Light Distribution Model for an Annular Reactor with a Cylindrical

reflectors are used in the reactors to recycle photons, which are otherwise ... that considers the reflector as a second light source in addition to t...
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Ind. Eng. Chem. Res. 2005, 44, 3471-3479

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Light Distribution Model for an Annular Reactor with a Cylindrical Reflector Quan Yang, S. O. Pehkonen, and Madhumita B. Ray* Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore

Accurate prediction of the light distribution field is important for designing large-scale photoreactors. So far, many incident light models have been developed that can be used for an accurate assessment of the light distribution field in annular photoreactors. Sometimes coated reflectors are used in the reactors to recycle photons, which are otherwise wasted; however, in these situations, the performance of the above models has not been tested. In this study, a new light distribution model based on a line source with diffuse emission model has been developed that considers the reflector as a second light source in addition to the original light installed along the centerline of the annular photoreactor. The performance of the new model is satisfactory in comparison with the experimental data obtained using chemical actinometry in a gas-phase photoreactor. Introduction A low yield of radiant energy absorption is quite common in photochemical reactions. The resulting high energy cost has been one of the main obstacles to the development of industrial processes despite several appealing features of photochemical processes, such as selectivity and low temperature of operation. To increase the radiative power absorbed within the reactor, and consequently the achievable conversion, a reflecting surface is often placed around the lamp-reactor assembly in such a way that at least some of the photons that would otherwise be wasted could be recycled and made available for absorption by the target pollutant. There are several typical reactor and reflector assemblies. One is the flat-plate reactor with a parabolic reflector, which generates a one-dimensional light field with almost “isoactinic” conditions.1 This assembly can be used for gathering kinetic information and is considered suitable for scale-up because one can minimize the spatial variations in light intensity. Consequently, absorbed radiation effects could be duly quantified by means of a one-dimensional radiation-field model, simplifying the estimation of the associated parameters in a kinetic study.2 However, the one-dimensional radiation field is seldom applicable in industry. In a second type of reactor, the lamp is mounted along one focal axis of the elliptical reflector and the reactor is assembled along the other focal axis.3,4 This installation is usually employed to generate a high intensity of light, particularly in bench-scale studies. In yet other types of reactor and reflector assemblies, a tubular lamp is surrounded by several tubular reactors and the reactor tubes, in turn, are surrounded by a reflector with a circular cross section. This reactor was conceived for operating photochemical reactions under pressure.4 In most cases, reflectors are mounted outside the reactor to avoid tarnishment and chemical decomposition of the reflector surfaces if the reflector directly contacts the chemicals. Another popular design, where * To whom correspondence should be addressed. Tel.: +656874-2885. E-mail: [email protected].

the cylindrical reflector is installed inside the annular photoreactor, was found to be effective in enhancing the pollutant conversion in specific cases.5 Among all of the designs, this is one of the easiest designs for installing and dismantling the reflector. Assessment of the light distribution field provides important information for designing a photoreactor because the initial rate of photochemical decomposition is proportional to the local volumetric rate of energy absorption.3 However, because of the presence of processes such as light absorption, dissipation, and reflection, a three-dimensional light distribution field needs to be developed for an accurate depiction of the light field. Although light distribution in some reactor and reflector systems has been evaluated in several studies,6-8 a detailed assessment of the light distribution field in an annular photoreactor fitted with a cylindrical reflector has not been carried out earlier. In our previous study, we have evaluated the performances of different light emission models, namely, a line source with spherical emission (LSSE) model,9 a line source with diffuse emission (LSDE) model,10 and an extensive source with volumetric emission model,11 by comparing experimental results obtained using a novel application of chemical actinometry. It was found that the LSDE model was the least computationally intensive yet was sufficiently accurate to be used for reactor scale-up.12 In this study, we have modified the LSDE model to calculate the local light intensity in an annular photoreactor fitted with a cylindrical reflector and compared the model performance with experimental measurements of the local light intensity. Model Development: Modification of the LSDE The LSDE was originally presented by Akehata and Shirai in 1972.10 This model assumes the lamp to be a line source of the same length, where each point in the line emits radiation in all directions. The energy emitted follows a cosine law; thus, the emitter in the lamp line releases its maximum energy in the direction that is normal to the UV source. In this sense, it is called a diffuse emission model. The validity of the LSDE model

10.1021/ie040098g CCC: $30.25 © 2005 American Chemical Society Published on Web 04/19/2005

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Figure 2. Schematic of the cylindrical reflector comprising differential light-emitting areas.

Figure 1. Schematic of the LSDE model.

has been subsequently experimentally verified initially by Akeheta and Shirai10 and later by Yang et al.12 It is worthwhile to mention that the LSDE model and the “diffuse” emission concept were developed to improve the performance of the LSSE model with a fluorescent lamp.3 As shown in Figure 1, if X represents an arbitrary point source, then the local intensity at a point (Y) in the reactor contributed by the emitter X can be calculated by the following equation:

i)

SL cos(γ) π2F2

[(

exp 1 -

rR  ∆x r λ

)]

(1)

where λ (cm-1) stands for the absorption coefficient of the medium in the reactor and ∆x is the incremental length of the line source. The Beer-Lambert law is incorporated into eq 1 because the light attenuates when it travels in the medium present in the reactor. Thereafter, the local light intensity contributed by all emitters can be obtained by integrating eq 1 over the lamp length, as shown in eq 2. The LSDE model was proven to be very

I)

SL cos(γ)

∫0L

2 2

πF

[(

exp 1 -

rR  dx r λ

)]

(2)

successful in the light intensity prediction when reflection was negligible.10,12 However, a reflector is occasionally installed in the photoreactor to recycle the photons. When the light reaches the surface of the annular photoreactor inner wall or the reflector, some of it is absorbed, while some is reflected back to the reaction space; this is somewhat difficult to evaluate mathematically because of the effects of both the reactor and reflector configurations. In this study, the local light intensity in the radiation field is separated into two parts: direct contribution by the light source and indirect contribution by the inner wall of the photoreactor or by the reflector. To evaluate the light contribution from the reflector or the inner wall, the reflecting surface is divided into numerous small areas (shown in Figure 2). The assumptions in the evaluation of the light distribution by both the light source and the reflecting surface in an annular photoreactor are listed as follows:

(i) Direct light from the lamp emits radiation in a diffused way and in every direction as described by the LSDE model (shown in Figure 1); therefore, the local light intensity at an arbitrary point within the reactor due to the direct light source is determined by the lamp power and the relative position of an arbitrary point to the light source. (ii) Every differential area on the reflector surface acts as a point source of light. It emits energy in every direction in the hemisphere and in a diffused way. Similar to direct light, the local light intensity at an arbitrary point within the reactor caused by the differential reflecting surface is determined by the emitting energy from the reflecting differential area and the relative position of an arbitrary point to this area. (iii) The emitting energy from the differential reflecting area is determined by the total energy received by the differential reflecting area and the reflectivity coefficient of the reflector. (iv) The total energy received by the differential reflecting area is completely contributed by the direct light source; thus, its value is calculated as described in step i. (v) The overall local light intensity at an arbitrary point contributed by the reflector is achieved by integrating the contribution by each differential area over the entire surface of the reflector. (vi) Although successive reflections always occur in the photoreactor, it is reasonable to consider only the first reflection. On the basis of experiments where the ray from a point source travels in one direction normal to the direct source, it attenuates to less than 10% of the original strength when it reaches the wall (less than 15 cm from the lamp). So, the energy of the first reflection compared to the original emission is already very small, and it will further decrease when it travels back from the reflector surface in the opposite direction. (vii) The final local light intensity at an arbitrary point is the sum of both the direct and indirect contributions. It should be noted that light from the reflecting surface emits energy in a hemisphere because light cannot escape from the annular photoreactor, whereas light from the direct light source, which is installed along the centerline of the photoreactor, emits in every direction of the entire sphere. The variables used in the model are as follows: (1) the configuration of the annular photoreactor, such as the diameter R and length L; (2) reflectivity coefficients of the reflector material; (3) characteristics of the UV lamp, such as the power of the light source and lamp dimensions; (4) extinction coefficient, λ (cm-1), of the medium in the photoreactor. The Model As mentioned earlier, the surface of the cylindrical reflector is divided into numerous small and equal segments (shown in Figure 2).

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Figure 4. Top view of the plane AEF.

of the photoreactor being z0 and z, respectively. Therefore, points A and B can be represented by [a¸ , ι, z0] and [0, R, z], respectively, when line CB or OE is used as the zero axis line. When Figures 3 and 4 (Figure 4 is a subsection of Figure 3) are compared, the following can be developed:

Figure 3. Schematic of an arbitrary emitter on the reflector surface and an arbitrary point in the photoreactor.

The differential area of a segment is

ds ) [π(2R)L]/nm

(3)

where n ) L/∆z and m ) 2π/∆δ. If constants n and m are sufficiently large, the small differential area can be regarded as a light-emitting point on the surface of the reflector. Suppose that an arbitrary point B (shown in Figure 3) is the emitting light source located on the surface of the reflector and A represents an arbitrary point within the photoreactor, the local light intensity of point A contributed by the emitting point B can be determined by the distance AB (F) and the angle β defined in Figure 3. On the basis of the assumptions made in the original LSDE and an energy balance in the hemisphere, the local light intensity at point A due to point B is given as

I)

I0[2 cos(β) exp(-Fλ)ds] π 2 F2

(4)

where I0 stands for the emitting energy from the differential reflecting area, and its value will be presented later. The LSDE model is recognized as a threedimensional model in the literature because every point source in the line is assumed to release its energy in three-dimensional space.1,2 In both the original LSDE model and the proposed model for the reflector, light sources are comprised of many point sources, and their contributions are later added or integrated. In this regard, the cosine law is directly applicable to the point source considered on the reflector surface. It should be noted that, according to the energy balance, the factor of 2 in eq 4 disappears if the point source emits light in the entire sphere. To obtain the value of AB (F) and the angle β, we assume cylindrical coordinates, with O (or C) being the origin and the distances between points A and B and the bottom plane

AF ) AO sin(a¸ ) ) ι sin(a¸ )

(5)

FO ) AO cos(a¸ ) ) ι cos(a¸ )

(6)

AE2 ) AF2 + (FO + OE)2 ) [ι sin(a¸ )]2 + [ι cos(a¸ ) + R]2 (7) AC2 ) AO2 + OC2 ) ι2 + (z - z0)2

(8)

AB2 ) F2 ) AE2 + BE2 ) [ι sin(a¸ )]2 + [ι cos(a¸ ) + R]2 + (z - z0)2 (9) β ) arccos[(BC2 + AB2 - AC2)/(2BC × AB)] ) arccos{[R2 + [ι sin(a¸ )]2 + [ι cos(a¸ ) + R]2 + (z z0)2 - ι2 - (z - z0)2]/[2R{[ι sin(a¸ )]2 + [ι cos(a¸ ) + R]2 + (z - z0)2}0.5]} (10) What follows is a brief discussion on the determination of I0, as shown in eq 4. The local light intensity on the surface of the reflector contributed by the direct light source (i.e., the lamp), Id, can be calculated by the LSDE model as

Id )

∫0Lπ2[R2 + (zL - x)2]1.5 exp{-[R2 + (z S R

(

x)2]0.5λ 1 -

rR R

)} dx (11)

However, because of light absorption by the reflector material, not all of the energy reaching the reflector surface is reflected. To obtain I0, Id must be multiplied by the reflectivity coefficient:

I0 ) IdΓ

(12)

where Γ refers to the reflectivity coefficient of the reflector material. The contribution of the other emitters on the reflector surface to the local light intensity at an arbitrary point A can be calculated using the same method as discussed earlier. Finally, the total contribution from the reflecting

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Figure 5. Schematic of an arbitrary emitter at the end of the cylindrical photoreactor and an arbitrary point in the photoreactor.

surface can be obtained by integrating the entire reflector surface. A set of equations was developed to calculate the contribution of the two ends of the source according to Figure 5. Point B in Figure 5 represents an arbitrary light point on the inner surface of the left end of the photoreactor, while A represents an arbitrary point in the photoreactor. Line O1D is parallel to line OA.

Figure 6. Shadow zone caused by UV lamp.

OC ) O1B ) r1

(13)

BC ) z

(14)

∠DO1B ) ∠AOC ) ω

(15)

Figure 7. Schematic of the photoreactor with two sampling ports on top.

AO ) r

(16)

Table 1. Parameters Used in the Model

Thus

AC ) xAO2 + OC2 - 2AO × OC cos(ω)

(17)

Because ∠BCA ) π/2.0, ∠CBA ) tan-1(AC/BC) ) tan-1(AC/z). Last, the local light intensity at an arbitrary point within the photoreactor contributed by the direct light source was determined by employing the LSDE model10 directly as shown in eq 11. The overall local light intensity at an arbitrary point within the photoreactor is achieved by adding the contribution from the reflecting surface to the contribution from the direct light source.

Ilocal,total ) Ilocal,direct + Ilocal,indirect

(18)

During light transmission, the reflected light cannot reach all parts of the reactor space because of the blockage by the UV lamp, as shown in Figure 6. Suppose J is an arbitrary emitting point on the inner surface of the reflector and point N is an arbitrary point in the shadow zone described by the arc KL, then point N cannot receive the reflected light from point J. If point N is in the shadow zone, ∠NJM must be less than ∠KJM [)arcsin(rR/R)]. The line JM passes through the center O, and the lines KJ and MJ are tangents to the UV source. Parameters used in this new model are summarized in Table 1. The numerical results were obtained using code written in VCPP (6.0), and the CPU used in this simulation was a 868 MHz Intel Pentium III. Experimental Section 1. Light Distribution Field in an Annular Photoreactor with a Reflector. The annular photoreactor

parameter

symbol

value

length of the reactor (cm) radius of the reactor (cm) radius of the UV lamp (cm) radius of the quartz tube (cm) reflectivity coefficient of the reflector (%) extinction coefficient of the medium (cm-1) constant shown in eq 3 constant shown in eq 3

L R rRr rR Γ  n m

64.5 15.0 1.35 2.125 0-40 0-0.5 200 200

was fabricated from stainless steel with a radius of 15.0 cm and a length of 64.5 cm. Monochromatic UV lamp together with a quartz tube covering the lamp was installed along the centerline (i.e., axis) of the annular reactor. The UV light source was 30 in. long with 100% radiation at 253.7 nm (model 17491; Aquafine Corp., Valencia, CA). Two sampling ports are located on the top surface of the test annular photoreactor. Because the radial light intensity profile along the longitudinal axis does not change significantly,12 there were only two representative axial sampling points located on the top surface of the reactor; one point (the first sampling port) is near the end of the annular reactor, and the other (the second sampling port) is at the center. The setup is shown in Figure 7. The outer diameter of the reflector is equal to the inner diameter of the annular reactor. Three cylindrical reflectors, which were fabricated of copper, stainless steel, and aluminum, were installed in the annular photoreactor. The light distribution field in the annular photoreactor was investigated by chemical actinometry. Potassium ferrioxalate, the most common actinometer used in the ultraviolet region, was used successfully in our previous research and was also been used in this study.12 A detailed description of the actinometry chemistry has been provided elsewhere.14-18 A spherical quartz cell with an outside radius of 0.85 cm, an inner radius of 0.8 cm, and a volume of 2.2 mL

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was used as a small batch reactor to measure the local light intensity at a fixed point. The small cell received light from all directions. Quartz was chosen as the fabrication material because of its good UV light transmittance. The small quartz reactor can only move vertically along the radius of the reactor after it is introduced to the reactor through the sampling ports. Thus, the location of the designated point can be described by the radius and the longitudinal axis of the reactor. The volume of the test reactor is 45 569 cm3, while the volume of the spherical cell is 2.2 cm3, resulting in a volume ratio of 20 710. Thus, the intrusive effects of the small cell on the aerodynamics of the reactor and the local light intensity are expected to be minimal. It is desirable to use a quartz cell as small as possible; however, because of fabrication constraints, the actual outer radius of the cell is around 0.85 cm. The gradient in the light intensity along the radius in a homogeneous photoreactor filled with air is not very large, and the light intensity decreases to 10% of its original value after traveling 12 cm in the reactor.10,12 Thus, treating the quartz cell as a point in the light field will not introduce a significant error. The quantity of the ferrous ion formed within a given irradiation time was deduced from the absorbance change, which was measured using a spectrophotometer (UV Mini-1240; Shimadzu Corp., Kyoto, Japan) at 510 nm. The reflection increases the local light intensity, and experiments were conducted in order to investigate the change in the light intensity distribution in the reactor with the inner wall coated with the three different reflectors. In addition, the entire inner wall of the photoreactor was painted black to minimize the reflection by the reactor wall itself.19 During the experiments, the UV lamp was switched on and allowed to stabilize for 30 min. Thereafter, 2.2 mL (V1) of a freshly made potassium ferrioxalate solution was pipetted into the quartz cell. Subsequently, the cell was introduced to designated positions in the reactor through the sampling ports (Figure 7). After some time (t), the cell was drawn out and 1.0 mL (V2) of the irradiated solution was transferred to a 10.0-mL (V3) volumetric flask, followed by the addition of 4 mL of a 1,10-phenanthroline (1.0 g L-1) solution and 0.5 mL of a sodium acetate buffer.18 The volume was then made up to 10.0 mL with deionized water. The solution was kept in the dark for at least 1 h to allow for full color development. The absorbance of the iron(1,10-phenanthroline)32+ was measured at 510 nm and compared with a reference. The reference was prepared in the same way, except that it had not been irradiated. The photon rate impinging on the detecting quartz cell during irradiation is given as

P0,λ )

NV1V3∆D510 V2lµ510φAC,λt

(19)

where ∆D510 is the difference in absorbance between the sample and the reference. Because all other variables in eq 19, except the absorbance and the irradiation time, were kept constant, the determination of an absolute photon rate was not necessary. Rather, the slope defined by the following equation can be used to describe the photon:

slopeλ ) ∆D510/t

(20)

Thus, the photon rate has the same meaning as the local light intensity, considering that 100% of the light from the UV lamp is at 253.7 nm. Furthermore, if one assumes the local light intensity, which is the greatest at the surface of the lamp, to be 1, then the local light intensity at any point in the reactor could be simplified as a relative slope, as shown in eq 21. It should be noted that, although thorough

sloperelative ) slopeλ/slopeλ,surface

(21)

mixing is preferred during the reaction, it was difficult to achieve because minimal shaking causes the small quartz reactor to sway from the designated point. However, the absence of mixing has been reported to have a negligible influence on the ferrioxalate actinometry results.14 It should also be noted that it is necessary to use appropriate concentrations of the ferrioxalate solution in order to ensure that all of the photons impinging on the small batch reactor are completely absorbed. A concentration range of 0.006-0.17 mol L-1 has been reported to be employed to measure the light intensity,14 and a 1 cm depth of a 0.006 M solution absorbs 99% or more of the light of wavelengths up to 390 nm.15 For longer wavelengths, at which the absorption coefficient of potassium ferrioxalate is relatively low, the 0.15 mol L-1 solution is usually more appropriate. In our previous study,12 it was found that the concentration of potassium ferrioxalate between 0.006 and 0.03 mol L-1 had no effect on the experimental results. Thus, 0.006 mol L-1 potassium ferrioxalate was used for subsequent experiments. At the same time, caution should be taken to ensure that the conversion of Fe3+ is less than 5%.14,15 The linear relationship between the absorbance and the irradiation time was used to verify the concentration range and the irradiation time. Four otherwise identical experiments (except irradiation times) were performed to calculate the relative local light intensity at each designated point. It was ascertained that nonlinearity did not occur during the irradiation. Finally, all of the experiments were conducted in a dark room illuminated by two red-safe lights because even small doses of visible light might cause uncertainty in the actinometry data. Quartz was chosen because it exhibits a good lighttransmitting ability in the ultraviolet region as discussed in our earlier study.12 In addition, a small thickness of the quartz tube (approximately 0.5 mm) also minimizes light attenuation. Moreover, the refraction and reflection exhibited the same influence on the local light intensity at every measurement point; thus, the influence is the same for each point and can be neglected because the relative light intensity was evaluated in this study. Because the light intensity on the surface of the quartz sheath, which covered the UV source, cannot be measured using the small quartz tube reactor because of its finite volume, a small cylindrical stainless steel reactor with a 5.5-cm radius and a 10.0cm length was fabricated. The same UV lamp as that used in the previous section was also used in this section. However, only 10.0 cm of the lamp was used effectively; the rest was outside the reactor and was covered by aluminum foil. The actinometry solution was introduced into the small reactor and circulated. Because the molar extinction coefficient of water is quite small in comparison with that of potassium ferrioxalate, the decomposition

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size. Third, the inner wall of the collimator was painted black in order to minimize reflections. Last, the length of the collimator should be larger than a recommended value (i.e., 20 cm).20 3. Measurement of Reflectivity Coefficients. Reflection of UV radiation from several surfaces was measured using the apparatus shown in Figure 8a,b. Incident radiation from a collimated source was imposed at 22.5°, 45°, and 67.5°, respectively, to the planar surface of each reflecting material. Materials evaluated for these measurements included stainless steel (SS 304), copper (C11000), aluminum (1100-H14), and black painted stainless steel. Reflected radiation was measured with the detector oriented at 22.5°, 45°, and 67.5° to the metal surface and parallel to the longitudinal axis of the collimator. The incident intensity was measured by positioning the surface of the detector perpendicular to the axis of the collimator at the same total distance from the source as that in the measurements of reflected radiation. The intensities of reflected and incident radiation were measured at the same total distance from the source; thus, the reflectivity coefficient of each material is defined as the ratio of the reflected intensity to the incident intensity. A digital radiometer, which only measures 253.7-nm light (model EW-09811-54; Cole-Parmer Instrument Co., Chicago, IL), was employed for the light intensity measurement. Results and Discussion Figure 8. Schematic of the collimator for measurement of reflectivity.

rate of potassium ferrioxalate can be used to calculate the total photon flux entering the reactor during a given irradiation time. On the basis of this value, the lamp power and the local light intensity on the surface of the quartz sheath can be determined. The detailed calculation methodology can be found in our earlier study.12 2. Fabrication of the Collimator and Measurement of the Reflectivity Coefficient. To produce uniform radiation, a specially designed collimator was fabricated, which minimized reflection and promoted the development of a well-behaved, quantified radiation source. The design and fabrication of the collimator is based on the design of Blatchley.20 The collimator system consists of two parts: one is the UV lamp box, and the other is the collimator. The dimensions of the wooden box are 12.0 cm × 12.0 cm × 72.0 cm, and the dimensions of the wooden collimator are 3.2 cm × 3.0 cm × 27.5 cm. The details of the construction of the lamp box and the collimator assembly have been described elsewhere.20 The UV lamp was installed in the wooden box to avoid exposure to operators. Some light rays from the UV source passed through the channel in the collimator. However, the light rays that were not parallel to the axis of the collimator were absorbed by the inner walls, and only those rays parallel to the collimator axis can reach the detector shown in Figure 8a. To ensure that all rays not parallel to the axis of the collimator were completely eliminated, several measures were taken. First, the wood, which is assumed to have a very low reflectivity coefficient, was used to fabricate both the box and the collimator in order to minimize the possibility of reflected radiation reaching the detector. Second, the interior of the collimator consisted of a series of wooden plates with vertically aligned circular holes of uniform

The measured incident intensity mentioned above is 0.29 mW/cm2, and the reflected intensities measured for the four different reflectors at different angles are listed in Table 2. The reflectivity coefficients of different materials were calculated using the above method, and their values are also given in Table 2. It should be noted that the quantity of reflected radiation is not completely determined by the nature of the reflecting materials themselves. The roughness of the surface due to corrosion and physical deforming may play a nonnegligible role, and the reflectivity coefficient is also dependent on the wavelength of light.20 From the experiments, it can be observed that the reflectivity coefficients at the three angles for the same reflector do not change. Aluminum shows good reflectivity (40.0%), followed by stainless steel (28.0%). It is surprising that the black painted stainless steel still exhibited a reflectivity coefficient of 4.0%,19 the same as copper. After incorporation of the reflectivity coefficients into the model developed above, simulated local light intensities were predicted and compared with the experimental data in Figure 9a,b. Figure 9a shows radial local light intensity profiles for the first sampling port (5.5 cm from one end), and the results for the second sampling port (close to the center and 29 cm from the other end) are presented in Figure 9b. It can be observed from these figures that the simulated results are in good agreement with the experimental data for all cylindrical reflectors used in this study. A significant aspect of this model is that no experimentally or empirically adjustable parameters are required. It is also apparent from Figure 9a,b that the local light intensity along the radius increases significantly with the reflector. The above experiments were conducted in an empty annular photoreactor; thus, it is assumed that the extinction coefficient of the medium present in the photoreactor is zero. However, if the medium present

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3477 Table 2. Measured Light Intensity and Calculated Reflectivity Coefficients at 254 nm material measured light intensity (mW/cm2) at 22.5° measured light intensity (mW/cm2) at 45° measured light intensity (mW/cm2) at 67.5° calculated reflectivity coefficient (%) reflectivity coefficient (%)a a The reflectivity coefficients are Optical_Parabolic_Mirrors&comp)2069.

from

copper

stainless steel

0.01 0.01 0.01 4.0 9.4

0.10 0.11 0.10 28.0 19.5

the

literature.20

aluminum 0.13 0.13 0.13 40.0 up to a maximum of 97% for upper UV, visible, and infraredb b

black-painted stainless steel 0.01 0.01 0.01 4.0 not available

http://www.globalspec.com/specifications/spechelpall?name)

Figure 10. Simulated radial local light intensity profile in the photoreactor in the presence of an absorbing medium.

Figure 9. Relative local light intensity vs radius in different cases.

in the annular photoreactor has a nonnegligible extinction effect, the extinction coefficient must be incorporated into the model. The simulated results with the extinction coefficients included in the model are shown in Figure 10, where the intensity profile was calculated for the second sampling port, with an aluminum reflector (the reflectivity coefficient is 40%, as listed in Table 2).

In Figure 10, it is apparent that when the extinction coefficient of the medium is very high (for example, 0.5 cm-1), the two relative local light intensity profiles (i.e., curves 5 and 6) along the radius before and after the installation of the reflector overlap, and the installation of the reflector does not improve the local light intensity. From the simulated results, it is also observed that the increments along the radius after reflector installation are almost at the same level when the extinction coefficient is less than 0.05 cm-1, as can be seen from the difference between curve 3 and curve 2 and the difference between curve 1 and curve 4. The local light intensity distribution fields with and without the aluminum reflector are shown in parts a and b of Figure 11, respectively. Because of symmetry, only half of the longitudinal axis is used in the two figures. It can be seen that, at the center of the reactor, the local intensity is increased by 40% because of reflection while the light intensity in the vicinity of the reflecting surface increases by approximately 55%. From the two figures, one can also observe that the local light intensity decreases considerably in the axial direction at the end of the photoreactor. It can also be observed that the light intensity contours in the two figures are very similar, except that the absolute values of the relative local light intensities are higher in Figure 11a than the corresponding values in Figure 11b, which shows the obvious contribution of the reflected rays to the local light intensity. It should be noted for Figure 11a,b that the extinction coefficient of the medium was assumed to be zero in the simulation.

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Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 Ilocal,total ) total relative local light intensity Ilocal,direct ) relative local light intensity contributed by the cylindrical UV lamp Ilocal,indirect ) relative local light intensity contributed by the cylindrical reflector I0 ) emitting energy from the differential reflecting area, einstein s-1 cm-2 Id ) relative local light intensity based on the LSDE, einstein s-1 cm-2 L ) length of the cylindrical photoreactor, cm l ) optical path length of the spectrophotometer cuvette, cm N ) Avogadro’s number P0 ) photon rate, photons s-1 R ) inner radius of the annular photoreactor, cm r, r1 ) radius shown in Figure 5, cm Γ ) reflectivity coefficient of the metal rR ) radius of the quartz tube covering the UV lamp, cm rRr ) radius of the UV lamp, cm SL ) output of the UV light source, einstein s-1 cm-1 t ) irradiation time, s µ ) molar extinction coefficient of iron(1,10-phenanthroline)32+, L mol-1 cm-1 V ) volume of the reactor, cm3 z ) distance shown in Figure 3, cm z0 ) distance shown in Figure 3, cm z1 ) distance shown in Figure 5, cm a¸ , β, γ, δ, ω ) angle shown in Figures 1-5, rad ι ) distance shown in Figure 3, cm F ) distance shown in Figure 3, cm φ ) quantum yield Subscripts AC ) actinometer λ ) wavelength

Literature Cited Figure 11. Simulated light field in the annular photoreactor (a) with and (b) without an aluminum reflector.

Conclusions A mathematical model was developed to investigate the light distribution field in an annular photoreactor with a cylindrical reflector. The local light intensity at any point in the photoreactor is comprised of both a direct source (i.e., the lamp) and an indirect source (i.e., the reflector). The LSDE model was modified to incorporate the reflectivity of the reactor wall, and the model was used to calculate the light intensity profiles for different cases. Subsequently, the model predictions were successfully compared with the experimental data. With an aluminum reflector, the local intensity at the center of the reactor can increase by 40% in the case of the low extinction coefficient for the medium. The model indicates that the application of the reflector is not beneficial when the extinction coefficient of the medium is moderately high (e.g.,  ) 0.5 cm-1) or the radius of the photoreactor is too large (e.g., 15 cm as was used in this study) because in both cases the light that can reach the reactor wall is quite small. Nomenclature λ ) extinction coefficient of the medium present in the reactor, cm-1 D ) absorbance ds ) differential area of the reflecting surface, cm2 i, I ) local light intensity, einstein s-1 cm-2

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Resubmitted for review October 14, 2004 Revised manuscript received March 1, 2005 Accepted March 3, 2005 IE040098G