Modeling and Experimental Verification of a Flat-Plate Solar

3592

Ind. Eng. Chem. Res. 1998, 37, 3592-3601

Modeling and Experimental Verification of a Flat-Plate Solar Photoreactor Germa´ n H. Rossetti,†,‡ Enrique D. Albizzati,† and Orlando M. Alfano*,‡ Facultad de Ingenierı´a Quı´mica, Universidad Nacional del Litoral (UNL), Santiago del Estero 2654, 3000 Santa Fe, Argentina, and Instituto de Desarrollo Tecnolo´ gico para la Industria Quı´mica (INTEC), Consejo Nacional de Investigaciones Cientı´ficas y Te´ cnicas (CONICET), and Universidad Nacional del Litoral (UNL), Gu¨ emes 3450, 3000 Santa Fe, Argentina

A nonconcentrating, flat-plate solar photoreactor has been modeled and experimentally verified. The mathematical model considers that the reactor glass window receives direct and diffuse (isotropic) solar radiation. The model was solved numerically and predictions were compared with photodecomposition rate data, employing the uranyl oxalate actinometer. The reaction was conducted in an isothermal, perfectly mixed reactor placed inside a batch recycling system. The experimental values were compared with theoretical predictions and good agreement was obtained, the maximum deviation being 12%. The effect of the actinometer concentration and of the solar zenith angles (for horizontal and tilted reactors) on the actinometer decomposition rate was investigated. Results indicated that the uranyl oxalate reaction rate increases when (i) the initial actinometer concentration increases at almost constant solar zenith angle and (ii) the zenith angle decreases at the same initial actinometer concentration. 1. Introduction The utilization of the ultraviolet (UV) portion of the solar spectrum to drive the chemical destruction of organic pollutants in contaminated air and wastewaters has gained an increasing interest in the last two decades.1-4 These treatment technologies, usually called advanced oxidation technologies (AOTs), are based on the generation of hydroxyl radicals (OH•), a powerful oxidizing agent, by combination of ultraviolet radiaton (artificial or solar) and an oxidizing chemical. According to the AOT considered (UV/titanium dioxide, UV/ hydrogen peroxide, UV/ozone, UV/Fenton’s reagent, etc.), homogeneous or heterogeneous reacting media inside the photoreactor are present. Both concentrating (or “several-suns”) and nonconcentrating (or “one-sun”) photoreactors have been used for collecting the incident ultraviolet solar radiation. Recent developments have proven that one-sun reactors are more efficient than concentrating reactors since they effectively use both direct and diffuse components of UV solar radiation.5-7 It is worth noting that according to the solar zenith angle, the diffuse component in the UV range can be equal to or greater than the direct component of UV solar radiation for cloudless sky conditions. Additional contributions on solar detoxification of wastewater using nonconcentrating reactors can be found in the work published by Klausner and Goswami,8 Wyness et al.,9 March et al.,10 Nogueira and Jardim,11 and van Well et al.,12 among others. The extensive literature on this subject is largely concerned with reaction yields, paths, and mechanisms. However, only a limited amount of work has been * To whom correspondence should be addressed. Fax: 54 42 550944. E-mail: [email protected]. † UNL. ‡ INTEC, CONICET, and UNL.

reported in the literature on the modeling of radiation absorption by a reacting system, solving the complete radiative transfer equation. Some examples where the interactions between the solar radiation and a participating plane medium (slab geometry) have been studied can be found in the papers published by Stramigioli et al.13 and Cengel and Ozisik.14 On the other hand, radiation field modeling applied to participating and reacting systems in slab geometries was also studied by Spadoni et al.,15 Santarelli et al.,16 Camera Roda and Santarelli,17 and Stramigioli et al.18 Additional theoretical and experimental contributions for flat-plate photoreactors, employing tubular UV sources of polychromatic energy and parabolic reflectors, can be found in Alfano et al.,19,20 Cabrera et al.,21,22 and Brandi et al.23 Among the papers mentioned in the previous paragraph, only the work published by Stramigioli et al.13 and Cengel and Ozisik14 have specifically considered solar radiation as an energy source of the process; nonetheless, these authors have not carried out an experimental verification of the models proposed for describing the radiation transport in these systems. In the first paper13 only the direct component of the solar radiation incident on the flat-plate photoreactor is taken into account (i.e., the corresponding diffuse component is neglected). On the other hand, in the second work14 both components of solar radiation are considered, but this approach was aimed at the theoretical prediction of the solar energy absorption in a solar pond to obtain the transient temperature distribution in the water from the solution of the energy conservation equation. In other words, in the participating medium only radiation absorption took place, but there was no photochemical reaction. As was previously said, solar energy is not considered in the rest of the literature mentioned.15-23 The results presented in the first group of references15-18 are mainly

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Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998 3593

concerned with the theoretical analysis of the radiation field in a participating and reacting medium, and with the study of the radiation scattering and different boundary conditions on the reactor behavior. The second group of papers19-23 are involved with the theoretical modeling and the experimental verification of flat-plate photoreactors irradiated with UV lamps and reflectors. The main objective was the analysis of the scattering effects on the volumetric rate of energy absorption starting from the radiative transfer equation; they used chemical actinometers in order to perform the experimental study. It should be noted that reflection, refraction, and absorption effects produced on the window where the radiation enters were not considered in detail by these authors. These phenomena, which may be important in systems where the incoming radiation impinges on the glass plate with different angles of incidence, have been usually considered by means of an averaged reactor wall transmission coefficient. In the present work, we report the modeling of the radiation field inside a nonconcentrating, flat-plate solar photoreactor for a homogeneous, participating, and reacting medium. It is assumed that the reactor glass plate is irradiated with direct and diffuse (isotropic) solar radiation, only radiation absorption in the reacting medium taking place (i.e., scattering and emission are neglected). A detailed analysis of the reflection, refraction, and absorption phenomena produced on the glass window of the solar radiation entrance (boundary condition of the radiative transfer equation) is included, considering the direct and diffuse components of incident solar radiation for any solar zenith angle. Afterward, we compute the local volumetric rate of energy absorption (LVREA), and this radiation variable is subsequently used to describe the photodecomposition of uranyl oxalate aqueous solutions (a well-known chemical actinometer). The reaction is conducted in a perfectly mixed reactor placed inside the loop of a batch recycling system. Finally, the complete model is numerically solved, and predictions are compared with reaction rate experimental data obtained with the chemical actinometer. It must be noted that the main objective of this work has been to propose and verify a general methodological approach for this type of solar reactors. To carry out the experimental verification of the model, a specific reacting system (a chemical actinometer), where only radiation absorption and a photosensitized reaction with available and reliable kinetic data take place, has been considered. 2. Reactor Model Radiation Field. To evaluate the radiation intensity inside the flat-plate solar photoreactor, a plane-parallel participating and reacting medium was modeled (Figure 1), assuming that only radiation absorption occurs (i.e., scattering and emission are neglected). In addition, it is assumed that a volumetric absorption coefficient (κλ) as a function of wavelength is known. For this one-dimensional system, the mathematical formulation of the radiation problem can be obtained, starting from the general form of the photon transport equation. If nλω represents the density of photons with a wavelength range between λ and λ + dλ, having a direction of propagation within the differential solid angle dω centered on the direction Ω, we have24

Figure 1. Variables involved in the radiation field model.

∂nλω + ∇‚(nλωcΩ) ) eλω - aλω ∂t

(1)

The spectral specific intensity Iλω can be related to nλω by the following equation:

Iλω ) chνnλω

(2)

Then, substituting eq 2 into eq 1 and solving

1 ∂Iλω + ∇‚(IλωΩ) ) Eλω - Aλω c ∂t

(3)

Usually, the first term of the left-hand side of eq 3 can be neglected since 1/c , 1 (steady-state condition). Besides, as mentioned before, scattering and emission are also neglected for this homogeneous medium. Therefore, eq 3 is reduced to

∇‚(IλωΩ) ) -Aλω

(4)

where Aλω only includes the radiation absorption phenomenon. Considering a linear isotropic constitutive equation to characterize the absorption term (Lambert’s equation) and the fact that Ω is a constant, the result is

Ω‚∇Iλω + κλIλω ) 0

(5)

Assuming a one-dimensional system (Iλω is only a function of x) and recalling that Ω‚i ) µ, eq 6 is obtained:

µ

∂Iλω(x) + κλIλω(x) ) 0 ∂x

0 0)

(B.1)

(µ < 0)

(B.2)

where functions F0(µ,φ) and FL(µ,φ) are given by the following expressions:

F0(µ,φ) )

[1 -

Fa-p(µ*i )]qD,λ

[1 - Fp-w(µ′r)]τλ(µ′r)

∫µ1

[1 - Fa-p(µ*)][1 - Fp-w(µ′)]τλ(µ′)

× 1 - τλ2(µ′)Fa-p(µ′)Fp-w(µ′) exp(-κλL/µ)µ dµ (B.8)

cr

From eq B.8 the following expression to evaluate the radiation flux at the reactor bottom is obtained:

qB,λ )

{

qD,λ

1

∫0 Fw-p(µ) exp(-2κλ/µ)µ dµ 1

1 - 2FB

[1 - Fa-p(µ*i )][1 - Fp-w(µ′r)]τλ(µ′r) 1 - τ2λ (µ′r)Fa-p(µ′r)Fp-w(µ′r)

nw2 2qS,λ 2 na

∫µ1

1 - τλ2(µ′r)Fa-p(µ′r)Fp-w(µ′r) δ(µ - µr) δ(φ - φr) +

a

λ

a-p

p-w

( )

κλ qB,λ Fw-p(µ)FB exp - L (B.3) π µ qB,λ FL(µ,φ) ) FB π

(B.4)

The radiation flux at the reactor bottom (qB,λ), included in the third term on the right-hand side of eq B.3 and on the right-hand side of eq B.4, will be evaluated below. Local Volumetric Rate of Energy Absorption (LVREA). From eq 9 in the paper, the LVREA can be obtained from the expression

∫4πIλω(x) dω ) κλ ∫02π dφ ∫01 I+λω(x) dµ + 2π 0 κλ ∫0 dφ ∫-1 Iλω(x) dµ (B.5)

Considering eqs B.1-B.4 and performing the integration of eq B.5, we finally get eq 11 of the paper. Radiation Flux at the Reactor Bottom. The radiation flux reaching the reactor bottom is evaluated from its definition:

qB,λ )

∫02π dφ ∫01I+λω(L)µ dµ

(B.6)

From eq B.1 evaluated at x ) L, one can obtain

( )

I+ λω(L) ) F0(µ,φ) exp -

κλ L µ

(B.7)

Substituting eq B.7 into eq B.6 and solving the resulting equation, we get

×

exp(-κλL/µr) +

[1 - Fa-p(µ*)][1 - Fp-w(µ′)]τλ(µ′)

cr

µr

[1 - Fp-w(µ′)]τλ(µ′) [1 - Fa-p(µ*)]qS,λ nw2 + 2 π n 1 - τ 2(µ′)F (µ′)F (µ′)

eaλ (x) ) κλ

∫01Fw-p(µ) exp(-2κλ/µ)µ dµ +

1 -τλ2(µ′)Fa-p(µ′)Fp-w(µ′)

}

exp(-κλL/µ)µ dµ

× (B.9)

Local Net Radiation Flux (LNRF). From its definition (eq 10 of the paper), the LNRF may be represented by

∫02π dφ ∫-11 Iλω(x)µ dµ ) ∫02π dφ ∫01 I+λω(x)µ dµ + ∫02π dφ ∫-10 I-λω(x)µ dµ

qn,λ(x) )

(B.10)

Substituting eqs B.1-B.4 into eq B.10 and solving the resulting integral, we finally obtain eq 12 of the main body of the paper. Literature Cited (1) Ollis, D. F., Al-Ekabi, H., Eds. Photocatalytic Purification of Water and Air; Elsevier: Amsterdam, The Netherlands, 1993. (2) Legrini, O.; Oliveros, E.; Braun, A. M. Photochemical Processes for Water Treatment. Chem. Rev. 1993, 93, 671-698. (3) Helz, G. R., Zepp, R. G., Crosby, D. G., Eds. Aquatic and Surface Photochemistry; CRC Press: Boca Raton, FL, 1994. (4) Proceedings of the Fourth International Conference on Advanced Oxidation Technologies for Water and Air Remediation and of The Third International Conference on TiO2 Photocatalytic Purification and Treatment of Water and Air, Orlando, Fl, Sept 1997. (5) Ollis, D. F. Solar-Assisted Photocatalysis for Water Purification: Issues, Data, Questions. In Photochemical Conversion and Storage of Solar Energy. Pelizzetti, E., Schiavello. M., Eds.; Kluwer Academic Publ.: The Netherlands, 1991; pp 593-622. (6) Bockelmann, D.; Goslich, R.; Weichgrebe, D.; Bahnemann, D. Solar Detoxification of Polluted Water: Comparing the Efficiencies of a Parabolic Trough Reactor and a Novel Thin-FilmFixed-Bed Reactor. In Photocatalytic Purification and Treatment of Water and Air. Ollis, D. F., Al-Ekabi, H., Eds.; Elsevier: Amsterdam, The Netherlands, 1993; pp 771-776. (7) Bockelmann, D.; Weichgrebe, D.; Goslich, R.; Bahnemann, D. Concentrating versus Non-Concentrating Reactors for Solar Water Detoxification. Solar Energy Mater. Sol. Cells 1995, 38, 441-451. (8) Klausner, J. F.; Goswami, D. Y. Solar Detoxification of Wastewater Using Nonconcentrating Reactors. AIChE Symp. Ser. 1993, 89, 445-452. (9) Wyness, P.; Klausner, J. F.; Goswami, D. Y.; Schanze, K. S. Performance of Nonconcentrating Solar Photocatalytic Oxidation Reactors, Part I: Flat-Plate Configuration. J. Sol. Energy Eng. 1994, 116, 2-7.

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Received for review December 16, 1997 Revised manuscript received April 27, 1998 Accepted May 31, 1998 IE9709188