Kinetics rate model of the photocatalytic oxidation of trichloroethylene in air over TiO2 thin films

Separation and Purification Technology 67 (2009) 226–232

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Kinetics rate model of the photocatalytic oxidation of trichloroethylene in air over TiO2 thin films Gianluca Li Puma a,∗ , Ignasi Salvadó-Estivill a , Timothy N. Obee b , Stephen O. Hay b a

Photocatalysis & Photoreaction Engineering, Department of Chemical & Environmental Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom United Technologies Research Center, Hartford, CT, USA

b

a r t i c l e

i n f o

Article history: Submitted for the special issue of Separation and Purification Technology honoring Professor Po Lock YUE Keywords: Photocatalysis Titanium dioxide Air pollution Reaction kinetics VOC

a b s t r a c t The photocatalytic oxidation of trichloroethylene (TCE) over a TiO2 thin film was investigated in a flowthrough photocatalytic reactor. The effects of TCE concentration and water vapor concentration on the oxidation rates were investigated. Rate models based on variations of the Langmuir–Hinshelwood kinetic model were found to represent the results unsatisfactorily. Therefore, a general rate equation for the oxidation of TCE was derived from an elementary reaction mechanism of TCE photocatalytic oxidation over TiO2 . The model, based on chlorine atom attack of the TCE molecule, yields a relatively complex equation including the explicit dependence on water vapor concentration, TCE concentration, photon flux and quantum yield. The rate equation yields half-order dependence on the photon flux at high photon fluxes and first-order dependence at low photon fluxes and reduces to first-order dependence on TCE and inverse dependence on water vapor under specific conditions. The kinetic parameters of the photocatalytic oxidation of TCE on TiO2 thin film were estimated by fitting the model to the experimental results. The approach demonstrated in this paper represents a more rational method of kinetic analysis than the mechanical adoption of a Langmuir–Hinshelwood type rate equation often reported in the literature. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Most people in industrialized and developing countries spend a considerable time in indoor environments where the concentrations of pollutants may be 2–5 times higher, and occasionally 100 times higher, than outdoors [1]. The contamination of indoor environments from trace concentrations of volatile organic compounds (VOCs) is of particular concern because of their long-term effects on humans. Sources of VOC in the indoor environments include building materials (e.g., paint, sealants, flooring, furniture, and upholstery) products (e.g., cleaning materials, solvents, and cooking fumes) and the occupant activities [2]. Furthermore, short-term effects of VOC contamination can be manifested through the wellknown “sick building syndrome” which is cause of absenteeism and poor performance in the work place. Indoor environments include habitable structure or conveyance, such as homes, schools, offices, factories and vehicles. A recent study of indoor air quality in indoor Hong Kong homes, offices, schools, shopping malls and restaurant identified aromatics and chlorinated hydrocarbons among the most common VOC [3].

∗ Corresponding author. Tel.: +44 115 9514170; fax: +44 115 9514115. E-mail address: [email protected] (G. Li Puma). 1383-5866/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2009.03.011

Among chlorinated hydrocarbons, trichloroethylene (TCE) is one of the most common and a carcinogenic compounds [4,5]. Its main use in industry is as a metal degreaser in the aviation and in the microelectronics industry. In commercial and domestic environments, it is often used as a dry cleaning agent. In the chemical industry, it is employed as an intermediate in fluorochemical and polyvinyl chloride (PVC) production. Photocatalytic oxidation (PCO) has been proposed as a mean of indoor air purification which allows destruction of VOC to levels perceived to be safe [6,7]. The oxidation reaction is carried over irradiation of a semiconductor photocatalyst, commonly titanium dioxide (TiO2 ), in the presence of water vapor and an electron acceptor (usually atmospheric oxygen). The PCO of TCE in gas-phase has been extensively studied in the literature. Significant work has been carried in terms of identification of reaction intermediates, in the elucidation of reaction kinetics mechanisms and in the estimation of reaction kinetics coefficients [8–21]. However, there is disagreement in the literature with regards to the kinetics rate equation which can model adequately the PCO of TCE. Table 1 summarizes selected rate equations of the PCO of TCE in different photocatalytic reactors. The most common rate equations proposed in the literature are based on variation of the Langmuir–Hinshelwood rate equation and most often (not always) appears to have been adopted without an analysis of the elementary reactions taking place.

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Table 1 Rate equations reported in literature for TCE photocatalytic oxidation in gas-phase. Rate equation KT [TCE]

−rTCE = kT1 I n 1+K1

T1 [TCE]

−rTCE = k



k1 [TCE] 1+k1 /[TCE]+k3 [H2 O]

−rTCE = k 1/K



k2 [O2 ]/[H2 O] 1+k2 [O2 ]/[H2 O]+k4 [H2 O]

PTCE

2

Constants values

Experimental conditions

Reference

kT1 = 7.28 pmv−1 cm−2 s−1

Tubular reactor, P25 on fibre textile

[22]

K = 0.00438 pmv−1 = 22.82 × 103 M−1 n = 0.52

4.02 mg cm−2 , 0 < I < 6.12 W m−2

k = 101 ␮mol s−1 m−2 = 2.02 × 10−5 mol s−1 g−1

TCE +PTCE

Fixed bed dynamic photoreactor. Anatase (Aldrich) spread on filter paper. VReactor = 3.14 cm3 , Ailluminated = 2.09 cm2 , I = 4.1 × 10−9 Ein cm−2 s−1 Annular reactor, P25 wash coated on walls, 0.5 mg cm−2 , I = 5.3 mW cm−2

[23]

[10]

KTCE = 0.022 mTorr−1 −rTCE =

a[TCE] 1+b[TCE]

a = 2.9 × 10−5 m3 s−1 g−1 b = 109 m3 mol−1 = 10.9 × 104 M−1

Glass tubular reactor, TiO2 on pellets

[24]

−rTCE =

kK[TCE] 1+K[TCE]

k = 1.4 ppm s−1 g−1

[20]

K = 0.12 ppm−1

Tubular reactor, (6 Pyrex glass cylinders), TiO2 Nihon Aerosil on walls 10 black lights (60 W)

−rTCE =

kKTCE [TCE] 1+KTCE [TCE]+KP [P]+KCO [CO2 ]

kTCE = 3.561 × 10−8 mol s−1 g−1 (RH ≤ 0.8%)

Rectangular reactor with baffles

[25]

KTCE = 4.388 × 105 M−1 (RH ≤ 0.8%) kTCE = 5.872 × 10−8 mol s−1 g−1 (RH = 24.4%) KTCE = 1.275 × 105 M−1 (RH = 24.4%) kTCE = 3.825 × 10−8 mol s−1 g−1 (RH = 61.7%) KTCE = 7.123 × 104 M−1 (RH = 61.7%)

3.5 g TiO2 powder I = 2.34 mW cm−2 T = 25 ± 0.1 ◦ C

k0 = 1.0216 × 10−6 mol s−1 g−1 , ˛ = 0.61

Cylindrical reactor, P25 on glass beads, 1.2 < [TCE] < 6.4 ␮M, 9.4 < [H2 O] < 1222.2 ␮M, 0.09 < I < 0.45 mW cm−2 , T = 50◦ C

2

 −rTCE = k0 I ˛

k1 CTCE 1+k1 CTCE +k2 CH O 2



k4 CH O 2

1+k3 CTCE +k4 CH O 2



K1 = 0.1074 ␮M−1 , K2 = 0.0005 ␮M−1 K3 = 0.2281 ␮M−1 , K4 = 0.3955 ␮M−1

This shortcoming and the inadequacy of the L–H rate type equations to model PCO kinetics have been recently highlighted in the literature by works of Minero [27], Serpone [28] and Ollis [29]. In this paper, we review some of the kinetics rate models proposed for TCE photocatalytic oxidation over titania-coated surfaces, and compare their adequacy in representing experimental results obtained in a differential flow-through reactor. We then employ a detailed elementary kinetic model of TCE PCO and formulate a TCE rate equation based on this mechanism. It is not the intention of this paper to be exhaustive in the mechanistic aspects of TCE photocatalytic oxidation, for this reason a generally accepted model based on chlorine atom attack of the TCE molecule is employed [8]. The method has been used previously to model successfully rate data of PCO of perchloroethylene [30] and TCE [31]. For these reason we have followed a similar approach with appropriate modifications to model the PCO of TCE and determined kinetics parameters which should be applicable to reactor of different geometries utilizing the same titania coating and operating under similar experimental conditions. 2. Experimental A schematic view of the photocatalytic reactor used for the gasphase PCO of TCE is reported elsewhere [32]. It consisted of a flat 25-mm wide, 457-mm long, aluminum reactor that allowed the controlled distribution of the contaminated air flow over the catalyst. A 25 mm × 305 mm glass plate coated with the photocatalyst was located 76 mm from the inlet of the reactor and 76 mm from the outlet. The reactor was covered with a quartz glass (3.2 mm thick) sealed with a Viton gasket. This formed a 25 mm × 2 mm flow passage across the whole length of the reactor. The reactor inlet and outlet consisted of 25 mm × 25 mm × 25 mm bed containing glass beads which were designed to minimize back-flow diffusion and to achieve uniform, fully developed laminar flow over the photocatalytic plate.

[26]

The reactor was irradiated by two 15 W blacklight blue fluorescent lamps (SpectroLine XX-15A, UVA peak at 352 nm). The radiation intensity at the photocatalytic surface was regulated by adjusting the distance between the lamps and the reactor. UV radiation was measured with a UVA power meter (Oriel UVA Goldilux). High purity nitrogen gas was passed through a water bubbler to set the desired water vapor level. Ultra high purity water produced by a NANOpure Diamond UV water purification system (18.2 M cm−1 , ≤1 ppb TOC) was used in the bubbling bottle to saturate the gas. TCE (Fisher, for analysis, >99.8%) contaminant was generated through a thermostatted diffusion-controlled vaporizer. An ultra high purity (99.999%) oxygen gas flow was combined with the nitrogen and contaminant flows to produce the desired carrier gas mixture (15% oxygen, 85% nitrogen). The gas flow rates were adjusted using calibrated flowmeters. Thermocouples were used to measure the temperature of the inlet and exit streams. The concentrations of water vapor were measured using a photo-acoustic detector (Bruel & Kjaer 1302). The concentration of TCE was measured using a gas chromatograph (HP-5890 II) equipped with a ECD detector and a megabore column (Restek RTX-502.2). 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 BET; composition 78% anatase and 22% rutile by X-ray diffraction) in distilled water was deposited over a microscope glass plate. The glass plates were dipped in the suspension several times, air dried between dipping and then dried at 70 ◦ C for 2 h in an oven. The process was repeated until a catalyst loading of 7.4 g m−2 (film per side) was achieved. The contaminated gas stream entered the reactor by first passing through a bed of glass mixing beads. Next, the gas flow entered a 25 mm by 2 mm entrance region of sufficient length (76 mm in length) to produce a fully developed laminar velocity profile. The gas flow then passed over the surface of the titania-coated glass plates. Finally, the gas passed through a 25 mm by 2 mm exit region

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(76 mm in length) and the second bed of glass beads before exiting the reactor. The reactor was operated at a total gas flow rate of 4.0 L min−1 to ensure that mass transfer limitations were eliminated and that the operation of the reactor was under the kinetics controlled regime [32]. In a typical experiment, the TCE concentration in the reactor was initially allowed to reach 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. 3. Results and discussion The reactor was operated at steady state, under differential conditions (conversion less than 10%) and in the kinetics controlled regime. The TCE oxidation rate was estimated from steady-state experiments as follow: −rTCE =

Q (CTCE,in − CTCE,out ) A

(1)

where Q is the total flow rate at the reactor inlet, CTCE,in and CTCE,out are the concentration of TCE at the inlet and outlet of the reactor, and A is the area of the titania-coated glass-plate. 3.1. Fitting literature reaction kinetics models to experimental results Experiments at different TCE inlet concentrations (Fig. 1) and water vapor concentrations (Fig. 2) were performed and the TCE reaction rate was calculated from Eq. (1). Table 2 presents kinetic models for the photocatalytic oxidation of TCE in air over TiO2 thin films, which have been proposed in the literature. These are essentially based on variation of the Langmuir–Hinshelwood (L–H) rate model, including monomolecular and bimolecular models with competitive and non-competitive adsorption on the catalyst sites. In Table 2 it is also included an early empirical model based on the power-law rate equation. The model presented in Table 2 assumed that the reaction products do not influence the observed oxidation rates and that only TCE and water vapor are the only important species. Since the experiments were carried out under differential conditions, the experimental rate data estimated using Eq. (1) could directly be fitted by the rate equations presented in Table 2. A nonlinear least squares regression function (nlinfit) in MATLAB was

Fig. 2. Effect of water vapor concentration on the rate of PCO of TCE. Incident photon flux (UVA) = 15.5 W m−2 . [TCE]inlet = 4.1 × 10−2 ␮M.

used for this purpose to fit simultaneously the experimental results in Figs. 1 and 2 while minimizing the overall error. Although some of the models could represent the dependence of the oxidation rate from the inlet TCE concentration, they unsuccessful modelled the rate data as a function of the water vapor concentration. Table 3 reports the best fitting kinetics parameters for each of the models and the corresponding error. Model M1 based on an empirical rate equation could represent the results in Fig. 1 with an acceptable degree of accuracy, however, failed to model the results in Fig. 2. Model M2 based on the monomolecular L–H rate equation could also fit the data in Fig. 1, however, does not allow for a dependence of the rate from water vapor. Model M3 is based on the competitive adsorption of water and TCE on equal type of sites. This model fitted the data in Fig. 1 very well and predicted the general trend that should be expected in Fig. 2 with regard to the dependence of the rate on water vapor. Model M4 is based on the adsorption of water and TCE on different type of sites. This model failed to predict the dependence of rate from water vapor concentration and also the dependence of the rate from TCE at high concentration levels. Model M5 could predict the general trends in Figs. 1 and 2, however, a certain degree of error was observed. 3.2. TCE reaction mechanism and derivation of reaction rate equation The appropriate method of searching for a suitable rate equation for the PCO of TCE should begin with the formulation of a suitable reaction mechanism. Table 4 shows an elementary reaction mechanism for TCE photocatalytic oxidation based on the work by Nimlos et al. [8]. On the basis of this scheme the oxidation of TCE Table 2 Kinetic models of gas-phase photocatalytic oxidation of TCE.

Fig. 1. Effect of inlet TCE concentration on the rate of PCO of TCE. Incident photon flux (UVA) = 15.5 W m−2 . [H2 O] = 244 ␮M.

Kinetic model

TCE rate equation

M1: empirical

˛ −rTCE = I · kCTCE CH

M2: L–H monomolecular

−rTCE = I · k 1+KTCE

M3: L–H bimolecular – single site competitive

−rTCE = I · k

M4 L–H bimolecular – two types of sites – non-competitive

−rTCE = I · k (1+KTCE

M5: L–H bimolecular – two types of sites – competitive

−rTCE = I · k (1+K

Reference

ˇ

[33]

2O CTCE TCE CTCE

K

[22]

KTCE KH O CTCE CH O 2 2 (1+KTCE KH O CTCE CH O )2 2 2 K

K

C

[26]

H2 O H2 O CTCE TCE CTCE ) (1+KH2 O CH2 O )

[6]

K4 CH O K1 CTCE 2 1 CTCE +K2 CH2 O ) (1+K3 CTCE +K4 CH2 O )

[26]

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229

Table 3 Best fitting kinetics parameters for each of the models in Table 2. Values obtained by nlinfit (Matlab). Model

Parameter

Value

95% confidence interval

Units

M1

k ˛ ˇ

0.523 0.68 −0.10

2.660 0.083 0.929

␮mol m−2 s−1 W−1 m2 ␮M0.58 – –

M2

k KTCE

1.91 0.197

0.180 0.034

␮mol m−2 s−1 W−1 m2 ␮M−1

M3

k KTCE KH2 O

6.33 0.335 1.55 × 10−2

2.910 0.583 3.41 × 10−2

␮mol m−2 s−1 W−1 m2 ␮M−1 ␮M−1

M4

k KTCE KH2 O

2.64 0.195 1.07 × 10−2

0.257 3.49 × 10−2 n/a

␮mol m−2 s−1 W−1 m2 ␮M−1 ␮M−1

M5

k K1,TCE K3,TCE K2,H2 O K4,H2 O

4.97 0.644 0.167 2.29 × 10−2 1.07 × 10−2

0.711 2.60 – 0.109 –

␮mol m−2 s−1 W−1 m2 ␮M−1 ␮M−1 ␮M−1 ␮M−1

is mainly due to Cl atom attack which after its generation undergoes a chain regeneration mechanism. However, photocatalytically generated hydroxyl radicals are needed to generate Cl atoms. Reaction R0 is the generation of electron-hole couples, upon irradiation with UVA, which can recombine to release heat (R12) or can be trapped by surface adsorbed species after migration to the surface. Photogenerated holes react with adsorbed water to produce hydroxyl radicals (R1). Photogenerated electrons react with adsorbed oxygen to produce superoxide anion radicals (R2). Reactions R3 to R6 relate to the mechanism of Cl atom formation. R3 is the reaction of TCE with hydroxyl radicals and finishes with the generation of Cl atoms and formation of dichloroacetic acid (DCAA). R7 is the reaction of TCE with a Cl atom to break the double bond to form an alkyl radical. This radical further reacts with oxygen to form peroxyl radical (R8) which combines with another peroxyl radical to form an alkoxyl radical (R9). The alkoxyl radical can rupture the C–C bond to form phosgene and a dichloromethyl radical (R10) or can lose a Cl atom to form dichloroacetyl chloride (DCAC) (R11) one of the most important intermediates in TCE photocatalytic oxidation [9]. The chain reactions (R7–R11) may explain the high reaction rates seen for the gas-phase photocatalytic oxidation of TCE relative to photocatalytic oxidation of non-chlorinated

organic compounds (e.g., toluene), where the chain reaction would be less likely. The termination reactions of Cl atoms with other radicals, water or the reaction walls (all these species denoted with M) have been grouped in a single reaction (R13). It is worth noting that the TCE reaction mechanism presented is by no means complete since we have not taken into account the role of the superoxide anion radical and further reactions of hydroxyl radical with DCAC to form phosgene [8]. Furthermore we have not distinguished between free and adsorbed radical species consequently we have not explicitly balanced sites in each step to derive the kinetic equations which follows. The proposed TCE degradation mechanism is based on Cl atom to be the most important species which reacts with adsorbed TCE molecules [8,17,34]. As a result, R7 is considered to be much faster than R3 and the rate of TCE photocatalytic oxidation can be written as: −rTCE ≈ k7 [TCE]ad [Cl]•

(2)

The pseudo steady-state approximation on the electrons, the holes, the Cl atoms the OH radicals and the radical species is then applied. Furthermore, competitive adsorption of TCE and H2 O on the same type of sites is considered and it is assumed that pseudo-

Table 4 TCE reaction mechanism. Process Initiation

Reaction steps h

TiO2 −→TiO2 + e− + h+ h+ + H2 Oad → OH • + H + − h+ + HOad → OH • e− + O2 → O2−



Reaction rates

No.

rg

(0) +

k1 [H2 O]ad [h ]

(1)

k2 [O2 ][e− ]

(2)

Cl• generation

HC2 Cl3 + OH • → HC2 Cl3 OH • HC2 Cl3 OH • + O2 → HC2 Cl3 OHOO• 2HC2 Cl3 OHOO• → 2HC2 Cl3 OHO• + O2 HC2 Cl3 OHO• → HC2 Cl2 OHO + Cl•

k3 [TCE]ad [OH• ] k4 [HC2 Cl3 OH• ][O2 ] k5 [HC2 Cl3 OHOO• ]2 k6 [HC2 Cl3 OHO• ]

(3) (4) (5) (6)

Chain propagation

HC2 Cl3 + Cl• → HC2 Cl4 • HC2 Cl4 • + O2 → HC2 Cl4 OO• 2HC2 Cl4 OO• → 2HC2 Cl4 O• + O2 HC2 Cl4 O• → COCl2 + HCCl2 • HC2 Cl4 O• → HC2 Cl3 O + Cl•

k7 [TCE]ad [Cl• ] k8 [HC2 Cl4 • ]ad [O2 ] k9 [HC2 Cl4 OO• ]2 k10 [HC2 Cl4 O• ] k11 [HC2 Cl4 O• ]

(7) (8) (9) (10) (11)

Ending reactions

e− + h+ → heat Cl• + M → products

k15 [h+ ][e− ] k16 [Cl• ][M]

(12) (13)

Non-radical reaction Reactants adsorption/desorption Water adsorption

COCl2 + H2 O → CO2 + 2HCl HC2 Cl3 + S ↔ HC2 Cl3 H2 O + S ↔ H2 Oad

kA (KTCE [TCE][S] − [TCE]ad ) kA (KW [H2 O][S] − [H2 O]ad )

(14) (15) (16)

Notes: Trichloroethylene: HC2 Cl3 ; dichloroacetyl chloride: HC2 OCl3 ; phosgene: COCl2 .

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equilibrium exists between the adsorbed species and the species in the gas. Jacoby et al. [9,10] concluded that the degradation rates of TCE is not influenced by DCAC, the main intermediate of TCE, and suggested that these two species do not compete for the same adsorption sites. In consequence, the effect of DCAC on TCE degradation rate can be eliminated. A balance on the total number of catalyst active sites is also performed. After rearrangement it may be shown that Eq. (2) becomes: −rTCE =

˛1 [TCE][H2 O] 2 (1 + KTCE [TCE] + KW [H2 O])





˛2 (1 + KTCE [TCE] + KW [H2 O]) −1 1 + rg [H2 O]

×

This equation resemble the one derived by Esterkin et al. [31] for TCE photocatalytic oxidation, however, here we adopt quantum efficiencies and incident photon flux rather than primary quantum yield and LSRPA. Eq. (9) can be further simplified if we assume that: KTCE [TCE] 1 + KW [H2 O]

which is valid when the catalyst is not saturated with TCE and when a linear dependence of the rate from TCE concentration is observed. This is normally found at low TCE concentrations as shown in Fig. 1 in the range from 0 to 2 ␮M. As a result, Eq. (9) in the linear range becomes:

(3) −rTCE =

where rg is the local superficial rate of electron-hole formation on the titania-coated glass-plate, and ˛1 and ˛2 are kinetic coefficients. ˛1 = − ˛2 =

k1 k2 k7 KTCE KW [O2 ][S]2 2k12 k13 [M]

(5)

with [S] the total concentration of active sites. The local rate of electron-hole formation rg is a function of the primary quantum yield ˚ (the number of electrons-hole couples generated per photon absorbed) and of the local surface rate of photon adsorption (LSRPA) e on the titania-coated glass-plate:

2 ˚ e d

(6)



˛2 (1 + KW [H2 O]) −1 1 + ϕ I [H2 O]

2

3.3. Simplification of TCE rate equation: limiting cases of low and high photon flux The literature suggests that under low photon flux the rate of photocatalytic oxidation of organic compounds over TiO2 surfaces is first-order on the incident photon flux, and at high photon fluxes is half-order. Following the method shown by Imoberdorf et al. [30] Eq. (11) can be simplified further to consider these two cases of irradiation with high and low photon fluxes. At high photon flux the term in brackets in Eq. (11) can be simplified as follows:





(1 + KW [H2 O]) 1 + ˛2 ϕ I −1 [H2 O]

where  is the wavelength. Owning to the difficulty in estimating the LSRPA (the major problem is the need for the estimation of the reflection and absorption coefficient of TiO2 thin films which in turn are a function of the physical and electronic properties of the films), and considering that the LSRPA should be proportional to the local incident photon flux I over the titania-coated glass-plate, we can rewrite Eq. (6) in terms quantum efficiency ϕ (the number of electrons-hole couples generated per incident photon) as follows:

2 ϕ I d



(1 + KW [H2 O]) ˛2 ϕ I [H2 O]

∼ =

(12)

which shows half-order dependence on the reaction rate from the incident photon flux. This limiting case has been described by Upadhya and Ollis [35]. Conversely, at low photon flux



˛2 ϕ I

(7)

(1 + KW [H2 O]) [H2 O]



1

(13)

and therefore we can approximate the term under the square root in Eq. (11) in a Taylor’s series truncated to the first term. It follows:

1

Averaging the quantum efficiency throughout the wavelength spectrum with enough energy to excite the catalyst, it follows:

2 ϕ I d ∼ =

rg =

(1 + KW [H2 O])



(11)

1

rg =

˛1 [TCE][H2 O]

(4)

4k12 k1 k2 KW [O2 ][S]

rg =

(10)



ϕ I ∼ = ϕ I

(8)



1

where ϕ is the wavelength averaged quantum efficiency and I is the wavelength averaged incident photon flux, which in general is a function of position over the titania-coated glass-plate. In the experimental set-up the radiation field over the plate was measured radiometrically and was found to be approximately constant, therefore, the dependence of rg from position was neglected. Replacing Eq. (8) in Eq. (3) it follows: −rTCE =

˛1 [TCE][H2 O] (1 + KTCE [TCE] + KW [H2 O])



×

1 + ϕ I

2



˛2 (1 + KTCE [TCE] + KW [H2 O]) −1 [H2 O]

(9)





(1 + KW [H2 O]) 1 + ˛2 ϕ I −1 [H2 O]

∼ =



˛2 ϕ I

(1 + KW [H2 O]) 2[H2 O]

 (14)

Replacing in Eq. (11) we have: −rTCE = I

˛[TCE] (1 + KW [H2 O])

(15)

with ˛=

k7 KTCE [S] ˛1 ˛2 ϕ = 2 k13 [M]

(16)

which shows linear dependence of the rate from the incident photon flux and an inverse relationship with respect to concentration of water in the gas-phase. Therefore Eqs. (9) or (11) can represent the entire range of photon fluxes from low to high providing the observed reaction is kinetically controlled.

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231

Fig. 5. Fitting of Eq. (9) to experimental results in Fig. 1. Fig. 3. Fitting of Eq. (15) to experimental results in Fig. 1 in the low concentration range.

Fig. 6. Fitting of Eq. (9) to experimental results in Fig. 2. Fig. 4. Fitting of Eq. (15) to experimental results in Fig. 2 in the low concentration range.

3.4. Fitting TCE rate equations to experimental results and estimation of kinetic parameters The experimental results of oxidation rate versus TCE concentration in Fig. 1 show linear dependence at low TCE concentrations. Furthermore the photon flux (15.5 W m−2 UVA) is weak, as a result the limiting case described by Eq. (15) was adopted. Non-linear least squares fitting of Eq. (15) to the experimental data shown in Figs. 3 and 4 yielded the kinetic parameters ˛ and KW which are presented in Table 5. The results for the dependence of the rate on

TCE concentration were well represented by the model. The results describing the dependence of rate on water concentration were approached by the model. The underlying trend was well described by the model although an error was noted. With the knowledge of the values of the kinetic parameters ˛ and KW in Table 5, the complete TCE rate equation (Eq. (9)) was fitted to the experimental results with the limiting condition imposed by Eq. (16). The best fitting results are presented in Figs. 5 and 6. The model appears to represent the experimental data with a reasonable degree of accuracy in the entire range of the process variables investigated. Confidence limits for the model parameters are shown. Table 6 reports the values of the kinetic parameters for the PCO of TCE in the range of process variable investigated. The

Table 5 Kinetic parameters for the PCO of TCE valid at low TCE concentrations (Eq. (15)). Parameter ˛ KW

Value 0.95 1.07 × 10−2

95% confidence interval 0.13 9.29 × 10−3

Units −1

␮mol W ␮M−1

−1

s

−1

␮M

R2 (TCE)

R2 (H2 O)

0.9962

0.9912

R2 (TCE)

R2 (H2 O)

0.9909

0.9922

Table 6 Kinetic parameters for the PCO of TCE valid in the entire range of process variables investigated (Eq. (9)). Parameter ␣1 ␣2 × ϕ KTCE KW

Value 18.9 0.100 0.335 1.07 × 10−2

95% confidence interval 2.3 0.035 0.083 9.29 × 10−3

Units −1

−1

␮M m s W−1 m2 ␮M−1 ␮M−1

␮mol

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kinetic model presented in this paper with the parameters in Table 6 represents a more rational model for the prediction of the oxidation rate of TCE over immobilized TiO2 compared to semi-empirical rate equations adopted in the literature. 4. Conclusions In this paper, we have summarized the rate equations proposed in the literature for the PCO of TCE and compared these models to kinetic data collected in a differential reactor. The inadequacy of some of these models to fit rate data has been demonstrated. Often in the literature L–H type rate equations have been applied mechanically to model kinetics data of photocatalytic reactions. This has been done without considering a detailed mechanism of the elementary reaction taking place. In this paper we have shown a simple analysis of the kinetics of PCO of TCE and demonstrated a suitable method for the estimation of the kinetic parameters. The rate equation and the values of the kinetic parameters should therefore be applicable to reactor of different reactor geometries utilizing the same titania coating and operating under similar experimental conditions. This type of analysis is, in the view of the authors, essential in successful design and scale-up of photocatalytic reactors. Acknowledgements This paper was presented orally at the Symposium on “Advanced Technologies for Environmental Remediation” in honor of Professor Po Lock Yue on the Occasion of his Retirement, Hong Kong, China, 15 June 2007. G. Li Puma would like to thank the Department of Chemical Engineering at the Hong Kong University of Science & Technology for financial support to attend the symposium. He would also like to thank Professor Po Lock Yue for the support given over 15 years of close collaborations and wish him a happy retirement. Finally, the authors acknowledge the Business-Engineering and Science Travel Scholarships (BESTS) from the Transferable Business Skills Programme (Roberts Money Postgraduate Training) for financial support. References [1] US EPA, US Consumer Product Safety, Commission Office of Radiation and Indoor Air (6604J), The inside story. A guide to indoor air quality. EPA Document # 402-K-93-007, April 1995. [2] IEH, Indoor air quality in the home: final report on DETR Contract EPG 1/5/12 (Web Report W7) Leicester, UK, Institute for Environmental and Health (at http://www.le.ac.uk/ieh/publications/publications.html posted November 2001). [3] S.C. Lee, H. Guo H, W.M. Li, L.Y. Chan, Inter-comparison of air pollutant concentrations in different indoor environments in Hong Kong, Atmos. Environ. 36 (2002) 1929–1940. [4] Colorado Department of Public Health and Environment, Trichloroethylene Health Effects Fact Sheet, January 2005 (at http://www.cdphe.state.co.us/hm/ tcefs.pdf). [5] US EPA, Office of Research and Development, Trichloroethylene Health Risk Assessment: Synthesis and Characterization. EPA Document # 600/P-01/002A, August 2001 (at http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=23249). [6] J. Peral, X. Domenech, D.F. Ollis, Heterogeneous photocatalysis for purification, decontamination and deodorization of air, J. Chem. Technol. Biotechnol. 70 (1997) 117–140. [7] T. Obee, N.M.D. Brown, 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. 29 (1995) 1223–1231. [8] M.R. Nimlos, W.A. Jacoby, D.M. Blake, T.A. Milne, Direct mass spectrometry studies of the destruction of hazardous wastes. 2. Gas-phase photocatalytic oxidation of trichloroethylene over TiO2 : products and mechanisms, Environ. Sci. Technol. 27 (1993) 732–740.

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