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Photocatalysis and radiation absorption in a solar plant
Salmr£no~lWanmots nnd ,~alarC,e k
ELSEVIER
Solar EnergyMaterials and Solar Cells 44 (1996) 199-217
Photocatalysis and radiation absorption in a solar plant D. Curc6 b S. Malato
a
j. Blanco
a
j. G i m r n e z b,*
a Centro de lnuestigaciones Energ~ticas, Medioambientales y Tecnol6gicas, Plataforma Solar de Almeda, Apartado 22, 04200 Tabernas, Almeda, Spain b Departamento de Ingenieda Qulmica, Facultad de Qulmica, Universidad de Barcelona. C/Martl i Franqu£s 1, 08028 Barcelona, Spain
Abstract Recently, many papers have appeared in literature about photocatalytic detoxification. However, progress from laboratory data to the industrial solar reactor is not easy. Kinetic models for heterogeneous catalysis can be used to describe the photocatalytic processes, but luminic steps, related to the radiation, have to be added to the physical and chemical steps considered in heterogeneous catalysis. Thus, the evaluation of the radiation, and its distribution, inside a photocatalytic reactor is essential to extrapolate results from laboratory to outdoor experiments and to compare the efficiency of different installations. This study attempts to validate the experimental set up and theoretical data treatment for this purpose in a Solar Pilot Plant. The procedure consists of the calibration of different sunlight radiometers, the estimation of the radiation inside the reactor, and the validation of the results by actinometric experiments. Finally, a comparison between kinetic constants, for the same reaction in the laboratory (artificial light) and field conditions (sun light), is performed to demonstrate the advantages of knowing the radiation inside a large photochemical reactor. Keywords: Catalysis;Concentratedsolar radiation;Photochemistry; Solar concentrators;Titaniumdioxide
I. Introduction Destruction of pollutant compounds through light-assisted heterogeneous catalysis is a widely discussed topic in the literature [1-5].
* Corresponding author. Fax: 34 3 402 1291. 0927-0248/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0927-0248(96)00059- I
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In a photocatalytic process, the catalyst (usually a semiconductor) absorbs energy of a definite wavelength interval from the incident light, generating electron/hole pairs [6-8]. Part of these charges can be transferred to the semiconductor surface, promoting redox reactions. It has been reported [1-5] that a large number of pollutants are degraded to carbon dioxide a n d / o r other environmentally compatible products if they are in contact with these free charges or intermediate species, such as radicals, which have been generated by these free charges. Photocatalytic detoxification has the advantage, in front of conventional processes, of avoiding the use of other chemical substances, such as oxidants or reductors [9]. The catalyst can be removed from water and the energy for the process can proceed from a clean and cheap supplier, the Sun [1-4]. In a photodetoxification process, the relevant aspects are: the contaminant, the catalyst, and the incoming radiation. From an engineering point of view, the last one is the most important, because several difficulties arise when results from the laboratory are extrapolated to pilot plant scale, and from there to large industrial facilities. Problems related to scale changes and radiation effects on reactors are given by the following factors: (1) geometry and reactor materials, and (2) power and emission spectrum of the radiation source. Taking into account the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models for heterogeneous catalysis, the reaction rate ( r a, tool i ~ s-~) for a photocatalytic process can be written in a general way: r~ = - k f ( c a ) ,
(1)
where k is the global kinetic constant, and f(c~) is a function of the reactant concentration (ca). Some considerations should be outlined about the application of Eq. (l) to describe the kinetics of photocatalytic processes: (a) It is clear that the form of f ( c , ) will depend on the reactions tested and on the experimental conditions. Several expressions for f(c~) are found in literature corresponding to the kinetic studies on the photocatalytic treatment of several pollutants [1-4,10-21]. One of the most widely used in the treatment of organics comes from the consideration of only two elementary reaction steps: adsorption and chemical reaction [20]. Thus, f(c~) can be expressed as K . ca/(l + K . c~), where K is an adsorption constant. Other special cases, for instance the photocatalytic reduction of chromium(VI), lead to exponential expressions such as: f(c~) = c~/2 [5,9,21-23]. This latter expression comes from more complex equations, deduced by applying the LHHW models [23]. (b) Another consideration is the possible photochemical decomposition of the pollutant by light, without the presence of the catalyst, since this leads to more complex kinetic equations for f(ca). In the case of Cr(VI), as in the photocatalytic treatment of other metals like Hg(II), it has been demonstrated that the reaction occurs only when light and semiconductor are used together [9,22-24]. Thus, the homogeneous photochemical reaction in the liquid phase does not occur. (c) In the photocatalytic processes, the reaction rate depends on the radiation absorbed (F~h,~) by the catalyst. This introduces an important difference with respect to the processes of heterogeneous catalysis without light. In this last case, the global kinetic
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201
constant does not vary from one experimental device to another, if the flow models are the same. However, in the photocatalytic processes the change of the experimental device can imply a change in the global kinetic constant. These changes are related to the light used in each case, the reactor geometry and other factors influencing the radiation absorbed by the catalyst. As a consequence of all this, the global kinetic constant, in a photocatalytic process, depends on Fab~ which is related to the catalyst concentration c c. In addition, Fabs also depends on the absorptivity of the other chemicals present in the reactor, since these species can absorb (without reaction) radiation useful for the desired photochemical reaction. Thus, the global kinetic constant can be expressed, in a general form, as follows: k = f ( c c ,Ca,Fabs).
(2)
It is necessary to determine the Fabs associated with the experimental conditions to compare and scale-up results. To calculate Fab~ we need to know the radiation entering the photoreactor (Fer) and to use radiation models for heterogeneous systems. At the same time, as mentioned above, Fab~ depends on the catalyst concentration (cc), and on the absorptivity of the reaction medium, which is related to the reactant concentration (Ca). Thus, the radiation absorbed by the catalyst can be related to the entering radiation by a factor (Fi): (3)
Fab~ = F ~ F , .
The value of this factor could be calculated in three different ways: (a) theoretical models, (b) turbidimetric models, and (c) the effective absorptivity method. A typical example of the first method applied to photocatalysis is proposed by Spadoni et al. [25]. However, this method requires the calculation of certain parameters, like the Albedo one, which is difficult to obtain. Other theoretical models have been introduced [26,27]. In this case, the particles are considered perfectly spherical and non-conducting, and their application to a semiconductor slurry is difficult. At the same time, these slurries, in the case of high concentration, produce multiple light scattering and very often the particles have different sizes. The simulations based on turbidimetric models were used by Yokota et al. [28]. For their application, it is essential to calculate the optical parameters related to the suspension characteristics: particles size, liquid phase absorptivity, etc. The radiation absorbed by the catalyst is then calculated mathematically. The effective absorptivity method is based on the use of a function of Lambert-Beer type: Fab s = F e r [ 1 -
exp( - / z L c c ) ] ,
(4)
where/z is the suspension absorptivity coefficient, L is the light pathway length, and c¢ is the catalyst concentration. This method is very simple to apply and it gives, in some cases, a first estimation of Fabs [23,29]. However, it presents some disadvantages. For instance, it does not allow calculation of the light scattering, which is not measured by radiometric or actinometric techniques. The effect, on light absorption, of the changes in the particles size is not considered. It is difficult to use if the radiation is absorbed by the liquid phase.
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From theoretical and practical points of view, the calculation of F~ is very important. If the experimental conditions (radiation source, spectral distribution, catalyst, contaminant concentration, reactor geometry) are very similar between laboratory and pilot plant, this factor is identical. However, /;~r is always different for every experimental condition, and the calculation of the radiation inside the photoreactor is essential to scale-up results. In the laboratory experiments Fer is usually evaluated in two different ways: (a) Emission models [30] and loss coefficients of the reactor walls and application to the emission spectrum of the radiation source. (b) Actinometric experiments based on chemical reactions in which the rate depends on the power and spectral distribution of the incident light. If the Sun is used as photons source, the results are usually related to the amount of incident radiation per unit of collecting surface (W m 2), but this method does not allow comparison with laboratory results. In the following pages we discuss a method to evaluate the outdoor experiments in the same way as the laboratory ones. The procedure is: (1) radiometer calibration, (2) calculation of the radiation entering and the radiation absorbed in the photoreactor, (3) actinometric experiments, and (4) estimation of the kinetic constant for a chemical reaction.
2. Experimental The installation used for the calculation of Fer belongs to the solar experimental complex Plataforma Solar de Almerfa [31,43]. Fig. 1 illustrates the basic layout, composed of 12 parabolic collectors, four tanks for mixing the solutions and a centrifugal pump. The photoreactor consists of several borosilicate glass tubes (56 mm I.D., 2 mm thick) connected in series and fixed at the collector focus (Helioman-type module, see Fig. 2). The flow model for the experimental system was characterized using stimulus-response techniques [32-34]. Thus, a tracer (inert species) was injected in the reactor inlet and its distribution of concentration was analyzed at the outlet. By this experimental technique, it was demonstrated that, for the flow-rate range tested (500-2000 l/h), the system can be described by a plug flow model [31]. For the experimental conditions tested, temperature does not influence the reaction rate [9,23,35,36]. The same can be said referring to the mass transfer steps [9,23]. The actinometric experiments were carried out with the oxalic-uranyl system [35], used worldwide. The oxalic acid was analyzed by titration with potassium permanganate 0.1 N. The characteristics of the actinometric solution are as follows: - oxalic acid 0.05 M (prepared with H2C204-2HzO A.G.) - uranyl 0.01 M (prepared with (NO3)2UO2-6H20 A.G,) UO~ + h~ (UO~ +)* (excitation step) (UO~+) * + HzC204 ~ UO~ + + CO + CO 2 + H20(oxidationstep)
D. Curc6 et aL / Solar Energy Materials and Solar Cells 44 (1996) 199-217
203
43- Cooling system
Pump ,4
Fig. I. Detoxification Loop Scheme. Several tanks for solutions preparation with different operational modes depending on the experimental conditions. 12 Helioman modules concentrate the radiation inside borosilicate glass tubes by a two-axis sun-tracking system.
Fig. 2. Helioman-type module.
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Table 1 Chemical actinometry characteristics 3.(rim)
P-a (cm- t )
qba (mol/eins)
295 305 315 325 335 345 355 365 375 385 395 405 415 425 435 445 455 465 475 485 495 505 515 525 535
19.630 13.270 9.610 5.790 3.650 1.670 0.810 0.410 0.370 0.370 0.370 0.370 0.350 0.340 0.325 0.258 0.187 0.110 0.055 0.029 0.016 0.009 0.006 0.004 0.003
0.57 0.56 0.56 0.54 0.51 0.51 0.50 0.49 0.49 0.52 0.54 0,56 0,57 0.58 0.58 0.57 0.54 0.47 0.37 0.29 0.22 O.18 0.12 0.08 0.02
Some characteristics of the actinometric solution (absorptivity coefficient and quantum yield) are listed in Table 1. Data appearing in Table 1 come from experimental results obtained in our laboratory, completed with data appearing in literature [35,36]. The quantum yield is independent of the incident light intensity and reaction temperature [35,36]. The quantum yield can vary for high conversions and when the proportion oxalic-uranyl was varied. In our case, conversion was always lower than 13% (except in one experiment, when is reached 20%) and the proportion oxalic-uranyl was always 5:1, as in our laboratory experiments and in experiments described in the literature. The actinometric solution absorptivity, at each wavelength, is: (Absorbedphotons/incidentphotons) = 1 - exp( - / x ~ D ) ,
(5)
where D is the photoreactor I.D. and /z~ is the absorptivity coefficient for the actinometric solution. This absorptivity coefficient remains constant over time since oxalic acid does not absorb radiation in the wavelength range tested (300-535 nm), and uranyl is not consumed by the reaction [36,37]. The quantum yield at each wavelength is defined as: (mols H2C204 reacted/einstein absorbed) = qb~.
(6)
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205
It has been demonstrated that oxalic acid decomposition follows a zero-order kinetics [35,36]. This means that the reaction rate is a function only of the radiation absorbed (Fab~), which in turn is related to the radiation entering (Fer), the quantum yield and the absorptivity coefficient. As these characteristics are wavelength dependent, and the radiation source is not monochromatic, the calculation has to be performed using summatory terms. Under these conditions, the decomposition reaction rate can be written as follows: h = 535 ra=
E q~xFer,A[1-exp(-/xaD)], h = 300
(7)
where Fer,~ is the radiation entering a unit volume of the reactor for each wavelength (interval of 1 nm). The area of the reflective surface of the helioman solar light collector is 32 m 2, while the volume of the reactor is 41.4 1. Thus, the relationship Area/Volume is 0.733 m 2 1and the radiation per unit area is transformed to volume units using this factor.
3. Results and discussion Measurements of spectral solar irradiance, taken over one day using a precision spectroradiometer (LICOR 1800) from 300 nm (minimum wavelength of the Sun radiation received on the surface of the earth), are displayed in Fig. 3, where the incident power per unit area and unit wavelength (Wx, in W m -2 nm -~) is depicted versus the
One Day Between 10:30 and 15:30 0,6 '7
E r-I=
0,4
I---
O
a.
0,2
o 300 31o 320 330
340 350
360
370 380 390 400
Wavelength (nm) Fig. 3. UV-Direct Solar spectrum at the Plataforma Solar de Almer~a. Spectra measured at different times of the day.
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0,03!
~'E¢~0,025t ~ 0,o2 ,-,°
One Day Between 10:30 and 15:30 ( 8 Different Moments of the Day) * Average S p e c t r u ~
/
//~
0,015
:~
0,01
O Z 0,005
o 300
310
320
330
340
350
360
370
Wavelength (nm)
380
390
40(
Fig. 4. NormalizedUV-Direct Solar spectrumand averagespectrum.
wavelength (A). The spectra can be normalized by dividing the W~ at each wavelength by the value obtained from the integration fW~dA between 300 and 400 nm. This wavelength range corresponds to the spectrum interval measured by the pyrheliometer used in the measurement of the UV-Direct power (as explained in the next section). The results are shown in Fig. 4, where it can be seen that the plotting is the same for all the spectra registered during the same day. This excellent agreement indicates that the light wavelength distribution between 300 and 400 nm did not change during the day at the Plataforma Solar de Almerfa. Besides this, the UV-Direct spectral distribution is not expected to change throughout the year for a selected site [38,39], because the relative distribution of this low wavelength radiation is not affected by changeable atmospheric conditions. The major variables that determine the solar irradiance are molecular (Rayleigh) scattering, absorption and scattering by aerosols, absorption and scattering by ozone, and absorption by clouds. Most of these are fixed for a selected site, and the others (clouds, water vapour) do not affect the spectrum between 300 and 400 rim. Thus, Fig. 4 shows the relative UV spectral distribution at the Plataforma Solar de Almer~a (PSA). This is used as a standard for the evaluation of the UV radiation available at the PSA, focused on photochemical and photocatalytic applications. The spectra are drawn up to 404 nm because of the pyrheliometer measuring range, as we explain in the next paragraph, but all the previous considerations are applicable up to 404 nm. Measurements of direct-normal ultraviolet solar radiation have been taken since the beginning of 1991 using a pyrheliometer (Intern. Light, Sed-400) located on solar tracking system (EPPLEY, ST-l). These UV-Direct radiation data are used for the
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
207
Table 2 Spectroradiometer (300-400 nm integral) and W-Direct radiometer measurements Local time 10:31 10:48 11:00 12:41 12:56 12:59 15:25 15:34
Pyrheliometer
Spectroradiometer
(Wm -2)
(W m - 2 )
13.69 16.57 17.43 25.97 27.06 26.96 17.78 17.68
11.68 15.29 16.01 24.49 25.53 25.42 15.62 16.00
Error (%) 17.2 8.4 8.9 6.0 6.0 6. l 13.8 10.5
evaluation of all the photochemical experiments carried out at the PSA, since it is the most suitable way to measure the UV radiation at the same time as the experiments are performed. The correct evaluation requires exact knowledge of the pyrheliometer cut-off point. The technical specifications of this instrument did not state the UV interval used for the original calibration and, for this reason, field measurements of both radiometers (spectroradiometer and pyrheliometer) working at the same time were carded out. The results are reported in Table 2. The spectroradiometer data are the summatory of all the individual radiation values between 300 and 400 nm. The total UV power measured by the pyrheliometer was always greater than that given by the spectroradiometer and the percentage of error was not constant. This may indicate that the pyrheliometer cut-off point is slightly higher than 400 nm. Therefore, it is also necessary to consider an upper limit higher than 400 nm for the spectroradiometer data. Thus, upper limits from 401 to 405 nm were considered for spectroradiometer data. The total radiation measured between 300 nm and these upper limits is indicated in Table 3, where it is also compared with the measurements given by the pyrheliometer, previously indicated in Table 2.
Table 3 Pyrheliometer measurements compared to different spectroradiometer integrating intervals Pyrheliometer
Spectroradiometer
(W m - 2 )
1-401 (W m -~ ) 300 < A < 4 0 1
1-402 (W m -2 ) 300< A<402
1-403 (W m - 2 ) 300 < A < 4 0 3
1-404 (W m - 2 ) 300 < A < 404
1-405 (W m -2 ) 3 0 0 < A < 405
13.69 16.57 17.43 25.97 27.06 26.96 17.78 17.68
11.99 15.69 16.42 25.06 26.12 26.01 15.99 16.39
12.33 16.13 16.87 25.69 26.77 26.66 16.40 16.81
12.67 16.57 17.33 36.34 27.43 27.32 16.81 17.24
12.03 17.01 17.79 26.99 28.11 27.98 17.24 17.67
12.38 17.46 18.25 27.64 28.78 28.65 17.66 18.11
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Table 4 Average error and maximum variability between the pyrheliometer and different spectroradiometer integrating intervals
Average error A max
1-401 (W m -2 ) 300< A<401
1-402 (W m - 2 ) 300 < A < 4 0 2
1-403 (W m - 2 ) 300 < A < 4 0 3
1-404 ( W m 2) 300< A<404
1-405 (W m - 2 ) 300< A<405
14.2 5.6 6.2 3.6 3.6 3.6 11.2 7.9 7.0 10.6
11.0 2.7 3.3 1.1 1.1 1.1 8.4 5.2 4.2 9.9
8.1 0.0 0.0 1.4 1.4 1.3 5.8 2.5 2.6 8,1
5.1 2.6 2.l 3.9 3.9 3.8 3.1 0.0 3.1 5.1
2.3 5.4 4.7 6.4 6.4 6.3 0.0 2.4 4.3 6.3
Table 5 Fraction of power associated to each wavelength (Fig. 4) A (nm)
fa ( n m - i )
h (nm)
f~ ( n m - ~)
300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350 352
0.000102 0.000222 0.000417 0.000617 0.001004 0.001329 0.00185 0.002342 0.002769 0.003241 0.003749 0.004272 0.005 0.005761 0.006576 0.006956 0.00726 0.007417 0.007487 0.007702 0.008125 0.008392 0.008401 0.008503 0.008822 0.009206 0.009655
354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404
0.009856 0.009735 0,009639 0,009966 0.010713 0.011747 0.012692 0.013158 0.013093 0.012705 0.012697 0.013323 0.013829 0.013426 0.01255 0.012178 0.012726 0.013748 0.014311 0.014295 0.014208 0.015356 0.018054 0.021249 0.023404 0.024166
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Table 4 shows the errors (%) of these measurements with respect to those of the pyrheliometer. The maximum difference (A) between the errors is also indicated in each case. From these data it can be concluded that the pyrheliometer measures the UV radiation in the range between 300 and 404 nm. The power associated with a given wavelength (A) can be calculated by multiplying the pyrheliometer total measurement by the fraction of power (fx) associated with this wavelength (see Table 5). This fraction, for each wavelength, is given by the average of the values depicted in Fig. 4, which depicts the relative UV spectral distribution, obtained from Fig. 3 data, as described previously. The photochemical reactor located in the PSA concentrates the incident solar radiation by parabolic mirrors covered by a high UV-reflectivity aluminized film designed for this kind of applications. Although its reflectivity is not constant throughout the UV range (300-400 nm), the difference between maximum and minimum is less than 3%, thus we have considered a fixed value of 84.7% [31]. This value corresponds to a perfectly uniform and clean surface, but the mirrors are continuously outdoors, and lose their original reflectivity with time. To take this into account, the surface characteristics are measured frequently by a reflectometer (WEDEL, FH-PTL). This instrument gives information about the surface behaviour for light reflection and its changes over the time. The values obtained indicate the reflectivity (R R) at any time, and vary between 0 and 1. The reflectometer covers a range of wavelengths higher than 300-400 nm, but it was found that the reflectivity of the aluminized surface was practically the same for all wavelengths. Thus, the data (R R) given by the reflectometer can be used in the useful range (300-400 nm). However, this value has to be corrected by a factor
0,03
1 UV Direct Spectrum (300-404 nm) 0,025 2 U V Spectrum Reflected by PSA AFFilm
'E
3 UV Spectrum Inside Glass Tubes
0,02 a.
~
/ /
/
0,015
O,Ol 0,005
o 300 310 320 330 340 350 360 370 380 390 400 Wavelength
(nm)
Fig. 5. Average spectrum (Fig. 4) and calculated average spectrum inside the photoreactor considering the mirror surface efficiency and the glass tube transmissivity.
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D. Curc6 et aL /Solar Energy Materials and Solar Cells 44 (1996) 199-217
(1.22) calculated from the reactor geometry and the instrument specifications [31], taking into account that the reflections do not take place at a single point (the reactor has a large area). The ultraviolet radiation refected by the parabolic surface reaches the reactive phase through the walls of the glass tubes where the liquid flows (see Fig. 5). This glass has very good UV-light transmissivity properties [31]. In the following sections more details about and a method for the calculation of F~r are explained. In a photocatalytic reaction, the rate usually depends directly on the light absorbed by the catalyst (Fab~, einstein 1-l sec- l) [40] or on its square root ,t ,~-I/z'~ ab~ " [41]. If kinetics is order one with respect to the reactant concentration, and the reaction rate is directly dependent on the radiation absorbed, for a monochromatic light source, the reaction rate can be expressed as: ra, x = -- kaFat,s,xCa,
(8)
where ra, A is the reaction rate (tool 1 1 s - i ) at a wavelength A, k~ is the kinetic constant (1 eins-l), Fab~,x is the absorbed radiation at A (eins 1-J s-J), and c a is the reactant concentration (tool 1- l ). The radiation absorbed by the catalyst is related with the radiation entering the photoreactor (F~r) by Eq. (3), thus: ra, a = -kaFer,xFlC a.
(9)
It is clear that F~ must be lower than 1, because not all the radiation entering the photoreactor can be absorbed by the catalyst. In addition, the radiation entering the photoreactor can be related to the incident radiation, by the expression (for each wavelength): Fer,x = F u ~ . x ( S / V ) I I i . x ( F i , x ) ,
(10)
where Fu~,X is the incident radiation per specular surface unit (eins m -2 s-l), S / V is the ratio between reflectors surface and reactor volume (m 2 1-1), and IIi,x(Fi, ~) is the product of different efficiency coefficients of the experimental system (reflectivity, transmissivity, etc). The incident radiation (Fus) can be calculated, given the incident power per square meter (WT), from Planck's equation:
LWT~ h~Ua
Fu~.X = - - ,
(11)
where A is the wavelength (m), h is Planck's constant (6.626 10 -34 J s), c is the speed of light (3 108 m s-l), Na is Avogadro's number (6.022 10z3), and fx is the fraction of power associated with a single wavelength (see Table 5), and fxWT is the incident radiation at wavelength A. According to the previous Eqs. (9), (10), and (11), and assuming that the photochemical reaction in homogeneous medium can be neglected, the reaction rate can be rewritten, as function of the incident radiation measured by the radiometer (WT), in the form: ra, ~ = - kaF,( S / V ) (hcUa) -I Af~WT Hi,h ( F i x ) c,.
(12)
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\J
211
,ubularpnotoreactor
~ refl~ting mirror Fig. 6. Photoreactor losses scheme.
This equation can be applied to a polychromatic radiation source by summing the ra.a corresponding to each wavelength for the whole wavelength range considered (300-404 nm), then: A =
404
E
ra=-kaFI(S/V)(hcNa)-IWTCa
(13)
(i'( Fi,)f) •
A = 300
In addition, if the semiconductor used as catalyst has a band-gap lower than 404 nm, the previous equation must be restricted to this wavelength limit (Ag): A~A s
ra=-kaFI(S/V)(hcNa)-iWTC
a ~., ( Hi.,( Fi,AIAI,).
(14)
A = 300
The factor IIi,~(Fi, a) is the product of all the system loss coefficients: /-/i,A(F/,A) =
(15)
Fc F~Fr,,~Ft.,~,
where Fc is the collector construction factor (0.91), Fs is the sun tracking error factor (0.92), Fr.a is the mirror reflectivity factor, the value of which is measured periodically by a reflectometer (R R, see below) with a correction constant (F,. a = 1.22 R R) and F~,a is the glass transmissivity, an UV-dependent factor [31]. A scheme of all these correction factors is reported in Fig. 6. Thus, Eq. (13) can be rewritten in the following form: A=Ag
E
ra=-kRFI(S/V)(hcNa)-IWTFcFsl'NNRRCa
(Ft,xAfx).
(16)
h = 300
Most of these parameters are fixed for our reactor, so we
use
FDETOX.Xg:
A=Ag
FOETOX,a,= ( S/V)( hcNa)-l FcF~l.22RR E X = 300
(F,,aAfa),
(17a)
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D. Curc6 et al./ Solar Energy Materials and Solar Cells 44 (1996) 199-217
where ( S / V ) band-gap is:
is 0.773 m 2 1-l, thus FDETOX,Ag for a catalyst with a 385 or 404 nm
FDETOX,385 = 1.86 10-6RR,
(17b)
FDETOX,404 = 2.94 10-6RR .
(17c)
And Eq. (16) is reduced to the following simple expression: G = - ka Fj Wv FDETOX,AgCa.
(18)
The definition of FDETOx or any other empirical efficiency parameter for a photochemical reactor needs the following steps: (a) Definition of all the efficiency factors involved in the radiation distribution. (b) Relationship between power flux and photon flux by spectral measurements. (c) Light concentration ratio ( S / V ) of the system. (d) Catalyst band-gap Ag (if the reaction is photocatalytical) and liquid phase absorptivity (if necessary). (e) Experimental demonstration of these calculations by the appropriate actinometric experiments. Several actinometries were carried out at the PSA to demonstrate the good fitting of the previous equations. The value of FDETOX,Ag(dependent only on the mirror reflectivity) and the UV-Direct radiation will be enough for the continuous evaluation of the radiation entering the reactor if these equations can be used with confidence. Due to the high cost of the acfinometric solution (uranyl salt) and the low conversion desired (less than 20%) only o n e helioman module (6th, Fig. 1) and a small tank (two hundred litres approx.) connected to all the reactor instruments were used. The solution was recirculated until the perfect mixing of the products was achieved and afterwards the module was focused. The oxalic acid concentration was analyzed after one pass through the reactor at the same time as solar radiation was registered with the pyrheliometer and the spectroradiometer. Table 6 summarizes the experimental conditions of these actinometries. The calculation procedure is as follows: (a) During the experiment the solar spectrum between 300 nm and 535 nrn is registered (active interval of the solution, see Table 1). (b) All the system efficiencies and S / V ratio are applied to the spectral data. (c) In this case, the reaction is zero order with respect to the oxalic acid concentration, i.e., c a in Eq. (9) disappears. In addition, F 1 could be assimilated, in a non-disper-
Table 6 Chemical actinometries summary. Experimental conversion compared to calculated conversion Actinometry 1 2 3 4 Experimental Period Residence time (s) Oxalic acid Initial conc. (M) Oxalic acid Final conc. (M) Conversion (%) Calculated conversion (%)
10:49/11:02 137 4.82 10-2 4.2 10-z 13 16
12:38/12:48 103 4.65 10-2 3.70 10-2 20 17
13:51/13:57 66 5.17 10 2 4.75 10-~8 10
15:18/15:27 106 5.45 10-2 5.12 10-2 6 7
D. Curc6 et a l . / Solar Energy Materials and Solar Cells 44 (1996) 199-217
213
sive medium, to [1 - e x p ( - p.~D)], and k a to the quantum yield ~ . Thus, Eq. (13) can be rewritten as follows: A~535
ra=-(S/V)(hcNa)-IW4
~_, ( I I i , x ( F i , a ) h f ~ a [ 1 - e x p ( - I ~ x D ) ] ) ,
(19)
h = 300
where Wr' and fx' have the same meaning as W r and fx in the new 300-535 nm range. (d) The procedure for the calculation, by Eq. (19), of the expected conversion (X in %) for the oxalic acid is the following:
c ( t f ) = c( t o) + ~_, t i r(t 0 = 0, t n = one - pass residence time),
(20)
i=0 n
c(tf) = C( to) - ( S / V ) (
hcNa) -1 ~.,( W~,iti) i=0
A=535
X
~., ( l - l i . a ( F i , a ) h f ~ d P a [ 1 - e x p ( - I z a D ) ] ) ,
(21)
h = 300
X = 100
c(to) - c(te) C( to )
(22)
Table 6 shows a comparison between the values of the conversion, X, calculated from Eq. (22), where c(t e) is either the experimental value, or the value obtained from Eq. (21). We consider FDETOx enough confident because the values of the conversion obtained using experimental concentrations or these ones coming from photon flux equations (see Eq. (21)) are quite similar. As an example, the reaction considered is the photocatalytic reduction of Cr(VI) to Cr(III). This reaction has a half order kinetics with respect to the Cr(VI) concentration at pH < 2, and using TiO 2 Degussa P-25 as catalyst [9,22,23]. Thus, the reaction rate can be expressed (according to Eq. (9)) as:
r, = dc / d t = - kaFer F1 cl/2.
(23)
The catalyst band-gap is 385 nm, thus Fer must be calculated from FDETOX,385.The system has different tanks and pipes for solution recirculation, but the only illuminated part is the reactor (glass tubes). Therefore, the factor Fer refers only to this illuminated part (reactor). Thus, if we work under perfect mixing flow conditions, ~ichieved by using few heliomans and high flow-rates, it is necessary to correct the volume in the following manner:
d c / d t = - k~Fcr F,( Vu/Vt) c ~/2 ,
(24)
where V u is the useful volume (glass tubes) and Vt is the total volume (glass tubes, tank and connection pipes). If we apply FDETOX,385,taking into account Eqs. (16), (17), and (18):
d c / d t = - k~ r l W T ( t ) FDETOx , 3 8 5 ( V u / / V t ) c1/2,
(25)
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D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
and integrating: C1/2 "~ C1/2 -- ( 1 / / 2 ) kaF1FDETOX ,385(gu//Vt) ,~tiWT(t),
(26)
where Co is the Cr(VI) initial concentration. Results are shown in Fig. 7 for an experiment with a TiO 2 concentration of 2 g 1-1. The kinetic constant (k a F 1) fitted using equation 26 was 65 ppm 1/2 1 eins-1. The values obtained at PSA were compared with these ones obtained at the laboratory level. Thus, a k~ F 1 value of 68 ppm 1/2 1 eins- 1 was obtained for experiments carried out in a Solarbox, using a Xe lamp (spectrum very close to the solar one) and flat reactors [42]. It can be concluded that, using different reactor geometries, the values obtained for k a F 1 are very close at the laboratory and pilot plant levels. This means that the method proposed takes into account the characteristics of the different experimental systems. Thus, the kinetic constants obtained can be more useful for the change of scale. Another application of this method could be found in the pentachlorophenol, TiO 2 mediated, photocatalytic degradation at the PSA Solar Detoxification Reactor, previously reported [43]. This compound follows an apparent first-order rate equation when the initial concentration (c o) is small: l n ( c 0 / c ) = kapt,
(27)
where t is the illumination time corresponding to each sample. Fittings of the data of two different experiments, carried out under the same conditions but at different moments of the day (early in the morning and at noon), give kap = 0.239 min- t and kap = 0.368 min- t, respectively. The same fittings can be performed, but using the expression:
In co/c = k'a e,
(28)
1 ~ . ~ .
¸
.
•
f "0
2i
• •
experimental
- - fitted o o
0,02
0,04 Radlation
0,06
0,08
0,1
(eins/l)
Fig. 7. Cr(VI) photoreduction as function of incident radiation per unit volume of the photoreactor.
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
215
where:
El+ , = E, + F~r,,+ l(ti+, - ti),
(29)
and considering that E (eins l - l ) is the radiation received by each sample, Fer is calculated by Eqs. (10)-(17), and t is the illumination time. Thus, using these last equations, the values obtained were kap = 187 eins-1 1 and kap = 173 eins-I 1. The discrepancy between the results of experiments performed in different radiation conditions disappears if this method is applied.
4. Conclusions A method for radiation evaluation inside a solar reactor is proposed together with a validation method. Before the beginning of the outdoor experiments with the Sun as radiation source, it is necessary to study the efficiency of the experimental set-up and the available solar spectrum if comparison with other reactors and experimental conditions is desired. The calculation of the kinetic constants in terms of rate per useful radiation can help us to determine the influence of other parameters involved in the reaction efficiency.
Acknowledgements The authors are grateful to the Comisi6n Interministerial de Ciencia y Tecnologla (CICYT) (project AMB95-0885-C02-02) for funds received to carry out this work.
References [1] M. Schiavello (Ed.), Photocatalysis and Environment. Trends and Applications, NATO ASI Series, Series C: Mathematical and Physical Sciences, Vol. 237 (Kluwer Academic Publishers, Dordrecht, 1988). [2] N. Serpone and E. Pelizzetti (Eds.), Photocatalysis, Fundamentals and Applications (Wiley, New York, 1989). [3] D.F. OUis and H. A1-Ekabi (Eds.), Photocatalytic Purification and Treatment of Water and Air (Elsevier Science, Amsterdam, 1993). [4] D.E. Klett, R. Hogan and T. Tanaka (Eds.), Solar Engineering (The American Society of Mechanical Engineers, New York, 1994). [5] J. Sabat6, M.A. Anderson, M.A. Aguado, J. Gim6nez, S. Cervera-March and C.G. Hill, Jr., Comparison of TiO 2 powder suspensions and TiO 2 ceramic membranes supported on glass as photocalytic systems in the reduction of chromium(VI), J. Molecular Catalysis 71 (1992) 57. [6] M. Gr'~itzel(Ed.), Energy Resources through Photochemistry and Catalysis (Academic Press, New York, 1983). [7] M. Schiavello (Ed.), Photoelectrochemistry, Photocatalysis and Photoreactors: Fundamentals and Development, NATO ASI Series, Series C: Mathematical and Physical Sciences, Vol. 146 (Riedel, Dordrecht, 1985). [8] S.L. Nathan and M.L. Rosenbluth, Theory of semiconductor materials, in: N. Serpone and E. Pelizzetti (Eds.), Photocatalysis, Fundamentals and Applications, Ch. 3 (Wiley, New York, 1989). [9] M.A. Aguado, J. Gim6nez and S. Cervera-March, Continuous photocatalytic treatment of Cr(VI) effluents with semiconductor powders, Chem. Eng. Comm. 104 (1991) 71.
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[10] H. Al-Ekabi and N. Serpone, Kinetic studies in heterogeneous photocatalysis. 1. Photocatalytic degradation of chlorinated phenol in aerated aqueous solutions over TiO 2 supported on glass matrix, J. Phys. Chem. 92 (1988) 5726. [11] H. Gerischer and A. Heller, The role of oxygen in photooxidation of organic molecules on semiconductor particles, J. Phys. Chem. 95 (1991) 5261. [12] H. Gerischer and A. Heller, Photocatalytic oxidation of organic molecules on TiO 2 particles by sunlight in aerated water, J. Electrochem. Soc. 139 (1992) 113. [13] Y. Mao, C. Schoeneich and K.D. Asmus, Identification of organic acids and other intermediates in oxidative degradation of chlorinated ethanes on TiO 2 surfaces en route to mineralization: A combined photocatalytic and radiation chemical study, J. Phys. Chem. 95 (1993) 10080. [14] R. Terzian, N. Serpone, C. Minero and E. Pelizzetti, Photocatalyzed mineralization of creols in aqueous media with irradiated titania, J. Catal. 128 (1991) 352. [15] M. Trillas, J. Peral, X. Domenech and J. Gimenez, Photocatalytic oxidation of phenol and 2,4-dichlorophenol over TiO2, in: D.E. Klett, R.E Hogan and T. Tanaka (Eds.), Solar Engineering, (The American Society of Mechanical Engineers, New York, 1994) p. 171. [16] T. Nguyen and D.F. Ollis, Complete heterogeneously photocatalyzed transformation of 1,1- and 1,2-dibromoethane to CO 2 and HBr, J. Phys. Chem. 88 (1984) 3386. [17] K. Okamoto, Y. Yamamoto, H. Tanaka and A. Itaya, Heterogeneous photocatalytic decomposition of phenol over TiO 2 powder, Bull. Chem. Soc. Japan 58 (1985) 2015. [18] K. Okamoto, Y. Yamamoto, H, Tanaka and A. Itaya, Kinetics of heterogeneous photocatalytic decomposition of phenol over anatase TiO 2 powder, Bull. Chem. Soc. Japan 58 (1985) 2023. [19] C.S. Turchi and D.F. Ollis, Photocatalytic degradation of organic water contaminants: Mechanisms involving hydroxyl radical attack, J. Catalysis i22 (1990) 178. [20] J. Cunningham and P. Sedlak, Initial rates of TiO2-Photocatalysed degradation of water pollutants: Influences of adsorption, pH and photon-flux, in: D.F. Ollis and H. A1-Ekabi (Eds.), Photocatalytic Purification and Treatment of Water and Air (Elsevier Science, Amsterdam, 1993) p. 67. [21] H. Yoneyama, Y. Yamashita and H. Tamura, Heterogeneous photocatalytic reduction of dichromate on n-type semiconductor catalysts, Nature 282 (1979) 817. [22] M.A. Aguado, J. Gimenez, R. Simarro and S. Cervera-March, A new continuous device to perform S-L-G photocatalytic studies, Solar Energy 49 (1992) 47. [23] M.A. Aguado, Modelado de procesos de tratamiento fotocatalRico de cromo y mercurio en disoluci6n, Doctoral Thesis (University of Barcelona, 1990). [24] M.A. Aguado, S. Cervera-March and J. Gim6nez, Continuous photocatalytic treatment of mercury(II) on titania powders. Kinetics and catalyst activity, Chem. Eng. Sci. 50 (1995) 1561. [25] G. Spadoni, E. Bandini and F. Santarelli, Scattering effects in photosensitized reactions, Chem. Eng. Sci. 33 (1978) 517. [26] H.C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957). [27] D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier Science, Amsterdam, 1969). [28] T. Yokota, Y. Takahata, H. Nanjo and K. Takahashi, Estimation of the light intensity in a solid-liquid photoreaction system (Private Communication, 1985). [29] V. Augliaro, L. Parmisano and M. Schiavello, Photon Absorption by aqueous TiO 2 dispersion contained in a stirred photoreactor, AIChE J. 37(7) (1991) 1096. [30] H.A. Irazoqui, J. Cer&i and A.E. Cassano, Radiation profiles in a empty photoreactor with a source of finite spatial dimensions, AICHE 19(3)(1973)460. [31] J. Blanco et al., Final configuration of PSA solar detoxification loop, Technical Report TR06/91 (Plataforma Solar de Almerla, Almerla, 1991). [32] D.M. Himmelblau and K.B. Bischoff, Process Analysis and Simulation (Wiley, New York, 1968) p. 59. [33] O. Levenspiel, Chemical Reaction Engineering, 2nd ed. (Wiley, New York, 1972) p. 253. [34] Ch.G. Hill, Jr., An Introduction to Chemical Engineering Kinetics and Reactor Design (Wiley, New York, 1977) p. 388. [35] J.F. Rabek, Experimental Methods in Photochemistry and Photophysics, Vol. 2, Ch. 27 (Wiley, New York, 1982).
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[36] A.E. Cassano, Uso de actin6metros en reactores tubulares continuos, Revista de la Facultad de Ingenierfa Qulmica, Santa Fe (Argentina) 37 (1968) 469. [37] M. Vicente and S. Esplugas, Calibrado del fotorreactor anular, Afinidad 40 (1983) 453. [38] F. Cbenlo and F. Fabero, An~lisis de la distribuci6n espectral de la radiaci6n solar en Madrid, ISES Espa~a, V Congreso Iberico y IV Congreso Iberoamericano, Madrid, October 1990. [39] J.C. Riordan, Influence of atmospheric conditions and air mass on the ratio of ultraviolet to total solar radiation, SERI/TP-215-3895, August 1990. [40] T. Sakata and T. Kawai, Photosynthesis with semiconductor powders, in: M. Gr'~itzel (Ed.), Energy Resources Through Photochemistry and Catalysis (Academic Press, New York, 1983) p. 353. [41] H. Al-Ekabi and N. Serpone, Mechanistic implications in surface photochemistry, in: N. Serpone and E. Pelizzetti (Eds.), Photocatalysis, Fundamentals and Applications, Ch. 14 (Wiley, New York, 1989). [42] D. Curc6, Kinetic and radiation models for photocatalytic processes, Doctoral Thesis (University of Barcelona, 1994). [43] C. Minero, E. Pelizzetti, S. Malato and J. Blanco, Large solar plant photocatalytic water decontamination: degradation of pentachlorophenol, Chemosphere 26 (1993) 2103.
ELSEVIER
Solar EnergyMaterials and Solar Cells 44 (1996) 199-217
Photocatalysis and radiation absorption in a solar plant D. Curc6 b S. Malato
a
j. Blanco
a
j. G i m r n e z b,*
a Centro de lnuestigaciones Energ~ticas, Medioambientales y Tecnol6gicas, Plataforma Solar de Almeda, Apartado 22, 04200 Tabernas, Almeda, Spain b Departamento de Ingenieda Qulmica, Facultad de Qulmica, Universidad de Barcelona. C/Martl i Franqu£s 1, 08028 Barcelona, Spain
Abstract Recently, many papers have appeared in literature about photocatalytic detoxification. However, progress from laboratory data to the industrial solar reactor is not easy. Kinetic models for heterogeneous catalysis can be used to describe the photocatalytic processes, but luminic steps, related to the radiation, have to be added to the physical and chemical steps considered in heterogeneous catalysis. Thus, the evaluation of the radiation, and its distribution, inside a photocatalytic reactor is essential to extrapolate results from laboratory to outdoor experiments and to compare the efficiency of different installations. This study attempts to validate the experimental set up and theoretical data treatment for this purpose in a Solar Pilot Plant. The procedure consists of the calibration of different sunlight radiometers, the estimation of the radiation inside the reactor, and the validation of the results by actinometric experiments. Finally, a comparison between kinetic constants, for the same reaction in the laboratory (artificial light) and field conditions (sun light), is performed to demonstrate the advantages of knowing the radiation inside a large photochemical reactor. Keywords: Catalysis;Concentratedsolar radiation;Photochemistry; Solar concentrators;Titaniumdioxide
I. Introduction Destruction of pollutant compounds through light-assisted heterogeneous catalysis is a widely discussed topic in the literature [1-5].
* Corresponding author. Fax: 34 3 402 1291. 0927-0248/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0927-0248(96)00059- I
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In a photocatalytic process, the catalyst (usually a semiconductor) absorbs energy of a definite wavelength interval from the incident light, generating electron/hole pairs [6-8]. Part of these charges can be transferred to the semiconductor surface, promoting redox reactions. It has been reported [1-5] that a large number of pollutants are degraded to carbon dioxide a n d / o r other environmentally compatible products if they are in contact with these free charges or intermediate species, such as radicals, which have been generated by these free charges. Photocatalytic detoxification has the advantage, in front of conventional processes, of avoiding the use of other chemical substances, such as oxidants or reductors [9]. The catalyst can be removed from water and the energy for the process can proceed from a clean and cheap supplier, the Sun [1-4]. In a photodetoxification process, the relevant aspects are: the contaminant, the catalyst, and the incoming radiation. From an engineering point of view, the last one is the most important, because several difficulties arise when results from the laboratory are extrapolated to pilot plant scale, and from there to large industrial facilities. Problems related to scale changes and radiation effects on reactors are given by the following factors: (1) geometry and reactor materials, and (2) power and emission spectrum of the radiation source. Taking into account the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models for heterogeneous catalysis, the reaction rate ( r a, tool i ~ s-~) for a photocatalytic process can be written in a general way: r~ = - k f ( c a ) ,
(1)
where k is the global kinetic constant, and f(c~) is a function of the reactant concentration (ca). Some considerations should be outlined about the application of Eq. (l) to describe the kinetics of photocatalytic processes: (a) It is clear that the form of f ( c , ) will depend on the reactions tested and on the experimental conditions. Several expressions for f(c~) are found in literature corresponding to the kinetic studies on the photocatalytic treatment of several pollutants [1-4,10-21]. One of the most widely used in the treatment of organics comes from the consideration of only two elementary reaction steps: adsorption and chemical reaction [20]. Thus, f(c~) can be expressed as K . ca/(l + K . c~), where K is an adsorption constant. Other special cases, for instance the photocatalytic reduction of chromium(VI), lead to exponential expressions such as: f(c~) = c~/2 [5,9,21-23]. This latter expression comes from more complex equations, deduced by applying the LHHW models [23]. (b) Another consideration is the possible photochemical decomposition of the pollutant by light, without the presence of the catalyst, since this leads to more complex kinetic equations for f(ca). In the case of Cr(VI), as in the photocatalytic treatment of other metals like Hg(II), it has been demonstrated that the reaction occurs only when light and semiconductor are used together [9,22-24]. Thus, the homogeneous photochemical reaction in the liquid phase does not occur. (c) In the photocatalytic processes, the reaction rate depends on the radiation absorbed (F~h,~) by the catalyst. This introduces an important difference with respect to the processes of heterogeneous catalysis without light. In this last case, the global kinetic
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
201
constant does not vary from one experimental device to another, if the flow models are the same. However, in the photocatalytic processes the change of the experimental device can imply a change in the global kinetic constant. These changes are related to the light used in each case, the reactor geometry and other factors influencing the radiation absorbed by the catalyst. As a consequence of all this, the global kinetic constant, in a photocatalytic process, depends on Fab~ which is related to the catalyst concentration c c. In addition, Fabs also depends on the absorptivity of the other chemicals present in the reactor, since these species can absorb (without reaction) radiation useful for the desired photochemical reaction. Thus, the global kinetic constant can be expressed, in a general form, as follows: k = f ( c c ,Ca,Fabs).
(2)
It is necessary to determine the Fabs associated with the experimental conditions to compare and scale-up results. To calculate Fab~ we need to know the radiation entering the photoreactor (Fer) and to use radiation models for heterogeneous systems. At the same time, as mentioned above, Fab~ depends on the catalyst concentration (cc), and on the absorptivity of the reaction medium, which is related to the reactant concentration (Ca). Thus, the radiation absorbed by the catalyst can be related to the entering radiation by a factor (Fi): (3)
Fab~ = F ~ F , .
The value of this factor could be calculated in three different ways: (a) theoretical models, (b) turbidimetric models, and (c) the effective absorptivity method. A typical example of the first method applied to photocatalysis is proposed by Spadoni et al. [25]. However, this method requires the calculation of certain parameters, like the Albedo one, which is difficult to obtain. Other theoretical models have been introduced [26,27]. In this case, the particles are considered perfectly spherical and non-conducting, and their application to a semiconductor slurry is difficult. At the same time, these slurries, in the case of high concentration, produce multiple light scattering and very often the particles have different sizes. The simulations based on turbidimetric models were used by Yokota et al. [28]. For their application, it is essential to calculate the optical parameters related to the suspension characteristics: particles size, liquid phase absorptivity, etc. The radiation absorbed by the catalyst is then calculated mathematically. The effective absorptivity method is based on the use of a function of Lambert-Beer type: Fab s = F e r [ 1 -
exp( - / z L c c ) ] ,
(4)
where/z is the suspension absorptivity coefficient, L is the light pathway length, and c¢ is the catalyst concentration. This method is very simple to apply and it gives, in some cases, a first estimation of Fabs [23,29]. However, it presents some disadvantages. For instance, it does not allow calculation of the light scattering, which is not measured by radiometric or actinometric techniques. The effect, on light absorption, of the changes in the particles size is not considered. It is difficult to use if the radiation is absorbed by the liquid phase.
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From theoretical and practical points of view, the calculation of F~ is very important. If the experimental conditions (radiation source, spectral distribution, catalyst, contaminant concentration, reactor geometry) are very similar between laboratory and pilot plant, this factor is identical. However, /;~r is always different for every experimental condition, and the calculation of the radiation inside the photoreactor is essential to scale-up results. In the laboratory experiments Fer is usually evaluated in two different ways: (a) Emission models [30] and loss coefficients of the reactor walls and application to the emission spectrum of the radiation source. (b) Actinometric experiments based on chemical reactions in which the rate depends on the power and spectral distribution of the incident light. If the Sun is used as photons source, the results are usually related to the amount of incident radiation per unit of collecting surface (W m 2), but this method does not allow comparison with laboratory results. In the following pages we discuss a method to evaluate the outdoor experiments in the same way as the laboratory ones. The procedure is: (1) radiometer calibration, (2) calculation of the radiation entering and the radiation absorbed in the photoreactor, (3) actinometric experiments, and (4) estimation of the kinetic constant for a chemical reaction.
2. Experimental The installation used for the calculation of Fer belongs to the solar experimental complex Plataforma Solar de Almerfa [31,43]. Fig. 1 illustrates the basic layout, composed of 12 parabolic collectors, four tanks for mixing the solutions and a centrifugal pump. The photoreactor consists of several borosilicate glass tubes (56 mm I.D., 2 mm thick) connected in series and fixed at the collector focus (Helioman-type module, see Fig. 2). The flow model for the experimental system was characterized using stimulus-response techniques [32-34]. Thus, a tracer (inert species) was injected in the reactor inlet and its distribution of concentration was analyzed at the outlet. By this experimental technique, it was demonstrated that, for the flow-rate range tested (500-2000 l/h), the system can be described by a plug flow model [31]. For the experimental conditions tested, temperature does not influence the reaction rate [9,23,35,36]. The same can be said referring to the mass transfer steps [9,23]. The actinometric experiments were carried out with the oxalic-uranyl system [35], used worldwide. The oxalic acid was analyzed by titration with potassium permanganate 0.1 N. The characteristics of the actinometric solution are as follows: - oxalic acid 0.05 M (prepared with H2C204-2HzO A.G.) - uranyl 0.01 M (prepared with (NO3)2UO2-6H20 A.G,) UO~ + h~ (UO~ +)* (excitation step) (UO~+) * + HzC204 ~ UO~ + + CO + CO 2 + H20(oxidationstep)
D. Curc6 et aL / Solar Energy Materials and Solar Cells 44 (1996) 199-217
203
43- Cooling system
Pump ,4
Fig. I. Detoxification Loop Scheme. Several tanks for solutions preparation with different operational modes depending on the experimental conditions. 12 Helioman modules concentrate the radiation inside borosilicate glass tubes by a two-axis sun-tracking system.
Fig. 2. Helioman-type module.
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Table 1 Chemical actinometry characteristics 3.(rim)
P-a (cm- t )
qba (mol/eins)
295 305 315 325 335 345 355 365 375 385 395 405 415 425 435 445 455 465 475 485 495 505 515 525 535
19.630 13.270 9.610 5.790 3.650 1.670 0.810 0.410 0.370 0.370 0.370 0.370 0.350 0.340 0.325 0.258 0.187 0.110 0.055 0.029 0.016 0.009 0.006 0.004 0.003
0.57 0.56 0.56 0.54 0.51 0.51 0.50 0.49 0.49 0.52 0.54 0,56 0,57 0.58 0.58 0.57 0.54 0.47 0.37 0.29 0.22 O.18 0.12 0.08 0.02
Some characteristics of the actinometric solution (absorptivity coefficient and quantum yield) are listed in Table 1. Data appearing in Table 1 come from experimental results obtained in our laboratory, completed with data appearing in literature [35,36]. The quantum yield is independent of the incident light intensity and reaction temperature [35,36]. The quantum yield can vary for high conversions and when the proportion oxalic-uranyl was varied. In our case, conversion was always lower than 13% (except in one experiment, when is reached 20%) and the proportion oxalic-uranyl was always 5:1, as in our laboratory experiments and in experiments described in the literature. The actinometric solution absorptivity, at each wavelength, is: (Absorbedphotons/incidentphotons) = 1 - exp( - / x ~ D ) ,
(5)
where D is the photoreactor I.D. and /z~ is the absorptivity coefficient for the actinometric solution. This absorptivity coefficient remains constant over time since oxalic acid does not absorb radiation in the wavelength range tested (300-535 nm), and uranyl is not consumed by the reaction [36,37]. The quantum yield at each wavelength is defined as: (mols H2C204 reacted/einstein absorbed) = qb~.
(6)
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205
It has been demonstrated that oxalic acid decomposition follows a zero-order kinetics [35,36]. This means that the reaction rate is a function only of the radiation absorbed (Fab~), which in turn is related to the radiation entering (Fer), the quantum yield and the absorptivity coefficient. As these characteristics are wavelength dependent, and the radiation source is not monochromatic, the calculation has to be performed using summatory terms. Under these conditions, the decomposition reaction rate can be written as follows: h = 535 ra=
E q~xFer,A[1-exp(-/xaD)], h = 300
(7)
where Fer,~ is the radiation entering a unit volume of the reactor for each wavelength (interval of 1 nm). The area of the reflective surface of the helioman solar light collector is 32 m 2, while the volume of the reactor is 41.4 1. Thus, the relationship Area/Volume is 0.733 m 2 1and the radiation per unit area is transformed to volume units using this factor.
3. Results and discussion Measurements of spectral solar irradiance, taken over one day using a precision spectroradiometer (LICOR 1800) from 300 nm (minimum wavelength of the Sun radiation received on the surface of the earth), are displayed in Fig. 3, where the incident power per unit area and unit wavelength (Wx, in W m -2 nm -~) is depicted versus the
One Day Between 10:30 and 15:30 0,6 '7
E r-I=
0,4
I---
O
a.
0,2
o 300 31o 320 330
340 350
360
370 380 390 400
Wavelength (nm) Fig. 3. UV-Direct Solar spectrum at the Plataforma Solar de Almer~a. Spectra measured at different times of the day.
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0,03!
~'E¢~0,025t ~ 0,o2 ,-,°
One Day Between 10:30 and 15:30 ( 8 Different Moments of the Day) * Average S p e c t r u ~
/
//~
0,015
:~
0,01
O Z 0,005
o 300
310
320
330
340
350
360
370
Wavelength (nm)
380
390
40(
Fig. 4. NormalizedUV-Direct Solar spectrumand averagespectrum.
wavelength (A). The spectra can be normalized by dividing the W~ at each wavelength by the value obtained from the integration fW~dA between 300 and 400 nm. This wavelength range corresponds to the spectrum interval measured by the pyrheliometer used in the measurement of the UV-Direct power (as explained in the next section). The results are shown in Fig. 4, where it can be seen that the plotting is the same for all the spectra registered during the same day. This excellent agreement indicates that the light wavelength distribution between 300 and 400 nm did not change during the day at the Plataforma Solar de Almerfa. Besides this, the UV-Direct spectral distribution is not expected to change throughout the year for a selected site [38,39], because the relative distribution of this low wavelength radiation is not affected by changeable atmospheric conditions. The major variables that determine the solar irradiance are molecular (Rayleigh) scattering, absorption and scattering by aerosols, absorption and scattering by ozone, and absorption by clouds. Most of these are fixed for a selected site, and the others (clouds, water vapour) do not affect the spectrum between 300 and 400 rim. Thus, Fig. 4 shows the relative UV spectral distribution at the Plataforma Solar de Almer~a (PSA). This is used as a standard for the evaluation of the UV radiation available at the PSA, focused on photochemical and photocatalytic applications. The spectra are drawn up to 404 nm because of the pyrheliometer measuring range, as we explain in the next paragraph, but all the previous considerations are applicable up to 404 nm. Measurements of direct-normal ultraviolet solar radiation have been taken since the beginning of 1991 using a pyrheliometer (Intern. Light, Sed-400) located on solar tracking system (EPPLEY, ST-l). These UV-Direct radiation data are used for the
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
207
Table 2 Spectroradiometer (300-400 nm integral) and W-Direct radiometer measurements Local time 10:31 10:48 11:00 12:41 12:56 12:59 15:25 15:34
Pyrheliometer
Spectroradiometer
(Wm -2)
(W m - 2 )
13.69 16.57 17.43 25.97 27.06 26.96 17.78 17.68
11.68 15.29 16.01 24.49 25.53 25.42 15.62 16.00
Error (%) 17.2 8.4 8.9 6.0 6.0 6. l 13.8 10.5
evaluation of all the photochemical experiments carried out at the PSA, since it is the most suitable way to measure the UV radiation at the same time as the experiments are performed. The correct evaluation requires exact knowledge of the pyrheliometer cut-off point. The technical specifications of this instrument did not state the UV interval used for the original calibration and, for this reason, field measurements of both radiometers (spectroradiometer and pyrheliometer) working at the same time were carded out. The results are reported in Table 2. The spectroradiometer data are the summatory of all the individual radiation values between 300 and 400 nm. The total UV power measured by the pyrheliometer was always greater than that given by the spectroradiometer and the percentage of error was not constant. This may indicate that the pyrheliometer cut-off point is slightly higher than 400 nm. Therefore, it is also necessary to consider an upper limit higher than 400 nm for the spectroradiometer data. Thus, upper limits from 401 to 405 nm were considered for spectroradiometer data. The total radiation measured between 300 nm and these upper limits is indicated in Table 3, where it is also compared with the measurements given by the pyrheliometer, previously indicated in Table 2.
Table 3 Pyrheliometer measurements compared to different spectroradiometer integrating intervals Pyrheliometer
Spectroradiometer
(W m - 2 )
1-401 (W m -~ ) 300 < A < 4 0 1
1-402 (W m -2 ) 300< A<402
1-403 (W m - 2 ) 300 < A < 4 0 3
1-404 (W m - 2 ) 300 < A < 404
1-405 (W m -2 ) 3 0 0 < A < 405
13.69 16.57 17.43 25.97 27.06 26.96 17.78 17.68
11.99 15.69 16.42 25.06 26.12 26.01 15.99 16.39
12.33 16.13 16.87 25.69 26.77 26.66 16.40 16.81
12.67 16.57 17.33 36.34 27.43 27.32 16.81 17.24
12.03 17.01 17.79 26.99 28.11 27.98 17.24 17.67
12.38 17.46 18.25 27.64 28.78 28.65 17.66 18.11
208
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
Table 4 Average error and maximum variability between the pyrheliometer and different spectroradiometer integrating intervals
Average error A max
1-401 (W m -2 ) 300< A<401
1-402 (W m - 2 ) 300 < A < 4 0 2
1-403 (W m - 2 ) 300 < A < 4 0 3
1-404 ( W m 2) 300< A<404
1-405 (W m - 2 ) 300< A<405
14.2 5.6 6.2 3.6 3.6 3.6 11.2 7.9 7.0 10.6
11.0 2.7 3.3 1.1 1.1 1.1 8.4 5.2 4.2 9.9
8.1 0.0 0.0 1.4 1.4 1.3 5.8 2.5 2.6 8,1
5.1 2.6 2.l 3.9 3.9 3.8 3.1 0.0 3.1 5.1
2.3 5.4 4.7 6.4 6.4 6.3 0.0 2.4 4.3 6.3
Table 5 Fraction of power associated to each wavelength (Fig. 4) A (nm)
fa ( n m - i )
h (nm)
f~ ( n m - ~)
300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350 352
0.000102 0.000222 0.000417 0.000617 0.001004 0.001329 0.00185 0.002342 0.002769 0.003241 0.003749 0.004272 0.005 0.005761 0.006576 0.006956 0.00726 0.007417 0.007487 0.007702 0.008125 0.008392 0.008401 0.008503 0.008822 0.009206 0.009655
354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404
0.009856 0.009735 0,009639 0,009966 0.010713 0.011747 0.012692 0.013158 0.013093 0.012705 0.012697 0.013323 0.013829 0.013426 0.01255 0.012178 0.012726 0.013748 0.014311 0.014295 0.014208 0.015356 0.018054 0.021249 0.023404 0.024166
209
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
Table 4 shows the errors (%) of these measurements with respect to those of the pyrheliometer. The maximum difference (A) between the errors is also indicated in each case. From these data it can be concluded that the pyrheliometer measures the UV radiation in the range between 300 and 404 nm. The power associated with a given wavelength (A) can be calculated by multiplying the pyrheliometer total measurement by the fraction of power (fx) associated with this wavelength (see Table 5). This fraction, for each wavelength, is given by the average of the values depicted in Fig. 4, which depicts the relative UV spectral distribution, obtained from Fig. 3 data, as described previously. The photochemical reactor located in the PSA concentrates the incident solar radiation by parabolic mirrors covered by a high UV-reflectivity aluminized film designed for this kind of applications. Although its reflectivity is not constant throughout the UV range (300-400 nm), the difference between maximum and minimum is less than 3%, thus we have considered a fixed value of 84.7% [31]. This value corresponds to a perfectly uniform and clean surface, but the mirrors are continuously outdoors, and lose their original reflectivity with time. To take this into account, the surface characteristics are measured frequently by a reflectometer (WEDEL, FH-PTL). This instrument gives information about the surface behaviour for light reflection and its changes over the time. The values obtained indicate the reflectivity (R R) at any time, and vary between 0 and 1. The reflectometer covers a range of wavelengths higher than 300-400 nm, but it was found that the reflectivity of the aluminized surface was practically the same for all wavelengths. Thus, the data (R R) given by the reflectometer can be used in the useful range (300-400 nm). However, this value has to be corrected by a factor
0,03
1 UV Direct Spectrum (300-404 nm) 0,025 2 U V Spectrum Reflected by PSA AFFilm
'E
3 UV Spectrum Inside Glass Tubes
0,02 a.
~
/ /
/
0,015
O,Ol 0,005
o 300 310 320 330 340 350 360 370 380 390 400 Wavelength
(nm)
Fig. 5. Average spectrum (Fig. 4) and calculated average spectrum inside the photoreactor considering the mirror surface efficiency and the glass tube transmissivity.
210
D. Curc6 et aL /Solar Energy Materials and Solar Cells 44 (1996) 199-217
(1.22) calculated from the reactor geometry and the instrument specifications [31], taking into account that the reflections do not take place at a single point (the reactor has a large area). The ultraviolet radiation refected by the parabolic surface reaches the reactive phase through the walls of the glass tubes where the liquid flows (see Fig. 5). This glass has very good UV-light transmissivity properties [31]. In the following sections more details about and a method for the calculation of F~r are explained. In a photocatalytic reaction, the rate usually depends directly on the light absorbed by the catalyst (Fab~, einstein 1-l sec- l) [40] or on its square root ,t ,~-I/z'~ ab~ " [41]. If kinetics is order one with respect to the reactant concentration, and the reaction rate is directly dependent on the radiation absorbed, for a monochromatic light source, the reaction rate can be expressed as: ra, x = -- kaFat,s,xCa,
(8)
where ra, A is the reaction rate (tool 1 1 s - i ) at a wavelength A, k~ is the kinetic constant (1 eins-l), Fab~,x is the absorbed radiation at A (eins 1-J s-J), and c a is the reactant concentration (tool 1- l ). The radiation absorbed by the catalyst is related with the radiation entering the photoreactor (F~r) by Eq. (3), thus: ra, a = -kaFer,xFlC a.
(9)
It is clear that F~ must be lower than 1, because not all the radiation entering the photoreactor can be absorbed by the catalyst. In addition, the radiation entering the photoreactor can be related to the incident radiation, by the expression (for each wavelength): Fer,x = F u ~ . x ( S / V ) I I i . x ( F i , x ) ,
(10)
where Fu~,X is the incident radiation per specular surface unit (eins m -2 s-l), S / V is the ratio between reflectors surface and reactor volume (m 2 1-1), and IIi,x(Fi, ~) is the product of different efficiency coefficients of the experimental system (reflectivity, transmissivity, etc). The incident radiation (Fus) can be calculated, given the incident power per square meter (WT), from Planck's equation:
LWT~ h~Ua
Fu~.X = - - ,
(11)
where A is the wavelength (m), h is Planck's constant (6.626 10 -34 J s), c is the speed of light (3 108 m s-l), Na is Avogadro's number (6.022 10z3), and fx is the fraction of power associated with a single wavelength (see Table 5), and fxWT is the incident radiation at wavelength A. According to the previous Eqs. (9), (10), and (11), and assuming that the photochemical reaction in homogeneous medium can be neglected, the reaction rate can be rewritten, as function of the incident radiation measured by the radiometer (WT), in the form: ra, ~ = - kaF,( S / V ) (hcUa) -I Af~WT Hi,h ( F i x ) c,.
(12)
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
\J
211
,ubularpnotoreactor
~ refl~ting mirror Fig. 6. Photoreactor losses scheme.
This equation can be applied to a polychromatic radiation source by summing the ra.a corresponding to each wavelength for the whole wavelength range considered (300-404 nm), then: A =
404
E
ra=-kaFI(S/V)(hcNa)-IWTCa
(13)
(i'( Fi,)f) •
A = 300
In addition, if the semiconductor used as catalyst has a band-gap lower than 404 nm, the previous equation must be restricted to this wavelength limit (Ag): A~A s
ra=-kaFI(S/V)(hcNa)-iWTC
a ~., ( Hi.,( Fi,AIAI,).
(14)
A = 300
The factor IIi,~(Fi, a) is the product of all the system loss coefficients: /-/i,A(F/,A) =
(15)
Fc F~Fr,,~Ft.,~,
where Fc is the collector construction factor (0.91), Fs is the sun tracking error factor (0.92), Fr.a is the mirror reflectivity factor, the value of which is measured periodically by a reflectometer (R R, see below) with a correction constant (F,. a = 1.22 R R) and F~,a is the glass transmissivity, an UV-dependent factor [31]. A scheme of all these correction factors is reported in Fig. 6. Thus, Eq. (13) can be rewritten in the following form: A=Ag
E
ra=-kRFI(S/V)(hcNa)-IWTFcFsl'NNRRCa
(Ft,xAfx).
(16)
h = 300
Most of these parameters are fixed for our reactor, so we
use
FDETOX.Xg:
A=Ag
FOETOX,a,= ( S/V)( hcNa)-l FcF~l.22RR E X = 300
(F,,aAfa),
(17a)
212
D. Curc6 et al./ Solar Energy Materials and Solar Cells 44 (1996) 199-217
where ( S / V ) band-gap is:
is 0.773 m 2 1-l, thus FDETOX,Ag for a catalyst with a 385 or 404 nm
FDETOX,385 = 1.86 10-6RR,
(17b)
FDETOX,404 = 2.94 10-6RR .
(17c)
And Eq. (16) is reduced to the following simple expression: G = - ka Fj Wv FDETOX,AgCa.
(18)
The definition of FDETOx or any other empirical efficiency parameter for a photochemical reactor needs the following steps: (a) Definition of all the efficiency factors involved in the radiation distribution. (b) Relationship between power flux and photon flux by spectral measurements. (c) Light concentration ratio ( S / V ) of the system. (d) Catalyst band-gap Ag (if the reaction is photocatalytical) and liquid phase absorptivity (if necessary). (e) Experimental demonstration of these calculations by the appropriate actinometric experiments. Several actinometries were carried out at the PSA to demonstrate the good fitting of the previous equations. The value of FDETOX,Ag(dependent only on the mirror reflectivity) and the UV-Direct radiation will be enough for the continuous evaluation of the radiation entering the reactor if these equations can be used with confidence. Due to the high cost of the acfinometric solution (uranyl salt) and the low conversion desired (less than 20%) only o n e helioman module (6th, Fig. 1) and a small tank (two hundred litres approx.) connected to all the reactor instruments were used. The solution was recirculated until the perfect mixing of the products was achieved and afterwards the module was focused. The oxalic acid concentration was analyzed after one pass through the reactor at the same time as solar radiation was registered with the pyrheliometer and the spectroradiometer. Table 6 summarizes the experimental conditions of these actinometries. The calculation procedure is as follows: (a) During the experiment the solar spectrum between 300 nm and 535 nrn is registered (active interval of the solution, see Table 1). (b) All the system efficiencies and S / V ratio are applied to the spectral data. (c) In this case, the reaction is zero order with respect to the oxalic acid concentration, i.e., c a in Eq. (9) disappears. In addition, F 1 could be assimilated, in a non-disper-
Table 6 Chemical actinometries summary. Experimental conversion compared to calculated conversion Actinometry 1 2 3 4 Experimental Period Residence time (s) Oxalic acid Initial conc. (M) Oxalic acid Final conc. (M) Conversion (%) Calculated conversion (%)
10:49/11:02 137 4.82 10-2 4.2 10-z 13 16
12:38/12:48 103 4.65 10-2 3.70 10-2 20 17
13:51/13:57 66 5.17 10 2 4.75 10-~8 10
15:18/15:27 106 5.45 10-2 5.12 10-2 6 7
D. Curc6 et a l . / Solar Energy Materials and Solar Cells 44 (1996) 199-217
213
sive medium, to [1 - e x p ( - p.~D)], and k a to the quantum yield ~ . Thus, Eq. (13) can be rewritten as follows: A~535
ra=-(S/V)(hcNa)-IW4
~_, ( I I i , x ( F i , a ) h f ~ a [ 1 - e x p ( - I ~ x D ) ] ) ,
(19)
h = 300
where Wr' and fx' have the same meaning as W r and fx in the new 300-535 nm range. (d) The procedure for the calculation, by Eq. (19), of the expected conversion (X in %) for the oxalic acid is the following:
c ( t f ) = c( t o) + ~_, t i r(t 0 = 0, t n = one - pass residence time),
(20)
i=0 n
c(tf) = C( to) - ( S / V ) (
hcNa) -1 ~.,( W~,iti) i=0
A=535
X
~., ( l - l i . a ( F i , a ) h f ~ d P a [ 1 - e x p ( - I z a D ) ] ) ,
(21)
h = 300
X = 100
c(to) - c(te) C( to )
(22)
Table 6 shows a comparison between the values of the conversion, X, calculated from Eq. (22), where c(t e) is either the experimental value, or the value obtained from Eq. (21). We consider FDETOx enough confident because the values of the conversion obtained using experimental concentrations or these ones coming from photon flux equations (see Eq. (21)) are quite similar. As an example, the reaction considered is the photocatalytic reduction of Cr(VI) to Cr(III). This reaction has a half order kinetics with respect to the Cr(VI) concentration at pH < 2, and using TiO 2 Degussa P-25 as catalyst [9,22,23]. Thus, the reaction rate can be expressed (according to Eq. (9)) as:
r, = dc / d t = - kaFer F1 cl/2.
(23)
The catalyst band-gap is 385 nm, thus Fer must be calculated from FDETOX,385.The system has different tanks and pipes for solution recirculation, but the only illuminated part is the reactor (glass tubes). Therefore, the factor Fer refers only to this illuminated part (reactor). Thus, if we work under perfect mixing flow conditions, ~ichieved by using few heliomans and high flow-rates, it is necessary to correct the volume in the following manner:
d c / d t = - k~Fcr F,( Vu/Vt) c ~/2 ,
(24)
where V u is the useful volume (glass tubes) and Vt is the total volume (glass tubes, tank and connection pipes). If we apply FDETOX,385,taking into account Eqs. (16), (17), and (18):
d c / d t = - k~ r l W T ( t ) FDETOx , 3 8 5 ( V u / / V t ) c1/2,
(25)
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D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
and integrating: C1/2 "~ C1/2 -- ( 1 / / 2 ) kaF1FDETOX ,385(gu//Vt) ,~tiWT(t),
(26)
where Co is the Cr(VI) initial concentration. Results are shown in Fig. 7 for an experiment with a TiO 2 concentration of 2 g 1-1. The kinetic constant (k a F 1) fitted using equation 26 was 65 ppm 1/2 1 eins-1. The values obtained at PSA were compared with these ones obtained at the laboratory level. Thus, a k~ F 1 value of 68 ppm 1/2 1 eins- 1 was obtained for experiments carried out in a Solarbox, using a Xe lamp (spectrum very close to the solar one) and flat reactors [42]. It can be concluded that, using different reactor geometries, the values obtained for k a F 1 are very close at the laboratory and pilot plant levels. This means that the method proposed takes into account the characteristics of the different experimental systems. Thus, the kinetic constants obtained can be more useful for the change of scale. Another application of this method could be found in the pentachlorophenol, TiO 2 mediated, photocatalytic degradation at the PSA Solar Detoxification Reactor, previously reported [43]. This compound follows an apparent first-order rate equation when the initial concentration (c o) is small: l n ( c 0 / c ) = kapt,
(27)
where t is the illumination time corresponding to each sample. Fittings of the data of two different experiments, carried out under the same conditions but at different moments of the day (early in the morning and at noon), give kap = 0.239 min- t and kap = 0.368 min- t, respectively. The same fittings can be performed, but using the expression:
In co/c = k'a e,
(28)
1 ~ . ~ .
¸
.
•
f "0
2i
• •
experimental
- - fitted o o
0,02
0,04 Radlation
0,06
0,08
0,1
(eins/l)
Fig. 7. Cr(VI) photoreduction as function of incident radiation per unit volume of the photoreactor.
D. Curc6 et al. / Solar Energy Materials and Solar Cells 44 (1996) 199-217
215
where:
El+ , = E, + F~r,,+ l(ti+, - ti),
(29)
and considering that E (eins l - l ) is the radiation received by each sample, Fer is calculated by Eqs. (10)-(17), and t is the illumination time. Thus, using these last equations, the values obtained were kap = 187 eins-1 1 and kap = 173 eins-I 1. The discrepancy between the results of experiments performed in different radiation conditions disappears if this method is applied.
4. Conclusions A method for radiation evaluation inside a solar reactor is proposed together with a validation method. Before the beginning of the outdoor experiments with the Sun as radiation source, it is necessary to study the efficiency of the experimental set-up and the available solar spectrum if comparison with other reactors and experimental conditions is desired. The calculation of the kinetic constants in terms of rate per useful radiation can help us to determine the influence of other parameters involved in the reaction efficiency.
Acknowledgements The authors are grateful to the Comisi6n Interministerial de Ciencia y Tecnologla (CICYT) (project AMB95-0885-C02-02) for funds received to carry out this work.
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