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Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O2/CO2 Atmosphere Andreas Richter,* Petr A. Nikrityuk,* and Matthias Kestel CIC Virtuhcon, Department for Energy Process Engineering and Chemical Engineering, Technische Universität Bergakademie Freiberg, Fuchsmühlenweg 9, 09596 Freiberg, Germany ABSTRACT: In this work, the behavior of a 200-μm spherical carbon particle moving in a hot environment mainly consisting of O2 and CO2 was investigated numerically. The main goal of this work was to study the influence of the particle velocity, temperature, and composition of the surrounding gas on the carbon consumption rates. The particle investigated was placed in a uniform oxygen/carbon dioxide mixture at different Reynolds numbers corresponding to different laminar flow regimes. The ambient temperature was systematically varied in the range of 1000−3000 K, and the mass fraction of O2 was varied between 0.12 and 0.36. To solve the Navier−Stokes equations for the flow field coupled with the energy and species conservation equations, a finite volume solver was applied. In addition to the solid carbon, the model incorporates six gaseous chemical species (O2, CO, CO2, H2, H2O, and N2). The semiglobal reaction mechanism includes the forward and backward water−gas-shift reaction, one reaction for CO combustion, and four heterogeneous reactions. The ambient medium was assumed to be nearly dry (YH2O = 0.001). The numerical results were carefully validated against experimental data published in the literature (Bejarano and Levendis, Combust. Flame 2008, 153, 270−287). In particular, it was shown that taking into account losses from radiation (gas− gas, gas−solid) brings the results closer to the experimental data. Additionally, the influence of the gas−gas radiation effect on the integral characteristics of the oxidizing particle was studied. In particular, the results are discussed with a focus on the systematic variation of the ambient-gas temperature and Reynolds number. We found out that increasing the Reynolds number enhances species transport to the particle surface and shifts particle oxidation from a diffusion-controlled to a kinetically controlled regime.

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INTRODUCTION According to the latest analyses of environmental data, carbon dioxide is considered to be responsible for global warming, because it is a greenhouse gas, alongside steam, methane, and other causes.1 To avoid irreversible risks and environmental costs, CO2 emissions must be reduced. One possible means of reducing CO2 emissions is to use the oxycombustion of coal with flue gas recirculation and carbon sequestration. In this process, the fossil fuel is burned in a mixture of oxygen and recycled flue gas, which consists primarily of water and CO2. For a review of technological developments, we refer the interested reader to the works of Buhre et al.2 and Wall et al.3 A number of works have been published about the numerical modeling of a pilot-scale oxy-fuel combustor including predictions of the heat-transfer and pollutant-formation characteristics (e.g., Chui et al.4). Because of the multiscale character of the processes involving solid carbonaceous materials inside combustors and gasifiers, the use of computational submodels describing particle−gas interactions is unavoidable, and the correct prediction of the burning rate and particle temperature based on such submodels is an essential part of successfully modeling oxy-coal combustors. A comprehensive overview of common char combustion submodels can be found in the article by Edge et al.5 The main challenge in designing a burnout model is to adequately model the char combustion, the particle−gas and gas−gas radiation, the impact of particle velocity on char combustion, and the chemistry of char conversion. However, an analysis of existing computational burnout submodels reveals that the influence of particle velocity on the carbon consumption and © 2013 American Chemical Society

particle temperature, among other factors, is not well understood.6 Numerical simulations of single burning particles can highlight different physical phenomena and correlations and, thereby, help to better elucidate the complex combustion physics. Before 1980, Amundson and co-workers7,8 performed a large number of numerical studies investigating diffusion and reaction in a stagnant boundary layer around a spherical carbon particle using the pseudo-steady-state approach. Only diffusion-limited regimes were investigated. It was shown that the two-film model developed by Burke and Schumann9 is capable of adequately predicting the combustion of a coal particle at higher temperatures. For an extended review of works produced before 1980, see Sundaresan and Amundson.10 As progress in computational fluid dynamics (CFD) was made at the beginning of the 1990s, reacting carbon particles received a great deal of attention from researchers using simplified Navier−Stokes (N−S) equations coupled with species and energy conservation equations. One example of this kind of approach was reported by Lee et al.,11 who carried out a numerical investigation of single-particle combustion in hot air. In that work, they focused on transient phenomena and considered different Reynolds numbers, confirming that the particle’s burning mode is sensitive to the Reynolds number. Higuera12 carried out a numerical study of the effects of particle Received: Revised: Accepted: Published: 5815

October 11, 2012 March 7, 2013 March 14, 2013 March 14, 2013 dx.doi.org/10.1021/ie302770j | Ind. Eng. Chem. Res. 2013, 52, 5815−5824

Industrial & Engineering Chemistry Research

Article

see the review in ref 6. The computational cell-averaged temperature is used as an input parameter in such submodels. The large temperature range used in this work is explained by the fact that it covers kinetically controlled and diffusioncontrolled regimes for all Reynolds numbers, to demonstrate global trends that are valid for a large range of ambient-gas temperatures. Furthermore, the mass fraction of O2 was varied between 0.12 and 0.36. Altogether, we considered five different temperatures, three different atmospheres, and eight different Reynolds numbers, yielding a total of 120 configurations. Before proceeding with a description of the mathematical model, we first introduce several assumptions that were made to solve the problem. The consumption time scale of the particle is always large compared to the convective and diffusion time scales for the gas phase; thus, the pseudosteady-state approach can be used.10,17,18 Because of the steadystate character of the model, volatilization is not considered. Furthermore, buoyancy effects of the particle are neglected. The particle consists of carbon only and is nonporous. To consider intraparticle reactions that occur in porous structures, a random-pore model could be applied, but this would require intrinsic kinetics.19 To our best knowledge, CFD-based particle-resolved models using intrinsic kinetics for char conversion under the influence of the ambient-gas flow are not available in the literature. Additionally, recent publications have demonstrated that the flow field can penetrate porous particles.20 Because of the lack of available models and as a first step, we consider the interplay between char combustion and the flow field for solid particles. The chemistry is modeled using semiglobal heterogeneous and homogeneous reactions written as follows

size and velocity, temperature, and gas composition on burning rates, using simple chemistry. Recently, Kestel et al.13 examined the influence of water vapor on the carbon consumption rate and the surface temperature of a single particle moving in an air-based atmosphere. In contrast to these works, studies dealing with the numerical investigation of coal particles in hot CO2 atmospheres are rare. Higuera12 noticed an increase in the gasification rate in the presence of CO2 in the environmental gas. However, using a surface kinetics code, Hecht et al.14 found that the CO2 gasification reaction acts to reduce the char particle temperature and the rate of char oxidation. In particular, they showed that the CO2 gasification reaction also increases the char conversion rate for low O2 concentrations but decreases char conversion for combustion at high O2 concentrations. It should be noted that the influence of particle velocity was not considered. More general comparisons of particle combustion in hot air and O2/ CO2 atmospheres are given in refs 6 and 15. In summary, it is clear that no systematic studies have been performed on the impacts of the particle velocity and surrounding temperature on the carbon consumption of char particles moving in hot O2/CO2 environments. For that reason, this work is focused on the numerical investigation of the combustion of a 200-μm spherical char particle moving in a hot environment consisting of O2 and CO2 at different ratios. The main goal was to study the effects of the particle velocity and the temperature and composition of the surrounding gas on the carbon consumption rate and the particle-surface temperature. In addition, the choice of Reynolds number (Re) and surrounding gas temperature (T∞) allows for the improvement of existing burnout models that are used, for example, in discrete particle model simulations of large-scale facilities.

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CO +

MODEL ASSUMPTIONS AND GOVERNING EQUATIONS The particle investigated is assumed to be placed in a uniform oxygen/carbon dioxide mixture with low mass fractions of N2 (YN2 = 0.01) and water (YH2O = 0.001). The application on which we focus is entrained-flow reactors. Even if the Reynolds numbers referring to gas flows are large in such systems, the particle Reynolds numbers are generally small because of the small particle sizes.16 In particular, for 200-μm particles, the typical particle Reynolds numbers are in the range between 0.1 and 100. Larger particle Reynolds numbers have been reported for fluidized-bed and fixed-bed applications only. For that reason, we focus on particle Reynolds numbers, Re, between 1 and 200, corresponding to laminar flow regimes. Strictly speaking, the oxidation of residual carbon is an unsteady process. However, comparing the carbon flow velocity (known as Stefan flow, ṁ /(Apρ) with the velocity of the particle shows that the latter has a higher value. From this point of view, in this work, we consider the steady-state burnout up to Re = 200 to investigate the interplay between the particle velocity and the composition and temperature of the ambient gas. In parallel with the variation of the particle Reynolds number, the ambient-gas temperature was systematically varied in the range of 1000−3000 K. The choice of ambient temperature as the dominant input parameter is explained by the fact that, in CFD-based simulations of industrial-scale pulverized-coal (PC) combustors or gasifiers, submodels are used to model char burnout on a particulate scale; for details,

1 O2 + H 2O → CO2 + H 2O 2

(R1)

CO + H 2O → CO2 + H 2

(R2)

CO2 + H 2 → CO + H 2O

(R3)

C + CO2 → 2CO

(R4)

C+

1 O2 → CO 2

(R5)

C + O2 → CO2

(R6)

C + H 2O → CO + H 2

(R7)

The corresponding pre-exponential factors A and activation energies E for these heterogeneous and homogeneous reactions are listed, together with the corresponding literature sources, in Table 1. The reactions include water as a catalytic species. The influence of water vapor was recently considered by Kestel et al.,13 who showed numerically that, even for low water concentrations, the catalytic effect of water vapor cannot be neglected. With the aforementioned assumptions, the steady-state conservation equations for the mass and momentum transport take the form

∇·(ρu ⃗) = 0

(1)

∇·(ρuu⃗ ⃗) = −∇p + ∇·τ

(2)

where p is the pressure, u⃗ = (ux, ur) is the velocity vector, and τ is the stress tensor. In this work, we consider gas flows in the range of Re ≤ 200 only, so the two-dimensional axisymmetric T

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dx.doi.org/10.1021/ie302770j | Ind. Eng. Chem. Res. 2013, 52, 5815−5824


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Gas-to-gas radiation plays a major role in chemically reactive flows, as we show in the next section. Here, the P-1 radiation model is applied.25 The incident radiation G is estimated by solving the transport equation

Table 1. Reaction Mechanisms for Homogeneous and Heterogeneous Reactions E (J/kmol)

n

1.6736 × 108

0

Turns18

8.368 × 107

0

1.205 × 10

0

Jones and Lindstedt41 −

R4 R5

2.24 × 1012 m2.25 kmol−0.75 s−1 2.75 × 109 m3 kmol−1 s−1 9.98 × 1010 m3 kmol−1 s−1 4.605 m s−1 K−1 3.007 × 105 m s−1

A

1.751 × 10 1.4937 × 108

1 0

R6 R7

593.83 m s−1 K−1 11.25 m s−1 K−1

1.4965 × 108 1.751 × 108

1 1

reaction R1 R2 R3

8

8

ref

⎛ ∇G ⎞ 2 4 ⎟ − αG + 4αn σT = 0 ∇·⎜ ⎝ 3α ⎠

(9)

where n is the refraction index of the medium and σ is the Stefan−Boltzmann constant. The absorption coefficient α is estimated following the weighted-sum-of-gray-gases model as

42

Libby and Blake Caram and Amundson7 Date43 Libby and Blake42

α=−

ln(1 − ε) , s

s > 10−4 m

(10)

I

α=

21,22

form of these equations is valid. The stress tensor comprises the dynamic viscosity η and is calculated as

{

τ = η [∇u ⃗ + (∇u ⃗)T ] −

2 ∇·u ⃗ 3

}

i

I

ε=

∇·(ρuh⃗ ) = ∇·(λ∇T − qrad ⃗ )−

∑ i

Mi

Ri

4 2 −∇·qrad ⃗ = αG − 4αn σT

Dij = 0.0188

1 ⎞ ⎟ Mj ⎠

pζij 2 Ω D (7)

Here, Dij denotes the diffusion coefficient for a binary mixture; X is the mole fraction; ΩD is the diffusive collision integral, which describes the interaction between molecules; and ζij is the average collision diameter for the binary mixture. For details, see ref 23. The net rate of production of the ith species, Ri, is computed as the sum of the Arrhenius reaction sources over the Nr reactions in which the species is involved Nr

R i = Mi ∑ R ̂ i , r r=1

(13)

Because heterogeneous reactions affect the mass and energy balance at the interface, in the end, they have a significant influence on the boundary conditions for the gas species and the temperature. The convective and diffusive mass fluxes of the gas-phase species at the surface are balanced by the production/ destruction rates of gas-phase species by surface reactions.28 The surface temperature of the particle depends on the balance between the heat release due to the heterogeneous reactions and the convective, diffusive, and radiative heat exchange with the surrounding area. All three mechanisms are considered here. At the surface, the velocity component tangential to the wall is assumed to be zero (no-slip), and in the normal direction, Stefan flow can be present, which characterizes the mass flux between the surface and the gas. For details about the boundary conditions and the approximation of the transport properties, please see ref 13. Reference 13 also discusses the solution of the partial differential equations (PDEs) (eqs 1−6) using ANSYS Fluent, version 13.0.24 It should be noted that the solution of PDEs 1−6 does not imply any assumptions about the flame form or location. Discretization and Software Validation. In this work, we utilize body-fitted, quadrilateral meshes. To avoid blockage effects, the domain extends 40d in the radial direction, 30d in the upstream direction, and 100d in the downstream direction, where d is the particle diameter. The first 20 rows of finite volumes around the particle have a length only of 0.01d, and the particle is discretized with 100 finite volumes along the halfcircumference, which ensures a sufficiently high resolution of near-wall effects. Grid independence was verified using additional calculations with coarser and finer grids. The numerical grid that we used for the study is illustrated in

(6)

⎛1 T 3⎜ M + ⎝ i

(12)

where αi is the absorption coefficient of the ith gray gas and αε,i is the emissivity weighting factor for the ith fictitious gray gas emissivity. In the model applied, the distance s is the characteristic length of each individual finite volume. All values for αi and αε,i are given in refs 26 and 27. Following the given equations, the radiative source term can be calculated using

(4)

where Yi is the mass fraction and Di is the mass diffusion coefficient of species i. In the energy conservation equation, λ is the thermal conductivity, T is the temperature, h is the enthalpy, h0 is the enthalpy of formation, qr⃗ ad is the gas-phase radiation source, and M is the molecular weight. The diffusion coefficient for species i in the mixture, Di, is computed using the local mole fraction of the individual species of the mixture 1 − Xi Di = , ∑j , j ≠ i (Xj /Dij)

∑ αε ,iαips i=0

(5)

hi0

(11)

Here, ε is the total emissivity over the distance s and is calculated as

where RG is the universal gas constant and pop is the operating or reference pressure. The species and energy transport equations are ∇·(ρuY ⃗ i ) = ∇·(ρDi∇Yi ) + R i

s ≤ 10−4 m

i=0

(3)

The density follows the incompressible ideal-gas law pop ρ= Y R GT ∑i Mi

∑ αε ,iαip ,

(8)

The corresponding Arrhenius molar rates, R̂ , are given in the work of Kestel et al.13 The heat capacities of the single species are calculated using polynomial expressions, with coefficients taken from ref 24. The values for λ, η, and D are calculated using kinetic theory. 5817



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Figure 1; the computational domain and numerical setup are presented in Figure 2.

Figure 1. Numerical two-dimensional and axisymmetric mesh.

Figure 2. Computational domain and numerical setup.

Before we proceed with the description of the software and model validation against experimental data published in the literature, a few words should be said about the classical benchmark tests, namely, analytical one-film and two-film models; see the detailed derivation of these models in ref 18. These tests are basically used as first-step validation benchmarks for nonmovable, nonporous oxidizing carbon particles; for example, see refs 13, 29, and 30. In the cited references, the validation of the model against the analytic two-film model is reported. The advantage of analytic models for the validation of codes or software is their transparency in terms of input parameters and the transport properties used in simulations. The same cannot be said about many experimental data published in the literature. Nevertheless, the validation against experimental data provides more insight into the real processes occurring on and near the particle surface. The experimental data considered in this work consist of two sets of experiments performed independently by Rodriguez and Raiko31 and Bejarano and Levendis.32 For validation of the setup for a turbulent flow around a burning graphite rod,33 see ref 34. In ref 31, Rodriguez and Raiko measured the surface temperatures of single char particles in a drop-tube furnace. They investigated different O2/N2 and O2/CO2 atmospheres with oxygen concentrations between 3% and 50% and different gas-flow temperatures. The Reynolds number was equal to 1. In Figure 3, measurements for 200-μm particles in O2/N2 and O2/ CO2 atmospheres at 1273 K are compared with results based on the numerical model described in the preceding section. The agreement is relatively good; most of the results are within the measurement accuracy range. The minimum deviation is 0.5%, the maximum deviation is 10.7%, and the average deviation is 5.3%. Analysis of Figure 3 reveals the large error that occurs if gasto-gas radiation is neglected in the model. For O2/CO2 atmospheres in particular, the difference between the results with and without gas-to-gas radiation is between 8% and 36%, and for O2/N2 atmospheres, it is between 3% and 26%. To strength our validation work, we carried out additional numerical simulations to compare the results with experimental

Figure 3. Validation against experimental data published by Rodriguez and Raiko.31 T∞ = 1273 K, Re = 1.

data published by Bejarano and Levendis,32 who studied the combustion of single lignite and bituminous coal particles in different O2/N2 and O2/CO2 atmospheres with different oxygen concentrations and gas-flow temperatures. In this validation case, we compared particle-surface temperatures predicted numerically against experimental data for lignite coal at approximately 50% burnout.32 Data were selected for an operating temperature of 1400 K in the drop-tube furnace and a particle size of 75−90 μm. O2/N2 and O2/CO2 atmospheres were considered. The oxygen content was varied between 20% and 60% (mole fraction), which largely covers the range of oxygen concentrations that we consider in this article. In the drop-tube furnace, the Reynolds number was guessed to be on the order of 1, and the effect of pyrolysis gases on the char burnout temperatures at approximately 50% burnout time was assumed to be negligible. Figure 4 depicts the comparison between the experimental data of Bejarano and Levendis32 and our numerical results for O2/N2 and O2/CO2 atmospheres. This comparison reveals an acceptable agreement between the different data sets, if we take into account the fact that a so-called surface-reaction based model was used in simulations. In particular, the deviation lies between 3.8% and 5.7% for O2/CO2 and between 1.4% and 2.8% for O2/N2 atmospheres. A further examination of the impact of particle porosity on the results achieved for validation against experiments is given in the Discussion section. Finally, we also calculated the burnout time based on a shrinking-core model35 in which the particle density was kept constant. Following our estimations, the burnout time lies between 25 and 150 ms, depending on the oxygen content. These values cover the burnout times reported by Bejarano and Levendis,32 which were between 10 and 100 ms. The particle burning rates predicted in the present work are between 0.15 5818



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Figure 5. CO2 distribution for partial oxidation at Re = 1. In each panel, the minimum and maximum are marked. YO2,∞ = 0.24, YCO2,∞ = 0.749.

around the particle. Because of these mechanisms, the flame sheet is detached from the particle at higher ambient temperatures (see Figure 5b). In the region between the particle and the flame sheet, the mass fraction of oxygen is approximately zero. To highlight this process in more detail, Figure 6 compares the rates of the homogeneous and heterogeneous reactions as

Figure 4. Validation against data published by Bejarano and Levendis.32 T∞ = 1400 K, Re = 1.

and 1.2 kg/(m2 s). These values are comparable to the 0.1 and 0.7 kg/(m2 s) values reported by Stauch and Maas36 for a 100μm particle at Re = 0.

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PARTIAL OXIDATION OF A SINGLE CARBON PARTICLE IN A 24% O2/75% CO2 ATMOSPHERE Influence of Ambient Temperature. Next, we investigate the partial combustion of a char particle with d = 200 μm as a function of T∞. Because the particle surface temperature is not fixed but a function of surface reactions and surface radiation, the ambient-gas temperature is the independent parameter in our investigations. The composition of the ambient atmosphere is fixed (YO2 = 0.24, YCO2 = 0.749, YN2 = 0.01, YH2O = 10−3). The fluid velocity corresponds to a Reynolds number of 1. In this article, we define this configuration as a reference case for subsequent studies. Figure 5 presents contour plots of the mass fraction of CO2 predicted for the reference case at ambient temperatures of T∞ = 1500 K and 2500 K. It can be seen that the flame-sheet thickness remains approximately constant. At T∞ = 1500 K, some oxygen can reach the particle surface, so exothermic heterogeneous reactions R5 and R6 are active and, along with the homogeneous reaction R1, produce CO2 in the vicinity of the particle surface, which explains the CO2 maximum at the particle surface in Figure 5a. At higher temperatures, the CO oxidation consumes all of the oxygen available. For that reason, no oxygen can be found at the particle surface. The Boudouard reaction (reaction R4), which consumes CO2 produced by the CO oxidation and provides additional CO, is the dominant heterogeneous reaction. This explains the lower CO2 content around the particle, which is illustrated in Figure 5b. The CO produced diffuses away and reacts with O2 to form CO2 (reaction R1) in the flame sheet

Figure 6. Reaction rates for homogeneous (black) and heterogeneous (red) reactions at Re = 1.

functions of T∞. For T∞ = 1000 K, the kinetic rate of reaction R1 (CO combustion) is some orders of magnitude higher than those of the other two homogeneous reactions. For the heterogeneous reactions, reactions R4−R6 mostly affect the partial oxidation process, so the influence of gasification reaction R7 is nearly negligible. As illustrated in Figure 6, reaction R1 remains the most important homogeneous reaction, if the ambient temperature is increased. At higher temperatures, the influence of the Boudouard reaction (reaction R4) increases, and this reaction significantly dominates the heterogeneous reactions. For example, for T∞ = 3000 K, the reaction rate of the Boudouard reaction is 3 orders of magnitude larger than the rate of gasification reaction R7, and reactions R5 and R6 are no longer active. As described previously, this phenomenon is caused by the fact that all of the 5819



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oxygen is combusted within the flame sheet, so no oxygen can be found at the particle’s surface. Because the Boudouard reaction is endothermic, the temperature in a thin layer around the particle is decreased for higher ambient temperatures. The temperature difference at the surface, Ts − T∞, is decreased (see Figure 9), and in the case of T∞ = 3000 K, the surface CO2 concentration is slightly below the concentration in the ambient-gas flow (not illustrated here). It should be noted that the flame can be blown out depending on Re and T∞. The numerical model is able to capture this effect, so a separate flame sheet is not assumed a priori. In particular, for a low oxygen concentration, low gas temperature, and high Reynolds number, no flame could be detected (not shown here). For a 400-μm particle at Re values of 0.64 and 6.38, Higuera12 demonstrated that a flame exists and is attached to the particle, which confirms the flame structures shown in Figure 5. Influence of Convection. In this section, the influence of gas velocity on coal char combustion is considered. The atmospheric composition corresponds to that in the previous section. Figure 7 illustrates the partial oxidation of a single char

Figure 8. Reaction rates for homogeneous (black) and heterogeneous (red) reactions at Re = 100.

values, the flame sheet is much smaller, shifted to the wake region and partially detached from the particle surface. At sufficiently low gas temperatures or high gas-flow velocities, the flame is suppressed or can be blown out. This is the reason for the large impact of Re on homogeneous reactions at low temperatures (see, for example, the influence on water−gasshift reactions R2 and R3 at T∞ = 1000 K). If the temperatures are sufficiently high, this effect becomes less important. This effect and the impact of the enhanced convective mass transfer can be seen in Figure 9. This figure also shows that the

Figure 7. Partial oxidation of a single char particle at Re = 100. Mass fraction of CO2 for T∞ = 2500 K. The minimum and maximum are marked. YO2,∞ = 0.24, YCO2,∞ = 0.749.

particle at Re = 100. It can be observed that, because of the gas flow, the flame sheet around the particle is detached from the particle and is shifted to the downstream side of the particle. From previous works, it is known that the relative velocity between the gas flow and the particle influences the combustion processes through several phenomena.13,37,38 The increased bulk flow causes an increased convective transport of reactants in the vicinity of the particle. The viscous boundary layer and, thus, the characteristic length for the diffusive transport of species to and from the particle’s surface are reduced.12 Additionally, the size and position of the reacting zones (e.g., flame sheet) are significantly changed. To explain the differences between the processes at Re = 1 and Re = 100, in Figure 8, we plot the rates of the homogeneous and heterogeneous reactions at Re = 100. A comparison of Figures 8 and 6 reveals that, because of the enhanced convective mass transfer at Re = 100, the heterogeneous reaction rates are increased by factors of 2−8. The gas flow shifts the flame sheet to the wake region of the particle. In the forward stagnation region at Re = 100, the boundary layer is very thin, and oxygen can be transported to the particle wall by diffusion. Because of this process, in contrast to the case at Re = 1, reactions R5 and R6 remain active and decrease only slightly with increasing T∞. For this reason, not only the Boudouard reaction but also reactions R5 and R6 affect the heterogeneous combustion. At large Re

Figure 9. (Top) Temperature difference between the surface and ambient gas and (bottom) carbon consumption rate for different Re values (YO2,∞ = 0.24).

char particle reacts significantly for all Reynolds numbers considered. For T∞ = 1000 K, the increase of Re from 1 to 200 leads to 50% higher surface temperatures (392 K), and for T∞ = 3000 K, the same increase in Re leads to surface temperatures that are increased by 250% (221 K). The impact of the endothermic Boudouard reaction increases for higher ambient temperatures, so the temperature decreases in a thin layer around the particle. Therefore, the linear relation between Ts − T∞ and T∞ has a proportionality factor between −0.48 and −0.41 (see Figure 9, top). The influence of the gas velocity can also be observed for the carbon consumption rate, displayed in Figure 9 (bottom). It can be seen that the carbon mass flux increases as the Reynolds number or gas temperature increases. 5820



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In particular, the difference between Re = 1 and Re = 200 is 270% for an ambient temperature of 1000 K and 210% for 3000 K.

increased beyond this limit, the surface temperature deviates between 3.6% (110 K) and 12.2% (254 K) if the oxygen concentration in the gas flow is reduced. The carbon consumption rate (see Figure 10, bottom) is strongly affected by the oxygen concentration. The carbon consumption rate changes by 26−60% as YO2,∞ is increased or decreased. A higher gas flow increases the particle’s surface temperature and carbon consumption, as discussed in previous sections. The next question is how the gas flow affects the correlation between the ambient O2 concentration (YO2,∞) and the particle surface temperature or carbon consumption. Upon examination of Figure 10, one can see that, at higher Reynolds numbers, the dependences on the gas composition and temperature remain similar. The proportionality factor between Ts − T∞ and T is in the range between −0.53 and −0.33 (not illustrated). The surface temperature increases by 12.8% for T∞ = 1000 K and by 5.1% for T∞ = 3000 K for YO2,∞ = 0.36. A decrease in the oxygen concentration results in lower surface temperatures, more precisely, 1100 K for T∞ = 1000 and 180 K (5.8%) for T∞ = 3000 K. The carbon consumption rate changes by 31− 53% as YO2,∞ is increased or decreased. This effect is nearly independent of T∞.

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CHAR OXIDATION WITH VARYING O2/CO2 CONCENTRATIONS Finally, we study the influence of the atmospheric composition on the partial oxidation of single char particles in the case of three different atmospheres consisting of oxygen mass fractions of 0.12, 0.24, and 0.36 balanced with CO2. Figure 10 (top)

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DISCUSSION

At present, not all physical effects are well-understood and taken into account in the investigation of single particles. This is especially the case for the effect of the relative particle velocity on the combustion/gasification rate (see the recent works and reviews, e.g., refs 5 and 12). Thus, the basic feature explored in this work (in comparison to that investigated in the 1980s) is the solution of the “convection” problem using the Navier−Stokes (N−S) equation coupled with species concentration and heat conservation equations, including the effect of radiation. From this point of view, this work is a consequent improvement on existing works (e.g., refs 11−13, 39, and 40). In particular, this work • uses the full form of the N−S equation coupled with the energy conservation and species conservation equations using complete sets of boundary conditions taking into account heterogeneous chemical reactions, • uses the Stefan flow condition on the boundary between the chemically reacting solid and the surrounding gas, • validates the model against experimental data published in the literature for a wider range of parameters than in previous works, and

Figure 10. Influence of the O2/CO2 ratio on the temperature difference (top) and carbon consumption rate (bottom). The gas flow was at Re = 1 () and Re = 100 (− − −).

shows the particle temperature difference as a function of YO2,∞ and T∞. As discussed previously, Ts − T∞ is proportional to T∞. If the gas at Re = 1 is considered, the proportionality factor is in the range between −0.51 and −0.24, depending on YO2. An increase of 0.12 in YO2 leads to a 14.5% higher surface temperature (259 K) at T∞ = 1000 K and a 3.2% higher surface temperature (99 K) at T∞ = 3000 K. If YO2,∞ is decreased, the situation is different. At low ambient temperatures (T∞ = 1000 K), the ignition of the particle is suppressed, which results in 790 K lower surface temperatures. If the ambient temperature is

Figure 11. Influence of surface structure on the temperature distribution inside and around a single particle. Setup follows experimental data published by Bejarano and Levendis.32 YO2,∞ = 0.4, T∞ = 1400 K. 5821



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• takes into account gas−gas radiation using the P-1 radiation model. Next, we discuss the assumption that the particle is completely nonporous. It is well-known that char particles feature a complex inner structure with an extended inner surface compared to the outer particle surface.35 In this work, we applied the assumption of a nonporous particle, which is, strictly speaking, not valid for a real char particle, if the so-called kinetically controlled regime (regime I) or pore-diffusion regime (regime II) is dominant (see, for example, the book by Szekely et al.35). At the same time, at higher temperatures, when the diffusion-controlled regime (regime III) is valid, our model is an acceptable approximation. Finally, it should be pointed out that the classical classification of oxidation regimes for a porous particle is valid for a single-component gas− particle system. If a multicomponent gas reacts with a porous particle, several regimes can exist simultaneously for each gas species (see, for example, the recent work by Nikrityuk et al.38). A detailed numerical investigation of such structures could be helpful, but is not feasible because of the large modeling effort required. To demonstrate and discuss some of the phenomena related to particle porosity, we repeated the validation against results published by Bejarano and Levendis32 using a pseudoporous geometry approximated by defining a two-dimensional axisymmetric problem. In this case, we modeled the effect of macroporosity using a geometry consisting of six gaps arranged at equal distances along the particle surface (see Figure 11a). These gaps represent macropores that have access to the outside of the char. Heat transfer inside the solid particle was taken into account. The gaps lead to an increased surface area inside the particle. Figure 11 illustrates the velocity and temperature field in and around these gaps. Inside the gaps, no oxygen is present, so the Boudouard and gasification reactions (reactions R4 and R7, respectively) are the dominant heterogeneous reactions. For this reason, the temperature inside the gaps is decreased. The heterogeneous reactions cause Stefan flow inside the gaps, which leads to small jets at the particle surface. Because of the extended endothermic reactions inside the gaps, the average surface temperature is decreased, as illustrated in Figure 12. Compared to the results for solid particles, agreement with the measurements is improved. The deviation is between 1.5% and 3.8% for O2/CO2 and between 0.5% and 1.4% for O2/N2. With these phenomena in mind, it can be summarized that the modeling of porous particles is far more challenging and remains largely unsolved.

Figure 12. Validation against ref 32 including pseudoporous particle.

An analysis of simulations revealed that the particle velocity plays a significant role in the enhancement of char oxidation due to the increase in convective mass transfer. In particular, a comparison between the reference case predicted for Re = 1 and the case for Re = 100 showed that the heterogeneous reaction rates were increased by factors of 2−8. At a Reynolds number of 200, the surface temperature and carbon consumption rate increased by 50−250% and 210−270%, respectively. On the other hand, a change in ambient oxygen concentration from 0.12 to 0.36 was found to increase the particle surface temperature by 3−15% and the carbon consumption rate by 26−60%. Finally, it should be noted that the findings presented in this work can be used when developing submodels for use in modeling large-scale reactors.

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AUTHOR INFORMATION

Corresponding Author

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*E-mail: [email protected] (A.R.), petr.nikrityuk@vtc. tu-freiberg.de (P.A.N.).

CONCLUSIONS In this work, the partial oxidation of a 200-μm char particle in hot O2/CO2 atmospheres was investigated using a CFD approach. Special attention was paid to the effects of ambient temperature and particle velocity on the burning rate of a char particle. The chemistry was modeled using semiglobal reactions, with three homogeneous and four heterogeneous reactions. A comparison with measured data published in the literature showed good agreement between the numerical and experimental measurements and supported the validity of the proposed model. We demonstrated that gas-to-gas radiation, which has been assumed to be negligible in some works, reduces the particle surface temperatures by between 8% and 36% for ambient temperatures between T∞ = 1000 K and T∞ = 3000 K, respectively.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was funded by the Saxon Ministry of Science and Fine Arts within the framework of Virtuhcon (Project 47531.50-02-0390-09/1).

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NOMENCLATURE A = pre-exponential factor d = particle diameter D = diffusion coefficient E = activation energy G = incident radiation term dx.doi.org/10.1021/ie302770j | Ind. Eng. Chem. Res. 2013, 52, 5815−5824


Article

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h = enthalpy h0 = enthalpy of formation ṁ = mass flow rate ṁ ′ = mass flux M = molecular weight n = refraction index p = pressure q⃗rad = gas-phase radiation source R = production term RG = universal gas constant R̂ = Arrhenius molar rate of creation and destruction Re = Reynolds number s = path length for radiation model T = temperature u⃗ = (ux,ur)T = velocity vector Y = mass fraction Greek Symbols

α = absorption coefficient αε = emissivity weighting factor ε = emissivity ζ = average collision diameter η = viscosity λ = thermal conductivity ρ = density σ = Stefan−Boltzmann constant τ = stress tensor ΩD = diffusive collision integral Subscripts

i = ith species op = operating r = radial direction rad = radiation s = surface x = x direction ∞ = bulk-flow quantity

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