Ind. Eng. Chem. Res. 1990, 29, 1278-1283
1278
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, I, 33-63. Coburn, L. A,; Englande, A. J.; Lockwood, M. P.; Collins, T. Kraft Bleach Plant Effluent Treatment by Ultraviolet Oxidation Processes. Tappi Proc. 1984,272-286,1984 Environmental Conference. De Barnardez, E. R.; ClariB, 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. 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.
Legan, R. W. Ultraviolet Light takes on CPI Role. Chem. Eng. 1982, 89,95-100. Peyton, G. R.; Huang, F. Y.; Burlesson, J. L.; Glaze, W. H. Destruction of Pollutants in Water with Ozone in Combination with Ultraviolet Radiation. I. General Principles and Oxidation of Tetrachloroethylene. Environ. Sci. Technol. 1982a, 16,448-452. Peyton, G. R.; Huang, F. Y.; Burlesson, J. L.; Glaze, W. H. Destruction of Pollutants in Water with Ozone in Combination with Ultraviolet Radiation. 11. Natural Trihalomethane Precursors. Environ. Sci. Technol. 1982b, 16, 454-458. 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. Receiued for review April 18, 1989 Revised manuscript received January 18, 1990 Accepted February 5, 1990
Design and Experimental Verification of a Tubular Multilamp Reactor for Water and Wastewater Treatment Manuel Vicente,+ Orlando M. Alfano, Santiago Esplugas,?and Albert0 E. Cassano* INTEC,T Casilla de Correo No. 91, 3000 Santa Fe, Argentina
A model for the design of a multilamp tubular photoreactor employed for water and wastewater treatment was developed. A test reaction was used to achieve an experimental corroboration of the model. It was shown that under normal conditions a two-dimensional mass balance is sufficient to describe the system and that the additional numerical complexity required by a three-dimensional model is not justified. Deviations between model predictions with constant and variable radiation attenuation coefficients were also studied. For low values of the flow rate (conversions higher than lo%), good predictions were obtained only with the second approach. By use of the well-known oxalic acid-uranyl sulfate actinometer, the reactor model was successfully verified, showing good agreement with the experimental data. The results thus obtained indicate that the proposed procedure can be used to improve the design and operation of this type of reactor. In a previous work (Alfano et al., 1990),the multilamp, tubular, cylindrical flow reactor with multicylindrical, circular cross-section reflectors was analyzed from the viewpoint of the radiation field generated inside the reactor boundaries. The local values of in the absence of chemical reaction were obtained as the sum of the radiation directly received by the reactor from the lamp and that arriving at the reaction zone indirectly after reflection at the reflector walls; i.e., hlT
= lqlD -k
hlIn
(1)
As was established by Irazoqui et al. (1976), the local rate of initiation of a single-photon absorption photochemical reaction can be written in terms of the product of the primary quantum yield (@) times the local volumetric rate of energy absorption (LVREA) designated by ea. In turn, in homogeneous media, ea is proportional to the product of the local value of the attenuation coefficient (IL) times the local value of the modulus of the radiation flux density vector (lql). For polychromatic light, an integration over the wavelength range of interest must also be performed (Claril et al., 1988). When an overall quantum yield is used (a phenomenological constant employed to characterize the overall kit Present address: Departamento de Ingenieria Quimica, Facultad de Quimica, Universidad de Barcelona, Barcelona, Espaiia. 1Instituto de Desarrollo TecnolBgico para la Industria Quimica (INTEC). Universidad Nacional del Litoral (UNL) and Consejo Nacional de Investigaciones Cientificas y TBcnicas (CONICET), Santa Fe, Argentina.
0888-5885/90/2629-1278$02.50/0
netics of a photochemical reaction), a similar approach produces an expression for the overall reaction rate. Thus, the rate of reaction can be written as R = @plqlT (2) where here gives the moles of product formed or reactant decomposed per einstein of radiation energy absorbed. Since in the general case p is a function of concentration, eq 2 results in a function of the spatial variables and concentrations inside the reactor. This work analyzes the performance of the system for a reaction of simple kinetics. The study was aimed at developing criteria to introduce simplifications in the mathematical model describing the reactor. The first one is concerned with the possibility of using two-dimensional mass balances to describe a process that from the point of view of the radiation field is three-dimensional. The second simplification seeks for operating conditions under which the assumption of a constant attenuation coefficient provides good results when compared with those obtained with the rigorous approach based upon an attenuation process depending on reactant and/or product concentration. This criterion is analyzed in terms of reactor conversion. Finally, an experimental verification is performed by using the well-known photodecomposition of the oxalic acid and uranyl sulfate reacting mixture as a test reaction. Mathematical Model Many photochemical reactors can be modeled by using the species mass balances and the radiation balance. 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1279 Thermal effects may have significant effects in some particular cases (when the reaction is highly exothermic, for example), and then the thermal energy conservation equation will also be needed. We know that in this system, when p # 0, angular asymmetries in the radiation field are present. Then, three-dimensional mass balances will be used initially. For a cylindrical coordinate system located at the center and bottom of the tubular reactor, we can write the mass conservation equations for any species under the following assumptions: (i) negligible thermal effects, (ii) steady-state conditions, (iii) laminar, Newtonian flow, (iv) constant physical properties, (v) Fickian constitutive equations for the diffusive fluxes in the multicomponent system, and (vi) negligible axial diffusion as compared with the convective flux. When written in dimensionless form, they become
The results at the reactor outlet will be expressed in terms of the flow-average exit concentration as follows:
The three-dimensional (3-D) mass balance represented by eqs 3-8 can be simplified, particularly in the integration procedure, if angular symmetry can be assumed. Some indications about the feasibility of this approximation were described in Alfano et al. (1990). Here, comparisons between a 3-Dmodel and a 2-D model will be performed to reach more definitive conclusions. When the simplification is plausible and angular symmetry is an accepted assumption, the second term of the right-hand side of eq 3 vanishes, eqs 4,5, and 8 remain unchanged, and eqs 6 and 7 are not required since
a+i/ap = o with the following boundary and initial conditions: (4)
V L VP, Y = 1,
a+i/ar = 0 a+i/ar = 0
Vl, Vr, P =O,
a+i/aP
(6)
V l , VP, Y = 0,
Vl,
Vr, B
= */4,
VT, VP) l =0,
=0
Wi/W Jii
=1
=0
(5) (7) (8)
Here, boundary conditions (4)) (61, and (7) are the result of symmetry considerations. Boundary condition ( 5 ) is derived from the assumption of nonpermeable reactor walls (i.e., wall reactions are neglected). Since the reactor is substantially longer than the lamp, the initial condition at f = 0 is clearly justified. The assumption of laminar regime is not always necessary, and certain applications could be performed under turbulent conditions. The model can be easily extended to other flow conditions without further conceptual or computational difficulties. Operating conditions such as piston flow are just a particular case of this model, and since they are simplifications, they can be incorporated to the model with minor changes in its formulation. In our case we have performed our work under laminar conditions because of the following: (i) We are trying to achieve well-measurable conversions in the actinometric reactions used to test the model, and with this purpose not too low mean residence times are required. (ii) We are trying to work under conditions where the velocity profiles and the diffusional fluxes can be well-defined and computed. Laminar flow conditions are very suitable for achieving this purpose, particularly if one recognizes that turbulent flow not always implies piston flow for concentrations. It should be noted that in eq 3 Oi includes the rate of initiation, which is a function of the exponential term representing the attenuation of radiation. Hence, eq 3 is a partial integrodifferential equation (PIDE). We have already described the additional complexities derived from the existing link between the attenuation of radiation and the extent of the reaction (Romero et al., 1983). Thus, the reaction extent at each point inside the reactor is a function of the whole concentration field, and the numerical scheme will require an iteration procedure superimposed on the solution method for the partial differential equation. The existence of four sources of radiation and consequently four reflectors must also be incorporated to the required evaluation of the radiation field.
(10)
everywhere. However, it must be pointed out that this approximation in the mass balance does not necessarily imply that the radiation field can also be two-dimensional. In fact, in this case it must remain three-dimensional. To incorporate a three-dimensional radiation field into a two-dimensional mass balance, a projection of the radiation attenuation phenomenon on the plane used to establish the two-dimensional computational mesh is required. A cylindrical projection methodology for annular photoreactors was first proposed by Romero et al. (1983). Its extension for this particular system is summarized in the Appendix. For the two-dimensional model, the flow-average exit concentration is calculated with the classic formula
In order to allow an experimental corroboration of the model, a test reaction will be used. The well-known oxalic acid-uranyl sulfate actinometer was chosen with this purpose. Under precisely controlled operating conditions (Leighton and Forbes, 1930; Forbes and Heidt, 1934; Volman and Seed, 1964; Heidt et al., 1979; De Bernardez and Cassano, 1985),the chemical response to the influence of a radiation field is well-known. The absorption of light is undertaken by a uranyl oxalate complex, and the photochemical reaction is photosensitized by the uranyl ions. In spite of having a rather complex reaction mechanism, it is well-known that the overall effect is the photolysis of the oxalic acid to produce CO, C02, HCOOH, and HzO. The rate of decomposition can be written as
Rox = -aPoxea = -a O X P IQl
(12)
where @ox is the “overall” quantum yield. The point values of the absorbed energy expressed by ea are a function of the concentration of the uranyl ions and are independent of the oxalic acid concentration only under restricted conditions (Leighton and Forbes, 1930; De Bernardez and Cassano, 1985). Clearly, if the radiation attenuation required to compute IqI is a function of the oxalic acid concentration, there exists a coupling of the radiation balance with the mass balance. Results and Discussion The reactor model was solved for a reacting solution with an initial concentration of 0.001M uranyl sulfate and 0.005 M oxalic acid. A precise description of the reacting system is shown in Table 1. It includes the reactor, the reactor jacket, the lamps (which have almost monochromatic
1280 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 Table I. Parameter Values of the Reacting type of parameter parameter reactor length dimensions of the inner radius of the reactor photoreactor distance from lamp base to reactor base jacket length outer radius of the jacket radius of the reflector reflector length distance from lamp axis to reactor axis distance from reflector axis to reactor axis lamp nominal input power characteristics predominant wavelength output power at 253.7 nm
optical properties actinometric reaction
Xox(S=1)
System value employed LR = 100 cm RR = 0.92 cm zo = 33 cm
+ox
05
Ld = 46 cm RJ = 2.7 cm RM = 2.17 cm L R ~ 34 cm DL = 3.76 cm
n n v v
05
00
Y
10
(a)
D M = 2.94 cm
P=15W X = 253.7 nm = 2.37 x 10-5 einstein/s RL = 0.80 cm lamp radius LL = 34 cm lamp length av reflection coeff (reflector) (rM) = 0.65 (TR) 2 1 av transmittance (reactor) initial concn of oxalic acid Coo, = 0.005 M CO,, = 0.001 M initial concn of uranyl sulfate overall quantum yield (253.7 a,,, = 0.6 mol/ einstein nm) attenuation coeff (253.7 nm) p = 6.5 cm-' Do, = 10" cm2/s oxalic acid diffusion coeff T = 20 O C operating temp
10
0' 0 ° ' 80 %
O5
t
lei, 1
00 00
variable p
05
Y
10
(bl Figure 2. Oxalic acid radial concentration profiles for (a) constant and (b) variable p.
For laminar flow tubular reactors, the problem was studied by De Bernardez and Cassano (1985), and they found that when the limit of 20% conversion at every point inside the reactor cannot be fulfilled, an oxalic acid concentration dependence must be incorporated into the attenuation coefficient for the uranyl ion complex. They have experimentally found that, for X = 253.7 nm and C, = lo+ mol ~ m - the ~ , following expression holds:
1
j '\
f0
1.1 (cm-')
--------
Figure 1. Oxalic acid output conversion as a function of the volumetric flow rate for 6 = 0 and j3 = n/4.
emission), the reflectors, and the most significant parameters for the reaction rate. Computed Results. Figure 1 shows the oxalic acid output conversion as a function of the volumetric flow rate using the two-dimensional mass balance model for the extreme values of /3 (/3 = 0 and /3 = ?r/4). Differences between both results are very small. (Values computed with the three-dimensionalmass balance fall between both curves.) Since differences are never larger than 2%, it can be concluded that the additional numerical complexity required by the 3-D model is not justified. The 2-D model will be used henceforward. A second simplification was also attempted. If 1.1 could be assumed independent of the oxalic acid concentration, the attenuation or radiation can be decoupled from the extent of the reaction. This could be done if the conversion never exceeds 20% anywhere (De Bernardez and Cassano, 1985). If this is not the case, the nature of the uranyl complex that absorbs radiation changes. Difficulties are even more severe for much larger conversions (for instance, for conversions beyond 75%) because secondary reactions, not taken care of in the model, may influence the experimental results.
= 2.36
+ 3.37 X 106Cox- 9.58 X 1O"CO2 + 1.29 X 10"C0,3 - 6.53 X 1021Co,4(13)
with Coxexpressed in mol ~ m - ~ . When the concentration-dependent attenuation coefficient must be used, coupling between 1.1 and $ox exists. If this is the case,the procedure to incorporate the 3-D nature of the attenuation of radiation in the 2-D mass balance is not as simple as it is when p = constant (see the Appendix). Figure 2 shows oxalic acid radial concentration profiles for different values of the axial position. Figure 2a plots the results for 1.1 = constant (1.1 = 6.5 cm-l) and Figure 2b for 1.1 according to eq 13. It is clear that, for regions close to the reactor wall, conversions are higher than 20%. In fact, for the second half of the reactor length, in an annular cylinder externally bounded by the reactor wall, the oxalic acid has been totally converted. This is equivalent to a reduction in the true reactor volume since radial mixing does not compensate the oxalic acid defect concentration. Since a variable attenuation coefficient accounts for a decrease in 1.1 with oxalic acid econversion, the model can correctly represent a deeper penetration of radiation inside the reactor. The immediate consequence is the prediction of higher conversions. The existence of very steep radial gradients for both cases and a better accounting of the more realistic attenuation phenomenon for the second ( p = variable) are clearly depicted in Figure 2. Figure 3 conclusively shows the differences between the two cases for axial variations of the oxalic acid conversion. Deviations are magnified for low flow rates since in these cases overall conversions are always higher. One could also
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1281
03 0
x ox 02
01
O O,
,
10
Figure 3. Oxalic acid axial conversion profiles for constant and variable k. 05variable p
x&
anstant
=l
p
experiments
Figure 5. Variables involved in the calculation of the three-dimensional attenuation process.
eration of the photoreactor with the test reaction employed in a very accurate way.
02
Conclusions
00
I
I
8
1
Q ( cm3/s 1
Figure 4. Oxalic acid exit conversion: comparison between model predictions and experimental data.
say that for the upper values of the flow rates, in a first approximation,the model with p = constant could be used.
Experimental Results The reactor and the reacting conditions have already been described in Table I. The reactor was operated under steady state from the viewpoint of lamp operation, temperatures, flow rates, and output concentration. All parts of the experimental setup were isolated from the light with the exception of the reactor and reflectors. The reacting solution was circulated through a system made exclusively of quartz, Pyrex glass, and Teflon and/or PVC connections. Circulation was obtained with a centrifugal pump made of glass. Several samples were taken at different times for each reactor operating condition to ensure that steady state had been achieved. They were analyzed by conventional volumetric titrations. Figure 4 shows the experimental results. Model predictions with p = constant and p = variable are also included. For overall oxalic acid exit conversions higher than 1090,only the second case produced good agreement with the experiments. What is really significant is that in spite of the complexity of the model to interpret the contributions of direct and indirect radiation, as well as the mathematical procedure devised to incorporate the 3-D attenuation into the 2-D mass balance, the proposed approch predicts the op-
A model for the design of a multilamp, multireflector photoreactor that is employed in water and wastewater treatment has been developed. The rigorous modeling of this system requires the consideration of direct and reflected radiation from four lamp-reflector devices symmetrically located about the tubular reactor. In the general case, coupled, three-dimensionalmass and radiation energy balances must be solved due to the angular asymmetries of the radiation field. Similarly, the spatial variations of the attenuation coefficient (due to concentration changes) must be considered, leading to an even greater complexity in the coupling between the mass and the radiation balances. The first simplification was introduced by Alfano et al. (1990). There, the whole radiation problem was reduced to an approach that requires the consideration of a single lamp-reflector device and the evaluation of the radiation field in an angular interval between 0 and ?r. In this work, two additional simplifications have been studied in order to establish their ranges of application as a function of some operating parameters affecting the reactor performance. It was shown that under normal conditions a 2-D mass balance will be sufficient, thus avoiding the need for a more complex 3-Dmodel. It was also shown that the three-dimensional nature of the radiation attenuation process must be kept, but the problem is amenable of a geometrical treatment that permits its accurate representation in a 2-D mass balance. It was also theoretically and experimentally shown that only for low conversions could a model with a constant attenuation coefficient be used with confidence. However, in these cases, a significant reduction in the mathematical complexity of the system can be gained. By use of a well-established test reaction, the reactor model was successfully checked, showing good agreement with experiments. These results indicate that the proposed mathematical model can be reliably used to improve the
1282 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 /
A
J/ = C/C OOx, concentration, dimensionless
Oi= RiLR/(v)Coox,reaction rate of the ith species, dimensionless
Subscripts D = direct radiation i = for the ith species I = incidence point In = indirect radiation J = jacket property L = lamp property m = relative to a multicomponent mixture ox = oxalic acid R = reactor property Rf = reflector property T = total value ur = uranyl ion 0 = point of entrance at the reactor wall
(b)
Superscripts O = inlet value ' = value projected on the plane x-y
Figure 6. Projection of the radiation attenuation process on the plane ( r , 0) for (a) Ibrl 6 7r/2 and (b) I@,[> n / 2 .
Special Symbols ( ) = average value
design and performance of this type of reactor.
Appendix. Numerical Computation of a Three-Dimensional Attenuation of Radiation
Acknowledgment We are grateful to Elsa I. Grimaldi for her assistance in editing this paper. We are also grateful to CONICET and to UNL for financial aid.
The key point is the evaluation of an exponential attenuation integral that appears in the rate of initiation of every photochemical reaction and is represented by the following expression:
Nomenclature C = concentration, mol D = diffusion coefficient, cm2 s-l DL = distance from lamp axis to reactor axis, cm DRf = distance from reflector axis to reactor axis, cm E = output power, einstein s-l ea = local volumetric rate of energy absorption, einstein cm-3 S-1
Ge = R R / LR, geometric number, dimensionless I = incidence point L = length, cm P = nominal input power, W Pe = RR(u)/Di,, Peclet number, dimensionless q = radiant energy flux density vector, einstein cmW2 s-l Q = volumetric flow rate, cm3 s-l r = cylindrical coordinate, cm R = radius, cm Ri = reaction rate of the ith species, mol cm-3 s-l s = linear coordinate along the radiation path with origin at the incidence point, cm 5" = temperature, K U = v / ( u ) , velocity, dimensionless u = velocity, cm s-l X = conversion, dimensionless z = rectangular coordinate; also cylindrical coordinate, cm zo = distance from lamp base to reactor base, cm Greek Letters (3 = cylindrical coordinate, rad y = r/RR, radial coordinate, dimensionless r = reflection coefficient, dimensionless { = z/LR, axial coordinate, dimensionless 0 = spherical coordinate, rad X = wavelength, cm p = attenuation coefficient, cm-' p* = linear coordinate along the radiation path, cm T = transmittance, dimensionless 4 = spherical coordinate, rad dr = angle defined by eq A-4 or A-5 @ = quantum yield, mol einstein-'
The intregal must be solved for the total length of the radiation path that every ray travels inside the reactor, from the point of entrance at the reactor wall (po*) to the point where the reaction rate must be evaluated (pI*). Let us define a new variable s along the ray with origin at the incident point I. Its positive direction is opposite to the direction of penetration of the radiation ray inside the reactor. Hence,
A relationship between the value of s and the cylindrical coordinate system (r, 0,z ) used in the description of the mass balance is required (Figure 5). From plane trigonometry, if the dimensionless cylindrical coordinates for point I are yI, PI, {I, the relationship sought for is the following: cos ,+r A (y2- y12sin2 #,)'/21 (A-3) sin 8 According to the coordinate system used to evaluate the radiation field (see Alfano et al. (1990)), the value of is 4r =4 for direct radiation (-4-4) = PI - 4 for indirect radiation (A-5) To evaluate the integral of eq A-2, the value of iliat each point along s must be known. This requirement applies to every point of the plane mesh (7,{) used in the numerical solution of the mass balance. To do it, every point along s must be rotated about the reactor center axis and located on the integration mesh (Figure 6). In every case, the sign of the square root that appears on eq A-3 must be decided. Case I: l&l 6 7r/2 (Figure 6a). In this case, for values of y > yI, the term inside parentheses is always positive. Only positive values of the square root have physical = -[-yI 1
Znd. Eng. C h e m . 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
