Znd. Eng. Chem. Res. 1990, 29, 1283-1289
1283
meaning. The integral of eq A-2 can be numerically evaluated according to N
&';($i)
ds
C ~ ( $ n )Ans
(A-6)
n=n1
Case 11: l&l > */2 (Figure 6b). In this case, in order to take into account the attenuation from so to s1and from s1 to s = 0, both signs of the square root will be required. Hence,
The integral from s1 to so is entirely analogous to case
I. Let us look at the first integral of the right-hand side
of eq A-7. For values of y < yI, eq A-3 has two solutions. Each one of them has physical meaning if the negative sign is used for values of s from s* to s = 0 and the positive sign when s goes from s* to s1 (Figure 6b). In addition to this, the term between parentheses could take on negative values and the square root not be a real number. Values for which the term between parentheses takes on negative values correspond to points inside the reactor that cannot be reached by a ray that has a trajectory like the one defined from so to s = 0 and for which the parameter s has been defined. These values could be represented, for example, by those correspondingto a circumference of radius y = y.+ll* in Figure 6b. The value of y that makes the term inside parentheses equal to zero is given by * = 171 sin AI (A-8) Once the lower possible value of y (y = y *) is known, the method can be applied without difficulty. In Figure 6b, s+~.and s-,,. indicate the way in which the numerical approximation calculates this point. The final expression results:
Literature Cited Alfano, 0. M.; Vicente, M.; Esplugas, S.; Cassano, A. E. Radiation Field Inside a Tubular Multilamp Reactor for Water and Wastewater Treatment. Znd. Eng. Chem. Res. 1990, first in a series of three in this issue. Claril, M. A.; Irazoqui, H. A.; Cassano, A. E. A priori Design of a Photoreactor for the Chlorination of Ethane. AZChE J. 1988,34, 366-382. De Bernardez, E. R.; Cassano, A. E. A priori Design of a Continuous Annular Photochemical Reactor. Experimental Validation for Simple Reactions. J. Photochem. 1985,30, 285-301. Forbes, G . S.; Heidt, L. J. Optimum Composition of Uranyl Oxalate Solutions for Actinometry. J. Am. Chem. SOC. 1934, 56, 2363-2365. Heidt, L. J.; Tregay, G . W.; Middleton, F. A. Influence of pH upon the Photolvsis of the Uranvl Oxalate Actinometer Svstem. J. P h p . Chem. 1979, 74, 187~-1882. Irazoqui, H. A.; Cerdl, J.; Cassano, A. E. The Radiation Field for the Point and Line Source Approximation and the Three-Dimensional Source Models: Applications to Photoreactions. Chem. Eng. J. __ 1976,11, 27-37. Leighton, W. G.; Forbes, G . S. Precision Actinometry with Uranyl Oxalate. J. Am. Chem. SOC.1930.52, 3139-3152. Romero, R. L.; Alfano, 0. M.; Marchetti; J. L.; Cassano, A. E. Modelling and Parametric Sensitivity of an Annular Photoreactor with Complex Kinetics. Chem. Eng. Sci. 1983, 38, 1593-1605. Volman, D. H.; Seed, J. R. The Photochemistry of Uranyl Oxalate. J . Am. Chem. SOC.1964,86, 5095-5098.
Received f o r review April 18, 1989 Revised manuscript received January 18, 1990 Accepted February 5 , 1990
Effect of the Reflector Shape on the Performance of Multilamp Photoreactors Applied to Pollution Abatement Santiago Esplugas,' Manuel Vicente,t Orlando M. Alfano, and Albert0 E. Cassano* ZNTEC,! Casilla de Correo No. 91, 3000 Santa Fe, Argentina
This work studies the influence of the shape and dimensions of the reflectors of a multilamp tubular photoreactor on the reactor yield with the purpose of achieving a maximum use of the radiant energy emitted by the lamps. Accordingly, a parametric study of the reacting system is performed by employing an Extense Source with Voluminal Emission (ESVE) model for each lamp, and a comparison of the radiation incidence efficiency of three different types of reflector cross sections, circular, parabolic, and elliptical, is presented. The theoretical predictions are experimentally tested by means of the potassium ferrioxalate actinometric reaction. It is concluded that, for a better use of the radiation emitted by the lamps, it is convenient to employ elliptical reflectors. Besides, it is shown that reflectors of circular cross section may also reach a high efficiency provided their location and dimensions are properly designed. An attractive design of photochemical reactors for industrial applications can be found in the multilamp tubular photoreactor (Braun et al., 1986; Alfano et al., 1990; Vicente et al., 1990). This photoreactor has a tubular, t Present address: Departamento de Ingenieria Quimica, Facultad de Quimica, Universidad de Barcelona, Barcelona, Espaiia. t Instituto de Desarrollo Tecnoldgico para la Industria Quimica (INTEC). Universidad Naciond del Litoral (UNL) and Consejo Nacional de Investigaciones Cientificas y Tgcnicas (CONICET), Santa Fe, Argentina.
cylindrical reactor made of quartz surrounded by several tubular sources of ultraviolet radiation; typically, as exemplified in this work, four lamps are symmetrically located about the reactor centerline. To save energy and increase operation safety (protection from UV radiation), the reactor-lamp system is isolated from the surroundings by means of four cylindrical reflectors of circular cross section. Given the geometry of the reactor-lamp system, direct radiation coming from the lamps, and indirect radiation after reflection on the reflector walls, will impinge upon
o a a s - ~ s s ~ ~ ~ o ~ ~ s ~ ~ - i ~1990 8 3 American $ o ~ . ~ oChemical / o Society
1284 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
the reactor. From the yield of the radiation power consumption viewpoint, due to the importance of indirect radiation (Alfano et al., 1990), it seems relevant to study the effects of the shape and dimensions of the reflecting mirrors on the reactor performance. Energetical Aspects of t h e System One of the most important features in the design of a photochemical reactor is that associated to its energy yield. The energy yield of a photoreactor can be defined as the ratio between the amount of desired product obtained in the reactor and the amount of energy required to operate the radiation source. In other words, it is the probability that a given amount of energy, supplied to the lamp, reaches the reactor and becomes absorbed by the reactant to yield the desired product. For a better analysis of the factors influencing the photoreactor energy yield, the process can be imagined as a sequence of steps, each one with a probability of occurrence amenable to measurement (Cerdd et al., 1977). They are defined as follows. (1)The probability that the lamp power consumption may result in an energy emission in the desired region of the radiant energy spectrum. It is related to the emission spectrum and to the energy yield of the lamp: p~ = (energy emitted in Ah)/(energy consumption by the source) = WE/P (1) WE is the flow of photons or power emitted by the radiation source in the interval of the reactant absorption wavelengths, in einsteins/second, and P is the electric power consumed by the lamp, in watts. (2) The probability that this portion of the radiation energy spectrum be available for absorption in the reaction volume when the latter is assumed to be a blackbody: pr = (energy available for absorption in AX)/(energy emitted in Ax) = Wr/ WE (2) where WI is the flow of photons impinging upon the reactor surface, in einsteins/second. (3) The probability that this amount of available energy for absorption in the reaction volume be absorbed in the actual reactor by the desired reactant. It is related to the radiation absorption of reactants, products, and inerts: pA = (energy absorbed by proper reactant in Ax)/ (energy available for absorption in Ah) = WA/ WI (3) WAis the flow of photons absorbed by the desired reactant, in einsteins/second. (4)The probability that the desired reactant, excited by the absorbed energy, may undergo the expected transformation into the desired product. It is usually known as overall product quantum yield (a): pp = (amount of the desired product)/(energy absorbed by the reactant in Ax) = &/ W , (4) Qp is the extensive rate of product generation, in moles/ second. The product of these four probabilities gives the value of the energy efficiency of any photochemical reactor:
(5) While a proper design of a process will take into account the optimization of all these probabilities, the quality of a device to incorporate radiant energy to the reaction volume will depend exclusively upon the value of pI. To achieve a better understanding of the physical meaning of 71, it should be thought that the reaction 7 =~ E W ~ A ~ P
volume used for its direct experimental determination must operate as a blackbody. Thus, the numerator of 11 gives, for each lamp-reflector-reactor arrangement, the value of the maximum energy available for absorption at the reactor. As such, it excludes nearly all effects directly ascribable to the reactant or to the reaction. Its value depends explicitly upon (i) the geometrical characteristics of the lamp, the reflector, and the reactor and (ii) the physical properties of the reactor and reflector materials. For this reason it is useful to compare different sizes and shapes of reactor configurations. On the other hand, pA depends on the optical characteristics of the reacting system, pp on the kinetics of the photochemical reaction, and vE, primarily on the emission characteristic of the radiation source. Since the question under analysis is what shape of the reflector is the best, this work is aimed at studying pr, which is called incidence efficiency. The problem consists in finding the functional relationship between the incidence efficiency of a given photoreactor and its optical and geometrical characteristics, i.e., to relate the incident radiant energy flux upon the limiting surface of the reaction volume (reaction surface) with the reactor, lamp, and reflector dimensions, as well as with the optical parameters of the reflector and the reactor wall. The experimental determination of the incidence efficiency requires several special considerations. The reaction surface can be considered as a blackbody if, and only if, the actinometric reaction has a value of qA as close to one as possible. For this reason, an actinometer with practically 100% absorption for all the radiation spectral range of interest must be used. The value of VE can be obtained from the lamp manufacturer’s specifications. vp is a well-known value for an actinometric reaction. Hence, the incidence efficiency can be directly computed from experimental measurements of the total efficiency, p. Thus, experimental values of p1 will only be distorted by the possible inaccuracies of the kinetic information and measurements, as well as in equipment specifications and construction. Geometrical Aspects of the System We would like to compare three possible reflectors that differ among themselves only in the shape of their cross sections: (i) elliptical cross section, (ii) parabolic cross section, and (iii) circular cross section. All other parts of the system will be kept unchanged. With the purpose of performing the comparison among the three reflectors, a slight change must be introduced into the system originally studied by Alfano et al. (1990). The line of intersection of two adjacent cylindrical reflectors of circular cross section lies on a circle. Originally, the radius of this circle was considered equal to the jacket radius ( R J . If we now try to substitute the circular reflectors by others of elliptical or parabolic cross section, a steric difficulty arises because, without changes, they would either intersect the lamp or turn the distance between the lamp and the reflector insufficient. To sort out this difficulty, the radius of intersection of the different reflectors (R,) has been set slightly longer than RJ (Figure 1). This radius, Ro,allows a rational comparison among the three reflectors. From now on, it will be called the reflector reference radius. For a geometrical arrangement of one reactor of radius R R with four lamps of radius RL, the centers of which are at a distance DLof the reactor center, and with a reflector reference radius Ro (Figure l),it can be shown that there exists only one ellipse with one focus located at the center of the reactor and the other at the center of the lamp, there
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1285
R, =
Figure 1. Geometrical variables involved in the theoretical analysis of the reactor-lamps-reflectors system.
exists only one parabola with its focus located at the center of the lamp, and there exist infinite circumferences, each one with a different radius R,. The semiaxes of the ellipse corresponding to the elliptical reflector are a=
Ro + (DL2 + Ro2 - 21J2DLRo)'J2 2
b = [a2- (DL/2)2]'/2
(6)
(8)
The focal parameter, p , corresponding to the parabola results:
+
(DL2 Ro2 - 21/2DLRo)'/2- (DL - Ro2'l2/2)
P=
(9)
As for the case of the ellipse, the reflector cannot cut the lamp; consequently, there exists a security distance (ds), equal to (ds), = P - RL (10) Comparing eqs 8 and 10, it can be seen that the distance (ds), is critical since
is normally a small value. If the security distance used for the ellipse is smaller than 0.1464Ro, we could not position a parabolic reflector in the same system because it would intersect the lamp. Concerning the circumference, there is one for each distance (ds), to be considered. The center of the circumference is separated from the center of the reactor by a distance equal to h = DL + RL - R, + (ds), (12) The value of the radius R, is
where
(7)
Since the reflector cannot intersect the lamp, a "security distance", (ds),, must be defined. It is the minimum distance required between the surface of the lamp and that corresponding to the reflector. It may be expressed as (ds), = a - RL - DL/2
Evaluation of the Incidence Efficiency In order to evaluate the value of qI, it is necessary to solve the radiation balance. To do so, a series of hypotheses about the emission by the radiation source must be made. For mercury and neon transparent lamps, the radiation emission may be considered isotropic and voluminal, while in fluorescent lamps the emission is diffuse and superficial (Akehata and Shirai, 1972). For an arc-type lamp, the Voluminal Emission Extense Source model (Irazoqui et al., 1973), which considers the lamp as an emitting volume, has proved to produce good agreement with experimental results in a variety of reactor configurations (Cassano and Alfano, 1989). However, it must be recognized that it presents some mathematical complexity, especially for reflected radiation, but simpler models, such as the linear model with spherical emission (Jacob and Dranoff, 1970),cannot be used to treat reflected radiation (De Bernardez et al., 1986). To evaluate the incidence efficiency, qI, it is necessary to determine WI for each one of the geometries at issue. The required equations obtained with the ESVE model are the following:
qp = K(rRf) (TR)J@"AP'E~(@) m$ [COS
e,(@) - COS fli(@)IGf"(6)d@ (16)
Here, j is a generic subindex defining the type of reflector (e for elliptical, p for parabolic, and c for cylindrical). The functions included in the integrand and the limiting angles for these integrals have been previously reported in the literature as follows: direct radiation (Irazoqui et al., 1973); reflected radiation for the ellipse (Cerdl et al., 1973, 1977); reflected radiation for the parabola (Alfano et al., 1985);and reflected radiation for the circle (Alfano et al., 1987, 1990).
Computational Results Figure 2 shows the influence of the reflector type (elliptical and parabolic) on the incidence efficiency (71) for direct and indirect radiation and the variations of both with the reactor radius. The ESVE model has been used for both direct radiation and reflected radiation. The reactor length has been taken to be equal to the length of the radiation source, and a lamp radius corresponding to a typical germicidal lamp has been adopted. In the reactor-lamp configuration, a separation distance between both centers has been chosen so as to leave enough free space between the surface of the reactor and the surface of the four lamps. Similarly, a reflector reference radius has been adopted in order to ensure the placement of an elliptical and a parabolic reflecting surface with the required security distance and prevent undesired effects produced by thermal dissipations from the lamp. The
1286 Ind. Eng. Chem. Res., Vol. 29, No. 7 , 1990 Table I. Characteristics of the Reacting System parameter type dimensions of the photoreactors
lamp characteristics optical properties actinometric reaction
0.15
values employed
Rn = 1.0 cm DL = 4.0 cm (ds), = 1.90 cm u = 5.30 cm p = 2.39 cm germicidal G3OT8 RL = 1.27 cm WE = 8.3 W (at 253.7 nm) (rRr)N 0.65 9 = 1.25 mol/einstein Cope3t = 0.02 kmol/m3
ref
LR = 59.0 cm Ro = 6.2 cm (ds), = 1.03 cm b = 4.91 cm
P=30W LL = 81.3 cm
General Electric, 1967
(TR) 1 (at 253.7 nm)
ALCOA, 1964; Koller, 1966 Murov, 1973; Hatchard and Parker, 1956
I r
I R,
/ R,
:O 46
71,c e10 -
0 00
Figure 2. Effect of the reactor radius on the photoreactor incidence efficiency.
parameters corresponding to the reactor-lamps-reflectors configurations and the values of the optical properties used in the calculation are described in Table I. As expected, when the reactor radius increases, the incidence efficiency also increases, but this improvement is much more pronounced in the case of an elliptical reflector with contributions of reflected radiation much higher than those of direct radiation. Thus, the indirect radiation coming from an elliptical reflector is approximately 70% higher than that coming directly. For a parabolic reflector, instead, the values of the indirect radiation are approximately 20% smaller than that corresponding to direct radiation. Figure 3 shows the variation of the incidence efficiency for indirect radiation, for different sizes of the reactor and for different circular reflectors. The ratio of the distance between reactor and lamp centers to the reflector reference radius is DL/Ro = 0.645. Starting from purely geometrical considerations, it can be shown that a value of (ds),/Ro equal to 0.166 corresponds to a circumference circumscribing the parabola, while a value of (ds),/Ro.equal to 0.313 corresponds to a circumference circumscribing the ellipse (see dashed lines). By comparing Figures 2 and 3, it can be noted that the incidence efficiency for circles that match these values are very close to those of the parabola and the ellipse, respectively. In Figure 3, we can also observe that there exists an optimal security distance giving rise to a maximum in the incidence efficiency. The position of this maximum value does not depend on the reactor radius and nearly corresponds to the circle circumscribing the ellipse. It should be remarked that the indirect radiation efficiency increases a great deal with the reactor radius, particularly when the security distance takes on its optimum value. These results may be very useful for designing a commercial equipment because they allow the manufacturing of a device of maximum efficiency (elliptical reflectors) and
ot
03
(ds), / R,
05
Figure 3. Optimal security distance for circular reflectors (indirect radiation).
minimum complexity of construction (circular reflectors). Another relevant parameter is the separation distance, DL, between the center of the reactor and those of the lamps. This value coincides with the separation of the two focii of the ellipse when an elliptical reflector is used. Figure 4a shows the variation of the indirect radiation incidence efficiency with this distance for both an elliptical and a parabolic reflector. The direct radiation incidence efficiency is also included. As the separation between the reactor and the lamps increases, the direct incidence efficiency decreases, and practically, the values of the indirect incidence efficiency for the elliptical and parabolic reflectors are not modified. In the whole interval of values of DL, the elliptical reflector has a better performance. In Figure 4a, a value of the ratio reactor radius/reference radius (RR/Ro)equal to 0.16 has been used;the same effect is expected for other values of the reactor radius. From the design point of view, it should be convenient to choose the smallest possible value of DL compatible with the possibilities of mechanical construction and operation of the reacting system. The radiation source radius presents a great influence on the incidence efficiency, as shown in Figure 4b. The ratio of the distance between the reactor center and the lamp center to the reference radius (DL/R,) is equal to 0.645, and the ratio of the reactor radius to the reference radius (RR/RO) is equal to 0.16. From the indirect radiation yield viewpoint, the lamp of the smallest radius produces the best yield, especially when the reflector is elliptical. Rays are better focused on the reactor when the lamp radius is smaller. The small influence produced by the lamp radius on direct radiation can also be observed. Figure 4c shows the influence of the reflector reference size on the incidence efficiency. A ratio of the distance between the center of the reactor and that corresponding to the lamp to the reactor radius (DL/RR) equal to 4.0 has
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1287 015
Experimental Results
71 010
005
000
I
I
0.6
I
I
I
0.8
0.7
DL /Ro
71 0.2
01
In order to compare the incidence efficiency theoretical predictions with the experimental results, two multilamp photoreactors with elliptical and parabolic reflectors were built. Based on the main conclusions obtained in the section above, it was decided to build an elliptical multilamp reactor of maximum incidence efficiency. The materials employed (see Table I) were the following: germicidal lamps with emission in the ultraviolet region (in general they are of small diameter), quartz tubes for the reactor (of the largest possible diameter compatible with a bench-scale equipment), and small values of the reflector reference radius and of the separation distance between focii (compatible with the mechanical construction of the system and the reactor operation). The parabolic multilamp reactor was built with the aim of comparing and verifying systems of maximum and minimum incidence efficiency. It must be recalled that the parabolic reflector appears in theory to be the least efficient arrangement and that circular reflectors may approach the performance of either limiting cases by moving the location of their tenters. As a comparison basis between both geometries, the reflector reference diameter and the reactor and lamp dimensions were kept constant. In order to test the incidence efficiency predictions with experiments, several actinometric verifications have been performed by using the potassium ferrioxalate reaction (Parker, 1953; Hatchard and Parker, 1956). The actinometry was performed in a flow reactor. It was fed with potassium ferrioxalate aqueous solution (0.02 M) so that it can be safely assumed that this actinometric solution acts as a blackbody ( f A 1). Through the measurement of the actinometer decomposition at the reactor outlet, it is possible to experimentally determine the number of photons entering the photoreactor and, consequently, the incidence efficiency. The analysis of the reaction product, Fe2+, was performed with the classic phenanthroline spectrophotometric method. The experiments were carried out with no reflecting mirrors to measure direct radiation and using four elliptical or parabolic reflectors to measure the total radiation in each case. Reflectors were made of aluminum, specularly finished, and provided with Alzac treatment. Parts a-c of Figure 5 show the experimental results corresponding to the actinometric measurements without using the reflectors, using the elliptical reflectors, and using the parabolic reflectors, respectively, together with the representation corresponding to the predictions of the mathematical model (solid lines). The Fe2+concentration at the reactor outlet as a function of the mean residence time (7,) is represented. Since it is considered that all the energy arriving at the reactor is used for the reaction, the relation must be a line going through the origin. This linear relationship is no longer fulfilled if, as a result of high conversions inevitably produced in the proximities of the reactor wall, the absorption of radiation by the photolysis products becomes increasingly important. In order to avoid this problem and to make sure that the actinometric solution acts as a blackbody, as well as to avoid problems with undesired secondary reactions (Hatchard and Parker, 1956), the experiments were designed so that average exit conversions never exceeded 10%. It can be observed in the figures that in the three cases under study the agreement between the values predicted by the model and the experimental ones is very good. From the straight line obtained with the experimental results, it is possible to calculate the incidence efficiency
=
0.0
0.1
0.15
11 0.10
0.05
0.00
2
3
RO/DL
(C) Figure 4. Effect of the geometrical variables on the photoreactor incidence efficiency: (a) distance from lamp axis to reactor axis, (b) lamp radius, and (c) reflector reference radius.
been used. Of course, the reference radius does not affect the direct incidence efficiency, but it does influence the indirect one in such a way that as the reference radius increases, the incidence efficiency decreases both for the elliptical reflector and for the parabolic one as well. It is then desirable that the value of the reference radius be as small as possible. In the whole interval of the Ro values, the elliptical reflector is the one achieving the highest value of the incidence efficiency.
1288 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 Table 11. Comparison of Predicted and Experimental Incidence Efficiencies prediction with ESVE exptl ‘70 incidence model value error efficiency 0.0765 0.0874 12.5 direct radiation total radiation elliptical reflectors 0.207 0.203 2.0 total radiation parabolic reflectors 0.138 0.153 9.8
-
Model Experiments
cl 10
05
I
I
0
I
20
Tr ( 5 )
40
(a)
In eq 18, m is the slope of the line that can be obtained from the experimental measurement of CF~Z+ vs T,. Since VR is known and ZqpAWEA can be calculated from reported values of the overall quantum yield ( ~ p , and ~ ) the lamp manufacturer’s specifications ( WQA),71 can be readily obtained from
mVR A
0
Experiments
TP,A
(19) E,A
From the reported value of ~ p(Parker, , ~ 1953; Hatchard and Parker, 1956; Murov, 1973) and the spectral distribution of the lamp output energy, WEA,for the system made of four germicidal G30T8 lamps, the following value was found:
10
cfp,AwE,A A
= 6.86 x
mol E4-l
(20)
Consequently, from eqs 19 and 20, the experimental values of qI for the different reflectors are easily obtained. This information has been summarized in Table 11, where the corresponding theoretical values and percent errors are also included for each case. As can be observed, good agreement between the experimental data and the model predictions has been obtained, with an error nowhere greater than 13%.
04
Conclusions A parametric study of the influence of the shape and dimensions of the reflectors used in tubular multilamp photoreactors has been performed based upon the ESVE model, whose predictive quality was experimentally validated. The models developed have been tested by using actinometric verifications with potassium ferrioxalate aqueous solutions. Good agreement between theoretical and experimental results has been obtained. From the work performed, the following can be concluded. Maintaining all equipment parameters constant, the elliptical reflector is the one providing the highest values of the incidence efficiency. For an optimal use of the radiation emitted by the lamps, elliptical reflectors should be used, increasing the reactor radius at the maximum and reducing the values of the reflector reference radius and of the lamp radius to the minimum compatible with equipment construction and lamp availability. For cylindrical reflectors of circular cross section, there is an optimal value at ita centerline position that maximizes the indirect radiation efficiency. Depending on the geometry of the reactor-lamp system, the optimum may be very close to the value corresponding to an elliptical reflector.
I
00 0
5
T,(S) (C) Figure 5. Comparison of predicted and experimental values of the actinometric reaction for (a) direct radiation, (b) total radiation with elliptical reflectors, and (c) total radiation with parabolic reflectors.
for direct radiation, for the total radiation with elliptical reflectors, and for the total radiation with parabolic reflectors. Performing a macroscopic mass balance in the reactor for species Fe2+,we have QCFQ+= ~ Z V P , A ~ E , J (17) A
where an assumption has been made that all radiant energy arriving at the reactor surface that defines the reactor volume is used to produce the photochemical reaction (Q, = 1). Hence, the linear relationship between the concentration of product and the mean residence time can be expressed as follows: CFe2+
=
~)I(CVP,AWE,A A
7* =
VR
m7,
(18)
Acknowledgment We are grateful to Elsa I. Grimaldi for her assistance in editing this paper and to Antonio C. Negro for his valuable participation in the experimental runs. We are also grateful to CONICET and to UNL for their financial aid.
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1289
S. Esplugas gratefully acknowledges the financial support provided by CAICYT (Spain).
Special Symbol ( ) = average value
Nomenclature a = ellipse semimajor axis, cm b = ellipse semiminor axis, cm C = concentration, mol cm-3 ds = security distance, cm DL = distance from lamp axis to reactor axis, cm h = distance from circumference center to reactor axis, cm L = length, cm m = slope of the mass balance defined by eq 18, mol m 3 s-l p = parabola focal parameter, cm P = nominal input power, W q = radiant energy flux density, einstein cm-2 s-l Q = volumetric flow rate, cm3 s-l R = radius, cm V = volume, cm3 W = flow of photons, einstein s-l z = rectangular coordinate; also cylindrical coordinate, cm
Literature Cited
Greek Letters
fl = cylindrical coordinate, rad
r = reflection coefficient, dimensionless
= energy efficiency 0 = spherical coordinate, rad K = characteristic property of lamp emission, einstein cm-3 sr-l X = wavelength, cm p = spherical coordinate, cm 7, = mean residence time, s T = transmittance, dimensionless 4 = spherical coordinate, rad = quantum yield, mol einstein-I Q = extensive rate of product generation, mol s-l 9
Subscripts
A = absorption c = circumference e = ellipse E = emission I = incidence J = jacket property L = lamp property p = parabola P = production R = reactor property Rf = reflector property 0 = reflector reference property Superscripts
D = direct radiation In = indirect radiation initial value ’O == value projected on the plane x-y
Akehata, T.; Shirai, T. Effect of Light-Source Characteristics on the Performance of Circular Annular Photochemical Reactor. J . Chem. Eng. Jpn. 1972,5,385-391. ALCOA. Technical Bulletin, New Kensington, PA, 1964. Alfano, 0. M.; Romero, R. L.; Cassano, A. E. A Cylindrical Photoreactor Irradiated from the Bottom-I. Radiation Flux Density Generated by a Tubular Source and a Parabolic Reflector. Chem. Eng. Sci. 1985,40,2119-2127. Alfano, 0. M.; Vicente, M.; Cassano, A. E.; Esplugas, S. The Multilamp Tubular Photoreactor. Presented at the 4th Mediterranean Congress on Chemical Engineering, Barcelona, Spain, Nov 11-13, 1987. Alfano, 0. M.; Vicente, M.; Esplugas, S.; Cassano, A. E. Radiation Field Inside a Tubular Multilamp Reactor for Water and Wastewater Treatment. Ind. Eng. Chem. Res. 1990,first in a series of three in this issue. Braun, A.; Maurette, M. T.; Oliveros, E. Technologie Photochimique; Presses Polytechniques Romandes: Laussane, Switzerland, 1986;Chapter 4,pp 143-189. Cassano, A. E.; Alfano, 0. M. Photoreactor Design. In Handbook of Heat and Mass Transfer; Cheremisinoff, N. P., Ed.; Gulf Houston, TX, 1989; Vol. 3, Chapter 16,pp 583-670. Cerdl, J.; Irazoqui, H. A.; Cassano, A. E. Radiation Fields Inside an Elliptical Photoreflector with a Source of Finite Spatial Dimensions. AIChE J. 1973,19,963-968. Cerdl, J.; Marchetti, J. L.; Cassano, A. E. Radiation Efficiencies in Elliptical Photoreactors. Lat. Am. J. Heat Mass Transfer 1977, 1, 33-63. De Bernardez, E. R.; Claril, M. A.; Cassano, A. E. Analysis and Design of Photoreactors. In Chemical Reaction and Reactor Engineering; Carberry, J., Varma, A,, Eds.; Marcel Dekker: New York, 1986; Chapter 13,pp 839-921. General Electric Co. Technical Bulletin, Cleveland, OH, 1967. Hatchard, C. G.; Parker, C. A. A New Sensitive Chemical Actinometer-11. Potassium Ferrioxalate as a Standard Chemical Actinometer. h o c . R. SOC.London 1956,A235, 518-536. Irazoqui, H.A.; Cerdl, J.; Cassano, A. E. Radiation Profiles in an Empty Annular Photoreactor with a Source of Finite Spatial Dimensions. AIChE J. 1973,19,460-467. Jacob, S. M.; Dranoff, J. S. Light Intensity Profiles in a Perfectly Mixed Photoreactor. AIChE J. 1970,16,359-363. Koller, L. R. Ultraviolet Radiation; Wiley: New York, 1966. Murov, S. L. Handbook of Photochemistry; Marcel Dekker: New York, 1973. Parker, C. A. A New Sensitive Chemical Actinometer-I. Some Trials with Potassium Ferrioxalate. Proc. R. SOC.London 1953, A220, 104-116. Vicente, M.; Alfano, 0. M.; Esplugas, S.; Cassano, A. E. Design and ExDerimental Verification of a Tubular Multilamp Reactor for Water and Wastewater Treatment. Ind. Eng. Chem. Res. 1990, second in a series of three in this issue.
Received for revieu April 18, 1989 Revised manuscript received January 18, 1990 Accepted February 5, 1990
