454
Ind. Eng. Chem. Res. 1989,28, 454-470
Tiegs, D.; Gmehling, J.; Rasmussen, P.; Fredenslund, A. VaporLiquid Equilibria by UNIFAC Group Contributions. 4. Revision and Extension. Ind. Eng. Chem. Res. 1987,26, 159. Timmermans, J. Physico-Chemical Constants of Pure Organic Compounds; Elsevier: Amsterdam, 1950; Vol. I. Weeks, R. W., Jr.; McLeod, M. J. Permeation of Protective Garment Materials by Liquid Halogenated Ethanes and a Polychlorinated Biphenyl. Los Alamos Scientific Laboratory Report LA-8572-MS, 1980.
Weeks, R. W., Jr.; McLeod, M. J. Permeation of Protective Garment Material by Liquid Benzene and by Tritiated Water. Am. Ind. Hygiene Assoc. J. 1982, 201, 43. Wilhoit, R. C.; Zwolinski, B. J. Physical and Thermodynamic Properties of Aliphatic Alcohols; American Chemical Society: Washington, DC, 1973; Vol. 11. Received for review November 12, 1987 Accepted January 17, 1989
PROCESS ENGINEERING AND DESIGN Hydrodynamic Changes and Chemical Reaction in a Transparent Two-Dimensional Cross-Flow Electrofluidized Bed. 2. Theoretical Results Charles V. Wittmann Department of Chemical Engineering, Illinois Institute of Technology, Chicago, Illinois 60616
Theoretical explanations of some of the experimental results of part 1 are given. In the presence of the electric field, caused by a direct current (dc) applied on the fluidized bed and a bone-dry gas, an electric polarization of the particles is assumed. This behavior in turn causes an electric polarization a t the bubble surface. A theory based on potential flow of the emulsion phase around the elliptical bubbles which takes into account the electric work of these surface charges explains the decrease of the rising velocity of the bubbles with increasing field strength. T h e results show a linear effect of the field strength. This saturation of the polarization with a maximum charge of 8.3 X C kg-l is attributed mainly to triboelectric effects. The bed expansion with increasing field strength a t constant gas flow rate is explained by the additional electric forces a t the electrode walls which support part of the bed weight. In this case, a slightly modified Ergun’s correlation predicts an increase in voidage. Results give a variation of the wall shear stress with power 0.93 of the field strength. The increase in conversion of ozone in the EFB reactor with increasing field strength is explained by the simultaneous variations of the bubble velocity, bed height, and bubble frequency in a three-phase model: bubble, cloud, and emulsion, which are all assumed to be in plug flow. The value for the reaction rate constant K, = 0.346 s-l, which is the single adjustable parameter, agrees with the decrease in exit concentration of about 22%. Both variations of the bubble velocity and the bed height increase the total mass transfer out of the bubble phase. The former also increases the reaction in the cloud phase and the latter the one in the emulsion phase. T h e drastic decrease in bubble frequency decreases the gas bypassing and substantially increases the reaction in the emulsion phase. Various aspects of the influence of an applied electric field on a fluidized bed have been reviewed, and new quantitative experimental results have been presented in part 1 of this work (Wittmann and Ademoyega, 1987). Theoretical explanations of the peculiar phenomena in such an “electrofluidizedb e d (EFB) have been few. Katz and Sears (1969) invoked polarization within the particles caused by the electric field as well as “surface polarization charges”. In this view, the polarized particles are aligned in the field with the positive side of one particle next to the negative side of an adjacent particle, giving rise to attractive interparticle forces. The pressure drop through the bed at “stabilization breakup” was correlated with (A V ) 2supporting this theory. Johnson and Melcher (1975) conje_ctur_edabout-a macroscopic force per unit volume of bed P-VE where P is the polarization density of the particles and E the macroscopic electric field. At the particle scale, these latter authors thought that the electric energy 0888-5885/89/2628-0454$01.50/0
due to this polarization was of a magnitude comparable to the one of the kinetic energy associated with particle fluctuations as well as its potential energy due to gravity and thus was capable of causing the observed hydrodynamic changes in the bed. In a theoretical interpretation of the application of an EFB to aerosol collection, Zahedi and Melcher (1976) considered a bed of electrically polarized particles. Dietz and Melcher (1978a) claimed that electric forces due to polarization of the particles are not large enough to affect the hydrodynamic and gravitational forces acting on the particles. For these forces to dominate, they required the conditions R, < 100 pm and t,*/++ I10. They attributed the hydrodynamic changes in an EFB to interparticular forces resulting from an electric current a t the surface of the particles, which constricts at the contacts between two particles. This theory applies to the EFB in the “frozen” or “electropacked” state; i.e., the bed is no C 3 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 4,1989 455 longer fluidized due to the strong electric field. In this theory, at the particle scale, they did consider a variable electric field, calculated to describe the current flow; it was, however, approximated in a region close to the particleparticle contact by the dielectric breakdown strength in air, Em-. The interparticle attractive forces and shear stress on the walls in the cross-flow configuration resulting from this theory are given by eq 1 and 2, respectively.
was increased and a maximum at about 0.01 g of water per gram of air or 70% relative humidity at room temperature. With ammonium sulfate particles fluidized in a Plexiglas equipment, Kisel'nikov et al. (1967) observed an increase with humidity. Using glass beads in a grounded metallic apparatus, Bafrnec and Bena (1972) recorded a strong monotonic decrease when the humidity was increased, reaching 0 after a relative humidity of 60%. Both Ciborowski and Wlodarski (1962) and Kisel'nikov et al. f, = (0.415)4~cf*R~~E,~"~~E~~.~ (1) (1967),who all used an apparatus with dielectric walls and a grounded metallic gas distributor, found an increase in W the ball potential with the bed height. 7, = 0.05(1 - t)fflv,--~*Em,,0.E[AV/w]1.2 (2) RP In the above experiments, it is assumed that the fluidized particles are electrostatically charged, and collision It is noteworthy that expressions 1and 2 do not depend with the metal ball transfers a part or all of this charge on the surface conductivity, us,of the particles, and thus to the ball and to the grounded distributor. Bafrnec and all "semiinsulating" particles of a given size, i.e., with an Bena (1972) claimed to have proved this assumption by electrically insulating bulk and a conductive surface, should showing that the ball and the particles have the same behave in the same fashion. At lower relative humidities, polarity when directing a charge of known polarity to the Johnson and Melcher (1975) found a lesser effect of the ball. It is conceivable that, for some materials, collision applied electric field, which would suggest that us has a of the particles with a ball probe creates new charges, decreasing effect on f ,and 7, in these conditions. In the although these should be of different polarity. Hendricks case of air saturated with water vapor, droplets are likely (1973) gave a good review of the different ways in which to form which, according to Loeb (1965), can reduce . ,E particles can be charged. In a fluidized bed with and In the conditions where the bed is packed due to the without applied electric field, several electrostatic pheelectric field and when using several kinds of particles, nomena can occur. Dietz and Melcher (1978a) obtained experimental results Triboelectric, or contact charging in general, often occurs for 7, from a Couette viscometer, which correlated well at the interface of two solids in contact, when these solids with the dependence on the applied potential, AV, given are made of different materials with different Fermi levels. by eq 2. These results also yielded values for the total Harper (1967) and Inculet (1973) gave detailed reviews of number of contacts of a particle, NT, in a range between this controversial subject. In the case of the materials used 5 and 13. Dietz and Melcher (1978b) correlated experiin the experiments of part 1, if the triboelectric series of mental results of pressure overshoot at incipient fluidiHendricks (1973) applies, glass and silica particles should zation caused by the applied field with eq 2 and obtained become charged negatively and the inside of the Plexiglas very good agreement by using values close to NT = 6 in (lucite) walls positively. However, silica gel particles may the case of glass beads. These latter authors also conbehave quite differently than quartz particles. As a result ducted experiments without support a t the bottom of the of this phenomenon, all particles in the bed should acquire bed in which they determined the minimum applied poa net charge of the same polarity. tentials required (1)to stop the particles from raining from the lower part and (2) to support the entire bed, when in Triboelectric charging can also result in a usual fluidized both cases the flow rate was reduced and extrapolated to bed from the collision of the particles with each other. But, zero. Very good agreement was obtained with eq 1 and as also pointed out by Bafrnec and Bena (1972), if there 2 when NT = 3 was used for case 1 and NT close to 6 for is only one kind of particle present, the charges and their case 2. polarity which are produced are random, and the total The conditions of the experiments under investigation charge of the bed due to this process is zero. One can think (part 1)are different from the ones of the theory of Dietz of perfectly nonconducting particles where each has a and Melcher (1978a,b). In these conditions, electrostatic random distribution of surface charges of alternating pocharging and polarization of the dielectric particles cannot larity. In the case of a nonnegligible surface conductivity, be ignored. such a phenomenon should not occur. Although some of their results appear nonreproducible, Ciborowski and Charging of Particles in Fluidized Beds Wlodarski (1962) recorded an increase in the minimum fluidizing flow rate at low humidities with a simultaneously In gas fluidized beds without applied electric field, observed agglomeration of particles. This phenomenon electrostatic phenomena have been studied by numerous could be explained by the existence of charged particles authors who measured the electric potential of a metallic of different polarities attracting each other. ball immersed in the bed (Ciborowski and Wlodarski, 1962; If a strong electric field is applied to the fluidized bed, Kisel'nikov et al., 1967; Bafrnec and Bena, 1972). All these it is likely that the collision of two particles, although they authors found that this potential increased after fluidiare made of the same material, does not produce surface zation began and reached a steady state in a time ranging charges of random polarities but that the electrons are from 2 min to 2 h. Kisel'nikov et al. (1967) showed that transferred in the opposite direction of the applied field the particle material strongly influences this time, as well during contact. Inculet (1970) has shown that, when the as the magnitude of the steady-state potential obtained. colliding particles in the field are not made of the same Ciborowski and Wlodarski (1962), who obtained similar material, a nonsymmetric charge distribution is observed. results, claimed that these were not reproducible. All Shih et al. (1987) simulated an EFB containing particles former authors also found that this steady state potential made of different materials which acquired net charges. increased with increasing gas flow rate. There is disHowever, for particles made of the same material, after agreement about the influence of the humidity of the separation, rotation of the particles in the applied field, fluidizing gas on this potential. In their glass equipment, and new collisions, the surface charge distribution of with every dielectric particles used, Ciborowski and Wloperfectly insulating particles would still be random. In darski (1962) reported a sharp increase when the humidity
456
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 SEMICONDUCTING SURFACE
INSULATING OR SEMI - CONDUCTING BULK /'
Figure 1. Polarization of surface charges.
their analysis, Dietz and Melcher (1978a,b)emphasized the existence of a nonnegligible surface conductivity of the dielectric particles in the presence of humid air. In the experiments of part 1,although oxygen with no more than 10 ppm of water has been used as the fluidizing gas, the surface conductivity of the dielectric particles utilized is also believed to be nonnegligible. The silica gel particles, which gave a slightly more pronounced bed expansion, are highly porous and have a molecular structure containing SiOH acidic groups (Iler, 1979) which easily adsorb a considerable amount of water. Thus, these particles should have a nonnegligible surface conductivity even in a very dry gas. The triboelectric charges created on such particles, when immersed in a high electric field, should migrate at the particle surface to reach the dipole configuration of Figure 1. Some collisions are likely to discharge the particles, especially when these are lined up in the electric field. However, as long as the bed is not frozen, the colliding particles in the electric field should have a timeaveraged dipole configuration. If the bulk conductivity is also nonnegligible, as it may be in the case of silica gel with water adsorbed in the pores, the polarization should even be increased. Particle charging by ionic phenomena is also possible. Henry (1953) and Harper (1967) have considered an ionic interchange at the interface during contact charging of dielectrics. The contact between the gases and the solids may involve ions. A low concentration of ions can exist in gases, e.g., 02and H30+in the atmosphere. In the case of the experiments under investigation where oxygen with 10 ppm or less of water was used as fluidizing gas, atmospheric ions can be present. In this case, one kind of these ions could be selectively adsorbed on the solid particles, especially on porous silica gel. Then the particles acquire a net charge. This phenomenon is well-known for solids immersed in liquids and gives rise to the Helmholtz double layer at the solid surface (Delahay, 1965; Hendricks, 1973; Inculet, 1973). Contacting of' a neutral gas with a high velocity over a solid such as the "polyacid" silica gel may give the ionization reaction with HzO to produce H30+ in the gas. A double layer would also result in this process. In relation to this explanation, Kisel'nikov et al. (1967) obtained substantially higher ball potentials with the salt ammonium sulfate than with the polymer particles fluidized in the bed. The previous processes, in which all the particles acquire a net charge of the same polarity, do explain the buildup of the ball potential in fluidized beds. In this case, an increase in gas velocity increases the rate of formation of these charges due to a higher kinetic energy during collisions and a higher frequency of collisions or a higher friction. However, these processes also imply that the particles repulse each other. In a bed with an applied field, they would move to one electrode. In the case where bubbles are present, these would interface with particles which have all the same polarity, and thus, the bubbles themselves would be directed toward this same electrode
in a very sensitive fashion. In the EFB experiments of part 1, none of these phenomena were observed. On the contrary, attractive forces between particles were clearly identified. There was no noticeable motion of the particles toward one electrode. The bubbles did change shape and slow down in the electric field, but they did not move toward any of the electrode walls. Thus, the phenomena leading to a net and uniform charging of the particles were dismissed in the present theory. Bulk polarization of the dielectric particles in the field of the EFB had been considered by all previous authors. The relative permittivity of the silica gel particles used in the experiments under investigation has been determined in a cylindrical dielectric cell, and a value of tp*/tO* = 4.4 per solid volume was found. From previous studies (Kurosaki, 1954; Thorp, 1959) the value of tp* varies with the specific gravity of the silica gel particles as well as with the amount of water adsorbed. Considering the average radius of the particles used, R, = 97 pm, the requirements of Dietz and Melcher (1978a) for R, and t *, in the order of having a significant influence of the bufk polarization, are not failed by much. The previous analysis has shown that additional surface charges created by frictional effects should considerably enhance the polarization of the particles in the electric field on a time-averaged basis. The conditions of the experiments under investigation differed from the ones of the theory of Dietz and Melcher (1978a,b) in the following. (1)The particles were still fluidized, i.e., the EFB was not frozen. Bubbles were present, and the particles were moving, implying that the interparticle contact time was low compared to the time of no contact. (2) If an electric current was flowing through the bed, it was too low to be measured with the high-voltage generator used under normal conditions. A t a very high voltage, the current intensity would, however, gradually build up just before a spark developed between the electrode walls. One could otherwise have attempted to use quantitative information on the electric current to check if the theory of Dietz and Melcher (1978a,b) still applies for these conditions. (3) A very small humidity of not more than 10 ppm was used in the fluidizing gas, which enhances triboelectric charging of the particles. As a result of this analysis, in this paper, bulk polarization as well as polarization of the triboelectric charges on the dielectric particles will be considered.
Rising Velocity of Bubbles in the EFB Davies and Taylor (1950) showed experimentally that large three-dimensional (3D) bubbles of air rising in liquids have a spherical cap. Assuming inviscid flow around these bubbles at a constant internal pressure, they derived their relative rising velocity as
u,,= 2/3@,)'/2 and obtained excellent experimental agreement. Using rods immersed in water, Grace and Harrison (1967) obtained bubbles having the shape of an ellipsoid of revolution about the major axis, or prolate, and these bubbles rose faster in the direction of the major axis than the corresponding spherical cap bubbles. With the same assumptions of inviscid flow and constant pressure inside the bubble, these latter authors derived relative velocities of bubbles with the shapes of prolate ellipsoids in 3D and of elliptical cylinders in 2D, which rose in the direction of the major axis. There are similarities between the behavior of bubbles in fluidized beds and of large gas bubbles in inviscid liquids (Davidson and Harrison, 1963). In the experiments of part 1,bubbles with the shapes of elliptical cylinders rising in
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 457 a
Y I a
+
E
C.
\
Figure 2. (a) Polarized particles in the emulsion phase. (b) Charged bubble surface. (c) Charge distribution on the bubble surface.
the direction of the minor axis were obtained. In the “emulsion” phase which flows around the bubbles, the voidage, t, depends on the electric field, but it is assumed to be independent of location. Hence, following Davidson and Harrison (1963), this phase can also be treated as an incompressible fluid. Furthermore, following the latter authors, we assume that, in the case of the EFB, the emulsion phase behaves like an inviscid liquid and has an irrotational flow field. With these assumptions, the theory of Davidson and Harrison (1963) applies to the EFB when the total potential, P, includes an electric term. This potential flow occurs around the bubbles having the shape of elliptical cylinders, which is given a priori from experiments. The steady-state equation of motion for the emulsion phase becomes r
-vP = -vp
Figure 3. Elliptical coordinates for the deformed bubbles.
spherical, or circular in 2D, the charge distribution can be taken as q E cos y, referring to Figure 2c. This charge is also the one of a differential bubble surface element dA = d ds at point P to which the particle is tangent. Thus, the charge on dA is dq = QE cos y d ds = q E sin 0 d ds (4) This distribution is symmetrical with respect to the bubble’s minor axis such that dq = 0 a t the apex of the bubble. As the bubble rises, it displaces the positive charges on its surface to the positive electrode and the negative charges to the negative electrode, thus performing work, WE. To describe the bubble, elliptical coordinates are used and point M in Figure 3 is located by the coordinates r]
(54
y = c sinh $. sin
r]
(5b)
On the ellipse of Figure 3, = to,and its focal distance, 2c, is such that c2 = u2 - b2,with the coordinates of points A and B such that u = c cosh toand b = c sinh to. In the derivation of the rising velocity, a stationary bubble in a moving emulsion is considered following Davies and Taylor (1950); thus, -Ubr becomes the uniform velocity of the emulsion far away from the bubble. Using the appropriate complex potential, Milne-Thomson (1960) derived the velocity distribution, ii(t,r]), of an inviscid fluid flowing around an elliptical cylinder, such that the undisturbed velocity, U, at infinity makes an angle, a, with the major axis of the ellipse as shown in Figure 3, which gives at any point M sinh2 (5 - to)+ sin2 (r] - a )
+ p,g’ + B E 2
(3b) With the assumption of dominating forces resulting from the electric polarization, the particles tend to line up in the field, attracting each other, as shown in Figure 2a. At the bubble-emulsion interface, the discontinuity results in a charged bubble surface as shown in Figure 2b. Boland and Geldart (1972),in the case of no applied electric field, have detected electric charges during the passage of a bubble in front of a fixed probe built in the wall of a fluidized bed. So0 (1974) considered a dielectric medium around the bubbles and calculated the electric stress at the bubble interface but concluded that these forces do not affect the bubble motion. In the present case, the applied electric field and the resulting phenomena give rise to a d.ifferent situation. For a polarized particle assumed
x = c cosh [ cos
ii2
=
u2[
%][
sinh2 to+ sin2 9
]
(6)
In the present case, the bubbles rise in the direction of the minor axis and a = ~ / 2 .Thus, at point P on the ellipse, we have
b 2 / c 2+ sin2 r] Integration of eq 3 along a stream of emulsion of differential thickness dh and flowing a t the bubble interface from point B to point P gives 1 2
-[ap2
- 6~3~1 + g[Yp - YBI +Jppdp/pe + WE = 0 w
(8)
458
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989
where WE is the work done by the electrical forces (WE > 0) per unit mass of emulsion. Following previous authors, the assumptions of a constant pressure inside the bubble and a stagnation point at B give 72iip2
+ g[yp
b] +
-
WE
(9)
=0
If we assume that the charge on the bubble surface does not substantially alter the applied electric field, E , the electric force per unit bubble area acting on the bubble surface at point P is obtained from eq 4 as &E = E& sin 0 (10) In the emulsion stream considered in eq 8, the charge per unit interface area, qE, is proportional to the charge per unit volume, The electric work is then
oE.
f L p 6E ds
WE =
e
=
Let
qE,
=
LLpEQEsin 0 ds
(11)
Pe
(12)
YB
The substitution of oq 1 2 into eq 9 gives cp2 =
2b(g - QEE)(1 - sin
(13)
7)
Comparing eq 7 and eq 13 gives =
2b(g - q & ) ( l - sin q)
[SI[$
+ sinzq][
cos2 q
]
(14)
-
Following Davidson and Harrison (1963), who assume that only the top area of the bubble is important, let q n/2, or if E = x / 2 - q , let E 0, giving
-
lim va/2
+
1 - sin 7
cos2 q
1 - cos t 1 = lim -= 6-0
sin2 E
2
and eq 14 reduces to
It is assumed that the changes inside and at the surface of the particles depend on the electric field following the monotonically increasing function, or otherwise constant, of eq 16. Then, as E is increased, the square root term of eq 15 reduces Ubr: qE=mn
X>O;
n 1 0
(16)
In the case of spherical bubbles rising in a fluidized bed without applied electric field, the rising velocity of the bubble can be obtained from the theory of Davies and Taylor (1950) using an appropriate equivalent bubble diameter (Kunii and Levenspiel, 1969) or equivalently a multiplicative adjustment factor, f . We will assume that the same is possible in the case of an applied electric field where the factor f does not change significantly with the field. With eq 15 and 16, this assumption gives
The measured rising velocity of the bubbles is the absolute velocity, ut,. In a usual fluidized bed without an applied field, when the gas flow rate, Qo, is above the value required in the minimum fluidizing state, Qa, it is usually assumed that the "excess gas" passes through the bed as
for Q =
U,, cm s-' 31.6" 29.3 27.7 24.2 21.4 19.9
"This value is the intercept of the linear least-squares fit for A V = 0 shown in Figure 11 of part 1 and not the experimental value U , = 31.2 em s-'.
bubbles. Based on the work of Nicklin et al. (1962) and Nicklin (1962) for air bubbles in water, the absolute velocity, Ub, of the bubbles has been related to Ub,(Davidson and Harrison, 1963; Kunii and Levenspiel, 1969) by the relation
and eq 11 reduces to (see Figure 2c)
WE = qEESYp-dY = q&[b - yp]
Ub:
Table I. Bubble Shapes, Size, a n d Rising Velocity 2.0 L min-' av 2b, AV, av 2a, bla = b/(l kV em b / a ) 2 ,cm (1 em 0 1.87 1.63 0.872 0.233 2 1.91 0.848 0.237 1.62 4 1.95 1.51 0.774 0.240 6 2.12 1.54 0.726 0.258 8 2.28 1.42 0.623 0.270 10 2.99 1.32 0.442 0.317
ub
=
ubr
+ UO - Umfo
(18)
In the case of the EFB of this study, there are only a few isolated bubbles. Also, as it will be shown in the next section, when the applied field increases, more gas flows through the emulsion phase. Thus, eq 18 is replaced by the approximation ub = Ub,. Among all the data giving rising velocities of bubbles (see Figure 11 of part l),the one for the flow rate Q = 2.0 L min-l, which showed little scattering, is used. The bubble shapes corresponding to this flow rate were reported in part 1 in the form of a major and minor axis, 2a and 2b, respectively. These data are summarized in Table I together with the corresponding rising velocity. Table I shows the increase in the eccentricity, e, of these elliptical cylinders with increasing field strength. Model eq 17 shows that, when b 0 and a is large, i.e., bubbles with the shape of thin cracks, ub, decreases as b1I2,assuming no dependence on E. However, as shown in Table I for the range of the data, the effect of the flattening of the bubbles in the electric field actually causes a small increase in the rising velocity. Nevertheless, this effect is overshadowed by the effect of the electric work. The value off is determined from the data of Table I for AV = 0 and Ub = 31.6 cm s-l which gives f = 2.09. Equation 17 can be rearranged into the form
-
The remaining data for AV > 0 have been correlated by eq 19, and the result is shown in Figure 4, which gives a reasonable agreement between the data and model eq 17. From a linear least-squares parameter estimation, we find n + 1 = 0.988 and X = 8.30 X (m s-~)(Vm-l)-(n+l).This result implies that n = 0, which shows that the charge is not affected by the electric field. In summary, we obtain the results =0 = Q E = 8.30 x c kg-' We recall that q E corresponds to the maximum charge in the polarized distribution around the particles. The value obtained above agrees remarkably well with the ones given by So0 (1974) for this type of material and where a net particle charge is assumed. It also compares to the value given by Hendricks (1973) for the spray charging of water droplets. If bulk polarization of the particles would be important, one would expect to find n = 1 (e.g., Bottcher (1952)). Thus, triboelectric charging appears to be pre-
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 459 301
I
I
I
I
I
I
Table 11. Physical Constants and Experimental Conditions of the EFB Bo= 2000 cm3 min-’ A = 13.26 cm2 d, = 194 pm 9,= 0.8 p s = 0.70 g cm-3 g cm-3 (0, at 20 OC, 1 atm) p B = 1.331 X p = 2.03 X lo4 g cm-’ 5-l (02 at 20 OC, 1 atm) D = 0.2 cm2 s-l (03in O2 a t 20 “ C )
I
I
Table 111. Basic EFB Equations
€
201
02
I
I
I
0 4
I
06
log ( A V )
I
I
08
I
I
I I O
a
b
C
Ab’: 0
av=o
0 Qa, when the applied field strength is increased, the bed expands with a linear increase in bed height, Lf.This increase is limited by the “freezing” of the bed, and just before this state, new minimum fluidizing conditions are obtained at the given applied potential, AVO,such that Qo = Qmf(AV0).The different cases showing the bed expansion are schematically presented in Figure 5. As the bed height increases with the applied field strength, simultaneously the bubble frequency, v, decreases considerably; the bubble velocity, ub, decreases, as shown in the previous section; but the bubble volume, ub, remains almost constant. The corresponding variations of these measured parameters presented in part 1 are summarized in Table IV. As a consequence of these variations, eq 21 shows that the gas flow rate through the bubble phase, Qb, decreases substantially. Since the total flow rate, Q, remains constant, the gas flow rate through the emulsion phase Q, = Q - Qb increases. Equation 22 shows that the bubble residence time, Ob, increases due to both the increase in L f and the decrease in ub. The results show that the increase in Ob is smaller than the decrease in Qb. Thus, considering eq 23, the total bubble phase volume, vb, decreases. Equation 24 shows that the volume fraction of bubble phase, 6, decreases even further. Equation 24 also shows that 6 is independent of
460 Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 Table V. Values of Computed Parameters in the Bed Expansion AV, kV Qb,cm3 s-l ob, s v b , cm3 Nb 0 14.6 1.25 18.3 5.89 1.39 16.2 5.13 2 11.7 4 12.0 1.51 18.1 6.02 18.2 5.47 6 10.3 1.76 17.6 5.33 8 8.58 2.05 16.4 4.07 10 7.25 2.26
"In
-
for Variable A V 6
c
0.0349 0.0301 0.0328 0.0322 0.0302 0.0275
0.546 0.559 0.570 0.580 0.592 0.603
El" 285 262 230 208 188 172
Ea" 2.03 1.90 1.72 1.60 1.48 1.39
W" 287 281 272 265 258 253
Y? 17.6 40.9 55.7 69.4 79.0
g cm-2 s-~.
Lf. But, the decrease in 6 and the increase in Lf are two conjugated phenomena which increase the voidage, t, of the emulsion phase, as shown by eq 25. This equation uses as a reference the state of the bed represented by case b of Figure 5 in which there is no applied field and a gas flow rate Qo > Qmfosuch that there are a few isolated bubbles rising in the bed. The actual variations of these calculated parameters, for the gas flow rate Q = Qo = 2.0 L min-', are given in Table V. In order to compute the minimum superficial gas velocity, ud0, required to fluidize a packed bed of particles, several authors (e.g., Leva (1959), Kunii and Levenspiel (1969))Richardson (1971)) have extended the correlation of Ergun (1952) to a bed in the minimum fluidizing conditions. The pressure loss given by the correlation is equated with the weight of the bed, yielding an equation in umfo.If this value is known, the force balance can be used to find the corresponding bed voidage, tmfo. In the present analysis, as an approximation, Ergun's equation will be further extended to all the cases of Figure 5 where Q = Qo > Q& in a slightly modified form. It is well-known that when Qo increases above the critical flow rate, Qmfo, the pressure drop does not increase substantially in a typical fluidized bed. This phenomenon invalidates Ergun's equation when the voidage is assumed to be constant. The modification introduced below dampens this predicted pressure increase. This approximation can also be justified by the scarcity of the bubbles in the cases considered, and their number further decreases as AV is increased. For the flow rate Qo and no applied electric field, the weight of the bed is given by
0.40 g cmW3, as given by the manufacturer. With the parameters of eq 27a-c, eq 26 reduces to eq 28
co = (P, - Pg)g
C$03 - Cl(l - z0)
-
C2 = 0
(274
(28)
where zo = to + a., A numerical solution of eq 28 readily gives the value z0 = 0.581 corresponding to the voidage to = 0.574 a t AV = 0 used as the reference in eq 25. When the electric field is applied, an additional friction or shear force acts on the bed along both electrodes, which tends to support the bed (Dietz and Melcher, 1978a,b). Equation 26 has to include an additional term which describes this force. It is assumed that it depends on the mth power of the applied field E = (AV)/w and that it is proportional to the electrode area. Also, it is assumed that it acts in the vertical direction through a constant friction factor, ff, such that it counteracts the weight of the bed and, for a high enough AV, eventually supports the bed entirely without any gas flow a t all (Dietz and Melcher, 197813). Thus, we obtain
W = ALq(1 - t o ) ( l - ~ o ) ( P ,- Pg)g The term tolio is neglected compared to to, introducing a relative error of 6o which is at most 3% for Qo = 2.0 L min-', as shown in Table V. In the case of A V = 0, the force balance is then written as c
By analogy with the right-hand side of eq 26 for the bed weight, the left-hand side giving the pressure drop considers a voidage which includes the fraction of bubble phase. This modification of Ergun's equation dampens the pressure increase for increasing flow rate since, as uo increases, the fraction of the bubble phase, 60, increases also. With a sphericity value & = 0.8 and a packed voidage of 0.43, related by the correlation of Brown et al. (1950), the specific gravity of the silica gel particles has been This . yields a bulk value of computed as ps = 0.70 g ~ m - ~
where 2 = t + 6 and m I0. For variable 2 in the neighborhood of 0.5, derivative calculations show that the variation of the term containing C1in eq 29 predominates. Thus, as AV increases, the right-hand side decreases, and considering the term in C1, t has to increase, which is in overall agreement with the experimental results on bed expansion. The quantified variations o f t are presented in Table V. Although the effect of 6 is small, eq 29 shows that its decrease with AV further contributes to the increase of t. Table V presents results in terms of the parameters
w = Co(1 -z)
(30~)
It shows that the values of E2are only 1% of those of E l , implying that in Ergun's equation the viscous dissipation largely predominates over kinetic energy losses, as could
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 461 I 9
18
17
16
7 0
0 -
I 5
14
13
0 2
0 4
0 8
06
log ( A V )
10
(kV)
Figure 6. Correlation of the bed expansion with eq 31.
have been predicted for the small flow rate. With the parameters of eq 30a-c, eq 29 can be rearranged into the form log Y , log (W - El - E,) = log w
+ m log (AV)
(31)
where w=-
2ffC wm+l
Figure 6 shows the experimental data from Table V which have been correlated by eq 31. This figure shows a good agreement between the data and model eq 29. The slightly downward concavity may be attributed to a less good approximation by the modified Ergun's equation a t lower values of AV. From a linear least-squares fit plotted in Figure 6, we obtain the power m, giving T,
= ff{[AV/~u]'.~~
(1969), we will consider three distinct phases: (1) the bubble phase; (2) the cloud phase around the bubbles; (3) the emulsion phase. As shown previously, the applied electric field changes the hydrodynamics of each of these phases which in turn affect the conversion. The present model will ignore bubble coalescence, which is not very important due to the relatively small number of bubbles present in the conditions investigated. As was also shown (part l),the substitution by cobaltimpregnated silica gel changes the bed expansion very little. All the other characteristics required in the present model were obtained experimentally with pure silica gel, and thus we will consider here the bed expansion obtained for pure silica gel. In order to compensate for the slightly smaller relative bed expansion with this material, a little more material was used in the experiments. In the model proposed by Kunii and Levenspiel (1969) which applied to a vigorously bubbling bed, the conversion was calculated by assuming that no gas leaves the emulsion phase. It was shown that, for the EFB under investigation, most of the gas passes through the emulsion phase and it cannot be ignored in the overall exit stream which it dilutes. The catalytic reaction only takes place in the particles, and it is assumed that there are no solids inside the bubbles. In order to describe the mass transport in a usual fluidized bed, it is often assumed that there is plug flow in the bubble phase with mass transfer through the bubble-cloud interface. This assumption is also made in the present model. The cloud phase rises with the bubbles. As a logic extension, the plug flow assumption is thus also made for the cloud phase with mass transfer through the cloud-emulsion interface. It is assumed that the voidage in the cloud phase is the same as in the emulsion phase. This model is then consistent with the developments of the previous section, since, with respect to the voidage, the cloud phase is indistinguishable from the emulsion phase. The flow pattern for mass transport is harder to describe in the emulsion phase due to the agitation of the particles and even their downward flow in some areas. An axial dispersion model can be considered. However, in the EFB of this study, the ratio Lf/(wd)'f2 is high, and thus we will also assume plug flow in this phase. In these conditions, the steady-state mass balances for ozone in each phase give eq 33a-c which express the rate of change of the ozone (334
[
(32)
This power is very close to the linear dependence found in eq 20 for the interparticular attractive force. Finally, this power also compares to the value m = 1.2 given by Dietz and Melcher (1978a,b) as shown in eq 2, although their result applied to an EFB in different conditions.
Conversion in the EFB Reactor A. The Model. This section intends to model the catalytic conversion of ozone into oxygen obtained in the EFB, when the silica gel was activated by impregnation with cobalt (part 1). Several investigators have related the hydrodynamic behavior of a fluidized bed to the chemical reaction occurring in it. Various models describing a heterogeneous catalytic reaction in a fluidized bed have been proposed and summaries published (Calderbank and Toor, 1971; Yates, 1983). Following Kunii and Levenspiel
-dCe =-
fibhe
6
(1- c)
+ i]%Cc
Kr (C, - Ce) - (1- c)-Ce
(33b)
(33c) dz cue 1 _-6(1 + p) cue C b = cc = c e = ci, at z = 0: (34) concentration with the bed height, z. The known inlet concentration is the initial condition given by eq 34. The parameters of eq 33 which are not already defined in Table I11 are given in Table VI. Equation 33b includes a bubble wake of total volume V8,,. Equation 33c actually applies to the gas in the emulsion phase which percolates through the particles. Equations 33b,c assume a first-order decomposition reaction of ozone within the solids with a rate constant K,. It is assumed that the cloud phase rises with the same velocity as the bubble phase, i.e., u, = U b , as
462 Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 2 50
Table VI. Parameters for the Ozone Mass Balances u, = Qc
(35)
=
(36)
PtQb
Qo-
u = -Qe= e
tuc= 6 c r b
A,
Qb-
[l - 6(1
u, = U e / e ff
=
v8,w/vb
Qc
+ P)]A
I
I
I
I
I
-
r:
I
(37)
4
(38)
1
(39)
3 M O D E L PREDICTIONS W I T H E X P E R I M E N T A L
expressed in eq 35. Equation 36 is derived from the assumption of eq 35 and the definition of eq 40, and it gives the gas flow rate through the cloud phase. Equation 41 is based on the Davidson model and is given by Davidson and Harrison (1963) as well as by Kunii and Levenspiel (1969). Equations 42 and 43, which express the mass transfer between phases, are given by Kunii and Levenspiel (1969) and apply actually to 3D spherical bubbles. These latter expressions are used as approximations, and for a more rigorous description, only mass-transfer coefficients based on 2D ellipsoids would be suitable. To remain consistent in the latter approximations, db of eq 42 and 43 has been computed as the equivalent diameter of a 3D spherical bubble. A closer look at Table VI shows that, when eq 36-38 are combined on one hand and when eq 40 and 41 are combined on the other hand, two equations are obtained in which the two unknown parameters /3 and U, are given implicitly. The elimination of U, and the use of eq 21 and 24 gives the ratio /3 as the solution of linear eq 44 which uses only parameters defined in Table 111.
The parameters of eq 33 vary as the hydrodynamic characteristics of the EFB change with increasing field strength. The variations of some parameters introduced in Table VI are given in Table VII. This latter table shows that these parameters do not change drastically, except for /3 which increases by a factor of 2.20 when the applied potential varies from 0 to 10 kV. Also, the magnitude of /3 shows that the gas flow rate through the cloud phase cannot be ignored. Equations 33a-c form a system of three linear first-order ordinary differential equations in the three unknowns c b , Cc, and C,. With the initial condition given by eq 34, a unique analytical solution can be derived (see, e.g., Amundson (1966)). Reliable numerical methods of solution for such problems are also readily available. For the constant flow rate Q = Qo = 2.0 L min-', all the parameters of eq 33a-c are either known or can be calculated, except for cy and the reaction rate constant, K,. Due to the elliptical shape of the bubbles for increasing field strength, the bubble wake is hard to define. For this reason, the bubble wake is ignored in this analysis, which implies that a = 0. A parameter estimation has been done for K , by comparing the solution of eq 33a-c with the experimental
DATA F O R Ub, L,, U , vb AS I N P U T
A
I50 0
EXPERIMENTAL DATA
2
6
8
10
AV(kV)
Figure 7. Model predictions and experimental data for the average outlet concentration of ozone from the EFB reactor.
values of the outlet concentration of ozone for variable field strength. The average outlet concentration predicted by the model and given by eq 45 is compared
The feed concentration was obtained from ozone generator calibrations, giving Ci, = 1500 ppm. With the optimally estimated value for the reaction rate constant K , = 0.346 the results of a numerical integration, using the RungeKutta-Verner routine from IMSL named DVERK, gave the average outlet concentrations shown in Figure 7. These results show a good agreement with the experiments, giving a linear decrease for increasing field strength (part 1). The optimal numerical value obtained for K, also compares very well with the values of Kobayashi et al. (1966) who decomposed ozone in a regular fluidized bed using the same catalyst. Thus, the simple plug flow model for all three phases is a good enough model for the behavior of this EFB reactor. The minor discrepancies between data and model predictions may be due to the fact that the hydrodynamic bed characteristics used were for pure silica gel rather than catalyst. The use of 3D mass-transfer coefficients for spherical bubbles may also introduce a small error. It should be pointed out that small changes in the values of K, give substantially different values for the conversion at each value of the field strength, and the rate of change of concentration with the field strength is not adjustable independently. The average outlet concentration given by the line in Figure 7, which represents a linear least-squares approximation of all experimental data points and model predictions a t each value of AV, decreases by 22% when the potential increases from 0 to 10 kV.
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 463 Table VII. Values of the Parameters of Table VI for Q = Q o= 2.0 L min-' and Increasing Field Strength AV, k V Qe, cm3 s-l ug,cm s-l U,,cm s-l P (Kbc)b, 8-l 1.37 2.50 0.172 0 17.3 10.4 2 4 6 8 10
20.2 19.8 21.4 23.1 24.4
1.58 1.56 1.68 1.81 1.91
Table VIII. Values of Parameters of Equations 46a-d A V = 10 kV p' (u,)b, cm s-l uc, cm s-l AV=O 0.172 2.97 17.3 3.06 10.7 UblAV-10 kV o.287 2.94 19.0 L$AV-10 kV 0.155 YIAV-10 kV
A V = 10 kV
0.266 0.379
4.67 4.55
17.6 12.0
2.83 2.73 2.90 3.06 3.17
0.214 0.219 0.272 0.334 0.379
10.8 11.0 10.9 11.2 10.6
(K&, K1 5.17 5.00 5.02 4.50 4.30 3.79
in the Sensitivity Analysis and Two Experimental Cases: A V = 0 and 1- c 0.454 0.464 0.400 0.444 0.397
u,, cm s-l 1.37 1.33 1.36 2.06 1.91
8 0.0349 0.0554 0.0349 0.0134 0.0275
1-
+ 8)
0.9591 0.9287 0.9597 0.9830 0.9621
(K&, 10.4 10.3 10.4 12.1 10.6
(Koe)b,8-l 5.17 4.06 5.42 5.21 3.79
Table IX. Values of the Lumped Parameters of Equations 46a-c0
UblAV-lOkV
0.5171 0.3277 0.3674 0.5335
LdAV-10 kV YIAV-10 kV
A V = 10 k V
3.365 3.524 2.775 2.331
1.329 1.844 1.243 0.8316
0.009 108 0.015 05 0.007 288 0.008 846 0.011 43
0.1378 0.181 2 0.144 4 0.055 05 0.056 54
0.1152 0.1200 0.101 4 0.082 77 0.071 68
In cm-'.
B. Parameter Sensitivity Analysis. The model thus validated enables us to analyze quantitatively the effects of the hydrodynamic changes in the bed for increasing field strength. Tables I11 and VI show that four key parameters can be identified from which all other parameters can be computed. These parameters are (1)the bubble frequency, v ; (2) the bubble volume, ub; (3) the bubble velocity, Ub; and (4) the bed height, Lp The results of Table IV have shown the simultaneous variations of these parameters as the field strength is increased, and the results of Table IV have shown also that ub remains almost constant. In a parameter sensitivity analysis of their effect on the ozone conversion, the three parameters Ub, Lf, and v are allowed to vary independently. In order to see the effect of one parameter, the two other parameters, as well as ub, are kept constant and equal to their value at AV = 0, while this one parameter is allowed to vary as measured when AV varies from 0 to 10 kV. These results are compared to the experimental cases a t AV = 0 and 10 kV in which the parameters &, Lf, and v vary simultaneously, including Ub. a. Composite Model Parameters. It is advantageous to rewrite eq 33a-c in a simplified form and in a form where the assumption that cy = 0 is implied:
-dCe =-
(Kce)b
dz
u,
6 1- 6(1
+ p)
K* (C, - C,) - (1- E)-C, Ue
(46~)
The terms of eq 46a-c will be referred to as "intrinsic" rate process terms and their absolute values will be implied; e.g., if the intrinsic mass transfer of eq 46a decreases, the slope of C b becomes less negative. The variations of the parameters of eq 46 in the sensitivity analysis of U b , Lf, and v and the experimental cases a t AV = 0 and 10 kV are recorded in Tables VI11 and IX. These values show that in the experimental case at AV = 10 kV, antagonistic effects are obtained. Specifically,Table VI11 shows considerable variations in 8, (uc)b, uc, u,, 6, (Kce)b, and a smaller but nonnegligible variation in e. The decrease in 1- E is almost completely due to Lf. Because of the small value of 6 compared to 1, as also shown in Table VIII, U b and v do not affect e very much, as predicted by eq 25. The sharp increase of p is due essentially to U b and, to a little lesser extent, to v, but there is a small dampening effect due to Lf. Similarly, there is a considerable increase of (u,)b, due especially to v, with a small contributing effect by U b and a small dampening effect by Lf. The decrease of u, is due to u b , but it is also dampened by Lf.The increase of u, is due to v. In addition, Table VI11 and eq 24 show that the decrease of 6 due to v is substantially dampened by u b . The decrease of (Kce)bis mainly due to u b and is dampened by Lf, but there is also a decreasing effect caused by u b a t AV = 10 kV which is not considered in the sensitivity analysis. b. Concentration Profiles in the Three Phases. As mentioned previously, an analytical solution of eq 46a-c for c b , C,, and C, and can be derived in terms of three eigenvalues and three eigenvectors. However, the eigenvalues are the three roots of a cubic equation, and the complexity of the algebraic formulation would not allow exhibition of the effects of the individual parameters: Ub, Lf, and v. Therefore, numerical integrations are also performed in the parameter sensitivity analysis. For each set of parameter values used a t a given value of AV, the concentration profiles including the outlet concentrations are computed. At the inlet, eq 46a-c give
464
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 Table X. Values of the Sums Defined by Equations 48a-d"
(474 AV=O LblAVclOkV LflAV=10 kV
ulAV=10 kV
A V = 10 kV
SI
s 2
s 3
s 4
3640.8 2395.3 3726.5 3157.8 2352.7
7854.7 6700.5 7677.3 8209.1 7683.5
28749 27 900 31714 30088 32513
20895 21 199 24037 21879 24830
"In ppm cm.
Regardless of the field strength, we always have u, > ue. Thus, the initial slopes are always such that dCC dz
d21i;o> dCb
=
lzio
> -d Ce dz
lzi0
An accurate analysis of the variations in the outlet concentrations can be given in terms of the overall physicochemical rate processes involved. For this purpose, it is useful to introduce the sums
S3 = s L0 f C cdz S4 = L L f C edz
where
K, (AC,), = (1 - t)-S4
(50f)
Ue
The expressions defined by eq 50a-f give the contribution of specific physicochemical rate processes to the outlet concentrations from the three phases, referred to as CTOC. In the case of the experimental conditions at AV = 0 and 10 kV, the ozone concentration profiles in the three phases predicted by the model are given in Figure 8. These variations can be related to the effects produced by the separate variations of the parameters ut,,Lf, and v, for which the concentration profiles are shown in Figure 9. The values of the sums defined by eq 48a-d and the ones of the CTOC defined by eq 50a-f, both obtained in the parameter sensitivity analysis of ub, Lf, and v as well as
for the experimental cases at AV = 0 and 10 kV, are given in Tables X and XI, respectively. Table XI also includes in the last column the percentage of decrease in outlet concentration in each phase, i = bubble, cloud, and emulsion: i. Separate Variations of the Parameters. The separate decrease of produces substantially lower values of Cb throughout this phase. It leaves the profile of C, almost unchanged for z < 6 cm and lowers it sizably at larger values of z , including the outlet. The profile of Ce is almost unchanged; it is raised a little in the middle of the bed and is very slightly lowered toward the outlet. These variations are respectively due to an increased intrinsic mass-transfer bubble-cloud for Cb at smaller values of z and an increased intrinsic reaction in the cloud phase for C, at intermediate values of z , resulting from increased residence times in these phases through the lower values of ub and u,. The compounded effects, as expressed by the CTOC of these processes given in Table XI, show the same variations. The separate increase of Lf actually produces raised profiles for all three concentrations, Cb, C, and c,, in the range 0 < z < Lf0. These variations are caused by a decrease in intrinsic reaction at every location in both cloud and emulsion phases through the higher value of t. These phenomena in turn produce a decrease in intrinsic masstransfer bubble-cloud for Cb a t values of z such that z < 10 cm, due to a decrease of the driving force Cb - C, and raise the profile of cb. However, the increase in Lf also produces an increase in residence time in all three phases. As a consequence, S1is increased, in spite of the decrease in the driving force, Cb - C,, as shown in Table X, and the CTOC of the mass transfer in the bubble phase is increased. The increase of S1 also increases the CTOC of the mass-transfer bubble-cloud in the cloud phase. But the CTOC of the mass-transfer cloud-emulsion in the cloud phase is mainly increased due to (Kce)b,and not S2 which decreases. The increase in residence time also increases S3 and S4,in addition to the effect of the raised profiles of C, and C,. But these variations do not affect the CTOC of the reaction in the cloud and emulsion phases due to the antagonistic effect of t . As a result, the exit concentrations of the bubble and the cloud phases are decreased, and the exit concentration of the emulsion phase is almost unchanged. The separate decrease of v produces, at small and intermediate values of z , substantially raised profiles for all three concentrations, c b , C,, and Ce. These variations are even larger than the ones caused by Lf.However, for large values of 2, all three profiles are lowered, with crossover points between 23 and 32 cm. Yet, only the decrease in the emulsion phase is substantial. The initially raised profile of C, is due to a decrease of the intrinsic reaction in this phase, itself caused by a decrease in residence time through ue. The lowering of C, at higher values of z is due to the extremely sharp drop in 6 which causes a big reduction in the intrinsic mass transfer into this phase and which dwarfs the effects of the reaction. These variations
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 465
900 0
I
I
1
2
I 3
I
4
5
6
7
6
9
z (cm)
0
0
BUBBLE PHASE CLOUD P H A S E EMULSION P H A S E
-
- CASE U
IO00
-
Fl a
-
-
V
-
500
t
01 1 IO
t
1 I
I
I
I
I
I5
20
25
30
35
I 40
1
0
45
z (cm)
20 IO
25
30
35
40
45 0
15
z (cm)
Figure 8. Calculated profiles for the ozone concentration in the three phases of the EFB reactor a t two values of the applied field: a, top; b, bottom.
Figure 9. Calculated profiles for the ozone concentration in the three phases of the EFB reactor with the separate variations of the parameters: a, top; b, bottom.
are carried over into the two other phases through the driving forces in the intrinsic mass-transfer terms, with a dampened effect.
ii. Simultaneous Variations of the Parameters. In the experimental cases, when AV increases from 0 to 10 kV, Figure 8 shows that the concentration profiles in each
466 Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 Table XI. Contributions of the Processes to the Outlet Concentration in the Phases" case concn -(ACbc)b (4cbc)c -(ACcA -(ACAc AV=0 Cb -1193.2 cc +12 730.0 -13 702.7 -261.9
+1082.3
c e
ublAV=10
k\'
Cb
+8 060.0
c; Cb
cc
-8902.8
Ch
cc Cb
cc
+1214.3
-2544.6
+1108.8
-2436.7
-1221.3 +13 130.9
-14 155.3
-231.1
-1208.8 +8 165.6
c, 1 V = 10 kV
-2407.0
-419.9
c e
ylAV=10 kV
-(AC,),
-1238.7
C, LflAV=10 kV
(GA
-9 149.9
-263.3 +281.8
-1629.1
+434.4
-1779.9
-1255.2 +5 484.7
-6 389.6
-371.5
Caut or PDOC 306.8 265.4 175.3 15.0% 10.6% 2.86% 9.12% 7.92% 1.71% 5.21% 4.91% 12.6% 20.2% 15.5% 11.4%
"In ppm.
of the three phases are raised for 0 < z < L,, but near the outlet, z = Lf, all are lowered. The effects, with enhancements and antagonisms, produced by each of the three parameters, ub,Lf, and Y, can be shown when these profiles are compared to the ones of Figure 9. The values of the PDOC given in Table XI clearly show that the separate effects of each of the three parameters contribute to lower the outlet concentration in each phase, but they are not additive due to antagonisms. Near the origin, the variations in the slope of the three profiles are given by eq 47a-e. Tables VI11 and IX show that the decrease of 1 - e caused mainly by Lfis less important than the decrease of u, caused by ut,, and thus, the initial slope of C, becomes more negative. This result seems to be in contradiction with Figure 8a. However, an enlargement shows that, up to about z = 0.05 cm, the profile of C, for AV = 10 kV is indeed below the one for A V = 0. As given by Table VIII, u, increases substantially due to v. Thus, the initial slope of C, becomes less negative due to both v and Lf, respectively, through u, and 1 - e. The enhancing effects of these two parameters are shown in Figure 8a when compared to Figure 9a. For values of z not too near the origin, it is more convenient to analyze the variations of the concentration profile in the emulsion phase first, with references to eq 46c. A t smaller values of z , i.e., z I 5 cm, the profile of C, is an extension of the effects on the initial slope. At intermediate and larger values of z , the profile of C, is considerably affected by v, which drastically decreases the intrinsic mass-transfer cloud-emulsion into this phase, through 6. This variation causes a decrease in the slope of c,, although it is dampened by ut,.The effect of Lf through 1 - E , giving a lower intrinsic reaction, also dampens the decrease in slope and keeps the profile of C, raised. The values of the CTOC in Table XI show the dominance of v with dampening effects of ub and L,. Also, the CTOC of the mass transfer decreases more than the CTOC of the reaction, and thus, the outlet concentration from the emulsion phase is decreased. Roughly, the profile of C, is the result of the superposition of the following features: decreasing ub has an inertia effect; increasing Lfstretches it to larger values of z in an affine transformation parallel to the z axis; decreasing v raises it at small and intermediate values of z but lowers it at larger values of 2 . The concentration profile in the cloud phase can be analyzed with references to eq 46b. At smaller values of z not too near the origin, it is mostly affected by the variations of the two intrinsic mass-transfer terms. Es-
pecially v renders the net intrinsic mass transfer less negative through the driving force, C, - C,. Lfhas a similar effect of a lesser magnitude, and both parameters act in concert to produce an increase in the slope of C, and a raised profile. These variations are shown in Figure 8a, when compared to Figure 9a. At these smaller values of z , the behavior of C, is similar to the one of C,. A t larger values of z , the slope of c, decreases due to ub, which increases the intrinsic reaction in this phase, through a much lower u,. The latter variation is enhanced by v, again through C, - C, in the intrinsic mass transfer, as well as by Lf,through a higher (&&. The values of the CTOC in Table XI show a small variation in the net negative mass transfer, for which Lfdampens the relative increase caused by ub. The CTOC of the reaction is substantially increased to a value between the ones obtained when & and Lf varied separately. As a result, the outlet concentration from the cloud phase decreases. To summarize, the profile of C, is roughly affected in the following way: the decrease of ub lowers it at larger values of z ; the increase of Lf stretches it to larger values of z in an affine transformation parallel to the z axis and lowers it at larger values of z ; the decrease of v raises it at smaller and intermediate values of z and lowers it slightly near the outlet. The concentration profile in the bubble phase is determined by the mass-transfer bubble-cloud, as given by eq 46a. A t smaller values of z not too near the origin, in spite of the drastic decrease in U,, the intrinsic mass transfer is reduced, due to the increase of C, explained above. However, at these values of z , Figure 8a, when compared to Figure 9a, shows that the slope of Cb is between the ones produced by the separate variations of v and Lf.This result shows that ub considerably antagonizes the effects of each v and L f , which both decrease the intrinsic mass transfer through the raised profile of C,. At larger values of z , the reduction in the increase of C,, as also explained above, acts together with Ub to increase the intrinsic mass transfer and to decrease the slope of cb. Table XI shows that the CTOC of the mass transfer in the bubble phase is increased due to each of the three parameters in the order ub > Lf> v, but not additively. In summary, the profile of C, is the superposition of the following features: the decrease of Ub lowers it considerably; the increase of L f stretches it to larger values of z in an affine transformation parallel to the z axis and lowers it considerably a t larger values of z ; the decrease of v raises it at smaller values of z and lowers it a little near the outlet. c. Total Rates in the EFB Reactor. The behavior of the EFB reactor can be described in terms of total
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 467 Table XII. Total Rates of the Processes in the EFB Reactor" case phase Fin kTbc AV=O b 21 926 -17 442 2 055 26019 21 926 3 370 24 705 21 926 2 039 26 035
C
e b
UblAV=lO kV
C
LdAV-10
e b
kV
C
e
b
ylAV-10 kV
8 397 1243 40 360 10 881 2 490 36 629
C
e b
A V = 10 kV
C
e
+17442 -18 106 +18 106 -17 852 +17 852 -6 767 +6 767
-9 105 +9 105
kTw
-Rc
-18 774 +18 774
-359
-19 999 +19999
-943
-19 244 +19 244
-314
-7 582 +7 582
-218
-10608 +lo608
-617
-Re
FO",
-41 909
4484 364 3040 3820 534 2795
-42 294
4074 333 2985
-41 753
-43 833
-43 463
1630 210 4109 1776 370 3774
"In (ng of O3s-')/(g L-l).
mass-transfer rates, Tij,from phase i to phase j and total reaction rates, Rk, in phase k. These rates are given by
Tbc = Qb(ACbc)b = Qc(ACbc),
(514
Tce =
(51b)
Qc(Acce)c
Rc =
=
Qe(Acce)e
Qc(Acr)c
Re = Qe(ACr)e
(51~) (5W
With eq 50a-f and appropriate equations in Tables I11 and VI, the total rates can be expressed as
= 6A (Kbc)b s 1
(524
Tce = 6A(Kce)bS2
(5%)
Tbc
R, = @ ( l - E)AK,S~ Re = [ l - 6(1 + p)](1 - €)AKrS4
(52~) (524
The numerical values of these rates in the parameter sensitivity analysis of ub, Lf, and v, and for the experimental cases at AV = 0 and 10 kV, are given in Table XII. For a complete description, Table XI1 also gives the ozone inflows into the three phases, Fk,in = QkCin,and the corresponding ozone outflows, Fk,out = QkCklL* k = b, c, e. The discussion will concentrate on the experimental cases when AV varies from 0 to 10 kV. For the bubble phase, the drastic decrease of v decreases the ozone inflow almost equivalently through Qb given by eq 21. However, for AV = 10 kV as shown in Table XII, the small increase in ub, which has been ignored in the sensitivity analysis, prevents an as big a decrease in Qb as in the case where v decreased alone. The flow rate, Qb, directly quantifies the so-called "gas bypassing" in the form of bubbles. As shown by eq 52a, Tbcis affected by 6 and S1.The sharp decrease of v causes an equal decrease of 6, but the latter variation is antagonized by ub. Table X shows that SI is sharply decreased by ub and by v to a lesser extent. Overall, Table XI1 shows that Tbcis drastically decreased by v, with ub, and to a small extent Lf, antagonizing this variation. The decrease in ozone inflow is more drastic than the decrease in Tb,. The result is a considerable decrease in ozone outflow from this phase by a factor of 1/2.5, which is nearly the same as in the case where v varied alone. For the cloud phase, the more than doubling of 0,the small increase in E, and the small increase of u b at A v = 10 kV override the decrease of v and produce an increased ozone inflow into this phase through Q,, as given by eq 36 and shown in Table XII. Equation 52b shows that the variations of 6 affect TCein the same way as Tb,. Table
X shows that S2is decreased substantially by u b , as was SI,but v increases S2,as opposed to S1. Overall, S2is only decreased a little. The decrease of (Kce)b,caused by ub but also by the increase of u b a t AV = 10 kV, also affects T,. Overall, however, the decrease of SI is larger than the one of S2and (Kce)bcombined, and the decrease of 6 is not large enough to reverse the effects of these variations which cause a larger decrease of Tbcthan of T,, as shown in Table XII, and the net transfer into the cloud phase becomes more negative. As given by eq 52c, R, is mostly affected by the large variations of 0and 6 shown in Table VIII. Lf does not affect R,, as the decrease in 1- E is cancelled by the increase in SB.ub increases both 0 and 6, thus considerably increasing R,, while v causes a sharp decrease in 6, dampening this increase, as shown in Table XII. But all the variations in the cloud phase balance out, and the ozone outflow from this phase is almost unchanged. For the emulsion phase, the ozone inflow is substantially increased due to the very large decrease of inflow into the bubble phase. As mentioned above, this variation in turn is due to the large decrease in v, and it would have even been greater if u b had not increased at AV = 10 kV. Simultaneously, T,, is cut by almost one-half due to the sharp decrease in 6 caused by v, as discussed previously. As given by eq 52d, Re is affected by the variations in 6, 1- E , and also the profile parameter S4. Table XI1 shows a substantial increase in Re due to both parameters Lf and v, with v having a stronger effect. The increase of Re due to Lf acts through the large increase of S4but includes an antagonizing effect by 1 - 6 . The increase of Re due to v acts through the sharp decrease of 6, as well as the increase of 8,. u b causes small increases in 1 - e and s4but also a large increase in 6, which cancels the net effect on Re. Overall, however, since the ozone inflow in this phase is so much increased, the result is a small increase in ozone outflow from this phase by a factor of 1.2. To summarize, as AV increases from 0 to 10 kV, starting from original inflows which are about equal for the bubble and the emulsion phases and with the one of the cloud phase at 1/10 of that value, half of the inflow of the bubble phase is redirected into the emulsion phase and a small fraction of it adds to the inflow of the cloud phase. The overall performance of the EFB reactor can be measured by the sum Rc + Re, which, when computed with the results of Table XII, ranks the cases in the following order: ( A v = 0) < LfIlokV < UblIOkV < V(10kV < ( A v = 10 kV) This result shows that each separate variation of the three parameters, ub, Lf, and v, contributes to the increase in overall conversion and gives their order of importance. The
468 Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989
results for R, and Re also show that the effects of the separate variations are not additive, as numerous dampening antagonisms occur. The total rate results also show that, at high field strength, when the bubble phase is considerably reduced, the emulsion phase tends to impose the overall outlet concentration. Summary and Conclusions 1. The decrease of the rising velocity of the bubbles in the EFB with increasing electric field strength can be explained by the assumption of potential flow in the emulsion phase, as in the Davidson model, with the addition of an electrical potential. The shape of the bubbles can be approximated by cylindrical ellipsoids which rise in the direction of the minor axis. Their eccentricity, which increases with the electric field strength, has been taken from the experimental data. In the quietly bubbling bed in which the interparticle contact time is small, the particles are assumed to be polarized in the high electric field and to have no net charge, causing a polarization at the bubble surface. When these bubbles rise in the emulsion phase, they perform an electrical work which increases with the field strength and slows down the bubbles. This theory allows for the derivation of an expression for the rising velocity in terms of the bubble shape and the field strength. This result shows that for very large values of the eccentricity, i.e., crack shaped bubbles, the velocity decreases with increasing eccentricity. However, in the region of the experimental data, the flattening of the bubbles with increasing field strength actually causes a small increase in velocity. This effect is completely overshadowed by the effect of the electrical work. The theoretical result could be successfully correlated with the experimental data on bubble rising velocities. The results show that the polarization charges of the particles are independent of the applied field. This phenomenon can be explained by the predominance of the polarization of triboelectric surface charges over bulk polarization. The amount of triboelectric surface charges depends on friction only, which in turn depends essentially on the gas flow rate and not on the applied field. A saturation is then obtained in the high field. As a result, the interparticular attractive forces are linear with the applied field strength. 2. The bed expansion for increasing field strength and constant gas flow rate can be explained by the balance of three forces which act on the quietly bubbling bed. These forces are as follows: (1)the weight of the bed; (2) the pressure drop which has been described by a slightly modified Ergun’s correlation; (3) the shear stress at the electrodes created by the electric field, which increases with the field strength and which partially supports the bed weight. The experimental data on bed hydrodynamics show that the decrease in bubble phase fraction is completely overshadowed by the increase in voidage in the emulsion phase which is directly related to the bed expansion. These data could be successfully correlated with an electric shear stress at the wall which varies with the field strength raised to the power 0.93. This result compares well with the linear dependence of the interparticular force on the field strength found previously. 3a. The catalytic conversion of ozone in the EFB can be modeled by using the observed hydrodynamic changes with increasing field strength. This is accomplished in a model which considers three phases, a bubble phase, a cloud phase, and an emulsion phase. Plug flow is assumed in all three phases. An overall exit concentration is computed as a flow rate weighted average of the phases. With the catalytic reaction rate constant as the single adjustable paranpter. the overall ozone conversion predicted by the
model, for variable field strength and constant gas flow rate, matches well the experimental data. When the potential increases from 0 to 10 kV corresponding to a field strength increase from 0 to IO5 V m-l, the ozone outlet concentrations predicted and measured decrease linearly by 22% f 2%. The optimal value of the reaction rate constant used in the model is in good agreement with previous work done with the same catalyst. 3bl. The model allows for a quantitative analysis of the effects caused by the variation of three measured parameters; (1)the bubble rising velocity, ub; (2) the bed height, Lf; (3) the bubble frequency, v. The concentration profiles and the outlet concentrations can be described with intrinsic rate process terms per unit flow rate through the specific phases. Each separate variation of these three parameters decreases the outlet concentration in each of the three phases. The effect of the simultaneous variations on the concentration profiles is a superposition of the effects caused by the separate variations. Antagonistic effects on the rate processes produce nonadditive variations in the concentration profiles and the outlet concentrations. As a net result, in all three phases the profiles are raised throughout the original height of the bed, but the outlet concentrations of the expanded bed are decreased. 3b2. The EFB reactor can be described in terms of the total rates of the physicochemical processes involving the three phases. Both the decrease in u b and the increase in Lf increase the total transfers from the bubble phase into the cloud phase, as well as from the cloud phase into the emulsion phase. Moreover, the decrease in u b increases the flow rate through the cloud phase and increases the total reaction in this phase. The increase in Lf increases the total reaction in the emulsion phase. The decrease in v produces a drastic decrease of the flow rate through the bubble phase, mainly to the advantage of the emulsion phase, and considerably reduces the so-called “gas bypassing”. In turn, this variation increases the total reaction in the emulsion phase considerably, due to the additional “contacting” in this phase. As a result, the variations of each of the three parameters contribute to the increase in total reaction in the EFB reactor, with an order of importance as follows: v > u b > L,. However, these effects are not additive. The effect of v antagonizes the ones of ub, producing the increase of flow rate through the cloud phase and the total reaction in this phase. The effect of v reverses the ones of both ub and L f ,producing the increase of all total mass transfers. At high field strength, the sharp reduction of the bubble phase causes the emulsion phase to control the outlet concentration of the EFB reactor. Acknowledgment The author is very thankful for a financial contribution from the State of Illinois through Professor D. Gidaspow of the Illinois Institute of Technology. The author also thanks B. Ademoyega, MSChE, for help with some calculations in the section on conversion. Nomenclature A = cross section of the EFB (=wd),cm2
bubble interface area per unit volume of bubble, cm-’ a = half major axis of elliptical bubble, cm b = half minor axis of elliptical bubble, cm C, = concentration of ozone in phase k , k = b, c, and e, ppm C = average concentration of ozone, ppm c = focal distance of elliptical bubble, cm D = molecular diffusivity of ozone in oxygen, cm2 s-’ (ib =
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 469 d = bed depth, immaterial dimension, cm d b = equivalent diameter of the bubbles, cm d, = equivalent diameter of particles, cm E = strength of applied electric field ( = A V / w ) , V m-l E,, = field strength in a region near the interparticular contact, V m-l Eo = field strength along the axis of a particle chain, V m-l El, E2 = expressions defined by eq 30a,b, g cm-2 s - ~ e = eccentricity of elliptical bubble, dimensionless FE = interparticular attractive electric force, g cm Fk = ozone inflow or outflow into or from phase k, ppm of O3 cm3 s-1 f = correction factor introduced in eq 17, dimensionless ff = friction factor of particles at the electrodes, dimensionless f, = electric force between two particles along the axis of a particle chain, g cm s - ~ g = acceleration of gravity, cm ( K d b = ebkb,, K1 (Kce)b = cbkce, S-l K , = reaction rate constant, s-l k , = mass-transfer coefficient of ozone from phase i to phase j , cm s-l Lf = bed height, cm Nb = number of bubbles in the bed, dimensionless NT = total number of contacts of a particle, dimensionless P = dipole moment per unit volume of particles, C m-2 P = total potential for the flow in the emulsion phase, g cm-2 9-2
p = apparent hydrostatic pressure in the emulsion phase, g
cm-l s - ~ Q = total gas flow rate through the EFB, cm3 s-l Qk = gas flow through phase k , k = b, c, and e, cm3 s-l Qd = total gas flow rate in the minimum fluidizing conditions at AV, cm3 s-l q = electric charge on the bubble surface, C & = charge density in the emulsion phase, C m-, qE = maximum electric charge on the bubble surface per unit mass of emulsion phase, C kg-l GE = as above per unit volume of emulsion phase, C m-3 = as above per unit external area of particle, C m-2 Rb = radius of curvature of the spherical cap of the bubble, cm Rb = equivalent radius of a spherical bubble, cm R , = equivalent radius of bubble + cloud, cm Rk = total rate of reaction in phase k of the EFB, k = c and e, ppm of 0, cm3 s-l R, = equivalent radius of particles (=d,/2), cm Si = sums defined by eq 48, ppm of O3 cm s = arc length at the bubble surface, cm Tij = total mass transfer in the EFB from phase i to phase j , ppm of O3 cm3 s-l U = velocity of the emulsion phase far away from the elliptical cylinder, cm s-l ub = absolute rising velocity of the bubbles, cm s-l ub, = relative rising velocity of the bubbles, cm s-l uk = absolute velocity of the gas in phase k , k = c and e, cm S-1
ii = velocity distribution of the emulsion phase around an elliptical cylinder, cm s-l u = superficial gas velocity in the EFB corresponding to a total flow rate Q, cm s-l ( u c ) b = velocity defined by eq 46d, cm s-l uk = superficial gas velocity in phase k , k = c and e, cm s-' umf = minimum fluidizing gas velocity at AV, cm s-l vk = total volume of phase k in the EFB, k = b, c, and e, cm3 VT = total volume of the EFB (VT = A&) V8,w= total volume of bubble wake in the EFB, cm3 ub = volume of a single bubble, cm3 W = force per unit volume exerted by the weight of the bed, g cm-2 s - ~ WE = electric work of the rising bubble per unit mass of emulsion phase, g cm2 s - ~
w = bed width or distance between electrodes, cm x = rectangular coordinate in the elliptical bubble Yb = expression defined by eq 19, cm Y, = expression defined by eq 31, g cm-2 s - ~ y = rectangular coordinate in the elliptical bubble z = height variable in the EFB, cm Greek Letters a = wake volume ratio defined by eq 39, dimensionless p = cloud volume ratio defined by eq 40, dimensionless
AV = electric potential difference applied between the electrodes, kV AVO= applied potential required to obtain the minimum fluidizing conditions for the total gas flow rate Qo, kV (ACij), = contribution of the mass transfer from phase i to phase j to the outlet concentration in phase k = i or j , with i # j and i and j = b, c, and e, ppm (Ac,),= contribution of the reaction in phase k to the outlet concentration of phase k = c and e, ppm 6 = volume fraction of bubble phase in the EFB, dimensionless t = volumetric gas fraction in the emulsion phase of the EFB, dimensionless cp* = permittivity of the particle material, C V-' m-l tf* = permittivity of the fluidizing fluid, C V-' m-l { = constant defined by eq 29 7 = elliptical coordinate 8b = residence time of the bubble phase, s X = constant defined by eq 16, C kg-' (V m-l)-n = viscosity of the gas, g cm-l s-l v = bubble frequency, number of bubbles s-l E = elliptical coordinate p e = bulk specific gravity of the emulsion phase, g cm-, pg = specific gravity of the gas, g cm-3 pa = specific activity of the particles, g cm-, u = constant defined by eq 20, C u, = electric surface conductivity of the particles, mho T~ = shear stress at the electrodes, g cm-' s - ~ &E = electric force acting on the bubble per unit area of bubble surface, g cm-' s - ~ 6 E = electric force acting on the bubble per unit volume of emulsion phase, g cm-2 & = sphericity factor of the particles, dimensionless w = constant defined by eq 31, g cm-2 s - ~V-" Subscripts E = electric b = bubble phase c = cloud phase e = emulsion phase mf = at minimum fluidizing conditions O=atAV=O Registry No. O,, 10028-15-6.
Literature Cited Amundson, N. R. Mathematical Methods i n Chemical Engineering-Matrices and Their Application; Prentice-Hall: Englewood Cliffs, NJ, 1966. Bafmec, M.; Bena, J. Chem. Eng. Sci. 1972, 27, 1177. Boland, D.; Geldart, D. Powder Technol. 1972,5, 289. Bottcher, C. J. F. Theory of Electric Polarisation; Elsevier: Amsterdam, 1952. Brown, G . G.; Foust, A. S.; Brown, G. M.; Katz, D. L.; Brownell, L. E.; Schneidewind, R.; Martin, J. J.; White, R. R.; Williams, G. B.; Wood, W. P.; Banchero, J. T.; York, J. L. Unit Operations; Wiley: New York, 1950; p 214. Calderbank, P. H.; Toor, F. D. Fluidized Beds as Catalytic Reactors. In Fluidization; Davidson, J. F., Harrison, D., Eds.; Academic: New York, 1971. Ciborowski, J.; Wlodarski, A. Chem. Eng. Sci. 1962, 17, 23. Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: New York, 1963. Davies, R. M.; Taylor, Sir G. Proc. R . SOC.London 1950, A200, 375. Delahay, P. Double Layer and Electrode Kinetics; InterscienceWiley: New York, 1965.
Ind. Eng. Chem. Res. 1989,28, 470-475
470
Dietz, P. W.; Melcher, J. R. AIChE Symp. Ser. 1978a, 74(175), 166. Dietz, P. W.; Melcher, J. R. Ind. Eng. Chem. Fundam. 1978b,17,28. Ergun, S. Chem. Eng. Bog. 1952, 48, 89. Grace, J. R.; Harrison, D. Chem. Eng. Sci. 1967, 22, 1337. Harper, W. R. Contact and Frictional Electrification; Clarendon Press: Oxford, 1967. Hendricks, C. D. Charging Macroscopic Particles. In Electrostatics and its Applications; Moore, A. D., Ed.; Wiley: New York, 1973. Henry, P. S. H. Br. J. Appl. Phys., Suppl. 1953,2, S31. Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. Inculet, I. I. Colloid Interface Sci. 1970, 32, 395. Inculet, I. I. Static Electrification of Dielectrics and at Material's Interfaces. In Electrostatics and its Applications; Moore, A. D., Ed.; Wiley: New York, 1973. Johnson, T. W.; Melcher, J. R. Ind. Eng. Chem. Fundam. 1975,14, 146. Katz, H.; Sears, J. T. Can. J. Chem. Eng. 1969, 47, 50. Kisel'nikov, V. N.; Vyalkov, V. V.; Filatov, V. M. Int. Chem. Eng. 1967, 7, 428. Kobayashi, H.; Arai, F.; Izawa, N.; Miya, T. Kagaku Kogaku 1966, 30, 656. Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969.
Kurosaki, S. J. Phys. Chem. 1954,58, 320. Loeb, L. B. Electrical Coronas-Their Basic Physical Mechanisms; University of California Press: Berkeley, 1965. Leva, M. Fluidization; McGraw-Hill: New York, 1959. Milne-Thomson, L. M. Theoretical Hydrodynamics, 4th ed.; The McMillan Company: New York, 1960. Nicklin, D. J. Chem. Eng. Sci. 1962, 17, 693. Nicklin, D. J.; Wilkes, J. 0.;Davidson, J. F. Trans. Znst. Chem. Eng. 1962, 40,61. Richardson, J. F. Incipient Fluidization and Particulate Systems. In Fluidization; Davidson, J. F., Harrison, D., Eds.; Academic: New York, 1971. Shih, Y. T.; Gidaspow, D.; Wasan, D. T. AIChE J . 1987,33, 1322. Soo, S. L. Powder Technol. 1974, 10, 211. Thorp, J. M. Trans. Faraday SOC.1959,55, 442. Wittmann, C. V.; Ademoyega, 0. Ind. Eng. Chem. Res. 1987, 26, 1586. Yates, J. G. Fundamentals of Fluidized-Bed Chemical Processes; Butterworths: London, 1983. Zahedi, K.; Melcher, J. R. Air Pollut. Control Assoc. J . 1976, 26,345.
Received for reuiew December 21, 1987 Accepted December 15, 1988
GENERAL RESEARCH Reactions of Carbonyl Sulfide and Methyl Mercaptan with Ethanolamines Mahmud A. Rahman,t Robert N. Maddox,*J and G. J. Mains* Department of Chemical Engineering and Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078-0537
Carbonyl sulfide and methyl mercaptan were interacted with anhydrous monoethanolamine (MEA), diglycolamine (DGA), diethanolamine (DEA), di-2-propanolamine (DIPA), methyldiethanolamine (MDEA), and dimethylethanolamine (DMEA). The reaction products were analyzed by 'H and I3C NMR. T h e protonated amine:thiocarbamate salt was detected for MEA, DEA, and DGA. The DIPAthiocarbamate product could not be isolated, and no evidence for reaction products from MDEA or DMEA interaction with carbonyl sulfide could be obtained. The contact of MEA, DEA, DGA, DIPA, MDEA, and DMEA with methyl mercaptan did not lead to a reaction. However, pronounced shifts and lump formations of the hydroxyl and amine protons in the 'H NMR spectra indicate that Lewis acid-base adducts are synthesized between the amine and mercaptan molecules. The pressure measurements also corroborate this NMR evidence. The removal of acid gases such as carbonyl sulfide (COS) and methyl mercaptan (CH,SH) is an essential process in the natural gas and petroleum gas processing industry. Monoethanolamine has been a traditional solvent for removal of carbonyl sulfide (Kohl and Riesenfeld, 1979; Maddox, 1977; Danckwerts and Sharma, 1966). However, loss of MEA in the regenerator is a well-known fact: the loss due to an irreversible reaction with COS. Recently, di-2-propanolamine has gained stature as a major COS solvent in the ADIP and Sulfinol processes (Kohl and Riesenfeld, 1979; Maddox, 1977). The amine solvents which are of industrial importance and considered in this study are monoethanolamine (MEA), diethanolamine
* Author t o whom correspondence should be addressed. 'Department of Chemical Engineering. Department of Chemistry.
*
0888-5885/89 /2628-0470$01.50/0
(DEA), /3,/3'-(hydroxyamino)ethyl ether (diglycolamine, DGA), di-Zpropanolamine (DIPA), methyldiethanolamine (MDEA), and dimethylethanolamine (DMEA). The objective of this study is to determine the reaction products of the reactions between COS and the amines and to investigate the possibility of a reaction between methyl mercaptan and amines. Reactions of Carbonyl Sulfide with Amines The removal of carbonyl sulfide from mixtures of gases by reactive liquid solvents is an important industrial operation. The relevant reactions with a primary amine are RNHz + COS
-
RNHCOS-
RNHz + H+
-
+ H+
RNH3+
(1) (2)
where R is generally an alkanolamine radical. This reac0 1989 American Chemical Society
