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Kinetic study of decomposition of peroxypropionic acid in liquid phase through direct analysis of decomposition products in gas phase
Chemical Engineering Science 62 (2007) 5007 – 5012 www.elsevier.com/locate/ces
Kinetic study of decomposition of peroxypropionic acid in liquid phase through direct analysis of decomposition products in gas phase Sébastien Leveneur a,b,∗ , Tapio Salmi a , Niko Musakka a , Johan Wärnå a a Laboratory of Industrial Chemistry, Process Chemistry Centre, Abo ˚ ˚ Akademi, FI-20500 Abo/Turku, Finland b LRCP-Laboratoire des Risques Chimiques et Procédés, INSA Rouen, Place Emile Blondel, BP8, 76131 Mont-Saint-Aignan Cedex, France
Received 16 June 2006; received in revised form 7 December 2006; accepted 10 December 2006 Available online 29 December 2006
Abstract Decomposition of peroxypropionic acid (PPA) takes place in the liquid phase, but the main products of decomposition, carbon dioxide and oxygen are transferred to gas phase. An analytical method was developed to determine the decomposition of PPA in liquid phase by means of chemical analysis of gas phase. The method is based on on-line mass spectroscopy (MS). A mathematical model for the semi-batch gas–liquid system was developed. The model comprised both kinetic and mass transfer effects. A comparison between experimental results and results predicted from the mathematical model revealed that the model can describe the essential effects of decomposition kinetics. 䉷 2007 Elsevier Ltd. All rights reserved. Keywords: Kinetics; Mass transfer; Mathematical modelling
1. Introduction Peroxypropionic acid (PPA) has potential importance from an industrial viewpoint. Because of its oxidative properties, it can be used in the destruction of organophosphorus (as paraoxon) and sulfurated pollutants. However, like many peroxo-compounds, it decomposes in the liquid phase. Traditionally, liquid-phase decomposition kinetics is measured by analyzing the liquid-phase components off-line. The method is, however, slow and cumbersome. Therefore, we developed a rapid on-line method, which is based on the analysis of the decomposition products released into the gas phase. The method is based on quadrupole mass spectrometry (MS). The experimental system consists of a semi-batch reactor coupled to an online-MS. Reactor modelling aspects are considered. 2. Experimental setup The experiment setup is described in detail in the doctoral thesis of Musakka (2004). A schematic experimental setup ∗ Corresponding author. Laboratory of Industrial Chemistry, Process Chem-
˚ ˚ istry Centre, Abo Akademi, FI-20500 Abo/Turku, Finland. Tel.: +358 2 215 4983; fax: +358 2 215 4479. E-mail address: sleveneu@abo.fi (S. Leveneur). 0009-2509/$ - see front matter 䉷 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.12.040
used to investigate the PPA decomposition is displayed in Fig. 1. The system consisted of two parts: the liquid phase in batch and the gas phase in continuous mode. The carrier gas was fed into a 500 ml glass reactor and leaves the reactor with the gas-phase decomposition products. About 200 g of a PPA solution was poured into the reactor, the carrier gas flow rate was adjusted to 10 ml min−1 at 20 ◦ C. Temperature of the cooling condenser was adjusted to −20 ◦ C to avoid the evaporated liquid-phase components (e.g. water, propionic acid, PPA) to enter the MS. It is sufficient to apply an atmospheric pressure in the reactor to remove the decomposition product; helium is used as a carrier gas. In the purpose of preventing any metal contamination, each part of the reactor was cleaned by a phosphate-free detergent (DeconexR 22PF). The gas–liquid mass transfer characteristics were studied by varying the stirring rate. It was adjusted to be high enough (150 rpm) thus suppressing the liquid–gas mass transfer resistance, but avoiding vortex formation at the gas–liquid interface. 3. Chemical analysis The liquid phase was analyzed offline by titrations and NMRspectroscopy. For measuring the PPA and hydrogen peroxide
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Fig. 2. Calculated results from the tracer experiment.
Fig. 1. Schematical representation of the experimental setup used for decompositions studies.
The mass balance of an arbitrary component (i) in the liquid phase is written in a quantitative form as follows: n˙ Li,in + ri V0L = n˙ Li.out + NLi A +
concentrations, the Greenspan and MacKellar (1948) method was used. Propionic acid was titrated with sodium hydroxide. The mole fractions of carbon dioxide, oxygen and ethane were calculated from the intensities attributed to their mass numbers: 44, 32 and 27, respectively. Since liquid-phase components interfere with these mass numbers, we have to take into account these interferences when calculating the mole fractions of the different gas components. The mole fraction of a component X (e.g. CO2 , O2 ) was calculated from I X − f B IB , xX = kX .xcg Icg where fB is the fragmentation coefficient of the liquid phase component. The fragmentation coefficients were determined by measuring the intensities of the mass numbers of the liquid phase components present in the peroxypropionic acid solution. 4. Characterization of flow characteristics The flow pattern of the gas phase was determined by tracer experiments, by introducing a pulse of another inert gas (here: Ar) into the main inert gas flow (here: He) and recording the pulse at the reactor outlet by MS. The tracer concentration in a tank reactor with complete backmixing (CSTR) is given by the well-known expression c = c0 e−t/t¯.
(1)
The straight line in the logarithmic plot (Fig. 2) implies that the gas phase of the reactor system is completely backmixed. 5. Mass balances for gas and liquid phases In this work, a tank reactor with a continuous flow out from the reactor is considered. The gas outflow contained the decomposition products and helium, which was used as a carrier gas. Under the present circumstances, the vapor pressure of the liquid phase was negligible (the outlet gas was fed through the reflux condenser, Fig. 1).
dnLi . dt
(2)
For the simplest approach, the interfacial component flux (NLi ) is expressed by the law of Fick: ∗ NLi = kLi (cLi − cLi ),
(3)
where the asterisk denotes the equilibrium concentration at the gas–liquid interface. The equilibrium concentration is de facto determined by the gas solubility. The volume of the reaction mixture can be regarded as constant. Thus the amount of substance (nLi ) and concentration (cLi ) are related by nLi = cLi V , which gives dnLi dcLi = V dt dt
(V = constant).
Because the liquid phase is in batch, we get n˙ Li,in = n˙ Li.out = 0. Furthermore, the mass transfer area-to-volume ratio is denoted by A = a0 . V0L
(4)
Consequently, the balance is simplified to dcLi ∗ ), = ri − kLi a0 (cLi − cLi dt
(5)
where the derivative dcLi /dt stands for the accumulation of a component i. For non-volatile components, the mass transfer coefficient kLi is zero. ∗ is obtained The concentration at the liquid–gas interface cLi from solubility data of gases, by using the modified Henry’s ∗ /c∗ ≈ c /c∗ . law: Ki = cGi Gi Li Li The mass balance of a gas-phase component is NLi A = n˙ G +
dnGi dnGi = cGi V˙G + . dt dt
(6)
According to (3) and (4), we obtain ∗ kLi a0 V0L (cLi − cLi ) = cGi V˙G +
dnGi . dt
(7)
S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
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Table 1 Behavior of liquid-phase components in the decomposition of PPA
Hydrogen peroxide PPA Propionic acid Sulfuric acid Hydrogen peroxide PPA Propionic acid Sulfuric acid Hydrogen peroxide PPA Propionic acid Sulfuric acid
Reaction temperature (◦ C)
Reaction time (min)
Initial concentration (mol L−1 )
Final concentration (mol L−1 )
25 25 25 25 35 35 35 35 45 45 45 45
235 235 235 235 291 291 291 291 277 277 277 277
4.41 1.89 3.64 0.36 4.29 1.86 3.70 0.41 3.41 1.47 3.04 0.31
4.39 1.75 3.64 0.36 4.47 1.68 3.87 0.41 3.57 1.31 3.15 0.31
Since the volume of the gas phase is constant and the relation nGi = cGi VG (VG = constant) is valid, we get: dnGi /dt = VG dcGi /dt, which gives cGi kLi a0 V0L dcGi ∗ (cLi − cLi )− , = dt VG G
(8)
where G = VG /V˙G and VG = Vinert . The behavior of a component in the liquid and gas phase is described by the Eqs. (5) and (8). For non-volatile components, kLi = 0 and just the liquid-phase balance is needed. Other simplifications can be done, since the reactions itself are slow compared to the interfacial mass transfer in the vigorously stirred tank. 5.1. Simplified mass balances The derivatives dCi /dt are low, so the kinetics of the decomposition is slow. We can presume that reactions occur essentially in the bulk phase and neglect reactions in the liquid film (see also Table 1 and discussion thereafter). The following simplifying notations are introduced: kLi a0 = L ,
∗ cLi − cLi = c
and
cGi . Ki
This expression for cLi is substituted into Eq. (11) giving the following equation: ri − cGi /G dcGi = , dt /Ki + 1
(12)
where = V0L /VG and cLi = cGi /Ki for all components in the calculation of ri . Eq. (12) is valid for gas-phase components. For non-volatile components in liquid phase, we have dcLi = ri . dt
(13)
The benefit of the simplified mathematical model equations (12) and (13) is that just kinetic and equilibrium parameters are needed, but mass-transfer parameters are discarded.
6.1. Experimental data
and
After adding Eqs. (9) and (10), we get dcGi cGi dcLi + = ri − . dt dt G
cLi =
6. Results and discussion
V0L = . VG
By editing Eqs. (5) and (8) by the above notations we get dcLi = (ri − L c) (9) dt cGi dcGi . = L c − dt G
phases are related by the equilibrium ratio (Ki ):
(10)
(11)
Mass transfer is assumed to be rapid compared to the kinetic phenomena. Thus the concentrations in gas and liquid bulk
The experiments were carried out with a solution containing (wt%): 25% of propionic acid, 15% of PPA, 3% of sulphuric acid, 15% of hydrogen peroxide and water. The graphs obtained from on-line MS analysis show the experimental data (Fig. 3). CO2 and O2 were the main products detected in the gas phase and the amount of carbon dioxide was always higher than the amount of oxygen. Carbon monoxide and ethane were detected, too. Their amounts decreased as the temperature increased. The graph O2 versus CO2 shows that there is a linear relationship between these components. For lower temperatures, the molar ratios were xCO2 ≈ xO2 but at 45 ◦ C the ratio became xCO2 ≈ 2xO2 . The results indicate that parallel reactions take place and the importances of some reactions depend on the temperature.
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S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
Fig. 3. Decomposition products at different temperatures.
Table 1 shows the concentration evolution for each component during the reactions in the liquid phase. One can notice that the liquid-phase variations are small. Indeed, the concentrations of propionic acid and hydrogen
peroxide increase slightly during reaction, whereas one can notice that the decomposition of PPA decreases. From Table 1 it can be evaluated that the initial rate of PPA decomposition was about 6×10−4 mol L−1 min−1 , indicating a very slow reaction.
S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
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Table 2 Kinetic parameters of the model Parameter (L mol−1 s−1 )
Rate constant of the reaction (III), k3 Activation energy of reaction (III), Ea3 (J mol−1 ) Rate constant of the reaction (IV), k4 (L mol−1 s−1 ) Activation energy of reaction (IV), Ea4 (J mol−1 ) Rate constant of the reaction (V), k5 (L mol−1 s−1 ) Activation energy of reaction (V), Ea5 (J mol−1 ) Retarding effect of oxygen, KO2
Estimated parameters
Estimated std. error
Est. relative std. error (%)
Parameter/std. error
0.172.10−04
0.766.10−05
44.5 4.6 44.9 3.4 51.4 208.1 53.5
2.2 21.8 2.2 29.0 1.9 0.5 1.9
0.132.10+06 0.177.10−04 0.150.10+06 0.677.10−06 0.139.10+05 0.179.10+04
0.608.10+04 0.796.10−05 0.518.10+04 0.348.10−06 0.290.10+05 0.960.10+03
Fig. 4. Fit of the model to the experiments (mole fraction versus time) carried out with 15%PPA solutions at temperatures 25–45 ◦ C.
6.2. Data fitting Based on our experimental data, the following stoichiometry was assumed in the quantitative treatment of the data: 2H2 O2 → 2H2 O + O2 , H+
The overall reactions do not reflect the intrinsic reaction mechanism, because complicated radical reactions take place. For this reason, an empirical approach is proposed for the rate expression of the reactions, for instance,
(I)
PPA + H2 O ↔ PA + H2 O2 , (II) 2PPA → 2PA + O2 , (III) (IV) for modeling PPA → EtOH + CO2 , 2PPA → 2C2 H6 + 2CO2 + O2 , (V) 2PPA → 2EtOH + 2CO + O2 , (VI) where PA is propionic acid. Because Eq. (III) is a linear combination of Eqs. (I) and (II), the rate expression for these reactions will be replaced by the rate expression of reaction (III).
Rj =
kj cPPA ccat , 1 + KO2 cO2
where j resents the index of the reaction. According to literature, molecular oxygen acts as a radical scavenger and thus retards the rates of the decomposition. The parameter KO2 takes into account this effect. The solubility parameters Ki were determined from separate solubility measurements (Ahlkvist et al., 2003). The
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temperature dependences of the rate constants are described by a modified Arrhenius equation: Ea 1 1 k = kref exp − , − R T Tref where kref = Ae−(Ea/RT ref ) , Tref is the reference temperature, typically the average temperature of the experiments. The goal of this modification is to minimize the correlation between the frequency factor and the activation energy during the parameter estimation. The parameter estimation was carried out by Modest software (Haario, 1994), by using Simplex and Levenberg–Marquardt algorithms. The ordinary differential equations (12) and (13) were solved repetitively during the parameter estimation by the backward difference method designed for stiff differential equations. For the modelling, reaction (VI) was ruled out. Only the rate constants (k3 , k4 and k5 including their temperature dependencies) and the parameter KO2 were estimated. The results from the modeling are summarized in Table 2 and some data fitting is shown in Fig. 4. The coefficient of determination of this model is 99.6%, so the values calculated are statistically reliable. If we look the estimated relative standard error, one can see that except for the activation energy of reaction (V), all of them are low. The kinetic parameters estimated indicate that reactions (III) and (IV) are the most important. 7. Conclusion The proposed method based on on-line analysis of released gas-phase products by rapid quadrupole mass spectrometry is reliable for studying the kinetics of the decomposition reactions. The method can be applied both for qualitative and quantitative purposes. It is useful as the effect of temperature, concentration, pressure, impurities and stabilizers can be studied on the percarboxylic acid decomposition kinetics. In addition, the method can be used to determine the kinetic parameters quantitatively. A detailed modelling of the reactor system and well-defined flow conditions are required. A more detailed approach to understand the decomposition mechanism of perpropionic acid and the formation of carbon monoxide is required in future. Notation a0 A
mass transfer-to-volume ratio, m2 m−3 area of liquid–gas interface, m2
c Ea fi Ii k k kLi K KO2 n n˙ N R t t V V˙ x
concentration, mol L−1 activation energy, J mol−1 fragmentation coefficient of a component, i intensity of a component i, A rate constant, L mol−1 s−1 calibration coefficient mass transfer coefficient for i in the liquid phase, m s−1 equilibrium parameter parameter for the retarding effect of oxygen amount of substance, mol flow of the amount of substance, mol s−1 flux, mol m−2 s−1 reaction rate, mol L−1 s−1 time, s mean residence time, s volume, m3 volumetric flow rate, m3 s−1 mole fraction
Greek letters L
liquid volume-to-gas ratio ∗ , mol L−1 CLi − CLi −1 kLi .a0 , s residence time, s
Subscripts and superscripts ∗ cat cg i
interfacial (equilibrium) value catalyst carrier gas component index
References Ahlkvist, J., Salmi, T., Eränen, K., Musakka, N., 2003. Bestämning av syrets och koldioxidens löslighet i organiska vätskor, Laboratoriet för teknisk ˚ kemi, Abo Akademi. Greenspan, F.P., MacKellar, D.G., 1948. Analysis of aliphatic per acids. Analytical Chemistry 20 (11), 1061–1062. Haario, H., 1994. MODEST—User’s Guide. Profmath Oy, Helsinki. Musakka, N., 2004. Experimental study and mathematical modelling of ˚ organic decomposition reactions in liquid phase. Doctoral Thesis, Abo Akademi.
Kinetic study of decomposition of peroxypropionic acid in liquid phase through direct analysis of decomposition products in gas phase Sébastien Leveneur a,b,∗ , Tapio Salmi a , Niko Musakka a , Johan Wärnå a a Laboratory of Industrial Chemistry, Process Chemistry Centre, Abo ˚ ˚ Akademi, FI-20500 Abo/Turku, Finland b LRCP-Laboratoire des Risques Chimiques et Procédés, INSA Rouen, Place Emile Blondel, BP8, 76131 Mont-Saint-Aignan Cedex, France
Received 16 June 2006; received in revised form 7 December 2006; accepted 10 December 2006 Available online 29 December 2006
Abstract Decomposition of peroxypropionic acid (PPA) takes place in the liquid phase, but the main products of decomposition, carbon dioxide and oxygen are transferred to gas phase. An analytical method was developed to determine the decomposition of PPA in liquid phase by means of chemical analysis of gas phase. The method is based on on-line mass spectroscopy (MS). A mathematical model for the semi-batch gas–liquid system was developed. The model comprised both kinetic and mass transfer effects. A comparison between experimental results and results predicted from the mathematical model revealed that the model can describe the essential effects of decomposition kinetics. 䉷 2007 Elsevier Ltd. All rights reserved. Keywords: Kinetics; Mass transfer; Mathematical modelling
1. Introduction Peroxypropionic acid (PPA) has potential importance from an industrial viewpoint. Because of its oxidative properties, it can be used in the destruction of organophosphorus (as paraoxon) and sulfurated pollutants. However, like many peroxo-compounds, it decomposes in the liquid phase. Traditionally, liquid-phase decomposition kinetics is measured by analyzing the liquid-phase components off-line. The method is, however, slow and cumbersome. Therefore, we developed a rapid on-line method, which is based on the analysis of the decomposition products released into the gas phase. The method is based on quadrupole mass spectrometry (MS). The experimental system consists of a semi-batch reactor coupled to an online-MS. Reactor modelling aspects are considered. 2. Experimental setup The experiment setup is described in detail in the doctoral thesis of Musakka (2004). A schematic experimental setup ∗ Corresponding author. Laboratory of Industrial Chemistry, Process Chem-
˚ ˚ istry Centre, Abo Akademi, FI-20500 Abo/Turku, Finland. Tel.: +358 2 215 4983; fax: +358 2 215 4479. E-mail address: sleveneu@abo.fi (S. Leveneur). 0009-2509/$ - see front matter 䉷 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.12.040
used to investigate the PPA decomposition is displayed in Fig. 1. The system consisted of two parts: the liquid phase in batch and the gas phase in continuous mode. The carrier gas was fed into a 500 ml glass reactor and leaves the reactor with the gas-phase decomposition products. About 200 g of a PPA solution was poured into the reactor, the carrier gas flow rate was adjusted to 10 ml min−1 at 20 ◦ C. Temperature of the cooling condenser was adjusted to −20 ◦ C to avoid the evaporated liquid-phase components (e.g. water, propionic acid, PPA) to enter the MS. It is sufficient to apply an atmospheric pressure in the reactor to remove the decomposition product; helium is used as a carrier gas. In the purpose of preventing any metal contamination, each part of the reactor was cleaned by a phosphate-free detergent (DeconexR 22PF). The gas–liquid mass transfer characteristics were studied by varying the stirring rate. It was adjusted to be high enough (150 rpm) thus suppressing the liquid–gas mass transfer resistance, but avoiding vortex formation at the gas–liquid interface. 3. Chemical analysis The liquid phase was analyzed offline by titrations and NMRspectroscopy. For measuring the PPA and hydrogen peroxide
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S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
Fig. 2. Calculated results from the tracer experiment.
Fig. 1. Schematical representation of the experimental setup used for decompositions studies.
The mass balance of an arbitrary component (i) in the liquid phase is written in a quantitative form as follows: n˙ Li,in + ri V0L = n˙ Li.out + NLi A +
concentrations, the Greenspan and MacKellar (1948) method was used. Propionic acid was titrated with sodium hydroxide. The mole fractions of carbon dioxide, oxygen and ethane were calculated from the intensities attributed to their mass numbers: 44, 32 and 27, respectively. Since liquid-phase components interfere with these mass numbers, we have to take into account these interferences when calculating the mole fractions of the different gas components. The mole fraction of a component X (e.g. CO2 , O2 ) was calculated from I X − f B IB , xX = kX .xcg Icg where fB is the fragmentation coefficient of the liquid phase component. The fragmentation coefficients were determined by measuring the intensities of the mass numbers of the liquid phase components present in the peroxypropionic acid solution. 4. Characterization of flow characteristics The flow pattern of the gas phase was determined by tracer experiments, by introducing a pulse of another inert gas (here: Ar) into the main inert gas flow (here: He) and recording the pulse at the reactor outlet by MS. The tracer concentration in a tank reactor with complete backmixing (CSTR) is given by the well-known expression c = c0 e−t/t¯.
(1)
The straight line in the logarithmic plot (Fig. 2) implies that the gas phase of the reactor system is completely backmixed. 5. Mass balances for gas and liquid phases In this work, a tank reactor with a continuous flow out from the reactor is considered. The gas outflow contained the decomposition products and helium, which was used as a carrier gas. Under the present circumstances, the vapor pressure of the liquid phase was negligible (the outlet gas was fed through the reflux condenser, Fig. 1).
dnLi . dt
(2)
For the simplest approach, the interfacial component flux (NLi ) is expressed by the law of Fick: ∗ NLi = kLi (cLi − cLi ),
(3)
where the asterisk denotes the equilibrium concentration at the gas–liquid interface. The equilibrium concentration is de facto determined by the gas solubility. The volume of the reaction mixture can be regarded as constant. Thus the amount of substance (nLi ) and concentration (cLi ) are related by nLi = cLi V , which gives dnLi dcLi = V dt dt
(V = constant).
Because the liquid phase is in batch, we get n˙ Li,in = n˙ Li.out = 0. Furthermore, the mass transfer area-to-volume ratio is denoted by A = a0 . V0L
(4)
Consequently, the balance is simplified to dcLi ∗ ), = ri − kLi a0 (cLi − cLi dt
(5)
where the derivative dcLi /dt stands for the accumulation of a component i. For non-volatile components, the mass transfer coefficient kLi is zero. ∗ is obtained The concentration at the liquid–gas interface cLi from solubility data of gases, by using the modified Henry’s ∗ /c∗ ≈ c /c∗ . law: Ki = cGi Gi Li Li The mass balance of a gas-phase component is NLi A = n˙ G +
dnGi dnGi = cGi V˙G + . dt dt
(6)
According to (3) and (4), we obtain ∗ kLi a0 V0L (cLi − cLi ) = cGi V˙G +
dnGi . dt
(7)
S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
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Table 1 Behavior of liquid-phase components in the decomposition of PPA
Hydrogen peroxide PPA Propionic acid Sulfuric acid Hydrogen peroxide PPA Propionic acid Sulfuric acid Hydrogen peroxide PPA Propionic acid Sulfuric acid
Reaction temperature (◦ C)
Reaction time (min)
Initial concentration (mol L−1 )
Final concentration (mol L−1 )
25 25 25 25 35 35 35 35 45 45 45 45
235 235 235 235 291 291 291 291 277 277 277 277
4.41 1.89 3.64 0.36 4.29 1.86 3.70 0.41 3.41 1.47 3.04 0.31
4.39 1.75 3.64 0.36 4.47 1.68 3.87 0.41 3.57 1.31 3.15 0.31
Since the volume of the gas phase is constant and the relation nGi = cGi VG (VG = constant) is valid, we get: dnGi /dt = VG dcGi /dt, which gives cGi kLi a0 V0L dcGi ∗ (cLi − cLi )− , = dt VG G
(8)
where G = VG /V˙G and VG = Vinert . The behavior of a component in the liquid and gas phase is described by the Eqs. (5) and (8). For non-volatile components, kLi = 0 and just the liquid-phase balance is needed. Other simplifications can be done, since the reactions itself are slow compared to the interfacial mass transfer in the vigorously stirred tank. 5.1. Simplified mass balances The derivatives dCi /dt are low, so the kinetics of the decomposition is slow. We can presume that reactions occur essentially in the bulk phase and neglect reactions in the liquid film (see also Table 1 and discussion thereafter). The following simplifying notations are introduced: kLi a0 = L ,
∗ cLi − cLi = c
and
cGi . Ki
This expression for cLi is substituted into Eq. (11) giving the following equation: ri − cGi /G dcGi = , dt /Ki + 1
(12)
where = V0L /VG and cLi = cGi /Ki for all components in the calculation of ri . Eq. (12) is valid for gas-phase components. For non-volatile components in liquid phase, we have dcLi = ri . dt
(13)
The benefit of the simplified mathematical model equations (12) and (13) is that just kinetic and equilibrium parameters are needed, but mass-transfer parameters are discarded.
6.1. Experimental data
and
After adding Eqs. (9) and (10), we get dcGi cGi dcLi + = ri − . dt dt G
cLi =
6. Results and discussion
V0L = . VG
By editing Eqs. (5) and (8) by the above notations we get dcLi = (ri − L c) (9) dt cGi dcGi . = L c − dt G
phases are related by the equilibrium ratio (Ki ):
(10)
(11)
Mass transfer is assumed to be rapid compared to the kinetic phenomena. Thus the concentrations in gas and liquid bulk
The experiments were carried out with a solution containing (wt%): 25% of propionic acid, 15% of PPA, 3% of sulphuric acid, 15% of hydrogen peroxide and water. The graphs obtained from on-line MS analysis show the experimental data (Fig. 3). CO2 and O2 were the main products detected in the gas phase and the amount of carbon dioxide was always higher than the amount of oxygen. Carbon monoxide and ethane were detected, too. Their amounts decreased as the temperature increased. The graph O2 versus CO2 shows that there is a linear relationship between these components. For lower temperatures, the molar ratios were xCO2 ≈ xO2 but at 45 ◦ C the ratio became xCO2 ≈ 2xO2 . The results indicate that parallel reactions take place and the importances of some reactions depend on the temperature.
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S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
Fig. 3. Decomposition products at different temperatures.
Table 1 shows the concentration evolution for each component during the reactions in the liquid phase. One can notice that the liquid-phase variations are small. Indeed, the concentrations of propionic acid and hydrogen
peroxide increase slightly during reaction, whereas one can notice that the decomposition of PPA decreases. From Table 1 it can be evaluated that the initial rate of PPA decomposition was about 6×10−4 mol L−1 min−1 , indicating a very slow reaction.
S. Leveneur et al. / Chemical Engineering Science 62 (2007) 5007 – 5012
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Table 2 Kinetic parameters of the model Parameter (L mol−1 s−1 )
Rate constant of the reaction (III), k3 Activation energy of reaction (III), Ea3 (J mol−1 ) Rate constant of the reaction (IV), k4 (L mol−1 s−1 ) Activation energy of reaction (IV), Ea4 (J mol−1 ) Rate constant of the reaction (V), k5 (L mol−1 s−1 ) Activation energy of reaction (V), Ea5 (J mol−1 ) Retarding effect of oxygen, KO2
Estimated parameters
Estimated std. error
Est. relative std. error (%)
Parameter/std. error
0.172.10−04
0.766.10−05
44.5 4.6 44.9 3.4 51.4 208.1 53.5
2.2 21.8 2.2 29.0 1.9 0.5 1.9
0.132.10+06 0.177.10−04 0.150.10+06 0.677.10−06 0.139.10+05 0.179.10+04
0.608.10+04 0.796.10−05 0.518.10+04 0.348.10−06 0.290.10+05 0.960.10+03
Fig. 4. Fit of the model to the experiments (mole fraction versus time) carried out with 15%PPA solutions at temperatures 25–45 ◦ C.
6.2. Data fitting Based on our experimental data, the following stoichiometry was assumed in the quantitative treatment of the data: 2H2 O2 → 2H2 O + O2 , H+
The overall reactions do not reflect the intrinsic reaction mechanism, because complicated radical reactions take place. For this reason, an empirical approach is proposed for the rate expression of the reactions, for instance,
(I)
PPA + H2 O ↔ PA + H2 O2 , (II) 2PPA → 2PA + O2 , (III) (IV) for modeling PPA → EtOH + CO2 , 2PPA → 2C2 H6 + 2CO2 + O2 , (V) 2PPA → 2EtOH + 2CO + O2 , (VI) where PA is propionic acid. Because Eq. (III) is a linear combination of Eqs. (I) and (II), the rate expression for these reactions will be replaced by the rate expression of reaction (III).
Rj =
kj cPPA ccat , 1 + KO2 cO2
where j resents the index of the reaction. According to literature, molecular oxygen acts as a radical scavenger and thus retards the rates of the decomposition. The parameter KO2 takes into account this effect. The solubility parameters Ki were determined from separate solubility measurements (Ahlkvist et al., 2003). The
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temperature dependences of the rate constants are described by a modified Arrhenius equation: Ea 1 1 k = kref exp − , − R T Tref where kref = Ae−(Ea/RT ref ) , Tref is the reference temperature, typically the average temperature of the experiments. The goal of this modification is to minimize the correlation between the frequency factor and the activation energy during the parameter estimation. The parameter estimation was carried out by Modest software (Haario, 1994), by using Simplex and Levenberg–Marquardt algorithms. The ordinary differential equations (12) and (13) were solved repetitively during the parameter estimation by the backward difference method designed for stiff differential equations. For the modelling, reaction (VI) was ruled out. Only the rate constants (k3 , k4 and k5 including their temperature dependencies) and the parameter KO2 were estimated. The results from the modeling are summarized in Table 2 and some data fitting is shown in Fig. 4. The coefficient of determination of this model is 99.6%, so the values calculated are statistically reliable. If we look the estimated relative standard error, one can see that except for the activation energy of reaction (V), all of them are low. The kinetic parameters estimated indicate that reactions (III) and (IV) are the most important. 7. Conclusion The proposed method based on on-line analysis of released gas-phase products by rapid quadrupole mass spectrometry is reliable for studying the kinetics of the decomposition reactions. The method can be applied both for qualitative and quantitative purposes. It is useful as the effect of temperature, concentration, pressure, impurities and stabilizers can be studied on the percarboxylic acid decomposition kinetics. In addition, the method can be used to determine the kinetic parameters quantitatively. A detailed modelling of the reactor system and well-defined flow conditions are required. A more detailed approach to understand the decomposition mechanism of perpropionic acid and the formation of carbon monoxide is required in future. Notation a0 A
mass transfer-to-volume ratio, m2 m−3 area of liquid–gas interface, m2
c Ea fi Ii k k kLi K KO2 n n˙ N R t t V V˙ x
concentration, mol L−1 activation energy, J mol−1 fragmentation coefficient of a component, i intensity of a component i, A rate constant, L mol−1 s−1 calibration coefficient mass transfer coefficient for i in the liquid phase, m s−1 equilibrium parameter parameter for the retarding effect of oxygen amount of substance, mol flow of the amount of substance, mol s−1 flux, mol m−2 s−1 reaction rate, mol L−1 s−1 time, s mean residence time, s volume, m3 volumetric flow rate, m3 s−1 mole fraction
Greek letters L
liquid volume-to-gas ratio ∗ , mol L−1 CLi − CLi −1 kLi .a0 , s residence time, s
Subscripts and superscripts ∗ cat cg i
interfacial (equilibrium) value catalyst carrier gas component index
References Ahlkvist, J., Salmi, T., Eränen, K., Musakka, N., 2003. Bestämning av syrets och koldioxidens löslighet i organiska vätskor, Laboratoriet för teknisk ˚ kemi, Abo Akademi. Greenspan, F.P., MacKellar, D.G., 1948. Analysis of aliphatic per acids. Analytical Chemistry 20 (11), 1061–1062. Haario, H., 1994. MODEST—User’s Guide. Profmath Oy, Helsinki. Musakka, N., 2004. Experimental study and mathematical modelling of ˚ organic decomposition reactions in liquid phase. Doctoral Thesis, Abo Akademi.