Fuel 96 (2012) 168–175

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Fuel

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A new char combustion kinetic model – Part 2: Empirical validation

Andrés Rojas a, Juan Barraza b,⇑, Richelieu Barranco c, Edward Lester c

a Departamento de Ingeniería Química, Universidad Nacional de Colombia Sede Manizales, Manizales, Colombiab Escuela de Ingeniería Química, Universidad del Valle, A.A 25360 Cali, Colombiac Department of Chemical and Environmental Engineering, The University of Nottingham, Nottingham NG7 2RD, UK

a r t i c l e i n f o

Article history:Received 24 February 2011Received in revised form 19 January 2012Accepted 20 January 2012Available online 7 February 2012

Keywords:CharCombustion modelIntrinsic reactivity

0016-2361/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.fuel.2012.01.044

⇑ Corresponding author. Tel.: +57 2 3312935; fax: +E-mail address: juan.barraza@correounivalle.edu.c

a b s t r a c t

A new kinetic model for the combustion reactivity of char from pulverized coal was developed by meansof dimensional analysis using the Rayleigh method. This model was published in Fuel 88 (2009) 2335–2339, ‘‘A new char combustion kinetic model. Part 1. Formulation’’. In this work, the required parametersto validate the kinetic model were derived from experimental data from chars produced in a drop tubereactor using three devolatilization times (100, 150 and 300 ms), three devolatilization temperatures(900, 1000 and 1100 �C in a nitrogen environment) and three bituminous coals (two Colombian coals,La Yolanda and El Cerrejón, and one UK coal, Thoresby). The empirical results show that there is goodagreement with the obtained experimental results, which can be predicted by the intrinsic reactivityof the coals.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The efficient use of pulverized coal is crucial to the utility indus-try, particularly as concerns over global warming increase. Improv-ing efficiency necessitates better understanding of the mechanismsfor the coal combustion process. The heterogeneous nature of coaland the multistage mechanisms that govern coal combustion com-plicate the successful modelling of this process. In modellingterms, a three-step semi-global mechanism was proposed by Hurtand Calo [1] where a simple rate law describes the major trends inreaction order, activation energy, and CO/CO2 ratio from 600 to2000 K.

Coal combustion mechanisms can be modelled using computerbased simulations. A model called CBK8 describes a large set ofdata on extinction and near-extinction for chars from pulverizedcoals of various rank at gas temperatures from 1100 to 1600 Kand oxygen concentrations from 3 to 19% v/v. The model withthe same parameter set also describes the thermogravimetric anal-ysis (TGA) at 500 �C for a wide range of US coals, thus unifyingreactivity measurements spanning over 1000 �C in particle tem-perature and 4–5 orders of magnitude in reaction rate [2]. Thesemodels can be used as part of the development and design ofnew furnaces [3], or optimization of operation conditions [4] forboilers or for simply predicting the combustion behaviour of newcoals [4]. These computer models can use complex codes, involvingnumerical models of char combustion with sub-models for otherrelevant processes such as fluid flow, heat transfer, and chemical

ll rights reserved.

57 2 3392335.o (J. Barraza).

reaction kinetics. Combustion models must tackle the complexityof the carbon–oxygen reaction mechanism, whose kinetics areknown to be influenced by ash [5], petrographic (maceral groups)properties of coal [6], particle size [7], diffusion phenomena [8],distribution and size of pores [9], flame temperature [1] and charcharacteristics [10]. These phenomena are difficult to capture ina single combustion model since it then requires multiple inputparameters, both mathematical and empirical.

A reasonable approach for practical char combustion modelling,therefore, is to postulate global mechanisms that yield kinetic lawswith the proper mathematical form to reproduce the major fea-tures of the kinetic data, while accepting that assumptions aremade that ignore some experimental artifacts [11].

This paper extends the work by the authors in the previous Fuelpaper [12] by providing the parameters for a new intrinsic kineticmodel for char combustion reactivity in pulverized coals. Thisintrinsic kinetic model was obtained by the dimensionless methodof Raleigh [13] and it is the relationship between three dimension-less numbers. The first dimensionless number represents charcharacteristics such as surface area, apparent density, intrinsicreactivity and devolatilization time (this parameter is associatedwith residual volatile matter in the char). The second number rep-resents combustion characteristics (activation energy and combus-tion temperature). The third dimensionless number corresponds tothe coal characteristics using either the maceral content or per-centage of unreactive material (%Unreactives or %U). %Unreactivesis determined using an automated image analysis program thatmeasures the reflectance profile of the whole coal and then quan-tifies the proportion of material, regardless of maceral type, thatwill likely to be most unreactive during combustion [14–19].

A. Rojas et al. / Fuel 96 (2012) 168–175 169

2. Method

2.1. Coal origin and char preparation

Two Colombian coals (La Yolanda and El Cerrejón) and one UKcoal (Thoresby) were selected in this study. El Cerrejón representsa coal that is successfully traded on the world market as a combus-tion coal. Thoresby is standard UK high volatile bituminous coalwith typical combustion characteristics for a UK coal. Yolanda isa less well known Colombian coal with a higher rank than a typicalUK or export coal for power generation but with very high vitrinitebut with a lower %Unreactives values than the other two coals. Theproximate analysis was carried out in a thermogravimetric ana-lyzer LECO TGA 601; the contents of C, H and N elements in theultimate analysis were determined by an elemental analyzer (LECOCHN2000); S content was determined in a LECO SC 32 sulphurom-eter analyzer; and the oxygen content was obtained by difference.Maceral contents for coal samples were obtain by manual analysisusing an optical microscope (Leitz Ortholux II POL-BK) with a32 �magnification oil-immersion lens. Random Vitrinite reflec-tance was measured using a photometer and 100 separate mea-surements, each being taken from a homogenous area of vitriniteon individual particles. All these coals were ground to pf specifica-tion (75% under 75 lm). The �75 lm fraction was fed to a droptube reactor operating at three temperatures (900, 1000 and1100 �C) under a N2 environment, and at three residence times(100, 150 and 300 ms).

2.2. Surface area and apparent density analysis of coals and chars

The specific surface area of the coal and char samples was mea-sured using a MicromeriticsASAP 2010 analyzer. Between 0.2 and0.3 g of sample was degassed for at least 10 h at 120 �C. The surfacearea of the degassed sample was then calculated from the nitrogenadsorption isotherm (77 K) using the BET equation. The apparentdensity of the coal and char samples was determined in a CarloErba Macropore Unit 120 poresimeter.

Table 1Proximate, ultimate, petrographic and other properties of coals.

Parameter Coals

ElCerrejón

Thoresby LaYolanda

Proximate analysis (wt.%, dry basis)Ash 11.68 22.75 15.61Volatiles 35.55 26.69 28.82Fixed carbon 52.77 50.56 55.57Fuel ratio 1.48 1.89 1.93

Ultimate analysis (wt.%, dry basis)C 82.35 79.5 85.41H 5.92 5.73 5.58N 1.32 1.39 1.32S 0.88 2.21 1.38O (difference) 9.53 11.17 6.31H/C ratio 0.86 0.87 0.78

2.3. Microscopy analysis of coals

Image analysis of the coal samples was carried out using imageanalysis system which combines oil immersion microscopy withKontron KS400 automated image analysis software [14,17–24].This program determines the relative reflectance of a whole coalsample, presented as a histogram in the grey-scale range of 0–255, where a grey-scale of 0 is black and 255 is white. 150 imagesare measured for total reflectance and the value for %Unreactives,(which is mainly composed of inertinite and higher reflectancesemifusinite material. Some mineral matter can be included in thisreflectance range but most is washed out during the block polish-ing stage) is calculated to be the % of pixels with a reflection great-er than 190.Clays minerals generally has a reflectance range similarto that of liptinites but the mounting procedure again reduces theamount that is present in the final polished block.

O/C ratio 0.09 0.11 0.06

Maceral analysis (% mineral-matter free basis)Vitrinite 80.4 78.4 95.6Liptinite 0.8 3.2 0Semi-fusinite 7.6 7.8 1.6Fusinite 11.2 10.6 2.8Random vitrinite reflectance (vol.%) 0.55 0.70 0.98Reactive inertinite (vol.%) 14.27 12.18 2.76Reactive inertinite fraction, x 0.81 0.77 0.69%Unreactives (vol.%) 3.7 3.7 0.2Specific surface area (m2/g) 13.2 8.1 2.7Apparent density to 0.1013 MPa (g/cm3) 0.65 0.74 0.71

2.4. Isothermal combustion rates in a TGA

The combustion characteristics of each char sample were mea-sured using a Perkin-Elmer TGA 1 thermogravimetric analyzer(TGA). All TGA experiments were conducted using an isothermalmethod. Char samples were heating in an inert-gas (nitrogen) envi-ronment with a flow rate of 30 ml/min up to the work temperature(700, 800 or 900 �C). The gas supply is switched to air once thistemperature is reached.

3. Results and discussion

3.1. Coal and char characterization

The characteristics of the three coal samples are shown in Table1. According to the vitrinite random reflectance, La Yolanda coal isthe highest rank, while El Cerrejón coal is the lowest rank. LaYolanda coal has the highest vitrinite content, Thoresby coal hasthe highest liptinite content and El Cerrejón coal presents the ma-jor inertinite content (semi-fusinite + fusinite).

Surface area, apparent density and activation energy of chars,whose were obtained at three residence time and three devolatil-ization temperatures, are shown in Table 2. Most of the char sam-ples appear to have, at a fixed devolatilization time, a lower surfacearea than the original coal with an increase in apparent density asdevolatilization temperature increase. This behaviour may be dueto the swelling of the char particle. In terms of activation energy,La Yolanda chars showed lower activation energy.

3.2. Reaction kinetic model

A reaction kinetics model was developed to determine the coalreactivity a function of char, coal and combustion characteristics(model 1 – Macerals), as shown in Eq. (1):

Rctv

r2nA3n�1g

¼ k0Ea

RT

� �a V þ Lþ xIMM þ ð1� xÞI

� �b

ð1Þ

Where a and b are empirical constants for the global kinetic reac-tion model, Rc is the chemical reaction rate coefficient ing cm�2 s�1 atm-n, tv is the char devolatilization time in s, Ag is thespecific surface area of char pores in cm2 g�1, r is the apparent den-sity of the char in g cm�3, n is the global reaction order, k0 is theempirical constant for the new kinetic combustion model, Ea isthe apparent activation energy in J mol�1 K�1, I, L and MM are theinertinite, liptinite and mineral matter concentration of the originalcoal respectively in % v/v, x is the reactive inertinite fraction and R isthe universal gas constant in atm cm3 mol�1 K�1.

Table 2Surface area, apparent density and activation energy of chars.

Sample Devolatilization time (ms) Surface area (m2/g) Apparent density (g/cm3) Activation energy (kJ/mol)

900 �C 1000 �C 1100 �C 900 �C 1000 �C 1100 �C 900 �C 1000 �C 1100 �C

El Cerrejón 100 16.8 3.4 7.7 0.54 0.56 0.57 7.42 4.75 4.82150 12.3 2.7 8.2 0.55 0.58 0.59 6.79 7.45 5.19300 17.0 5.3 8.2 0.59 0.61 0.62 5.39 7.91 11.00

Thoresby 100 3.8 8.7 6.5 0.57 0.58 0.58 6.73 4.57 6.08150 2.3 7.8 14.7 0.59 0.59 0.60 8.49 8.78 7.44300 13.6 9.2 12.9 0.62 0.63 0.63 5.04 9.36 6.34

La Yolanda 100 1.3 1.5 1.5 0.71 0.77 0.80 1.65 2.74 1.64150 2.3 1.6 1.7 0.76 0.87 0.88 1.24 5.12 10.55300 2.8 1.8 1.2 0.80 1.06 0.92 4.39 3.96 9.49

R2 = 0.9918

0.5

0.6

0.7

0.8

0.9

1

0.2 0.4 0.6 0.8 1 1.2

Random mean vitrinite reflectance, VRo, %

Iner

tinite

rea

ctiv

e fr

actio

n

Fig. 1. Relationship between the inertinite reactive fraction and the coal range [25].

170 A. Rojas et al. / Fuel 96 (2012) 168–175

An alternative model (model 2 – %Unreactives) was developed[25], in such a way that it was substituted the dimensionless num-ber, which replaced the coal maceral composition elements with%Unreactives, %U, the number for the non-reactive fraction. Thisalternative model is given by the following equation:

Rctv

r2nA3n�1g

¼ k0Ea

RT

� �a 100�%U%U

� �b

ð2Þ

Then, the combustion rate for two previous models is given by:

r00c ¼1As

dmdt¼ �k0

r2nA3n�1g

tv

!Ea

RT

� �a V þ Lþ xIMM þ ð1� xÞI

� �b

mn ð3Þ

r00c ¼1As

dmdt¼ �k0

r2nA3n�1g

tv

!Ea

RT

� �a 100�%U%U

� �b

mn ð4Þ

where As is the reaction surface area in cm�2, dm/dt is the rate ofchar mass loss during combustion in g s�1, m is the char remainingmass in g and r00 is the char combustion rate in g cm�2 s�1.

4. Determination of data involved in the kinetic model

Different methods to evaluate the required parameters, in orderto validate the model, such as reactive inertinite fraction, maceralcontent, reaction order, energy activation, surface area, apparentdensity and intrinsic reactivity, are shown below:

4.1. Reactive inertinite fraction and maceral content data

It is well established that not all inertinite is inert during thecombustion processes of pulverized coal [24,25], and it was foundthat the reactive inertinite fraction does not depend on the quan-tity of present inertinite, but on the coal ‘rank’, as measured withvitrinite reflectance [28–31]. The expression for calculating thereactive inertinite fraction for coals with a rank of between 0.45%and 1.14% is shown in the following equation:

x ¼ �0:2749VRoþ 0:9596 ð5Þ

where x is the reactive inertinite fraction and VRo is the coal vitri-nite reflectance. It was found that the reactive inertinite fraction un-der conditions of pulverized coal combustion decreased with theincrement of the coal range [26,27]. Given that the vitrinite reflec-tance values of the coal used in this work are inside of the rangeof applicability of Eq. (5), it was an acceptable way to determinethe inertinite reactive fraction for each coal. The inertinite reactivepercentage, IR or xI, and the reactive inertinite fraction, x, for threecoals are presented in Table 1. The relationship between reactiveinertinite fraction and vitrinite reflectance (together with theregression line given by the previous equation), is given by Thomaset al. [27] and is shown in Fig. 1.

4.2. Reaction order and energy activation data

The rate of mass loss by char combustion can be consideredusing the following equation:

rc ¼ �dmdt¼ kmn ð6Þ

where k is the kinetic constant of reaction given by the Arrheniusequation, m is the remaining mass in the char, and n is the reactionglobal order. Eq. (6) is integrated considering that for a zero time ofreaction the residual mass of fuel is the initial mass, m0, which is fedto the equipment, whereas for at any time t the residual mass of fuelis m. Therefore, Eq. (7) is obtained for any reaction order, n, differentfrom 1:

m1�n �m1�n0 ¼ ðn� 1Þkt ð7Þ

When Eq. (6) is integrated for a reaction order equal the unit, Eq. (8)is created;

Lnm0

m

� �¼ kt ð8Þ

m and m0 are given in dry ash free basis (daf) and they are obtainedby the thermogravimetric analysis. At time zero the combustionprocess starts at the fixed temperature as the nitrogen flow is chan-ged to an air flow. The determination of the reaction order relies onmass and time using Eq. (7), assuming different reaction orderswith intervals of 0.1 between 0 and 3. For the case that the reactionorder is the unit, the calculations are carried out with Eq. (8). A rela-tionship seen in Fig. 2 between reaction order and combustion time.Reaction orders can be determined using the slopes p of the profilesin Fig. 2. The kinetic constant of reaction can be obtained from thevalue of the slope using the following equation:

-7

-5

-3

-1

1

3

5

7

9

0.0 3.5 7.0 10.5

m1-

n -m

o1-n an

d L

n(m

o/m

).

Time, min

n=0

n=0.1n=1.0

n=0.2

n=0.3

n=0.4

n=0.5n=0.6n=0.n=0.8n=0.9n=0.97

n=1.1

n=1.2

n=1.3

n=1.4

n=1.5

n=1.6

n=1.7La Yolanda's char produced at 900ºC, 150ms

Fig. 2. Variation of Eqs. (7) and (8) with the reaction order.

A. Rojas et al. / Fuel 96 (2012) 168–175 171

k ¼ pn� 1

ð9Þ

The reaction order value for each char is given in Table 3.Yolanda derived chars tend to burn with zero order kinetics, exceptfor chars obtained at 1100 �C, during isothermal burnout at 700and 800 �C. The chars from Thoresby and El Cerrejón coal are com-parable in terms of kinetics. At 700 �C both show 0.1 kinetic order(except El Cerrejón’s char at 1100 �C and 300 ms, which is 0.2).Isothermal burnout at 800 and 900 �C showed kinetics of zero or-der for all samples. These zero order values agree with the valuesreported in the literature at 1000 K [32]. Zero order kinetics for lig-nite derived chars lignite coal have also been reported [33–35]alongside kinetics of 0.5 for chars from anthracites coal increasingto first order kinetics for chars from sub-bituminous coal [36]. Theunits of the kinetic constant of reaction are given by the corre-sponding values of the reaction order. So, for a reaction orderof zero the units of k are mg/s, for n = 0.1, mg0.9/s and n = 0.2,mg0.8/s. The energy to start the combustion of the char samples(activation energy, E) is determined from three kinetic constants,which were obtained when each char was burned isothermally at700, 800 and 900 �C. Those kinetic constants of reaction, k, aregiven by the Arrhenius equation in the following equation:

k ¼ Ae�E=RT ð10Þ

A graph of logk against 1/T was used to calculate the apparentactivation energy, E, and the frequency factor A. The activation

Table 3Reaction order for three chars a function of combustion temperature, devolatilization tem

Combustiontemperature (�C)

Devolatilizationtemperature (�C)

La Yolanda

100 ms 150 ms 300 ms

700 900 0.0 0.0 0.01000 0.0 0.0 0.01100 0.1 0.1 0.1

800 900 0.0 0.0 0.01000 0.0 0.0 0.01100 0.1 0.1 0.1

900 900 0.0 0.0 0.01000 0.0 0.0 0.01100 0.0 0.0 0.0

energy results for each char from the different coals are presentedin Table 2. The data shows that the highest values of activationenergy was presented in chars obtained during devolatilization at1000 �C, which may be due to the lower volatile matter remainingin the chars when the coals are pyrolyzed at higher temperatures.When comparing the activation energy values of the three coals, LaYolanda’s chars have lower activation energy compared to theother two coals. For our case, activation energy does not simplyrepresent the reactivity of the coal, since the proposed model ofreactivity (Eq. (1)) incorporates coal, char and combustion charac-teristics, which are not included in the determination of the activa-tion energy.

4.3. Surface area and apparent density data

Tables 1 and 2 show the specific surface area results for thecoals and their respective chars. It is necessary consider that someof the measurements of surface area and density are not only proneto considerable error but very dependent on the method of produc-tion of the chars. Values were determined by nitrogen adsorptionat 77 K and using the BET equation. Most of the char’s samples ap-pear to have a lower surface area than the original coal. There areseveral reasons why this reduction of surface area may have oc-curred: (a) overlapping or coalescence of pores as the coal is heated[37,38]; (b) a decrease in pores longitude caused by the erosion ofits internal walls [38]; and (c) ‘fouling’ as a result of tar condensa-tion and volatile residual on the char surface blocking pores [37].Activation of carbon material can generate high surface areas (inexcess of 500 m2/g [39]) but this requires longer periods of timewhere the carbon is exposed to a heat in a partially oxidizing envi-ronment where pores can be opened by burning off residual inhomogeneities [40,41]. In this work, the DTF was operated in anitrogen atmosphere.

Apparent density results for the chars are also presented in Ta-ble 2. As the coal particles lose large quantities of volatiles to formchars, their density values appear to increase. In all three cases,apparent density increases with increasing DTF residence time.Temperature has a less pronounced effect on density. La Yolandaproduces chars with the highest apparent density (it had the high-est initial carbon content as a coal and reasonably high ash con-tent) while the chars from the El Cerrejón coal have the lowestapparent density.

4.4. Chemical reactivity data

The chemical reactivity of each char sample is determinedthrough the reaction kinetic coefficient, k, which was obtainedfor each combustion temperature, specific surface area, Ag, whichis determined by nitrogen adsorption (BET) and the fuel massburned (m0) in the combustion process by means of the thermo-gravimetric analysis. Those parameters are related to the followingequation:

perature and devolatilization time.

Thoresby El Cerrejón

100 ms 150 ms 300 ms 100 ms 150 ms 300 ms

0.1 0.1 0.1 0.1 0.1 0.10.1 0.1 0.1 0.1 0.1 0.10.1 0.1 0.1 0.1 0.1 0.20.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0

Table 4Chemical reactivity, Rc, of the combustion of three chars.

TGA combustiontemperature (�C)

DTF devolatilizationtemperature (�C)

La Yolanda Thoresby El Cerrejón

100 ms 150 ms 300 ms 100 ms 150 ms 300 ms 100 ms 150 ms 300 ms

700 900 4.29 2.38 1.84 3.03 4.88 0.87 0.62 0.89 0.601000 3.69 3.26 2.87 1.40 1.51 1.27 3.01 3.96 1.911100 3.59 5.22 7.03 1.78 0.78 0.89 1.35 1.21 2.24

800 900 4.20 2.30 1.99 1.81 2.94 0.50 0.39 0.93 0.381000 3.73 3.42 2.88 0.83 0.85 0.71 1.88 2.33 1.181100 6.49 5.31 7.57 1.09 0.48 0.54 0.78 0.76 0.79

900 900 4.68 2.62 2.22 1.91 3.03 0.50 0.41 0.55 0.371000 3.83 3.78 2.82 0.80 0.88 0.74 1.80 2.35 1.181100 3.94 3.38 4.50 1.07 0.46 0.51 0.74 0.71 0.72

172 A. Rojas et al. / Fuel 96 (2012) 168–175

Rc ¼k

Agm0ð11Þ

The chemical reactivity units vary according to the reaction or-der, so, for n = 0, the units are g/(m2 min), for n = 0.1, g0.9/(m2 min)

Table 5Parameters of chemical reactivity according to Eq. (13).

Chars from coal k0 a b

La Yolanda 2.00 � 10�4 ± 1.6 � 10�5 0.461 ± 0.115 0.266 ± 0.073Thoresby 2.28 � 10�4 ± 1.8 � 10�5 1.300 ± 0.448 0.248 ± 0.054El Cerrejón 2.10 � 10�4 ± 2.2 � 10�5 1.130 ± 0.111 0.258 ± 0.044All coals 2.00 � 10�4 ± 1.8 � 10�5 0.459 ± 0.045 0.242 ± 0.054

(a)

(b)

R2 = 0.350

0

0.03

0.06

0.09

0.12

0.15

0 0.03 0.06 0.09 0.12 0.15

Pred

icte

d va

lues

Observed values

R2 = 0.933

0.00

0.02

0.04

0.06

0.08

0.10

0 0.02 0.04 0.06 0.08 0.1

Observed values

Pre

dict

ed v

alue

s

Fig. 3. Calculated and observed value of the chemical reactivity, Rc, for chars from (a) Y

and for n = 0.2, g0.8/(m2 min). In general, the chemical reactivityunits are given by g1�n/(m2 min). Now, it can be determined thechemical reactivity in units of g/(g min), through the followingexpression:

R0cg

g min

� �¼ Rc

ggnm2 min

� �� Ag

m2

g

� �� ½m0hgi�n ð12Þ

The chemical reactivity for the combustion of the three chars isgiven in Table 4. It was found that for all the operation conditions,chars from La Yolanda coal presented the highest chemical reactiv-ity values followed by El Cerrejón chars and Thoresby chars. As it isshown in Table 4, only small changes can be seen, which might re-sult from the degree of accuracy of the method or from small vari-ations in the degree of devolatilization found in the chars [47].

(c)

(d)

R2 = 0.885

0

0.02

0.04

0.06

0.08

0 0.02 0.04 0.06 0.08

Observed values

Pred

icte

d va

lues

R² = 0.714

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Pred

icte

d va

lues

Observed values

La Yolanda

Thoresby

El Cerrejon

olanda coal (b) Thoresby coal (c) Yolanda coal (d) three coals, according to Eq. (1).

A. Rojas et al. / Fuel 96 (2012) 168–175 173

4.5. Validation of the correlation

To confirm the validity of the proposed char combustion kineticequation, a variety of various char samples were examined. Eq. (1)can be rewritten to create:

Rc ¼ k0r2nAg3n�1

tv

!E

RT

� �a V þ Lþ xIMM þ ð1� xÞI

� �b

ð13Þ

For the validation of this expression, a non-lineal least-squaremethod was used to find the values of the constants k0, a and b,that minimized the sum of the squares of the vertical deviations(Dvs) for all experimental data. The vertical deviation is given by:

Dv ¼ RciðObservedÞ � RciðCalculatedÞ ð14Þ

Using the Walsh and Diamond method [42], the function objective(Fobj) to minimize is:

Table 6Parameters of chemical reactivity according to Eq. (16).

Char from coal k0 a b

La Yolanda 1.78 � 10�4 ± 1.18 � 10�5 0.460 ± 0.109 0.108 ± 0.022Thoresby 2.20 � 10�4 ± 5.83 � 10�6 1.299 ± 0.005 0.129 ± 0.005El Cerrejón 2.57 � 10�4 ± 1.42 � 10�6 1.133 ± 0.003 0.116 ± 0.001All coals 1.90 � 10�4 ± 7.60 � 10�6 0.474 ± 0.062 0.104 ± 0.013

(a)

(b)

R² = 0.349

0.00

0.03

0.06

0.09

0.12

0.15

0.00 0.03 0.06 0.09 0.12 0.15

Pred

icte

d va

lues

Observed values

R² = 0.933

0.00

0.02

0.04

0.06

0.08

0.10

0.00 0.02 0.04 0.06 0.08 0.10

Pred

icte

d v

alue

s

Observed values

Fig. 4. Calculated and observed value of the chemical reactivity, Rc, for chars from (a) Y

Fobj ¼XN

i¼1

Dv2

¼XN

i¼1

Rci � k0r2nAg3n�1

tv

!E

RT

� �a V þ Lþ xIMM þ ð1� xÞI

� �b" #" #2

ð15Þ

where N is the number of experimental observations.The values of the parameters, k0, a and b, with their respective

uncertainties for each coal, are presented in Table 5. The observedand calculated values of the chemical reactivity for the La Yolanda,Thoresby and El Cerrejón coals are shown in Fig. 3a–c respectively.The lineal regression coefficients in these figures show good agree-ment for the observed and calculated values of chemical reactivityfor El Cerrejón and Thoresby (R2 = 0.885 and 0.933, respectively).However, La Yolanda coal gave a poor regression coefficient(R2 = 0.350). This may be due to its higher vitrinite reflectance(approximately 1%) which was that was not used as a parameterin the validation of the chemical reactivity equation. This couldmean that there might be problems when using the model to com-pare coals across a wider rank range. Fig. 3d shows the observedand calculated values of chemical reactivity for all the chars. Theoverall regression coefficient was far from unity (R2 = 0.714). Thevalues that minimized the function objective for all the chars usingthe model represented by Eq. (13) are also shown in Table 5. Smalldifferences exist between the parameter values for each coal type.

In order to broaden the potential applicability of the model, analternative Equation (model 2 – %Unreactives) was developed (Eq.

(c)

(d)

R² = 0.885

0.00

0.02

0.04

0.06

0.08

0.00

Pred

icte

d va

lues

Observed values

R² = 0.752

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Pred

icte

d V

alue

s

Observed Values

La Yolanda

Thoresby

0.02 0.04 0.06 0.08

El Cerrejon

olanda coal (b) Thoresby coal (c) Yolanda coal (d) three coals, according to Eq. (2).

R² = 0.9632

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.02 0.04 0.06 0.08 0.1 0.12

Rc,

Mod

el 1

- m

acer

als

Rc, Model 2 - %U

Fig. 5. Chemical reactivity, Rc, correlation between model 1 – Maceral and model 2–%Unreactives.

174 A. Rojas et al. / Fuel 96 (2012) 168–175

(2)), which integrates the ‘‘unreactive’’ number (%U) into thedimensionless number that considers the coal characteristics. %Uis a value based on the reflectance of the whole coal and is deter-mined by image analysis [16,21,43–45]. This number representsthe percentage of less reactive components in the coal regardlessof maceral type. Eq. (2) can be rewritten as it is shown in the fol-lowing equation:

Rc ¼ k0r2nAg3n�1

tv

!E

RT

� �a 100�%U%U

� �b

ð16Þ

Eq. (16) was also validated using Eqs. (14) and (15). The values ofthe parameters, k0, a and b, with their respective uncertainties foreach coal, are presented in Table 6. The observed and calculated val-ues of the chemical reactivity for the La Yolanda, Thoresby and ElCerrejón coals are shown in Fig. 4a–c respectively. The lineal regres-sion coefficients presented in these figures also show good correla-tion for El Cerrejón and Thoresby (R2 = 0.885 and 0.933,respectively), whereas La Yolanda coal gives the lowest regressioncoefficient (R2 = 0.349). As it is seen, those results are similar com-pared to those obtained under Eq. (13), which uses maceral contentas a dimensionless number. Fig. 4d shows the observed and calcu-lated values of chemical reactivity for all the chars. Values that min-imized the function objective for all the chars using the modelrepresented by Eq. (16) are also shown in Table 6. As it is shown,results of the parameters k0, a and b of the individual coal are quitesimilar.

Under the experimental conditions of this work, it can be seenthat model 1 – Macerals is in good agreement with the experimen-tal results using coals of high volatile matter content, whereas thatmodel 2 – %Unreactives, described in Eq. (2) shows a better agree-ment with the experimental values of the reactivity parameter forall chars. %Unreactives value was developed for predicting finalburnout performance in combustion systems [22,46,47], and itmight be that different thresholding (or more thresholds) wouldbe more suitable for the kinetic models. However, the reactivityprofile that is used to generate the %Unreactives number can alsobe used to quantify macerals and vitrinite reflectance by usingthe peaks and position of peaks from the reflectance profile[15,21–22]. This approach would allow a universal parameter tobe created that includes reactivity, maceral composition and vitri-nite reflectance, thus extending the validity of the model to a largerrange of coal (sub-bituminous to medium volatile bituminous).The values of the dimensionless number which validates Eqs.(13) and (16) are shown in Table 7. The results indicate that themain difference for both models is the dimensionless number thatis derived for coal characteristics. A comparison between the reac-tivity parameters obtained by the models is shown in Fig. 5. It isworth noting a good agreement exists between both models, whichis represented by the high regression coefficient (R2 = 0.96). Theintroduction of further thresholding levels for% U would allow alarger rank range of coals to be considered which would inevitablyreduce its correlation with the dimensionless number for macerals,since coals can have a wide range of maceral compositions across awide range of ranks [16].

Finally, Eqs. (13) and (16), which evaluate a, b and k0 constants,are most complete than Eqs. (6) and (10), which evaluates the con-

Table 7Dimensionless number range for Eqs. (13) and (16).

Eq. (13) Eq. (16)

11:74 < r2n A3n�1g

tv

� �< 472:44 11:74 < r2n A3n�1

g

tv

� �< 472:44

0:13 < EaRT

� < 1:36 0:13 < Ea

RT

� < 1:36

4:76 < VþLþxIMMþð1�xÞI

� �< 9:55 26:17 < 100�%U

%U

� < 587:24

stants k, A and E, due to those equations include petrographic andstructural parameters of the chars.

5. Conclusions

Two versions of a new intrinsic kinetic model have been devel-oped for predicting char combustion reactivity from pulverizedcoals. Both models showed the relationship between three dimen-sionless numbers. The first dimensionless number represents charcharacteristics; the second one is related to combustion character-istics and the third one corresponds to the coal characteristics.Both models were validated to predict the intrinsic reactivity ofthree coals, two from Colombia and one from UK, and they showedthat exist a good correlation between experimental and predictedvalues for high volatile bituminous coals. More validation work isneeded to prove that this model can be used to predict combustionreactivity. A more comprehensive parameter will be developedfrom the %Unreactives profile that takes into account vitrinitereflectance (rank of the coal), maceral content and total reactivity.This parameter will allow the model to be used on a larger rankrange of coals.

Acknowledgments

The authors wish to thank Colombian Institute of Science (COL-CIENCIAS) for their financial support of this work. Also the techni-cal support of the Universidad del Valle and The University ofNottingham is acknowledged.

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