Mathematical Modeling of the Photochemical Reactor Degradation of

48 products - Ollis and Al-Ekabi, 1993; Halmann, 1996; Walling,. 1975). ... of many organic pollutants (Ruppert and Bauer, 1993). Moreover, the p-NTS ...
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Ind. Eng. Chem. Res. 1998, 37, 347-356

347

Mathematical Modeling of the Photochemical Reactor Degradation of p-Nitrotoluenesulfonate E. Balanosky and J. Kiwi* Institut de Chimie Physique II, Ecole Polytechnique Fe´ de´ rale de Lausanne (EPFL), Lausanne 1015, Switzerland

This study involves the Fenton photo-assisted degradation of p-nitrotoluenesulfonate (p-NTS). The most important chemical variables affecting the reaction have been identified. A mathematical model has been constructed for the optimal conditions necessary to achieve photocatalytic degradation of p-NTS. A polynomial and an exponential function have been constructed and developed for this purpose. These function(s) allow the optimization of the energy, time, and chemicals needed during the degradation of a given amount of the pollutant. The photo-assisted degradation was observed to render the recalcitrant p-NTS susceptible to undergoing a secondary biological degradation. Contour plots giving the minima of the TOC values attained during the degradation process have been determined through the polynomial or exponential functions found. These minima are referenced to the critical parameters involved in the degradation. The overlapping of minima in two of these 2D contour plots gives the minimum value of the TOC as a function of three variables. These functions are represented in 3D surfaces for specific sets of variables. The validity of the exponential model is shown in this study to reach to much lower TOC values far beyond the application range of the polynomial model and therefore it is better suited for the problem under consideration. The kinetics of the photo-assisted process were found not to be significantly affected by the intensity of the applied light or the absorption of the solution. The excitation of the Fe3+-ion chromophore in solution was the factor determining the kinetics and efficiency of the photodegradation. Quantum yields for the degradation of p-NTS were determined as a function of the wavelength of irradiation to substantiate this observation. The evolution of aromatic and aliphatic intermediates within the degradation time was looked into. Intermittent illumination was applied during the degradation with consequent energy savings since the degradation still took place within reasonable degradation times. Batch and flow runs were carried out in the photoreactor. An estimate of the cost and efficiency for the electrical energy used during the degradation of p-NTS is outlined. Introduction This study aims to develop a mathematical model for the optimization of the conditions required to achieve degradation of p-NTS through Fenton-assisted reactions. The Fenton reagent is one of the most powerful and common sources of •OH radicals (Helz et al., 1994; Ollis and Al-Ekabi, 1993; Halmann, 1996; Walling, 1975). It has been widely employed during the last decade in the field of Advanced Oxidation Technologies. During this work we investigated the light-enhanced treatment of p-NTS-contaminated solutions. This substance belongs to the nonbiodegradable class of pollutants. It is found in effluents of the Swiss chemical industry having nitro and sulfate groups as electronwithdrawing groups (Pitter and Chudoba, 1990). It has been shown that UV/visible radiation accelerates the Fenton reaction, improving the abatement rates of many organic pollutants (Ruppert and Bauer, 1993). Moreover, the p-NTS photodegradation mediated by TiO2/H2O2 in batch systems was reported recently in a published work of our laboratory (Minsker et al., 1993). Degradation through photoreactors using the Fenton * Author to whom correspondence is addressed. Fax: 0041 21 6934111. Phone: 00412 21 6933621. E-mail: [email protected].

reagent has only been explored in a few studies (Scott and Ollis, 1994; Cassano et al., 1995). Not much engineering work has been devoted to this subject either, and even less work has focused on reactors involving homogeneous photocatalysis. During the present work, after obtaining the experimental data for the important parameters intervening in the degradation, the aim of this study was (a) to construct a simple mathematical function for the treatment of the experimental data. This avoids complicated programming during the optimization procedure for a given set of experimental conditions, (b) to use the rather expensive photons of the pretreatment for the shortest time possible, up to the point where biocompatibility has been achieved, and (c) to couple the initially pretreated solution with biological degradation until the degradation of the pollutant is complete. Experimental Section Photoreactor. A 36 W Philips (1.20 m long and 26 mm in diameter, TLD 36 W/08) black actinic light source was employed in such a way that its center passed through the focal axis of the reactor. Most of the degradation runs employed this light source. The lamp radiated at wavelengths between 330 and 390 nm. This is important since the scattering effects were observed

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to be less important in a solution having high optical absorption. A medium-pressure 400 W Hg lamp (Photochemical Reactors No. 3040) was also used in some runs having 40% of the UV output at 366 nm. The lamp radiated at wavelengths between 330 and 390 nm. This is important since the scattering effects were observed to be less important in a solution having high optical absorption. The reactor mixing flask had a 1 L volume equal to the volume of solution used in batch mode experiments. During the flow through experiments the p-NTS solution was fed into a system from the 18 L reservoir and H2O2 was added by means of a peristaltic pump into the 1 L mixing flask. Materials. p-NTS was a gift from Ciba (Monthey). FeCl3‚6 H2O and H2O2 (Fluka 30% w/w) were p.a. and used as received. The Fe3+ ions were added at the beginning of each run. The consumption of H2O2 during the reaction was followed by the Merckoquant test for peroxides (Nadtochenko and Kiwi, 1996). An extremely low residual H2O2 was attained during the first stage (see Figure 5). It was never allowed to exceed 0.2 mg/L after the pretreatment stage. Analysis in Solution. Total organic carbon (TOC) was monitored during this study with a Shimadzu 500 instrument provided with an automatic autosampler. High-pressure liquid chromatography (HPLC) was carried out with a Varian 9100 LC unit equipped with a 9065 diode array. The column used was a 5 µm Spherisorb ODS-2, and the mobile phase consisted of an ammonium acetate solution in an acetonitrile-water solvent. The ammonium acetate was 0.3 N at zero time. At 20 min the mobile phase was 70% ammonium acetate and 30% acetonitrile. After 30 min, the mobile phase consisted of 100% ammonium acetate. The peak of p-NTS was observed to elute in the HPLC spectrogram after ∼20 min. Spectrophotometric measurements were carried out with a Hewlett-Packard 386/20 N diode array. Chemical actinometry was carried out by means of an Aberchrome 540 chemical actinometer (Heller and Langan, 1981) in the wavelength range of λ ) 310-340 nm. The determination of the quantum yield (Φ) at various λ’s was carried out with of a high-intensity Baush and Lomb monochromator blazed at 350 nm. The incident beam had an area of 1 cm2. Test of Bacterial Activity. The Zahn-Wellens (see OECD Guidelines, 1981) test was used on pretreated solutions in the dark, at room temperature, and under continuous O2 purging for 5 days. This test used a high concentration of bacterial sludge of 1 g/L. This activated sludge from the Lausanne STEP station was aerated for 24 h with 50 mL/min flow of air. The equivalent of a dry bacterial concentration of 1 g/L was used to evaluate the biological degradation. Results and Discussion Optimization of the Variables Intervening in the Degradation of p-NTS in an Immersion Type Flow Photoreactor. Photochemical degradation of p-NTS was optimized by following the TOC decrease in solution as a function of the most important variables affecting the degradation. The high concentrations of p-NTS used as substrate in Figure 1a-d relate to the concentrations of p-NTS found in the effluents near the manufacturing sites. The results are shown in Figure 1a-e where the TOC decrease during the degradation is seen as a function of time, varying systematically with the variables: (a) concentration of the p-NTS substrate,

(b) rate of flow of H2O2 addition, (c) concentration of Fe3+ ion used, (d) type and intensity of the light source used, (e) pH of the solution. Batch mode operation was used in the 1 L reactor containing the initial components. H2O2 was added at the rates given in the caption to each individual figure. A pattern for the experimental results shown in Figure 1a-e indicates that for a typical run containing p-NTS (500 mg/L or 1.9 × 10-3 M or TOC 160 mg of C/L) the initial TOC was seen to decrease by about 60% to ∼60-70 mg of C/L after ∼30 min. Figure 1d shows the results of the batch mode operation of the reactor during the degradation of p-NTS in acid solutions at a pH of 2.6, in the dark and under irradiation, applying one or two actinic lamps or an Hg lamp at p-NTS concentrations as already used for the results given in Figure 1b,c. Flow Experiments in a Loop System: Continuous and Intermittent Light Irradiation. Figure 2a shows a schematic diagram for the continuous flow reactor. Figure 2b shows the batch mode operation of the reactor: in trace a the degradation of solutions containing high levels of p-NTS (TOC ∼ 400 mg of C/L) in the dark and trace b the photodegradation under continuous illumination for the same solution with a double actinic light (5 mW/cm2). Control photolysis with no Fe3+ ion or H2O2 added in solution did not lead to p-NTS degradation in the reactor operated in flow or batch mode. The results for a flow mode operation of the reactor using a 20 L tank for the initial solution of the p-NTS and Fe3+ ion used and adding 150 µL/min/L are shown in trace c. An initial concentration of p-NTS (TOC ∼ 170 mg of C/L) has been taken for the later run to compare these results with the results obtained in Figure 1c. The flow rate used was 200 mL/min or 12 L/h. The residence time in the reactor was relatively short and equivalent to 0.083 h. The rate of the TOC decrease with time was observed to be similar to that observed previously in the batch mode operation. The full mineralization of this solution (not shown in trace c) was achieved in ∼8 h. The 62 mmol of p-NTS in the 18 L tank required ∼800 mmol of H2O2. This is an oxidant to pollutant ratio of 12.9:1 and suggests the stoichiometry in the flow reactor as

C7H6O5NS + 13H2O2 + 19/2O2 f 7CO2 + 29/2H2O + HNO3 + H2SO4 (1) Trace d shows the TOC decrease for a slightly more concentrated solution of p-NTS (260 mg of C/L). Trace d shows the results for a slightly more concentrated solution of p-NTS where an initial reaction period in the dark was applied for 20 min. Only then was double actinic light illumination applied, also for 20 min. The switching off and on of the light was repeated for 20 min periods up to 120 min (see Figure 2). The final level of TOC reduction after 120 min was seen to be close to the level reached when continuous illumination was applied (trace b) but for a solution with significantly lower initial TOC content (trace d). The beneficial effects of active intermediates formed in batch reactions in the dark have recently been reported by Pignatello (Sun and Pignatello, 1993) during the degradation of dichlorophenoxyacetic acid (2,4-D). HPLC experiments to identify the intermediate formed during the dark reaction have been carried out, referencing the observed peaks with known compounds. The aromatic species

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Figure 1. (a) TOC decrease with time for irradiated solutions with a double actinic light source containing Fe3+ (10-3 M) at pH ) 2.6 and H2O2 (150 µL/min/L) as a function of the concentration of p-NTS. (b) TOC decrease as a function of time for irradiated solutions containing p-NTS (500 mg/L) and Fe3+ (10-3 M) as a function of the rate of addition of H2O2 in micromoles per liter during the run. (c) TOC decrease with time for irradiated solutions containing p-NTS (500 mg/L) and H2O2 added at the rate of 150 µl/min/L as a function of Fe3+ ion: (A) 2.5 × 10-4 M; (B) 5 × 10-4 M; (C) 10-3 M. The pH of the runs was 2.6. (d) TOC decrease as a function of time for irradiated solutions of p-NTS (500 mg/L), H2O2 (300 µL/min/L), and Fe3+ (10-3 M) as a function of the type of light and intensity used: dark, one actinic light, two actinic lights, and a medium-pressure Hg lamp. (e) TOC decrease for irradiated solutions similar to those used to give the results in part d as a function of solution pH.

observed during the initial degradation have been identified as belonging to benzoquinone and benzoquinone-like isomers. The column use was the same as the one employed to follow p-NTS. Close peaks formed close to the benzoquinone peak indicated that other intermediates were formed consisting of nitro and sulfate isomers of benzoquinones. This is an expected result since benzoquinone is the most oxidized form of quinones and will form in solutions in the presence of H2O2. Disappearance of Aromatic Groups during the Photodegradation of p-NTS in the Photo-assisted Fenton Reaction. Figure 3 shows that after 30 min of irradiation, the p-NTS added initially to the solution

has entirely disappeared. This peak was detected by comparing the peak during our experiments with the calibration curve obtained for pure p-NTS in solution. A separate peak appeared in the HPLC spectrogram and was followed at λ ) 229 and 254 nm with a retention time of 5.9 min. The scanning of this peak in the diode detector array revealed a single aromatic compound different from p-NTS. This aromatic compound was seen to reach a maximum at 5 min and decayed over 40 min as seen in Figure 3. These types of aromatic intermediates such as the quinone-like compounds reported in the preceding section are commonly found during the chemical and biological degradation of toluene and phenol (Minsker et al., 1994;

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Figure 3. Disappearance of p-NTS during actinic irradiation as detected by HPLC for a solution containing: p-NTS (500 mg/L), H2O2 added at the rate of 150 µL/min/L and Fe3+ (10-3 M). Concomitantly the appearance and disappearance of aromatics and aliphatics are also shown as a function of time.

Figure 2. (a) Schematic diagram for a continuous flow reactor system. (b) TOC decrease with time for a reactor solution p-NTS (400 mg/L), Fe3+ (10-3 M), and H2O2 (150 µL/min/L) (A) dark run batch mode, (B) actinic irradiation with a double actinic light in batch mode, (C) degradation of a solution 170 mg of C/L in a flow reactor, (D) batch mode degradation of a solution with an initial TOC of 260 mg of C/L showing the periods of light irradiation (L, see arrows) followed by dark periods at the position of the full circles.

Halmann, 1996). Smaller peaks in the HPLC spectrogram could not be identified against available commercial compounds.

Aliphatic compounds increase to a maximum at ∼30 min and are seen to decrease afterward, as detected at λ ) 230 nm where a double peak was observed with a retention time of 2.5 min. These signals have been observed as characteristics for a very large number of aliphatic compounds with carbon number C1-C6. The concentrations for the aromatic and aliphatic compounds reported in Figure 3 were calculated taking into consideration the decrease in TOC observed concomitantly during the degradation. After 30 min only aliphatics were observed at λ ) 230 nm and their concentration relative to the initial p-NTS was calculated after measuring the decrease of the TOC value within 30 min. No C1-C6 pure aromatics were specifically identified since these short aliphatic chains seem to contain nitro and sulfate groups not found in commercial samples to compare with. The ratio of this TOC to the initial TOC was used as the scaling factor to correlate the p-NTS concentration with the concentrations of aromatics and aliphatics during the reaction. Quantum Yield of Disappearance of p-NTS as a Function of Wavelength. The quantum yield Φ (the rate at which the p-NTS molecules disappear divided by the number of photons absorbed per unit time) is reported in Figure 4. The photon flux incident on the inner front window has been measured by the Aberchrome actinometer cited in the Experimental Section (Heller and Langan, 1981). This dependence has been observed to provide useful information about the ab-

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Figure 4. Initial quantum yield taken after 30 min for p-NTS disappearance (observed by HPLC) as a function of the wavelength for a solution: p-NTS (500 mg/L), H2O2 (10-3 M), and Fe3+ (10-3 M). For other details see text.

sorption of the chromophore active in the homogeneous degradation. Monochromatic light from a Xe lamp was applied on the photocell between 350 and 600 nm for 30 min to obtain the quantum yields reported in Figure 4. The values of Φ were obtained by dividing the number of p-NTS molecules abated (by the HPLC technique) by the number of photons‚cm-2 s-1, at each wavelength. Figure 4 reveals that the more energetic photons (λ < 380 nm) are more effective in abating p-NTS during the photo-assisted Fenton degradation. The spectral absorption of p-NTS beginning at λ ) 400 nm toward higher energies as well as the absorption of the Fe3+ ion at these wavelengths explains the form of Φ for the p-NTS disappearance up to 474 nm observed in Figure 4. Dissolved Fe(III) complexes have been reported to photolyze with non-negligible quantum yields up to 550 nm (Faust and Hoigne´, 1990; Langford and Carey, 1975) and would explain in a qualitative way the rise in the spectrum from λ ≈ 475 nm toward longer wavelengths as shown in Figure 4. Combined Photochemical Pretreatment and Biological Degradation of p-NTS. Solutions containing p-NTS (500 mg/L) were pretreated in the photochemical reactor under irradiation with Fe3+ ion (10-3 M) and H2O2 (10-3 M). It had to be verified whether the present technique was adequate to abate the high concentrations used for this nonbiodegradable compound (500 mg/ L). The results are presented in Figure 5. The effect of the pretreatment time on the biological degradation of p-NTS was assessed by the Zahn-Wellens test

Figure 5. Decrease in TOC with time when a solution containing p-NTS (500 mg/L), H2O2 (10-3 M), and Fe3+(10-3 M) is pretreated in a reactor with double actinic light at 1/4 and 1/2 h and subsequently treated biologically with activated sludge. For other details see text.

(OECD, 1981). Biological treatment of p-NTS had been explored previously in our laboratory (Minsker et al., 1994). Such treatment was not effective within a 2 month period of growing cultures in different media. The biodegradation was measured by following the decrease of the dissolved organic carbon (DOC) as a function of time. This test resembles the conditions found in field processes involving aerobic waste-water treatment of industrial effluents. The objective was to establish the validity of the pretreatment under real field conditions. The activated sludge solutions were checked during the biological degradation of the p-NTSgenerated intermediates against a control suspension of bacteria containing 1 mg/mL, dry weight, of activated sludge. Activated sludge was added to solutions pretreated for 15 and 30 min, and the dissolved organic carbon (DOC) was monitored for 5 days. A control solution with only bacterial sludge was used as the reference. The solution was continuously oxygenated with O2 (5 mL/min), and the solution levels were checked daily in order to maintain a pH close to 7. The DOC values shown in Figure 5 reflect the residual carbon in the solution when the sewage sludge was filtered through a 0.45 µm filter. An increase in the DOC values for solutions pretreated for 30 min is observed. This is due to the effect of the residual toxicity still left in the concentrated p-NTS solution (used for pretreatment) on the activated sludge. After the initial growth period, the DOC is seen

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Figure 6. Contour plots obtained with the polynomial expression for the experimental data reported in Figure 1b,c for the pair of variables: Fe3+, H2O2.

to decrease monotonically for up to 120 h (5 days) due to bacterial degradation in such a way that practically all p-NTS is consumed. This is readily seen by the close proximity after 120 h of the DOC of the pretreated sample to that of the control sample of activated sludge (bacteria). The same general trend is observed in Figure 5 for the solution pretreated for 15 min. Mathematical Modeling of the Chemical Variables Affecting the Photodegradation. (a) Polynomial Model. The experiments represented in Figure 1a-d were then used as a basis for the polynomial model shown in Figures 6-8. Each graph represents a set of 36 pairs of values for TOC and 4 of the important experimental variables affecting the degradation: the concentration of p-NTS, the concentration of Fe3+ ion used, the rate of flow of H2O2 added (or the total amount of H2O2 added during the time of each reaction per liter of solution), and the intensity (I) of the light used during the degradation. Some years ago the methodology for building a statistically significant model was devised (Box et al., 1978) for a set of well-chosen experiments. This approach allowed one to optimize the design and to assess the interaction between the different variables in various types of experiments. The mathematical model is empirical, and the polynomial expansion is used as the first choice. This model allows for the drawing of contour plots (curves of constant response value) and, once tested, for prediction of the values of the response(s) at any point in the experimental region of interest (Khuri and Cornell, 1987). This methodology has been applied to investigate and identify the four main variables that appear to contribute significantly to the degradation process: H2O2, Fe3+ ions, p-NTS concentration, and the intensity of applied light. This approach took the experimental data in pairs, X1 and X2, for the reaction parameters [H2O2], [Fe3+], [p-NTS], and the intensity of the light used. In a simplified way reduced-centered dimensionless variables were worked out in order to avoid having different units for the different variables. Each reduced-centered variable Xi was specifically associated with a physical

variable ui in such a way that Xi ) (ui - uio)/∆ui where uio is the value of ui at the center of the experimental region and ∆ui ) (uimax - uimin)/2. The response function Z (TOC values) is represented by a quadratic polynomial of the form

Z ) bo +

∑biXi + ∑biiXi2 + ∑∑bijXiXj

(2)

where bo ) ∑Zi/N, the average of the values of TOC over N experimental points, bi’s are the coefficients for the main effect of the variable Xi, bii’s are the coefficients for the quadratic effect of the variable Xi, and bij is the coefficient for the first-order interaction effect of Xi, and Xj. The method for calculating the coefficients bi and bij is based on coefficient bi’s representing a first-order effect. A set number of experiments is taken (6) with 8 TOC values corresponding to each value of Xi, that is, 48 values in total. In each case the TOC values are multiplied by the values of the corresponding Xi. The 48 products found are added up and divided by 48 to find the respective bi coefficient. Coefficients noted by bii’s represent the quadratic effect. For each case the TOC values obtained were multiplied by the square of the corresponding Xi and the 48 products were added up and divided by 48. To find the bij coefficients representing the first-order interaction effect between Xi and Xj, the TOC values found were multiplied by Xi and Xj in each case and subsequently the 48 products were added up and then divided by 48. The values of the Xi variables were taken as follows:

Xi ) ([H2O2} - 18)/18 in mL/L Xi ) ([p-NTS] - 750)/750 in mg/L Xi ) ([Fe3+] - 300)/300 in mg/L Xi ) (intensity - 52.5)/52.5 in mW/cm2 Contour plots were then obtained using the IGOR 3.0 program in a Power Macintosh 8200/120 in order to locate regions for the minima of Z as a function of the

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Figure 8. 3D surface plot from the polynomial expression for TOC vs (H2O2, Fe3+) showing the 2D planes inside the cube in each case.

Figure 7. (a) Minimum regions for TOC as a function of three experimental parameters obtained by the overlap of the contour plots in a polynomial model for TOC vs (H2O2, Fe3+, and p-NTS) and (b) for TOC vs (intensity, Fe3+, and p-NTS).

possible combinations of the variables taken in pairs. The variation of TOC vs (H2O2, Fe3+) is presented in Figure 6. Similar plots can be drawn for TOC vs (H2O2, p-NTS), TOC vs (p-NTS, Fe3+), and TOC vs (p-NTS, intensity). They were obtained by calculating the coefficients of the polynomial expression in eq 2 and subsequently drawing the contour corresponding to the respective pairs of variables under study. The central regions at the four contour plots indicate four regions in which the TOC values attain minimum values. By

means of the model used the TOC (mg C/L) values are seen to decrease in Figure 6 from 230 to 40. These contour plots show the minimum region of the function Z (see eq 1) attained through the optimization of two experimental parameters taken in pairs (Figure 6). The time variable during the polynomial optimization is not shown but is implicit in Figure 6 within a 2 h reaction time. Parts a and b of Figure 7 show the overlap of the contour plots of TOC vs (H2O2, Fe3+, p-NTS) and TOC vs (p-NTS, Fe3+, intensity). In this way the overlap of two pairs of selected variables gives the minimum of TOC as a function of three variables. Parts a and b of Figure 7 with double vertical axes were necessary to plot this overlap. These figures clearly indicate the relative and absolute minimum areas for the function of Z (see eq 2) for the three variables considered in the positive region of the axes employed. The large shaded areas in the negative region have no physical meaning. They are only mathematical solutions to the equation employed. The areas denoted by 40 in Figure 7a and 70 in Figure 7b represent the absolute minima for the TOC values attained during the degradation starting from solutions of p-NTS, Fe3+ ion, and the integrated amount of H2O2 shown in this figure. The values for the individual components making up the solution are shown in the striped areas in Figure 7a,b. These areas represent the minima for the TOC values, that are possible to attain for p-NTS degradation under the given experimental conditions. Figure 8 shows the three-dimensional (3D surfaces) variation of TOC vs (H2O2, Fe3+). It shows on the top and bottom faces of each cube the contours depicting the plots already presented in Figure 6. The contour plots shown previously were the 2D projections of Figure 8. Such projections help to visualize the complex relation between the three variables affecting the photodegradation during the reaction time. Time is a common variable for the 2D and 3D surfaces presented in this study. The range of Xi used to generate the contour plots and 3D surfaces (Figures 6 and 8) is shown in Table 1. (b) Exponential Model. Because it was experimentally observed that the TOC decrease with time followed an exponential decay function, it was thought that modeling with such a function would better fit the experimental results obtained. Such a model would also

354 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 Table 1. Range of Xi Values (Contours and 3D Surfaces) Xi -2 [H2O2] (mL/L) [pNTS] (mg/L) [Fe3+] (mg/L) intensity (mW/cm2)

nonphysical value nonphysical value nonphysical value nonphysical value

-1

0

1

0 18 36 0 750 1500 0 300 600 0 52.125 104.25

2 54 2250 900 156.375

Figure 9. Contour plots obtained via the exponential expression for the experimental data reported in Figure 1b,c for the pair of variables: Fe3+, H2O2.

allow one to predict the optimal experimental region to achieve lower TOC simulated values than relatively high TOC values predicted in Figure 7a,b through the polynomial model. The exponential model could be written as

∑(biXi + ∑biiXi2 + ∑∑bijXiXj)]]

Z ) bo[exp[s

(3)

where the coefficients are the same as those defined in eq 2 and s is a scaling factor that adjusts the fitting of the curves for the initial and final concentrations of the reagents used. Figure 1a-d presented a near-exponential decrease for TOC with time as a function of the four variables considered. Therefore, an exponential model should give a better fit of the experimental data reported in the TOC vs time curves in Figure 1a-e. Figure 9 show the contour plots obtained from the exponential model of the four functions of Z mentioned above. The same procedure was followed in the exponential model as in the polynomial model. Each graph represents a set of 36 pairs of values for TOC and one

Figure 10. (a) Minimum regions for TOC as a function of three experimental parameters obtained by the overlap of the contour plots in the exponential model for TOC vs (H2O2, Fe3+, and p-NTS) and (b) TOC vs (intensity, Fe3+, and p-NTS).

of important experimental variables affecting the degradation: the concentration of p-NTS, the concentration of Fe3+ ion used, the rate of flow of H2O2 added (or total amount of H2O2 at time t per liter of solution), and the light intensity used during the degradation. By means of the model used the values of TOC (mg of C/L) are seen to decrease in Figure 9 from 280 to 10. Figure 9 shows minimum TOC regions of 10 and 15, a factor of 4 lower than that obtained with the polynomial model.

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Figure 5). The measure of the relative efficiency of the degradation has been given in some cases by the “electrical energy per order” (EE/O). This has been defined as the electrical energy (kWh) required to reduce the concentration of the pollutant(s) by 1 order of magnitude in 1000 U.S. gal (3784 L) of water (Serpone et al., 1993). For a process in a flow reactor as shown in Figures 2c and 5 it is possible to estimate

EE/O ) 1000P{60R log(ci/cf)} ) 1.3

Figure 11. 3D surface plot from the polynomial expression for TOC vs (H2O2, Fe3+) showing the 2D planes inside the cube in each case.

(4)

where P is the lamp power in kilowatts, R is the number of gallons per minute, and ci and cf are initial and final concentrations over the treatment time. A considerable reduction in electrical energy consumption during the process has been accomplished recently by turning on and off the light during the process as shown by batch mode utilization of the reactor for p-NTS degradation in Figure 2d. This approach takes advantage of the effect of light irradiation on the active intermediates formed in the dark (11). Work along these lines in flow-through systems is underway in our laboratory and will be reported in the near future. Conclusions

Therefore, this model allows us to predict the optimum conditions for the decrease of TOC to 4-7% of its initial value, in terms of some of the four parameters considered. It is readily seen that this treatment of the data is a better approximation to the real behavior as compared to the polynomial model. Parts a and b of Figure 10 show the overlap regions of the contour plots to give the absolute and relative minima for the variation of TOC vs (H2O2, p-NTS, Fe3+) and TOC vs (intensity, Fe3+, and p-NTS). Figure 11 shows the 3D surfaces of the variation of the four abovementioned functions of Z taken in pairs of variables, respectively. The contours shown at the top and bottom faces of the cubes enclosing the surfaces are the same as those represented in Figure 9; the latter ones are the 2D projections of surfaces in Figure 11. Minimum regions were found which allowed a model of the optimal degradation of pollutant up to lower TOC values than those seen with the polynomial model, as shown previously in Figure 7a,b. During chemical pretreatment of recalcitrant compounds, prior to biological degradation, when more than 75% of the pollutant initial C-content had been abated, the solution became biocompatible and could be disposed of in a biological treatment plant (Vogelpohl, 1996). The exponential treatment of the data is therefore highly suited for the modeling of this type of pretreatment as presented in this study. Efficiency of the Degradation and Its Relation to Electrical Energy Consumption and Economic Viability. Figure 2c shows a TOC reduction from 180 to ∼80 mg of C/L, in 30 min. The electrical power used by two actinic lamps during this time was then equivalent to 36 W/h or 7.99 kWh/m3. The cost of the electricity to reach a TOC value of 50 mg of C/L is ∼40 U.S. cents/m3. This is taking the cost of electricity at 0.05 US$/kWh. Since the biological degradation is considered a no-cost process, then the latter estimate for the energy cost will be valid for the complete degradation of p-NTS after 30 min of pretreatment (see

A systematic study of the main variables affecting the degradation of p-NTS was carried out. This enabled us to construct the mathematical functions of the model to evaluate the critical variables intervening in the photocatalytic degradation of this pollutant. Photoassisted Fenton reactions were seen to accelerate the degradation compared to reactions in the dark. The combination of photo-activated pretreatment followed by biodegradation leads to complete p-NTS degradation (Figure 5). The oxidation of the pollutant in the first stage by the •OH radical yields intermediates that are susceptible to biological abatement. A mathematical modeling for the optimization during the degradation has been worked out with polynomial and exponential functions. The exponential model approximates better to the experimental results obtained as a function of the four main variables used in this study. This treatment of the experimental data permits the minimization of the time, light intensity, and amount of chemicals used during the light-enhanced Fenton process. Acknowledgment This work was supported by INTAS Cooperation Contract 94-0642 and the European Community Environment Program under Contract No. ENV-CT95-0064 (OFES No. 96.0350 Bern). Literature Cited Box, G.; Hunter, P.; Hunter, J. Statistics for Experimenters: an Introduction to Design, Data Analysis and Model Building; Wiley-Interscience: New York, 1978. Cassano, A.; Martin, C.; Brandi, R.; Alfano, O. Photoreactors Analysis and Design: Fundamentals and Applications. Ind. Eng. Chem. Res. 1995, 34, 2155. Faust, C.; Hoigne´, J. Photolysis of Fe(III) hydroxy-complexes as sources of •OH radicals in clouds, fog and rain. Atmos. Environ. 1990, 24, 79.

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Received for review June 18, 1997 Revised manuscript received October 28, 1997 Accepted October 28, 1997 IE9704410