Environ. Sci. Technol. 2010, 44, 2056–2063
Simulation of UV Photoreactor for Degradation of Chemical Contaminants: Model Development and Evaluation SIAMAK ELYASI* AND FARIBORZ TAGHIPOUR Chemical and Biological Engineering Department, University of British Columbia, 2360 East Mall, Vancouver, BC V6T 1Z3, Canada
Received August 13, 2009. Revised manuscript received January 31, 2010. Accepted February 2, 2010.
Models simulating the performance of UV reactors enhance our understanding of the fundamental principles governing the operation of these units. When modeling the performance of UV reactors, governing equations for all related phenomena are derived and solved. This research presents a step-by-step methodology to setup and solve the governing equations determining the performance of UV reactors and to evaluate the results. A computational fluid dynamic (CFD) model was developed in order to simulate UV photoreactors in the Eulerian framework for chemical removal using a UVbased hydroxyl radical initiated oxidation process. Verifying the results of the integrated CFD model, a novel method was developed using a modified planar laser-induced fluorescence technique for measuring tracer concentration profiles inside the UV reactor. In addition, the components of the CFD modelshydrodynamics and radiationswere evaluated using experimental profile throughout the entire reactor. This verified procedure can be applied to the simulation and optimization of UV photoreactors with various geometries and operating conditions.
1. Introduction UV technology, in combination with an oxidant such as hydrogen peroxide, provides an effective method of water and wastewater treatment. This photoinitiated oxidation process (also referred to as the UV-based advanced oxidation process, AOP) can be applied when treating optically clear water or wastewater that contains contaminants with concentrations of less than 1000 ppm (1). In UV-based AOP, hydroxyl radicals which are generated through the reaction of UV radiation with hydrogen peroxide play a major role in oxidizing persistent chemicals. A mathematical model simulating the performance of UV reactors can contribute to our understanding of UV technology for water treatment, allowing us to obtain the full benefit of UV photoreactors. The modeling of a UV photoreactor is a challenging area of research because of the multiphysics nature of this type of reactor. The model should allow for the effects of fluid movement and mixing (hydrodynamics), the distribution of radiant energy (radiation field), the rate of deterioration of * Address correspondence to either author. Tel.: (+1) 604-8223238. Fax: (+1) 604-822-6003. E-mail:
[email protected] (S.E.);
[email protected]. 2056
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the chemicals (photochemical/chemical kinetics), and the interaction of these phenomena with one another. The UV reactor performance model (semimechanistic approach) consists of a system of partial differential equations governing various phenomena in the UV reactor that should be solved simultaneously. Due to the complexity of the reactor geometry and interaction of many phenomena, analytical solutions do not exist, and a numerical solution is the only practical approach, using relevant techniques such as computational fluid dynamics (CFD). The modeling results for reactor performance should be validated against experimental data (hydrodynamics, radiation, and species concentration) to ensure their applicability to reactor design and optimization. A number of researchers have developed models of photoreactor performance (e.g., see refs 2-7); however, they have used conventional methods for model evaluation. These methods compare the modeling predictions with the experimental results for the overall reactor performance, which is determined by comparing the ratio of the outlet to the inlet concentration of the reactor. This method does not reveal any discrepancies that might exist between the model predictions and the experimental values for velocity, radiant energy, and concentration of species inside the photoreactors. Some other researchers (8, 9) have compared the hydrodynamics from the reactor performance model with experimental velocity data inside the photoreactor obtained using particle image velocimetery (PIV). But, in these cases, the CFD model predictions have been typically validated using PIV experimental data for only a few strategic locations inside the photoreactors, instead of throughout the entire reactor domain. In this research, a general methodology is presented for developing an integrated CFD model of UV reactor performance and evaluating all parts of the model separately. The results of each part of the integrated model (hydrodynamic, radiation, species concentration) are evaluated separately against experimental values in a UV photoreactor in order to develop a more practical and reliable integrated model. The approach can be summarized as follows: • The simulated velocity field is compared with PIV measurements at every point, and velocity vector profiles for the entire reactor cross-section are presented. • The radiation field is modeled and compared with measured values, which are recorded using a photodiode sensor located at discrete positions throughout for the entire domain of the reactor. • The photoreaction rate of a chemical used as a model contaminant for the UV-advanced oxidation process is measured in a bench-scale photoreactor under controlled conditions to obtain a photoreaction kinetic model. • An integrated model of hydrodynamics, radiation, and conservation of a chemical species is developed to determine the concentration profile throughout the reactor. The integrated model is evaluated using concentration data obtained with a newly developed and modified planar laser-induced fluorescence (PLIF) method. This powerful technique reveals the concentration profile throughout the entire domain of the reactor and can be useful to evaluated the full model. The strategy presented can be employed for any type of UV reactor in order to obtain a reliable integrated model for performance simulation. 10.1021/es902391t
2010 American Chemical Society
Published on Web 02/12/2010
2. Theory 2.1. Mass and Momentum Conservation (Hydrodynamics). The velocity field can be obtained by solving the equations of mass and momentum conservation. The general forms of the conservation of mass and momentum (Navier-Stokes equation) are ∂ (F) + ∇ · (Fu) ) 0 ∂t
(1)
∂ (Fu) + ∇ · (Fuu) ) ∇p - ∇ · τ + Fg + F ∂t
(2)
where t, F, u, p, τ, g, and F are time, medium density, velocity vector, pressure, viscous stress tensor, gravitational acceleration, and external body force, respectively. An analytical solution of the system of partial nonlinear differential equations is not available for complex geometries, so these must be solved numerically. The three-dimensional, timedependent numerical solution of eq 2 (direct numerical simulation (DNS)) is only applicable for a very small computational domain and a laminar flow regime due to the extensive computational resources required. For the turbulent regime, an acceptable engineering approach to solve eq 2 is the use of statistical methods or the classical approach that solves the Reynolds averaged Navier-Stokes (RANS) form of the equations (10). In the RANS approach, the Reynolds stress tensors are semiempirically correlated using algebraic (11), one-equation (12), two-equation (e.g., standard k-ε (13), RNG k-ε (14), realizable k-ε (15), or standard k-ω (16)), or multiple equation models of turbulence such as the Reynolds stress model (RSM) (17-19). 2.2. Radiant Energy Conservation. The simplified form oftheradiationtransferequation(RTE)(20)istheBeer-Lambert Law that is applicable in many UV reactors, due to a lack of scattering (no significant concentration of particulates) and emission (relatively low temperature) throughout the medium. The differential form of the Beer-Lambert Law for steady-state conditions is dI(s, Ω) + k(s, Ω)I(s, Ω) ) 0 ds
(3)
where I and k are the intensity and the absorption coefficient for a specific solid angle (direction) Ω and position vector s. For a photoreactor, changes in intensity depend not only on the medium absorption coefficient but also on the refraction/reflection through/from different materials in the medium, such as the quartz body of the UV lamp, the quartz protector of the UV lamp (sleeve), and the body of the reactor. These refraction/reflection phenomena should be integrated into eq 3. The photoreaction rate is a function of the radiant power obtained by integrating the intensity over the entire solid angle (4π). Considering all the above-mentioned effects, the radiant power per unit area, or fluence rate, at a point for one specific wavelength is (21) G)
∫
4π
0
(
n
1
I0(Ω) exp[-
n
(
∑ i)1
Li)2
∑∫ i)1
overLi
m
ki(s, Ω) ds]
∏T
i
i)1
)
dΩ
(4)
where Li, I0, ki, and Ti are the path length of a ray through the ith medium, intensity at source, absorption coefficient of medium i, and fraction of the ray transmitted from one medium to another, respectively. The fluence rate is the key parameter in the photoreaction rate correlation.
2.3. Species Mass Conservation. For each individual chemical (species m) in the computational domain, the mass conservation equation is ∂ (x F) + ∇ · (xmFu) ) -∇ · jeff + Sm ∂t m
(5)
where x, jeff, and S are mass fraction, effective diffusive flux, and source/sink term of species m, respectively. The diffusive term can be derived using Fick’s law with the molecular diffusion coefficient of the species in the medium. It was shown in our previous work that a turbulent Schmidt number of 0.7 is an appropriate value to be used for calculating the effective diffusive flux (22). The source/sink term depends on the nature of the reaction occurring in the domain of the reactor. Adding an oxidant (e.g., hydrogen peroxide) to the UV-based photoreactor produces hydroxyl radicals, very strong oxidants that can oxidize many chemical contaminants. Three potential primary reactions occur in parallel for the degradation of a chemical contaminant: (1) direct oxidation of chemical contaminant with oxidant; (2) photolysis by UV radiation; and (3) reaction with hydroxyl radicals (23). The value of the sink term in the species conservation equation for the reactant is the sum of these three reaction rates. For many chemicals, the rates of reactions are available (24); however, for certain chemicals, the rates need to be measured. In addition, if a chemical of interest (contaminant) exists in the presence of other impurities (which is the case in many practical applications), the rates may be affected and, hence, should be measured experimentally. The reaction rates can be determined using a bench-scale collimated-beam UV photoreactor under controlled conditions (i.e., well-mixed with a known radiation field). It is important to note that the photoreaction rate is a function of the radiant power (fluence rate) distribution in the medium. Therefore, the fluence rate should be simulated prior to photoreaction rate modeling. In addition to the fluence rate, which appears in the source term of the species mass conservation equation, the velocity also appears in the convection term of this equation. Therefore, the velocity field needs to be simulated. As a result, for developing an integrated model of reactor performances, which reveals the concentration profile of species, it is essential to also develop models of hydrodynamics and radiation distribution.
3. Experimental Methods 3.1. Flow-Through Pilot-Scale Photoreactor. A flowthrough pilot-scale photoreactor was studied for UV reactor modeling and model evaluation under different flow conditions. The dimensions of the reactor were selected to meet the criteria for planar laser-induced fluorescence that were recommended by Menton and Lipp (26) in order to minimize the optical absorbance. The body of the reactor was built from glass (5 mm thickness), instead of clear polymeric material such as polymethacrylate, to prevent its transparency being affected by either UV radiation or chemicals adsorption over the experiment period. At the bottom of the reactor, a quartz sleeve was attached to hold a large UV lamp (low pressure, 200 W, arc length 1.07 m, with more than 90% of its emission at 255 ( 5 nm, from Emperor Aquatics). A hole at the end of the sleeve with air suction at the other end, with flow rate of 0.0013 ( 0.003 m3/s and inlet/outlet temperatures of 22 ( 1/25 ( 1 °C, maintained an ambient skin temperature on the surface of the sleeve and maintained isothermal conditions. Figure S1 (of the Supporting Information) shows the dimensions and configuration of the pilot-scale reactor. 3.2. Material. A fluorescent chemical, Rhodamine WT, abbreviated as RhWT, was selected as the chemical candidate VOL. 44, NO. 6, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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for photoreactor modeling and model evaluation. RhWT, with the CAS registry number 37299-86-8 and the index name Xanthylium, 9-(2,4-dicarboxyphenyl)-3,6-bis(diethlamino)-, chloride, disodium salt in a 20 wt % aqueous solution was supplied by Turner Designs Inc. Potassium iodide, potassium iodate, and borax were used to calibrate the UV radiant energy passing through a collimated-beam bench-scale photoreactor (used for kinetic measurements). The bench-scale photoreactor contains a low pressure UV lamp with more than 90% of its emission at 255 ( 5 nm from Emperor Aquatics. Hydrogen peroxide was used as an oxidant and was measured using potassium iodide, sodium hydroxide, and ammonium molybdate tetrahydrate. Ammonium molybdate tetrahydrate was supplied by Acros Organics, and all of the other chemicals were supplied by Fisher Scientific. 3.3. Concentration Measurement. The absorbance of different weight percentages of RhWT (10 ppb to 10 ppm) at different hydrogen peroxide concentrations was measured at 555.5 nm (maximum absorbance) using a Cary 100 UV-vis spectrophotometer to obtain its extinction coefficient (21). The concentration of hydrogen peroxide in the solution was measured using the method presented by Klassen et al. (25). Hydrogen peroxide can oxidize iodide solutions under alkaline pH conditions and generates an I3- ion. The absorbance of the solution at 352 nm was used to backcalculate the concentration of hydrogen peroxide. 3.4. Velocity Measurement. Particle image velocimetry was applied to measure the velocity field. The flow-through photoreactor was installed in a piping network consisting of pumps, piping, instrumentation, a storage tank, and a particle image velocimetry (PIV) setup. Figure S2 (of the Supporting Information) shows a schematic diagram of the PIV setup. The same setup was used to measure the concentration profile by planar induced-laser fluorescence (PLIF). The PIV setup employed was the “FlowMap 2D” system from Dantec Dynamics which consists of software for capturing and processing images; a 12-bit digital camera (“HiSense MKII” from Hamamatsu Photonic K.K.) equipped with a narrow-band filter at 532 nm; and a laser pulse source at 532 nm (“Laser Solo III-15 Hz” from NewWave Research Company). PIV measurement criteria (27, 28) were taken into consideration in order to minimize errors during the experiments. Seeding the fine particles (polyamide with diameters of 10-20 µm) causes the reflection of light produced by the pulsed laser source. During the very short lifetime of the pulse (5-10 ns), the displacement of the particle is almost zero, and it can be concluded that the scattered light represents the location of the particles captured by the digital camera. After a short period of time, a second image is captured using a second laser pulse. Comparison of the two images (cross correlation) using a proper length scale reveals the length and direction of the velocity vector in the plane of the laser sheet. To reduce the noise, a Gaussian window function with a coefficient of 1 was used. Because window functions do not use the information near the edges of an interrogation area, a 25% overlap (4 pixels) of the interrogation window of 16-by-16 pixels was considered in the calculations. In addition, to broaden the narrow correlation peaks and remove the effect of the neighboring points in the correlation plane, a lowpass Gaussian filter with a coefficient of 1.5 was applied to the frequency domain of the Fourier transform calculation (27). Using the aforementioned criteria, a 0.25 m length of the reactor (from reactor inlet) was studied using PIV. This zone was divided into three sections. For each section, 400 double images were captured at two different mass flow rates of 0.005 ( 0.002 and 0.014 ( 0.002 kg/s. The values are reported with 95% confidence intervals. The 400 images were processed to reveal the average velocity field. Finally, the velocity 2058
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fields from the three sections were stitched together to represent the velocity profile inside the reactor (0.25 m length of the reactor). 3.5. Radiant Energy Measurement. A radiometer (IL1700, from International Light Technologies) and a solar blind UV sensor (SIC01M-C, from Roithner Laser Technik) were used to measure the irradiance rate at different points inside the reactor (where no liquid was run through the reactor, which was filled with air). The top side of the reactor was removed, and the sensor was inserted into the flow pathway of the reactor. The midplane inside the reactor was scanned, changing the position of the sensor inside the reactor (see Figure S3 of the Supporting Information). 3.6. Photoreaction Rate Measurement. The photoreaction rate of RhWT (as a model contaminant) and hydrogen peroxide (as an oxidant) in the presence of UV radiant energy was measured in a customized UV collimated-beam photoreactor under controlled conditions. The reactor consisted of: two midsize UV lamps on an aluminum reflector below a beam collimator; a double-jacketed reactor of 250 mL, with a round quartz window (3 mm thickness) at the bottom; and a variable speed stirrer at the top. The photoreactor sample port (bottom) was connected to the flow-through cuvette of a UV-vis spectrometer (Cary 100) via the circulating pump. Prior to measuring the photoreaction rate of the RhWT, the actinometry solution of iodide/iodate and the online spectrometer were used to accurately determine the UV radiant power passing through the collimated-beam photoreactor (29). The concentration of RhWT solution was 126 ( 1 ppb, and the hydrogen peroxide concentration was 10.14 ( 0.05 ppm. These were measured as a function of absorbed radiation to find the photoreaction rate (see Figure S4 of the Supporting Information) (21). 3.7. Concentration Profile of RhWT Measurement (PLIF). Fluorescent chemicals (e.g., RhWT) upon absorption of light at a given wavelength (e.g., 532 nm) can generally emit light at higher wavelengths (e.g., 580 nm). The intensity of the emitted light depends directly on the concentration of the fluorescent chemical. This behavior allows the measurement of the fluorescent chemical concentration profile using the same setup as for PIV. The technique is referred to as planar laser-induced fluorescence (PLIF). Replacing the narrow-band filter of the camera in the PIV setup with a high-pass filter (>550 nm) can convert the PIV setup to a PLIF setup. Due to the nature of pulsed lasers, the beam energy is not spatially uniform. In addition, the laser energy varies over time in consecutive pulses ((7% as measured in our experiments). To increase the accuracy of the measurements by considering these variations, the laser beam was split into two parts using a beam splitter. The energy of one beam was measured using another 12-bit digital camera with a narrow-band (532 nm) filter from a reflective surface as the reference. The other beam excited the fluorescent solution through the reactor and this was captured using the second camera with a high-pass filter (>550 nm). This technique provides a way of accounting for the pulse-to-pulse variation in laser energy and, hence, increases the accuracy of the concentration measurements. For the PLIF calibration process, different solutions of RhWT (10-130 ppb) with a constant hydrogen peroxide concentration (9.65 ( 0.56 ppm) were pumped through the reactor (while the UV lamp was off), and 400 images were captured for each concentration using both cameras. The value of each pixel on the resulting image, after subtracting the dark base (no laser source) was divided by the total value of reflected light (captured by the second camera) to allow normalization based on the reference beam. Finally, the normalized value for each pixel was plotted in relation to the
FIGURE 1. PIV results at mid cross-section of the reactor for two different mass flow rates: 0.005 (A) and 0.014 (B) kg/s. The results are shown for the first half of the reactor, in which hydrodynamics is most important, due to the flow being far from fully developed. Because of the light scattering and reflection, unrealistic velocity vectors were generated from some parts of the reactor; these have been removed (blank areas). concentration of RhWT to determine a linear correlation for that pixel. This resulted in a two-dimensional (2D) calibration map. A stock solution of hydrogen peroxide (10.30 ( 0.05 ppm) and RhWT (126 ( 1 ppb) at 21.4 ( 0.3 °C was fed into the reactor while the UV lamp was stabilized. Two different flow rates of 0.006 ( 0.002 and 0.015 ( 0.002 kg/s were tested. For each operating condition, the inlet, middle, and outlet of the reactor were studied, and 400 images were captured for each section. The average of the normalized images, after subtracting the glowing background image, was used to calculate the RhWT concentration profiles inside the flow-through UV photoreactor. This procedure was applied for three zones through the entire length of the reactor.
4. CFD Model Setup The details of the CFD model set up are provided in the Supporting Information.
5. Results and Discussion 5.1. Evaluation of the Hydrodynamic Model. 5.1.1. Velocity Field Measurement (PIV). The results of the PIV measurement for the two flow rates for the entrance region of the reactor are shown in Figure 1. For each image, the length of the arrows is proportional to the velocity magnitude. The value of R2 (the square of the correlation coefficient between two observed data values) for the average of 400 and 350 images for each of the two flow rates was close to 1, suggesting that 400 images were statistically sufficient for averaging. The flow pattern within the UV reactor begins at the inlet jet and passes over the hemisphere of the sleeve in the inlet section where it diverts to the main section of the reactor. Due to the high gradient of momentum in different directions of the jet stream, a back-circulation of the fluid at the inlet zone is produced causing recycle of fluid near the top of the reactor. Higher inlet velocities (with higher gradients) result in greater vorticity and flow rate of the recycled flow and, consequently, reduce the path height of the main fluid at the bottom of the reactor (close to sleeve)(see Figure S5 of the Supporting Information). 5.1.2. Simulation of Hydrodynamics. The average Reynolds numbers corresponding to the flow rates over the entire cross-section at the round inlet of the photoreactor (Figure S1 of the Supporting Information) are 530 ( 230 and 1480 ( 280 for cases A and B, respectively. Due to variations in the velocity at each cross-section, the local Reynolds number differs on any vertical line (from top to bottom) within the reactor, but the maximum Reynolds number cannot exceed
the inlet average Reynolds number. As a result, in case A, the flow regime is laminar throughout the entire reactor length; in case B, however, the area close to the bottom of the reactor (near the sleeve) is in the transition regime, whereas the area far from the sleeve is laminar. The aforementioned observations were modeled using different viscous models (laminar, transitional,andturbulent)withdifferentnumericalapproaches. The CFD results from laminar and standard k-ω transitional flow simulations using the first-order discretization method yielded the best fit of the PIV data for cases A and B, respectively (Figure 2). Overall, the flow patterns were well-predicted by the model. In order to show the deviation of the simulation results from the experimental measurements (PIV), the velocity vectors of the simulation results were subtracted from the PIV measurement for each corresponding point for the two different cases (see Figure S6 of the Supporting Information). Considering the scale of the images, the error corresponding to the PIV measurements, and the instrumental errors, there is a good correspondence for both cases, although with better agreement for case B. In the inlet zone, none of the models could predict the high circulation flow accurately. In addition, there is a narrow band below the contour of the turning points for which both models predicted a smaller velocity field than was found experimentally. The overall degree of agreement can be evaluated using the coefficient of determination (R2) between the PIV velocity vectors and those of simulation, which is expressed as
R2 ) 1 -
∑ (Vx - Vx ∑ (Vx - Vx PIV
PIV
SIM)
2
+ (VyPIV - VySIM)2
2
+ (VyPIV - VyPIV,Ave)2
PIV,Ave)
(6)
where Vx and Vy are the x and y components of the velocity vector, respectively, and indices PIV, SIM, and Ave represent the PIV measurements, simulation results, and the average of the measured values (PIV) throughout the entire domain, respectively. The R2 for cases A and B are 0.86 and 0.92, respectively (a perfect match would result in R2 ) 1.0). Better statistical agreement was found between the simulation results and experimental values for case B. It is expected that the simulation and experimental concentration profiles, which are highly affected by the velocity field, will show better agreement in case B, as well. 5.2. Evaluation of the Radiation Model. Considering the UV lamp as a line or volume source (I0 modeling in eq 4), the UV radiant emission from the source can be modeled VOL. 44, NO. 6, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Simulated velocity profile (CFD results) at mid cross-section of the reactor for two different flow rates: 0.005 (A) and 0.014 (B) kg/s.
FIGURE 3. Irradiance rate at different distances indicated by ], 0, ×, ∆, and * for distances 1, 10, 20, 30, and 50 mm from the surface of the lamp, respectively. Experimental values for the radiation power (symbols) vs the 1D model-predicted values (continuous lines) and the 3D model, cylindrical emitter with 7 mm diameter, values (dashed lines). using measured boundary conditions. It is important to note that the UV lamp does not behave as a uniform emission source because the moving air (used in this experiment as a coolant in the gap of the sleeve and lamp to maintain ambient temperature on the outer sleeve surface) changes the temperature gradient along the side of the lamp plasma dramatically. This causes a nonuniform emission that is lower closer to the lamp tip, where air enters the gap. As a result, radiant power should be measured close to the surface of the lamp/sleeve to calculate the intensity of the UV lamp at the source (boundary conditions). In addition, for a more realistic model, reflection from the body of the reactor should be integrated into the model. A comparison of the experimental and modeling results for the irradiance rate inside the air-filled reactor (absorption coefficient is equal to zero) is shown in Figure 3. Modeling the radiation (considering refraction and reflection from the reactor walls), with the radiant source as a volumetric or linear emitter, provided a reasonable agreement with the experimental results. However, the results from the linear source model were more satisfactory over the various distances from the lamp. As a result, the line source (1D) model was selected for modeling the radiation field inside the reactor, taking into account the absorption coefficient of RhWT and hydrogen peroxide (4.48 m-1), the reflection/refraction from/through the sleeve and the lamp quartz body, as well as the reflection from the side walls of the reactor (21). The simulated fluence rate profiles inside the photoreactor are shown in Figure S7 (of the Supporting Information). In the areas about 3 cm above the lamp sleeve surface, the fluence rate is six times less than in the area close to the surface of the sleeve. 5.3. Kinetic Model Determination. The total rate of reaction of the rhodamine WT with hydrogen peroxide in 2060
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the presence of UV is the summation of the three primary rates of direct oxidation, direct photolysis, and reaction with hydroxyl radicals (generated from UV photo oxidation of hydrogen peroxide). The rate of direct oxidation and direct photolysis were found to be insignificant. The total photoinitiated oxidation rate of RhWT and hydrogen peroxide after receiving H J/m2 UV fluence was measured to be (21) ln
(
)
CRhWT ) (-4.757 ( 0.092) × 10-3H 130
(7)
where CRhWT is the concentration of RhWT after receiving H (J/m2) fluence. This correlation was developed for the concentration of RhWT of less than 130 ppb (initial concentration of RhWT) and hydrogen peroxide at 10 ppm. Considering the volume of the bench-scale collimated-beam photoreactor (in which the reaction rate was measured) and the agitation effect of the impeller, the photoreactor is a wellmixed batch reactor. Using the chain rule, the rate of reaction for such reactor from eq 7 can be written as (21) dCRhWT ) (-4.757 ( 0.092) × 10-3GabsCRhWT dt
(8)
where Gabs is the absorbed fluence rate. Considering the temperature of reaction rate tests during the experimental measurements (21 ( 1 °C), eq 8 is valid only for ambient temperature. Passing cooling air over the UV lamp in the PLIF measurements maintained the temperature of reaction zones at 21 ( 1 °C. During all tests, the skin temperature of the sleeve while the UV lamp was operated did not exceed 24 °C, and hence, the isothermal assumption using eq 8 is valid.
FIGURE 4. Concentration profile of rhodamine WT (ppb) in the UV reactor with the laser energy at a steady-state condition for two different mass flow rates: 0.006 (A) and 0.015 (B) kg/s.
FIGURE 5. Concentration profile of rhodamine WT in the UV photoreactor calculated by the integrated model for two different mass flow rates: 0.006 (A) and 0.015 (B) kg/s. Concentrations less than 80 ppb are shown as white. 5.4. Evaluation of the Integrated Model. The concentration profile of RhWT is the result of the interaction of hydrodynamics, fluence rate, and reaction rate. Therefore, measuring the concentration profile throughout the entire reactor is the best indicator for the evaluation of the photoreactor model performance. As far as the authors are aware, no experimental measurement of the concentration profile in a photoreactor has been reported in the open literature. Figure 4 shows the measured concentration of the RhWT profile through the midcross-section of the photoreactor. The concentration profile through the entire length of the reactor was studied by investigating three sections of the reactor from inlet to outlet separately. The three images (averaged from 400 images for each zone) were combined and stitched together. Due to the technical limitations in keeping the setup perfectly consistent while studying different zones, it was not possible to obtain a perfect match in the areas where two adjacent images overlapped. The values close to the boundaries of the reactor walls were masked because they did not represent the true concentrations (as a consequence of reflections from the white glue joints in these regions of the reactor). For all images, a horizontal median filter of rank 40 was applied to remove the shadowing effects of the laser sheet in the images. Radiation measurement in the inlet zone (-5 to 1 cm from the tip of the lamp) showed a very low level of radiant energy (almost zero). This implies that the rate of conversion
of RhWT was very low. In other words, higher concentrations of RhWT are expected in this zone, in contrast to what was observed experimentally (Figure 4). This can be explained by considering the flow pattern in the reactor (Figure 1), which plays a major role in controlling the concentration. Low velocity (flow) of fluid at the reactor inlet zone increases the residence time of chemicals and consequently enhances the conversion consequently. In addition, the recycled flow of low concentration fluid from downstream to upstream dilutes the concentration of the inlet stream. As a result, lower concentrations levels of RhWT are expected at the inlet zone. In the area closer to the lamp (sleeve) where the fluence rate is at its maximum level, a minimum concentration of RhWT should be observed. These features are clearly demonstrated in Figure 4. Error in concentration can occur where the concentration gradient is high, with higher concentration at top is higher (due to a high absorption of laser light at the reactor exit) than at the bottom. Therefore, the measurements in the outlet sections are expected to have a relatively high degree of uncertainty for all cases and this explains the similar concentration profiles found for both cases in Figure 4, at the end of the reactor. The integrated model of reactor performance simulated the concentration profile in the UV reactor by solving the governing equations of mass, momentum, radiant energy, and species conservation. The results are shown in Figure 5. The main features of the concentration profile through
FIGURE 6. Concentration difference (CPLIF - CSimulation) in parts per billion for two different mass flow rates: 0.006 (A) and 0.015 (B) kg/ s. Concentration differences higher than 30 ppb are shown as white. VOL. 44, NO. 6, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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the reactor is well-predicted by the model. The difference between the modeling and experimental results of RhWT concentration for the two flow rates (cases A and B) are shown in Figure 6. The reliability of the simulation results (Figure 6) should be compared with the uncertainty associated with the calibration map for calculating the concentration contours in the PLIF procedure (see Figure S8 of the Supporting Information). Overall, there is close agreement between the modeling and experimental results throughout the entire cross-section of the reactor. The relatively high degree of disagreement at the lower end of the reactors is likely due to the difficulties in PLIF measurements as a result of light reflection in these regions. The differences between the model predictions and the experimental results are in the range of measurement uncertainty (see Sources of Uncertainty and Errors in the Supporting Information). The agreement is better for case B, likely due to a better prediction of the velocity profile. For both cases, in a small zone at the end of the reactor, adjacent to the UV lamp, the difference in concentration shows a notable deviation. In that zone, the significant vertical concentration gradient causes an error in the PLIF measurement. Overall, the disagreement between the results can be attributed to the uncertainty associated with experiments, such as instrumental error and error of the PLIF method, as well as the errors associated with numerical methods and model parameters. The PLIF method presented here cannot be used directly for industrial photoreactors; considering it requires the body of the reactor to be manufactured from optically accessible (transparent) material. In addition, for reactors with relatively large diameter, a scanning method should be employed to first find the concentration close to the reactor wall and then continue the scanning up to the center of the reactor, taking into account any absorbance correction. However, this technique could be directly used for small pilot scale transparent reactors for better understanding of the reactor behavior or for evaluating the general-purposed integrated models of reactor performance. To summarize, conventional methods for evaluating photoreactor models typically rely exclusively on concentration measurements at the reactor inlet and outlet. These methods cannot show the discrepancies between the model predictions and real values inside the photoreactor, nor can they reveal the causes of the deviation. The methods utilized in this research can be applied to evaluate photoreactor models, as well as models of similar systems. This approach evaluates the accountability of each component of the integrated model as well as the results of the integrated model for the entire computational domain. As a result, the discrepancy for each component is revealed, and the model can be applied to a wide range of operating conditions. This approach reduces uncertainty in the integrated model setup and provides a solution for individual phenomena. Consequently, it decreases the bias of the final integrated model solution. Considering the uncertainties in the measurements of velocity, fluence rate, and concentration, overall, the favorable agreement between the experimental data and the simulated results for each governing equation (momentum, mass, and radiant energy), and the integrated system of equations (species mass conservation) verifies the reliability of the presented methodology.
Appendix A Nomenclature CRhWT ) concentration of rhodamine WT (ppb) F ) volumetric external forces (N/m3) G ) fluence rate (W/m2) 2062
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Gabs ) absorbed fluence rate (W/m2) g ) gravitational acceleration (m/s2) H ) local absorbed fluence (dose) by microorganisms or chemicals (J/m2) I ) average radiant intensity of entire spectrum (W/sr) I0 ) average radiant intensity of entire spectrum at source of radiation (W/sr) jeff ) effective molecular diffusive rate (kg/s · m3) k ) absorption coefficient of the medium for the whole spectrum (1/m) ki ) absorption coefficient of medium, ith (1/m) Li ) pathway length of ray through medium, ith (m) p ) pressure (Pa) R2 ) coefficient of determination Sm ) source term of species m (kg/s · m3) s ) position vector (m) t ) time (s) u ) velocity vector (m/s) Vx ) x component of velocity vector (m/s) Vy ) y component of velocity vector (m/s) xm ) mass fraction of species m F ) density (kg/m3) τ ) viscous stress tensor (Pa) Ω ) solid angle (steradians)
Supporting Information Available CFD model setup (30), source of uncertainty and errors, and Figures S1-S8. (Figure S1) The photoreactor used for PLIF measurements (all internal dimensions are expressed in cm). (Figure S2) Schematic view of pilot-scale photoreactor, which consists of: product reservoir (1), feed reservoir (2), stirrer (3), centrifugal pump (4), flow/ pressure/temperature meter (5), photoreactor (6), laser source (7), digital camera (8), PIV/PLIF control unit (9), data acquisition system (10), and online spectrophotometer (11). (Figure S3) Reflector glasses over the UV lamp in the quartz sleeve. The apparatus consists of two window glasses (1), a UV photodiode extension arm (2), a UV sensor (3), a UV lamp (4), a quartz sleeve (5), and the position of the hole in the sleeve (6). (Figure S4) Schematic diagram of bench-scale collimated-beam UV photoreactor: parabolic reflector (1), UV lamp (2), collimator (3), double jacket rector (4), stirrer (5), and thermometer (6). (Figure S5) Velocity (x-component) profile and contour of turning points at different sections of the reactor for two different flow rates. Vertical lines indicate different xpositions in centimeters. (Figure S6) Velocity difference (vectors), VPIVVSIM, and x-components of velocity reactor. Vertical lines indicate x-position, and curves show zero axial velocity difference (VxPIV-VxSIM). The color bar (linear scale) indicates the velocity difference (vectors) from 0.015 (red) and 0.03 (red) to 0 m/s (blue) for cases A and B, respectively. The arrows show the flow directions. The velocity measurements near the surfaces are removed (white regions) because of the high uncertainty in the measurement due to the reflections. (Figure S7) Fluence rate (W/m2) profile at the mid-cross-section of the photoreactor. (Figure S8) Uncertainty in the RhWT concentration profile measurement (ppb) with a 95% confidence interval in the UV reactor for two different mass flow rates: 0.006 (A) and 0.015 (B) kg/s. The color bar (linear scale) indicates the concentration uncertainty from (30 (red) to 0 ppb (blue), and the arrows show the flow directions. This material is available free of charge via the Internet at http://pubs.acs.org.
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