Detailed analysis of the CO oxidation chemistry around a coal char particle under conventional and oxy-fuel combustion conditions

Combustion and Flame 162 (2015) 478–485

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

Detailed analysis of the CO oxidation chemistry around a coal char particle under conventional and oxy-fuel combustion conditions Cristina Gonzalo-Tirado, Santiago Jiménez ⇑ LIFTEC (CSIC-University of Zaragoza), María de Luna 10, 50018 Zaragoza, Spain

a r t i c l e

i n f o

Article history: Received 23 May 2014 Received in revised form 17 July 2014 Accepted 1 August 2014 Available online 3 September 2014 Keywords: CO flame Continuous-film model Char combustion Char-CO2 gasification Oxy-fuel combustion

a b s t r a c t The purpose of this article is to analyze in detail the homogeneous chemistry involving the CO oxidation in the gas around a burning char particle. Namely, the model presented in a previous work (GonzaloTirado et al., 2014) [1] has been applied to the case of a 120 lm and a 600 lm subbituminous char particle in a 24% O2, 1673 K atmosphere under both conventional and oxy-fuel combustion conditions. The CO + OH M CO2 + H reaction is shown to be the prevailing reaction in the conversion of the CO in the boundary layer; the high CO2 concentrations typical of oxy-combustion affect the equilibrium in this reaction and reduce its overall rate, which explains the lower ‘intensity’ of the flame in those conditions. As for the release/absorption of heat in the gas, the reactions in which the OH radicals participate as reactants or products are predominant; the OH chemistry is somehow more intense in N2 and higher flame temperatures and OH concentrations are thus attained in conventional combustion conditions. Relatively low moisture concentrations in the bulk gas are sufficient to activate this boundary layer chemistry; with [H2O] larger than 3% no substantial changes are observed in the CO conversion. The combustion history of the particles has been also studied. A logical sequence oxidation–gasification is observed; whereas the CO-to-CO2 oxidation occurs first contiguous to the particle, the onset of char-CO2 gasification results in a detachment of the flame from the surface and a decrease in the oxidation rate, especially for large particles. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction It is well known that the combustion of a coal particle is a very complex process, since it involves simultaneously both heterogeneous and homogeneous reactions, which makes its understanding and modelling very difficult. The majority of the studies dedicated to the simulation of char conversion have been based on the application of simplifying assumptions regarding the homogenous reactions in the gas around the particle, such as the single-film (e.g., [2– 6]), the double-film [5,7,8] or the global kinetics [9,10] approaches. The single-film theory assumes that the gaseous reactions are frozen, hence not influencing the process; on the contrary, the double-film theory considers they occur in a thin flame front at an infinitely fast rate. Finally, most of the studies applying global kinetics made use of Howard et al.’s [11] kinetics for the global (‘virtual’) reaction CO + 1/2 O2 ? CO2, whose rate depends on the temperature and the O2, CO and H2O concentrations. Whereas these simplified models, and especially the single-film approach, dominate the commercial applications, more complex models have ⇑ Corresponding author. Fax: +34 976506644. E-mail address: [email protected] (S. Jiménez).

been proposed in the past, involving a number of homogeneous reactions (e.g., [12–14]). In a previous study [1], the authors used a detailed model to evaluate the performance of the above-mentioned three simpler models for different coal chars in a wide range of combustion conditions in a manner similar to that of Hecht et al. [14], who checked the accuracy of single-film model results for fine particles; that analysis concluded that the global kinetics or infinite rates for the CO-to-CO2 conversion are not generally suitable to properly describe how the CO oxidation occurs and influences both the mass and heat transfer towards/from the particle surface. In this work, the focus is set on the details of the CO conversion across the gas around a burning char particle in the pseudo-steady state reached after the initial transient, but also in the latter stage. One aspect specifically explored here is the effect of water vapour on the oxidation of CO. In this respect, Annamalai and Ryan [15] pointed out that in dry air the CO oxidation is very slow even at flame temperatures and can be described through the global scheme: CO + 1/2 O2 ? CO2, whereas when water vapour is present, as typically in coal combustion, the wet oxidation scheme must be used instead: CO + OH ? CO2 + H. This is connected with the previous work of Adomeit and co-workers [12], who presented a theoretical study of the magnitude of the catalytic effect of

http://dx.doi.org/10.1016/j.combustflame.2014.08.002 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

C. Gonzalo-Tirado, S. Jiménez / Combustion and Flame 162 (2015) 478–485

479

Nomenclature Aj C Cpg Di dp E Eac Eag G _C m _ C;gasif m _ O2;s m _ O2;gas m Niter nj Pj,s r R RCO r* r*50

frequency factor for heterogeneous oxidation or gasification (kg m2 s1 Pan) char content (kg of char/kg of particles) gas specific heat (J kg1 K1) mass diffusivity of the species i (m2 s1) particle diameter (m) heat released (<0) or consumed (>0) by the gaseous reactions (J m1 s1) activation energy for oxidation (J mol1) activation energy for gasification (J mol1) percentage of char consumed by gasification (%) overall burning rate (kg C m2 s1) char consumption due to heterogeneous gasification (kg C s1) oxygen consumed in the particle’s surface due to heterogeneous oxidation (kg O2 s1) overall amount of oxygen consumed by the homogeneous reactions in the gas-phase (kg O2 s1) number of iterations required for the convergence in the inner or outer loop of the computation algorithm apparent reaction order with respect to O2 or CO2 partial pressure of O2 or CO2 at the surface of the particle (Pa) radial coordinate (m) universal gas constant (J mol1 K1) rate of each reaction converting CO to CO2 (kmol CO m1 s1). normalized radial coordinate (2r/dp) dimensionless radial coordinate at which 50% CO has been converted to CO2

moisture by using an 18-reaction gas-phase mechanism; they found that the conversion of CO to CO2 is practically frozen in the absence of H2O and enhanced in its presence. Mitchell et al. [13] also suggested, based on computational results, that the CO + OH reaction plays an important role in the CO oxidation around burning char particles, the OH concentration being dependent on the moisture concentration in the bulk gas. Finally, Goel et al. [16] found that the presence of water vapour or hydrogen is required to get a significant amount of CO oxidized in the boundary layer, especially at low gas temperatures, through the simulation of different cases with a model including char oxidation and a 56 gaseous reaction kinetics scheme. The combustion history of a char particle under both conventional and oxy-fuel combustion is studied in this work. For this purpose, several simulations in O2:N2 and O2:CO2 atmospheres have been performed with the detailed char conversion model already mentioned, using data for an Indonesian subbituminous coal previously reported by this research group [6]. The model considers both oxidation and char-CO2 gasification at the external surface of the particle, as well as a reduced GRI-Mech 3.0 mechanism [1,17] for the description of the homogeneous chemistry. In the first part of the study, extensive work has been conducted to analyze thoroughly the predominant reactions in the gas around the particle in terms of contribution to CO conversion and energy release; these results have also served to understand the way in which the high CO2 concentrations typically attained in oxycombustion affect the CO oxidation in the surroundings of the particle. As mentioned above, additional calculations have been performed to further analyze the relevance of the gas-phase reactions for variable water vapour concentrations in the bulk gas. Finally, the onset of the CO-to-CO2 oxidation and the activation of the char gasification have been examined through

Sg,i Sg,T t T U u Yi

qg kg [CO] [CO2] [H] [H2O] [OH]

gas-phase reactions source term for the mass balances of species i (kg i m3 s1) gas-phase reactions source term for the gas energy balance (J m3 s1) time (s) temperature (K) Unburnt fraction, U = C/C0 flow velocity (m/s) mass fraction of the species i gas density (kg m3) gas thermal conductivity (W m1 K1) concentration of CO (kmol m3) concentration of CO2 (kmol m3) concentration of H radicals (kmol m3) concentration of H2O (kmol m3) concentration of OH radicals (kmol m3)

Subscripts bulk bulk gas gas refers to i species j refers to O2 oxygen O2:N2 refers to O2:CO2 refers to p particle

the gas-phase oxidation (j = c) or gasification (j = g) conventional combustion oxy-combustion

Superscripts 0 initial time

the evaluation of the temporal evolution of the radial profiles of the main species and the gas temperature, as well as the heterogeneous oxidation and gasification rates. 2. Char conversion model and simulations The simulations have been performed using the detailed combustion model presented in [1], for which only a brief description is given here. The code implemented solves the combustion history of a single, spherical char particle immersed in a quiescent environment at atmospheric pressure. At the surface, carbon can react with either O2 or CO2 to form only CO through the global reactions C + 1/2 O2 ? CO and C + CO2 ? 2 CO; char-H2O gasification is not considered here, among other reasons due to the lack of kinetics data for this reaction, as already explained in [1]. Apparent kinetics, with parameters obtained in a previous experimental study for an Indonesian sub-bituminous coal [6], are used to model the heterogeneous reactions so that the carbon consumption rate is calculated as a function of the partial pressure of the reactant (O2 and/or CO2) at the surface of the particle and the particle temperature: n

Rj ¼ Aj  Pj;sj  expðEaj =RT p Þ

ð1Þ

A reduced GRI-Mech 3.0 mechanism [1,17] is used to describe the gaseous chemistry in the particle’s surrounds, which results in the consideration of 114 reactions and 29 species in the gas; the accuracy of several reductions of the complete GRI-Mech 3.0 (and the corresponding computational costs) is briefly discussed in Appendix A. The initial properties of the char (density and composition) are the same as in [1]. At each time step both the mass and energy transfer through the boundary layer (Eqs. (2) and (3))

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are solved; diffusion and convection (i.e. the so-called Stefan flow) are taken into account, as well as the transient and the source terms associated to the gas-phase reactions.

ð3Þ

The finite-volume method has been used to discretize these conservation equations in a grid with 100 concentric layers and variable distance between the nodes; a double iterative scheme (for the mass fraction, Yi,(r), in an inner loop, and the temperature, T(r), in an outer loop) has been applied to guarantee convergence. The software Cantera [18] is used to compute the source terms, as well as the gas properties at the different nodes. The continuity equation is also computed in order to determine the flow velocity, u, for the convective terms in Eqs. (2) and (3). The time step used depends on the combustion conditions; they vary within 0.8– 3 ms in the cases reported in this paper. After each time step, the oxidation and gasification rates are determined and the particle temperature is calculated from a particle energy balance; also, the fuel properties are updated. The calculation finishes when the unburnt fraction, U, reaches 0.001. For simplicity, a constant particle diameter is assumed during all the combustion history in these simulations; minor variations in the results shown are expected, in any case, since the measured dependence of the diameter on the unburnt fraction is low for the coal considered here [6]. As explicitly indicated in Eqs. (2) and (3), the model solves the combustion history of the char particle, so that in every case a transient period followed by a stage in which the particle temperature and burning rate reach nearly constant values is observed. All the results presented in this paper for the latter pseudo-steady state correspond to values taken at U = C/C0  0.2. In the first part of this work, an analysis of the predominant homogeneous reactions in the pseudo-steady state has been made, based on the results for the reference case of a 120 lm sub-bituminous coal char particle burning in a 1673 K, 24% O2 (15% H2O) environment under conventional (8% CO2, N2 to balance) and oxy-fuel (no N2, CO2-rich) combustion conditions. The reactions involved in the CO conversion to CO2 have been examined thoroughly, as well as those with a significant impact on the boundary layer energy balance. Also, a specific study has been performed to ascertain the effect of the water vapour concentration in the bulk gas on the relevance of the gaseous chemistry, with simulations of the combustion of a 120 lm particle with different molar fractions of H2O, both considering and neglecting the homogeneous reactions (i.e. single-film approach, setting the source terms Sg,i = Sg,T = 0 in Eqs. (2) and (3)). Finally, the main processes involved in the initial transient stage of the char combustion are illustrated by the case of two char particles, 120 lm and 600 lm in diameter, in a conventional combustion atmosphere (same conditions as above). The onset of the heterogeneous oxidation and gasification has been examined in detail; also the evolution of the radial profiles of O2, CO2 and temperature in the boundary layer has been analysed to better understand how the CO conversion starts and evolves along the char particle combustion history.

RCO (kmolCO.m-1.s-1)

   @ðqg  Cpg  TÞ 1 @ @T ¼ Sg;T r 2 qg  u  Cpg  T  kg  þ 2 @t r @r @r

ð2Þ

CO + OH <-> CO2 + H

3

CO + HO2 <-> CO2 + OH (x20) CO + O2 <-> CO2 + O (x20)

2 10-6

1 10-6

O2:N2 O2:CO2 1

10

100

r* Fig. 1. Rate of the main reactions converting CO to CO2 in the boundary layer surrounding a 120 lm subbituminous coal char particle immerse in a 24% O2, 15% H2O, 1673 K environment. Results correspond to both conventional (8% CO2, N2 to balance) and oxy-fuel (CO2 to balance) combustion. Note that, except for the CO + OH M CO2 + H reaction, the rates have been multiplied by a factor of 20.

steady state, RCO, for the reference case previously described (dp = 120 lm, Tbulk = 1673 K, 24% O2) with N2 and CO2 as alternative main gaseous component. These rates are expressed in terms of CO reacting per unit of time and radial thickness, kmol CO m1 s1, which in the authors’ opinion are convenient units to properly compare the relative importance of the reactions at different locations (r* = 2r/dp) and conditions (O2:N2 and O2:CO2), and facilitates the relation of these rates to the accumulated curves shown in Fig. 2, as commented below. As evident in Fig. 1, the CO oxidation is practically dominated by its reaction with OH, with the other reactions playing a very minor role in this respect. The spatial distribution of this reaction is significantly different in N2 and CO2, in spite of the similar CO production at the particle’s surface in both cases (1.5% difference, as derived from the data inserted in Fig. 2): in N2-rich atmospheres, the CO oxidation occurs closer to the particle and in a more ‘intense’ manner, whereas it is extended to regions located further when CO2 is the main carrier. The same pattern is observed in Fig. 2, where the accumulated percentage of CO converted at increasing distances from the particle is shown; r*50, defined as the normalized radial coordinate at which 50% of the CO exiting the particle has been converted to CO2 serves as ‘average flame location’. In each case (i.e. O2:N2 and O2:CO2), Fig. 2 basically corresponds to the integral of the CO + OH reaction curve in Fig. 1, although there is an apparent ‘shift’ between the maxima in Fig. 1

100

.

mC=0.2791 kgC.m-2.s-1 G=32.47% gasified Tp=2126 K

80

60

.

mC=0.2695 kgC.m-2.s-1 G=39.30% gasified Tp=1968 K

r*50=6.7 r*50=4.4

40

20

0

3. Results and discussion

CO + O + M <-> CO2 + M (x20)

10-6

0 100

CO converted (accumulated, %)

   @ðqg  Y i Þ 1 @ @Y i ¼ Sg;i r 2 qg  u  Y i  qg  Di  þ 2 r @r @t @r

4 10-6

O2:N2 O2:CO2 1

10

100

r* 3.1. Reactions in the gas-phase Figure 1 shows the rate at which the main reactions involving CO contribute to its oxidation across the boundary layer in the

Fig. 2. CO converted (accumulated) across the boundary layer for the two cases _ C ), percentage described in Fig. 1. The pseudo-steady state overall reaction rates (m of char consumed by gasification (G), particle temperature (Tp) and average flame location (r*50) are indicated.

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C. Gonzalo-Tirado, S. Jiménez / Combustion and Flame 162 (2015) 478–485

and the maximal gradient in Fig. 2 due to the logarithmic scale used in the X-axis. In order to further explore these phenomena, Fig. 3 shows the direct and reverse rates of the CO + OH M CO2 + H reaction for the cases of combustion in N2 and in CO2. Each of the individual reactions is faster in CO2, in spite of the slightly lower concentrations of OH and H (shown in Fig. 4, top) and temperatures (in Fig. 4, bottom) that are in fact reached in that gas, pointing to

CO + OH -> CO2 + H CO2 + H -> CO + OH

8 10-8

6 10-8

4 10-8

2 10-8

0

O2:N2 O2:CO2 1

10

100

r* Fig. 3. Forward and reverse rate of the overall reaction CO + OH M CO2 + H corresponding to the simulations presented in Figs. 1 and 2 (dp = 120 lm, 1673 K, 24% O2, N2 or CO2 as alternative main component).

8 10-5 [OH]O2:N2 [H]O2:N2 [OH]O2:CO2 [H]O2:CO2 [OH]O2:CO2 ( DO2,gas)

4 10-5

3

Concentration (kmol/m )

6 10-5

2 10-5 0 4 10-3 [CO]O2:N2 [CO2]O2:N2 [CO]O2:CO2 [CO2]O2:CO2

3 10-3 2 10-3 1 10-3 0

1 102

O2:N2 O2:CO2 O2:CO2 ( DO2,gas)

2100 2000

>0

0 -1 102

Heat consumed

<0

Heat released

-2 102 -3 102 -4 102 -5 102

O2:N2

-6 102 1 102

1900

E (J.m-1.s-1)

Tgas (K)

2 102

E (J.m-1.s-1)

Reaction rate (kmol.m -1.s-1)

1 10-7

the differences in [CO] and [CO2] as the main causes for the differences observed in Fig. 3. Figure 4 (middle) further reduces the list of dominant factors to basically one, the CO2 concentration across the reactive layer, about five times higher when CO2 acts as the main carrier in the conditions explored here. This explains the fact that the reverse reaction rate plotted in Fig. 3 is more similar to the forward one in CO2 than in N2, which results in an equilibrium shifted towards CO in the CO2-rich atmosphere. Following back this reasoning, the presence of higher CO2 concentrations reduces the CO net oxidation rate in oxy-combustion, which finally leads to less intense and more extended CO flames in CO2 than in N2, as evident in Fig. 2 and already observed in a previous work [19] for a wide range of particles and conditions. Figure 5 displays a quantification of the rate of the prevailing reactions responsible for the energy release and consumption in the gas-phase in O2:N2 and O2:CO2. All these reactions are more intense (except the oxidation of CO by O, which actually has little relevance in the energy balance) and lead to a higher overall energy release in N2. As a result, higher gas temperatures are reached in O2:N2, as previously reported in this work (Fig. 4, bottom) and in [19]. A careful inspection of these charts also reveals that most reactions (curves in black in the plot) involve OH radicals as reactant or product; the fact that the OH chemistry in CO2-rich atmospheres is somehow less intense is related to the lower OH concentrations reached in this mixture, compared to the N2 case (Fig. 4, top). The OH production depends, among other factors, on the O2 and H2O available, which are the same in the bulk gas for both O2:N2 and O2:CO2; however, it is well known that the diffusivity of O2 in CO2 is lower than in N2, which may by itself explain the lower production of OH under oxy-combustion. This hypothesis has been validated by repeating the oxy-combustion simulation with an oxygen diffusivity similar to that in N2 (i.e. DO2  (DO2:CO2/ 0.8)  DO2:N2); as shown in Fig. 4, a considerable increase in the OH concentration and gas temperature (up to values near those in O2:N2) is observed due to the enhancement of the oxygen transfer. Interestingly, these (hypothetical) changes do not alter the spatial distribution of the CO conversion in O2:CO2 (accumulated percentage displayed in Fig. 2), which further supports the relevance of the CO2 concentration in the CO oxidation profile. In order to check the potential relevance of the higher specific heat capacity of CO2 with

1800 1700 1600 1

10

100

r*

0 -1 102 -3 102 -4 102 -5 102 -6 102

Fig. 4. Radial profiles of gas temperature and CO, CO2, OH and H concentration in the gas around a 120 lm char particle burning in a 24% O2, 1673 K environment. Results are presented for both conventional (15% H2O, 8% CO2, N2 to balance) and oxy-fuel (15% H2O, CO2 to balance) combustion conditions. The dotted curves denoted with "DO2,gas correspond to simulation of ‘virtual’ oxy-combustion conditions where the oxygen diffusivity has been approximated to that in N2 (i.e. in conventional combustion conditions); see text for details.

O + CO <-> CO2 H + O2 + H2O <-> HO2 + H2O H + O2 <-> O + OH OH + H2 <-> H + H2O 2OH <-> H2O2 2OH <-> O + H2O CO + OH <-> CO2 + H OH + HO2 <-> O2 + H2O Source term

-2 102

O2:CO2 1

10

100

r* Fig. 5. Rates of energy released and absorbed in the homogeneous reactions for the O2:N2 (above) and O2:CO2 (below) cases presented in Fig. 1. The corresponding global source term in the energy balance (Sg,T in Eq. (3), in J m1 s1) is also represented.

C. Gonzalo-Tirado, S. Jiménez / Combustion and Flame 162 (2015) 478–485

respect to N2, and additional test was performed in the oxy-combustion conditions with a gas heat capacity similar to that in N2; negligible variations in the computed flame peak temperature (<2 K) were observed. In a real boiler, coal particles go through different zones with variable H2O vapour concentration. As indicated above, char-H2O gasification has not been considered in the study, however the water concentration may in principle affect the OH production and thus the CO + OH M CO2 + H conversion reaction in the particle’s surrounds. This aspect has been investigated through a series of simulations with the 120 lm base-case in N2 and CO2 and different molar fractions of H2O in the bulk gas (0–25%); the change in [H2O] is exclusively balanced with the concentration of the main carrier (N2 or CO2), whereas the concentration of O2 (24%) and CO2 (8% in the O2:N2 cases) is kept constant. The resulting percentage of char consumed through char-CO2 gasification, G, is shown in Fig. 6; this value is related to the location and influence of the flame since when it approaches the surface the CO2 transferred towards the surface is enhanced and so does the gasification rate [1]. The absolute burning rates and average flame locations (r*50) are also indicated in the graph for the 1% and 25% H2O cases. In the absence of a flame (single-film model, S.F.), the fraction of char gasified is practically independent of the moisture concentration in N2 since the CO2 transferred from the bulk gas (where [CO2] = 8%) is similar in all cases; however, in oxy-fuel combustion, it slightly decreases as the concentration of H2O increases due to the associated reduction in the CO2 bulk gas concentration. When the detailed kinetics are used (D.K.), the flame significantly approaches the particle surface in both atmospheres when the moisture concentration increases, as indicated by the values of r*50 included in Fig. 6. Two regions are evident in each plot: when the H2O molar fraction is lower than 3% in the bulk gas, the sensitiveness of G towards [H2O] is very marked; for higher moisture levels the slope of the curve considerably decreases and the percentage of char gasified asymptotically reaches a steady value. When absolutely no H2O is available, still some CO reacts in the boundary layer, but through the reactions CO + O + M M CO2 + M and CO + O2 M CO2 + O, which

G (%)

D.K. 30

.

mC=0.2607 r*50=8.6

20

0% H2O 1% H2O 4% H2O 8% H2O 15% H2O 25% H2O

0.15

0.1

0.05

0

1

10

100

r* Fig. 7. Radial profiles of the CO2 molar fraction in the surroundings of a 120 lm char particle for different H2O concentrations in the bulk gas. Conditions as in Fig. 6, combustion in O2:N2 only.

as shown in Fig. 1 are much slower than the reaction with OH so that the solution is very similar to that given by the single-film approach. This behaviour can also be observed in Fig. 7, where radial profiles of CO2 molar fraction are represented for different moisture concentrations in conventional combustion conditions simulated with the detailed kinetics model; the presence of minor amounts of moisture already results in the appearance of a CO flame. These trends are in good agreement with the computational results of Adomeit et al. [12], who reproduced the experiments of Matsui et al. [20] with a planar stagnation-point configuration and found that the conversion of CO to CO2 is practically frozen in dry air and that the CO2 mass fraction at the particle surface does not vary much above a (relatively low) concentration of water vapour in the bulk gas. A posteriori, moisture is thus not expected to be a limiting factor for the development of a CO flame in conditions typical of real boilers, where the concentrations of H2O are typically above 10%. 3.2. Transient behaviour Figure 8 (included as Fig. 9 in the animation S1) shows the evolution of the overall burning rate and particle temperature, as well as the surface oxidation and gasification rates, for the base-case of a 120 lm char particle from injection at room temperature in a 1673 K, 24% O2, N2-rich environment; a number of approximate unburnt fractions, U = C/C0, are indicated in the upper X-axis as a

.

mC=0.2875 r*50=3.9

40

0.2

YCO2

482

S.F.

10

U (approx.)

O2:N2 0 0.35

.

mC (kgC.m-2.s-1)

.

S.F.

10

.

O2:CO2 0

0

5

10

0.56

0.30

2200

0.3

mC=0.2779 r*50=5.2

mC=0.2594 r*50=16.2

20

0.82

15

20

0.25

Global

1650

Oxidation

1100

0.2 0.15 0.1

550

Gasification

25

H2O (%, molar basis) Fig. 6. Percentage of char consumed through char-CO2 gasification (G) vs. H2O molar concentration in the bulk gas. Conditions as in previous figures: a 120 lm char particle, 24% O2, 1673 K in N2 (8% CO2, above) and CO2 (below). Results considering (D.K. model) and neglecting (S.F. model) the gas-phase reactions. The _ C , in kg C m2 s1) and average flame location (r*50) are absolute burning rate (m indicated for the 1% and 25% H2O D.K. cases.

Tp (K)

G (%)

30

0.99

Particle temperature

D.K.

40

1

0.05 0

0

0.02

0.04

0.06

0.08

0.1

0

t (s) Fig. 8. Temporal evolution of the particle temperature and the oxidation, gasification and overall reaction rate of a 120 lm char particle burning in a 24% O2, 1673 K (15% H2O, 8% CO2, N2 to balance) environment. Approximated values of the unburnt fraction are indicated in the upper X-axis as a reference.

483

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0.3

U (approx.) 1.6 10

0.25

1 -7

1.4 10-7

0.2

U=0.94

m (kg.s-1)

YCO2

1.2 10-7

.

0.15

0.99

0.88

0.74

0.5

0.75

. mO2,s . mO2,gas . m C,gasif

1 10-7 8 10-8 6 10-8 4 10-8

0.1

1

10

2 10-8

100

r*

0.25

Fig. 10. Evolution of the oxygen consumed at the surface and in the gas around a 600 lm char particle, together with the corresponding rate of char gasified by CO2. 24% O2, 1673 K (15% H2O, 8% CO2, N2 to balance). Approximated values of the unburnt fraction are indicated in the upper X-axis as a reference.

diffusion limit in which the combustion of this particle (size, coal reactivity, conditions) takes place. The decrease in char oxidation rate is much smaller, and hardly appreciable, in the case of the 120 lm particle (Fig. 8), basically because this one burns further from the diffusion limit. These phenomena may also be observed in Fig. 11 (top), which displays the radial profiles of O2 around and at the surface of the particle: the initial progressive decrease in the O2 surface concentration is a consequence of the onset of char oxidation and the low levels rapidly reached reflect the proximity to the diffusion limit; the shape of the profiles, which in that first stage is basically 0.28 0.24

YO2

0.2 U=0.94

0.16 0.12 0.08 0.04 0 0.35 0.3

YCO2

reference. After an initial heating period, the heterogeneous oxidation is activated first (at Tp  800 K according to the kinetics used) and further contributes to the particle’s heating. The delay observed in the onset of char gasification by CO2 (at Tp  1200 K, here) is exclusively due to the higher activation energy of this reaction (Eag = 148.5 kJ/mol vs. Eac = 108 kJ/mol) since, as shown in Fig. 9, CO2 is available at the particle surface at all times. The latter figure is thought to clearly illustrate the process: first char oxidation and CO conversion near the particle result in the accumulation of CO2 in the particle surrounds; then, the CO2 at the surface is consumed soon after the activation of the gasification, leading to a more ‘localised’ CO2 peak from where it diffuses towards the particle and the bulk gas. Similar trends are observed for a particle in O2:CO2 (not shown here), although in this case the contribution of gasification is significantly larger, as already shown in Fig. 6 and previous works [1,19]. It is perhaps interesting to note that the activation of the endothermic gasification does not imply a decrease in Tp, although the particle temperature finally reached (2126 K in this case, as shown in Fig. 2) is considerably lower than the one expected when the heterogeneous gasification is not considered (2386 K for the same conditions). An equivalent analysis of the combustion history of a 600 lm char particle in the same conditions is presented in Fig. 10 (and animation S2, which also includes the next figure cited). The plot compares the evolution of the oxygen consumed at the particle surface by heterogeneous oxidation and in the gas around the particle; the evolution of the gasification rate (in kg C s1) is also shown as a reference. As in the previous case, there is a delay in the start of the latter reaction with respect to char oxidation. Before the gasification is activated, the consumption of oxygen is split in two equal parts at the particle’s surface and in the gas-phase, as expected in the sequential mechanism used (C(s) + 1/2 O2 ? CO, CO + 1/2 O2 ? CO2). As evident in the graph, the onset of char gasification results in an increase of the oxygen consumed by the gaseous reactions, which again is expected because in the latter process O2 does not react at the particle’s surface but in the gas (C(s) + CO2 ? 2 CO, CO + 1/2 O2 ? CO2), and in a significant decrease (30%) of the char oxidation rate – O2 consumption at the surface. A similar reduction was reported by Makino and Law [10], who studied the transient stage in the combustion of a 2 mm coal particle by means of a char combustion model based on Howard’s global kinetics. The net outwards convective flow (Stefan flow) hardly contributes to this decrement, which is basically associated to the intense consumption of oxygen in the CO flame around the particle and the vicinity to the oxygen

0

t (s)

0.25

U=0.94

0.2 0.15 0.1 U=0.94

2200 1925

Tgas (K)

Fig. 9. Evolution of the CO2 mass fraction radial profile during the combustion process; conditions as in the previous figure. The profiles are represented for the specific values of the unburnt fraction, U: 1, 0.9999, 0.999, 0.998, 0.997, 0.9955, 0.994, 0.99, 0.98, 0.96, 0.94, 0.92, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3 and 0.2. As a reference, the profile corresponding to U = 0.94 is indicated in the plot.

0

1650 1375 1100 825 550 275 1

10

100

r* Fig. 11. Evolution of the gas temperature and the O2 and CO2 mass fraction radial profiles for the case described in Fig. 10. The profiles correspond to the specific values of the unburnt fraction used in Fig. 9. The curve corresponding to U = 0.94 is indicated as a reference.

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determined by diffusion, shows slight changes after the start of CO2 gasification (a decrease in [O2] in 2 < r* < 50) for U < 0.94, attesting the relevance of the oxygen consumption in the boundary layer. The presence of the flame is also apparent in Fig. 11 (bottom), although it should be noted that the position of the temperature peaks does not necessarily coincide with those reported for the CO2 mass fraction profiles shown in Fig. 11 (middle); as explained above, this is related to the fact that although the reaction CO + OH M CO2 + H dominates the CO–CO2 conversion, other reactions involving OH radicals also play an important role in the gas energy balance. The slight changes in the O2 profiles observed after the onset of CO2 gasification, and thus in the concentration of OH, have a direct correspondence in the later evolution of the CO2 profiles, which indicate more detached and extended flames. It is probably worth noting that the figures shown so far in this section (and the Supplementary Videos S1 and S2) are intended to illustrate the combustion of a coal particle after its volatiles have been released, namely the evolution of the gas properties around the particle from the onset of char oxidation to the pseudo-steady state reached soon after the start of the char gasification by CO2. A detailed description of the oxidation ignition itself is certainly beyond the scope of this study (and, in any case, would require more complex heterogeneous mechanisms, as in e.g., [21], than the apparent kinetics used here), but the resulting uncertainty is thought to affect only the very first moments of char oxidation, and not the general history and the conclusions stated here. As for the fact of considering a pure char particle, and not a coal particle which first heats up and devolatilizes, prior simulations (e.g., [22]) and experiments (e.g., [23,24]) support the separation of devolatilization and char oxidation; a shift in time is obviously expected, but this should not affect the sequence presented in the previous figures. As a complementary analysis, which might be of interest for potential implementations of similar codes, the number of iterations, Niter, required by both the inner (Yi) and outer (T) loop for the case studied in Fig. 8 has been represented in Fig. 12; for this particular case, the total computation time on a desktop PC is 15 min. The number of iterations in the outer loop is minimal, except for the first time steps. As for the outer loop, the number of iterations registered shows a close correlation with the rates presented in Fig. 8: initially, several time steps with large Niter are required to compute all the mass fraction profiles in detail; then, Niter decreases until the onset of the heterogeneous oxidation and the conversion of CO in the boundary layer. The activation of

the gasification does not have a noticeable effect on the number of iterations, which decrease in good correspondence with the stabilization of the particle temperature and overall burning rate. 4. Conclusions In this paper, the mechanisms of CO oxidation in the surroundings of a coal char particle in pulverized fuel combustion conditions has been studied in detail. Also, the evolution of the particle and its surrounding gas from the activation of char oxidation has been analysed. Some of the conclusions obtained are: – When moisture is present, the CO oxidation in the boundary layer mainly proceeds through the homogeneous reaction CO + OH M CO2 + H. The equilibrium of this reaction is more shifted towards CO in CO2-rich atmospheres (as in oxy-combustion); as a consequence, the CO-to-CO2 reaction zone (the CO flame) is less intense and more extended in CO2 than in N2. – In the absence of H2O, the gaseous chemistry is practically frozen since the prevailing reactions converting the CO (CO + O + M M CO2 + M and CO + O2 M CO2 + O) are much slower than the reaction with OH; for this reason, the solution approaches that obtained with the single-film model. – The presence of moisture is necessary to enable the CO + OH M CO2 + H conversion reaction; however, for H2O concentrations higher than 3% in the bulk gas, the homogeneous chemistry displays little dependence on that concentration. – Higher flame temperatures are attained in O2:N2 than in O2:CO2; this is related to the OH production and consumption reactions, which are more intense in conventional combustion. The higher diffusivity of O2 in N2 than in CO2 is responsible for the enhancement in the oxygen transferred from the bulk gas and thus the intensification of the OH chemistry in the boundary layer in N2. – Among the two heterogeneous reactions considered, char oxidation is activated first in the combustion process; the larger activation energies of the char-CO2 gasification cause a delay in the onset of the latter. Once the gasification starts, a reduction in the oxidation rate is observed, especially for large particles, due to the enhanced consumption of O2 in the boundary layer. – The CO-to-CO2 conversion takes place in the boundary layer already at the start of the char oxidation; it starts close to the particle and is detached from the surface soon after the activation of the gasification.

U (approx.) 120

1

0.99

0.82

0.56

0.30

Acknowledgments

8

6 80 4

60 40

2

Niter (outer loop, T)

Niter (inner loop, Y i )

100

20 0

0

0.02

0.04

0.06

0.08

0.1

0

t (s) Fig. 12. Evolution of the number of iterations required by the computer code to reach convergence in the inner (Yi) and outer (T) loop. Case of a 120 lm char particle burning in a 1673 K, 24% O2 (15% H2O, 8% CO2, N2 to balance) environment (i.e. that in Figs. 8 and 9).

The authors acknowledge the funding received from the Spanish Government through Grants ENE2007-64658/CON and CSD2010-00011 (CONSOLIDER program). Appendix A. Computation times and accuracy of different reduced gaseous chemical mechanisms and computational tolerances The purpose of this appendix is to illustrate the dependence of the computed burning rates and particle temperatures on the model used to calculate the combustion history of a char particle. In particular, results are presented for the reduced mechanism (without hydrocarbons) used in this work, but also when the complete GRI-Mech mechanism (i.e. 325 reactions and 53 species) and two other reduced mechanisms are used: one in which only the NOx chemistry is neglected (thus considering 219 reactions and 36 species) and another one where both the nitrogen-containing

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Table A1 Computation time and accuracy when the combustion history of a 120 lm and a 600 lm subbituminous char particle (Tbulk = 1673 K, 24% O2, 15% H2O, 8% CO2, N2 to balance) is computed with a model including the full GRI-Mech mechanism and when hydrocarbons, N-containing species or both types of species are extracted from the mechanism.

a

Computation time (min)

_ C (kg m2 s1) m

Tp (K)

_ C (%) Dm

DTp (K)

Case of a 120 lm particle D.K. (no HCs & Ns) D.K. (no HCs)a D.K. (no Ns) D.K. (full)

7 9 21 25

0.2790 0.2794 0.2793 0.2793

2125.4 2126.7 2127.9 2127.9

0.11 +0.04 0

2.5 1.2 0

Case of a 600 lm particle D.K. (no HCs & Ns) D.K. (no HCs)a D.K. (no Ns) D.K. (full)

50 80 261 287

0.0605 0.0606 0.0606 0.0606

1876.5 1877.6 1877.5 1877.4

0.17 0 0

0.9 0.2 0.1

Model used in the calculations shown in this paper.

Table A2 Dependence of the D.K. model results (without HCs) on the tolerances used in the inner and outer loop; variations referred to the case with the tolerances used within this work. Conditions as in Table A1 (120 lm particle).

0.1 (Yi) and 0.1 (T) 0.1 (Yi) and 1 (T)a 0.5 (Yi) and 1 (T) 1 (Yi) and 1 (T) a

Computation time (min)

_ C (kg m2 s1) m

Tp (K)

_ C (%) Dm

DTp (K)

10 9 3 2.3

0.2790 0.2794 0.2775 0.2770

2126.2 2126.7 2122.9 2122.3

0.14

0.5

0.68 0.86

3.8 4.4

Tolerances used in the calculations shown in this paper.

and hydrocarbon species and their reactions are disabled (i.e. with 34 reactions and 12 species). The difference between all these models is thus the degree of detail in the homogeneous chemistry description, with the complete model being a priori the most accurate one; for this reason it is taken as a reference to evaluate the deviations in the calculation of the burning rate and particle temperature. Table A1 shows the predicted burning rate and particle temperature, together with the corresponding computation time, for the four alternative mechanisms applied to the case of a 120 lm and a 600 lm char particle in 24% O2:N2. As expected, the computation time increases with the complexity of the model. Also, although the version without the HCs was used to compute the cases presented in this paper and in previous works (e.g., Molina et al. [25]), apparently the mechanism could have been further reduced with a reasonably low cost in terms of accuracy (e.g. <1 K in temperature, 600 lm case) and a noticeable reduction in computation time. The results of a preliminary study regarding the dependence of the predictions’ accuracy on the tolerances used in the inner (for Yi(r)) and outer (for T(r)) loop are also presented in this appendix. As already explained in [1], these tolerances, defined as the maximum relative differences between successive iterations considering all nodes and species, were set to 0.1% and 1%, respectively. Table A2 shows the results obtained when these tolerances are varied in the case of simulating the combustion of a 120 lm particle (same conditions as in Table A1). When the tolerance used for the energy balance in the gas is more restrictive, negligible variations are observed in the predicted burning rates and particle temperatures with respect to the case of using a tolerance of 1. When the tolerance criterion is relaxed for Yi, some differences are observed in the predictions, but, in any case, the results suggest that this tolerance may have been further increased while still keeping a reasonable accuracy and with a noticeable reduction of the computation time. It is probably worth noting that the code has not been optimised for speed, and that significant reductions in the computation times quoted are surely attainable with refined implementations; nevertheless, the ratios readily derivable from the times in Tables A1 (and A2) are considered valid indications of the complexity associated to

each mechanism/tolerance set, and might (hopefully) provide useful information for future implementers of similar codes. Appendix B. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.combustflame. 2014.08.002. References [1] C. Gonzalo-Tirado, S. Jiménez, R. Johansson, J. Ballester, Combust. Flame 161 (2014) 1085–1095. [2] M.A. Field, D.W. Gill, B.B. Morgan, P.G.W. Hawksley, Combustion of Pulverized Coal, The British Coal Utilization Research Association, Leatherhead, UK, 1967. [3] B. Coda, L. Tognotti, Exp. Therm. Fluid Sci. 21 (2000) 79–86. [4] J.J. Murphy, C.R. Shaddix, Combust. Flame 144 (2006) 710–729. [5] F.J. Higuera, Combust. Flame 152 (2008) 230–244. [6] C. Gonzalo-Tirado, S. Jiménez, J. Ballester, Combust. Flame 159 (2012) 385– 395. [7] H.S. Caram, N.R. Amundson, Ind. Eng. Chem. Fundam. 16 (2) (1977) 171–181. [8] A. Makino, Combust. Flame 90 (1992) 143–144. [9] S.V. Sotirchos, N.R. Amundson, Ind. Eng. Chem. Fundam. 23 (1984) 191–201. [10] A. Makino, C.K. Law, 21st Symp. (Int.) Combust. (1986) 183–191. [11] J.B. Howard, G.C. Williams, D.H. Fine, 14th Symp. (Int.) Combust. (1973) 975– 986. [12] G. Adomeit, G. Mohiuddin, N. Peters, 16th Symp. (Int.) Combust. (1976) 731– 743. [13] R.E. Mitchell, R.J. Kee, P. Glarborg, M.E. Coltrin, 23th Symp. (Int.) Combust. (1990) 1169–1176. [14] E.S. Hecht, C.R. Shaddix, J.S. Lighty, Combust. Flame 160 (2013) 1499–1509. [15] K. Annamalai, W. Ryan, Prog. Energy Combust. Sci. 19 (1993) 383–446. [16] S. Goel, C.H. Lee, J.P. Longwell, A.F. Sarofim, Energy Fuels 10 (1996) 1091–1098. [17] G.P. Smith, S.D. Golden, M. Frenklach, et al., GRI-MECH 3.0, 2001, Available at . [18] D. Godwin, Cantera: An Object-Orient Software for Reacting Flows, . [19] C. Gonzalo-Tirado, S. Jiménez, Proc. Combust. Inst. (2014). . [20] K. Matsui, A. Koyama, K. Uehara, Combust. Flame 25 (1975) 57–66. [21] J.C. Chen, Combust. Flame 107 (3) (1996) 291–298. [22] J. Ballester, S. Jiménez, Combust. Flame 142 (2005) 210–222. [23] Y. Liu, M. Geier, A. Molina, C.R. Shaddix, Int. J. Greenhouse Gas Control 5S (2011) S36–S46. [24] J. Riaza, R. Khatami, Y.A. Levendis, L. Álvarez, M.V. Gil, C. Pevida, F. Rubiera, J.J. Pis, Combust. Flame 161 (2014) 1096–1108. [25] A. Molina, E.G. Eddings, D.W. Pershing, A.F. Sarofim, Proc. Combust. Inst. 29 (2) (2002) 2275–2281.