Ind. Eng. Chem. Res. 2007, 46, 7637-7644
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A Rational Approach to the Design of Photocatalytic Reactors Giovanni Camera Roda* and Francesco Santarelli Dipartimento di Ingegneria chimica, mineraria e delle tecnologie ambientali, UniVersita´ degli studi di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy
A model to assess the performances of an annular photocatalytic reactor has been developed by investigating different operational conditions through an analysis based on the proper dimensionless parameters (namely, the optical thickness, the Thiele modulus and two among the well-known Damko¨hler and Peclet numbers, which are properly redefined). Different dependences of the reaction kinetics on the local rate of radiant energy absorption are also considered. Because the progress of the reaction is affected by the radiation field, all these parameters are dependent on the catalyst concentration and then indirectly on the catalyst load. The conditions under which an optimal value for the catalyst concentration may exist are determined, thus contributing to provide insight to one aspect that is quite controversial in the literature. Introduction It is expected that, soon, photocatalytic processes will be widely used as an effective tool for the treatment of water that has been polluted by traces of toxic and/or persistent chemicals.1 Therefore, a large amount of attention has been given to studying the kinetics of the degradation of the organic pollutant substrate, as well as investigating the parameters that affect the performance of the systems (lamp/reactor) used. Results are undoubtedly interesting but suffer from a lack of generality,2,3 because they are presented in terms of dimensional parameters, which are significant to the specific situations investigated and, consequently, are valid under the same limitations. More-general criteria then are needed to assess the role that the operational variables have in determining and possibly optimizing the performance of a reactor. A significant example of the previous statement is given by the different conclusions presented by the authors who investigated, in slurry systems, the effects of catalyst load on the conversion and possible existence of an optimal value for this quantity. According to a large number of authors,3-11 the rate of removal of the substrate increases monotonically with the catalyst load and approaches an asymptotic value. The value of the catalyst load at which the asymptotic behavior appears is obviously dependent on the specific situation investigated; however, in any case, it is related to situations where a strong attenuation of the radiation field occurs within the reactor. In other experiments and works,2,3,11-19 a maximum of the rate of removal results at a specific value of the catalyst load. This behavior is generally justified by the significant attenuation of the radiation by the photocatalyst particles when their concentration is increased beyond a given value. This “shielding effect” might thwart the positive effect of an increase of the available catalyst sites, obtained by increasing the catalyst load. However, the maximum is strangely observed by the various researchers at catalyst concentrations that give very dissimilar attenuations of the radiation in the reactor, and this disagreement has not yet been justified. In a similar way, the dependence on the particular investigated situation limits the general validity of the analysis of the effects, * To whom correspondence should be addressed. E-mail address:
[email protected].
which are caused by (i) the flow rate of the stream to be treated2,20 and (ii) the order of the reaction, with respect to the local rate of radiant energy absorption. The discrepancies that emerge in the conclusions of the cited investigations are not considered as a sign of inaccuracy but are simply the outcome of attention to operational conditions with a different relative weight of the relevant parameters. Therefore, the present contribution is an effort to investigate the behavior of a photocatalytic reactor on the basis of the dimensionless parameters that are currently used in the transport phenomena and/or in the reaction engineering analysis to find answers to some open questions. Mathematical Model: Basic Equations A photocatalytic reaction has been considered to occur within an annular reactor with a fluorescent UV-A lamp placed on its axis. Because of the axial symmetry of the investigated situations, a two-dimensional problem results for both the radiation and the pollutant concentration fields. The geometry of the system can be represented by the following dimensionless variables:
k)
Rint R
R*lamp ) L* )
Rlamp R L R
where Rint is the internal radius of the annular region, R the external radius of the annular region, Rlamp the radius of the emitting lamp, and L the length of the irradiated annular reactor. The investigation has been developed through the following steps of the analysis: (a) radiative field and distribution of the rate of radiant energy absorption within the reactor; (b) conversion per pass when the reactor operates in a continuous mode; and (c) overall conversion when the reactor is inserted in a recycle/ batch system. Radiative Field and Distribution of the Rate of Radiant Energy Absorption. It is well-known that a peculiar feature of the photocatalytic processes is the essential role of the
10.1021/ie070302a CCC: $37.00 © 2007 American Chemical Society Published on Web 06/09/2007
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Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007
radiation field as an inherent element of the process. This feature is common to all the photochemical processes and requires a specific treatment that has a scaring effect on most of the people interested in photochemical and photocatalytic reactions and is often handled with simplified and questionable approaches. A rigorous analysis of the radiative transfer can be developed starting from the basic treatment presented in the textbooks on this subject21,22 or from the comprehensive analysis of the role of radiative transfer in photochemical processes.23-26 In the case of photocatalytic processes, the radiation field is dependent on the catalyst concentration after the geometry of the reactor and the location and the emission properties of the lamp are assigned. Even if the catalyst load is currently used to account for the radiation absorption, its intensive value, the catalyst concentration, is definitely more appropriate for this purpose, because it enters the constitutive equations for the optical properties of the participating particles. After the radiative transfer equation (RTE) has been solved and the distribution of the radiation intensity has been obtained, it is possible to determine the local rate of radiant energy absorption (e˘ ′′′) as
e˘ ′′′ ) κ
∫4π Iω dω
where ω represents any direction of the travelling radiation. The relevant optical parameters that affect the radiative transfer are (1) the optical thickness, given as τ ) βR(1 - k), where β ) κ + σ is the extinction coefficient (here, κ is the absorption coefficient, and σ is the scattering coefficient), (2) the single scattering albedo, ω0 ) σ/β, and (3) the phase function p(ω f ω′) for elastic scattering from the ω-direction to the ω′-direction. After the catalyst has been chosen, the albedo ω0 and the phase function are assigned, because the absorption and scattering coefficients (and, then, the total extinction coefficient β) are dependent linearly on the catalyst concentration.27 Therefore, the effects on the photons distribution due to the catalyst load can be investigated more properly, only in terms of the optical thickness, because this parameter accounts for the combined effect of the catalyst concentration (and then, indirectly, the catalyst load) and of the dimensions of the reactor.28 Continuous Annular Photoreactor-Conversion per Pass. Two flow conditionss fully developed laminar flow and turbulent flowshave been considered for the annular photoreactor when it operates in a continuous mode, assuming that the reaction rate is given by the kinetic equation
R ) K(e˘ ′′′)RCA
(1)
where e˘ ′′′ is the local rate of radiant energy absorption (here, e˘ ′′′ will be considered to be due to a monochromatic radiation or representative of the value averaged in a range of wavelengths), R is the order of the reaction (with respect to e˘ ′′′), and CA is the substrate concentration. The assumption of a firstorder reaction, with respect to the pollutant concentration, is consistent with the low concentration values that are typical of most of these processes. (a) Laminar Flow in the Reactor. When the Reynolds number (which is defined as Re ) [2〈Vz〉R(1 - k)F]/µ) is
