Ind. Eng. Chem. Res. 2007, 46, 6235-6243
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Estimation of Multicomponent Reaction Kinetics of p-Nitrophenol Ozonation in a Bubble Column Markku Kuosa,* Arto Laari, Antti Solonen, Heikki Haario, and Juha Kallas Lappeenranta UniVersity of Technology, Department of Chemical Technology, P. O. Box 20, FI-53851 Lappeenranta, Finland
In this work, the reaction kinetics of p-nitrophenol ozonation in a bubble column at low pH of water was studied. The reaction kinetic parameters, rate coefficients, and stoichiometric coefficients were estimated by using nonlinear optimization. The reaction rate equations were written by applying a part of the reaction scheme of Yu and Yu (Ozone Sci. Eng. 2001, 23, 303-312). The concentration of the unknown intermediate compounds is presented as a residual COD (chemical oxygen demand) calculated from the measured COD and the theoretical COD for the known species. The decomposition rate of p-nitrophenol on the pathway producing hydroquinone was found to be about two times faster than the decomposition rate on the pathway producing 4-nitrocatechol. The ozone self-decomposition by hydroperoxide ions seems to be the plausible cause for the relatively high ozone consumption at low pH. The identifiability and reliability of the estimated parameters were analyzed with the Markov chain Monte Carlo (MCMC) method. MCMC methods are Bayesian statistical methods that can be used for analyzing the distribution of parameters in nonlinear models in order to extend and support the information given by traditional regression analysis. Introduction The chemistry of ozonation in a water solution is rather complex. The reactions of ozonation involve direct molecular reactions of O3 with dissolved compounds and transformation of O3 into secondary oxidants such as hydroxyl radicals (OH•), hydroperoxyl radicals (HO2•), and further species such as •O3-, HO3•, etc. Modeling of all these reactions requires large amounts of kinetic data, which is not necessarily available or applicable due to the different natures of waters. In this study, a method has been developed to estimate the reaction rate and stoichiometric coefficients of a multicomponent reaction model in ozonation, taking also gas-liquid mass transfer and reactor hydrodynamics into consideration. Another important objective of the work was to study parameter reliability to avoid poorly identified parameters or overparametrization. Nitrophenol, and phenols in general, have been the subject of relatively numerous studies of ozonation in recent decades. This results from their toxicity and the supposed or proved carcinogenic effects on living organisms. The intermediates of the ozone-phenol reaction are quite well-known, but the reaction schemes and particularly the reaction rate coefficients in the reaction schemes are poorly known. Phenols are known to react slowly with ozone at low pH. Hoigne´ and Bader1 reported a value of ∼100 dm3/ (mol s) at pH 2 for the second-order p-nitrophenol-ozone reaction. They extrapolated the reaction rate coefficient to be 14 × 106 dm3/(mol s) at pH 8. Shi et al.2 have studied the effect of mass transfer and pH on p-nitrophenol removal. Beltran et al.3 have studied the degradation kinetics and mass transfer at different kinetic regimes of p-nitrophenol ozonation. Masschelein and Goossens4 studied the influence of the O3-gas transfer rate on the reaction in the kinetics in ozonation of nitrophenols. Guiza et al.5 studied the degradation of pnitrophenol with O3 and with O3 combined with Fe(III). Adams et al.6 and Hsu et al.7 studied the effect of preozonation of the p-nitrophenol solution at pH 7 on biodegradability. Oturan * To whom correspondence should be addressed. E-mail:
[email protected].
et al.8 determined the rate constants for hydroxylation reactions of p-nitrophenol and its hydroxylated derivates by OH• radicals. There are plenty of publications on the enhancement of p-nitrophenol ozonation by the use of photocatalysis, Fe(III) with UV radiation, activated carbon, ultrasound, high voltage pulsed corona discharge, etc. Materials and Methods Experimental Setup and Analytics. Bubble column reactors are often used to carry out gas-liquid or gas-liquid-solid reactions because of their efficiency and simplicity. Therefore, a bubble column is also very suitable for ozonation studies. In the current work, experiments were performed in a bubble column with a total height of 2.05 m and an inner diameter of 0.11 m. The height of the liquid surface in the column was 1.3 ( 0.1 m. The upper part of the column formed a gas head space with a height of 0.75 ( 0.1 m. The bubble column was operated as a semibatch reactor. The gas was fed into the column from the bottom through a porous polypropylene plate with a pore diameter of 300-400 µm. The superficial velocity of the gas was 0.0164 m/s at 101.325 kPa. The input gas ozone concentration was adjusted to be in the range of 5.13 × 10-5 to 1.46 × 10-4 mol/dm.3 The gas-phase ozone concentration was measured spectrophotometrically at the inlet and at the outlet of the column. The dissolved ozone concentration in the water was measured at one point in the reactor by using an Orbisphere 3660 dissolved ozone analyzer. For this, some water was drawn through the column wall at a height of 0.4 m from the column bottom and pumped through a flow chamber with a flow rate of about 350-400 cm3/min. The measured liquid ozone concentrations ranged from 0 to 1.07 × 10-5 mol/dm.3 The liquid samples to be analyzed for the reaction intermediates were taken at 0.8 m from the bottom of the column over the course of time. A solution made by dissolving p-nitrophenol into deionized water with a conductivity of 1-5 µS/cm was used as the liquid phase in the experiments. The temperature of the column was maintained at 20 ( 0.1 °C. The concentrations of p-nitrophenol and various reaction intermediates were analyzed by using the high-performance
10.1021/ie070423a CCC: $37.00 © 2007 American Chemical Society Published on Web 08/21/2007
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liquid chromatography (HPLC) instrument Hewlett-Packard model 1100 with the column YMC-Pack Pro C18 (150 mm × 4.6 mm). The p-nitrophenol concentrations were in the range 6.5 × 10-4 to 1.1 × 10-3 mol/dm3 at the beginning of the ozonation run. Liquid samples were analyzed also for the pH, chemical oxygen demand (COD), and total organic carbon (TOC). Nitrate and nitrite were also analyzed quantitatively with the ion chromatography instrument Dionex DX-120 using the IonPac AS14 anion-exchange column. The experimental data were collected from eight different experimental runs. The ozone concentration was measured from all runs both in gas and as dissolved ozone in water. The concentrations of p-nitrophenol and hydroquinone were measured from five different runs (runs 1, 4-6, and 8). The COD was analyzed from two runs (runs 3 and 7), and the nitrate was analyzed from two runs (runs 2 and 7). Model Equations for Mass Transfer and Hydrodynamics. In the simulation of the bubble column, the reactor hydrodynamics model is in a key role. For bubble columns, the hydrodynamics can be presented by using the complete mixing model, the axial-dispersion model, the cell model with back flow, and the CFD (computational fluid dynamics) models. Because of the hydrodynamic conditions in this study, the axialdispersion model (ADM) was used for the gas phase to estimate and validate the reaction kinetics. From the physical point of view, the ADM is a fully empirical model giving the unknown mixing properties of the system as an axial-dispersion coefficient. Nevertheless, the dispersion model can predict gas- and liquid-phase residence time distributions with accuracy sufficient for most technical cases (Schlu¨ter et al.).9 However, because the gas flow was relatively small, the case was practically plug flow on the gas side. According to an earlier study (Kuosa et al.),10 complete mixing on the liquid side could be assumed at the applied gas superficial velocity of 0.0160 m/s. The model consists of a system of partial differential equations (eqs 1-3) including terms for mass transfer and reaction. Mass balance in the liquid phase can be presented as
(1 - G)
∂[i]L ) Ni - (1 - G)ri z < 1.3 m ∂t
and for ozone in the gas phase above the liquid surface:
∂[O3]G ∂2[O3]G ∂[O3]G ) -UG + EGT 1.3 < z < 2.05 m ∂t ∂z ∂z2 (3) The gas above the liquid surface was estimated to have mixed tank conditions (EGT ≈ 1.0 × 106). The following initial and boundary conditions apply:
([O3]Ginlet - [O3]calc) ∂[O3]G | ) -U ∂z Z)0 EG
∂[i]L ∂[i]L |Z)0 ) | )0 ∂z ∂z Z)1.3m
(4) (5)
(6)
In eq 5, [O3]calc is the concentration computed by the method of lines in the first of the 14 cells on the gas side. To solve the system of differential equations, the column was divided into 14 cells in the axial direction on the gas side so that there were 10 equations, 2 that applied to the gas phase below the liquid surface level, 1 equation (eq 1) for each component i that applied to the liquid phase, and 4 equations (eq 3) that described the gas flow dynamics in the upper part of the column. The total number of equations, the sum of the number of differential eqs 1, 2, and 3, was 19. The reaction was supposed to take place dominantly in the liquid bulk. NO3 is obtained from the equation n
N O 3 ) k La
∑i ([O3]i* - [O3])
(7)
where n ) 10 is the number of cells on the gas side. The saturation concentration of ozone in water is determined by the Henry’s equation.
[O3]i* )
PO3,i H
(8)
Values for the volumetric mass transfer coefficient kLa ) 0.042 1/s and the pseudo-Henry’s law coefficient H ) 7.98 × 106 (Pa dm3)/mol were obtained from the measured ozone concentrations in the gas and liquid by the Beltran method.9 These values were used to determine the reaction kinetic parameters in parameter estimation. The obtained values are in good agreement with earlier estimates obtained by nonlinear optimization (Kuosa et al.11). The gas holdup was calculated from experiments by measuring the height of the liquid level in the column, with and without passing gas.
G )
∂[O3]G ∂[O3]G ∂2[O3]G ) -UG - NO3 + GEG G ∂t ∂z ∂z2 z < 1.3 m (2)
t > 0,
t > 0,
∂[O3]G )0 | ∂z Z)L
(1)
where i represents the concentration of each component i and Ni is the absorption flux. For organics and nitrate ion, Ni ) 0 For ozone in the gas phase,
t ) 0, 0 e z e L [O3]L ) 0, [O3]G ) 0
t > 0,
hT - h0 hT
(9)
p-Nitrophenol Reactions with Ozone Reaction Scheme. A reaction scheme for p-nitrophenol ozonation has been presented by Yu and Yu.12 In their scheme, there are two main reaction pathways from p-nitrophenol. One pathway is via the intermediates 4-nitrocathecol and catechol to volatile acids. The other pathway is via hydroquinone and p-quinone. A simplification of their scheme that has been taken into this study is presented in Figure 1. CODres represents the residual COD of the intermediate species, which is the measured total COD from which the theoretical COD of p-nitrophenol and hydroquinone have been subtracted. Reaction Model. The reactions of ozone with nitrophenol and the intermediates can be assumed to follow overall secondorder reaction kinetics, first order for ozone and organic solutes (Hoigne´ and Bader1,3 and Langlais et al.13). The ozone selfdecomposition has an important role usually only in basic conditions (Langlais et al.13 and Sotelo et al.14). However, it was found that, in the current case, it is necessary to include ozone self-decomposition into the reaction model to satisfy the measured ozone and oxygen demand mass balances. The observed self-decomposition can be explained to be caused by
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ozone self-decomposition reaction terms calculated from concentrations of p-nitrophenol and ozone (rate coefficient k4) and hydroquinone and ozone (rate coefficient k7) to achieve the measured ozone consumption. Reaction rate eqs 19-23 were written in the following mode:
ri ) -
d[i]
)
dt
∑ kiγi[O3][i]
(18)
i*O3
Figure 1. Ozone reaction scheme used in the model.
the complex radical chain reactions, which eventually lead to the escape of oxygen from the reaction system. For the reaction scheme of Figure 1, the following reaction equations can be written, taking into consideration the stoichiometric coefficients for ozone. In the following equations, the abbreviation NP represents p-nitrophenol and HQ represents hydroquinone The ozone reactions with p-nitrophenol and hydroquinone can be written basically as
NP + γiO3 f A
(10)
HQ + γjO3 f A
(11)
where A represents the known and the unknown intermediates with a degree of oxidation determined by the stoichiometric coefficients γi and γj. Reactions 10 and 11 can also be expressed as COD using the theoretical oxygen consumptions for NP and HQ calculated from their molecular structure and the residual COD calculated on the principle explained earlier. Using this approach, the complete reaction model can be presented as k
1 NP + 32 O3 98 HQ + NO3-
k2
γNPNP + γ1O3 98CODres k3
γHQHQ + γ2O3 98 CODres
(12) (13) (14)
k
3COD + O 958 CO + H O res 3 2 2 2
(15)
k
6 CODres + 32 O398 2NO3-
(16)
k ,k
4 7 O3 98 23O2
(17)
The nitrate ion was assumed to be produced dominantly from reactions 1 and 5 (eqs 12 and 16). In eq 16, the coefficients 2/3 and 2 come from the presumption that the major part of nitrogen is in the nitrite group or in the nitrite ion. This means that it takes 1/3 mol of O3 to oxidize 1 mol of nitrite to nitrate. Because of the fact that the analyzed nitrite ion concentrations were found to be very low near the detection limit, the nitrite ion could be neglected from the end products being included in the CODres. γi is the stoichiometric coefficient for ozone. In the reaction rate equations, the stoichiometric coefficients γNP and γHQ are the theoretical oxygen demands for p-nitrophenol and hydroquinone, respectively. With this procedure, eqs 13 and 14 can be written as reaction equations for the COD and ozone. The CODres produced in eqs 13 and 14 can be written as (γNP γ1(3/2))NP and (γHQ - γ2(3/2))HQ and can be found in eq 21. The γi(3/2) represents the theoretical COD reduction by γi mol of O3. Here, NP and HQ are the mol of p-nitrophenol and hydroquinone, respectively. Equation 17 represents additional
γi represents the stoichiometric or theoretical coefficient.
d[NP] ) k1[O3][NP] + k2[O3][NP] dt
(19)
d[HQ] ) -k1[O3][NP] + k3[O3][HQ] dt
(20)
rNP ) rHQ ) rCODres ) -
d[CODres] 3 ) -k2 γNP - γ1 [O3][NP] dt 2 3 k3 γHQ - γ2 [O3][HQ] + 2 3 k5 [O3][CODres] + k6[O3][CODres] (21) 2
(
(
rNO3 ) -
)
)
d[NO3] ) -k1[O3][NP] - k52[O3][CODres] dt
(22)
d[O3] 2 ) k1 [O3][NP] + dt 3 k2γ1[O3][NP] + k3γ2[O3][HQ] + k4[O3][NP] + 2 k5[O3][CODres] + k6 [O3][CODres] + k7[O3][HQ] (23) 3
r O3 ) -
The parameters γNP ) 7.25 (mol of O2)/(mol of NP) and γHQ ) 6.5 (mol of O2)/(mol of HQ) represent the theoretical COD of p-nitrophenol and hydroquinone, respectively. The coefficient 3/2 in eq 21 is the theoretical amount of mol of COD depleted by 1 mol of O3. k4 and k7 represent the reaction rate coefficients for the unknown reactions consuming ozone. Those reactions are the ones between ozone and the species that cannot be presented in terms of COD. The reaction rate coefficients from k1 to k3 and k5 as well as k6 are the coefficients of eqs 12-16 of direct reaction and the radical reaction chain of the ozone and solute. The radical-type chain reaction was first introduced by Hoigne´ and co-workers.15-17 The reaction between ozone and the OH- ion13,14,18 has a minor role in acidic solutions. Experimental Results and Discussion During the first 5000-7000 s of the experiment, the dissolved ozone concentration was zero, and after that, it started to increase rapidly (Figure 2). Typically the pH changed from 5.5 to 2.5 during the experiments in 2.6-2.8 h. In Figure 2, the measured ozone concentrations in gas at the inlet and at the outlet of the column and the dissolved ozone concentration are presented. The ozone concentration in gas at the column inlet varies during the experiments depending on the conditions in the ozone generator. However, the variation in the ozone concentration is taken into consideration in the model and does not cause any error in the simulations. Beltra´n et al.3 obtained a stoichiometric ratio of ∼3 for the amount of ozone consumed per mol of p-nitrophenol at pH 6.5. In this study, the ratio of the mol of consumed ozone per mol
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Figure 2. Estimated and measured ozone concentrations. Gas inlet: run 5 -0-, run 6 -O-, run 8 -]-; gas outlet: estimated, run 5 - -, run 6 s, run 8 •••; measured, run 5 0, run 6 O, run 8 ]; dissolved: estimated, run 5 ---, run 6 - -; measured, run 5 /, run 6 +.
Figure 3. Estimated and measured p-nitrophenol and COD concentrations. p-Nitrophenol: estimated, run 1 - -, run 4 s, run 6 - -, run 3 ---; measured, run 1 O, run 4 /, run 6 0; COD: estimated, run 3 s, run 4 - -; measured, run 3 +; CODres: estimated, run 3 ---, run 4 - -.
of decomposed p-nitrophenol was found to be ∼4, calculated for the situation where all p-nitrophenol has been consumed. The reaction eqs 12-16, written for the reactions between ozone and the solutes, represent ozone decomposition reactions giving the reaction products so that the amount of consumed oxygen calculated from the ozone depletion is according to the stoichiometry needed to oxidize each reactant to products. In some particular reactions and circumstances, the theoretical stoichiometry COD/O2 calculated from the reacting ozone could be 1:1. However, in the reaction schemes involving complex radical chain reactions, this seems not to be the case. It was found to be necessary to include an additional ozone self-
decomposition reaction term (eq 17) to the model so that all the ozone consumed in the experiments could be consumed also in the model. The theoretical O2 consumption calculated from the ozone mass balance was about four times that calculated from the change of COD. This results most probably from radical chain reactions producing hydrogen peroxide and HO2-. As a result of these reactions, a part of the O3 eventually leaves the process as O2. According to Hoigne´ and Bader,18 in solutions containing benzene or some of the substituted benzenes, the radical-type chain reaction led to significant rates of decomposition already at pH values > 2.5. The effect of the radical chain reactions on ozone decomposition was also verified in the
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Figure 4. Estimated and measured hydroquinone concentrations. Measured, run 1 +, run 4 O, run 5 0, run 6 b, run 8 *; estimated, run 1 -x-, run 4 -, run 5 ---, run 6 s, run 8 - -.
current study. A remarkable decrease was detected in the p-nitrophenol decomposition rate at pH 2.1 by use of a radical scavenger tert-butanol. The additional ozone reaction rate term in eq 23 (rate coefficients k4 and k7) was calculated as a second-order reaction from ozone, p-nitrophenol, and hydroquinone concentrations. This comes from the assumption that the ozone decomposition is dependent on the concentrations of ozone, p-nitrophenol, and hydroquinone. Basically, O3 reacts with OH- or with hydroperoxide ions, the ionic form of hydrogen peroxide, to initiate a radical-type reaction chain. In this case, the reaction with OHhas minor importance because of the low pH. The existence of hydrogen peroxide is probably due to the 1.3-dipolar cycloaddition reaction in opening the aromatic ring.13,19,20 If ozone decomposition by radical reactions is dependent on the pnitrophenol concentration, it has to be supposed that the reaction of ozone with catechol and 4-nitrocatechol is fast, which is suggested by the low concentrations of these compounds. During this research, the analyzed maximum concentration of hydroquinone was typically
