kinetics of heavy metal vaporization from coal in a fluidized bed by an inverse model

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERINGAsia-Pac. J. Chem. Eng. 2010; 5: 266–273Published online 25 May 2009 in Wiley InterScience(www.interscience.wiley.com) DOI:10.1002/apj.278

Special Theme Research Article

Kinetics of heavy metal vaporization from coal in afluidized bed by an inverse model

Jing Liu,1* Xuefeng Liu,1 D. Gauthier,2 S. Abanades,2 G. Flamant,2 Jianrong Qiu1 and Chuguang Zheng1

1State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, China2Processes, Materials, and Solar Energy Laboratory (CNRS-PROMES), Font-Romeu, France

Received 18 August 2008; Revised 14 January 2009; Accepted 15 January 2009

ABSTRACT: This study addresses the kinetics of heavy metal vaporization during fluidized bed thermal treatment ofcoal. Both direct and inverse models were developed in transient conditions. The direct model predicts the time courseof the metal concentration in the gas from the vaporization rate profile. The inverse model was developed and validatedto predict the metal’s vaporization rate from its concentration in the outlet gas. A method to derive the kinetic law ofheavy metal vaporization during fluidized bed thermal treatment of coal from the global model and the experimentalmeasurements is derived and illustrated. A first-order law was fitted for the mineral matrix and a second-order lawwas fitted for coal. This method can be applied to any matrix, whether it is mineral matrix or organic matrix. 2009Curtin University of Technology and John Wiley & Sons, Ltd.

KEYWORDS: coal; heavy metal; vaporization; kinetics; fluidized bed

INTRODUCTION

The accumulation of toxic heavy metals (HMs) gen-erated by coal combustion presents a serious threatto the environment. Extensive studies were devel-oped with respect to their abundance, physico-chemicalform, toxicity, and partitioning behavior in the com-bustion/environmental control systems.[1–5] Some of theheavy metals will be volatilized during coal combustionand the extent to which metals are volatilized variesgreatly. The degree of metal volatilization involvesmany factors, including the initial speciation and con-centration of metal, the type of coal, the treatment tem-perature and duration, the gas composition and flowrate, and the presence of other chemicals such as chlo-rine, sulfur, or alumino-silicate compounds. Theoreti-cally, the process is governed by the laws of thermo-dynamics, reaction kinetics, and mass and heat transferoperations.[6] It is essential to understand the vaporiza-tion behavior of HMs during coal combustion in orderto better understand their behavior and better controltheir emissions.

The vaporization of HMs has been studied mainlyby direct analysis of the different residues producedby combustion.[7–9] Mechanism studies[10,11] showed

*Correspondence to: Jing Liu, State Key Laboratory of Coal Com-bustion, Huazhong University of Science and Technology, Wuhan430074, China. E-mail: [email protected]

that HM behavior in fluidized bed combustion can-not be based only on the mass balance measurements.The thermodynamic calculations were applied to predictthe partitioning of a metal during thermal treatment.[12]

However, there is experimental evidence that equi-librium calculations overpredict the amount of metalvaporized.[13] The main reason is that mass transfer lim-itations are not taken into account in such models andthat the required assumptions (particularly the closed-system approach) are not accurate for coal combustionprocesses.

Many fluidized bed models were developed,[14–17]

which range from the ones with pseudo-homogeneousphases to complex ones with three phases or assembliesof bubbles. Helble[18] developed a semiempirical modelof HM emission, in which fundamental laboratoryresults and also field emission data were included. Hoet al .[6] have identified kinetic laws to describe metalbehavior during fluidized bed thermal treatment of soil.This model is based on the heat and mass transferlaws and on experimental results to simulate the metalvaporization process. Experiments were used to identifykinetics in the model.

In summary, there are a large number of experimen-tal data from on-site boilers and laboratory facilities.Researchers have provided qualitative mechanisms forelemental vaporization such as volatility and associ-ations of elements. However, to our knowledge, thekinetic law on the vaporization of metals from coal

2009 Curtin University of Technology and John Wiley & Sons, Ltd.

Asia-Pacific Journal of Chemical Engineering KINETICS OF HEAVY METAL VAPORIZATION FROM COAL IN A FLUIDIZED BED 267

in a fluidized bed is lacking. On the basis of well-controlled experimental studies for coal, this articleidentifies the kinetic law of a metal vaporization fromcoal combustion. Experiments were carried out in awell-instrumented, bubbling, fluidized bed reactor formeasuring the metal concentration in the exhaust gas.The method developed to identify the kinetic law formetal release from coal is presented. The direct math-ematical model predicts the time course of the metalconcentration in the gas from the vaporization rate pro-file, but which are not practicable because this vapor-ization rate cannot be measured in reactor burning coal.The inverse model intends to predict the metal’s rateof vaporization from its concentration in the outlet gas.Two cases are detailed: metals in a mineral matrix andmetals in an organic/mineral matrix (coal).

EXPERIMENTAL PROCEDURES

A schematic diagram of the experimental setup[19] isshown in Fig. 1. The reactor is a 0.105-m ID and a0.40-m high cylinder, topped by a 0.2-m disengagingheight. The reactor was electrically heated, and Kthermocouples measured the temperature at severaldepths in the bed, as well as at the inlet and outlet.Every measurement was recorded on a PC. Oncethe reactor was in steady state, a given mass ofparticles spiked with a metal was injected into the

bed. Temperature measurements proved that, becauseonly a small quantity of such reacting particles wasinjected in the bed at high temperature (850 ◦C), thetemperature does not change very much: actually, therewas a decrease of about 10 ◦C with mineral particles,but an increase of 10 ◦C to 20 ◦C with coal due toexothermic combustion. The measurements also showedthat the reactive sample penetrated deep into the bed,since the temperature change was the same whateverthe height is. The synthetic gas composition in theexperiments (by volume) is 4.8% O2, 70.8% N2, 8.8%CO2, 400 mg · Nm−3 SO2, and 15.6% H2O.

During experiments, solid samples can be taken fromthe bed at given times and collected in a vessel foranalysis by means of a tube plunged in the fluidizedbed and an aspiration pump. This method, which canbe implemented only in the case of mineral matrices,provides the temporal profile of a metal’s concentrationin the mineral matrices (q(t)). The metal concentrationin exhaust gases is measured on-line by inductivelycoupled plasma optical emission spectrometry (ICP-OES). For that purpose, the gas outlet is connected tothe nearby ICP and is carried back to the ICP througha heated line (maximum temperature 450 ◦C).

Both mineral and organic matrices (coal) were metal-spiked by impregnating them with a metal compound:a weighted batch of substrate was mixed for 5 h withthe appropriate volume of metallic species solution.Samples were then dried at 80 ◦C for at least 24 h.

Sheath argon

Mass-flowcontrollers

Air

N2

CO2

Primary

Pump

Air or synthetic gas

(Air + N2 + CO2)

Flue gas

Filter

ICP

Peristaltic pump(secondary sampling)

Gas sample

Calibration

Condenser(pump protection)

Fluidized bedreactor

T ≈ 250°C

Gas preheater

≈ 650°C

850°C

+

+

Coal injection

Solid samplesextractionsystem

Plasma gas

Figure 1. Experimental setup. This figure is available in colour online at www.apjChemEng.com.

2009 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2010; 5: 266–273DOI: 10.1002/apj

268 J. LIU ET AL. Asia-Pacific Journal of Chemical Engineering

The metal content was measured by ICP-OES aftermicrowave-assisted acid digestion.

MODELING METHODOLOGY

Direct model

The classical Kunii and Levenspiel’s model[20] was builtup for beds of Geldart group A particles in whichclouds are very thin. The modified version of Kunii andLevenspiel’s model[16] was adapted, which is especiallyfitted to treat beds of Geldart group B particles inwhich clouds are very thick, to the problem of HMvaporization (by taking into account the phenomena ofHM adsorption and condensation of metal on particles).

The main assumptions of the model are:

(1) the bed is composed of two phases, the bubbles con-taining a small amount of solid (subscript B in theequations) and the emulsion phase, correspondingto the rest of the bed (subscript E);

(2) bubbles have a uniform diameter;(3) gas flow in the emulsion phase is at minimum

fluidization, gas is in plug flow everywhere;(4) there exists a mass transfer between both phases,

and the global mass transfer coefficient is estimatedfrom the relation[16]:

KBE = 4.5Umf

DB(1)

The bed is assumed to be isothermal, so the inter-nal phenomenon within a solid particle (heat and masstransfer, chemical reactions) would have no effect onthe results. This macroscopic approach uses only theglobal flux of generation of species at the external sur-face of the particles. Therefore, it may be extended toother combustion systems, in which solid–gas masstransfer occurs. Temperature measurements at differ-ent depths in the bed showed that this assumption wastrue for alumina (the bed’s temperature decreased about10 ◦C when at 850 ◦C) and of particles of coal (bed’stemperature increased 10–20 ◦C). The variations of thevolumetric flow rate due to chemical and physical con-versions were neglected. First, the metal’s vaporizationflux was weak compared to the gas flow of fluidization.Secondly, for organic matrices, the gas flow resultingfrom combustion did not significantly affect the globalflow rate of gas, since the mass of sample injected intothe bed represented less than 1% of the total mass ofthe bed. Finally, the gas velocity (U ) was consideredconstant in the bed.

The model predicts the HM concentration in thebubble and the emulsion phases as a function of bedheight. For species i and an elemental step [h , h + dh],the mass balances in each phase are the following:

Bubble phase:

−FB

(U ∗

B∂CBi

∂h+ ∂CBi

∂t

)= −FBγBq rBi ρp

+ FBKBE(CBi − CEi ) + FBγB(ρp θ vspiked

+ ρsand(1 − θ)vsand) (2)

Emulsion phase:

−(1 − FB)

(Umf

∂CEi

∂h+ ∂CEi

∂t

)

= −(1 − FB)(1 − εmf)θrEiρp − FBKBE(CBi

− CEi ) + (1 − FB)(1 − εmf)

(ρpθvspiked + ρsand(1 − θ)vsand) (3)

where γB represents the volume fraction of solid par-ticles dispersed in the bubbles. Its empirical value is0.005[16]; θ is the volume fraction of reacting solid(particles spiked with heavy metal) in the bed (ratioof reacting solidto the total volume of solid); rEi andrBi correspond to the vaporization rates of i speciesin each phase (mg · s−1 · kg−1); they are considered thesame and equal to r in the following (rEi = rBi = r).vspiked and vsand are the adsorption rates on reacting par-ticles and sand, respectively (mg · s−1 · kg−1). Actually,these terms of adsorption are negligible, since adsorp-tion on sand is always very small[21,22] and the mass ofsand is much larger than the mass of reacting sample.

UB∗ is given by Davidson and Harrison[14]:

U ∗B = UB + 3Umf (4)

UB = U − Umf + 0.711√

gDB (5)

Where Umf is the minimum fluidization velocity atbed temperature, UB is the bubble’s rise velocity, andU is the superficial gas velocity.

Mori and Wen’s correlation[23] calculates the bubblediameter along the bed:

DB = DBm − (DBm − DB0) exp

(−0.3h

DC

)(6)

Where DBm represents the maximum diameter ofbubble once completely coalesced:

DBm = 0.652[AC(U − Umf)]2/5 (7)

DB0 corresponds to the initial diameter of bubble.Cooke et al .[24] proposed the following relationship todetermine DB0 at the surface of a perforated plate havingn0 holes per surface unit of distributor:

DB0 =[

6

π

U − Umf

n0

]0.4

g−0.2 (8)



In this model, although the bubble’s diameter in-creases with the bed’s height, a mean diameter isconsidered, and it is calculated by:

DB = 1

H

∫ H

0DBdh (9)

In Eqns (2) and (3), FB is the volume fraction of bedconsisting of bubbles, it is obtained from Davidson andHarrison’s equation[14]:

FB = H − Hmf

H= U − Umf

UB(10)

The void fraction of bed under static conditions iscalculated from the initial height of bed H0, the samplemass Mp, and the sand mass Msand:

ε0 = 1 −(

Mp

ρp+ Msand

ρsand

)1

ACH0(11)

where Ac is the cross-sectional area of the bed. Theheight of bed at minimum fluidization (Hmf) is deter-mined from the initial height of bed (H0), the voidfraction of bed at static condition (ε0), and the voidfraction of bed at minimum fluidization (εmf):

Hmf

H0= (1 − ε0)

(1 − εmf)(12)

The boundary conditions are that at the surface ofdistributor:

h = 0 : CBi = CEi = 0 (13)

The concentration of species i at the bed’s surface(h = H ), i.e. in the outlet gas (assuming that the speciesdoes not condense on the reactor’s walls), is

Coi = [FB.CBi + (1 − FB).CEi ]h=H (14)

The expanded height of bed (at normal fluidization)H is determined by an iterative procedure. After His initialized, the mean diameter of a bubble, DB (seeEqn (9)) and its rising velocity, UB (see Eqn (5)) wascalculated. Then, Eqn (10) was used to calculate Hagain, and so forth until convergence.

Inverse model

When coal or organic matrices are burning, the con-centrations of each metal in the outlet gas are the onlyexperimental measurements available, since the burningsolids cannot be sampled. The kinetics of vaporizationof a metal from coal (at the particle level) can thenbe obtained by applying the inverse model developedbelow. The purpose of the inverse model is to predict

the metal’s vaporization rate, knowing its concentrationin the outlet gas. Thus, the vaporization rate may bedetermined whatever the matrix is, even if it is burning.

On-line analysis gives the emission intensity profile,which can be normalized (I /Imax). It is the same as thatof concentration (Co

∗ = Co/Co max) since intensity andconcentration are proportional. Thus, Eqns (2) and (3)were written under dimensionless forms by dividing byCo max/FB, and were expressed with Eqns (16) and (17).The dimensionless vaporization flux f (s−1) is relatedto the vaporization mass flow rate r (mg · kg−1 · s−1):

f = γBθ rρp

Co max/FB(15)

The model’s equations can be written as:

∂C ∗Bi

∂h+ 1

U ∗B

∂C ∗Bi

∂t= f

U ∗B

− KBE

U ∗B

(C ∗Bi − C ∗

Ei ) (16)

∂C ∗Ei

∂h+ 1

Umf

∂C ∗Ei

∂t= (1 − εmf)

f

γBUmf

+ FB

1 − FB

KBE

Umf(C ∗

Bi − C ∗Ei ) (17)

C ∗oi =

[C ∗

Bi + (1 − FB)

FB.C ∗

Ei

]h=H

(18)

where the dimensionless concentrations CE∗ and CB

∗are defined as:

C ∗E = CE

Co max/FBand C ∗

B = CB

Co max/FB(19)

KINETIC LAW OF HM VAPORIZATION: CASEOF ALUMINA

Direct model simulation

In the case of mineral matrix, the metal’s concentra-tion in the solid particle can be determined experimen-tally by analyzing solid samples withdrawn from thefluidized bed. The profile of experimental data of Cdconcentration from intermittently sampled solid parti-cles can be fitted to get the equation of Cd concen-tration in the solid particles (q(t)). Then the equationof (q(t)) was differentiated to get the vaporization rate(r = dq(t)/dt). The vaporization rate was used as inletparameter in the direct model to calculate the Cd con-centration in the outlet gas (Co), as shown in Fig. 2.

The values of various parameters used in the simula-tion are listed in Table 1. In the first few seconds, Cdconcentration in the outlet gas increased sharply, whentime was about 3 seconds, Co has a maximum, and thenit decreased with time.



0 5 10 15 20 25 30 35 40 45 50 55 60 650

50

100

150

200

Cd

conc

entr

atio

n in

the

outle

t gas

,C

o (m

g·N

m-3

)

Time (min)

T = 0.057 min (3 sec),

Co,max = 200.76mg·Nm-3

Figure 2. Results of direct model. Time course of the Cdconcentration in outlet gas from alumina.

Table 1. Values of the model’s parameters of thefluidized bed.

Parameters Value

Superficial gas velocity, U (m · s−1) 0.51Void fraction at minimum fluidization, εmf 0.5Void fraction at normal fluidization condition, ε 0.74Initial diameter of bubble, DB0 (mm) 8.87Mean diameter of bubble, DB (mm) 27.4Bubble’s rise velocity, UB (m · s−1) 0.71Initial height of bed, H0 (m) 0.15Expanded height of bed, H (m) 0.31Volume fraction of bubbles, FB 0.48Global exchange coefficient, KBE (s−1) 27.92

Inverse model simulation

Using the gaseous concentration profile at the outlet gas(Co) as inlet parameter, the Cd vaporization flux (fromporous alumina particles) from the fluidized bed wasdetermined by applying the inverse model (see Fig. 3).

The vaporization rate is relatively fast at the initialstage of the treatment but slows down and eventuallylevels off later. The decrease in the rate of metal vapor-ization is apparently caused by the formation of lessvolatile metal compounds (CdO · Al2O3) according toAl2O3 + CdCl2 + H2O → CdO · Al2O3 + 2HCl.[21,22]

From Eqn (15), since the parameters γB, θ , ρp, Co max,and FB were known for alumina matrix, Cd vaporizationrate (r) can be calculated. Then, Cd concentration in thesolid particles (qi ) for each time ti can be obtained fromthe relation qi − qi−1 = r · �t and then compared withthe experimental data. Figure 4 plots the comparisonbetween this calculated Cd concentration in the solidparticles and the experimental values obtained from theanalysis of solid samples. The theoretical profile of Cdconcentration in the solid particles is clearly consistent

0 5 10 15 20 25 30 35 40 45 50 55 60 650.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

Cd

vapo

riza

tion

flux

f (

S-1)

Time (min)

T = 0.052 min (3 sec),

fmax = 0.0175s-1

Figure 3. Results of inverse model. Time course of Cdvaporization flux (f ).

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75300

400

500

600

700

800

900

Cd

conc

entr

atio

n in

the

part

icle

s,q

(mg·

Kg-1

)

Time (min)

Experimental Cd concentration fromsolid sample analysis

Cd concentration from modeling

Figure 4. Comparison between Cd concentration in thesolid particles (q) obtained from modeling and experiment.

with the experimental results. This very good fit provesthat results from on-line gas analysis can be used toestimate the rate of vaporization of metals by applyingthe inverse model.

Kinetic law of Cd vaporization from alumina

The vaporization rate (r = dq/dt) and the profile ofmetal’s concentration in solid particles (q) for each timeare known. Hence the kinetic law can be deduced fromthe relation between the vaporization rate (r = dq/dt)and the profile of metal’s concentration in solid particles(q), as shown in Fig. 5.

The corresponding Cd concentration decrease in thesolid particles in the second part is very small (about3 mg · kg−1) comparing to the first part (about 500 mg ·kg−1), and the time is very short (smaller than 3 s), sothe second part can be neglected.



350 400 450 500 550 600 650 700 750 800 850 9000.0

0.2

0.4

0.6

0.8

1.0

1.2C

d va

pori

zatio

n ra

te, r

(m

g·kg

-1·s

-1)

Cd concentration in the particles, q (mg·Kg-1)

Figure 5. Cd vaporization rate (r) vs. Cd concentration inthe solid particles (q).

The kinetic law is:

dq

dt= 0.00241q − 0.91316, (t ≥ 3 s),

it is a first-order law (20)

or assuming:dq

dt= k(q − αq0)

n, (21)

where q0 is initial Cd concentration in solid parti-cles, q0 = 856 mg · kg−1, k = 0.00241, α = 0.442646,n = 1.

KINETIC LAW OF HM VAPORIZATION:CASE OF COAL

Experimental results

The net intensity of emission (i.e. after withdrawingthe background intensity), more precisely the normal-ized intensity (I /Imax) of spectral lines of metal, wasmeasured vs time. Whatever the matrix is, the metal’sconcentration in the gas exhibited a peak almost instan-taneously after the reacting sample was injected into thefluidized bed. For coal that containing organic species,the profiles of vaporization of metals in the exhaustgas are the only data available, since the burning solidscannot be sampled. Normalized profiles of the concen-tration of the three metals are shown in Fig. 6.

Inverse model simulation

The on-line gaseous intensity of Cd, Pb, and Zn wasfitted and for each metal, the vaporization dynamicswas obtained by applying the inverse model to the

0 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e co

ncen

trat

ion

Co*

(=

I/I m

ax)

Duration of treatment (min)

Cd

Pb

Zn

2

Figure 6. On-line gaseous intensity of Cd, Pb, and Zn duringcoal combustion vs duration of treatment.

00.000

0.005

0.010

0.015

0.020

Vap

oraz

ition

g fl

ux f

(s-1

)

Time (min)

CdPbZn

2 4 6 8 10 12 14 16

Figure 7. Results of inverse model. Time course of thevaporization flux of metal (f ) from coal.

experimental measurements (Fig. 7). With synthetic gascontaining HCl, the vaporization tendencies of Cd andPb are similar and the release process is short. Znvaporizes somewhat slower than Cd and Pb. This trendindicates that Zn is difficult to be vaporized due to theformation of thermally stable forms with mineral matterin raw coal.

Kinetic law of Cd vaporization from coal

Comparing to mineral matrix, it is more difficult toobtain the kinetic law of HM vaporization in organicmatrix (coal) because the profile of metal’s concen-tration in solid particles (q) for each time cannot bemeasured by experiment. The HM relative concentra-tion in outlet gas (Co) is the only measured data. Co maxis not known, so the vaporization rate (r) cannot be



obtained from Eqn (15) directly. Another method to getr has been developed.

According to Equation (15), f = γBθ rρpCo max/FB

,

assuming: r = a · f (22)

a = C0 max

FB · γB · θ · ρP(23)

γB, θ , ρp, and FB are known. Therefore, for differ-ent values of a , q (t) profiles can be deduced from therelation qi − qi−1 = r · �t , as shown in Fig. 8. Vapor-ization percentage is shown in Table 2 for differentvalue of a.

If the vaporization percentage is known, the valueof “a’ can be deduced, and then the kinetic law canbe identified. When coal sample is burned at 850 ◦C,the final Cd concentration (qfinal) is 516 mg · kg−1, thevaporization percentage is 65.6%. The value of “a”is thus 380. Then, from Eqn (15), Co max is equal to116.42 mg · Nm−3.

Figure 9 shows the relationship between the vapor-ization rate (r = dq/dt) and the profile of metal’s con-centration in solid particles (q). Finally, the kinetic lawcan be obtained only from the experimental data of HMrelative intensity by the inverse model, as soon as q0,and qfinal in solid samples are known. This method canbe applied to any matrix, whether it is mineral matrixor organic matrix. From Fig.ure 9, the kinetic law can

0 4 8 10 12 14 16300400500600700800900

1000110012001300140015001600

Cd

conc

entr

atio

n in

coa

l, q

(mg·

kg-1

)

Time (min)

a220

a260

a300

a340

a380

a420

2 6

Figure 8. Cd concentration (q0 = 1500 mg · kg−1) in coalvs time.

Table 2. Vaporization percentage for different valuesof ‘‘a’’.

a 220 260 300 340 380 420

Vaporizationpercentage (%)

38.0 44.9 51.8 58.7 65.6 72.5

400 600 800 1000 1200 1400 16000

2

4

6

8

Cd

vapo

riza

tion

rate

, r (

mg·

kg-1

·s-1

)

Cd concentration in coal, q (mg·kg-1)

Cd vaporization rate, r

polynomial fit (order = 2)

polynomial fit (order = 3)

Figure 9. Comparison of polynomial fit of Cd vaporizationrate (r) vs Cd concentration.

be assessed:

dq

dt≈ −23.44523 + 0.06051 · q − 2.96182

· 10−5 · q2 (24)

or assume :dq

dt≈ k(q − αq0)

n + β (25)

where q0 is initial Cd concentration in solid parti-cles, q0 = 1500 mg · kg−1, k = −2.96182 × 10−5, n =2, α = 0.681, β = 7.46.

Or more accurately,

dq

dt= −1.85309 − 0.01768 · q + 5.62921 · 10−5

· q2 − 2.90413 · 10−8 · q3 (26)

CONCLUSION

A study was carried out to investigate the kinetic lawof toxic metal release from coal during their thermaltreatment. Both direct and inverse models were devel-oped to predict HM vaporization in transient conditions.This procedure was first validated with mineral matricesspiked with metal. It was then implemented with coal.Then kinetic laws were determined from the relationof vaporization rate (r = dq/dt) and HM concentra-tion in solid particles (q). A first-order law was fittedfor the mineral matrix and a second-order law (simpli-fied) was fitted for coal. The kinetic law obtained inthis way could be integrated in a global model of coalcombustion in order to simulate the effects of operat-ing parameters on the metal’s behavior. This inversemethod can be applied to any matrix, whatever mineralmatrix or organic matrix.



Acknowledgements

This work was supported by National Natural ScienceFoundation of China (50606013, 20877030) and by 973Program of China (2006CB705806, 2006CB200304).Portions of this work were conducted under Sino-FrenchAdvanced Research Program (E06-03).

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kinetics of heavy metal vaporization from coal in a fluidized bed by an inverse model

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