Environ. Sci. Technol. 1991, 25, 2065-2070
Kinetics and Transport Parameters for the Fixed-Bed Catalytic Incineration of Volatile Organic Compounds Albert C. Frost, John E. Sawyer, and Jerry C. Summers Allied Signal Inc., Tulsa, Oklahoma 74104
Yatish 1.Shah* and Carlos G. Dassori College of Engineering and Applied Sciences, The University of Tulsa, Tulsa, Oklahoma 74104
rn The accurate sizing of a commercial catalytic incinerator from laboratory data requires a comprehensive mathematical model for the reactor. Allied Signal has developed one such model, which is capable of (a) predicting Langmuir-Hinshelwood rate constants and the alumina layer mass-transfer coefficient through a nonlinear regression fitting of the experimental data obtained in a laboratory adiabatic, fixed-bed reactor and (b) sizing a commercial reactor for the desired performance for given sets of kinetic and transport parameters. The model considers axial dispersion of both mass and heat as well as mass-transfer resistance a t the gas-solid interface. The mathematical model correlated the experimental data for the conversions of n-hexane, n-octane, n-decane, and n-dodecane well over wide ranges of superficial gas velocities, bed depths, temperatures, and inlet concentrations. Introduction Catalytic incineration has become a desirable way to control the emission of volatile organic compounds (VOCs). Its relatively low operating temperature requires less fuel and less expensive materials of construction than does thermal incineration. The proper design of a fixed-bed reactor for catalytic incineration requires the knowledge of kinetic and transport parameters, and an appropriate mathematical description of the reactor behavior. This description has usually been in the form of a simple isothermal model having a single global rate constant ( I ) . A more sophisticated model is presented in this paper that incorporates a Langmuir-Hinshelwood kinetic expression, a bulk film mass-transfer coefficient for the gas flowing around the catalyst pellets, a solid mass-transfer coefficient for any layer of refractory support (e.g., alumina) that may be covering the noble metal, and the dispersion coefficients for the mass and heat along the length of the reactor. The model can also be modified slightly to describe these same rate processes in a monolithic bed. This model is used to estimate four Langmuir-Hinshelwood constants and the mass-transfer coefficient for the alumina layer covering the platinum from laboratory temperature-conversion data for n-hexane, n-octane, ndecane, and n-dodecane. The curves generated by the model using these derived rate constants closely match the experimental curves for conversions over a wide range of space velocities, bed depths, and temperatures. Such a capability makes the model a valuable tool for predicting the performance of commercial reactors. Mathematical Model The present model for the fixed-bed reactor containing spherical particles is somewhat similar in character to the one presented by Carberry and Wendel (2). It incorporates
* Present address: College of Engineering, Drexel University, Philadelphia, PA 19104. 0013-936X/91/0925-2065$02.50/0
a different fluid-solid mass-transfer mechanism and uses simpler heat equations, which reduces the number of unknown constants that need to be derived from the data. It makes the following assumptions: (1) The reactor is operated under adiabatic and steady-state conditions. (2) There are no radial concentration or temperature gradients. (3) The axial mass and temperature dispersions are characterized by the usual dispersion coefficients. (4)The mass-transfer resistance through the gas film surrounding each catalyst particle is characterized by the usual bulk film mass-transfer coefficient. The corresponding heat-transfer resistance is neglected. (5) The noble metal is deposited on a refractory oxide (e.g., alumina) support as a single film. This film can reside either on the outside surface of the support or at some discrete distance within the support. The mass transfer through the resulting alumina layer is described with a solid mass-transfer Coefficient. The corresponding heattransfer resistance is once again neglected. (6) The intrinsic reaction rate for the oxidation of the VOCs follows the Langmuir-Hinshelwood kinetic expression. The oxygen concentration is assumed to be in excess and is not explicitly incorporated into the expression. (7) The heat of reaction for the VOCs and the heat capacity of the gas stream are independent of temperature. (8) The temperature dependence of the gas flow rate, concentration, and density are governed by the ideal gas law. (9) The temperature dependence of the bulk film mass-transfer coefficient follows the relationship described by Thoenes and Kramers (3). (10) As shown by Oh et al. ( 4 ) for an effective diffusion coefficient in an alumina particle, the temperature dependence of the solid mass-transfer coefficient is assumed to be proportional to the absolute temperature raised to the 1.4 power. Figure 1 illustrates a schematic of the concentration profile across the exterior bulk gas film and the alumina layer that covers the film of noble metal. It is worth noting that while the alumina layer may slow down the rate of a simple first-order reaction, it may actually increase the rate of a Langmuir-Hinshelwood reaction, particularly for the case where the reactant is strongly adsorbed (5). Governing Equations With the previous assumptions, a differential material balance for the reacting VOC species can be expressed as
At steady state, the mass-transfer rates can be equated to the rate of reaction as
0 1991 American Chemical Society
k,a,(C - C*J = D,a\/L*(C*, - C,)= (1 - c)wrA (2) Environ. Sci. Technol., Vol. 25, No. 12, 1991 2065
Pe, = u&/D.
r,
(23)
= (1 - f)wrAL/Cnuo
(24)
I? = P/P"
(25)
a = u/u"
(26)
Peh = p°CpunL/X,
(27)
kg = kg/kog
(28)
D,= D,/Dos
(29)
which leads to the dimensionless expressions G A S P H A S E ALUMINA LAYER Flpure 1.
alumina.
Mass transfer resistances across the bulk gas film and the
where the intrinsic kinetic reaction rate is expressed by a Langmuir-Hinshelwood equation of the type
a,kg(C*, FA =
- C) = Ba,(C. - C*J
= iA
(31)
+ 8)) exp(y'/(l + S))]*
(32)
Da(1 - c.1 exp(-y/(l [1 + a ( 1 - C,)
with the boundary conditions at z = 0 (l/Pe,)(dc/dz) Equations 1-3 are subjected to the boundary conditions at x = 0 u(Co- C) = -De (dC/dx) (4)
at x = L
dC/dx = 0
at z = 1
(dT/dx) = 0
(7) (8)
Finally, the continuity equation leads to (d/dx)(pu) = 0
(9)
The above equations can be dedimensionalized by using the expressions
c = (C,
- C)/C0
(10)
C. = (Cn - CJ/Co
(11)
c* = (Co - C*.)/Cn
(12)
2
= x/L
2066
(13)
a, = k;a,L/uo
(14)
Bi = D*,a',.L/L*u,
(15)
D*. = D,'"(T/FF'
(16)
R = k',Co
(17)
Da = (1 - t)wk,L/uo
(18)
Y = E/R,To
(19)
Y' = q/R,To
(20)
8 = (T- Tn)/To
(21)
B = (-~R)co/PocpTo
(22)
Environ. Sci. Technol., Vol.
25. No. 12. 1991
(34)
Similarly, the differential heat balance equation can be expressed as subject to the boundary conditions
at z = 0
pa8 = (1 /Pe,)(dS/dz)
at z = 0
at x = L
dC/dz = 0
(33)
(5)
The differential heat balance for the reactor can be expressed as
subjected t o the boundary conditions at x = 0 pcpu(To - 7') = -A, (dT/dx)
=UC
d8/dz = 0
(36) (37)
Finally, the continuity equation can be expressed as (d/dz)(pa) = 0 (38) The temperature dependence of the gas density is based on the ideal gas law. The gas-solid mass-transfer coefficient, the gas viscosity, and the temperature coefficient for the VOC-air diffusivity are calculated from correlations presented by Theones and Kramers (3),Reid et al. (6),and Benton and Hewitt (3, respectively. Mass and heat Peclet numbers for the reaction conditions examined in this study are based on the particle diameter and are estimated to have a value of 2 (8). The above equations do not consider the effect of temperature change on the gas-phase concentration. The equations are strictly appropriate only when heat generation and temperature rise are small. In the present analysis the above described model is fitted to the experimental temperature-conversion data by optimizing tried values for the four rate parameters in the LangmuirHinschelwood kinetic expression and for the mass-transfer coefficient for the alumina layer covering the noble metal. IMSLs DBCLSF optimization routine is used to obtain the nonlinear regressive fitting along the entire range of the temperature-conversion curve. This optimization routine relies on IMSLs DBVPFD boundary value problem solver routine to find each of the calculated conversions for each set of reiterated rate constants. The calculations start with a set of values for the parameters and the system of differential equations is solved by DBVPFD mathematics routine. As a result, the exit conversion that satisfies the boundary conditions is obtained. These results are taken by the mathematics subroutine DBCLSF, which is essentially the implementation of the Marsquordt algorithm, and a better set of param-
PREHEAT
CATALYST REACTOR
U
I
3 I
TO VENT
I
I
FIO
t T o w
Flgure 2. Experimental apparatus.
eters is computed. The process is repeated until no further improvement of the fitting is found. The result is the set of parameters that best fit the data with the predictions of the model. Once the five rate constants are found in this manner, they can be fed back into the program to determine design parameters for commercial reactors. These design parameters can be either the space velocity required for a new reactor to attain a targeted conversion or the conversion that will result from an existing reactor having a fixed catalyst volume and a fixed volumetric flow rate. The form of the model that solves for the space velocity of a new commercial reactor uses both routines and reiterates in reactor diameter (for a given bed depth) until the prescribed destruction efficiency is achieved. The form of the model that solves for the destruction efficiency of an existing commercial reactor requires only a single pass through the DBVPFD program. Experimental Section Reactor System. A schematic of the experimental system is outlined in Figure 2. It shows that metered air and nitrogen streams are passed through water and liquid hydrocarbon saturators, respectively, before they are combined with an additional nitrogen stream to form the inlet feed stream to the reactor. The relative amounts of these streams are such that the combined feed stream has a 50% relative humidity at room temperature and contains 12% oxygen. The total volumetric flow rate is checked with a piston-type flow rate calibrator (Tracor Atlas, Inc.). The water-saturated air stream and the additional nitrogen stream are passed through a preheater before they are joined by the hydrocarbon-saturated nitrogen stream at the inlet of the reactor. The combined stream then passes down through the catalyst bed (typically 1.0 in. in diameter and 4.0 in. long). The effluent stream is cooled through a coil before it is split into two parts; one part goes directly to vent and the other to a sample pump that pressurizes it to 6 psig. A small portion of this pressurized stream is fed to the FID, while the rest is passed through a back-pressure regulator and out to vent. This arrangement gives a rapid analytical response and a means of keeping the pressure at the outlet
of the reactor to very close to ambient pressure. Run Procedure. The FID reading for the inlet hydrocarbon concentration is obtained by analyzing the inlet stream as it is bypassed around the reactor. During this time the preheater and reactor are heated to approximately 200 O F . The run starts when the bypassed fluid is directed through the reactor and the temperatures of the preheater and reactor are increased at a rate of 85 "F/h. The temperatures at the top (inlet), wall, and bottom (outlet) of the bed are recorded with the corresponding FID reading at every 25 O F temperature rise. The outlet temperature is adjusted in respect to the inlet temperature to reflect the expected temperature rise resulting from the oxidation of the VOCs, while the wall temperature is maintained at an intermediate temperature. Most of the runs are made at low VOC concentrations and, hence, with temperature rises that are less than 75 O F . The experimental data were obtained for n-hexane, n-octane, n-decane, and n-dodecane with a 2-4-in. catalyst bed, at 15000-45000 h-' GHSVs and in the temperature range of 260 to 750 O F . The inlet concentration was varied from 37 to 234 ppm. Catalyst. The catalyst was in the form of a 0.12-in.diameter alumina spheres with the platinum distributed as a sharp Gaussian curve slightly below the outer surface, with a resultant average layer loading of approximately 0.2 wt % platinum. The fresh BET surface area was 100 m2/g and the fresh pore volume totaled 1.09 mL/g, 69% of which was wider than 1000 A. It was activated by heating to 1300 O F for 16 h in air that had been saturated with water at room temperature and subsequently subjecting it to a 950 O F , 2000 ppm, 67 vol % propylene/33 vol % propane stream for 4 h. Results Figure 3 shows the fits of the mathematical model to the n-decane and n-dodecane data a t 15 000 h-l GHSV. The value for the transport parameter DFfu \/L* was determined by applying the model to the experimental data for n-dodecane for the conditions where mass transfer is the rate-controlling step. This is at the high-temperature plateau region of the temperature-conversion curve, where the kinetic rate is assumed to be infinitely fast and only Environ. Sci. Technol., Vol. 25, No. 12, 1991
2067
Table I. Derived Rate Constants from Data Shown in Figure 8 (GHSV = 30000 h-l) component
k,, m3/kg.s
n-C6
9.2 x 103 6.2 x 104 5 . 2 x 105
fl-C8
nGo n-G2
E, kJ/kmol
2.1 x 2.9 x 3.0 x 4.0 x
1.0 x 107
104 104 104 104
k'*, m3/kmol
1.6 10.0
5.6
X
lo2
10.0
qv kJ/kmol
D,lefa\/L*, s-l
4.7 x 104 3.3 x 104 1.1 x 104 1.2 x 104
127.7 110.4 96.4 88.0
GHSV=15000 h - '
~.
Model Prediction Experimental Data
-
,
I
-7 I , , I I
,
,
Intel Temperature(K) Figure 3. Fit of n-decane and n-dodecane data with model.
the bulk gas film and alumina layer mass-transfer steps control the reaction process. Since the bulk gas film mass-transfer coefficient is estimated from the literature, the alumina layer mass-transfer coefficient is the only unknown in the solution of the mathematical equations. The value for D p f u:/L* obtained in this manner was 88 s-l at 225 O F , which was in good general agreement with a 190 s-l; a value calculated from the effective diffusivity for CO in a Ptlalumina catalyst reported by Oh et al. ( 4 ) . It should be mentioned that Diefa\/L* is estimated from a small difference between two large numbers (the predicted conversion minus the experimental conversion) and consequently is sensitive to experimental error. While this experimental error affects the absolute magnitude of D p f u 'JL*, the absolute magnitude has a negligible effect on the fitting of the data below the plateau portion of the temperature-conversion curve. It is difficult and time consuming to solve for DFfu\/L* simultaneously with the four Langmuir-Hinschelwood constants. The reason for this is shown by Figure 4 which plots the absolute value of the mean relative deviation of the fit [(predicted conversion for any assigned value for Dsrefa'v/ L* - experimental conversion)/ (experimental conversion)] as a function of different assigned values for the alumina mass-transfer coefficient for n-dodecane. When this coefficient is set at a value lower than the exact calculated value (indicated by the sharp minimum in Figure 4), it itself is rate limiting and has a pronounced effect on the mean relative deviation. However, when the coefficient is set at a value higher than the calculated value, it quickly loses its rate-determining influence over to the bulk gas film coefficient, and the mean relative deviation starts to level off. This resulting plateau causes an unacceptable large increase in computer time when attempts are made to calculate the alumina mass-transfer coefficient simultaneously with the four Langmuir-Hinshelwood constants. Since the major component of the diffusion through the alumina layer is believed to be bulk film diffusion through the macropores ( 4 ) , the alumina layer mass-transfer coefficients for the other hydrocarbons were estimated by multiplying the coefficient for the n-dodecane by the bulk 2088
Environ. Sci. Technol., Vol. 25, No. 12, 1991
Diffusion Resist.Parameter [log(Df'a;/L*)] Figure 4. Effects of changing Diefa',lL perimental values.
on predicted minus ex-
- Model Prediction
4" - 15K 70
a
60
2" - 45K 30 20
i -
10 -
0
/ /
LA,, , - , Normal Hexane
28, 26
-
,
I 1
Hexane
24-
Q
22-
's
To
8 la-
CO
L6-
g
1.4
-
700 F 100 ppm
d p = 118"
50
40
oa-
V
a4 -
30
0.6
10
2o
4
I
350
450
550
Inlet Temperature
650
750
(K)
Figure 8. Fit of n-hexane, n-octane, ndecane, and ndodecane data with model at GHSV = 30000 h-'. 90
-
80
-
4 in.-13.06 slpm 234.25 ppm
4 in.-24.78 slpm 214.69 ppm
70-
8
60-
6
50-
6
40-
.3
6
10
0
ExperimentalData
I
changes in the adsorption constants were less dramatic. The apparent activation energies ( E )listed in Table I were 50-70% lower than the approximately 74 kJ/mol activation energy derived from simple power law rate expressions (9, 10) for alkanes higher than butane. Such discrepancies could be expected in view of the fact that the apparent activation energy in the Langmuir-Hinshelwood equation is separated from the temperaturedependent adsorption effects present in the dnominator, whereas the activation energy in the power law equation incorporates these temperature-dependent adsorption effects. The adsorption constant present in the denominator of the Langmuir-Hinshelwood equation used in this paper incorporates terms for the adsorption of both the hydrocarbon and oxygen. Consequently, its value by itself has no clear meaning. However, it is worth noting the general agreement between the reported values for the apparent heat of adsorption, q , listed in Table I and the heats of condensation for n-hexane and n-octane. The lower q values for the n-decane and n-dodecane may be due to a large experimental error associated with the scarcity of low-temperature, low-conversion data for these two species. The model described in this article is a predictive model, since it is developed from the first set of principles of mass and energy balances. The fit of the model to the experimental data with two different flow rates through two different bed volumes (see Figure 5), with two different flow rates through the same bed volume (see Figure 7 ) ,and with other data a t a 15000 h-l GHSV supports the predictability of the model. Additionally, the rate parameters obtained in this study compare well with the values reported in the literature. The model can be used to design a commercial reactor, as long as the assumptions made in the development of the model are valid. Unfortunately, at the present time we do not have data from a commercial operation to assess the validity of this claim. Conclusions The mathematical model developed to extract four Langmuir-Hinschelwood rate constants and an alumina layer mass-transfer coefficient fitted the experimental data well for n-hexane, n-octane, n-decane, and n-dodecane over wide ranges of conversions for different bed depths and superficial velocities. Glossary a"
Bi
specific interface area, m-l defined in eq 15 Environ. Sci. Technol., Vol. 25, No. 12, 1991 2069
C
c
Db
DO
DPf D,
D*, D
L* Peh
Pem
TO
P’e f
U UO
ii Ob X
z
IMSL DBSLSF, DBVPFD GHSV
voc
2070
gas-phase reactant concentration in bulk gas, kmol/m3 dimensionless concentration defined by eq 10 inlet concentration, kmol/m3 heat capacity, kJ/kg.K gas-phase reactant concentration a t the active catalyst film, kmol/m3 dimensionless concentration defined by eq 11 dimensionless concentration defined by eq 12 diameter of catalyst particle, m dimensionless parameter defined by eq 18 diameter of catalyst bed, m axial dispersion coefficient for mass, m2/s reference constant in eq 16 effective diffusion coefficient in alumina layer, m2/s dimensionless parameter defined by eq 16 apparent energy of activation, kJ/mol heat of reaction, kJ/kmol frequency factor, m3/kmol frequency factor, m3/kg.cal.s gas-phase mass-transfer coefficient, m/s dimensionless gas-phase mass-transfer coefficient defined by eq 28 gas-phase mass-transfer coefficient for inlet gas, m/s reactor length, m alumina layer thickness, m Peclet number defined in eq 27 Peclet number defined in eq 23 apparent heat of adsorption, kJ/kmol universal gas constant, 8.313 kJ/kmol.K rate of reaction, kmol/g.cal.s dimensionless parameter defined by eq 24 temperature, K inlet bed temperature, K reference temperature, K, in eq 16 superficial gas velocity, m/s superficial velocity of inlet feed gas, m/s dimensionless velocity, defined by eq 26 volume of catalyst bed, m3 axial direction, m dimensionless axial direction defined by eq 13 mathematics library for Fortran subroutine for mathematical applications two subroutines of the above mentioned library
gas hourly space velocity volatile organic compound
Environ. Sci. Technol., Vol. 25, No. 12, 1991
Greek Characters dimensionless parameter defined in eq 14 dimensionless parameter defined in eq 22 dimensionless parameter defined in eq 19 7’ dimensionless parameter defined in eq 20 Y € bed voidage, dimensionless axial dispersion coefficient for heat, kJ/m2-s A8 density, kg/m3 P dimensionless density as defined by eq 25 P density of inlet feed gas, kg/m3 Po 0 dimensionless temperature defined by eq 21 0 active catalyst loading of noble metal, kg/m3 of catalyst D parameter defined in eq 17 Registry No. n-C6,110-54-3; n-Cs,111-65-9; n-C,,, 124-18-5; n-Clz, 112-40-3.
Literature Cited (1) Chen, J.; Heck, R.; Burns, K. Commercial Development of Oxidation Catalyst for Gas Turbine Cogeneration Applications. Presented a t the 82nd Annual Meeting and Exhibition, Air and Waste Management Association,Anaheim, CA, 1989. (2) Carberry, J. J.; Wendel, M. M. A Computer Model of the Fixed Bed Catalytic Reactor: The Adiabatic and Quasiadiabatic Cases. A I C h E J . 1963, 9(1), 139. (3) Thoenes, D.; Kramers, H. Mass Transfer from Spheres in Various Regular Packings to a Flowing Fluid. Chem. Eng. Sci. 1958, 8 , 271. (4) Oh, S. H.; Baron, K.; Sloan, E. M. Effects of Catalyst Particle Size on Multiple Steady States. J . Catal. 1979, 59, 272. (5) Morbidelli, M.; Servida, A. Optimal Catalyst Activity Profiles in Pellets. 2. The influence of External Mass Transfer Resistance. Ind. Eng. Chem. Fundam. 1982,21, 278. (6) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. T h e Properties of Gases and Liquids, 2nd ed.; McGraw-Hill: New York, 1987. (7) Benton, C.; Hewitt, L. Prediction of Fluid Properties, 1st ed.; Plenum Press: New York, 1985. (8) Froment, G.; Hofmann, H. In Chemical Reaction and Reaction Engineering; Carberry, J. J., Varma, A. M., Eds.; Dekker: New York, 1987; pp 391-392. (9) Yu Yao, Y. F. Oxidation of Alkanes over Noble Metal Catalysts. Ind. Eng. Chem. & EC Proc. Res. Dev. 1980,19, 293. (10) Schwartz, A.; Holbrook, L. L.; Wise, H. Catalytic Oxidation Studies with Platinum and Palladium. J . Catal. 1971,21, 199.
Received f o r review May 13, 1991. Accepted July I, 1991.
