Modeling of single coal particle combustion in O₂/N₂ and O₂/CO₂ atmospheres under fluidized bed condition

Abstract

A one-dimensional transient single coal particle combustion model was proposed to investigate the characteristics of single coal particle combustion in both O₂/N₂ and O₂/CO₂ atmospheres under the fluidized bed combustion condition. The model accounted for the fuel devolatilization, moisture evaporation, heterogeneous reaction as well as homogeneous reactions integrated with the heat and mass transfer from the fluidized bed environment to the coal particle. This model was validated by comparing the model prediction with the experimental results in the literature, and a satisfactory agreement between modeling and experiments proved the reliability of the model. The modeling results demonstrated that the carbon conversion rate of a single coal particle (diameter 6 to 8 mm) under fluidized bed conditions (bed temperature 1088 K) in an O₂/CO₂ (30:70) atmosphere was promoted by the gasification reaction, which was considerably greater than that in the O₂/N₂ (30:70) atmosphere. In addition, the surface and center temperatures of the particle evolved similarly, no matter it is under the O₂/N₂ condition or the O₂/CO₂ condition. A further analysis indicated that similar trends of the temperature evolution under different atmospheres were caused by the fact that the strong heat transfer under the fluidized bed condition overwhelmingly dominated the temperature evolution rather than the heat release of the chemical reaction.

Keywords

coal / oxy-fuel / fluidized bed / combustion / simulation

Introduction

In the foreseeable future, coal is still one of the most important fuel sources in the energy mix of China [¹,²]. However, CO₂ produced by coal combustion may deteriorate greenhouse effect, threatening the ecology. Recently, a number of low-carbon energy technologies have been investigated [³–⁵]. Oxy-fuel combustion is regarded as a potential low-carbon option to coal-fired power plants. In oxy-fuel combustion, oxidizer is changed from air (O₂/N₂) to either pure oxygen or an oxygen/recycled flue gas mixture, in which a gas product mixture with a relatively high CO₂ concentration that is possible to capture the CO₂ from the flue gas is generated. The oxy-fuel technology has been studied in a number of combustion processes, especially in the pulverized coal (PC) combustion process. For example, laboratory-scale studies have been conducted on the oxy-fuel combustion of bituminous coal under the conditions of PC combustion by Levendis and coworkers [⁶–⁸]. Riaza et al. [⁹] have studied the combustion behavior of anthracite and semi-anthracite coal particles. The results show that the combustion intensity under the O₂/CO₂ condition is similar to that under air condition once the oxy-fuel condition is well controlled. These studies have shed some light on oxy-fuel combustion, but they are still limited to the PC combustion condition.

In addition to oxy-fuel PC combustion, oxy-fuel fluidized bed (FB) combustion has become a hot topic recently (e.g., Refs. [¹⁰,¹¹]). Leckner and Gómez-Barea [¹²] have operated oxy-fuel combustion under circulating fluidized bed (CFB) boiler conditions and found that a 30 vol% of O₂ in CO₂ is sufficient enough to maintain the bed temperature. Seddighi et al. [¹³] have observed a higher CO emission during the combustion process in a 4 MW_th CFB boiler under oxy-fuel conditions than that under air-fired conditions. Besides, NO_x, SO₂, and CO emissions of CFB boilers under oxy-fuel operation condition have been studied [¹⁴–¹⁶] and consistent conclusions have been reached. Moreover, experimental studies have been conducted to reveal the particle motion effect on combustion temperature and char conversion [¹⁷–¹⁹]. Recently, a 30 MW (thermal power) CFB boiler has been operated under both oxy-fuel combustion and air-fired combustion conditions at Ciuden, in Spain [²⁰], further confirming the feasibility of oxy-fuel FB combustion in industrial scale experiments. Although great efforts have been made, several key scientific issues in oxy-fuel FB combustion have yet to be completely understood [²¹], including fuel combustion characteristics and the dominating mechanism controlling the overall thermal conversion process of a fuel particle.

The strong heat and mass transfer under FB condition complicates the combustion process [²²]. Understanding of the fuel conversion and motion mechanism is the key to the proper design of FB reactors [²³]. Numerous modeling studies have been conducted on particle motion and thermal conversion. Modeling studies on the pyrolysis of single coal particles coupled with heat transfer and chemical kinetics have been reviewed by Saxena [²⁴] and Solomon et al. [²⁵]. Chern and Hayhurst [²⁶] have also modeled the pyrolysis process of coal particle using a progressing temperature front, and concluded that pyrolysis mainly occurs in a thin layer propagating from the surface of the particle to its center. Scala and Chirone [²⁷,²⁸] have numerically investigated the thermal conversion process of a single fuel particle in a FB at 1123 K and found that the char gasification reactions are enhanced under oxy-fuel conditions. Guedea et al. [²⁹] have studied the devolatilization and combustion of large coal particles in a thermo-gravimetric and proposed a model to predict the devolatilization process in both O₂/N₂ and O₂/CO₂ atmospheres. Bu et al. [³⁰] have developed a single coal paricle FB combustion model to investigate the combustion characteristics in terms of ignition and combustion temperature of single coal particles under oxy-fuel combustion conditions. In addition, modeling and theoretical analyses on the combustion temperature oscillation caused by the movement of the coal/char particles have also been performed by Salinero et al. [³¹].

The real combustion process of coal particles in FBs consists of water evaporation, devolatilization, heterogeneous and homogeneous reaction, as well as internal/external heat and mass transfer. Indeed, only very limited simulation studies have considered these sub-processes in a single coal particle combustion model under the oxy-fuel FB condition. Moreover, the identification of the key process is rarely seen in previous studies. The dominant mechanisms controlling the coal combustion characteristics under oxy-fuel FB conditions are still unclear. Therefore, investigations into the combustion characteristics of fuel particles in oxy-fuel FBs are urgently needed. In this paper, a heating model and a reaction model of single coal particle under FB conditions were proposed, including the heat and mass transfer, carbon conversion, drying, volatiles reaction, and devolatilization processes, etc. aiming to quantitate the combustion characteristics of a single coal particle combustion in air and oxy-fuel atmospheres and to identify the key mechanism controlling the combustion process under the oxy-fuel FB condition.

Modeling

The model proposed is a one-dimensional transient model describing the conversion of a single fuel particle under bubbling bed conditions using spherical coordinates, in which, the sub-processes including the moisture evaporation, devolatilization, char heterogeneous reaction, heat conductivity, convection and radiation are considered. The homogeneous reaction is limited to occur inside a thin reaction sheet, outside of which the gas mixture is chemically inert [³²].

To simplify the model, several assumptions frequently adopted e.g., in Ref. [³⁰] have been made as follows which still keep the key process correct and physically sound in the overall combustion process.

1) The fuel particle retains its spherical shape and is isotropic during the entire combustion process;

2) Fragmentation, swelling, and change of shape of the particle are assumed not to take place during combustion;

3) The temperature of moisture evaporation is assumed to be 373 K;

4) The ideal gas assumption applies.

Based on these assumptions mentioned above, the fuel particle combustion model has been developed in the following sequence.

Chemical kinetic model

In general, the temperature of the fuel particle keeps increasing due to the heating from the hot FB atmosphere. The volatile matter releases subsequently and diffuses away from the particle surface to a certain thin sheet where homogeneous reactions take place. In the present paper, the chemical kinetic model is a scheme consisted of a semi-empirical devolatilization reaction, three heterogeneous reactions, and three homogeneous reactions. The reaction scheme is listed in Table 1, and the detailed kinetic parameters of this model are tabulated in Table 2. It is noted that the heterogeneous reaction calculation needs the value of the specific area (s) of the fuel particle, which is calculated using the typical random pore model [³³] as Eq. (1).

s=s_{\mathrm{0}}(\mathrm{1}-X_{\mathrm{c}})\sqrt{\mathrm{1}-\psi \ln (\mathrm{1}-X_{\mathrm{c}})},

(1)\psi ={\displaystyle \frac{\mathrm{4}\mathrm{\pi }{L}_{\mathrm{0}}(\mathrm{1}-{\epsilon }_{\mathrm{0}})}{s_{\mathrm{0}}^{\mathrm{2}}}}=\mathrm{2.5},

where X_c denotes the carbon conversion rate, and \psi, the structural parameter which is 2.5 in the present paper.

In the computation, the heat release of the devolatilization (R1) is set as ΔH= 3.0×10⁵ J/kg according to Ref. [34].

Heating model of fuel particle

During the combustion process, the mass (density) and temperature of the fuel particle can be described by the one-dimensional conservation equations as

(2){\displaystyle \frac{\partial {\rho }_{\mathrm{par}}}{\partial t}}=-S_{\mathrm{rm}},

(3){\displaystyle \frac{\partial \left({\rho }_{\mathrm{par}}{c}_{\mathrm{p}}{T}_{\mathrm{par}}\right)}{\partial t}}=-{\displaystyle \frac{\mathrm{1}}{r^{\mathrm{2}}}}\hspace{0.17em}{\displaystyle \frac{\partial }{\partial r}}\left({\lambda }_{\mathrm{par}}{r}^{\mathrm{2}}{\displaystyle \frac{\partial T_{\mathrm{par}}}{\partial r}}\right)+{\displaystyle \sum S_{\mathrm{rh}}},

where ρ_par, λ_par, and T_par are the particle mass density, thermal conductivity, and temperature, respectively. S_rm and S_rh respectively denote the mass and heat source terms resulted from the water vaporization, particle pyrolysis and chemical reaction, which can be given by

(4)S_{\mathrm{rm}}=\left(k_{\mathrm{vap}}+k_{\mathrm{pyro}}+\mathrm{\Delta }M\right)/V,

(5){\displaystyle \sum S_{\mathrm{rh}}}=\left(k_{\mathrm{vap}}·\mathrm{\Delta }{H}_{\mathrm{vap}}+k_{\mathrm{pyro}}·\mathrm{\Delta }{H}_{\mathrm{pyro}}\right)/V,

where k_vap and k_pyro are the rates of vaporization and devolatilization while ΔM denotes the consumption rate of carbon (C); V is the particle volume; and ΔH_vap and ΔH_pyro represent the vaporization heat (\mathrm{\Delta }{H}_{\mathrm{vap}}=\mathrm{2.26}\times {\mathrm{10}}^{\mathrm{7}}\mathrm{J/kg}) and the devolatilization heat (\mathrm{\Delta }{H}_{\mathrm{pyro}}=\mathrm{3}\mathrm{.0}\times {\mathrm{10}}^5\mathrm{J/kg}) [³⁴] used in Eqs. (4) and (5).

To solve the above equations, the initial conditions are expressed as Eqs. (6) and (7).

(6)t=\mathrm{0},{\rho }_{\mathrm{par}}={\rho }_{\mathrm{par},\mathrm{0}},

(7)t=\mathrm{0},0\le r\le r_{\mathrm{par}},T_{\mathrm{par}}=T_{\mathrm{par},\mathrm{0}},

where r_par denotes the radius of fuel particle. The boundary conditions to solve Eqs. (2) and (3) are expressed as Eqs. (8) and (9).

(8)t\hspace{0.17em}>\hspace{0.17em}\mathrm{0},r=\mathrm{0},{\displaystyle \frac{\partial T_{\mathrm{par}}}{\partial r}}=\mathrm{0},

(9)t\hspace{0.17em}>\hspace{0.17em}\mathrm{0},r=r_{\mathrm{par}},A_{\mathrm{par}}{\lambda }_{\mathrm{par}}{\displaystyle \frac{\partial T_{\mathrm{par}}}{\partial r}}{|}_{r=r_{\mathrm{par}}}=A_{\mathrm{par}}\epsilon \sigma (T_{\mathrm{b}}^{\mathrm{4}}-T_{\mathrm{par}}^4)+h_{\mathrm{in}}{A}_{\mathrm{par}}(T_{\mathrm{rs}}-T_{\mathrm{par}})-{\displaystyle {\sum }_{j=\mathrm{2}}^{\mathrm{4}}{w}_{s,j}\mathrm{\Delta }{H}_{s,j}}\mathrm{\Delta }t,

where A_par is the particle surface area; h_in denotes the heat transfer coefficient between the fuel particle and the reaction sheet; ε and s are the emissivity and Stefan-Boltzmann constant, respectively; and Δt is the time-step. The convection and radiation from the FB reactor as well as the heat released from the char burning are all taken into account in Eq. (9). The calculation of heat transfer coefficient h_in is introduced in Section 2.5.

Model of moisture evaporation

Given that the moisture is released in a thin layer that separates the wet particle region from the dried external region, the evaporation layer can be defined at a position, r_ef, whose temperature is 373 K based on Assumption 3). The evaporation rate k_vap is determined by the heat transfer from the particle to the evaporation layer through the conduction, as

(10)k_{\mathrm{vap}}\mathrm{\Delta }{H}_{\mathrm{vap}}\mathrm{\Delta }t=\mathrm{4}\mathrm{\pi }{r}^{\mathrm{2}}{\lambda }_{\mathrm{par}}{\displaystyle \frac{\partial T_{\mathrm{par}}}{\partial r}}{|}_{r=r_{\mathrm{ef}}}.

Devolatilization/pyrolysis model of fuel particle

Based on Assumptions 1) and 2), the Loison-Chauvin model from Ref. [³⁵] is used to calculate the mass ratio of volatiles released from the devolatilization process. The formulas are listed as Eq. (11).

(11)\begin{array}{l}{\mathrm{CH}}_{\mathrm{4}}=\mathrm{0.201}-\mathrm{0.469}\phi V+\mathrm{0.241}\phi V^{\mathrm{2}},\hfill \\ {\mathrm{H}}_{\mathrm{2}}=\mathrm{0.157}-\mathrm{0.869}\phi V+\mathrm{1.338}\phi V^{\mathrm{2}},\hfill \\ {\mathrm{CO}}_{\mathrm{2}}=\mathrm{0.153}-\mathrm{0.900}\phi V+\mathrm{1.906}\phi V^{\mathrm{2}},\hfill \\ \mathrm{CO}=\mathrm{0.423}-\mathrm{2.653}\phi V+\mathrm{4.845}\phi V^{\mathrm{2}},\hfill \\ {\mathrm{H}}_2\mathrm{O}=\mathrm{0.}\mathrm{409}-\mathrm{2}\mathrm{.389}\phi V+\mathrm{4}\mathrm{.554}\phi V^{\mathrm{2}},\hfill \end{array}

where fV denotes the mass fraction of the fuel volatiles determined from the proximate analysis on dry, ash-free basis. The volatile matter components determine the chemical stoichiometric coefficients of the devolatilization reaction (R1). Considering the requirement to solve the change of mass and heat transfer equations, k_pyro can be determined by Eq. (12).

(12)k_{\mathrm{pyro}}={\displaystyle \frac{\mathrm{d}{m}_{\mathrm{v}}}{\mathrm{d}t}}.

Volatile homogeneous reaction sheet

The volatiles released diffuse outwardly to meet and react with oxygen away from the particle’s surface. In this model, the homogeneous reactions are assumed to be a group of one-step global reactions. Detailed kinetics of these reactions have been introduced in Tables 1 and 2 in Section 2.1. All the homogeneous reactions occur within a narrow reaction sheet due to the fast reaction rate assumption. The narrow reaction sheet (also called H-zone), as shown in Fig. 1, is located at a certain distance away from the particle surface [³²].

The thickness and the volume of the H-zone are given by Turns as expressed in Eqs. (13) and (14) [³²].

(13)r_{\mathrm{rs}}=\mathrm{MIN}({\displaystyle \frac{\mathrm{Nu}}{\mathrm{Nu}-\mathrm{2}}},\mathrm{5})r_{\mathrm{par}},

(14)V_{\mathrm{rs}}=\mathrm{MIN}\left({\displaystyle \frac{\mathrm{4}}{\mathrm{3}}}\mathrm{\pi }\right(r_{\mathrm{rs}}^{\mathrm{3}}-r_{\mathrm{par}}^3),\mathrm{26}\times {\displaystyle \frac{\mathrm{4}}{\mathrm{3}}}\mathrm{\pi }{r}_{\mathrm{par}}^{\mathrm{3}}),

where r_rs and V_rs are the radius and volume of the H-zone while Nu is the Nusselt number. When Nu approaches to 2 (a small Re_mf number), r_rs increases rapidly. To avoid numerical instabilities, a limited thickness is artificially set to be the maximum 5r_par in Eq. (13). Nu is calculated using Eq. (15) [³⁰,³⁶].

(15)\mathrm{Nu}=\mathrm{2}+\mathrm{0.6}{\left({\displaystyle \frac{{\mathrm{Re}}_{\mathrm{mf}}}{{\epsilon }_{\mathrm{mf}}}}\right)}^{\mathrm{1}/\mathrm{2}}{\mathrm{Pr}}^{\mathrm{1}/\mathrm{3}},

where Pr is the gas Prandtl number and ε_mf is the bed voidage at the minimum fluidization state.

The particle surface temperature T_par and the temperature of the homogeneous layer T_rs are then determined by solving two energy equations. The first energy conservation equation is Eq. (9), which describes the heat exchange between the H-zone and the particle surface. The second one is the energy conservation equation for the H-zone temperature T_rs, as expressed in Eq. (16),

(16){\displaystyle {\sum }_{j=\mathrm{5}}^7{w}_{\mathrm{h},j}\mathrm{\Delta }{H}_{\mathrm{h},j}{V}_{\mathrm{rs}}\mathrm{\Delta }t=\mathrm{4}\mathrm{\pi }{h}_{\mathrm{g}}{r}_{\mathrm{rs}}^2}(T_{\mathrm{b}}-T_{\mathrm{rs}})-h_{\mathrm{in}}{A}_{\mathrm{par}}(T_{\mathrm{rs}}-T_{\mathrm{par}}),

where w_h,j and ΔH_h,j are the reaction rate and reaction heat of homogeneous reactions in H-zone; and h_in is calculated using Eq. (17).

(17)h_{\mathrm{in}}={\displaystyle \frac{\mathrm{4}\mathrm{\pi }{\lambda }_{\mathrm{par}}}{A_{\mathrm{par}}({\displaystyle \frac{\mathrm{1}}{r_{\mathrm{par}}}}-{\displaystyle \frac{\mathrm{1}}{r_{\mathrm{rs}}}})}},

where h_g is the heat transfer coefficient between the reaction sheet and the FB atmosphere. Besides, Eq. (18) holds.

(18){\displaystyle \frac{\mathrm{1}}{h{A}_{\mathrm{par}}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}\mathrm{\pi }{h}_{\mathrm{g}}{r}_{\mathrm{rs}}^{\mathrm{2}}}}+{\displaystyle \frac{\mathrm{1}}{h_{\mathrm{in}}{A}_{\mathrm{par}}}}.

According to FB reactor conditions, the h between the fuel particle and the FB atmosphere can also be determined by using Nu number as in Eq. (19).

(19)h={\displaystyle \frac{\mathrm{Nu}{\lambda }_{\mathrm{par}}}{\mathrm{2}{r}_{\mathrm{par}}}}.

Species conservation equations for the H-zone and the simplified equation for the particle surface reaction are also solved in the model. Thus, the concentration of species i near the fuel particle can be obtained using Eqs. (20) and (21).

(20){\beta }_{\mathrm{g}}(c_{\infty ,i}-c_{\mathrm{h},i})={\displaystyle {\sum }_{j=\mathrm{2}}^{\mathrm{4}}{w}_{\mathrm{s},j}{v}_{i,j}+}{\displaystyle {\sum }_{j=\mathrm{5}}^{\mathrm{7}}{w}_{\mathrm{h},j}{v}_{i,j}{V}_{\mathrm{rs}}+}{\alpha }_i{w}_{\mathrm{1}},

(21){\beta }_{\mathrm{in}}(c_{\mathrm{s},i}-c_{\mathrm{h},i})={\displaystyle {\sum }_{j=\mathrm{2}}^{\mathrm{4}}{w}_{\mathrm{s},j}{v}_{i,j}}{V}_{\mathrm{rs}},

where β_in is the mass transfer coefficient [³²] between the particle and H-zone, and β_g, the mass transfer coefficient between H-zone and the FB atmosphere; v_i,j denotes the chemical stoichiometric coefficient of species i in reaction j, while w_s,j (heterogeneous reactions) and w_h,j (homogeneous reactions) are the reaction rates of reaction j; c_s,j, c_h,j and c_{\infty ,j} are the mass concentration of species i at the particle surface, H-zone, and infinite far space respectively. The convective flux due to the Stefan flow is ignored in the model. The mass transfer coefficients β_in and β_g are given by

(22){\displaystyle \frac{\mathrm{2}{r}_{\mathrm{par}}}{\mathrm{Sh}D{A}_{\mathrm{par}}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}\mathrm{\pi }{\beta }_{\mathrm{g}}{r}_{\mathrm{rs}}^{\mathrm{2}}}}+{\displaystyle \frac{\mathrm{1}}{{\beta }_{\mathrm{i}\mathrm{n}}{A}_{\mathrm{par}}}},

(23){\beta }_{\mathrm{in}}={\displaystyle \frac{\mathrm{4}\mathrm{\pi }D}{A_{\mathrm{par}}\left(\frac{\mathrm{1}}{r_{\mathrm{par}}}-\frac{\mathrm{1}}{r_{\mathrm{rs}}}\right)}},

(24)\mathrm{Sh}=\mathrm{2}{\epsilon }_{\mathrm{mf}}+\mathrm{0.6}{\left({\displaystyle \frac{{\mathrm{Re}}_{\mathrm{mf}}}{{\epsilon }_{\mathrm{mf}}}}\right)}^{\mathrm{0.5}}{\left(\mathrm{Sc}\right)}^{\mathrm{0.3}},

where D is the gas diffusion coefficient of the gas phase (using the value of N₂ diffusion coefficient in the O₂/N₂ condition and that of CO₂ in the O₂/CO₂ condition for simplicity); Sh is the Sherwood number, and Sc, the Schmidt number.

Heterogeneous reaction model of char conversion

The char consumption rate of \mathrm{\Delta }Mis obtained by using

(25)\mathrm{\Delta }M={\displaystyle {\sum }_{j=\mathrm{2}}^{\mathrm{4}}{w}_{\mathrm{s},j}}M{W}_{\mathrm{c}},

where MW_c is the molecular weight of carbon.

Model input parameters

According to Herrin and Deming [³⁷], the thermal conductivity of the fuel particle at 298.15 K is estimated as expressed in Eq. (26).

(26){\lambda }_{\mathrm{par},\mathrm{0}}={\mathrm{0.6}}^{\phi M}\times {\mathrm{4.56}}^{\phi A}\times {\mathrm{0.23}}^{\phi V+\phi C},

where \phi M, \phi A, \phi V, and \phi C are the mass fractions of moisture, ash, volatiles, and fixed carbon of the coal particle. Besides, the heat capacity at the constant pressure of the fuel particle at 298.15 K is given by Eq. (27).

(27)c_{\mathrm{par,0}}=\mathrm{4200}\times (\mathrm{0.189}C+\mathrm{0.874}H+\mathrm{0.491}N+\mathrm{0.36}O+\mathrm{0.215}S\mathrm{),}

where C, H, N, O, and S are the amounts of elements in the fuel particle of dry ash-free basis. At different temperatures, the thermal conductivity and the heat capacity model provided in Ref. [³⁸] are adopted in the present paper, as shown in Eqs. (28) and (29).

(28){\lambda }_{\mathrm{par}}=\{\begin{array}{ll}{\lambda }_{\mathrm{par},\mathrm{0}}\hfill & T_{\mathrm{par}}\le \mathrm{673},\hfill \\ {\lambda }_{\mathrm{par},\mathrm{0}}+\mathrm{2.24}\times {\mathrm{10}}^{-\mathrm{5}}{(T_{\mathrm{par}}-\mathrm{673})}^{\mathrm{1.8}}\hfill & T_{\mathrm{par}}>\mathrm{673},\hfill \end{array}

(29){\rho }_{\mathrm{par}}{c}_p=\{\begin{array}{ll}{\rho }_{\mathrm{par},\mathrm{0}}{c}_{p,\mathrm{0}}\hfill & T_{\mathrm{par}}\le \mathrm{623},\hfill \\ {\rho }_{\mathrm{par},\mathrm{0}}{c}_{p,\mathrm{0}}-\mathrm{2.29}\times {\mathrm{10}}^{\mathrm{3}}(T_{\mathrm{par}}-\mathrm{623})\hfill & T_{\mathrm{par}}>\mathrm{623}.\hfill \end{array}

As given in Table 3, the model parameters are set the same as those in Ref. [³⁰] to make a direct comparison between the experimental data of Bu et al. [¹⁹,³⁰] and the present results computed. In Eqs. (28) and (29), the initial values of thermal conductivity and heat capacity of the fuel particle are listed in Table 4. The proximate and ultimate analyses data are listed in Table 5.

Numerical solver

An implicit and transient code are developed with the integration of the integral finite-volume method to solve conservation equations with initial and boundary conditions. The uniform grid is applied in this code. In the computation, the grid and time step independence tests are conducted first. In particular, 20, 40, 60, 80, 100, and 120 for grids number and 0.01s, 0.001s, 0.0001s, and 0.00001s for time step are tested respectively. The criterion for the grid and time step independence is set to be<0.1% of the results between two different cases. According to independence tests, the grid number is set as 100 in the radial direction, and the time step-size is 0.001 s. Considering the trade-off between the computation accuracy and the computation resources required, the Tri-diagonal matrix algorithm is integrated into this code to solve nonlinear conservation equations. In the computation, the discrepancy of particle temperature between two consecutive cases is used to define whether the particle combustion is completed or not (This criterion is set to be<0.01 K).

Results

Model validation

This model is validated by comparing the particle temperature computed with the experimental data in Ref. [¹⁹]. It is noted that the temperature is measured out in a bubbling bed with a coal particle size range of 6 to 8 mm. More details of the experiments can be found in Ref. [¹⁹]. The validation results are demonstrated in Fig. 2. Generally, it is observed that the particle surface temperature computed and the center temperature are in good agreement with the data measured in both the O₂/N₂ and the O₂/CO₂ atmosphere. Further, considering the evaporation process in the model, a plateau appears on the particle center temperature curves during the initial period, which agrees with the experimental observations.

The sensitivity of the devolatilization and homogeneous reaction to the overall combustion process is numerically verified. Figure 3 presents the particle temperature evolutions by both the original computation and the revised computation. The original one includes the full sub-process while the revised computation is set to exclude the devolatilization model. Only a very slight discrepancy between the original computation and the revised computation is found in Fig. 2 between the cases with and without the devolatilization model, implying that the devolatilization and the homogeneous reaction is not the controlling mechanism for the temperature evolution in the overall combustion process. In the section that follows, numerical studies and analyses are conducted to identify the dominant mechanism for the combustion process.

Particle temperature and carbon conversion

The temperature and carbon conversion are good indicators to characterize the combustion process. Thus, the particle temperature and carbon conversion rate are further numerically studied and the analysis is extended to four different types of coal particles to trend-wisely confirm the evolution curves. Although only one group of kinetic parameters would not perfectly describe the chemical reaction process, the computation in such a way avoids the uncertainty caused by the complexity of the coal and still kept the key points sound when the detailed kinetic parameter data are not available. Figure 4 demonstrates the computed center and surface temperature of different types of fuel particles in the O₂/CO₂ atmosphere with an O₂ volume fraction of 30%. The temperature evolutions of the four types of coal particles are found to be similar to each other. On the contrary, the carbon conversion process presents considerable differences, namely, the carbon conversion is faster if the fixed carbon of the coal is lower, as exhibited in Fig. 5.

Figure 6 compares carbon conversion in an O₂/N₂ atmosphere and those in the O₂/CO₂ atmospheres. The O₂ mole fraction varies in this part of modeling as X_{{\mathrm{O}}_2} = 21%, 30%, and 40%. It is found that the rates of carbon conversion remarkably depends on X_{{\mathrm{O}}_2} for the cases in the O₂/N₂ atmospheres, as displayed in Fig. 6(a). It is straightforward that the higher X_{{\mathrm{O}}_2} in the fluidized bed has promoted the heterogeneous oxidation reaction between carbon and O₂. However, for the cases in the O₂/CO₂ atmospheres as plotted in Fig. 6(b), the dependence of the carbon conversion rate on X_{{\mathrm{O}}_2} is not as strong as those in the O₂/N₂ atmospheres. To clarify this difference, the reaction rates of two key carbon conversion reactions, i.e., the oxidation reaction C+ O₂ = aCO+ bCO₂ and the gasification reaction C+ CO₂ = 2CO are compared and the results are depicted in Fig. 7. It is demonstrated that the oxidation reaction dominates the carbon conversion under both O₂/N₂ and O₂/CO₂ conditions. The gasification reaction plays a more important role in the cases under O₂/CO₂ conditions than in those under O₂/N₂ conditions. When the particle temperature reaches a rather high value (e.g.,>1000 K), the gasification reaction is even as important as the oxidation reaction for the carbon conversion under O₂/CO₂ conditions, and thereby the X_{{\mathrm{O}}_2} effect is minor under O₂/CO₂ conditions, as shown in Fig. 6(b). The results shown in Figs. 6 and 7 also imply that a part of O₂ and CO₂ from the environment can diffuse though the homogeneous reaction sheet to the particle surface under the fluidized bed condition. This is consistent with the finding in Refs. [¹⁵,³⁰,³⁹].

Comparison of fuel combustion between O₂/N₂ and O₂/CO₂ atmospheres

Figures 8 and 9 present direct comparisons of temperature evolution (Fig. 8) and carbon conversion (Fig. 9) in both O₂/N₂ and O₂/CO₂ atmospheres. The discrepancy of the temperature evolution between the two atmospheres is found to be negligible, as shown in Fig. 8, while the discrepancy of the carbon conversion rate between the two atmospheres is significantly large. Naturally, the question will be raised why such a big difference in the chemical reaction can only slightly affect the temperature evolution. To answer this question, a non-dimensional heat ratio (Q^{*}), defined as the ratio of the heat release of the heterogeneous reactions to the total amount of heat transferred from the hot fluidized bed environment to the particle, is used to quantify the controlling process. The mathematical expression for Q^{*} is as demonstrated in Eq. (30).

(30)Q^{*}={\displaystyle \frac{Q_{\mathrm{r}}}{Q_{\mathrm{t}}}},

where Q_r denotes the heat release of the heterogeneous reactions and Q_t, the total heat transfer including radiation and heat convection from the hot environment. These two terms can be calculated using Eqs. (31) and (32),

(31)Q_{\mathrm{r}}=\left|{\displaystyle {\sum }_{j=\mathrm{2}}^{\mathrm{4}}{w}_{\mathrm{s},j}}\Delta H_{\mathrm{s},j}\right|,

(32)Q_{\mathrm{t}}=\left|A_{\mathrm{par}}\epsilon \sigma (T_{\mathrm{b}}^{\mathrm{4}}-T_{\mathrm{par}}^{\mathrm{4}})+h_{\mathrm{in}}(T_{\mathrm{h}}-T_{\mathrm{par}})\right|.

Figure 10 presents the evolution of Q^{*} as a function of time. Although the Q^{*} curve peaks at the time around 25 s, the Q^{*} value is within the range from 0 to 0.11, indicating that the heat transfer is at least an order of magnitude greater than the reaction heat release. As a result, the fuel particle temperature cannot obviously exceed the bed temperature because the heat process is mainly controlled by the heat transfer. This also answers the question why a big difference in the chemical reaction (carbon conversion) has only slightly affected the temperature evolution.

Analysis of volatile fraction and homogeneous reactions

Figure 11 shows the profile of the mole fraction (X_i) of the volatiles as a function of time inside the homogeneous reaction sheet in the O₂/CO₂ atmosphere of anthracitic coal. In the beginning, the particle temperature is sufficiently low to freeze the devolatilization reaction and thus X_{{\mathrm{H}}_2\mathrm{O}}, X_CO, X_{{\mathrm{H}}_2} approximates to 0. As the particle temperature increases, volatiles and moisture are first released and diffused to the homogeneous reaction sheet, followed by sharp increases in X_{{\mathrm{H}}_2\mathrm{O}}, X_CO, and X_{{\mathrm{H}}_2} and decreases in X_{{\mathrm{C}\mathrm{O}}_2} and X_{{\mathrm{O}}_2} due to the fast homogeneous reaction. In addition, the trade-off of X_CO and X_{{\mathrm{C}\mathrm{O}}_2} are found due to the competition among R2, R3, and R7 reactions. The homogeneous reaction evolution agrees with the finding in Section 3.2, further confirming that the gasification reaction plays an important role in terms of the reaction for the cases under the O₂/CO₂ FB combustion condition.

Conclusions

The combustion of a single coal particle in both O₂/N₂ and O₂/CO₂ atmospheres under the fluidized bed combustion conditions was numerically investigated and the following conclusions were made.

The gasification reaction may play an important role in the oxy-fuel fluidized bed combustion process. The carbon conversion rate of the single coal particle under the fluidized bed combustion conditions in the O₂/CO₂ (30:70) atmosphere is promoted by the gasification reaction. The carbon converstion rate is considerably greater than that in the O₂/N₂ (30:70) atmosphere.

The strong heat and mass transfer under the fluidized bed conditions dominates the particle temperature. The particle temperature evolutes similarly, no matter it is under the O₂/N₂ condition or the O₂/CO₂ condition. The further analysis indicates that the similar trend of temperature in different atmospheres is caused by the fact that the strong heat transfer under fluidized bed conditions overwhelmingly dominates the temperature evolution rather than the heat release of the chemical reaction.

References

[1] Wang H, He J. China’s pre-2020 CO₂ emission reduction potential and its influence. Frontiers in Energy, 2019, 13(3): 571–578

[2] Wang W, Li Z, Lyu J, Zhang H, Yue G, Ni W. An overview of the development history and technical progress of China’s coal-fired power industry. Frontiers in Energy, 2019, 13(3): 417–426

[3] Kanniche M, Gros-Bonnivard R, Jaud P, Valle-Marcos J, Amann J M, Bouallou C. Pre-combustion, post-combustion and oxy-combustion in thermal power plant for CO₂ capture. Applied Thermal Engineering, 2010, 30(1): 53–62

[4] Kunze C, Spliethoff H. Assessment of oxy-fuel, pre- and post-combustion-based carbon capture for future IGCC plants. Applied Energy, 2012, 94: 109–116

[5] Leung D Y C, Caramanna G, Maroto-Valer M M. An overview of current status of carbon dioxide capture and storage technologies. Renewable & Sustainable Energy Reviews, 2014, 39: 426–443

[6] Kazanc F, Khatami R, Manoel Crnkovic P, Levendis Y A. Emissions of NO_x and SO₂ from coals of various ranks, bagasse, and coal-bagasse blends burning in O₂/N₂ and O₂/CO₂ environments. Energy & Fuels, 2011, 25(7): 2850–2861

[7] Khatami R, Stivers C, Joshi K, Levendis Y A, Sarofim A F. Combustion behavior of single particles from three different coal ranks and from sugar cane bagasse in O₂/N₂ and O₂/CO₂ atmospheres. Combustion and Flame, 2012, 159(3): 1253–1271

[8] Khatami R, Stivers C, Levendis Y A. Ignition characteristics of single coal particles from three different ranks in O₂/N₂ and O₂/CO₂ atmospheres. Combustion and Flame, 2012, 159(12): 3554–3568

[9] Riaza J, Khatami R, Levendis Y A, Álvarez L, Gil M V, Pevida C, Rubiera F, Pis J J. Single particle ignition and combustion of anthracite, semi-anthracite and bituminous coals in air and simulated oxy-fuel conditions. Combustion and Flame, 2014, 161(4): 1096–1108

[10] Piotrowska P, Zevenhoven M, Davidsson K, Hupa M, Åmand L E, Barišić V, Coda Zabetta E. Fate of alkali metals and phosphorus of rapeseed cake in circulating fluidized bed boiler. Part 2: cocombustion with coal. Energy & Fuels, 2010, 24(8): 4193–4205

[11] Piotrowska P, Zevenhoven M, Davidsson K, Hupa M, Åmand L E, Barišić V, Coda Zabetta E. Fate of alkali metals and phosphorus of rapeseed cake in circulating fluidized bed boiler. Part 1: cocombustion with wood. Energy & Fuels, 2010, 24(1): 333–345

[12] Leckner B, Gómez-Barea A. Oxy-fuel combustion in circulating fluidized bed boilers. Applied Energy, 2014, 125: 308–318

[13] Seddighi K S, Pallarès D, Normann F, Johnsson F. Progress of combustion in an oxy-fuel circulating fluidized-bed furnace: measurements and modeling in a 4 MW_th boiler. Energy & Fuels, 2013, 27(10): 6222–6230

[14] Tan Y, Jia L, Wu Y, Anthony E J. Experiences and results on a 0.8 MW_th oxy-fuel operation pilot-scale circulating fluidized bed. Applied Energy, 2012, 92: 343–347

[15] Duan L, Sun H, Zhao C, Zhou W, Chen X. Coal combustion characteristics on an oxy-fuel circulating fluidized bed combustor with warm flue gas recycle. Fuel, 2014, 127: 47–51

[16] Varol M, Symonds R, Anthony E J, Lu D, Jia L, Tan Y. Emissions from co-firing lignite and biomass in an oxy-fired CFBC. Fuel Processing Technology, 2018, 173: 126–133

[17] Hernberg R, Stenberg J, Zethraus B. Simultaneous in situ measurement of temperature and size of burning char particles in a fluidized bed furnace by means of fiberoptic pyrometry. Combustion and Flame, 1993, 95(1-2): 191–205

[18] Joutsenoja T, Heino P, Hernberg R, Bonn B. Pyrometric temperature and size measurements of burning coal particles in a fluidized bed combustion reactor. Combustion and Flame, 1999, 118(4): 707–717

[19] Bu C, Leckner B, Chen X, Pallarès D, Liu D, Gómez-Barea A. Devolatilization of a single fuel particle in a fluidized bed under oxy-combustion conditions. Part A: experimental results. Combustion and Flame, 2015, 162(3): 797–808

[20] Lupion M, Alvarez I, Otero P, Kuivalainen R, Lantto J, Hotta A, Hack H. 30 MW_th CIUDEN oxy-cfb boiler–first experiences. Energy Procedia, 2013, 37: 6179–6188

[21] Lyu J, Yang H, Ling W, Nie L, Yue G, Li R, Chen Y, Wang S. Development of a supercritical and an ultra-supercritical circulating fluidized bed boiler. Frontiers in Energy, 2019, 13(1): 114–119

[22] Garcia-Gutierrez L, Hernández-Jiménez F, Cano-Pleite E, Soria-Verdugo A. Improvement of the simulation of fuel particles motion in a fluidized bed by considering wall friction. Chemical Enginee-ring Journal, 2017, 321: 175–183

[23] Zhu S, Zhang M, Huang Y, Wu Y, Yang H, Lyu J, Gao X, Wang F, Yue G. Thermodynamic analysis of a 660 MW ultra-supercritical CFB boiler unit. Energy, 2019, 173: 352–363

[24] Saxena S C. Devolatilization and combustion characteristics of coal particles. Progress in Energy and Combustion Science, 1990, 16(1): 55–94

[25] Solomon P R, Serio M A, Suuberg E M. Coal pyrolysis: experiments, kinetic rates and mechanisms. Progress in Energy and Combustion Science, 1992, 18(2): 133–220

[26] Chern J S, Hayhurst A N. Does a large coal particle in a hot fluidised bed lose its volatile content according to the shrinking core model? Combustion and Flame, 2004, 139(3): 208–221

[27] Scala F, Chirone R. Fluidized bed combustion of single coal char particles at high CO₂ concentration. Chemical Engineering Journal, 2010, 165(3): 902–906

[28] Scala F, Chirone R. Combustion of single coal char particles under fluidized bed oxyfiring conditions. Industrial & Engineering Chemistry Research, 2010, 49(21): 11029–11036

[29] Guedea I, Pallarès D, Díez L I, Johnsson F. Conversion of large coal particles under O₂/N₂ and O₂/CO₂ atmospheres—experiments and modeling. Fuel Processing Technology, 2013, 112: 118–128

[30] Bu C, Leckner B, Chen X, Gómez-Barea A, Liu D, Pallarès D. Devolatilization of a single fuel particle in a fluidized bed under oxy-combustion conditions. Part B: modeling and comparison with measurements. Combustion and Flame, 2015, 162(3): 809–818

[31] Salinero J, Gómez-Barea A, Fuentes-Cano D, Leckner B. Measurement and theoretical prediction of char temperature oscillation during fluidized bed combustion. Combustion and Flame, 2018, 192: 190–204

[32] Nikrityuk P, Meyer B. Gasification Processes: Modeling and Simulation. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2014

[33] Bhatia S, Perlmutter D. A random pore model for fluid-solid reactions: I. Isothermal, kinetic control. AIChE Journal, 1980, 26(3): 379–386

[34] Chern J S, Hayhurst A N. A model for the devolatilization of a coal particle sufficiently large to be controlled by heat transfer. Combustion and Flame, 2006, 146(3): 553–571

[35] Loison R, Chauvin F. Rapid coal pyrolysis. Chemical Industry (Paris), 1964, 91 (in French)

[36] Rowe P N, Clayton K T, Lewis J B. Heat mass transfer from single sphere in an extensive flowing fluid. Transactions of the Institution of Chemical Engineers, 1965, 43: 14–31

[37] Herrin J M, Deming D. Thermal conductivity of US coals. Journal of Geophysical Research–Solid Earth, 1996, 101(B11): 25381–25386

[38] Maloney D J, Monazam E R, Woodruff S D, Lawson L O. Measurements and analysis of temperature histories and size changes for single carbon and coal particles during the early stages of heating and devolatilization. Combustion and Flame, 1991, 84(1–2): 210–220

[39] Duan L, Li L, Liu D, Zhao C. Fundamental study on fuel-staged oxy-fuel fluidized bed combustion. Combustion and Flame, 2019, 206: 227–238

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