Environ. Sci. Technol. 2003, 37, 5783-5791
Modeling of Thin-Film Slurry Photocatalytic Reactors Affected by Radiation Scattering GIANLUCA LI PUMA* School of Chemical, Environmental and Mining Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
Photocatalytic oxidation over titanium dioxide is a “green” sustainable process for treatment and purification of water and wastewater. A dimensionless model for steadystate, continuous flow, thin-film, slurry (TFS) photocatalytic reactors for water purification using solar radiation and UV lamps is presented and validated. The model is applicable to TFS flat plate and annular photoreactors of (a) falling film or (b) double-skin designs, operating with three ideal flows: (1) falling film laminar flow (FFLF), (2) plug flow (PF) and (3) slit flow (SF). Model parameters can be estimated easily from real systems, and solutions can be obtained with modest computational efforts. A modified twoflux absorption-scattering model models the radiation field in the photoreactor. Model simulations show that at a scattering albedo higher than 0.3, radiation scattering can significantly affect conversions obtained at different values of optical thickness. However, at lower values, the effect of scattering on conversions is negligible. The conversions with the idealized flow systems follow the sequence FFLF > PF > SF. SF operation should always be avoided. The model estimates the optimum value of optical thickness that maximizes conversion in a photocatalytic reactor. Optimal design of TFS photocatalytic reactors using the photocatalyst TiO2 Degussa P25 requires an optical thickness in the range from 1.8 to 3.4 depending on flow conditions and reaction kinetics.
Introduction Photocatalytic oxidation (PCO) over a solid photocatalyst (TiO2) is a “green” sustainable process for purification of contaminated water and treatment of wastewater (1). The main features of this process are as follows: (i) ambient temperature oxidation process; (ii) use of mild oxidant (O2); (iii) safe and stable photocatalyst (TiO2); (iv) use of light (UV or solar radiation) as the only energy input; (v) destruction of pollutants to ppb levels; (vi) generation of highly powerful hydroxyl radicals. The strength of this oxidant is responsible for the titania’s broad activity toward a large classes of contaminants (e.g., aromatics, halogenated hydrocarbons, pesticides, endocrine disrupting chemicals, inorganics, and many others) (2, 3), and for the inactivation of microorganisms and toxins (e.g., coliforms, viruses, microcystins) (4, 5). However, its technological application is limited by several reasons, an important one of which is the lack of efficient photocatalytic reactor configurations and simpler mathematical models for design and scale-up of photoreactors. * Corresponding author phone: +44 (0) 115 9514170; fax: +44 (0) 115 9514115; e-mail:
[email protected]. 10.1021/es0300362 CCC: $25.00 Published on Web 11/13/2003
2003 American Chemical Society
As a result, most of the photocatalytic reactors used in research and development are designed using semiempirical methods. Among the different types of scalable photocatalytic reactors proposed in the literature (6) thin-film, slurry (TFS) photocatalytic reactors provide an excellent configuration for efficient excitation of the semiconductor photocatalyst (TiO2). TFS photocatalytic reactors operate at much higher catalyst concentrations than conventional photoreactors because of the high opacity of TiO2 slurry suspensions. This property, linked to the fact that these reactors have a very large illuminated catalytic surface area per unit volume of reactor and minimal mass transfer limitations (7), yields an increase in the number of hydroxyl radical generated per unit volume of reactor. This maximizes the efficiency of photon utilization, oxidation rates and reactor throughput. TFS photocatalytic reactors are therefore suitable for industrial scale applications of PCO. The most common configurations of TFS photocatalytic reactors are that of falling film or thin-film annular/flat reactors (6, 8). Other less conventional designs include the fountain photocatalytic reactor (9). Falling film configurations have the advantage over thin-film annular/flat reactors of a very high mass transfer rate of the reducing agent oxygen. They also do not suffer from the filming problem of the radiation entrance wall which occurs in photoreactor irradiated through a transparent window such as in thin-film annular/flat photoreactors. However, the latter reactor configurations are preferred when the solutions to be detoxified contain high concentrations of volatile organic carbon (VOC) which will simply be lost from the system in falling film reactors. The modeling of photocatalytic reactors requires a complex analysis of the radiation field in the photoreactor (6, 10, 11). This analysis, linked to the modeling of the fluiddynamics and the reaction kinetics, results in integrodifferential equations which almost invariably require demanding numerical solutions (12). Further advances of PCO on an industrial scale will be facilitated by the availability of simpler mathematical models that retain the essential elements of a rigorous model and that can be easily used for scale-up and design. An example of a suitable simplified radiation model is the two-flux radiation model (13, 14). Recently, we have presented an alternative simpler approach to the analysis of TFS photocatalytic reactors which brings in complete and experimentally validated dimensionless models for falling film and a fountain photocatalytic reactors (9, 15-18). Furthermore, we have provided a systematic and generic methodology for the design and modeling of steadystate continuous flow TFS photocatalytic reactors for water purification using solar and artificial sources of radiation shown in Table 1. We have also presented modeling results for a number of reactor geometries and ideal flow operation modes under the assumptions that the effect of light scattering could be neglected (19). As it will be shown in this paper, this assumption may be acceptable with TFS photoreactors operating at optimal values of optical thickness (i.e. high catalyst concentration) and with catalyst with scattering albedo less than approximately 0.3. However, with catalysts with a scattering albedo greater than 0.3, the effect of light scattering becomes important and cannot be neglected in the model. In the present paper, a dimensionless mathematical model of steady-state continuous flow TFS photocatalytic reactors for water purification using solar and artificial sources of radiation that accounts for the effect of light scattering is VOL. 37, NO. 24, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. TFS Photocatalytic Reactors and Idealized Flow Operation Modesa
Geometry. In the TFSFW configuration, the length of the flat plate is H and the width is T. In the TFSIW configuration, the lamp is perfectly centered with respect to the reactor and the reactor geometry is described by the following parameters:
H L L β) R
R)
(1) (2)
For a TFSIW photoreactor we have
δ,R R ≈1 R+ξ
a
FFLF is falling film laminar flow, PF is plug flow, and SF is slit flow.
presented and experimentally validated. Furthermore, modeling results of the effect of radiation scattering on conversions under a number of different flow conditions and reaction kinetics are shown and discussed. To take into account the effect of light scattering without compromising the simplicity of the model, the rigorous approach to modeling radiation fields advocated by the group of Cassano (10-12) was simplified to include a two-flux absorption-scattering model by Brucato and Rizzuti (14) with simpler radiation attenuation terms. This modeling approach of the radiation field was shown to be satisfactory previously for the modeling of a fountain photocatalytic reactor (9, 17, 18).
Modeling of TFS Photocatalytic Reactors Two configurations of TFS photocatalytic reactors are shown in Table 1: (i) TFSFW - the liquid flows along a flat wall (FW), as a falling film or between parallel plates and the reactor is irradiated by lamps equally distributed above and with a light reflector or directly by solar radiation and (ii) TFSIW - the liquid flows along the internal wall (IW), of a cylindrical reactor as a falling film or in an annulus with the lamp mounted along the central axis. A dimensionless mathematical model for the steady-state, continuous flow, TFS reactors of Table 1 is presented in Table 2. This model is the extension of the model developed by the author (19) to include the case in which the light scattering phenomena are not negligible. This condition practically occurs at scattering albedo higher than 0.3 as will be explained later. The essential assumptions and peculiarities of this model are given below. Further details of the model have been given elsewhere (19), thus these are not presented here. 5784
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(3) (4)
Thus, the effect of curvature on photon fluxes and fluid flow can be safely neglected, and the same coordinate system (ξ, z) can be used to model the reaction space, in both cylindrical and planar geometry. Steady-State Ideal Flow Systems. Three cases of steadystate, unidirectional, continuous flow are considered in the model to simulate the different reactor configurations shown in Table 1: falling film laminar flow (FFLF), plug flow (PF) and slit flow (SF). For all three ideal flow systems, the Reynolds number is defined in the same manner. The thickness of the liquid film for laminar or turbulent flow falling film photoreactors can be determined from correlations in the literature (20). For TFS annular/parallel plates photoreactors δ is the dimension of the annulus/gap. The liquid phase is a Newtonian fluid with constant physical properties. The catalyst particles are considered to be uniformly distributed within the liquid film; however, the concentration of solids is not so high as to cause substantial changes in the rheological properties of the fluid. Radiation Field. In the TFSFW configuration, the intensity of the incident radiation is uniform and described by its value averaged over the useful range of the incident radiation spectrum. In the TFSIW configuration the emission of radiation from the lamp is modeled using the Linear Source Spherical Emission (LSSE) model (21). The lamp is considered to be a line source. Each point on this line is assumed to emit radiation in every direction and isotropically. There is no light absorption, scattering, or emission in the space between the lamp and the thin-film. In the reaction space, i.e., the thin-film, the modeling approach advocated by Cassano (10-12) based on a rigorous analysis of the radiation field in the photoreactor was simplified to include a two-flux absorption-scattering model (14) with simpler radiation attenuation terms. It is assumed that the useful photons entering the liquid film travel through the liquid film only along parallel planes orthogonal to the liquid flow (LSPP model). These photons are absorbed or scattered by the solid photocatalyst particles only. In Table 2, f(ω,τ) is a dimensionless function introduced to account for radiation scattering (17, 18). This function depends on the scattering albedo ω and on the optical thickness τ where σ and κ are the specific mass scattering and absorption coefficients respectively, averaged over the useful spectrum of the incident radiation
∫ σ) ∫
λmax
λmin λmin
∫ κ) ∫
σλIλdλ
λmax
λmax
λmin λmax
λmin
(5) Iλdλ
κλIλdλ (6) Iλdλ
TABLE 2. Mathematical Model of TFS Photocatalytic Reactors
where λmin and λmax are respectively the minimum and maximum wavelengths of the incident radiation that can be absorbed by the photocatalyst.
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suspension (i.e., with the observed degree of agglomeration of TiO2 in the suspension). The two-flux model shows that the incident radiation at a point (ξ, z) in the liquid film is equal to the sum of the radiation that travels in the forward direction and the fraction that travels in the backward direction due to backscattering. The expression for f(ω,τ) for the case of pure backscattering can be derived from the study of Brucato and Rizzuti (14) which provides an approximate tool to model the radiation field. For the case of a purely absorbing medium (ω ) 0), f(ω,τ) reduces to 1 and the expression for the radiation intensity in the reaction space reduces to the Beer-Lambert law. Conversely, for a purely scattering medium (ω ) 1) with σ f ∞, f(ω,τ) ) 2 and all incident radiation is backscattered at the front window of the reactor. Further comments on f(ω,τ) have been reported elsewhere (17, 18). The application of this one-dimensional radiation model has previously been shown to be satisfactory for TFS photocatalytic reactors. It has been found that the modeling of the radiation field in the reaction space by the more complex LSSE radiation model (two-dimensional model) did not yield any significant benefit to the accuracy of the overall reactor model (15). Thus, the one-dimensional radiation model was used in the present model since it yields simpler mathematical equations. Reaction Kinetics. The kinetic equation used in the model has the same form as that reported in our previous papers (15-18). At each point in the reaction space, the rate of the reaction of a substrate j is considered to be proportional to the local volumetric rate of photon absorption (LVRPA) (µIξ,z) raised to the mth power and to the nth power of the local substrate concentration Cj. The method for obtaining m and n is based on the approximation that the conversion per pass is small (15). Iξ,z is the total incident radiation at a point (ξ, z) of the liquid film, and µ is the absorption coefficient averaged over the spectrum of the incident radiation. kT is a constant that takes into account all other factors that may affect the overall quantum yield, with the exception of the substrate concentration and the LVRPA. Justification for using a power law kinetic equation in preference to a more popular Langmuirian rate equation has been given elsewhere (15). The Langmuir type of kinetic model does not offer significantly better representation of the rate data of photocatalytic reactions; therefore for simplicity the power law model was selected. The objective was not to rigorously represent the reaction mechanism but to provide a satisfactory model of the rate data. The present kinetic rate equation does not include the effect of reaction intermediates, since most of the applications of photocatalytic detoxification involve lightly contaminated water in which the effect of the intermediates can often be neglected. However, if the intermediates affect the kinetics of destruction of the primary substrate these effects will be seen only when the concentration of the primary substrate has been reduced considerably near the end of the steeper part of the degradation curve (e.g., 70% conversion). In this situation, the present kinetic equation will only be valid for the partial conversion of the primary substrate. Dimensionless Design Equation for TFS Photocatalytic Reactors. The dimensionless design equation in Table 2 was derived from the material balance for a substrate j written for an annular (TFSIW) or transversal (TFSFW) slice within the liquid film and neglecting the transversal diffusive flux term. The design equation is expressed in terms of the Damko¨hler number, NDa, which in this case has the meaning of the ratio of the overall reaction rate, calculated at the inlet concentration and at the maximum photon flux, to the maximum input mass flow rate of the reactant. NDa , 1 indicates that the disappearance of the substrate j is much 5786
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slower than the convective transport through the reactor. However, it should be observed that in the presence of radiation scattering, NDa increases by the factor [f(ω,τ)]n compared to the case without scattering because the net photon flux at z* ) 0.5 increases due to the contribution of backscattering. This effect is discussed further in the model simulation section (Figure 4). The integration of the design equation with boundary conditions
B.C. (1) z* ) 0 C /j ) 1
(7)
yields the radial distribution of the dimensionless concentration of substrate j at the reactor outlet section, CH* j from which the conversion can be calculated. A is a dimensionless coefficient that is dependent only on the geometry of the reactor and m (Table 2). Analytical solution of the expression for A for the TFSIW configuration is possible only when m ) 1. In photocatalytic oxidation, this situation has been experimentally verified at low irradiation intensities of less than 10-3 Ein m-2 s-1 (22). If the reaction rate is solely dependent on the absorption of radiation (n ) 0) and is first-order (m ) 1), the present model yields an analytical solution for the reactor conversion. The derivation of the mathematical model in dimensionless form allows photoreactor scale-up by dimensional analysis. If a small-scale or pilot plant TFS photocatalytic reactor is optimized with respect to the dimensionless parameters of the TFS model, scale-up to a larger unit could be obtained using similarity concepts. Absorption of Radiation. The effective radiant power absorbed within the reaction space Wabs can be obtained by integrating the LVRPA with respect to the volume occupied by the liquid film:
Wabs )
∫ (µI V
ξ,z)dV
(8)
The effective fraction of radiant power absorbed within the reaction space (radiation transmission factor) is ψ. The expressions of Wabs and ψ are shown in Table 2 for both the TFSFW and the TFSIW configurations. It should be noted that in the presence of radiation scattering, both Wabs and ψ decrease by the factor (1 - ω) f(ω,τ) compared to the case without radiation scattering (19). Once the absorption of radiation Wabs is known, the apparent quantum yield of a reaction could be determined.
Experimental Validation of Model The present model was validated with the experimental results of the oxidation of salicylic acid in aqueous suspensions of TiO2 (Degussa P25) using the pilot plant laminar falling film slurry photocatalytic reactor as reported in Li Puma and Yue (16). The value of the specific mass extinction coefficient (κ + σ) for suspensions of TiO2 (Degussa P25) in deionized water, averaged over the range of wavelengths 300380 nm, was found to be 1296 m2 kg-1 and was measured as shown in Li Puma and Yue (16). Using the specific absorption coefficients for TiO2 (Degussa P25) reported elsewhere (23) the average specific absorption coefficient calculated by eq 6 was found to be κ ) 338 m2 kg-1. The scattering albedo ω was therefore 0.74. Although the specific absorption coefficient should be measured for the prevailing conditions of the slurry suspension (i.e., with the observed degree of agglomeration of TiO2 in the suspension), it is not expected that its value differs much from the above. In fact, the degree of agglomeration of TiO2 primarily affects the value of the scattering coefficient rather than that of the absorption
Figure 1 shows a comparison of the fitting of the model results to the experimental results for the conversion of salicylic acid as a function of the Damko¨hler number with different reactor geometries. For each geometry, the process parameters investigated included the effect of the intensity of the incident radiation (range 57.7-126.4 W m-2) and of the inlet concentration of salicylic acid (range 10.3-99.1 kg m-3). Furthermore, Table 3 shows a comparison of the fitting of the model results to the experimental results as a function of the optical thickness and of the Reynolds number. The model calculations were found to correlate well with the experimental data, in all cases were within the experimental errors, and were consistent with the experimental validation of the present model.
Model Simulations FIGURE 1. Comparison of model results and experimental results for the oxidation of salicylic acid in aqueous suspensions of TiO2 (Degussa P25) in a pilot plant laminar falling film slurry photocatalytic reactor. Lines are results from the present model; symbols are experimental results from ref 16.
TABLE 3. Comparison of Model Results and Experimental Results of the Oxidation of Salicylic Acid in Aqueous Suspensions of TiO2 (Degussa P25) in a Pilot Plant Laminar Falling Film Slurry Photocatalytic Reactora τ
χ (exp) (%)
χ (model) (%)
0.06 0.31 0.62 1.24 1.7
14.63 25.62 29.41 34.10 36.49
13.42 25.11 31.05 34.25 36.16
NRe
χ (exp) (%)
χ (model) (%)
291 684 1258 1434 1415
12.54 16.22 22.76 28.52 37.38
13.93 16.64 21.72 27.63 36.33
a Experimental results and model parameters from ref 16 with ω ) 0.74, kT ) 8.335 × 10-8 kg(1-n) s-1 W-m m(3m+3n-3).
coefficient, and its effect was accounted for by the experimental measurements of the extinction coefficient (κ + σ) (16). The kinetic parameters m and n of salicylic acid degradation were equal to those reported elsewhere (m ) 0.5, n ) -0.44) (16). The adjustable parameter kT was calculated by fitting the present model to the experimental results in Li Puma and Yue (16) of the effect of the intensity of the incident radiation and the initial concentration of salicylic acid on conversion. The value of kT was found to be 8.335 × 10-8 kg(1-n) s-1 W-m m(3m+3n-3) with a standard deviation of 0.637 × 10-8 kg(1-n) s-1 W-m m(3m+3n-3).
The present model was used to predict the conversion of a TFS photocatalytic reactor under different flow conditions, reaction kinetics, and scattering albedo. Kinetic Parameters m and n. The kinetic parameters m and n of the mathematical model measure the dependence of the reaction rate of a substrate j on the LVRPA and the substrate concentration, respectively. There are limiting cases in which the value of m and n can be reasonably estimated without the need to perform lengthy experiments. Studies of the photocatalyzed rate of organics versus the intensity of the incident radiation (or the absorbed radiation measured by actinometry) have shown that at weak intensities (typically less than 10-3 Ein m-2 s-1) the observed rate of oxidation of organics is first-order in radiation intensity (22); however, at higher intensities (more common case) a square root dependence of the rate is generally found (2). In the present model these two limiting cases correspond to assigning the value of m ) 1 and m ) 0.5, respectively. The Langmuirian fitting of the rate data of photocatalytic reactions (2) suggests the other two limiting values for the parameter n: high substrate concentration (typically > 100 ppm) (n ) 0) and low substrate concentration (typically < 10 ppm) (n ) 1). These limiting cases for m and n were used to illustrate the effect of kinetics on the model simulation results. Idealized Flow and Radiation Scattering. The results of the model simulations for the idealized flow conditions in Table 2 are presented for the TFSIW reactor configuration. For these simulations a set of realistic model parameters were used (Table 4) (16). The limiting cases described above for the values of the kinetic parameters m and n were used. For each set of values of m and n, the value of the kinetic parameter kT was selected such that the maximum conversion with the FFLF system in the absence of light scattering (ω ) 0) was 80%, to elucidate the full effect of the flow conditions on reactor performance. In practice, in photocatalytic oxidation of organic pollutants, such a conversion can be realized by recirculating a fraction of the outflow back to the reactor inlet or connecting multiple reactors in series. Thus, the general conclusions of the present analysis remain accurate. The simulation results for the conversion of a substrate j as a function of optical thickness at different values of the
TABLE 4. Model Parameters Used in the Simulations geometry UV lamp (36W Philips blacklight) substrate concentration Reynolds number film thickness recycle ratio TiO2 extinction coeff (Degussa P25)
R ) 22.222, β ) 1.333, H ) 1.6 m Iw ) 76.64 W m-2 Cj0 ) 10 ppm NRe ) 1454 δ ) 4.808 × 10-4 m η)0 (σ + κ) ) 1296 m2 kg-1 VOL. 37, NO. 24, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Model simulation for the conversion of a substrate j as a function of the optical thickness and scattering albedo for different idealized flow conditions. Kinetic parameters: m ) 1 (low radiation intensity), n ) 0 (high substrate concentration), kT ) 1 × 10-7 kg(1-n) s-1 W-m m(3m+3n-3). (a) FFLF; (b) PF; (c) SF. Other model parameters from Table 4.
FIGURE 3. Model simulation for the conversion of a substrate j as a function of the optical thickness and scattering albedo for different idealized flow conditions. Kinetic parameters: m ) 0.5 (high radiation intensity), n ) 1 (low substrate concentration), kT ) 4.32 × 10-3 kg(1-n) s-1 W-m m(3m+3n-3). (a) FFLF; (b) PF; (c) SF. Other model parameters from Table 4.
scattering albedo and different kinetics are shown in Figures 2 and 3 and Figures S1 and S2 (see Supporting Information) respectively for FFLF, PF and SF systems. Figures 2 and 3 and Figures S1 and S2 show that in every situation the conversion in the reactor reaches a maximum at an optimal value of optical thickness. Starting from small values of optical thickness, the conversion initially increases due to an increase of the irradiated catalytic surface area per unit volume of reactor until an optimum has been reached. The optimal condition corresponds with the most favorable
correspondence of the transversal profiles of the fluid velocity and LVRPA. Mathematically this can be expressed as
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∫∫ 1
0
1
0
[(LVRPA)m × fluid residence time] dξ*dz* ∝
∫∫ 1
0
1
0
/ (I ξ*,z* )m
v/z
dξ*dz* ) max (9)
This optimum is, however, dependent on the value of the model parameter m, which measures the dependence of the
reaction kinetics from the absorption of radiation and on the value of ω. As m increases the model becomes more sensitive to changes in the radiation field. If optical thickness is increased above the optimal value, the conversion decreases because of unfavorable correspondence of the fluid velocity and LVRPA that is largely caused by a decrease of radiation absorption at positions deep into the thin-film. At very high values of optical thickness (τ > 10) a situation may be reached in which the radiation is effectively absorbed in the outer layer of the thin-film with little absorption at the deeper sections of the thin-film. The model simulations show that in every situation radiation scattering significantly affects the conversions obtained at different values of optical thickness. As the scattering albedo ω is increased the conversions decrease significantly in all three cases of ideal flow, with the most prominent effects observed for the cases in which m ) 1 (Figure 2 and Figure S1, Supporting Information) as expected. This is caused by losses of photons from the reacting systems due to radiation scattering which in the present model occurs at the position ξ* ) 0. Furthermore, the model simulations show that at optimal value of optical thickness, the effect of radiation scattering can be significant when ω is higher than 0.3 and must be accounted for when ω is 0.5 or higher. Thus, if this limit is not exceeded by means of controlled synthesis of TiO2 powders, the effect of radiation scattering can be safely neglected, and simplified models of the radiation field in the reactor can be used (19). The model simulations show that for each set of kinetic parameters and independently from the values of the scattering albedo and optical thicknesses, the conversions obtained with the three different idealized flow systems follow the sequence FFLF > PF > SF. The reasons for this have been explained in full elsewhere (19, 24) and can be attributed to the degree of correspondence of radiation field and fluid residence time. For example, in the FFLF system there is a very good degree of correspondence of radiation field and fluid residence time since the fluid elements with the lowest residence times near ξ ) 0 receive maximum intensity of radiation, and the fluid elements with the longer residence times near ξ ) 1 receive the lowest intensity of radiation. In this study it is further noticed that as the scattering albedo increases the difference in conversions observed with the three flow systems diminishes. Furthermore, this differential is larger when m ) 1 than when m ) 0.5. The reason for this is explained further below. The model simulations reveal that radiation scattering does not affect appreciably the value of optimal optical thickness that result in maximum substrate conversion when m ) 0.5 (Figure 3 and Figure S2, Supporting Information). The optimal value of optical thickness was found to be 2.8 for the FFLF system and equal to 2 for PF and SF systems. However, a shift in the locus of the optimal value of optical thickness with radiation scattering was observed when m ) 1 (Figure 2 and Figure S1, Supporting Information). A relatively small shift was found in the range of scattering albedo from 0 to 0.6: for example Figure 2 shows τoptimal ) 2.2 -3.0 with FFLF system, τoptimal ) 1.8-2.2 with PF and SF systems. However, a larger shift was observed in the range of scattering albedo from 0.7 to 0.9: for example Figure 2 shows τoptimal ) 3.4-8.2 with FFLF system, τoptimal ) 2.6-5.8 with PF system, and τoptimal ) 2.4-3.0 with SF system. Thus, it appears that when the reaction kinetics are highly dependent on the radiation field (m ) 1) a shift in the optimal value of the optical thickness with radiation scattering should be observed. The shifting effect is clearly more distinct in the FFLF system. The reasons for these results can be explained by showing the model simulation of the dimensionless LVRPA for a transversal cross section of the thin-film as a function
FIGURE 4. Model simulation of the dimensionless LVRPA for a transversal cross section of the thin-film (z* ) 0.5) as a function of the scattering albedo and at constant optical thickness (τ ) 1). Other model parameters from Table 4.
FIGURE 5. Radiation transmission factor as a function of the optical thickness at different scattering albedo. Model parameters from Table 4. of the scattering albedo and at constant optical thickness. Figure 4 shows that as ω increases photons penetrate less */ becomes into the film and as a result the profile of Iξ*,z* steeper near the radiation entrance wall and less intense near the back of the thin-film. These results are consistent with those obtained with complex radiation scattering models (25). Radiation scattering always produces (i) a reduction of the total energy absorbed within the reactor (see Figure 5), (ii) a reduction in the penetration depth of the photons and (iii) a steeping of the profile of the LVRPA at the reactor entrance. To compensate for these three negative effects higher conversions can only be obtained if the liquid film is made optically thicker, e.g., by increasing the catalyst concentration, to maximize the absorption of photons in the irradiated transversal section of the thin-film. This effect is more noticeable in the FFLF system since there is a higher correspondence of radiation field and fluid residence time. In contrast, the SF is less sensitive to this effect because of the complete noncorrespondence of radiation field and fluid residence time for sections from ξ* ) 0 to ξ* ) 0.5 of the thin-film which are those that receive most of the radiation. For the same reasons, as the scattering albedo increases the difference in conversions observed with the three flow VOL. 37, NO. 24, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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systems diminishes since there is a worsening of the degree of correspondence of radiation field and fluid residence time which has a more noticeable effect in the FFLF system. Radiation Transmission Factor. The effect of the scattering albedo on the transmission of radiation from the radiation source (UV lamp) to the slurry suspension is shown in Figure 5 for different values of the optical thickness. The transmission factor increases with the optical thickness until an asymptotic plateau is reached which occurs at progressively lower values as the scattering albedo increases. This suggests that the optimum range of optical thickness of TiO2 (Degussa P25), considered solely from the point of view of the radiation field, is in range from 2 to 4. Above τ ) 4 in practice no photons can escape from the back wall (ξ ) 1) of the thin-film (14), and all radiation losses occur from backscattering at ξ ) 0. One peculiarity of this conclusion is that although a simplified analysis of the radiation field has been used in the present model, the profile of the curve presented here is almost indistinguishable with that reported in Brandi et al. (26) who have solved the full radiative transfer equation to calculate the radiation field of a flat plate photoreactor 10 mm in thickness. Their results also show that the plateau of the reactor volume averaged LVRPA is reached at a concentration of TiO2 (Degussa P25) of approximately 0.3 g/L which corresponds to a value of the optical thickness of 3.9 calculated using the same value of the extinction coefficient as this work. Optimum Optical Thickness. The results shown therefore suggest that for most applications, an optimal design of TFS photocatalytic reactor requires the optical thickness of the reactor to be in the range from 1.8 to 3.4 depending on the type of flow system and on the dependence of the reaction kinetics from the LVRPA (parameter m). This conclusion has been confirmed experimentally by a number of authors as shown in Table S1 (see Supporting Information) using a variety of photocatalytic reactors and TiO2 (Degussa P25). Economic analyses on case studies of TiO2 photocatalysis for water purification suggest that this technology is economically viable when the contaminated water has 10 ppm or less of organic content (27). Under the above conditions the Langmuirian fitting of the rate data of many organic pollutants suggests n ) 1 in the present model. Furthermore, since it is generally unusual to operate at low intensity of irradiation, it follows that m ) 0.5 in many cases. Thus for the most common set of kinetic parameters (m ) 0.5, n ) 1) an optimum in the design of a TFS photocatalytic reactor would be obtained when the optical thickness is equal to 2.8 with the FFLF system and is equal to 1.8-2.2 in the PF system (Figure 3). SF operation mode should positively be avoided. This paper has shown an elegant and systematic analysis of thin-film slurry photocatalytic reactors for water treatment and purification by TiO2 photocatalysis. It has provided a mathematical model in “dimensionless form” that can be easily used for scale-up and design of photoreactors of different geometries irradiated by UV lamps or by solar radiation. The effect on reactor performance of radiation scattering by the solid photocatalyst has been particularly emphasized throughout the paper. Current models of photocatalytic reactors available in the literature are either too rigorous or too simplistic to be used effectively for the design and scale-up of photocatalytic reactors. The present model retains the essential elements of a rigorous approach, while providing simple solutions, which will aid in the development of photocatalytic oxidation technology for water treatment and purification.
Nomenclature a
velocity coefficient: a ) 0 for FFLF and PF, and a ) 0.5 for the SF, dimensionless
A
geometrical coefficient, dimensionless
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ccat
photocatalyst concentration, kg m-3
C
substrate concentration, kg m-3
C*
dimensionless substrate concentration () C/CO)
H
reactor length, m
I
radiation intensity (or radiative flux), W m-2
Iλ
radiation intensity divided wavelength of radiation, W m-3
max I ξ)0
maximum value of radiation intensity at surface ξ ) 0, W m-2
/ I ξ*,z*
dimensionless radiation intensity or dimenmax sionless LVRPA ()Iξ,z/Iξ)0 )
kT
kinetic constant, kg(1-n) s-1 W-m m(3m+3n-3)
L
lamp length, m
m
order of reaction with respect to LVRPA, dimensionless
n
order of reaction with respect to substrate concentration, dimensionless
NDa
Damko¨hler number, dimensionless
NRe
Reynolds number, dimensionless
Q0
volumetric flow rate through system inlet, m3 s-1
QR
volumetric flow rate through reactor, m3 s-1
r
radial coordinate, m
rj
rate of reaction with respect to substrate j, kg s-1 m-3
rl
lamp radius, m
R
distance between lamp axis and first illuminated surface of the film in the TFSIW configuration, m
T
reactor width in the TFSFW configuration, m
v
fluid velocity, m s-1
v*
dimensionless fluid velocity () vz/vmax ) z
V
volume of reaction space, m3
W
radiant power, W
z
axial coordinate, m
z*
dimensionless axial coordinate () z/H)
Greek letters R
geometrical parameter () H/L) dimensionless
β
geometrical parameter () L/R) dimensionless
γ
conversion per pass, dimensionless
Γ
mass flow rate per unit width of reactor wall, kg m-1 s-1
δ
film thickness, m
η
recycle ratio, dimensionless
κ
specific mass absorption coefficient averaged over the spectrum of the incident radiation, m2 kg-1
λ
radiation wavelength, m
µ
absorption coefficient averaged over the spectrum of the incident radiation () ccat × κ), m-1
kinematic viscosity, m2 s-1
ξ
film thickness coordinate, m
ξ*
dimensionless film thickness coordinate () ξ / δ)
simulation for the conversion of a substrate j as a function of the optical thickness and scattering albedo for different idealized flow conditions (Figures S1 and S2). This material is available free of charge via the Internet at http:// pubs.acs.org.
π
ratio of circumference to diameter of a circle (= 3.1428)
Literature Cited
ν
m-3
F
fluid density, kg
σ
specific mass scattering coefficient averaged over the spectrum of the incident radiation, m2 kg-1
τ
optical thickness () (σ + κ) ccatδ), dimensionless
χ
total conversion for the system, dimensionless
ψ
radiation transmission factor () Wabs/WL) dimensionless
ω
scattering albedo () σ/(σ + κ)) dimensionless
Subscripts abs
absorbed
j
substrate
l
lamp
r
direction along the radial coordinate
R
position at r ) R
w
lamp wall
z, z*
direction along the axial coordinate
λ
wavelength
ξ, ξ*
direction along the film transversal coordinate
Superscripts average
average value
*
dimensionless variable
H
reactor outlet
max
maximum value
O
system inlet
R
through reactor
Acknowledgments The author is grateful to NATO (Grant SfP-977986) and the UK EPSRC (Grant GR/R19427/01) for the financial support to produce this work.
Supporting Information Available Optimum optical thickness for oxidation of selected pollutants in slurry suspension of TiO2 (Table S1) and model
(1) Ollis, D. F. C. R. Acad. Sci. Paris, Serie IIC, Chimie/Chemistry 2000, 3, 405-411. (2) Hoffmann, M. R.; Martin, S. T.; Choi, W.; Bahnemann, D. W. Chem. Rev. 1995, 95, 69-96. (3) Ohko, Y.; Iuchi, K. I.; Niwa, C.; Tatsuma, T.; Nakashima, T.; Iguchi, T.; Kubota, Y.; Fujishima, A. Environ. Sci. Technol. 2002, 36, 4175-4181. (4) Lawton, L. A.; Robertson, P. K. J.; Cornish, B. J. P. A.; Jaspars, M. Environ. Sci. Technol. 1999, 33, 771-775. (5) Watts, R. J.; Kong, S.; Orr, M. P.; Miller, G. C.; Henry, B. E. Water Res. 1995, 33, 95-100. (6) Alfano, O. M.; Bahnemann, D.; Cassano, A. E.; Dillert, R.; Goslich, R. Catal. Today 2000, 58, 199-230. (7) Turchi, C. S.; Ollis, D. F. J. Phys. Chem. 1988, 92, 6852-6853. (8) Li Puma, G.; Yue, P. L. Environ. Sci. Technol. 1999, 33, 32103216. (9) Li Puma, G.; Yue, P. L. Ind. Eng. Chem. Res. 2001, 40, 51625169. (10) Cassano, A. E.; Martin, C. A.; Brandi, R. J.; Alfano O. M. Ind. Eng. Chem. Res. 1995, 34, 2155-2201. (11) Brandi, R. J.; Alfano, O. M.; Cassano, A. E. Environ. Sci. Technol. 2000, 34, 2623-2630. (12) Brandi, R. J.; Alfano, O. M.; Cassano, A. E. Chem Eng. Sci. 1999, 54, 2817-2827. (13) Raupp, G. B.; Nico, J. A.; Annangi, S.; Changrani, R.; Annapragada, R. AIChE J. 1997, 43, 792-801. (14) Brucato, A.; Rizzuti, L. Ind. Eng. Chem. Res. 1997, 36, 47484755. (15) Li Puma, G.; Yue, P. L.Chem. Eng. Sci. 1998, 53, 2993-3006. (16) Li Puma, G.; Yue, P. L. Chem. Eng. Sci. 1998, 53, 3007-3021. (17) Li Puma, G.; Yue, P. L. Chem. Eng. Sci. 2001, 56, 2733-2744. (18) Li Puma, G.; Yue, P. L. Chem. Eng. Sci. 2001, 56, 721-726. (19) Li Puma, G.; Yue, P. L. Chem. Eng. Sci. 2003, 58, 2269-2281. (20) Perry R. H.; Green, D. W. Perry’s Chemical Engineering Handbook, 6th ed.; McGraw-Hill Inc.: New York, 1984; pp 5-59. (21) Jacob, S. M.; Dranoff, J. S. Chem. Eng. Prog. Symp. Ser. 1966, 62, 47-55. (22) Ollis, D. F. In Photochemical Conversion and Storage of Solar Energy; Pelizzetti, E., Schiavello, M., Eds.; Kluver Academic Publishers: Dordrecht, 1991; pp 593-622. (23) Cabrera, M. I.; Alfano, O. M.; Cassano, A. E. In Proceedings of the International Conference on Oxidation Technologies for Water and Wastewater Treatment, Clausthal-Zellerfeld, Germany, 1215 May, 1996. (24) Ollis, D. F.; Turchi, C. Environ. Prog. 1990, 9, 229-234. (25) Alfano, O. M.; Cabrera, M. I.; Cassano, A. E. Chem Eng. Sci. 1994, 49, 5327-5346. (26) Brandi, R. J.; Alfano, O. M.; Cassano, A. E. Chem Eng. Sci. 1996, 51, 3169-3174. (27) Blanco, J.; Malato, S. Solar Detoxification; UNESCO Natural Sciences World Solar Programme, 2001.
Received for review March 10, 2003. Revised manuscript received July 18, 2003. Accepted September 29, 2003. ES0300362
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