Ind. Eng. Chem. Res. 2002, 41, 6409-6412
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Photocatalytic Powder Layer Reactor: A Uniformly Mixed Gas Phase Occurring in a Catalytic Fixed-Bed Flow Reactor David F. Ollis* Chemical Engineering Department, North Carolina State University, Raleigh, North Carolina 27695-7905
Integral conversion photocatalysis rate data in gas-solid studies have often been obtained through the use of a powder layer downflow laboratory reactor illuminated from above. The photocatalyst particles, characteristically 20-40 nm in primary particle size and ∼1 µm in agglomerate size, are illuminated to a characteristic depth of the reciprocal of the absorption coefficient, resulting in opacity at 30-50 µm in a loose-packed powder layer. We establish here that this photocatalytic membrane reactor behaves as a well-mixed system; thus, reaction kinetic models can be directly tested for any degree of reactant conversion, without prior need for rate integration. Photocatalytic Powder Layer Reactor Photocatalyst gas-solid rate equations have been deduced or fitted to data from powder layer reactors,1-8 monolith reactors,3,9-11 fluidized beds,12,13 channel plate reactors,14 reticulated (ceramic) foam reactors,15 fiber mesh reactors,16 and coated tubes,17,18 among others. The simplest configuration among these is that of the powder layer reactor, popularized by Teichner’s group1 in the late 1960s (Figure 1). Here, a layer of semiconductor oxide photocatalyst particles is either deposited or physically affixed at the upper surface of a nonreactive, porous ceramic frit. Reactor analyses of this flow configuration are few. Formenti et al.1 utilized this configuration in their studies of hydrocarbon partial oxidation, in which the primary kinetic figures of merit were percent conversion of reactant and percent selectivity to partial oxidation vs total oxidation. A first analysis including intensity variation with bed depth was reported by Peral and Ollis.2 Their analysis considered a humidified air feedstream, lightly contaminated by 1-100 ppm of hydrocarbon or oxygenate pollutant. Their experimental conditions included a slow superficial velocity (23-40 cm/min) and an average surface area of 5 × 105 cm2/g of TiO2, corresponding to a particle size of about 30 nm. Under these conditions, the estimated maximum difference between bulk flow and surface concentrations was ∼10-3%, indicating a negligible external mass-transfer resistance. Later microscopy of typical commercial titania semiconductor oxide particles19 showed that the primary 20-30-nm particles were agglomerated into secondary particles with on the order of 1-3-µm average diameters. If the same external mass-transfer correlation is again used for the larger secondary particles, a negligible gas-solid external mass-transfer resistance is again found. Given the equivalence of the surface and bulk gas concentrations at any bed depth z, these authors then modeled the axially nonuniformly illuminated photocatalytic reactor with an assumed Langmuir-Hinshelwood rate form. Thus
where
* E-mail:
[email protected]. Phone: 919-515-2329. Fax: 919-515-3495.
When an optically opaque powder layer is used (typical case), the exponential term on the right side becomes
Figure 1. Powder layer photoreactor.
u
dC - rate(z) ) 0 dz
(1)
KC rate(z) ) -k(I) 1 + KC and
k(I) ) koIR ) ko(Ioe-βz)R ) koIoRe-Rβz Here, z is the bed depth, I is the intensity, I0 ) I(z)0), β is the absorption coefficient, and 0.5 < R < 1.0. The dependence of the rate of photocatalyzed reactions on intensity is well-established: it is R ) 1 for low intensities and R ) 0.5 for higher intensities, usually above 1 solar near-UV equivalent (about 1 mW/cm2). Integration of eq 1 provides
ln
( )
koKIoR C (1 - e-RβL) ) K(Co - C) Co Rβu
10.1021/ie020038f CCC: $22.00 © 2002 American Chemical Society Published on Web 09/07/2002
(2)
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Ind. Eng. Chem. Res., Vol. 41, No. 25, 2002
0, and we have
mated from the Einstein equation as
()
( )
koIR C ln ) K(Co - C) - K Co uRβ (total light absorption) (3) The apparent validity of this equation was tested2 by establishing the linearity of plots of ln(C/Co) vs (Co C). In turn, these plots provided a slope of +K and an intercept of -(koKIoR/Rβu). We now consider the evaluation of the relatively fundamental rate law parameters ko and K. The intensity exponential R can be independently established; β, the absorption coefficient for TiO2, is known; and Io is measurable at the catalyst upper surface. Thus, the Langmuir-Hinshelwood rate parameter values for ko and K were established by fitting eq 3 to data sets for compounds such as acetone, butanol, xylene, and formaldehyde.2 Convenient though this fit might be, the powder layer photocatalytic reactor of Figure 1 is but a recent example of a packed-bed, heterogeneous catalytic reactor, analyses of which reach back to the mid-1950s in the pioneering work of Dankwerts19 and Wehner and Wilhelm.20 These early workers considered radially uniform packed beds with axial dispersion. Their early analyses furnish two results of interest here: (1) Regardless of whether the reactor entrance condition is taken to be that of Dankwerts or of Wehner-Wilhelm, the analytic concentration profile obtained within the bed is the same. (2) The bed entrance concentration, C(O+) was less than the far upstream condition, Co. Further, their bed concentration profile, considered below, shows that, in the limit as the axial reactor Peclet number approached 0, the axial concentration profile tended to become absolutely flat. In the parlance of chemical engineering, the reactor behaved as though it were perfectly mixed. These early results are markedly different from our prior plug-flow assumption for the powder layer reactor, and we now consider a reinterpretation. In our laboratory studies, the volumetric flow rate was typically 70-120 cm3/min passing through about 3 cm2 of illuminated cross section of catalyst, giving a superficial velocity v of (70-120 cm3/min)/(3 cm2) ) 23-40 cm/min ≈0.38-0.67 cm/s ) v. For an illuminated powder bed length (depth) of 10-50 µm for our agglomerated Degussa P25 TiO2 powder, the resulting axial Peclet number is thus approximately
(0.6 cm/s)(5 × 10-3 cm)
Pea ≡ uL/D
xx2 ) (Dett)0.5 ) [(0.1 cm2/s)(0.1 s)]0.5 ) 0.1 cm Thus, in 0.1 s, the ratio of diffusional displacement to displacement by bulk flow is r ) (10-1 cm)/(5 × 10-3 cm) ) 20. Hence, diffusional transport is more effective than bulk flow in leveling any axial concentration gradients created by reaction within the active catalyst layer. To deduce the correct reaction rate form, the concentration C in the “well-mixed” reactor must be known. The small Pe number limit establishes that the reactor is a CSTR, and this conclusion also indicates that the reactor concentration is the same as the easily measurable exit concentration. We revisit the Wehner-Wilhelm condition to establish the accuracy of this conclusion. Returning to the concentration profile within the reactor, Wehner and Wilhelm provided boundary conditions for the fractional concentration f, where f ) C/Co (upstream feed concentration) at z ) 0
f(0) ) go[(1 + a) exp(aPe/2) - (1 - a) exp(-aPe/2)] (4a) and at z ) 1
f(1) ) 2ago exp(Pe/2) where
go ) 2/[(1 + a)2 exp(aPe/2) - (1 - a)2 exp(-aPe/2)] (4c) and
a ) (1 + 4R/Pe)1/2
Pea(max) ) 0.03 In all cases, Pea < 3 × 10-2 ) 0.03. Because the Peclet number is the ratio of convective to diffusive transport, diffusive transport is utterly dominant in the powder layer reactor, and the concentration profile is flat, i.e., uniform, as occurs in a well-stirred reactor (CSTR) configuration. Said differently, the average gas transit time t through the powder layer reactor is t ) L/v ) (5 × 10-3 cm)/(0.055 cm/s) ) 0.1 s. In this time, the corresponding molecular mean free diffusional displacement is esti-
(4d)
For our small Pe case where Pe < Pe(max) ) 3 × 10-2, we calculate the fractional conversion at each end of a uniformly active catalyst bed. Taking ex ) 1 + x + x2/2 + ... for small x, results in
F(0) ) ago(2 + Pe + a2Pe2/2) which is identical, within a2Pe2/2, to the other boundary condition
(10-1 cm2/s)
or
(4b)
f(1) ) 2ago(1 + Pe/2) ) ago(2 + Pe) Because a ) (1 + 4R/Pe)1/2 ≈ 12 (see later examples) and Pe ) 3 × 10-2, we have a2Pe2/2 ≈ 0.065. The maximum percent difference in the entrance and exit fractional concentrations is thus about
100 ×
0.065 a2Pe2/2 ) × 2 2 2 + Pe + a Pe /2 2 + 3 × 10-2 + 0.065 100 ) 3.1%
thus justifying the flat profile approximation deduced from earlier Pe and transit time discussions. For kinetic evaluation of the dimensionless first-order rate constant R, we have the fractional conversion at
Ind. Eng. Chem. Res., Vol. 41, No. 25, 2002 6411
when f(1) ) 0.5, a result that differs from the axial conversion result by only 1.5%. The corresponding plug-flow model used earlier provides
the reactor exit, f(1)
f(1) ) ago(2 + Pe) where, ignoring terms beyond O(Pe)
k)-
2 go ) a[4 + Pe(1 + a2)] Thus
f(1) )
2 + Pe 2 + Pe + 2R
(5)
Because Pe ) uL/De and R ) kL/u, we have
C(1) ) f(1) ≡ Co
1 2(kL/u) 1+ uL 2+ D
[
]
(7)
For example, under typical integral conversion conditions such that f(1) ) 0.5 (50% conversion) and Pe ) 3 × 10-2, one obtains
(
Pe (2 - 1) ) 1.015 2
)
and thus
(
)
5 × 10-2 cm/s u ) 10 s-1 k ) R ) 1.015 L 5 × 10-3 cm Error Estimate: Axial Dispersion vs CSTR and PFR Models. Having established that the behavior of the photocatalytic membrane reactor is that of a virtual CSTR, we can replace the original reactor differential equations of axial dispersion with chemical reaction19,20 by a simple algebraic CSTR balance on reactor volume V:
F[Co - C(1)] ) V (rate/vol) u u kaxial ) R ) 1.015 L L with the rate constant calculated according to the simpler CSTR analysis for the same first-order reaction. Now we have
F[Co - C(1)] ) VkC(1) so
[
] [
]
uA 1 F Co k) -1 ) -1 V C(1) LA f(1) or
k)
u L
kKC(1) F[(Co) - C(1)] ) V 1 + KC(1)
(8a)
1 1 θ ) + Co - C(1) kKC(1) k
(8b)
or
kL Pe 1 -1 )1+ u 2 f(1)
R) 1+
a result with an error of 32.2%. Nonlinear Rate Equations: Revisiting Langmuir-Hinshelwood. Photocatalyzed gas-solid reactions have often been fitted to the L-H rate form. We thus have for our powder layer reactor and the L-H kinetic form
(6)
where C(1)/Co is known from data. The unknown dimensionless rate constant, R, is given by
R≡
u u ln f(1) ) 0.693 L L
where θ ) V/F is the superficial gas-phase residence time. This form applies to L-H kinetics with a rate constant k that is uniform throughout the bed. Such is not the case with the intensity-dependent rate constants of heterogeneous photocatalysis, and we consider the final alteration needed to make use of the simple and convenient CSTR algebraic equation for evaluation of rate data from powder layer photocatalytic reactors. Variation of Intensity with Position in Layer. While the reactant is well-mixed within the reactor, the strong absorbance of light by the TiO2 photocatalyst provides total absorption (i.e., optical density OD > 2) within a bed depth of L ) 50 µm. Consequently, the intensity I, and thus the local rate constant k(z), is still a function of position z. The average rate constant over the volume is
k h)
∫0L
k(z) dz ) ko L
∫0L
)
IoR exp(-Rβz) dz L
(9)
koIoR LRβ
where 0.5 e R e 1.0, β is the titania (TiO2) absorption coefficient, and total absorption of light is assumed. This average rate constant, k h , is the parameter determined from the CSTR eqs 8a and 8b noted above for L-H kinetics. From its value, the fundamental quantity ko can be calculated from formula 9 above. The intensity exponent R is typically constant for Io < 0.5 solar near-UV equivalents (nUV solar) (R ) 1.0) or Io > 5 solar near-UV equivalents (R ) 0.5). When the predominant intensity variation lies in the transition regime, typically
0.5 nUV solar < Io < 5 nUV solar a constant fractional power (e.g., R ) 0.67) has been used to fit particular data sets and can provide a reasonable estimate for eq 9. A fundamental treatment for trichloroethylene data22 indicates that the location of this intensity transition regime may depend on the reactant concentration.
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Reaction-Induced Diffusion Gradients? In addition to the Peclet number influence, we ask whether the presence of the photocatalytic reaction itself provides a sufficiently strong consumption of reactant to generate any substantial diffusion gradient within the catalyst layer. The classic test for this question is the value of the Wagner-Weisz-Wheeler modulus, Mw, given by eq 1021
Mw )
L2 -rate De C
(
)
where the rate is given in units of moles per unit volume of catalyst per second. For our typical conditions
L ) 50 µm, Co ) 100 ppmv, De ) 10-1 cm2/s and
r(50% conversion) ) (10 cm3/min)Co(0.5)/[(3 cm2)L] we calculate
Mw < 0.02-0.2 indicating a negligible reaction-induced concentration gradient. Conclusions A photocatalytic membrane (or powder layer) gassolid reactor has been analyzed through the use of the axial reactor Peclet number to establish the apparent reactor equivalent for the pertinent conditions of slow flow rate and thin catalyst layer. The analysis shows the following: (1) The maximum Peclet number is 3 × 10-2; hence, the reactor operates as the equivalent of a well-stirred tank (uniform concentration throughout). (2) Given the rapid diffusive mixing, the apparent rate constant is simply the average rate constant over the nonuniformly irradiated reactor volume. (3) Despite the nonuniform irradiation, the intrinsic rate constant, ko, and the apparent binding constant, K, are easily obtained from a simple well-mixed reactor (CSTR) model, provided that the catalyst absorbance and rate intensity dependence are known. Nomenclature C ) molar concentration Co ) upstream concentration C(0) ) reactor entrance concentration C(1) ) reactor exit concentration De ) effective gas-phase diffusivity (cm2/s) f ) fractional conversion F ) volumetric gas flow rate k(I) ) intensity-dependent rate constant ko ) intensity-independent portion of the rate constant k h ) volume-average rate constant K ) apparent binding constant, L-H equation Mw ) Wagner-Weisz-Wheeler modulus ) L2(rateobs/DeC), where rateobs is in units of moles per unit catalyst volume per unit time L ) photocatalyst bed depth Pea ) axial Peclet number (≡ uL/De) R ) dimensionless rate constant (kL/u) v ) powder layer reactor volume u ) axial gas flow superficial velocity z ) axial position in catalyst layer
R ) intensity exponent in rate equation β ) catalyst absorbance (cm-1)
Acknowledgment This research was supported by the state of North Carolina. Literature Cited (1) Formenti, M.; Meriadeau, P.; Teichner, S. J. Heterogeneous Photocatalysis. Chem. Tech. 1970, 1, 680. (2) Peral, J.; Ollis, D. F. Photocatalytic oxidation of gas-phase organics for air purification. J. Catal. 1992, 136, 554. (3) Sauer, M.; Ollis, D. F. Photocatayzed oxidation of ethanol and acetaldehyde in humidified air. J. Catal. 1996, 158, 570. (4) Sauer, M. L.; Hale, M. A.; Ollis, D. F. Heterogeneous photocatalytic oxidation of dilute toluene-chlorocarbon mixtures in air. J. Photochem. Photobiol. 1975, A88, 169. (5) Peral, J.; Ollis, D. F. TiO2 photocatalyst deactivation by gasphase oxidation of heteroatom organics. J. Mol. Catal. Chem. 1997, 115, 347. (6) Luo, Y.; Ollis, D. F. Heterogeneous photocatalytic oxidation of trichloroethylene and toluene mixtures in air: Kinetic promotion and inhibition, time-dependent catalyst activity. J. Catal. 1996, 163, 1. (7) d’Hennezel, O.; Ollis, D. F. Trichloroethylene-promoted photocatalytic oxidation of air contaminants. J. Catal. 1997, 167, 118. (8) d’Hennezel, O.; Ollis, D. F. Surface pre-chlorination of anatase TiO2 for enhanced photocatalytic oxidation of toluene and hexane. Helv. Chim. Acta 2001, 83, 3511. (9) Hossain, M. M.; Raupp, G. V. Radiation field modeling in a photocatalytic monolith reactor. Chem. Eng. Sci. 1998, 53, 3771. (10) Hossain, M. M.; Raupp, G. B.; Hay, S. O.; Obee, T. N. Three-dimensional developing flow model for photocatalytic monolith reactors. AIChE J. 1999, 45, 1309. (11) Hossain, M. M.; Raupp, G. B. Polychromatic radiation field model for a honeycomb monolith photocatalytic reactor. Chem. Eng. Sci. 1999, 54, 3027. (12) Lim, T. H.; Heong, S. M.; Kim, S. P., et al. Degradation characteristics of NO by photocatalysis with TiO2 and CuO/TiO2. React. Kinet. Catal. 2000, 71, 223. (13) Lim, T. H.; Heong, S. M.; Kim, S. P., et al. Photocatalytic decomposition of NO by TiO2 particles. J. Photochem. Photobiol. A 2000, 134, 209. (14) Sitkiewicz, S.; Heller, A. Photocatalytic oxidation of benzene and stearic acid on sol-gel derived TiO2 thin films attached to glass. New J. Chem. 1996, 20, 233. (15) Changrani, R.; Raupp, G. B. Monte Carlo simulation of the radiation field in a reticulated foam photocatalytic reactor. AIChE J. 1999, 45, 1085. (16) Pichat, R.; Didier, J.; Hoang-Van, C., et al. Purification/ deodorization of indoor air and gaseous effluents by TiO2 photocatalysis. Catal. Today 2002, 63, 363. (17) Nimlos, M. R.; Wolfrum, E. J.; Brewer, M. L., et al. Gasphase heterogeneous photocatalytic oxidation of ethanol: Pathways and kinetic modeling. Environ. Sci. Technol. 1996, 30, 3102. (18) Suzuki, U. Y.; Warsito, A. M.; Uchida, S. Chem. Lett. 2000, 130. (19) Danckwerts, P. V. Continuous flow systems: Distribution of residence times. Chem. Eng. Sci. 1953, 2, 1, (20) Wehner, J. F.; Wiilhelm, R. H. Boundary conditions of flow reactor. Chem. Eng. Sci. 1956, 6, 89. (21) Levenspiel, O. Chemical Reaction Engineering, 3rd ed.; John Wiley and Sons: New York, 1999; p 388. (22) Upadhya, S; Ollis, D. F. A simple kinetic model for the simultaneous concentration and intensity dependence of TCE photocatalyzed destruction. J. Adv. Oxid. Technol. 1998, 3 (2), 1.
Received for review January 17, 2002 Revised manuscript received June 20, 2002 Accepted June 21, 2002 IE020038F
