Energy Efficiency in Photocatalytic Reactors for the Full Span of

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Ind. Eng. Chem. Res. 2009, 48, 9864–9876

Energy Efficiency in Photocatalytic Reactors for the Full Span of Reaction Times 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 Facultad de Ciencias Quı´micas, Programa de Ingenierıá Quı´mica, UniVersidad Autońoma de Zacatecas, Me´xico

OH• radicals react in photocatalytic reactors via adsorbed species on the catalytic surface through complex reaction mechanisms leading to complete mineralization of organic molecules. Our research group has recently contributed with kinetic modeling of the photocatalytic network using a parallel-series reaction network. This kinetic approach helps toward the assessment of the photocatalytic thermodynamic efficiency factors (PTEF) and quantum yields (QY). Efficiency calculations consider stoichiometric relationships involving observable chemical species and OH• groups. These stoichiometric equations set the OH• requirements for reaching a particular intermediate species and for the complete mineralization of them. On this basis, the PTEF and QY factors for phenol photoconversion point toward a high degree of photon utilization as in the case of Photo-CREC units and, as a result, confirm the value of photocatalysis for the conversion of organic pollutants in water. 1. Introduction Heterogeneous photocatalysis has emerged as a viable alternative to remove water waste hazardous pollutants, converting them at the end into CO2 and mineral acids.1 Phenol has been extensively used as a model pollutant to both, understand the photocatalytic reaction mechanisms and test the performance of various photocatalytic reactors. Kinetic models for the photocatalytic oxidation of phenol and other phenolic compounds have been mainly based on the initial rates of reaction. Such kinetic models fail to account for the formation and the conversion of reaction intermediate species. Recently, our research team2,3 developed a series-parallel kinetic model based on measurable aromatics and aliphatic acid intermediates. A different number of OH• radicals is required to reach a specific species in the parallel-series network. Regarding energy efficiencies for ranking various photoconversion reactor configurations, their importance has been emphasized in a number of studies.4-13 In spite of this, determination of photocatalytic reactor efficiency has remained a challenge due to the many variables involved, such as reaction rates, reaction mechanism, OH• free radicals participating in the reaction steps, kinetic constants, adsorption parameters, irradiation field, light absorbed by the photocatalyst, and amount and type of photocatalyst. Serrano and de Lasa14,15 proposed a photochemical thermodynamic efficiency factor (PTEF), a key parameter relating the energy needed to produce OH• radicals over the irradiated energy absorbed by the photocatalyst. Our research group has further progressed in energy efficiency assessments with better reaction networks, enhanced kinetic modeling, and irradiation field assessments. As a result, accurate and comprehensive determination of photocatalytic reactor efficiencies can be provided. In the present study, it is shown that in the Photo-CRECWater II (chemical reactor engineering center)16 both PTEF and the quantum yields (QY) can be obtained using a parallel-series network, kinetic models, and stoichiometric equations. This * To whom correspondence should be addressed. E-mail: hdelasa@ eng.uwo.ca. † Universidad Autońoma de Zacatecas. ‡ The University of Western Ontario.

allows the calculation of the total OH• consumed at various extents of model pollutant photoconversion. 2. Experimental Setup Figure 1 illustrates the components and special features of the Photo-CREC-Water II reactor. The Photo-CREC-Water II reactor is constituted by the following components: a lamp (1), a glass inner tube with a diameter of 3.2 cm (2), an inner tube with a 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). The reactor has 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 being circulated and irradiated from the central region of the inner tube, where the near UV lamp is placed.16 An interchangeable inner Pyrex glass tube varying in thickness and diameter enables the Photo-CREC-Water II to modify

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.

10.1021/ie900353n CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009

Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009 Table 1. Characteristics of Photo-CREC-Water II component

specifications

value

unit characteristics annular reactor

stirred tank

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

3.2-cm-diameter 5.6-cm-diameter lamps windows (fused silica)

thickness thickness lamp radius, lamp length window radius

Total organic content (TOC) was measured using a Shimadzu total organic analyzer TOC-5050. HPLC analyses were carried out using a Waters 1525 HPLC.

1.74 cm; 2.82 cm

3. Energy Efficiency Factors

4.45 cm 44 cm 2.5 L 1.4 L 3.5 L

In the photocatalytic processes, it is important to account for the pollutant adsorption phenomena on the catalyst surface and to establish a kinetic model to estimate the reaction and adsorption parameters, the global reaction rate and the reactor efficiency. Serrano et al.17 analyzed the different affinity of the chemical species on the TiO2 surface, and they concluded that some compounds adsorb strongly and slowly, following a nonadsorption equilibrium behavior, while others, in the case of phenol and other phenolic compounds, adsorb quickly but weakly, following an equilibrium adsorption, described by the Langmuir adsorption isotherm. The definition of the photochemical thermodynamic efficiency factor (PTEF)14,15 considers the ratio between the energy utilized for the OH• radical formation and the energy absorbed by the photocatalyst. In the present study, this definition is modified including a γ parameter representing the fraction of the photon energy absorbed by TiO2 with a wavelength smaller than the one required for superseding the semiconductor band gap.

reactor inner tube 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

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Wirr

0.35 g

Qabs

0.14 g/L 16 L/min 1.625 W

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 it is used to modify the flow rate. In order to facilitate radiometric and spectroradiometric 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 fourpoint 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 a 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 added to the mixture. More H2SO4 solution was added 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. 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 was 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.

PTEF ) ηOH )

-rOH · ,T∆HOH•Wirr Qused ) Qabsγ Qabsγ

(1)

with rOH•,T being in moles per minute-gram of irradiated catalyst, Wirr in grams of irradiated catalyst, ∆HOH• in Joules per mole, Qabs in Joules per minute, and γ without units. According to eq 1, the main parameters to estimate the PTEF are the values of the rate of reaction of the free radical OH• (rOH•,T), enthalpy of OH• radical formation (∆HOH•), the absorbed photons by the catalyst (Qabs), and fraction of the absorbed energy contributed by photons with λ < 380 nm (γ) (Appendix I). In a “j” chemical reaction step in a photocatalytic reaction network, one can consider OH• groups and two species with a different extent of oxidation, with “i” species (CnHmOo) being the one at the lower oxidation state and “h” species (CxHyOz) being the one at the higher oxidation state. These two species have to satisfy the oxygen, carbon, and hydrogen elemental balances as needed by reaction stochiometry. One should bear in mind that this stochiometric equation is a chemical path independent state function. 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

(2)

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 (Elemental carbon balance) νi,jm + νOH•,j - νh,jy - 2νH2O,j ) 0 (Elemental hydrogen balance) νi,jo + νOH•,j - νh,jz - νH2O,j ) 0 (Elemental oxygen balance) It is interesting to note that usually the atomic balance for carbon can be solved first, decoupled from the other two

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Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009

Figure 2. Phenol degradation and its aromatic intermediates.3

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. rOH•,j ri,j ) νi,j νOH•,j

then, rOH•,j )

νOH•,j r νi,j i,j

(3)

Furthermore, 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 2. This rate can be represented by the following equation: rOH•,T )

∑r

OH•,j

)

∑

νOH•,j r νi,j i,j

Figure 3. Comparison between the measured TOC and the calculated TOC (OC-AR line) for 30 ppm C in phenol. CO2 profiles are in a different scale (six times larger than the one shown on the y-axis).3

(4)

where rOH•,j is the rate of consumption of OH• radicals in step j of the reaction scheme containing several steps, 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. 4. Parallel-Series Reaction Network Figures 2 and 3 report the experimental results obtained with phenol at an initial concentration of 440 µmol/L (30 ppm C in phenol) in a Photo-CREC-Water II. Salaices et al.2 and Ortı´z et al.3 proposed a parallel-series reaction network for photocatalytic reactions based on the observable chemical species, such as the one described in Figure 4. Support for the parallel-series model can be found in the following observations: (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.

Figure 4. Reaction network for RN2. Note: step 7 is not considered in the accounted OH• groups given that it is an isomerization step not requiring OH• groups: phenol ) Ph ) C6H6O; o-dihydroxybenzene ) o-DHB ) C6H6O2; p-dihydorxybenzene ) p-DHB ) C6H6O2; aliphatic acids ) Ac ) C2H4O2.

5. Kinetic Model under a Parallel-Series Reaction Network A photocatalytic reaction system can be modeled on the basis of a number of applicable assumptions as follows: The controlling steps for the photochemical conversion of phenol are the intrinsic chemical reaction steps. 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.17 All the experiments are performed starting from adsorption equilibrium conditions between the photocatalyst and the model pollutant, in this case phenol. Accordingly, the expressions for the rate of change of the i species in step j can be written in the form of a LangmuirHinshelwood relationship2,1 as follows: dCi,j ) νi,j dt

ki,jKiCi

(5)

n

1+

∑KC

j j

j)1

where ki,j is the intrinsic kinetic constant for species i in step j, in moles per minute-gram of irradiated catalyst, Ki is the adsorption constant in liters per mole, and Ci is the liquid phase concentration in moles per liter.


In addition and considering that the experiments in which the photochemical transformations were carried out, involved an irradiated section and a photocatalytic reactor operated in the batch mode, 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

1+

(6)

j

n

∑KC

j j

j)1

)

V Wirr

(6a)

∑ν

i,jr * i,j

(7)

j

However and if one attempts to use eq 1 for PTEF calculations, it is necessary to relate the total reaction rate of OH• radical consumption, (rOH•,T) with the rate of consumption of the model compound species and the rates of production and consumption of the detectable intermediates species. Considering the reaction rate definition for the i species and step j (see eq 6), one can conclude that ri,j becomes

{

}

1 V dCi,j (1 + K *) i Wirr dt νi,j

r *i,j )

(8)

As a result one can see that a more rigorous consideration of reaction rate definition requires the modification of eq 6 including a (1 + K*)term reflecting the influence of adsorption i as defined in Appendix IV. Furthermore, the reaction rate for OH• radicals (rOH•,T) in terms of the concentrations of species in the liquid phase can be expressed, in agreement with eq 4, as rOH•,T )

∑r

•

OH ,j

)

∑

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

{ {

∑

PTEF )

∑

PTEF )

νOH•,j νi,j

2

QY )

PTEF ηOH•

Two kinetic models with different degrees of complexity were established in previous contributions.3 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. 6.1. PTEF and Quantum Yield for Reaction Network 1 (RN1). Reaction network 1 involves aromatic cyclic species being produced and consumed during the phenol photodegradation and before the ring-opening such as phenol (Ph), orthodihydroxybenzene, (o-DHB) and para-dihydroxybenzene (pDHB). The RN1 reaction network (Figure 5) 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 eq 2 as follows: 1

C6H6O + 28OH• 98 6CO2 + 17H2O Reaction 1 (14) 2

C6H6O + 2OH• 98 C6H6O2 + H2O Reaction 2

}}

(9)

(16)

j

4

}}

{ {

V dCi,j (1 + K*) i Wirr dt

νi,j

2

{{

(15)

3

-rOH•,T∆HOH•Wirr Qused ) Qabsγ Qabsγ

νOH•,j

(13)

6. PTEF and Quantum Yield Evaluation at Any Irradiation Time


5

C6H6O2 + 26OH• 98 6CO2 + 16H2O Reaction 5

∆HOH•Wirr

j

}}

dCi,j (1 + K*) i dt Qabsγ

(17)

(10)

(18)

Qabsγ

∑

(12)

C6H6O2 + 26OH• 98 6CO2 + 16H2O Reaction 3

Substituting eq 9 in eq 1 yields PTEF ) η )

PTEF ) QYηOH•

Details of ηOH• calculation are given in Appendix II.

with ri,j* in moles per minute-gram of irradiated catalyst, dCi/dt in moles per liter-minute, V in liters, and Wirr in grams. Thus, Wirr dCi ) dt V

(quantum yield) and ηOH• being the fraction of photon energy used in forming an OH• radical:

Then, QY can be calculated as

(∑ )

ki,jKiCi

9867

6

∆HOH•V

C6H6O2 98 C6H6O2 Reaction 6

j

(19)

(11)

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

For instance and according to stoichiometric eq 14,18 the reaction rates for step 1 (R1) and for the radical OH• in step 1 (rOH•,1) are

9868


rOH•,1 νOH•,1 rph,1 -28 r ) ,r • ) r ) ) 28rph,1 νph,1 νOH•,1 OH ,1 νph,1 ph,1 -1 ph,1 (20)

dCi,j ) dt

νi,jkiCi

(24)

n

1+

∑KC

j j

j)1

Using the same approach, equations can be established for the other reaction steps in order to establish the consumption of OH• radical in each step, rOH•,j, as a function of the i organic species.

For example, for the reaction of phenol in step 1 -k1Cph dCph,1 ) dt 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (25)

νOH•,1 νOH•,2 rph,1, rOH•,2 ) r , νph,1 νph,2 ph,2 νOH•,3 νOH•,4 r , rOH•,4 ) r , rOH•,3 ) νo-DHB,3 o-DHB,3 νph,4 ph,4 νOH•,5 r , rOH•,6 ) 0 rOH•,5 ) νp-DHB,5 p-DHB,5

Then, substituting the species concentration derivatives for each reaction step, as considered in eq 25, it yields

As a result, replacement of the stoichiometric coefficients given in eqs 14-19 yields the following:

26k3Co-DHB(1 + K*o-DHB) + 26k5Cp-DHB(1 + K*p-DHB)] V 1 + KphCph + Ko-DHBCortho + Kp-DHBCp-DHB Wirr (26)

rOH•,1 )

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

(21)

Substituting eqs 21 and 9 into 4 yields the total rate of OH• consumption in terms of the changes of concentration for the liquid phase detectable species: rOH•,T ) rOH•,1 + rOH•,2 + rOH•,3 + rOH•,4 + rOH•,5 + rOH•,6 rOH•,T ) 28rph,1 + 2rph,2 + 26ro-DHB,3 + 2rph,4 + 26rp-DHB,5 (22)

[

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) (23) 26 dt

rOH•,T )

]

Therefore one can see that in order to establish the rate of consumption of OH• groups one has to express the various rate of change of liquid phase species concentrations. As shown by Salaices et al.2 and Ortiz et al.,3 these changes for i species in the step j can be described with a Hinshelwood type rate equation as

rOH•,T ) - [(2k2Cph + 2k4Cph + 28k1Cph)(1 + K*ph) +

Consequently, with eq 26, 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 1 or 11. PTEF )

-rOH•,T∆HOH•Wirr ) Qabsγ

[(2k2Cph + 2k4Cph + 28k1Cph)(1 + K*ph) + 26k3Co-DHB(1 + K* o-DHB) + 26k5Cp-DHB(1 + K* p-DHB)] V∆HOH 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB Qabsγ

(27)

Thus, one can evaluate the PTEF using eqs 27, 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. With this end, the enthalpy of formation of OH• is estimated at 98 300 J/mol (Appendix III), considering PTEF ) QYηOH•. Given the fraction ηOH• (Appendix II) is 0.271, the QY can be calculated as QY )

PTEF 0.271

(28)

In summary, using this methodology both the PTEF and quantum yields (QY) can be established for the complete span of irradiation times. 6.2. Calculation of PTEF and Quantum Efficiency for Reaction Network 1 (RN1). Specific examples of PTEF and quantum yields calculations are developed using eqs 27 and 28 and the procedures described in this section. Figure 6 shows experimental results obtained in typical photocatalytic degradation experiments. First, the data in Figure 6 is fitted to the following equations (29-31). The values for the estimated parameters (kinetic and adsorption constants) are reported in Table 2. Figure 5. Reaction network 1 (RN1). Note: step 6 is not considered in the accounting of OH• groups because this step is an isomerization and it does not affect the required OH• groups: phenol ) Ph ) C6H6O; o-DHB ) C6H6O2; p-DHB ) C6H6O2.

dCph -(k2 + k1 + k4)Cph ) dt 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (29)


(k2Cph - k3Co-DHB - k6Co-DHB) dCortho ) dt 1 + KphCph + Ko-DHBCo-DHBKp-DHBCp-DHB

9869

r5

C6H6O2 + 2OH• + 2H2O 98 3C2H4O2 Reaction 5 (30)

(36) r7

dCpara k4Cph + k6Co-DHB - k5Cp-DHB ) dt 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (31) dCCO2 dt

k1Cph + k5Cp-DHB + k3Co-DHB ) 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (32)

C6H6O2 98 C6H6O2 Reaction 7

(37)

r9

C6H6O2 + 26OH• 98 6CO2 + 16H2O Reaction 9 (38) r10

3C2H4O2 + 24OH• 98 6CO2 + 18H2O Reaction 10 (39)

Figure 7 reports the changes of PTEF with the irradiation time for the three concentration profiles reported in Figure 6. It can be observed that PTEFs and quantum yields expressed on a percentage basis remain high, always above 10% and 40%, respectively, during a considerable irradiation period (first 400 min of irradiation, for 440 µM/L of initial pollutant concentration), decreasing later on progressively during the remaining 350-680 min of irradiation. Thus, one can see that there is relatively even and good photon utilization during this first phase of photoconversion, with this photon efficiency being reduced toward the end of the irradiation period. Thus and on this basis, one can perform PTEF and QY calculations using eqs 27 and 28. The results obtained are reported in Figures 7 and 8. 6.3. PTEF and Quantum Yields for Reaction Network 2 (RN2). Furthermore, a more adequate and descriptive reaction network for phenol photocatalytic conversion can be considered with the reaction network 2 (RN2). RN2 described in Figure 4 involves a parallel-series network and includes the intermediate aliphatic acids species. It is expected that 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 RN2 using a single pseudospecies3 which includes acetic, formic, oxalic, fumaric, and maleic acids as follows: Cac ) CAcAc + CFoAc + COxAc + CMeAc + CFuAc According to Ortiz et al.3 and given that acetic acid is the most predominant of the aliphatic acids, it was considered that acetic acid is the species representing the aliphatic lump in the ensuing stoichiometric equations.

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 (40) Considering also that rOH•,1 rph,1 ) , νph,1 νOH•,1 rOH•,1 )

νOH•,1 r , νph,1 ph,1

rOH•,5 )

νOH•,5 r , νo-DHB,5 o-DHB,5

rOH•,2 )

νOH•,2 r , νph,2 ph,2

rOH•,7 ) 0,

rOH•,3 )

rOH•,9 )

νOH•,3 r νph,3 ph,3

νOH•,9 r νp-DHB,9 p-DHB,9

νOH•,10 r νac,10 ac,10

Using the stoichiometric coefficients already known, from eqs 33-39) rOH•,1 ) 28rph,1 rOH•,2 ) 2rph,2 rOH•,3 ) 2rph,3 rOH•,5 ) 2ro-DHB,5 rOH•,7 ) 0 rOH•,9 ) 24 26rp-DHB,9 rOH•,10 ) rac,10 3

(41)

Substituting these last expressions in eq 40 for the OH• balance rOH•,T ) (rOH•,1 + rOH•,2 + rOH•,3 + rOH•,5 + rOH•,7 + rOH•,9 + rOH•,10)

(

) 28rph,1 + 2rph,2 + 2rph,3 + 2ro-DHB,5 + 26rp-DHB,9 + 24 r 3 ac,10

)

Besides, using eqs 41 and 9 for each compound and based on the network of Figure 4, the following results:

r1

C6H6O + 28OH• 98 6CO2 + 17H2O Reaction 1 (33) r2

(34)

r3


νOH•,1 -28 r r ) ) 28rph,1 νph,1 ph,1 -1 ph,1

rOH•,10 )

Then, the summary of stoichiometric equations for all reaction steps is


rOH•,1 )

(35)

[

dCph,1 dCph,2 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) (42) 26 dt dt

rOH•,T )

]

9870


Figure 6. Photocatalytic degradation of phenol and behavior of the intermediates for three experiments.3

Regarding the 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] 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB V∆HOH• (43) Qabsγ

6.4. Calculation of PTEF and Quantum Efficiency for RN2. Using the data of Figure 9 related with the degradation of 300, 400, and 590 µmol/L (µM), the following kinetic model was fitted: dCph ) -(k1Cph + k2Cph + k3Cph)/denom dt

(44)

dCo-DHB ) (k2Cph - k5Co-DHB - k7Co-DHB)/denom dt

(45)

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

(46)

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

The PTEF was evaluated using a similar procedure as that used for the RN1 network: (a) employing eq 43 and the parameters from Table 3, (b) using eq 13 for QY calculation. The estimated parameters from experiments are 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.3 Figures 10 and 11 report the PTEF and QY profiles for the experiments performed at three different initial concentrations. One can notice in Figures 10 and 11 that the calculated PTEF and QY for the RN2 are about 25% smaller than those calculated with RN1with the main difference being the inclusion of the aliphatic acids. Thus, the accounting of aliphatic acid mildly reduces the rate of some steps allowing a somewhat slower consumption of OH• radicals and making as a result the overall photoconversion process slightly less efficient. It can also be observed in Figures 10 and 11 that both PTEF and QY display changes with irradiation time increasing first, reaching a maximum later, and decreasing at the very end. This type of PTEF and QY “dome” shaped curve is the result of the Table 2. Parameters Estimated Using Three Experiments Simultaneously, Assessed with Equations 29-31

(47)

where denom ) 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB

estimate k1 ) kphfCO2 1/min k2 ) kphfo-DHB 1/min k4 ) kphfp-DHB 1/min k3 ) ko-DHBfCO2 1/min k5 ) kp-DHBfCO2 1/min k6 ) korthofpara 1/min Kph 1/µM Ko-DHB, Kp-DHB 1/µM

6.6078 × 3.8491 × 2.7000 × 4.9962 × 6.0498 × 1.2030 × 0.000724 0.000724

10-4 10-3 10-3 10-3 10-3 10-3


9871

Table 3. Estimated Parameters from Three Experiments Assessed with Equations 44-47 estimate k1 ) kphfCO2 1/min k2 ) kphfo-DHB 1/min k3 ) kphfp-DHB 1/min k5 ) ko-DHBfLuAc 1/min k9 ) kp-DHBfCO2 1/min k10 ) kLuAcfCO2 1/min k7 ) ko-DHBfp-DHB 1/min Kph, Ko-DHB, Kp-DHB 1/µM

Figure 7. PTEFs using parameters from Table 2 and RN1. Initial concentrations in micromoles per liter: 300 ()), 440 (0), 600 (∆).

Figure 8. Comparison of QYs using parameters from Table 2 and RN1. Initial concentrations in micromoles per liter: 300 ()), 440 (0), 600 (∆).

increased intermediate species reactivity and susceptibility due to being further oxidized. This leads to a better utilization of OH• groups and as a result to an increase of both PTEF and

1.1854 3.6138 2.3912 2.1566 5.2050 7.9872 1.0794 7.2400

× × × × × × × ×

10-3 10-3 10-3 10-3 10-3 10-4 10-3 10-4

QY, during the first period of irradiation. This enhanced consumption of OH• groups continues until the total concentration of organic species is depleted enough and, as a consequence, there is a progressive reduction of OH• species utilization efficiency. 6.5. Reviewing PTEF and QY Energy Efficiencies. The PTEFs and QYs are calculated in this study, following a carefully 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. Furthermore in order to define the PTEF using eqs 27 and 43, one has to establish Eav, the average photon energy for the polychromatic beam of the near UV lamp used in the present study, and ∆HOH•, the enthalpy of formation of the OH• groups. Regarding the Eav, the average photon energy absorbed by the TiO2 suspension, which is defined with an upper 388 nm wavelength limit, the one required for superseding the TiO2 band gap, its calculation is the result of an average process involving the irradiative lamp flux measured at a set distance from the lamp surface as follows:

Figure 9. Photocatalytic degradation of phenol and behavior of the intermediates for three experiments.

9872


∫ ∫

hc Eav )

λmax)388nm

λmin

λmax)388nm

λmin

I(λ)

dλ λ

(48)

I(λ) dλ

Appendix II provides additional details for the Eav evaluation with a resulting photon averaged energy of 362 598 J/(mol photon). Concerning the enthalpy of OH• radical group formation, this parameter is reassessed using a classical thermodynamic approach. In this respect a more appropriate initial state is selected for oxygen, setting it in solution rather than in the gas phase, as in a previous study.14 This modification of the initial state mildly increases the enthalpy of formation of the OH• groups from 94 600 to 98 300 J/mol. While this variation is only about 4%, it has still to be considered to establish PTEF with the adequate precision. Once the enthalpy of OH• and Eav were carefully chosen and by using eqs 43 and 28 for the RN2 model, the calculation of PTEF and QY is allowed yielding values during the initial irradiation period in the 7-19% and 25-69% ranges, respectively. One can notice that these efficiencies are significantly higher than the 2% and 6.89% for PTEF and QY previously reported.15 This important difference is assigned to the approach used for the accounting of OH•s consumed in the photoconversion. As shown in the present study, this counting shall not be restricted to the OH•s needed in the very first photocatalytic oxidation step (e.g., phenol evolving into dihydroxybenzene). Instead the total number of OH• radical groups disappearing in various photocatalytic steps has to be considered. This requirement of OH• radicals is in agreement with a parallel-series

Figure 10. PTEF based on RN2 and using parameters from Table 3. Initial concentrations in micromoles per liter: 300 ()), 440 (0), 600 (∆).

reaction network and is established with stoichiometric coefficients which comply with oxygen, carbon, and hydrogen element balances. It is worth mentioning that these results are encouraging for the application of photocatalysis for removal of waste hazardous pollutants given they point toward high photocatalytic conversion efficiencies in the Photo-CREC-Water II unit. It is expected that these high efficiencies will also be obtained in scaled photocatalytic reactors built using the same principles, as in Photo-CREC-Water II units. These results also demonstrate about the value of a methodology that can establish energy efficiencies for the complete span of irradiation times. To implement this methodology, it is shown that it is necessary to monitor the model compound as well as the intermediates species concentrations, to calculate the OH• enthalpy of formation, to evaluate the average energy of the emitted photons below the 388 nm wavelength, to postulate an applicable reaction network with its associated kinetic parameters, and to establish suitable stoichiometric coefficients. 7. Conclusions (a) Evaluation of energy efficiency factors, in the case of PTEF and QY, requires the calculation of both the fraction of absorbed energy and the average photon energy emitted with a wavelength below 388 nm. (b) This evaluation also calls for a reacting 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 studies3 and based in a parallel-series reaction network (RN1 and RN2) are used in these assessments. (c) Calculation of these energy efficiencies also shall include the estimation of the total OH• radicals consumed at every irradiation time. To accomplish this, state functions based stoichiometric coefficients derived from carbon, hydrogen, and oxygen elemental balances are assigned to each of the identifiable reaction steps. (d) Determination of QY in Photo-CREC-Water II reactors shows quantum efficiencies in excess of 60% under some conditions. These high QY point toward the good degree of photon utilization in these units. (e) These high PTEFs and QY are very encouraging and set up excellent prospects for the extensive future use of photocatalysis for water treatment and reactor scale up. Acknowledgment The authors wish to show appreciation to NSERC-Canada for their financial support to this project. B.S. would like to specially thank PRODERIC 2007-I and PIFI 2007-33-07 from Mexico for their generous support. Appendix I: Fraction of Qabs Available for Photocatalytic Transformations

Figure 11. QY based on RN2 and using parameters from Table 3. Initial concentrations in micromoles per liter: 300 ()), 440 (0), 600 (∆).

As indicated in eq 1, the evaluation of the PTEF requires the definition of a γ parameter expressing the fraction of absorbed photon energy available for the photocatalytic conversions. In order to calculate this parameter, the emission spectrum of the lamp measured at 6.57 cm from the lamp is used as shown in Figure A1.1:116 With this data the following calculation is performed selecting as the upper limit for this evaluation a 388 nm wavelength which


ηOH

∆HOH• ) ) Eav

9873

J mol photon mol OH• ) 0.271 J mol OH• 362 589 mol photon (A2.3) 98 300

Appendix III: Calculation of the Reaction Enthalpy for the Free Radical OH•

Figure A1.1. Spectrum of lamp irradiative flux measured at 6.57 cm. away from the lamp.1 Shaded area represents the fraction of photons with a wavelength smaller than 388 nm.

is the one that correspond to a photon energy of 3.2 eV that is the one required for superseding the TiO2 band gap: γ)

∫ ∫

hV

λmax)388nm

λmin λmax)469nm

λmin

TiO2 98 h+ + e-

I(λ) dλ

This electron/hole pairs promotes the formation of a hydroxyl radical as follows:

Appendix II: Fraction of Photon Energy Required to Form OH• Radicals The fraction of photons (1 Einstein) emitted by a near UV lamp generating 1 mol of free radicals OH• can be established using a spectrophoto radiometer spectrum. Once the irradiation spectrum is defined (refer to Figure A1.1), one can calculate the average emitted photon energy (Eav) using the following relationship:

∫ ∫

λmax

λmin

I(λ)E(λ) dλ

λmax

λmin

(A2.1) I(λ) dλ

In the case of the spectra under consideration, the numerical integration of eq A2.1 is restricted to the λmax ) 388 nm upper wavelength. Photons with larger wavelengths do not have enough energy to supersede the TiO2 bang gap and as a result to contribute to the photocatalytic transformation. As a result and considering E(λ) ) hc/λ

∫ ∫

hc Eav )

λmax)388nm

λmin

λmax)388nm

λmin

I(λ)

dλ λ

){

-34

]{

} (A2.2)

J photon s 6.023 × 1023 photon mol photon J ) 362 598 mol photon

[

Eav ) 6.02 × 10-19

H2O(l) f OH-(l) + H+(l)

(A3.2)

h+ + OH-(l) f OH•(l)

(A3.3)

Following this first step, there are a number of possible paths to describe the ensuing steps such as19,20 e- + O2(aq) f O2-

(A3.4)

O2- + H+ f O2H•

(A3.5)

H+ + O2- + O2H• f H2O2(l) + O2(aq)

(A3.6)

hV

H2O2(l) 98 2OH•(l)

}

Given that the enthalpy required for producing an OH• group (Appendix III) is 98 300 J/mol OH• instead of 94 600 J/mol OH•, as reported by Serrano and de Lasa,14 thus

(A3.7)

A linear combination of eqs A3.2-A3.7, with eqs A3.5-A3.7 multiplied by the factor 1/2, allows demonstrating that the overall stochiometry for the formation of the radical OH•(l) can be represented as 1 H2O(l) + O2(aq) f 2OH•(l) 2

I(λ) dλ

Js m 3.0 × 108 photon s -7 3.31 × 10 m J -19 ) 6.02 × 10 photon

(6.63 × 10 )

(A3.1)

(A1.1) I(λ) dλ

Evaluation of the γ fraction with the data of Figure A1.1 gives 0.893.

Eav )

The assessment of the enthalpy of formation of OH• radicals is a critical parameter for estimating the PTEF, as shown by Serrano and de Lasa.14 A revised evaluation of the enthalpy of formation of the OH• is reported in this appendix. The basic mechanism of heterogeneous photocatalysis is related to the excitation of TiO2 and/or other semiconductors with a photon of light (either from the sunlight or an artificial source). This excitation promotes an electron from the valence band to the conduction band of the semiconductor generating electron/hole pairs. This process is sketched as follows:

(A3.8)

Thus, the enthalpy of formation of OH• radicals, is a thermodynamic nonpath dependent state function, which is only affected by the initial and final conditions and can be calculated as 1 1 ∆H°OH•(l) ) ∆H°f,OH•(l) - ∆H°f,H2O(l) - ∆H°f,O2(aq) 2 4 (A3.9) The enthalpies of formation of the chemical species involved can be estimated as reported in refs 21-23 as ∆H°f,H2O(l) ) -285 830 J/mol

9874


∆H°f,O2(aq) ) -11 700 J/mol

(A4.5)

n

∑KC

1+

∆H°f,OH•(v) ) 38 950 J/mol

j j

j)1

However given that in eq A3.9 ∆H°f,OH•(l) is involved instead of ∆H°f,OH•(v), this parameter has to be revised using the OH• radical condensation enthalpy. Regarding this correction, there is limited information for assessing the condensation enthalpy for the OH• radical. Thus, a possible approach is to consider the condensation enthalpy for the OH- ion given the analogous expected condensation properties.

In this respect, one can notice that qi ) qi(Ci) and Ci ) Ci(t), and as a result, the total derivative of qi is given as

Thus, given that the condensation enthalpy for the OH• radical is assumed to be the same as that of OH ion, the enthalpy of formation for the radical OH• in the liquid phase can be estimated as

Appendix IV: Derivation of Equations for K*i Calculation Following refs 1 and 17, an expression can be provided to calculate the total reaction rate for i species, accounting for the species fractions distributed in both liquid and adsorbed phases: Ni,T ) Ni,L + Ni,ads

∑ KKC

i j j

j,j*i

(

)

(A4.7)

)

(A4.8)

2

n

∑ KC

1+

∂qi ) ∂Cj

j j

j)1

(

-KjKiqmCi

2

n

∑KC

1+

j j

j)1

Substituting these partial derivatives in the total concentration change of the i species yields dCi dCi,T W dqi ) + dt dt V dt dCi,T dCi ) + dt dt

W V(1 +

∑ KC)

{

(Kiqm + qm

n

2

j j

(A4.9)

∑ KKC) i j j

j,j*i

j)1

∑ KKq C

j i m i

j,j*i

dCj dt

dCi dCi,T ) + dt dt

W V(1 +

∑ KC)

{

(Kiqm + qm

n

2

j j

∑ KKC) i j j

j,j*i

j)1

∑ KKq C

j i m i

j,j*i

dCi dCi,T ) + dt dt

W n

V(1 +

∑ KC) j j

2

dCj dCi dt dt dt dCi

{

dCi (Kiqm + qm dt

Ni,ads ) Wqi and Ci,T ) Ci +

Furthermore analytical differentiation of eq A4.3 leads to the reaction rate of the compound i in the step j as dCi dCi,T W dqi ) + dt dt V dt

j i m i

j,j*i

(A4.12)

(A4.13)

W V(1 +

∑

{

(Kiqm + qm

n

KjCj)

2

∑ KKC) i j j

j,j*i

j)1

If one assumes adsorption equilibrium between phases in the equation as

}

Where K*i )

(A4.4)

i

dCi dCi,T ) {1 + K*} i dt dt

(A4.3)

(A4.11)

i j j

∑ K K q C dC

(A4.2)

}

dCi dt

j,j*i

dCj

Wqi V

(A4.10)

∑ KKC) -

j)1

Ni,L Ni,ads Ni,T ) + V V V

}

dCi dt

Also,

(A4.1)

where Ni is in moles. These amounts of i species, distributed in the liquid and adsorbed phases, can be expressed as concentrations in each of the phases as follows:

(A4.6)

And for i * j

]

On this basis, a 98 300 J/mol heat of formation is established starting from dissolved oxygen and water. This value slightly differs from a 94 600 J/mol reported calculated from oxygen in the gas phase and water.14 It is considered that this ∆H°OH•(l) revision is required to establish PTEF with the adequate rigor.

j)1

Kiqm + qm

∂qi ) ∂Ci

As a result and once the values for ∆H°OH•(l) are obtained, eq A3.9 can be used to get the ∆H°OH(l)

[

∂qi dCj j dt

∑ ∂C

Thus to evaluate the total derivative as in eq A4.6 one has to establish the ∂qi/∂Ci partial derivatives

∆H°f,OH•(l) ) ∆H°f,OH•(v) + ∆H°condensation,OH• ) -47 540 J/mol (A3.10)

1 ) -47 540 - (-285 830) 2 1 (-11 700) J/mol ) 98 300 J/mol 4

n

dqi ) dt

∆H°f,OH-(aq) - ∆H°f,OH-(v) ) -229 994 J/mol + 143 500 J/mol ) -86 490 J/mol

∆H°OH•(l)

KiqmCi

qi )

KjKiqmCi

dCj dCi

}

(A4.14)


In the present study where reacting species are phenol (ph), o-DHB, and p-DHB, the following results: qph )

KphqmCph 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB (A4.15)

∂qph dCph ∂qph dCo-DHB ∂qph dCp-DHB dqph ) + + dt ∂Cph dt ∂Co-DHB dt ∂Cp-DHB dt (A4.16) Kphqm + Ko-DHBKphqmCo-DHB + Kp-DHBKphqmCp-DHB ∂qph ) ∂Cph (1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB)2 (A4.17) -Ko-DHBKphqmCph ∂qph ) ∂Co-DHB (1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB)2 (A4.18) -Kp-DHBKphqmCph ∂qph ) ∂Cp-DHB (1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB)2 (A4.19) Replacing eqs A4.17-A4.19 in A4.16 results in the following: dCph dCph,T W dCph ) + dt dt V dt Kphqm + Ko-DHBKphqmCo-DHB + Kp-DHBKphqmCp-DHB

{

[ [ [

-Ko-DHBKphqmCph (denom)2 -Kp-DHBKphqmCph (denom)2

] ]

(denom)2 dCo-DHB + dCph dCp-DHB dCph

]

+

}

(A4.20)

denom ) 1 + KphCph + Ko-DHBCo-DHB + Kp-DHBCp-DHB dCph dCph,T ) {1 + K*ph} dt dt

(A4.21)

where K*ph )

{

W V

[ [

] ]

Kphqm + Ko-DHBKphqmCo-DHB + Kp-DHBKphqmCp-DHB -Ko-DHBKphqmCph (denom)2

]

}

+ (denom)2 dCo-DHB -Kp-DHBKphqmCph dCp-DHB + dCph dCph (denom)2 (A4.22)

[

Using a similar approach one can also show that, dCo-DHB dCo-DHB,T ) {1 + K*o-DHB} dt dt

(A4.23)

9875

K*o-DHB )

{

[ [

{

W V Ko-DHBqm + Ko-DHBKphqmCph + Kp-DHBKo-DHBqmCp-DHB -Ko-DHBKphqmCo-DHB

]

(denom)2 dCph + dCo-DHB

+

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

[

]

dCp-DHB dCp-DHB,T ) {1 + K*p-DHB} dt dt

-Kp-DHBKphqmCp-DHB

]

(denom)2 dCph + dCp-DHB

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

[

]

}

(A4.24) (A4.25)

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

K*p-DHB )

[ [

]

]

+

}

(A4.26)

Notation C ) speed of light, 3.0 × 108 m/s CA ) concentration of compound A, mol/L Ci ) concentration of the i chemical species, mol/L Ci,j ) concentration of the i chemical species in reaction step j, mol/L Ci,T ) total concentration of the i chemical species, mol/L CCO2 ) concentration of CO2, mol/L CH2O ) concentration of H2O, mol/L COH• ) concentration of OH• radical, mol/L Ci,eq ) 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 TiO2 ki ) apparent kinetic reaction constant for step i, 1/min K*i ) dimensionless adsorption constant (eq 8) Ki ) adsorption equilibrium constant, L/mol h ) Planck’s constant, 6.63 × 10-34 J/s I(λ) ) intensity of light, W/cm2 Ni,ads ) number of moles of adsorbed species i, mol Ni,T ) total number of moles of species i in fluid and solid phases, mol Ni,L ) number of moles of species i in the liquid phase, mol qi,m ) maximum adsorbed concentration of component i, mol/gads qi,ads ) concentration adsorbed species i at equilibrium, mol/gads Qabs ) rate of irradiated energy absorbed in photocatalytic reactor, J/s Qused ) rate of irradiated energy used for the formation of OH• radicals, J/s rOH•,T ) total reaction rate of OH• radicals, mol/(g catirr s) rA,j ) reaction rate of A in step j, mol/(g catirr s) rOH•,j ) reaction rate of OH• radical in step j, mol/(g catirr s) ri,j* ) rate of change of i species in step j (always positive, mol/ (g catirr s) ri,j ) reaction rate of component i in step j, mol/(g catirr min) ri ) reaction rate of component i, mol/(g catirr min) ri,T ) total reaction rate of component i, mol/(g catirr min) ri,j* ) rate of change of i species in step j (always positive, mol/ (g catirr s) rph,j ) reaction rate of phenol in step j, mol/(g catirr min)

9876


ro-DHB,j ) reaction rate of ortho-dihydroxybenzene in step j, mol/ (g catirr min) rp-DHB,j ) reaction rate of para-dihydroxybenzene in step j, mol/(g catirr min) rac,j ) reaction rate of carboxylic acids in step j, mol/(g catirr min) 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 ∆H°f,i ) standard enthalpy of formation for the component i, J/mol 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-DHB,j ) stoichiometric coefficient of ortho-dihydroxybenzene in reaction step j νp-DHB,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 yields 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

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ReceiVed for reView March 3, 2009 ReVised manuscript receiVed June 18, 2009 Accepted June 23, 2009 IE900353N

Energy Efficiency in Photocatalytic Reactors for the Full Span of

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