Photocatalytic Thermodynamic Efficiency Factors. Practical Limits in

6824

Ind. Eng. Chem. Res. 2010, 49, 6824–6833

Photocatalytic Thermodynamic Efficiency Factors. Practical Limits in Photocatalytic Reactors Benito Serrano,‡ Aaroń Ortı´z,† Jesu´s Moreira,† and Hugo I. de Lasa*,† Faculty of Engineering, Chemical Reactor Engineering Centre, The UniVersity of Western Ontario, London, ON, N6A5B8, Canada, and Unidad Academica de Ciencias Quı´micas, Programa de Ingenierıá Quı´mica, UniVersidad Autońoma de Zacatecas, Me´xico

The photocatalytic thermodynamic efficiency factor (PTEF) is a parameter that can be used in photocatalytic reactors to establish photon energy utilization as the ratio of the energy used to generate OH• free radicals and the energy absorbed by the TiO2 photocatalyst. The PTEF evaluation requires the assessment of the total rate of OH• free radicals at any given time during the photoconversion of organic species. A key parameter in this assessment is the availability of the complete spectrum of measurable chemical species including various intermediates. Quantification of different chemical species and their evolution with irradiation time allow via stoichiometric relationships the calculation of the OH• radicals consumed in the photocatalytic reactor. PTEFs and quantum yields (QY) were reported recently for phenol photocatalytic conversion in water media (free of iron ions) displaying 71% and 19% maximum QYs and PTEFs, respectively.19 In the present study, the QY and PTEF are reviewed further, considering the photoconversion of phenol in water media enhanced by iron ions. It is shown using the more realistic RN2 model that the maximum QYs and PTEFs reach up to 85% and 23% levels, respectively. These encouraging efficiency factors demonstrate the favorable prospects of photocatalysis and Photo-CREC Water reactors operated under optimum photocatalyst loading conditions (0.14 g/L), with only a small fraction of the total absorbed photons potentially lost in photon recombination. 1. Introduction Heterogeneous photocatalysis belongs to the advanced oxidation processes (AOP), a technique based on the formation of nonselective highly reactive radicals as initiators of the oxidative degradation. The use of an oxidant, a semiconductor material, and UV promotes oxidation reactions through the cyclic formation and consumption of hydroxyl radicals, which attack the organic compounds.1 An organic molecule can potentially be degraded to carbon dioxide CO2, water H2O, and mineral acids. Phenol has been extensively used as a model compound to both understand the photocatalytic reaction mechanisms and to test the performance of various photocatalytic reactors.2 Kinetic models for the photocatalytic oxidation of phenol and other phenolic compounds have been mainly based on initial rates of reaction. Such kinetic models fail to account for the formation of reaction intermediates species. More recently a series-parallel kinetic model based on some measurable aromatic and aliphatic acid intermediates was developed.3-6 These models involve variable quantities of OH• free radicals in the different steps. Regarding energy efficiencies for ranking photoconversion reactors, their importance has been emphasized in a number of studies.7-16 In spite of this, the determination of photocatalytic reactor efficiency has remained a challenge because of the many variables involved, such as reaction rates, reaction mechanism, OH• free radicals involved in various reaction steps, kinetic constants, adsorption parameters, irradiation field, light absorbed by the photocatalyst, amount and type of photocatalyst, type of organic or inorganic species to be converted. To address this issue, the photochemical thermodynamic efficiency factor (PTEF) was proposed as the ratio of the energy * To whom correspondence should be addressed. E-mail: hdelasa@ eng.uwo.ca. ‡ Universidad Autońoma de Zacatecas. † The University of Western Ontario.

used to produce the OH radical used in the photocatalytic reaction to the energy absorbed by the photocatalyst.17,18 In the very first approach, the efficiency factors were calculated using the information from the first minutes of photoconversion and calculating the initial reaction rate. Values in the range of 1-2% were obtained. In more recent studies however our research team argued about the need of rigorous consideration of reaction networks, enhanced kinetic modeling, and irradiation field assessments of all parameters involved and much higher energy efficiencies were calculated.3-5,19 With this aim a methodology for the evaluation of the OH• group consumed based on the measurable species changes and the OH• radical stoichiometric requirements for every oxidation step was established.19 Iron was doped either in the photocatalyst or in the aqueous solution with the aim of reducing the recombination of the electron-hole charges and the band gap energy. Iron ions dissolved in aqueous TiO2 slurries were used to favor phenol photoconversion,5 decreasing mineralization time without altering the series-parallel network model as originally reported in the literature.3 It was found that ferric ions were reduced to ferrous ions very rapidly in the solution and remained in this state throughout the rest of the photoconversion reaction. These results suggest that it is actually the Fe ions as Fe2+ ions that promote higher photoconversion reaction rates, as Fe3+ is quickly reduced to Fe2+ with Fe2+ being reoxidized to Fe3+ on the catalyst surface once the charge is scavenged from the Fe2+ to form superoxide radical (O2-) species. This appears to be a similar process to that occurring in the platinization of TiO2, where Pt reduces the recombination rate by transferring the electron to the O2 molecule to form the superoxide radical. It is the goal of this study to consider the phenol photoconversion enhanced by iron ions to test the experimentally observed upper limits of PTEFs and QYs. In this context, this

10.1021/ie9017034  2010 American Chemical Society Published on Web 03/08/2010

Ind. Eng. Chem. Res., Vol. 49, No. 15, 2010

6825

Figure 1. Schematic representation of the Photo-CREC Water-II reactor: (1) MR or BL lamp, (2) replaceable 3.2-cm-diameter Pyrex glass inner tube, (3) replaceable 5.6-cm-diameter Pyrex glass inner tube, (4) fused-silica windows, (5) UV-opaque polyethylene outer cylinder, (6) stirred tank, (7) centrifugal pump, and (8) air injector.

contribution provides valuable information and establishes the observable extent of absorbed photon recombination.

Table 1. Characteristics of Photo-CREC Water-II component

specifications

value

Unit Characteristics

2. Experimental Setup The Photo-CREC Water-II reactor is configured with two concentric cylindrical tubes: the internal tube is made out of glass, and the external tube is made out with polyethylene. These tubes form an annular region where the slurry is circulated and irradiated from the central region of the inner tube, where a near-UV lamp, 1.27 cm of radius, 40 cm of length, 15 W black light blue lamp, UVP-XX-15BLB, spectral energy distribution in the 300-405 nm wavelength region, is placed in the central channel of the reactor.19,21 Figure 1 illustrates the components and special features of Photo-CREC Water-II reactor: a lamp (1), a glass inner tube with diameter of 3.2 cm (2), an inner tube with diameter of 5.6 cm (3), silica windows (4), a PVC outer tube (5), a stirred tank (6), a centrifugal pump (7), and an air injector (8). An interchangeable inner Pyrex glass tube varying in thickness and diameter enables the Photo-CREC Water-II to modify the dimension of the annular cross-section and adjust the flow conditions in the annular reactor space. Pyrex glass is used because it has a good near UV light transmission properties (in excess of 90% of the UV radiation greater than 315 nm in wavelength) and has a low cost. A centrifugal pump circulates the fluid throughout the system and is used to modify the flow rate. To facilitate radiometric and spectro-radiometric measurements, the unit is equipped with seven circular windows equally spaced (6.4 cm) along the outer tube wall. Since an operation with a large optical thickness and radiation measurements is considered, the outer reactor tube is made of UV-opaque polyethylene to minimize radiation reflection. The reactor is also equipped with a four-point flow distributor injector at the reactor entrance. These features ensure uniform injection and intense mixing. The injection points are located in the top section of the reactor at 90°-radial and 45°azimuthal position. Table 1 reports the dimensions of the reactor components. For each experiment of the present study, a predefined amount of reactant was weighed and dissolved in 50 mL of water. It was then added to a known volume of water, whose pH had been previously adjusted to the desired value of 4 by using an H2SO4 solution. Next, the photocatalyst TiO2 (30 nm, Degussa P25) which had been previously dissolved in 100 mL of water and stirred for 10 min, was incorporated to the mixture. More

annular reactor

internal radius 1, internal radius 2, external radius, height V for 3.2-cm-diameter V for 5.6-cm-diameter V

stirred tank reactor inner tube 3.2-cm-diameter 5.6-cm-diameter lamps

thickness thickness lamp radius, lamp length window radius

windows (fused silica)

1.74 cm; 2.82 cm 4.45 cm 44 cm 2.5 L 1.4 L 3.5 L 0.23 cm 0.32 cm 1.27 cm, 40 cm 0.5 cm

Operating Conditions weight of irradiated catalyst catalyst concentration water recirculation flow photon energy absorbed by the TiO2 suspension

Wirr

0.35 g

Qabs

0.14 g/L 16 L/min 1.625 W

H2SO4 solution was used if needed to adjust the pH to the desired value of 4 and more water was added to complete a volume of 6 L in total. Finally, Fe ions were incorporated via a Fe solution containing 5 mg/L of Fe (either as Fe3+ or Fe2+) and premixed with TiO2 in 100 mL for 30 min; this mixture was added to the previously described slurry aqueous mixture.5 The reactants were allowed to be in contact with the catalyst for 30 min or more before the near-UV lamp was turned on. During this period of time, henceforth referred to as the dark period, the reacting media was pumped around the system at a rate of 16 L/min and the air flow rate was set to 6 L/min, which provided the necessary oxygen for the reaction and prevented the catalyst from settling in the mixing tank. After this period, the lamp was turned “on” and the timer reset to zero to start measuring the reaction time. All other operating conditions (air flow rate, reacting media flow rate, 0.14 g/L catalyst weight) were kept constant, except for the pH. All experiments were carried out at room temperature (22 ( 1 °C). Samples were taken at different time intervals to track the concentration of the reactants and intermediates. Each sample was filtered using 0.2 µm Mandel filters before being analyzed. TOC was measured using a Shimadzu total organic analyzer TOC-5050. HPLC analyses were carried out using a Waters 1525 HPLC. The photon energy absorbed by the TiO2 suspension was estimated using a physical method and a macroscopic irradiation

6826


balance, Pa ) Pi - Pbs - Pt where Pa is the rate of absorbed photons, Pi is the rate of photons reaching the reactor inner surface, Pbs is the rate of back scattered photons exiting the system, and Pt is the rate of transmitted photons. The various terms in this macroscopic balance were calculated as follows: (a) Pi ) Po - Pa-wall, where Po is the rate of photons emitted by the lamp and Pa-wall is the rate of photons absorbed by the wall of the inner cylinder; (b) Pbs ) Pi - Pt|Cf0+, where Pt|Cf0+ is the rate of photons transmitted when the catalyst concentration approaches to zero; (c) Pt ) Pns + Pfs with Pns representing the rate of transmitted nonscattered photons and Pfs is the rate of forward transmitted scattered radiation. The terms Po and Pi were estimated with the so-called lamp test unit and the apparatus radiometer and spectrophoto radiometer. The rest of the terms were calculated using the indicated expressions of the macroscopic balance. More details can be consulted in the cited references.2,21,22 3. Discussion 3.1. Evaluation of OH Consumed in Photocatalytic Reactors. The evaluation of the OH• radical groups consumed in a photocatalytic reactor is a key issue for determining both QYs and PTEFs. A possible “indirect” and reliable method consists of (a) assessing measurable chemical species at every step of the reaction, (b) relating the disappearance of them with the OH• radicals consumed in compliance with stoichiometry. This OH• “balancing” using the stoichiometric equations, pathindependent state functions, allows establishing the OH• requirements for every single step without needing a detailed mechanistic description of how this oxidation event actually takes place. Thus, in a photocatalytic reaction network for the “j” chemical reaction step, one can consider that both OH• groups and two organic species are involved, with a different degree of oxidation. The “i” species (CnHmOo) is the species at the lower oxidation state while the “h” species (CxHyOz) is the one with the higher oxidation state. These two species have to comply with oxygen, carbon, and hydrogen elemental balances as needed by reaction stochiometry. Thus, this stoichiometric equation sets the OH• requirements for the photocatalytic step j followed by the photocatalytic transformation to evolve from the i (CnHmOo) species to the h (CxHyOz) as νi,jCnHmOo + νOH,jOH f νh,jCxHyOz + νH2O,jH2O

(1)

ri,j rOH•,j ) νi,j νOH•,j

νOH•,j r νi,j i,j

(2)

Furthermore and on the basis of the above a total rate of reaction of OH• radicals rOH•,T can be calculated as the sum of all rates of OH• consumed by organic chemical species (model compound and all intermediate species) in each one of the reaction steps such as the step j described with eq 1. Thus, the rOH•,T rate can be represented by the following equation: rOH•,T )

∑r

OH•,j

)

∑

νOH•,j r νi,j i,j

(3)

where rOH•,j is the rate of consumption of OH• radicals in step j of the reaction network, ri,j is the reaction rate of the compound i in step j, and νi,j is the stoichiometric coefficient of compound i in step j. Note that sometimes this coefficient can be zero with this depending on the contribution or not of the species i in a specific reaction step j. Thus, it is shown that the total rate of OH• consumption can be calculated using an “indirect method” as in eq 3 involving the summation of the rates of every single oxidation step multiplied by the ratio of the corresponding stoichiometric coefficients. 3.2. PTEF and QY Efficiency Factors. The photochemical thermodynamic efficiency factor (PTEF)17,18 is a parameter relating the energy utilized for the OH• radical formation and the absorbed energy by the photocatalyst. This definition has to be modified including a γ parameter which represents the fraction of the photon energy absorbed by TiO2 with a wavelength smaller than the one required for superseding the semiconductor band gap.19 PTEF ) ηOH )

-rOH•,T∆HOH•Wirr Qused ) Qabsγ Qabsγ

(4)

with rOH•,T being in mol min-1 gcatirr-1, Wirr is in gcatirr, ∆HOH• is in J mol -1, Qa is in J min-1, and γ is without units. According to eq 4, the main parameters to estimate the PTEF are the values of the rate of consumption of the free radical OH• (rOH•,T), the enthalpy of OH• radical formation (∆HOH•), the absorbed photons by the catalyst (Qabs) and the fraction of the absorbed energy contributed by photons with λ < 380 nm (γ). Regarding rOH•,T, it can be accounted at every network step using eq 5, the rate of i species oxidation in step j:19

with νi,j and νh,j representing the stoichiometric coefficients for CnHmOo and CxHyOz, respectively, for the j step with νi,jn - νh,jx ) 0

then, rOH•,j )

ri,j ) -

(elemental carbon balance) (1a)

{

}

1 V dCi,j (1 + K*) i Wirr dt νi,j

(5)

Thus, eq 3 becomes νi,jm + νOH•,j - νh,jy - 2νH2O,j ) 0 (elemental hydrogen balance),(1b)

rOH•,T )

∑r

OH•,j

νOH•,j r ) νi,j i,j νOH•,j V dCi,j (1 + K*) i νi,j2 Wirr dt

∑

)

∑

νi,jo + νOH•,j - νh,jz - νH2O,j ) 0 (elemental oxygen balance)(1c) It is interesting to note that usually the carbon atomic balance can be solved first, decoupled from the other two equations, and then the remaining two balances can be solved subsequently for the unknowns νOH,j and νH2O,j. On this basis, the following stoichiometric relationships can be considered for the step j:

{ {

}}

(6)

j

Futhermore replacing eq 6 in the PTEF definition given by eq 4 gives

PTEF )

∑

νOH•,j νi,j

2

{ {

}}

V dCi,j (1 + K*) i Wirr dt Qabsγ

j

∆HOH•Wirr

(7)


6827

Figure 2. Experimental profiles for the Fe-assisted photocatalytic 440 µmol/L phenol oxidation.4

The PTEF can be also portrayed as the product of QY and ηOH•,17 with QY representing the fraction of photons absorbed by the photocatalyst leading to the formation of OH• radicals (quantum yield) and ηOH• the fraction of photon energy used in forming an OH• radical: PTEF ) QYηOH•

(8)

Then the QY can be calculated as QY )

PTEF ηOH•

(9)

with ηOH assessed at 0.271 mol photon/mol OH•.19 Thus, both the PTEF and the QY can be calculated at every stage of the photocatalytic conversion using eqs 8 and 9, the evolution of various species concentrations and several important adsorption, stoichiometric, thermodynamic, and irradiation parameters such as Ki, νi,j, ∆HOH•, Wirr, Qabs, γ, and ηOH. 3.3. The Parallel-Series Reaction Network. A photocatalytic conversion of organic pollutants based on the observable chemical species can be assumed to take place via a parallelseries reaction network.3,4 Figures 2 and 3 report the experimental results obtained with phenol at an initial concentration of 440 µmol/L (30 mg/L of C in phenol) in a Photo-CREC Water-II. Figures 2 and 3 support this parallel-series reaction network given the following: (a) the phenol concentration decays progressively with a close to first order kinetic rate, reaching an essentially zero concentration at the end of the run, (b) the detectable liquid phase concentrations of intermediate species initially rise and later on diminish until they are virtually depleted, (c) full depletion of intermediate species occurs at times close to the complete disappearance of phenol, (d) the TOC drops monotonically following an essentially zero order reaction showing that there is already complete oxidation of phenol with CO2 formation at short reaction time. In addition in a photocatalytic processes, it is important to account for the pollutant adsorption phenomena on the catalyst surface and to establish a kinetic model accounting for both reaction and adsorption. Affinity of different chemical species on the TiO2 surface was previously analyzed.20 Some compounds adsorb strongly and slowly, following a nonadsorption equilibrium behavior, while others, as in the case of phenol and

Figure 3. Comparison between measured TOC and calculated TOC (OCAR line) for 440 µmol/L of phenol. Note: CO2 formed profiles are in a different scale (six times larger than the one shown on the y-axis).4

other phenolic compounds, adsorb quickly but weakly, following an equilibrium adsorption described by the Langmuir adsorption isotherm. 3.4. Kinetic Modeling in Photocatalytic Reactors. Phenol photocatalytic conversion can be modeled on the basis of a number of applicable assumptions as follows: (i) The controlling steps for the photochemical conversion of phenol are the intrinsic chemical reaction steps. (ii) All chemical species are converted during irradiation at conditions close to adsorption equilibrium (quasi-equilibrium). Phenol adsorbs rapidly and weakly as it was established in a previous contribution.20 (iii) All the experiments are performed starting from adsorption equilibrium conditions between the photocatalyst and the model pollutant, in this case phenol. On the basis of these assumptions a balance equation for each chemical species i can be expressed as follows: V dCi ) Wirr dt with r*i,j )

(

(∑ ) νi,jr*i,j

ki,jKiCi n

1+

(10)

j

∑KC

j j

j)1

)

V Wirr

(11)

6828


reaction 2 2

C6H6O + 2OH• f C6H6O2 + H2O

(14)

reaction 3 3

C6H6O2 + 26OH• f 6CO2 + 16H2O

(15)

reaction 4 4


(16)

reaction 5 5

C6H6O2 + 26OH• f 6CO2 + 16H2O

(17)

reaction 6 6

C6H6O2 f C6H6O2 Figure 4. Reaction network 1 (RN1). Phenol ) Ph ) C6H6O, o-DHB ) C6H6O2, p-DHB ) C6H6O2. Note: The step 6 is not considered in the accounting of reacted OH• groups given this step is an isomerization and it does not affect the required OH• groups.

with r*i,j in mol min-1 gcatirr-1 (always positive), dCi/dt in mol L-1 min-1, V in L, and Wirr in grams.

∑ν

i,jr* i,j

(12)

j

As a result it can be shown that the use of the evolution of the Ci chemical species with irradiation time provides valuable data for the evaluation of the various kinetic parameters of eq 11. These kinetic parameters can be used in conjunction with eqs 7 and 8 to calculate both PTEF and QY at various reaction times. 3.5. PTEF and Quantum Yield Evaluation at Any Irradiation Time. Two kinetic models with different degrees of complexity were established in previous contributions.4 The first RN1 reaction network considers the formation and disappearance of aromatic species and CO2. The second model RN2 reaction network predicts the rate of formation and disappearance of aromatic species, short-chain carboxylic acids, as well as CO2 formation. 3.5.1. PTEF and Quantum Yield for Reaction Network 1 (RN1). The reaction network 1 (RN1) involves aromatic cyclic species being produced and consumed during the phenol photodegradation and before the ring-opening such as phenol (Ph), ortho-dihydroxybenzene (o-DHB), and para-dihydroxybenzene (p-DHB). The RN1 reaction network (Figure 4) considers the formation of CO2 either directly from phenol or as a result of the mineralization of ortho-dihydroxybenzene and para-dihydroxybenzene. The stoichiometric coefficients for each network reaction step have to be defined to comply with the carbon, hydrogen, and oxygen element balances as described in eqs 1a-1c) as follows: reaction 1 1

Thus, and in agreement with the stoichiometry, the OH• consumption rates are related to the rates of consumption of species in the various steps as rOH•,1 ) 28rph,1 rOH•,2 ) 2rph,2 rOH•,3 ) 26ro-DHB,3 rOH•,4 ) 2rph,4 rOH•,5 ) 26rp-DHB,5 rOH•,6 ) 0(19) Substituting eqs 19 and 5 into 3, yields the total rate of OH• consumption in terms of the changes of concentration for the liquid phase detectable species:

Thus, dCi Wirr ) dt V

(18)

C6H6O + 28OH• f 6CO2 + 17H2O

(13)

rOH•,T ) [rOH•,1 + rOH•,2 + rOH•,3 + rOH•,4 + rOH•,5 + rOH•,6] (20) rOH•,T ) [28rph,1 + 2rph,2 + 26ro-DHB,3 + 2rph,4 + 26rp-DHB,5] (21)

[

dCph,2 dCph,1 V (1 + K*ph) + 2 (1 + K*ph) + 28 Wirr dt dt dCph,4 dCo-DHB,3 (1 + K*o-DHB) + 2 (1 + K*ph) + 26 dt dt dCp-DHB,5 (1 + K*p-DHB) (22) 26 dt

rOH•,T )

]

One should notice that K*ph is a parameter accounting for the adsorption of phenol on the photocatalyst surface. This parameter also considers the effect of the other chemical species on phenol adsorption. K*p-DHB and K*o-DHB have similar physicochemical meaning. Their expressions are reported in the manuscript Appendix. Their derivation was reported in Serrano et al.19 Therefore one can see that in order to establish the rate of consumption of OH• groups one has to be able to express the various rates of change of liquid phase species concentrations. As shown by Salaices et al.3 and Ortiz et al.,4 these changes for i species in the step j can be described with a Hinshelwoodtype rate equation (refer to eq 11). For example, for the reaction of phenol in step 1, dCPh,1 -k1Cph(1 + K*ph) ) (23) dt 1 + KphCph + Ko-DHBCortho + Kp-DHBCpara Then, by substituting the species concentration derivatives for each reaction step, as considered in eq 22, it yields


rOH•,T ) (((2k2Cph + 2k4Cph + 28k1Cph)(1 + K*ph) + 26k3Co-DHB(1 + K*o-DHB) + 26k5C′p-DHB(1 + K*p-DHB))/ V (24) (1 + KphCph + Ko-DHBCortho + Kp-DHBCpara)) Wirr Consequently, with eq 24, the rOH•,T can be calculated knowing the intrinsic kinetic constants, the adsorption constants, and the species concentrations. Following this, the PTEF can be established as given by eqs 4 and 7: -rOH•,T∆HOH•Wirr ) (((2k2Cph + 2k4Cph + Qabsγ 28k1Cph)(1 + K*ph) + 26k3Co-DHB(1 + K*o-DHB) + 26k5Cp-DHB(1 + K*p-DHB))/(1 + KphCph + Ko-DHBCo-DHB + V∆HOH Kp-DHBCp-DHB)) (25) Qabsγ

PTEF )

Therefore, one can evaluate the PTEF using eq 25, the reaction network kinetic parameters, the species concentration profiles, the adsorption constants, the reactor volume, the photon energy absorbed by the photocatalyst, and the fraction of photons with a wavelength smaller than 387 nm. Once the PTEF is established, the quantum yields can be calculated using ηOH• ) 0.271:19 QY )

PTEF 0.271

(26)

In summary, using this methodology both the PTEF and quantum yields (QY) can be calculated for the complete span of irradiation times.

6829

Table 2. Parameters Estimated Using Three Experiments and Assessed with eqs 27-29 300 µmol/L 440 µmol/L 600 µmol/L kphenol-CO2, L/min kphenol-ortho, L/min kpheno-para, L/min kortho-CO2, L/min kpara-CO2, L/min kortho-para, L/min Kphenol, Kortho, Kpara L/(µmol/L) qmax mol/g cat.

0.0011 0.0065 0.003 0.0125 0.0125 0.0008 0.000724 0.000548

0.0011 0.0065 0.003 0.0085 0.0085 0.0008 0.000724 0.000548

0.0007 0.0052 0.003 0.006 0.006 0.0008 0.000724 0.000548

3.5.2. Calculation of PTEF and Quantum Efficiency for Reaction Network 1 (RN1). Specific examples of PTEF and quantum yields calculations are developed using eqs 25 and 26 already reported in section 3.5.1 and using the procedures described in this section. Figure 5 shows the experimental results obtained in typical phenol photodegradation experiments with iron ions added. Equations (27-29) are fitted to the experimental data and a separate group of parameters is obtained for each initial concentration level. This approach is preferred to the one considered by Serrano et al19 where a single set of parameters was obtained for the complete range of initial concentrations. While the derived parameters are in both cases numerically close, the method of the present study allows estimating more accurately the chemical species time-derivatives, main contributors to the PTEF and QY factors, at every reaction step. dCPh -(k2 + k1 + k4)Cph ) dt 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCd-HHB (27) dCortho (k2Cph - k3Co-DHB - k6Co-DHB) ) dt 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (28) dCpara k4Cph + k6Co-DHB - k3Cp-DHB ) dt 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (29)

Figure 5. Experimental and predicted profiles for the 5 mg/L Fe-assisted photocatalytic oxidation of 300, 440, and 600 µmol/L phenol solution using the KM1 model.4

The values for the estimated parameters (kinetic and adsorption constants) are reported in Table 2. Figures 6 and 7 were obtained using the above-calculated kinetic constants and the various stoichiometric, adsorption, thermodynamic, irradiation parameters: Ki, νi,j. ∆HOH, Wirr, Qabs, γ, and ηOH. One can observe that the PTEF and quantum yields expressed on a percentage basis surpass the 33% and 100%

Figure 6. PTEFs using parameters from Table 2 and RN1. Initial phenol concentrations in µmol/L: 300 (∆), 440 ([), 600 (0); 5 mg/L of iron ions.

Figure 7. Comparison of QY values using parameters from Table 2 and RN1. Initial phenol concentrations in µmol/L: 300 (∆), ([), 600 (0); 5 mg/L of iron ions.

6830


levels, respectively, during a first irradiation period (50-300 min). These parameters decrease progressively later during the second irradiation period. Thus, one can see that there is overall a good level of photon utilization with photon efficiency exceeding the QY limit of 100%. 3.5.3. PTEF and Quantum Yields for Reaction Network 2 (RN2). On the basis of this data a reaction network 2 (RN2) can be postulated. RN2 reaction network described in Figure 8 involves a parallel-series network and includes the intermediate aliphatic acids species. It is expected that the RN2 accounts for more chemical intermediate species, provides a more realistic description of the reaction network, and produces as a result more accurate values for the photocatalytic efficiency factors. One should notice that aliphatic acid species are lumped in the RN2 using a single pseudospecies3 which includes acetic, formic, oxalic, fumaric, and maleic acids as follows: Cac ) CAcAc + CFoAc + COxAc + CMeAc + CFuAc

(30)

According to Ortiz et al.4 and given acetic acid is the most predominant of the aliphatic acids, it was considered acetic acid as the species representing the aliphatic lump in the ensuing stoichiometric equations. Then, the summary of stoichiometric equations for all reaction steps is reaction 1 r1

C6H6O + 28OH• f 6CO2 + 17H2O

(31)

reaction 2 r2


(32)

reaction 3 r3


(33)

rOH•,1 ) 28rph,1 rOH•,2 ) 2rph,2 rOH•,3 ) 2rph,3 rOH•,5 ) 2ro-DHB,5 rOH•,7 ) 0 rOH•,9 ) 26rp-DHB,9 24 rOH•,10 ) rac,10 rOH•,11 ) 26ro-DHB,11(40) 3 Substituting these last expressions in eq 39 for the OH• balance gives rOH•,T ) (rOH•,1 + rOH•,2 + rOH•,3 + rOH•,5 + rOH•,7 + rOH•,9 +

(

rOH•,10 + rOH•,11) ) 28rph,1 + 2rph,2 + 2rph,3 + 2ro-DHB,5 + 26rp-DHB,9 +

24 r + 26ro-DHB (41) 3 ac,10

)

Besides, using eqs 41 and 5 for each compound, and on the basis of the network of Figure 8, we get

[

dCph,2 dCph,1 V (1 + K*ph) + 2 (1 + K*ph) + 28 Wirr dt dt dCo-DHB,5 dCph,3 (1 + K*ph) + 2 (1 + K*o-DHB) + 2 dt dt dCp-DHB,9 dCac,10 (1 + K*p-DHB) + 8 (1 + K*ac) + 26 dt dt dCo-DHB,11 • (1 + Ko-DHB ) (42) 26 dt

rOH•,T ) -

]

Regarding RN2 network, one can envision that a similar procedure as the one used for PTEF calculations with the RN1 network model can be employed assuming K*ac ) 0. Thus, the following equation can be obtained: PTEF ) (((28k1Cph + 2k2Cph + 2k3Cph)(1 + K*ph) + 2k5Co-DHB(1 + K*o-DHB) + 26k9Cp-DHB(1 + K*p-DHB) + 8k10Cac + 26k11Co-DHB(1 + K*o-DHB))/(1 + KphCph + V∆HOH• Ko-DHBCo-DHB + Kp-DHBCp-DHB)) (43) Qabsγ

reaction 5 r5

C6H6O2 + 2OH• + 2H2O f 3C2H4O2

(34)

reaction 7 r7

C6H6O2 f C6H6O2

3.5.4. Calculation of PTEF and Quantum Efficiency for RN2. Using the data of Figure 9 related with the degradation of 300, 400, and 590 micromoles of phenol per liter (µmol/L) the following kinetic model was fitted,

(35)

dCph ) -(k1Cph + k2Cph + k3Cph)/denom dt

reaction 9 r9

C6H6O2 + 26OH• f 6CO2 + 16H2O

(36)

dCo-DHB dt

(44)

) (k2Cph - k5Co-DHB - k7Co-DHB - k11Co-DHB)/denom

(45) reaction 10 r10

3C2H4O2 + 24OH• f 6CO2 + 18H2O

(37)

dCp-DHB ) (k3Cph + k7Co-DHB - k9Cp-DHB)/denom (46) dt

reaction 11 •

r11

C6H6O2 + 26OH f 6CO2 + 16H2O

dCac ) (k5Co-DHB - k10Cac)/denom dt

(38)

Using a similar methodology than the one described for RN1, the total rate of consumption of OH• (rOH•,T) can be obtained in terms of the consumption of OH• radical in each step as follows: rOH•,T ) rOH•,1 + rOH•,2 + rOH•,3 + rOH•,5 + rOH•,7 + rOH•,9 + rOH•,10 + rOH•,11(39) Moreover, employing the stoichiometric coefficients already known from equations 31-38 results in

(47)

where denom ) 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB Furthermore, a more adequate and descriptive reaction network for phenol photocatalytic conversion can be considered on the basis of all observable species incorporating the aliphatic acids as reported in Figure 9. Again in this case, the various kinetic parameters were adjusted to reproduce the concentrations profiles to each curve generated with a different initial phenol concentration, as


6831

Figure 8. Reaction network 2 (RN2), phenol ) Ph ) C6H6O, o-dihydroxybenzene ) o-DHB ) C6H6O2, p-dihydorxybenzene ) p-DHB ) C6H6O2, aliphatic acids ) Ac ) C2H4O2. Note: The step 7 is not considered in the account of reacted OH• groups given that this is an isomerization step not requiring OH• groups.

reported in Table 3. Note that the adsorption equilibrium constant for the carboxylic acids is not accounted because of its low value and its negligible statistical significance.4 As stated before for RN1, even if these parameters were close in magnitude to the ones established for the complete range of concentrations, it was judged that this method was more appropriate to calculate the species time-concentration derivatives at various irradiation times. Then, the PTEF was evaluated using a similar procedure than the one used for the RN1 network: (a) employing eq 42 and the parameters from Table 3, (b) using eq 9 for QY calculations. Figures 10 and 11 report the PTEF and QY profiles for the experiments performed at three different initial concentrations and accounting for the carboxylic acid species.

One can notice that the calculated PTEF and QY for the RN2 which includes the aliphatic acids yields efficiency values in excess to 20% and 75%, respectively, for the irradiation period in the 50-200 min range. Thus, accounting for the aliphatic acids mildly reduces the rate of some steps allowing a slower pace in the OH• radical consumption, yielding an overall photoconversion process slightly less efficient. Consequently the RN2 network is considered more accurate and representative of the species involved, provides high and accurate energy efficiencies in Photo-CREC Water-II reactors.

Figure 10. PTEF based on RN2 and using parameters from Table 3. Initial phenol concentrations in µmol/L: 300 (∆), 440 ([), 600 (0); 5 mg/L of iron ions.

Figure 9. Experimental and predicted profiles for the 5 mg/L Fe-assisted photocatalytic oxidation of 300, 400, and 500 µmol/L phenol solution using the KM2 model. Table 3. Estimated Parameters from Three Experiments Assessed with eqs 44-47 300 µmol/L 440 µmol/L 600 µmol/L kphenol-CO2, L/min kphenol-ortho, L/min kpheno-para, L/min kortho-CO2, L/min kpara-CO2, L/min kortho-para, L/min kacid-CO2, L/min kortho-acid, L/min Kphenol, Kortho, Kpara, L/(µmol/L) qmax, mol/g cat

0.0012 0.004 0.0035 0.0019 0.018 0.000537 0.009 0.011 0.000724 0.000548

0.0011 0.0055 0.0035 0.0011 0.011 0.000537 0.0025 0.006 0.000724 0.000548

0.0008 0.004 0.003714 0.0008 0.007 0.000537 0.0019 0.003 0.000724 0.000548

Figure 11. QY based on RN2 and using parameters from Table 3. Initial phenol concentrations in µmol/L: 300 (∆), 440 ([), 600 (0); 5 mg/L of iron ions.

6832


3.6. Review of the PTEF and QY Values with Iron Ion Addition. As described in the previous sections of the present study the PTEF and QY values can be calculated via a careful counting of the OH• radicals consumed at every stage of the photocatalytic conversion. To compute the OH• radicals consumed, both stoichiometric and kinetic equations are required as those provided by the “parallel-series” reaction network. Even if using this method for the photocatalytic conversion of phenol free of iron ions, gives encouraging PTEF and QY values,19 the objective of the present study is to demonstrate that even higher efficiencies are possible using iron ions in water media, Measured efficiencies of the upper QY and PTEF theoretical limits are 100% and 27.1%, respectively, where every photon contributes to the formation of one OH group or 27.1% of the complete photon energy is used for the formation of an OH group. The results obtained with the more reliable RN2 show that these PTEF and QY theoretical values are close indeed in the Photo-CREC Water reactor to these limits with relatively little loss of efficiency assigned to a small extent of photon recombination.

K*ph ) W V

K*o-DHB

(b) Energy efficiency evaluations also call for a reaction network, an adequate kinetic model, and experimentally obtained concentration profiles for both the model compound and the intermediate species. Two kinetic models developed in previous research studies4 and based in a parallel-series reaction network (RN1 and RN2) are used in these assessments. (c) Energy efficiency calculations are successfully developed in this study for the iron ion enhanced photocatalytic conversion of phenol in water media. Very high energy efficiencies neighboring the maximum theoretical values of 100% QY are successfully confirmed. (d) Determination of QY values in Photo-CREC Water-II reactors shows quantum efficiencies in excess of 70% under prolonged irradiation periods which points toward high degrees of photon utilization and very limited photon recombination. (e) These high PTEFs and QYs are very encouraging and set up excellent prospects for the extensive future use of photocatalysis in water treatment scaled-up units.

Acknowledgment The authors wish to show appreciation to NSERC-Canada for their financial support to this project. B. Serrano would like to specially thank PRODERIC 2007-I and PIFI 2007-33-07 from Mexico for their generous support.

Appendix K*i constants can be calculated with eqs A1, A2, A3 as follows:19

Kphqm + Ko-DHBKphqmCo-DHB + Kp-DHBKphqmCp-DHB

[ W ) V

K*p-DHB )

4. Conclusions (a) Energy efficiency factor evaluations, in the case of PTEF and QY, require the calculation of the total OH• radicals consumed at every time point of the photocatalytic conversion and of stoichiometric coefficients derived from carbon, hydrogen, oxygen elemental balances assigned to each of the identifiable reaction steps.

{[

{[

[

W V

[

[

]

]

Ko-DHBqm + Ko-DHBKphqmCph+ Kp-DHBKo-DHBqmCp-DHB

(denom)2 -Ko-DHBKphqmCo-DHB 2

(denom)

{[

]

+ (denom)2 -Ko-DHBKphqmCph dCo-DHB + dCph (denom)2 -Kp-DHBKphqmCph dCp-DHB (A1) dCph (denom)2

[

]

+

dCph + dCo-DHB

]

}

-Kp-DHBKo-DHBqmCo-DHB dCp-DHB (A2) dCo-DHB (denom)2

Kp-DHBqm + Kp-DHBKphqmCph+ Kp-DHBKo-DHBqmCo-DHB

(denom)2 -Kp-DHBKphqmCp-DHB 2

(denom)

[

]

}

]

]

dCph + dCp-DHB

]

+

}

-Kp-DHBKo-DHBqmCp-DHB dCo-DHB (A3) dCp-DHB (denom)2

with denom ) 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB Nomenclature C ) speed of light, 3.0 × 108 ms-1 CA ) concentration of compound A, mol L-1. Ci ) concentration of the i chemical species, mol L-1 Ci,j ) concentration of the i chemical species in reaction step j, mol L-1 Ci,T ) total concentration of the i chemical species, mol L-1 CCO2 ) concentration of CO2, mol L-1 CH2O ) concentration of H2O, mol L-1. COH• ) concentration of OH• radical, mol L-1. Ci ) concentration of compound i in equilibrium. E ) energy of a photon at a given wavelength, J. Eav ) average energy of a photon, J. h+ ) hole generated in the valence band of the TiO2. ki ) apparent kinetic reaction constant for step i, min-1 K*i ) dimensionless adsorption constant (eq 88) Ki ) adsorption equilibrium constant, L mol-1 h ) Planck’s constant, 6.63 × 10-34 J s-1 I(λ) ) intensity of light, W cm-2 Ni,ads ) number of moles of adsorbed species i, moles Ni,T ) total number of moles of species i in fluid and solid phases, moles Ni,L ) number of moles of species i in liquid phase, moles qi,m ) maximum adsorbed concentration of component i, mol gads-1 qi,ads ) concentration adsorbed at equilibrium, mol gads-1 Qabs ) rate of irradiated energy absorbed in photocatalytic reactor, J s-1 Qused ) rate of irradiated energy used for the formation of OH• radicals, J s-1 rOH•,T ) total reaction rate of OH• radicals, mol gcatirr-1 s-1 rA,j ) reaction rate of A in step j, mol gcatirr-1 s-1 rOH•,j ) reaction rate of OH• radical in step j, mol gcatirr-1 s-1

Ind. Eng. Chem. Res., Vol. 49, No. 15, 2010 -1

-1

ri,j ) reaction rate of component i in step j, mol gcatirr min r*i,j ) rate of chemical change, mol min-1 gcatirr-1 (always positive) ri ) reaction rate of component i, mol gcatirr-1 min-1 ri,T ) total reaction rate of component i, mol gcatirr-1 min-1 rph,j ) reaction rate of phenol in step j, mol gcatirr-1 min-1 ro-DHB,j ) reaction rate of ortho-dihydroxybenzene in step j, mol gcatirr-1 min-1 rp-DHB,j ) reaction rate of para-dihydroxybenzene in step j, mol gcatirr-1 min-1 rac,j ) reaction rate of carboxylic acids in step j, mol gcatirr-1 min-1 t ) time, min V ) reactor volume, L W ) weight of adsorbent material gads Wirr ) irradiated photocatalyst weight, g Greek Symbols ηOH ) fraction of photon energy to form OH• radicals. γ ) fraction of the absorbed energy contributed by photons with λ < 380 nm ∆HOH• ) enthalpy of OH• radical formation in a photochemical reaction J mol-1 ∆H°f,i ) standard enthalpy of formation for the component i, J mol-1 λ ) wavelength, nm λav ) average wavelength, nm νA,j ) stoichiometric coefficient of compound A in reaction step j νOH,j ) stoichiometric coefficient of OH• radical in reaction step j νH2O,j ) stoichiometric coefficient of H2O in reaction step j νh,j ) stoichiometric coefficient of component h in reaction step j νi,j ) stoichiometric coefficient of component i in reaction step j νph,j ) stoichiometric coefficient of phenol in reaction step j νo,j ) stoichiometric coefficient of ortho-dihydroxybenzene in reaction step j νp,j ) stoichiometric coefficient of para-dihydroxybenzene in reaction step j νac,j ) stoichiometric coefficient of carboxylic acids in reaction step j Subscripts ads ) adsorbed av ) average cat ) catalyst in ) initial condition, t ) 0 irr ) irradiated m ) maximum p ) para o ) ortho ph ) phenol Ac ) carboxylic acids. AcAc ) acetic acid. FuAc ) fumaric acid. FoAc ) formic acid. LuAc ) lumped carboxylic acids OxAc ) oxalic acid. MeAc ) malonic acid. Acronyms PTEF ) photochemical thermodynamic efficiency factor RN1 ) reaction network 1 RN2 ) reaction network 2 QY ) quantum yield CREC ) chemical reactor engineering center o-DHB ) ortho-dihydroxybenzene p-DHB ) para-dihydroxybenzene OC-AR ) calculated organic carbon for aromatic compounds OC-acids ) calculated organic carbon for carboxylic acids

6833

Literature Cited (1) Frank, S. N.; Bard, A. J. Heterogeneous photocatalytic oxidation of cyanide and sulfite in aqueous solutions at semiconductor powders. J. Phys. Chem. 1977, 81, 1484–1488. (2) de Lasa, H.; Serrano, B.; Salaices, M. Photocatalytic Reaction Engineering; Springer: New York, 2005. (3) Salaices, M.; Serrano, B.; de Lasa, H. Photocatalytic conversion of phenolic compounds in slurry reactors. Reaction kinetic modeling. Chem. Eng. Sci. 2004, 59, 3–15. (4) Ortiz, A.; Serrano, B.; Salaices, M.; de Lasa, H. Photocatalytic oxidation of phenol: Network, kinetic modeling and parameter estimation. Ind. Eng. Chem. Res. 2007, 46 (23), 7394–7409. (5) Ortiz-Gomez, A.; Serrano-Rosales, B.; de Lasa, H. Enhanced mineralization of phenol and other hydroxylated compounds in a photocatalytic process assisted with ferric ions. Chem. Eng. Sci. 2008, 63, 520– 557. (6) Ortiz-Gomez, A.; Serrano-Rosales, B.; Moreira-del-Rio, J.; de Lasa, H. Mineralization of phenol in an improved photocatalytic process assisted with ferric ions: Reaction network and kinetic modeling. AdVances in Chemical Engineering; Academic Press: Amsterdam, The Netherlands, 2009; Vol. 36, Chapter 3, pp 69-110. (7) Bolton, J. R.; Cater, S. Homogeneous photodegradation of pollutants on contaminated water: An introduction. Aquatic and Surface Photochemistry; Hels, G., Zepp, R., Crosby, D., Eds.; 1994; Lewis Publications: Boca Raton, FL, pp 467. (8) Bockelmann, D.; Goslich, R.; Weichgrebe, D.; Bahnemann, D. Solar Detoxification of Polluted Water: Comparing the Efficiencies of a Parabolic Trough Reactor and a Novel Thin-Film Fixed Bed Reactor. In Photo Catalytic Purification of Water and Air; Ollis, D., Al-Ekabi, H., Eds.; Elsevier: New York, 1993; pp 771-777. (9) Sun, L.; Bolton, J. R. Determination of the quantum yield for the photochemical generation of hydroxyl radicals in TiO2 suspensions. J. Phys. Chem. 1996, 100, 4127–4134. (10) Riegel, G.; Bolton, J. R. Photocatalytic efficiency variability in TiO2 particles. J. Phys. Chem. 1995, 99, 4215–4224. (11) Davydov, L.; Smirniotis, P. G.; Pratsinis, S. E. Novel differential reactor for the meassurement of overall quantum yields. Ind. Eng. Chem. Res. 1999, 38 (4), 1376–1383. (12) Salinaro, A.; Emeline, A. V.; Zhao, J.; Hidaka, H.; Riabchuk, V. K.; Serpone, N. Terminology, relative photonic efficiencies and quantum yields in heterogeneous photocatalysis. Part I, suggested protocol (technical report) IUPAC. Pure Appl. Chem. 1999, a71 (2), 321–335. (13) Salinaro, A.; Emeline, A. V.; Zhao, J.; Hidaka, H.; Riabchuk, V. K.; Serpone, N. Terminology, relative photonic efficiencies and quantum yields in heterogeneous photocatalysis. Part II, experimental determination of quantum yields (technical report), IUPAC. Pure Appl. Chem. 1999, b71 (2), 303–320. (14) Serpone, N.; Terzian, R.; Lawless, D.; Kennepohl, P.; Sauv, G. On the usage of the turnover numbers and quantum yields in heterogeneous photocatalysis. J. Photochem. Photobiol. A 1993, 73, 11–16. (15) Serpone, N. Relative photonic efficiencies and quantum yields in heterogeneous photocatalysis. Photochem. Photobiol. A 1997, 104, 1–12. (16) Serpone, N.; Salinaro, A.; Emeline, A.; Ryabchuk, V. Turnovers and photocatalysis. A mathematical description. J. Photochem. Photob. A 2000, 130, 83–94. (17) Serrano, B.; de Lasa, H. Photocatalytic degradation of water organic pollutants. kinetic modeling and energy efficiency. Ind. Eng. Chem. Res. 1997, 36, 4705–4711. (18) Serrano, B.; de Lasa, H. Photocatalytic degradation of water organic pollutants. pollutant reactivity and kinetic modeling. Chem. Eng. Sci. 1999, 54, 3063–3069. (19) Serrano, B.; Ortiz-Gomez, A.; Moreira-del-Rio, J.; de Lasa, H. Energy efficiency in photocatalytic reactors for the full span of reaction times. Ind. Eng. Chem. Res. 2009, 48 (22), 9864–9876. (20) Serrano, B.; Salaices, M.; Ortiz, A.; de Lasa, H. Quasi equilibrium and non equilibrium adsorption in heterogeneous photocatalysis. Chem. Eng. Sci. 2007, 62, 5160–5166. (21) Salaices, M.; Serrano, B.; de Lasa, H. I. Experimental evaluation of photon absorption in an aqueous TiO2 slurry reactor. Chem. Eng. J. 90, 2002, 219–229. (22) Salacies, M.; Serrano, B.; de Lasa, H. Photocatalytic conversion of organic pollutant. extinction coefficients and quantum efficiencies. Ind. Eng. Chem. Res. 2001, 40, 5455–5464.

ReceiVed for reView October 30, 2009 ReVised manuscript receiVed January 15, 2010 Accepted January 25, 2010 IE9017034

Photocatalytic Thermodynamic Efficiency Factors. Practical Limits in

Recommend Documents