Comprehensive Modelling and Simulation of Fluidized Bed Boilers and Gasifiers

Comprehensive modelling and simulation of fluidized bed boilers and gasifiers

M. L. de Souta-Santos IPT-lnstituto de Pesquisas Tecnolbgicas do Estado de Slo Paul0 S/A (DEMIAET), Cidade Universithia, Caixa Postal 7141, Slo Paula-SP, Brazil (Received 12 May 1988; revised 19 April 1989)

A comprehensive mathematical model and computer program to simulate a fluidized bed boiler or a fluidized bed gasifier have been developed. The program can predict several important parameters that describe the operation of the equipment such as: composition and temperature profiles for all gas and solid phases in the bed and freeboard; solid particle size distributions at any point; heat transfer between all phases and tubes or walls at any point; gas pressure losses, etc., as well as the usual engineering equipment performance data. The basic structure of the model includes a system of 46 differential equations, which represent the mass and energy balance for all phases at any point of the equipment. The results generated by the simulation were compared with values measured during the operation of fluidized bed units by Babcock & Wilcox and by the National Coal Board. Average deviations of between 2 and 5% for several parameters were achieved. This represents an improvement in the use of simulation as an engineeringhesign tool for such equipment.

(Keywords: fluidized beds; modelling; gasification)

Several studies on mathematical modelling of fluidized bed combustion and gasification have been published. From the analysis of previously published mathematical models and simulations of fluidized bed boilers and gasifiers, it is possible to justify the development of the present model.

The work published so far does not cover many important aspects and phenomena of the process. Devolatilization reactions are either not considered or are taken as an instantaneous processlP6. Other authors assume that the rate of volatiles release is homogeneously distributed throughout the bed’ or that the rate is proportional to the feeding rate or to the mixing rate of solid#- lo.

The dynamics of drying processes for the various solids added to the reactor, are not considered in most of the existing workrP9. Chemical reactions other than carbon and CO combustion are not considered’*3,5*6*8.

Despite its importance on various aspects of the process, no published simulation model of the FBC boiler has included the kinetics of limestone calcination. The possibility of dealing with different carbonaceous solids according to physical structure or reactivity is not well documented, nor is heat transfer between different kinds of particles.

A continuous differential mathematical treatment of the mass and energy balances for the bed and freeboard sections contrasts with the overall’*’ ‘-i3, compart- mented”’ ‘*16 or differential balances for imagined separated sections of the bed5-7,‘7-20.

MATHEMATICAL MODEL

Basic hypotheses and model strategy The program simulates the steady-state regime

operation of a fluidized bed combustor boiler or a fluidized bed gasifier, where the carbonaceous material,

001~2361/89/121507-15$3.00 0 1989 Butterworth & Co. (Publishers) Ltd.

inert bed material and/or limestone are fed in continuously. Any variations in conditions are assumed to occur only in the vertical or axial ‘z’ direction (Figure 1). At the base of the bed (z = 0), the two-phase mode12’,22 has been assumed, although this model can be criticized’6,23,24 for beds working at ‘slow bubble’ or at ‘fast growing bubble’ regimes. Most boilers and gasiliers work at ‘fast bubble regime’, and the program provides

GAS AND SMALL PARTI -

PLENUM

Figure 1 Schematic diagram of a fluidized bed reactor

FUEL, 1989, Vol 68, December 1507

Comprehensive modelling and simulation of fluidized bed boilers and gasifiers: M. L. de Souza-Santos

STACK GAS ENTRAINMENT Lir TOP OF FREEBOARD.

t 4

-2.2,

1-- -------I

I -R-S < HEAT. I HEAT a , mm%

MASS. ’ (~+~=OQRN=+JR t HEAT.

Rt3Cl-lONW 4 OAS IN THE

IuaES HEAT: , FREEBOARD.

LIMESlONE. * /

I c wmOMNms ( HEAT a MASS

I ’ (HETEROQBEOUS ,HFA TUBES

WALL& HEAT. RE&.TlONS.) ’ ’ T.> a

REACTIONSI WALLS.

I P-F

INERT SOWD @FAT: t I

< HEAT 8 I ) DRYINS.

MASS. I( HEAT. 1

P-E P-F I

I SOLIDS. ,

6 HEAT a MASS.

QA9 IN THE

P-F

Q&S IN THE

EMULSIW.

(NB

REACTIONS1

I P-F

HEAT 8 MASS.

FREEBOARD.

-.-. .-.-.-.-.-._. r.~~~~.F~~-.-.-.-._._._.‘“;”

a GASIFICATION POWTS.

UC. = UNIFORM COMPOSITION.

Figure 2 Simplified diagram of the model basic structure

an automatic check of the fluidization condition. Fluidization parameters change with changes in the temperature and composition in the emulsion and bubble phases, throughout the bed height.

Species taking part in the emulsion phase are: interstitial gas; carbonaceous solid; inert material and/or limestone. The bubble phase is free of solid particles and the clouds are incorporated in the emulsion phase. It is assumed that plug-flow regimes operate for the gas in the bubble and for the interstitial gas of the emulsion phase. The gas flow in the freeboard is also treated as a plug-flow regime. Limestone and inert material (normally sand and free ash from the carbonaceous material) are assumed to have a homogeneous composition throughout the bed, but temperatures which change with bed height. This is also assumed for the carbonaceous solid with respect to its fixed carbon composition, which is calculated by a reiterative procedure.

To verify the influence of the feed point position, the drying process and the devolatilization reactions are allowed to progress only in regions near the feeding point in the bed, Within the freeboard, all solids are treated as flowing in the vertical direction with a decreasing flow rate due to the return of particles to the bed, i.e., due to entrainment and to chemical reactions. Bubble size is a function of the bed height. For the beds with immersed tubes, the maximum bubble size is limited by the minimum horizontal distance between neighbouring tubes in the tube bundle region.

The heterogeneous reactions between gases and carbonaceous solid can be described by two possible mechanisms : the unreacted-core or shrinking-core model; or the exposed-core or segregated-ash model. The drying of solids and the devolatilization of carbonaceous material are assumed to be complete within the bed.

1508 FUEL, 1989, Vol 68, December

The unreacted core model is followed for these processes, regardless of the model adopted for the other reactions. The unreacted core model is also assumed for the gas-solid reactions in the freeboard. The gas is assumed to be transparent with respect to radiative heat transfer. To illustrate the assumptions described, Figure 2 shows a simplified diagram of the model structure.

Basic equations The system of differential mass and energy balances is

summarized in the Appendix and includes 46 coupled equations for each section, which must be solved by the simulation strategy.

Boundary conditions The condition of the gas stream injected through the

distributor (z=O) is known, so the total gas flow rate, Fo, its composition, Wc,j, and temperature, To, are set. Therefore, it is possible to write:

W GE,j.z=O- - WGB,j,z=O= wG,j.z=OT l~j$13 m

and

T -T -T GE,z=Q - G&z=0 - G,z=Q (2)

The partition (at z = 0) of the gas flow between emulsion and bubble phases, follows the two-phase theory. For heights where z >O, the fIow through these phases is dictated by the mass balances. The boundary conditions for the lowest part of the freeboard are the same as for the top of the bed.

The boundary conditions for the temperature of the various solids at the base of the bed are calculated by equating the heat flux transferred by convection and the


heat transferred by conduction at the bed base:

dT, A - be&z=0 dz z=. =rbed--dist(TA,z=o- Gist) (3)

and

2 (Twist-TG.s=o)=Clbed-dist(TA,r=O-Tdist) (4)

The heat transfer coefficient between bed and distributor is taken from Zhang and Ouyang24.

Therefore, Tp.,,, = o is achieved by a convergence routine based on the above equations.

Chemical reactions The model includes the set of possible chemical

reactions listed below:

CH,,,O,,,N,I,S,,,+ j+y-?+?+a,, >

02+

(28-1)C02+(2-2jl)CO+~H,O+a,,NO+

a1sS02 (R-l)

CH,,,O,,,N$%,,+ (1 -aAH +

1 +y-a,,-a,, >

H,+CO+~N,+a,,H,S

CLQ,,%,S,,, +CO2 +

2CO+a,,H,O+a,,NH,+a,,H,S

+ ?_a (

16-%a17-a18 >

H2

(R-2)

(R-3)

CH,,,O,,,N,,,S,,,+ (

2-~+a,,+~a,,+a,, H,* >

CH,+a,,H,O+a,,NH,+a,,H,S (R-4)

CH,,,0,,,N,,,Sa18+(2-a,,)NO *

CO,+ H, (R-5)

Volatiles -+ tar (R-6)

Here the volatiles, and therefore tar, are represented by: C6,,H6,,06,,N,,,S6,,.

Volatiles + 6,CO, + 6,CO + i&O2 + b4N2 + &H,O

+&HZ + tj,CH, + 6,SO, + t&NO +tj10C2H6

+tj,,H,S+ti,,NH, (R-7)

Volatiles+ (

. .

6,,8+$-~+$+ti,, >

0, +

(26,,/?-l)CO,+(2-26,,~)CO+~H20+6,,N0

+&$O* (R-8)

Moist carbonaceous solid -+ dry solid + H,O (R-9)

CaCO, + CaO + CO, (R-10)

2CaO + 2S0, + 0, + 2CaS0, (R-11)

Moist limestone + dry limestone + H,O (R-12)

Moist inert + dry inert + H,O (R-13)

CO+H,O i&O,+H, (R-14)

2co + 0, *2co, (R-15)

2H, + 0, +2H,O (R-16)

CH, + 20, *CO, + 2H,O (R-17)

2C,H, + 70, +4CO, + 6H,O (R-18)

4NH, + 50,*4NO + 6H,0 (R-19)

2H,S + 30, P2S0, + 2H,O (R-20)

N,+O, +2NO (R-21)

b,,C02+b;SH20+bl,NO+b,,S02 (R-22)

Tar + 6,CO, + b&O + i&O2 + b4N2 + b,H,O

+ bSH2 + b&H, + b,SO, + ti,NO + tjloC2H,

+b,,H2S+li,2NH, (R-23)

Tar + coke (R-24)

The forms presented in reactions (R-l) and (R-2) were taken from DeSai and Wen25, and forms in reactions (R-3)-(R-5) were adapted from the work of Kim and Joseph26. The stoichiometry coefficient, /$ will depend on the particle temperature27. Calculations of the stoichiometry coefficients in reactions (R-6)-(R-8), (R-23) and (R-24) should be accomplished by convergence calculations that involve estimating the devolatilization products*‘.

Reaction kinetics

Models for gas-solid reactions. The unreacted and exposed core models have been described29 for the carbonaceous gas-solid reaction. In this work these models have been generalized to deal with devolatilization reactions, drying of solids, calcination of limestone, and sulphur absorption.

The simulation program allows the user to choose between the two models, depending on the processed solid characteristics. However, inside a fluidized bed the severe attrition seldom allows the carbonaceous solid particle to retain the formed ash layer as the surface reactions proceed. Therefore, with few exceptions, the exposed core model should be chosen. In any case, a simple experimental test is enough to indicate the best decision.

The picture is different for drying of solids, devolatilization of carbonaceous solids, calcination of limestone or sulphur absorption by CaO: this is because no fragile shell develops during these processes (only dried, devolatilized or reacted external layers of the particles are formed). Therefore, in all these cases the program calculates the reaction rates for these processes using an adaptation of the unreacted core model.

The general expression for the gas-solid reaction using the unreacted core model is:

(5)



Table 1 Correspondence between the heterogeneous reaction, i, and its respective representative component, j, and solid phase m

Gas-solid reaction i

Representative Representative Solid unreacted component phase solid j m component

1 2 3 4 5 6 7 8 9

10 11 12 13

3 5 1 6 9

20 20 20

5 1 8 5 5

2 23 2 25 3 26

14 14 14 14 14 20 20 20 21 22

Table 2 Kinetic coefficients for some of the considered reactions

Reaction k,,i Unit .WR (K) Ref.

R-l & R-8 17.67 Pa-is-i 13597 69 R-14 2.78 x lo3 kmol-’ m3 s-i 1510 70 R-15 1.0 x lo5 kmol-0.75 m2.r5 16000 64

Ki.5 s-i

R-16 5.159 x lOi kmol’,’ rn“.’ K’.5 s-l 3430 64 R-17 & R-18 3.552 x 1014 kmol-’ m3 s-l K 15700 64 R-19 9.78 x 10” kmol-O.g m2.‘sW1 19655 65 R-21 1.815 x lOi kmol-0.5 m1.S s-i 67338 66 R-22 59.8 kmol-0,5 m1.5 Pa-0.3 12200 61

s-i K-i

where l<i<13, lGjd16and l<m<3.Theconnection between the three indices i, j and k, which describe the choice of the representative component (j) in the solid phase (m) of the reaction (i), is shown in Table 1. This table also indicates the component chosen to represent the solid material of the unreacted core for each reaction.

The parameter resistance terms, &, shown in Appendix A, account for: diffusion through the gas boundary layer surrounding the particle; diffusion through the formed non-active shell surrounding the unreacted core; and diffusion through the core combined with the kinetics.

In the exposed core model, the gas-solid reaction rate is given by Equation (5), in which Cz,i, the resistance through the ash layer, is zero.

Individual kinetic coefficients. The Arrhenius coefficients for several considered reactions are given in Table 2. Although it is recognized that several factors influence the reactivity of the carbonaceous solid3’, a reasonable correlation between the reactivity and the basic composition of the carbonaceous solid (the volatiles/ fixed-carbon ratio), has been found31. Basically, this involves a correction coefficient that is multiplied by the kinetic coefficients of the reactions R-i (i=2, 3 or 4) that have been evaluated for a reference coal. This allows the kinetic coefficients for the respective reactions with the given carbonaceous material to be determined:

E. ki = ki,ref I

ki,mf

The parameter k is given by:

iti=ig; (7)

where

f,= mass fraction of fixed carbon

mass fraction of volatile matter (8)

The coefficients are described in Table 3. The kinetic coefficients for reactions (R-3) and (R-4) are given in Appendix A. The coefficients are shown in Table 4, and equilibrium parameters for various reactions are listed in Table 5.

Devolatilization reactions. Because of the comprehensive approach used here, the devolatilization or pyrolysis reactions cannot be completely separated from the other reactions and processes in the system. The kinetics of the devolatilization reactions ((R-6), (R-7), (R-23) and (R-24)), have been included independently for the case of wood34. The coefficients are reported in Table 6.

Table 3 Auxiliary parameters used for solid-fuel reactivity estimation. The composition of the Illinois coal is reproduced from Yoon et ~1.‘~ and the Spanish lignite from Adlnez et a1.32

Reaction I 6 Reference coal fr,_r

R-2 & R-4” Illinois 1.32 .tX3 4.49 x lo+ - 1.736 03 3.97 x 1o-5 0.491

R-3 Lignite 1.93 1.33 x 1o-3 - 4.454 7.67 x lo-’ 2.152

’ The same correction was assumed for reactions R-2 and R-4

Table 4 Arrhenius coefficients related to the reactions R-2, R-3 and R-4

Coefficient index ko Unit J?/R (K) Coal Ref.

2 31

32

33

41 42

6.05 x 1O-3 Pa-‘s-i 21150 Illinois 71 1.91 x 1o-3 Pa-‘s-l 16840 Spanish 32

lignite 1.33 x 1o-8 Pa-’ - 7220 Spanish 32

lignite 3.13 x 10-s Pa-’ - 5050 Spanish 32

lignite 2.345 x lo-” PaeZ s-l 13670 Illinois 72 4.742 x lo-” Pa-’ - 11096 Illinois 72

Table 5 Equilibrium constants for some reactions

Reaction K0.i Unit AH,/R (K)

Relationship with partial pressures Ref.

R-2 R-3 R-4 R-14 R-15 R-16 R-21

3.139 x 10” Pa 16344 PZPSP;’ 73 1.238 x lOi Pa 20294 p;p; 1 74 1.453 x lo-” Pa-’ -11005 p,p;* 73 0.0265 -3958 pIpsp;lp;l 74 8.264 x lo-” Pa-’ - 68080 p: p;zp; 1 75 8.109x lo-l3 Pa-’ - 60230 p: p; 2p; 1 75

19.254 21570 p;p;‘p;’ 15


Comprehensive modelling and simulation of fluidized bed boilers and gasifiers: M. 1. de Souza-Santos

Table 6 Arrhenius coefficients for devolatihzation reactions

Reaction Type of material k, (Pa-’ s-t) E/R (K) Ref.

R-6”

R-7”

R-23b

R-24*

bituminous coal subbituminous coal lignite wood bituminous subbituminous lignite wood bituminous subbituminous lignite wood bituminous subbituminous lignite wood

w,,, 1.1 x los/P Wtar 7.5 x lO'/P Wtsr 5.1 x 104/P 4.125 x 106/P Weas 1.1 x 105/P Wsas 7.5 x 104/P Wgas 5.1 x 104/P 1.435 x 104/P 9.7 x lo9 3.5 x 10’0 8.0 x 10” 9.7 x lo9 5.3 x lo4 2.5 x lo4 1.1 x lo3 5.3 x lo4

- 10669 -9406 -8155

- 13555 - 10669 -9406 -8155

- 10657 - 14590 - 13964 - 13339 - 14590

- 3524 - 2766 -2009 - 3524

33 33 33 34 33 33 33 34 33 33 33 34 33 33 33 34

’ Tr,r must be used in calculations b Tos must be used, and k, units are s-r

It is assumed that the devolatilization reactions follow the unreacted core model, in which the already devolatilized material acts as the reacted shell. Therefore, the pre-exponential coefficients were related to pressure, as in the unreacted core model equation. This led to the definition of a pseudo partial pressure for the volatiles in the solid:

p20=P WPLW,l (9)

The rate of production of gases due to the devolatilization reactions depends on the distribution of stoichiometric coefficients, as shown by reaction (R-7). The stoichiometry also depends on an approximate formula for the tar and the correlations used to compute this are shown in Appendix A.

Drying processes. In the devolatilization reactions (R-6), (R-7) and (R-8), the drying processes are treated by the unreacted core model. It is obvious that in this case the term ‘reaction rate’ is meaningless, and therefore [3,i (for i=9, 12, 13) is equal to zero. The equilibrium partial pressure of water for the drying process is the saturation partial pressure at the respective solid temperature.

Calcium carbonate decomposition. The calcination of limestone, represented by reaction (R-IO), provides calcium oxide, which is the active solid in the absorption of SO2 (reaction (R-11)). The thermodynamics of the calcination show that at high partial pressures of carbon dioxide equilibrium35 can be attained. This condition would stop the calcination process.

The kinetics of the limestone calcination reaction are given by36.37:

k 10

_ 3.07 x 10” ~ exp(-24670/T,,,) (Pa-’ SK’) (10) P:

where pT is given by Equation (A34). The kinetics of this reaction have been studied3s,39, and the kind of limestone is known to influence the rate of reaction. The formation of CaSO, tends to block the pores of the limestone particles and reduce the reactivity of limestone. Therefore, reaction rate is a function of temperature, limestone conversion and particle size. The correction factor for the reactivity, I, may be calculated40-41 as

function of the calcium fractional conversion and the limestone particle diameter by interpolation among various curves relating these three parameters. This is used in the present work and the kinetic coefficient is written as:

k,,=Fexp(-4OgO/T,,,,)~ (Pa-’ s-l) (11)

No correlation has been found to account for the effect of temperature on the reactivity, although the presence of chemical compounds, other than calcium based compounds, may be important. The thickness of the CaSO, layer is determined by the calcium conversion in the bed and found by convergence of the mass balance throughout the bed.

Shift reaction. The water-gas shift reaction rate is given by42 :

Combustion of gases. The kinetics of gas combustion are summarized in Table a in Appendix A.

Mass and heat transfer The performance of a mathematical model for a

fluidized bed combustor or gasifier is very sensitive to the mass and heat transfer between the various phases in the system - . 5 ’ A list of the references used to calculate the more important heat and mass transfer processes considered in the model, among other correlations, is given in Table 7.

The radiative heat transfer between the various solids is calculated by:

E d4 m RSESE,m,n = W::V;,,- T;,,) -1

dz (13)

where 1 <m<3 and 1 <n<3. It was assumed that a

Table 7 List of sources used to describe various phenomena considered in simulation model. Full details can be found elsewhere**

Phenomena Ref.

Minimum fluidization voidage Bed expansion Emulsion voidage and solids-solids heat transfer Bubble size as function of z Bubble rise velocity Bubbles-emulsion gas M-T Solids-emulsion gas M-T Bubbles-emulsion gas H-T and pressure loss in bed Solids-emulsion gas H-T Tubes-emulsion gas H-T Tubes-bubbles H-T Tubes-bed total H-T Internal tube H-T Tubes-solids H-T Bed-distributor H-T Heat transfer to surroundings Solid circulation” Production of tine particles due to attrition Entrainment and elutriation Transport disengaging height Cyclone efficiencies Distributor, pressure loss

‘Adaptation is shown by Equation (A35) H-T, Heat transfer; M-T, mass transfer

43 43 44 15 22 45 46 47 48, 49 50 50 51 52 53 24 54 55 56 57 57 58 59



Figure 3 Basic logic diagram of the simulation program

particle of type m is surrounded by all kinds of particles and therefore ‘sees’ the n type particles by an area fraction, f,“.

Particle size distribution The effects are:

1. reduction of particle size due to chemical reactions; 2. reduction of particle size due to attrition among the

various particles; 3. variation due to entrainment and elutriation of

particles from the bed.

To compute the combined effects of these factors, a mass balance for the size level, 1, of particles of type m is set, and an iterative routine is followed. The balance is given by:

The auxiliary equations are presented in Appendix A. For the sake of simplicity, the solid friability coefficients have been taken as constants56, despite the fact that some recent works@-62 have shown that they are not truly constant.

The routine to compute the size distribution starts from the highest size level for which there is no mass increase due the generation of lines by attrition. As the next size is l= lm - 1, the new value of Sm,,,,, can be used to calculate l- m,lm, and the process can be repeated until 1= 1.

DESCRIPTION OF THE SIMULATION PROGRAM

A simplified block diagram of the computer simulation program, based on the present mathematical model, is presented in Figure 3. The basic necessary input data for the simulation program are: 1. complete physical and chemical characterization of the

fed carbonaceous, limestone, and inert solids,

2.

3.

including their mass flows and particle size distributions; complete characterization of the gaseous agent injected through the distributor, including mass flows; complete description of the equipment geometry, e.g. basic dimensions, tube bank position in the bed and in the freeboard, geometry of the distributor, description of the insulation system and of the cyclone system (if used).

Real operation data and comparison with simulations The task of obtaining operational data is a difficult

one, due to confidentiality, unreliability, inaccuracy, and incompleteness. In spite of these problems, some data were collected to use as references for comparisons between real operation and simulation results. As an example, the data from Babcock & Wilcox Co. (USA) fluidized bed unit (B&W)63 have been chosen, because they allow more complete comparisons between simulation and real operation. The data are the same as used by other workers5,6.

Plant operational data are described elsewhere28*63. Some basic data regarding plant operation and the equipment are shown in Table 8, while Tables 9-l 4 below show the computation results.

Figures 4-15 show several important features of the operation of the Babcock & Wilcox unit.

CONCLUSIONS

A comprehensive mathematical model and computer program that simulate the operation of fluidized bed boilers and gasihers consuming carbonaceous solids have been developed. The computer program based on the mathematical model, has been tested for some commercial

Table 8 Details of B&W equipment and operation (test no. 26)‘sS6’

Detail Value

Coal proximate analysis (w.b. %) Moisture 5.0 Volatiles 40.0 Fixed carbon 50.1 Ash 9.9

Coal ultimate analysis (d.b.) C 0.7320 H 0.0510 0 0.0790 N 0.0090 s 0.0300

Boiler Equivalent diameter 1.118 m Bed height” 0.700 m Freeboard height” 3.442 m Feeding point height” 0.305 m

Tube bank No. tubes in bed 30 No. tubes in f.b. 30 Pitch 0.114 m Length of each tube 0.991 m Height of 1st tube” 0.33 m Outside diameter 0.0483 m Inside diameter 0.0409 m

No. orifices in distributor 1504 Flow of coal 0.0505 kg s- ’ Flow of limestone 0.01215 kg s-l Air flow 0.6952 kg s-r

a Measurements from distributor


Comprehensive modeling and simulation of fluidized bed boilers and gasifiers: M. L. de Souza-Santos

and pilot plants. Comparisons between simulation generated results and real operational data have shown only small deviations for almost all parameters. Some specific comments on the simulation model and indications for future developments are given below.

Table 9 Composition of gas leaving freeboard (stack gas) during operation of Babcock & Wilcox unit, test no. 26

Gas composition (molar %, dry basis)

Real Present Data from Component operation simulation Refs. 5 and 6

CO, 13.8 13.00275 7.9 to 12.55 co 0 to 0.9 o.OOoO3 0.25 to 0.49 0, 3.9 3.83350 3.93 to 9.23 N, 81.2 83.05625 n.d. NO 0.03 0.03789 n.d. SO, 0.08 0.06946 n.d. HZ n.d. o.Ot3013 n.d. CH, n.d. 1.3 x 10-15 n.d. C,H, n.d. <1.0x 1o-4o n.d. H,S 0 to 2.4 x lo-“ 1.2 x lo-’ n.d. NH, n.d. 2.2 x lo- iz n.d. Tar n.d. <1.0x 1o-4o nd.

n.d., Not determined

Table 10 Carbonaceous solid compositions during operation of Babcock & Wilcox unit, test no. 26 (simulation results)

Mass percentage (wet basis)

Component Fed

C 40.260 H 2.805 0 4.345 N 0.495 S 1.650 Ash 5.445 Volatiles 40.000 Moisture 5.000

Average in Top of bed freeboard

10.932 14.806 0.76165 1.0315 1.1798 1.5979 0.13441 0.18204 0.44803 0.60679

86.544 81.776 0.0000 0.0000 0.0000 0.0000

Basic hypothesis and mathematical approach The modification to the two-phase model, which

includes the cloud region in the emulsion and allowing this phase to depart from the minimum fluidization condition, has proved to be a good representation for the fluidization dynamics. The conceptual separation of the cloud region seems to be unnecessary.

The highly coupled mass and energy transfer processes, combined with the various chemical process and particle flows and size variations, are the basis of the fluidized carbonaceous solid combustion or gasification. The so-called gasification reactions cannot be excluded even for a combustion model, because they contribute not only to the generation of important final and intermediate

Table 11 Total solid composition in bed during operation of Babcock & Wilcox unit, test no 26

_

Average in bed (mass, X)

Component Experimental Simulation

C 0.21 CaCO, 0.91 CaO 46.34 CaSO, 42.84 Moisture 0.00 Inert 9.70b

_

0 Includes all components in the carbonaceous solid b Uncertain value (calculated by difference)

0.110 0.000

50.529 49.281

0.0000 0.80

Table 12 Entrainment flows of particles at the top of the freeboard during operation of Babcock & Wilcox unit, test no. 26

_

Flow (g s-r)

Solid Operation Simulation

Carbonaceous 4.46 2.9985 Limestone 3.46 4.8000 Free ash 4.78 5.6997 Carbonaceous plus free ash 9.25 8.6983 Total 12.70 13.498

Table 13 Various process parameters for operation of the Babcock & Wilcox unit, test no. 26

Process parameter

Mass flow of flue gas (kg s-i) Total flow solids leaving bed (including entrainment at the top of the bed) (kg s-i) Minimum fluidization voidage in centre of bed Overall voidage in centre of bed Minimum fluidization velocity in centre of bed (m s-r) Superficial velocity in centre of bed (m s- ‘) Bed transversal area (m’) Carbon conversion (fraction of fed carbon) (%) Mass of bed (kg) Transport disengaging height, TDH (from bed surface) (m) Freeboard space (m) Calcium to sulphur (Ca/S) ratio in bed Calcium conversion (%) Sulphur retention (based on fed sulphur) (%) Static bed depth (m) Rate of energy input to system (kW) Percentage of energy input lost to external environment through walls Pressure loss across distributor (Pa) Pressure loss across bed (Pa)

Real operation

0.790 nd. n.d. n.d. n.d.

2.5” 0.9817

95.8 n.d. nd.

2.742 2.2

28.09 58.7

n.d. 1713.9 n.d. n.d. n.d.

_

Simulation

0.7525 79.772 0.520 0.8080 0.635 2.691 0.9817

98.158 444.8

4.049 2.742 2.287

28.9864 57.449 0.411

1713.9 1.048

412 3029

@ Probably calculated at bed base nd., Not determined



Table 14 Some parameters related to heat transfer during operation of the Babcock & Wilcox unit, test no. 26

Parameter Real operation

Total heat transfer to tubes in system (kW) 788.4“ Heat transfer to tubes inside bed (kW) n.d. Heat transfer to tubes in freeboard (kW) n.d. Total mass flow of steam generated by the system (ks s-l) 0.0 Total heat loss to external surroundings (kW) 113.1b Heat loss in bed section (kW) n.d. Heat loss in freeboard section (kW) n.d. Overall heat transfer coefficient between tubes and bed in centre of bundle (W m-’ K-l) n.d. Overall heat transfer coefficient between tubes and free board in centre of bundle (W mm2 K-l) n.d. Wall temperature of tubes in bed (centre of bundle) (K) n.d. Wall temperature of tubes in freeboard (centre of bundle) (K) n.d. Percentage of heat loss to surroundings in relation to heat transfer to tubes n.d. Temperature of water leaving tubes (K) 400 Temperature of external wall at top of bed section (K) n.d. Temperature of external wall at top of freeboard section (K) n.d. Heat transfer coefiicient between external wall and surroundings (top of bed section) (W m-* K-l) n.d. Heat transfer coefficient between external wall and surroundings (top of freeboard) (W me2 K-l) n.d.

’ Babcock and Wilcox report gives only total value for heat transfer to tubes, including tubes in stack gas cooling system b Losses to water jacket ’ Losses to external surroundings n.d.. Not determined

Simulation

655.11 397.31 257.80

0.0 17.97’ 4.25

13.72 69.28 5.35

702.5 455.3

2.699 395.3 356.7 347.2 21.56 20.68

Figure 4 Schematic view of the Babcock and Wilcox (B&W) test unit

products, but they also play a fundamental part in the energy balances. Small variations in the temperature profile can cause significant variations in the bed fluid dynamics, carbon conversion, gas compositions, particle size distributions in the bed and freeboard, entrainment, etc. The reverse is also true, i.e. imprecise determinations of e.g. emulsion-bubble flow partition, bubble size and bubble growth or particle size distributions, can lead to great deviations in other parameters. The conditions vary tremendously from point to point in the fluidized bed, and therefore only comprehensive models that solve the combined set of differential mass and energy balances are able to achieve a realistic simulation of a fluidized bed boiler or gasifier. Therefore, the fact that the present simulation program is capable of being processed to generate information that describes, within reasonable degree of deviations, the behaviour of a real operation, is in itself a strong indication of the coherence of the mathematical structure. It also shows that apparently independent correlations taken from the literature, which


; 1300

: c’

1200

; 1100

P p Doe

900

800

700

600

500

400

300

I I

/ /

/

0.00 0.14 0.28 0.42 0.56 I 70

HEIGHT (ml

Figure 5 Bed temperature profiles for B&W, test no. 26: E, emulsion gas; B, bubble gas; C, coal; L, limestone; +, measured average; *, tube bank region

describe various phenomena of the processes, can be put together in a logical building exercise that uses basic differential mass and energy balances, to give an important tool that allows real equipment operation to be predicted.

The vertical one-dimensional differential mass and energy treatment, for the bed and freeboard section, proved to be a reasonable mathematical approach to the simulation.

Temperature projZes

The model allows the computation of individual temperature profiles for gas in the emulsion, bubbles, carbonaceous, limestone and inert solids throughout the bed and freeboard. This information is vital for safe design, allowing the identification of high temperature


800

600

.I,

300 I * 7 I. IO

water jacket

I I 1.65 2.20

I I 2.75 3.30

HEIGHT (m)

Figure 6 Freeboard temperature profiles for B&W, test no. 26: G, gas; C, coal; L, limestone; + , measured average; *, tube bank region

0. 125- \ C \

0.100 - ‘,

OL-__-_____--_

0.69 I. 36 2.07 2.76 3.45

HEIGM Lrn)

Figure 7 Concentration profiles in the system for B&W, test no. 26: A, coal feeding point; *, tube bank region

regions in the solid phases or on the tubes. The former can, in some conditions, lead to bed collapse if the temperature is higher than the ash softening point, and the latter to erosion of the tube surface.

y- 35.0 0

z 31.5

0

2 20.0

s ,= 24.5

: : 21.0

% J 17.5

%

14. t )-

Although variations in temperature for each phase have been verified, the average value does not vary too much throughout the entire system (Figures 5 and 6). The temperature of the carbonaceous solid reaches its maximum at points near the distributor where these particles meet layers of high 0, concentration (Figure 5). As there is close contact, the temperature of the gas and solids in the emulsion tends to be almost the same in regions just above the distributor (Figure 5).

j- IO. !

7. c

3.:

0.c

mF - )O

Freeboard

I I I 0.69 1.38 207 2.76 3.45

HEIGHT Cm)

For fluidized bed combustion boilers, the simulation shows that the bubble phase temperature tends to

Figure 9 Concentration profiles in the system for B&W, test no. 26: A, coal feeding point

increase slowly towards the emulsion gas and particle temperatures from the bottom to the top of the bed (Figure 5). This behaviour is typical. The bubble temperature eventually passes the emulsion average temperature, mainly in regions near the top of the bed, and is more likely to occur in gasification processes. Sharper increases in the bubble phase temperature can be achieved near the tube bundle if the space between the tubes is smaller than the bubble diameter. This is mainly due to an increase in the bubble phase area for heat and mass transfer (Figure 5).

The temperature of the gaseous phase tends to increase just above the bed surface due to fast combustion of CO and other gases previously stored in the lean 0, emulsion phase that now contacts the rich 0, bursting bubble phase (Figure 6). No appreciable variations of temperature have been computed in the freeboard above the region

2 0.00150 ,

2 p 0.00135

2 0.00120

E (r 0.00105

5 $ o.oOQ90

I-+

bed

+_--_ ---

NO

.J I Wrd

0.00 0.69 1.36 2D7 2.76 3.45

HEIGHT (ml

Figure 8 Concentration profiles in the system for B&W, test no. 26: A, coal feeding point; *, tube bank region

T- 1

,H2S



3 0.225

0.00 0.14 0.26 0.42 0.56 0.70

HEIGHT (ml

Figure 10 Concentration profiles in the emulsion and bubble phases for B&W, test no. 26: A, coal feeding point, *, tube bank region; E, emulsion phase; B, bubble phase

= 1.0

E a 0.9- E 2 o.a- s

0.7 -

0.6

0. 5

0.4

0. 3

0. 2

0. I

0.0 0 I 2 3 4 5

PARTICLE DIAMETER (mm)

Figure 11 Coal particle size distribution for B&W, test no. 26: F, as fed to the bed; D, in the bed; TF, at the top of freeboard

near the bed surface (Figure 6). The temperature profiles in the bed are especially sensitive to the rate of solid circulation. Equation (A35) is useful as a first attempt to calculate individual solid circulation, but more research in this area is necessary.

Concentration profile of gases As expected, the simulations predicted a much sharper

decrease of 0, concentration and increase of CO, concentration in the emulsion phase than in the bubble phase (Figure IO). Greater CO concentration peaks are shown in the emulsion than the bubble phase. At higher points in the bed, the concentration of CO tends to vanish, even in the emulsion, due to the diffusion of 0,

from the bubble phase (Figure IO). CH,, H,, H,S, NH,, tar and C,H, (in the test ethane was fed continuously with the fluidizing air) are produced mainly by the devolatilization process (Figures 7 and 9). This is shown by the sharp increase in their concentrations near the feeding point in the bed. Their concentrations drop to almost nil a few centimetres from the feeding point and therefore no appreciable concentrations are detected in the freeboard. This behaviour is characteristic of combustors with the feeding port inside the bed. When the feeding point is above the bed surface it is possible that a noticeable concentration could be detected at the

2 P 1.0

2 E 0.9

w I

0.8

0. 7

0.6

0.5

0.4

0. 3

0.2

0. I

0.0

-I

c 0.0 0.6 1.2 1.8 2.4 3.0


Figure 12 Limestone particle size distribution for B&W, test no. 26: F, as fed; D, bed; TF, at the top of freeboard

g 1.0 ,

L $0.9- IL

3 0.8- 9

0.7 -

0.6 1

0.0 0.S 1.8 2.4 ; 0


Figure 13 Total average particle size distribution, -, in the bed, and ---, at the top of the freeboard for B&W, test no. 26: +, experimental determinations for the solids in the bed; A, experimental determinations for the top of the freeboard



top of the freeboard. This simulation can deal with this case.

When bituminous and semi-bituminous coal were used, SO, was produced mainly by the combustion of the carbonaceous solid rather than by devolatilization (Figure 8). No appreciable changes in the gas composition were detected in the freeboard. This is a characteristic of deep beds, which provide space for most chemical transformations to occur before the gas currents reach the top of the bed. This could change if the operation allowed a relatively low carbon conversion, which could react in the freeboard section (some work6* has shown NO, decline in the freeboard due to this cause).

The predicted composition of gas leaving the freeboard agrees with the real operational data within a 5% average deviation. However, greater deviations have been obtained for the SOa concentrations. As the deviations do not follow a consistent pattern, future work should concentrate on the study of SO2 absorption by limestone and limestone reactivity. Also, as the rate of SO, absorption by CaO is strongly influenced by the limestone temperature, improvements in the calculation of the solid temperature profiles would lead to better predictions of SOZ concentrations.

2 0.090 gl

s 0.081 P b

&

0.009 - $I> __Q--_. = --_a-__

0. GQO . -- 1 I 1 1

1.10 I .65 2.20 2.75 3.30

HEIGHT (ml

Figure 14 Gas and solid flows in the freeboard for B&W, test no. 26: G, gas (scale factor: 0.1); C, coal; L, limestone (scale factor: 0.001); A, free ash

Composition of solids The various elements in the carbonaceous particles,

apart from ash, decrease more or less proportionally with the carbon during the processing. The aImost complete consumption of volatiles from the solid carbonaceous was verified in all cases. No moisture survives in the average processed solid. In some operations, the carbon in the volatiles can constitute the major contribution to the maintenance of combustion in the bed. It is possible, therefore, that in some cases the elutriated carbonaceous particles can have their carbon in the ‘fixed carbon’ consumed mainly in the freeboard.

The best results were obtained using the exposed core (or ash free) model for the carbonaceous solid-gas reactions ((R-l) to (R-5)) and with the unreacted-core model for all other solid reactions or decompositions.

Particle size distributions The mathematical model is capable of predicting the

particle size distributions and flow for all golids in the bed and through the freeboard. These parameters are calculated for each individual solid and for the mixture (Figures I1 and 12). The average particle diameter in the bed can be either greater or smaller than the respective fed stream. This is due to the competing effects: chemical reactions, attrition and recycling of particles on one side and entrainment of fines to the freeboard, leaving the larger ones in the bed, on the other side (Figure 13).

T o.m- 4.0 F 09 ct 0.72 - _- s= -_J-

_,~_\______’ 5

-3.6

2 0.64- ’ 1 L-

,+UElT

2

- -3.2 z

/ 0.56- /

I 0.48 - - 2.4

/ 0.40 -y 2 - 2.0

0.32

i -r--t---- i

I. 6 --

0.24 1.2

0.00 I 1 r- I * 0.0

0.00

Ak $

0.14 0.28 0.42 0.56 0.70

HEIGHT (ml

Figure 15 Gas flows (E, through emulsion phase; B, through bubble phase; T. total of E+B). bubble velocitv (UB) and bubble diameter (DB) throughout the bed: A, coal feeding point; *, tube bank region

Table 15 Entrainment flows of particles at the top of the freeboard during the tests of the NCB test rig

Solid

Mass flow (g s-l) ____~___

Test no. 3 Test no. 5 Test no. 6

Experimental Simulated Experimental Simulated Experimental Simulated

Carbonaceous n.d. 12.07 n.d. 26.98 n.d. 0.75

Limestone n.d. 0.10 n.d. 0.82 n.d. 0.13

Free ash n.d. 4.44 n.d. 1.39 n.d. 0.80

Total 16.0 16.61 23.6 35.19 2.08 1.68

n.d., Not determined



The effect of recycling particles on the average diameter in the bed and on the entrainment of particles to the freeboard is shown in Table 15, which reproduces experimental and simulation results of a NCB plant (test nos. 3 and 5 used particles recycling to the bed). Complete data are available elsewhere28.

ACKNOWLEDGEMENTS

The author would like to thank A. B. Hedley and P. Foster of the University of Sheffield for their suggestions, and the CNPq (Conselho National de Desenvolvimento Cientifico e Tecnoiogico, Brazil) for the support given.

REFERENCES

1

2

3

4

5 6 7

8

9 10

11

12

13

14

15 16 17 18 19

20

21

22

23

24

25

26

27 28

29 30 ,31

32 33

34

Gibbs, B. M. Institute of Fuel Symposium Series, 1978, 1, A5.1-A510 Horio, M., Rengarajan, P, Krishnan, R. and Wen, C. Y. in ‘Fluidized Bed Combustor Modelling’, NASA Report No. NAS3-19725, 1977 Park, D., Levenspiel, 0. and Fitzgerald, T. J. AIChE Symp. Ser. 1981, 77(277), 116 Raman, P., Walawender, W. P., Fan, L. T. and Chang, C. C. Ind. Eng. Chem. Proc. Des. Deo. 1981,2Q (4), 686 0verturf.B. W. and Reklaitis, G.V. AIChEJ. 1983,29 (5), 813 Overturf, B. W. and Reklaitis, G. V. AIChE J. 1983,29 (S), 820 Weimer. A. W. and Clough, D. E. Chemical Engineering Science 1981,36, 549 Baron, R. E., Hodges, J. L. and Sarotim, A. F. AIChE 70th Annual Meetina. NY. USA. 1977 Rajan, R. and Ken, C. Y. ArChE J. 1980,26 (4), 642 Chang, C. C., Fan, L. T. and Walawender, W. P. AIChE Symp. Ser. 1984, 80, 80 Avedesian, M. M. and Davidson, J. R. Transactions of the Institute of Chemical Engineers 1973, 51, 121 Gordon, A. L. and Amundson, N. R. Chemical Engineering Science 1976, 31 (12), 1163 Gordon, A. L., Caram, H. S. and Amundson, N. R. Chemical Engineering Science 1978, 32 (6), 713 MIT Energy Laboratory, Massachusetts Institute of Technology, Report to US Dept. ofEnergy, contract No. E(49-18)-22951978 Mori, S. and Wen, C. Y. AIChE J. 1975, 21, 109 Horio, M. and Wen, C. Y. AIChE Symp. Ser. 1977, 13, 9 Chen, T. P. and Saxena, S. Fuel 1977,56,401 Chen,T. P. and Saxena, S. C. AIChE Symp. Ser. 1978,74,149 Saxena, S. C., Grewal, N. S. and Venhatoramana, M. University of Illinois at Chicago Circle, Report No. FE-1787-10 to US Dept. of Energy Tojo, K., Chang, C. C. and Fan, L. T. Ind. Eng. Chem. Proc. Des. Deu. 1981, 20 (3), 411 Toomey, R. D. and Johnstone, H. F. Chemical Engineering Progress 1952,48 (5), 220 Davidson, J. F. and Harrison, D. in ‘Fluidized Particles’, Cambridge University Press, 1983 Catipovic, N. M., Jovanovic, G. N. and Fitzgerald, T. 3. AIChE J. 1978,24 (3) 543 Zhang, G-T. and Ouyang, F. Ind. Eng. Chem. Process. Des. Dev. 1985, 24 (2), 430 DeSai, P. R. and Wen, C. Y. MERC/CR-78/3, U.S. Dept. of Energy, Morgantown (WV) Tech. Information Center, 1978 Kim, M. and Joseph, B. Ind. Eng. Chem. Proc. Des. Deu. 1983, 22,212 Rossberg, M. Z. Elektrochem. 1956,60, 952 de Souza-Santos, M. L. Ph.D. Thesis, University of Sheffield, UK, 1987 Yoon, H., Wei, J. and Denn, M. M. AIChE J. 1978,24 (5), 885 van Heek, K. H. and Muhlen, H. J. Fuel 1985,64, 1405 Kasaoka, S., Sakata, Y. and Tong, C. International Chemical Engineering 1985, 25 (I), 160 Adknez, J., Miranda, J. L. andGavil&n, J. M. Fuel 1985,64,801 Wen, C. Y. and Chen, L. H. Journal of The Chinese Inst. of Chem. Engineers 1983, 14, 173 Thurner, F. and Mann, U. Ind. Eng. Chem. Proc. Des. Deu. 1981, 20, 482

35

36

37 38

39

40

41

42

43

44

45 46

47

48

49

50

51

52

53

54 55 56 57 58

59

60

61

62 63 64

65

66

67

68

69 70

71

72

73

74

Kubashewski, O., Evans, E. L. and Alcock, C. B. ‘Metallurgical Thermochemistry’, Pergamon Press, London, UK, 1967, p. 422 Asaki, Z., Fukunaka, Y., Nagase, T. and Kondo, Y. Transaction 1974,5,381 Borgwardt, R. H. AlChE J. 1985.31 (l), 103 Borgwardt, R. H. Environmental Science and Technology 1970, 4 (l), 59 Borgwardt, R. H., Drehmel, D. C., Kittleman, T. A. er al. ‘Selected Studies on Alkaline Additives for Sulfur Dioxide Control’, EPA-RTP, 1971 Rajan, R., Krishnan, R. and Wen, C. Y. AZChE Symp. Ser. 1978, 74,112 Rajan, R., Krishnan, R. and Wen, C. Y. in ‘Simulation of Fluidized Bed Coal Combustors’, West Virginia Univ., Morgantown, WV, USA, NASA CR-159529, 1978 Franks. R. G. E. in ‘Mathematical Modelline in Chemical Engineering’, Wiley, NY, USA, 1967 Babu, S. P., Shah, B. and Talwalkar, A. AIChE Symp. Ser. 1978, 14, 176 Delvosalle, C. and Vanderschuren, J. Chem. Eng. Sci. 1985, 40 (5), 769 Sit, S. P. and Grace, J. R. Chem. Eng. Sci. 1981, 36, 327 La Nauze, R. D., Jung, K. and Kastl, J. Chem. Eng. Sci. 1984, 39 (ll), 1623 Kunii, D. and Levenspiel, 0. in ‘Fluidization Engineering’, J. Wiley, NY, USA, 1969 Kothari, A. K. M.Sc. Thesis, Illinois Institute of Technology, Chicago, USA, 1967 Gelperin, N. I., Einstein, V. G. and Kwasha, V. B. ‘Fluidization Technique Fundamentals’, Izd. Khimia, Moscow, USSR, 1967 Xavier, A. M. and Davidson, J. F. in ‘Fluidization’ (Eds. J. F. Davidson and D. L. Keairns), Cambridge University Press, 1978, p. 333 Gallo, J. G., Quassim, R. Y. and Saddy, M. Fluidized Combustion Conference, Energy Research Inst., Univ. of Cape Town, 1981 Isachenko, V. P., Osipova, V. A. and Sukomel, A. S. ‘Heat Transfer’, Mir, Moscow, USSR, 1977 Botteril, J. S. M. ‘Fluidized Beds, Combustion and Applications’ (Ed. J. R. Howard), Applied Science Publishers, 1983 Hughes, R. and Deumaga, V. Chem. Eng. 1974,27, 95 Talmor, E. and Benenati, R. F. AIChE J. 1963, 9, 536 Merrick, D. and Highley, J. AZChE Symp. Ser. 1974, 70, 366 Wen, C. Y. and Cheh, L. H. AIChE J. 1982,28, 117 Leith, D. and Mehta, D. in ‘Cyclone Performance and Design’, Atmospheric Environment, Pergamon Press, 1973, Vol. 7, pp. 527-549 Ho, T.-C., Chen, T. K. and Hopper, J. R. AIChE Symp. Ser. 1984,80, 34 Chirone, R., D’Amore, M. and Massimilla, L. 20th Symp. (Int.) on Combustion, The Combustion Institute, Ann Arbor, 1984 Salatino, P. and Massimilla, L. Chem. Eng. Sci. 1985, 40 (lo), 1905 Vaux, W. G, and Schruben, J. S. AIChE Symp. Ser. 1983,79,97 Babcock & Wilcox, EPRI FP-308, Vol. II, 1976 Vilienskii, T. V. and Hezmalian, D. M. ‘Dynamics of the Combustion of Pulverized Fuel (Dinamika Gorenia Prilevidnovo Tolpliva)‘, Energia, Moscow, USSR, 1978, p. 246 Branch, M. C. and Sawyer, R. F. 14th Symp. (Int.) on Combustion, The Combustion Institute, Pittsburg, PA, USA, 1972, pp. 967-974 Quan, V., Marble, F. E. and Kliegel, J. R. 14th Symp. (Int.) on Combustion, The Combustion Institute, Pittsburg, PA, USA, 20-25 August 1972, pp. 851-860 Siminski, V. J., Wright, F. J., Edelman, R. B., et al. AFAPLTR 72-74, Vols. I and II, Air Force Aeropropulsion Lab., Wright Patterson Air Force Base, Ohio, USA, 1972 Brikci-Nieassa. M. Ph.D. Thesis. Universitv of Sheffield, UK, 1982 - Sergeant, G. D. and Smith, I. W. Fuel 1973,52, 52 Biba, V., Macak, J., Klose, E. and Malecha, J. fnd. Eng. Chem. Proc. Des. Deo. 1978, 17 (I), 92 Gibson, M. A. and Euker, C. A. ‘Mathematical Modeling of Fluidized Bed Coal Gasification’, paper presented at AIChE Meeting, Los Angeles, CA, USA, 1975 Johnson, J. L. in ‘Kinetics of Coal Gasification’, Wiley, NY, USA, 1979 Hottel, H. C. and Howard, J. B. in ‘New Energy Technology’, MIT Press, Cambridge, MA, USA, 1971 Parent, J. .D. and Katz, S. ‘Equilibrium Compositions and



15

Enthalpy Changes for the Reaction of Carbon, Oxygen and Steam’, IGT Research Bulletin, 1948 Kanury, A. M. ‘Introduction to Combustion Phenomena’, Gordon & Breach Science, London, UK, 1975

NOMENCLATURE

aj stoichiometry parameter A area (m’) b, 6, tj stoichiometry parameters c C d D E

f”

f’

{“,

f

f bexp

s

G H

ki

k,i

Ki

Ko,i

L

Mj P P

ri

R Rs

R GE

R GB

S

s

molar concentration (kmol mm3) specific heat (J kg-l K- ‘) diameter or equivalent hydraulic diameter (m) diffusivity coeficient (m2 s- ‘) rate of energy produced( +), consumed(-) or transferred per unit of length of the vertical direction (W m-l) activation energy (J kmol- ‘) mass fraction of particles : e.g. fi = mass fraction of carbonaceous material particles among all the solids fraction based on the number of particles in the bed fraction based on the area of particles in the bed fraction based on the volume of particles in the bed mass fraction of the entrained particles at the top of the bed that return as forced recycle to the bed factor of bed expansion from the minimum to the operating fluidizing conditions43 fuel ratio (fixed carbon d.b/volatile matter d.b) mass flow (kg s-‘) mass flux (kg me2 s-l) enthalpy (J kmol- ‘) Arrhenius constant for reaction i (dimension depends on the reaction) pre-exponential Arrhenius constant for reaction i (same dimension as k) equilibrium constant for reaction i (dimension depends on the reaction) pre-exponential equilibrium constant for reaction i (same dimension as K) length (m) molecular mass of component j (kg kmol- ‘) partial pressure (Pa) pressure (Pa) rate of chemical reaction i (for gas-solid reactions: kmol me2 (of particle surface) s- ’ ; for gas-gas reactions: kmol mm3 (volume of gas phase) s-‘) universal gas constant (J kmol- ’ K- ‘) rate of production of chemical component due to solid-gas reactions (base=area of solid phase referred to in inferior index) (kg m- 2 s- ‘) rate of production of chemical component due to gas-gas reactions occurring in gas phase of emulsion (base=volume of gas phase in the emulsion) (kg mm3 s- ‘) rate of production of chemical component due to gas-gas reactions occurring in bubble phase (base = volume of bubble phase) (kg rnM3 s- ‘) mass fraction in particle size distribution mass fraction in particle size distribution referred to the individual species. The mass fraction distribution within each species m is given by

%LI

S S' T T* u V W

Xdist

Yj Z

a

F

A

9

V

P

0

z

f D

WBE

kl,I and the mass fraction in the mixture is s,,~. They are related by: s,,,~=S,,,~, mass fraction of particles in the bed smaller than

size dp,m,l bed sectional area (m2) surface area (m2) temperature (K) reference temperature (298.15 K) superficial gas velocity (m s- ’ ) volume (m3) mass fraction in solid or gas phases thickness of the distributor plate (m) molar fraction of component j vertical coordinate (m) coefficient of heat transfer (W mm2 K- ‘) stoichiometry coefficient rate of fines production due to particle attrition

(kgs-‘) indicates variation related to the accompanying variable void fraction in the bed surface emissivity resistance factor to chemical reactions (Pa m3 s kmol- ‘)

effectiveness factor for a reaction in the core or relative to cyclone efficiency limestone reactivity thermal conductivity (W m- ’ K- ‘) fraction of conversion of chemical component in the system coefficient of stoichiometry density (kg mw3) Stefan-Boltzmann constant (W mm2 Kd4) fraction of the particle radius occupied by the unreacted core material friability constant (m- ‘) total mass in the bed (kg) coefficient of mass transfer between bubble and emulsion (s- ‘)

Subscripts

amb ash

relative to the external ambient to the reactor relative to the ash content in the proximate analysis of carbonaceous material (wet basis) relative to the average condition at a point z on the bed or freeboard relative to the bed (normally to define a property as an average at a point in the bed) relative to the bubble phase relative to the unreacted or not still affected internal core of a solid particle relative to heat transfer by convection dry or calculated at dry basis relative to the distributor or distributor surface in contact with the bed relative to the bed or at the top of the bed, as in ZD relative to the emulsion phase relative to the freeboard section or at the top of the freeboard, as in zF relative to gas phase

A

bed

B core

C d dist

D E F

G GE GB i I

relative to gas in the emulsion relative to the gas in the bubble relative to the reaction R-i entering the system or section


Comprehensive modeling and simulation of fluidized bed boilers and gasifiers: M. 1. de Souza-Santos

j

J K 1

lm

L m

mf M N

! shell

S T vol

V W

Y

relative to the component j. Gas components: l=CO,; 2=CO; 3=0,; 4=N,; 5=HzO; 6=H,; 7=CH4; 8=SO,; 9=NO; 10=CzH,; ll=H,S; 12=NH,; 13 = Tar. Solid components in the carbonaceous particles: 14=C; 15=H; 16=0; 17=N; 18=0; 19= Ash; 20 = Volatiles; 21= Moisture. Solid components in the limestone particles: 22 =CaCO,; 23 = CaO; 24 = CaSO,; 25 = Moisture. Solid component in the inert particles: 26=SiO,; 27 = Moisture relative to the internal surface relative to recycling of particles to the bed relative to the level in the particle size classification (1 increases with the particle size) maximum number of levels in the size particle classification of the solid type m leaving the system or the indicated section relative to the solid type m (1 =carbonaceous material, 2 = limestone, 3 = inert) at the minimum fluidizing condition relative to mass transfer between phases due to the solid turnover in the bed relative to the solid particles relative to chemical reactions relative to radiative heat transfer relative to the reacted or processed external shell that covers the core of a solid particle relative to solid phase in the emulsion relative to the tubes relative to the volatiles content in the proximate analysis of carbonaceous material (wet basis) relative to the devolatilization processes relative to the wall (e.g. WOTD = relative to the outside wall of the tubes in the bed) relative to particle entrainment

Superscript * relative to the equilibrium condition

APPENDIX A

Basic and auxiliary equations This section gives the basic differential equations that

describe the mass and energy balances for each component or phase. Some important auxiliary equations are also listed. More details may be obtained from the references cited in Table 7 or Ref. 28.

Mass balances for the emulsion phase:

dvoE R ,- GE.> dz

dAB +G~GBGE,jx l<j<13 (AlI

Mass balances for the bubble phase:

dvi G dFGB,i _ R dbz dz

GB,j x- MGBGJ2.i x 1 <j< 13 (A2)

Total solid component conversions:

14<j<27 (A3)

Table a Description of the correlations used to compute the rates of the gas-gas reactions with the general form

Reactions (i) a b 6 C E d a Ref.

15 16 17 18 19 20

21 22

1.52 13 0.25 5 0.5 64 1.5 6 1.5 3 1 - - 64 1713 l--64 1 13 0 :: 0.86 3

l--64 1.04 - - 65

0 11 0.86 3 1.04 - - Assumed similarity with 19

0 4 1 3 0.5 - - 66 -1 13 0.5 3 1 67

’ Multiply by p”.3

R dA PE,m&

SE,m.j dz

14<j<27 (A4)

Energy balance for the emulsion phase:

FGECGE dTGE= - dz

&GE+ 5 (&~EGE.III+~~sEGE,~IJ m=l

+J%GBGE+&GBGE-&GETD+EGEWD 645)

Energy balance for the bubble phase:

FGBCGB~=-EQGB-&GBGE+&GBGE-ECGBTD dz

(A6) Energy balances for the solid phases:

d&m _E F~.mCs~.rn )=

dz QSE,m-ECS~~~,m -E~s~~~,m

- '%sETD.~- "$1 (ERsEsE,~,~+~c~E~E,~,~)

l<m<3 (A7)

Mass balances for the components in the freeboard:

1 <j<27 (A8)

Energy balances for gases in the freeboard section:

FGFCGF dTGF= dz

- EQGF+ i ~%sFGF,~+EMsFGF,~) m=l

--ECGFTF+EGFWF (A%

Energy balances for the solids in the freeboard:

F d&m PF,mCsF,m dz A=- EQSF,.,,- E CSFGF,m -'%s~~F,rn

3

-&SFTF,~- 1 E~~~~~,m,n n=l

1 <m,<3 (AlO)

Freeboard overall solid type m mass balance:

FLD,m=F~,m+FK,m+Fy,m,z=zo-Fy,m,z=zF (All)

F K,m,l- y,m,z=z~%y,m,l -F 6412)



Rate of fines generation (see Equation (14)):

f-,,I = VL‘yn(U - V&,,,_L&l,, (A13)

Rate of component production or consumption (Equation Al):

24

RGE,j= C Vj,iMjTiITGE l<j<l3 (A14) i= 14

Rate of solids production or consumption (Equation Al):

R %n~.i=~~~ vj,i”jrilTsE.m 1 <m<3, 1 <j<27 (A15)

Rate of mass transfer between emulsion and bubbles (Equation A 1):

G MGBGE.jzdBaBECGMj (YGB,j-YGE.j)

6 (‘416)

Rate of component production or consumption in the bubble phase (Equation A2):

24

RGB,j= C Vj.iMjrilTGB l<j<l3 (A17) i=14

Rate of energy production by gas-gas reactions in the emulsion (Equation A5):

E -f dG/,, QGE- RGE,jHjlTGE __

j=l dz VW

Rate of energy transfer associated with mass transfer between the solids and gases in the emulsion (Equation A5):

Ehl - f RSE,,,j(HjIT,,,~-HjI=~,E) % SEGE.m - j=l

(A19)

Rate of energy transfer associated with mass transfer between the emulsion and the bubble (Equation A5):

E MGBGE= jil GMGBGE.j(HjlTGu- HjlTm) 2 0420)

Rate of energy production or consumption due to heterogeneous reactions (Equation A7):

E QSE.m = jfl RSE,m,j Hj 1 Tsc.,,, 2 6421)

Assumed average temperature at a point in the emulsion:

T =T~+(TGE-~*)F,EcGE+(TGB--*)F,BcGB GE

FGE cGE + FGB CGB 6422)

Some fluidization parameters:

F u, = _GE

PGESE (A23)

s=sE+sB (A24)

s, = Slfbexp * (A25)

&E = hf &

C-1

0.15

(A26) u mf

Resistance coefficients used to describe the heterogeneous

reactions (Equation 5):

+$!% SEGE.m

i =(d~~,m)2Cl-~i)RTPE,m 2J

12tiDshell,i

13,i= ’ tliT?kiCSl,i

(~27)

(A2g)

(~29)

Some special kinetic coeficients:

k,= k 33

f +k,,p, +k,,p,

k = k,rPb

4 l+k,,p,

Devolatilization related coefficients (Table 6):

F W

v,13 tar = F

C FV,j j=l

(A30)

(A31)

(~32)

W gas = 1 - Wtar (A33)

CO2 equilibrium partial pressure used in Equation (10):

pt = 3.336 x 1O’P exp -__ (A34)

Solid rate circulations:

F F = PpJn(l - %lfw - %I,)

x exp( - 6630d,,,,)fzS ldm<3 (A35)

Differential surface particle areas in the emulsion (Equation Al):

dA A 25!LsE(1-&E)f~ pem l<m&3 dz

(A36) P&m

Differential surface particle areas in the freeboard (Equation A8):

dA A L5E=SF(1-EF)f;~ ldmS3 dz

C437) PF.m

Differential surface area of the bubbles (Equation A2):

d& x=s,+ B

(A38)

Differential volume occupied by the gas in the emulsion (Equation Al):

d&E ---=SEEE dz

(A39)

Differential volume occupied by the bubbles (Equation A2):

db_s dz

B (A40)

Total gas flow at each point of the referred phases:

FG= g Fj F,= y Fj (A41) j=l j=14


Comprehensive Modelling and Simulation of Fluidized Bed Boilers and Gasifiers

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