Kinetic Modeling of Polychlorinated Dibenzo-p-dioxin and

Aug 27, 2008 - National Homeland Security Research Center (E343-06), U.S.. Environmental ... Kinetic studies can be used to correlate PCDD/F formation...
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Environ. Sci. Technol. 2008, 42, 7218–7224

Kinetic Modeling of Polychlorinated Dibenzo-p-dioxin and Dibenzofuran Formation Based on Carbon Degradation Reactions E M A N U E L A G R A N D E S S O , * ,†,‡ SHAWN RYAN,§ BRIAN GULLETT,† ABDERRAHMANE TOUATI,| ELENA COLLINA,‡ MARINA LASAGNI,‡ AND DEMETRIO PITEA‡ Office of Research and Development, National Risk Management Research Laboratory (E305-01), U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711, Department of Environmental Sciences, Milano-Bicocca University, Piazza della Scienza 1, 20126 Milano, Italy, Office of Research and Development, National Homeland Security Research Center (E343-06), U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711, and ARCADIS Geraghty & Miller, Inc., 4915F Prospectus Drive, Durham, North Carolina 27713

Received May 6, 2008. Revised manuscript received July 8, 2008. Accepted July 21, 2008.

Combustion experiments in a laboratory-scale fixed bed reactor were performed to determine the role of temperature and time in polychlorinated dibenzo-p-dioxin (PCDD) and polychlorinated dibenzofuran (PCDF) formation, allowing a global kinetic expression to be written for PCDD/F formation due to soot oxidation in fly ash deposits. Rate constants were calculated for the reactions of carbon degradation, PCDD/F formation, desorption, and degradation. For the first time, values for activation and thermodynamic parameters for the overall reactions have been calculated for PCDD/F formation, desorption, and destruction reactions. Good agreement was found between the calculated rate constants for carbon degradation and for PCDD/F formation, indicating that the two processes have a common rate-determining step. Moreover, PCDD/F formation was found to be still active after long reaction times (24 h). These results points out the importance of carbon deposits in the postcombustion stages that can account for emissions long after their formation (memory effects). The calculated formation rates were 7-15 times higher than those reported in the literature from fly ash-only experiments, indicating the importance of both soot and a continuous source of chlorine. A comparison between full-scale incinerator rates and model calculated rates indicates that our model based on carbon degradation kinetic can be a tool to estimate emissions.

* Corresponding author phone: +1-919-541-1321; fax: +1-919541-0554; e-mail: [email protected]. † National Risk Management Research Laboratory (E305-01), U.S. EPA. ‡ Milano-Bicocca University. § National Homeland Security Research Center (E343-06), U.S. EPA. | ARCADIS Geraghty & Miller, Inc. 7218

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Introduction The formation of polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) has been studied in laboratory-scale experiments in order to understand the reactions controlling the combustion process and optimize the design and operating conditions of fullscale plants. Despite numerous examinations on the behavior of PCDD/Fs under different experimental conditions, few investigations have been carried out to predict their rates of formation in real combustion (e.g., incineration) facilities. Kinetic studies can be used to correlate PCDD/F formation/ destruction rates to those of the reagents. Taking into account that de novo synthesis has been identified as one major source of PCDD/Fs (1, 2), several authors studied the formation/destruction reactions as a function of temperature and time from the carbonaceous material in fly ash (FA). With regard to catalyzed reactions, PCDD and PCDF maximum formation temperatures were found between 300 and 470 °C (3, 4). Linear formation as a function of time was observed up to 60 min in experiments at 300 °C (5, 3), followed by a rapid net formation decrease at longer reaction times (6). Although these studies provided important information on the conditions relevant to PCDD/F formation, they did not provide an exhaustive set of data at different times and temperatures in the low-temperature range for the development of a kinetic model. Collina et al. (7) proposed to study carbon gasification kinetics in FA in order to understand the de novo synthesis reaction. They suggested that the carbon decrease was the result of two simultaneous processes. The first process (rate constant k2) is the direct oxygen transfer to a vacant carbon active site leading to immediate carbon gasification to CO2; the second process is dissociative oxygen chemisorption (k1) followed by the gasification (k3) of C(O) complex intermediates, probable precursors of PCDD/Fs. They modeled the production of C(O) at different temperatures, showing that the maximum concentration of oxygenated complexes with reaction time of about 4 h was in the temperature range 250-400 °C. The rate constants k1, k2, and k3, together with activation and thermodynamic parameters, were calculated. Other models related the rate of PCDD/F formation to some process variables including carbon or copper concentration in fly ash, partial pressure of oxygen, and reaction temperature (8, 9). The data used for validation of the models were derived from literature-reported de novo laboratory tests in flow reactors where the carbon had a residence time from minutes to hours. Reported rates measured in laboratory tests are 0.1-1 ng of PCDD/F (g of FA)-1 s-1, yet the rates in incinerator furnaces are 10-1000 ng of PCDD/F (g of FA)-1 s-1 (10). The latter rates were calculated by considering gasphase residence times, on the order of a few seconds, but they did not take into account carbon deposits, which can react for long time (minutes-hours) in the ducts of combustors. Therefore, the relationship between the de novo laboratory-scale results and rates in real facilities remains undemonstrated. The nature of particulate carbon has been shown to have a significant role in the de novo formation of PCDD/Fs (11-13). Recent laboratory studies pointed out that in situformed soot is a persistent carbon source for PCDD/F emissions and the presence of FA in the soot deposit is necessary as a catalyst and chlorinating agent (12, 14). In the present work, we performed experiments at different temperatures and times with the specific aim to develop a global kinetic expression for PCDD/F formation. Experi10.1021/es8012479 CCC: $40.75

 2008 American Chemical Society

Published on Web 08/27/2008

FIGURE 1. Schematic drawing of the multitemperature reactor (MTR) used, not to scale. mental conditions similar to those present in full-scale incinerator facilities were chosen in order to simulate the postcombustion zone, transition conditions (i.e., startups/ shutdowns), and “memory effects” (persistently higher emissions for a period after a transient event). For this reason, soot was added in the reacting bed, as well as a continuous chlorine source and water vapor in the gas stream.

Experimental Section Experimental Setup. The experiments were conducted in a multitemperature reactor (MTR), which consisted of four fixed-bed reaction tubes (0.8 cm inner diameter) with independent temperature controls and a common gas input and allowed for simultaneous reactivity studies at four different temperatures. A schematic drawing of the system is shown in Figure 1. In order to add water vapor in the gas stream, a flow of N2 (4 L min-1) was used to strip out the vapor from an impinger placed in a water bath at 55.5 °C. In order to allow for HCl formation, chlorine was mixed with water vapor at high temperature: a flow of Cl2 was added to the water impinger exit flow and passed through a reactor at 800 °C (residence time ) ∼0.4 s). The exit gases (N2, H2O, Cl2, and HCl) were then mixed with oxygen and additional N2: the resulting gas mixture was passed through each reactor of the MTR at a flow rate of 0.6 L min-1 (NTP ) normal temperature, 0 °C, and pressure, 1 atm). The gas flows to the system, with the exception of Cl2, were controlled with Sierra Series 840 mass flow controllers (MFC). The chlorine feed was controlled with a Hasting Teflon flowmeter. The temperatures in the four heated zones of the experimental facility were measured by 4 K-type thermocouples. Sampling and analyses were performed according to a slightly modified version of U.S. EPA Method 0023a (15). A sampling train was placed after each reactor; the collection components of the exhaust gas stream consisted of a condenser and a solid sorbent (XAD-2). The flow rate through the system was maintained constant by use of two pumps, one for each reactor pair, each connected to a meter box for flow rate measurements. After the experiments, the reaction beds containing the solid-phase fraction of PCDD/Fs, together with the XAD-2 resins and condenser rinses containing the vapor-phase fraction of PCDD/Fs, were extracted and analyzed with a high-resolution gas chromatograph (HRGC)/low-resolution mass spectrometer (LRMS)

(Agilent). A 60 m J&W DB dioxin column and single-ion monitoring (SIM) were used for mono- to octa-PCDD/F analyses. Materials. The bed materials (volume ) 1.1 cm3) were obtained from mixtures of oxidized FA (OX) and chlorinated soot. Table 1 reports the composition of these mixtures (OXSoot). Glass beads (1.5 g) were added to about 0.5 g of OXSoot to comprise the bed material, which may more closely simulate actual incinerator conditions where the gas stream flows through the fly ash (16). Chlorinated soot was produced in a quartz furnace followed by a filter, by use of an ethylene flame (Φ ) 0.86), and 200 ppm of Cl2 was added to the combustion gas flow. The formation of a prechlorinated soot matrix in these experimental conditions was previously observed by Wikstro¨m et al. (12). The OX was derived from raw FA [EPA FA, with composition reported elsewhere (17)] collected from an electrostatic precipitator of a grate-fired MSWI (municipal solid waste incinerator) located in the United States. The OX was prepared by thermal treatment of the raw FA at 500 °C in air for 24 h. The glass beads were thermally treated at 500 °C in air for 24 h to remove any potential impurities. The initial carbon content (C0) in each bed material is reported in Table 1 calculated as the percentage (w/w) of OXSoot. The OX carbon content was only 0.03% (17), so its contribution to the calculated carbon content C0 was neglected. Moreover, it was assumed that the soot added in the bed consisted of pure carbon. The untreated bed materials were characterized for PCDD/F content: analysis of the toluene extract of 0.0178 g of chlorinated soot showed only trace amounts (1.91 nmol g-1) of monochlorodibenzofuran; the PCDD content of the OX was 0.010 nmol g-1, while PCDFs were below the detection limit (∼0.5 ng sample-1 for each compound); no PCDD/F were detected in the glass beads. The gas flow added in the system consisted of oxygen (8.0 ( 0.1)%, water vapor (6.0 ( 0.8)%, gaseous Cl2 (200 ppm), and N2. Experimental Conditions. Table 1 reports the experimental conditions (identified by entry number) together with OXSoot identification, temperature, and time. The OXSoot mixture named A (Table 1) was used to study PCDD/F formation at different times (10-480 min) and temperatures (280-415 °C). The OXSoot mixtures with different carbon contents (0.5-1.4% w/w, B-E in Table 1) were prepared to evaluate the effect of C0 in experiments at constant temperature (350 °C) and time (30 min). Data Fitting. Analyses were run with the software Statistica 7.1, StatSoft Italia srl (2005), by use of an iterative nonlinear estimation procedure (18).

Results and Discussion PCDD/F Formation as a Function of Time and Temperature. Table 1 reports PCDD and PCDF concentrations, expressed as nanomoles per gram of OXSoot, as well as their sum, ΣPCDD/F, and ratio, PCDF:PCDD. For the experiments at 10 min and T ) 280 or 320 °C (entries 1 and 2), the concentrations were low and close to the detection limits. At 10, 30, and 60 min, PCDD/F formation continuously increased from 280 to 380 °C; at higher times, the trend appeared to achieve a constant concentration value at each temperature (Table 1). The two data points at 320 (entry 20) and 380 °C (entry 18) that do not follow the trend may have been due to experimental condition variability (flow and bed mixing variability). At 280-380 °C formation reached maxima between 47 and 66 nmol (g of OXSoot)-1 (entries 19-23); on the contrary, the highest PCDD/F formation at 415 °C (entries 5, 10, and 15) was 28 nmol (g of OXSoot)-1 at 30 min and decreased at 60 min. This fact, together with the observation of high carbon burnout in the VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Bed Types and Compositions, Experimental Conditions, and PCDD/F Results for Each Experimenta entry

OXSoot

soot (g)

carbon content (%)

t (min)

T (°C)

PCDDb (nmol g-1)

PCDFb (nmol g-1)

ΣPCDD/Fb,c (nmol g-1)

PCDF: PCDD

ηd (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A A A A A A A A A A A A A A A A A A A A A A A Be Ce De Ee

0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0025 0.0040 0.0060 0.0069

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.50 0.80 1.20 1.38

10 10 10 10 10 30 30 30 30 30 60 60 60 60 60 120 120 120 180 180 180 180 480 30 30 30 30

280 320 350 380 415 280 320 350 380 415 280 320 350 380 415 320 350 380 280 320 350 380 280 350 350 350 350

0.02 0.06 0.15 ( 0.02 0.49 ( 0.08 0.82 0.5 ( 0.1 1.4 ( 0.2 1.9 ( 0.5 1.8 ( 0.9 2.00 1.46 3.48 4.62 5.55 1.79 5.96 7.41 4.90 3.8 ( 0.3 5.62 7.92 5.89 6.81 1.63 1.66 1.42 1.95

0.14 0.61 3.5 ( 0.6 11.36 ( 0.09 15.42 3.4 ( 0.8 10.8 ( 0.8 18 ( 3 22 ( 4 26.05 12.64 27.03 36.95 48.00 24.45 38.66 50.67 42.64 28 ( 2 35.84 57.98 49.61 39.84 17.66 18.40 13.10 15.60

0.16 0.67 3.8 ( 0.7 11.8 ( 0.2 16.24 3.9 ( 0.9 12.2 ( 0.9 20 ( 4 24 ( 5 28.04 14.10 30.51 41.58 53.55 26.24 44.61 58.08 47.54 32 ( 2 41.46 65.91 55.49 46.65 19.29 20.06 14.52 17.54

7.0 10.2 23.3 23.2 18.8 6.8 7.7 9.5 12.2 13.0 8.7 7.8 8.0 8.6 13.7 6.5 6.8 8.7 7.3 6.4 7.3 8.4 5.9 10.8 11.1 9.2 8.0

0.000 23 0.0010 0.005 0.017 0.023 0.006 0.018 0.029 0.035 0.040 0.020 0.044 0.060 0.077 0.038 0.064 0.084 0.068 0.046 0.060 0.095 0.080 0.067 0.028 0.029 0.021 0.025

a The standard deviation for the repeated experiments is reported. b PCDD, PCDF, and ΣPCDD/F concentrations are referred to 1 g of OXSoot. c ΣPCDD/F indicates the sum of PCDD and PCDF. d η is the carbon conversion efficiency to ΣPCDD/F. e OXSoot B-E contain respectively 0.5%, 0.8%, 1.2%, and 1.4% initial carbon.

FIGURE 2. Experimental dependence on time of carbon concentration at different temperatures. bed already after 30 min (Figure 2), indicates that decomposition reactions (for both carbon and PCDD/F) influenced yields at this temperature. In all the experiments, PCDF amounts were higher than PCDD, in agreement with the usual results found in the emissions from MSWI (16). PCDF:PCDD ratio reflects a combined temperature and time effect. At 10 min, the ratio increased very quickly with increasing temperature (entries 1-4); with longer reaction time, the differences in the ratio values with increasing temperatures became progressively lower. At 180 min (entries 19-22) the ratio was relatively constant, with a value of 7.4 ( 0.8. 7220

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PCDD and PCDF formation as a function of temperature and time follows a similar trend. At short reaction times the formation increases, and at longer times the formation tends to decrease. Both PCDDs and PCDFs reach maximum formation at 350 °C and 120 min. These similarities suggest that their formation could be globally influenced by the same parameters, such as carbon, catalyst amount, and type, yet at different rates. However, the change in the PCDF:PCDD ratio could also indicate that a different pathway cannot be excluded. For each temperature the incremental rate calculated for PCDD or PCDF is given in Table S1, Supporting Information.

These data update the calculated values in ref 19. The rate increase in the first minutes of the experiments indicates the presence of an induction period. Since the reactors were heated in a nitrogen flow before the experiments, we believe the induction period is not related to unstable temperature conditions. On the other hand, it could be due to the time needed for chlorine and oxygen to reach steady conditions in the bed, as well as to the time needed for activation of the metal in the OX. In fact, OX has been treated at high temperature in air and it is likely to contain metal oxides, which could be converted into more active catalytic species, such as metal chlorides and oxychlorides, through reaction with the gas phase (and/or solid-phase inorganic chloride, i.e. NaCl). To evaluate whether the initial reaction kinetics were controlled by the initial carbon content, C0, experiments 24-27 (Table 1) were performed at T ) 350 °C and t ) 30 min with 0.5% e C0 e 1.4% (OXSoot types B-E, Table 1). These C0 values were chosen to span the carbon concentration before the incremental PCDD/F formation rate started to decrease, suggesting an apparent carbon limitation. Results of these experiments (Table 1) showed that the PCDD/F concentrations in OXSoot after 30 min were substantially similar, indicating that they did not depend on initial carbon concentration (i.e., carbon was not a limiting factor in our experimental conditions). The highest formation rates over the first 60 min of experiment at 280, 320, 350, and 380 °C were 138.8, 251.0, 276.0, and 389.7 ng of PCDD/F (g of OXSoot)-1 min-1, respectively (Table S1). Other experiments (5) with FA at 300 °C and t ) 60 min reported rate values of about 20 ng of PCDD/F (g of FA)-1 min-1. Our calculated rates were about 7-15 times higher, probably due to the presence of soot in the reaction beds, which can be more reactive than FA native carbon (unburned unextractable carbon in the FA) (12, 14). Moreover, our gas flow provided a continuous source of Cl2 to be transferred to the carbon (soot or smaller aromatic compounds), likely via metal chlorides (3), which results in a PCDD/F increase, based on demonstrated Cl2 effects (20). The carbon conversion efficiency (η) was calculated with the assumption that the soot added in the reaction bed consisted completely of carbon (Table 1; Figure S1, Supporting Information). In runs performed on OXSoot A, the initial carbon concentration was 8.34 × 105 nmol of C (g of OXSoot)-1; the maximum theoretical amount of possible PCDD/F skeletons was 6.95 × 104 nmol of PCDD/F (g of OXSoot)-1. With respect to this reference number, the highest η was 0.095% (entry 21) and the lowest conversion efficiency (entry 1) was 0.00023%, about a 500-fold variation. Carbon Degradation. Carbon degradation in OXSoot A (carbon content 834 µmol of C g-1, from the assumption that soot consisted of carbon only) was calculated from the online measurement of CO and CO2. Preliminary results have been reported in Grandesso et al. (19), and the experimental data are shown in Figure 2. At 280, 320, and 350 °C, carbon degradation was not completed in 150 min; at these temperatures, respectively 54%, 49%, and 20% of the initial carbon was still remaining in the bed. At 380 °C, the carbon degradation was completed within 150 min (less than 1% carbon left). At 415 °C, carbon degradation was monitored up to 50 min, when only 6% carbon was left in the bed. However, after 30 min only 3% carbon decrease occurred, indicating already a very slow degradation. Kinetic Modeling. As discussed before, PCDD or PCDF variations with temperature and time were qualitatively similar. This result is probably due to the major contribution of de novo synthesis in our system, in which carbon from soot, not from flame products, was present (13). Since PCDD and PCDF formation mechanisms seemed to be comparable,

the kinetics of their formation was interpreted in terms of the sum of their concentrations (Table 1). In a previous paper, Collina et al. (7) proposed a kinetic mechanism for FA native carbon oxidation. It was hypothesized that the nature of the interaction between native carbon and the FA surface is the key factor for C oxidation and C(O) complex formation and gasification. In this paper, on the basis of the theory of carbon intermediates formation (21), we are developing a more extensive model that includes PCDD/F formation and decomposition. PCDD/F are byproducts of carbon oxidation on FA surface in presence of oxygen and chlorine (22). Once formed, they can desorb from the carbonaceous structure and can be transferred into the vapor phase. Otherwise, they remain in the solid phase and can lead to decomposition and/or dechlorination reactions. In the same way, compounds in the vapor phase can undergo decomposition and/or dechlorination reactions. The overall process of PCDD/F formation can be schematically represented by C + O2 + Cl f CO + CO2 + (PCDD/F)s + other products where carbon, C, is partly oxidized to CO and CO2 and partly reacts to form PCDD and PCDF in the solid phase, (PCDD/ F)s. We indicate the carbon that gives (PCDD/F)s as CDF, in eq 1. Cl represents the active chlorine species for PCDD/F formation, primarily metal chlorides and oxychlorides (14, 20). In our system, chlorine is mainly supplied by the gas flow and in minor amounts by chlorinated soot and OX. However, metal chlorides are likely formed when the gas-flow chlorine reacts with the metal oxides in the reaction beds (23). Here, we use the following “gross” reaction scheme, based on the mechanism proposed by Huang and Buekens (8): ka/

CDF + O2 + Cl 98 (PCDD/F)s

(1)

ksv

(PCDD/F)s 98 (PCDD/F)v

(2)

kp

(PCDD/F)s,v 98 P

(3)

The reaction equations are formal (i.e., they are not stoichiometrically balanced). Equation 1 is the formation reaction, which occurs in the solid phase (s); eq 2 will be named as desorption and eq 3 as degradation. (PCDD/F)s and (PCDD/F)v represent dioxins and furans from formed-incarbon degradation reactions and adsorbed in the solid phase (s) or transferred in the vapor phase (v), respectively. P indicates products formed from the solid or vapor phase for decomposition reactions. According to the proposed reaction scheme, the rate equation for the carbon fraction involved in PCDD/F formation, CDF, is -d[CDF]/dt ) k/a[CDF]nC[O2]nO[Cl]nCl

(4a)

where nC, nO, and nCl are the reaction orders for carbon, oxygen, and chlorine, respectively. As the O2 and Cl2 were supplied in great excess at a controlled concentration, the oxygen and chlorine terms in eq 4a are constants in each experiment. From experimental data of carbon degradation (Figure 2), a first-order kinetic expression was chosen. On this basis, CDF was supposed to decrease following the same order (nC ) 1) and eq 4a becomes -d[CDF]/dt ) ka[CDF]

(4b)

where ka ) ka*[O2]nO[Cl]nCl. VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Calculated Values of Carbon Degraded and Rate Constants at Different Temperatures T (°C)

[CDF]0 (nmol of C g-1)

ka (min-1)

ksv (min-1)

kp (min-1)

280 320 350 380 415a

624 600 912 648 492

5 × 10-3 1.3 × 10-2 1.2 × 10-2 2.8 × 10-2 3.8 × 10-2

1.45 × 10-4 2.3 × 10-4 4.6 × 10-4 1.01 × 10-3 1.5 × 10-3

1.45 × 10-6 1.2 × 10-5 2.5 × 10-5 4.1 × 10-5 1.4 × 10-4

R2 0.990 0.991 0.998 0.997

C0 (µmol of C g-1)

k′a (min-1)

R2

854 ( 4 822 ( 8 808 ( 10 876 ( 12 868 ( 2

(4.28 ( 0.05) × 10-3 (5.1 ( 0.1) × 10-3 (1.20 ( 0.3) × 10-2 (2.57 ( 0.06) × 10-2 (9.90 ( 0.04) × 10-2

0.997 0.985 0.987 0.994 0.994

a The kinetic constants were evaluated by Arrhenius equation; see text. The value of [CDF]0 was estimated by comparison of experimental and calculated values for PCDD/F concentrations.

FIGURE 3. Experimental and calculated (eq 10) dependence on time of the PCDD/F concentrations at the different temperatures. The fitting is calculated from the values reported in Table 2. The respective rate equations for (PCDD/F)s and (PCDD/ F)v formations are

The formation of (PCDD/F) ) (PCDD/F)s + (PCDD/F)v is calculated by

d[(PCDD/F)s]/dt ) ka[CDF] - (ksv + kp)[(PCDD/F)s] (5)

ksv ka - ksv [(PCDD/F)] ) + exp(-kat) [CDF]0 ksv + kp (ksv + kp) - ka kakp exp[-(ksv + kp)t] (10) (ksv + kp)[(ksv + kp) - ka]

-d[(PCDD/F)v]/dt ) ksv[(PCDD/F)s] - kp[(PCDD/F)v] (6) Due to the very low gas residence time (t ) 0.11 s) and relatively low temperature in the MTR, the contribution to the decomposition reaction of (PCDD/F)v is assumed to be negligible. The system of differential equations 4a-6 is solved analytically with the following boundary conditions at t ) 0: [CDF] ) [CDF]0, [(PCDD/F)s] ) [(PCDD/F)s]0 ) 0, and [(PCDD/ F)v] ) [(PCDD/F)v]0 ) 0. [CDF]0 represents the fraction of initial carbon concentration that reacts according to eq 1 (i.e., 12 mol of C gives 1 mol of PCDD/F and thus is expressed as nanomoles of C per gram of OXSoot). The CDF concentration decrease with time is given by [CDF] ) [CDF]0exp(-kat)

(7)

and [(PCDD/F)s] and [(PCDD/F)v] formation are given by [(PCDD/F)s] )

[(PCDD/F)v] )

ka[CDF]0 {exp(-kat) - exp[-(ksv + kp)t]} (ksv + kp) - ka (8)

[

kaksv[CDF]0 1 - exp(-kat) (ksv + kp) - ka ka 1 - exp[-(ksv + kp)t] ksv + kp

]

(9)

In eqs 7-9, the concentrations are expressed as nanomoles of C per gram of OXSoot. 7222

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The model of eq 10 contains four parameters, ka, ksv, kp, and [CDF]0; because the first term as well as the pre-exponential terms are combinations of kinetic constants, they likely depend on temperature. The experimentally determined values of [(PCDD/F)] versus time (Table 1) at temperatures between 280 and 380 °C were fitted to eq 10 by a nonlinear estimation procedure (18). The goodness of fits was estimated on the basis of the standard deviation of the parameters as well as the determination coefficients (R2). Table 2 reports the calculated values of [CDF]0 together with the rate constants (ka, ksv, and kp) and R2. The good agreement between the experimental data and the kinetic model is shown in Figure 3. The activation and thermodynamic parameters calculated from Arrhenius and Eyring equations are reported in Table 3. The difference between activation or thermodynamic parameters was confirmed by use of a statistical procedure for comparing slopes and intercepts of the regression lines, applied at 95% confidence level (24). At 415 °C the kinetic constants (Table 2) were extrapolated from an Arrhenius equation developed with kinetic constants in the temperature range 280 °C - 380 °C. A first-order kinetic expression was chosen to model the carbon degradation (Figure 2): [C] ) [C]0exp(-ka′t)

(11)

TABLE 3. Activation (from Arrhenius Equation) and Thermodynamic (from Eyring Equation) Parameters ka

ksv

kp

Activation Parameters ln A (min-1) Ea (kJ mol-1) R2

5(1 46 ( 7 0.939

4(1 58 ( 6 0.971

9(2 101 ( 10 0.974

Thermodynamic Parameters K-1

mol-1)

(kJ ∆Hq (kJ mol-1) R2 ∆Gq a (kJ mol-1) % ∆Sq ∆Sq

a

-(0.22 ( 0.01) 41 ( 7 0.924 178 ( 10 77 ( 6

-(0.230 ( 0.009) 53 ( 6 0.966 195 ( 8 73 ( 4

-(0.19 ( 0.02) 96 ( 10 0.971 212 ( 14 55 ( 6

∆Gq at an average temperature of 622 K (349 °C).

where ka′ is the kinetic constant for carbon degradation. The calculated ka′ values are reported in Table 2 together with the determination coefficients, which were always greater than 0.98, indicating a good data fit. The rate constant values ka′ and ka are in good agreement, leading to the hypothesis that carbon oxidation and PCDD/F formation, in our system, have a common rate-determining step. Following eq 10, the reaction time, tmax, at which the maximum PCDD/F concentration, [PCDD/F]max, is formed was analytically calculated at each temperature. The highest [PCDD/F]max has been calculated at T ) 350 °C and it is equal to 75.1 nmol of PCDD/F (g of OXSoot)-1 (Table S2, Supporting Information). Taking into account that the initial carbon concentration is 834 µmol of C (g of OXSoot)-1, the calculated maximum PCDD/F yield is 0.108%. This value is in good agreement with the maximum observed experimental yield (entry 21), 0.095% (Table 1 and Figure S1). Equation 10 also specifies the relative contribution of PCDD/F formation and desorption/decomposition reactions, which are described respectively by the second and third terms of the equation (Figures S2 and S3, Supporting Information). The formation term has a large negative initial value and a steep variation with time increase; at each temperature, as t f 24 h it tends to zero. The desorption/ decomposition term has a smaller initial negative value and a smooth variation with time, indicating a lower contribution to the total yields. The formation terms equal the desorption/ decomposition at a “crossing time”, tcross, which is dependent on temperature. The estimated tcross values are reported in Table S2, together with the corresponding PCDD/F concentrations, [PCDD/F]cross. With higher temperatures, PCDD/F formation in the solid phase (eq 1) increases but the tcross values decrease (i.e., desorption and decomposition reactions become increasingly more important at shorter times). Thus, at a given residence time, the residual [PCDD/F]s concentration in the carbon lowers even if the temperature increases. This result is relevant with respect to the formation on the FA in MSWI energy recovery and environmental control units (“cold zones”), where FA have residence times as long as our calculated tcross. Values for activation and thermodynamic parameters have been reported for octachlorodibenzofuran decomposition and dechlorination reactions (25, 26), whereas values for PCDD/F formation and destruction comparable to those in Table 3 are not reported in the literature. However, we suggest that the estimated activation and thermodynamic parameters should be considered as apparent quantities. In fact, all these parameters refer to only a part of the overall reactions (i.e., those concerning CDF gasification); moreover, even for this partial reaction pathway we do not have any information

about the number and typology of the reactions and the reactants/products. The PCDD/F formation (ka) processes are characterized by an apparent molar free energy of activation [∆Gq ) 178 kJ mol-1 at 622 K (349 °C), the mean temperature at which the experiments have been carried out] mainly determined (77%) by a large negative activation entropy value (∆Sq ) 0.22 kJ mol-1 K-1). The relatively low activation enthalpy (∆Hq ) 46 kJ mol-1) is in the range of diffusion-limited reactions rather than typical of chemical steps. The negative ∆Sq and the very small A factor (about 150 min-1) point out that the transition states are more compact and stiffer than the reagents, indicating the so-called “tight” transition states. In the PCDD/F decomposition (kp) processes, ∆Sq and ∆Hq contributions to ∆Gq are similar (about 50%) but the activation enthalpy value (96 kJ mol-1) indicates the importance of chemical steps. The Ea and ∆Hq ratios between the decomposition and formation reactions are 2.2 ( 0.4 and 2.3 ( 0.5, thus indicating that PCDD/F are stable compounds in the experimental temperature range. Finally, the parameters for the desorption processes (ksv) are compared to those determined for dibenzofuran, dibenzo-p-dioxin, and biphenyl thermal desorption in diffusion-controlled conditions (26). The latter are of the same order of magnitude but smaller than the desorption energy parameter of the present work, as is expected for nonchlorinated species (10). The results show that in our laboratory experiments PCDD/F are formed at the temperatures typical of the MSWI cold zones and are stable over times as long as 15 h. Carbon deposits in the cold zones can reside under stationary conditions over a very long time and are a primary cause of PCDD/F formation (27, 28). During this time, the flue gas flow can either resuspend particulate matter or promote PCDD/F desorption or both. FA and soot resuspension and PCDD/F desorption have a big impact in MSWI emissions, in both vapor and solid phases, and have to be considered in order to explain memory effects. Several studies comparing laboratory-measured rates with those determined from industrial plants (10, 27, 29, 30) concluded that calculated rates from de novo synthesis laboratory experiments were too low to explain estimated incinerator PCDD/F emissions. However, the assumption of FA and soot residence time on the order of seconds in gas ducts does not take into account memory effects, in which fresh deposits can have residence times on the order of minutes. The consequence is that calculated rates from incineration based on in-flight residence times were highly overestimated. Our calculated formation rates with their long reaction times can be compared to formation rates in actual MSWI facilities. Hunsinger et al. (31) report data of ash deposits measured between soot blowing operations in a pilot waste incinerator designed for a waste feed of 20 Mg h-1. The average amount of boiler fly ashes deposited in 8 h was 240 kg with an average residence time of 4 h. PCDD/F were produced at a rate of about 30 mg h-1. In such a plant we can assume that the carbon concentration in the ash does not change during time: carbon is not a limiting factor for PCDD/F formation. We analytically calculated from eq 10 the initial formation rates as reported in Table S1. Considering an average FA/soot temperature of 320 °C in their boiler, our PCDD/F formation rate is 253 ng of PCDD/F g-1 min-1, which in the presence of 240 kg of ash and a carbon content of 1 mg g-1 gives 364 mg of PCDD/F h-1. This result is ∼10 times higher than the one found in the MSWI described. However, when the various assumptions and approximations of these calculations, scale effects between laboratory setup and a real plant, and the favorable conditions for PCDD/F formation used in our experiments (such as the use of soot and high gaseous chlorine concentrations) are all taken into account, we can consider the difference between the two rates acceptable. We believe that VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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our model based on carbon degradation kinetics can be a tool to estimate emission variations from a full-scale facility. This result emphasizes the importance of carbon as a major parameter affecting emissions and the need for full-scale MSWI to minimize carbonaceous deposit accumulation.

Acknowledgments We thank Christelle Briois at the Universite´ d’Orle´ans (France), Dennis Tabor at the U.S. EPA, and Matt Clayton from ARCADIS Geraghty & Miller for valuable help and for useful discussions.

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Supporting Information Available Incremental ratios for PCDDs and PCDFs, initial formation rates and carbon conversion efficiency calculated from experimental data, and details on data analysis: from eq 10, calculated PCDD/F at tmax and at tcross and figures of dependence on time of the second and third term. This material is available free of charge via the Internet at http:// pubs.acs.org.

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