Ind. Eng. Chem. Res. 1997, 36, 3315-3322
3315
Modeling of NOx Absorption into Nitric Acid Solutions Containing Hydrogen Peroxide D. Thomas* and J. Vanderschuren Chemical Engineering Department, Faculte´ Polytechnique de Mons, B 7000 Mons, Belgium
A mathematical model was developed for the isothermal absorption of nitrogen oxides into nitric acid solutions containing hydrogen peroxide. This model, based on the two-film theory of absorption with chemical reactions, includes diffusive transport and equilibrium between species in the gas phase and simultaneous absorption of the NOx components with fast irreversible reactions in the liquid phase. Kinetic parameters relative to the absorption of the different NOx species were determined at increasing acidities and for a low concentration of H2O2 from test runs performed in a small packed column at 20 °C and atmospheric pressure for various NOx partial pressures up to 500 Pa and the whole range of NOx oxidation ratios. Only the parameter relative to trivalent NOx was found to increase with the HNO3 molarity, the other ones remaining constant. Interpretation of the experimental results according to the model showed that the hydrolysis is the main controlling step for tetravalent nitrogen oxides and that among the trivalent components nitrous acid is likely to be a major transporting species. Nitrous acid is also formed in the gas phase, due to reaction with water:
Introduction The removal of NOx in gaseous waste products, discharged from nitric acid towers, power plants, or chemical reactors using nitric acid, is usually achieved by means of dry as well as wet techniques. The absorption of dilute NOx can be made by using various scrubbing reactants. Jethani et al (1990) made recently a critical review of the NOx abatement wet processes. The main drawbacks of wet techniques are the low solubility of nitric oxide and in the case of nonregenerable systems the production of effluent liquids which must be treated if they are not marketable. To increase the overall absorption rate of NOx, oxidizing agents were introduced successfully either in the gas phase (ozone, chlorine dioxide, hydrogen peroxide, ...) (Takahashi et al., 1979; von Wedel et al., 1991; Kasper et al., 1996) or in the liquid phase (potassium permanganate, sodium chlorite, ...) (Joshi et al., 1985). An oxidizing process using hydrogen peroxide in the scrubbing solution appears to be very attractive, as it results in the production of valuable nitric acid without generating any other polluting byproduct. A number of authors already investigated the use of aqueous solutions of hydrogen peroxide for industrial applications (Adrian and Verilhac, 1976; Downey, 1980; Cooper, 1984; Deo, 1988; Curtius, 1989; Buck et al., 1991; Pirkl and Hofmann, 1992), but the published information was very little detailed. Therefore, we decided to study more thoroughly the phenomenon and the kinetics of NOx absorption with H2O2. Absorption of NOx is a very complex phenomenon due to the numerous chemical reactions involved in the process. NOx gas is a mixture of several components, NO, NO2, N2O4, and N2O3, and the following reactions occur in the gas phase:
2NO + O2 f 2NO2
(1)
2NO2 a N2O4
(2)
NO + NO2 a N2O3
(3)
S0888-5885(96)00436-8 CCC: $14.00
NO + NO2 + H2O a 2HNO2
(4)
but the literature does not clearly indicate whether this formation is achieved at equilibrium or not. Moreover, considerable disagreement exists among the various reported data about the kinetics of HNO2 formation (Newman and Carta, 1988). The different gaseous components are absorbed into the liquid phase. In the case of pure water or aqueous solutions of nitric acid, the following reactions can be considered:
N2O3 + H2O f 2HNO2
(5)
N2O4 + H2O f HNO2 + HNO3
(6)
2NO2 + H2O f HNO2 + HNO3
(7)
The HNO2 formed in the liquid phase is readily decomposed, with the release of NO, according to a reaction usually written as
3HNO2 a HNO3 + 2NO + H2O
(8)
Some important features relative to the effect of the addition of hydrogen peroxide to the solution were found and discussed in a previous paper (Thomas et al., 1996): (1) In the presence of hydrogen peroxide, the decomposition of HNO2 is prevented as it is oxidized to HNO3 according to the global reaction:
HNO2 + H2O2 f HNO3 + H2O
(9)
which increases the overall NOx absorption rate. As a matter of fact this reaction is known to proceed through a sequence including peroxynitrous acid as the intermediate species (Halfpenny and Robinson, 1952; Benton and Moore, 1970). © 1997 American Chemical Society
3316 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
(2) The nitric acid concentration in the absorbent liquid has a positive influence on the fractional absorption of NOx with hydrogen peroxide. Hydrogen ions were found to catalyze the oxidation reactions by H2O2 in the liquid phase. (3) Absorption of dilute NOx remains possible into fairly concentrated nitric acid solutions up to 8 M (42% weight). (4) NOx absorption rates are independent of the hydrogen peroxide concentration up to 0.2 M. The kinetics of the overall absorption process of NOx can therefore be assumed zero order with respect to the hydrogen peroxide concentration, in the range of the used concentrations of reagent. Some kinetic studies were already performed concerning the liquid-phase oxidation by hydrogen peroxide of NOx species: nitrous acid HNO2 (Halfpenny and Robinson, 1952; Anbar and Taube, 1954; Benton and Moore, 1970) and nitric monoxide, NO (Baveja et al., 1979). However, for the design of NOx absorption towers fed with solutions containing H2O2, the knowledge of the kinetics of all the global chemical reactions involved is needed to predict the enhancement of masstransfer rates in the liquid phase. Therefore the objective of the present work was to determine the kinetic parameters which characterize the absorption of the different NOx components into nitric acid solutions containing H2O2.
experimental results were used to determine the required kinetic parameters according to the following model. Mathematical Model Numerous mathematical models of NOx absorption into water or diluted nitric acid were developed for both packed and plate columns (Counce and Perona, 1980, 1983; Lee et al., 1989; Wiegand et al., 1990; Suchak et al., 1991). These models were applied especially for the process design of HNO3 production towers and tried to describe the combined effects of several equilibria, rates of mass-transfer, and chemical reactions in the NOxHNO3-H2O system. The present model is an adaptation of that of Counce and Perona (1983) for packed columns, on the basis of the two-film theory of absorption with chemical reaction. It considers fast irreversible reactions of NOx species with H2O2 in the liquid phase. Equations of the Gas Phase. The gas-phase composition of NOx along the column is characterized by the partial pressures of the two chemical species NO* and NO2* which include the actual components NO, NO2, N2O3, N2O4, and HNO2. The partial pressure of HNO3 is always very low and neglected. The partial pressures of the NOx species are calculated from known values of pNO* and pNO2*, using the definitions in (10) and (11) and the following equilibrium relations:
Experimental Determinations The experimental system, including a small laboratory column of i.d. 0.045 m and height 0.455 m, packed with 10 mm glass raschig rings, has been described previously (Thomas et al., 1996). Flow rates were maintained at constant values for all the experiments, 0.175 m3/s‚m2 for the gas and 5.34 × 10-3 m3/s‚m2 for the liquid. The gaseous mixture, made of nitrogen oxides and nitrogen saturated with water vapor at the experimental temperature, was analyzed by chemiluminescence, giving the total NOx and the “chemical” nitric oxide NO* contents:
pNO* ) pNO + pN2O3 + 0.5pHNO2
(10)
The partial pressure of high oxidation state NOx species (“chemical” nitrogen dioxide NO2*) is the difference between the total NOx and partial NO* contents:
pNO2* ) pNOx - pNO* ) pNO2 + pN2O3 + 2pN2O4 + 0.5pHNO2 (11) The proportion of NO2* in total NOx, called the oxidation ratio OR, is an important characteristic of the gas. Absorption of dilute NOx up to partial pressures of 500 Pa was performed into aqueous and nitric acid solutions containing a small, but in excess, concentration of H2O2 (0.02 M), at atmospheric pressure and at a temperature of 20 ( 0.5 °C. The absorption rate was measured for the whole range of NOx oxidation ratios in the gas phase and different concentrations of HNO3 (0-4 M) in the scrubbing liquid. The concentrations of nitrite and nitrate ions in the solution were determined by electrophoretic capillary ion analysis; the total acidity and the H2O2 were checked by classical titration and iodometry, respectively. All
pN2O4 ) K2pNO22
(12)
pN2O3 ) K3pNOpNO2
(13)
These equilibrium relations are assumed to apply at all points of the bulk gas phase, of the gas film, and also at the gas-liquid interface. Most commonly used equilibrium constants K2 and K3 are reported by Joshi et al. (1985):
log10 K2 )
2993 - 11.232 (kPa-1) T
(14)
log10 K3 )
2072 - 9.240 (kPa-1) T
(15)
Given the uncertainties relative to the gas phase formation rate of HNO2, the trivalent species N2O3 and HNO2 are grouped as a single effective compound noted N2O3*. The steady-state diffusive transport of any absorbing species A across the gas film is equal to
RA ) -
DGA dpA dpA ) -kGA RTδ dξ dξ
(16)
where ξ is a dimensionless coordinate inside the gas film. Utilizing this expression and the equilibrium relations 12 and 13, the gradients of N2O4 and N2O3 can be evaluated in the gas film in terms of NO and NO2 as
dpN2O4 dξ dpN2O3 dξ
) 2K2pNO2
) K3pNO
dpNO2 dξ
dpNO2
(17)
dξ
+ K3pNO2
dpNO dξ
(18)
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3317
From the relations 10 and 11, the fluxes of chemical species are written as
RNO2* ) RNO2 + RN2O3* + 2RN2O4
(19)
RNO* ) RNO + RN2O3*
(20)
Substitution of eqs 16-18 into 19 and 20 and rearrangement lead to the expressions of the fluxes of NO2* and NO* through the gas film with the use of four parameters containing appropriate gas-phase masstransfer coefficients as
dpNO + xx -RNO2* ) ww dξ dξ dpNO2 dξ
+ zz
dpNO dξ
(21)
(22)
and finally:
dpNO2 dξ
xxRNO* - zzRNO2* )
RNO2 )
x
2 k2NO2DNO2 p 1.5 ) OKPNO2piNO21.5 3 H 3 iNO2
wwzz - xxyy
dpNO -wwRNO* + yyRNO2* ) dξ wwzz - xxyy
(23)
(24)
Equations in the Liquid Phase. For modeling purposes, the following global reactions between dissolved NOx species and H2O2 are supposed to take place in the liquid phase:
2NO2 + H2O2 f 2HNO3
(25)
N2O4 + H2O2 f 2HNO3
(26)
N2O3* + 2H2O2 f 2HNO3 + H2O
(27)
Obviously the absorption of nitrous acid formed in the gas phase is also accompanied by a global chemical reaction with H2O2, according to (9) but, as already said before, trivalent species N2O3 and HNO2 are treated together as a fictitious species N2O3*. Nitric oxide which is sparingly soluble and nonreactive in water can nevertheless react with H2O2 (Baveja et al., 1979):
2NO + 3H2O2 f 2HNO3 + 2H2O
(28)
The steady-state mass flux of each absorbing component A across the liquid film is expressed, according to the film theory of absorption accompanied by a fast irreversible reaction (Danckwerts, 1970), by
(30)
NO2
RN2O4 )
RN2O3* )
dpNO2
-RNO* ) yy
assuming large Hatta numbers and Henry equilibrium laws at the gas-liquid interface:
xk1
xk1
N2O3*
DN2O4 piN2O4 ) OKPN2O4piN2O4 (31)
N2O4
HN2O4
DN2O3 piN2O3 ) OKPN2O3*piN2O3
HN2O3
(32)
The factors multiplying the pi’s include all parameters needed for the design of scrubbing towers. We call them the overall kinetic parameters (OKP). The OKPs are preferred to conventional enhancement factors or Hatta numbers because they overcome the uncertainties about the Henry constants of different NOx species. Moreover they do not contain the mass-transfer coefficients kL and are therefore theoretically independent of the hydrodynamic conditions prevailing in the column. The absorption of NO, remaining always very low and being not substantially enhanced by increasing excess of H2O2 or by the presence of HNO3 in the liquid (Thomas, 1996), is taken into account by the expression
RNO ) kLNOciNO
(33)
with a zero bulk concentration, given the presence of H2O2. This expression is different from that of Baveja et al. (1979) who found first orders with respect to both reactants. Calculation of the Absorption Performances of the Whole Column. For simulation purposes, the packed column was divided into small height incremental volumes so that the average component pressures may be used in rate equations for interphase transport. The change in gas and liquid flow rates were neglected, as well as heat effects, and the gas phase was assumed to be ideal. In an incremental volume gas-phase equilibria were first calculated from pNO* and pNO2*. In the presence of oxygen, nitric oxide, NO, undergoes an irreversible oxidation which is second order with respect to NO and first order with respect to oxygen (see the rate constant k1 in Joshi et al., 1985). The extent of conversion, XNO, in an incremental column volume dV is computed and used to adjust the concentrations of NO* and NO2*. The equation for plug flow conditions is
k1(pNO)in(pO2)in dV
[
(29)
1 1 + b + 1 1 - XNO 1 + bXNO b 1 ln (34) b+1 1 - XNO b+1
According to our experimental results, all the reactions 25-28 are assumed to be zero order with respect to H2O2. The orders with respect to the dissolved NOx are postulated to be the same for reactions with H2O2 as for water: reaction 25 is second order with respect to NO2 and reactions 26 and 27 are both first order with respect to N2O4 and N2O3, respectively. The following expressions for the absorption rates are then used,
which can be solved by bisection. In the case of the laboratory column, XNO can be neglected as the inlet content of oxygen and the residence time of the gas are small. Next the gradients of NO2 and NO in the gas film were evaluated by integration of eqs 23 and 24 with the Runge-Kutta method in order to determine interfacial partial pressures. As these gradients are functions of the “chemical fluxes” which are themselves dependent
RA ) EAkLAcAi
G
)
]
3318 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
on the interfacial partial pressures, an iterative method was necessary to solve the problem. Expressions 3033 were used to determine the individual fluxes of NO2, N2O4, N2O3*, and NO, respectively. The steady-state mass balance equations for the incremental column volume allowed the calculation of the NO2* and NO* partial pressures at the outlet of the element:
(pNO2*)out ) (pNO2*)in - (RNO2 + 2RN2O4 + RN2O3*)
adVRT + (pNO)inXNO (35) G adVRT G (pNO)inXNO (36)
(pNO*)out ) (pNO*)in - (RNO + RN2O3*)
In terms of total partial pressure
(pNOx)out ) (pNO*)out + (pNO2*)out
(37)
Starting from bottom, this calculation, achieved element by element, gave finally the content of NO* and NO2* of the gas leaving at the top and the overall NOx removal performances of the column characterized by two parameters: the overall fractional absorption of NOx, A, and the absorption selectivity of tetravalent NOx, S. Mass-Transfer Characteristics of the Packing. The simulation of the column could only be made for given OKPs. It also required the knowledge of the mass-transfer characteristics of the packing for the used experimental gas and liquid flow rates (Thomas, 1996). The gas mass-transfer coefficients, kGA, were determined by absorbing SO2 into a sodium hydroxide solution. Corrections of diffusivities were applied to convert to the system of the NOx/N2 mixture. Measurements of the liquid-phase mass-transfer coefficients, kLA, were made by absorbing pure CO2 in water and correcting them with the liquid diffusivities of the NOx species. The determination of a was performed by absorbing dilute CO2 into concentrated sodium hydroxide solutions, in the conditions of the fast chemical reaction regime. The kinetic constant for the reaction between CO2 and OH- was given by Nijsing et al. (1959). The value of the effective area was found to be quite similar to the value estimated from the experimental study of Rizzuti et al. (1981), conducted in a small column packed with 10 mm glass Raschig rings. Determination of the Overall Kinetic Parameters To determine the OKP values relative to the various NOx species, numerous experiments were conducted in the laboratory column with aqueous and nitric acid solutions (0.5-4 kmol/m3) containing a small excess of H2O2 and flowing in a single pass through the column. For a given nitric acid molarity, the overall kinetic parameters of NO2 and N2O4 were first determined from approximately 30 absorption tests with gases containing from 10 to 500 Pa of tetravalent NOx at a maximum oxidation ratio close to 95%. The value of the OKP relative to N2O3* was then assessed with some 30 or 40 test runs made for a large range of NOx partial pressures and oxidation ratios. A grid method was
Figure 1. Variation of the OKP values with the HNO3 concentration of the scrubbing solution.
applied to find the OKP values by minimization of the mean deviation between experimental and calculated values using the following objective function:
OF )
∑i (0.5|Ai
1 n
exp
- Aicalc| + 0.5|Siexp - Sicalc|)
(38)
Actually both parameters, A and S, included in the objective function with equal weights played equally important roles in the minimization. The species N2O3*, taking a slight but non-negligible part in the absorption of NOx at an OR of 95%, needed successive adjustments of the OKP values. For NO2 and N2O4 (see Figure 1), we found OKP values which, roughly, do not vary appreciably with the nitric acid concentration whereas the factor relative to N2O3* increases regularly with the acidity. These values are compared in Tables 1 and 2 with those obtained by different authors for NOx absorption into water. These tables also include the Hatta numbers derived from the values of kL and of the kinetic constants k estimated from the determined OKPs. The Hatta numbers greater than 3 allow the confirmation of a posteriori that the reactions between NOx and H2O2 are fast, according to the assumption made in the model. With the exception of NO, absorption of other NOx species proceeds with fast kinetics, so that the volumetric absorption rates are only dependent on the effective surface area a and that they do not include the liquid mass-transfer coefficients kL. Figure 2 illustrates the influence of the acidity on the calculated contributions of the various species to the NOx absorption. These were computed from the individual fluxes by summing up the partial pressure differences obtained for all elementary volumes. It appears that the contributions of tetravalent species are slighty decreasing with the increase of the HNO3 concentration while the contribution relative to trivalent NOx is increasing with the acidity. Moreover, due to their high solubility, the compounds which exist in lower concentrations in the gaseous phase (N2O4 and N2O3*) take part subtantially to the overall absorption, which remains true for NOx partial pressures lower than 500 Pa (Thomas, 1996). The developed model and the OKP values were found to provide a good fit of the absorption data for a large range of operating conditions, the average absolute error (mean value of OF) being less than 5%. As a typical example, Figure 3 compares the computed values of parameters A and S to the experimental ones, for a total partial pressure of NOx of 500 Pa and different nitric acid solutions containing a small excess of H2O2. The
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3319 Table 1. Overall Kinetic Parameters for Tetravalent NOx
references
t (°C)
Takeuchi et al. (1977) Sada et al. (1979) Komiyama and Inoue (1980) this work (mean value)
25 25 15 20
x
2 k D /H3 (kmol/m2 s kPa1.5) 3 2NO2 NO2 NO2 27.7 × 10-7 22.6 × 10-7 8.39 × 10-7 15.37 × 10-7
xk references
t (°C)
Hoftyzer and Kwanten (1972) Kameoka and Pigford (1977) Komiyama and Inoue (1980) Pirkl et al. (1993) this work (mean value)
25 25 15 25 20
DN2O4
1N
2O4
HN2O4
HaNO2
2 k x 3 )
DNO2ciNO
2NO
2
2
kLNO
2
HaNO2 > 3 if piNO2 > 47 Pa
(kmol/m2 s kPa)
HaN2O4 )
xk
DN2O4
1N
2O4
kLN O
2 4
9.2 × 10-6 6.8 × 10-6 14 × 10-6 7.15 × 10-5 14.22 × 10-6
12
Table 2. Overall Kinetic Parameters for Trivalent NOx
references
t (°C)
[HNO3] (kmol/m3)
xk
1N
DN2O3
2O3
HN2O3
(kmol/m2 s kPa)
Corriveau (1971) Weisweiler and DeiB (1987) Newman and Carta (1988)
25 25 25
0 0 0
N2O3 without H2O2 1.59 × 10-5 2.9 × 10-5 2.5 × 10-4
this work
20
0 2 4
N2O3* with H2O2 2.86 × 10-4 1.23 × 10-3 1.63 × 10-3
Figure 2. Calculated contributions to the absorption of NOx species as a function of the HNO3 concentration; (pNOx)in ) 500 Pa; OR ) 50%.
HaN2O3 )
xk
1N
DN2O3
2O3
kLN O
2 3
360 1549 2058
Figure 4. Efficiency of NOx absorption into sodium hydroxide and HNO3 solutions containing H2O2; (pNOx)in ) 500 Pa.
The assumption that the overall kinetic parameters are not functions of the hydrodynamic conditions achieved in the column (see expressions 30-32) has been verified, and the OKP values validated as the model developed hereabove has worked with fair success in predicting the NOx removal efficiency of a pilot-scale column (2 m high with an i.d. of 0.215 m) packed with 25 mm plastic Pall rings and operated in various conditions with different liquid flow rates (Thomas and Vanderschuren, 1996; Thomas, 1996). Discussion of the Results Figure 3. Comparison of computed and experimental absorption performances for different nitric acid concentrations; (pNOx)in ) 500 Pa.
predictions seem to be quite good for all absorption rates. Experiments made with high oxidation ratios and giving absorption selectivities of NOx(IV) close to 100% are perfectly simulated. For lower selectivities, the model gives slightly too large values of S.
In order to understand the mechanism of NOx absorption into solutions containing H2O2 additional experiments of NOx absorption were performed with a 1 M sodium hydroxide solution. The results obtained are presented together with those relative to HNO3 solutions containing H2O2 in Figure 4. At high oxidation ratios, the absorption rates are quite similar in all solutions. As a matter of fact, the absorption phenomenon of tetravalent NOx appears to
3320 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
Figure 6. Mechanism of NOx absorption into nitric acid solutions containing H2O2.
Figure 5. Variation, with the HNO3 concentration, of the disappearing percentage of nitrite ions.
be controlled by the hydrolysis of the species NO2 and N2O4 since OKPs do not vary with the nitric acid concentration; OKP values are close to those obtained for water without H2O2 (see Table 1); there is little or no effect of added base on the absorption rate. At intermediate oxidation ratios, it is clear that trivalent NOx species play an important role in the absorption and a maximum of the overall absorption efficiency was observed for sodium hydroxide solutions. Similar to tetravalent NOx species, one may assume that the hydrolysis of the dinitrogen trioxide N2O3 is the ratecontrolling step. In alkaline solutions, the HNO2 formed in the gas phase undergoes during absorption an instantaneous proton transfer reaction:
HNO2 + OH- f NO2- + H2O
(39)
that greatly enhances the rate of dissolution as suggested by Carta (1984). Nitrous acid is likely to play an analogous role of major transporting species in the absorption of NOx into H2O2 solutions. As the oxidation reaction of nitrous acid by hydrogen peroxide (reaction 9) is catalyzed by hydrogen ions (Halfpenny and Robinson, 1952), the increase with the acidity of both the OKP of N2O3* and the contribution of that species to the absorption (Figure 2) is then easily understandable. Additional evidence of the rate-controlling step of the absorption process is given in Figure 5. The capillary ion analysis was applied for the determination of nitrite ions in the nitric acid solution containing H2O2 at the output of the column. It can be seen that the disappearing rate of NO2- is greatly increased by the HNO3 concentration. Above 0.5 M of HNO3, almost all the nitrous acid has been oxidized by H2O2, proving that the nitrous acid oxidation is very fast in the presence of HNO3. The role of hydrogen peroxide, added to the scrubbing liquid, appears to be dual: to prevent the HNO2 decomposition by oxidizing this component in the liquid phase and to enhance the absorption rate of the HNO2 formed in the gas phase, because its dissolution is accompanied by a rapid reaction with H2O2 in the liquid phase, catalyzed by hydrogen ions. The mechanism of NOx absorption into nitric acid solutions containing hydrogen peroxide can be finally represented as in Figure 6. Conclusions Kinetics of NOx absorption into aqueous and nitric acid solutions containing hydrogen peroxide was studied at 20 °C in a small laboratory packed column.
A mathematical model was developed of which the main features are simultaneous diffusion of the different components which remain at equilibrium everywhere in the gas phase including the gas film, grouping trivalent NOx, N2O3 and its hydrolyzed form HNO2, as a single effective species (N2O3*), and fast irreversible reactions in the liquid phase. These reactions are zero order with respect to H2O2 in a range of small concentrations, second order with respect to NO2, and first orders with respect to N2O3* and N2O4. Overall kinetic parameters for the absorption of different NOx species were determined. Taking into account the catalytic effect due to HNO3 on the NOx absorption in the presence of H2O2, the variation of these parameters with the HNO3 concentration was studied up to 4 M. It was found that the OKPs of tetravalent oxides NO2 and N2O4 remain constant and that the dissolution is likely to be controlled by the hydrolysis. The factor relative to N2O3* is regularly growing with the acidity due to the important contribution of gaseous HNO2 which undergoes during dissolution in liquid phase a fast oxidation with H2O2, enhanced by the nitric acid concentration. A satisfactory agreement was observed between the model predictions and the experimental observations for a large range of operating conditions. The kinetic parameters were also validated by means of absorption results obtained in a pilot-scale column and can therefore be used for the design of any absorption tower for the reduction of dilute NOx emissions by means of nitric acid solutions of H2O2. Acknowledgment Dr. D. Thomas is grateful to the FNRS (National Fund for Scientific Research of Belgium) for a grant of “Aspirant”. Nomenclature a ) effective gas-liquid specific interfacial area, m-1 A ) any absorbing component A ) overall NOx absorption efficiency ) [(pNOx)in (pNOx)out]/(pNOx)in b ) -(pNO)in/2(pO2)in cA ) bulk-liquid concentration of component A, kmol m-3 cAi ) interfacial concentration of component A, kmol m-3 dV ) incremental column volume, m3 DGA ) gas-phase diffusivity of component A, m2 s-1 DLA ) liquid-phase diffusivity of component A, m2 s-1 EA ) enhancement factor of component A G ) volumetric gas flow rate, m3 s-1 Ha ) Hatta number (see definition in Tables 1 and 2) HA ) Henry’s constant for component A, m3 Pa kmol-1 k1 ) third-order reaction rate constant for the oxidation of gaseous NO, Pa-2 s-1
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3321 k1A ) first-order rate constant, s-1 k2A ) second-order rate constant, m3 kmol s-1 kGA ) gas-phase mass-transfer coefficient for component A, kmol m-2 Pa-1 s-1 kLA ) liquid-phase mass-transfer coefficient for component A, m s-1 K2 ) equilibrium constant defined by pN2O4/pNO22, Pa-1 K3 ) equilibrium constant defined by pN2O3/pNOpNO2, Pa-1 L ) liquid flow rate, m3 s-1 M ) molarity of nitric acid solution, kmol m-3 n ) number of experiments OF ) objective function to minimize OKP ) overall kinetic parameter OR ) experimental oxidation ratio of NOx in the gas phase ) (pNO2*)/(pNOx) pA ) bulk-gas partial pressure of component A, Pa piA ) interfacial pressure of component A, Pa R ) gas constant, m3 Pa kmol-1 K-1 RA ) absorption rate of component A, kmol m-2 s-1 T ) temperature, K S ) absorption selectivity of tetravalent nitrogen oxides ) [(pNO2*)in - (pNO2*)out]/[(pNOx)in - (pNOx)out] XNO ) fractional conversion of NO ) [(pNO)in - (pNO)out]/ (pNO)in
ww ) kGNO2 + 4kGN2O4K2pNO2 + kGN2O3K3pNO xx ) kGN2O3K3pNO2 yy ) kGN2O3K3pNO zz ) kGNO + kGN2O3K3pNO2 Subscripts exp/calc ) experimental/calculated value in ) inlet of the elementary volume or of the column out ) outlet of the elementary volume or of the column Greek Letters δ ) gas film thickness, m ξ ) dimensionless distance inside the gas film
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Received for review July 22, 1996 Revised manuscript received November 4, 1996 Accepted May 13, 1997X IE960436G X Abstract published in Advance ACS Abstracts, July 1, 1997.
