A Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer

Transcription

1 J. Chin. Inst. Chem. Engrs. Vol. 33 No Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer Yi-Hung Chen [1] Ching-Yuan Chang [] Yue-Hwa Yu [3] and Pen-Chi Chiang [4] Graduate Institute of Environmental Engineering National Taiwan University Taipei Taiwan 16 R.O.C. Chun-Yu Chiu [5] Department of Environmental Engineering an-yang Institute of Technology I-an Taiwan 61 R.O.C. Young Ku [6] Department of Chemical Engineering National Taiwan University of Science and Technology Taipei Taiwan 16 R.O.C. Jong-Nan Chen [7] Graduate Institute of Environmental Engineering National Chiao-Tung University Hsin-Chu Taiwan 3 R.O.C. bstract The dynamic process of disinfection with ozone in a bubble column is studied for model establishment. Bubble columns have been widely used for ozone disinfection in plants and laboratories. Ozone is produced by passing oxygen-enriched gas through an ozone generator and introduced into the bottom of a column equipped with a gas-diffuser. There certainly exists a temporary and unsteady period before the ozone disinfection system reaches steady state. vailable ozone disinfection models employed to describe dissolved ozone and surviving microorganism profiles have commonly been developed for steady state. Moreover oxygen mass transfer has usually been neglected in previous ozone disinfection models. However this information is desirable for the proper operation of ozone disinfection in a bubble column. Thus the objective of this study was to model and investigate the dynamic ozone disinfection process in a bubble column with oxygen mass transfer. dynamic axial dispersion model is proposed and was employed to predict the variation of the ozone microorganism and oxygen concentrations along the column. The results of prediction were obtained based on the conditions of Mariñas et al. (1993. E. coli was chosen as the model microorganism. The dynamic model of ozone inactivation is useful for proper prediction of the variables of an ozone disinfection system in a bubble column. Key Words Ozone Ozone disinfection Bubble colu mn Dynamic model Hydrodynamics INTRODUCTION Ozone which is one of the most effective oxidants has been widely applied in water treatment and disinfection (Chang et al. 1. It is commonly produced by electrical discharge into pure oxygen or oxygen-enriched gas through an ozone generator. The mixture of gases composed of oxygen and ozone is then transferred to water by bubbling it through the bulk solution. The efficiency of disinfection is usually dependent on the dissolved ozone concentration. Certainly quantification of the concentration variation of dissolved ozone and surviving microorganism is critical to the rational design and optimization of microbial inactivation. Bubble column reactors (BCRs have been commonly used in plants and laboratories for ozone contacting in the United States and throughout the world (anglais et al Compared with other ozone contactors BCRs offer the advantages of no moving parts high liquid phase content for the treatment reasonable mass transfer rates under low energy input little required space and relatively low cost (Deckwer and Schumpe Bubble columns [1] [] To whom all correspondence should be addressed [3] [4] [5] [6] [7]

2 54 J. Chin. Inst. Chem. Engrs. Vol. 33 No. 3 are typically constructed with 18 to ft water depths to achieve 85 to 95 percent ozone transfer efficiency. The ozone-containing gas is introduced into the bottom of the column. The direction of liquid flow may be cocurrent or countercurrent. Certainly there exists a temporary and unsteady period before the ozone disinfection system reaches steady state. vailable ozone disinfection models employed for the description of ozone and microorganism profiles have commonly been developed for steady state (Smith and Zhou Such information about the dynamic process of ozone disinfection is still scarce. ccordingly predictions of the qualities of treated water such as the degree of microbial inactivation in the early stage of ozone disinfection are usually not available and the time required for steady state establishment remains to be determined (WW and SCE The degree of inactivation of the microorganism is described by the surviving ratio of the initial microorganism concentration. The major factors of ozone disinfection are C and t c where C is the concentration of dissolved ozone in mg/ and t c is the contact time in minutes. The United States Environmental Protection gency (USEP has promulgated the C t c regulation to assure adequate disinfection. The factors C and t c can be taken as the average value of the dissolved ozone concentration in the column and the t 1 value respectively where t 1 is determined by the tracer test representing the minimum time required for 9 percent of the inlet to be exposed to the disinfectant within the column (anglais et al Furthermore one of the advantages of ozone disinfection is that it contributes the dissolved oxygen (Evans 197 because oxygen may be used in the follow-up process after the ozone has been decomposed (McGhee The ozone concentration is usually relatively low in the carrier gas containing the majority of the oxygen. However the oxygen mass transfer has usually been neglected in the previous ozone disinfection models. This is because the solubility of oxygen is quite a bit lower than that of ozone. Oxygen is thus usually taken as an inert gas for the ozone-oxygen mixture. Therefore there is a lack of information about the dissolved oxygen concentration in the ozone disinfection process. The objective of this study was to model and investigate the dynamic ozone disinfection process in a bubble column with oxygen mass transfer. Three major factors were considered for the dynamic ozone disinfection model: (1 hydrodynamic behavior ( gas-liquid mass transfer and (3 microorganism ozonation reaction kinetics. dynamic axial dispersion model (DDM is proposed that takes into account these three major factors. Based on the DDM the dynamic variations of the ozone microorganism and oxygen concentration profiles can be predicted. Fig. 1. Two-film model for mass transfer of ozone and oxygen. The proposed model can provide useful information about the dynamic disinfection process with ozone in a bubble column. THEORETIC NYSIS Modeling the dynamic processes of ozone disinfection in a bubble column requires quantification of the rates of mass transfer and chemical reactions associated with the hydrodynamic condition of the system. The mass transfer of ozone (denoted as and oxygen (denoted as O from the gas to liquid phase can be described by the two-film model (Danckwerts 197 as illustrated in Fig. 1. s indicated by Danckwerts the predictions of mass transfer based on the film and penetration models are very similar. However the computation related to the film model is simpler because it involves ordinary rather than partial differential equations. Noting that the diffusivities of ozone and oxygen in the gas phase are about 1 4 times higher than those in the liquid phase one may assume that the resistance of mass transfer is solely contributed by the liquid phase. s the ozone is dissolved in water it may be consumed via self-decomposition to oxygen (O 3 3O (Hewes and Davison Regarding spontaneous ozone decomposition in water and ozone consumption in the presence of a microorganism (N one may propose the following pseudo first-order and secondorder rate expressions respectively (Chick 198; Kuo and Huang 1995; ezcano et al and 1: dc / dt k C α k C N (1 d N N dn / dt k C N ( N

3 Yi-Hung Chen Ching-Yuan Chang Yue-Hwa Yu Pen-Chi Chiang Chun-Yu Chiu Young Ku and Jong-Nan Chen: 55 Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer dc dt 3k C /. (3 / d With ozone decomposition and oxygen formation the mass transfer rates of ozone and oxygen may be enhanced and retarded respectively. The ratios of the mass transfer rates of ozone and oxygen with ozone decomposition and oxygen formation to those without may be desigated as the enhancement factor of ozone decomposition (E r and the retarding factor of oxygen formation (R fo respectively. ccording to the film model the E r and R fo of ozone and oxygen respectively can be calculated according to Eqs. (4 (1 in dimensionless form: d θ F / dx M θ F + M Nθ F ( N F / N d d θ x θ CG CG ( ugcg εg εgeg t C Er ka( C (4 H C ( N F / N / dx M Nθ F ( N F / N (5 R fokoa( C. H OF dx M O θ OF θ / θ (6 F θ F d( N F / N / dx x 1 θ F θ N F / N N / N θ θ E R OF r fo (7 (8 ( dθ / dx ( θ θ (9 F x ( dθ / dx ( θ θ. (1 OF x The dimensionless variables and parameters of Eqs. (4 (1 are defined in the nomenclature. The hydrodynamic condition of contactors affects the concentration profiles and hydraulic efficiency (t 1 /t. dynamic axial dispersion model is developed to describe the dynamic processes of ozone disinfection in a bubble column. ssumptions of the model are as follows (Mariñas et al. 1993; Zhou et al. 1994; Huang et al. 1. (1 The homogeneous bubbling flow regime holds. The dispersion coefficients gas holdup and mass transfer coefficients are constant along the height of column. ( The end effect of the column is neglected. (3 Pressure varies linearly with the column height owing to the hydrostatic head. (4 Henry s law applies. (5 Reactions in the gas phase are neglected. The axial dispersion model has been commonly used and is valid for the flow conditions in almost all types of bubble column reactors (Kaštánek et al However the assumption of the homogeneous bubbling flow regime is tenable for smaller gas velocity (u G <3 cm/s as explained by Deckwer (199. review of the previous studies on ozone contacting processes such as those of Mariñas et al. (1993 and Chen et al. ( with u G.5 and cm/s respectively indicates that the operating conditions of the gas velocity are in the homogeneous bubbling flow regime. Based on the above assumptions the overall mass balance of the gas phase may be described by Eq. (11. The left-hand side term represents the variation of the local gas concentration while the right-hand side terms stand for the dispersion effect convection and ozone and oxygen mass transfers respectively: O (11 pplying the ideal gas equation and noting that the hydrostatic pressure (P decreases linearly with the axial coordinate (z from the bottom of the column one has C G P RT PT + ε ρ g( z PT β P RT RT (1 with β P 1+ α P (1 z / and α P ε ρg /( fppt. Substituting Eq. (1 into Eq. (11 and putting the result in dimensionless form one may obtain Eq. (13 for the dimensionless superficial gas velocity (U G with U G u G /u G : for du dz G α P U β P R fo G St E GO r St 1+ α P β P G 1+ α P β O P y ( θ y ( θ θ θ. (13 z h B with the boundary condition (BC z U 1. (14 G For h B < z 1 UG. The dimensionless height of gas bubbles ( h B with h B hb / at time τ ( t/t which can be calculated by Eq. (15 has a maximum value of one: B dh R dτ ug U G z h B with the initial condition (IC (15 τ. (16 h B Further the dimensionless gas phase governing equations for ozone (θ with θ C /C and oxygen (θ with θ C /C can be expressed by Eqs. (17 and (18 respectively:

4 56 J. Chin. Inst. Chem. Engrs. Vol. 33 No. 3 τ τ R 1 θ ( UGθ ug[ PeG E R r St G ( θ ( θ θ ] 1 θ ( UGθ ug[ PeG R fo St GO θ ]. (17 (18 The dimensionless liquid phase governing equations for ozone (θ with θ C /(C /H the microorganism (N/N and oxygen (θ with θ C Olb /(C /H O should consider the chemical reaction terms according to Eqs. (1 (3 and are as follows: τ ( N / N τ τ 1 Pe + E r Da θ St N ( θ + s ( N / N θ θ Da θ 1 ( N / N ( N / N + s Pe Da ( N / N 1 Pe (19 Nθ ( + R fo θ St O ( θ + s θ + Da θ O (1 In Eqs. (19 (1 s +1 or 1 for countercurrent or cocurrent flow respectively. The ICs of Eqs. (17 (1 are τ θ θ θ θ θ N/N 1. ( The applicable BCs are as follows. t the bottom z : θ 1+ θ + PeG PeG. (3 ( / s + 1 N N (4a s θ 1 θ θ ( N / N t z h B : 1 Pe 1 + Pe 1 ( N / N 1+. (4b Pe (5 s θ + 1 θ ( N / N θ 1 Pe 1 Pe 1 ( N / N 1 (6a Pe ( / s 1 N N.(6b In the above equations the definitions of the dimensionless variables and parameter groups are listed in the nomenclature. Note that the Peclet numbers represent the flow conditions. s the values of the Peclet numbers become large the system tends to approach the plug flow. For small values of the Peclet numbers the flow behaves like complete mixing. Furthermore the Stanton and Damköhler numbers stand for the significance of mass transfer and chemical reaction respectively. Equations (13 (6 represent the governing equations of DDM for the ozone disinfection process in a bubble column. The present work is general and considers: (1 the dynamic state ( the oxygen mass transfer (3 the chemical reactions (4 the effects of chemical reactions (ozone decomposition and disinfection on mass transfer and (5 the superficial gas velocity variation. The steady state studies of Smith and Zhou (1994 neglected the oxygen mass transfer (St GO St O and the effects of chemical reactions on the mass transfer. The dynamic and axial variations of the ozone microorganism and oxygen concentration profiles are predicted by solving Eqs. (4 (1 and (13 (6 simultaneously. The finite difference method based on the Taylor series was employed with the Turbo C program in this study. Equations (4 (8 were firstly solved using the iterative method to obtain the values of θ F N F / N and θ OF in the film yielding the values of E r and R fo from Eqs. (9 and (1 at time τ. The obtained E r and R fo were substituted into Eq. (13 along with Eq. (14 to compute U G. Equations (15 (6 were then solved using the forwarddifference method to compute the values of the variables in the next time step of τ + τ from the available values at τ. This is followed by the computation of E r R fo and U G at τ + τ. The computation was conducted up to the steady state. The grids along z to 1 and the size of the time step adopted in the program were 11 points and 1-5 respectively.

5 Yi-Hung Chen Ching-Yuan Chang Yue-Hwa Yu Pen-Chi Chiang Chun-Yu Chiu Young Ku and Jong-Nan Chen: 57 Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer RESUTS ND DISCUSSION The results of dynamic ozone disinfection in a bubble column obtained in this study are divided into two parts: (1 the hydrodynamics effect on the characteristic time of the ozone contact system and ( the dynamic variations of the concentration profiles of ozone the microorganism and oxygen. For comparison and application purpose the operating conditions used by Mariñas et al. (1993 for treating Colorado River water in a pilot scale bubble column were assigned as the basic values. These are: t 6 min 16 ft 4.88 m d R in 16. cm Q 4.4 gal/min /min Q G (5 C 1 atm.6 ft 3 /min.64 /min C wt. % T 13 C turbidity.5 ntu ph 8.3 and a corresponding applied ozone dosage of 1 mg O 3 gas/ liquid. These values represent typical operation conditions of an ozone contactor in water treatment practice. Escherichia coli (E. coli which has been identified as an etiological agent responsible for waterborne diseases was chosen as the model microorganism. The inactivation kinetics of E. coli with ozone are proposed as Eqs. (1 and ( with the following parameters (Hunt and Mariñas 1997 and 1999: k N EaN N exp( (7 RT 11 α mg O 3 /CFU. (8 N In Eqs. (7 and (8 E an ( 371 J/mol N ( /(mg s R ( J/(mol K and T (in K are the activation energy frequency factor ideal gas constant and absolute temperature respectively. The kinetics were found to be ph independent. s for the value of DaN in Eq. (19 it is related to the initial concentration of the microorganism (N. The effect of N on the ratio of the rate of ozone consumption under inactivation of E. coli (α N k N C N to that under ozone self-decomposition (k d C with k d exp( / RT s -1 is shown in Fig.. The results indicate that at T 5 C E. coli inactivation with ozone is significantly correlated 7 with ozone consumption when N > 1 CFU/ where CFU denotes the colony forming units. The ratio of α N k N N /kd decreases with the temperature of the water at the same N (Fig.. ccording to regulations governing water sources for manufacturing drinking water in Taiwan the maximum allowable concentration of E. coli is 1 CFU/. Note 5 that the value of DaN is.84 in the conditions of 5 Mariñas et al. (1993 when N 1 CFU/. Therefore the value of α N k N N (.3 s -1 as 5 N N 1 CFU/ is much smaller than that of k d in general disinfection cases. Da N N/N (.84 as N N as compared to Da (1.71 for the Fig.. log(α N k N N / k d vs. log(n for Escherichia coli 11 inactivation with ozone. α N mg 8 O3/CFU k N exp( 371 / RT s 1 k d exp( / RT s -1 - T 5 C; T 15 C; - - T 5 C; T 35 C. case of Fig. 4 may then be neglected when computing ozone consumption in Eq. (19. The same approach with Da N was also noted by Smith and Zhou (1994. ccordingly the E r of ozone and R fo of oxygen can be found by Eqs. (9 and (3 respectively (Chen et al. : with E R r fo sinh 1 Ha Ha 3 D D C ( H O ( C / H ( C sinh C Ha k D k. d Ha Ha cosh Ha C / H C (9 C ( H C ( H O cosh Ha C C -1 (3 ccording to the results of Chen et al. ( the values of E r and R fo are significantly different from unity when k d is greater than s -1 (with Ha.3. Thus the values of E r and R fo can be reasonably taken as unity for common cases of ozone 5 self-decomposition with k d 1 to s -1 Ha.1 to.3 <.3. However it is better to take into account the effect of Da N for the case of high microorganism concentration. Otherwise the predicted concentration of the residual ozone and the degree of inactivation of the microorganism may be overestimated.

6 58 J. Chin. Inst. Chem. Engrs. Vol. 33 No. 3 Fig. 3. Hydraulic indices vs. Pe in bubble column. t 1 /t 9 ; t 1 /t ; - t 5 /t. (a Hydrodynamics effect on the characteristic time of the ozone contacting system Some hydraulic indices have commonly been used for ozone contactors such as t 1 / t a measurement of the degree of short-circuiting in the column t 5 / t the index of the mean detention time and t 9 / t 1 the Morril index indicating the degree of mixing (Bishop et al The hydrodynamic performance of ozone contactors mainly depends on t 1 / t. Figure 3 shows the variation of t 1 / t t 5 / t and t 1 / t 9 with Pe ( u /( ε E. s Pe falls below 1 the value of t 1 / t 9 approaches a constant value of.5 representing the hydrodynamics of complete mixing. On the other hand t 1 / t 9 increases significantly as Pe increases from 1 to 1 resulting in a change of the regime from complete mixing to plug flow. The value of t 1 / t also increases significantly from.1 to.95 as Pe increases from.1 to 1 which is similar to the trend of the variation of t 9. However the increase of t 5 / t with Pe 1 / t is moderate rising from.69 to 1.. The flow hydrodynamics approach plug flow with larger values of t 1 / t and t 5 / t in a bubble column. The USEP has outlined a recommended method for calculating the Ct c value based on the assumption of t 1 / t.8 listed in ppendix O of the Guidance Manual for the Surface Water Treatment Rule. anglais et al. (1991 referred to the results of evenspiel (197 and proposed values of t 1 / t varying from. to.5. Martin et al. (1995 reported values of t 1 / t 5 of a general bubble column of about.45 to.6 which correspond to Pe of 3.5 to 11 and t 1 / t of.37 to.55 (Fig. 3. Do- Quang et al. ( noted that the values of t1 /t of twelve full-scale ozonation plants were between.41 and.67. ccordingly the appropriate recommended (b Fig. 4. Variation of θ with z in the bubble column. u 1.35 cm/s u G.51 cm/s y.133 C 7.8 g/m 3 C 3 g/m 3 k d.475 s -1 k.13 cm/s k a. s -1 k O a.3 s -1 H.55 H O 7.3 ε G.6 ε.997 Pe 9.8 Pe G St.735 St G St O.831 St GO.798 α P.47 Da 1.71 Da N Da O.46 R ug ines: prediction with τ and steady state (ss. ( : experimental data of Mariñas et al. (1993 at steady state. (a countercurrent; (b cocurrent. value of t 1 / t is about.5 for bubble contactors in practice. Dynamic variations of the concentration profiles of ozone microorganism and oxygen Simulation of ozone disinfection was studied from the beginning to steady state. Figure 4 depicts typical concentration profiles of dissolved ozone

7 Yi-Hung Chen Ching-Yuan Chang Yue-Hwa Yu Pen-Chi Chiang Chun-Yu Chiu Young Ku and Jong-Nan Chen: 59 Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer (a (b Fig. 5. Variation of θ / θ ss with τ at different positions in the bubble column. kn 89.9 /(mg s Da N 4397 while other conditions are the same as those in Fig. 4. (a countercurrent; (b cocurrent. ines: prediction. - z.; z.4; - - z.6; z.8; z effluent of liquid. (θ as a function of the dimensionless axial coordinate z and operating time τ. The value of k Oa of oxygen is estimated based on k a of ozone according to the surface renewal theory (Danckwerts 197; Biń The values of parameters for modeling except those of oxygen and the microorganism were also used in previous studies (Huang et al and 1. For the countercurrent flow bubble column the highest ozone concentration was at the bottom and it decreased monotonically as z increased. comparison of the predicted values with the experimental data is presented in Fig. 4(a which shows satisfactory agreement except near the bottom of the column. The experimental θ values near the bottom are approximately constant indicating intensive mixing in the zone due to the use of a spherical diffuser (Mariñas et al If the flows was cocurrent a maximum value of θ would occur somewhere in the middle portion of the column and shifts upward with increasing ozonation time (Fig. 4b. The value of θ at the water inlet of column for the cocurrent system is large due to the presence of axial dispersion. It is seen that the shapes of the ozone concentration profiles in the transient state are similar to those in steady state for both countercurrent and cocurrent flow contactors. The ozone residual in the effluent for the countercurrent flow contactor (at z is much higher than that for the cocurrent one (at z 1. However the cocurrent flow contactor has a higher average value of θ than the countercurrent one dose. lthough the calculated values of E r and R fo are close to unity for the case with k d.475 s -1 the enhancing and retarding effects of ozone and oxygen and oxygen mass transfer are all included in the dynamic simulation. Figure 5 shows the time variation of θ /θ ss which represents the saturation degree of the steady state value at different positions of the column. θ approaches the steady state value faster near the inlet of input ozone gas (the bottom of the column for both the countercurrent and cocurrent flow contactors. The bubble column needed at least 3t to reach steady state in the experiments conducted by Mariñas et al. (1993. This is confirmed by the results shown in Fig. 5 indicating the time needed for the establishment of steady state. The time scale for reaching steady state usually ranges from about 1.5 to 3t according to the simulation results shown in Fig. 5 and the experimental data of Chen et al. (. Chen et al. further indicated that the ozone contacting process in a countercurrent bubble column reached steady state faster with higher values of the Peclet number ozone decomposition rate and mass transfer rate. The effluent liquid concentration of the countercurrent flow contactor with the effluent at the bottom of the column reaches steady state faster than dose that of the cocurrent flow contactor with the effluent at the top of column. For instance it takes.5 and 1.4 of τ to reach.95 θ ss of the effluent for the countercurrent and cocurrent flow contactors respectively. Thus when the liquid contacts with a higher concentration of gaseous ozone it has a higher level of dissolved ozone and approaches steady state faster. Different species of microorganisms may exhibit different degrees of resistance to reaction with ozone. smaller value of k N indicates that the microorganism is more resistant to ozone. E. coli is

8 6 J. Chin. Inst. Chem. Engrs. Vol. 33 No. 3 z (a (a (b Fig. 6. The degree of microorganism inactivation at different inactivation rate constants of ozone disinfection in the bubble column. k N 89.9 /(mg s Da N 4397 while other conditions are the same as those in Fig. 4.(a countercurrent; (b cocurrent. -.1k N ;.1 k N ; - -.1k N ; k N ; k N. generally more sensitive than other microorganisms such as Pseudomonas aeruginosa Shigella sonnei and Salmonella typhimurium (ezcano et al Figure 6 shows the variation of the log (N/N of ozone disinfection with z at different values of the inactivation rate constant in the bubble column. It is found that the surviving ratio of the microorganism in the effluent increases by several orders of magnitude as the value of the inactivation rate constant decreases by only one order. Thus the degree of disinfection with ozone strongly depends on the inactivation kinetics. The concentration of the microorganism increases and decreases monotonically with (b Fig. 7. Variation of log[ ( N Nss /( N Nss ] of E. coli inactivation with τ at different positions in the bubble column. kn 89.9 /(mg s Da N 4397 while other conditions are the same as those in Fig. 4. (a countercurrent; (b cocurrent. - z.; z.4; - - z.6; z.8; z effluent. from the bottom to the top of the column for the countercurrent and cocurrent flow contactors respectively. The degree of microorganism inactivation in the countercurrent flow contactor increases significantly as the liquid flows downward and approaches the bottom of the column due to the high dissolved ozone concentration. In contrast the degree of microorganism inactivation increases uniformly upwards along the cocurrent flow contactor due to the more uniform distribution of dissolved ozone. Furthermore Fig. 7 shows the time needed to

9 Yi-Hung Chen Ching-Yuan Chang Yue-Hwa Yu Pen-Chi Chiang Chun-Yu Chiu Young Ku and Jong-Nan Chen: 61 Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer approach steady state for microorganism inactivation different τ values are shown in Fig. 8. The concen- (a (b Fig. 8. Concentration profile of θ at different τ for ozone disinfection in the bubble column. kn 89.9 /(mg s Da N 4397 while other conditions are the same as those in Fig. 4. τ and steady state. (a countercurrent; (b cocurrent. with ozone in the bubble column. The value of (N N ss /(N N ss is equal to one at τ and zero at steady state. Similar to the variation trend of dissolved ozone the concentration of surviving microorganism near the bottom of the column approaches steady state faster. The concentration of the surviving microorganism in the liquid effluent at the bottom of the countercurrent flow contactor reaches steady state faster than does that at the top of the cocurrent one. The dissolved oxygen profiles of the column at Fig. 9. Concentration profile of θ at steady state for ozone disinfection in the bubble column. kn 89.9 /(mg s Da N 4397 while other conditions are the same as those in Fig. 4. ines: prediction. (1 - ( (3 - - ( : countercurrent (with O mass transfer countercurrent (without O mass transfer cocurrent (with O mass transfer cocurrent (without O mass transfer. ( experimental data of Mariñas et al. (1993. tration of dissolved oxygen decreases with z from the bottom to the top of the column during the transition to steady state for countercurrent flow. The dissolved oxygen of cocurrent flow has a local maximum value at some specific z value of the column (denoted as z max. The location of z max for cocurrent flow shifts upward during the transition state as τ increases and reaches the top of the column at the steady state. s a result the effluent and average concentrations of dimensionless dissolved oxygen ( θ for the cocurrent ( and countercurrent (.46.7 flow contactors at steady state are not significantly different. The average concentration of θ was calculated by taking the arithmetic mean of the values at 11 axial points with uniform mesh along the contactor. Moreover the level of dissolved oxygen clearly increases due to ozone disinfection processes and has a maximum value in the effluent at steady state. It may be worth mentioning that neglecting oxygen mass transfer in the model for the computation of θ in the effluent liquid in both the transient and steady states results in relative errors of less than 4.5 % (Chen et al.. The effect of oxygen mass transfer on the concentration profile of θ at steady state is shown in Fig. 9. It is seen that the change in the θ profile with and without oxygen mass transfer is small. For engineering applications oxygen

10 6 J. Chin. Inst. Chem. Engrs. Vol. 33 No. 3 mass transfer may be neglected in the simulation of ozone disinfection which is consistent with the conclusion of Chen et al. (. However it should be noted that information about the dissolved oxygen concentration which is useful for ozone contacting processes can not be obtained if the oxygen is assumed as an inert gas. The results obtained here show that the DDM proposed in this study is useful for the prediction of ozone disinfection processes. The validity of the present model when reduced to the simple cases of ozone contacting has been confirmed by the existing data of Mariñas et al. (1993 and Chen et al. (. For further comparison of model prediction with experimental data additional experiments on ozone disinfection would be helpful. CONCUSION dynamic model has been proposed to describe ozone disinfection processes in a bubble column. The model considers oxygen mass transfer. The profiles of the ozone microorganism and oxygen concentrations during ozone disinfection can be well predicted from the beginning to steady state. Some conclusions may be drawn as follows. (1 The values of t 1 / t and t 5 / t vary from.1 to.95 and from.69 to 1. respectively for Pe.1 to 1. The appropriate recommended value of t 1 / t is about.5 in practice. The hydrodynamics is close to complete mixing for Pe < 1 while it gradually approaches plug flow as Pe increases. ( Both the dissolved ozone and surviving microorganism concentrations approach steady state faster near the bottom than near the top of the column. For the liquid effluent the variation of the concentrations reaches steady state faster in the countercurrent flow contactor than in the cocurrent flow contactor. (3 The degree of inactivation of the microorganism with ozone strongly depends on the inactivation kinetics. The surviving microorganism concentration varies monotonically along the bubble column and has a minimum value in the effluent. (4 The concentration of dissolved oxygen varies monotonically in the bubble column at steady state and has a maximum value in the effluent. The effluent and average dissolved oxygen concentrations in the bubble column at steady state for the countercurrent and cocurrent flows are not significantly different. CKNOWEDGEMENT This study was support by the National Science Council of Taiwan under grant No E NOMENCTURE a specific gas-liquid interfacial area based on the volume of liquid and gas 1/m N -1 frequency factor mg -1 s C concentration of dissolved ozone mg/ C C concentrations of ozone of holdup and inlet gases M or mg/ or wt. % C C F dissolved ozone concentrations in bulk liquid and liquid film M or mg/ C i dissolved ozone concentration of liquid at gas-liquid interface M or mg/ C G total gas concentration in gas phase M or mg/ C C concentrations of oxygen of holdup and inlet gases M or mg/ C C OF dissolved oxygen concentrations in bulk liquid and liquid film M or mg/ C C at initial time M or mg/ C Oi dissolved oxygen concentration of liquid at gas-liquid interface M or mg/ CFU colony forming units d R diameter of bubble column in or m D D N molecular liquid diffusion coefficients of ozone and microorganism m /s D O molecular liquid diffusion coefficient of oxygen m /s Da Damköhler number of self-decomposition reaction of ozone ε k d / u Da N Damköhler number of inactivation reaction of ozone ε α N k N N / u Da N Damköhler number of microorganism ε k N C /( uh Da O Damköhler number of oxygen 3 ε kd C HO /( uch DDM dynamic axial dispersion model E an activation energy J/mol E G E axial dispersion coefficients of gas and liquid m /s E r enhancement factor of ozone mass transfer defined as Eq. (9 f P unit conversion factor 1135 Pa (atm -1 g standard acceleration of gravity 9.8 m/s h B height of rising gas bubbles at time t m h B dimensionless form of h B h B / Ha dimensionless Hatta number k d D k H H O Henry s law constants of ozone and oxygen C / C i C / C O i MM -1-1 k N inactivation rate constant mg -1 s k d decomposition rate constant of ozone 1/s k k O physical liquid-phase mass transfer coefficients of ozone and oxygen m/s liquid height of bubble column at steady

11 Yi-Hung Chen Ching-Yuan Chang Yue-Hwa Yu Pen-Chi Chiang Chun-Yu Chiu Young Ku and Jong-Nan Chen: 63 Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer M M N M N state ft or m dimensionless ozone decomposition reaction rate parameter of ozone k d D / k dimensionless ozone disinfection reaction rate parameters of ozone and microorganisms α N k N N D / k kn C D /(H k D N M O dimensionless ozone decomposition reaction rate parameter of oxygen 3k d C H O D /(C H k D O ntu neohelometric turbidity unit N N F numbers of surviving microorganisms in bulk liquid and liquid film CFU/ N ss steady state value of N CFU/ N initial number of activate microorganisms CFU/ P hydrostatic pressure as a function of location of column in Eq. (1 atm P T gas pressure at free space atm Pe G Pe Peclet numbers of gas and liquid phases u G /( E G εg u /( E ε Q G gas flow rate ft 3 /min or /min Q liquid flow rate gal/min or /min R gas constant.8 atm K -1 mol -1 or J K -1 mol R fo retarding factor of oxygen mass transfer defined as Eq. (1 R ug gas-liquid velocity ratio s u Gε /( uεg sign ( +1 for countercurrent; 1 for cocurrent flow St G St GO gas Stanton numbers of ozone and oxygen k a /( ugh k Oa /( ugho St St O liquid Stanton numbers of ozone and oxygen k a / u k Oa / u t time s t c contact time min or s mean liquid phase residence time u min or s t 1 time needed for 1 percent of tracer mass to exit column min or s t 5 time needed for 5 percent of tracer mass to exit column min or s t 9 time needed for 9 percent of tracer mass to exit column min or s T temperature K u G superficial gas velocity (up flow m/s or cm/s u G z h B ug at z h B m/s or cm/s u G inlet superficial gas velocity m/s or cm/s u superficial liquid velocity m/s or cm/s U G dimensionless superficial gas velocity u u G / G U U G z h G at z h B B x distance from gas-liquid interface of liquid film m x dimensionless x x/ x M x M thickness of liquid film / O / O m y y O mole fractions of inlet gases of ozone and oxygen z axial coordinate of column from bottom m dimensionless form of z z/ z location of z with maximal value of z max θ Greek symbols α N ozone demand per E. coli cell consumed mg O 3 /CFU α P pressure ratio ε ρg /( f PPT β P location variable 1 +α P ( 1 z / ε G ε relative gas and liquid holdups θ dimensionless C C / C θ dimensionless C C lb /(C /H θ ss steady state value of θ θ F dimensionless C F C F /(C /H θ dimensionless C C / C dimensionless C C Olb /(C /H O θ θ ( C C /[( C / HO C] ( θ θ /(1 θ θ θ at initial time C /( C / HO θ OF dimensionless C OF C OF /(C /H O ρ liquid density kg/m 3 τ dimensionless time t / REFERENCES WW and SCE (merican Water Works ssociation and merican Society of Civil Engineers Water Treatment Plant Design 3 rd Ed. McGraw-Hill New York (1998. Biń. K. pplication of a Single-Bubble Model in Estimation of Ozone Transfer Efficiency in Water Ozone Sci. Eng. 17(5 469 (1995. Bishop M. M. J. M. Morgan B. Cornwell and D. K. Jamison Improving the Disinfection Detention Time of a Water Plant Clearwell J. WW 85(3 68 (1993. Chang C. Y. Y. H. Chen H. i C. Y. Chiu Y. H. Yu P. C. Chiang Y. Ku and J. N. Chen Kinetics of Decomposition of Polyethylene Glycol in Electroplating Solution by Ozonation with UV Radiation J. Environ. Eng. SCE 17(1 98 (1. Chen Y. H. C. Y. Chang C. Y. Chiu W. H. Huang Y. H. Yu P. C. Chiang Y. Ku and J. N. Chen Dynamic Model of Ozone Contacting Process with Oxygen Mass Transfer in a Bubble Column J. Environ. Eng. SCE t

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13 Yi-Hung Chen Ching-Yuan Chang Yue-Hwa Yu Pen-Chi Chiang Chun-Yu Chiu Young Ku and Jong-Nan Chen: 65 Dynamic Model of Ozone Disinfection in a Bubble Column with Oxygen Mass Transfer Mariñas et al. (1993 (E. coli