A Simplified Model Accounting for the Combustion of Pulverized Coal

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A simplified model accounting for the combustion of pulverized coal char particles in a drop tube furnace Patrick Gilot, Alain Brillard, Jean-François Brilhac, and Cornelius Schönnenbeck Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01756 • Publication Date (Web): 29 Aug 2017 Downloaded from http://pubs.acs.org on August 30, 2017

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A simpli…ed model accounting for the combustion of pulverized coal char particles in a drop tube furnace

a

Patrick Gilota , Alain Brillarda , Jean-François Brilhaca and Cornelius Schönnenbecka Laboratoire Gestion des Risques et Environnement EA2334, Université de Haute-Alsace, Institut J.-B. Donnet, 3bis rue Alfred Werner, F-68093 Mulhouse Cedex France Abstract A simple model is proposed which predicts the evolution versus time of the temperature and of the carbonaceous material conversion of a coal char particle during its combustion in a drop tube furnace under a very high heating rate of 1500 K/s. The values of the intrinsic reactivity parameters are obtained performing thermogravimetric analyses of the coal char particles in a thermobalance under a low heating rate of 10 K/min. In this simple model, the local evolutions of the particle porosity and density are not accounted for as only their mean values are considered at any time of the combustion process. The oxygen concentration gradient within the particle is accounted for, once a particle e¤ectiveness factor related to the Thiele modulus is estimated. Comparisons between the experimental and simulated temperatures of the particle are performed for three regulation temperatures of the drop tube furnace and the combustion regimes are analyzed in terms of the e¤ectiveness factor of the particle. Keywords. Coal char combustion, Drop tube furnace, Modelling, Intrinsic reactivity, Thermogravimetric analysis

1

Introduction

Coal combustion is largely a¤ected by the burning rate of the carbonaceous residue (char) obtained after the fast pyrolysis step. Modelling the coal combustion in pulverized coal-…red boilers and furnaces requires the determination of both the kinetic and oxygen transport parameters. The determination of the kinetic parameters is a complicated challenge for the following reasons: 1. Char has a complex porous structure which depends on its formation conditions and continuously changes during the combustion process.

1

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2. Coal particle combustion involves a strong coupling between oxygen transport within and outside the particle and combustion of the carbonaceous material, which is highly a¤ected by combustion conditions such as heating rate and oxidizing environment. 3. The kinetic parameters, advantageously determined under kinetically controlled combustion, must be accurate enough to be used for the simulation of a combustion process, especially when combustion is controlled by kinetics. In a thermobalance, the sample temperature is well controlled and the mass loss is measured with high accuracy during the whole combustion process, as described in.1 Further, the active surface area is rate controlling, see2 and combustion occurs in the zone I burning regime. The char particle burns in a uniform way and the evolution of the porous structure during the combustion process may be represented by the random pore model proposed by Bhatia and Perlmutter in.3 On the contrary, in industrial furnaces where high heating rates (up to 105 K/min) and temperatures (up to 2000 K) are at work, strong di¤usional limitations appear. Both internal and external di¤usional limitations must thus be taken into account in a model devoted to the description of the combustion of char particles in industrial furnaces. Further, a complex situation occurs during an intermediate burning regime, where combustion is non-uniform within the particle with local evolutions of the surface area, apparent density, pore diameter, pore volume. . . Thiele modulus and an e¤ectiveness factor are currently used in the available models in order to simulate the combustion process which occurs in zone II, see,4 for example. In the present study, coal char particles have been produced from a South African bituminous coal through a pyrolysis process in a drop tube furnace. Then the combustion under an oxidative atmosphere of the collected coal char particles has been performed in the drop tube furnace, which simulates the conditions occurring in industrial furnaces. The particle temperature has continuously been measured by a two colors pyrometer located at the bottom of the drop tube furnace, see Figure 1 b). The values of the kinetic parameters associated to the coal char combustion have been determined through a thermogravimetric analysis performed under a low heating rate of 10 K/min and under an oxidative atmosphere. The main purpose of the present work is to propose a simple model which intends to simulate both the temperature and the carbonaceous material conversion of the coal char particle during the combustion process in a drop tube furnace. This simple model mainly consists of only two basic equations: an energy and an oxygen transport balances, which are written assuming uniform properties of structural parameters and temperature inside the particle. In this model, pore growth and coalescence are accounted for in order to derive a relation between the surface area and the carbonaceous material conversion, that we will simply call conversion throughout this work, when no confusion may occur. The porous structure of the particle is here characterized by a structural parameter. An evaluation of the Thiele modulus is performed.

2


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The oxygen concentration gradient within the particle is accounted for, once a particle e¤ectiveness factor related to the Thiele modulus is estimated. But the local evolutions of the particle porosity and density are not accounted for in this model, as only their mean values are considered at any time of the combustion process. The combustion of coal particles and of coal char particles in furnaces or boilers has already been analyzed and modelled by many authors and for a long time. In,5 the author combines a Thiele analysis and a random pore model in order to describe the combustion of coke particles in an atmospheric ‡uidized bed combustor. A sophisticated model has been proposed by Mitchell in,6 in order to simulate the physical changes of char particles occurring during a combustion process. Local values of the parameters have here been considered, which allow to locally use the random pore model for the description of the local evolution of the surface area. A model accounting for coal combustion has been studied in,7 where the motion of representative coal particles is analyzed together with the evolution of the temperature. The oxy-fuel combustion of coarse size coal char in a ‡uidized bed has been modelled in,8 through a generalized fully transient, one-dimensional and non-isothermal oxy-fuel combustion model, using a volume reaction model. The devolatilization process of a single coal particle and the combustion of the residual char have been modelled in.9 In these two last works, the authors introduced two sets of governing equations for the solid particle phase (component mass balance of gas species, total molar balance of gas mixture and energy balance) and for the gas boundary layer (component mass balance, total molar balance and energy balance). On the basis of 5 gas species and 3 main chemical reactions, this leads to a system of 8+7 equations which describe the coupled evolutions of the temperatures (gas and particle), of the mass fractions, of the total molar ‡ux of gas mixture, of the instantaneous mass concentration of carbon in solid char and of the total concentration of gaseous mixture. For the resolution of this large system of evolution equations, the authors used the COMSOL Multiphysics software. In,10 the authors proposed a fully transient and coupled kinetic, heat-transfer model accounting for the pyrolysis of large coal particles. The combustion of a gasi…ed semi-char in a drop tube furnace has been analyzed in,11 using a pore development process and an e¤ectiveness factor. A random pore model with intraparticle di¤usion has been introduced in12 for the description of char particles combustion. Di¤erent operating conditions of coal combustion occurring in a large-scale furnace have been simulated in13 through a CFD model. A coal combustion model has been presented in14 which is based on a kinetic model where the chemical reaction rate is considered as a function of coal intrinsic reactivity and fuel mass for a global reaction of order n. An oxy-fuel combustion has been simulated in15 through a CFD model. The model which is described in the present study is much simpler than many of the models presented in the above indicated papers. It only requires the resolution of a system of two coupled balance equations accounting for the heat transfer eq (3) and the oxygen transport eq (4). In order to validate this simple model, comparisons between the simulated and observed temperatures of 3


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a particle introduced in the drop tube furnace are proposed at three regulation temperatures of the drop tube furnace (1100, 1200 and 1300 C). The resolution of these equations is not time-consuming and does not require a dedicated software. The simulated and experimental particle temperatures do not quite well superimpose, although the di¤erences between the simulated and experimental temperatures lie in the admitted uncertainties and which are con…rmed in the present context through repeatability combustion experiments. It should indeed be noticed that pyrometry measurements of the particle temperature in a drop tube furnace often lacks of precision, mainly because of the radiations emitted by the reactor walls, see16 who gives 50 C as the uncertainty for particle temperatures measured in drop tube furnaces during coal pyrolysis and the results concerning the combustion of anthracite char coals in an isothermal plug ‡ow reactor under di¤erent oxygen concentrations in.17 Nevertheless, the trends of the particle temperature curves are well predicted using this simple model when physical parameters such as the particle radius, oxygen concentration. . . are modi…ed. The simple model which is proposed may thus be considered for a quick and rough description of the particle behavior during the combustion process in a drop tube furnace.

2

Material

A South African bituminous coal has been used for the pyrolysis experiments in a drop tube furnace. The proximate and ultimate analyses of this coal and of the coal char which is produced from this coal through a pyrolysis process in the drop tube furnace are indicated in Table 1, the measures being performed on the basis of the associated ISO standards. Table 1 Proximate and ultimate analyses of the coal considered in the present study (O is computed by di¤erence) and of the coal char produced from the coal by pyrolysis.

Coal Proximate analysis (wt%, ar) Volatile matter 24.0 Ash 13.8 Fixed Carbon 54.7 Moisture 7.5

Ultimate analysis (%, daf) C 67.64 H 3.77 N 1.81 S 0.76 O 26.02

Coal char Proximate analysis (wt%, ar) Volatile matter 0.7 Ash 20.0 Fixed Carbon 78.5 Moisture 0.8

Ultimate analysis (%, daf) C 76.63 H 0.89 N 1.26 S 0.53 O 20.69 ar: as received, daf: dry and ash-free basis. 4


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The High Heating Value of the coal used in the present study was measured at 27.3 MJ/kg, on dry basis. The density of the coal char material was measured as: ( bulk )rm = 296:6 kg/m3 .

3 3.1

Experiments and methods Coal pyrolysis and char combustion at high heating rates in a drop tube furnace

The vertical furnace which was used for the coal pyrolysis and then for the coal char combustion is heated by six lanthane chromite bars, allowing a power of 12 kW, see Figure 1.

Figure 1. A schematic representation of the drop tube furnace used for the present study for the coal char production a) and for the char combustion b). The maximal furnace temperature which can be obtained is 1600 C and it can be regulated adjusting electrical resistances, through a thermocouple located between the external wall of the reactor and the internal wall of the furnace. The reactor (60% alumina and 40% silica) has an internal diameter of 5 cm and a length of 140 cm. Before their introduction in the reactor, the coal particles were …rst crushed and sieved to the 36-72 m size fraction, with a mean diameter of 50 m. This granulometry perfectly corresponds to that of pulverized coal particles usually used in industrial boilers. The coal particles were fed into the drop tube furnace through an injection probe at a rate equal to 17 10 3 kg/hr, Figure 1 a). When entering in the injection probe, the coal particles were obeying a transient velocity regime during a very short time length, after which they were carried through the reacting zone of the drop tube furnace at the gas velocity. This gas velocity is computed in terms of the ‡ow and of the temperature. The

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falling time is then computed. The reaction time for devolatilization of coal particles was about 1 s for a gas temperature of 1573 K, corresponding to a 1 m drop and a gas ‡ow of 400 l/hr. The devolatilization yield was determined at 39% (daf), using the ash tracer method. The uncertainties related to the devolatilization yields ranged from 0.045 to 0.110, according to the determined devolatilization yields corresponding to di¤erent drop heights in the drop tube furnace. These estimates have been obtained taking the uncertainties related to the ash contents measured in the raw material and in the char residue, as well as the water content in the raw material. The relative uncertainties associated to the value obtained for the devolatilization yield of the char prepared for combustion experiments (with 1 m drop) were taken equal to 7.4%, leading to a devolatilization yield equal to 0:39 0:03 (daf). The coal char particles were collected at the bottom of the drop tube furnace in the con…guration indicated in Figure 1 a). Without any injection of char particles in the drop tube furnace in the con…guration of Figure 1 b), the temperature of the regulation thermocouple was set at three given values: 1000, 1200 and 1300 C, in order to investigate the gas temperature along the reactor vertical axis. Char particles were injected in the drop tube furnace in the con…guration indicated in Figure 1 b) for combustion under an oxidative atmosphere (88% nitrogen, 12% oxygen). They were injected with a primary gas ‡ow (40 l/hr) through a water cooled injector and entrained by a preheated secondary nitrogen ‡ow (360 l/hr) preheated at 900 C. During each injection sequence, an amount of 2 mg of char particles was introduced in the reactor. As for the coal particles, when entering in the injection probe, the coal char particles were obeying a transient velocity regime during a very short time length, after which they were carried through the reacting zone of the drop tube furnace at the gas velocity. This gas velocity is computed in terms of the ‡ow and of the temperature. The falling time is then computed. Di¤erent falling heights have been tested. The particle temperature was continuously measured during the combustion process with a two colors pyrometer IMPAC ISR 12-LO placed at the bottom of the drop tube furnace and pointing vertically towards the extremity of the injection probe, see Figure 1 b). As indicated in its manual, the accuracy of this two colors pyrometer is given as 0.4% of the measured value plus 1 C, if the temperature is less than 1500 C, that is about 6 C. The devolatilization process occurring during the pyrolysis of the coal particles led to swelling phenomena. The diameters of the collected coal char particles have been observed using a granulometry laser procedure performed at room temperature and the diameters of the dominant subpopulation were lying in the range 100-160 m, to be compared with the diameter range of the parent coal particles, namely 36-72 m. The collected coal char particles have then be smoothly sieved in this diameter range (mean value 130 m) for the further combustion experiments. Such a swelling phenomenon has already been observed in10 for coal particles submitted to a pyrolysis process, with pictures of the coal particles at di¤erent stages of the pyrolysis process.

6


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Successive identical coal char particle drops with temperature measurements were performed in order to analyze their repeatability.

3.2

Char combustion in a thermobalance

A preliminary thermogravimetric experiment was performed on roughly 100 mg of collected char particles. It was performed under nitrogen and under a temperature ramp equal to 10 C/min. During the temperature increase until 300 C (that is before the start of the combustion process), about 3% of the initial mass were lost. This mass loss was attributed to hydrocarbons and moisture which may have previously condensed on the surface of the sample during its collection from the bottom of the drop tube furnace devoted to pyrolysis experiments. The hydrocarbons plus water content of the raw char material (rm) was thus estimated as ( HC;W )rm = 0:03 0:01. The kinetics of char combustion were studied in a thermobalance (Setsys TG12 Setaram). About 8 mg of char collected from the drop tube furnace and sieved to the 100-160 m granulometry were placed in a small cylindrical crucible (5.91 mm of internal diameter and 2.6 mm of internal height). Due to the thinness of the material layer, the internal di¤usional limitations may be neglected, as already described in.18 The surface of the powder material was levelled o¤ at the mouth of the crucible in order to minimize the external di¤usional limitations to oxygen transport towards the surface of the material layer. The oxidizing gas (90% nitrogen, 10% oxygen) was ‡owing at 166.7 cm3 /min (normal conditions). The sample was heated from ambient temperature to 950 C at 10 K/min. Runs were also performed with an empty crucible to assess the e¤ects of drag and buoyancy on the weight measurements. Corrections associated to thermogravimetric analysis with an empty crucible were thus brought (subtracted) to the experimental results concerning the coal char particles, in order to obtain reliable thermograms. Because of the adsorbed water and hydrocarbons on the char sample and assuming that no combustion of the carbonaceous material occurs before 300 C, see the preceding discussion, time 0 of the char combustion was taken when the temperature was reaching 300 C. The sample mass measured at that temperature was taken as the initial sample mass. All the parameters related to this initial sample have the superscript 0. The void volume fraction fvoid of the sample is taken equal to 0.5 and the apparent density (density of a char particle) of the initial material may be computed as: 0p = ( bulk )rm 1 ( HC;W )rm = (1 fvoid ) = 575:4 kg/m3 . From the thermogram, the instantaneous conversion of the carbonaceous material in the thermobalance, de…ned as XC;t (t) = 1 mC (t) =m0C , is computed as a function of time (or temperature) from the following expressions: 0 m0C = m0 1 m0 0ash , where m0 is the mass of ash and mC (t) = m (t) the initial material present in the crucible at time 0, m (t) is that which is read on the thermogram at time t. The ash content 0ash in the initial solid is taken equal to 0:245 0:005, as the precision concerning 0ash deduced from the thermogram is approximately equal to 2%. This value may slightly vary from 7


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one sample to another one, due to heterogeneities. The temperature ramp is described through: T = at + T0 , for the constant heating rate a (10 K/min) and where T0 is the initial temperature at time 0.

3.3

Measurement of the speci…c surface area of the coal char particles

The coal char surface area was measured with a Micromeritics device using CO2 adsorption, following the IUPAC recommendations indicated in.19 For microporous samples with a relatively low total porosity, like carbons or carbonaceous residue, adsorption with N2 requires low pressures at very low (cryogenic) temperatures. This may lead to degassing problems and lack of precision. The sample was degassed at 150 C under vacuum during one day before CO2 adsorption. The CO2 adsorption was realized at 273 K under higher pressures. The Dubinin-Radushkevich equation described in20 was used in order to obtain the volume of the micropores. Then the speci…c surface area of the micropores was deduced. The speci…c surface area of the initial coal char material was estimated as: A0 = 99500 1000 m2 /kg, according to the precision (equal to 1%) indicated in the operating manual. For kinetics investigations, the evolution of the speci…c surface area of the coal char material during combustion was determined measuring the surface area of partially burnt samples obtained at di¤erent conversions, see Figure 2.

4 4.1

4.1.1

Calculations Determination of the kinetic parameters through a thermogravimetric analysis performed under an oxidative atmosphere Hypotheses

The particle radius is supposed to be constant along the combustion process. The char combustion is supposed to be kinetically controlled by the CO2 surface area, which is tentatively correlated to the conversion XC;th . The evolution of the speci…c surface area during combustion, related to the pore structure evolution, is thus accounted for. The pore structure is represented in the random pore model described in4 through a structural parameter which has to be determined. The presence of mineral matter leading to ash residue after the combustion process is accounted for in order to deduce the mass of the carbonaceous part of the sample. But a possible catalytic e¤ect of these minerals is not considered. 4.1.2

Equations

Assuming a …rst-order reaction with respect to oxygen, the carbonaceous material consumption rate is written as RC;th = MC ks AC mC (CO2 )1 , where the ki8


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netic constant ks is given an Arrhenius expression: ks = (ks )0 exp ( E= (Rg T )), (CO2 )1 is the inlet oxygen concentration and AC is the speci…c surface area based on the mass of carbonaceous material and whose increase is tentatively related to the carbonaceous material conversion XC;th in the thermobalance through Bhatia’s relation q ln (1 XC;th ); (1) AC = A0C 1

according to4 and.21 The calculated speci…c surface area A0C of the initial char, based on the carbonaceous part, is related to the measured speci…c area A0 0 0 through A0C = A0 = 1 ash . For the initial coal char material, AC is taken 2 equal to 131800 m /kg. The relative uncertainties concerning this value of 0 0 A0C are evaluated through A0C =A0C = A0 =A0 + ash = 1 ash ' 0:02, 0 according to the previous indications. This leads to AC ' 6600 m2 /kg. The variation of XC;th with respect to time is governed by the di¤erential equation RC;th dXC;th = = (CO2 )1 MC ks A0C (1 dt m0C

XC;th )

q 1

ln (1

XC;th ): (2)

For the determination of the kinetic parameters (ks )0 and E in the kinetic constant ks , a Scilab code has been built which …rst solves the equation (2) with initial values of these kinetic parameters. Then, this code includes an optimization procedure which determines the optimal values of the kinetic parameters through the minimization of the "error" taken as error =

J X

2

(XC;th )exp (tj )

(XC;th )sim (tj )

;

j=1

where (XC;th )exp (tj ) and (XC;th )sim (tj ) are the experimental and simulated conversions of the carbonaceous material in the thermobalance at time tj . Instead of taking all the experimental measure times, only around 150 of them are selected, regularly distributed along the overall experiment duration tmax . This reduces in a signi…cant way the computing times.

4.2 4.2.1

Modelling the combustion of the coal char particle during its fall in the drop tube furnace Hypotheses of the model

As already indicated, the char particle is supposed to leave the injection probe at 323 K and to fall inside the reactor at the same velocity as the gas. The gas temperature pro…le along the reactor axis has been measured and set in the model. A boundary layer accounts for the di¤usional limitations in the oxygen transport from the gas ‡ow to the particle surface. The particle is supposed to be heated by radiation from the walls of the reactor and by the reaction 9


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enthalpy. A convective heat ‡ux, represented by a coe¢ cient h, is exchanged between the particle surface and the gas. The reaction enthalpy accounts for the formation of both CO and CO2 . The molar ratio CO=CO2 is estimated as a function of temperature as in.22 No temperature gradient is considered within the particle, in agreement with the discussion presented in16 for a coal particle. The presence of non-carbonaceous minerals is accounted for in order to estimate the heat capacity of the char particle. The combustion process is supposed to be controlled both by kinetics and by oxygen di¤usion inside the particle and in a boundary layer. Estimating the particle e¤ectiveness parameter p allows to calculate the theoretical particle combustion rate. This parameter p is controlled by the porous structure and the temperature is calculated at every time step. Both Fick and Knudsen di¤usions are accounted for. A mean pore radius is estimated for the calculation of the Knudsen di¤usion. The porous structure evolution is modelled by eq (1) up to 11% conversion, as already proposed by Bhatia and Vartak in21 and.3 Fragmentation is not considered here and a constant particle radius is thus supposed. The probability of particle fracture during the particle fall is indeed surely low because of the small residence time of the particles and of the absence of shocks between particles. SEM pictures of coal char particles injected in a drop tube furnace under di¤erent atmospheres are presented in.25 4.2.2

Equations

Position of the particle The position of R t the particle during its fall is calculated as a function of time through xp = 0 ug dt, where ug is the gas velocity which depends on the gas ‡ow Fg0 and whose expression is known at 298 K:

ug = (Tg =298) Fg0 =

(dr =2)

2

.

Heat transfer The energy balance during the char particle heating up in the drop tube furnace is written as

m0C (1

XC ) (Cp )C + m0p

+4 Rp2 h (Tg

Tp ) +

0 ash

@Tp = 4 Rp2 "p TR4 @t O2 0 + R HCO : 2 1 + =2

Tp4

(Cp )ash

0 R HCO

(3)

The initial values of carbon and particle masses are calculated as: m0C = 0 0 04 3 1 ash and mp = p 3 Rp , respectively. The thermal parameters (Cp )C and (Cp )ash used in eq (3) are given the following expressions m0p

(Cp )C

=

(Cp )ash

=

3Rg 1200 exp MC Tp 754 + 0:586 (Tp

exp (1200=Tp ) 1200=Tp 273) ;

1

2

;

see.23 The char emissivity "p is taken equal to 0.85. The convective coe¢ cient h is calculated from (h)Tm = N u ( g )Tm = (2Rp ), taking the Nusselt number 10


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N u equal to 2. Tm is the mean temperature of the boundary layer: Tm = (Tp + Tg ) =2. The gas thermal conductivity ( g )Tm is related to Tm through 0:5 ( g )Tm = 0:0207 (Tm =273) (1 + 113=273) = (1 + 113=Tm ). The reaction enthalpies for CO and CO2 formations are taken as 0 R HCO 0 R HCO2

= =

103 103

110:5 393:5

6:38 (Tp 13:1 (Tp

298) ; 298) :

The CO=CO2 ratio is approximated as a function of the gas temperature through: = 102:5 exp ( 25000= (Rg T )), see.22 Oxygen ‡ux The oxygen ‡ux expression:

O2

= kd 4

Rp2

O2

entering the particle is de…ned through the

(CO2 )Rp

(CO2 )1 , where (CO2 )1 is computed

as: (CO2 )1 = (XO2 )1 P= (Rg Tg ), where (XO2 )1 is the inlet oxygen molar fraction. Due to the hypothesis of a quasi-steady state combustion regime, the oxygen ‡ux related to the carbonaceous material consumption rate is given as: O2 = RC = ( mC ), with RC = p ks mC AC (CO2 )Rp = and = ( + 1) = ( =2 + 1). = p ks mC AC + 1= kd 4 Rp2 . The O2 is thus given as: O2 = (CO2 )1 = oxygen mass transfer coe¢ cient is de…ned as: kd = Sh (DO2 )(F:bl) = (2Rp ) with: 1:75

(DO2 )(F:bl) = 1:78 10 5 (Tm =273) . The Sherwood number Sh is taken equal to 2. The speci…c area p AC of the particle is calculated according to the following ln (1 XC ), if XC < 0:11; AC = 300000 m2 /kg, expressions: AC = A0C 1 16 if XC 0:11, see and the discussion in section 5.1. O2 is …nally given through O2

=

3 0 p ks p 4

Rp3 A0 (1

(CO2 )1

XC )

p

1

ln (1

XC )

+

1 kd 4 Rp2

:

Computation of the particle e¤ectiveness factor The particle e¤ectiveness factor p is related to the Thiele modulus through p

=

3

1 tanh

1

:

Introducing x = r=Rp leads to the following dimensionless equation for the oxygen transport within the particle 1 @ x2 @x

x2

@XO2 @x

= Rp2

k s AC C XO2 ; e DO 2

(4)

which leads to the following expression of the Thiele modulus

= Rp

s

ks AC C = Rp e DO 2

s

k s A0

0 p

(1

XC )

p

1

e DO 2

11


ln (1

XC )

:

(5)

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e In eq (4), DO is the e¤ective oxygen di¤usivity within the porous structure. 2 This di¤usivity, which accounts for both Fick and Knudsen di¤usions, is given e e e through: 1=DO = 1=DK + 1=DFe , with DK = DK p = p and DFe = DF p = p . 2 The Knudsen di¤usivity is related to the mean pore radius

rp =

2rf AC

p

;

(6)

C

p through: DK = 4rp 2Rg Tp = ( MO2 )=3. The roughness factor rf is taken equal to 2, as in.6 The particle porosity p is a function of the particle density: p = 1 p = cr , where cr is the density of carbon crystallites, whose values are given: 1.4 g/cm3 and 1.82 g/cm3 in24 and 1.33 g/cm3 in.6 A mean value of 1.5 g/cm3 is taken in the present model. The Fickian di¤usivity DF is expressed as: 1:75 DF = 1:78 10 5 (Tp =273) . The density C of the carbonaceous part of the 0 particle is related to the conversion XC through: C = 0p (1 XC ) 1 ash . 0 The particle density p is expressed as: p = 0p 1 XC 1 . ash In the experiments realized in the drop tube furnace, the initial time t = 0 is chosen when the char particle leaves the injection probe, which leads to the initial conditions: Tp = 323 K, XC = 0, xp = 0 m. The problem under consideration in the present work thus mainly consists of two equations: an energy balance written for the particle (3) and an oxygen mass transport balance within the particle (4), assuming that the structural parameters (porosity, density, pore radius) involved in this model are uniform inside the particle. The temperature is also supposed to be uniform in the particle. Eq (3) allows to determine the particle temperature. Eq (4) allows to calculate the oxygen concentration gradient within the particle and to de…ne the Thiele modulus through (5), which is then used for the computation of the e¤ectiveness factor of the particle p , leading to the determination of O2 , which realizes the coupling between oxygen mass transport and energy balances. Numerical resolution of the problem using a Fortran software A Fortran code has been developed which solves eq (3) through an explicit Euler scheme with respect to the time parameter. Starting from the above-indicated initial conditions, this code successively computes the values of the di¤erent quantities ug , m0c ; : : : ; p , ; : : : ; p , as previously exposed. The application of the explicit Euler scheme leads to the value of Tp through eq (3), then that of the conversion XC at time t + dt through XC (t + dt)

= =

XC (t) + dXC (t) 0 XC (t) p + dt (CO2 )1 MC ks AC (1 1 ln (1 XC (t)):

XC (t))

The time step dt was taken equal to 2 10 4 s. The key point of this code is the resolution of the equation (4) which is written in spherical coordinates. A simple and e¢ cient second-order …nite di¤erence method has been elaborated for this resolution which is described in.26

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5 5.1

Results and discussion Determination of the kinetic constant ks through a thermogravimetric analysis of the coal char particle

Measurements performed on the partially burnt coal char samples revealed that during the combustion process the speci…c surface area was increasing up to a maximal value equal to 300000 m2 /kg, corresponding to a carbonaceous material conversion equal to 11%, and then remained constant up to a total conversion, see Figure 2.

Figure 2. The experimentally measured (crosses) and computed (squares) through Bhatia’s relation (eq (1)) speci…c surface area of partially burnt coal char particles. The constant value of 300000 m2 /kg was thus imposed in the model for XC bigger than 0.11. For XC < 0:11, Bhatia’s relation (eq (1)) was used to simulate the values of the speci…c surface area. When XC increases from 0 to 0.11, the temperature remains low enough during most of the corresponding interval 0-0.1 s, which means that the char combustion can be considered under kinetic control, validating the use of Bhatia’s relation. Taking = 37, eq (1) was found to reasonably represent the increasing evolution of the surface area. The following conditions were thus imposed: if XC 0:11: = 37:0; A0C = 131800 m2 /kg and if XC > 0:11: = 0:0. As exposed later on, this hypothesis will not lead to wrong simulations of the combustion process, see also the discussion in section 5.2.5. For the determination of the optimal values of (ks )0 and E which appear in the Arrhenius expression of the kinetic constant ks , the Scilab code which has been described in Section 4.1.2 has been applied in the temperature range 485-635 C, thus eliminating the domains of temperature corresponding to a very low conversion of the carbonaceous material and to conversions close to 1, for which large uncertainties may exist. The optimal kinetic constant is found 13


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equal to: ks = 1050 exp ( 153200= (Rg T )). The determination of the kinetic constant ks is a¤ected by the knowledge of the initial speci…c surface area A0 and of its variations along the combustion process. Classical statistical tools lead to the following standard deviations of E: 2400 J/mol. The activation energy will thus be taken equal to 153200 2400 J/mol. Of course, the value of A0 , computed from CO2 adsorption isotherms, remains questionable, especially when the complete description of the porosity is not performed. Regarding the variations of the speci…c surface area, modelled by eq (1) and using the structural parameter , this approach may be considered as a possible way to get a draft estimate of the porosity evolutions. A possible opening of closed pores during the combustion process is not considered in the random pore model, see.3 Despite the uncertainty about the porosity representation, it appears a priori important to account for the variations of the active surface area. Nevertheless, the value of 153200 2400 J/mol of this active surface area is in a reasonable agreement with that of 134000 J/mol which is cited in27 for a bituminous coal.

5.2 5.2.1

Char combustion in the drop tube furnace Experimental gas temperature

The gas temperature was measured with a thermocouple located at di¤erent points along the reactor axis for three di¤erent regulation temperatures 1100, 1200 and 1300 C without any char injection. The injected gas entered the reactor at the end of the injection probe at about 900 C and then was heated by the reactor walls. Then the gas was reaching a temperature plateau at the temperature of the isothermal part of the walls, see Table 2, column 2. Table 2 Gas temperature plateau measured (thermocouple) without particle injection and initial temperatures recorded by the pyrometer during particle combustion for three regulation temperatures (all the temperatures are measured in C ).

Regulation temp. 1100 1200 1300

Temp. plateau 1035 1132 1242

Initial pyrometer temp. 1048 1133 1236

These uniform wall temperatures were measured between 58 to 68 C smaller than the regulation temperature, depending on the regulation temperature, probably due to heat losses across the inlet and outlet sections of the reactor. After this plateau, the gas temperature decreased up to the outlet section of the reactor. 5.2.2

Experimental particle temperatures

For each regulation temperature, the particle temperature has been recorded by the two colors pyrometer for at least nine successive injection sequences. For 14


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each regulation temperature, large variations of the particle temperatures have been observed either in the slopes of the increasing part of the curves or in the values of the maximal temperature. For the regulation temperature equal to 1200 C, the maximal di¤erence between the lowest and highest maximal temperatures is equal to 63.3 C (between 1289.1 and 1352.4 C, with a mean value of 1326.4 C and a standard deviation equal to 25.0 C). These maximal temperatures occur at times which vary between 0.258 and 0.334 s, with a mean value equal to 0.289 s and a standard deviation equal to 0.027 s. Solomon gives in16 50 C as the uncertainty for particle temperatures measured in drop tube furnaces during coal pyrolysis. The overall duration of the combustion process remains the same in the di¤erent experiments for each regulation temperature. Quite similar observations can be done in the cases of combustions performed under 1100 and 1300 C regulation temperatures. The precise causes of these variations are di¢ cult to identify but an important lack of repeatability of the particle injection process may occur. The initial pyrometer temperatures (see Table 2, third column) are close to the plateau temperature, whatever the regulation temperature. This means that the pyrometer also detects the wall temperature which is the highest temperature in the reactor in the absence of combustion. When the particle enters the reactor, its temperature highly increases and the pyrometer rapidly detects this temperature when it becomes higher than that of the walls. After a temperature peak, the particle temperature decreases and reaches the same temperature as that observed before the particle entrance. For each regulation temperature, a particular curve called the mean curve was selected among the set of experimental temperature curves, choosing the maximal pyrometer temperature as criterion. This mean curve exhibits a maximum which is roughly the mean of all the maxima. On Figure 3, these mean curves are presented for the three regulation temperatures 1100, 1200 and 1300 C.

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Figure 3. Mean temperature curves during combustion of char particles in a drop tube reactor for the three regulation temperatures of 1100, 1200 and 1300 C. In this Figure 3, time 0 was arbitrarily chosen. As expected, the temperature maximum increases with the regulation temperature. Surprisingly, the slope of the increasing part of the curve corresponding to the 1300 C regulation temperature seems abnormally low in comparison to the two other slopes. 5.2.3

Comparison between the experimental and simulated particle temperatures and simulation of the conversion

The model described in subsection 4.2 has been used in order to predict the particle temperature during its combustion in the drop tube furnace and the evolution of the conversion versus time. In the simulations, the initial time 0 was here set when the particle enters the reactor at a temperature of 50 C. Figures 4 a) to 4 c) compare the experimental and simulated evolutions of the particle temperature for the three regulation temperatures.

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Figure 4. Comparison between model calculations and measurements of the particle temperature versus time during the particle drop in a drop tube reactor for a regulation temperature of (a) 1100 C; (b) 1200 C; (c) 1300 C. As already discussed, for the experimental curve representing the temperature returned by the pyrometer, the time 0 at which the particle leaves the injection probe is not precisely known. The pyrometer signal starts increasing when the particle temperature reaches the ‡at small initial part of the pyrometer signal. The pyrometer signal and the simulated temperature curve are forced to cross at the point corresponding to the start of the pyrometer signal increase, through a simple translation of the pyrometer signal along the time axis. In Figures 4 a), b) and c), the starting time of the experimental temperature observations has been uni…ed to 0.183 s. The pyrometer temperature signal and the simulated particle temperature exhibit a quite good agreement on Figure 4 b) which corresponds to the 1200 C regulation temperature. The maximal temperatures are quite close in the two curves (44 C di¤erence, corresponding to a percentage deviation approximately equal to 3%) and the combustion durations (about 0.5 s) are in a good agreement. In the case of Figure 4 a) (1100 C regulation temperature), the agreement is not so good, especially when considering the maximal temperature (73 C di¤erence, corresponding to a percentage deviation approximately equal to 6%). But remembering the di¤erences between the lowest and highest observed temperatures of the particle inside the drop tube furnace (75 C di¤erence), the results of the present model may be considered as valid. Further, the combustion durations are in a good agreement (about 0.8 s), still in this case of a regulation temperature of 1100 C. In the case of Figure 4 c) (1300 C regulation temperature), the pyrometer signal does not seem to be realistic because of a too low slope of the increasing part of the signal (136 C di¤erence, corresponding to a percentage deviation approximately equal to 10%). The experimental temperature curve indicated in Figure 4 c) (and also in Figure 3) is yet the mean curve of repeated combustion experiments under the regulation temperature of 1300 C. Nevertheless, the simulated temperature curve seems to be very realistic in the three cases, with a maximal temperature which increases and a combustion duration which decreases when the regulation temperature increases from 1100 to 1300 C. The evolutions of the conversion versus the particle position along the reactor axis are presented in Figure 5 for the three regulation temperatures.

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Figure 5. Simulations of the carbonaceous material conversion as a function of the particle position, for the three regulation temperatures (1100, 1200, 1300 C). As expected, a larger acceleration of the combustion process occurs when the regulation temperature increases. The combustion process is complete after a particle drop of about 30, 15 and 10 cm, for the three regulation temperatures 1100, 1200 and 1300 C, respectively. 5.2.4

Combustion regime of the particle

The value of the e¤ectiveness factor p allows to determine the combustion regime of the particle. Figure 6 represents the evolution of p versus time or versus the conversion XC for the three regulation temperatures 1100, 1200, 1300 C.

Figure 6. Evolutions of the e¤ectiveness factor p of the char particle during its drop in a drop tube reactor for three regulation temperatures (1100, 1200, 1300 C), as a function of (a) time; (b) conversion.

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At the very beginning of the particle drop, the e¤ectiveness factor remains almost equal to 1, as the combustion rate is here very small due to low particle temperatures. After this initial stage, a fast decrease of the e¤ectiveness factor is observed, due to a fast particle heating. For the 1300 C temperature regulation, the factor reaches a minimum value 0.1, which means that a mixed di¤usional and kinetic regime occurs, with a very large di¤usional contribution. For the 1200 C temperature regulation, the minimum value is 0.15. This mixed di¤usional and kinetic regime occurs during a short time (Figure 6 a) and prevails during a large conversion range, roughly between 0.1 and 0.6 for the 1200 and 1300 C regulation temperatures (see Figure 6 b). Then, the e¤ectiveness factor p increases up to 1. The di¤usional limitations here decrease due to porosity increase and above a conversion between 0.6 and 0.9, depending on the regulation temperature. Combustion is here close to be controlled by kinetics. Limitations to oxygen di¤usion are at work during a large part of the combustion process. When the di¤usional limitations for oxygen transport within the particle are high, combustion is very close to occur within a shell at the particle surface. This can be veri…ed calculating the oxygen concentration versus the radial position (CO2 )r = (CO2 )Rp (Rp =r) sinh ( r=Rp ) = sinh ( ). On Figure 7 corresponding to the 1200 C regulation temperature, three oxygen concentrations pro…les within the particle are presented, which correspond to the times at which the three conversions respectively equal to 0.096, 0.594 and 0.831 are reached.

Figure 7. Instantaneous oxygen concentration as a function of the radial position within the char particle at three times corresponding to three di¤erent conversions (0.096, 0.594 and 0.831) during the particle combustion in a drop tube reactor for a regulation temperature of 1200 C. At the beginning of the combustion process, that is at a time corresponding to 9.6% conversion, when only 9.62% of the carbonaceous material is consumed, the O2 concentration exhibits a very fast decrease close to the particle surface. 19


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Only the particle volume between r=Rp = 0:7 and the surface is concerned by combustion. When 59.4% of the carbonaceous material is consumed, the combustion front has only progressed towards the particle center up to r=Rp = 0:6. Finally, when 83.1% of the carbonaceous material is consumed, the particle center is also concerned by combustion. As expected, these oxygen concentrations gradients are more pronounced when the regulation temperature increases (curves not presented here). The di¤erent combustion regimes depend on the Thiele modulus given by eq (5). According to the hypotheses of the model, the value of the Thiele modulus is uniform in the whole particle in which the porous structure is supposed to remain uniform during the whole combustion process. The values of the Thiele modulus corresponding to the three conversions 0.096, 0.594, 0.831 are equal to 17.9, 10.6 and 3.8, respectively. 5.2.5

In‡uence of the speci…c surface area

In order to investigate the e¤ect of the speci…c surface area, another simulation of the combustion process has been realized assuming that the maximal value of the speci…c surface area is now equal to 400000 m2 /kg instead of 300000 m2 /kg, which represents a signi…cant change. However, the simulation of the combustion with a 1200 C regulation temperature with this higher value of the speci…c surface area returned that the maximal combustion temperature was only increased by 4 C and that the position of this maximum on the reactor axis was almost unchanged, as well as the corresponding conversion. This absence of sensitivity of the model towards the speci…c surface area is partially due to the fact that the combustion process is for a large part controlled by oxygen di¤usion, limiting the in‡uence of the kinetic parameters. Another reason is that the increase of the speci…c surface area decreases the mean pore radius rp , given in eq (6), which introduces an antagonistic e¤ect on the combustion rate. The above-indicated approximate values of the speci…c surface area can thus be accepted.

6

Conclusions

A simple model has been proposed which simulates the evolution during a combustion process of the temperature of a coal char particle injected in a drop tube furnace. This model mainly consists of two equations: an energy balance for the particle and an oxygen mass transport balance within the particle. It assumes uniform particle density and porosity, pore radius and temperature inside the particle. In the present model, the internal di¤usional limitations for oxygen transport which occur during the combustion process are taken into account through an e¤ectiveness factor of the particle which depends on the Thiele modulus, hence on the particle temperature. The oxygen transfer to the surface of the particle through a concentration boundary layer is also taken into account through an oxygen mass transfer coe¢ cient which depends on the

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particle temperature. Especially devoted to the simulation of the particle temperature during its fall in the drop tube furnace, this simple model is also able to predict the evolution of the conversion during the combustion process and the impact of di¤erent structural parameters acting on the combustion process. The agreement between the simulated and measured particle temperature looks relatively poor, although the di¤erences between the simulated and experimental particle temperatures lie in the uncertainties which are admitted for such experiments and which are con…rmed in the present study through repeatability combustion experiments. The resolution of the two equations involved in this model do not require time-consuming computations and they may be solved using a Fortran software. This model is much simpler than the comprehensive model which has been introduced in9 and in,10 for example, which is based on 8+7 equations. Of course, this simple model does not give as many details as the comprehensive one. The quite high di¤erences between the experimental and simulated particle temperatures are surely due to both the di¢ culty to obtain pertinent experimental measurements of the particle temperature in such conditions (that is using a two colors pyrometer) and to the poor knowledge of some physical properties of the char particle such as emissivity and thermal properties and their variations along the combustion process. Of course, the simpli…ed particle structure - a unique pore model - which is here considered may also lead to the observed relatively poor agreement. The particle structure drastically evolves locally during the combustion process and parameters such as particle porosity, pore size, apparent carbon density and speci…c surface area should be considered as local quantities which evolve inside the particle along this combustion process. Due to di¤usional limitations of oxygen transport, a combustion front progresses from the surface to the centre of the particle. A porosity gradient thus appears within the particle. A unique pore model trivially does not account for this phenomenon. The only way to account for the evolution of the porous medium during the combustion process should be to consider local parameters depending on the radial position (carbon density, particle density, speci…c surface area, particle porosity, oxygen di¤usivities. . . ) and to model local combustions occurring in successive elemental spherical annular volumes inside the particle. A more sophisticated model, using local quantities within the particle, is currently in progress in the lab. Nevertheless, the simpli…ed model which has been presented could be useful for a quick and rough description of the particle behavior during the combustion process. Acknowledgments The authors thank Mrs. Fatiha Mechati, Mrs. Sandrine Lesieur, Mrs. Damaris Kerhli and M. Olivier Allgaier for their fruitful contributions to the present study. The authors also thank Dr. L. Porcheron (EDF R&D), E. Thunin (EDF R&D) and Dr. P. Pilon (EDF R&D) for their support and helpful discussions along this study. The authors thank the anonymous referees whose comments contributed to improve a previous version of the work. 21


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Nomenclature a Ac A0 A0c

Constant heating rate for TGA (10 C= min) Speci…c surface area of the carbonaceous part Speci…c surface area of the initial material Speci…c surface area of the carbonaceous part of the initial material (CP )c Calori…c capacity of carbon (CP )ash Calori…c capacity of ash CO2 Oxygen concentration within the char particle (CO2 )Rp Oxygen concentration at the particle surface (CO2 )1 Oxygen concentration far from the particle dr Diameter of the reactor of the drop tube DF Fick di¤usivity of oxygen DK Knudsen di¤usivity of oxygen DFe E¤ective Fick di¤usivity of oxygen e E¤ective Knudsen di¤usivity of oxygen DK e E¤ective di¤usivity of oxygen within the particle DO 2 (DO2 )F;bl Di¤usivity of oxygen in the boundary layer E Activation energy fvoid Void volume fraction in the bulk material Fg0 Gas ‡ow h Convective heat transfer coe¢ cient ks Kinetic constant kd Mass transfer coe¢ cient of oxygen (ks )0 Frequency factor m Mass of the sample (TG) Initial mass of the char particle m0p m0 Initial mass of the sample (TG) at 300 C mC Mass of carbon within the char particle Mass of carbon within the char sample (TG) Initial mass of carbon within the char particle m0C Initial mass of carbon in the sample (TG) at 300 C MC Molar weight of carbon MO 2 Molar weight of oxygen Nu Nusselt number (here taken equal to 2) P Pressure within the reactor r Radial coordinate rp Mean pore radius RC Carbonaceous material consumption rate of oxygen RC;th Carbonaceous material consumption rate of oxygen in the thermobalance Rp Particle radius Rg Perfect gas constant

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K/s m2 /kg m2 /kg m2 /kg J/kgK J/kgK mol/m3 mol/m3 mol/m3 m m2 /s m2 /s m2 /s m2 /s m2 /s m2 /s J/mol m3 /s m/s2 m/s m/s m/s kg kg kg kg

kg kg/mol kg/mol Pa m m kg/s kg/s m J/molK

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Sh t T Tg Tm

Sherwood number (here taken equal to 2) Time s Gas and sample temperature (TG) K Gas temperature (Entrained ‡ow reactor) K Mean temperature in the boundary layer around a particle K T0 Reference gas temperature (573 K) K Tp Particle temperature (Drop reactor) K TR Temperature of the reactor walls K ug Gas velocity m/s x Dimensionless radial coordinate within the particle xp Coordinate for particle position in the drop reactor m XC Carbonaceous material conversion ratio XC;th Conversion ratio in the thermobalance XO2 Oxygen molar fraction (XO2 )1 Oxygen molar fraction far from the particle z Parameter for estimation of thermal capacity 0 Reaction enthalpy for CO formation J/mol R HCO 0 Reaction enthalpy for CO2 formation J/mol R HCO2 Combustion e¤ectiveness factor p "p Char particle emissivity (taken as 0.85) Gas thermal conductivity W/mK g Thiele modulus of the particle Molar oxygen ‡ux mol/s O2 Molar stoichiometric factor molC/molO2 Density of carbonaceous particle material kg/m3 C True density of carbon kg/m3 cr Particle density kg/m3 p 0 Initial apparent particle density kg/m3 p ( bulk )rm Bulk density of the raw material kg/m3 Stefan-Boltzmann constant W/m2 K4 Molar ratio CO=CO2 Tortuosity factor of the particle p (here taken equal to 2) 0 Ash content in the initial char particle ash ( HC;W )rm HC and water content within the raw material Particle porosity p Structural parameter AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes The authors declare no competing …nancial interest.

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A Simplified Model Accounting for the Combustion of Pulverized Coal

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