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Numerical Investigations of CO/CO2 Ratioin Char CombustionWei He a , Rong He a , Takamasa Ito b , Toshiyuki Suda b & Jun'ichiSato ca Department of Thermal Engineering, Tsinghua University, Beijing,Chinab Research Laboratory, IHI Corporation, Yokohama, Japanc IHI Inspection & Instrumentation Co., Tokyo, Japan

Available online: 24 May 2011

To cite this article: Wei He, Rong He, Takamasa Ito, Toshiyuki Suda & Jun'ichi Sato (2011): NumericalInvestigations of CO/CO2 Ratio in Char Combustion, Combustion Science and Technology, 183:9,868-882

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NUMERICAL INVESTIGATIONS OF CO/CO2 RATIOIN CHAR COMBUSTION

Wei He,1 Rong He,1 Takamasa Ito,2 Toshiyuki Suda,2 andJun’ichi Sato31Department of Thermal Engineering, Tsinghua University, Beijing, China2Research Laboratory, IHI Corporation, Yokohama, Japan3IHI Inspection & Instrumentation Co., Tokyo, Japan

The CO/CO2 ratio of reactions during char combustion was investigated numerically. The

simulations used the pore model with fractal properties, a gas diffusion model suitable for

fractal pores, and a carbon-oxygen reaction model to describe the char oxidation. The CO/

CO2 ratio in the primary reactions was derived assuming Gaussian distributions of the acti-

vation energies and Maxwell distribution of the oxygen molecular velocity. The numerical

simulations of the char combustion for various particle sizes, pore structures, and tempera-

tures revealed that the effects of the secondary reactions and the pore structure on the CO/

CO2 ratio are the main reasons why different researchers obtain different experimental

results for of the CO/CO2 ratio.

Keywords: Char oxidation; CO=CO2 ratio; Fractal; Pores

1. INTRODUCTION

Char combustion is very important in coal combustion, as it produces most ofthe heat release during combustion. Experiments have indicated that the char com-bustion products always include CO2 and CO gases. There have been many discus-sions in the literature as to whether CO or CO2 is the primary char combustionproduct (Arthur, 1951; Ayling and Smith, 1972; Phillips et al., 1970; Roberts andSmith, 1973; Rossberg, 1956; Tognotti et al., 1990; Walker et al., 1959). The twomain opinions are that CO2 is the primary product with the generated CO2 thenreacting with the carbon surface to form CO and that CO is the primary productwith the generated CO then reacting with the O2 in the gas phase to produce CO2.The discussions of these two mechanisms have led to agreement that both CO2

and CO can be primary products in the carbon-oxygen reaction (Hart et al.,1967), which is expressed by the CO=CO2 ratio.

The chemical reaction energy produced when CO2 is the product of thecarbon-oxygen reaction is quite different from when CO is the product. Therefore,

Received 5 May 2010; revised 22 January 2011; accepted 4 March 2011.

Address correspondence to Rong He, Department of Thermal Engineering, Tsinghua University,

Beijing 10084, China. E-mail: rhe@mail.tsinghua.edu.cn

Combust. Sci. and Tech., 183: 868–882, 2011

Copyright # Taylor & Francis Group, LLC

ISSN: 0010-2202 print=1563-521X online

DOI: 10.1080/00102202.2011.569803

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the char particle temperature history largely depends on the CO=CO2 ratio(Goel et al., 1996). A small difference in the CO=CO2 ratio of the char oxidation pro-ducts can result in differences of hundreds of degrees in the combustion temperature(Tognotti et al., 1990). Therefore, the CO=CO2 ratio must be better understood toexplain the char combustion mechanism. During char combustion, the primaryCO2 and CO produced in heterogeneous reactions usually reacts in secondary reac-tions of COþO2 and CþCO2. Therefore, analyses of the CO=CO2 ratio for the pri-mary heterogeneous reactions must be careful to not contaminate the results with theeffects of secondary reactions. Measures such as adding an inhibitor or using highflow rate are used to avoid secondary reactions (Arthur, 1951; Day and Walker,1958; Rossberg, 1956). Some experiments have shown that the CO=CO2 ratio varieswith temperature, oxygen pressure, and particle size (Froberg and Essenhigh, 1979;Kurylko and Essenhigh, 1973; Mathias et al., 2003; Tognotti et al., 1990), while someother researchers only showed an exponential relation between the ratio and tem-perature, such as CO=CO2¼A exp(�B=T) (Amariglio and Duval, 1966; Du et al.,1991) where T is the temperature.

A rigorous explanation for the CO=CO2 ratio based on theoretical models isnot yet available. A plausible explanation is that the CO=CO2 ratio is a functionof temperature and depends on many other factors (e.g., reaction devices, catalyticeffect of the impurities, particle pore structure, experimental measurement errors,oxygen pressure, secondary reactions) that may explain the huge differences betweendifferent researchers. The effects of these many factors mixed together make it diffi-cult to find the effect of a particular factor.

This paper gives an expression for the CO=CO2 ratio derived theoreticallyusing the kinetic theory of gases with numerical simulations to investigate theCO=CO2 ratio for different pore structures, oxygen pressures, and temperatures.The expression for the CO=CO2 ratio, which includes parameters determined bycomparison with low temperature experimental results (Du et al., 1991), could beexpanded to high temperatures range. The numerical method can easily separatethe secondary reactions from the primary reactions, which is hard to do experimen-tally, especially for secondary reactions inside char pores. The numerical method canalso easily isolate the effect of the pore structures from other factors. Thus, thesenumerical results are used to explain the mechanisms that drive the CO=CO2 ratioleading to a more general expression for the ratio.

2. NUMERICAL MODELS

2.1. Pore Models

Char particles are typical porous media with fractal properties (Avnir et al.,1983; Avnir et al., 1985; He et al., 1998; Pfeifer and Avnir, 1983; Salatino et al.,1993). The pores of coal char particles are not only diffusion channels for the gas-eous reactants and products, but also provide surfaces and spaces for the chemicalreactions. Hence, the pore structure has an important influence on the coal charcombustion characteristics.

The effects of the pore structure on the gas diffusion are illustrated byFigures 1a and 1b, which show two coal char pore models having similar porosities

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and specific surface areas, but very large differences in the diffusion and reactionproperties. These differences are due to the complexity of the pore structure, andcan be described by their fractal dimension. Therefore, the fractal properties of poresinfluence the reaction and the CO=CO2 ratio.

This analysis used char models with fractal properties generated by a randomwalk algorithm proposed by Liang et al. (2007). Numerous char particle models withdifferent porosities and fractal dimensions can be obtained by changing the randomwalk parameters. These pore models not only reflect the fractal properties of the charpores, but also look very much like the actual pores (Liang et al., 2007).

There are many methods to define the fractal dimensions of porous char par-ticles. Here, the fractal dimensions of porous chars were measured using the mercuryporosimetry test, with the fractal dimensions defined as (He et al., 1998):

dSðrÞdr

/ r�D ð1Þ

where r is the pore radius, S(r) is the accumulated surface area, dS(r)=dr is the sur-face probability distribution function, and D is fractal dimension of the porous char.The fractal dimension, D, was obtained by taking the logarithm of both sides ofEq. (1), with D as the negative of the slope of Ln(dS(r)=dr�Ln(r). This definitionreflects some of the pore geometry characteristics, especially the effects of the geo-metric structure on the fluid diffusion into the pores.

2.2. Diffusion Model

The pore shapes in char particles are very complex with fractal characteristics(Avnir et al., 1983; Avnir et al., 1985; He et al., 1998; Pfeifer and Avnir, 1983;Salatino et al., 1993). This pore structure has a significant impact on the diffusionof the reactants and the products through the pores. However, traditional char com-bustion models have been based on the classic diffusion laws of Fick’s law andKnudsen’s law, which do not describe the effect of the pore fractal characteristicson the char combustion. In fact, gas diffusion in fractal medium does not followedFick’s law and Knudsen’s law (Costa et al., 2003; Gefen et al., 1983; Levitz, 1997).Cao and He (2010) developed a gas diffusion model in fractal pores using the kinetictheory of gases to study gas diffusion in fractal porous media. The results with this

Figure 1 Gas diffusion in two pores with similar porosities and specific surface areas.

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diffusion model were found to be more representative of the actual diffusing process.Thus, this model is used here to describe the gas diffusion in the particle model basedon its fractal properties.

2.3. Reaction Model

Carbon oxidation is a complex process involving many elementary steps,including adsorption, formation of (C-O) complexes, desorption, and other steps(Annamalai and Ryan, 1993; Haynes, 2001). The main objective of this analysis isto study the effects of the pore structure on the CO=CO2 ratio. Thus, the analysisis simplified by using a one-step reaction model (Higuera, 2008) to describe thechemical reaction occurred during the char combustion instead of a multiple elemen-tary reaction model. In this way, the analysis can focus on the pore structure effect,without large errors in the chemical effects. The chemical reactions for the char com-bustion used in this model are

CðsÞ þ1

2O2ðgÞ ! COðgÞ DH0 ¼ �111:5 kJ=mol ðaÞ

CðsÞ þO2ðgÞ ! CO2ðgÞ � 393:8 kJ=mol ðbÞ

COðgÞ þ1

2O2ðgÞ ! CO2ðgÞ � 282:2 kJ=mol ðcÞ

CðsÞ þ CO2ðgÞ ! 2COðgÞ � 170:8 kJ=mol ðdÞ

Reactions (a), (b), and (d) are heterogeneous reactions, while Reaction (c) is ahomogeneous reaction. Reactions (a) and (b) are primary reactions occurring on thecarbon surface, while (c) and (d) are secondary reactions.

The reactions between the solid carbon and gaseous oxygen are heterogeneousreactions described using the classical simple collision theory (SCT; Fowler andGuggenheim, 1949). The SCT theory is based on molecular-kinetic theory, withthe chemical reaction a result of molecular collisions that cannot occur if the colli-sion intensity of the molecules does not exceed an energy threshold (Fowler andGuggenheim, 1949).

The distances between the solid molecules are very short, with the solid mole-cules vibrating in a small range near a fixed location. Therefore, the translationalenergy of the O2 molecules can be assumed to represent the collision intensitybetween the O2 molecules and the solid carbon surface. The reaction only occurswhen an oxygen molecule collides with the carbon surface with a translational energyexceeding a given threshold (Fowler and Guggenheim, 1949). The translationalenergy of the oxygen molecules satisfies the Maxwell velocity distribution (Reif,1965):

f ðeÞ ¼ 2p1

pkT

� �32

exp � ekT

� �e12 ð2Þ

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where e is the translational energy of the gas molecule (kJ=mol), kis the Boltzmannconstant and T is the gas temperature (K). The proportion of oxygen molecules withtranslational energy between E and Eþ dE is f(E)dE.

Due to the complex surface structure of the carbon material, the adsorptionand desorption of (C-O) complexes on the carbon surface possess a broad rangeof binding energies and exhibit noticeable differences in the activation energies(Du, 1990; Niksa and Kerstein, 1986). Therefore, the threshold energies for Reac-tions (a) and (b) are not fixed, but are expressed by a probability distribution. Duet al. (1990) used the temperature programming desorption (TPD) technique toinvestigate the dynamics of (C-O) complexes on carbon surfaces to show that theactivation energy distribution approximately satisfies a Gaussian distribution. There-fore, the energy thresholds for Reactions (a) and (b) are approximated by Gaussiandistributions.

Suppose that Reactions (a) and (b) are mutually independent. Let /1(E1) and/2(E2) represent the energy threshold distribut ion functions for Reactions (a) and (b):

/1ðE1Þ ¼ 1ffiffiffiffiffiffiffi2pr1

p exp � ðE1�E1Þ22r2

1

� �

/2ðE2Þ ¼ 1ffiffiffiffiffiffiffi2pr2

p exp � ðE2�E2Þ22r2

2

� �8<: ð3Þ

where E is the mean value (kJ=mol) and r is the standard deviation (kJ=mol). Whenan oxygen molecule with translational energy e collides with a carbon atom, therecan be (a) no reaction, (b) a reaction producing CO, or (c) a reaction producingCO2. The threshold energies of Reactions (a) and (b) are E1 and E2, which satisfyprobability distributions and /1(E1) According to simple collision theory (Reif,1965), if the translational energy e of an oxygen molecule is less than E1 and E2, thisoxygen molecule does not react with the carbon. If E1< e<E2, Reaction (a) occurs,but not Reaction (b). Similarly, if E2< e<E1, Reaction (b) occurs.

The probability of each combination is then:

(a) e�E2�E1. This collision will not result in any reaction. According to the basicmultiplication and addition principles of probability theory (Chow, 1988), theprobability is

P1 ¼Z þ1

e/2ðE2Þ

Z þ1

E2

/1ðE1ÞdE1

� �dE2 ð4Þ

(b) e�E1�E2. This collision will also not result in any reaction and its probabilityis

P2 ¼Z þ1

e/1ðE1Þ

Z þ1

E1

/2ðE2ÞdE2

� �dE1 ð5Þ

(c) E2� e�E1. This collision will produce CO2 and its probability is

P3 ¼Z þ1

e/1ðE1ÞdE1 �

Z e

0

/2ðE2ÞdE2 ð6Þ

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(d) E1� e�E2. This collision will produce CO and its probability is

P4 ¼Z e

0

/1ðE1ÞdE1 �Z þ1

e/2ðE2ÞdE2 ð7Þ

(e) E1�E2� e. This collision will produce CO2 and its probability is

P5 ¼Z e

0

ðE2ÞZ E2

0

/1ðE1ÞdE1

� �dE2 ð8Þ

(f) E2�E1� e. This collision will produce CO and its probability is

P6 ¼Z e

0

/1ðE1ÞZ E1

0

/2ðE2ÞdE2

� �dE1 ð9Þ

With P1þP2þP3þP4þP5þP6¼ 1. For these combinations, let x0 be thenonreaction probability, x1the probability to produce CO and x2 the probabilityto produce CO2. Then

x0ðeÞ ¼ P1 þ P2 ¼Rþ1e /1ðE1ÞdE1 �

Rþ1e /2ðE2ÞdE2

x1ðeÞ ¼ P4 þ P6 ¼R e0 /1ðE1ÞdE1 �

Rþ1e /2ðE2ÞdE2

þR e0 /1ðE1Þ

R E1

0 /2ðE2ÞdE2

� �dE1

x2ðeÞ ¼ P3 þ P5 ¼Rþ1e /1ðE1ÞdE1 �

R e0 /2ðE2ÞdE2

þR e0 /2ðE2Þ

R E2

0 /1ðE1ÞdE1

� �dE2

8>>>>>>><>>>>>>>:

ð10Þ

In char pore models, each gas element contains many oxygen molecules andother gas molecules. Not all the oxygen molecules that collide with the carbonsurface react with the carbon, but only those molecules with translational energieslarger than the threshold energies E1 or E2. The molecular translational energies attemperature T can be calculated by Eq. (1). Then define Pnon as the ratio of non-reacting molecules to all molecules, PCO as the ratio of molecules producing CO toall molecules and PCO2

as the ratio of molecules producing CO2 to all molecules.Then

Pnon ¼Rþ10 x0ðeÞf ðeÞde

PCO ¼Rþ10 x1ðeÞf ðeÞde

PCO2¼

Rþ10 x2ðeÞf ðeÞde

8><>: ð11Þ

The CO=CO2 ratio for this primary reaction is

CO

CO2¼

2Rþ10 x1ðeÞf ðeÞdeRþ10 x2ðeÞf ðeÞde

ð12Þ

The factor 2 in Eq. (12) is because the stoichiometric ratio between O2 and COin Reaction (a) is 0.5. Equation (12) then gives the CO=CO2 ratio in one element attemperature T. Usually, for pulverized coal, the particles are quite small and the

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temperature gradient inside a particle is small enough so that Eq. (12) can approxi-mate the primary CO=CO2 ratio for the whole particle based on the particle tempera-ture. Equation (12) describes the CO=CO2 ratio for the primary reaction as a functionof only the temperature and chemical nature of the char and not the particle structure.

The four parameters r1; r2;E1; and E2 and in Eq. (12) are unknown but canbe determined by comparing the numerical results with experimental data as dis-cussed in the next section. In the numerical simulations, the secondary Reactions(c) and (d) are assumed to occur simultaneously with primary Reactions (a) and(b). The oxidation of CO in reaction (c) can be calculated by (Howard et al.,1973):

d½CO�=dt ¼ �1:3� 1011½CO�½H2O�1=2½O2�1=2 expð�15105=TÞ ð13Þ

where [H2O] is approximately equal to 0.0025mol=L, which is the saturated watervapor content of air at 1 atm and 308.15K. The reaction rate for Reaction (d) canbe calculated as (Annamalai and Ryan, 1993):

d½CO2�=dt ¼ �0:034 p0:34s ½CO2� expð�109000=RTÞ ð14Þ

where P5 is the CO2 pressure (atm); [CO], [CO2], [H2O], and [O2] are the gas con-centrations (mol=L); and R is the universal gas constant.

3. RESULTS AND DISCUSSION

Many researchers believe that the CO=CO2 ratio increases with increasing reac-tion temperature. Above 1300K, CO is the dominant product of the primary reac-tions (Smoot, 1993). At temperatures of 1600�1700K, the CO2 content is onlyaround 15%, while at 1800K the CO2 can be neglected (Mitchell, 1988). But, below1073K the CO=CO2 ratio is low to about 0.3 (Lewis and Simons, 1979). r1, r2, E1,and E2 in Eq. (12) were determined based on the experiments results of Du et al.(1991) for carbon soot oxidation at low temperatures. Their experimental resultswere used because (a) soot is high-purity carbon so the catalytic effect of impuritiesis small; (b) the experimental temperature range was 670–890K, so Reactions (c) and(d) are slower than Reactions (a) and (b) by several orders of magnitude so the CO=CO2 ratio is less contaminated by the secondary reactions; and (c) the soot particlesin these experiments were very small (about 43 nm), so the gas diffusion resistance inthese small particles is very large and the pore effect and the secondary reactions inthe pores can be neglected. Thus, the results of Du et al. (1991) can be assumed torepresent the primary CO=CO2 ratio at these temperatures.

The particle models used in numerical simulation were constructed using100� 100� 100 cubic elements. Pores in these particle models were generated usinga random walk algorithm (Liang et al., 2007). A typical pore model is shown inFigure 2 where the black cubes are solid carbon elements and the white cubes arepore elements. To compare with the experiments of Du et al. (1991), the char modelhad a particle size of 50 nm, a porosity of 31.9%, and a fractal dimension of 0.807.Comparison of the overall CO=CO2 ratio (including the primary and secondary reac-tions) from the numerical simulations with this char model with the experimental

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results gave the parameters in Eq. (12) as

E1 ¼ 60:5 kJ=mol; r1 ¼ 2:0 kJ=molE2 ¼ 54:0 kJ=mol; r2 ¼ 4:5 kJ=mol

�ð15Þ

The value of parameter E2 (¼54 kJ=mol) is cited from He et al. (2002), and theother three parameters are determined by multidimensional least-squares regressionalgorithm. The algorithm was realized using Matlab program to do some iterate cal-culations, with the initial values of E1 ¼ 60 kJ=mol, r2¼ 2.0 kJ=mol, and r1¼ 2.0 kJ=mol. The numerical and experimental results are compared in Figure 3 where thesquares are the experimental data and the triangles are the numerical results. Becausethe pore effects in such small particles are very limited, other char models with dif-ferent porosities and fractal dimensions would give similar results. The CO=CO2

ratio in the primary reactions from Eq. (12) with the parameters in Eq. (15) is quiteclose to the numerical results calculated using with the char pore model includingboth the primary and secondary reactions. The simulated char particle size is closeto the experimental soot particle size, but different chemical reaction mechanismsin the char and the soot may results in some differences.

Figure 3 Comparison of numerical results with Du et al.’s (1991) experimental data.

Figure 2 Typical numerical pore model.

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The primary CO=CO2 ratio from Eq. (12) is based on a theoretical derivation.Because high temperature experiments to determine the CO=CO2 ratio are difficult,most experiments are at low temperatures. The model in Eq. (12) was verified byexperimental data in Figure 3, at a low temperature range, which is when char com-bustion situations occur, especially in fluidized and fixed beds. At high temperaturessuch as in a pulverized coal furnace flame, although Eq. (12) can theoretically beused, it lacks experimental validation. An available empirical formula for high tem-peratures is different from Eq. (12). For example, the empirical formula CO=CO2¼ 120 exp(�3200=T) from Du et al. (1991) differs from Eq. (12; Hayhurstand Parmar, 1998).

In this study we sought to investigate the effect of the pore structure, so weonly considered the secondary reactions insight the particle pores, without the sec-ondary reactions occurring outside of the particle because they have no relationshipwith the pore structure. Figure 4 shows the CO=CO2 ratio changes over time usingthe fractal particle model for four different situations. The results show that whenthe secondary reactions are not considered, the CO=CO2 ratio does not change overtime and is not related to the pore structure. When the secondary reactions areincluded, the CO=CO2 ratio gradually tends toward a stable value as the primaryand secondary reactions reach equilibrium. This shows that the primary CO=CO2

ratio is associated with the temperature and the chemical nature of the char and isnot related to the partial pressure of the oxygen. Thus, correlation between the over-all CO=CO2 ratio and the pore structure is due to the effect of the pore structure onthe secondary reactions.

There have been various discussions of the effects of the oxygen pressure on theoverall CO=CO2 ratio. Some experiments showed no effects (Arthur, 1951; Pfeiferand Avnir, 1983; Rossberg, 1956), while others showed that the CO=CO2 ratiodecreased with increasing oxygen pressure (Avnir et al., 1983; Avnir et al., 1985;Tognotti et al., 1990). The single-particle experiments by Tognotti et al. (1990) on

Figure 4 CO=CO2 ratio changes over time at 1100K (Char model: size¼ 10mm, porosity¼ 30.75%, fractal

dimension¼ 1.123).

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an electrodynamic balance showed that the overall CO=CO2 ratio is smaller at higheroxygen pressures, with negligible differences at low temperatures (T< 1000K), butsignificant differences at high temperatures (T> 1000K). The present numericalresults also show this trend, with the secondary reactions and the overall CO=CO2

ratio decreasing with increasing oxygen pressure. At low temperatures the CO=CO2 ratios are quite close for different oxygen pressures, but at high temperaturesthe differences are quite large, as shown in Figure 5. At low temperatures the second-ary reactions are relatively slow and can be neglected, while at high temperatures thesecondary reactions are much faster. Therefore, low-temperature experiments maynot show the effect of oxygen pressure on the CO=CO2 ratio, while high-temperatureexperiments have an obvious effect of oxygen pressure.

The secondary reactions depend strongly on the gas diffusion. If the gas dif-fusion inside the pores is slow, there may be more time for secondary products toform in the pores. For the same pore structure, the gases in large particles also havelarge reaction times inside the pores to produce more secondary products, whichreduce the CO=CO2 ratio, as illustrated in Figure 6. Figure 6 also shows that experi-ments with smaller particles size are better for determining the parameters in Eq. (15)because of the limited secondary reactions.

For the same particle size, different pore structures allow the diffusion charac-teristics, which affect the secondary reactions. Figure 7 shows the predicted overallCO=CO2 ratios for different char models with the same particle sizes but differentporosities and fractal dimensions. The results show how the pore structures affectthe gas diffusion and, hence, the time for the gases to react within the pores. Thisaffects the secondary reactions in the pores, resulting in different overall CO=CO2

ratios.The secondary reactions significantly affect the overall CO=CO2 ratio

and always occur, especially at high temperatures. The secondary reactions occurin- and outside of pores, with the reactions inside the pores extremely difficult to

Figure 5 Effect of oxygen partial pressure on overall CO=CO2 ratio. Char model: size¼ 10 mm,

porosity¼ 29.9%, fractal dimension¼ 0.96.

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measure in experiments. In addition, char particles from different parent coalsusually have different pore structures that also influence the gas diffusion in thepores. Therefore, different experimental conditions lead to varying conclusions forthe CO=CO2 ratio. Thus, the theoretical model in Eq. (12) for the CO=CO2 ratiodeveloped from the primary reactions can be used to more accurately predictionthe overall CO=CO2 ratio. Equation (12) may also more accurately predict theCO=CO2 ratio at high temperatures, which is difficult to measure experimentally.

The Eq. (12) was derived based on SCT model, with assumed that the energythreshold values for the heterogeneous Reactions (a) and (b) approximately are

Figure 7 Overall CO=CO2 ratios for different char models. Particle size¼ 50mm; oxygen partial

pressure¼ 0.2 atm. Char model 1: porosity¼ 19.2%, fractal dimension¼ 1.40; Char model 2: porosity¼31.9%, fractal dimension¼ 0.81; Char model 3: porosity¼ 40.3%; fractal dimension¼ 1.33.

Figure 6 Effect of particle size on overall CO=CO2 ratio. Temperature¼ 1300K; oxygen partial

pressure¼ 0.2 atm; porosity¼ 31.9%; fractal dimension¼ 0.81.

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Gaussian distributions. The SCT model is established on the molecular-kinetictheory, it considers the chemical reaction as a result of the molecules collision (Fow-ler and Guggenheim, 1949). Although there are some differences between the SCTmodel and the actual process which involve chemisorption and overdesorption pro-cesses. However, by adjusting the parameters of the SCT model, the producing ratesof CO and CO2 can be controlled close to the actual state. Besides, at high tempera-ture, the chemisorptions rapidly desorpted and the intermediate process are veryshort, in this case, so at this situation the SCT model is close to the actual situation.In pulverized coal (PC) boiler, the burning char particles temperature rise quickly tohigh temperature, which makes the chemisorptions desorbed rapidly. Therefore, Eq.(12), based on the SCT model, can describe the CO=CO2 ratio at different tempera-tures with proper accuracy.

4. CONCLUSIONS

The CO=CO2 ratio of the primary reactions for char combustion was investi-gated, including the effect of the secondary reactions. The initial reactions of oxygenwith carbon produce CO and CO2 in the primary reactions. Then the CO and CO2

products can react with either oxygen or carbon in secondary reactions. The CO=CO2 ratio for the primary reactions is derived based on the classic Maxwell molecu-lar velocity distribution and a Gaussian distribution of the activation energies. Theparameters for the Gaussian distributions of the activation energies were determinedby comparing numerical results with previous experimental data. The numericalmodel includes the oxygen diffusion and reactions in fractal char pore models.

The char particle temperature is closely related to the secondary reaction rates,with higher temperatures resulting in more secondary reactions. Thus, the tempera-ture influences the reaction rate, the primary CO=CO2 ratio and the diffusion rate.The reaction rate, the CO=CO2 ratio, and the diffusion also affect the reaction heatrelease rate and the heat convection, thus affecting the particle temperature. Thechar particle pores, which act as diffusion channels for the gases and provide loca-tions for the chemical reactions, have a significant impact on the chemical reactions,the gas diffusion resistance and the global CO=CO2 ratio.

Simulations of char combustion for different particle sizes, pore structures, andtemperatures were used to analyze the effects of the secondary reactions on the CO=CO2 ratio to explain how different studies have measured very different CO=CO2

ratios. A theoretical equation was derived for the CO=CO2 ratio, with parametersdetermined from low-temperature experiments that gives relatively accurate primaryCO=CO2 ratios at low temperature. More high temperature experiments are neededto determine the parameters for high temperatures. Even so, this equation still givesbetter qualitative trends at high temperature.

ACKNOWLEDGMENTS

The work was financially supported by the IHI Corporation (Japan), theNational Natural Science Foundation of China (No. 50676048) and the ChinaSpecial Funds for Major State Basic Research Projects (No. 2006CB200305).

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NOMENCLATURE

D pore fractal dimensionE1 threshold energy of reaction (a)E2 threshold energy of reaction (b)E1 mean value of the Gaussian distribution /1(E1) (kJ=mol)E2 mean value of the Gaussian distribution /2(E2) (kJ=mol)k Boltzmann constantPnon ratio of non-reacting moleculesPCO ratio of molecules producing COPCO2

ratio of molecules producing CO2

Ps CO2 pressure (atm)r pore radius (m)S accumulated specific pore surface area (m2=kg)T gas temperature (K)x0 non-reaction probabilityx1 probability of producing COx2 probability of producing CO2

r1 standard deviation of the Gaussian distribution /1(E1) (kJ=mol)r2 standard deviation of the Gaussian distribution /2(E2) (kJ=mol)e translational energy of gas molecule (kJ=mol)f(e) Maxwell velocity distribution/1(E1) Gaussian distribution/2(E2) Gaussian distribution

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