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Activated carbon injection for mercury capture is already a. *Corresponding author phone: +39 081 7682242; fax: +39 081. 5936936; e-mail: [email protected]...
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Environ. Sci. Technol. 2001, 35, 4367-4372

Simulation of Mercury Capture by Activated Carbon Injection in Incinerator Flue Gas. 1. In-Duct Removal FABRIZIO SCALA* Dipartimento di Ingegneria Chimica, Universita` degli Studi di Napoli “Federico II”, P.le Tecchio, 80, 80125 - Napoli, Italy

A detailed model for the in-duct mercury capture in incinerator flue gas by powdered activated carbon injection is presented. Material balances on mercury in both gaseous and adsorbed phases are carried out along the duct length and inside the activated carbon particles, taking into account mass transfer resistances and adsorption kinetics. The set of the coupled partial differential equations is transformed by means of an orthogonal collocation technique and integrated using a Runge-Kutta method with adaptive stepsize control. The model has been applied to several sorbents of practical interest, whose parameters have been evaluated from available literature data. The values and range of the operating variables have been chosen in order to simulate typical incinerators operating conditions. Results of simulations indicate that large sorbent loadings in the duct are needed to obtain high mercury removal efficiencies, due to the short residence times. As a consequence very low utilization of the sorbents is achieved in any case. To minimize the sorbent feed rate it is particularly advisable to use a reactive sorbent and to lower the operating temperature as much as possible. Improvements in the mercury capture performance can be obtained also by increasing the in-duct particles residence time and by decreasing the sorbent particles size. Model results are compared with available relevant full scale data.

Introduction In the United States the 1990 Clean Air Act Amendments listed 189 hazardous air pollutants, produced by a variety of industrial and combustion sources. Among these pollutants mercury has drawn special attention by the international community. In particular in 1997 the U.S. Environmental Protection Agency (EPA) completed a comprehensive Mercury Study Report to Congress (1). The increased attention to mercury emissions with respect to other trace metals is due to two main reasons: 1. the increasing level of bioaccumulation in the environment and particularly in the foodchain of this toxic metal with potential risks for human health and 2. the difficulty to limit mercury emissions from anthropogenic sources due to the high volatility of mercury species. Although mercury emissions occur naturally, major pollution is caused by human activities (1-6). Recent studies recognized that about 70-85% of the total anthropogenic *Corresponding author phone: +39 081 7682242; fax: +39 081 5936936; e-mail: [email protected]. Present address: Istituto di Ricerche sulla Combustione - C.N.R. - P.le Tecchio, 80, 80125 - Napoli, Italy. 10.1021/es010065h CCC: $20.00 Published on Web 10/06/2001

 2001 American Chemical Society

mercury emissions are caused by combustion sources, mainly coal-fired utilities and waste incinerators (municipal, hazardous, and medical) (1, 5). The latter source has attracted particular attention because the concentration of mercury in the stack gas is relatively high, and significant deposition near the emission sources has prompted public concern (710). Mercury emissions from incinerators are related to the presence of mercury containing devices or materials in the waste. In particular metallic mercury and mercury oxide are the prevalent forms in municipal waste (10, 11). At the typical combustion temperatures all the mercury, regardless of its initial chemical form, is readily vaporized as elemental mercury and exits the combustion chamber with the flue gas (2, 11). Upon cooling mercury is mostly homogeneously and/ or heterogeneously transformed into volatile oxidized mercury species as a consequence of the large excess air and the presence of large amounts of chlorinated compounds in the gas (11-13). Both thermodynamic equilibrium calculations (14, 15) and experimental measurements (16-18) in incinerators flue gases showed that the main mercury emitted species is HgCl2. Contrary to other trace metals, this volatile compound does not undergo condensation and passes through traditional air pollution control systems with moderate to low capture efficiencies and is eventually emitted in the atmosphere (9, 12, 19, 20). It has been shown that mercury in flue gases is partly captured by adsorption on the unburned carbon in fly ash (2, 12, 21); well-designed incinerators, however, have little unburned carbon in fly ash so that this capture mechanism is often negligible (19, 22). Oxidized mercury emitted in the atmosphere is readily solubilized in cloudwater and rainwater and transported to soil, rivers, and lakes where it is transformed into more toxic organic species (for example methyl mercury) and assimilated by animals and plants (2, 8). In the last years industrialized countries have been setting progressively tighter limits for mercury emissions from waste incinerator facilities. In particular the European Community has set a 0.05 mg/Nm3 mercury emission limit in 1994 on new hazardous waste incinerators (Directive 94/67), while it is currently under way extension of this limit to all waste incinerators (Directive proposal C372/98). Italy, as well as other European countries, has already set this emission limit in 1997 for new municipal waste incineration plants (Decree of the Ministry of Environment n.503-19/11/1997). To meet local emission limits specific technologies for mercury capture have to be applied to incinerators. Following bench-scale (23-25), pilot-scale (26), and full-scale (10, 27, 28) experimental research carried out in the past decade, powdered activated carbon injection in flue gas upstream of a particulate matter control device (PMCD) has been indicated as the best available technology for mercury capture in incinerators flue gas (1). This technology offers a number of advantages over other possible technologies, like the following: high mercury capture efficiency; production of a nonhazardous and noncorrosive solid byproduct (possibly regenerable); limited fire or explosion hazards; simple and low cost process design, operation, and maintenance; and possibility of retrofitting existing plants. Noteworthy activated carbon has also been reported to effectively capture other flue gas pollutants such as dioxins and furans. This technology is particularly cost-effective when the flue gas treatment system employs dry sorbent injection for acid gas control; in this case activated carbon can be simply mixed with the sorbent and injected in the duct upstream of the PMCD. Activated carbon injection for mercury capture is already a VOL. 35, NO. 21, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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commercial technology and has been applied with success to a number of incinerators worldwide. Despite the considerable experimental research carried out to date, however, no model simulation of mercury adsorption by activated carbon injection in incinerators flue gas has been attempted yet. The scope of the present work was to develop a detailed predictive tool for this process taking into account all relevant mechanisms and evaluating parameters from available literature data. This paper will be focused on mercury capture in the duct between the activated carbon feeding point and the PMCD. Results obtained in this paper will be relevant to plants where the PMCD is an electrostatic precipitator. A companion paper (29) will focus attention to the additional mercury capture on a fabric filter, in the case that this is the relevant PMCD of the plant.

Theory The system is schematized as a straight duct of constant diameter starting from the activated carbon feeding point and ending at the PMCD. The model is based on the following assumptions: 1. The relevant mercury species in the gas phase is mercuric chloride (HgCl2), and no other mercury species are present. 2. The adsorption process is not dependent on the flue gas composition apart from mercuric chloride concentration; in particular it is assumed that hydrochloric acid and sulfur dioxide concentrations are respectively sufficiently high and sufficiently low not to give rise to significant presence of elemental mercury. 3. Activated carbon particles are supposed to be spherical and all of the same size and to be uniformly dispersed in the gas phase. 4. The system is at the steady state, and both the gas and solid flow rates are constant. 5. The temperature is constant and uniform through the system and pressure losses are neglected, so that gas velocity is constant along the duct. 6. Mercury adsorption on the duct walls is negligible, i.e., equilibrium conditions are reached between the gas phase and duct walls so that no net exchange of mercury is present. 7. Mercury adsorption heat effects are neglected due to the trace level concentrations. Fluid Dynamics. The flue gas is assumed to travel in plug flow along the duct. To establish if the slip velocity between the activated carbon particles and the gas is relevant, the terminal velocity of the particles was evaluated for the particle sizes of interest. To this end the Stokes regime assumption was made. Results indicated that terminal velocities are always more than 1 order of magnitude lower than typical flue gas velocities so that it is reasonable to assume that particles travel at the same velocity as the flue gas. Particle Reynolds number resulted always lower than one justifying the assumption of the Stokes regime. Analysis of Relevant Mass Transfer Mechanisms. The process of mercuric chloride vapor adsorption on activated carbon can be schematized as a series of three steps: 1. mass transfer from the bulk gas to the external surface of the activated carbon particle through the gas boundary layer, 2. mass transfer from the external surface to the interior of the particle through the pore structure, and 3. surface adsorption on the internal surface area of the particle. The first step can be treated in the classical way by means of an external mass transfer coefficient whose calculation passes through the evaluation of the particle Sherwood number. Keeping in mind the previous result that the particle slip velocity is always much lower than the gas velocity, a reasonable assumption is that the Sherwood number is equal to the limiting theoretical value of 2 relative to the stagnant boundary layer condition. It was evaluated that this assumption would give negligible errors in the evaluation of Sh at most practical conditions and a maximum error of the order of 10% at the largest particle size considered (100 µm). 4368

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As regards the second step, pore diffusion can be caused by two distinct mechanisms: gaseous diffusion inside the pore network and surface diffusion along the pore walls. While the first mechanism is always present, the second one is only relevant at high adsorbate coverages, that is when approaching monolayer adsorption conditions (30); in these conditions the mobility of the adsorbed phase is comparable to that of the gas phase. To check if these conditions can be reached during the mercury capture process, a calculation was carried out in order to find the maximum coverage possible for the activated carbons considered. To this end conservative conditions were used by considering the maximum uptake capacity (ωmax) of mercury (Table 1). Given the dimension of a single HgCl2 molecule (6.5 Å × 3 Å) and the sorbents pore surface area data (23, 24), for the virgin activated carbon a maximum coverage of about 8% can be anticipated, while for the two sulfur impregnated ones higher values are obtained, anyway lower than 25% and 50%, respectively. Taking into account that in practical conditions, due to the short contact times, the particle mercury uptake is always much lower than the maximum theoretical one surface diffusion can be assumed to be negligible as compared to gaseous diffusion. This latter mechanism is typically treated by means of an effective pore diffusion coefficient (Deff) given by a combination of molecular (Dm) and Knudsen (DKn) diffusivities

Deff )

(

P 1 1 + τP Dm DKn

)

-1

(1)

where the particle pore tortuosity (τP) is usually approximated as the reciprocal of the particle porosity (P), as τP ) 1/P. The Knudsen diffusivity is given by

DKn )

x8RT 32π

dpore 3

(2)

This expression is based on the simplifying assumption that the treatment can be carried out by means of a single average pore diameter (dpore), although many activated carbons exhibit a bimodal pore size distribution. Adsorption Kinetics. Mercuric chloride adsorption on the internal surface of virgin and sulfur impregnated activated carbon particles has been clearly identified as a physical adsorption mechanism (24). A number of theoretical and empirical equations can be used to model the adsorption process. In this work the Lamgmuir theory will be used for the following reasons: 1. Langmuir isotherms were successfully used to correlate experimental data (23, 24). 2. The Langmuir theory allows for the simple expression of the rate of adsorption in addition to the equilibrium isotherm. 3. The only experimental kinetic and thermodynamic data found in the literature for mercuric chloride adsorption on activated carbon are expressed according to the Langmuir theory (23, 24). The net rate of mercury adsorption on the activated carbon particle surface can be written as the difference between the adsorption rate and the desorption rate

dω ) k1(ωmax - ω)c - k2ω dt

(3)

where ω is the local mercury uptake on the sorbent and c is the local gas mercury concentration. At the equilibrium this rate equation leads to the Langmuir isotherm

ωeq ) ωmax

Kceq 1 + Kceq

(4)

where the adsorption eqilibrium constant is related to the kinetic parameters by K ) k1/k2.

TABLE 1. Adsorptive and Physical Properties of the Sorbents Considered sorbent DARCO G60 DARCO G60 + 7.8% Na2S DARCO G60 + 18.7% Na2S SORBALIT fly ash

T, °C

k1, m3/gs

k2, 1/s

ωmax

120 150 200

0.25 0.2 0.1 6.0E-2 3.0E-2 0.45 0.37

1.5E-3 4.2E-4 1.7E-4 2.4E-4 1.5E-4 6.16E-3 5.5E-4

0.113 3.87E-2 2.53E-2 0.106 0.160 3.04E-2 1.03E-3

150

Model Equations. The mercury mass balance in the gas phase inside the particle pores (in radial coordinates) reads

(

)

∂c ∂2c 2∂c P - Deff 2 + + FP[k1(ωmax - ω)c - k2ω] ) 0 (5) ∂t r ∂r ∂r where FP is the sorbent particle density and eq 3 was used. Giving the plug flow and the no slip velocity assumptions, the mercury mass balance in the bulk gas phase in the duct reads

|

dcB 3ΘACDeff∂c )dt FPRP ∂r

(6)

(RP,t)

where cB is the gas bulk mercury concentration, ΘAC is the activated carbon loading per unit volume in the bulk gas, and RP is the sorbent particle radius. The system of three coupled differential equations (eqs 3, 5, and 6) has the following initial and boundary conditions

ω(r, 0) ) 0; c(r, 0) ) 0; cB(0) ) cBIN

|

∂c ∂r

; (0,t ) 0)

|

∂c ∂r

) (RP, t)

(7)

KG [c (t) - c(RP,t)] Deff B

(8)

where the mass transfer coefficient is given by KG ) DmSh/ 2RP. The average mercury uptake in the activated carbon particles in a duct section is simply given by

ω j (t) )

(cBIN - cB) ΘAC

(9)

to solve the system of partial differential equations it is useful to adimensionalize the equations by means of the following new adimensional variables

γ ) c/cBIN; γB ) cB/cBIN; φ ) ω/ωmax; ξ ) r/RP; 2

τ ) tDeff/PRP (10) giving 2

dφ PRP ) [c INk (1 - φ)γ - k2φ] dτ Deff B 1

(

)

(3′)

2

FPRP ωmax IN ∂γ ∂2γ 2∂γ + + [cB k1(1 - φ)γ - k2φ] ) 0 2 ∂τ ξ ∂ξ ∂ξ DeffcBIN (5′)

|

dγB 3ΘACP∂γ )dτ FP ∂ξ

(6′) (1,τ)

with the initial and boundary conditions:

|

∂γ ∂ξ

GP, kg/m3

EP

dpore, Å

0.65

60

0.7 0.4

200 60

750 830 940 650 1360

φ(ξ, 0) ) 0; γ(ξ, 0) ) 0; γB(0) ) 1 ) 0; (0,τ)

|

∂γ ∂ξ

) (1,τ)

(7′)

KGRP [γ (τ) - γ(1,τ)] Deff B

(8′)

Solution Procedure. The boundary-value partial differential equation (eq 5′) was reduced to a set of n initialvalue ordinary differential equations in τ using an orthogonal collocation technique (31). To this end the solution was approximated by a linear combination of Lagrange polynomials, and the collocation points were chosen as the zeroes of Legendre polynomial of the same order as the number of internal collocation points. The resulting system of 2n + 1 (2n + eq 6′) ordinary differential equations was integrated using a fifth-order Runge-Kutta method with adaptive stepsize control. The number of collocation points (n) and the Runge-Kutta stepsize were adjusted in order to give a total accuracy of 10-4 in the value of the output variables. Accordingly a value of n ) 5 was used for the calculations. Parameters Estimation. The model has been applied to one virgin activated carbon and two sulfur impregnated carbons. For comparison also a commercial sorbent (Sorbalit) and a fly ash have been considered. Sorbalit is a pelletized sorbent composed of cement, lime, activated carbon, and proprietary sulfur compounds used for the simultaneous removal of mercury and acid gases. The fly ash considered has been collected on the fabric filter of a full scale municipal solid waste incinerator and has an unburned carbon content of about 0.6 wt % (21). Adsorptive and physical properties of the sorbents considered were taken from literature (21, 23, 24, 32) and are reported in Table 1. Molecular diffusivity of mercuric chloride in the flue gas was estimated by means of the Chapman-Enskog theory and was calculated to be 0.14 × 10-4 m2/s, 0.16 × 10-4 m2/s, and 0.19 × 10-4 m2/s at 120 °C, 150 °C, and 200 °C, respectively.

Results and Discussion The procedure followed to analyze model results has been that of selecting a set of operating variables as a base case for computations and to assess the influence of the relevant input variables on the process by varying them one at a time. Table 2 reports the operating variables for the base case and the range of variation of each variable. The values and range of the input variables have been chosen in order to simulate as closely as possible typical incinerators operating conditions. The virgin activated carbon sorbent (DARCO G60) has been selected for base case computations. Figures 1 and 2 report the gas bulk mercury concentration decrease and the average mercury uptake on the sorbent as a function of residence time in the duct for different particle sizes (Figure 1) and different system temperatures (Figure 2). The gas bulk mercury concentration has been normalized with the inlet bulk concentration, while the sorbent mercury uptake with ωmax. Both figures show that, as expected, the longer the particle residence time in the duct the larger the mercury capture. Figure 1 clearly points out that small sorbent particles achieve larger mercury capture at all residence times. Below a certain particle size, however, in this case about 20 VOL. 35, NO. 21, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Base Case Values and Range of Variation of the Operating Variables for Computations base case range

3

T, °C

dP, µm

cIN B , µg/m

tD, s

ΘAC, g/m3

150 120-200

20 5-100

500 100-1000

10 1-10

10 0.01-100

FIGURE 3. Gas mercury concentration profiles inside the sorbent particles at different particle sizes (left) and temperatures (right). Sorbent: DARCO G60; cBIN ) 500 µg/m3; ΘAC ) 10 g/m3; tD ) 1.0 s.

FIGURE 1. Gas bulk mercury concentration decrease (left) and average mercury uptake on the sorbent (right) as a function of particle residence time in the duct for different particle sizes. Sorbent: DARCO G60; T ) 150 °C; cBIN ) 500 µg/m3; ΘAC ) 10 g/m3.

FIGURE 4. Gas bulk mercury removal as a function of sorbent loading in the duct at different particle sizes. Sorbent: DARCO G60; T ) 150 °C; cBIN ) 500 µg/m3; tD ) 10 s.

FIGURE 2. Gas bulk mercury concentration decrease (left) and average mercury uptake on the sorbent (right) as a function of particle residence time in the duct for different operating temperatures. Sorbent: DARCO G60; dP ) 20 µm; cBIN ) 500 µg/m3; ΘAC ) 10 g/m3. µm, there is not much effect in lowering the particle size. The effect of the system temperature is more important: curves in Figure 2 show that a temperature decrease from 200 °C to 120 °C has a dramatic influence on the mercury capture, which increases from about 20% to about 90% after 10 s of residence time. In analyzing the uptake curves (on the right-hand side of the figures) it should be noted that results have been normalized with ωmax, whose value increases with decreasing the temperature. It is interesting to observe that the sorbent mercury uptake figures are some orders of magnitude lower than ωmax, thus confirming the assumption that the surface diffusion mechanism in the sorbent pores is always negligible. Figure 3 reports the gas mercury concentration profiles inside the sorbent particles after 1.0 s of residence time at different particle sizes and temperatures. The mercury concentration has been normalized with the bulk concentration at the same residence time. The curves show that for large particle sizes intraparticle diffusion resistance is mostly controlling the mercury uptake rate, while for small particle sizes the rate is under kinetic control. A decrease of the process temperature leads to an increase of the intraparticle 4370

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FIGURE 5. Gas bulk mercury removal as a function of sorbent loading in the duct at different temperatures. Sorbent: DARCO G60; dP ) 20 µm; cBIN ) 500 µg/m3; tD ) 10 s. diffusion resistance contribution due to the augmented adsorption kinetic rate. Boundary layer diffusion resistance is always limited as demonstrated by the mercury concentration values at the particle surface (r/RP ) 1) being close to the bulk ones. Figures 4 and 5 report the gas bulk mercury removal as a function of the sorbent loading in the duct at 10 s of residence time at different particle sizes (Figure 4) and temperatures (Figure 5). The curves show that in order to obtain mercury removal efficiencies of the order of 90-95%, large loadings of the order of 10-100 g/m3 have to be used with the sorbent at hand. The best operating conditions are achieved with small particles (dP < 20 µm) and low temperatures (120 °C).

FIGURE 6. Gas bulk mercury removal as a function of sorbent loading in the duct for different sorbents. T ) 150 °C; dP ) 20 µm; cBIN ) 500 µg/m3; tD ) 10 s. The influence of the mercury gas inlet concentration was investigated in the range of values reported in Table 2. No appreciable influence on the mercury removal results was observed at any operating condition. A close examination of eq 5 clarifies the reason for this behavior. At the short residence times considered, the desorption term (k2ω) in eq 5 is always negligible with respect to the other terms so that the equation becomes linear in the mercury concentration. As a consequence mercury removal (1 - cB/cBIN) results practically independent of the inlet gas mercury concentration. Figure 6 reports the gas bulk mercury removal as a function of the sorbent loading in the duct at 10 s of residence time for the different sorbents considered. In the figure the external diffusion limit curve, corresponding to the ideal case of infinitely fast adsorption kinetic rate, has been drawn for comparison. At any sorbent loading in the duct this curve represents the maximum theoretical mercury removal obtainable in these particular operating conditions. Comparison of the different curves shows that not much difference exists between the virgin activated carbon and the sulfur impregnated ones. It seems that sulfur impregnation, though increases the maximum mercury uptake capacity (Table 1), does not change appreciably the initial adsorption kinetic rate. Sorbalit performs slightly better than the other sorbents, while the fly ash considered has a very bad mercury capture behavior. Finding a more reactive sorbent should give the possibility to considerably economize in the sorbent feed rate. It should be kept in mind, however, that in order to achieve a determined mercury removal efficiency, it is not possible to go beyond the external diffusion limit curve. For example for the case reported in Figure 6 a 90% mercury reduction cannot be obtained anyhow with sorbent loadings lower than about 0.3 g/m3. It is important to note, moreover, that for more reactive sorbents it is crucial to employ the smaller particle size possible in order to reduce diffusional resistances. On the whole model results indicate that for the in-duct mercury capture in incinerator flue gas a large quantity of sorbent is needed to obtain a high mercury removal efficiency, as a consequence of the short contact times. Very low utilization of the sorbents is predicted. Minimization of the sorbent feeding rate is achievable by using a reactive sorbent, by lowering the operating temperature, by increasing the in-duct particle residence time, and by decreasing the sorbent particle size. Comparison with Available Full Scale Data. As reported previously, results in this paper will be relevant to incinerators where the PMCD is an electrostatic precipitator. Very scarce experimental activity has been reported in the literature on

mercury reduction in this kind of plants. The only comprehensive research project has been carried out by EPA on a municipal waste combustor in Camden County, NJ (28). Limited experimental results are also available for some tests conducted on a municipal waste combustor in Davis County, UT (33). The overall trends of the model computations compare favorably with experimental results reported forthe full scale facilities. In particular it was demonstrated that the lower the duct and the electrostatic precipitator temperatures the higher the mercury capture efficiency. Mercury gas concentration was not found to influence appreciably the capture efficiency. Unfortunately in the reports the sorbent particle size used and the in-duct residence time were not reported nor the influence of their variation investigated. The variable with the greatest influence on the mercury capture performance was found to be the carbon feed rate, that is the sorbent loading in the duct. Both the studies used a lignite-based activated carbon (DARCO FGD) for most experimental runs, whose kinetic and thermodynamic data for mercuric chloride adsorption are not available in the literature. Mercury capture efficiencies of the order of 8090% were obtained with carbon loadings of the order of 0.5 g/m3 in the duct, indicating that this activated carbon is more reactive than the sorbents considered for model calculations. The authors, however, report that experimental results are significantly influenced by the very large quantity of fly ash (with large unburned carbon content) present in the flue gas that provided above 50% mercury reduction even without any activated carbon injection (28).

Acknowledgments Funding by the Italian Agency for Environmental Protection (ANPA) and by the European Social Fund is gratefully acknowledged.

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(24) Karatza, D.; Lancia, A.; Musmarra, D.; Pepe, F.; Volpicelli, G. Hazard. Waste Hazard. Mater. 1996, 13, 95. (25) Krishnan, S. V.; Gullett, B. K.; Jozewicz, W. Environ. Prog. 1997, 16, 47. (26) Schager, P. The Behaviour of Mercury in Flue Gases; Ph.D. Dissertation, Chalmers University of Technology: Go¨teborg, Sweden, 1990. (27) Nebel, K. L.; White, D. M.; Parrish, C. R.; Zirkle, T. G.; Palazzolo, M. A.; Hartman, M. W. Emission Test Report: OMSS Field Test on Carbon Injection for Mercury Control; report EPA-600/SR92-192; 1993. (28) White, D. M.; Kelly, W. E.; Stucky, M. J.; Swift, J. L.; Palazzolo, M. A. Emission Test Report: Field Test of Carbon Injection for Mercury Control, Camden County Municipal Waste Combustor; report EPA-600/SR-93-181; 1994.

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(29) Scala, F. Environ. Sci. Technol. 2001, 35, 4373-4378. (30) Ruthven, D. M. Principles of Adsorption & Adsorption Processes; Wiley: New York, 1984. (31) Villadsen, J.; Michelsen, M. L. Solution of Differential Equation Models by Polynomial Approximation; Prentice Hall: Englewood Cliffs, NJ, 1978. (32) Lancia, A.; Karatza, D.; Musmarra, D.; Pepe, F. J. Chem. Eng. Jpn. 1996, 29, 939. (33) Chandler, A. J.; Rigo, H. G. Proc. 89th Annual Meet. Air Waste Manage. Assoc.; Nashville, TN, paper RP122.01; 1996.

Received for review March 2, 2001. Revised manuscript received August 6, 2001. Accepted August 27, 2001. ES010065H