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Chemical Engineering and Processing 48 (2009) 1212–1221

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

nfluence of t-butanol on multicomponent reaction kinetics and mass transfer in-nitrophenol ozonation at low pH

arkku Kuosa ∗, Juha Kallasepartment of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20 FIN-53851 Lappeenranta, Finland

r t i c l e i n f o

rticle history:eceived 8 December 2008eceived in revised form 24 February 2009ccepted 20 April 2009vailable online 3 May 2009

eywords:

a b s t r a c t

The influence of t-butanol on multicomponent reaction kinetics and mass transfer in p-nitrophenol ozona-tion is studied at pH 2. The rate coefficients and mass transfer coefficient kLa are estimated with nonlinearparameter estimation. Different reaction kinetic models were used to exclude the possible effect of themodel on the obtained kLa when using data from solutions with different t-butanol concentrations. Two ofthe reaction kinetic models include residual COD, which is the total COD from which the COD of the knownspecies is subtracted. It could be determined that the presence of t-butanol in the solution increases the

zoneubble columnydrodynamicsass transfer

-Butanol

hold-up and kLa. Evidence suggesting that radicals have a noticeable role in p-nitrophenol ozonationkinetics at low pH was found. The reliability and identifiability of the estimated parameters are studied.

© 2009 Elsevier B.V. All rights reserved.

-Nitrophenoleaction kineticsarameter estimation

. Introduction

Ozone has proven to be a very effective chemical for the degra-ation of species that are persistent in biological waste waterreatment. However, the manufacturing of ozone requires a largemount of energy, which makes optimization of the ozonation pro-ess necessary, and the development of reliable hydrodynamic andeaction kinetic models essential. In liquid phase ozone reacts withissolved compounds via direct molecular reaction or via secondaryxidants, such as hydroxyl radicals (OH•), hydroperoxyl radicalsHO2

•) and further compounds like •O3−, HO3

•, etc. To quantifyhe extent of oxidation during an ozonation process, it is neces-ary to combine the characterization of the ozonation process withhe available kinetic information. The oxidation of a dissolved com-ound M during an ozonation process can be formulated as follows,upposing that the dissolved compound reacts with O3 or OH•:

d[M]dt

= k1[M][O3] + k2[M][OH·] (1)

The fraction fOH of M reacting with OH radicals can be calculated

s [1]

OH = k2Rc

k1 + k2Rc(2)

∗ Corresponding author. Fax: +358 621 2199.E-mail address: markku.kuosa@lut.fi (M. Kuosa).

255-2701/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2009.04.008

where Rc is the ratio of the concentrations of OH radicals andozone.

In many works in the literature, the molecular action of ozoneby direct reaction has been investigated using t-butanol as a freeradical scavenger to ensure only a direct reaction pathway. Severalauthors have shown that the addition of t-butanol affects the hydro-dynamic conditions affecting the ozone mass transfer. Neglectingthe effect of t-butanol may lead to large errors in the determinationof reaction kinetic constants. According to López-López et al. [2], t-butanol reduces the surface tension and increases the mass transfercoefficient (kLa). Beckelkacem and Debellefontaine [3] have shownthat t-butanol improves the oxidation process during maleic acidozonation, as it increases the mass transfer rate. Camarasa et al.[4] found that small amounts of alcohol prevented coalescence ofsmall bubbles in an air–water system. There is evidence in litera-ture that alcohols in general [5], as well as some hydrotropes andadditives, for example acetate have these same kinds of effects inwater solution.

According to the ozonation literature, radicals play a minor rolein ozonation at low pH due to the low concentrations of the hydroxylion (OH−).

In general, the addition of t-butanol slows down the reaction

rates of organic molecules like phenols in ozonation, especially athigh pH, where the production of radicals is fast. However, accord-ing to Hoigné and Bader [6], the radical type reaction in solutionscontaining benzene or some of the substituted benzenes, leads tosignificant rates of decomposition already at pH values higher than

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M. Kuosa, J. Kallas / Chemical Enginee

.5. In the literature there is little information about the effect ofadical scavengers on the rates of different reaction paths in theecomposition of organic molecules. Some researchers [6,7] con-lude that a concentration of t-butanol equal to 10−3 mol/(dm3)s sufficient for radical mechanism inhibition. The majority of theesearch in the literature concerning mass transfer and the hydro-ynamic properties of the solution in ozonation with t-butanol haseen conducted using “pure” water. So there is need to study these-butanol–water solutions with additional solvents.

p-Nitrophenol is a commonly identified compound in wasteaters of the dye, textile and intermediary product industries, andelongs to the EEC List I of hazardous pollutants and the U.S.E.P.A.riority Pollutant List. Nitrophenol, and phenol in general, has beenhe subject of numerous studies of ozonation in recent decadesecause of their toxicity and their supposed or proven carcino-enic effects on living organisms. A brief review of the literaturen p-nitrophenol ozonation has been presented in a previous study8].

In that study, a method was developed to estimate the reactionate and stoichiometric coefficients of a multicomponent reaction

odel in ozonation, taking also gas–liquid mass transfer and reactorydrodynamics into consideration. p-Nitrophenol was used as theodel component. To remove the uncertainty concerning the effect

f the changing pH during the experiments, new experiments werearried out (Kuosa et al. [9]) at the constant pH of 2. It was found outhat the model estimated well the reaction kinetics at this constantH.

The objective of this work was to determine how the additionf t-butanol affects the reaction rates on different reaction paths inodel component p-nitrophenol ozonation. The ozonation exper-

ments were conducted at pH 2.0 to determine whether radicalnhibition in fact occurs to a remarkable degree at low pH. A fur-her goal was to examine how different amounts of t-butanol affecthe p-nitrophenol decomposition rate. In addition, the influencesf different amounts of t-butanol on the volumetric mass transferoefficient kLa and gas hold-up in a p-nitrophenol solution weretudied.

. Experimental set-up and analytics

In the current work, the experiments were performed in a rect-ngular bubble column with a total height of 2.0 m, depth of 0.03 mnd width of 0.16 m. The height of the liquid surface in the columnas 1.35–1.75 ± 0.1 m depending on the experimental run. Thus, thepper part of the column formed a gas head space with a height of.65–0.25 ± 0.1 m. The bubble column was operated as a semi-batch

eactor. The gas was fed into the column from the bottom through aorous polypropylene plate with a pore diameter of 300–400 �m.he superficial velocities of the gas were 0.017, 0.023 and 0.028 m/st 101.325 kPa. The input gas ozone concentration was adjusted toe in the range of 1.16 × 10−5 to 1.22 × 10−4 mol/dm3. The gas phase

able 1xperimental runs with t-butanol.

un t-Butanol concentration(mol/dm3)

p-Nitrophenol Hydroquinone COD NO3

2.25 × 10−2 × × ×2.25 × 10−2 × × ×2.25 × 10−2 ×2.25 × 10−2 ×2.25 × 10−3 × × ×2.25 × 10−3 × × ×2.25 × 10−3 × ×2.25 × 10−3 × ×2.25 × 10−3 ×

0 2.25 × 10−3 ×1 2.25 × 10−4 × ×

nd Processing 48 (2009) 1212–1221 1213

ozone concentration was measured spectrophotometrically at theinlet and outlet of the column. The dissolved ozone concentrationin the water was measured directly from the water at single pointnear the column wall at the height of 0.5 m in the reactor by usingan Orbisphere 3660 dissolved ozone analyzer. The measured liquidozone concentrations ranged from 0 to 4.16 × 10−6 mol/dm3. Theliquid samples to be analyzed for the reaction intermediates weretaken at 0.5 m from the bottom of the column over the course ofrun time. A solution made by dissolving p-nitrophenol into deion-ized water with the conductivity of 1–5 �S/cm was used as theliquid phase in the experiments. The temperature of the column wasmaintained at 20 ± 0.1 ◦C. The pH 2.0 was adjusted by the additionof sulphuric acid. Depending on the experimental run 2.25 × 10−4,2.25 × 10−3 or 2.25 × 10−2 mol/dm3 t-butanol was added into thesolution.

The concentrations of p-nitrophenol and various reactionintermediates were analyzed by using a high-performance liq-uid chromatography (HPLC) instrument Hewlett Packard mod1100 with the column LUNA C18(2) (150 mm × 4.6 mm). Thep-nitrophenol concentrations were in the range 6.0 × 10−4 to1.2 × 10−3 mol/dm3 at the beginning of the ozonation run.

The liquid samples were also analyzed for pH, COD and TOC. Inaddition, nitrate and nitrite were analyzed quantitatively with theion chromatography instrument Dionex DX-120 using the IonPacAS14 anion-exchange column.

The experimental data were collected from 11 differentexperimental runs, four runs with a t-butanol concen-tration of 2.25 × 10−2 mol/dm3, six runs with t-butanolof 2.25 × 10−3 mol/dm3, and one run with t-butanol of2.25 × 10−4 mol. The ozone concentration was measured fromall runs both in gas and as dissolved ozone in water. The con-centrations of p-nitrophenol were measured from four runs andhydroquinone was measured from two runs. COD was analyzedfrom six runs and nitrate from 7 runs. The runs with the butanolconcentrations, the analyzed components and the superficialvelocities are shown in Table 1. The runs without t-butanol andtheir experimental conditions are presented elsewhere (Kuosaet al. [9]). The inlet gas ozone concentration was set to differentvalues by adjusting the voltage in the ozone generator. Due tothe technical characteristics of the generator, it was not possi-ble to maintain constant ozone concentration in the gas feed.However, the varying concentration was taken into account inthe reactor model and did not cause any error in the modelpredictions.

3. Model equations for mass transfer and hydrodynamics

Based on the hydrodynamic conditions in this study, an axialdispersion model was used for the gas phase to estimate and vali-date the reaction kinetics. As the gas flow was relatively small, thecase was, however, practically plug flow on the gas side. According

− Ozone gas inlet Ozone gas outlet Dissolved ozone Superficialvelocity (m/s)

× × × 0.023× × × 0.023× × × 0.023× × × 0.023× × × 0.020× × × 0.017× × × 0.023× × × 0.023× × × 0.028× × × 0.017× × × 0.023

1 ering and Processing 48 (2009) 1212–1221

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214 M. Kuosa, J. Kallas / Chemical Engine

o an earlier study [10], complete mixing on the liquid side can bessumed at the applied gas superficial velocities.

The model consists of a system of partial differential equations(3)–(5)), including terms for mass transfer and reaction. The massalance in the liquid phase can be presented as

1 − εG)∂[i]L

∂t= Ni − (1 − εG)ri, z < hw (3)

here [i] represents the concentration of each component i and Nis the absorption rate. For organics and the nitrate ion Ni = 0.

For ozone in the gas phase:

G∂[O3]G

∂t= −UG

∂[O3]G

∂z− NO3 + εGEG

∂2[O3]G

∂z2, z < hw (4)

nd for ozone in the gas phase above the liquid surface (head space):

∂[O3]G

∂t= −UG

∂[O3]G

∂z+ EGT

∂2[O3]G

∂z2, hw < z < hc (5)

The gas above the liquid surface was assumed to have mixedank conditions (EGT = 1.0 × 106 m2/s).

The following initial and boundary conditions apply:

= 0, 0 ≤ z ≤ hc, [O3]L = 0, [O3]G = 0 (6)

> 0,∂[O3]G

∂z

∣∣∣∣Z=0

= −U([O3]G,inlet − [O3]calc)

EG(7)

t > 0,∂[O3]G

∂z

∣∣∣∣Z=hc

= 0

t > 0,∂[i]L

∂z

∣∣∣∣Z=0

= ∂[i]L

∂z

∣∣∣∣Z=hw

= 0(8)

In Eq. (7) [O3]calc is the concentration in the first cell on theas side computed by the method of lines. To solve the systemf differential equations, the column was divided into 14 cells inhe axial direction on the gas side, so that there were 10 equationsEq. (4)) applying to the gas phase below the liquid surface level,ne equation (Eq. (3)) for each component i applying to the liquidhase, and four equations (Eq. (5)) describing the gas flow dynam-

cs in the upper part of the column. The total number of differentialquations, the sum of the number of Eqs. (3)–(5), was 19.

The reaction was assumed to take place dominantly in the liquidulk. NO3 was obtained from the equation:

O3 = kLa

n∑i

([O3]∗i − [O3]) (9)

here n = 10 is the number of cells on the gas side.The saturation concentration of ozone in the water was deter-

ined by Henry’s equation.

O3]∗i =PO3,i

H(10)

The gas hold-up was calculated from the experiments by mea-uring the height of the liquid level in the column, with and withoutassing gas.

G = hT − h0

hT(11)

. p-Nitrophenol reactions with ozone

.1. Reaction scheme

A reaction scheme for p-nitrophenol ozonation has been pre-ented by Yu and Yu [11]. There are two main reaction pathwaysrom p-nitrophenol in their scheme. One pathway is via the inter-

ediates 4-nitrocathecol and catechol to volatile acids. The other

Fig. 1. The ozone reaction scheme used in the model.

pathway is via hydroquinone and p-quinone. A simplification oftheir scheme adopted in this study is presented in Fig. 1. CODres

represents the residual COD of the intermediate species, whichis the measured total COD from which the theoretical COD of p-nitrophenol and hydroquinone have been subtracted.

4.2. Reaction model

The reactions of ozone with nitrophenol and the intermediatescan be assumed to follow overall second-order reaction kinetics,and first order for ozone and organic solutes [6,12]. Phenols areknown to react slowly with ozone at low pH, Hoigné and Bader [6]report a value of about 100 (dm3 s)/mol at pH 2 for the second-orderp-nitrophenol-ozone reaction.

For the reaction scheme in Fig. 1, the following reaction equa-tions can be written, taking into consideration the stoichiometriccoefficients for ozone to retain mass balance. In the followingequations the abbreviation NP represents p-nitrophenol and HQrepresents hydroquinone.

The ozone reactions with p-nitrophenol and hydroquinone canbe written as

NP + �iO3 → A (12)

HQ + �jO3 → A (13)

where A represents the known and the unknown intermediateswith a degree of oxidation determined by the stoichiometric coef-ficients � i and � j. Reactions (12) and (13) can also be expressedas COD using the theoretical oxygen consumptions for NP and HQcalculated from their molecular structure and the residual COD cal-culated on the principle explained above. With this approach, thecomplete reaction model can be presented when taking the massbalances into account as

NP + 23 O3

k1−→HQ + NO3− (14)

�NPNP + �1O3k2−→CODres (15)

�HQHQ + �2O3k3−→CODres (16)

32 CODres + O3

k5−→CO2 + H2O (17)

CODres + 23 O3

k6−→2NO3− (18)

Ozone may also self-decompose in some conditions accordingto the equation

O3k4−→ 3

2 O2 (19)

The self-decomposition of ozone usually has an important roleonly in basic conditions [12,13]. However, it seems that in somecases it is necessary to include an ozone self-decomposition terminto the reaction model to satisfy the measured ozone and oxy-gen demand mass balances. This self-decomposition of ozone can

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M. Kuosa, J. Kallas / Chemical Enginee

e explained as being caused by complex radical chain reactions,hich eventually lead to the escape of oxygen from the reaction

ystem.The nitrate ion was assumed to be produced dominantly from

eactions (1) and (6) (Eqs. (14) and (18)). In Eq. (18), the coefficients/3 and 2 come from the presumption that the major part of nitro-en is in the nitrite group or in the nitrite ion. This means that itakes 1/3 moles of O3 to oxidise 1 mol of nitrite to nitrate. Due to theact that the analyzed nitrite ion concentrations were found to beery low, near the detection limit, the nitrite ion could be neglectedrom the end products included in the CODres. � i is the stoichio-

etric coefficient for ozone. In the reaction rate equations, thetoichiometric coefficients �NP and �HQ are the theoretical oxygenemands for p-nitrophenol and hydroquinone. With this proce-ure, Eqs. (15) and (16) can be written as reaction equations forhe COD and ozone. The CODres produced in Eqs. (15) and (16) cane written as (�NP − �1 (3/2))NP and (�HQ − �2 (3/2))HQ and can be

ound in Eq. (23). � i(3/2) represents the theoretical COD reductiony � i mol of O3. Here NP and HQ are the moles of p-nitrophenolnd hydroquinone. Eq. (19) represents an additional ozone self-ecomposition reaction term calculated from the concentrations of-nitrophenol and ozone (rate coefficient k4) to achieve the mea-ured ozone consumption. The reaction rate (Eqs. (20)–(24)) can beritten in the following mode:

i = − d[i]dt

=∑

i /= O3

ki�i[O3][i] (20)

here � i represents the stoichiometric or theoretical coefficient.

NP = − d[NP]dt

= k1[O3][NP] + k2[O3][NP] (21)

HQ = − d[HQ]dt

= −k1[O3][NP] + k3[O3][HQ] (22)

CODres = − d[CODres]dt

= −k2

(�NP − �1

32

)[O3][NP] − k3

(�HQ − �2

32

)[O3][HQ]

+ k532

[O3][CODres] + k6[O3][CODres] (23)

NO3 = − d[NO3]dt

= −k1[O3][NP] − k52[O3][CODres] (24)

O3 = − d[O3]dt

= k123

[O3][NP] + k2�1[O3][NP] + k3�2[O3][HQ] + k4[O3][NP]

+ k5[O3][CODres] + k623

[O3][CODres] (25)

The parameters �NP = 7.25 mol O2/mol NP andHQ = 6.5 mol O2/mol HQ represent the theoretical COD of p-itrophenol and hydroquinone, respectively. The coefficient 3/2

n Eq. (23) is the theoretical number of moles of COD depletedy 1 mol of O3. k4 represents the reaction rate coefficient for thenknown reactions consuming ozone. These reactions are the onesetween ozone and the species that cannot be presented in termsf COD. The reaction rate coefficients from k1 to k3 and k5 and

6 are the coefficients of Eqs. (14)–(18) of direct reaction and theadical reaction chain of the ozone and solute. The radical-typehain reaction was first introduced by Hoigné, Staehelin and Buhler14–16]. The reaction between ozone and the OH− ion [12,13,16]lays a minor role in acidic solutions.

nd Processing 48 (2009) 1212–1221 1215

The lack of hydroquinone concentration data for runswith t-butanol concentrations of 2.25 × 10−3 mol/dm3 and2.25 × 10−4 mol prevented the use of the reaction model ofEqs. (14)–(18). The decomposition reactions in p-nitrophenolozonation can be also written as

NP + �3O3k8−→CODres (26)

32 CODres + O3

k9−→products (27)

The CODres produced in Eq. (26) can be written as (�NP − �3(3/2))NP. For reactions (26) and (27), the reaction rate (Eqs.(28)–(30)) can be written in the mode of Eq. (20) as

rNP = − d[NP]dt

= k8[O3][NP] (28)

rCODres = − d[CODres]dt

= −k8

(�NP − �3

32

)[O3][NP] + k9

32

[O3][CODres] (29)

rO3 = − d[O3]dt

= k8�3[O3][NP] + k9[O3][CODres] (30)

5. Parameter estimation

The reaction rate coefficients ki of the reactions between ozoneand p-nitrophenol and between ozone and the intermediates, thestoichiometric coefficients � i, and the volumetric mass transfercoefficient kLa were obtained by parameter estimation with Modest6.0 parameter estimation software [17]. In the parameter estima-tion, the partial differential equations (Eqs. (3)–(5)) were solvednumerically and integrated by the method of lines presented bySchiesser and Silebi [18]. In the parameter estimation, the objec-tive function was the weighted sum of the squares of the residualsbetween the model and the data:

l(ˇ) = ||y − yp||2 =n∑

i=1

(yi − yip)2wi (31)

where yi represents the measured concentration of ozone in thegas phase at the outlet of the column, the dissolved ozone, p-nitrophenol, hydroquinone, NO3

− and COD concentrations.The yip for the total COD was computed according to the follow-

ing equation:

yCODp = [CODres] + �NP[NP] + �HQ[HQ] (32a)

or using Eq. (32b) if hydroquinone is not included separately in themodel:

yCODp = [CODres] + �NP[NP] (32b)

In the case of the runs with a t-butanol concentration of2.25 × 10−2 mol/dm3, the rate coefficients and stoichiometric coef-ficients of the model of Eqs. (14)–(18) and those of the model ofEqs. (26) and (27) were estimated. In the case of the runs with at-butanol concentration of 2.25 × 10−2 mol/dm3 using the model ofEqs. (14)–(18) and t-butanol concentration 0 mol/dm3 using modelof Eqs. (26) and (27) the kLa was estimated simultaneously withother estimated model parameters. Due to the complexity of thereaction system, the solution easily ran into numerical instabili-ties when the data from the runs with t-butanol and the model

of Eqs. (26) and (27) were used, making it difficult to estimate allthe estimable parameters simultaneously. The parameter estima-tion was, therefore, carried out in two separate stages. In the firststage, the kLa for each run was estimated using dissolved and gasoutlet ozone concentrations as object variables, while the ozone

1216 M. Kuosa, J. Kallas / Chemical Engineering and Processing 48 (2009) 1212–1221

ol concentration is 2.25 × 10−3 mol/dm3. Superficial velocity of the gas is 0.023 m/s.

dt

r

kssgtkoolmlTdsawa

r

vstdHcm

TE

P

kkkkkk��k

Fig. 2. MCMC analysis for kLa and k′ . Left: without t-butanol. Right: the t-butan

ecomposition was computed using the first-order kinetics equa-ion

O3 = k′[O3] (33)

′ is the pseudo first-order reaction rate coefficient estimatedimultaneously with kLa. MCMC analysis of kLa and k′ is pre-ented in Fig. 2. It can be interpreted that any high enough k′ valueives an approximately an equal kLa. This results from the rela-ively low dissolved ozone concentration. With this method, theLa was also estimated for the run with a t-butanol concentrationf 2.25 × 10−4 mol/dm3. In Fig. 3 it can be seen that in the modelf reaction Eq. (33) estimated ozone concentrations do not fol-

ow the measured values accurately, although they are of the sameagnitude. This suggests that ozone decomposition does not fol-

ow first-order kinetics in p-nitrophenol ozonation with t-butanol.he estimated values in the range 0.25–0.54 with relative stan-ard errors 42.3–54.8% were obtained for k′. Approximately theame values for kLa were obtained using the ozone concentrations experimental variables both at the inlet and outlet of the column,ith only dissolved ozone concentration as the observed variable

nd computing the decomposition rate of ozone with equation

O3 = G([O3]G,inlet − [O3]G,outlet)(1 − εG)Vw

(34)

With this reaction model, the coefficient of determination (R2

alue) was low due to the high relative deviation from the mea-ured values of the dissolved ozone concentrations, but because

he measured concentrations were low, the absolute values of theeviations also remained low. The pseudo-Henry’s law coefficient(7.98 × 106 Pa dm3/mol) was estimated from the measured ozone

oncentrations in the gas and in the liquid phase [8] by the Beltránethod [7].

able 2stimated values of the parameters for the model of reaction Eqs. (14)–(19).

arameter, dimension Estimated value without t-butanol Estimated STD (relative

1 (dm3/mol s) 97.2 23.7 (24.3%)2 (dm3/mol s) 104 21.4 (23.9%)3 (dm3/mol s) 286 74.4 (26.0%)4 (dm3/mol s) 9.17 × 10−3 63.3 (875 × 103%)5 (dm3/mol s) 8.32 0.44 (5.4%)6 (dm3/mol s) 0.76 × 10−7 6.35 × 10−3 (83.1 × 101 3.39 0.27 (8.1%)2 1.26 × 10−3 0.33 (261 × 103%)La (1/s) 0.027 0.11 × 10−2 (4.0%)

Fig. 3. Estimated and measured ozone concentrations using the first-order reactionmodel. Estimated: — gas outlet; - - - dissolved. Measured: + gas outlet; © dissolved.

Using the reaction model of Eqs. (14)–(18), the optimization rou-tine fits the LSQ (least squares) objective function with a 99.5%

coefficient of determination (R2 value) for the case of the runs witha t-butanol concentration of 2.25 × 10−2 mol/dm3. The estimatedrate coefficients and stoichiometric coefficients and their standarderrors are presented in Table 2 for the case of a t-butanol concen-

) Estimated value, 2.25 × 10−2 mol/dm3 t-butanol Estimated STD (relative)

10.1 1.80 (17.8%)29.8 4.71 (15.8%)

111.1 26.3 (23.7%)0 (assumed) Not estimated0.42 0.14 (33.2%)

4%) 6.57 × 10−3 1.07 × 10−3 (16.3%)4.77 0.51 (10.6%)0.22 × 10−5 1.1 × 10−2 (51 × 104%)0.052 0.40 × 10−2 (7.7%)

ring and Processing 48 (2009) 1212–1221 1217

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17(5

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)2.

690.

10(3

.9%

)3.

570.

18(5

.0%

)4.

48

0.23

(5.2

%)

M. Kuosa, J. Kallas / Chemical Enginee

ration 2.25 × 10−2 mol/dm3, and compared with the parametersbtained from the case without t-butanol (see Kuosa et al. (acceptedor publication) for details of the experimental conditions in p-itrophenol–water runs). In Table 3 the rate coefficients obtainedith the model of Eqs. (26) and (27) and a t-butanol concentration

f 0, 2.25 × 10−3 and 2.25 × 10−2 mol/dm2 are presented with stan-ard errors. Using the reaction model of Eq. (33) in the estimationf kLa only from the gas outlet and the dissolved ozone data, the2 varied from 79% to 95%, depending on the run. In Table 4, theLa estimated using the reaction models of Eqs. (33) and (34) areresented for runs with and without t-butanol. All runs used forarameter estimation were performed at a gas superficial velocityf 0.023 m/s.

When comparing the kLa values of Tables 2–4 and consideringig. 2, it can be deduced that kLa is increased when t-butanol isissolved in the reaction solution. Furthermore, in Table 4, taking

nto consideration the standard errors, it seems that in practicehere is no difference in kLa between the t-butanol concentra-ions of 2.25 × 10−4 and 2.25 × 10−2 mol/dm3. This suggests thexistence of a limit value for kLa, a finding which is consistentith the results of López-López et al. [6], their limit value being

.0 × 10−3 mol/dm3 for pure water at pH 5. The kLa values in thearameter estimations in Table 3 in the cases of a t-butanol con-entration of 2.25 × 10−3 and 2.25 × 10−2 mol/dm3 were taken fromables 2 and 4, and when possible, by avoiding choosing the high-st or lowest value obtained with each t-butanol concentration.he sum of the decomposition rate coefficients of p-nitrophenol1 and k2 from Table 2 is 201.2 dm3/mol for the solution with-ut t-butanol and 39.9 dm3/mol for the solution with a t-butanoloncentration of 2.25 × 10−2 dm3/mol. The p-nitrophenol decom-osition coefficients are presented also in Table 3. Taking intoonsideration standard errors, they differ little. However, the lowerhe obtained p-nitrophenol decomposition rate, the higher the radi-al scavenger concentration. The average is 90.6 (dm3 s)/mol, whichs near the value 100 (dm3 s)/mol reported by Hoigné and Bader6] at pH 2.0. The difference of the decomposition rate coefficientsbtained with different reaction models comes from the model esti-ated concentration of dissolved ozone on the basis of the data

vailable.The interpretation of the stoichiometric coefficient� i (i = 1, 2

r 3) which expresses the amount by which COD is reducedn the reaction chain, is not unambiguous, due to the effect ofolymerization and the effect of components that cannot be pre-ented as COD, for example. In Table 3, the �3 value of 2.69ppears reasonable when compared to the �1 value of 3.39 and2 being equal to about zero, when taking into consideration the

elative values of k1 and k2 in Table 2. The higher values 3.57nd 4.48 for �3 can be explained by a more total absence ofadicals, which probably favors the reaction path p-nitrophenol-itrocathecol instead of the path p-nitrophenol-hydroquinone. Theame phenomenon is suggested by the relative values of k1 and k2,ee Table 2. The relation k1/k2 has a value 2.1 with p-nitrophenolzonation with initial pH 5 [8]. The standard error for k9 is rel-tively low in the case without t-butanol. The lower values for9 can be explained by the low reaction rate of t-butanol withzone.

. Experimental results and discussion

.1. Hold-up

The gas hold-up calculated by Eq. (11) is presented in Fig. 4.egardless of the scattering at the higher superficial velocities itan be determined that the hold-up rises as a function of superficialelocity and also as a function of t-butanol concentration. Ta

ble

3Es

tim

ated

valu

eso

t-B

uta

nol

con

cen

tr

Para

met

er,d

imen

s

k 8(d

m3/m

ols)

k 9(d

m3/m

ols)

�3

1218 M. Kuosa, J. Kallas / Chemical Engineering and Processing 48 (2009) 1212–1221

Table 4Estimated kLa with t-butanol and without t-butanol.

Reaction model equation and t-butanol concentration kLa (1/s) Standard error Relative standard error (%) R2 value (%)

34 (0 mol/dm3) 0.031 3.22 × 10−3 10.5 Low33 (0 mol/dm3) 0.031 1.17 × 10−3 3.8 88.934 (2.25 × 10−4 mol/dm3) 0.046 3.24 × 10−3 7.1 Low33, (2.25 × 10−4 mol/dm3) 0.043 5.48 × 10−3 7.9 79.434 (2.25 × 10−3 mol/dm3) 0.039 4.0 × 10−3 9.5 Low33 (2.25 × 10−3 mol/dm3) 0.035 3.1 × 10−3 8.9 86.034 (2.25 × 10−2 mol/dm3) 0.034 2.2 × 10−3 6.5 Low33 (2.25 × 10−2 mol/dm3) 0.040 1.9 × 10−3 4.9 94.8

Table 5Correlation matrix in the case ozonation with 2.25 × 10−2 mol/dm3 t-butanol.

k1 k2 k3 k5 k6 kLa �1 �2

k1 1.00k2 0.78 1.00k3 0.90 0.55 1.00k5 0.57 0.76 0.38 1.00k6 0.70 0.99 0.44 0.76kLa −0.67 −0.86 −0.58 −0.63�1 0.107 −0.02 0.22 −0.05�2 −0.10 −0.43 0.06 −0.83

6

o

are presented.

Fdw

Fig. 4. Gas hold-up with different t-butanol concentrations.

.2. Comparison of the measured and estimated concentrations

The estimated and measured concentrations of the dissolvedzone and at the gas outlet are presented in Fig. 5. It can be seen that

ig. 5. Ozone concentrations of three separate runs. Left: two runs using the model of reaissolved (—), gas outlet (-·-). Run 6: dissolved (––), gas outlet (�), gas outlet. Right: run 2 uith t-butanol concentration of 2.25 × 10−2 mol/dm3, dissolved (- - -), gas outlet (�).

1.00−0.83 1.00−0.07 −0.002 1.00−0.48 0.45 0.09 1.00

the model of reaction Eqs. (26) and (27) estimates the ozone con-centrations rather well. However, there is some deviation betweenthe measured and estimated values in the beginning of each run.On the right-hand side of Fig. 5 it can be seen that the model ofEqs. (26) and (27) estimates somewhat better the dissolved ozonethan the more complicated reaction model of Eqs. (14)–(19). Thedifference may be explained by the accuracy of the model in esti-mating the dissolved ozone concentrations on the basis of availabledata. Both multicomponent reaction models, the model of reactionEqs. (26) and (27), and that of reaction Eqs. (14)–(19) estimate quiteaccurately the p-nitrophenol concentration. On the left-hand sideof Fig. 6, the measured and estimated values of p-nitrophenol con-centrations are presented for the case of a t-butanol concentrationof 2.25 × 10−3 mol/dm3. On the right side of Fig. 6, the measured andestimated p-nitrophenol, hydroquinone and NO3

− concentrations

The measured and estimated COD are presented in Fig. 7.Although the measured concentration values are quite scatteredin some cases in Figs. 6 and 7, it can be determined that on averagethe model estimates these values quite acceptably.

ction Eqs. (26) and (27) with t-butanol concentration 2.25 × 10−3 mol/dm3. Run 5:sing the models of reaction Eqs. (14)–(19), dissolved (—), gas outlet (-·-), and 26–27

M. Kuosa, J. Kallas / Chemical Engineering and Processing 48 (2009) 1212–1221 1219

Fig. 6. Left: the measured (run 5, ©+; run 6, +) and estimated (run 5, �; run 6, —) p-nitrophenol concentrations using the model of reaction Eqs. (26) and (27) with t-butanolc timated (run 1, —; run 2, -·-) p-nitrophenol, measured (run 1, *; run 2, ♦) and estimated( (run 1, —; run 2, · · ·) NO3

− concentrations using the model of reaction Eqs. (14)–(19) witht

7

dmp(fpe0boT

adeaws

Table 6Correlation matrix in the case ozonation without t-butanol.

k8 k9 kLa �3

k8 1.00

Fm

oncentration 2.25 × 10−3 mol/dm3. Right: the measured (run 1, �; run 2, ×) and esrun 2, —; run 1, �) hydroquinone and measured (run 1, �; run 2, ©) and estimated-butanol concentration of 2.25 × 10−2 mol/dm3.

. Identification of the parameters and MCMC analysis

In parameter estimation it is important that the parametersepend on each other as little as possible. There are differentethods to obtain information about the interdependence of the

arameters: using a correlation matrix, the object function methodsee Ref. [19]) and MCMC (Markov chain Monte Carlo) analysis,or example. In general, the standard errors of kLa obtained inarameter estimation in this study were relatively small. When-ver all the off-diagonal elements in the correlation matrix exceed.9 in magnitude, the estimates are highly correlated and tend toe inaccurate [20]. The correlation matrices showed acceptabler low interdependence between kLa and other parameters (seeables 5 and 6).

The question of the identifiability of the parameters (how goodnd unique the estimate is) and the accuracy of the model pre-

ictions can be answered with MCMC methods. In MCMC, thestimation problem is handled in a Bayesian way: the parametersre treated as random variables that have a statistical distributionith many possible values. Instead of a single fit, MCMC analy-

is determines ‘all’ parameter values (i.e. a representative sample

ig. 7. Left: the measured (*, ©) and estimated (—, - - -) COD using the model of reactioeasured (*, ©) and estimated (—, - - -) COD using the model of reaction Eqs. (14)–(19) w

k9 0.33 1.00kLa −0.93 −0.53 1.00�3 −0.92 −0.09 0.78 1.00

of their distribution) that give a good fit to the data. The size ofthe measurement error can be estimated with classical statisticsusing the residuals, or it may be sampled. For more details, see Refs.[21–23]. MCMC-analysis of the two used models are presented inFigs. 8 and 9. It can be deduced from the shapes of these param-eter pair plots that kLa is well identified. Also the rate coefficientsof the model of reaction Eqs. (26) and (27) seem to be well iden-tified (Fig. 9). In the case of the reaction model of Eqs. (14)–(18)

there is some uncertainty in the rate coefficients, for example theparameter pair plot (k2, k6) where the interdependence can be seenclearly. However, even in these cases the optimum can be found(Fig. 8).

n Eqs. (26) and (27) with t-butanol concentration 2.25 × 10−3 mol/dm3. Right: theith t-butanol concentration of 2.25 × 10−2 mol/dm3.

1220 M. Kuosa, J. Kallas / Chemical Engineering and Processing 48 (2009) 1212–1221

Fig. 8. MCMC analysis for the estimated parameters in the case with 2.25 × 10−2 mol/dm3 t-butanol.

Fig. 9. MCMC analysis for the estimated parameters in the case ozonation without t-butanol.

ring a

8

mftmkthlarTip

A

a

[EE

EGH[hh

[kkkklnN[[[[

[

[[PRtUVwyy

[

[

[

M. Kuosa, J. Kallas / Chemical Enginee

. Conclusions

In this study, kLa and reaction kinetic coefficients were esti-ated with nonlinear parameter estimation. The data was obtained

rom p-nitrophenol ozonation runs at pH 2.0 with and without-butanol. kLa was estimated using four different reaction kinetic

odels to exclude the possible effect of the model on the obtainedLa when using the data from runs with different t-butanol solu-ions. It could be determined that adding t-butanol increased theold-up and kLa. These results support the findings presented in the

iterature. The decomposition rate of p-nitrophenol in ozonation isffected only slightly by t-butanol at pH 2.0 but the presence of thisadical scavenger seems to affect the production of residual COD.he correlation matrices and MCMC analysis were useful in assess-

ng the observation reliability and identifiability of the estimatedarameters.

ppendix A. Nomenclature

specific interfacial area in the unit volume of phase mix-ture (m2/m3)

CODres] concentration of residual COD (mol/dm3)G coefficient of axial dispersion in the gas phase (m2/s)GT coefficient of axial dispersion in the gas phase in single

phase flow (m2/s)L coefficient of axial dispersion in the liquid phase (m2/s)

volumetric gas flow (dm3/s)pseudo-Henry’s law constant ((Pa dm3)/mol)

HQ] concentration of hydroquinone (mol/dm3)T total height of the liquid surface with the passing gas (m)0 total height of the liquid surface without the passing gas

(m)i] concentration of component i (mol/dm3)L individual liquid side mass transfer coefficient (m/s)La volumetric mass transfer coefficient (1/s)1 − k6 reaction rate coefficient (mol/(dm3 s))′ pseudo first-order reaction rate coefficient (1/s)

objective functionnumber of observations

O3 ozone absorption rate (mol/(dm3 s))NO3

−] concentration of nitrate ion (mol/dm3)NP] concentration of p-nitrophenol (mol/dm3)O3]G ozone concentration in the gas phase (mol/dm3)O3]G,inlet ozone concentration of the gas at the inlet of the column

(mol/m3)O3]GO ozone concentration of the gas at the outlet of the column

(mol/m3)O3]L ozone concentration in the liquid phase (mol/dm3)O3]* saturation concentration of ozone in liquid (mol/m3)O3 ozone partial pressure (Pa)2 coefficient of determination

time (s)

G superficial velocity of the gas (m/s)w volume of reactor below water surface level (dm3)i weight for observed value

observationi observation

[

[

nd Processing 48 (2009) 1212–1221 1221

yp observed variable predicted by the modely average value of all yiz coordinate in direction of column height (m)ˇ estimated parameter�1, �2, �3 stoichiometric coefficients�HQ theoretical COD of hydroquinone (mol O2/mol)�NP theoretical COD of p-nitrophenol (mol O2/mol)εG gas hold-up� standard deviation of the pure experimental error

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