Modeling and experimental studies on single particle coal devolatilization and residual char combustion in fluidized bed

Modeling and experimental studies on single particle coal devolatilization and residual char combustion in fluidized bed

Fuel 90 (2011) 2132–2141 Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Modeling and experimental st...

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Fuel 90 (2011) 2132–2141

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Modeling and experimental studies on single particle coal devolatilization and residual char combustion in fluidized bed Anup Kumar Sadhukhan a, Parthapratim Gupta a,⇑, Ranajit Kumar Saha b a b

Chemical Engineering Department, National Institute of Technology, Durgapur 713 209, West Bengal, India Chemical Engineering Department, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India

a r t i c l e

i n f o

Article history: Received 3 May 2010 Received in revised form 14 December 2010 Accepted 3 February 2011 Available online 17 February 2011 Keywords: Devolatilization Char Combustion Kinetic model Heat transfer model

a b s t r a c t Single particle devolatilization followed by combustion of the residual coal char particle has been analyzed in a batch-fluidized bed. The kinetic scheme with distributed activation energy is used for coal devolatilization while multiple chemical reactions with volume reaction mechanism are considered for residual char combustion. Both the models couple kinetics with heat transfer. Finite Volume Method (FVM) is employed to solve fully transient partial differential equations coupled with reaction kinetics. The devolatilization model is used to predict the devolatilization time along with residual mass and particle temperature, while the combined devolatilization and char combustion model is used to predict the overall mass loss and temperature profile of coal. The computed results are compared with the experimental results of the present authors for combustion of Indian sub-bituminous coal (15% ash) in a fluidized bed combustor as well as with published experimental results for coal with low ash high volatile matter. The effects of various operating parameters like bed temperature, oxygen mole fraction in bulk phase on devolatilization time and burn-out time of coal particle in bubbling fluidized bed have been examined through simulation. Ó 2011 Published by Elsevier Ltd.

1. Introduction Coal is the primary source of energy in developing countries including India and is likely to remain so in foreseeable future. Hence combustion of coal attracted a considerable amount of theoretical and experimental investigations. Fluidized bed combustion is one of the advanced technologies for utilizing medium sized coal particles efficiently due to its advantages in coal preparation and handling and the easier removal of ash resulting from the combustion of high ash coal. It is also considered to be a promising technology for emission control of gaseous pollutants. Coal when put inside a fluidized bed at temperature in excess of about 350 °C undergoes a rapid thermal decomposition called devolatilization, during which a fraction of coal, in the range of 30–50% by weight, is released in the form of volatiles depending on the volatile content of the original coal sample. Typically, the major constituents are CH4, CO, CO2, H2O, H2, C2H6 and other traces of higher hydrocarbons [1]. The volatiles subsequently may burn in presence of oxygen adjacent to the particle surface causing further increase in particle temperature, which accelerates the volatile evolution process. The characteristic time for release of volatiles

⇑ Corresponding author. Tel.: +91 343 2755314; fax: +91 343 2547375. E-mail address: [email protected] (P. Gupta). 0016-2361/$ - see front matter Ó 2011 Published by Elsevier Ltd. doi:10.1016/j.fuel.2011.02.009

from a coal particle depends on the volatile content of original coal sample, particle size and bed temperature. Komatina et al. [2] studied the temperature history of a coal particle during devolatilization inside a fluidized bed using Nitrogen as fluidizing medium. Chern and Hayhurst [3] presented a kinetic model for millimeter-sized coal particle incorporating heat transfer from fluidizing gas to coal particle without considering the volatile combustion as the fluidizing gas was nitrogen. Among various kinetic models on coal devolatilization the model demonstrated by Anthony and Howard [4] and distributed energy chain model by Niksa [5] have wide range of applicability. Most of the models for coal combustion in fluidized bed neglect the release of volatiles all together and deal with combustion of devolatilized char. Andrei et al. [6] proposed that the characteristics of volatile evolution are of prime consideration for design of efficient coal injection system for fluidized bed combustor. In an air-fluidized bed only some devolatilizing particles are seen to float on the surface of the bed, the volatiles burn with oxygen and a flame is formed above the particle. However inside a fluidized bed, the particles are found mostly in the particulate phase, where the bed materials quench the combustion volatiles and flame is not formed around the particle. A flame may form around the particle inside the bed, if it enters the bubble phase, which was experimentally observed by Prins et al. [7]. Borghi et al. [8] presented a single particle model for devolatilization followed by

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Nomenclature V V⁄ mk MV Nt ct cp Dk dp E Fv M r rs Rl Rep Rv S T t tv Xc

mass fraction of volatiles (–) volatile mass fraction after long time (–) mass fraction of component k (mol m3) molecular wt of volatiles (kg mol1) total molar flux (mol s1 m2) total concentration of gaseous mixture (mol m3) molal specific heat (J mol1 K1) diffusivity of component k (m2 s1) particle diameter (m) activation energy (J mol1) average volatile evolution rate (kg s1) molecular weight of gaseous component (kg mol1) radial co-ordinate (m) radial distance from center to particle surface (m) chemical reaction rate for Eqs. (7)–(9) (mol s1) particle Reynolds number (–) rate of devolatilization reaction (kg m3 s1) specific surface area (m2 m3) temperature (K) time (s) devolatilization time (s) carbon conversion in devolatilized char

residual char combustion of coal in fluidized bed, considering the combustion of entire evolved volatiles around the particle. Cherm and Hayhurst [9] argued that in presence of oxidizing environment inside the fluidized bed, although the volatiles burn around the particle very rapidly, the flow of fluidizing gas and bed material might carry much of the liberated energy away from the particle. Hence only a fraction of the liberated energy due to volatile combustion will be utilized to heat up the coal particle and particle temperature will be much less than that theoretically predicted. During devolatilization the coal particle undergoes many structural changes which continue during the combustion of the residual char itself. According to Wang and Bhatia [10], the char particle comprises microporous grains surrounded by mesopores and macropores. The heterogeneous gas–solid reactions take place on micropore surface while macropores serve as channel for transportation of gaseous reactants and products. Hence the combustion of porous devolatilized char inside the fluidized bed proceeds with reactions throughout the entire volume, called volume reaction model (VRM) [11], sometimes called shrinking reactive core model [12]. According to this model, the particle size remains nearly constant with the carbon taking part in reactions leaving behind inert ash, and causing particle density to fall with carbon conversion. The micro porosity, internal pore surface area and the accessible porosity of char gradually change during the course of combustion. Among various structural models the random pore model by Bhatia and Perlmutter [13] is one of the widely accepted models to predict the variation of pore surface area with conversion. The present study aims at investigating experimentally the combustion characteristics including devolatilization followed by residual char combustion in fluidized bed with Indian sub-bituminous coal containing 19% ash. A kinetic model based on distributed activation energy has been used for coal devolatilization. The transient devolatilization model considers volatile evolution followed by combustion of volatiles very near to the particle. The model is capable of predicting the particle temperature and the time of devolatilization for a given particle size and bed temperature. Volume reaction model with multiple chemical reactions and

Greek characters DHvc heat of combustion of volatiles (J mol1) DHdv heat of reaction for coal devolatilization (J mol1) e char porosity (–) er emissivity of the char (–) emf bed porosity at minimum fluidization (–) ckl reaction stoichiometry for component k for reaction no l (–) f fraction of the enthalpy from combustion reaching particle (–) k thermal conductivity (J m1 K1 s1) r Stefan–Boltzmann constant (J m2 s1 K4) rT standard deviation activation energy (J mol1) g molar ratio of CO/CO2 w pore parameter (–) q density (kg m3) Subscripts s solid phase g gas phase e effective property

pore diffusion has been employed for char combustion. The details on intra-particle pore diffusion is addressed with experimentally measured pore characteristics like pore volume, pore surface area, porosity and average pore size at various carbon conversion of devolatilized char. The combined single particle model consists of three sub-models: (1) kinetic model of coal devolatilization and volatiles combustion, (2) fully transient char combustion model and (3) fully transient heat transfer model during devolatilization and char combustion. These sub-models are inter-connected and solved simultaneously using implicit finite volume method by a FORTRAN code developed in-house. A fairly good agreement has been observed between the model prediction and experimental results of the present authors and others. 2. Mathematical model In this section the sub-models for kinetics of coal devolatilization, residual char combustion and energy balance during devolatilization and char combustion are described. A spherical particle with no decrepitation has been used where coal devolatilization is followed by combustion of residual char. During devolatilization volatiles come out from the porous internal structure of coal particle and burn with oxygen in air around the particle, forming a volatile flame. The flame prevents oxygen from reaching the particle surface. Soon the volatile evolution rate decreases and finally the volatile flame disappear. Now the oxygen concentration at particle surface starts to rise and combustion of residual char starts. 2.1. Kinetic model for coal devolatilization The distributed activation energy model of Anthony and Howard [4] is chosen for coal devolatilization as it eloquently incorporates large number of simultaneous reactions and species. The activation energy E is assumed to be a Gaussian distribution function with a mean of E0 and standard deviation rE. The instantaneous yield of volatiles, V and it evolution rate, Rv may be calculated as:

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Z ðE0 þ2rE Þ ðV   VÞ 1 ¼ pffiffiffiffiffiffiffi  V rE 2p ðE0 2rE Þ  Z t   exp k0  expðE=Rg TÞ  dt 0 " ( )# ðE  E0 Þ2  dE  exp  2r2E

Rv ¼

1 pffiffiffiffiffiffiffi rE 2p

"Z

(

ðE0 þ2rE Þ

k0 expðE=Rg TÞ  exp 

ðE0 2rE Þ

ð1Þ

) # ðE  E0 Þ2 dE 2r2E



 ðV  VÞ ð2Þ ⁄

V is used as a model fitting parameter after Borghi et al. [8]. 2.2. Heat transfer model during devolatilization As the coal particles enter the hot fluidized bed the particles are heated up due to convective and radiative heat transfer from the bed. At about 350 °C volatiles start evolving followed by homogeneous gas phase combustion. In this study it is assumed that the flow of fluidizing gas and bed material might carry much of the liberated energy due to volatiles combustion [9]. Only a fraction f (0.0 < f < 1.0) of the liberated energy from volatile combustion will be utilized to heat up the coal particles. The energy balance equation for the particle may be written as:

  @ðqs T s Þ ke 1 @ 2 @T s 1 þ ¼ r Rv  ðDHdv Þ @t cps cps r 2 @r @r

ð3Þ

The particle temperature at which it enters the bed is the initial condition. At the particle center the heat flux is zero, while at the particle surface the following boundary condition is used.

ke



@T s F v  ð DH v c Þ ¼f þ rer  T 4s  T 4b þ hc  ðT s  T b Þ 2 @r r¼rs 4pR

ð4Þ

2.3. Char combustion model Field et al. [14] proposed that for char particles below 100 lm the external mass transfer resistance is not significant and combustion reaction is kinetically controlled. However in fluidized bed combustor, most of the char particles are large enough (dp > 1.5 mm). Hence the overall combustion is influenced by external diffusion of reactant O2, product CO/CO2 and internal pore diffusion within the char particle along with surface chemical reaction rate [15]. Experimental studies by Dennis et al. [15] in fluidized bed using char particles in the size range of 1.5–8.0 mm revealed that the combustion proceeds mainly on particle surface and product is a mixture of CO and CO2. Arthur [16] proposed that during oxidation of carbon in char above 1000 °C, the product is entirely CO and in a temperature range of 400–900 °C the composition of the product gases may be given by

g ¼ CO=CO2 ¼ 2512 expð6240=TÞ

ð5Þ

For the purpose of oxygen balance for char combustion reaction the overall reaction may be written by incorporating g as:

2g þ 2 2g 2 C þ O2 ! CO þ CO gþ2 gþ2 gþ2 2

ðReaction : 1Þ

ð6Þ

The experimental and theoretical evidences reveal the fact that in a fluidized bed temperature of more than 750 °C the particle temperature exceeds 1000 °C and hence the combustion product is mostly CO. From the analysis of combustion gas and particle temperature, Dennis et al. [15] proposed that most of the carbon

monoxide produced during combustion is oxidized within the particle pores and close to particle external surface. However, many researchers argued that CO does not burn entirely within internal pores and gas boundary layer. Biggs and Agarwal [17] concluded that as the boundary layer is very thin in fluidized bed operation, a part of the CO burns inside the particle pores and the rest outside the boundary layer. The fraction of CO burning within and/or outside the boundary layer depends on operating conditions like gas velocity and operation temperature. In the present model no a priori assumption has been made on this account to ensure the applicability of the model in general. The wet homogeneous reaction mechanism similar to Biggs and Agarwal [17] is used for CO combustion in presence of trace amount of water vapor in air. A part of the CO2 thus generated may diffuse back at char surface and react with carbon to form CO again. A more detailed discussion on the reaction mechanism is available in Gupta et al. [18].

C þ CO2 ! 2CO ðReaction : 2Þ

ð7Þ

CO þ 1=2O2 ! CO2

ð8Þ

ðReaction : 3Þ

After a short duration carbon at the surface gets consumed completely leaving behind an ash layer. Further combustion is sustained within the internal pore surface area where intra-particle diffusion assumes importance. The rate of heterogeneous reactions (Eqs. (7) and (8)) depends on specific pore surface area, S(Xc) expressed per unit volume of the char particle at carbon conversion Xc at any time instant and is obtained experimentally. The variation of specific surface area S(Xc) with carbon conversion (Xc) modeled using random pore model of Bhatia and Perlmutter [13] may be presented as

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SðX c Þ ¼ S0  ð1  X c Þ 1  w lnð1  X c Þ

ð9Þ

where S0 is the specific surface area at zero carbon burn-off for devolatilized char and w is the dimensionless parameter known as pore parameter whose value depends on the nature of the coal char. In this study it is assumed that the char particle is surrounded by the gas mixture of O2, CO, CO2, H2O and N2. Only the carbon reacts leaving behind the ash skeleton intact and particle size remains constant during the entire period of combustion. 2.3.1. Conservation equations Conservation equations for gaseous species in porous particle phase

@ 1 @ 2 ðe  qg;s mk;s Þ þ 2 ðr Ntg;s Mav mk;s Þ @t r @r   X l¼3 1 @ 2 @mk;s r eRl ckl Mk þ ¼ Dke;s qg;s 2 r @r @r l¼1

ð10Þ

Total molar balance of gas mixture: 3 X 5 X @ðe  ct;s Þ 1 @ 2 þ 2 ðr Ntg;s Þ ¼ ckl  e  Rl @t r @r l¼1 k¼1

ð11Þ

Energy balance equation:

@ðcps qs T s Þ 1 @ 2 þ 2 ðr Ntg;s M av ;s cpg;s T s Þ @t r @r   X l¼3 1 @ 2 @T s þ r eRl  ðDHl Þ ¼ ke 2 r @r @r l¼1

ð12Þ

The mass balance of carbon in the solid char particle:

  dW c gþ1 ¼ 2 R1 þ R2  M c dt gþ2

ð13Þ

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The conservation equations in gas boundary layer has the forms as:

@ 1 @ 2 ðq mk Þ þ 2 ðr Ntg Mav mk Þ @t g r @r   1 @ @mk r2 ¼ qg Dke 2 þ ck3 R3  Mk r @r @r 5 X @ðct Þ 1 @ 2 ck3  R3 þ 2 ðr Ntg Þ ¼ @t r @r k¼1

@ 1 @ 2 ðC pg qg T g Þ þ 2 ðr N tg M av T g C pg Þ @t r @r   1 @ @T g r2 þ R3 ðDH3 Þ ¼ kg 2 r @r @r

Sh ¼ ð14Þ

ð15Þ

ð16Þ

2.3.2. Initial and boundary conditions The ambient air composition and temperature are chosen as initial conditions for both particle phase and gas boundary layer. At the particle center both mass and energy flux are equated to zero, while the boundary conditions at the edge of boundary layer near the free stream are equated to the bulk condition of fluidized bed. The other boundary conditions are presented below. At particle surface the boundary conditions for particle phase:

@mk;s Dke;s  qg;s þ Ntg;s M av ;s mk;s r¼rs @r r¼rs @mk ¼ Dke  qg þ Ntg Mav mk r¼rs @r

ð17Þ

r¼r s

Ntg;s ¼ Ntg @T s þ Ntg;s M av ;s cpg;s T s r¼rs  r2r ðT 4s  T 40 Þ ke r¼r s @r r¼rs @T g ¼ kg þ Ntg Mav cpg T g r¼rs @r r¼rs

ð18Þ

ð19Þ

The species mass fractions and temperature for gas boundary layer at the particle surface is equated to that in the porous particle phase [11]. 2.3.3. Expression of physico-chemical parameters The specific heat of gas mixture and heat of reactions are considered to be function of temperature and compositions. The heat transfer coefficient between the devolatilizing char particle and surrounding gases in presence of bed materials in fluidized bed is generally [19] the sum of hgc, gas-convection and hpc, particle-convection due to the presence of particulate phase. The contribution of the hgc becomes increasingly important in fluidized beds of larger particles or dilute-phase fluidization. hgc is estimated from Parmar and Hayhurst correlation [19] using an effective thermal conductivity of the particulate phase and a porosity-dependent drag coefficient. hpc depends on new particles being brought into contact with the heat-transfer surface, residing there and then being replaced by fresh particles and is modeled using correlation by Mickley and Fairbanks [20]. During char combustion in fluidized bed the mass transfer boundary layer thickness may be estimated from a number of correlations available including that of Prins et al. [7]. Hayhurst and Parmar [21] carried out a series of char combustion experiments in fluidized bed with varying operating gas velocity and temperature using graphite and coal char and presented a new correlation for estimating the Sherwood number:

Sh ¼ 2emf þ 0:61 ðRep Þ0:48  ðScÞ1=3

Dennis et al. [22] proposed a relationship between Sh and the mass transfer boundary layer thickness:

ð20Þ

2emf

s

þ acush 

dchar d

ð21Þ

where s is the tortuosity, which allows for the tortuous path for diffusion through the bed of particles and acush is the fraction area of the char covered by a gas cushion. In the present study the Sherwood number is estimated by Eq. (20) and the thickness of the mass transfer boundary layer is estimated using Eq. (21). The diffusivity and the viscosity of the individual gaseous components are calculated as a function of temperature using the Chapman–Enskog equation. The effective diffusivity of gaseous components within the porous char particle is calculated taking into consideration the Knudsen diffusivity, porosity and tortuosity factor of the char particle. The viscosity of gas mixture is estimated using the semi-empirical formula of Wilke [23]. The Wilke and Eucken equation [24] has been used to compute the thermal conductivity of gas mixture and the effective thermal conductivity of porous char particle is calculated considering the porous texture of the particle with pores filled up with gas mixture [25]. 3. Numerical method The principal variables Ts, mk,s, mk, and Tg are functions of time and radial position. These are obtained by solving the respective differential equations (Eqs. (3), (12), (10), (14), and (16)) simultaneously along with the initial and boundary conditions. Finite volume technique using implicit formulation was successfully employed to solve the sets of coupled partial differential equations along with nonlinear boundary conditions by present authors [11,12,18,24] where the merits of FVM were discussed elaborately. For spatial discretisation equal radii approach is adopted. The discretised equation in the control volume around each grid point is presented by a set of linear algebraic equations. An integrated FORTRAN code is developed to solve the model equations using TriDiagonal Matrix Algorithm where the convergence criterion is selected as 104 for all normalized principal variables. 4. Experimental Sub-bituminous coal of Indian origin is used for experiments in fluidized bed combustion. Individual particles are filed off to make them spherical with sphericity of 0.81–0.85. Five different particle sizes (average particle diameters of 6.0 mm, 4.36 mm, 3.0 mm, 2.18 mm and 0.92 mm) are selected for the experiments in fluidized bed for devolatilization study while three samples (4.36 mm and 2.18 mm) are chosen for combined devolatilization followed by residual char combustion. A 6.0 mm coal particle is also selected to study the center temperature history of a single coal particle during devolatilization and combustion in fluidized bed. A finesheathed Chromel–Alumel thermocouple is inserted into a fine hole drilled up to the center of the coal particle and plugged by iron-cement to ensure uniform combustion conditions and the central point temperature is measured continuously. The sample particles are air dried in crucibles in an oven at a temperature of 110 °C for two hours. The coal sample contains 27.0% VM, 58.1% fixed carbon and 14.9% ash on dry basis, while the ultimate analysis shows 86.41% C, 1.82% N, 4.51% H, 0.15% S and 7.15% O. The fluidized bed consists of a bed of silica sand (355–425 lm, static bed height of 100 mm and expanded bed height of 132 mm) in an Inconel alloy column, 82 mm in diameter, fitted with a distributor having 1.6 mm diameter holes and 1.2% open area. It is enclosed in a chamber constructed of refractory bricks mortared with castable refractory and insulated with asbestos sheet. LPG is

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with the microbalance at the top of the combustor by a very fine nichrome wire. The weight of the empty basket along with suspension system is determined at the test temperature and gas flow rate to note any possible flow-induced drag on the basket. The basket containing 2–5 coal particles are weighed, put inside the combustor and the mass is continuously monitored. The particle when put inside the combustor is heated up, devolatilization starts and volatile flame is produced at the top end of the particle. The yellowish volatile flame is visible through a mirror arrangement. Due to volatile combustion the particle surface temperature increases rapidly, thus accelerating the volatile evolution rate. Gradually the volatiles evolution rate slows down and eventually stops. The disappearance of volatile flame indicates the devolatilization time, tv, for different particle sizes at various bed temperatures. The devolatilization time is cross checked with the devolatilization time obtained from residual mass vs. time curve. It is followed by combustion. Samples of devolatilized char and partially burnt chars are taken out at different time instants and quenched in liquid nitrogen immediately. Only a few coal particles are used in

Table 1 Volatile yield V⁄ at various temperature and particle size. dp (mm) V⁄ at 700 °C V⁄ at 850 °C

6.0 0.20 0.27

4.36 0.22 0.28

3.0 0.24 0.29

2.18 0.25 0.30

0.92 0.26 0.32

burned outside the column to heat it to a desired temperature. An air blower provides air through an air preheater into the fluidized bed. The temperature of the bed is measured by a chromel–alumel thermocouple and controlled to within ±5 °C with the help of two separate on off controller attached with the gas flow line from the two LPG cylinder. Two operating bed temperatures 700 °C and 850 °C are chosen for experimentation with Umf 0.087 and 0.082 m/s respectively with superficial gas velocity U  2.5Umf. The bed is in bubbling fluidization regime. More detailed description and schematic are available elsewhere [25]. An experimental method similar to Peeler and Poynton [26] and Borah et al. [27] is employed. An Inconel wire basket is attached

30 Experimental 700 0C Experimental 850 0C Predicted

Devolatilization time (s)

25 20 15 10 5 0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Particle diameter (mm) Fig. 1. Comparison of predicted and experimentally obtained devolatilization time: devolatilization and combustion in fluidized bed (yO2 = 0.21).

1.0

m / m0 (-)

0.9

0.8

0.7

Experimental 2.18 mm dia.

0.6

Experimental 4.36 mm dia. Model prediction

0.5 0

5

10

15

20

25

30

Time (s) Fig. 2. Comparison of predicted and experimentally obtained residual mass: devolatilization in fluidized bed (yO2 = 0.21, Tb = 700 °C).

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5.1. Testing and comparison of devolatilization model

each run, which ensures constant oxygen concentration in the bulk phase, corroborated by analysis of gas samples from the bed. Biggs and Agarwal [17] used similar operating conditions to study the burning characteristics of porous coal char in a fluidized bed. Partially burnt char samples at different carbon conversion are analyzed for specific pore surface area. Nitrogen adsorption technique at 196 °C with automatic sorption analyzer Autosorb-1 (Model No. ASIC-9) by Quantachrome instruments is employed for the purpose. A mercury porosimeter (Pore-Master-GT, model PM 33-6) is used to determine the macroporosity of coal, devolatilized char and partially burnt char samples. The details on experiments are available in the previous work by the present authors [28]. Experiments were repeated 3–4 times for each run and the reproducibility is found to be within ±5%.

In order to determine the final volatile yield V⁄ the coal particles are heated in an atmosphere of flowing nitrogen at desired temperature for a period of more than 1 h. Table 1 shows the V⁄ for different particle sizes at a given temperature. The predicted devolatilization time for Indian sub-bituminous coal for different particle size at different fluidized bed temperatures depends on the parameter f, the fraction of volatiles undergoing combustion. f is obtained as 0.52 by fitting the experimentally observed devolatilization time with the model using Levenbarg Marquardt method. Fig. 1 compares the experimental devolatilization time with model predictions for five coal particles of different size at two bed temperatures of 700 °C and 850 °C. At both bed temperatures the model predicts the experimental results well with relative mean errors of 0.045 and 0.048 respectively (Fig. 1). It is observed during the experiments that the duration of volatile flame increases with an increase in particle size and decrease in bed temperature. The devolatilization time also depends on the volatile content of coal and bulk oxygen concentration in the bed.

5. Results and discussion The coal combustion model presented here consists of two sub-models, coal devolatilization and char combustion models.

1.0

m / m0 (-)

0.9

0.8

0.7 Experimental 2.18 mm dia Experimental 4.36 mm dia Model predicted

0.6

0.5 0

4

8

12

16

20

Time (s) Fig. 3. Comparison of predicted and experimentally obtained residual mass: devolatilization in fluidized bed (yO2 = 0.21, Tb = 850 °C).

1.0

m / m 0 (-)

0.8

0.6

0.4

Experimental 2.18 mm dia. Experimental 4.36 mm dia.

0.2

Model prediction

0.0 1

10

100

1000

Time (s) Fig. 4. Comparison of predicted and experimentally obtained residual mass: devolatilization and combustion of coal in fluidized bed (yO2 = 0.21, Tb = 700 °C).

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1.0

Experimental 2.18 mm dia Experimental 4.36 mm dia Model predicted

m / m0 (-)

0.8

0.6

0.4

0.2

0.0

1

10

100

1000

Time (s) Fig. 5. Comparison of predicted and experimentally obtained residual mass: devolatilization and combustion of coal in fluidized bed (yO2 = 0.21, Tb = 850 °C).

1.0 Experimental 3.0 mm dia.

0.8

Experimental 1.85 mm dia.

m / m0 (-)

Model Prediction

0.6

0.4

0.2

0.0

1

10

100

1000

Time (s) Fig. 6. Comparison of model prediction with experimental residual mass Andrei et al. [6]): devolatilization and combustion of coal in fluidized bed (yO2 = 0.08, Tb = 750 °C).

1.0 Experimental 3.0 mm dia.

0.8

Experimental 1.85 mm dia.

m / m0 (-)

Model prediction 0.6

0.4

0.2

0.0

1

10

100

1000

Time (s) Fig. 7. Comparison of model prediction with experimental residual mass Andrei et al. [6]: devolatilization and combustion of coal in fluidized bed (yO2 = 0.08, Tb = 900 °C).

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1200

Temperatue (0C)

1000 800 600 400 0 Experimental at 700 C 0 Experimental at 850 C

200

Model prediction 0 1

10

100

1000

Time (s) Fig. 8. Comparison of predicted and experimental center temperature profile: devolatilization and combustion of coal in fluidized bed (yO2 = 0.21, dp = 6 mm).

1200 900 0C

0

Temperatue ( C)

1000 850 0C 700 0C

800

600 Surface temperature Center temperature

400

200 1

10

Time (s)

100

1000

Fig. 9. Comparison of predicted temperature profiles: devolatilization and combustion of coal in fluidized bed (yO2 = 0.21, dp = 3 mm).

The devolatilization model is tested with experimental results of residual mass fraction during devolatilization of coal in air-fluidized bed. The experimental temporal residual mass loss profiles for 2.18 and 4.36 mm particles compare well with predicted results at bed temperatures of 700 °C (Fig. 2) and 850 °C (Fig. 3). The relative mean errors are 0.040 and 0.045 at 700 °C, while the same are 0.032 and 0.038 at 850 °C for 2.18 and 4.36 mm particles respectively.

5.2. The char combustion model The measured pore surface area of devolatilized char is 16.1 m2/cm3. The value of w is estimated from experimental data on pore surface area at various carbon conversions of residual char by regression analysis and is found to be 8 and 6 at 700 and 850 °C respectively. The data from mercury porosimeter shows that the porosity coal increases from 0.12 (virgin coal) to 0.30 (devolatilized char), while fully formed ash layer has porosity as high as 0.72. The variation of porosity with carbon conversion in char is modeled using liner interpolation. A detailed mathematical description is available in [27].

5.2.1. Testing and comparison of combined model The combined model is tested with experimental results of the present authors for devolatilization and char combustion of Indian sub-bituminous coal in a fluidized bed (21% O2). The experimental results and model predictions of temporal residual mass loss profile for 2.18 and 4.36 mm particles at bed temperature of 700 °C (Fig. 4) and 850 °C (Fig. 5) show that they agree well. The relative mean errors are 0.065 and 0.058 at 700 °C and 0.069 and 0.062 at 800 °C for two particle sizes respectively. From Figs. 4 and 5 it is evident that at the same bed temperature the fractional residue for small particles is always lower than the corresponding values for larger particles, and for the same particle size, it always lower at higher bed temperature. The estimated relative mean error is less than 0.048. The combined devolatilization and char combustion model is further compared with the experimental results of Andrei et al. [6] for combustion of Montana Lignite having volatile content of 35% in fluidized bed (8% oxygen) at 750 °C for different particle sizes (Figs. 6 and 7). A good agreement is observed for both cases with relative mean errors of 0.040 and 0.045 at 750 °C (Fig. 6) and 0.050 and 0.052 at 900 °C (Fig. 7). Fig. 8 compares the predicted center temperature profiles of a 6 mm coal particle using the combined model with data measured

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experimentally by the present authors at two different operating bed temperatures. Though the model predicts a temperature peak due to volatiles combustion, this is not very prominent experimentally, perhaps due to high response time of the thermocouple. However the overall prediction is good with the relative mean errors of 0.054 and 0.048 at 700 °C and 850 °C respectively 5.3. Simulation studies The model may be used to predict the combustion characteristics under different process conditions. The effects of various process parameters on combustion of coal of Indian origin in a fluidized bed are assessed from the simulation studies. Bubbling fluidized beds are normally used to burn low grade fuels with high volatile matter, typically pyrolysis and combustion of low grade coal and biomass [29]. Operating conditions are chosen after bubbling fluidized bed with the oxygen mole fraction in the range of 0.06–0.09 and the particle size of 3 mm. A few simulations are discussed in the following sections. 5.3.1. Particle surface temperature Fig. 9 compares the surface and center temperature profiles for 3 mm particle at different bed temperatures. Two peaks are observed in particles where combustion proceeds in ignition regime, i.e. with CO burning in the boundary layer. A similar phenomenon of two peaks was observed by Timothy et al. [30] through simulation studies for high volatile bituminous coal particles. Levendis et al. [31] observed two peaks experimentally for combustion of bituminous coal. The first temperature profile shows a peak at the end of the devolatilization period. The heat of combustion of volatile heats up the particle and the rate of volatile release is accelerated causing quicker particle heat up. Towards the end of devolatilization, volatile release rate gradually decreases and eventually almost stops causing sharp decrease in particle temperature. Subsequently the flame disappears and char combustion starts. The heat of reaction for heterogeneous surface reaction is much less than that for homogeneous volatiles combustion causing particle temperature to fall. However a second peak is observed during char combustion period and the peak is more prominent (Fig. 9) at higher bed temperature when the char combustion proceeds in ignition regime. Due to extinction towards the end of char combustion, the particle finally attains the bed temperature. For very fine particles, the second peak is not very prominent as the char combustion continues through heterogeneous reactions only. The peaks are more prominent in particles of intermediate size (say 3 mm) as the devolatilization is faster. 5.3.2. Effect of oxygen in bulk gas of fluidized bed The simulation study reveals that at 700 °C the burn-out time of 3 mm coal particle in fluidized bed in presence of 21% oxygen is found to be 576 s and it rises to 2014 s if the oxygen content is reduced to 6%. The corresponding times are 145 s and 490 s respectively for fluidized bed operating at 1050 °C. This information will help assess the role of oxygen on burning efficiency of the combustor. It is observed that at low bed temperatures the burnout time increases drastically at lower oxygen content of the bulk phase, but at higher temperature the effect is not so prominent. The results are of significance as oxygen enrichment has been assuming greater importance in recent times. 6. Conclusion 1. It is observed that the duration of volatile flame is longer for larger particle size at a given bed temperature. However, it also depends on the bed temperature, volatile content of coal and bulk gas oxygen concentration of the bed.

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