Two-Dimensional Modeling of a Flat-Plate ... - ACS Publications

Sep 21, 2007 - The continuity equation for convection and diffusion in two dimensions, under un-steady-state conditions, was coupled with radiation fi...
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Ind. Eng. Chem. Res. 2007, 46, 7489-7496

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Two-Dimensional Modeling of a Flat-Plate Photocatalytic Reactor for Oxidation of Indoor Air Pollutants Ignasi Salvado´ -Estivill,† Alberto Brucato,‡ and Gianluca Li Puma*,† Photocatalysis & Photoreaction Engineering, School of Chemical and EnVironmental Engineering, The UniVersity of Nottingham, UniVersity Park, Nottingham NG7 2RD, United Kingdom, and Dipartimento di Ingegneria Chimica dei Processi e dei Materiali (DICPM), UniVersita` degli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy

In this paper we present a two-dimensional (2-D) analysis of a narrow-slit, flat-plate, single-pass, flowthrough photocatalytic reactor for air purification. The continuity equation for convection and diffusion in two dimensions, under un-steady-state conditions, was coupled with radiation field modeling and photocatalytic reaction kinetics to model the transient and steady-state behavior of the reactor. The model was applied to the photocatalytic oxidation of trichloroethylene (TCE) in humidified air streams under different experimental conditions. The kinetic parameters determined by a three-dimensional (3-D) computational fluid dynamics model of the reactor were used in the 2-D model simulations. Under the experimental conditions in the reactor, the 2-D model was shown to approximate closely the experimental results of the oxidation of TCE and to give predictions that approach very well those of the 3-D model. The 2-D model, when applicable, provides a simpler and less time-consuming approach than the 3-D model with computational times reduced by a significant amount. Introduction In most developed and many developing countries, people spend on average 90% of their time indoors.1 Rates of respiratory disease and incidence of allergic responses such as asthma have increased in recent years, and there is concern that some of this increase can be associated with changes in the quality of the air in the indoor environment.2,3 The elimination of low/trace-concentration gaseous indoor air pollutants is of particular concern because of their long-term effects on humans. An example is the widespread use of trichloroethylene (TCE) as an additive in adhesive glues, rust remover, typewriter correction fluids, paint removers, and cleaner fluids for electronic equipment.4 On the basis of mechanistic research, it has been found that TCE exposure can cause several adverse health effects, such as neurotoxicity, immunotoxicity, liver and kidney toxicity, endocrine effects, and several forms of cancer.4,5 TCE is classified as “highly likely to produce cancer in humans” by the EPA.5 The efficient removal of indoor airborne particles and volatile organic compounds (VOCs) in public and private buildings would also allow for a reduction in outdoor air supply rates. Consequently, when air conditioning (heating or cooling) is necessary, substantial energy savings may be realized. UV photocatalytic air purifiers have the potential to achieve the necessary reductions in indoor VOC levels.6,7 One of the unresolved issues in the commercial application of this photocatalytic oxidation (PCO) technology to the treatment of contaminated indoor air is the availability of robust and flexible tools to aid the scaleup, design, and optimization of photocatalytic reactors.8 These tools are also essential for evaluating intrinsic kinetic parameters from experimental results collected in integral flow reactors (observed reactant conversion * To whom correspondence should be addressed. Phone: +44 (0) 115 9514170. Fax: +44 (0) 115 9514115. E-mail: gianluca.li.puma@ nottingham.ac.uk. † The University of Nottingham. ‡ Universita` degli Studi di Palermo.

higher than 5%). It is essential to determine kinetic parameters with proper consideration of the radiation field and convection/ diffusion effects in the reactor. In the absence of the above considerations caution should be exerted on kinetic parameters determined from the experiments, since the parameters will be specific to the particular photoreactor employed and in general will not be applicable to reactors of different sizes and geometries. An accurate mathematical model of the photocatalytic reactor is necessary to determine accurate kinetic parameters of the photocatalytic oxidation of air pollutants. This involves coupling the radiation field model with the momentum balance, the mass balance, and a suitable reaction mechanism. Significant work can be found in the literature with regard to the photocatalytic oxidation of VOCs over photocatalysts supported on solid walls. Imoberforf et al.9,10 have recently presented complete models of flat-wall and multiannular photoreactors in which reactant convection, diffusion, and reaction were coupled with an appropriate analysis of the radiation field to model the oxidation of perchloroethylene in humid air over TiO2 films. Hossain et al.11 presented a complete model to simulate formaldehyde oxidation in a monolith photocatalytic reactor. Mohseni and Taghipour12 employed computational fluid dynamics (CFD) to model the transport equation of vinyl chloride in an annular photocatalytic reactor. More recently, Salvado-Estivill et al.13 combined CFD modeling with radiation field modeling and photocatalytic reaction kinetics to model the decomposition of TCE in a flat-plate, single-pass, flow-through photocatalytic reactor. The main aim was to determine kinetic parameters independent of reactor geometry, radiation field, and fluid dynamics that would be applicable to the design and scaleup of photocatalytic reactors for indoor air purification. Although the power of CFD modeling is immense and recommended in the modeling of complex reactor geometries with nonideal flow patterns, its correct use is not always straightforward. Furthermore, CFD modeling may require the use of proprietary software. Mathematical models should ideally capture the essential elements of the photocatalytic process without introducing a high degree of complexity.

10.1021/ie070391r CCC: $37.00 © 2007 American Chemical Society Published on Web 09/21/2007

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Figure 1. Planar and side views of the flat-plate photocatalytic reactor (right). Experimental setup for the photocatalytic oxidation experiments (left).

In this paper, we present a two-dimensional (2-D) analysis of a narrow-slit, flat-plate, single-pass, flow-through photocatalytic reactor for air purification. The rationale is to provide a simpler and more user-friendly approach than CFD modeling (three-dimensional, 3-D) of the reactor. The continuity equation for convection and diffusion in two dimensions under un-steadystate conditions was coupled with radiation field modeling and photocatalytic reaction kinetics to model the transient and steady-state behavior of the reactor. The model was applied to the photocatalytic oxidation of trichloroethylene in humidified air streams under different experimental conditions. Flat-Plate Photocatalytic Reactor Figure 1 presents planar and side views of the photocatalytic reactor used for the gas-phase PCO of organic substrates. It consisted of a flat 75 mm wide, 600 mm long, stainless steel reactor that allowed the controlled distribution of the contaminated air flow over the catalyst. A 75 mm × 100 mm glass plate coated with the photocatalyst was located 270 mm from the inlet of the reactor and 170 mm from the outlet. The reactor was covered with a borosilicate glass (7.7 mm thick) sealed with a Viton gasket. This formed a 75 mm × 2.5 mm flow passage across the whole length of the reactor. The reactor inlet and outlet were designed to minimize back-flow diffusion and to achieve uniform, fully developed flow over the photocatalytic plate. The reactor was irradiated with up to five blacklight blue fluorescent lamps (Philips TL 8W/08 F8T5/BLB, 0.0155 m bulb diameter, 0.26 m bulb length, and 1.2 W UV-A output). The lamp emitted a minute fraction of the total radiation at 324 and 325 nm and the rest between 343 and 400 nm with a maximum irradiance peak at 365 nm.14 The centerlines of the lamps were separated by 0.039 m. The radiation intensity at the photocatalytic surface was regulated by varying the number of lamps switched on (one, three, or five) and by adjusting the distance between the lamps and the reactor. UV radiation was measured with a radiometer (Cole-Parmer), equipped with a 365 nm sensor. The experimental setup consisted of carrier gas (oxygen) and VOC delivery systems, the reactor, and the analytical unit. The carrier gas line was split into two streams, one of which was bubbled through water to set the humidity for the reaction. The relative humidity of the rejoined streams was measured by a

thermohygrometer (Testo 635). The gas flow rates were adjusted using calibrated flow meters (Cole-Parmer). The VOC was continuously injected into the system as a liquid, using an infusion syringe pump (Cole-Parmer). The temperature at the point of injection upstream was monitored by a temperature controller (Cole-Parmer) and maintained slightly above the boiling point of the VOC. At the reactor inlet the temperature of the gas was 35 ( 2 °C. The temperature gradient of the gas over the section of the reactor occupied by the catalytic plate was 1.3 °C, and the average temperature was 31 ( 2 °C. Visual observations and pressure measurements confirmed that no condensation of the vapors took place within the reactor. TCE (Fisher, for analysis, >99.8%) was used as a model pollutant. Ultra-high-purity water produced by a NANOpure Diamond UV water purification system (18.2 MΩ cm-1, e1 ppb TOC) was used in the bubbling bottle to saturate the gas. Ultra-high-purity oxygen carrier gas (99.999%) was provided by BOC gases. The outlet gas mixture was separated using a GS-GASPRO capillary column (30 m, 0.32 mm i.d.) installed in a gas chromatograph (Agilent Technologies, GC-6890N) equipped with a thermal conductivity detector (200 °C) and a flame ionization detector (250 °C), with helium as the carrier gas. Reactor inlet and outlet gas samples were injected at 200 °C through an automatic sampling system. The valves allowed the injection of 0.25 mL gas samples from either the inlet or the outlet of the photoreactor every 2 min. The reactor outlet stream was vented to the atmosphere. A 7 wt % suspension of TiO2 Degussa P25 (primary particle size 20-30 nm by TEM, specific surface area 52 m2 g-1 by the BET method, composition 78% anatase and 22% rutile by X-ray diffraction) in ethanol was deposited over the glass plate, left overnight at room temperature to evaporate the solvent, and dried at 120 °C for 2 h in an oven. Another layer was added to obtain a catalyst loading of 7 g m-2. In a typical experiment, the TCE concentration in the reactor was initially allowed to reach the steady state, which was monitored by continuous analysis of the reactor inlet and outlet compositions, reactor temperature, and inlet pressure. Then the UV lamps were switched on, and the reactor effluent was monitored until the concentration of TCE at the outlet reached a constant value. The conversion was calculated from the inlet and outlet TCE concentrations. The oxidation of TCE was

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carried out at 8% relative humidity since this was found to yield the highest TCE conversion in the reactor.15

concentration. (b) No flow through the top glass cover at z ) d

(∂CA/∂z)|z)d ) 0

2-D Modeling of the Flat-Plate Photocatalytic Reactor Momentum Balance. Laminar flow in a narrow slit was considered. CFD simulation of the reactor using Fluent 6.2 confirmed the flow to be laminar and fully developed in the section occupied by the photocatalytic plate.13 The velocity profile across the vertical direction is represented by16

2z - d 3 Vx ) 〈V〉 1 2 d

( (

2

))

(1)

where 〈V〉 is the average gas velocity, z is the distance from the surface of the catalyst, and d is the thickness of the slit. Material Balance. The un-steady-state material balance for species A in the reactor is16

where CA is the molar concentration of species A, v is the fluid velocity vector, JA is the diffusion molar flux, and RA is the volumetric rate of generation of A. Inserting Fick’s law, for a constant diffusivity (D) in the reactor [JA ) -D(∇CA)], eq 2 becomes

∂CA ) -(∇‚CAv) + D(∇2CA) + RA ∂t

(3)

In rectangular coordinates, this is

The following assumptions are made: (a) Infinite plate in the y direction since the width of the reactor was 30 times the height. As a result, the lateral component of the fluid velocity (Vy) is not present and no concentration gradients exist in the y direction. (b) Fully developed laminar flow regime. This implies that the component Vz is equal to zero and Vx does not change in the axial direction. (c) Negligible diffusion in the axial direction compared to transport by convection. This cancels the diffusion term in the x direction. (d) The reaction occurs on the surface of the catalyst only. Therefore, the last term in eq 4 is not present and the rate of consumption of A is added a posteriori as a boundary condition. Under these assumptions, eq 4 is simplified as follows:

( )

∂CA ∂2CA ∂CA - Vx )D 2 ∂t ∂x ∂z

(5)

Boundary and Initial Conditions. The boundary conditions to integrate eq 5 in the reactor volume are as follows: (a) Pollutant adsorption and reaction on the catalytic surface (z ) 0)

D(∂CA/∂z)|z)0 ) -rA

(6)

where rA is the rate of formation of A per unit surface area. This is in general a function of the light intensity and reactant

(7)

The initial conditions are

at t ) 0, CA ) CA0 at any x and z

(8)

at x ) 0, CA ) CA0 at any z and t

(9)

The conversion of A in the reactor is calculated from

XA ) 1 - (

∫0d VxCAL dx)/(CA0∫0d Vx dx)

(10)

Reaction Rate and Radiation Field Model. The rate term in eq 6 would need to be determined by a reaction kinetics scheme for the photocatalytic oxidation of TCE. In this work, we adopt the Langmuir-Hinshelwood-type TCE rate equation proposed by Jacoby et al.17,18 to model the rate of disappearance of TCE over the catalyst at constant humidity. However, since the rate should depend on the local surface rate of photon absorption (LSRPA), which in turn is a linear function of the incident photon flux, we extend the rate equation as follows:

-rA ) -rTCE ) 〈I(x,y)〉n

kKCTCE(z)0) 1 + KCTCE(z)0)

(11)

where 〈I(x,y)〉 is the average radiation intensity at the surface of the catalyst considered here with regard to the 2-D model

〈I(x,y)〉 ) (

∫catalyst surface I(x,y) dx dy)/(∫catalyst surface dx dy)

(12)

k is the apparent rate constant, which encompasses the true surface reaction rate constant, the optical properties of the photocatalytic film (absorption and reflection), and the effect of relative humidity and intermediates. K is the adsorption constant of TCE with the catalyst, and CTCE(z)0) is the volumetric concentration of TCE in the gas phase at the surface of the catalyst. The exponent n in eq 11 depends on the efficiency of electron-hole formation and recombination at the catalyst’s surface and takes a value between 0.5 and 1 provided that the reaction is kinetically controlled.17 At weak intensities the observed oxidation rate is first-order with respect to the radiation intensity and shifts to half-order once the rate of electron-hole formation becomes greater than the photocatalytic rate, favoring electron-hole recombination.19 The actual mechanism of TCE photocatalytic oxidation is still under discussion, and several kinetic expressions have been proposed in the literature, the majority of which do not consider the effects of the main intermediate product: dichloroacetyl chloride (DCAC). Jacoby et al.17 demonstrated that TCE molecules successfully competed with DCAC for oxidative species available on the catalytic surface. According to their experimental data, the TCE reaction rate did not depend on the DCAC concentration, which led the authors to conclude that DCAC and TCE adsorb on different types of surface sites. Therefore, since in our experiments the concentration of reaction intermediates was undetectable, the effect of DCAC was neglected. The incident radiation intensity at any position (x, y) on the surface of the photocatalytic plate was modeled by the linear source spherical emission (LSSE) model with the following assumptions: (1) isothermal conditions; (2) negligible absorption, scattering, or emission of radiation by the gaseous media occupying the space between the lamps and the catalyst; (3) negligible attenuation coefficient of the borosilicate glass which

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Figure 2. Lamp arrangement showing coordinates of the LSSE model.

covers the reactor; (4) negligible lamp radius compared to the distance of the lamp to the photocatalytic plate; (5) lamp axes parallel to the reactor. According to the LSSE model20

[ (

)

)]

(

r LI w x - xL,0 x - xL,0 - L I(x,y)|z)0 ) arctan - arctan 4R R R

(13)

where rL (m) is the radius of the lamp, Iw (W m-2) is the radiation intensity measured at the lamp wall, x (m) is the axial coordinate, y (m) is the reactor lateral coordinate, xL,0 (m) is the distance of the lamp ending from the axis origin, L (m) is the length of the lamp, and R (m) is the distance between the lamp axis and the point of interest on the surface of the plate (Figure 2). In the presence of multiple lamps, with N lamps axially mounted above the reactor, the distance between the axis of lamp i and a point (x, y) on the surface of the photocatalytic plate can be defined as

Ri ) [Z2 - (ylamp,i - y)2]1/2

(14)

where ylamp,i is the distance of the lamp axis from the origin (Figure 2). The radiation intensity on the surface of the photocatalyst equals the sum of the contributions from each lamp. It follows that

I(x,y)|z)0 )

∑

(I(x,y)|z)0)i )

( [ ( ) N lamps

∑

N lamps

rLIw,i 4Z

x - xL,0

arctan

Ri

- arctan

(

)])

x - xL,0 - L Ri

(15)

∫343380nmnm Wλ dλ)/(∫320380nmnm WλPλ dλ)

Numerical Integration of Material Balance Equation 5 was integrated numerically by a finite volume approach. The convection and diffusion terms were discretized by the simplest first-order (upwind) and second-order (central difference) formulas, respectively. In this way advantage was taken of the intrinsic robustness of these schemes. Solution accuracy was gained through relatively fine discretization. In particular, 80 and 200 cells in the z and x directions, respectively, were found to safely ensure fully converged results. With regard to the time derivative, an explicit first-order Euler approach was adopted. The time interval was selected in such a way that the Courant number was smaller than 1 in all cells (∆t e ∆x/Vx,max) while the stability of the diffusional term was also ensured [∆t e (∆y2/D)/8)]. At every time step the distribution of reactant concentration at the catalytic surface CTCE(z)0) was computed by locally solving the boundary condition (eq 6, first-order-discretized) together with the reaction kinetics (eq 11). This was accomplished by iterative refinement starting from the local converged value obtained in the former time step. Steady-state conditions were simulated by either letting the transient solutions evolve until the steady state was attained or more conveniently by direct solution of the linear algebraic set of equations obtained when eq 5 was discretized in the absence of the accumulation term. All computations were carried out using MatLab v. 7.1.0 software.

i

Equation 15 is strictly valid for monochromatic irradiation only. However, with polychromatic irradiation, as in this work, eq 15 can still be used by replacing Iw,i with its value averaged across the useful spectrum of the incident radiation, 〈Iw,i〉. The wavelength range which applies to the present case is λmin ) 320 nm, the minimum wavelength emitted by the lamp, and λmax ) 380 nm, the highest wavelength that can photoactivate the TiO2 photocatalyst. In practice the experimental photon flux I was measured with a UV radiometer fitted with a 365 nm sensor. Therefore, 〈Iw,i〉 was estimated by eq 16,

〈Iw,i〉 ) Isensor(

elsewhere.13 The difference between the measured and the calculated values of the intensity on the surface of the catalyst was less that 2%.

(16)

where Isensor (W m-2) is the incident radiation measured with the radiometer, Pλ is the relative spectral response of the 365 nm sensor, and Wλ (W) is the radiant power of the lamp at wavelength λ. The LSSE radiation model was experimentally validated in the reactor, and the results have been reported

Experimental Results and Validation of the Model We have previously shown that the transition from a mass transfer controlled regime to reaction kinetics partial control occurred at a fluid flow rate of approximately 1.72 L min-1 (Re > 46).13 As a consequence, the experiments designed to evaluate the activity of the catalyst for TCE photocatalytic oxidation were carried out at a flow rate of 2.3 L min-1 (Re ) 61) to operate the reactor in the predominant reaction controlled regime. The diffusion coefficient of TCE in air was taken to be 7.9 × 10-6 m2 s-1.21 The reaction kinetics were not saturated with respect to the irradiation level as shown previously.13 Consequently, the coefficient n in eq 11 was taken to be equal to 1 in the simulations. Table 1 shows kinetic parameters of TCE photocatalytic oxidation, estimated by a 3-D CFD model of the reactor13 which encompassed the nonuniform radiation intensity distribution over the photocatalytic plate calculated by the LSSE model (Figure 3). These parameters will be replaced in eq 11 and used in the 2-D model of the reactor applied to

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Figure 3. Distribution of radiation intensity on the surface of the catalytic plate, predicted by the LSSE model in the presence of the borosilicate glass reactor cover, for five lamps, three lamps, and one lamp (Z ) 0.122 m, 〈Iw〉 ) 73.5 W m-2). Average intensities: 13.53 W m-2 with five lamps, 8.78 W m-2 with three lamps, 3.06 W m-2 with one lamp. Table 1. Kinetic Parameters of TCE Photocatalytic Oxidation over TiO2 (Degussa P25) Thin Films Deposited on Glassa model

n

k (mol m-2 s-1 W-1 m2)

K (m3 mol-1)

TiO2 loading rate

UVA intensity range (W m-2)

relative humidity (%)

3-D model13

1

3.80 × 10-5

7.00

7 g m-2 of Degussa P25 on glass

3-14

8.0

a

Data determined by 3-D CFD modeling of the

reactor.13

TCE oxidation. Thereafter, the difference between 2-D and 3-D model predictions is evaluated for the experimental conditions in the reactor to provide confidence limits for the 2-D model. Radiation Intensity Profiles. Figure 3 shows the distribution of radiation intensity on the surface of the catalytic plate for three different irradiation conditions as predicted by the LSSE model. Gradients in the radiation intensity in the axial and lateral directions were present. The modeling of the reactor by 3-D CFD considered the actual distribution of radiation intensity on the surface of the catalytic plate. However, the average intensity over the entire surface of the catalyst was used in the 2-D simulations (eq 12). This was calculated to be 13.53 W m-2 with five-lamp irradiation, 8.78 W m-2 with three-lamp irradiation, and 3.06 W m-2 with one-lamp radiation. Transient Response and Concentration Profiles. The solution of the un-steady-state material balance (eq 5) over the time domain allows the prediction of the transient behavior of the reactor. Figure 4 shows the evolution of TCE conversion over time from the start of lamp irradiation for three different irradiation configurations. It also compares the concentration profiles of TCE at the steady state predicted by the 2-D model. The model predicts that the steady state is reached in 0.7 min under the experimental conditions in the reactor. At the steady state, the spatial profiles of TCE show strong gradients in both the vertical and the axial directions. The gradient of TCE in the vertical direction is zero at the inner surface of the glass plate since TCE cannot be transported through it. Conversely,

it equals the reaction rate at the surface of the catalytic plate. As expected, stronger axial gradients of TCE are realized in the region near the catalytic plate compared to the region near the glass plate. Effect of the Radiation Intensity, TCE Feed Concentration, and TCE Molar Flow Rate. Figure 5 shows the experimental results of TCE conversion at different radiation intensities and TCE inlet concentrations. The 2-D model with kinetic parameters from Table 1 fits the experimental results satisfactorily. Model predictions with (10% and (20% uncertainty on the parameter k are also shown to provide the sensitivity of the model to changes of this kinetic parameter. Figure 6 shows 2-D model fitting of TCE conversion at different TCE molar flow rates carried out in the predominant reaction controlled operational regime (Re > 46). In these experiments the inlet TCE concentration was kept approximately constant by increasing the TCE feed rate proportionally to the increase in the volumetric flow rate. The model was found to represent the experimental results satisfactorily. Comparison between 2-D and 3-D Reactor Models. Table 2 shows TCE conversions predicted by the 2-D model and the 3-D CFD model described elsewhere.13 The two models agree very closely, confirming the validity of the 2-D model assumptions listed earlier. However, the 3-D model, the more precise of the two since it includes the full representation of the fluid dynamics and radiation field, predicts conversions a fraction higher than the 2-D model. One reason for this is the presence

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Figure 4. 2-D model prediction of transient behavior of TCE conversion in the reactor and steady-state TCE concentration maps above the photocatalytic plate (color scale in mol m-3) (flow rate 2.3 L min-1, CTCE,0 ) 40.5 µM). Average intensities: 13.53 W m-2 with five lamps, 8.78 W m-2 with three lamps, 3.06 W m-2 with one lamp.

Figure 5. TCE conversion as a function of the radiation intensity (average value on the catalyst surface). Lines are 2-D model predictions. The flow rate is 2.3 L min-1. Kinetic parameters are from Table 1.

of a gradient in fluid velocity (Vy) in the 3-D model (ignored by the 2-D model) that allows for longer fluid residence times in the regions near the lateral walls and therefore larger conversions. It should be emphasized that if the width to thickness ratio of the slit had been much smaller than in the present reactor, the 2-D model would have led to larger underpredictions of the 3-D model results. The contribution of axial (x direction) and lateral (y direction) diffusion to transport of species through the reactor was considered in the 3-D CFD model, but it was neglected in the 2-D model.

Lateral diffusion should increase as the concentration of TCE at the reactor inlet is increased, since the presence of the lateral walls creates larger TCE gradients in the y direction. Lateral diffusion should also increase as the radiation intensity is increased, since faster reaction rates at the catalyst surface form larger TCE gradients in the y and z directions. As a result of lateral diffusion, more reactant is transported toward the region of the reactor near the lateral walls which have longer fluid residence times. Therefore, larger conversions should be obtained. The results in Table 2 show that the difference in TCE concentration at the reactor exit predicted by the 2-D and 3-D

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eq 11. Clearly this was not taken into account in this work since it was considered that the “gas-phase” adsorption of TCE over the catalyst was a rapid step. Furthermore, the model fitting of the experimental data in Figure 5 did not call for a more complex reaction kinetic mechanism. Nevertheless, the rate equation used in this work does not contain the dependence on other important factors, such as the adsorbed H2O concentration and reaction products. The investigation on the use of more complex kinetic mechanisms and TCE rate equations will be the subject of a forthcoming paper. Conclusions

Figure 6. Conversion as a function of the TCE molar flow rate. Comparison between experiment and the 2-D model (CTCE,0 from 30 to 35 µM, 〈I〉catalyst surface ) 3.06 W m-2, kinetic parameters from Table 1). Table 2. Comparison of TCE Conversions Predicted by 2-D and 3-D Modelsa CTCE,0 (µM)

〈I〉plate (W m-2)

X2-D (%)

X3-D (%)

CTCE,0 (X3-D - X2-D) (µM)

25.1

3.06 8.78 13.53 3.06 8.78 13.53 3.06 8.78 13.53

12.046 28.161 37.302 11.605 27.478 36.642 11.231 26.879 36.053

12.191 28.482 37.712 11.831 27.871 37.139 11.417 27.242 36.531

0.036 0.081 0.103 0.075 0.130 0.165 0.075 0.147 0.194

33.2 40.5

a Flow rate 2.3 L min-1. 〈I 〉 ) 73.5 W m-2. Kinetic parameters from w Table 1.

models (see the last column) increases as the inlet TCE concentration and the radiation intensity on the photocatalytic plate are increased. These results corroborate exactly with the explanation given. It should be noted however that in the 3-D model the effect of lateral diffusion on reactant conversion is mitigated by the presence of stronger radiation intensities near the center of the photocatalytic plate (Figure 3), creating a diffusion flux toward the center of the plate.13 From the results presented it can be concluded that the 2-D model can be used under the present experimental conditions for the derivation of reaction rate laws and reaction kinetic constants which are independent of radiation intensity and fluid dynamics. The parameters would therefore be more universally applicable to the design and scaleup of photocatalytic reactors for indoor air purification, providing that the same catalyst coating (type, thickness, and surface morphology) and experimental conditions (concentration of reagents and incident radiation spectra) are used in the scaled-up reactor. With regard to computational time in a standard specification PC, the 2-D model with a 80 × 200 grid required 70 s to solve eq 5 and 30 ms to solve the same equation in the absence of the accumulation term (steady state). The 3-D model needed approximately 20 min to perform the same calculation under steady-state conditions. The simple kinetic model adopted in this work (eq 11) assumed that the effect of radiation intensity is included in the term 〈I(x,y)〉n only. Therefore, the kinetic constants k and K should not depend on the radiation intensity. Recently, Ollis22 proposed a simple kinetic analysis of “liquid-phase” photocatalytic reactions and concluded that the adsorption rate constant K should also depend on the radiation intensity, implying that a radiation intensity term should appear in the denominator of

A two-dimensional model of a narrow-slit, flat-plate photocatalytic reactor was shown to approximate closely the experimental results of the oxidation of TCE. It was also shown that, under the present experimental conditions, the 2-D model approached very well the predictions of a much more complex 3-D CFD model of the reactor. The main advantages of the 2-D model are simplicity, lower implementation time and computational burden, and avoidance of the use of proprietary CFD software. However, the recognition of the 2-D model assumptions, namely, fully developed laminar flow, uniform irradiation of the catalytic plate, large width to thickness ratio, negligible axial diffusion, and lateral gradients, should always be kept in mind before use of the 2-D model for the estimation of kinetic parameters and reaction conversions in flat-plate experimental photoreactors. The reactor described here coupled with its mathematical modeling is particularly suited to precise determination of kinetic parameters of photocatalytic reactions directly from integral reactor experimental data. The 2-D model is not limited to the L-H rate law used in this work and can accommodate any rate law expression, thus allowing fast screening of reaction kinetic models. The 2-D model under the present circumstances can be used for the derivation of reaction rate laws and reaction kinetic constants which are independent of the radiation intensity and fluid dynamics and, therefore, more universally applicable to the design and scaleup of photocatalytic reactors for indoor air purification. Acknowledgment We acknowledge the Business-Engineering and Science Travel Scholarships (BESTS) from the Transferable Business Skills Programme (Roberts Money Postgraduate Training) and the UK EPSRC (Grant GR/S77875) for financial support. Nomenclature C ) substrate concentration, mol m-3 d ) thickness of the slit, m D ) diffusion coefficient, m2 s-1 J ) diffusion flux, mol m-2 s-1 k ) apparent rate constant, mol m-2 s-1 W-1 m2 K ) adsorption equilibrium constant, m3 mol-1 I ) radiation intensity (or radiative flux), W m-2 〈I〉 ) radiation intensity averaged across the photocatalytic surface area, W m-2 L ) lamp length, m n ) order of the reaction with respect to LSRPA, dimensionless N ) number of lamps, dimensionless P ) relative spectral response function, dimensionless r ) reaction rate per unit surface area, mol s-1 m-2 R ) distance of the lamp axis to a position of interest, m rL ) lamp radius, m RA ) volumetric reaction rate of species A, mol s-1 m-3

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t ) time, s V ) gas velocity, m s-1 v ) gas velocity vector, m s-1 〈V〉 ) average gas velocity (flow rate/cross-sectional area), m s-1 x ) reactor axial coordinate, m xL0 ) distance of the lamp end from the axis origin, m X ) conversion, dimensionless y ) reactor lateral coordinate, m W ) radiant power, W z ) reactor vertical coordinate, m Z ) vertical distance of the lamp axis from the photocatalytic plate, m

(7) Obee, T.; Brown, N. M. D. TiO2 photocatalysis for indoor air applications: effects of humidity and trace contaminant levels on the oxidation rates of formaldehyde, toluene and 1,3-butadiene. EnViron. Sci. Technol. 1995, 29, 1223. (8) Raupp, G. B.; Alexiadis, A.; Hossain, M. M.; Changrani, R. Firstprinciples modeling, scaling laws and design of structured photocatalytic oxidation reactors for air purification. Catal. Today 2001, 69, 41. (9) Imoberdorf, G. E.; Irazoqui, H. A.; Cassano, A. E.; Alfano, O. M. Photocatalytic degradation of tetrachloroethylene in gas-phase on TiO2 films: A Kinetic Study. Ind. Eng. Chem. Res. 2005, 44, 6075-6085. (10) Imoberdorf, G. E.; Irazoqui, H. A.; Alfano, O. M.; Cassano, A. E. Scaling-up from first principles of a photocatalytic reactor for air pollution remediation. Chem. Eng. Sci. 2007, 62, 793.

Greek letters

(11) Hossain, M. M.; Raupp, G.; Hay, S. O.; Obee, T. N. Threedimensional developing flow model for photocatalytic monolith reactors. AIChE J. 1999, 45, 1309.

λ ) radiation wavelength, m ∇ ) vector differential operator

(12) Mohseni, G. M.; Taghipour, F. Experimental and CFD analysis of photocatalytic gas phase vinyl chloride (VC) oxidation. Chem. Eng. Sci. 2004, 59, 1601.

Subscripts

(13) Salvado-Estivill, I.; Hargreaves, D. M.; Li, Puma, G. Evaluation of the intrinsic photocatalytic oxidation kinetics of indoor air pollutants. EnViron. Sci. Technol. 2007, 41, 2028. (14) Toepfer, B.; Gora, A.; Li Puma, G. Photocatalytic oxidation of multicomponent solutions of herbicides: reaction kinetics analysis with explicit photon absorption effects. Appl. Catal., B 2006, 68, 171. (15) Salvado, I.; Hargreaves, D. M.; Li Puma, G. Single-pass, flowthrough phocatalytic reactor for oxidation of volatile organic carbon in contaminated air. 10th International Conference on TiO2 Photocatalysis: Fundamentals and Applications, Chicago, IL, Oct 23-27, 2005. (16) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena, 2nd ed.; Wiley: New York, 2002. (17) Jacoby, W. A.; Blake, D. M.; Noble, R. D.; Koval, C. A. Kinetics of the oxidation of trichloroethylene in air via heterogeneous photocatalysis. J. Catal. 1995, 157, 87. (18) Jacoby, W. A.; Nimlos, M. R.; Blake, D. M.; Noble, R. D.; Koval, C. A. Products, intermediates, mass balances, and reaction pathways for the oxidation of trichloroethylene in air via heterogeneous photocatalysis. EnViron. Sci. Technol. 1994, 28, 1661. (19) Herrmann, J.-M. Heterogeneous photocatalysis: state of the art and present applications. Top. Catal. 2005, 34, 49. (20) Jacob, S. M.; Dranoff, J. S. Radial scale-up of perfectly mixed photochemical reactors. Chem. Eng. Prog. Symp. Ser. 1966, 62, 47. (21) Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H., Handbook of chemical property estimation methods: enVironmental behaViour of organic compounds; American Chemical Society: Washington, DC, 1990. (22) Ollis, D. F. Kinetics of liquid phase photocatalyzed reactions: An illuminating approach. J. Phys. Chem. B 2005, 109, 2439.

0 ) reactor entrance A ) generic species L ) reactor exit TCE ) trichloroethylene w ) lamp wall x ) direction of the reactor axial coordinate y ) direction of the reactor lateral coordinate z ) direction of the reactor vertical coordinate λ ) wavelength Literature Cited (1) Austin, B. S.; Greenfield, S. M.; Weir, B. R.; Anderson, G. E.; Behar, J. V. Modelling the indoor environment. EnViron. Sci. Technol. 1992, 26, 851. (2) IEH. Indoor air quality in the home: Final report on DETR Contract EPG 1/5/12, (Web Report W7), November 2001, Institute for Environment and Health, Leicester, UK. http://www.le.ac.uk/ieh/publications/publications.html. (3) U.S. EPA and U.S. Consumer Product Safety Commission, Office of Radiation and Indoor Air (6604J). The inside story. A guide to indoor air quality; EPA Document No. 402-K-93-007; Washington, DC, April 1995. (4) Colorado Department of Public Health and Environment. Trichloroethylene Health Effects Fact Sheet, January 2005. http://www.cdphe.state.co.us/hm/tcefs.pdf. (5) U.S. EPA, Office of Research and Development. Trichloroethylene Health Risk Assessment: Synthesis and Characterization; EPA Document No. 600/P-01/002A; Washington, DC, August 2001. http://cfpub.epa.gov/ ncea/cfm/recordisplay.cfm?deid)23249. (6) Peral, J.; Domenech, X.; Ollis, D. F. Heterogeneous photocatalysis for purification, decontamination and deodorization of air. J. Chem. Technol. Biotechnol. 1997, 70, 117.

ReceiVed for reView March 15, 2007 ReVised manuscript receiVed May 14, 2007 Accepted May 17, 2007 IE070391R