurrent), and flow regime (i.e., completely mixed, plug flow, and mixed flow). Ozone mass transfer, ozone self-decomposition, and ozone consumption by substrates in the liquid phase must also be specified. The ozone transfer efficiency from the gas to liquid phase is mainly controlled by physical parameters such as the temperature, gas flow rate, ozone partial pressure, and reactor geometry.1,2 Chemical parameters such as the pH, ionic strength, and composition of the aqueous solution also affect ozone transfer.1 The effect of physical parameters can be adequately represented by a partition coefficient, e.g., Henry’s coefficient, for describing the ozone distribution between the gas and liquid phases and KLa.3 The effect of chemical parameters can be represented by an adequate description of ozone decomposition in the aqueous phase.2 * To whom correspondence should be addressed. Tel.: +91 512 2597403. Fax: +91 512 2597395. E-mail: [email protected].

Models for completely mixed ozone contactors operating in semibatch mode have been developed by several researchers.4-10 The model by Anselmi et al.4 was a three-equation model describing concentrations of ozone in the bulk liquid, holdup gas, and volume above the liquid surface but neglecting ozone decomposition in the liquid or gaseous phases. The model proposed by Roustan et al.,5 which incorporated ozone decomposition reactions in the liquid phase, was an advance on the Anselmi model. The model proposed by Chiu et al.8 was an improvement on the previous two models, incorporating the mass-transfer enhancement factor (E) and its variation with time into the model formulation. A more recent model9 considered ozone reactions in the liquid and gas phases in the headspace above the liquid in the reactor to develop two types of models, where both liquid and gas phases are completely mixed and where the gas phase was plug flow. In addition, these models considered the effect of temperature, gas flow rate, ionic strength, and influent gaseous ozone concentration. However, the effect of the aqueous-phase pH and scavenger concentration on ozone decomposition and hence mass transfer was not explicitly considered. All models discussed above pertained to ozone mass transfer and decomposition in pure water. The model proposed by Qiu et al.10 incorporated ozone reactions with solutes (2,4-DCP and 2,6-DCP (dichlorophenol)) in the liquid phase into the model formulations, in addition to ozone self-decomposition. Models for continuous-flow ozone contactors have been developed by several researchers.11-14 Le Sauze et al.11 developed models for ozone mass transfer from

10.1021/ie020490z CCC: $27.50 © 2004 American Chemical Society Published on Web 02/24/2004

Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1419

the gas to liquid phase and liquid-phase ozone decomposition in plug-flow reactors, perfectly mixed reactors, reactors with axial dispersion in the aqueous phase, and reactors with three axial dispersion zones. Ozone mass transfer has been described in this paper using the twofilm theory and E and ozone decomposition using the empirical ozone consumption rate in natural waters determined by Yurteri and Gurol.15 Some experimental validations of the models are provided though the quantity of experimental data cited is low. Zhou et al.12 provided a comprehensive model for ozone contactors using a two-phase axial dispersion model (ADM) to integrate nondeal mixing, mass-transfer, and ozone decay processes as a whole. This model was tested with pilot-scale data and shown to provide excellent agreement. El-Din and Smith13 presented a semiempirical nonisobaric one-phase ADM of ozone contactors. This was achieved by assuming that variation of the gaseous ozone mole fraction along the column height is exponential, assigning a suitable empirical function for the same. Under the circumstances, only the differential equation for ozone in the liquid phase needs to be solved. Simulations using this model were compared with data reported by Zhou et al.12 and showed good agreement. A more recent attempt at modeling the ozone contactor was reported by Kim et al.,14 in connection with the design of the ozone contactor for inactivation of Cryptosporidium oocysts. This model was in many ways similar to the one described by Zhou et al.12 but neglected the effect of the water-column pressure on the ozone transfer efficiency and assumed that gas holdup, gas-phase dispersion, and gas-phase ozone decomposition were negligible. In all of the models discussed above, ozone selfdecomposition in the liquid phase has been incorporated into the model through empirical expressions. Numerous expressions have been developed over the years for this purpose and also to account for the effect of pH, alkalinity (radical scavenger concentration), and ozonedemanding solutes (e.g., natural organic matter, NOM) on the ozone decomposition rate in water. Examples of such expressions include the second-order ozone decomposition kinetics in pure water described by Gurol and Singer,16 where the second-order rate constant itself is a function of pH. In another important work, Yurteri and Gurol15 showed that ozone decomposition is first order in natural waters and expressed this rate constant as a function of pH, total organic carbon concentration, and alkalinity. In general, researchers agree that ozone self-decomposition in water is a function of both residual ozone concentration and pH, with a reaction order of between 0 and 2 with respect to the residual ozone and of between 0 and 1 with respect to the hydroxide ion,8 depending on specific conditions. In addition to the development of the empirical models described above, considerable progress has also been made in the area of mechanistic model development for ozone decomposition. Two mechanistic models describing ozone self-decomposition in the aqueous phase are popular. The first one is commonly known as the Hoigne-Staehelin-Bader (HSB) model.17-22 It is a compilation of radical reactions describing the decomposition of ozone at near-neutral pH levels. The other one is known as the Tomiyasu-Fukutomi-Gordon (TFG) model,23 which also consists of a compilation of radical reactions describing ozone decomposition, and is only applicable at high pH values. Some researchers

have attempted the verification of the two mechanistic models mentioned above through comparison with experimental data and existing empirical models. Chelkowska et al.24 compares the HSB and TFG models with an empirical model proposed by Tomiyasu et al.,23 with encouraging results. No experimental ozone decomposition data were presented in this paper. Westerhoff et al.25 simultaneously compared the HSB and TFG models and an empirical ozone decomposition model proposed by Gurol and Singer16 with experimentally derived data for pure water with and without scavenger and with waters containing NOM. On the basis of this study, it was concluded that the HSB model provided a better agreement with experimental data at nearneutral pH values. Sunder and Hempel26 described the extension of the HSB model to incorporate degradation of perchloroethylene (PCE)/trichloroethylene (TCE), in addition to ozone self-decomposition. This extended model was verified through experimental results obtained using a tubular reactor. On the basis of the literature reports discussed above, it is clear that advances in the modeling of ozone contactors, on the one hand, and the mechanistic modeling of ozone decomposition in the aqueous phase, on the other hand, have progressed independently of each other. Attempts to merge these two areas in order to obtain a comprehensive mechanistic model for describing ozone mass transfer and aqueous-phase reactions in bubble-type ozone contactors are currently ongoing. Andreozzi et al.27 modeled advanced oxidation processes for treatment of mineral oil contaminated waters in semibatch reactors. The modeling methodology incorporated a mechanistic description of aqueous ozone decomposition but assumed a steady-state condition for all radical species in the solution. This assumption is questionable. Also the effect of the E on the ozone mass transfer, which decreases with time because of the depletion of the substrate in semibatch reactors, was not considered during modeling. Beltran et al.28 reported a mechanistic model describing degradation of simazine by ozonation in bubble contactors. However, this model does not incorporate reactions involving inorganic carbon, which acts as a scavenger of hydroxyl radicals in most natural waters. Also, the set of reactions used for modeling purposes is incomplete, with the equilibrium reactions involving H+/OH- and H2O2/HO2- not being considered. This may lead to model simulations in which charge balance will not be maintained and thus may lead to unrealistic variations in the pH and other species concentrations in the model simulations. Other researchers reporting similar work include Hautaniemi et al.,29,30 dealing with degradation of chlorophenol, and Beltran et al.,31 dealing with alachlor. The work of Pedit et al.32 is the most complete of all of the attempts at ozone contactor modeling to date. In this work, an ozone contactor model for a tall bubble contactor was developed considering both ozone mass transfer and a mechanistic description of aqueous ozone decomposition, including degradation of TCE and PCE by ozonation. The ozone decomposition chemistry considered is exhaustive and includes reactions involving inorganic carbon as the scavenger and other reversible reactions. The only possible criticisms of this paper may be as follows. First, the developed model was not validated with a sufficient amount of experimental data from either laboratory- or pilot-scale reactors. Second, the possibility of gas-phase ozone decomposition in the

1420 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004

headspace above the reactor, which is a common occurrence in tall ozone contactors, is not considered. Third, the effect of the E on the ozone mass transfer has not been considered. Fourth, the effect of hydrostatic pressure in tall columns upon variation in the mass-transfer coefficient, gas holdup, dispersion coefficients, etc., along the column height has not been considered. The work described in the present paper is a continuation of the mechanistic modeling work as described above, specifically focusing on elucidating the effect of changes in the aqueous-phase pH and scavenger concentration on the ozone mass transfer and aqueousphase self-decomposition of ozone. The model was validated using carefully obtained experimental data at various pHs, scavenger concentrations, and influent gaseous ozone concentrations. The reasons for the discrepancy between experimental data and model simulations in some cases was also discussed with respect to the sensitivity of the ozone mass transfer and self-decomposition to changes in the temperature and ionic strength of the aqueous medium. Model Development Partitioning of Ozone between the Gas and Liquid Phases. Henry’s law describes partitioning of ozone between the gas and liquid phases.

P[O3] ) H[O3]X[O3]

(1)

The value of Henry’s constant is a function of the temperature as shown in Table 1. Henry’s law can also be written in terms of the solubility ratio (S), which is the ratio of the saturation ozone concentration in the aqueous phase to the gaseous ozone concentration, when both concentrations are expressed in mg L-1 (or mol L-1). In mathematical terms,

S)

[O3]sl in mg L-1 (or mol L-1) [O3]sl in mg L-1 (or mol L-1)

(2)

S calculated at various temperatures is also shown in Table 1. The calculated values match well values of 0.34, 0.24, and 0.17 for temperatures of 12, 21, and 31 °C, respectively, reported elsewhere.33 As discussed later, S plays an important part in the formulation of kinetic expressions for modeling ozone mass transfer. Rate of Ozone Mass Transfer. Ozone mass transfer from the gaseous to aqueous phase may be expressed by an equation of the form k′1

z [O3]l [O3]g y\ k′ 2

(3)

On the basis of the above equation, the rate of ozone transfer (RO3) from the gaseous to liquid phase may be expressed as

RO3 ) k′1[O3]g - k′2[O3]l

(4)

S[O3]g ) [O3]sl

(5)

From eq 2,

Thus, substituting eq 2 in eq 4,

RO3 )

k′1 [O ]s - k′2[O3]l S 3l

(6)

Again, as per Lewis-Whitman two-film theory, the same mass transfer of ozone between gas and liquid phases may be described as

RO3 ) KLa{[O3]sl - [O3]l}

(7)

When eqs 6 and 7 are compared, kinetic constants k′1 and k′2 can be expressed in terms of KLa as follows:

k′1 ) SKLa

(8)

k′2 ) KLa

(9)

These values will be used in the model calculations described later for quantifying ozone mass transfer. Ozone Reactions in the Aqueous Phase. As mentioned earlier, two competing mechanistic models for ozone self-decomposition are prevalent in the literature, the HSB and TFG models.2 The TFG model was only verified at high pH values (pH > 10) and hence may not be suitable for application at lower pH values. The HSB model, on the other hand, describes ozone decomposition at neutral pH values and was hence chosen for the model development described in this paper. In this regard, it has been demonstrated25 that the HSB model predicts ozone decomposition in “pure” Milli-Q water better than the TGF model at nearneutral pH values. The essential equations describing the HSB model are shown in Table 2. In the absence of other ozone-consuming solutes, the pH and bicarbonate/ carbonate alkalinity of the water are the two main variables that control ozone decomposition in the pure aqueous phase. Additionally, the following assumptions are made for model development. First, no ozone decomposition occurs in the gas phase; second, both the liquid and gas phases in the reactor are completely mixed. The validity of these assumptions will be discussed later in the paper. Equations Describing Ozone Mass Transfer and Reactions. As per the ozone mass-transfer relationship (eq 3) and equations describing aqueous ozone decomposition presented in Table 2, the total number of species to be considered for modeling purposes is 15, i.e., [O3]g, [O3]l, [OH-], [•O2-], [•HO2], [•HO2-], [•O3-], [•HO3], [•OH], [H2O2], [H+], [H2CO3*], [HCO3-], [CO32-], and [•CO3-]. For each of these species, a mass balance equation can be written as follows:

{rate of species accumulation} ) {rate of species input} - {rate of species output} {net rate of species destruction} + {rate of mass transfer} (10) Unlike the case of irreversible reactions, where only one kinetic rate constant is required to describe the rates of formation and destruction of various species, in the case of reversible reactions, rates for both the forward and backward reactions are required. However, such forward and backward reaction rates may not be available because such reactions are generally described by an equilibrium constant, which is the ratio of the forward to the backward reaction rate. The procedure adopted for incorporating an equilibrium relationship

Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1421 Table 1. Variation of Henry’s Constant and S for Ozone Partitioning between the Liquid and Gas Phases with Temperature temperature, °C Henry’s constant, H[O3], atm S (calculated)

0 1945 0.586

5 2490 0.466

10 3190 0.370

15 4200 0.286

20 5190 0.235

25 6555 0.190

30 8302 0.152

35 10375 0.124

Table 2. Ozone Reactions in Pure Water Containing Bicarbonate/Carbonate Alkalinity reaction 1

rate constant Initiation Reactions

O3 + OH- 9 8 •O2- + •HO2 k 1

2

O3 + HO2- 9 8 •O3- + •HO2 k

k2 ) 5.5 × 106 M-1 s-1 (Staehelin and Hoigne22)

2

3

Propagation Reactions

O3 + •O2- 9 8 O3- + O2 k

k1 ) 70 M-1 s-1 (Staehelin and Hoigne22)

3

k3 ) 1.6 × 109 M-1 s-1 (Buhler et al.34)

H+ + •O3- 9 8 •HO3 k

k4 ) 5.2 × 1010 M-1 s-1 (Buhler et al.34)

5

•HO 98 3 k 5

k5 ) 1.1 × 105 M-1 s-1 (Buhler et al.34)

6

O3 + •OH 9 8 •HO2 + O2 k

4

4

OH + O2 Promotion Reactions

6

7

H2O2 + •OH 9 8 •HO2 + H2O k

k7 ) 2.7 × 107 M-1 s-1 (Buxton et al.36)

7

8 9 10 11

-

HO2 +

•OH

9 8 k 8

•O 2

k8 ) 7.5 × 109 M-1 s-1 (Christensen et al.37)

+ H2 O

•HO 2

+ •OH 9 8 H2O + O2 k

•HO 2

+ •HO2 9 8 H2O2 + O2 k

k9 ) 1.0 × 1010 M-1 s-1 (Bielski et al.38)

7

Formation of H2O2

10

H2O + •HO2 + •O2- 9 8 H2O2 + O2 + OHk •HO 2

Reversible Reactions

f k12

y\ z H+ + •O2b

K12 ) kf12/kb12 ) 10-4.8 M (Behar et al.39)

k12

13

K13 ) kf13/kb13 ) 10-11.8 M (Staehelin and Hoigne22)

f k13

H2O2 + y\ z HO2- + H+ b k13

14

K14 ) kf14/kb14 ) 10-14 M (Stumm and Morgan40)

f k14

H2O y\ z OH- + H+ b k14

15

K15 ) kf15/kb15 ) 10-6.3 M (Stumm and Morgan40)

f k15

H2CO3* y\ z HCO3- + H+ b k15

16

K16 ) kf16/kb16 ) 10-10.3 M (Stumm and Morgan40)

f k16

HCO3- y\ z CO32- + H+ b k16

-

k10 ) 8.3 × 105 M-1 s-1 (Bielski et al.38) k11 ) 9.7 × 107 M-1 s-1 (Bielski et al.38)

11

12

k6 ) 1.1 × 108 M-1 s-1 (Sehested et al.35)

Scavenging Reactions

•OH

k17

98

•CO 3

17

HCO3 +

+ H2O

18

CO3- + •OH 98 •CO3- + OH-

19

•CO 3

k18

k19

+ •OH 98 •CO3- + OH-

in mass balance equations was to assign arbitrarily high forward and backward reaction rates, with the constraint that the ratio of the two rates be equal to the corresponding equilibrium constant. Under the circumstances, care must be taken to ensure that the arbitrary values chosen as above are at least an order of magnitude higher than the largest irreversible reaction rates that are encountered. This will ensure that concerned species related through equilibrium relationships remain in equilibrium even while participating in other reactions. Additionally, all equations (eq 3 and equations in Table 2) used for the development of mass balance equations are consistent in terms of mass, charge, and electron balance. Also, in the case of the steady-state solution, the “rate of species accumulation” (left-hand side of eq 10) is zero for all species. This will result in 15 nonlinear coupled simultaneous equations that were solved using (Bio)chemical Kinetics Simulation Software called GEPASI 3.41

k17 ) 1.0 × 107 M-1 s-1 (Buxton et al.36) k18 ) 4.0 × 108 M-1 s-1 (Buxton et al.36) k19 ) 3.0 × 109 M-1 s-1 (Westerhoff et al.25)

Simulation Results A detailed presentation of the simulation results involves specifying the steady-state reactor concentration of the 15 species identified earlier as participating in the ozone mass transfer and decomposition processes, for specified reactor input conditions. Because the rate of aqueous ozone decomposition depends on the solution pH and scavenger concentration, the effects of changes in these two parameters on ozone mass transfer and decomposition were simulated. Effect of the pH. Simulation results for a particular scavenger concentration (CT ) 1 mM) and pH values of 7, 8, and 8.8 are presented in Table 3 for demonstration of the effect of changes in the aqueous-phase pH on ozone mass transfer and decomposition. As per the results in Table 3, the steady-state aqueous ozone concentration in the reactor was highest at pH 7 and declined with increasing pH. This is in line with the expectation of greater ozone stability at lower pH values

1422 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 Table 3. Simulation of the Effect of pH on Ozone Decomposition in a Continuous-Flow Countercurrent Ozone Contactor (Ql ) 25 mL min-1, Qg ) 1 L min-1, KLa ) 0.1 s-1, S ) 0.20, [O3]ig ) 30 mg L-1, CT ) 1 mM) inorganic carbon concentration, CT ) 1 mM pH 7 no.

species

units

[O3]l mg L-1 [OH-] M [•O2-] M [•HO2] M [HO2-] M [•O3-] M [H+] M [•HO3] M [•OH] M [H2O2] M [H2CO3*] M [HCO3-] M [CO3--] M [•CO3-] M [O3]g mg L-1 mg L-1 [O3]sl ) S[O3]g charge balance: [2 + 3 + 5 + 6 + 12 + 2(13) + 14 - 7] carbon balance: [11 + 12 + 13 + 14]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

influent

pH 8 reactor

0 1 × 10-7 0 0 0 0 1 × 10-7 0 0 0 1.663 × 10-4 8.333 × 10-4 4.176 × 10-7 0 30

influent

pH 8.8 reactor

influent

5.96 9.95 × 10-8 2.64 × 10-14 1.68 × 10-16 4.11 × 10-13 1.06 × 10-12 1.01 × 10-7 5.06 × 10-14 2.37 × 10-13 2.61 × 10-8 1.66 × 10-4 8.29 × 10-4 4.13 × 10-7 4.11 × 10-6 29.82 5.99 -8.416 × 10-4 -8.416 × 10-4

0 1 × 10-6 0 0 0 0 1 × 10-8 0 0 0 1.95 × 10-5 9.76 × 10-4 4.89 × 10-6 0 30

5.68 9.80 × 10-7 1.45 × 10-12 9.38 × 10-16 1.76 × 10-10 7.04 × 10-10 1.02 × 10-8 3.40 × 10-12 1.10 × 10-11 1.13 × 10-6 1.92 × 10-5 9.42 × 10-4 4.63 × 10-6 3.34 × 10-5 28.80 5.83 -9.864 × 10-4 -9.864 × 10-4

0 6.31 × 10-06 0 0 0 0 1.58 × 10-09 0 0 0 3.06 × 10-6 9.66 × 10-4 3.06 × 10-5 0 30

10-3 M

10-3 M

10-3 M

10-3 M

10-3 M

reactor

2.54 6.62 × 10-6 1.95 × 10-11 1.87 × 10-15 4.26 × 10-9 3.69 × 10-8 1.51 × 10-9 2.63 × 10-11 6.11 × 10-11 4.05 × 10-6 2.71 × 10-6 8.99 × 10-4 2.98 × 10-5 6.82 × 10-5 20.58 4.12 -1.034 × 10-3 -1.034 × 10-3 10-3 M

Table 4. Some Salient Features of Simulations Presented in Table 3 units min-1

pH 7.0 10-4

pH 8.0

pH 8.8

rate of gaseous ozone input rate of gaseous ozone output rate of ozone mass transfer rate of aqueous ozone output

mol mol min-1 mol min-1 mol min-1

6.25 × 6.21 × 10-4 3.71 × 10-6 3.12 × 10-6

6.25 × 5.90 × 10-4 3.54 × 10-5 2.96 × 10-6

6.25 × 10-4 4.29 × 10-4 1.96 × 10-4 1.32 × 10-6

total by initiation by propagation by promotion

Rate of Ozone Decomposition mol min-1 5.89 × 10-7 % of total 11.9 % of total 54.5 % of total 33.6

3.25 × 10-5 22.7 50.8 26.6

1.95 × 10-4 38.7 50.5 10.9

2.24 × 10-5 37.4 62.6 0.691

1.74 × 10-4 12.6 87.4 0.890

Rate of [•OH] Radical Production or Consumption total mol min-1 3.34 × 10-7 consumption by promotion % of total 58.5 consumption by scavenging % of total 41.5 [•OH] radical produced/ozone consumed 0.567

as discussed by earlier researchers.25 Additionally, the steady-state aqueous ozone concentration at pH 7 approaches the corresponding saturation concentration, resulting in a precipitous decline in the rate of ozone mass transfer (see Table 4). With increase in pH, the aqueous ozone decomposition is hastened, and hence the steady-state aqueous ozone concentration at higher pH values was less than the corresponding saturated aqueous ozone concentration (see Table 3). This provides the necessary “driving force” for the enhancement of the rate of ozone mass transfer (see Table 4). A corollary to the above analysis is that a system at lower pH, which provides stability to the aqueous ozone, should also exhibit low concentrations of ozone decomposition products, i.e., a hydroxyl [•OH] radical, as compared to a high pH system. Simulation results of the hydroxyl [•OH] radical concentration with various pH values as shown in Table 3 indicate that this is indeed the case. The simulation results have been further examined through some additional calculations based on the results presented in Table 3, which are presented in Table 4. As per the results presented in this table, there is a 3 “order of magnitude” difference between the rates of ozone decomposition at pH 7 and 8.8. It is also observed that, at pH 7, 84% of ozone transferred to the liquid phase through mass transfer is not decomposed and goes out with the reactor effluent. This percentage falls to 8.35 and 0.67, respectively, when the pH is 8 and 8.8,

10-4

respectively. At pH 7, where ozone decomposition in the aqueous phase is low and mostly occurs through promotion and propagation reactions (eqs 6 and 3, respectively, in Table 2), the molar ratio between hydroxyl radical production and ozone consumption is nearer to 0.5. In contrast, at pH 8.8, ozone decomposition mostly occurs through initiation and propagation reactions (eqs 1 and 3 respectively, Table 2), and the molar ratio between hydroxyl radical production and ozone consumption is nearer to 1.0. At pH 7, a substantial proportion of the hydroxyl radicals are consumed through promotion reactions (eq 6 in Table 2), while at pH 8.8, most hydroxyl radical consumption is through scavenging reactions (eqs 17 and 18 in Table 2). This is probably due to the greater concentration of carbonate ions at higher pH, which was a greater affinity for hydroxyl radicals in comparison to bicarbonate ions. However, despite the above fact, because of the higher hydroxyl radical production at pH 8.8, the absolute rate of hydroxyl radical consumption through promotion reactions is much greater than that at pH 7. Effect of the Scavenger Concentration. Simulation results for a particular pH (pH 8) and scavenger concentrations of 0.01, 0.1, and 1 mM are presented in Table 5 for a demonstration of the effect of the change in scavenger concentration on ozone mass transfer and decomposition. As per the results presented in Table 5, the steady-state aqueous ozone concentration in the

Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1423 Table 5. Simulation of the Effect of the Scavenger Concentration (CT) on Ozone Decomposition in a Continuous-Flow Countercurrent Ozone Contactor (Ql ) 25 mL min-1, Qg ) 1 L min-1, KLa ) 0.1 s-1, S ) 0.20, [O3]ig ) 30 mg L-1, pH 8) pH 8 CT ) 0.01 mM no.

species

units

[O3]l mg L-1 [OH-] M [•O2-] M [•HO2] M [HO2-] M [•O3-] M [H+] M [•HO3] M [•OH] M [H2O2] M [H2CO3*] M [HCO3-] M [CO32-] M • [ CO3 ] M [O3]g M mg L-1 [O3]sl ) S[O3]g charge balance: [2 + 3 + 5 + 6 + 12 + 2(13) + 14 - 7] carbon balance: [11 + 12 + 13 + 14]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

influent

CT ) 0.1 mM

reactor

0 1 × 10-6 0 0 0 0 1 × 10-8 0 0 0 1.95 × 10-7 9.76 × 10-6 4.99 × 10-8 0 30

influent

CT ) 1 mM

reactor

influent

2.68 9.85 × 10-7 1.76 × 10-11 1.13 × 10-14 7.88 × 10-11 3.03 × 10-9 1.01 × 10-8 1.45 × 10-11 2.50 × 10-10 5.05 × 10-7 1.90 × 10-7 9.39 × 10-6 4.63 × 10-8 3.73 × 10-7 20.98 4.19 -1.08 × 10-5 -1.08 × 10-5

0 1 × 10-6 0 0 0 0 1 × 10-8 0 0 0 1.95 × 10-6 9.76 × 10-5 4.99x 10-8 0 30

3.89 9.84 × 10-7 7.72 × 10-12 4.96 × 10-15 2.35 × 10-10 2.10 × 10-9 1.01 × 10-8 1.01 × 10-11 9.88 × 10-11 1.50 × 10-6 1.90 × 10-6 9.39 × 10-5 4.63 × 10-8 3.70 × 10-6 24.26 4.85 -9.95 × 10-5 -9.95 × 10-5

0 1 × 10-6 0 0 0 0 1 × 10-8 0 0 0 1.95 × 10-5 9.76 × 10-4 4.89 × 10-6 0 30

10-5 M

10-4 M

10-3 M

10-5 M

10-3 M

reactor

5.68 9.80 × 10-7 1.45 × 10-12 9.39 × 10-16 1.76 × 10-10 7.04 × 10-10 1.02 × 10-8 3.40 × 10-12 1.10 × 10-11 1.13 × 10-6 1.92 × 10-5 9.42 × 10-4 4.63 × 10-6 3.34 × 10-5 28.80 5.83 -9.864 × 10-4 -9.864 × 10-4 10-3 M

Table 6. Some Salient Features of Simulations Presented in Table 5 units min-1

CT ) 0.01 mM 10-4

CT ) 0.1 mM

CT ) 1 mM

rate of gaseous ozone input rate of gaseous ozone output rate of ozone mass transfer rate of aqueous ozone output

mol mol min-1 mol min-1 mol min-1

6.25 × 4.37 × 10-4 1.88 × 10-4 1.40 × 10-6

6.25 × 5.05 × 10-4 1.20 × 10-4 2.03 × 10-6

6.25 × 10-4 5.90 × 10-4 3.54 × 10-5 2.96 × 10-6

total by initiation by propagation by promotion

Rate of Ozone Decomposition mol min-1 1.87 × 10-4 % of total 0.9 % of total 50.1 % of total 49.0

1.18 × 10-4 5.6 50.2 44.2

3.25 × 10-5 22.7 50.8 26.5

6.67 × 10-5 80.1 19.9 0.567

2.24 × 10-5 37.4 62.6 0.691

Rate of [•OH] Radical Production or Consumption total mol min-1 9.57 × 10-5 consumption by promotion % of total 96.5 consumption by scavenging % of total 3.5 [•OH] radical produced/ozone consumed 0.513

reactor was highest at the scavenger concentration of 1 mM and declined with a decrease in the scavenger concentration. This is due to the fact that, at lower scavenger concentrations, the promotion reactions that enhance ozone decomposition gain prominence (see the results in Table 6), resulting in a decreased stability of ozone in such systems, as compared to systems with higher scavenger concentration. Moreover, a comparison of the steady-state aqueous ozone concentration with the corresponding saturated ozone concentrations for the three cases (see Table 5) indicate that the differences in these values, or the driving force required for ozone mass transfer, were more in systems with lower scavenger concentrations. Hence, the rate of mass transfer was higher, and the gaseous ozone concentration effluent from the reactor was substantially lower in the case of such systems, as compared to systems with high scavenger concentrations. Systems with high scavenger concentrations that provide stability to aqueous ozone also exhibit lower concentrations of ozone decomposition products, i.e., the hydroxyl [•OH] radical, as compared to a low scavenger system (see Table 5). Additional analyses presented in Table 6 show that ozone decomposition is mostly through promotion and propagation reactions (eqs 6 and 3 in Table 2) at lower scavenger concentrations, while a decline in promotion at higher scavenger concentration results in substantial amounts of ozone decomposition by initiation reactions (eq 1 in

10-4

Table 2). Similarly, hydroxyl radical consumption is mostly through promotion at lower scavenger concentration (eq 6 in Table 2) and through scavenging (eqs 17 and 18 in Table 2) at higher scavenger concentration. As in the case of the results presented in Table 4, in systems where promotion reactions are predominant, the ratio between hydroxyl radical production and ozone consumption is near to 0.5, while in systems where scavenging is predominant, this ratio is nearer to 1. Experimental Methods The experimental setup consisted of a continuous-flow countercurrent bubble contactor as shown in Figure 1. Dimensions and other important characteristics of this reactor are given in Table 7. Ozone was generated in the gas phase by passing pure oxygen from an oxygen cylinder through an ozone generator (CDS/4C/AF; Indizone, Chennai, India). Arrangements were made for applying this ozone/oxygen mixture to the bottom of the reactor, where it bubbled through a porous ceramic plate and moved upward through the reactor. The gas flow into the reactor was controlled using an online mass flow controller (GFC171S; Aalborg Instruments & Controls Inc., Monsey, NY). The ozone concentration in the gas influent to or effluent from the reactor was measured using an online ozone monitor (Ozomat GM-6000OEM; Anseros, Tu¨bingen, Germany). The liquid phase

1424 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004

Figure 1. Schematic of the bubble contactor used for ozonation experiments. Table 7. Experimental Reactor Dimensions reactor shape reactor height, cm reactor diameter, cm reactor cross-sectional area, m2 depth of the liquid, cm length-to-diameter ratio

cylindrical 39 6.4 3.22 × 10-3 31 4.84

was introduced into the reactor from the top using a multichannel peristaltic pump (PA-MCP; IKA, Staufen, Germany). Liquid was also extracted at the same rate from the bottom of the reactor using the same pump, thus maintaining a continuous liquid flow in the reactor. All components of the experimental setup and the reactor were made of borosilicate glass, Teflon, or stainless steel to ensure that ozone consumption due to corrosion of components by ozone leading to the erroneous experimental results is fully eliminated. A schematic of the experimental setup is shown in Figure 2. Triple-distilled water was pre-ozonated to ensure that both inorganic and organic impurities were minimized to the extent possible. The average conductivity of this water was 2 µS, and the pH value was between 7 and 7.5 for fresly ozonated water. The pH and CT of this water was then adjusted to the desired value by the addition of desired amounts of NaHCO3/Na2CO3 and HCl/NaOH, followed by experimental verification of these values using a sample aliquot. Approximately 3 L of water purified and prepared as above was required for each experiment. The valves in the experimental setup were set as in case A or B (Figure 2) to measure the influent and effluent gaseous ozone concentrations, respectively. The ozonator was switched on after attaining steady-state liquid and gas flow in the reactor at predetermined rates. Attainment of a constant gaseous ozone concentration in the effluent side was taken as an indication that “steady state” has been attained in the reactor. Next, five aliquots of 5 mL each were taken at 5-min intervals from the reactor for the measurement of the aqueous ozone concentration in the reactor. Influent and effluent gaseous ozone concentrations were also measured at these times. Analytical Methods Gaseous ozone was directly measured using an UV absorbance based ozone-monitoring device (Ozomat GM6000-OEM; Anseros, Tu¨bingen, Germany). The aqueous

Figure 2. Schematic of the experimental setup used for ozonation experiments.

ozone was measured by the Indigo method42 or Method No. 4500-O3-A,43 with the final absorbance of the Indigo solution being measured spectrophometrically (20D+; Spectronic, Mumbai, India) using a 4-cm-path-length cell. Alkalinity was determined by the titrimetric method using methyl orange indicator (Method No. 2320 B43). The pH was measured using a combination pH electrode (CL-51; Toshniwal, Ajmer, India) connected to a digital pH meter (CL-54; Toshniwal, Ajmer, India). Experimental Verification of Simulation Results Analysis of the Reactor Characteristics. Tracer studies were conducted in order to verify the assumption that the liquid phase in the reactor is completely mixed (data not shown). No experiments were performed to test the validity of the assumption that the gas phase in the reactor is completely mixed. Literature review44 on this subject indicated that there is some dispute on whether the gas phase should be described as completely mixed or plug flow. Though a majority of researchers have modeled the gas phase in such reactors as completely mixed,4,5 others9 have used both kinds of flow regimes and concluded the plug-flow model to be superior. For the model described in this paper, the gas phase in the reactor was considered to be completely mixed, based on the assumption that in reactors with low length-to-diameter ratios (4.81) a choice either one way or the other makes little or no difference. Regarding the assumption of gas-phase decomposition of ozone being negligible, Wu and Masten9 indicated that, as per their experimental observation, the steady-state ozone

Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1425 Table 8. Experimental Determination of KLa at 25 °C pH

[O3]ig, mg L-1

[O3]g, mg L-1

S (T ) 25°C)

[O3]sl , mg L-1

[O3]l, mg L-1

KLa (s-1)

8.5 8.5 8.5 8.5 8.5

25.5 30.1 36.3 39.4 46.1

20.2 23.0 27.5 30.2 33.2

0.1897 0.1897 0.1897 0.1897 0.1897

3.83 4.36 5.22 5.73 6.30

3.0 3.2 3.8 4.2 4.4 average

0.106 0.102 0.103 0.100 0.113 0.105 ( 0.005

concentration at the entrance of and at the exit to the reactor headspace was unchanged corresponding to headspace detention times of up to 20 min. The retention time of ozone in the headspace of the reactor described here was calculated to be much less than 20 min. Experimental Determination of KLa. Experimental determination of KLa for the reactor under question was performed at a liquid flow rate (Ql) of 25 mL min-1. The gas flow rate (Qg) during the above studies was maintained constant at 1 L min-1. A typical experiment of this type was conducted with water at moderately high pH (∼8.5) and 1 mM scavenger concentration (CT). The influent gaseous ozone concentration, [O3]ig, the effluent gaseous ozone concentration, [O3]g, and the aqueous ozone concentration, [O3]l, in the reactor were measured as described earlier under steady-state conditions. On the basis of these values, KLa of the reactor could be calculated based on the mass balance of the gaseous ozone in the reactor

Qg{[O3]ig - [O3]g} ) V(KLa){[O3]sl - [O3]l} (11) Thus, KLa may be calculated as

KLa )

Qg{[O3]ig - [O3]g} V{[O3]sl - [O3]l}

)

Qg{[O3]ig - [O3]g} V{S[O3]g - [O3]l}

)

RO3 S[O3]g - [O3]l

(12)

The value of S in the above expression was 0.1897, corresponding to a temperature of 25 °C prevalent during these experiments. The steady-state values of [O3]g and [O3]l calculated for four values of [O3]ig are shown in Table 8. The value of KLa was calculated based on these data using eq 13 to be 0.105 ( 0.005 s-1 for Qg and Ql values of 1 L min-1 and 25 mL min-1, respectively. The general mass-transfer equation proposed by Dankwerts,45 when applied to ozone mass transfer in this case, results in the following expression:

{

[O3]l RO3 ) KLax1 + M [O3]sl 1+M

}

(13)

In this expression, M is defined as Dkw/kL2. As per the equation recommended by Johnson and Davis,46 D ) 1.71 × 10-9 m2 s-1. Beltran et al.3 reported the value of kL to be 3.1 × 10-4 m s-1 for clean water as in this case. As per Yurteri and Gurol,15 for raw surface water, kw ) 2.8 × 10-3 s-1 at slightly alkaline pH values. Using the above values, M was calculated to be 4.98 × 10-5. For such a low value of M, eq 13 is indistinguishable from eq 12, and hence no error will be incurred in using eq 12 for calculating the KLa value. Additionally, El-Din and Smith13 and Zhou et al.,12 during ozone reactor modeling, have neglected mass-

transfer enhancement as above in their calculations through similar reasoning. Also, Qiu et al.,10 during simulation of batch ozonation of the 2,4-DCP solution, have shown that E is high at the beginning of the experiment when the pollutant concentration is high but rapidly declines with pollutant destruction. Hence, it is justified to assume that, in the absence of pollutants in the aqueous phase, E can be neglected. Experimental Conditions for Ozonation Studies. Experimental ozonation studies were conducted under a variety of conditions obtained by varying influent gaseous ozone concentration [O3]ig, pH, and scavenger concentration (CT). The variables monitored during experiments were [O3]g and [O3]l. The gas flow rate (Qg) and liquid flow rate (Ql) values were held constant at 1 L min-1 and 25 mL min-1, respectively. For each experiment, sufficient time was allowed to elapse after the start of ozonation before readings/samples were taken to ensure the attainment of steady state. Generally, for each experiment, five readings/samples were taken at 5-min intervals. The average and standard deviation of these values were computed and used for model verification. In all, a total of 34 experiments of this type were performed. Experimental Results versus Mathematical Simulation. Simulations were run corresponding to the conditions used for obtaining experimental data. Comparison of measured and simulated aqueous ozone concentrations and measured and simulated effluent gaseous ozone concentrations are presented in Figures 3 and 4, respectively. Conditions corresponding to each data point, i.e., pH, scavenger concentration, and influent gaseous ozone concentration, and S, which is a function of the temperature, are also shown in the same figure. A line of unit slope is also drawn in both figures, such that a point lying on this line suggests perfect agreement between experimental data and simulation results. A point below this line suggests undersimulation of the experimental value, while a point above this line suggests oversimulation. A regression line is also drawn in the same figure to indicate the degree of agreement between experimental and simulated values. Discussion On the basis of the results presented in Figures 3 and 4, it may be concluded that the agreement between experimental data and simulation results is only moderate. The reported correlation coefficients in the above figures could have been enhanced significantly if some poorly correlating data points were omitted as possible “outliers”. However, that would have defeated the objectives of the discussion in this section, which is geared toward exploring the reasons behind the disagreement between some of the experimental data with simulation results. To begin such a discussion, one must first look at some of the assumptions made during the development of the simulation model and the possible impacts of the invalidity of these assumptions on the simulation

1426 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004

Figure 3. Comparison of the measured and simulated aqueous ozone concentrations. KLa ) 0.1 s-1 for all simulations. T ) 30 ( 5 °C. For both simulation and experiments, pH, S, and CT values are as given in the figure. [O3]ig values are given in parentheses corresponding to each data point in the figure. Error bars are based on the standard deviation of the measured values.

results. One assumption made while formulating the model was that the gas phase in the reactor was completely mixed. The effect of this assumption, if incorrect, would be to overpredict the effluent gaseous ozone concentration. However, the results in Figure 4 indicate that gaseous ozone concentration is underpredicted in many cases. Another assumption was that no ozone decomposition occurs in the gas phase. The net effect of invalidity of this assumption will also be overprediction of the effluent gaseous ozone concentration. It is postulated that differences in temperature and ionic strength values between the experimental and simulated results may account for most of the variability seen in Figures 3 and 4. It is well-known that the masstransfer coefficient (KLa) increases with increase in the temperature, while S of ozone decreases with temperature. Furthermore, sensitivity analysis9 showed that S is the parameter that is most sensitive in determining the concentration of aqueous ozone and hence effluent gaseous ozone concentration from the reactor. Also, the ionic strength and KLa are positively correlated. This is due to the reduction in the surface tension of water with an increase in the ionic strength,47 which results in a decrease in the bubble size and a corresponding increase in the specific interfacial area (a), thus increasing the KLa. S is, however, not significantly affected by the ionic strength in the range of 0.0-0.1 M investigated during this research.9,48

Figure 4. Comparison of the measured and simulated effluent gaseous ozone concentrations. KLa ) 0.1 s-1 for all simulations. T ) 30 ( 5 °C. For both simulation and experiments, pH, S, and CT values are as given in the figure. [O3]ig values are given in parentheses corresponding to each data point in the figure. Error bars are based on the standard deviation of the measured values. Table 9. Sensitivity Analysis for the Determination of the Effect of Changes in S and KLa Values on [O3]l and [O3]l Simulation Conditions (Qg ) 1 L min-1, Ql ) 25 mL min-1, CT ) 1.0 mM, pH 8.8, V ) 1 L, [O3]ig ) 30 mg L-1) KLa ) 0.1 s-1

[O3]l, mg L-1 [O3]g, mg L-1

S ) 0.1238 (T ) 35 °C)

S ) 0.1523 (T ) 30 °C)

S ) 0.1897 (T ) 25 °C)

2.04 24.24

2.25 22.75

2.49 21.02

S ) 0.1523 KLa ) 0.05 [O3]l, mg L-1 [O3]g, mg L-1

1.98 24.67

s-1

KLa ) 0.10 s-1

KLa ) 0.15 s-1

2.25 22.75

2.39 21.73

Model simulations were conducted at a constant KLa value of 0.1 s-1 and with S values varying between 0.13 and 0.18 for different experiments, corresponding to a temperature range of 25-35 °C encountered during these experiments. The ionic strength, which affects the value of KLa substantially, varied between 0.0 and 0.1. Sensitivity analysis was performed for ascertaining the effect of variations in S and KLa on the aqueous ozone concentration in the reactor and the effluent gaseous ozone concentration from the reactor. As per the results of this analysis presented in Table 9, a 5 °C variation in the temperature may affect the aqueous ozone concentration by 10% and the effluent gaseous ozone concentration by 7.6%. A 50% variation in the KLa value affects the aqueous ozone concentration by 12% and the

Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1427

effluent gaseous ozone concentration by 8%. These results are similar to those espoused by Wu and Masten.9 In conclusion, almost all variation between measured and simulated aqueous ozone and gaseous ozone concentrations shown in Figures 3 and 4 may be ascribed to variations in S and KLa, resulting from differences in the temperature and ionic strength, respectively, between simulation conditions specified and actual experimental conditions.

Acknowledgment We gratefully acknowledge the financial help provided by the Third World Academy of Sciences (TWAS), Trieste, Italy, for equipment purchase (Research Grant Agreement No. 99-205 RG/CHE/AS), Council for Scientific and Industrial Research (CSIR), India (Scheme No. 22/309), and Ministry of Human Resources Development (MHRD), Government of India, under the Research and Development Scheme for Year 2001-02 (Sanction Order No. 26-1/2202-TSV).

Summary and Conclusions The research presented in this paper includes formulation of an ozone contactor model incorporating ozone mass transfer from the gas to liquid phase and a mechanistic description of ozone self-decomposition in the liquid phase. The simulation results obtained from the modeling exercise have been verified with experimental data obtained at various pHs and radical scavenger concentrations. Questions may be raised about the need for incorporation of a mechanistic description of ozone decomposition in ozone contactor modeling when empirical descriptions of the same have been reported to be quite adequate in simulating aqueous and gaseous ozone concentrations in ozone contactors.12 In this regard, it must be understood that empirical descriptions of ozone decomposition are often adequate when the objective is the description of dissolved ozone concentration distribution in the ozone contactor under various conditions, as is required for ozone concentration times contact time, or CT, calculations in ozone contactors used for disinfection purposes. However, when ozone contactors are used for other purposes, such as the destruction of micropollutants, often the interaction leading to micropollutant degradation is not with molecular ozone but with hydroxyl radicals formed by ozone self-decomposition. Under such circumstances, the prediction of the micropollutant degradation profile can only be achieved through a mechanistic model for ozone decomposition and interaction of the resulting hydroxyl radicals with the micropollutants. The model developed in this paper describes ozone mass transfer from the gaseous to liquid phase and ozone self-decomposition in the aqueous phase. The aqueous phase considered is pure water containing only H+/OH- ions and radical scavengers (HCO3-/CO32-). However such a model might easily be extended to incorporate ozone decomposition through interaction with NOM by incorporating equations of the form kNOM,O

3

NOM + O3 98 products kNOM,[•OH]

NOM + [•OH] 98 ψ[•O2-] + products where ψ may vary between 0 and 1, with ψ ) 0 for pure scavengers and ψ ) 1 for pure promoters. Similar equations may also be incorporated to account for interaction of ozone and hydroxyl radicals with target micropollutants and their degradation products. In short, the model presented in this paper can be used as the basic “building block”, which through incorporation of additional equations may be used to describe the interactions resulting from application of ozone to complex solution matrixes.

Nomenclature D ) diffusion constant of ozone, m2 s-1 P[O3] ) partial pressure of ozone, atm RO3 ) rate of ozone mass transfer, mg L-1 s-1 H[O3] ) Henry’s constant for ozone, atm X[O3] ) saturation mole fraction of ozone corresponding to [O3]g, mol mol-1 [O3]sl ) saturated aqueous ozone concentration corresponding to [O3]g, mg L-1 [O3]g ) gas-phase ozone concentration effluent from the reactor, mg L-1 k′1 ) forward kinetic rate constant for eq 3, s-1 k′2 ) backward kinetic rate constant for eq 3, s-1 kNOM,O3 ) kinetic rate constant for the reaction between NOM and ozone, M-1 s-1 kNOM,[•OH] ) kinetic rate constant for the reaction between NOM and [•OH] radicals, M-1 s-1 k1 ) kinetic rate constant for eq 1 in Table 2, M-1 s-1 k2 ) kinetic rate constant for eq 2 in Table 2, M-1 s-1 k3 ) kinetic rate constant for eq 3 in Table 2, M-1 s-1 k4 ) kinetic rate constant for eq 4 in Table 2, M-1 s-1 k5 ) kinetic rate constant for eq 5 in Table 2, M-1 s-1 k6 ) kinetic rate constant for eq 6 in Table 2, M-1 s-1 k7 ) kinetic rate constant for eq 7 in Table 2, M-1 s-1 k8 ) kinetic rate constant for eq 8 in Table 2, M-1 s-1 k9 ) kinetic rate constant for eq 9 in Table 2, M-1 s-1 k10 ) kinetic rate constant for eq 10 in Table 2, M-1 s-1 k11 ) kinetic rate constant for eq 11 in Table 2, M-1 s-1 k17 ) kinetic rate constant for eq 17 in Table 2, M-1 s-1 k19 ) kinetic rate constant for eq 19 in Table 2, M-1 s-1 k18 ) kinetic rate constant for eq 18 in Table 2, M-1 s-1 kf12 ) forward kinetic rate constant for eq 12 in Table 2, s-1 f k13 ) forward kinetic rate constant for eq 13 in Table 2, s-1 kf14 ) forward kinetic rate constant for eq 14 in Table 2, s-1 f k15 ) forward kinetic rate constant for eq 15 in Table 2, s-1 kf16 ) forward kinetic rate constant for eq 16 in Table 2, s-1 kb12 ) backward kinetic rate constant for eq 12 in Table 2, M-1 s-1 b k13 ) backward kinetic rate constant for eq 13 in Table 2, M-1 s-1 kb14 ) backward kinetic rate constant for eq 14 in Table 2, M-1 s-1 kb15 ) backward kinetic rate constant for eq 15 in Table 2, M-1 s-1 b k16 ) backward kinetic rate constant for eq 16 in Table 2, M-1 s-1 [OH-] ) hydroxide ion concentration, M [O3]ig ) influent gaseous ozone concentration, mg L-1 Qg ) gas flow rate, L min-1 Ql ) liquid flow rate, mL min-1 kw ) specific ozone utilization rate constant, s-1

1428 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 kL ) local mass-transfer coefficient, m s-1 [•O2-] ) superoxide radical concentration, M [•HO2] ) hydroperoxide radical concentration, M [HO2-] ) hydroperoxyl ion concentration, M [•O3-] ) ozonide radical concentration, M [•HO3] ) hydrated ozonide radical concentration, M [•OH] ) hydroxyl radical concentration, M [H2O2] ) hydrogen peroxide concentration, M [H+] ) hydrogen ion concentration, M [H2CO3*] ) carbonic acid concentration, M [HCO3-] ) bicarbonate ion concentration, M [CO32-] ) carbonate ion concentration, M [•CO3-] ) carbonate radical concentration, M [O3]l ) aqueous ozone concentration inside and effluent from the reactor, mg L-1 CT ) inorganic carbon concentration, mM M ) squared Hatta number K12 ) equilibrium constant for eq 12 in Table 2, M K13 ) equilibrium constant for eq 13 in Table 2, M K14 ) equilibrium constant for eq 14 in Table 2, M K15 ) equilibrium constant for eq 15 in Table 2, M K16 ) equilibrium constant for eq 16 in Table 2, M KLa ) mass-transfer coefficient, s-1 S ) solubility ratio, M M-1 T ) temperature, °C V ) liquid volume in the reactor, L ψ ) stoichiometric factor for the production of [•HO2] radicals through interaction between NOM and [•OH]

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Resubmitted for review March 17, 2003 Revised manuscript received August 1, 2003 Accepted September 5, 2003 IE020490Z