Ind. Eng. Chem. Res. 1997, 36, 4705-4711
4705
Photocatalytic Degradation of Water Organic Pollutants. Kinetic Modeling and Energy Efficiency B. Serrano† and H. de Lasa* Chemical Reactor Engineering Centre, Faculty of Engineering Science, University of Western Ontario, London, Ontario, Canada N6A 5B9
Photocatalytic conversion of a model pollutant (methylene blue) is studied in a novel PhotoCREC reactor unit. The experiments developed allow us to investigate the suitability of an heterogeneous reaction model which accounts for the concentrations of the model pollutant both in the bulk and on the mesh-TiO2. In addition, a photochemical-thermodynamic efficiency factor (PTEF) is further examined, with the help of the enthalpy of •OH formation from water and oxygen and based on the analysis in the light energy absorbed by the mesh. The resulting PTEF is a dimensionless parameter and has to be calculated at high enough model pollutant concentrations, that is, at conditions where zero-order reactions prevail. The PTEF values found in the Photo-CREC unit with the incorporated recent technical improvements are in the 0.0182 level, and this represents quantum yields of 6.31% of the so-called ideal efficiency. Introduction The design of photocatalytic reactors for water decontamination is an area that still offers major technical challenges (Blanco and Malato, 1993; Pelizzetti et al., 1992; Ollis et al., 1989; Turchi et al. 1993; Matthews, 1993). While some of the physicochemical principles of the photocatalytic conversion process are relatively well understood (Pruden and Ollis, 1980; Turchi and Ollis, 1990; Gerischer and Heller, 1991; Bahnemann et al., 1991; Gerischer, 1993; Fox and Dulay, 1993), the reactor design and reactor engineering of the photocatalytic units still require major attention. This is particularly true in the context of scaled reactors which are required to be operated with high light energy utilization. Thus, there is need to develop new photocatalytic reactors and to establish criteria to compare the photoreactor performance on the basis of photochemical and thermodynamic principles (Yue, 1985). Reviewing proposed photocatalytic designs (Borello et al., 1989; Cabrera et al., 1994; Robertson and Henderson, 1990), it is apparent that proper illumination for a geometrical configuration, adequate mixing patterns inside the reactor, and high water-photocatalyst interaction are essential factors to achieve optimized operation. Recently, a novel Photo-CREC reactor was developed at CREC-UWO for the photodegradation of water pollutants using both phenol and methylene blue (de Lasa and Valladares, 1995). Photo-CREC is configured as a multistage unit, a concentric reactor with a 2.8-L water holdup. This unit has 16 irradiated baskets holding entrapped TiO2 particles in glass mesh. The TiO2 is held on the mesh by means of particle-surface physical forces. The unit is equipped with a 15-W monochromatic lamp (wavelength ) 365 nm). Energy Efficiency Factors The energy efficiencies of the photocatalytic processes have been evaluated using the electrical energy per order (EE/O) (Bolton et al., 1992), the quantum yields, and the quantum efficiencies (Valladares and Bolton, * Author to whom correspondence should be addressed. † Present address: Becario Externo CONACYT, Facultad Ciencias Quı´micas, Universidad de Zacatecas, Zacatecas, Mexico. S0888-5885(97)00104-8 CCC: $14.00
1993; Bockelmann et al., 1993). The EE/O contains the implicit assumption of a first-order kinetics. Energy efficiency estimations using the quantum yields require the calculation of the incident photons on TiO2, while the quantum efficiencies need the assessment of the absorbed photons in reactor media (Valladares and Bolton, 1993). Quantum yields and quantum efficiencies entail the implicit hypothesis that all the energy of the used photons contributes to the formation of •OH groups. Careful consideration of this matter, as it will be shown in the coming sections of the present study, is required for a proper evaluation of the energy efficiencies. Photochemical Thermodynamic Efficiency Factor (PTEF) Let us consider a photocatalytic reactor under source irradiation and quasi-isothermal conditions. In this unit, a Qm,abs energy rate is adsorbed by the supported TiO2 with only a fraction of this energy rate, Qused, being utilized for the desired goal of •OH radical formation. As a result, there is a fraction of the light energy absorbed, so-called Qlost, that will be unused and dissipated as thermal energy. Given the relevance of Qused and Qlost and their relative importance, it is significant to introduce a dimensionless PTEF, η, based on the Qused/Qm,abs ratio:
η ) Qused/Qm,abs
(1)
This criterion is of general applicability and is not restricted to a specific photoconversion process, this process being homogeneous or heterogeneous. The PTEF can be expressed for a photocatalytic process, using the following relationship:
η ) r*OH∆H* OHW/Qm,abs
(2)
where r*OH represents the rate of formation of the hydroxyl radicals (in mol (g of mesh)-1 s-1) ∆H*OH is the enthalpy involved (in J mol-1) in the •OH radical formation in a photocatalytic reaction, and W is the total amount of photocatalyst impregnated mesh (in g of mesh). Frequently, TiO2 photocatalysis is pictured as a pseudohomogeneous process with rates based on the bulk pollutant concentrations. In this case, the PTEF can be written as © 1997 American Chemical Society
4706 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
η ) rOH∆H*OHV/Qm,abs
(3)
where rOH ) r* OHW/V. It can be observed, from eqs 2 and 3, that PTEFs are not only a function of the •OH radical formation rates but are also related to the enthalpies of formation of the •OH radical. Regarding the rate of •OH radical formation, the rates of accumulation and consumption can be viewed, at any time in the process, as the addition of two terms:
rOH ) -rOH,c + rOH,acc
(4)
While the model pollutant consumption rate in the bulk can frequently be directly measured, the determination of rOH offers inherent problems. For example, a simple relationship between the rate of •OH consumption and the rate of model pollutant conversion cannot be invoked. The evaluation of the •OH radical formation rate requires that important distinctions be made between the consumed and accumulated OH groups: rOH ) -rOH,c + rOH,acc. Given that rOH,c ) ν∑(rp/νp) represents the summation of all rates of •OH consumption by all classes of organic chemical species on the catalyst surface (model pollutant and all intermediate chemical species), it follows that
[] rp
∑ νp
rOH ) -ν
+ rOH,acc
(5)
The stoichiometric numbers for each of these initial and intermediate steps are not known. Only at the very beginning of the photoconversion, when the surface concentration of all chemical species equals the surface concentration of the model compound and when the model pollutant is the only •OH scavenger, ν∑(rp/νp) ) νrmp,0/νmp, and it follows that
[ ]
rOH ) -
ν r + rOH,acc νmp mp,0
(6)
where rmp,0 represents the rate of disappearance of the model pollutant at time t ) 0. If experiments are performed starting from conditions where the pollutant and the impregnated mesh are at equilibrium, the hypothesized first-order rate based on surface model pollutant concentration can be expressed as rmp,0 ) -krq, and from eq 6 it results that
rOH ) ν*(krq) + rOH,acc with q ) qmKCeq/[1 + KCeq] (7)
cally a constant or so-called maximum value. This upper value for PTEF, [ν*krqm∆H*OHV/Qm,abs], is a characteristic of the photocatalytic unit which includes various reactor characteristics including illumination, light absorption, fluid dynamics, and mass transfer in a single thermodynamic efficiency factor. Under these conditions, the PTEF can be considered to be the product of two yields:
η ) φηOH
(10)
where φ ) {-Rν*[rmp,0]maxV}[NAhc/λ]/Qm,abs or alternatively φ ) {-Rν*[rmp,0]maxV}/{Qm,abs/[NAhc/λ]}, this is a quantum yield which provides the fraction of photons absorbed by the photocatalyst resulting in the formation of •OH radicals, and ηOH ) ∆H*OH/{R[NAhc/λ]} represents the fraction of photon energy used in formating •OH radicals. Thus, it is demonstrated that energy efficiency evaluation requires not only a quantum yield, φ, based on the Qm,abs by the TiO2, but also the fraction of photon energy used in forming •OH radicals, ηOH. The product of these two factors provides a proper assessment of the energy efficiency through the PTEF. Evaluation of the PTEF The basic mechanism of heterogeneous photocatalysis is related to the “excitation” of TiO2 or other metal oxides. Photocatalysts may be in suspension or immobilized onto a transparent matrix under irradiation from either natural sunlight or artificial low-energy UV light. It is generally agreed that this excitation promotes an electron from a level in the valence band of the solid to a highly delocalized level in the conduction band. It is thought that this creates an oxidizing site (a “hole”) and a reducing site (an “electron”), both localized at defect sites.
TiO2 + hν f h+ + e-
(11)
This photogenerated electron-hole pair can then be captured by reagents which are adsorbed on the photocatalyst surface. The hole can be filled by electron transfer either from an adsorbed pollutant molecule or from an adsorbed water molecule. In the latter case, a hydroxyl radical is formed:
H2O f OH- + H+
(12)
h+ + OH- f •OH
(13)
with ν* ) ν/νmp. When the model pollutant concentration with respect to other scavengers is very high (in large excess with respect to the other species), the model pollutant is going to consume all the •OH radicals and •OH accumulation is not allowed (rOH,acc ) 0). As well, at high pollutant concentrations, 1 + KCeq approaches KCeq (refer to eq 7), q ) qm, and rmp,0 shows a maximum value:
Furthermore, various steps can be formulated for the network of the ensuing reactions (Turchi and Ollis, 1990; Pellizzetti et al., 1992). An example follows:
rOH ) -ν*[rmp,0]max ) ν*(krqm)
(8)
and the PTEF becomes
η ) -ν*[rmp,0]max∆H* OHV/Qm,abs ) ν*krqm∆H*OHV/Qm,abs (9) Thus, if the initial pollutant concentration is increased progressively, the PTEF approaches asymptoti-
e- + O2 f O2-
(14)
O2- + H+ f •O2H
(15)
H+ + O2- + •O2H f H2O2 + O2
(16)
H2O2 + hν f 2•OH
(17)
A linear combination of eqs 11-17, with eqs 15, 16, and 17 multiplied by 1/2, applicable at low concentrations of intermediate species in this network, allows us to demonstrate that the overall stoichiometry of the formation of ∆H* OH radicals can be represented as
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4707
H2O(l) + 1/2O2(aq) f 2•OH(l)
(18)
Accordingly, the enthalpy of formation of •OH radicals from H2O and O2 is given as
∆H*OH ) ∆Hf(•OH) - 1/2∆Hf(H2O) - 1/4∆Hf(O2) (19) On this basis, the estimation of ∆H* OH, the enthalpy of formation of OH in aqueous media starting from H2O and dissolved O2, gives 94 600 J mol-1. The heats of formation involved in eq 19 were estimated from Wagman et al. (1982) and Kerr (1966). Moreover, given that ηOH (refer to eq 10) involves the energy of a photon at λ ) 365 nm, estimated as 327 000 J mol-1, and considering an R ) 1, this yields a ηOH, the fraction of photon energy used in forming •OH radicals, of 0.289. Thus, in the ideal case of a photoreactor with quantum yields (φ) equal to 1 and for λ ) 365 nm, an {η}ideal of 0.289 is obtained, and this represents the upper efficiency limit for a photocatalytic reactor using TiO2 and 365-nm wavelength.
Figure 1. Schematic representation of the photocatalytic reactor. (a) Compressed air, (b) air gas regulator, (c) oxygenator with air pipe distributor, (d) Gilson water pump, (e) valve for controlling water circulation, (f) concentric Photo-CREC unit with lamp placed in the center and 16 conical baskets spaced throughout the unit, (g) three-way valve, (h) lamp, (i) basket, (j) Pyrex glass tube, (k) external Plexiglas tube, (l) annular channel.
Experimental Methods In order to proceed with the experimental program and to thoroughly test the Photo-CREC reactor concept (de Lasa and Valladares, 1995), an earlier design was significantly modified. In the advanced version, the photocatalytic reactor (Figure 1) is constituted by an annular channel with 16 baskets positioned at a 45° angle. In this configuration, the Photo-CREC reactor has stainless steel spacers placed between the baskets. These spacers secure basket positioning and minimum light losses. The near-UV lamp is located in the central channel, providing 15 W of monochromatic light (365 nm). Water is circulated in the downflow direction, with the only exception being the period at the beginning of the run when an upflow water circulation is preferred to evacuate air pockets. Water exiting the reactor is discharged in the oxygenator. This unit is equipped with a perforated pipe air distributor and a magnetic stirrer, and this secures water saturation with oxygen. A variable-flow Gilson pump completes the experimental system. This pump is used to return the water to the upper section of the photoreactor unit, completing in this way the cycle of water oxygenation and recirculation. Regarding the TiO2-mesh preparation, the following technique was employed. First, the organic matter on the fresh fiber glass mesh, which could hinder TiO2 attachment, was removed using a nitric acid solution (70 wt %). To check the effectiveness of the method, the mesh was calcined at 550 °C for 5.5 h, and this revealed no weight change and, consequently, good organic matter removal. Following this, the mesh was mounted on the inner face of each one of the baskets to proceed to “in situ” impregnation. With this end, a TiO2 particle slurry (5 wt % TiO2 in a 30% methanol-water solution) was circulated at a 1720 mL/min flow rate for 10 h. The several described changes in the Photo-CREC allow better contact between water and the TiO2 and a significant catalyst loading on the impregnated fiber glass mesh (16.5 wt %). According to the the SEM-EDX results, the mesh was covered essentially 100% with TiO2. Concerning the experiments developed using methylene blue (MeB) as the model pollutant, each run involved the following:
Figure 2. Schematic representation of the lamp testing unit. (a) Lamp holder with inner surface (exposed to light) painted in black, (b) radiometer, (c) lamp, (d) rail with a 1-cm opening extending throughout the entire lamp length, (e) U-shaped tunnel allowing the radiometer to be axially displaced.
(a) Equilibrium Step. This is, as advanced by Matthews (1989), an important initial period. Light is turned “off” and water with the model pollutant is circulated through the photoreactor. During this period, only adsorption of the pollutant (methylene blue) on the mesh surface takes place. (b) Reaction Step. Once the adsorption equilibrium is reached, the light is turned “on” and the photoreaction conversion is initiated in earnest. The reaction step continues, with water recirculation and re-oxygenation of the water stream, until low levels of model pollutants are achieved. Samples from the experiments were collected at various times-on-stream and analyzed with the combined use of a PU8625 UV/vis spectrophotometer (644 nm) and a Shimadzu 5050 TOC model. This allowed us to follow both the disappearance of methylene blue and of various intermediate products. For example, for a 1.7 L/min water recirculation flow and an initial model pollutant concentration of 33 × 10-6 mol L-1, an 80% reduction of the MBe was achieved in 350 min, while the 80% reduction of TOC was attained in 850 min. Using the above-described equipment, experiments were conducted at several flow rates ranging from 0.2 to 1.7 L/min and model pollutant concentrations ((340) × 10-6 mol L-1). Other auxiliary equipment components were manufactured and employed to determine the fraction of light absorbed in the unit. With this end, the near-UV lamp (365 nm) was placed in a so-called lamp calibration unit (Figure 2). This unit was constituted by a lamp holder, painted in black, and a rail allowing a near-UV sensor (UVX radiometer) to be displaced at a fixed distance
4708 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 1. Reaction Constants (kr) for Different Initial Equilibrium Concentrations of Methylene Bluea init. equilib. conc. × 106, mol L-1
kr, g of mesh L-1 min-1
0.48 0.95 1.48 2.31 3.10 5.86 7.10 9.18
2.71 ( 0.55 2.40 ( 0.43 2.90 ( 0.55 2.60 ( 0.53 2.59 ( 0.29 3.04 ( 0.63 2.60 ( 0.46 2.55 ( 0.48
kads ) 0.0017 × 106 L mol-1 min-1, K ) 0.107 × 106 L mol-1, qm ) 2.0 × 10-6 mol (g of mesh)-1. a
from the light source. Integration of the measured light, using an imaginary cylindrical surface, provides the total light emitted by the lamp. Using this methodology, it was observed that the intensity emitted by the lamp changed as much as 50% in 1000 h of operation. Thus, it was judged that frequent lamp recalibrations were required for a better assessment of light energy emitted by the lamp, and this was of significance for energy efficiency calculations. Furthermore, and in order to quantify light losses (Qloss), both in the glass tube and at the glass-water interface, additional experiments were performed in the lamp calibration unit. The lamp was placed inside a glass tube having in the upper section a water reservoir which simulates reactor geometry, and this assembly was in turn positioned in the lamp calibration unit. It was found that from the 15 W of electric power of the monochromatic lamp, 1 W of emitted light was emitted and only 0.8 W of this light energy traversed the inner glass tube of the Photo-CREC unit evolving through the glass-water interface. Finally, and given that the PTEF factor is based on Qm,abs, the following was done: (a) Experiments were performed to quantify the light energy absorbed in the water solution using a standard spectrometric cell. It was found that there was an average 3% of light energy absorption for the highest concentrations employed ((30-40) × 10-6 mol L-1). (b) Experiments were performed to estimate the light energy reaching the mesh directly by employing a modified spectrometric cell. The modified cell had the same dimensions as a conventional one (2.8 cm × 1.3 cm), with the central section holding a mesh impregnated with TiO2. The results obtained showed that the impregnated mesh absorbed 73% of the incident energy (Qw,abs ) 0.728 W). In summary, while accounting for these various light energy losses, the overall fraction reaching the mesh was estimated as Qm,abs/Qw,abs ) 0.73. Consequently, it can be concluded that from the 0.8 W initially absorbed by the water, 0.728 W reached the mesh and only 0.53 W (Qm,abs ) 0.53 W) are abosrbed by the mesh-TiO2. Presumably all of this irradiation reaches the TiO2, this given the high TiO2 loading on the mesh surface. Reactor Model and Parameter Estimation Modeling of the photoconversion reaction, under conditions where external mass transfer can be neglected and with intense water recirculation, has to acknowledge different pollutant states: (a) pollutant adsorbed on the catalyst mesh (q); (b) pollutant evolving in the liquid phase (C). Given that photocatalytic reaction experiments were developed in the batch and were initiated when adsorption equilibrium was reached
and when light was turned on, the following equations can be considered for t > teq:
liquid phase dC W ) [-kadsC(qm - q) + kdesq] dt V
(20)
catalyst phase V dC dq )+ krq dt W dt
[
]
(21)
with initial conditions C ) Ceq and q ) qeq at t ) teq. Numerical solution of this set of equations was developed using a Runge-Kutta fourth-order method. The K and qm parameters of the Langmuir equation (eq 7) were estimated using a Marquart nonlinear regression and a number of runs (light turned off) at adsorption equilibrium conditions. Calculated values are K ) 0.11 × 10+6 L mol-1 and qm ) 2.02 × 10-6 mol (g of mesh)-1. In addition, the section of the concentration curve, representing the initial period of the adsorption process, together with eqs 20 and 21, and the same regression technique also provided the kads parameter. With this method, an average kads for a fixed volumetric recirculation flow of 1.720 L min-1 was calculated as 0.001 75 × 10+6 L (mol min)-1. Finally, and with model pollutant concentration decay experiments (light of the setup was turned on), the kr constant was assessed solving simultaneously both eqs 20 and 21 and regressing kr until proper fitting of the experimental decay curves with acceptable residual distribution was obtained. The values of kr reported for different initial pollutant equilibrium concentrations are reported in Table 1. It has to be mentioned that these calculations were developed employing data from the first 12 min, both for runs with light turned on and off. These are conditions where there is little influence of intermediate products and model pollutant photoconversion dominates the reactor behavior. Experimental Results As stated and to increase the reactor efficiency, a number of modifications was introduced in the PhotoCREC unit. These improvements optimized the contact between the TiO2, anchored on the fiber glass mesh, with both the near-UV light and the water stream. A new in situ impregnation method was developed. Fiber glass mesh was carefully attached to the meshsupporting baskets, and water-methanol solution (30% by weight) with suspended TiO2 was circulated through the unit. This allowed for high convective circulation of the slurry and firm attachment, presumably due to surface-related forces, of the catalyst to the fiber glass mesh. As a result, a tight and thick layer of TiO2 particles on the fiber glass mesh surface was obtained. This high coverage of the mesh was apparent from the SEM-EDX micrographs. EDX microanalysis, providing microanalysis information of 1-µm depths, yielded close to zero Si/Ti ratios. This very low Si/Ti ratio is an indication of the high degree of TiO2 coverage on the glass mesh surface. Confirmation of strong particle attachment of the TiO2 on the fiber glass mesh was also obtained given translucid water was obtained after the first washing and during all subsequent experiments. In this way, it was demonstrated that photocatalytic reactors using immobilized TiO2, anchored on fiber glass mesh, do not require any means of particle recovery such as is the case of slurry reactors, where TiO2 has to be separated
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4709
Figure 3. Change of the concentration of methylene blue in the bulk water phase with irradiation time at various water recirculation rates. Initial concentration of MeB: 12 × 10-6 mol L-1. Photoreactor unit: Photo-CREC.
Figure 4. Change of concentration of methylene blue in the bulk water phase with time at two initial concentrations: (9) 34 × 10-6 mol L-1, ([) 27 × 10-6 mol L-1. (a) Period of operation with light off; (b) period of operation with light on. Photoreactor unit: Photo-CREC. Water recirculation flow: 1.72 L min-1.
from the water stream following pollutant photoconversion. Several experiments were conducted (Figure 3), varying the water flow recirculation rate from 150 to 1720 mL/min. It was found that the same concentration profile was obtained for flow rates of 1200 mL/min and higher. Thus, it was concluded that at 1720 mL/min, there is no mass-transfer limitation. As a result, subsequent experiments were carried out at 1720 mL/ min. For the various experiments developed, at 1720 mL/ min water recirculation rate, there is an “absorption period” (light off), and once adsorption equilibrium is reached, a “reaction period” takes place (light on) (Figure 4). An interesting observation from the adsorption period is that the high degree of pollutant adsorption, about 75% of the model pollutant, is in the adsorbed state once the light is turned on. This is a
very important finding and points toward the need of heterogeneous modeling for the various photocatalytic steps (refer to eqs 20 and 21). Moreover, in order to ascertain the type of adsorption process involved, which was, as described above, very significant, adsorption experiments were developed varying the model pollutant equilibrium concentration (Figure 5) between 1 and 60 × 10-6 mol L-1. A Langmuir adsorption equilibrium-type isotherm was confirmed. As advised in the modeling section, the kr parameters were calculated for increasing initial equilibrium concentrations (Table 1). It can be observed that the values of the kr parameters remain in a relatively narrow range, and this supports the heterogeneous model which considers an intrinsic rate constant, kr, not being affected by the initial equilibrium concentration. With these kr and the corresponding qeq at Keq, the
4710 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Figure 5. Equilibrium isotherm for methylene blue and TiO2-mesh. Temperature: 20 °C. Water recirculation: 1.72 L min-1.
Figure 6. Change of PTEF with the initial equilibrium concentration of MeB. Temperature: 20 °C. Water recirculation: 1.72 L min-1.
rates of the reactions were assessed, and correspondingly, the PTEFs were calculated. Thus, the maximum PTEF was evaluated at high enough model pollutant concentrations, that is, at conditions where zero-order reactions apply. Figure 6 portrays the increasing PTEFs with increasing concentrations, and this yields a maximum value of 0.0182 and a quantum yield 0.0631. This is about 6.31% of the so-called “ideal” PTEF efficiency of 0.289. Conclusions The suitability of an heterogeneous reaction model for description of model pollutant photoconversion is demonstrated with experiments developed using a model pollutant (MeB) and a Photo-CREC reactor unit. In addition, a Photochemical-thermodynamic efficiency factor (PTEF) is further examined based on the analysis in the light energy absorbed by the mesh and
with the help of an enthalpy of •OH formation from water and oxygen. The dimensionless PTEF is calculated at high enough model pollutant concentrations, that is, at conditions where zero-order reactions prevail. PTEF in the Photo-CREC shows a maximum value of 0.0182, yielding a 0.0631 quantum yield, and this represents 6.31% of the so-called ideal PTEF efficiency. Acknowledgment We express our appreciation to the CONACYTsMe´xico and to the Universidad Auto´noma de ZacatecassMe´xico for the External Fellowship to Benito Serrano Rosales. We would also like to express our acknowledgment to the Natural Sciences and Engineering Research Council of Canada for the valuable financial contribution. Nomenclature C ) pollutant concentration in the solution (mol L-1) c ) light speed in a vacuum (2.997 × 1010) (cm s-1)
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4711 kads ) adsorption rate constant (L mol-1 min-1) kdes ) desorption rate constant (min-1) kr ) kinetic constant involved in eq 7 (g of mesh L-1 min-1) K ) adsorption equilibrium constants (L mol-1) h ) Planck constant (6.62 × 10-34 J s) hc/λ ) photon energy of wavelength λ (J photon-1) NA ) Avogadro’s number (6.023 × 1023 molecules mol-1) PTEF ) photochemical-thermodynamic efficiency factor q ) adsorbed pollutant concentration on the mesh + TiO2 (mol (g of mesh)-1) qm ) maximum adsorbed pollutant concentration (mol (g of mesh)-1) Qm,abs ) rate of light energy absorbed in the photocatalytic reactor mesh (J s-1) Qused ) rate of energy utilized for the desired goal of •OH radical formation (J s-1) Qlost ) energy rate of dissipation of unused thermal energy not achieving any useful photochemical conversion (J s-1) rOH ) rate of •OH radical formation (mol L-1 s-1) • -1 r* OH ) rate of OH radical formation (mol (g of catalyst) s-1) rOH,c ) rate of •OH radical consumed in the photocatalytic process (mol L-1 s-1) rOH,acc ) rate of •OH radical accumulated (mol L-1 s-1) rmp,0 ) rate of disappearance of the model pollutant at time t ) 0 (mol L-1 s-1) rp ) rates of pollutant photodegradation of the chemical species p (mol L-1 s-1) t ) irradiation time (min) V ) total water holdup (L) W ) total amount of impregnated mesh (g of mesh) Greek Symbols R ) number of photons required for the formation of an •OH radical η ) photochemical thermodynamic efficiency factor or Qused/ Qm,abs ηOH ) ∆H*OH/{R[NAhc/λ]}, fraction of photon energy used in forming •OH radicals ∆H*OH ) enthalpy of •OH radical formation in a photocatalytic reaction (J mol-1) λ ) wavelength (nm) φ ) -[Rν*rmpV] {NAhc/λ}/Qm,abs, quantum yield or fraction of photons absorbed by the photocatalyst resulting in •OH generation ν ) stoichiometric number for the •OH reacting with the model compound (negative number) νmp ) stoichiometric number for the model pollutant reacting with •OH (negative number) νp ) stoichiometric number for the pollutant chemical species reacting with •OH (negative number) ν* ) ν/νp ratio (positive number) Subscripts or Superscripts eq ) equilibrium condition between phases max ) maximum p ) pollutant
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Received for review February 3, 1997 Accepted July 29, 1997X IE970104R
X Abstract published in Advance ACS Abstracts, October 1, 1997.
