Models for the combustion of single solid fuel particles in fluidized beds: A review

Renewable and Sustainable Energy Reviews 68 (2017) 410–431

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Models for the combustion of single solid fuel particles in fluidized beds: A review ⁎

Xuguang Jiang , Dandan Chen, Zengyi Ma, Jianhua Yan State key laboratory of clean energy utilization, Zhejiang University, Hangzhou 310027, China

A R T I C L E I N F O

A BS T RAC T

Keywords: Single solid fuel particle Models Combustion Coal Biomass Solid waste (SW)

Combustion is a key process of energy utilization in fluidized beds. To achieve higher efficiency and lower pollution, a fundamental understanding of the complex combustion behavior is required. Mathematical modeling plays important roles in the exploration of the complex process and the prediction of combustion performance. Up to now, many models of the combustion of solid fuel particles have been presented. This study gives a detailed review of the proposed combustion models for common solid fuels, i.e., coal, biomass, and solid waste. The combustion models for coal and biomass have matured. However, models for solid waste have seldom been studied and need to be studied further. Considering the complex compositions of biomass and solid waste, a systematic model library based on many works should be proposed for them in the future. In addition, the transformation behavior of hazardous substance (F, Cl, and heavy metals) in solid waste should also be considered in combustion models in the future. Moreover, advanced measuring methods, such as laser measurements, should be used in future works to better understand the reaction mechanism during combustion and improve the accuracies of the models. An overall and accurate model library for the combustion of various type of solid fuels is expected to be established in the future, which will be helpful in the design, adjustment, and operation of combustion systems.

1. Introduction Combustion is one of the main forms of energy utilization, and coal is the primary energy resource in many countries. The combustion of coals has a large significance in the energy industry because it can effect both the efficiency of energy conversion and the generation of pollutants. Therefore, to achieve higher efficiencies and reduce pollution, it is necessary to know the detail process of coal burning and study the models that simulate the coal combustion process. As a clean coal technology, Fluidized Bed (FB) Combustion has been identified to be useful in pollution control. In addition, fluidized beds can be adapted to nearly every type of fuel, especially low heating value fuels. FB combustion is a promising technology in combustion fields. Currently, more and more attention has been focused on sustainable energy. The disposal of both biomass and solid waste has attracted the attention of the entire world in the past few years. Fluidized beds are thus considered to have a wide application range. Therefore, models of the combustion of biomass and solid waste (SW) in fluidized beds are also urgently in need of study. With the rapid development of computer science and mathematical methods, researchers from all over the world have been extensively

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studying models of the combustion of solid fuels. Because the combustion of solid fuel particles discussed in this paper occurs in fluidized beds, the models refer to relatively large particles. Therefore, this paper focuses mainly on models that represent the combustion of relatively large solid fuel particles in fluidized beds. Some excellent studies can be found all over the word in this aspect. In the 1980s, Agarwal et al. [1–4] from the University of Mississippi did a lot of work on the models for the drying and devolatilization processes of coal combustion in FBs. They were the first ones to perform studies of these aspects. Instead of an empirical model, they proposed a theoretical model for the drying and devolatilization of coal particles in FBs. The model they proposed usually assumes the heat transfer inside particle to be the rate-controlling mechanism. In the 2000s, Komatina et al. [5,6] from the University of Belgrade also studied models for drying and devolatilization. They focused on investigating the temperature inside the coal particle during combustion in an FB. Therefore, they designed an FB system to measure the temperatures in the centers of coal particles. This system was helpful for improving the models by comparing the measured temperatures with simulated data. Dennis et al. [7,8] from the University of Cambridge studied models for char combustion in FBs. They addressed

Corresponding author. E-mail address: [email protected] (X. Jiang).

http://dx.doi.org/10.1016/j.rser.2016.10.001 Received 23 December 2015; Received in revised form 16 July 2016; Accepted 2 October 2016 1364-0321/ © 2016 Elsevier Ltd. All rights reserved.

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τ Τvap χ ψ

Nomenclature A As Aj Ar c Cp CM* CMG CMS D E E0 G hm k k′ k0 km L l m n n1 n2 q r Rp R R S S′ T V V V∞ XC XM ΔH

Area (m2) Specific surface area (m2/m3) Pre-exponential factor: 1 – (mol/m2 s), 2 – (m/s), 3 – (m3/mol s) Archimedes number Content (%) Specific heat capacity (J/kg K) Metal equilibrium concentration (mol/m3) Metal concentration in gas phase (mol/m3) Metal concentration at particle surface (mol/m3) Gas diffusion coefficient (m2/s) Activation energy (J/mol) A mean of activation energy (J/mol) Control surface of cylinder (m2) Metal mass transfer coefficient (m/s) Rate constant (s−1) Reaction rate constant: 1 – (mol/m2 s), 2 – (m/s), 3 – (m3/mol s) Frequency factor (s−1) Mass transfer coefficient (m/s) Initial length of cylinder (m) Length of cylinder (m) Mass (kg) Reaction order Correlation parameter Correlation parameter Specific heat (J/kg) Distance from center of particle (m) Radius of particle (m) Universal gas constant (J/mol K) Reaction rate (mol/m3 s) Source term for heat transfer equation (J/m3 s) Source term for mass transfer equation (kg/m3 s) Temperature (K) Volume (m3) Volatile matter content (%) Ultimate yield of volatile matter (%) Conversion degree of carbon The molar fraction of metal Reaction heat (J/kg)

Subscripts 0 b bp c d de di e eff g i in j M p ref s vi v vap w wall

0 °C Fluidized bed Bed material particle Coal Drying Devolatilization Decomposition rate of species i Evaporation Effective Gas Species: 1 – O2, 2 – CO, 3 – CO2, 4 – C Initial Combustion reactions: 1 – heterogeneous, 2,3 – homogeneous Metal Particle Reference Surface of particle Evolution rate of species i Volatile matter Vaporation of metal Water Furnace wall

Abbreviations SW FB MSW SS CWT HHV TG DTG SHRM MHRM DAEM CR KAS FWO CPD FG-DVC

Greek symbols α δ λ ε ε′ Γ ν ν′ ρ σ σE

Time (s) Vaporization ratio of the metal Molar fraction Parameter for mode of specific surface area changes (Eq. (20))

Heat transfer coefficient (W/m2 K) Distance from control volume to surface of cylinder (m) Heat conductivity (W/m K) Emissivity Char particle porosity Shape factor, 0 for plates, 1 for cylinders, 2 for spheres Stoichiometric coefficient Velocity of gaseous species (m/s) Density (kg/m3) Stefan–Boltzmann's constant, 5.67×108 (W/m2 K4) Standard deviation activation energy (J/mol)

FRM MRM CRM PRM

Solid waste Fluidized bed Municipal solid waste Sewage sludge Coal washery tailings High heating value Thermo-gravimetry Derivative thermo-gravimetry Single heating rate method Multiple heating rate method Distributed activation energy model method Coats and Redfern method Kissinger–Akahira–Sunose method Flynn–Wall–Ozawa method Chemical Percolation Devolatilization Functional Group – Depolymerization, Vaporization, Cross-linking First-order reaction model Multiple-order reaction model Competing reaction model Parallel reaction model

studied models for the entire process of coal combustion in FBs. Chern et al. verified that there is a central core of virgin coal during coal particle combustion in FBs based on experimental observations. The core shrinks mostly with a constant velocity. They also found that the burning temperature of the char is partially controlled by CO oxidation. The shrinking core model was used in many other studies. Sadhukhan et al. proposed a devolatilization and char combustion model for the

the mass transfer processes of char particle combustion in FBs and suggested that the char burning rate is controlled by the diffusion of both O2 to the burning char and the gas products away from it into the particulate phase. They proposed a new correlation between the Sherwood number and the diameter of the burning char. In the 2010s, Chern et al. [9,10] from the University of Cambridge and Sadhukhan et al. [11,12] from the Indian Institute of Technology 411

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Fig. 1. Structure models of coal: (a) Krevelen model [22] and (b) Shinn model [23].

and Thunman et al. [16] from Chalmers University of Technology also proposed the combustion of a single wood particle. The model proposed by Porteiro et al. proposed a specific discretization scheme. Interior-particle processes (drying, devolatilization and char reactions), exterior-particle processes (diffusional and convective transport), and particle shrinkage were considered in this model. The model predictions agreed well with the experimental data. Thunman et al. proposed models that are suitable for several coal particle shapes, i.e., spheres, finite cylinders, and parallelepipeds. The model shows good agreement with experimental results for more than 60 samples. According to

combustion of a single coal in an FB, where the distributed activation energy model was chosen for devolatilization and the chemical reactions model was considered for the char combustion. Both models couple kinetics with heat transfer. These two models were used in many other studies. The model predictions were found to have good agreement with the experimental results. For biomass, in the 2000s, Yang et al. [13] from the University of Sheffield proposed a 2D model for the combustion of a single biomass particle. This model demonstrates the occurrence of a combustion wave and the release of tar. Porteiro et al. [14,15] from Universidad de Vigo 412

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Fig. 2. Stages in the combustion of a coal particle.

Fig. 5. Mean composition of MSW in China [27].

Thunman et al., shrinkage has a considerable influence on devolatilization and char combustion. In the 2010s, Haseli et al. [17–19] from Eindhoven University of Technology studied a model of wood particle combustion under high heating conditions. They focused on the kinetic constants for the devolatilization process and on the gas reactions for the combustion process. These two aspects have never been thoroughly discussed before, and the kinetic constant was proven to be important for the modeling of biomass particle combustion. However, there are not many related studies for solid waste considering its complicated components and various physical and chemical properties. Khiari et al. [20] elaborated a mathematical model that represents the combustion of a small wet sewage sludge particle. The drying of the particle and heterogeneous combustion of the char were both considered in this model; these factors have seldom been considered when modeling the combustion processes of sludge at that time. Mazza et al. [21] studied the combustion model for municipal solid waste (MSW) particles. In this model, a solid waste particle combustion model and a heavy metal vaporization model were both taken into account. A shrinking-core model was used to describe the vaporization behaviors of heavy metals, which are seldom considered in MSW combustion modeling. This study outlined a new field in MSW combustion simulation, e.g., heavy metal vaporization modeling, F and Cl vaporization modeling, and Dioxin vaporization modeling. In this paper, models for the combustion of single solid fuels (coal, biomass, and solid waste) are reviewed. For solid waste, three kinds of solid fuels, i.e., sewage sludge (SS), coal washery tailings (CWT) and municipal solid waste (MSW), are taken into account. First, the chemical structure and combustion mechanisms of solid fuels are introduced in this article. Then, both the kinetic model and the particle model of solid fuels combustion are reviewed. This paper studies the current statuses and prospects of combustion models for single solid

Fig. 3. Structures of the main components in biomass [24]: (a) cellulose, (b) hemicellulose, and (c) lignin.

Fig. 4. Decomposition mechanisms of the main components in biomass [25,26]: (a) cellulose, (b) hemicellulose, and (c) lignin.

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Table 1 The proximate analysis, ultimate analysis and HHV of typical solid waste. Components

MSW (Mean) [27]

SS [28] CWT

Food residue Wood waste Paper Textiles Chlorine-free plastics PVC Rubber From lignite [29] From bitumite [30]

Proximate analysis

Qgr,d kJ kg−1

Ultimate analysis (daf)

Mad

Ad

Vd

FCd

C

H

O

N

S

Cl

69.85 42.95 13.15 13.75 0.13 0.21 0.89 7.5 10.12 8.07

20.98 6.84 12.2 3.56 0.48 4.18 15.64 40.76 18.84 49.52

66.79 75.87 76.14 82.69 99.44 85.94 64.7 48.32 44.92 18.52

12.23 17.29 11.66 13.75 0.08 9.87 19.67 10.92 36.25 28.89

47.22 51.35 45.62 54.08 86.22 40.59 84.52 56.88 66.95 −

7.04 6.39 6.01 5.84 12.97 5 8.62 7.76 5.41 −

41.15 40.5 47.78 38.09 0.73 0.59 4.31 26.16 25.89 −

3.86 1.59 0.34 1.7 0.08 0.08 0.86 7.60 1.45 −

0.49 0.18 0.22 0.22 0.05 0.2 1.56 1.69 0.23 −

1.06 0.29 0.28 0.36 0 53.53 1.62 0.17 − −

15,386 19,461 15,894 20,162 43,448 21,172 29,789 10,341 21,604 14,470

with the increasing temperature and pressure. Humic acid functional groups and humate are also formed during this stage. Then, oxygen functional groups begin to decompose, which causes a reduction in the oxygen content of the coal. Finally, humic acids are gradually transformed into larger molecules through condensation, and aliphatic and alicyclic functional groups are also eliminated. Several structure models for coals have been proposed, among which two typical models were proposed by Krevelen [22] and Shinn [23], as shown in Fig. 1(a) and (b). Aromatic ring groups are the main components of coals. Three stages usually occur during coal combustion: drying, devolatilization, and char combustion, as shown in Fig. 2. Drying generally starts at ~100 °C, and both moisture and some light

fuel particles. Based on these statuses and prospects, the scope of future work can be explained. 2. Chemical structure and combustion mechanism of solid fuels 2.1. Coal To better understand the coal combustion process, the chemical structure of coal must be studied first. Coal is transformed from ancient plants under high temperature and high pressure conditions. The transformation process is called coalification. First, dehydration occurs

Fig. 6. TG curves for the combustion of coals: (a) anthracite [41], (b) bituminous coal [42], and (c) lignite [43].

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gases are evaporated during this stage. As the temperature increases, coal moves into the devolatilization stage when it gets enough energy to support the process. When the temperature reaches the burning point, volatile matter begins to burn and the aromatics are gradually transformed into char by condensation. The last stage is mainly about the combustion of the char...

in this article, hoping to fully understand the combustion mechanism of MSW and then explain the scope of future work.

2.2. Biomass

TG (Thermogravimetry) and DTG (Derivative thermogravimetry) analysis are common methods that are used to analyze the thermal behaviors of fuels. In TG analysis, the mass changes of a sample of a material are continuously recorded as functions of time and temperature so that the thermal behaviors of the sample can be obtained. DTG is the derivative of the TG curve, and it is usually used to observe the mas loss rates of samples. Fig. 6 presents TG curves during the combustion of typical coals,

3. Models for the combustion of coal 3.1. TG analysis and kinetic models

Generally, biomass is composed of three main natural polymeric materials and some minerals. The three main materials are cellulose (~50%), hemicellulose (10–40%) and lignin (10–40%), and their chemical structures are presented in Fig. 3. The cellulose molecule is a linear chain of several hundred to many thousands of simple repeated units. Hemicellulose is a copolymer composed of polysaccharides. Lignin is a cross-linked phenolic polymer, and its monomers are cross-linked by aliphatic or ether bridges.. Biomass has 3 special characteristics compared to coals. First, it has a lower carbon content and lower calorific value and is much easier to burn out. Second, it has a higher content of volatile matter, which makes it easier to start the combustion. The devolatilization stage thus constitutes the main part in the entire combustion process. Third, the density of biomass is lower than that of coal, which makes both the heat transfer and the mass transfer easier for biomass. Based on these 3 characteristics, models for the combustion of biomass particles must be different from those for coals. Fig. 4 shows the decomposition mechanism of the three main components in biomass during devolatilization. The final products of the 3 main polymeric materials can be summarized into three classes: gas, tar and char. However, the performances of these 3 materials in specific processes vary significantly. It is the specific processes that matter most in the combustion model for biomass particles. Thus, it is necessary to fully understand the devolatilization mechanisms of biomass to explain the correct model for its combustion.. 2.3. Solid waste There are many types of solid waste in the world including industrial waste, domestic waste, and agricultural waste. In this paper, three kinds of solid waste are considered, i.e., sewage sludge (SS), coal washery tailings (CWT) and municipal solid waste (MSW). Considering the complicated components of solid waste, detailed chemical structures of each component are not presented. Instead, this article focuses on the composition and material characteristics of typical solid waste fuels in this section. Professor Zhang [27] from Tsinghua University studied the main components of MSW in China. As shown in Fig. 5, MSW in China is composed of combustible fractions and non-combustible fractions. Table 1 gives the material properties of solid waste fuels, including SS, MSW, and CWT. Both the proximate and ultimate properties of solid waste vary from one component to another, especially for MSW. SS and CWT generally have high ash contents. The proximate and ultimate properties of CWT depend on the coal type before washing.. Up to now, only a few studies on models for the combustion of solids have been observed, most of which have focused on sewage sludge. For SS, models for the combustion of coals and biomass can be taken as a reference considering the similarities in their physical and chemical properties. Models for the combustion of CWT can also take coal as a reference because it is derived from coals. Moreover, to present a precise model in the future for combustion of both SS and CWT, attrition and fragmentation of particles must be taken into consideration due to their high ash contents. For MSW, it is hard to precisely simulate its combustion due to its sophisticated composition and the differences between each component. However, some kinetic analysis for the combustion of MSW have been studied using the TG method. Therefore, kinetic analysis has been reviewed for the first time

Fig. 7. Models for the combustion of a single fuel particle. (a) sphere [44]: (1) origin fuel, (2) dry fuel, (3) fuel after devolatilization and burning, (4) water evaporation surface, (5) dry fuel combustion surface; (b) cylinder [14]: numerical model.

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SHRMs are also known as model-based methods. The representative method for SHRMs is the Coats–Redfern method (CR method), which was proposed by Coats and Redfern [31,32]. In this method, a reaction mechanism model must be assumed first and the kinetic parameters are obtained using linear fitting. The CR method has relatively high error and is usually used in early studies. MHRMs are also called iso-conversional methods or model-free methods. Reaction mechanism models do not need to be assumed first, and the value of the activation energy is obtained based on the TG curves recorded at several different heating rates. The representative methods for MHRMs are the Kissinger–Akahira–Sunose method (KAS) and the Flynn–Wall–Ozawa method (FWO). The FWO method was proposed by Flynn et al. [33,34], and the KAS method was proposed by Kissinger et al. [35]. These methods can usually achieve higher accuracy than SHRMs. However, only the value of the activation energy can be obtained using these methods. Without the reaction order and the pre-exponential factor, an entire kinetic mechanism

Fig. 8. Flow chart for the calculation process at each time step [48].

i.e., anthracite, bituminous coal, and lignite. A sharp decrease in the TG curve is observed for all kinds of coal. This sharp decrease is attributed to the release of volatile matter and the combustion of this matter. As shown in Fig. 6(a), an obvious decrease in the TG curve before the devolatilization stage is found because lignite usually contains high moisture contents. Based on the TG analysis of all of the coals, three stages can be observed during the combustion of coals: a water evaporation stage, a devolatilization stage and a char combustion stage. Models for the combustion of coals were also proposed based on the three stages. Moreover, the peak temperature of each coal is different. The peak temperatures of anthracite, bituminous coal, and lignite are 620 °C, 480 °C and 400 °C, respectively. Therefore, the models must be different for the combustion of different coals.. The kinetic parameters for the combustion of coals are usually very important during the model study because it is directly related to the description of the processes for each stage. Generally, the kinetic parameters are obtained from TG curves using a series of methods. It is very important to choose the right method to accurately find the kinetic parameters. There are many different methods for the study of kinetic parameters based on TG curves. These methods can fall into three classes: single heating rate methods (SHRMs), multiple heating rate method (MHRMs) and distributed activation energy model methods (DAEMs).

Fig. 9. Experimental fluidized bed reactors: (a) [28] 1) Gas preheating section; 2) electrical furnaces; 3) ceramic insulator; 4) gas distributor; 5) thermocouple; 6) fluidization column; 7) steel basket; 8) manometer; 9) digital mass flowmeters; 10) air dehumidifier. (b) [5] 1) Fan; 2) N2; 3) Tubes; 4) Coal particle; 5) Fluidized bed; 6) Thermal insulation; 7) Electrical heater; 8) Thermocouple in particle center; 9) Fluidized bed reactor; 10) Thermocouple in fluidized bed; 11) Data acquisition system; 12) Gas analyzer; 13) Digital thermometer.

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on the temperature of the shell after the drying process. The devolatilization process consumes heat, and at the same time, it cools the coal particle shell. The combustion of volatile matter occurs in a diffusion flame around the particle. Char combustion of the coal particle is calculated based on the temperature of the shell in the final step. During this process, the temperatures of the shell is increased by the reaction heat. At each time step, related data are collected throughout the entire combustion process, e.g., temperatures, coal properties, and carbon contents.. Most models were proposed based on the shrinking core model, which presumes a diameter of the unreacted core that shrinks with time as shown in Fig. 7. A typical calculation procedure using the shrinking core model is presented in Fig. 8. The fuel particle is divided into many shells for the numerical calculation of the combustion model as shown in Fig. 7(b). Shrinking core models can frequently be observed in the combustion models for single solid fuel particles in the following sections. Two typical fluidized bed reactors used to study combustion models are presented in Fig. 9. Both Cano et al. [28] and Komatina et al. [5] conducted combustion experiments in bubbling fluidized bed combustors. According to Cano et al., the changes in fuel particles at different reaction times were studied by pulling them out of the rector using a steel basket. However, the temperature inside the fuel particle is difficult to measure in this way. In Komatina’s study, the coal particles were first drilled through their centers and fastened to thermocouples, and then, they were placed into the fluidized bed. However, it is difficult to study the characteristics of the fuel particle at different reaction times using this method. Thus, the two aspects of both Cano’s and Komatina’s methods must be taken into consideration when designing a fluidized bed reactor for model studies..

cannot be obtained. Therefore, Khawam and Flanagan [36] proposed a complementary method. According to this method, the active energy is first obtained based on an MHRM. The reaction order and the preexponential factor are then achieved using the idea given by Gotor et al. [37]. Gotor et al. proposed a new master plot method based on the integral kinetic equation. According to this method, the kinetic model and reaction order can be obtained by comparing the experimental plot with theoretical plots at various degree of conversion. The preexponential factor can be then calculated according to a related equation with a known kinetic reaction mechanism. DAEMs were proposed by Vand et al. [38] and applied to the pyrolysis of coals by Pitt [39]. DAEMs presume the occurrence of a series of parallel reactions and continuously distributed activation energies. DAEMs and MHRMs can complement each other due to their respective advantages. The application of MHRMs ensures accurate results for higher rank coals because the volatile content is relatively low. Lower rank coals usually have higher volatile matter contents, and the secondary pyrolysis may have an influence. Thus, DAEMs based on a series of parallel reactions can achieve accurate results if applied to lower rank coals [40]. 3.2. Models for the combustion of a single coal particle Many studies have been conducted to study the combustion models of single coal particles [6,8–12,44–52]. According to Section 3.1, three stages can be observed in the TG analysis of coal combustion: the water evaporation stage, the devolatilization stage and the char combustion stage. The combustion model of a single coal particle is also established based on these three stages. Some of these models can also be used for the combustion of biomass and solid waste, especially for the heat and mass transfer model of the entire process. Many researchers have proposed combustion models of biomass and solid waste based on the models of coals and made some progress with these models. Thus, in this section, some models used for biomass and solid waste are also introduced as models for coals because these models were proposed based on coal models, e.g., the heat transfer model proposed by Saastamoinen [46] for biomass and the drying model proposed by Kijo-Kleczkowska [44] for coal water suspensions. Therefore, no more specific introduction for the heat and mass transfer model, drying model, and char combustion model will be conducted in the sections for biomass and solid waste. Models for the combustion of different shapes of a single fuel particle are shown in Fig. 7: (a) sphere and (b) cylinder. According to Fig. 7(a), three periods can be found in the combustion process: a drying period, a devolatilization period, and a char combustion period. Three zones and two surfaces can be observed as the origin fuel zone, dry fuel zone, zone of fuel after devolatilization, water evaporation surface, and dry fuel combustion surface. As shown in Fig. 7(b), a discretization scheme for a cylinder was described. A distance (r) from the center of the particle to the control volume is assumed in this method. The control volume dV is defined as a hollow cylinder with an inner diameter (r–dr/2) and outer diameter (r+dr/2). The length of the control volume is l(r)=L−Rp+2r. The control surface is G(r) =dV(r)/dr=πr2l(r)/dr=2πr(L−Rp)+6πr2. This model is more suitable for particles with isotropy because the distance from the control volume to the surface of the cylinder is equal in each direction.. Fig. 8 gives the entire calculation process for the combustion of a single solid fuel particle, where three sub-models that were proposed based on the three periods during combustion can be found in the process. Heat transfer is calculated separately in each sub-model. The most important sub-models in the simulation models are reviewed in the following sections. At every time step, the calculation starts with convective and conductive heat transfer to the coal particle. The drying of the coal particle is then calculated based on the temperature of the shell, and the inner shell of the coal particle is cooled by the generated water vapor. The devolatilization of the coal particle is calculated based

3.2.1. Models for drying Drying is the first process during coal combustion, and only a few studies were conducted to study the drying models of coal particles in FBs [1–5,48,53,54]. Due to the high temperature, drying occurs after the coal particles enter the combustion reactor. The drying process is usually believed to end when all of the moisture has evaporated, and then, the devolatilization process begins. However, according to Agarwal et al. [2,4], there is no clear dividing line for drying and devolatilization, and instead, the two process always have a crossing period during the combustion process. According to the drying model presented by Agarwal et al. [1,3], only heat transfer was considered in the model. However, the mass transfer and diameter change were neglected; it was a simplified model. Winter et al. [48] presented a global combustion model for coal particles. In this model, three sub-models were introduced, and the

Fig. 10. Schematic diagram of a drying coal particle [6].

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n1 is a parameter proposed by Komatina et al., n1 = 0.095(dc / dp )0.125. Ar is the Archimedes number. The Komatina’s model introduced above is a simplified model, and there are some other key problems that are not taken into consideration in this model but are very important for the modeling of coal drying. For example, in Komatina’s model, only spherical coal particles are considered. However, coal particles with different shapes should be taken into account. Saastamoinen [46] proposed a heat transfer equation that is suitable for some common fuel particle shapes as follows:

influence of the moisture content on the drying characteristics was also discussed. Komatina et al. [5,6] also presented a drying model for coal particle combustion, and the fluidized bed reactor used in this study is shown in Fig. 9(b). The results based on this drying model were verified to be in good agreement with the experimental data. Komatina’s model is a typical, simple, unsteady drying model for single coal particles in an FB, and it was proposed based on the shrinking core model. Both the mathematic methods and the shrinking core theory of Komatina’s model are often applied to other models, so it is mainly introduced in this section. The drying model assumes that the particle is a sphere and that its diameter does not change during drying, which means that no attrition or fragmentation occurred during the drying process. The drying model is an unsteady model that was presented based on the shrinking core model as shown in Fig. 10. In this model, the moisture is assumed to evaporate in an infinitely thin interface, which is also considered as the dividing line for the different regions in coal particles as shown in Fig. 10. The wet-dry interface has a constant temperature (100 °C), and it propagates from the surface of the coal particle to its center. In this drying model, only heat transfer was considered, which is similar to the model proposed by Agarwal et al. Thus, the mass transfer is not considered inside the coal particle.. The heat transfer is introduced as the following equation:

ρCp

∂T 1 ∂ ⎛ ∂T ⎞ = 2 ⎜λr 2 ⎟ ∂τ r ∂r ⎝ ∂r ⎠

ρCp

(1)

where ρ is the density (kg/m ), Cp is the specific heat capacity (J/kg K), and λ denotes the heat conductivity (W/m K) of the coal particle. Eq. (1) is a general one dimensional unsteady heat conduction equation for a sphere, where the source term is neglected. The term on the left side represents the storage of energy, and the term on the right side represents the conduction heat transfer. Eq. (1) represents the heat balance of the coal particle and determines the temperature inside the coal particle. All of the processes during the coal particle combustion are simulated based on this equation. According to Fig. 10, the temperature change inside the coal particle is between re and R, and the corresponding boundary conditions are explained as

λ

∂T ∂r ∂T ∂r

= ρw qd r = re

dre dτ

λ

(1a)

(1b)

where q is the specific heat (J/kg), α is the heat transfer coefficient (W/ m2·K), and A denotes the area (m2). For the subscripts, w represents water, d represents drying, b represents fluidized bed, and s represents the surface of the coal particle. According to Eq. 1a, the heat transfer at the evaporation front mainly contains heat for both heating the fuel shell and vaporing water. Parameter qd is the specific heat for the heat transfer:

qd = [(1 − cw ) Cp, c + cw Cp, w ](Te − Tin ) + cw qe

0.4615 ⎛ −0.275 2.6505λ (Tb ) n1⎡ λg (Tb ) ⎤ d ⎞ ⎥ ⎜ c⎟ Ar ⎢ dp ⎣ λg (T0 ) ⎦ ⎝ dbp ⎠

4 = αA (Tb − Ts ) + εσ (Twall − Ts4 ) r = Rp

(5)

∂ρi = Si ′ ∂τ

(6a)

∂(ε′ρi ) 1 ∂ + 2 (r 2v′ρi ) = Si ′ ∂τ r ∂r

(6b)

where Eqs. (6a) and (6b) are used for the mass transfer of the solid phase (coal, char, and liquid water) and the gaseous phase (water vapor, gas, and tar), respectively. i represents the species. S′ is a source term, and it is different for different reaction phases (drying and devolatilization). For the drying process, the mass generation rate of water during the drying process is a key parameter of the source term in the mass transfer equation. Kijo-Kleczkowska [44] used an equation to describe the moisture evaporation rate as follows:

(2)

The first term on the right side of Eq. (2) represents the heat for heating the evaporation layer from its initial temperature to 100 °C. The second term is the heat for moisture evaporation. According to Eq. (1b), the heat transfer at the surface of particle is mainly determined by the convective heat transfer between the fluidized bed and the surface of the particle. The heat transfer coefficient (α) is proposed as

α=

∂T ∂r

Compared to Eq. (1b), the radiative heat transfer is added into the heat transfer at the surface of particle as shown in the second term on the right side of Eq. (5). For the mass transfer, a general equation that can be used for both the drying and devolatilization processes is given as follows:

= αA (Tb − Ts ) r = Rp

(4)

This equation changes with the particle shape: plate (Γ=0), cylinder (Γ=1) and sphere (Γ=2). Similar to Eq. (1), the term on the left side represents the storage of energy, and the first term on the right side represents the conduction heat transfer. In addition, two source terms are considered in Eq. (4) as described in the second and third terms on the right side. The two terms represent the heat consumed during the devolatilization process and the drying process, respectively. Eq. (4) is an improved version of Eq. (1). It takes the elements that were neglected in Eq. (1) into consideration, including the shape factor of the particles as well as the influence of the energy consumed during the devolatilization and drying processes on the heat balance. Moreover, the heat transfer equation is not only suitable for the drying process but also for the devolatilization process of a fuel particle in a fluidized bed. The boundary conditions are a significant factor in modeling. In Komatina’s model, only convective heat transfer is considered in the boundary conditions, while the radiative heat transfer is neglected. Generally, the boundary condition at r =Rp should be described as

3

λ

• • ∂T 1 ∂ ⎛ ∂T ⎞ = Γ ⎜λr Γ ⎟ + qde ρde + qw ρw ∂τ r ∂r ⎝ ∂r ⎠

dm w ΔT ρCp Ve = dτ Δτ ΔHe

(6c)

Based on this equation, the mass of releasing moisture with time can be established and used to compare with experimental data so that the model can be verified. 3.2.2. Models for devolatilization The shrinking core model, heat transfer equation and the boundary conditions of the drying model were introduced in the last section. The mathematical methods and heat transfer equations for the drying and devolatilization processes are nearly the same. Thus, detailed methods and equations are not presented in this section. Instead, this section

(3)

where λg(Tb) and λg(T0) represent the gas heat conductivity coefficient at FB reactor temperature and at 0 °C, respectively. dc and dbp represent the diameter of the coal and the bed material, respectively. 418

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dV = k (V ∞ − V ) n dτ

focuses on the mechanism models for the devolatilization of coal particles. Two types of models are usually used for coal devolatilization processes, i.e., structural models and empirical models [45]. For structural models, the CPD [55,56] and FG-DVC [57] models are two representative models. These structural models are generally complex and need to know the functional groups in the coal particles. In contrast, the empirical models are generally simpler compared to the structural models because they were proposed based on experiments and practices. The empirical models are believed to be capable of predicting the devolatilization behavior of coal particles during combustion process well, especially for large single coal particles. This article focuses on combustion in FBs where the fuel particles are usually large; thus, in this condition, an empirical model is more suitable for modeling the coal devolatilization. Therefore, several main empirical models are introduced in this section as follows:

where the kinetic rate constant can be described as a formula based on the particle diameter:

k = n1 dˆ

(7)

k = k 0 exp(−E /RT )

(8)

n2

(10)

According to Peeler et al., for the coal particles in this study, the multiple-order reaction model is proven to be capable of predicting the weight loss behavior well during the devolatilization process in a fluidized bed. However, similar to the first-order model, the kinetic parameter of the multiple-order reaction model also changes with the operating conditions. (iii) Competing reaction model (CRM) The competing reaction model is more sophisticated compared to the first-order reaction model and multiple-order reaction model. It was proposed to overcome the problem of these two models because they cannot predict the coal devolatilization behavior well under too many different conditions. Doolan et al. [64] proposed the competing reaction model based on the firstorder reaction model with some improvements as follows:

(i) First-order reaction models (FRMs) The first-order Arrhenius-type model is one of the earliest developed models describing coal devolatilization. It is relatively simple and has been used in many studies [58–62]. The general equation for this model can be described as follows:

dV = k (V ∞ − V ) dτ

(9)

dVi = k vi (Vi∞ − Vi ) − kdi Vi dτ

(11)

where subscript i denotes the generated species and kv and kd are the evolution and decomposition rate, respectively. In this model, the first term on the right hand of the equation is a normal first-order reaction model. The second term represents the decomposition of volatile matter. Compared to the FRM and MRM, one more element, the decomposition of volatile matter, was taken into consideration in the CRM. Cliff et al. [65] and Yang et al. [66] also used the competing reaction model in their studies. Jamaluddin et al. [67] compared the CRM to the FRM and the MRM. By taking the decomposition of volatile matter into account, the CRM was proven to be capable of covering a wider range if operating condition as well as obtaining a more accurate prediction of the final temperature and the volatile species. Compared to the FRM and the MRM, the CRM has made considerable progress in the accuracy of model prediction.

As the operating conditions change, the kinetic parameters of these models vary significantly because these parameters are obtained by curve fitting. A key drawback of this model is that a lot basic experiments should be performed first to obtain the kinetic parameters so that this model can be used for coal devolatilization. (ii) Multiple-order reaction model (MRM) The multiple-order reaction model was proposed by Peeler et al. [63] when studying the devolatilization process of a single large coal particle (1.4–29 mm) under fluidized bed conditions. The general equation for this model can be described in the following equation: Table 2 Multiple parallel reaction models of coal devolatilization [77].

ka

Ea

COAL1 (−C12H12−) 1 COAL1→5CHARH+.1 CHARC+.2H2+.9CH4+1C*2–5 2 COAL1→TAR*1 3 COAL1→5CHARH+.25CHARC+.5H2+.75CH4+1C2–5 4 COAL1→TAR*1 5 TAR*1→TAR1 6 TAR*1+CHARH→5.3CHARH+3CHARC+2.55H2+.4CH4 7 TAR*1+CHARC→4.3CHARH+4CHARC+2.55H2+.4CH4

2.0×108 1.0×108 1.0×1014 1.0×1014 2.5×1012 2.5×107 2.5×107

40,000 40,000 75,000 75,000 50,000 32,500 32,500

COAL2 (−C14H10O−) 8 COAL2→2CHARC+3.94CHARH+.25COAL1+.04BTX*+.31CH*4 +.11 C*2–5+.11(COH2)*+.15CO*2+·41H2O*+.18CO*+.265H2 9 COAL2→0.61CHARC+4.33CHARH+.21COAL1+.16BTX*+.27CH4 +.7CO+·1H2O+.2(COH2)*+.28H2 10 COAL2→TAR*2 11 COAL2→TAR2 12 TAR*2→TAR2 13 TAR*2+CHARH→1.5CHARC+7CHARH+1H2O*+.5CH4

6.0×1010 4.0×1018 5.0×1010 4.0×1017 2.4×109 4.5×109

36,000 63,000 36,000 63,000 39,000 30,000

COAL3 (−C12H12O5−) 14 COAL3→2.73CHARC+1.8CHARH+.22COAL1+.08BTX*+.2Ox−C +.1CH*4+.11 C*2–5+.2H2+.6(COH2)* +2·2H2O*+.1CO2+.4CO*2+1CO* 15 COAL3→COAL*3 16 COAL*3→1.5CHARH+.82CHARC+2.08CO+.25Ox−C+.14CH4+.7C2–5 +.5CO2+.47(COH2)* +.16BTX*+.25COAL1+1·2H2O+.29H2 17 COAL3→TAR*3+CO*2+ H2O 18 COAL3→TAR3+CO2+ H2O 19 TAR*3→TAR3 20 TAR*3+CHARH→4CHARH+2.5CHARC+.2CH*4+2(COH2)*+.8H2+.3C2–5

2.0×1010 5.0×1018 1.2×108 1.6×109 2.0×1018 5.0×109 1.4×108

33,000 61,000 30,000 33,000 61,000 32,500 30,000

a k=k exp(−E/RT) (units are cal, mol, 1, K, and s).

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be described well according to the mechanism models introduced above. With the addition of a heat transfer model, mass transfer model, and the initial and boundary conditions, the complete model for the devolatilization can be presented. The models introduced in this section are usually simpler than the structural models. However, some key parameters used in these models are obtained based on the average values from the experiments, which indicates that many experiments should be performed before using these models. Thus, the future work for the devolatilization models should focus on creating a wider experimental database and improving the accuracy of the models.

(iv) Distributed activation energy models (DAEMs) Please et al. [68] and Niksa et al. [69] used DAEMs to predict the coal devolatilization behavior during both combustion and pyrolysis conditions. They proved that DAEMs are capable of predicting coal devolatilization behavior well. Sadhukhan et al. [12] and Kijo-Kleczkowska [44] also used DAEMs for the devolatilization model as a part of the global model for coal combustion. The equations for DAEMs are usually described as

dm v dV (r , τ ) =− mc dτ dτ ⎡ V (r , τ ) = V0 ⎢1 − ⎣

f (E ) =

1 σE

∫0

(12) ∞

exp(−

∫0

τ

⎤ k 0 e−E / RT dτ ) f (E ) dE ⎥ ⎦

⎡ (E − E 0 ) 2 ⎤ ⎥ exp ⎢ − 2σE2 ⎦ ⎣ 2π

3.2.3. Models for char combustion Char combustion is a very important stage of combustion, and it has been studied by many researchers all over the world [8,11,12,78– 86]. Generally, char combustion is considered to occur when the devolatilization process is finished [80]. Guedea et al. [81] proposed a char combustion model that combined heat transfer and mass transfer. The first and second fragmentations were also considered in this model, and the model agreed well with experiment. Dennis et al. [7,8] invested the combustion kinetics of coal char in an FB and studied the influence of the Sherwood number on the particle diameter. They indicated the uncertainty about the proportion of the carbon burning directly to CO2 at the surface of the burning char. This is an important problem that still needs to be solved. Sadhukhan et al. [11,12] used a chemical reaction kinetic model to present char combustion for single coal particles in FB, and the results also proved to have satisfactory agreement with experiment. Manovic et al. [86] also used a similar chemical reaction kinetic model to present the char combustion for single coal particles in an FB similar to Sadhukhan et al. Both heat transfer and mass transfer were considered in this model. This model considered the primary CO/CO2 ratio in the char combustion process and solved the problem proposed by Dennis et al. to some extent. This model is very common and used in many studies; thus, it is introduced as a representative model for char combustion as follows:

(13)

(14)

where Eq. (12) refers to the relationship between the evolution mass rate of the volatile matter and its evolution volume rate, Eq. (13) is formula for the instantaneous yield of volatile matter, and Eq. (14) describes the activation energy of coal. DAEMs give new forms for the calculation of the activation energy. Only one activation energy can be obtained using the FRM, MRM and CRM. The one activation energy was obtained based on the entire reaction process, and it cannot represent the real activation energy of the elementary reaction. However, the combustion of coal is a sophisticated process, and there are many parallel and cross chemical reactions in this process. According to the DAEMs, the activation energy E is assumed to be a Gaussian distribution function, and it changes with the changing conversion degree. Thus, compared to the other models, the DAEMs make more accurate predictions based on their unique descriptions of the activation energy. Moreover, according to Kijo-Kleczkowska and Sadhukhan et al., the global models using DAEMs for the devolatilization part agree well with the experimental data. DAEMs turn out to have a wider range of applicability compared to the other models, and they can be expanded for the modeling of the devolatilization of other fuels, such as biomass and sewage sludge and not only coals. (v) Parallel reaction models (PRMs) The parallel reaction models (PRMs) are models that consist of a series of first-order reactions. According to Tomecze et al. [70], each volatile compound is usually generated through 4–6 firstorder reactions. A considerable number of studies have been conducted to study PRMs [54,71–75]. Agarwal et al. [76] indicated that PRMs can accurately predict the weight-loss and volatile evolution of large coal particles.

(i) Heat transfer and mass transfer models Heat transfer and mass transfer models are always the most important models for the entire combustion model. The typical mass transfer equation is shown as follows:

∂ci 1 ∂ ⎛ ∂c ⎞ = 2 ⎜r 2Deff, i i ⎟ + ∂τ r ∂r ⎝ ∂r ⎠

∑ νi,j Rj

(15)

where Deff,i denotes the effective diffusion coefficient [87] and νi,j and Rj represent the stoichiometric coefficient and the chemical reaction rate, respectively. The first term on the right side of Eq. (15) is a diffusion term, where the mass transfer of oxygen through the particle is considered. The second term on the right side of Eq. (15) is a source term, where the mass changes caused by chemical reactions are taken into consideration. Detailed chemical reaction models will be introduced in the following section. The typical heat transfer equation is shown as follows:

According to Sommariva et al. [77], there are also some typical multiple parallel reaction models for the devolatilization of coals as shown in Table 2. The multiple parallel reaction models can also be expanded for the modeling of the devolatilization of biomass and sewage sludge because these models are suitable for the active components in these two fuels. Generally, the devolatilization of single coal particles in an FB can

Cp, c

∂T 1 ∂ ⎛ ∂T ⎞ = 2 ⎜r 2λeff ⎟ + ∂τ r ∂r ⎝ ∂r ⎠

∑ ΔHj Rj

(16)

Table 3 Reported ratios of CO/CO2 [95,96,98,99]. Reference Arthur Rossberg Basu et al. Prins Linjewile and Agarwal Hurt and Calo Campbell, Mitchell and Ma

Year 1951 1956 1976 1987 1995 2001 2002

Carbon type

Reactor

Coal char, graphite Electrode carbon Anthracite coal Graphite Petroleum coke Bituminous coal, petrol coke, brown coal Lower Kittanning coal

420

Flow system Flow system Fluidized bed Fluidized bed Fluidized bed Various Flow system

Temp. (K) 730–1170 790–1690 1123 985–1110 970–1220 500–2270 773–873

CO/CO2 −6240/T

2510× 1860×−7200/T 0.38 0.17–0.50 0.00472×−4540/T k3/(k2×pO2) Coal: 12600×−11680/T

Calcd for 1073 K 7.48 2.27 0.38 0.17–0.50 0.32 5.6 Coal: 0.236

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Table 4 A summary of the different combustion models for coal particles in fluidized beds in recent years. Models

Year

Material

Fuel size

Reactor

Drying

Devolatilization

Char combustion

Manovic et al. [86] Sadhukhan et al. [12] Sadhukhan et al. [11] Gupta et al. [92] Chern et al. [10] Saastamoinen et al. [46] Wendt et al. [47] Zhao et al. [49] Kijo-Kleczkowska [44] Komatina et al. [6]

2008 2011 2010 2007 2012 2006 2002 1996 2011 2007

Lignite Subbituminous coal Ash coal Lignite Bitumite and lignite Various Coal Coal Coal water suspension Bituminous coal

5–10 mm 1–6 mm 3–5 mm ~1 mm 13–14 mm > 0.3 mm < 1 mm 10–16 mm < 1 mm 5–10 mm

Fluidized bed Fluidized bed High pressure Fluidized bed Fluidized bed Fluidized bed − Fluidized bed Fluidized bed Fluidized bed

− − − − − 100 °C − − 105 °C 100 °C

− DAEM − − Parallel reaction model Multiple-order reaction model 2D Model FG-DVC model DAEM −

Reaction Reaction Reaction Reaction Reaction − − − − −

where λeff denotes the effective heat conductivity coefficient and ΔHj denotes the energy for chemical reaction j. The first term on the right side of Eq. (16) is a conduction heat transfer term, where the heat transfer through the particle is considered. The second term on the right side of Eq. (16) is also a source term, where the changes in the temperature caused by chemical reactions are taken into consideration. Detailed chemical reaction models will be introduced in the following section. For the initial conditions for both the heat and mass transfer equations, all of the parameters are the same for the surrounding media. For the boundary conditions, the equations are listed as follows:

1, 1 1, 1, 1,

3 2, 3 2, 3 2

∂ci =0 ∂τ

(15a)

∂T =0 ∂τ

(16a)

r = Rp , −Deff, i

−λ

∂ci = k m (ci, s − ci, b ) + νi,1 R1(1 − ε′)/ As ∂r

∂T = α (Ts − Tb ) + (1 − ε′) ΔH1 R1/ As ∂r

(15b) (16b)

where km [88] represents the mass transfer coefficient, α [89] denotes

r = 0,

Table 5 A summary of the kinetic data for the different biomass species [100]. Type

Reference

Year

Material

Experimental condition

Temp. (K)

Kinetic constants*

Softwood

Samolada and Vasalos Wagenaar et al.

1991 1993

Fir wood Pine

Isothermal TGA

673–773 553–673 773–873

Chan et al.

1985

Pine

–

–

Liu and Fan

1998

Nanmu

TGA

Liu and Fan

1998

Paulownia

TGA

Thurner and Mann

1981

Oak sawdust

Isothermal

435–568 568–623 623–728 728–787 455–571 571–631 631–671 671–775 573–673

Di Blasi and Branca

2008

Beech

–

573–708

Gorton and Knight Ward and Brashlaw Nunn et al. Font et al.

2008 2008 1985 2008

Hardwood Wild cherry Sweet gum Almond shell

Isothermal Isothermal Non-isothermal –

677–822 538–593 600–1400 733–878

Swann et al.

2008

Maple plywood

353–823

Liu and Fan

1998

Willow

TGA DSC TGA

kg1+kt=2.40×104exp(−94/RT) kc1=3.05×7exp(−125/RT) kt=9.28×109exp(−149/RT) kg1=1.11×11exp(−177/RT) k=1.4×1010exp(−150/RT) kc1=1.08×7exp(−121/RT) kt=2×108exp(−133/RT) kg1=1.3×8exp(−140/RT) k=5.53×108exp(−116.57/RT) k=1.99×1024exp(−290.53/RT) k=5.91×105exp(−109.37/RT) k=2.30×1021exp(−320.37/RT) k=7.64×1011exp(−149.0/RT) k=1.44×1018exp(−215.21/RT) k=3.90×1020exp(−287.32/RT) k=7.42×1048exp(−645.17/RT) kg1=1.43×4exp(−88.6/RT) kt=4.13×106exp(−112.7/RT) kc1=7.38×5exp(−106.5/RT) kg1+kt=1.73×106exp(−106.5/RT) k=2.49×106exp(−106.5/RT) kg1+kt=1.5×1010exp(−149/RT) kc1=3.3×6exp(−112/RT) kg1=4.4×9exp(−153/RT) kt=1.1×1010exp(−148/RT) k=1.483×106exp(−89.52/RT) k=1.19×1012exp(−173.7/RT) kg1+kt=3.338×105exp(−69/RT) kc1=2.98×3exp(−73/RT) kt=5.85×106exp(−119/RT) kg1=1.52×7exp(−139/RT) k=1.885×106exp(−92.1/RT) k=2.0×1013exp(−170/RT) k=1.33×1011exp(−146/RT) k=2.54×108exp(−118.73/RT) k=2.53×1024exp(−296.93/RT) k=8.13×1014exp(−226.56/RT) k=4.41×1051exp(−711.36/RT)

Hardwood

*

Subscript g, t, and c represent gas, tar, and char, respectively.

421

446–595 595–658 658–699 699–768

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occur at the surfaces of char particles are only considered at the beginning of combustion. (ii) Chemical reaction models In the combustion models, the chemical reactions are very important because the heat balance inside the particle has a considerable influence on the temperature. Three main reaction equations are listed as follows [90–92]:

Reaction 1: [2(x + y)/(x + 2y)]C + O2 → [2x /(x + 2y)]CO + [2y /(x + 2y)]CO2 Reaction 2: C + CO2 → 2CO

Reaction 3: C + 0.5O2 → CO2 .

Fig. 11. DTG curves for several common biomass samples (Heating rate: 40 K/min) [102].

The reaction rates of these three reactions are defined as

R1 = k1 ′χO2 As

(17)

R2 = k2 ′cO2

(18)

R3 = k3 ′cCO cO0.5 c 0.5 2 H2 O

(19)

where χO2 denotes the oxygen mole fraction and s represents the surface area that can be used for reaction:

As = As, in (1 − XC ) 1 − ψ ln(1 − XC )

(20)

where s0 denotes the specific surface area at the beginning and XC denotes the carbon conversion efficiency. kj in Eqs. (17)–(19) can be described as

⎛ −E ⎞ kj = Aj exp ⎜ i ⎟ ⎝ Rg T ⎠

(21)

where the activation energy values are E1=179.4 kJ/mol [93], E2=247.4 kJ/mol [92], and E3=55.70 kJ/mol [86]. The pre-exponential factor values are A1=25.42 kmol/m2 s [93], A2=4.02×108 m/s [92], and A3=7.43×105 m3/mol s [94]. Another key parameter for the combustion model is the primary CO/CO2 ratio [95,96]. Generally, the temperature increases as the CO/ CO2 ratio decreases. The CO/CO2 ratio is also described by the Arrhenius type relation as

−ECO / CO2 x = ACO / CO2 exp( ) y Rg T

(22)

where the values ACO/CO2=2512 and E CO/CO2=51.88 kJ/mol are used according to Arthur [97]. Lackner et al. [96] reviewed the relations for the primary CO/CO2 ratio as shown in Table 3: Up to now, the combustion models for coal particles in FBs have been developed to be complete and perfect. Table 4 gives some typical combustion models in recent years. The main shortcomings of these models lie in the unknowns of the detailed gas species, gas ratios, and their generated orders during the combustion process. Therefore, future work for these models may focus on determining the reaction processes and mechanisms by using some advanced measurement methods such as laser measurement technologies. The accuracies of these models can only be improved based on a clearer understanding of the reaction mechanism during the combustion process.

Fig. 12. TG curves for main biomass components [101]: (a) cellulose, (b) hemicellulose, and (c) lignin.

4. Models for the combustion of biomass

the heat transfer coefficient, and As denotes the specific surface area. The first terms on the right sides of Eqs. (15b) and (16b) represent the mass transfer and convective heat transfer from the char particle to the fluidized bed, respectively. The second terms on the right sides of Eqs. (15b) and (16b) represent the mass and heat changes due to the heterogeneous chemical reactions that occurred at the surface of the char particle, respectively. These special mass and heat transfers that

4.1. TG analysis and kinetic models Kinetic models for the combustion of biomass can also be summarized into three categories similar to coals: SHRMs, MHRMs and DAEMs. Shi and Chew [100] listed the kinetic parameters of common 422

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Table 6 A summary of different combustion models for biomass particles in recent years. Models

Year

Material

Fuel size

Reactor

Drying

Devolatilization

Char combustion

Wang et al. [118] Sreekanth et al. [116] He et al. [132] Yang et al. [13] Porteiro et al. [14] Porteiro et al. [15] Galgano et al. [133] Thunman et al. [16] Haseli et al. [17] Haseli et al. [18] Haseli et al. [19] Park et al. [129]

2015 2008 2011 2008 2007 2006 2004 2002 2011 2011 2013 2010

Seaweed Casuarina Wood Willow Birch Wood Beech Various Beech Various Sawdust Wood

− 10–30 mm 5–25 mm 1–20 mm 5–25 mm 25 mm 40 mm 10–40 mm 1–10 mm ~1 mm ~1 mm 25.4 mm

Fluidized bed Fluidized bed Fixed bed Various − Fixed bed − Various − Various Various −

100 °C 100 °C 100 °C 100 °C 100 °C 100 °C − − − − − −

Multi-step reaction model Multi-step reaction model Multi-step reaction model Multi-step reaction model Multi-step reaction model Multi-step reaction model Shrinking core model Shrinking core model Multi-step reaction model Multi-step reaction model Shrinking core model Multi-step reaction model, Multi-components model

Shrinking core model − Reaction 1 2D model Reaction 1 Reaction 1 Shrinking core model Reaction 1, 2 Reaction 1, 3 − Reaction 1 −

model, and a char combustion model [8,46,100,103–121]. The drying model and the char combustion model for biomass are similar to those for coals. However, the devolatilization models of biomass and coals are different from each other due to their difference in physical and chemical characteristics. Thus, the devolatilization models for biomass are mainly introduced in this section. Devolatilization models for coals are mainly empirical models, e.g., first-order reaction models, m-order reaction models, and DAEMs. However, devolatilization models for biomass mainly focus on the different reaction processes, based on which the models can be divided into three main types as follows: 4.2.1. Multi-component models Multi-component models refer to the models for the three constituents in biomass. For cellulose, Bradbury et al. [122] presented a three-stage reaction model. In this model, cellulose is presumed to be converted into active cellulose in the first stage, and in the next two stages, this active cellulose is further decomposed, producing volatiles and char. Diebold et al. [123] proposed another widely recognized devolatilization model for cellulose as shown in Fig. 4(a). In this model, the active cellulose is also formed in the first stage, and then, it decomposes into primary vapors that undergo several further reactions to form secondary gases and secondary tar. Di Blasi et al. [124] studied a two stage reaction devolatilization model for hemicellulose as shown in Fig. 4(b). In this model, A denotes hemicellulose, B represents the intermediate product, and V1 and V2 denote the volatiles. The intermediate product is formed with a reduced degree of polymerization in the first stage and then decomposed into volatiles and char in the second stage. Antal et al. [125] studied a multistep reaction devolatilization model for lignin as shown in Fig. 4(c). In this model, at low temperatures (below 500 °C), lignin is converted into char and gas by dehydration reactions. At higher temperatures (above 500 °C), lignin monomers are formed first and then decomposed into tar due to secondary degradation. At very high heating rates, gas and reactive vapors are formed. The multi-component models divide the model for biomass combustion into three main parts based on its main components: a cellulose combustion model, a hemicellulose combustion model, and a lignin combustion model. Compared to the original coal combustion model, some progress has been made because the model has been adjusted to be more suitable for the chemical properties of biomass. However, this model still cannot describe the complex reaction mechanism of biomass, which is why the following two models were then proposed as improved versions.

Fig. 13. Multi-step reaction models for biomass devolatilization: (a) [14,18], (b) [126], (c) [127], (d) [128], and (e) [129].

biomass species as shown in Table 5. Moreover, the TG analysis for biomass is mainly introduced in this section. Fig. 11 gives the DTG curves for the pyrolysis of several common biomass materials. The devolatilization of biomass mainly occurs at approximately 350 °C, which is different from the devolatilization temperature range (400– 600 °C) for coals as shown in Fig. 6. Collard et al. [101] reviewed the TG analysis for the pyrolysis of three constituents in biomass as shown in Fig. 12. The main devolatilization temperatures of cellulose, hemicellulose and lignin are 300 °C, 280 °C, and 350 °C, respectively...

4.2.2. Multi-step reaction model In multi-step reaction models, the different final products of biomass can always be lumped into three categories, i.e., gas, tar and char, while the intermediate products and kinetic schemes are different from each other in different models. Multi-step reaction models are the

4.2. Models for the combustion of a single biomass particle The combustion model for biomass in an FB can also be divided into three parts similar to coals: a drying model, a devolatilization 423

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Fig. 14. TG and DTG curves of several common solid wastes during thermal treatment. (a) and (b): Sewage sludge [134], (c) and (d): Coal washery tailings [135], (e) RDF [136], and (f) Main components in RDF [137].

most commonly used models for biomass combustion as seen in Table 6 where the models for biomass combustion in recent years are reviewed. Porteiro et al. [14] and Haseli et al. [18] used the simplest model when studying the combustion model of biomass as shown in Fig. 13(a). In this model, secondary degradation is not considered,

Fig. 15. The devolatilization model of sewage sludge [20,140].

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Fig. 17. Schematic diagrams of the experimental systems used for studying the combustion model of a single CWT particle [30]: (a) tube furnace and (b) fluidized bed.

decomposed via the reaction of the volatiles and gases generated in the first stage. Park et al. [129] compared a multi-components model and two multi-step reaction models in their research. The results show that a two parallel reactions model assumes that the wood is formed into tar and intermediate solids, which further decompose, yielding char and gas. Based on the comparison, a new multi-step model for wood is proposed, as shown in Fig. 13(e). The model is a three parallel reactions model in which wood is presumed to be decomposed into gas, tar, and intermediate solids in the first reaction. In the second reaction, some tar is further converted into gas, and in the third reaction, the intermediate solid and the remaining tar are further converted into char. This complex model proves to have good agreement with the experimental data. This newly proposed three parallel multi-step reaction model is proven to be more accurate for the modeling of biomass devolatilization based on both theory and experimental data.

Fig. 16. Different regions in the model for the combustion of an MSW particle. [21].

and three products (gas, tar and char) are formed through a primary reaction. This model is usually applied in many simplified models when studying the combustion model of biomass particles. The devolatilization behavior of biomass particles can be described roughly based on this model; however, the accuracy of this model is lower than the models that take secondary degradation into consideration. Branca and Di Blasi [126] proposed the multi-step reaction of wood degradation as shown in Fig. 13(b) where A represents biomass, B and D represent intermediate products, C represents char, and V denotes the volatiles. The accuracy of this model is higher than that of the simplified model because secondary degradation is considered in this model.. According to Liden et al. [127], a two parallel reactions model was proposed as shown in Fig. 13(c). In this model, the wood is presumed to be decomposed into gas, tar and char in the first stage, and in the second stage, the tar is converted into gas through further decomposition. This model is also commonly used in studies. According to the model proposed by Koufopanos et al. [128], the primary and secondary reactions are studied as described in Fig. 13(d). In this model, the biomass is presumed to be decomposed in the first stage, producing volatiles, gases and char. In the second stage, the char is further

4.2.3. Distributed activation energy models (DAEM) In many studies, authors prefer to use DAEMs as the mechanism models for biomass devolatilization because of the complex agricultural origins of biomass. The theory of DAEM for biomass is the same as that for coals. Thus, no detailed description of the DAEMs is introduced in this section. Rostami et al., Sonobe et al., and Várhegyi et al. [102,130,131] all used DAEMs in their studies and proved that DAEMs can predict the devolatilization behavior of biomass well. Várhegyi et al. suggested that DAEMs are more suitable for experiments conducted under high heating rates. Rostami et al. suggested that the accuracies of the models can be improved by slightly changing the kinetic parameters. Table 6 presents combustion models for biomass particle proposed in recent years. Most of the models take the multi-step reaction model as the devolatilization model for biomass combustion. Most of the materials used in these studies of biomass combustion are wood, and other kinds of biomass are rarely seen in these models. In summary, models for the combustion of biomass particles still need to be improved in some aspects: first, these multi-step reaction models 425

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Table 7 A summary of the combustion models for solid waste particles in fluidized beds in recent years. Models

Year

Material

Fuel size

Reactor

Cano et al. [28] Khiari et al. [20] Mazza et al. [21] Huang et al. [30] Huang et al. [141]

2007 2007 2010 1985 1986

SS SS MSW CWT CWT

4–6 mm 2 mm − 12 mm 12 mm

Fluidized Fluidized Fluidized Fluidized Fluidized

bed bed bed bed bed

Drying

Devolatilization

Char combustion

− 100 °C − Quasi-steady Quasi-steady

− Multi-step model Multi-step model Two-step model Two-step model

Reaction 1 Reaction 1 Reaction 1 − Ash layer

wastes have been conducted. Sewage sludge accounts for the majority of these studies. According to Section 5.1, the combustion characteristics of sewage sludge are similar to those of biomass. Thus, the models for the combustion of biomass particles can be taken as a reference when studying combustion models of SS particles. Cano et al. [28] studied a model for the char combustion of a single sewage sludge particle in an FB as shown in Fig. 9(a). A small stainless steel basket was used to take the sewage sludge particle out of the fluidized bed at different residence times for analysis. This model was derived from the shrinking core model, and the shrinkage of the particles size was also taken into consideration. Khiari et al. [20] studied the global combustion model for sewage sludge particles in both FBs and thermogravimetric analyzers. Similar to the combustion models for coal and biomass, combustion models for sewage sludge can also be divided into three parts: a drying model, a devolatilization model, and a char combustion model. The drying and char combustion models of sewage sludge are similar to those of coals. The devolatilization model of sewage sludge (Fig. 15) is a multiple-step reaction model similar to the common models for biomass but slightly different. In this model, dried sludge is transformed into volatiles and intermediates that further decompose, yielding volatiles, char and ash. According to Khiari et al., combustion models for sewage sludge particles in two different conditions (FB and TGA) were compared. The burnout time in an FB is reduced because the heat transfer rate is enhanced in this condition.. Solid wastes usually contain some hazardous substances, e.g., F, Cl, and heavy metals, which are relatively rare in coals and biomass. Hazardous substances should be taken into account when studying the models for the combustion of solid waste particles because its transfer rule is very important for the environment. Lockwood et al. [138] and Han et al. [139] proposed the heavy metal transformation model for SS combustion. According to Lockwood et al., gas phase reactions of heavy metals are supposed to be taken into consideration. However, the related kinetic mechanism is incomplete. Thus, more studies should be conducted in this aspect in future works.

containing only primary and secondary degradation cannot usually predict the devolatilization behavior for biomass particles accurately because the effect of biochar activity on secondary degradation has not been explicitly explained. Second, the distributed activation energy model is suitable for biomass; however, it is still in the early stages of development, and its abilities need to be enhanced so that it can analyze the detailed decomposition processes of biomass into various gases, tars and chars. Finally, a comprehensive model for biomass combustion should be proposed in which global parameters should be taken into account, such as shrinkage and attrition. 5. Models for the combustion of solid waste 5.1. TG analysis and kinetic models Due to the increasing attention given to the environment, solid waste disposal has become a major problem. Thus, it is necessary to learn the combustion mechanism of solid wastes so that a combustion system for solid wastes can be proposed. It is hard to review all of the kinetic models of solid waste considering its complex components. In this paper, only three main classes of solid waste are studied: sewage sludge (SS), coal washery tailings (CWT), and typical wastes (RDF and MSW). Fig. 14 gives the TG and DTG analyses of the three kinds of solid waste during thermal treatment. Based on these kinetic analyses, the combustion mechanism of solid waste can be understood and the scope of future work can be explained.. Fig. 14 (a) and (b) give the TG and DTG curves of three kinds sludge during pyrolysis at 20 °C min−1: biochemical sludge (BS), physicochemical sludge (PCS), and sewage sludge (SS). Two peaks are found in the DTG curves of BS and SS, corresponding to water evaporation and devolatilization. The temperature of the devolatilization peak is approximately 350 °C, which is similar to the devolatilization temperature of biomass as shown in Fig. 11. For PCS, another peak is found at approximately 750 °C due to the decomposition of minerals. Fig. 14 (c) and (d) give the TG and DTG curves of CWT at various heating rates. Two peaks are also observed in the DTG curves and the devolatilization peak temperature is approximately 400 °C, which is similar to the devolatilization temperature of lignite as shown in Fig. 6(c). Fig. 14 (e) gives the TG and DTG curves of refuse-derived fuel (RDF) during pyrolysis process under a 10 °C min−1 heating rate. Five peaks are found in the DTG curve and their corresponding temperatures are 100 °C, 300 °C, 450 °C, 650 °C, and 900 °C. The first peak is due to water evaporation. Fig. 14 (f) gives the TG curves of the main components in RDF. The peak temperature for paper and PVC is approximately 300 °C and that of polyethylene and polypropylene is approximately 450 °C. The second peak in the DTG curve represents the conversion of paper and PVC, and the third peak refers to the conversion of polyethylene and polypropylene. Moreover, the fourth peak in the DTG curve represents the conversion of food residues, and the last peak is due to the decomposition of minerals.

5.2.2. Solid waste (SW) Few studies about the combustion models for municipal solid waste (MSW) particles have been conducted. A typical model was proposed by Mazza et al. [21] to represent the combustion behavior of MSW particles in FBs. This model combined combustion behavior and heavy metal vaporization behavior. The different particle regions in this model are given in Fig. 16. The shrinking core model is used for both MSW particle combustion and heavy metal vaporization phenomena as shown in Fig. 16(a).. The metal vaporization model proposed by Mazza et al. does not require diffusion phenomena. The vaporization front is assumed to progresses from the external toward the particle core, and it progresses simultaneously with the combustion front. Thus, the heavy metal vaporization rate should be calculated based on the vaporization front position. According to Mazza et al., the metal concentration, coupled with the vaporization front can be described as

5.2. Models for combustion of a single solid waste particle

−v′g Aref CMG (τ ) + h m Ap (CMS − CMG ) dCMG (τ ) = dτ Vref

5.2.1. Sewage sludge (SS) Up to now, few studies on the models of the combustion of solid 426

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Table 8 A summary of main general combustion models in fluidized bed. Reaction phase

Models

Drying and Devolatilization

ρCp

∂T ∂τ

=

1 ∂

Devolatilization

dmw dτ

=

Reference

Heat transfer

[6,46]

Mass transfer

[14,85]

Moisture evaporation rate Mechanism for coal

[13,44]

r 2 ∂r ⎝

⎧ ∂ρi ⎪ ∂τ = Si ′ ⎨ ∂(ε ′ ρ ) i ⎪ + ⎩ ∂τ Drying

⎛ 2 ∂T ⎞ ⎜λr ⎟+S ∂r ⎠

Main merit

1 ∂ r 2 ∂r

(r 2v′ρi ) = Si ′

ΔT ρCp Ve Δτ ΔHe

(1) First-order reaction model (FRM):

dV dτ

= k (V ∞ − V )

(2) Multiple-order reaction model (MRM): (3) Competing reaction model (CRM):

dVi dτ

dV dτ

=

[63]

= k (V ∞ − V ) n

kvi (Vi∞

[64]

− Vi ) − k di Vi

⎧ ⎡ ⎤ ∞ τ ⎪V (r , τ ) = V0 ⎢1 − ∫ exp(− ∫ k 0 e−E / RT dτ ) f (E ) dE ⎥ 0 0 ⎣ ⎦ ⎪ (4) Distributed activation energy model (DAEM): ⎨ ⎡ (E − E )2 ⎤ ⎪ 1 0 ⎪ f (E ) = σE 2π exp ⎢⎣− 2σ 2 ⎥⎦ ⎩ E (5) Parallel reaction model (PRM) (1) Multi-components model (2) Multi-step reaction model:

[58–62]

[12,44,68,69]

[70,76,77] Mechanism for biomass

[122–125] [14,18]

[126]

[127]

[128]

[129]

(3) Distributed activation energy model (DAEM): ⎧ G (τ ) G (τ ) + hm Ap (C S − C G ) ⎪ XM ′ = τvap XM dCM −v ′g Aref CM M M ⎨ X Mav (2 − 2τvap) = dτ Vref r + X Mav (2τvap − 1) ⎪ XM (r )′ = Rp ⎩ Char combustion

Cp, c ∂ci ∂τ

∂T ∂τ

=

= 1 ∂

1 ∂

⎛ 2 ∂T ⎞ ⎜r λeff ⎟ + ∑ ΔHj Rj ∂r ⎠

Mechanism for heavy metal in solid waste

Heat transfer

[102,130,131] [21]

[8,11,12,78–86]

r 2 ∂r ⎝

⎛ 2 ∂c ⎞ ⎜r Deff, i i ⎟ + ∑ νi, j Rj ∂r ⎠

Mass transfer

r 2 ∂r ⎝

Mechanism (continued on next page)

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Table 8 (continued) Reaction phase

Models

Main merit

Reference

[2(x + y)/(x + 2y)]C + O2 → Reaction 2: C + CO2 → 2CO Reaction 3: [2x /(x + 2y)]CO + [2y /(x + 2y)]CO2 C + 0.5O2 → CO2 Reaction 1:

biomass and solid waste particles. However, mechanisms that are different from coals should be used for biomass and solid waste due to their different physical properties, chemical components and structures, especially during the devolatilization process. According to Table 8, significant differences can be observed from the mechanisms for coal and biomass. However, models for solid waste combustion in FBs have rarely been studied. As increasing attention is paid to the environment, models for the combustion of solid wastes must be studied further. (2) In current studies, traditional measuring methods, such as flue gas analyzers, have most commonly been used when studying the combustion models of fuel particles. However, the gaseous species generated around the fuel particles during the combustion process cannot be obtained using only a flue gas analyzer. Thus, the detailed reaction mechanism during combustion cannot be understood. Advanced measuring methods, such as laser measurements, should be used in future works. The products around fuel particles generated at every instance can be obtained with the help of laser measurements. Thus, the primary CO/CO2 ratio for the char combustion model can be obtained based on experimental measurements instead of empirical equations. Additionally, the reaction mechanism during combustion can be understood better, and the mechanism model can be improved based on these data. The accuracy of the combustion model can thus be increased. (3) In current combustion models, the diameters of the particles are usually assumed to be constant, which is inconsistent with reality and directly affects the accuracy and precision of the models of the combustion process. In fluidized beds, attrition and shrinkage of fuel particles usually occurs due to the bed material friction. Thus, in future works, changes in particle structure (attrition and shrinkage) should be considered in the combustion models. (4) A systematic model should be proposed for fuels containing complex components such as biomass and solid wastes. Especially for solid waste, no model can fully explain its combustion process considering the complexity of its components. A lot more work should be done to study the combustion mechanism of each component in solid wastes to develop a systematic model where the combustion model of a solid waste can be obtained if its composition is known. Another key problem for solid wastes is that the transformation rules of hazardous substances (F, Cl, and heavy metals) should be considered in the combustion model. There have been almost no studies on the CWT combustion model in recent years. Further studies should be conducted taking the combustion models of coal and sewage sludge as references. According to previous studies, agglomeration and attrition phenomena have been obviously found during the combustion process of CWT in fluidized beds. Thus, the effects of agglomeration and attrition should be considered when studying its combustion model. If all of these suggestions are realized, an overall and accurate model library for the combustion of solid fuels will be established. For a single type of solid fuel, an accurate model can provide a better understanding of the complicated reactions in the particles. Thus, many common issues, e.g., low carbon conversion efficiency, high CO content, and NOx and SO2 pollution, can be solved by adjusting the operating conditions of the combustion equipment. Because this combustion equipment uses mixed fuels, the scheme for the ratio of each of type fuel and the combustion characteristics of the mixed fuels can be obtained quickly based on an overall model library. Moreover, the models for single fuel particles can be used as the bases for the

In addition, the evaluation of the equilibrium concentration of the heavy metals is made based on a linear distribution of heavy metal molar fractions with measured vaporization ratio. The heavy metal equilibrium concentration (CM*) can be calculated based on its molar fraction (XM). This fraction (XM) is a function of the radial position r:

′ = τvap XM XM is a constant: XM

XM varies with r: XM (r )′ =

(24)

X Mav (2 − 2τvap ) Rp

r + X Mav (2τvap − 1)

(25)

It can be inferred from the TG and DTG analysis in Section 5.1 that both RDF and MSW have complex components, and the combustion properties of each component are very different. Up to now, empirical models have been used for MSW particle combustion. However, to fully explain the combustion behavior of MSW particles, the combustion mechanism of each component and the interactions between each component in MSW should be studied. Thus, many more studies need to be performed in this aspect in the future. 5.2.3. Coal washery tailing (CWT) Studies about the combustion models for single CWT particles are really difficult to find. Professor Huang from Zhejiang University conducted studies on this topic in the 1980s [30,141]. Both tube furnaces and fluidized beds were used in Huang's study, as shown in Fig. 17. Professor Huang proposed a quasi-steady-state drying model of a CWT particle in a fluidized bed. A two-step reaction model was used for the devolatilization model. For the char combustion model, the agglomeration and ash layer diffusion were taken into consideration due to the high ash content in CWT. Table 7 gives the combustion models for three typical solid waste particles from studies from recent years.. Significant progress has been made in modeling the combustion process of a single particle of coal, biomass, and sewage sludge. As a kind of solid waste, CWT is in need of disposal, and its combustion mechanism and model should be fully understood. According to the TG and DTG analysis of CWT in Section 5.1, the combustion characteristics of CWT are similar to those of coals. In addition, CWT is composed of fine particles, which is similar to sewage sludge. Thus, combustion models for coal and sewage sludge could be taken as a reference when studying the combustion model of CWT. Moreover, the high ash content, the ash layer diffusion and the attrition of CWT particles must be considered in the combustion model. 6. Critical analysis and future research outlook Combustion models for single solid fuel particles (coal, biomass, and solid waste) in FBs are reviewed in this paper. A summary of the main general combustion models is listed in Table 8. Some critical analysis and the future research outlooks for these models are concluded as follows: (1) The combustion models for various types of solid fuels (coal, biomass, and solid waste) in FBs are analyzed in this study. Among these models, the combustion models for coals have progressed the most. Some models for coals can also be used for other solid fuels such as biomass and solid waste. For example, the general heat and mass transfer equations for the modeling of coal combustion can also be applied to biomass and solid waste modeling. The numerical scheme and the calculation process for coal particles are also suitable for 428

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numerical modeling of combustion equipment systems. More accurate combustion characteristics of the whole system can be obtained based on the model of a single particle. This achievement will be helpful for both designing a combustion system and adjusting the combustion system.

[28]

[29] [30]

Acknowledgments

[31]

Financial support is acknowledged from the National Basic Research Program of China (Grant 2011CB201500), the National High Technology Research and Development Program (863 Program) of China (Grant 2012AA063505), the Special Fund for National Environmental Protection Public Welfare Program (Grant 201209023-4) and the Program of Introducing Talents of Discipline to University (Grant B08026).

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