DYNAMIC MODELING OF BUBBLING FLUIDIZED BED

DYNAMIC MODELING OF BUBBLING FLUIDIZED BED COMBUSTORS Nevin Selc¸uk Department of Chemical Engineering Middle East Technical University 06531 Ankara, Turkey Tel: + 90 (312) 210 2603 Fax: + 90 (312) 210 1264 E-mail: [email protected]

DYNAMIC MODELING OF BUBBLING FLUIDIZED BED COMBUSTORS Nevin Selc¸uk Department of Chemical Engineering Middle East Technical University 06531 Ankara, Turkey Tel: + 90 (312) 210 2603 Fax: + 90 (312) 210 1264 E-mail: [email protected]

ABSTRACT Advantages of fluidized bed combustion technology such as the ability to burn a wide variety of fuels efficiently and to control pollutant emissions without flue gas treatment systems have led to a steady increase in its commercial use over the past decades. A fluidized bed combustor may sometimes be required to operate on fuels different from that it is designed for due to highly heterogeneous nature of particularly low quality coals or under off-design conditions. These changes usually lead to disruption of steady-state conditions, hence dynamic modeling becomes an essential requirement for the prediction of thermal and emission performances. This paper refers to the limited number of studies on dynamic modeling of bubbling fluidized bed combustors available in the open literature and describes in detail a dynamic model recently developed and tested from the viewpoint of predictive accuracy by comparing its results with measurements taken on the METU 0.3 MW Atmospheric Bubbling Fluidized Bed Combustor (ABFBC) Test Rig.

INTRODUCTION To date, research on mathematical modeling of fluidized bed combustors (FBCs) has focused on steady state models that provide tools for the design of a FBC around a given operating condition and prediction of its performance and emissions. Relatively little has been done in the area of dynamic modeling required for the design and implementation of a reliable control structure. A restricted number of studies on dynamic modeling of circulating FBCs is reported in the literature [1, 2]. Although bubbling fluidized bed boilers have been introduced to process and utility industries long before the circulating ones, the number of published studies on dynamic modeling of continuous bubbling FBCs is even more limited. Notable are models of a large shallow FBC [3, 4, 5], bench scale FBC [6, 7, 8] and a 3.5 MW FBC [9]. The model developed by Fan et al. [3] simulates the dynamic behavior of lateral distributions of oxygen and carbon particle concentrations in an isothermal bed. It is based on two-phase theory and diffusion controlled combustion of single sized carbon particles to carbon dioxide. Transient energy balances, reaction kinetics and elutriation losses are not considered. The model was later extended to incorporate transient energy balance on bed, but no solution was provided [4, 5]. Neither of these models has been experimentally validated. A dynamic model based on three-phase backmixing model, isothermal bed with varying char particle temperature, kinetically and diffusionally controlled combustion reactions to CO and CO 2 at the particle surface, shrinking particle model was proposed [6]. The same model but this time incorporating energy balance on bubble phase to take into account the nonisothermality of the bed was applied to the prediction of combustion of coal and/or combustible gas mixtures and validated against data from specific batch experiments [7, 8]. The model of Beasley and Golan [9] is a simple semi-empirical one proposed for engineering estimations. It is based on an overall energy balance around the whole combustor and excludes hydrodynamics and combustion kinetics. Comparisons between predicted and measured temperatures for step changes in coal feed show that the model fails for changes in coal feed rate over 10 %. A dynamic mathematical model of a continuous ABFBC has recently been developed on the basis of first principles and used to correlate data from a pilot-scale combustor [10]. The model accounts for bed and freeboard hydrodynamics, volatiles release and combustion, char particles combustion and their size distribution, and heat transfer. The solution procedure of dynamic model employs method of lines (MOL) approach for the solution of the governing nonlinear partial differential equations. The initial conditions required for each sub–model was provided from the simultaneous solution of governing equations of dynamic model with all temporal derivatives set to zero. Predictive accuracy of both steady state and dynamic models was assessed by applying it to the prediction of the behavior of METU 0.3 MW ABFBC Test Rig, and comparing their predictions with measurements taken on the same rig at steady state and transient conditions. Transient data were obtained by imposing changes to coal and air flow rates and measuring corresponding changes in oxygen and carbon monoxide concentrations at the exit of freeboard and in temperatures along the combustor against time. Comparisons of measurements and predictions show that the predictions of the model are physically correct and agree well with the measurements. This paper focuses on the description of this comprehensive model and the analysis of the dynamic response of the model during the transient operation of the pilot scale combustor and its validation against experimental data. MODEL DESCRIPTION The physical system to be considered is a continuously operated atmospheric bubbling fluidized bed combustor (ABFBC), equipped with a particle separator and bed ash removal system. Excess heat generated within bed is removed by means of water-cooled coils and heat transfer through combustor wall respectively. The dynamic behavior of the FBC under consideration is described by transient conservation equations for energy and chemical species in conservative form for both and freeboard sections. The correlations used in estimating physical parameters in the model are listed in Table 1. Five chemical species, O 2 , CO, CO2 , H2 O and SO2 are considered in the model. Chemical reactions included in the model together with their rate expressions are given in Table 2. Bed Model Bed model can be described in terms of bed hydrodynamics, volatiles release and combustion, char combustion and particle size distribution of bed char and bed char hold-up.

Table 1: Correlations used in the model References Mass transfer to particles in emulsion phase, k g

[14]

Heat transfer to particles in emulsion phase, h p

[15]

Specific elutriation rate constant, E
r

[16]

Terminal velocity of particles, u t

[17]

Bubble to emulsion mass transfer, Kbe

[17]

Minimum fluidization velocity, u m f

[18]

Bubble size, db

[13]

Emulsion phase velocity, u e

[19]

Bubble phase volume fraction, δ

[19]

Convective heat transfer coefficient of bed wall, h bw

[20]

Convective heat transfer coefficient of cooling tubes, h cw

[21]

Convective heat transfer coefficient of cooling water, h i

[22]

Exponential decay constant, a

[23]

Gas side heat transfer coefficient in freeboard, h g

[17]

Table 2: Reactions and rate expressions # 1 2 3 4 5

Reaction

Place


CO CO
1
2O
CO C
1
2O
CO H
1
2O
H O S
O
SO Cs
1
2O2

2

VM

2

2V M

VM

2

2

2

2

2

Rate Expression

Parameters

Reference

  17967
T
 475  10 exp  8052
T

kC  590Tp exp




char surface

kCCO2 s

gas phase

kCOCO0 23CCOCH0 25O

gas phase

instantaneous

-

-

gas phase

instantaneous

-

-

gas phase

instantaneous

-

-







kCO

5

p

g

[24] [25]

Bed Hydrodynamics Bed hydrodynamics is based on modified two-phase theory suggested by Grace and Clift [11], uo 

Qb Ao

 ut f  ue
1


δ

(1)

where throughflow velocity, u t f , can be expressed in terms of emulsion phase velocity, u e , using modified n-type two-phase theory of Grace and Harrison [12], ut f


n  1 u e δ

(2)

where n  2 for three-dimensional beds. Gas/solids in emulsion phase and gas in bubble phase are assumed to be well-stirred and in plug flow, respectively. An integrated average mean bubble size found from bubble size expression proposed by Mori and Wen [13], in the sections unoccupied by the tube bank and from constant and uniform bubble size determined by the clearance between horizontal tube bank is utilized. Bubbles are assumed to be free of solids.

Table 3: Devolatilization kinetic parameters v∞ , % (dry)

36.3

ko , s
1

1
3  1013

σ, J mol
1

4
7  104

2
4  105

Eo , J mol
1

Volatiles Release and Combustion Volatiles are assumed to be released uniformly in the emulsion phase. The amount released in bed is determined by using the volatile release model of Stubington et al. [26], and time resolved devolatilization profile of coal particles which necessitates a devolatilization kinetics model and determination of its kinetic parameters. The parallel independent reaction model of Anthony and Howard [27], is used to describe the devolatilization kinetics, v v∞

1










∞

exp 0









t

k
E dt

f
E dE

(3)

0

where k
E   ko exp

E RT 

f
E  




2π

1
2


1

σ

exp





E
Eo2

(4)

2σ2





(5)

These equations contain four parameters to be estimated from experimental data. These are ultimate yield of volatiles, v∞ , pre-exponential factor, k o , the mean, Eo , and standard deviation of the activation energy distribution, σ. Experimental data on devolatilization kinetics were obtained from thermogravimetric analysis (TGA). Thermal analyses were carried out in nitrogen atmosphere with raw sample screened through 60 mesh ASTM sieve (250 µm) at two heating rates, 10 Æ C/min and 20Æ C/min. Samples were heated from 30 Æ C to 900Æ C and then kept isothermal at 900Æ C for another half an hour. In order to determine the kinetic parameters the weight loss versus time data was converted to dry basis by subtracting the moisture content of coal from the recorded weight losses. Weight losses at the end of the TGA runs yielded v ∞ values. As for the pre-exponential factor, k o , the value derived by Merrick [28], for a range of coals was used. With values available for v ∞ and ko , Eo and σ values were found by using experimental data in conjunction with a nonlinear regression algorithm. The values resulting from the data on two heating rates were averaged and used in the devolatilization kinetics model. Four kinetic parameters utilized in the model are illustrated in Table 3. Figure 1 shows comparison between experimental and calculated weight loss data for Beypazarı lignite at the two heating rates and the parameters listed in Table 3. Reasonable agreement is obtained for each heating rate. The computation of the time-resolved devolatilization history of coal particles from model of Anthony and Howard [27], requires the specification of particle temperature in addition to the estimated kinetic parameters. Assuming that particles are thermally neutral, remain spherical and intact with constant thermophysical properties during devolatilization, particle temperature can be calculated from ∂T ∂t






α∂ ∂T r2 2 r ∂r ∂r



(6)

with the following boundary conditions at r  R

4 4
k ∂T  h p
Tg
T   σε
Tg
T  ∂r

at r  0

∂T ∂r

0

(7)

(8)

50 10 oC/min, calculated 10 oC/min, experimental 20 oC/min, calculated 20 oC/min, experimental

Weight loss, % (dry)

40

30

20

10

0 0

600

1200

1800

2400

3000

3600

4200

4800

5400

6000

6600

Time, s

Figure 1: Comparison of calculated and experimental weight losses for temperature ramps 10 K/min and 20 K/min for Aydın lignite In the presence of radial temperature profile and with the assumption of evenly distributed volatile matter in the particle, total amount of volatile matter released with respect to time can be obtained by averaging Equation (3) over the volume of the particle,

t  
∞
 vavg 3 R 2  1
exp k
E dt f
E dE r dr (9)
v∞ R3 0 0 0 For the determination of the amount of volatiles released in the bed section of the ABFBC, calculation of the time spent by the particle at different locations during its upward and downward motion in the bed and over the surface is required. This is provided by Stubington’s particle movement model [26]. In this model, it is assumed that particle movement is caused solely by bubbles and that a coal particle remains stationary in the bed until a bubble displaces it axially and radially to another stationary point higher up in the bed up to the bed surface. The mean axial rise velocity of a coal particle is obtained from the expression of Nienow et al. [29], ur  k
u0
um f 05

(10)

where k is a constant and equal to 0
19 for their system. The particle will reside in a position for a time period enough for two successive bubbles to pass through that position which is equal to the inverse of bubble frequency. Bubble frequency at any height in the bed is calculated from the expression of Cranfield and Geldart [30], f

 0
61h


072

(11)

where h is the height above the distributor and f is the bubble frequency. Assuming instantaneous rise of the coal particle to the next stationary position, the distance traveled by the particle is calculated as the stationary time multiplied by the mean axial rise velocity. When a coal particle reaches bed surface it moves to the wall and is carried back down into the bed to a certain distance by the general downward movement of inert bed particles, then it is picked up by a bubble and starts to rise again in a stepwise movement. The lateral distance moved by the particle at the bed surface is assumed to be proportional to the bubble size, x  kdb

(12)

and the proportionality constant, k, is an empirical value found to be 0.4 for the system under consideration. The particle descending velocity is found from the relationship given by Kunii and Levenspiel [17], ud



αδub 1
δ
αδ

(13)

where α  0
2. The average depth of penetration of a large coal particle circulating in the bed is determined from the correlation of Nienow et al. [29], dcir  1
2Hbed
u0
um f 05

(14)

Comparison of the cumulative time spent by a devolatilizing coal particle while it is standing at each stationary point in the bed with its devolatilization history yields the fraction of volatiles released in bed. The remaining volatiles are assumed to be released to freeboard while the particle is at the bed surface. With regard to combustion of volatiles released, volatile carbon and hydrogen are assumed to burn instantaneously to CO and H 2 O, respectively. The oxidation of CO takes place in both bubble and emulsion phases according to the rate expression of Hottel et al. [25]. Char Combustion Char particles are assumed to burn only to CO, as it is the major product of char combustion for typical FBC temperatures. Using the shrinking particle model and taking film mass transfer and the kinetics resistance into consideration, the rate of carbon oxidation at the particle surface can be obtained as rCe 

2 CO e 1k f  2ks 2

(15)

Film mass transfer coefficient, k f , is obtained from the equation suggested by Jung and La Nauze [14]. Kinetics of combustion of char particles is assumed to be represented by equation of Field et al. [24]. Average emulsion phase O 2 concentration is used to calculate combustion rate. The shrinkage rate of char particles is estimated from ℜ
r 


dr dt



1 x f c  xa MC rCe ρd x f c

(16)

The particle temperature is calculated by solving an energy balance around the particle, which is assumed to have uniform temperature, dTd dt



 o ℜ
r  3x f c ∆HR1 3  4 h p
Td
Tbed 
σεd
Td4
Tbed 
rMC c pd
x f c  xa  rρd c pd

(17)

Particle Size Distribution of Bed Char and Bed Char Hold-up Since carbon consumption rate depends on the surface area provided by the burning char particles, calculation of particle size distribution (PSD) and hold-up of char particles is of fundamental importance in the prediction of behavior of fluidized bed combustors. Under the assumption that attrition is negligible, the unsteady state population balance on char particles takes the following form: ∂Φ
r ∂t

 Ff Pf
r 


Fbd ΦW
r
Φ
rE
r  ∂∂r Φ
rℜ
r
3r Φ
rℜ
r

(18)

d

Φ
r  0

at r  rmax

(19)

Once the solution for Φ
r becomes available Wd , Pbed
r, Fco and Pco
r are obtained from the following expressions: Φ
r  Wd Pbed
r


Wd



rmax

rmin

Pbed
r 

(20)

Φ
rdr

(21)

Φ
r Wd

(22)


Fco 

rmax

Φ
rE
rdr

(23)

Φ
rE
r Fco

(24)

rmin

Pco
r  Mass and Energy Balance Equations

Transient conservation equations for chemical species in bubble and emulsion phases are described as follows: ∂n jb ∂t dn je dt





∂n jb RTbed nb Abed δℜ jb  Abed δKbe
C je
C jb 
PAbed δ ∂z

 

n jb dTbed Tbed dt



n jb ∂nb nb ∂t



RTbed ne Vbed
1
δεm f ℜ je
Vbed δKbe
C je
C jb 
n je
n jez
0 PVbed
1
δεm f n je dTbed n je dne   Tbed dt ne dt

(25)





(26)

These equations are subject to the following boundary conditions, at z  0

at z  0

n jb  y jb

n je  y je

na ue 1
δ εm f 1 ub δ

(27)

na ub δ 1 ue
1
δεm f

(28)

The expressions for the species generation or depletion terms appearing in Equations (25) and (26), ℜ takes the following forms for each species considered, j1

ℜ1e 


mvm xvl Vbed
1
δεm f

0
5

(29)

xCvm xH vm xSvm  0
5  MC MH2 MS




0 5nCe
0 5rCOe


ℜ2e 

j4




(30)


CO

ℜ2b 
rCOb

j3

and ℜ je ,


O2 

ℜ1b 
0
5rCOb

j2

j b

mvm xvl Vbed
1
δεm f

0
5

xCvm MC

(31)

 nCe


rCOe

(32)


CO2 

ℜ3b  rCOb

(33)

ℜ3e  rCOe

(34)

ℜ4b  0

(35)


H2 O

ℜ4e  j5



1

Vbed
1
δεm f

xH vm mvm xvl MH2

xH2 O  mF MH2 O

(36)


SO2 

ℜ5b  0 mvm xvl ℜ5e  Vbed
1
δεm f where, nCe 




3Wd Vbed
1
δεm f

rmax

rmin

x

Svm

(37)



(38)

MS Pbed
r ℜ
rdr r

(39)

On the assumption that the gas and the inert particles are at the same temperature and that the mass of combustion gases and char particles are negligible compared to the mass of inerts, a combined gas/solid phase energy balance can be written as,
Ta
LT dTbed 1  na c pa dT
πdT o Ucw
Tbed
Tw dx dt c piWi Tr 0
Tbed 6
Abwhbw
Tbed
Tbws

ne  nb ∑ y j c pg j dT
m f xw λo j
1

Tr


mcoc pi
Tbed
Tr 
mbd c pi
Tbed
Tr   Qrxn  Q p



(40)

where enthalpy generated by chemical reactions, Q rxn , and energy transferred from burning char particles, Q p , are obtained from following equations,  
Hbed
Hbed o Qrxn  Abed ∆HR2 εm f
1
δ rCOe dz  δ rCOb dz  m f xvm xvl

Qp 

3Wd ρd

x

o

0

xH vm xSvm Cvm o o o ∆HR3  ∆HR4  ∆HR5 MC MH3 MS




rmax

rmin





(41)

 dr

4 h p
Td
Tbed   σε
Td4
Tbed 

(42)

r

The combustor wall surrounding the bed have a mass sufficient to make its dynamic effect an important consideration in the temperature dynamics of the bed. The thermal inertia of the wall is taken into consideration by making one-dimensional heat transfer analysis. For a combustor with square cross-section and wall thickness of L bw , the temperature profile inside the wall is given by the following equation, Appendix A of Degirmenci [31], ∂Tbw ∂t





kbw ∂Tbw 5 2 ∂x ρbw c pbw
x  A0bed

∂2 Tbw 05 
x  Abed 2 ∂x2



(43)

Equation (43) is subject to the following boundary conditions: x0

hbw
Tbed
Tbw  
kbw x  Lbw

∂Tbw ∂x

Tbw  Tbwo

(44) (45)

In order to account for dynamics of the energy absorbed by the in-bed heat exchanger, a separate energy balance is performed on the cooling water. Neglecting the heat transfer resistance and mass of the tubes, the transient variation of the temperature of the cooling water is given by the following equation, Appendix A of Degirmenci [31], ∂Tcw ∂t



4dT o hcw
Tbed 2 dT i ρcw c pcw

∂Tcw cw ∂x


Tw 
πd4m2 cwρ T i

(46)

The inlet temperature of the cooling water is set as boundary condition to Equation (46). Surface temperature of tube wall, Tw , is calculated by solving a surface energy balance, hcw dT o
Tbed
Tw 
hi dT i
Tw
Tcw   0

(47)

Freeboard Model Solids Distribution The hold-up of particles in the freeboard is expressed with an exponential decay function [23], εs εso


az f 

 exp


(48)

where εso is the volume fraction of solids just above the surface of dense bubbling bed and is given by, εso  1
ε f

(49)

The volume fractions of char and inert particles of size r at bed surface are obtained from the following equations, respectively, εd o  εso

Wd Pbed
r∆rρd Wd ρd  Wi ρi

(50)

εio  εso

Wi Pbed
r∆rρi Wd ρd  Wi ρi

(51)

The entrainment flux of particles, K i , is calculated by assuming that it consists of a cluster flux, K ih , and a dispersed  as suggested by Hazlett and Bergougnou [32], noncluster flux, Ki∞

 Ki  Kih  Ki∞

(52)

and are obtained from empirical correlations proposed by Choi et al. [23]. The elutriation rate constant, E
r, defined in Equation (7) of [33], is then calculated from, E
r 

Abed  K Wd i∞

(53)

The elutriated particles are assumed to rise at the superficial gas velocity in the freeboard. Size distribution of entrained solid particles at any height in the freeboard is calculated by assuming that probability of finding particles of size r at any height is proportional to their presence in bed with proportionality constant being K ih , Fz Pz
r  Kih Abed Pbed
r

(54)

Multiplying both sides of Equation (54) by dr and integrating yields the flow rate of entrained particles and their size distribution as follows:
rmax Fz  Abed Kih Pbed
rdr (55) rmin

Pz
r  Abed Kih Pbed
rFz

(56)

Mass and Energy Balance Equations It is assumed that the gases in the bubble and emulsion phases mix instantaneously at the top of the bed and enter freeboard. The gas flow in freeboard is assumed to be in plug flow. Transient conservation equation for chemical species can be written from Equation (25) by excluding the interphase transfer as follows, ∂n j f ∂t





RT f n f ∂n j f A f
1
εs ℜ j f
PA f
1
εs ∂z





n j f ∂T f T f ∂t



n j f ∂n f n f ∂t

(57)

Boundary condition for Equation (57) is expressed as, at z f

0

n j f

 n j e  n j b

(58)

The expression for species generation/depletion term, ℜ j f , appearing in Equation (57) takes the following forms for the species considered, j1


O2 

ℜ1 f j2



xCvm xH vm xSvm mvm
1
xvl  
0
5  0
5  V f
1
εs MC MH2 MS


CO

ℜ2 f j3





xCvm mvm
1
xvl  0
5 V f
1
ε s  MC

j5

 nC f


0 5nC f
0 5rCO f






rCO f

(59)

(60)


CO2 

ℜ3 f j4



 rCO f


H2 O

(61)



ℜ4 f

mvm
1
xvl  xH vm 
V f
1
ε s  MH2

ℜ5 f




SO2 


mVvm

11

εxvl  f

s

x

Svm

(62)

(63)

MS

where nC f , the solid carbon consumption rate at any height in freeboard is the sum of carbon consumption rates for coarse and fine particles, as shown below,
rmax
 εsd Pz
r 2η x f c  Fco rmax Pco
r nC f 
ℜ f
rdr  ρd ℜ f
rdr (64) MC x f c  xa r A f rmin ru p
r rmaxe η in Equation (64) represents the contact efficiency between gas and solids in freeboard and it is calculated from the following equation proposed by Kunii and Levenspiel [34], η  1







ue 1

1
δ exp

6
62z f  u0

(65)

The gas temperature profile in freeboard is obtained by solving an energy balance which considers convective transport and, generation and loss of energy, ∂T f ∂t



RT 2 n RT 2 RT 2
T
T 
A
1
f ε fPT ∂T∂zf  PM Tf c R
A
f1
fε PTr ∂n∂zf f s r g r pg f s r

(66)

Equation (66) has the following boundary condition: at z f

0

Tf

 Tbed

(67)

R is the combined energy generation and loss rate per unit volume of freeboard. It is the sum of energy generated by chemical reactions, Rrxn , energy loss from freeboard walls, R fw , and energy transferred from/to char and ash particles present in the freeboard, R p . These terms can be expressed as follows, o Rrxn  ∆HR2 rCO f





mvm
1
xvl  xCvm xH vm xSvm o o o ∆HR3  ∆HR4  ∆HR5 V f
1
εs  MC MH2 MS

Rfw 


4dbed h f w
T f Abed
1
εs 


Tf w



(68)

(69)


rmaxe  Pzd
r  3Fco h p
Td
T f   σε
Td4
T f4  dr Abed ρd rmin ru p
r
rmax  Pzd
r   3εd h p
Td
T f   σε
Td4
T f4  dr r rmaxe
rmax  Pzi
r   3εi h p
Ti
T f   σε
Ti4
T f4  dr r rmaxe

Rp 

(70)

It is assumed that in freeboard char particles temperatures are equal to their temperatures in bed as calculated by Equation (17) and temperatures of inert particles remain at T bed . A surface energy balance is formulated to solve for the temperature of the freeboard wall, h f
T f


Tf w

Tf w
R Tf wo   0

(71)

w

where h f is calculated by using the approach of Kunii and Levenspiel [17], h f

hr  hg hz f
0

hr  hg


az f

 exp


2



(72)

SOLUTION PROCEDURE The input data required by the system model are the configuration of the rig and its internals, air and coal flow rates, coal analysis, all solid and gas properties, inlet temperatures of air, cooling water and feed solids and the size distribution function of feed solids deduced from sieve analysis. Apart from these input data, application of the model necessitates empirical and semi-empirical correlations from the literature for heat and mass transfer, combustion kinetics, elutriation and entrainment rates etc., listed in Tables 1 and 2. These expressions contain empirical or semi-empirical constants which may not always comply with the experimental conditions of the system to be modeled. Therefore it is the usual practice to adjust some of these constants until a compromise is found to reproduce the measured data as accurately as possible [35]. In this study, minimum number of fitting parameters was utilized. These were pre-exponential factor for carbon monoxide oxidation, exponential decay constant for entrained particles and elutriation rate constant. CO concentrations predicted by using the rate expression of Hottel et al. [25], was found an order of magnitude lower than the measurements. To match the measured CO concentration at the exit of the combustor, the rate constant from Hottel et al. was multiplied by 0.3 and this value was used for model validation. With regard to entrainment, direct use of the entrainment rate expression of Choi et al. [23], in the model resulted in higher char hold-up and hence lower O 2 concentrations in the freeboard compared to measurements. To match the measured O2 concentration at the exit of the freeboard, the decay constant of the entrainment rate expression of Choi et al. was multiplied by 5 and used in the simulations for model validation. Direct use of elutriation rate expression of Choi et al. in the steady state model yielded higher carryover flow rate at the cyclone exit. To match the measured carryover flow rates, elutriation rate constant of Choi et al. was multiplied by 0.38. A code was developed for the numerical solution of the governing equations presented. The code is based on the method of lines (MOL) solution of partial differential equations (PDEs) [36]. In the MOL approach the first stage in the solution of PDEs is to discretize the spatial derivatives and second stage is to integrate the resulting system of ordinary differential equations (ODEs) by a powerful ODE solver. In the application of the first stage, first order spatial derivatives in Equations (25), (43) and (46) are discretized according to biased–downwind scheme whereas the one in Equation (18) is discretized according to biased-upwind scheme to ensure problem stability. Second order derivatives are discretized according to centered scheme. Discretization schemes used are based on the five-point Lagrange interpolation polynomial to satisfy accuracy [37]. The resulting ordinary differential equations (ODEs) are integrated by a semi-implicit Runge-Kutta algorithm embedded in the ODE solver ROWMAP [38]. Initial conditions required for the solution of ODEs are provided by the steady state solution of the transient code. EXPERIMENTAL Experimental data for model validation were generated on a 0.3 MW ABFBC test rig burning lignite particles of wide size distribution in their own ash. The main body of the test rig is the modular combustor formed by five modules of

Table 4: Characteristics of Aydın lignite Sieve Analysis

Size (mm)

Weight (%)

Proximate Analysis

Ultimate Analysis

(as fired)

(dry)

Composition

Weight (%)

Composition

Weight (%)

8.000-4.750

7
96

Moisture

17
0

C

46
60

4.750-3.350

28
06

Ash

28
0

H

3
52

3.350-2.360

18
29

VM

33
0

O

14
34

2.360-1.700

19
45

FC

22
0

N

1
33

1.700-0.850

12
18

S(org)

0
36

0.850-0.600

3
58

S(prt)

0
15

0.600-0.300

4
19

S(slf)

0
05

Ash

33
76

0.300-0.000

6
28

HHV: 17
1 MJ kg

d 32 : 8
7  10
4 m

Density:

1140 kgm 3

Table 5: Operating conditions at steady state

Coal flow rate, kg s
1  103

Bed drain flow rate, kg s
1  103

Carryover flow rate, kg s
1  103 Air flow rate, mole s
1

0.34 5.94 6.32

Excess air, %

47

Superficial air velocity, m s
1

3.1

Average bed temperature, K

1126

Average freeboard temperature, K

1143

Combustion efficiency, %

95

O2 concentration at the stack, % (dry)

5.9

CO2 concentration at the stack, % (dry)

12.4

Bed cooling water flow rate, kg s
1 OHTC in bed, W m
2 K
1 OHTC in freeboard, W m
2 K
1 Bed height, m



24.9

0.38 238 59 1.2

Overall heat transfer coefficient

internal cross-section of 0.450.45 m and 1 m height. Inner walls of the modules are refractory lined and insulated. The first and fifth modules from the bottom refer to bed and cooler, respectively, and the ones in between are the freeboard modules. There exists two cooling surfaces in the modular combustor, one in the bed and the other in the cooler providing 0.35 m 2 and 4.3 m2 of cooling surfaces respectively. There are 14 ports for thermocouples and 10 ports for gas sampling probes along the combustor. Two ports for feeding coal/limestone mixture are provided in the bed module. One of the feeding ports is for under-bed feeding and is located at 22 cm above the distributor plate, the other is for in-bed feeding and is located 15 cm below the expanded bed height. In order to measure concentrations of O 2 , CO, CO2 , SO2 along the combustor at steady state, combustion gas

is sampled from the combustor and passed through gas conditioning system where the sample is filtered, dried and cooled. O2 concentration is measured by means of Leeds & Northrup Paramagnetic O 2 analyzer. CO and CO 2 are measured by Anarad AR-600 series IR analyzer. SO 2 is measured by Servomex series 1490 IR analyzer. The output signals from analyzers and process values such as temperatures, air and water flow rates, pressures and speed of screw conveyors are logged to a PC by means of a data acquisition and control system, Bailey INFI 90. Further details of the test rig are given in [39] and [40]. Experiments were carried out with Aydın lignite. Table 4 shows the properties of lignite burned in the rig. It burns in its own ash due to its high ash content. Table 5 illustrates the steady state operating conditions for the experiment. The transient response of the test rig was investigated by imposing changes to coal and air flow rates while keeping the rest of the parameters constant. The response of the system to changes was studied in terms of stack gas oxygen and carbon monoxide concentrations, gas temperatures and in-bed cooling water exit temperature. Transient responses of the system were monitored following successive step changes in coal and air flow rates and also pulse change in coal flow rate. Step changes in air and coal flow rates and durations depicted in Figure 2(a). Figure 2(b) shows the pulse change in coal flow rate (133 %) for a period of 45 s. RESULTS AND DISCUSSION Validation of Steady State Predictions The initial conditions required for the dynamic model were provided from the solution of the governing equations of the dynamic model with all temporal derivatives set to zero. This also leads to the prediction of the steady state performance of the rig. Comparisons between the predictions and measurements under steady state conditions in terms of concentration and temperature profiles are shown in Figures 3(a) and 3(b). Predicted profiles and measured values are found to be in reasonable agreement. Responses to Step Changes Figure 4(a) shows comparison between measured and predicted temporal variation of O 2 concentrations at the freeboard exit and also predicted transient bed exit O 2 concentration for step changes in air and coal flow rates. As can be seen from the figure, there is a good agreement between the measured and predicted O 2 concentrations. O 2 shows an immediate response to changes in air and coal flow rates. The increase in air flow rate and the decrease in coal flow rate results in an increase in O 2 concentration as expected. The reverse trend is observed for the decrease in air flow rate and for the increase in coal flow rate. The change in predicted O 2 concentration at the bed exit is more notable than the predicted change at the freeboard exit as O 2 is further depleted due to homogeneous and heterogeneous reactions in the freeboard. Figure 4(b) displays the responses in terms of CO concentrations. Predicted and measured transient CO concentrations at the freeboard exit show favorable comparison. The response of CO concentration is found to be smoother than that of O 2 due to the damping effect of oxidation of CO to CO 2 in the freeboard which is apparent from the comparison of predicted bed and freeboard exit CO concentrations. Figure 5(a) illustrates the thermal response of the system to successive step changes in air and coal flow rates in terms of bed temperature. As can be seen from the figure the prediction follows the same trend as measurement. The model underpredicts the bed temperature and the difference between the measured and predicted temperatures increases steadily and settles to 40 K toward the end of simulation period. Comparison between the responses of bed temperature and species concentrations shows that the response of bed temperature is more sluggish than that of species concentrations due to the large thermal inertia of inert bed material. Figure 5(a) also shows the predicted bed wall temperature to the same successive step changes. Slower response of bed wall temperature compared to bed temperature depicts the additional thermal inertia of refractory walls. Figure 5(b) illustrates the comparison between measured and predicted bed cooling-water exit temperatures. The measured transient response is reproduced by the model reasonably well. Figure 6(a) shows the predicted temporal variation of char weight in bed. As can be seen from the figure when the air flow rate is increased char hold-up in bed decreases initially due to the increases in elutriation loss and O 2 concentration which leads to an increase in the char combustion rate. As time progresses the bed temperature decreases through the rise in sensible heat loss with the gas. This leads to a fall in char combustion rate which in turn increases the bed char hold-up. Opposite trend is observed when the air flow rate is decreased. The decrease and increase in coal flow rate result in a fall and rise of bed char hold-up with time as the coal is the only source of char in bed. Figure 6(b) displays the change in bed char size distribution with time. As can be seen from the figure, for successive step changes

30

9.0

27

1

2

3

4

8.5 8.0

24 7.5 21 7.0 18 15 -600

AIR FLOW RATE, mole/s

COAL FLOW RATE, kg/s × 10 3

COAL AIR

6.5

-300

0

300

600

900

1200

1500

6.0 1800

TIME, s (a)

COAL FLOW RATE, kg/s × 10 3

60

50

40

30

20 -300

-200

-100

0

100

200

300

TIME, s (b)

Figure 2: Changes imposed on coal and air feed rates: (a) Successive step changes in coal and air feed rates, (b) pulse change in coal feed rate

24

BED

FREEBOARD

MOLE % (dry)

20

16

12

8

4

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

HEIGHT ABOVE THE DISTRIBUTOR PLATE, m (a)

1400

BED

FREEBOARD

PREDICTED MEASURED

1300

TEMPERATURE, K

1200 1100 1000 900 800 700 600 500 400 300 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

HEIGHT ABOVE THE DISTRIBUTOR PLATE, m (b)

Figure 3: Measured and predicted steady state (a) gas concentration (O 2 :, CO2 :∇, CO:), (b) temperature profiles along the combustor

O2 CONCENTRATION, mole % (wet)

15

PREDICTED (bed exit) PREDICTED (freeb. exit) MEASURED (freeb. exit)

13

11

9

7

5

1 3

2

0

180

360

540

720

900

3 1080

1260

4 1440

1620

1800

1620

1800

TIME, s (a)

CO CONCENTRATION, ppm (wet)

8000

PREDICTED (bed exit) PREDICTED (freeb. exit) MEASURED (freeb. exit)

7000 6000 5000 4000 3000 2000 1000 0

1 0

2 180

360

540

720

900

3 1080

1260

4 1440

TIME, s (b)

Figure 4: Comparison of measured and predicted transient (a) O 2 , (b) CO concentrations for successive step changes in air and coal feed rates (1: 14.3 % increase in air, 2: 12.5 % decrease in air, 3: 21.7 % decrease in coal, 4: 27.8 % increase in coal)

1200

PREDICTED BED TEMP. MEASURED BED TEMP. PREDICTED BED WALL TEMP.

TEMPERATURE, K

1175

1

1150

2

3

4

1125

1100

1075

1050

0

180

360

540

720

900

1080

1260

1440

1620

1800

1620

1800

TIME, s (a)

335

PREDICTED MEASURED

TEMPERATURE, K

330

325

320

315

1

0

2

180

360

540

720

900

3

1080

1260

4

1440

TIME, s (b)

Figure 5: Comparison of measured and predicted transient (a) bed temperature, (b) bed cooling-water exit temperature for successive step changes in air and coal feed rates (1: 14.3 % increase in air, 2: 12.5 % decrease in air, 3: 21.7 % decrease in coal, 4: 27.8 % increase in coal)

220

CHAR WEIGHT, kg × 10 3

200 180 160 140 120 100 80

1 0

2 180

360

540

720

3

900

1080

1260

4 1440

1620

1800

TIME, s (a)

3

4

2 1

(b)

Figure 6: Predicted transient bed char (a) hold-up and (b) size distribution for successive step changes in air and coal feed rates (1: 14.3 % increase in air, 2: 12.5 % decrease in air, 3: 21.7 % decrease in coal, 4: 27.8 % increase in coal)

in air and coal flow rates with the magnitudes less than 30 % the variation in bed char particle size distribution is not significant. Responses to Pulse Change Figure 7(a) shows comparison between the measured and predicted temporal variation of O 2 concentration at the freeboard exit for a pulse change in coal feed rate by 133%. As can be seen from the figure, reasonable agreement is obtained. With the sudden increase in coal flow rate O 2 concentration falls quickly to zero and then starts to increase but with a slower rate. The steep decrease is due to the combustion of volatile matter and the decelaration in the increase is due to the combustion of char particles. Figure 7(b) displays the response in terms of CO concentration. The model is found to reproduce the transient CO concentration reasonably well. Pulse addition of coal makes the system O2 deficient, hindering the CO oxidation which results in a steep increase in its concentration. As can also be seen from the figure, predicted CO concentration shows a faster response than the measured one. This is considered to be due to the simplifying assumption that the volatile C is released as CO only, rather than as a mixture containing hydrocarbons too. The responses to pulse addition of coal in terms of predicted and measured bed temperatures and bed cooling water exit temperatures are depicted in Figure 8(a) and 8(b), respectively. Favorable comparisons are observed. Sluggish response of bed temperature compared to species concentrations to pulse change in coal feed rate is similar to that found for step changes in coal and air flow rates, as expected. Predicted bed char hold-up in response to the pulse change in coal feed rate is shown in Figure 9(a). Char hold-up is found to increase with the coal feed rate and attains a maximum when the pulse change is stopped. The sharp decrease following the peak is due to the depletion of the accumulated char owing to the heterogeneous oxidation reaction. Figure 9(b) illustrates the variation in bed char size distribution for pulse change in coal flow rate. As can be seen from the figure bed char size distribution initially moves toward the smaller size range due to enhanced char combustion rate (Figure 7(a)) and then shifts toward the larger size range owing to the fall in char combustion rate and finally reaches its initial distribution. CONCLUSION A recently developed dynamic model of a 0.3 MW ABFBC was described. On the basis of comparisons between predictions and measurements it is demonstrated that the model serves as a useful tool in predicting responses of flue gas composition and temperatures to changes in fuel and air flow rates.

O2 CONCENTRATION, mole % (wet)

8

PREDICTED MEASURED 6

4

2

0

0

120

240

360

480

600

720

840

TIME, s (a)

CO CONCENTRATION, ppm (wet)

22000

PREDICTED MEASURED

20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

0

120

240

360

480

600

720

840

TIME, s (b)

Figure 7: Comparison of measured and predicted transient (a) O 2 , (b) CO concentrations for pulse change in coal feed rate

1200

TEMPERATURE, K

PREDICTED BED TEMP. MEASURED BED TEMP. PREDICTED BED WALL TEMP. 1150

1100

1050

0

120

240

360

480

600

720

840

TIME, s (a)

335

TEMPERATURE, K

PREDICTED MEASURED

330

325

320

315

0

100

200

300

400

500

600

700

800

900

TIME, s (b)

Figure 8: Comparison of measured and predicted transient (a) bed temperature, (b) bed cooling-water exit temperature for pulse change in coal feed rate

1100

CHAR WEIGHT, kg × 10 3

1000 900 800 700 600 500 400 300 200 100 0

0

100

200

300

400

500

600

700

800

900

TIME, s (a)

(b)

Figure 9: Predicted transient bed char (a) hold-up and (b) size distribution for pulse change in coal feed rate

NOMENCLATURE a

Decay constant, m
1

A

Cross-sectional area, m2

cp

Specific heat capacity, J kg
1 K
1

C

Concentration, mol m
3

d

Diameter, m

E

Activation energy, J mol
1

Eo

Mean of activation energy distribution, J mol
1

E(r)

Elutriation rate constant, s
1

f

Bubble frequency, s
1

f (E)

Activation energy distribution function for devolatilization, mol J
1

F

Char feed rate, kg s
1

Fz

Upward flow rate of entrained particles at any height z in freeboard, kg s
1

h

Individual heat transfer coefficient, J m
2 s
1 K
1

H

Height, m

∆H o

Heat of reaction at standard state, J mol
1

k

Proportionality constant in Equation (10), m 05 s
05 ; proportionality constant in Equation (12); first-order reaction rate constant for devolatilization, s
1 ; thermal conductivity, J m
1 s
1 K
1

kf

Film mass transfer coefficient, m s
1

ko

Pre-exponential factor for 1st order devolatilization rate constant, s
1 ;

ks

1st order surface reaction rate constant for char combustion, m s
1

Kbe

Interphase mass transfer coefficient, s
1

 Ki∞

Dispersed noncluster flux of entrained particles in size i, kg m
2 s
1

Kih

Cluster flux of entrained particles in size i, kg m
2 s
1

Ki

Total flux of entrained particles in size i, kg m
2 s
1

L

Length, m

m

Mass flow rate, kg s
1

M

Molecular or atomic weight, kg mol
1

n

Index of the dimension; molar flow rate, mol s
1

nC

Carbon consumption rate, mol m
3 s
1

P(r)

Size distribution function, m
1

Pz (r)

Size distribution of entrained particles at any height z in freeboard, m
1

Q

Volumetric flow rate, m 3 s
1 ; energy generation/loss rate, J s
1

r

Spatial independent variable, m

rC

Carbon consumption rate on the surface of char particle, mol m
2 s
1

rCO

Rate of CO combustion, mol m
3 s
1

R

Ideal gas constant, J mol
1 K
1 ; radius, m

R

Energy generation/loss rate in freeboard, J m
3 s
1

ℜ

Species generation/depletion rate, mol m
3 s
1

ℜ(r)

Shrinkage rate of char particles, m s
1

Rw

Thermal resistance across the freeboard wall, J m
2 s
1 K
1

t

Time, s

T

Temperature, K

uo

Superficial velocity in bed, m s
1

ub

Superficial bubble phase velocity, m s
1

ud

Particle descending velocity, m s
1

ue

Superficial velocity in emulsion phase, m s
1

um f

Superficial minimum fluidization velocity, m s
1

ur

Axial rise velocity, m s
1

ut f

Superficial throughflow velocity in bubbles, m s
1

U

Overall heat transfer coefficient, J m
2 s
1 K
1

v

Volatiles released, %

v∞

Ultimate yield of volatiles released, %

V

Volume, m3

W

Hold-up in the bed, kg

x

Mass fraction (dry basis); spatial independent variable, m

xvl

Fraction of volatiles released in the bed

y

Mole fraction

z

Spatial independent variable, m

Greek Letters α

Thermal diffusivity, m 2 s
1 ; parameter in Equation (13)

δ

Bubble phase volume fraction

ε

Voidage

εm f

Voidage at minimum fluidization conditions

εs

Solids volume fraction

ε

Emissivity

η

Contact efficiency

λo

Latent heat of vaporization at standard state, J kg
1

ρ

Density, kg m3

σ

Standard deviation of activation energy distribution, J mol
1 ; Stefan-Boltzmann constant, J m
2 s
1 K
4

Φ

Dummy variable defined in Equation (20)

Subscripts 32

Surface/volume mean

a

Air; ash

avg

Average

b

Bubble

bd

Bed drain

bed

Bed

bw

Bed wall

C

Carbon

co

Carryover

cw

Cooling water

d

Char

e

Emulsion

f

Feed coal; freeboard

fc

Fixed carbon

fw

Freeboard wall

g

Gas

H

Hydrogen

i

Inert; inner

j

Species index

max

Maximum

maxe

Maximum elutriated

min

Minimum

o

Outer; at the bed surface

p

Particle

r

Radiation; reference

rxn

Reaction

s

Surface; solid

S

Sulfur

T

Tube

vm

Volatile matter

w

Wall; water

References [1] Basu, P., Chem. Eng. Sci., 54:5547-5557 (1999) [2] Costa, B., Faille, D., Lamquet, O., Marchiondelli, C. and Spelta, S., 16th Int. Conf. on FBC, Paper No:36 (in CD-ROM), 2001 [3] Fan, L.T., Tojo, K. and Chang, C. C., Chem. Process Des. Dev., 18:333-337 (1979) [4] Chang, C.C., Fan, L.T. and Rong, S. X., Can. J. Chem. Eng., 60:272-284 (1982) [5] Chang, C. C., Rong, S. X. and Fan, L. T., Can. J. Chem. Eng., 60:781-795 (1982) [6] Sriramulu, S., Sane, S., Agarwal, P. and Mathews, T., Fuel, 75:1351-1362 (1996) [7] Srinivasan, R.A., Sriramulu, S., Kulasekaran, S. and Agarwal, P. K., Fuel, 77:1033-1049 (1998) [8] Kulasekaran, S., Linjewile, T. M. and Agarwal, P. K., Fuel, 78:403-417 (1999) [9] Beasley, D. E. and Golan, L. P., Chem. Eng. Comm., 79:115-130 (1989) [10] Selc¸uk, N. and Degirmenci, E. Comb. Sci. Tech., 166 (2001) [11] Grace, J. R. and Clift, R., Chem. Eng. Sci., 29:327-334 (1974) [12] Grace, J. R. and Harrison, D., Chem. Eng. Sci., 24:497-508 (1969) [13] Mori, S. and Wen, C. Y., AIChE Journal, 21:109-116 (1975) [14] Jung, K., and La Nauze, R. D., 4th Conf. (Int.) on Fluidization, 427-434 (1983) [15] Ranz, W. E. and Marshall Jr., W. R., Chem. Eng. Prog., 48:141-146 (1952) [16] Tanaka, I., Shinohara, H., Hirosue, H. and Tanaka, Y., J. Chem. Eng. Japan, 5:51-57 (1972) [17] Kunii, D. and Levenspiel, O., Fluidization Engineering (2nd Ed.), Butterworth-Heinemann, Boston, 1991 [18] Ergun, S., Chem. Eng. Prog., 48:89-94 (1952) [19] Gogolek, P. E. G. and Becker, H. A., Powder Technol., 71:107-110 (1992) [20] Kunii, D. and Levenspiel, O., 7th Conf. (Int.) on Fluidization, 47-58 (1992) [21] Denloye, A. O. O. and Botterill, J. S. M., Powder Technol., 9:197-203 (1978) [22] Sleicher, C. A. and Rouse, M. W., Int. J. Heat Mass Transfer, 18:677-683 (1975) [23] Choi, J. H., Chang, I. Y., Shun, D. W., Yi, C. K., Son, J. E. and Kim, S. D., Ind. Eng. Chem. Res., 38:2491-2496 (1999) [24] Field, M.A., Gill, D.W., Morgan, B.B. and Hawksley, P.G.W., Combustion of Pulverized Coal, The British Coal Utilisation Research Association, 1967 [25] Hottel, H. C., Williams, G. C., Nerheim, N. M., Schneider, G. R., 10th Symp. (Int.) on Combustion, 975-986 (1965). [26] Stubington, J. F., Chan, S. W., Clough, S. J., AIChE Journal, 36:75-85 (1990) [27] Anthony, D. B. and Howard, J. B., AIChE Journal, 22:625-656 (1976) [28] Merrick, D., Fuel, 62:534-539 (1983) [29] Nienow, A. W., Rowe, P. N. and Chiba, T., AIChE Symposium Series, 74:65-53 (1978) [30] Cranfield, R. R. and Geldart, D., Chem. Eng. Sci., 29:935-947 (1974)

[31] Degirmenci, E., Ph.D Thesis, Department of Chemical Engineering, METU, Turkey, 2000 [32] Hazlett, J. D. and Bergougnou, M. A., Powder Technol., 70:99-107 (1992) [33] Selc¸uk, N., Oymak, O., Degirmenci, E., Powder Technol., 87:669-271 (1996) [34] Kunii, D. and Levenspiel, O., Ind. Eng. Chem. Res., 29:1226-1234 (1990) [35] Hannes, J., Ph.D. Dissertation, RWTH Aachen, Germany, 1996 [36] Schiesser, W.E., The Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, New York, 1991 [37] Schiesser, W.E, “Variable Grid Spatial Differentiator in the Numerical Method of Lines”, Lehigh University, DSS/2 Manual No:9, 1988 [38] Weiner, R., Schmitt, B.A. and Podhaisky, H., “ROWMAP - A ROW-Code with Krylow Techniques for Large Stiff ODEs”, FB Mathematik und Informatik, Universit¨ad Halle, Tech. Report No. 39, 1996 [39] Selc¸uk, N., Degirmenci, E., Oymak, O., 14th Int. Conf. on FBC, 1163-1174, 1997 [40] Degirmenci, E. and Selc¸uk, N., 15th Int. Conf. on FBC, Paper No:100 (in CD-ROM), 1998