polychromatic radiation field model for a honeycomb monolith photocatalytic reactor

*Corresponding author. Tel.: 001 602 965 2828; fax: 001 602 965 0037;e-mail: [email protected].

Chemical Engineering Science 54 (1999) 3027}3034

Polychromatic radiation "eld model for a honeycomb monolithphotocatalytic reactor

Md. Moazzem Hossain, Gregory B. Raupp*

Department of Chemical, Bio and Materials Engineering, Arizona State University, Tempe, AZ 85287-6006, USA

Abstract

In this paper we extend our radiation "eld model previously developed to predict the monochromatic light intensity pro"le insidea photocatalytic square-channeled monolith reactor to predict the integral average polychromatic light intensity pro"le. In thisextended polychromatic formulation, the mathematical representation of the model accounts for a source that emits a distribution ofwavelengths and for wavelength-dependent optical properties (re#ectivity) of the active photocatalytic thin "lm coated on the innerwalls of the monolith channels. In the sense that these wavelength dependent properties of a given photocatalytic reactor system canbe independently measured, the polychromatic radiation "eld model contains no adjustable parameters. Model predictions for theintegral average light intensity transported through square monolith channels of varying length are in excellent quantitativeagreement with experimental measurements employing Degussa P25 titania-coated monolith channels and near ultraviolet lampsemitting light primarily in the 300}400 nm range.

The model reveals that axial light intensity gradients are severe, with the light intensity in the portion of the monolith channelbeyond about 3}4 aspect ratios in length falling to below 1% of the incident light intensity. At a given axial distance down themonolith channel, the e!ective light #ux that reaches the catalytic wall is approximately a factor of two lower than the total light #uxthrough the channel cross section near the channel entrance, and an order of magnitude lower than the total cross section light #uxnear the channel exit. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Photocatalytic oxidation; Reactor modeling; Titania photocatalysts; Indoor air quality; Monolith reactor; Polychromaticradiation

1. Introduction

Laboratory-scale photocatalytic oxidation (PCO) re-actors operating at ambient temperature and pressureare capable of destroying volatile organic compounds(VOCs) often found in indoor air environments, includ-ing, for example, formaldehyde (Peral and Ollis, 1992;Obee, 1996), toluene (Sauer et al., 1992; Obee, 1996),acetone (Peral and Ollis, 1992; Raupp and Junio, 1993),and ethanol (Nimlos et al., 1996). This capability hascatalyzed industrial interest in employing free-standingPCO units or PCO reactors integrated into heating,ventilation, and air conditioning (HVAC) systems asa means of improving indoor air quality (IAQ).

Because of the nature of the IAQ application, energye$ciency of the PCO units is a dominant design issue.Speci"cally, the reactors must be designed to providehigh ultraviolet (UV) light energy utilization while yield-ing low pressure drop operation and only an incrementalthermal load on the HVAC system due to UV lampelectrical energy conversion ine$ciencies. Because com-pact designs are desirable, the active surface area toreactor volume ratio is also an important design metric.Of the candidate con"gurations currently under consid-eration, honeycombed monoliths yield the lowest pres-sure drop, and provide a reasonable surface area per unitreactor volume. A titania-coated and an uncoatedsquare-channeled honeycomb monolith containing 25cells per square inch (CPSI) are shown in Fig. 1. Forreasons that will soon become apparent, the length tochannel width ratio of these photocatalytic monoliths aresubstantially lower than those typically employed inthermal catalytic monoliths.

0009-2509/99/$} see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 9 5 - 3

Fig. 1. Titania-coated and uncoated square channel 25 CPSI mono-liths.

Results from recent experimental (Sauer and Ollis,1994; Suzuki, 1993) and theoretical studies (Luo, 1994)suggest that the monolith con"guration for photocataly-sis may be a suitable candidate for HVAC applications.Accordingly, several large corporations interested incommercializing PCO for IAQ applications are focusingtheir research and development e!orts on channeledmonolith-based photocatalytic reactor designs (Suzuki,1993; Hall et al., 1997).

Although considerable work has been published de-scribing modeling of monolith reactors for thermal cata-lytic applications, few papers have been published thatdescribe models for photocatalytic monolith reactors.For air puri"cation applications, UV light absorption inthe #uid phase is negligible, and as a consequence, theradiation "eld is independent of the #uid #ow and reac-tant/product concentration "elds. This fact allows signi"-cant simpli"cation of the modeling e!ort in the sense thatthe radiation "eld model can be developed and validatedindependently of the convection}di!usion-reaction mono-lith model.

Luo (1994) developed a simple geometrically basedradiation "eld model to predict the integrated light inten-sity within monolith reactor channels. To simplify themodel geometry, the square cross-section channels em-ployed in practice were approximated as circular in crosssection in the model. This analytical model does notaccount for "nite thin "lm re#ectivity, and requires em-pirical adjustment of three parameters: (i) the catalystlayer light absorption coe$cient, (ii) the e!ective catalystlayer thickness, and (iii) the e!ective lamp radius.

In a recent publication (Hossain and Raupp, 1998) wedeveloped a fundamental mathematical model based onthe well-accepted principles of radiation heat transfer forpredicting the monochromatic radiation "eld in an ex-ternally irradiated photocatalytic monolith reactor. This

model is valid for light sources emitting a singlewavelength of light or a very narrow wavelength range(e.g. a low pressure Hg germicidal lamp where 98% of thelight emission is at 254 nm), or can be employed todescribe the integrated light intensity pro"le when usingmulti-wavelength sources by employing a single adjust-able parameter (the average re#ectivity of the active cata-lyst "lm). In this paper we extend this model to accountfor polychromatic radiation. This single channel modelcan be employed in a practical monolith comprisingmany parallel, non-interacting channels with appropriatespeci"cation of the external light #ux to each channelmouth.

2. Model development

In a photocatalytic monolith reactor, light enters theparallel monolith channels from an external source.When photons interact with the photoactive semicon-ducting solid titania particles coated on the wall withina given channel, they may be either absorbed or di!uselyre#ected. We assume that the titania "lm is of su$cientthickness to preclude transmission through the "lm.Fig. 2 illustrates the geometry of a single square crosssection channel of length ¸ and width =. The channelaspect ratio a is de"ned as ¸/=. Light incident ona di!erential wall area dA originates either directly froma di!erential source area dA

0, or indirectly upon re#ec-

tion from the opposite or two adjacent walls. Lightincident upon a virtual cross section A

csoriginates either

directly from a di!erential source area dA0, or indirectly

upon re#ection from the four walls. Note that modelvalidation requires a description of the cross sectionallight intensity, since the light intensity passing througha monolith can be readily measured, whereas directmeasurement of the wall intensities is problematic.

Our polychromatic radiation "eld model employs thefollowing assumptions:

(1) The monolith is irradiated externally by a lamp orlamps approximated by a time-invariant, polychro-matic light source.

(2) Light interaction with the #uid phase is negligible.(3) The photocatalytic thin "lm coating on the monolith

walls is uniform and su$ciently thick such that nolight transmits through the thin "lm.

(4) Light re#ection from the thin "lm coating is perfectlydi!use.

(5) Optical thin "lm properties (absorbance and re#ec-tance) are dependent on light wavelength j, but areindependent of the local light incidence angle.

The general model makes no assumptions regardingthe angular dependence of the light incident on themonolith channel. Assumption (4) of perfectly di!usere#ection should be valid as long as the ratio of the

3028 Md. Moazzem Hossain, G.B. Raupp/Chemical Engineering Science 54 (1999) 3027}3034

Fig. 2. Schematic diagram of a single channel monolith channel oflength ¸ and square cross section of width= showing the di!erentialareas contributing photon #ux to a di!erential wall area dA (top) anda virtual cross sectional area A

cs(bottom).

root-mean-square (rms) surface roughness to the lightwavelength is greater than 0.2 (Bennett 1963; Birkebaket al., 1967). For the titania washcoat "lms employed inthis study (which are also employed in commercialphotoreactors), this ratio is well above unity. Assumption(5) of incidence angle independence of the thin "lm op-tical properties is valid for local incidence angles from thenormal (03) to about 703, but should introduce a modestmodel inaccuracy since these properties vary stronglynear grazing incidence angles (753}903).

The mathematical representation of this model is sum-marized in the equations that follow. For an arbitraryUV source incident on the monolith mouth with inten-sity distribution I

0and speci"ed directionality ), the UV

#ux Iw(j) to the channel wall and the UV #ux I

cs(j)

through the channel cross section are given by:

Iw(j)"PA

0

I0(j, X) ) dF MdA; dA

0N

#2o(j) PA@!$

Iw(j) ) dF MdA; dA@

!$N

#o(j) PA@01

Iw(j) )dF MdA; dA@

01N, (1)

Ics(j)"PA

0

I0(j, X) ) dF MA

cs; dA

0N

#4o(j) PA@Iw(j) )dF MA

cs; dA@N, (2)

where o(j) is the titania thin "lm wavelength-dependentwall re#ectivity, dF are geometrically determined di!er-ential view factors, and the areas are as de"ned in Fig. 2.The "rst term in the right-hand-side of both equations

arises due to ballistic photon transport directly from thesource. The second term in Eq. (1) represents the lightre#ected from the adjacent walls, while the third termrepresents the light re#ected from the opposing wall.Note that Eq. (1) is implicit in I

w, and that Eq. (2) requires

the solution of Eq. (1).The equations given above are valid for any speci"ed

UV source, including di!use or directional (e.g. focused)sources. In the expected commercial HVAC air treatmentapplication, monoliths will be irradiated by a bank of#uorescent lamps and the air duct walls will be UVre#ecting aluminum. In this con"guration, the UV #ux atan individual monolith channel mouth is well approxi-mated by a uniform, di!use source. For the di!use sourceapproximation, the "rst integral in Eqs. (1) and (2) can beevaluated analytically, yielding the following equationsfor the dimensionless UV #ux U

w(j),I

w(j)/I

0(j) to the

channel wall and the dimensionless UV #ux Ucs(j),

Ics(j)/I

0(j) through the channel cross section:

Uw(j)"F MdA; A

0N#2o(j) PA@

!$

Uw(j) )dF MdA; dA@

!$N

#o (j) PA@01

Uw(j) )dF MdA; dA@

01N, (3)

Ucs(j)"F MA

cs;A

0N#4o(j)PA@

Uw(j) ) dF MA

cs; dA@N, (4)

where the F's are geometrically determined integral viewfactors. The necessary dimensionless integral and di!er-ential view factors (Siegel and Howell, 1992; Worth et al.,1996) given in terms of dimensionless axial distance de-"ned as X,x/= have been previously derived, and aresummarized in Eqs. (5)}(9):

FMdA;A0N"

1

n Ctan~11

X#

X

2ln

X2(X#2)

(X2#1)2

!

X

(X2#1)1@2tan~1

1

(X2#1)1@2D , (5)

dF MdA; dA@01

N"1

n( DX!X @ D2#1)~3@2

]tan~11

( DX!X@D2#1)1@2dX@ , (6)

dF MdA; dA@!$

N"!

1

4nln

DX!X@D2 ( DX!X@ D2#2)

( DX!X@D2#1)2dX@,

(7)

F MAcs; A

0N"

2X2

n ClnX2#1

XJX2#2#

2

X2JX2#1

]tan~11

JX2#1!

2

Xtan~1

1

XD , (8)

Md. Moazzem Hossain, G.B. Raupp/Chemical Engineering Science 54 (1999) 3027}3034 3029

Fig. 3. Spectral distribution of an 8W UV &black light' lamp. Dashed line: experimental measurement; solid line: empirical "t to Eq. (11).

dF MAcs; dA@N"

1

n Ctan~11

DX!X@D#

DX!X@D2

]lnDX!X@D2 ( DX!X@D2#2)

( DX!X@D2#1)2

!

DX!X@D( DX!X@D2#1)1@2

]tan~11

( DX!X@D2#1)1@2D dX@ (9)

The integration limits on X@ for the wavelength-depen-dent photon accounting statements [Eqs. (3) and (7)] arefrom 0 to a. These equations can be solved numericallyfor individual photon energies over the range of applic-able light wavelengths from j

.*/to j

.!9. The integral-

average light intensity pro"le can then be determined fora given spectral distribution of lamp power P(j) asfollows:

U!7%3!'%

"

Pj.!9

j.*/

P(j) )U(j) dj

Pj.!9

j.*/

P(j) dj. (10)

Inspection of the polychromatic model equations re-veals that the radiation "eld in monoliths is determineduniquely by the monolith aspect ratio a, the spectralpower distribution of the lamp P(j), and the wavelength-dependent thin "lm re#ectivity o(j). If the two constitut-ive relations P(j) and o(j) can be measured, the modelcontains no adjustable parameters. For solution of the

general Eqs. (1) and (2), the directionality of the UVsource must also be speci"ed.

3. Experimental details

A series of square-channeled ceramic CordieriteTMhoneycomb monoliths (Corning) with nominal cell dens-ities of 25 cells per square inch (CPSI) and lengths vary-ing from 0.25 to 2.0 in were coated with titania. Actualchannel widths are 0.165$0.002 in. The monoliths wereslurry dip-coated to form a continuous "lm of TiO

2particles (Degussa P25) with an average "lm thickness ofapproximately 20 lm as described in further detail in ouroriginal publication (Hossain and Raupp, 1998).

A di!use light source was approximated by a parallelbank of six 8 W #uorescent &black light' bulbs (NEC,F8T5-BLB) positioned 2.0 in in front of the monolith'sface. The light intensity incident on four parallel channelmouths and the light intensity transmitted throughthese channels were measured as described previously(Hossain and Raupp, 1998) with an integrating UVradiometer (Minolta UM-1) capable of detecting light ofwavelengths between j

.*/equal to 310 and j

.!9equal to

400 nm.We measured the spectral power distribution of the

UV lamps with a Spectro#uoro photometer (ShimadzuRF-1501). This measured distribution is shown in Fig. 3.The spectrum is characterized by a principal peakcentered at 365 nm and a secondary peak centered at403 nm. For purposes of radiation "eld simulation, thisdistribution was modeled assuming that a slightlyskewed Gaussian emission peak at 365 nm is superim-posed with a smaller Gaussian emission peak at 403 nm.


Fig. 4. Di!use re#ectivity of a dry Carlo Erba TiO2

wash-coat "lm. Points: experimental measurement; solid line: empirical "t to Eq. (12).

Mathematically, the power distribution is given by

P(j)"expG!C1

blnA1#

j!365

19.5sinh (b)BD

2

H#0.18 expG!C

j!403

7 D2

H , (11)

where b is the skewness parameter (Butler, 1980). A valueof 0.1 for b was found to yield the best statistical "t to thedata. Fig. 3 shows that the empirical model-predictedspectral power distribution provides an accurate repres-entation of the measured distribution over thewavelength range of interest (310}410 nm).

The wavelength dependent re#ectivity o(j) data wereprovided by Brucato (1998). The measured data were "twith the empirical model given by Eq. (12). A comparisonof the model prediction with experimental data is shownin Fig. 4.

o(j)"0.515#0.455 tanhCAj!420

20 B#1.85D . (12)

4. Solution of the model equations

To solve the governing dimensionless integral equa-tions (3) and (4) we discretized the wavelength range into5 nm intervals over the 310}400 nm range. This rangecorresponds to the detection range of the UV radiometeremployed to measure UV #uxes. For each wavelengthinterval, Eqs. (3) and (4) were solved numerically usingGauss}Legendre quadrature and the mean wavelengthdependent "lm re#ectivity given by Eq. (12). Eq. (3) wassolved "rst, and the computed wall #ux was then em-ployed in the solution of Eq. (4). All simulations em-

ployed 96 quadrature points; use of a larger number ofpoints had no e!ect on the quantitative solutions. Like-wise, decreasing the wavelength discretization interval to2 nm had no e!ect on the model solutions. After obtain-ing the wavelength-dependent #uxes over each interval,the integral average #ux was calculated using Eqs. (10)and (11).

5. Results and discussion

Fig. 5 compares experimental cross-sectional exit UVintegral average #uxes for a series of titania-coated 25CPSI monoliths of di!erent lengths (aspect ratios) withmodel predictions. High aspect ratio monoliths transmitrelatively little light. For example, for a monolith with anaspect ratio equal to six, the dimensionless #ux at themonolith exit is only approximately 1% of the entrance#ux. Within the uncertainty limits of the data, all pointsfall on the model-predicted curve. Recall that this excel-lent match is achieved without bene"t of adjustable para-meters. With con"dence that the model captures theunderlying physics of photon transport and absorptionin the monolith channels, in the following paragraphs weemploy model predictions to explore details of the UVradiation "eld and the e!ective light utilization withinthe monolith.

Fig. 6 shows the UV wall #ux pro"le as a function ofwavelength for a square channel monolith with an aspectratio equal to six. The UV intensity gradients are severe,with the falling below 10% of the inlet intensity withina length of 3}4 channel widths even for the highestwavelength light. The pro"les change in three ways as thelight wavelength (and hence re#ectivity) increases. First,the intensity pro"les become more uniform for higher


Fig. 5. Comparison of model predicted cross section #ux at the monolith outlet with experimental data for titania coated 25 CPSI monoliths.

Fig. 6. Dimensionless photon #ux to the monolith wall versus dimen-sionless axial distance for a square channel of aspect ratio equal to 6 asa function of light wavelength.

wavelength light as a consequence of less light absorptiondown the length of the channel. Second, gradients nearthe exit are steeper. This behavior is a manifestation ofthe fact that in this region the re#ected light contributionfrom the exit side gradually decreases as the exit is ap-proached, and becomes zero right at the exit point. Thee!ect is more pronounced for light wavelengths exhibi-ting higher re#ectivity. Third, the entrance discontinuityin light #ux due to geometric shadowing at the entrancebecomes less pronounced as the re#ected contribution tothe total #ux becomes more important with increasingre#ectivity.

The integral average light #ux pro"le falls between the365 nm and 385 nm wavelength curves, indicating that

the average re#ectivity over the entire range would fallbetween these two point values. This prediction is consis-tent with our previous "t of the data using the monochro-matic radiation "eld model (Hossain and Raupp, 1998),in which we extracted a single e!ective average re#ectiv-ity of 40%. Figs. 7 and 8 compare the predictions of thepolychromatic and monochromatic radiation "eld mod-els for the photon intensity pro"les to the monolith crosssection and wall, respectively. The models are in reason-able agreement, although the deviation between the twomodels is greater for the wall #uxes than for the crosssection #uxes.

In a photocatalytic reactor employing a semiconduc-tor photocatalyst, only the photons that possess energiesgreater than or equal to the band gap are of interest. Forthin "lm TiO

2, the band gap is approximately 3.2 eV,

corresponding to a light of wavelength of 387 nm. Forillustrative purposes, we assumed that 390 nm is themaximum light wavelength capable of activating thetitania, and used the model to predict the integrated lightintensity #ux to the monolith wall for only the e!ectivephotons (e!ective wall #ux). Fig. 9 compares the totalintegral average cross section UV #ux and the totalintegral average wall UV #ux with the e!ective wall #ux.This comparison dramatically illustrates the signi"canterror that would be induced if the total cross section #uxwere used rather than the e!ective integral average wall#ux in photocatalytic reactor modeling. At the channelmouth the total wall #ux is approximately half of thetotal cross section #ux; the di!erence in the two pro"lesbecomes greater down the length. The e!ective wall #uxat the channel mouth is about 93% of the total wall #ux,but at the channel exit (X"6) it is only about 77% of the


Fig. 7. Model-predicted dimensionless photon #ux to a monolith crosssection versus dimensionless axial distance for a square channel ofaspect ratio equal to 6. Solid line: polychromatic model; dashed line:monochromatic model with o"0.40.

Fig. 8. Model-predicted dimensionless photon #ux to the monolithwall versus dimensionless axial distance for a square channel of aspectratio equal to 6. Solid line: polychromatic model; dashed line, mono-chromatic model with o"0.40.

Fig. 9. Comparison of model-predicted cross section, wall, and e!ectivelight #ux distribution for a square channel of aspect ratio equal to 6.

total wall #ux. This behavior arises because of thethin "lm re#ectivity, and hence absorptivity, variationwith light wavelength. As the light passes through thechannel, light of lower wavelengths is absorbed preferen-tially and the ratio of the lower to higher wavelengthlight remaining decreases.

6. Conclusions

The fundamental polychromatic model presented herefor photon transport and absorption in a honeycombmonolith photocatalytic reactor irradiated externally bya di!use source reveals that the light intensity pro"le isuniquely determined by the channel aspect ratio, the wallcoating wavelength-dependent re#ectivity function, andspectral power distribution of the light source. Since

these quantities can be measured independently, themodel contains no adjustable parameters. Experimentalmeasurements of light transmitted through a series ofsquare-channeled monoliths are in excellent agreementwith model predictions. Axial light intensity gradients aresevere, with the portion of the monolith channel beyondabout 3}4 aspect ratios in length operating essentially &inthe dark'. At a given axial distance down the monolithchannel, the e!ective light #ux that reaches the catalyticwall is signi"cantly lower than the total light #ux throughthe channel cross section, with the magnitude of thedi!erence increasing down the length of the channel. Thisvalidated model can now be used con"dently as theradiation "eld sub-model for a full convection}di!usion-reaction photocatalytic monolith reactor model.

Acknowledgements

We gratefully thank Professor Alberto Brucato (Uni-versity of Palermo) for supplying the titania thin "lmre#ectivity vs. wavelength data, and Professor Vince Piz-ziconi and Je! Labelle (ASU) for assisting with the collec-tion of the lamp spectral power distribution data.

Notation

A area (source, wall or cross section)b skewness parameterdF di!erential view factorF integral view factorI photon intensity or #ux (photons/cm2)¸ monolith channel length (m)P lamp power (arbitrary units)= channel width (m)x axial distance (m)X dimensionless axial distance x/=


Greek characters

a channel aspect ratio ¸/=j light wavelength (nm)o re#ectivity of the channel wallU dimensionless photon intensity or #uxX source directionality (angular distribution of

light on monolith channel mouth)

Subscripts

ad adjacent wallscs cross sectiono sourceop opposite wallw wall

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polychromatic radiation field model for a honeycomb monolith photocatalytic reactor

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