Ind. Eng. Chem. Res. 2003, 42, 2479-2488
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Radiation Field in an Annular, Slurry Photocatalytic Reactor. 2. Model and Experiments Roberto L. Romero, Orlando M. Alfano, and Alberto E. Cassano* INTEC, Universidad Nacional del Litoral and CONICET, Gu¨ emes 3450, S3000GLM Santa Fe, Argentina
The radiation field in an annular, slurry photocatalytic reactor has been modeled and verified working with a pilot-plant reactor. A suspension of titanium dioxide in water flows through the annular reaction space, which is irradiated with a tubular, UV lamp placed at the central axis of the system. Two different types of titanium dioxide have been used: Aldrich and Degussa P25. Using a rigorous model, it is possible to precisely evaluate the radiation intensity at each point inside the reactor. The radiation distribution was verified by computing the forwardly transmitted radiative fluxes going out of the reactor walls at different axial positions and compared with radiometer measurements (“point” measurements). Predictions of the same fluxes were also verified with homogeneous actinometry employing potassium ferrioxalate (providing an average measurement of the outgoing fluxes over the reactor external surface). When predictions from the theoretical model are compared with experimental data, good agreement was obtained. 1. Introduction One of the concepts that has received an increasing degree of attention in environmental remediation has been the use of titanium dioxide as a catalyst for the light-induced photooxidation of pollutants. Catalysis by illuminated titanium dioxide is the result of the interaction of the electrons and holes generated in the photoactivated semiconductor with the surrounding medium; thus, as a consequence of light absorption, electronhole pairs are formed in the solid particle. They can recombine or participate in reduction and oxidation reactions that have as a result the decomposition of contaminants. In contrast with the profuse literature regarding the chemistry of these reactions, a parallel research effort applied to the engineering aspects of these processes has not been observed. Design methods are very scarce, and in most of the cases, they rely on empirical or semiempirical approximations. Ab initio methods of analysis are possible but not free from difficulties.1-5 Polychromatic radiation transport in participating media (with absorption, scattering, and chemical reaction) is properly represented by a set (in theory, an infinite set) of integrodifferential equations.6 Only for very simplified and somewhat idealized situations is it possible to get analytical solutions. Moreover, machine computation must resort to special numerical techniques that can be adapted from general transport theory and, particularly, neutron transport applications. Among the most attractive configurations for photocatalytic applications, the tubular, cylindrical reactor has often been used in solar trough collectors. On the other hand, if artificial light is to be used in combination with continuous-flow reactors, the cylindrical geometry of an annular reactor is perhaps the simplest and most efficient configuration. Cylindrical geometries pose a very challenging problem in that radiation transport in curvilinear coordinate systems gives rise to additional complications in the numerical procedures.1,7-9 * To whom correspondence should be addressed. Fax: 54 342 4559185. E-mail:
[email protected].
Understanding the radiation field in photocatalytic reactors is an important step toward the modeling of these reacting systems. In the liquid phase, the catalyst particles, TiO2 in its different varieties, are usually suspended in a fluid phase, although other reactor configurations have also been proposed such as packed and fluidized beds with an immobilized catalyst.10-13 Because TiO2 is activated by photon absorption in the UV range, the knowledge of the radiation field distribution inside the reactor is essential. This is so because in any kinetically controlled photoprocess the reaction rate depends, with different functional dependencies, on the local volumetric rate of photon absorption. In photocatalytic systems, when the catalyst is stable from the chemical (activity) and mechanical (particle size and agglomeration) points of view, the nonuniform radiation field is constant, i.e., independent of the reaction extent (time of operation), but a strong function of position in the reaction space. This spatial distribution can be properly calculated, as has been shown by Romero et al.1 It is then very important to validate the employed models with specially designed experiments. In this work, numerical results obtained with an upgraded version of the theoretical model are used to calculate radiation properties that can be measured without distortion of the light distribution in the reaction space, i.e., calculated fluxes coming out through the external wall of the reactor when it is filled with the catalytic suspension (Aldrich and Degussa P25). These fluxes are experimentally measured with two different approaches: (i) a global measurement with an actinometer solution flowing through a second annular space surrounding the reactor and (ii) point measurements with a fiber-optic, UV detector (and a radiometer) that can be moved and placed at different angular and axial positions on the external wall of the reactor. It is expected that if these values show good concordance with predictions, the radiation distribution inside the reactor, calculated by the model, can be used with confidence.
10.1021/ie020588d CCC: $25.00 © 2003 American Chemical Society Published on Web 01/03/2003
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Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003
will be extended in the 310-390 nm wavelength range. The gap between both reactor walls (Table 1) must be necessarily small because, under normally employed catalyst concentrations, absorption by titanium dioxide is very strong and, consequently, after a few millimeters (no more than 12 mm for concentrations as low as 0.5 × 10-3 g cm-3) there are no more photons to absorb. The annular space (1 cm) was filled with a spatially uniform suspension of the solid catalytic particles in water. The fluid phase (water in this work) is assumed to be transparent to the employed radiation in the above-mentioned wavelength range; hence, absorption may be the result of interaction of photons with the solid only. Two types of catalysts were experimentally investigated: (i) Aldrich titanium dioxide (99% anatase) and (ii) Degussa P25 (75% anatase) titanium dioxide. Table 2 provides the specific values of the absorption, scattering, and extinction coefficients for the TiO2 suspensions, as a funcion of wavelength.14 With highly absorbing solids, the concentration must be small (e0.5 × 10-3 g cm-3) to make meaningful measurements on the wall of the outer annular space. Moreover, for local measurements with a fiber-optic detector, the employed concentration must be lower.
Figure 1. Annular photocatalytic reactor. Table 1. Parameters of the Lamp-Reactor System system
parameter
annular reactor (Duran glass walls) external annular space (Duran glass walls) Philips TL/09 lamp
value
rin rou LR rin rou
3 cm 4 cm 70 cm 4.25 cm 4.95 cm
nominal power arc length (LL) lamp radius (rL) emission photochemical power emission range
80 W 150 cm 1.9 cm superficial and diffuse 5.9 × 10-5 einstein s-1 310-445 nm
2. The Reactor The reacting system is a cylinder of annular crosssectional area. This annular space surrounds a cylindrical tubular lamp longer than the reactor to avoid end effects that could distort the results of experiments designed to test the validity of the model (Figure 1). The lamp is a polychromatic source of the arc type having superficial and diffuse emission (TL 80W/09 from Philips). Emission by the lamp is mainly in the ultraviolet A range with a peak at 355 nm (Table 1). The inner reactor wall is made of Duran glass that cuts off any emitted radiation below 280 nm. Considering the wavelength ranges of (i) absorption by the catalyst (below 390 nm and down to rather low wavelengths), (ii) emission by the lamp (310-445 nm), and (iii) good transmission by the glass tube (300 nm e λ e 800 nm), one can consider that the scope of these experiments
3. Radiation Field Model Preliminary experiments, similar to those described in the next sections, indicated that the first model published by Romero et al.1 did not include the proper boundary conditions for the annular space. Essentially, in the previous model backscattering coming out through the inner wall, which modify the intensities of the radiation that arrives at the opposite inner reactor wall, was not incorporated into the inlet boundary condition; i.e., in the original model backscattered photons were considered lost, whereas in reality an important fraction of them enters the reactor in the opposite part of the reactor wall. Not all of them enter because very often the lamp wall is not transparent to the traveling photons in the wavelength range of interest. Also, reflections at the inner walls of the reacting system were not included in the previous model. In the laboratory, very often this boundary condition is obtained by using a homogeneous actinometer solution placed in, or circulated through, the reaction space. This reacting system, being homogeneous, cannot take into account the scattering produced by the titanium dioxide suspension (obviously, the backscattering at the inner reactor wall included). It will be seen in the next
Table 2. Spectral Distribution of Mass Absorption, Scattering, and Extinction Coefficients for TiO2 Suspensions Aldrich
Degussa P25
λ (nm)
κ/λ (cm2 g-1)
σ/λ (cm2 g-1)
β/λ (cm2 g-1)
κ/λ (cm2 g-1)
σ/λ (cm2 g-1)
β/λ (cm2 g-1)
315 325 335 345 355 365 375 385 395 405 415 435
8797 8922 8995 8340 6435 3045 951 379 239 193 146 100
27 080 27 551 28 333 30 019 32 957 37 262 39 819 41 054 42 006 42 580 42 627 42 673
35 877 36 473 37 328 38 359 39 392 40 307 40 769 41 433 42 245 42 773 42 773 42 773
18722 15872 11775 8082 4777 2548 1293 433 0 0 0 0
50 418 54 528 55 877 55 056 54 583 52 547 50 013 47 567 45 071 42 343 40 000 36 000
69 140 70 400 67 652 63 138 59 359 55 095 51 305 47 999 45 071 42 343 40 000 36 000
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Υλ,rinIλ,Lp(rin,z,µ>0,η,t), (2) the one generated by backscattering coming out of the reaction space from the opposite side of the reactor wall (excluding the fraction that is eclipsed by the opaque lamp), Υλ,rin2Iλ,bs(rin,z,µ0,η,t). Then
Iλ(rin,z,µ>0,η,t) ) Υλ,rinIλ,Lp(rin,z,µ>0,η,t) + Υλ,rin2Iλ,bs(rin,z,µ0,η,t) (3) Figure 2. Coordinate systems employed to describe the RTE in the reactor (adapted from Romero et al.1).
sections that the significance of this omission depends on the geometrical characteristics of the system, the type of lamp used (transparent to radiation or not), and the concentration of the employed catalyst. Moreover, when one looks for design methods applicable to practical reactors, the equipment is not available beforehand for these measurements. Then, the value must be calculated from a theoretical emission model making correct account of all contributing effects (emission by the lamp, backscattering from the TiO2 suspension, and reflections by the glass walls). The new formulation starts from the same fundamental principles. Essentially one must write, for monochromatic light, a radiation balance along a given direction of propagation in a pseudohomogeneous medium together with the appropriate boundary conditions.6 This balance is generally made with the following realistic assumptions for photocatalytic systems: (1) scattering is multiple but independent and (2) scattering is elastic. Under these conditions, along its traveling trajectory through a heterogeneous participating medium, a ray may lose radiation because of (i) absorption and (ii) out-scattering and may gain energy by (iii) internal emission and (iv) in-scattering. Internal emission is always neglected because the operating temperature is usually low. The resulting radiative transfer equation (RTE) is
∇‚[ΩIλ(x,Ω,t)] + κλ(x,t) Iλ(x,Ω,t) + σλ(x,t) Iλ(x,Ω,t) ) σλ(x,t) jeλ(x,t) + p(Ω′fΩ) Iλ(x,Ω′,t) dΩ′ (1) 4π Ω′)4π
∫
κλ and σλ are the absorption and scattering coefficients, respectively, and p(Ω′fΩ) the phase function for scattering.15 The lamp and the reactor have azimuthal symmetry (a situation that was confirmed in the performed experiments) and, consequently, in our case two spatial coordinates are used (r, z). Concerning the directional coordinates, they are expressed in terms of the direction cosines of the propagation direction Ω(µ,η) (Figure 2). Equation 1 must be solved with the boundary conditions that are defined by the incoming radiation from all of the surfaces that limit the reaction space. (i) At the top and bottom surfaces of the reactor, there is no radiation coming in:
Iλ(r,0,µ,η>0,t) ) Iλ(r,LR,µ,η0,η,t) can be calculated with an emission model for the lamp;6,16 Iλ,bs(rin,z,µ0,η,t) can be incorporated by employing the specular directional reflectivity that can be calculated with Fresnel’s equations.17 The value of Iλ,Rf(rin,z,µ>0,η,t) also needs the solution of the problem and must be obtained in an iterative way. (iii) At the external reactor wall, we consider reflection:
Iλ(rou,z,µ
