Development of semi-parallel reaction model of devolatilization and heterogeneous reaction for pulverized coal particles

Fuel Processing Technology 158 (2017) 104–114

Contents lists available at ScienceDirect

Fuel Processing Technology journal homepage: www.elsevier.com/locate/fuproc

Research article

Development of semi-parallel reaction model of devolatilization and heterogeneous reaction for pulverized coal particles Shota Akaotsu a,⁎, Junichi Tanimoto a, Tatsuya Soma a, Yasuhiro Saito a, Yohsuke Matsushita a, Hideyuki Aoki a, Akinori Murao a,b a b

Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6-6-07 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan Steel Research Laboratory, JFE Steel Corporation, 1 Kokan-cho, Fukuyama, Hiroshima 721-8510, Japan

a r t i c l e

i n f o

Article history: Received 3 August 2016 Received in revised form 10 December 2016 Accepted 12 December 2016 Available online xxxx Keywords: Pulverized coal combustion Devolatilization Mass transfer rate Semi-parallel reaction

a b s t r a c t A semi-parallel reaction model for the devolatilization and heterogeneous reaction of coal particles during pulverized coal combustion was developed. The quasi-steady mass transfer around a single coal particle with devolatilization and the oxidation of char were analyzed to investigate the effect of the convective flow generated by devolatilization on the mass transfer of the oxidant to the particle surface at various reaction temperatures and particle diameters. The oxidation rates of char with devolatilization were lower than those without devolatilization. This tendency became pronounced with increasing reaction temperature and particle diameter. This indicated that the convective flow generated by devolatilization inhibits the mass transfer of the oxidant to the particle surface and that the influence of the devolatilization depends on the reaction temperature and particle diameter. In addition, the oxidation rates estimated by the semi-parallel reaction model were compared with those obtained from the conventional sequential reaction model and parallel reaction model. In contrast to the other models, the semi-parallel reaction model more accurately represented the decrease in char oxidation rates with increasing devolatilization rate. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The predominant method of coal resource utilization is combustion. Pulverized coal combustion is used in coal-fired thermal power plants [1] and blast furnace operations [2]. Recently, new energy conversion systems such as gasification [3] and oxy-fuel combustion [4–6] have been developed. In general, immediately after pulverized coal particles are injected into a high temperature atmosphere, they are heated by radiative heat transfer from the furnace walls and convective heat transfer between the gas phase and particle surface. Thermal decomposition of the coal particle starts when its surface temperature reaches 700–900 K; then, a char is produced by coal pyrolysis. The release of volatile matter (VM) during pyrolysis results in an elevation of the particle temperature because of the ignition and combustion of the VM, thereby promoting the oxidation and gasification reactions of the char. As the reaction processes taking place during pulverized coal combustion involve instantaneous phenomena which are completed within only a few hundred milliseconds, they have been studied through numerical simulations as well as experimentally [7–11]. Computational fluid dynamics (CFD) is a powerful tool for the analysis of a flow field that includes the interactions between chemical reactions and a fluid ⁎ Corresponding author. E-mail address: [email protected] (S. Akaotsu).

http://dx.doi.org/10.1016/j.fuproc.2016.12.011 0378-3820/© 2016 Elsevier B.V. All rights reserved.

flow. In CFD analyses of pulverized coal combustion, the gas and particle phases are separated, and information about the coal particle, such as its trajectory and chemical reaction rates, can be calculated. Then, a reaction model for pulverized coal combustion must therefore be based on an actual combustion process, which will have significant impact on the flow field in the CFD analysis. On the basis of previous experiments, various reaction models have been developed and applied to numerical simulations. Hashimoto et al. proposed a tabulated devolatilization process (TDP) model to consider the effect of the heating rates of the coal particles on the devolatilization rates [12]. In this model, a database that included pre-exponential factors and activation energies of devolatilization for various heating rates was prepared and the devolatilization rates were extracted from the database. Huang et al. suggested that there are active sites for CO2 and/or H2O at the char surface [13]. In response to those results, Umemoto et al. developed a gasification reaction rate equation that considered the active sites with CO2 and H2O [14]. However, in previous studies, the devolatilization and char oxidation processes have been assumed to be independent. In other words, these processes have been treated as either sequential or parallel reactions in conventional simulations. Fig. 1 shows a schematic diagram of the mass transfer of the oxidant around a single coal particle. Fig. 1 (a, b) illustrates the histories of the devolatilization rate and oxidation rate of the char, assuming these reactions to be sequential or parallel.

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

105

Fig. 1. Schematic diagram of the mass transfer of oxidant (left) and the histories of devolatilization rates and oxidation rates of char in the sequential and parallel reaction models (right).

In the sequential reaction model, char oxidation does not occur until devolatilization is complete. Assuming that the reaction processes, including devolatilization and char oxidation, are sequential, Richter et al. numerically simulated the detailed chemical reactions around a single coal particle [15]. However, a disadvantage of this reaction model is that char oxidation is completely ignored in the early reaction period, even though the char particle has been heated due to the combustion of the VM. Howard and Essenhigh reported that devolatilization and char oxidation in the initial stage progress in parallel when the particle diameter is small [16]. Asotani et al. performed numerical simulations and predicted ignition behavior assuming that devolatilization and char oxidation are parallel processes [17]. In the parallel reaction model, devolatilization and char oxidation are assumed to occur simultaneously but to be independent of each other. Howard and Essenhigh also indicated that convective flow caused by the release of VM inhibits the mass transfer of the oxidant to the particle surface and that the concentration of oxidant at the particle surface is close to zero when the char particle is over 65 μm in diameter [18]. When the temperature at which devolatilization occurs is relatively high or char oxidation occurs at low temperature, devolatilization will influence the oxidation of the char, as shown in Fig. 2. In other words, the reactions are defined as “semi-parallel” reactions, in which the oxidation rate of the char decreases with the convective flow caused by devolatilization and increases with a decrease in the devolatilization rate. Unfortunately, in almost all the previous CFD studies of pulverized coal combustion, the assumptions about the relationship between the devolatilization process and char oxidation were not described. Specifically, it is unclear whether the assumed relationship between these reactions is sequential or parallel. Of course, the interaction between devolatilization and char oxidation is ignored in both cases. Even in ANSYS Fluent®, one of the most popular commercial CFD software applications, char oxidation begins after the VM is completely evolved [19]. Accordingly, the assumption of the relationship between devolatilization and char oxidation processes in CFD has not yet been established.

To understand basic coal combustion phenomena, a onedimensional approach employing a single coal particle is useful. Many researchers, using this approach, have considered detailed chemical reactions in the gas phase or at the particle surface [20–24]. However, most detailed simulations of a single coal particle are too difficult and overly complicated to apply to CFD, due to the high computational costs and limits of grid resolution. Therefore, the assumptions should be carefully determined to prevent inconsistencies between the onedimensional simulation and the CFD for pulverized coal combustion. In the present study, the relationship between devolatilization and the heterogeneous reaction of char was investigated, and a heterogeneous reaction model capable of considering the effect of devolatilization on the mass transfer of the oxidant is proposed for the CFD analysis. To investigate the effect of the devolatilization process on the mass transfer of the oxidant, the quasi-steady mass transfer around a single coal particle was numerically analyzed under the condition that devolatilization and char oxidation occur in parallel. Then, a parameter study was performed for various reaction temperatures and particle diameters, and the effect of the devolatilization process on the mass transfer of the oxidant to the particle surface was quantified. In addition, a semi-parallel reaction model of the devolatilization and heterogeneous reaction of char was developed by fitting a simple equation to the results of the parameter study. Finally, the difference in the oxidation rates between conventional reaction models and the semi-parallel reaction model was evaluated, and the implementation of this reaction model in the CFD of pulverized coal combustion was discussed.

2. Review of the restrictions for calculating coal reactions in CFD Fig. 3 shows an image of the target system in this study, i.e., the phenomena occurring in the computational grid of the CFD simulation. In the CFD analysis of pulverized coal combustion, development of the semi-parallel reaction model is restricted in two ways:

Fig. 2. Schematic diagram of the mass transfer of oxidant (left) and the histories of devolatilization rates and oxidation rates of the char in the semi-parallel reaction model (right).

106

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

Coal particle

Boiler

Computational grid in Euler-Lagrange approach

Target system in this study

Fig. 3. Image of the target system in this study.

• The information in a control volume, such as the distribution of chemical species and temperature, remains unknown. The length of the control volume is much larger than that of the particle diameter. Accordingly, we must use several assumptions to obtain the parameters in the vicinity of the particles. • Even if only representative particles are calculated, we must calculate at least a thousand to as many as ten thousand particles. Accordingly, we cannot perform a detailed simulation that includes the various chemical reactions for each coal particle. According to the first restriction, we carefully determined the assumptions and numerical conditions for a quasi-steady mass transfer analysis, and built the strategy in accordance with the second restriction. 3. Quasi-steady mass transfer analyses around a single coal particle

present calculations because the amount of moisture in Newlands coal is small and depends on ambient conditions. The diameter of each coal particle was set to 10–150 μm, and the reaction temperature was varied in range of 1000 to 2500 K. In this study, the temperatures of the particles and gas phase were assumed to be the same for the basic investigation of mass transfer involving devolatilization and char oxidation processes. We also checked the influence of this assumption on the results of the mass transfer analysis by the simple calculation of a single coal particle. The calculation method and conditions were the same as those enumerated in Section 3.2. The influence for large particles was found to be relatively large due to their large heat capacity. Although this problem can be overcome by solving energy equations for the gas and particle phases, we were concerned that the modelling would become impossible because of an excessive number of independent parameters. Fortunately, the devolatilization rate, which is sensitive to the heating rate, could be determined with PC Coal Lab® (Niksa Energy Associates), considering the heating rate of the particle. Therefore, we assumed that the particle temperature was the same as the gas temperature to avoid the complication of a parameter study because of too many independent parameters. This simplification enabled us to consider the effect of devolatilization on the mass transfer of the oxidant to the char particle surface and to develop a semi-parallel model of the devolatilization and oxidation of char for pulverized coal particles. 3.2. Chemical reactions In this study, the VM was assumed to comprise CO, CO2, H2O, HCN, N2, CH4, C2H2, and tar. The devolatilization rate for each chemical species i was expressed by a first-order reaction rate equation as follows:
 r dev;i ¼ K dev;i V i −V i ;

ð1Þ

  Edev;i ; K dev;i ¼ Adev;i exp − RT

ð2Þ

3.1. Computational domain and numerical conditions Fig. 4 shows a schematic diagram of the computational domain. The coal particle was assumed to be a sphere, and the change in particle diameter with devolatilization and char oxidation was ignored. The gas phase was described by a one-dimensional spherical coordinate system. The computational domain extended from the particle surface to a point 50 times the particle diameter from the particle center. The width of the control volume was set to 1 μm. The dependence of the individual boundaries located in the computational domain and the grid density on the numerical results was confirmed. Quasi-steady mass transfer analyses were performed assuming that the reaction temperature was constant over time and space. In a quasi-steady state, the VM continues to be released at a fixed rate, and the chemical species are transferred until the convective and diffusive flows balance each other. Since the devolatilization rate of the pulverized coal is in a quasi-steady state, the initial value of the reaction rate was used. The numerical conditions are summarized in Table 1. The present investigation considers a bituminous coal (Newlands coal) [25], and Table 2 presents its proximate and ultimate analyses. The moisture in the coal was neglected in the

0.5dp

r

0

Coal particle

49.5dp

Fig. 4. Computational domain around a single coal particle.

where V⁎ is the total amount of VM in the coal, and V is the discharge of VM from the coal. The pre-exponential factor (Adev), activation energy (Edev), the molecular weight of tar, and V⁎ were obtained by pyrolysis simulations using the commercial software, PC Coal Lab®. This software provides a detailed simulation of the pyrolysis behavior of coal based on the FLASHCHAIN® model [26], which considers the macromolecular structure of coal. Then, the heating rate of the coal particle must be estimated and inputted. In this study, the particle was heated at a rate of 105 K/s, based on the rate of a rapid heated system, such as a blowpipe. When PC Coal Lab® is applied for the CFD analysis, the pyrolysis conditions must be determined in advance of the main calculation. Actually, the heating rate is different from particle diameters, and the kinetic parameters of the devolatilization rate equation also would change. However, the particle trajectory in CFD is largely different for each particle, especially in a turbulent flow field. Thus, the simpler calculation of a single coal particle is commonly performed to estimate a representative heating rate, which could be input to PC Coal Lab®. Using TDP model, Hashimoto et al. performed CFD calculations for pulverized coal combustion that considered the differences in the thermal histories of each coal particle. In that case, the coal particles tended to exhibit nearly the same temperature histories (4.43 × 104–1.47 × 105 K/s) regardless of the particle diameter. Therefore, the assumption of uniform thermal histories for all particles would not have a significant impact on the results in this study. During the oxidation of char, the following two chemical reactions, i.e., partial and full oxidation, may occur. C þ 0:5 O2 →CO;

ðR1Þ

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

107

Table 1 Numerical conditions of mass transfer analyses for Newlands coal. Coal

Particle diameter (μm)

Particle density (kg/m3)

Reaction temperature (K)

Mole fraction of N2 (−)

Mole fraction of O2 (−)

Gas pressure (Pa)

Newlands

10–150

800

1000–2500

0.8

0.2

101,325

C þ O2 →CO2 :

ðR2Þ

The partial oxidation reaction (R1) mainly occurs at high temperature, while the full oxidation reaction (R2) dominates at low temperature [27]. In this study, only the partial oxidation reaction (R1) was assumed for char oxidation, for three reasons. First, the target system of this study is a pulverized coal combustion system in which the ambient temperature around the coal is high (above 1600 K). Second, under high-temperature conditions, the mass transfer rate of the oxidant would have a greater effect on the overall rate of char oxidation because the rate-controlling process would shift from the chemical reaction to the mass transfer of the oxidant. As will be discussed in Section 5.1, the effect of devolatilization on the overall rate of char oxidation was found to be more significant at high temperature than at low temperature. Accordingly, the modelling of the char oxidation rate is focused on relatively high-temperature conditions. These details are discussed in the Results & Discussion section. Finally, the char oxidation reaction is often assumed to consist of only the partial oxidation reaction in CFD calculations for pulverized coal combustion [28–30]. Therefore, this assumption is reasonable to integrate the developed reaction model into the CFD for pulverized coal combustion. The chemical reaction rate was expressed by Field's equation [31] as follows: r ¼ kPO2 Sp ;

ð3Þ

  E k ¼ A exp − ; RT

ð4Þ

where the pre-exponential factor, A = 14286 kg/(atm⋅m2 ⋅s), and activation energy, E = 142.4 kJ/mol, were obtained from the literature [32]. PO2 is the partial pressure of oxygen at the particle surface; this value was given by our numerical simulation. Sp is the external surface area of the char particle. Several researchers have performed onedimensional simulations of the reactions of a single coal particle that included a pore diffusion process [23,24], and described the importance of this process. Smith and Tyler introduced an effectiveness factor in the reaction rate equation and evaluated the “intrinsic reactivity” of char particles [33]. When we consider the pore diffusion process through an effective diffusion coefficient, both porosity and tortuosity factors are needed. However, these parameters change with the coal type and pyrolysis conditions. Even in the previous simulation that considered an effectiveness factor, constants were used as the porosity and tortuosity terms. The treatment of these factors is different for each investigator. Therefore, we reduced the complexity of our approach and omitted the unclear assumptions about the pore diffusion process in this study. The most important assumption in our study is that the chemical reactions in the gas phase are ignored. Recently, a number of researchers have focused on O2/CO2 atmospheres for oxy-fuel combustion systems, Table 2 Proximate and ultimate analysis of Newlands coal [16]. Volatile matter

Fixed carbon

Ash

C

56.67

15.13

84.63

d.b.(wt%) Newlands

28.20

H

O(diff.)

N

S

8.69

1.70

0.29

d.a.f.(wt%) 4.69

performing sophisticated simulations that included detailed chemical reactions in the gas and particle phases [24,34]. The motivation behind that research was to understand the basic mechanism and combustion behavior of a new combustion system. However, our motivation was to develop a usable reaction model for considering the CFD of pulverized coal combustion. Therefore, we did not consider chemical reactions in the gas phase, to minimize the inconsistencies and complexity associated with implementing the reaction model in the CFD analysis. 3.3. Governing equations The governing equations for the gas phase were the continuity equation, conservation equations for the chemical species, and the ideal gas law. The equations of the one-dimensional spherical coordinate system are given as follows:  1 ∂
2  x  ρu ¼ Sϕ x2 ∂x 

ð5Þ

0;X in gas phase þ r ; at particle surface i dev;i

ð6Þ

   ∂f m;i 1 ∂
2 1 ∂ 2 þ Sϕ   ρuf   ρD ¼ x x i m;i x2 ∂x x2 ∂x ∂x

ð7Þ

Sϕ ΔV ¼

νr i i

 Sϕ ΔV ¼

ρ¼

X

0; in gas phase ν i r þ r dev;i ; at particle surface

PM : RT

ð8Þ

ð9Þ

The governing equations for the gas phase were discretized on staggered grids with the finite volume method. The convection and diffusion terms in the conservation equations for chemical species were discretized by the power-law scheme [35]. The system of equations was solved using the tri-diagonal matrix algorithm. 4. Development of semi-parallel reaction model 4.1. Strategy for developing the semi-parallel reaction model As mentioned in Section 2, a detailed mass transfer analysis cannot be performed due to the huge number of particles in the CFD domain. Accordingly, we must parameterize the degree of the effect of devolatilization on char oxidation and propose a model equation to easily estimate the reaction rate of char oxidation with devolatilization. Then, the parameters we can use for the modelling are confined to those obtained from previous CFD analyses for pulverized coal combustion. For the char oxidation model in the CFD for pulverized coal combustion, the kinetic/diffusion reaction model proposed by Field [36] is the most popular. According to that model, the oxidation rate of pulverized coal char, r, was estimated by the overall reaction rate, which combined the chemical reaction rate of the char, rC, and the mass transfer rate of the oxidant from the bulk to the particle surface, rM, as follows: 1 1 1 : ¼ þ r rC rM

ð10Þ

108

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

The chemical reaction rate of the char was calculated using Eq. (3). The mass transfer rate of the oxidant to the particle surface was represented using the mass transfer equation proposed by Mulcahy and Smith [37]. These equations are often employed in CFD for pulverized coal combustion because they can account for the convection generated by the products from char oxidation as well as the diffusion of the oxidant around a single coal particle. However, the equations proposed by Mulcahy and Smith cannot consider the effect of the convection generated by devolatilization on the mass transfer of the oxidant to the particle surface. Thus, in this analysis, the mass transfer equation proposed by Mulcahy and Smith was not used to estimate the char oxidation rates with devolatilization; it was only used for the verification of this mass transfer analysis without devolatilization. The details of the equation are discussed in the Appendix A.

Eqs. (11) and (12), were solved by the 2nd-order Runge-Kutta method with a time step of 0.1 μs. Fig. 5 provides a schematic flowchart of each reaction model. In the case of the sequential model, devolatilization and char oxidation are assumed to be successive processes, as in previous numerical studies. In other words, the oxidation rate of the char is not calculated until the devolatilization is completely finished, regardless of the particle surface temperature. On the other hand, in the semiparallel and parallel models, the devolatilization rate and oxidation rate of the char are calculated simultaneously. Then, only in the semiparallel reaction model, the oxidation rate is modified to obtain the reaction rate considering the effect of the devolatilization process. 5. Results and discussion 5.1. The effect of devolatilization on the mass transfer of the oxidant

4.2. Comparison of the oxidation rate of the semi-parallel reaction with that of the conventional reaction model To confirm the superiority of the semi-parallel reaction model developed in the mass transfer analyses above, the oxidation rate of a single coal particle estimated by this model was compared to those obtained from the conventional sequential reaction model and the parallel reaction model. This calculation was different from the above numerical analyses. The calculation conditions are summarized in Table 3. The calculation conditions were set assuming an entrained bed boiler for coal power plants, as described previously [32]. The particle diameter was set to 150 μm and the temperatures of the gas phase and the wall were set to 1500 and 1200 K, respectively. In the case of the sequential reaction model, the oxidation reaction was assumed not to start until the ratio of the VM residual to the initial value fell below 0.01%. The governing equations are mass and energy conservation equations, as follows: dmp ¼ −r; dt mp C p;p

ð11Þ

dT p ¼ Q conv þ Q trad þ Q reac ; dt

ð12Þ

where r is calculated using Eq. (10). Qconv, Qtrad, and Qreac are the convective, radiative, and reaction heat transfers, respectively. They are calculated using the following equations.
 Q conv ¼ h T g −T p Sp ;

ð13Þ

  Q trad ¼ εp σ T 4w −T 4p Sp ;

ð14Þ

Q reac ¼ ξrΔh;

ð15Þ

where h , Tg , Tw , σ, and Δh are the convective heat transfer coefficient, the ambient gas temperature, the solid wall temperature, the Stefan– Boltzmann constant, and the heat of reaction, respectively. The emissivity of the particle, εp, was set to 0.9. The char particle was assumed to be in quiescent flow and the Nusselt number was set to 2.0. For the radiative heat transfer, only that between the char particle and the wall was considered. An appropriate value for the contribution ratio of the heat of reaction to the particle, ξ, has not been established. In previous studies [32,38,39], this value was often assumed to range between 0.3 and 1.0. In this study, ξ was set to 0.5. The ordinary differential equations,

Fig. 6 shows the distribution of the mole fraction of the oxidant around a single coal particle for each case (with and without devolatilization). Without devolatilization, the mole fraction of oxidant at the particle surface is almost the same as the bulk value. This indicates that the rate of oxidant consumption is low and that the apparent oxidation rate of the coal char depends on the chemical reaction rate of the char. On the other hand, with devolatilization, the mole fraction of the oxidant at the particle surface is lower than that without devolatilization. This is because the convective flow generated by devolatilization inhibits the mass transfer of the oxidant to the particle surface, and the apparent reaction rate of the coal depends on the mass transfer rate of the oxidant. The effect of reaction temperature on the distribution of the mole fraction of the oxidant will be discussed in detail. The distribution of the mole fraction of the oxidant around a single coal particle at temperatures of 1400 and 2000 K with devolatilization is shown in Fig. 7. Elevation of the reaction temperature results in an increase in the devolatilization rate, and hence, a remarkable decrease in the mole fraction of the oxidant at the particle surface. At 1400 K, the mole fraction of the oxidant decreases at a distance from the particle surface of r/dp = 1; whereas, it sharply decreases at r/dp = 3 at 2000 K. This is because the magnitude of the convective flow grows larger due to the increase in the amount of VM released from the particle surface. To enable a more detailed discussion of the effect of the convective flow, the distribution of gas velocity around a single coal particle at 1400 and 2000 K is shown in Fig. 8. In Fig. 8 (a), only char oxidation is considered, whereas both devolatilization and char oxidation are considered in Fig. 8 (b). A higher reaction temperature increases the char oxidation rate and devolatilization rate simultaneously; hence, the gas velocity at 2000 K is increased compared with that at 1400 K. Without devolatilization, the gas velocity at the particle surface is less than 1.4 m/s, compared to the ~20 m/s flow observed with devolatilization. Without devolatilization, the convective flow is caused by the generation of char oxidation products, but with devolatilization, the flow results from devolatilization as well as char oxidation. At 2000 K, the gas flux is 2.4 kg/(m2 ⋅ s) without devolatilization, and 8.4 kg/(m2 ⋅s) with devolatilization. These results suggest that the convective flow generated by devolatilization significantly inhibits the mass transfer of the oxidant to the particle surface. Next, the effect of particle diameter will be discussed. Fig. 9 shows the distribution of the mole fraction of the oxidant around a single coal particle with a diameter of either 50 or 100 μm with

Table 3 Calculation conditions for the comparison of reaction models. Particle diameter (μm)

Particle density (kg/m3)

Initial particle temperature (K)

Gas temperature (K)

Wall temperature (K)

Mole fraction of N2 (−)

Mole fraction of O2 (−)

Gas pressure (Pa)

150

800

300

1500

1200

0.8

0.2

101,325

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

START

START

Initialize

Initialize

t+Δt

t+Δt

Initialize t+Δt

Calc. Tp

NO End devolatilization?

NO End devolatilization? Yes

START

Calc. Tp

Calc. Tp

Yes

Calc. rdev

NO End devolatilization? Yes

Calc. rdev

Calc. r

Calc. r

109

Calc. r

Calc. rdev

Calc. r

Calc. r Calc. rinhibited

No

End time ? Yes END

(a) Sequential

No

No

End time ?

End time ? Yes

Yes

END

END

(b) Parallel

(c) Semi-parallel

Fig. 5. Flow diagrams of the iterative procedures for the sequential, semi-parallel, and parallel models.

devolatilization. The mole fraction of the oxidant at the particle surface is lower for the larger (100 μm) particle than the smaller (50 μm) one. In addition, the mole fraction of the oxidant decreases from the bulk to the particle surface; this tendency grows more pronounced as the particle diameter increases. This trend is attributed to the significant influence of the convective flow, which is due to an increase in the amount of VM for larger particles. Fig. 10 shows the distribution of the gas velocity around a single coal particle with devolatilization for particle diameters of 50 and 100 μm. The gas velocity increases with rising particle diameter. This is due to the assumption that the amount of VM released from the pulverized coal is proportional to the cube of the particle diameter, whereas the cross-sectional area that the gas traverses increases with the square of the particle diameter. Next, the effect of devolatilization will be quantitatively evaluated in terms of the oxidation rates of the char. Fig. 11 shows the Arrhenius plots of the oxidation rates of a char particle with a 50 μm diameter. Focusing on numerical solutions without devolatilization, the oxidation rates of char increase linearly with elevation of the reaction temperature

but approach the mass transfer rate of the oxidant above 2000 K. This means that the rate-controlling step shifts from the chemical reaction to the mass transfer of the oxidant. Regardless of the reaction temperature, the numerical solutions agree with the analytical solutions; therefore, the validity of the numerical solutions is confirmed. When devolatilization is considered, the oxidation rate of the char is lower than that without devolatilization because the convective flow caused by devolatilization inhibits the mass transfer of the oxidant; thereby, the mole fraction of the oxidant at the particle surface is reduced. In addition, the increase in chemical reaction rate due to high temperature results in the transition from chemical reaction control to mass transport control; thus, the oxidation rate of the char is decreased above 1600 K. The oxidation rates of chars with diameters of 50 and 100 μm with and without devolatilization are compared in Fig. 12. Although the oxidation rate of the char particle with a diameter of 50 μm is lower than that of 100 μm particle below 1400 K without devolatilization, the difference becomes small above 1600 K. This implies that the rate-

Fig. 6. Distribution of the mole fraction of oxidant around a single coal particle (T = 1400 K, dp = 50 μm).

Fig. 7. Comparison of the distributions of the mole fraction of oxidant with reaction temperatures of 1400 and 2000 K (dp = 50 μm).

110

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

(a) Without VM release.

Fig. 10. Comparison of the distributions of gas velocities at diameters of 50 and 100 μm (T = 1400 K).

and mass transfer rate of the oxidant to the particle surface was evaluated. Since no model was used for calculating the mole fraction of oxidant at the particle surface, the mass transfer rate of the oxidant cannot be directly calculated. Accordingly, the numerical solutions are assumed to follow the overall reaction rate equation, Eq. (10); then, the mass transfer rate of the oxidant was calculated from Eq. (16). 1 1 1 ¼ − : rM r rC

(b) With VM release. Fig. 8. Distribution of gas velocities around a single coal particle (dp = 50 μm).

controlling step shifts from the chemical reaction to the mass transfer of the oxidant. In this calculation, the chemical reaction rate is assumed to be proportional to the square of the particle diameter, and the mass transfer rate is proportional to the particle diameter. In addition, above 1400 K with devolatilization, the oxidation rate of the char particle with a diameter of 100 μm is lower than that of the 50 μm particle; whereas, below 1400 K, that of the 100 μm particle is higher than that of the 50 μm particle. To discuss the temperature at which the ratecontrolling step shifts, the relationship between the chemical reaction

Fig. 9. Comparison of the distributions of the mole fraction of oxidant at diameters of 50 and 100 μm (T = 1400 K).

ð16Þ

The ratio of the mass transfer rate of the oxidant to the chemical reaction rate, rM/rC, is shown in Fig. 13 for various reaction temperatures. The rate-controlling step is the chemical reaction when rM/rC is greater than unity, whereas the rate-controlling step shifts to the mass transfer rate of the oxidant when rM/rC becomes less than unity. The temperature at which the rate-controlling step shifts with devolatilization is lower than that without devolatilization. This is attributed to a decrease in the mass transfer rate of the oxidant due to devolatilization. With devolatilization, the rate-controlling step for the 100 μm particle shifts by 1100 K, whereas that of the 50 μm particle does not shift until 1700 K. This is because the chemical reaction rate per particle surface area is independent of particle diameter, whereas the mass transfer rate of the oxidant per particle surface area is inversely proportional to the particle diameter. Therefore, the effect of devolatilization on the oxidation rate of the char becomes larger with an increase in particle diameter.

Fig. 11. Arrhenius plots of oxidation rates of the char particles (the dotted and solid lines show analytical solutions and the plotted points show numerical solutions).

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

111

Fig. 12. Comparison of the oxidation rates of char particles with diameters of 50 and 100 μm.

Fig. 14. Effect of devolatilization on oxidation rate of char particles with various particle diameters, arranged by rdev/r.

5.2. Parameterization of the inhibition effect of convective flow due to devolatilization on the mass transfer of the oxidant

devolatilization, rdev/r, are shown in Fig. 14. Unfortunately, since the rate-controlling step of the apparent reaction changes depending on reaction temperature, I varies widely for different particle diameters. In this case, not only the values of rdev/r, but also the particle diameters, must be used to obtain the value of I. Fig. 15 shows the relationship between the ratio of inhibition and the ratio of devolatilization rates to mass transfer rates of the oxidant without devolatilization, rdev/rM. Note that the plotted points show the obtained data and the solid line is the fitted equation. To determine the fitting equation, the following three requirements were imposed: the fitting equation must approach the maximum ratio of the inhibition value, Imax = 1; the intercept is zero, corresponding to the fact that I is zero when the devolatilization rate is zero; and the parameters can be integrated into CFD simulations with a minimal number of fitting parameters. As a result, the selected equation is as follows:

The above investigations indicate that the convective flow caused by devolatilization hinders mass transfer of the oxidant and reduces the oxidation rate of the char in the cases of high temperature or large particles. Thus, the degree of decrease in the oxidation rate of the char due to the inhibition effect of devolatilization can be parameterized. As an index representing the effect of devolatilization on the oxidation rate of the char, a ratio of inhibition, I, was defined and introduced as follows: I ¼ 1−

r inhibited ; r

ð17Þ

where rinhibited and r denote the apparent reaction rates with and without devolatilization, respectively. As I moves closer to unity, the inhibition effect of devolatilization on the mass transfer of the oxidant is greater. To incorporate the oxidation rate of the char that considers the inhibition effect of devolatilization into CFD simulations, a semiparallel reaction model was developed. This reaction model was constructed from the parameters commonly used in conventional numerical simulations of pulverized coal combustion. For these parameters, the overall reaction rate without devolatilization, r, mass transfer rate, rM, and devolatilization rate, rdev, were used. The results obtained by arranging the ratio of inhibition, I, with the ratio of devolatilization rates for apparent reaction rates without

Fig. 13. Comparison of the reaction temperatures at which the rate-controlling step shifts for particles with diameters of 50 and 100 μm.

r dev

I ¼ 1−ðcÞ rM ;

ð18Þ

where c is the only model fitting parameter and has a value of 0.939 for this study's target coal (Newlands coal). As can be seen in Fig. 15, the fitting equation shows excellent agreement with I regardless of particle diameter and reaction temperature. However, there is a slight difference for rdev/rM between 25 and 60. Although the accuracy of the fitting equation could be improved by using other high-order functions, the implementation of these results in the CFD would become more complex due to the increases in the numbers of reference and fitting parameters. The equation, i.e., the semi-parallel reaction model, can simply estimate the

Fig. 15. Relationship between the ratio of inhibition and the parameter rdev/rM.

112

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

oxidation rate of the char, and it incorporates the inhibition effect of devolatilization on the mass transfer of the oxidant to the particle surface. Furthermore, since this model requires only parameters that can be easily obtained from conventional numerical simulations, this equation is suitable for the numerical simulation of pulverized coal combustion. Although results for other coals are not shown here, we have confirmed that the ratios of inhibition for other coals can be represented by adjusting the model parameter alone. 5.3. Implementation of the semi-parallel reaction model in the CFD for pulverized coal combustion In the semi-parallel reaction model, the appropriate oxidation rate of the char with devolatilization can be calculated from the inhibition ratio. The procedure to integrate the semi-parallel reaction model into the CFD for pulverized coal combustion is as follows:

(a) Sequential reaction model (conventional model).

1. Using the Eqs. (1) and (2), the devolatilization rate is estimated from the particle temperature at a certain time. 2. To obtain the overall reaction rate of the char without devolatilization, the chemical reaction rate and mass transfer rate of the oxidant are calculated using Eq. (3) and the equation proposed by Mulcahy and Smith [37]. 3. The ratio of the devolatilization rate to the mass transfer rate of the oxidant. rdev/rM, is calculated. 4. By substituting the ratio calculated in step 3 into Eq. (18), the inhibition ratio, I, is obtained. 5. The overall reaction rate of the char with devolatilization, rinhibited, can be obtained as follows:

r inhibited ¼ ð1−I Þr:

ð17Þ

To investigate the superiority of the semi-parallel reaction model developed in the mass transfer analyses above, the oxidation rate of a single coal particle estimated by this model was compared to those obtained from the conventional sequential and parallel reaction models. The details of the calculation conditions and governing equations were provided in Section 4.2. Fig. 16 shows the histories of the devolatilization rates and oxidation rates of the char using the semi-parallel, sequential, and parallel reaction models. For all reaction models, the devolatilization process is finished at t = 35 ms. Focusing on Fig. 16 (a), the char oxidation rate rapidly increases around t = 35 ms, just as the devolatilization process is finished. In the sequential model, it is assumed that the char oxidation reaction does not occur until devolatilization is complete. On the other hand, in Fig. 16 (b) and (c), the oxidation rates of the char gradually increase near t = 20 ms, and clear differences between the results of the sequential reaction model and those of the other models appear. Comparison of Fig. 16 (b) with (c) indicates that the behavior of the oxidation rate of the char in the semi-parallel reaction model seems to be the same as that of the parallel reaction model. This is because the char oxidation rate is low due to the low temperature during the devolatilization process, and the effect of devolatilization on the oxidation rate of the char seems to be small. To further discuss the details of these results, particle temperature histories are shown in Fig. 17. These histories show nearly the same trends across all the models. As shown in Fig. 17 the particle temperature reaches 1000 K at t = 20 ms and 1300 K at t = 35 ms. This result implies that char oxidation does not occur at all until the particle temperature reaches approximately 1300 K in the sequential reaction model. The estimated oxidation rate of the char with the sequential reaction model is clearly unrealistic because char oxidation is known to start at 600–700 K, as shown by Ito et al. [40]. Fig. 18 shows a comparison of the histories of the oxidation rates of the char for the semiparallel and parallel reaction models. During an elapsed time of t =

(b) Semi-parallel reaction model.

(c) Parallel reaction model (conventional model). Fig. 16. Histories of the devolatilization rates and oxidation rates of char.

15–25 ms, in which the devolatilization rate is high, the oxidation rate for the semi-parallel reaction model is slightly lower than that for the parallel reaction model. This is because the oxidation rate is decreased by the inhibition effect of devolatilization, and the semi-parallel reaction model can represent this effect. Although the difference seems to be small in this study, the effect of the semi-parallel reaction model would be large in other cases, such as the CFD in the vicinity of the burner. In addition, the most important point for the use of this reaction model is that we can perform CFD for pulverized coal combustion without additional arbitrary assumptions about the order of the coal combustion process. Therefore, the semi-parallel reaction model would be useful for CFD simulations based on the Euler–Lagrange approach.

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

Fig. 17. Histories of particle temperature.

113

as the devolatilization moved closer to completion. Therefore, the semi-parallel reaction model allows an estimation of the oxidation rate of the char, including the effect of devolatilization on the mass transfer of the oxidant. Applying the semi-parallel reaction model for the devolatilization and heterogeneous reaction of char to computational fluid dynamics for pulverized coal combustion would improve the accuracy of the simulations. Here, the proposed semi-parallel reaction model was developed based on several bold assumptions for gas-phase reactions and porous structure. Those simplifications reduced the complexity and complications of an excessive number of independent parameters, and increased our understanding of the basic transport phenomena around a coal particle. For future work, there is some possibility of refining the reaction model by including the gas-phase reactions and solving the energy equation. Acknowledgements

6. Conclusion The effect of the devolatilization process on the mass transfer of an oxidant to the particle surface during pulverized coal combustion was investigated, and a semi-parallel reaction model for char oxidation, including the inhibition effect of devolatilization, was developed. Then, char oxidation rates were estimated by the developed semi-parallel reaction model, and the predicted values were compared with those from conventional (i.e., sequential and parallel) models. The convective flow generated by devolatilization was found to inhibit the mass transfer of the oxidant, and the oxidation rate of the char was decreased due to the inhibition effect of devolatilization. The effect became more pronounced as the reaction temperature or particle diameter was increased. To parameterize the inhibition effect of devolatilization, the inhibition ratio, I, was defined, introduced, and rearranged using parameters commonly used in conventional numerical simulations. Regardless of reaction temperature and particle diameter, the inhibition ratio was approximately represented by a simple fitting equation. The sequential reaction model illustrated unrealistic behavior, i.e., char oxidation did not occur until the particle temperature reached 1300 K. On the other hand, the oxidation rates estimated by the semi-parallel and parallel reaction models gradually increased at the end of the devolatilization process, and the predicted value of the semi-parallel reaction model was lower than that of the parallel model. This decrease in the oxidation rate in the semi-parallel reaction model was due to the effect of devolatilization, and the difference in the oxidation rates between the semi-parallel and parallel reaction models became smaller

Fig. 18. Comparison of histories of oxidation rates of the char for the semi-parallel and parallel reaction models.

The authors gratefully acknowledge financial support by the Japan Society for the Promotion of Science KAKENHI 26820415. Appendix A The mass transfer rate of the oxidant with convection generated by oxidation can be estimated using the equation developed by Mulcahy and Smith [37] as follows:
#     " Di;0 ρ0  T 0:75 − ln 1−γ f v;i M  carbon  SP r M;i ≃ 0:5dP M T 0 νi γ

ðA:1Þ

where Di,0 is the diffusion coefficient of chemical species, i, at reference temperature, T0. γ is a model parameter represented by the following equations: γ≡

D X νi ; iD νi i

ðA:2Þ

where D is the mean diffusion coefficient defined by the relationship, P X Pi : ¼ iD D i

ðA:3Þ

Nomenclature A Adev Cp D D dp E fm fv h I k Kdev M m P p Q R r Sp Sϕ T u V x

pre-exponential factor for char oxidation pre-exponential factor for devolatilization specific heat of coal particle diffusion coefficient mean diffusion coefficient particle diameter activation energy mass fraction volume fraction convection heat transfer coefficient ratio of inhibition rate constant rate constant of devolatilization molecular weight mass total pressure pressure heat gas constant reaction rate external surface area volumetric source term for dependent variables ϕ reaction temperature velocity amount of volatile matter distance

(kg/(atm⋅m2 ⋅s)) (1/s) (J/(kg⋅K)) (m2/s) (m2/s) (m) (kJ/mol) (−) (−) (W/(m2 ⋅K)) (−) (kg/(atm⋅m2 ⋅s)) (1/s) (g/mol) (kg) (Pa) (Pa) (W) (J/(mol⋅K)) (kg/s) (m2) (kg/s) (K) (m/s) (kg) (m)

114

S. Akaotsu et al. / Fuel Processing Technology 158 (2017) 104–114

Greek symbols γ Δh ε ν ξ ρ σ ϕ

model parameter of mass transfer rate equation heat of reaction emissivity stoichiometric coefficient contribution ratio of heat of reaction to the particle density Stefan–Boltzmann constant dependent variables

(−) (J/kg) (−) (−) (−) (kg/m3) (W/(m2 ⋅K4))

Subscripts C carbon conv dev i M O2 reac trad 0

chemical reaction rate carbon convection devolatilization chemical species mass transfer rate of oxidant oxygen reaction thermal radiation reference

Superscript inhibited

reaction rate with devolatilization

References [1] E.S. Rubin, C. Chen, A.B. Rao, Cost and performance of fossil fuel power plants with CO2 capture and storage, Energy Policy 35 (2007) 4444–4454. [2] P.R. Austin, H. Nogami, J.-i. Yagi, A. Mathematical Model, Of four phase motion and heat transfer in the blast furnace, ISIJ Int. 37 (1997) 458–467. [3] J. Kopyscinski, T.J. Schildhauer, S.M.A. Biollaz, Production of synthetic natural gas (SNG) from coal and dry biomass – a technology review from 1950 to 2009, Fuel 89 (2010) 1763–1783. [4] B.J.P. Buhre, L.K. Elliott, C.D. Sheng, R.P. Gupta, T.F. Wall, Oxy-fuel combustion technology for coal-fired power generation, Prog. Energy Combust. Sci. 31 (2005) 283–307. [5] T. Wall, Y. Liu, C. Spero, L. Elliott, S. Khare, R. Rathnam, F. Zeenathal, B. Moghtaderi, B. Buhre, C. Sheng, R. Gupta, T. Yamada, K. Makino, J. Yu, An overview on oxyfuel coal combustion—state of the art research and technology development, Chem. Eng. Res. Des. 87 (2009) 1003–1016. [6] L. Chen, S.Z. Yong, A.F. Ghoniem, Oxy-fuel combustion of pulverized coal: characterization, fundamentals, stabilization and CFD modeling, Prog. Energy Combust. Sci. 38 (2012) 156–214. [7] C. Chen, M. Horio, T. Kojima, Numerical simulation of entrained flow coal gasifiers. Part I: modeling of coal gasification in an entrained flow gasifier, Chem. Eng. Sci. 55 (2000) 3861–3874. [8] H. Watanabe, M. Otaka, Numerical simulation of coal gasification in entrained flow coal gasifier, Fuel 85 (2006) 1935–1943. [9] N. Abani, A.F. Ghoniem, Large eddy simulations of coal gasification in an entrained flow gasifier, Fuel 104 (2013) 664–680. [10] O.T. Stein, G. Olenik, A. Kronenburg, F. Cavallo Marincola, B.M. Franchetti, A.M. Kempf, M. Ghiani, M. Vascellari, C. Hasse, Towards comprehensive coal combustion modelling for LES, Flow Turbul. Combust. 90 (2013) 859–884. [11] M. Rabaçal, B.M. Franchetti, F.C. Marincola, F. Proch, M. Costa, C. Hasse, A.M. Kempf, Large Eddy simulation of coal combustion in a large-scale laboratory furnace, Proc. Combust. Inst. 35 (2015) 3609–3617.

[12] N. Hashimoto, R. Kurose, S.-M. Hwang, H. Tsuji, H. Shirai, A numerical simulation of pulverized coal combustion employing a tabulated-devolatilization-process model (TDP model), Combust. Flame 159 (2012) 353–366. [13] Z. Huang, J. Zhang, Y. Zhao, H. Zhang, G. Yue, T. Suda, M. Narukawa, Kinetic studies of char gasification by steam and CO2 in the presence of H2 and CO, Fuel Process. Technol. 91 (2010) 843–847. [14] S. Umemoto, S. Kajitani, S. Hara, Modeling of coal char gasification in coexistence of CO2 and H2O considering sharing of active sites, Fuel 103 (2013) 14–21. [15] A. Richter, M. Vascellari, P.A. Nikrityuk, C. Hasse, Detailed analysis of reacting particles in an entrained-flow gasifier, Fuel Process. Technol. 144 (2016) 95–108. [16] J.B. Howard, R.H. Essenhigh, Mechanism of solid-partical combustion with simultaneous gas-phase volatiles combustion, Symp. Combust. 11 (1967) 399–408. [17] T. Asotani, T. Yamashita, H. Tominaga, Y. Uesugi, Y. Itaya, S. Mori, Prediction of ignition behavior in a tangentially fired pulverized coal boiler using CFD, Fuel 87 (2008) 482–490. [18] R.H. Essenhigh, J. Csaba, The thermal radiation theory for plane flame propagation in coal dust clouds, Symp. Combust. 9 (1963) 111–125. [19] ANSYS Mechanical APDL Theory Reference, Release 15.0, November 2013. [20] T.F.W.V.S. Gururajan, R.P. Gupta, J.S. Truelove, Mechanisms for the ignition of pulverized coal particles, Combust. Flame 81 (1990) 119–132. [21] L. Chun Wai, S. Niksa, The combustion of individual particles of various coal types, Combust. Flame 90 (1992) 45–70. [22] A.N. Hayhurst, The mass transfer coefficient for oxygen reacting with a carbon particle in a fluidized or packed bed, Combust. Flame 121 (2000) 679–688. [23] R.E. Mitchell, L. Ma, B. Kim, On the burning behavior of pulverized coal chars, Combust. Flame 151 (2007) 426–436. [24] T. Maffei, R. Khatami, S. Pierucci, T. Faravelli, E. Ranzi, Y.A. Levendis, Experimental and modeling study of single coal particle combustion in O2/N2 and oxy-fuel (O2/ CO2) atmospheres, Combust. Flame 160 (2013) 2559–2572. [25] Y. Matsushita, N. Mitsuhara, S. Matsuda, T. Harada, N. Kumada, Drying of brown coal using moisture analyzer with halogen heat source and simple drying rate equation, Kagaku Kogaku Ronbunshu 38 (2012) 123–128. [26] S. Niksa, A.R. Kerstein, FLASHCHAIN theory for rapid coal devolatilization kinetics. 1. Formulation, Energy Fuels 5 (1991) 647–665. [27] J. Arthur, Reactions between carbon and oxygen, Trans. Faraday Soc. 47 (1951) 164–178. [28] K. Yamamoto, T. Murota, T. Okazaki, M. Taniguchi, Large eddy simulation of a pulverized coal jet flame ignited by a preheated gas flow, Proc. Combust. Inst. 33 (2011) 1771–1778. [29] B.M. Franchetti, F. Cavallo Marincola, S. Navarro-Martinez, A.M. Kempf, Large Eddy simulation of a pulverised coal jet flame, Proc. Combust. Inst. 34 (2013) 2419–2426. [30] A. Bermúdez, J.L. Ferrín, A. Liñán, L. Saavedra, Numerical simulation of group combustion of pulverized coal, Combust. Flame 158 (2011) 1852–1865. [31] M.A. Field, Rate of combustion of size-graded fractions of char from a low-rank coal between 1200 K and 2 000 K, Combust. Flame 13 (1969) 237–252. [32] S. Nozawa, Y. Matsushita, Numerical investigation of the effect of the heterogeneous reaction model on the thermal behavior of pulverized coal combustion, Asia Pac. J. Chem. Eng. 8 (2013) 292–300. [33] I.W. Smith, R.J. Tyler, The reactivity of a porous Brown coal char to oxygen between 630 and 1812 °K, Combust. Sci. Technol. 9 (1974) 87–94. [34] E.S. Hecht, C.R. Shaddix, J.S. Lighty, Analysis of the errors associated with typical pulverized coal char combustion modeling assumptions for oxy-fuel combustion, Combust. Flame 160 (2013) 1499–1509. [35] S.V. Patanker, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Tayler & Francis Group, New York, 1980. [36] M.A. Field, D.W. Gill, B.B. Morgan, P.G.W. Hawkslay, The Combustion of Pulverized Coal, British Coal Utilization Research Association, 1968. [37] M.F.R. Mulcahy, I.W. Smith, Kinetics of combustion of pulverized fuel : a review of theory and experiment, Rev. Pure Appl. Chem. 19 (1969) 81–108. [38] R. Kurose, H. Makino, A. Suzuki, Numerical analysis of pulverized coal combustion characteristics using advanced low-NOx burner, Fuel 83 (2004) 693–703. [39] L. Qiao, J. Xu, A. Sane, J. Gore, Multiphysics modeling of carbon gasification processes in a well-stirred reactor with detailed gas-phase chemistry, Combust. Flame 159 (2012) 1693–1707. [40] S. Ito, T. Tanaka, S. Kawamura, Regeneration of used filter applied to coal gas cleaning, CRIEPI Report, W89031(in Japanese), 1990.