999
Ind. Eng. Chem. Res. 1992,31,999-1007 ture. Stud. surf. sci. &tal. 1986b,28, 859. Inui, T.; Makino, Y.; Okazumi, F.; Nagano, S.; Miyamoto, A. Selective Aromatization of Light Paraffims on Platinum Ion-Exchanged Gallium-Silicate Bifunctional Catalysts. Znd. Eng. Chem. Res. 1987a,26,647. Inui, T.; Okazumi, F.; Tarumoto, J.; Yamase, 0.; Matsuda, H.; Nagata, H.; Daito, N.; Miyamoto, A. Highly Selective Synthesis of High Octane-Number Gasoline from Light Olefins on Fe-Silicates. J. Jpn. Pet. Znst. 1987b,30,249. Inui, T.; Ishihara, Y.; Kamachi, K.; Matsuda, H. Pt Loaded High-Ga Silicates for Aromatization of Light Paraffm and Methane. Stud. Surf. Sci. Catal. 1989a,49, 1183. Inui, T.; Matsuda, H.; Takeguchi, T.; Chaisupakitsin, M. Highly Selective Conversion of Methanol to Aromatics on H-Ga-Silicate
Catalysts. Proceedings of the 2nd Japan-Korea Symposium on Catalysis. Tokyo, Institute of Technology: - . 1989;. Tokyo __ Tokyo, - . i989G; p is. Oblad, A. G.; Mills, G. A.; Heinemann, H. Polymerization of Olefins to Liauid Polvmers. J . Awwl. Chem. 1958,6. 341. Poutsma, M. I;. Mechanis'tic Considerations of Hydrocarbon Transformations Catalyzed by Zeolites. ACS Monogr. 1976,171, 437. Shibata, M.; Kitagawa, H.; Sendoda, Y.;Ono, Y.Transformation of Propene into Aromatic Hydrocarbons over ZSM-5 Zeolites. Stud. Surf. Sci. Catal. 1986,28, 717.
Received for review August 21, 1991 Accepted December 3, 1991
Mathematical Modeling of Methane Combustion in a Fluidized Bed Donald R. van der Vaart Virginia Polytechnic Institute and State University, Pennwood Laboratory, Route 9,Box 103, Charlottesville, Virginia 22902
The homogeneous combustion of methane in a fluidized bed is described using three increasingly complex reactor models which can be identified by their key features: (1) two phases with constant bubble size, (2) three phases with constant bubble size, and (3) three phases with bubble growth. A simple plug flow model is used to describe the freeboard region separately. T o compare the predicted methane concentration profiles with measured values, existing theory for in-bed gas sampling is considered. Without resorting to the use of adjustable parameters, the third model provides the best agreement between theory and experiment. Two factors were identified as crucial to the success of this model: (a) the accurate treatment of the time gas in the bubble needs to reach the bed temperature and (b) the change in the rate of mass transfer between the bubble and dense phases as the bubbles grow.
Introduction The nonideality of fluidized bed reactors has led to the development of a large number of modeling approaches. While many reactor models have been proposed based on these approaches, virtually all have been developed or verified for applications involving catalytic gas-phase reactions. In these cases, little or no reaction is assumed to take place in the bubble phase due to the small amount of catalyst present there. Hence, the overall conversion depends strongly on the rate of mass transfer between the emulsion phase, where gas-solid contacting is efficient, and the bubble phase. The homogeneous combustion of gas in a fluidized bed presents dramatically different characteristics since the bubble phase, with its small volumetric fraction of solid particles, now presents a more favorable reaction volume to the flammable mixture than does the cloud or emulsion phase. Because of this reversed role of the bubble and dense phases as compared with solid-catalyzed systems, the gas combustion system should provide a useful test of fluidized bed reactor models. This article presents a comparison of three reactor models with experimental data from the fluidized bed combustion of methane. Qualitatively, the combustion of methane behaves similarly to the propane system described by van der Vaart and Davidson (1986). Combustion is erratic at lower temperatures with explosions occurring in the freeboard as the bubbles containing the fuel gaslair mixture erupt from the surface. At higher temperatures, burning appears to occur within the bed in a quiet, stable manner. For methane combustion, Rao and Stepanchuk (1967) and Sadilov and Baskakov (1973) measured axial temperature gradients in the freeboard over a fluidized bed of sand. The latter study, in which an extremely fine, bare
thermocouple arrangement was used, reported much higher excursions, some even above the calculated flame temperature under the experimental conditions. A series of Soviet investigations on the behavior of methane combustion followed this work. More extensive temperature measurements by Baskakov and Makhorin (1975) and Makhorin and Glukhomanyuk (1975) were made in an attempt to measure temperature gradients caused by inbed ignition. At a bulk bed temperature of 1100 O C , temperature maxima were measured as high as 1480 "C near the distributor for a system with dp = 0.25-1.5 mm. These studies led to the development of a single-phase model by Yanata et al. (1975), who attempted to correlate the experimental data. More recently, Khinkis (1982) used a two-phase model to predict both temperature and concentration profiles for this system although no experimental resulta were compared with the model calculations. Experimentally, the gaseous combustion system is difficult to study since the traditional problems of measuring the gas-phase concentrations in the bubble/cloud and the emulsion phases of the reactor are now coupled with the large temperature gradients which could exist in these phases. At present, any experimental approach must be content with measuring the phenomenon through indirect means such as those described here.
Experimental Section A schematic of the experimental reactor is shown in Figure 1. To limit catalytic effects, all-ceramic materials were used in the reactor construction. The reactor was a 99.8%pure alumina (McDanel Refractory Co.) tube (7-cm i.d.) fitted with a 1-cm-thick,7-cm-0.d. porous alumina disk (fabricated by the Selee Corp.) as distributor. The disk was cemented inside the tube using a high-temperature
0 1992 American Chemical Society 0888-5885/92/2631-0999$03.~0/0
1000 Ind. Eng. Chem. Exhmst S h m u p
Res., VoL 31, No. 4,1992 L,
0
0.03
0.1s
0.1
Wpmw . h1
b
e.1
M.Mk(r (I)
*.a .
.
Figure 2. Concentration profdes of stable chemical species: TM = 1223 K, U - U, = 0.2 m/s, H, = 0.077 m, 3W35E-pm Band Figure 1. High-tampmature fluidized bed reactor.
cement (Sauerekn A w d Adheaive Cement, No.2 Paste) 80 that the top of the distributor was just above the bottom of the heating coils of the furnace. The plenum chamber was filled with a-alumina pellets of low surface area (3/ 16-in. UCI T-375) to reduce dead volume. Heating was provided hy a high-temperature split-tube furnace (Lindberg Model No.55332) with a single heated zone 46 cm long. A ceramic-sheathedtypeK thermocouple was placed in the bed approximately 4 cm above the distributor to measure the bed temperature. The temperature measured by this thermocouple, denoted by TM,represents an average temperature of the fluidizinggas in the bubble, cloud, and emulsion phases and the solid particles. Gas samples were drawn from various points along the axial direction and at the midway point between the wall and the centerline in the radial coordinate. An air-cooled quartz probe was used consisting of three concentric tubes. The gas sample was drawn through the innermost tube while cooling air (>0.7 L/s corresponding to a linear velocity of 21 m/s along the outside of the inner sampling tube) flowed down along the sample tube and up the outermost tube. The temperature of the exhaust gas was measured to be 130 O C . Under these conditions the reactions occurring in the sampled gas were assumed to be quenched upon entering the probe. A gas chromatograph (Hewlett-Packard5890) equipped with an electronic integrator ("3996A) was used to analyze for C&, CO, CO,, N2,and O2 using a two-column isolation technique. The bed material was extremely low-surface-area sand of high purity (99.6 w t 70SiOJ obtained from US. Sica Co. and sieved to 300-355 pm. An average particle diameter of 327 pm was used in all calculations. Using the correlation recommended by Broughton (1974), the minimum fluidizing velocity, U,, was calculated as a function of the bed temperature and was found to be approximately 0.04 m/s over the temperature range of this study. The bed height at m i n i u m fluidizing velocity was seen to be equal to the slumped-bed height, which was 0.077 m. Integration of the system of differential equations r e sulting from each model was performed using Gear's m e thod as available from IMSL as DIVPAG. Results A series of measmmenta were completed a t three bed temperatures (Le., 850,950, and 975 'C) all at an excess fluidizing velocity (U- U,) of 0.20 m/s (evaluated at the bed temperature). Only a stoichiometric mixture of methane in air was used in this study. The concentration profiles of each of the stable species are shown in Figure
Figure 3. Comparison of measured methane concentration protile with twmphase model: U - U, = 0.2 m/a, H, = 0.077 m, 3 W 355-run sand.
2 for a bed temperature of 950 "C. The water concentration was calculated by difference, assuming complete combustion. It should be noted that house air was used in these experiments and that argon is known to elute at the same retention time as oxygen. The effect of bed temperature on methane conversion is shown in Figure 3. In a separate seriea of experiments, a 3-mm-0.d. stainleas steel-sheathed thermocouple was used to measure the temperature gradients in the axial direction. Under conditions of over-bed ignition (i.e., TM = 850 "C), the freeboard temperature was measured to be 20 O C higher than TM with fluctuations of i 3 OC while a temperature 10 "C (il"C) helow TM was measured 0.01 m above the distributor. This agrees, qualitatively, with the previous studies and implies that combustion was occurring near the surface of the bed under these conditions. At 950 OC, a temperature rise of 6 OC was observed from 0.01 to 0.05 m above the distributor. A s i m i i gradient was measured at T w = 975 "C now from 0.01 to 0.03 m above the distributor. This indicates that combustion was occurring lower in the bed as TM was increased, which agrees with the concentration profiles given in Figure 3.
Reactor Models For obvious reasons, most fluidzed reactor models are intended to describe commercial-scale reactors. These beds are generally much deeper than laboratory unita and, coupled with other design differences, exhibit differences in their bubble characteristics. Specifically, for all but the larger particle size systems (dp> 1mm),bubbles in commercial reactors can reach a maximum stable bubble size
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1001 Table I. Expressions Used in All Models Daram eter
expression
rc,- = bubble radius at T," Ubr = relative rise velocity of bubbleb
U,, = absolute rise velocity of bubbleb
H = expanded bed heightb
(T.4)
2) (-)
Dab0Sg0.25
K b = bubble-to-emulsion mass-transfer coeffb
= 4*5(
+
5.85
(T.5)
K, = cloud-to-emulsion mass-transfer coeffe
(T.6)
6 = fraction of bed occupied by bubblesb
(T.7)
h, = gas-to-particle heat-transfer coeffd
hb = bubble-to-emulsion heat transfer coefC T
= residence time of particle in bubblee
rdd
= cloud radiusb
T
= (2.3rb/g)1/2
(T.10) (T.11)
"Darton et al., 1977. bDavidson and Harrison, 1963. 'Kunii and Levenspiel, 1990. dRanz and Marshall, 1952. 'Toei et al., 1972.
before they have traversed a significant fraction of the bed height. Hence, provided that most of the conversion does not occur in the bottom portion of the bed, the use of an average bubble size to describe these systems is reasonable. In contrast, bubbles in laboratory units experience continual growth due to coalescence throughout the reador. Clearly, the use of an average bubble size can only be a first approximation in these systems. If laboratory reactors are to be used to measure kinetic data for use in scale-up, this distinction could be important. Three models are presented here with the following gross characteristics: (a) two phases, bubble and emulsion with constant bubble size; (b) three phases, bubble, cloud, and emulsion with constant bubble size; and (c) three phases, bubble, cloud, and emulsion with variable bubble size. Common to all the models tested is the assumption of plug flow for the emulsion, bubble, or bubble/cloud phase. Additional assumptions common to all three models are (i) the bubble phase is nonisothermal, (ii) the initial temperature of the bubble gas is assumed to be 400 "C (the temperature measured in the plenum during operation), (iii) the temperature of the solids is constant and uniform throughout the bed, (iv) radiative heat transfer between the gas and the particles is ignored, (v) gas jets formed at the distributor are ignored (vi) the distribution of gases between the bubble and cloud/emulsion phases is governed by the two-phase theory of fluidization, and (vii) the bubbles and their clouds are spherical. Table I lists the specific relations used to describe the fluidized bed properties. Note that, for the two constant bubble size models (a and b), none of the quantities in the table are functions of x . Since the bubble gas temperature could vary dramatically from 400 "C to well over the bed temperature, temperature-dependent correlations were used to describe the physical properties of the gas. The use of a constant bubble radius often takes the form of an adjustable parameter in a variety of fluidized reactor
models. For the purpose of this comparison of models, the constant bubble size used in the fist two models was taken as an average value, (rb), to be calculated a priori. While different averages are possible, van der Vaart (1988) showed that, at least for propane combustion, bubble ignition depended on bubble residence time. Therefore, an average bubble radius, ( r b ) , was determined whose residence time equaled the average residence time, t, of bubbles which grow according to eq T.l.
To integrate the right-hand side (RHS) of eq 1, the expanded bed height must first be determined by eq T.4 (e.g., H was 0.125 m for the conditions of this study). The average bubble radius, ( r b ) , was then defined as that bubble whose absolute rise velocity, (Uabe),was H / f . Strictly speaking, ( r b ) should be calculated as a function of the bubble temperature since U - Urn,would vary accordingly. It will be shown that the bubble temperature does not reach Tbedimmediately upon entering the bed. The estimation of what the excess fluidizing velocity would actually be under such a transient condition would probably stretch the interpretation of the two-phase theory beyond ita bounds. For the purposes of this comparison, U - Urn,was assumed to be constant throughout the bed for all three models. Thus, ( r b ) was calculated to be 0.012 m at all three bed temperatures studied since U - U , was kept constant. It is interesting to note that, to the extent that bubbles seen bursting at the bed surface can be used to estimate bubble size, bubbles were estimated to be roughly 0.035-m i.d. at H = 0.125 m under the conditions of this study. The material and energy balances presented below will be used to describe the gas flow through the fluidized reactor from x = 0 to H. By way of defining the transition
1002 Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992
from the bubbling bed to the freeboard region ( x > H), M e r and Heertjea (1960) showed that the time-averaged void fraction of gas, e, increased rapidly as a function of the distance above H& To account for this increase within the framework of the models presented below, the void fiactions in the bubble, cloud, and emulsion phases where allowed to increase in a manner which correlates the data presented by Bakker and Heertjes (1960). Thus, an exponential decay in particle concentration was used for each phase from their values in the bed (i.e., 0.0015 for the bubble phase and 0.55 in the cloud and emulsion phases) to 0 at H. This was done for all three models for Hd < x C H. Finally, since each model will predict the concentration profile of methane in each of the phases treated (be it two or three), some method of mixing these individual concentrations must be used to calculate the predicted concentration of methane drawn by the sampling probe, thereby enabling the comparison of the predictions of the model with the experimental data. Intuition might suggest that the concentration determined by the probe is simply the weighted average according to the volumetric fraction of the various phases
0.04
0
1
\ 0
0.04
0.w
0.12
=R
(4) This expression predicts that the overall reaction rate is inversely proportional to the methane concentration. While this relationship is absurd in the limits, Dryer and Glassman (1972) noted the same dependence in a qualitative study of the induction phase. Equation 4 was used in all of the models discussed below for the experimental conditions shown in Figure 3. Unfortunately, the use of this global expression prevented the comparison of the experimental 02,CO, and COz profiles with the models. Clearly, a more complete reaction network would be warranted provided the reactor model shows merit. Two-Phase Model. This model is essentially the Davidson and Harrison (1963) model with the possible nonisothermality of the bubble-phase taken into account. It is assumed that the gas temperature in the emulsion
0.1
-
phase is constant. The methane molar balance in the bubble phase is Uabs dCb/dx = -&(Cb - c,) - Rb (5) while the energy balance over the bubble phase is v b m b
which is based on the time the probe spends in each phase. This “temporal” average reduces to the volumetric average (eq 2) for the special case when Urd = ubr. The same mixing average can be applied to the three-phase models (see the Appendix). Kinetics. Methane combustion has been extensively studied to the point that mechanistic reaction networks are available comprised of large numbers of elementary reactions. No attempt is made here to employ such a detailed reaction scheme within the reactor models described below. Instead, a global reaction rate expression for the disappearance of methane was sought which could adequately describe the overall combustion rate. Kozlov (1959) investigated methane combustion in small (empty) tubes (i.e., 1-5-mm id.) and developed the following global expression for the reaction of methane to carbon monoxide for both induction and postinduction phases
*
0416
Dlrtano a h tbo DLbrlk(.r (I) Figure 4. Comparison of measured methane concentration profde with three-phase model (constant bubble size): U U, = 0.2 m/s, H, = 0.077 m, 300-355-pm sand.
UabsVbCp,gPb d T b / h = for the two-phase system. However, Davidson (1984) showed that a more accurate averaging rule might be
0 ..,
- hb4?rrb2(Tb- T-)(6)
where T, is the bed temperature. Rather than using the heat transfer analogy of eq T.5, however, the heat-transfer coefficient, hbe,was calculated usingthe correlation of Toei et al. (1972) (eq T.9), who correlated their data for single A value of bubbles using both e,, = 1 X lo4 and 2 X 1.5 X 10” was assumed throughout this comparison although the resulta were not sensitive to eb in this range. The molar balance of methane in the emulsion phase is Ud d C , / h = -(1- 6)~dR - KbS(Ce - Cd (7) The coupled, differential equations (5-7) were numerically integrated for the initial conditions of the problem (initial mole fraction of methane in both phases equal to 0.0947 and To = 400 O C at x = 0). The results are compared to the experimental data for methane conversion in Figure 3. Both volumetric and temporal averages for the probe concentration are shown. Three-phase Model. Chavarie and Grace (1976) showed that eq T.5 overestimates bubble-to-emulsion phase mass transfer and that a more accurate estimate is given by including the cloud phase as proposed by Kunii and Levenspiel (1968). This introduces a more severe restriction to bubble-to-emulsion mass transfer because the cloud-phase gas remains associated with the bubble as shown by Davidmn and Harrison (1963). The additional phase adds the unknown, c&+which is given by the methane balance over the cloud: Uabs%nfVclddCcld/h = -V&bc(Ccld - c b ) - kc$dd(Ccld
- Ce) - emfVdd&ld
(8)
The methane balance in the bubble phase remains essentially unchanged from eq 5 after substituting C d for C,. Similarly, the emulsion-phase methane balance is unchanged from eq 7 with the mass-transfer coefficient now given by K, (given by eq T.6) and with Cd instead of Cb The bubble-phase energy balance is identical to eq 6. The concentration profdea of methane predicted by this model are shown in Figure 4 for the temperatures studied. Three-phase Model with Bubble Growth. While bubble growth has long been recognized and studied,
Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 1003 relatively few reactor models have included the phenomenon. Notable exceptions include the work by Calderbank and Toor (1971), Darton (1979), and van Swaaij (1985) in which two-phase models were expanded to account for bubble growth in isothermal reactors. Recently, Bortolozzi and Deiber (1990) studied the influence of bubble growth on the overall mass-transfer rate between the bubble gas and the emulsion phase using Davidson's potential-flow analysis. They used an isothermal coal gasifier as model system but did not compare their results to experimental data. The model presented here takes bubble growth into account in the context of an extremely exothermic gasphase reaction. Two mechanisms of bubble growth are included in determining the unknown bubble radius, rb, the first of which is coalescence. The possible change in the bubble temperature, however, would affect the coalescence rate as it is given by eq T.l (i.e., for a given temperature). This equation must be modified to include this effect. Perhaps the most straightforward method for describing this enhanced growth rate would be to simply multiply the excess fluidizing velocity by Tb/T,, where T, is the temperature used in calculating (U - Umf). This would result in the following equation for r,, the bubble radius at any temperature: Another method would be to simply assume that the expansion of the (spherical) bubble with the bubble temperature induces the change in coalescence rate. This leads to rc = (Tb/Tm)1'3rc,m
(10)
These two methods lead to similar expressions, but since the latter is somewhat more convenient it was used in the equations that follow. The second mechanism of bubble growth is the net molar change due to the difference in inlet and outlet stream temperatures. This mechanism is treated below. The unsteady state energy balance for the bubble phase is uabscp
d ( VbpR>b Tb
)
=
This treatment of bubble growth assumes that the process is continuous as implied by eq T.l. The same expression implies that the bubble size is a monotone-increasing function of x . Due to ita stochastic nature, bubble growth is neither continuous nor monotonic. As a first step toward treating bubble growth, however, an average growth process is justified. The expression for Tbcan be derived from a total molar balance on the bubble:
Note that the only contribution to the net molar flow through the bubble other than that due to coalescence is from the change in gas density described above; that is, no net change in moles due to reaction is included. This assumption is strictly only correct for the complete combustion of methane. A molar balance of methane, similar to eq 12, around the bubble gives the mole fraction of methane in the bubble, yb. As before, this system of equations describing the bubble phase is coupled to the cloud-phase-gas temperature and composition through heat and mass transfer. Similar balances must be made for the cloud phase to determine these functions. The unsteady-state energy balance over the cloud phase is
P
.ld)
=
(13) where h mf is the coefficient of heat transfer from the cloud gas to t i e solids. It is assumed to be the same as given in eq T.8 except that Re, is based on U , rather than Ubr. The heat-transfer area in this case is the surface area of the particles in the cloud phase, A,, given by
A, =
- %Id)
3Vcld(1 TP
(11) where the fourth term on the RHS of the equation describes the gas flow into the bubble due to coalescence. Here rc,bois the bubble radius at the initial bubble temperature, Tho. Note that Uab, Kbc,v b , and hbchave the same meaning as before except that they are now functions of x . Note, too, that the left-hand side (LHS) of the equation does not depend on Tb explicitly so that this equation does not give Tb but, instead, rb. The term describing the net change in enthalpy due to the convective flow through the bubble (first term on the RHS on the equation) is actually zero. It has been included here for completeness. This means that the total number of moles of gas in the bubble will increase if Tb> Tcld,giving rise to the second mechanism of bubble growth. This point distinguishes the growth of the bubble due to coalescence alone from that including chemical reaction.
The last term on the RHS of eq 13 describes the change in the cloud volume in the absence of any reaction. That is, Uh is the relative bubble rise velocity based on rc rather than on rb. It is still a function of x as is r,. As in the case of the bubble phase, the LHS of eq 13 does not depend on Tcldexplicitly but, instead, gives the unknown cloud radius, rcld. Similarly, a total molar balance around the cloud phase yields an equation for the cloud temperature, Tcld,while Ycld, the methane mole fraction in the cloud phase, is given by a methane balance. The gas flow in the emulsion phase is assumed to be in plug flow. The steady-state energy balance is
1004 Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992 8.1
J Y*Lrr
Y.lr
8.88 8.86
0.04
1 -
1000
0.81
500 00
0
8
8.U
8.n
8.12
ai6
8.a
DLtua .krr tL. Dbt~Ikcr (11 Figure 5. Comparison of measured methane concentration profile with three-phase model with bubble growth U - U, = 0.2 m/s, H, = 0.077 m, 3W356-am sand.
K - TT - 1 11113 23.
0.84
0.88
o.ia
8.16 T-1148. 8.2
DIatmce m b a t h Dlrtrlk* (I) Figure 7. Predicted bubble temperature profde, three-phase m with bubble growth: U - Ud = 0.2 m/s, H, = 0.077 m, 300-355wm sand.
combined on a volumetric basis to determine the inlet gas temperature and composition and were assumed to be in plug flow. The freeboard was assumed to be completely free of solids with a constant wall temperature. Thus, the energy balance for the freeboard is
0.82
I
-
i
1
0 0
8.04
8.n
- - 8.12
I *I
L16
8.2
DLtur .krr C L Dls8rlklr (I) Figure 6. Comparison of measured methane concentration profile with individual phaee profiles from three-phase model with bubble growth: Tw = 1223 K, U - U, = 0.2 m/s, Hd = 0.077 m, 300355-pm sand.
and cloud phases, it will be assumed that T, is sufficiently constant to assume that the density of the gas in the emulsion phase is constant. This assumption will be tested later, but for now, this assumption means that the emulsion-phasevolume is constant, thereby circumventing the need for total molar balance. The molar balance of methane in the emulsion phase is identical to eq 7 with C b replaced by Ccld where b and Kbe are functions of x . Thus, eight coupled ordinary differential equations describe the Unknown fUnctiOnS rb, Yb, Tbt rcld, Ydd, Tcid,Ye, and T, between x = 0 and H. The calculated methane concentration profiles corresponding to the experimental condtions are shown in Figure 5. The methane concentrations predidsd for each of the individual phases are shown in Figure 6 for TM = 950 OC. Also, the predicted bubble temperature profiles for all three bed temperatures are shown in Figure 7. The model predicted that both the cloud- and emulsion-phase gas reached the bed temperature immediately upon entering the bed and remained essentially isothermal throughout the bed thereby obviating the need for these two energy balanm (and justifyingthe above assumption). Simulationsof larger particle-size systems discussed below indicate that temperature gradients in the emulsion phase are possible due to the reduced heat-transfer surface area available in these systems. An experimental study is needed to test these results in which the fluidization parameters are varied over a wider range. Fmeboard Region. To treat the reacting gases after they leave the bubbling bed at x = H,a separate freeboard model was used for all three models. The gases were
The gas-to-wall heat-transfer coefficient was assumed to be 1.9 W/(m2*K)as given by a standard heat-transfer correlation. The methane balance in the freeboard is simply
This model calculates the unknowns yfi and Tfi for each of the three models (Figures 3-5) for x > H.
Discussion The complete chemical anal* (of stable species) shown in Figure 2 shows that the overall conversion of methane to carbon dioxide involves the intermediate formation of carbon monoxide. This fact led Kozlov (1959)to measure CO oxidation rates separately, prior to measuring the overall combustion of methane. Kozlov (1959)suggested that the first reaction (CH4oxidation to CO) is the limiting (global) reaction at temperatures below 1500 "C above which the second (global) reaction (CO oxidation to Cod limited the overall rate of combustion. The fact that only the overall (complete) combustion of methane is assumed here is probably one reason why such high peak temperatures are predicted (see Figure 7). Since approximately 30% of the total heat of combustion for methane is released by CO oxidation, its more gradual combustion (above 1500 "C) would tend to spread out the combustion zone, thereby reducing the peak temperature. It is interesting to note in this regard that a maximum CO concentration of only 21% of the inlet CH, concentration was measured while Dryer and Glassman (1972)measured a maximum of 60% of the inlet methane concentration. This might indicate that significant peak temperaturee are, indeed, being obtained in the fluidized bed thereby allowing the more rapid conversion of CO (ascompared with the mild temperature maximum reported by Dryer and Glassman (1972)for their much-diluted system). In this study, the lowest peak CO concentration was measured when combustion occurred in the freeboard, i.e., when Tw = 850 O C .
Ind. Eng. Chem. Res., Vol. 31, No. 4,1992 1005 When comparing the three models presented here, it is important to point out that no parameters were adjusted to fit the particular system used in this study. In light of this fact and the fact that the kinetic expression used for methane combustion was determined in a reactor configuration completely different to the one used here, the agreement between the predicted methane profile of the three-phase model with bubble growth and the experimental values is quite good. The fact that the three models are similar in structure illustrates the effect of adding each level of complexity. Comparison of the two- and three-phase models using an average bubble diameter demonstrates the importance of the increased resistance to mass transfer due to the inclusion of the cloud phase. Clearly, the tailing in the mole fraction of methane seen in the experimental results is more nearly represented by the three-phase model. It is also apparent that the temporal probe average yields a somewhat better fit than the volumetric average. In both of these constant bubble size models, however, the distance from the distributor at which ignition occurs is the same and is greater than indicated by the experimental findings. Apparently, the bubble gas is taking too long to reach its ignition temperature in these two models. By addition of bubble growth to the three-phase model, this time period is reduced because (a) the smaller bubbles rise more slowly through the bed and (b) they exhibit a more favorable surface to volume ratio for heat transfer. It is now apparent that the regression of the "average" bubble size (as parameter) could lead to a more accurate prediction of this system by the simpler two models. As a start along these lines, reducing the bubble radius from 0.012 to 0.008 m dropped the point of ignition 0.01 m. Apparently, much lower values would be needed to improve the agreement. The tailing effect is also more pronounced when bubble growth is included due to the influence of bubble growth on the mass-transfer rates. The complexity of the process is illustrated in Figure 6,which shows the methane mole fraction profiles for each of the three phases. Note that, initially, the mole fraction of methane is lowest in the emulsion phase owing to the fact that the temperature of the gas is immediately raised to the bed temperature and that the gas residence time is higher there than in the bubble or cloud phase. As the bubble temperature reaches the bed temperature (see Figure 7),the reaction is initiated, ultimately leading to the complete depletion of the methane in the bubble upon ignition. The concentration gradients between the three phases are now reversed so that methane is resupplied to the bubble from the emulsion and cloud phases. Eventually, methane mole fractions in the bubble and cloud are again higher than that in the emulsion phase simply due to the difference in relative residence times. The predicted conversion in the freeboard region is sharper (for Tbed= 850 "C) than the experimental conversion profile would indicate. It may be that the modeling of the freeboard as a perfect mixer as proposed by Yates and Rowe (1977)may improve the fit there. Finally, simulation of the system of Baskakov and Makhorin (1975)(with dp = 0.88 mm) by the three-phase model with bubble growth predicted that ignition would occur in the emulsion phase at approximately 1 mm from the distributor with a predicted T,, of 2300 K. If emulsion-phase ignition is possible, it could explain the fact that a temperature gradient was measured by Baskakov and Makhorin (1975)while no such (pronounced) maximum was measured in the system described in the present study. Emulsion-phase burning could be expected
to lead to a stationary reaction front in the bed which could be measured by a thermocouple. This is in contrast to the smaller particle size system described here which is predicted to exhibit temperature peaks only in the bubble phase. If the time the thermocouple spends in the bubble and emulsion phases is roughly equal, as is predicted by Davidson's (1984)probe theory, the temperature of the thermocouple could be expected to be much closer to that of the emulsion phase due to the more efficient heattransfer rate in that phase. Hence, a much smaller temperature gradient would be expected in the small-particle system. It is of interest to investigate whether a further reduction in particle size could lead to lower peak temperatures in the bubble phase as well.
Conclusions Comparison of the experimental results with the predicted methane concentration profiles for each of the three models leads to the following conclusions. (a) The change in heat-transfer rates and, more importantly, in the bubble rise velocity when bubble growth is treated accounts for a more accurate prediction of bubble ignition. (b) The additional mass-transfer resistance introduced by the inclusion of the cloud phase can explain much of the tailing in methane conversion measured at the two higher temperatures. (c) This tailing effect is even more pronounced when bubble growth is considered. (d) The high-temperature combustion of methane is well described by the thermal theory. In addition, while the two methods used to calculate the composition of the gas drawn by the in-bed probe lead to significantly different results, more experiments are needed to recommend either average. These conclusions imply that both the heat and mass transfer between the bubble and emulsion phases are more accurately described by the three-phase model with bubble growth. The former has important implications for homogeneous reactions and physical processes (e.g., fluidized bed drying) while the latter could be important for any fluidized bed process under study in a laboratory reactor including catalytic reactions. Acknowledgment
I gratefully acknowledge the support of the Gas Research Institute for this work under Contract No. 5089260-1905. Nomenclature A = cross-sectional area of reactor (m2) A, = surface area of solid particles (m2) A. = constant dependent on distributor plate (assumed to be 5.52 X 10" m2) Ci = concentration in phase i (mol/m3) C = molar specific heat capacity (J/(mol.K)) = specific heat capacity of solids (J/(kg.K)) Dab = diffusion coefficient (m2/s) d, = mean particle diameter (mm) g = gravitational acceleration (m/s2) h = heat-transfer coefficient (W/(m2.K)) hb = bubble-teemulsion heat-transfer coefficient (W/(m2-K)) hpbr = gas-to-particleheat-transfer coefficient based on &, (W/(m2.K)) hpmf= gas-to-single-particle heat-transfer coefficient based on urn, (W/(m2.K)) H = bed height (m) AH = heat of combustion of methane (J/mol)
1006 Ind. Eng. Chem. Res., Vol. 31, No. 4, 1992
Kbe= bubble-to-emulsion mass-transfer coefficient based on bubble volume (s-l) K,, = cloud-to-emulsion mass-transfer coefficient based on cloud volume (9-l) k = thermal conductivity (W/(mK)) kce = cloud-to-emulsion mass-transfer coefficient based on cloud surface area (l/(s.m)) P = pressure (Pa) rb = bubble radius (m) rC,- = bubble radius at T, in the absence of reaction (m) = mean particle radius (m) = homogeneous reaction rate in phase i (mol/ (m3.s)) S c l d = surface area of cloud (m2) t = time ( 8 ) f = average bubble residence time (s) Tb0= initial bubble gas temperature (K) Ti= temperature of phase i (K) T, = bed temperature (K) U = superficial fluidizing velocity (m/s) Uabs= absolute bubble rise velocity (m/s) Ub, = relative bubble rise velocity (m/s) u b r c = relative bubble rise velocity in the absence of reaction (m/s) U, = interstitial gas velocity (m/s) Urn,= minimum fluidizing velocity (m/s) V = volume (m3) r = axial distance from distributor (m) yMi= mole fraction of methane in phase i
;pi
Greek Letters 6 = volumetric fraction of bubbles ci = void fraction in phase i f b = volumetric fraction of solids in bubble phase emf = void fraction at minimum q i = height of phase i
fluidizing velocity
pg = ps =
molar density of gas (mol/m3) density of solids (kg/m3) 7 = residence time of solids in bubble (s) + = volumetric fraction of bubble and cloud volume in bubble void
Subscripts
b = bubble phase c = in the absence of chemical reaction cld = cloud phase e = emulsion phase fb = freeboard g = gas mf = evaluated at minimum fluidizing velocity p = particle probe = sampling probe s = solid w = reactor wall
Appendix. Calculation of Sample Concentration for Three-phase Model ‘If it is assumed that the rate of gas drawn through the chemical probe is constant, then the composition of the sampled mixture is
If the absolute rise velocity of the bubble and cloud is assumed to be Uab,this equation can be rewritten in terms of qi,denoting the height of phase i CeC.
c, =
Uabs
+ c b x - ‘Ib + C c l d x - ‘Icld Uabs
-+-+-
Uabs
‘le
‘Ib
‘Icld
Uabs
Uabs
Uabs
(A.2)
where the summations are over the time the sample is drawn. Now ‘Ib
6= ‘Ib
=
+ ‘Icld + ‘Ie
~
u - urn,
(A.3)
Uabs
so
using eq T.11. This can be compared with the expression used by Fryer and Potter (1972). Registry No. Methane, 74-82-8.
Literature Cited Bakker, P. I.; Heertjes, P. M. Porosity Distributions in a Fluidized Bed. Chem. Eng. Sci. 1960, 12 (4), 260-271. Baskakov, A. P.; Makhorin, K. E. Combustion of Natural Gas in Fluidised Beds. Inst. Fuel Symp. Ser. (London)1975,l; Fluidized Combustion Conference Vol. 1, paper C3. Bortolozzi, R. A.; Deiber, J. A. Mass Transfer Between Growing Air Bubbles and an Emulsion of Coal Particles in Fluidized Gasification and Combustion. Chem. Eng. Sci. 1990,45 (5), 118S1197. Broughton, J. Influence of Bed Temperature and Particle Size Distribution on Incipient Fluidisation Behaviour. Trans. Znst. Chem. Eng. 1974,52, 105-107. Calderbank, P. H.; Toor, F. D. Fluidized Beds as Catalytic Reactors. In Fluidization; Davidson, J. F., Harrison, D., Eds.; Academic Press: London, 1971; Chapter 8. Chavarie, C.; Grace, J. R. Performance Analysis of a Fluidized Bed Reactor. I. Visible Flow Behavior Znd. Eng. Chem. Fundam. 1975,14, 75-79. Chavarie, C.; Grace, J. R. Interphase Mass Transfer in a Gas-Fluidized Bed. Chem. Eng. Sci. 1976,31, 741-749. Darton, R. C. A Bubble Growth Theory of Fluidized Bed Reactors. Trans. Znst. Chem. Eng. 1979,57, 134-138. Darton, R. C.; LaNauze, R. D.; Davidson, J. F.; Harrison, D. Bubble Growth Due to Coalescence in Fluidized Beds. Trans.Znst. Chem. Eng. 1977,55, 274-280. Davidson. J. F. Fluidised Combustion: Review of Fundamentals. In Fluidised Combustion: Is It Achieving Its Romise? Institute of Energy: London, 1984; Vol. 2, Rev/l/l-7. Davidson, J. F.; Harrison, D. Fluidised Particles;Cambridge University Press: Cambridge, UK, 1963. Dryer, F. L.; Glassman, I. High Temperature Oxidation of CO and CHI. Symp. (Znt.) Combust. 1972, 14th, 987-1003. Fryer, C.; Potter, 0. E. Countercurrent Backmixing Model for Fluidized Bed Catalytic Reactors. Applicability of Simplified Solutions. Znd. Eng. Chem. Fundam. 1972,11,338-344. Khinkis, P. A. Mathematical Modeling of Exothermal Processes in Fluidized Bed of Inert Particles. Khim. Teknol. (Kieu)1982,5, 46-49. Kozlov, G. I. On High Temperature Oxidation of Methane, Symp (Znt.)Combust. 1959, 7th, 142-149. Kunii, D.; Levenspiel, 0. Bubbling Bed Model. Znd. Eng. Chem. Fundam. 1968, 7,446-452. Kunii, D.; Levenspiel, 0. Fluidized Bed Reactor Models. 1. For Bubbling Beds of Fine, Intermediate, and Large Particles. 2. For the Lean Phase: Freeboard and Fast Fluidization. Znd. Eng. Chem. Res. 1990,29, 1226-1234. Makhorin, K. E.; Glukhomanyuk, A. M. Research of Gas Combustion in Fluidized Bed Plants. Proceedings of the Fifth International Conference on Fluidized Bed Combustion; US DOE Washington, DC, 1975; Vol. 3, pp 268-273. Ranz, W. E.; Marshall, W. R., Jr. Evaporation from Drops; Part 11. Chern. Eng. h o g . 1952, 48 (4), 173. Rao, V. R.; Stepanchuk, V. F. Combustion of Gaseous Fuels in Fluidized Beds. Indian J. Chem. Eng. 1967, 5 (Aug), 245-248. Sadilov, P. V.; Baskakov, A. P. Temperature Fluctuations at the Surface of a Fluidized Bed with Gas Combustion Occurring Therein. Znt. Chem. Eng. 1973,13 (31,449-451. Toei, R.; Matauno, R.; Hotta, H.; Dichi, M.; Fujine, Y. The Capacitance Effect on the Transfer of Gas or Heat Between a Bubble and the Continuous Phase in a Gas-Solid Fluidized Bed. J. Chem. Eng. Jpn. 1972,5, 273-279. Van der Vaart, D. R. Freeboard Ignition of Premixed Hydrocarbon Gas in a Fluidized Bed. Fuel 1988, 67, 1003-1007.
Ind. Eng. Chem. Res. 1992,31, 1007-1012 Van der Vaart, D. R.; Davidson, J. F. The Combustion of Hydrocarbon Gas, Pre-Mixed with Air, in a Fluidized Bed. FLuZDZZATZON V , Elsinore, Denmark; Engineering Foundation: New York, 1986, pp 539-546. Van Swaaij, W. P. M. Chemical Reactors. In Fluidization; Davidson, J. F., Clift, R., Harrison, D., Eds.; Academic: London, 1985; Chapter 18. Yanata, I.; Makhorin, K. E.; Glukhomanyuk, A. M. Investigation and Modelling of the Combustion of Natural Gas in a Fluidized Bed
1007
of Inert Heat Carrier. Znt. Chem. Eng. 1975, 15 (l), 68-72. Yates, J. G.; Rowe, p. N. A Model for the Chemical Reaction in the Freeboard Region above the Fluidised Bed. Trans. Znst. Chern. Eng. 1977, 55, 137.
Received for review July 25, 1991 Revised manuscript received December 27, 1991 Accepted January 17, 1992
Catalytic Hydrogenation of Multiring Aromatic Hydrocarbons in a Coal Tar Fraction Roberto Rosal, Fernando V. DIez, and Herminio Sastre* Department of Chemical Engineering, University of Oviedo, 33071 Oviedo, Spain
The kinetics of the hydrogenation reaction of the main aromatic hydrocarbons found in a light fraction of an anthracene oil was studied employing two different commercial catalysts: reduced nickel and sulfided nickel-molybdenum. Kinetic expressions considering the effect of temperature and hydrogen pressure were obtained. The effect of sulfur concentration in the feed was also evaluated. Specific reaction rates and activation energies were calculated assuming first order with respect to all reagents including hydrogen in hydrogenation reactions. The concentrations of naphthalene, acenaphthene, phenanthrene, fluoranthene, and pyrene were fitted t o a first-order decay. The reaction path for anthracene involves a reversible reaction between 9,lO-dihydroanthracene and 1,2,3,4-tetrahydroanthracene.
Introduction
Table I. Properties of Catalysts
During liquefaction or coprocessing, coal undergoes a series of chemical and physical processes leading to a cleavage of bonds and a solubilization of the organic matter into liquid products. The upgrading of these fractions to remove heteroatoms is essential if they are employed as raw material in the manufacture of chemicals or synthetic fuels. Hydrodenitrogenation and hydrodesdfurization are required to prevent poisoning of the catalysts employed in subsequent reaction steps. On the other hand, liquids produced from coal must be upgraded in order to reduce their content in sulfur, nitrogen, and oxygen, which are recognized as a major source of environmental pollution and a cause of damage of equipment such as power plants and combustion engines. In these processes, a parallel hydrogenation of aromatic and polyaromatic compounds takes place to some extent. The saturation of aromatic rings is a previous step before nitrogen removal in the hydrodenitrogenation of aromatic compounds such as carbazole and acridine (Katzer and Sivasubramanian, 1979). The hydrogenation of aromatics is also important in the development of coal liquefaction technology itself (Davies, 1977; Chiba et al., 1987). The solvent behaves as a vehicle by means of which hydrogen from the gas phase is transferred to the liquefying coal. The donatable hydrogen depleted during extraction is then restored by catalytic hydrogenation. The partially hydrogenated hydrocarbons originating from two- to four-ring aromatics have been recognized as particularly good donor substances. Large quantities of such fused aromatics and methyl aromatics are found in the oils formed in coal liquefaction and in fractions from coal tar,like anthracene oil or creosote oil. Almost all the available results have been obtained by employing a pure compound or a mixture of a reduced number of components rather than a real fraction (Chu
* To whom correspondence should be addressed. 0888-5885192/ 2631- 1007$03.00/0
composition, % surf. area, m2/g mean pore diameter, A cumul desorption surf. area of pores between 10 and 300 A, m2/g cumul desorption pore vol of pores between 10 and 300 A, cm3/g
G-134-ARS, Siid-Chemie Ni 5 0 4 2 % SiOz 25% A120310% 285 68 274
M8-24, BASF NiO 4% MOO, 16% 207 67 189
0.41
0.31
and Wang, 1982). The kinetics of the hydrogenation of naphthalene and phenylnaphthalene has been reported employing a sulfided Co0-Mo03/yA1,03 catalyst at 325 "C and 75-atm hydrogen pressure (Sapre and Gates, 1982). The reaction of 1-methylnaphthalene starts with hydrodealkylation to yield naphthalene (Patzer et al., 1979). Several reaction paths have been proposed for the hydrogenation of anthracene (Wiser et al., 1970; Wiser, 1982) and phenanthrene (Shabtai et al., 1978; Girgis, 1988),but results are fragmentary due to the great complexity of the product. Quantitative networks for hydrogenation of fluoranthene and pyrene have been established in part (Lapinas et al., 1987; Girgis, 1988). Moreover, comparison between the data reported in the literature is difficult because each group of researchers employs different conditions and sometimes the reaction rates reported are not given in mutually consistent units. Most of the work has been performed at a fixed temperature, and, therefore, no information is available on the activation energies. This paper aims at the study of the hydrogenation of the main constituents of an aromatic fraction from coal tar distillation. Reactions taking place are fitted to simplified rate expressions.
Experimental Section Materials. Two commercial hydrogenation catalysts were employed: nickel on silica-alumina (G-134-ARS, 0 1992 American Chemical Society
