Regerative desulphurization in interconnected fluidized bed combustion of coal

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Regenerative Desulphurization in Interconnected

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adres: J . Dekker Hoefijzerstraat 20 2611 MP Delft 015 - 124162 opdrachtdatum: 10/10/1992 versiagdctum: 21/12/1992

Regenerative Desulphurization in Interconnected F1uidized Bed

Combustion of Coal

Joost Dekker Jouke Eijssen

SUMMARY

As part of a research on regenerative desulphurization in tluidized bed combustion of coal, a design has been made of a 100 MW power plant. Fluidized bed technology has been used because of it's capability of in-situ sulphur removal. To comply with emission regulations for coal fired power stations, as set by the Dutch Government, a CaO on "Y-A~03 sorbent has been added. This new sorbent, developed at the Delft University of Technology, ensures relatively fast sulphation and selective and fast regeneration. Although this sorbent has a good attrition resistance, an Interconnected Fluidized Bed (lFB) was designed to minimize conveyance attrition. Because, until now, no research had been done on this sorbent's behaviour in an IFB system operating at high temperature, the ambition has grown to built a pilot-plant for testing purposes.

In this report, a preliminary study is made of the possibility to downscale the commercial IFB coal eombustor design, to pilot-plant scale. In chapter 2, an engineering model for regenerative desulphurization is presented. By combining this with the hydrodynamics model of the IFB, derived in chapter 3, dimensioning calculations can be done. For this purpose two simulation models have been programmed in MathCad 2.52 . Special attention was paid to write a program that is readily transferable to, and can be easily adapted by other users. In ehapter 4, the ealculation procedure to design the comercial plant as weIl as a sensitivity analysis of the main parameters are given, together with a flrst intent to downscale this design to pilot-plant scale. The goal of writing a readily transferable (and adaptable) program has been achieved. With this model all calculations were made, leading to a 100 MW power plant. The combustor was found to be 385 m3

, compared to a regeneration bed of 10 m3• With this design, all emission regulations

are met. After down' sealing this design, credible dimensions of a pilot-plant were found, although the idea of four equal sized beds had to be discarded.

- i

-CONTENTS SUMMARY

CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

1 INTRODUCTION . . . 1

2 AN ENGINEERING MODEL FOR REGENERATIVE DESULPHURIZATION . . . .. 5

Coal combustion and sorbent sulphation .. . . 5

Modeling sorbent sulphation . . . 7

Sorbent regeneration . . . 17

Modeling sorbent regeneration . . . .. . . . . . . . . . . . .. 17

3 INTERCONNECTED FLUIDIZED BED HYDRODYNAMICS . . . . . . . . . . . . . .. 21 ,

Bed hydrodynamies. . . . .. . . 21

Segregation of sorbent and ash . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25

Sorbent transport through orifices. . . . . . . . . . . . . . . . . . . .. 27

Motivation of the used eorrelations and assumptions . . . . . . . . . . . . . .. 35

l)~,.\ ~ 4 MO G RESULTS . . . 41

Caleulating the IFB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41

Dimensional analysis and down-sealing . . . , 59

5 CONCLUSION AND RECOMMENDATIONS 71 6 LIST OF SYMBOLS . . . ... . . 73 Latin symbols 73 Greek symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79 7 REFERENCES 81 8 APPENDIX o.o . . . 85 Safety analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

MathCad Listing of Sulphation-Regeneration model . . . . . . . . . . . . . . 87

Mathcad Listing of Hydrodyanmics model . . . . . . . . . . . 111

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1 INTRODUCTION

Of the several air pollutants that plague the world, sulphur oxides have received special attention. Except for nitrogen oxides and maybe particulate matter (dust), few air pollutants have been stu-died as much. Because it's emission is heavy in all highly industrialized countries, it has become the center of attention of governmental regulatory agencies.

Practically all S02 and S03 comes from the combustion of naturally occurring sulphur compounds, often· constituents of an ore or a fossll carbonaceous material. The burning of oll and coal for heating and power production are potential sources of major sulphur oxide pollution. Other competitors as energy source, like hydroelectric and nuclear , do not produce S02' and constitute one way of reducing sulphur oxide emission. But even though, since the energy crisis of 1973, the impending shortage of oll and natural gas as weil as their polluting capacity were an incentive for the intensive development of new energy sources, these have remained of secondary importance. While even in the 70's sulphur oxides were normally not removed from the stack gas of carbonaceous fuel-burning plants, because they were considered too dilute, nowadays desulphuriz-ation is standard procedure. The technology of desulphurizdesulphuriz-ation has developed in different directions, each with its particular advantages and problems. Due to environmental pressures a complicated technology has evolved in a relatively short time.

The general approach in desulphurization process development has been to convert the sulphur to some form other than S02 that is easier to remove from the gas. lt is possible to make a distinction between throwaway and regeneration processes. Throwaway processes don't solve the pollution problem completely because atmospheric pollution is merely converted to a solid waste problem. The disposal task of coal-burning power plants is even made larger since now not only ash but also sulphated solid (or liquid) waste is produced.

Extensively used (dry) natural sorbents for desulphurization, like limestone and dolomite, are not satisfactory tor regeneration purposes. Main drawbacks are their high regeneration temperature and their attrition sensitivity. The existing synthetic sorbents always suffer from at least one of these problems.

At the Departmem of Chemical Engineering of the Delft University of Technology (DUT), a sorbent (SCO-5OO) has been developed which does not suffer any of these drawbacks. After testing sulphation, regeneration and attrition, this behavior was modeled and fitted in a steady state engineering model.

Because not only the sorbem, but also the design of the process should be aimed at minimizing attrition, Interconnected Fluidized Bed technology is studied.

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Figure 1: Interconnected Fluidized Bed system

-2-The basis of an Interconnected Fluidized Bed system (IFB) is the need of minimizing sorbent attrition and the need to integrate at least two different chemica! environments in one system. The traditional design of regenerative desulphurization in fluidized bed coal combustion suffered from extensive cataiyst attrition. This is mainly due to the high speed particle impact, originated in the pneumatic transport of the sorbent through a pipeline-system.

A scheme of an IFB system is shown in figure 1. The system consists of four fluidized beds which can be operated with four different gases at different gas velocities. In principle, bed one and three are operated at a high fluidization velocity and bed two and four at a lower fluidization velocity. This results in leao and dense beds with different bed heights. Because the separating wall between bed one and two is just below the dynamic bed height of bed one, particles will flow over from this bed to the second bed. Through an orifice at the bottom of the separating wall between bed two and three, these beds are connected. Because of the density difference between these beds, a pressure drop over the orifice exists, resulting in a particle flow from bed two to bed three. The particles are now again in a lean bed imd will, consequently, flow over the separating waU to bed four. From this bed they will travel through an orifice, to bed one, where the cycle is completed. Because of the low particle velocity through the system attrition will be minimized. When using this system for regenerative desulphurization in fluidized bed coal combustion, the advantage of minimal sorbent attrition is combined with ash/sorbent segregation, simplifying ash removal from the system. Also the necessity to use two different chemical environments in one system can be accomplished easily.

It is obvious that the coal combustion and S02-removal takes place in bed one. In bed two, the segregation of large ash-particles and sorbent will take place. The ash will siok to the bottom where it can be removed. Because the orifice, in the separating wall between bed two and three, is weU above the ash level, only sorbent will enter bed three. In this bed the regeneration of the sorbent takes place, after which the sorbent is transported to bed four. This bed is designed in such a way that, by changing the fluidization velo city in this bed, the sorbent flow through the complete system can be controlled.

In this report a commercial, IFB-based, coal combustor will be designed. Also the possibility of down scaling this design to pilot-plant scale will be studied. This pilot-plant shouldn't only be used for research on sulphur retention from coal combustion, but also for H:!S containing waste gas treatment. The main objectives of this pilot-plant design are the following:

a) Testing the SGC-500 sorbent in an IFB, at the same operating conditions as the

commercial IFB coal combustor

b) Testing the acceptor used in H:!S-gas removal, according to Wakkerl)

c) Testing the hydrodynamie behavior of the IFB under these operating conditions.

d) Testing the attrition of the used sorbent under these operating conditions.

This paper will only deal with a design based on SO:!-gas removal, and no sugestions will be given for design parameters based on H:!S-gas removal.

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-4-I

2 AN ENGINEERING MODEL FOK REGENERATIVE DESULPHURIZATION

Coal combustion and sorbent sulphation

As much as 40% of the combustibles in coal can be in the form of volatile materials. The burning of coal thus involves gas-solid and gas-gas reactions. Also a distinction can be made between the 'volatiles' sulphur and the 'char' sulphur. The volatile sulphur is mainly due to the organic sulphur, present as approximately 33-50% of the total coal sulphur content. The char sulphur originates in the pyritic (FeS,) sulphur and in the small sulphate (less than 5% caSO.) content. When coal is added to a fluidized bed the particles will heat up to the reactor temperature (850°C) in 1 to 10 seconds, depending on their size. At a temperature around 350°C the devolatilization of the coal starts. During devolatilization sulphur compounds as COS, H2S, CS2 and S02 are released, which, if enough oxygen is present, react ftuther to give the main released sulphur compound S02' The S02 may be in equilibrium with S03 and oxygen. During the devolatilization phase, 5 to 20 seconds. the combustion of the remaining char will start. The temperature of the

char particles will rise to 150-200°C above the bed temperature while mostly sulphur dioxide is released. According to literature data[2), the char burnout time for particles with diameters between 1 and 2 mm, ranges from 50 to 500 seconds depending on reaction and fluidization conditions. On the other hand the devolatilization time of coal is mostly less than 20% of the total coal burnout time. Because this is of the same order of magnitude as the mixing time in a fluidized bed (about 5 seconds), the 'volatiles-sulphur' is, contrary to the char sulphur, not released uniformiy throughout the whole bed. but around the coal feed point. If the sulphur compounds that are released as volatiles are to be captured by CaO, capture should occur in both the reducing atmosphere of the volatiles and in the oxidizing atmosphere of the air-rich regions in the bed. Because of the implications this has tor the design and operation of the fluidized bed combustor, it seems crucial to know the distribution of the released sulphur over the 'volatile' and 'non-volatile' phases. In this context the assumption that all organic sulphur is released during devolatilization has been veritied and shown to be correct[2). In addition it was found that 10-20 % of the pyritic sulphur is released with the volatiles, the remaining pyrite is oxidized during char eombustion. During ehar combustion also a negligible amount of sulphur is released due to the reaetion between sulphate and eoal ash.

Besides SOx a!so NOx is formed during the fluidized bed eombustion of eoa!. The NOx emission

from the combustor is a result of a eompetition between NOx formation and reduction whieh are

complex proeesses with many simultaneous reactions. A simplified ]ohnsson's[3.4) seheme is used

to deseribe the NO release. Due to the low bed temperature no NOx is tormed from the oxidation

of N₂ from the air and so the NOx emission is relatively low. A method under study to further

reduee the NOx emission is sub-stoichiometrie eoal eombustion. At these lower oxygen

concentra-tions SOx and NOx emissions are tound to be related. The lower the oxygen eoneentration is, the lower the sulphur retention and the NO concentration are. These interactions have not been

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Modeiing sorbept sulohation

A shrinking unreacted core model is proposed to describe the sorbent sulphation. This model assumes that reaction occurs fust at the outer skin of the particle after which the reaction zone moves into the non-porous solid particle while a 'shell' of completely converted and inert, porous solid material is produced. To be abie to use this model the thickness of the reaction zone ought to be small compared to the dimensions of the particle, as is the case with non-porous particles. For porous particles this model can be used when the reaction is fast. Diffusion into the core and chemical reaction occur in~~ giving rise to a thin diffuse reaction zone which advances to the center of the particle at a certain rate.

For the sulphation of a sorbent particle the overall rate of the process is defined by the following steps:

Step 1: Diffusion of gaseous reactant from the bulk through the filmlayer to the outer surface of the particle.

Step 2: Diffusion of gaseous reactant through the shell to the reaction front.

Step 3: Reaction of gaseous reactant with solid at the unreacted core surface. In the case of sulphation it is supposed that the conversion rate of CaO is first order i@ concentrati-on and proporticoncentrati-onal to the extern al surface area ~f the unreacted core.

Because no gaseous products are formed during sulphur capture, diffusion of product gases through the shell to the exterior surface (Step 4) and through the filmlayer into the bulk (Step 5) need not be considered.

Based on this shrinking unreacted core model, Wolft1SJ _{derives an equation for the conversion of a}

single sorbent panicle in a two step analysis. First a single typical partially reacted particle is examined to derive an expression relating SO"! concentration at the reaction front in the particle to the unreacted co re radius. fc' Second. an expression is derived describing the change of rc with time.

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Combining these two expressions gives an equation describing the conversion of one particle as a function of time. where: C_eao C02.1 CS02.1 ~,1

Ic.

re

r

r

r

: calcium content in fresh sorbent

: bulk gas O2 concentration bed 1

: bulk gas S02 concentration bed 1

, J

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: equilibrium constant S02 to S03 oxidation

: surface based reaction rate constant : unreacted core radius

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: stoichiometrie coeff. equal to 1 mol CaO/mol S03

: time based on residence time particle

and where aSOx.f and asox.a are defined as

CXSOx,s

where: 0 S02.f : diffusion coefficient of S02 in tilm

OS03.f : diffusion coefficient of S03 in film

0S02.. : diffusion coefficient of S02 in shell

0S03.. : diffusion coefficient of S03 in shell

~ : particle radius

o

:

thickness of filmlayer around particle

Combining this convers ion equation with the reactor hydrodynamics of a fixed bed reactor, Wolff

derives his SURE2 (Sulfur Retention) mode 's ~el, in which the tixed bed is approximated

by Ntanka in series. consists of t 0 differential equations) which have to be solved (for these Ntanka)

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(CSTR) this model becomes

where: CS02.0

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: inlet equivalent-S02 concentration

: concentration of particles in reactor : time

: gas volume in tank V r : reactor volume

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'-Furthermore steady state behaviour will be considered and thus there will be no changes in bulk gas S02 concentration. Also one average unreacted core radius, derived from the definition of the CaO convers ion

Where: : CaO convers ion

will be used, which will simplify the model equations substantially. The particle conversion

equation drops out of the model altogether, just as the time dependency of the bulk gas S02

-12-1

This sulpbation model is extended to include tbe formation of nitrogen oxides. Lin et al.(4

) derive tbe emission of NO from tbe basic mass balance equations of NH) and NO and find

wbere: CNO,1 : bulk gas NO concentration

Ic,. : rate constant NO to N_{z conversion}

Ic..

:

rate constant NH) to NO conversion

Ic., : rate constant NH) to N_{z conversion}

where the NH) and NO inlet concentrations are calculated from the nitrogen content of the coai:

CNO•O

(l-f)fN'<f> cool

<f>.f.l·M

N

C _NH).O = f..,1N

·<f>

cool

4>/.l·MN

where: Ac : carbon external surface area

Ae:..o : sorbent reactive surface area

CNH).O : inlet NH3 concentration

CNO .O : inlet NO concentration

d.,.b : diameter bottom ash particles fN : weight fraction nitrogen in coal

f v : weight fraction volatiles in coal

MN : molar weight nitrogen

Tl : residence time all particles bed 1

P.b : density bottom ash

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: weight fraction bottom ash in coal : yoidage bed I

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Sorbent regeneration

The sorbent can be regenerated by therma! decomposition at a temperature higher than 850°C in the absence of a reducing medium. This is not an attractive way because of the lower regeneration rate compared to reductive regeneration and because of sintering of sorbent at higher temperatu-res. Moreover, when operating the combustor bed (bed one) at 850°C it is for energetical reasons more favourable to maintain the sorbent at one temperature during its entire cycle. Herefore the choice was made to regenerate the sorbent in a reducing medium at 850°C. For economie reasons an off-gas with as high a concentration S02 as possible is wanted because it can then be used to produce sulphur or sulphuric acid. It is thus favourable to regenerate the sorbent with H2 and/or CO. Regeneration with CO is less efficient towards S02 than regeneration with ~. Regeneration with a CO/H2 mixture looks very promising as it can be achieved by substoichiometrie coa! combustion in the regeneration bed. In this design the sorbent will be regenerated by H2• The reactions that describe the regeneration process and the formation of by-products, are the following:

kl=O.95 mis

II dG=-93.98 kJ/mol

III dG=-35.32 kJ/mol

IV k4 =0.005 mis

The formation of CaS is undesirable because it decreases the available amount of active sorbent. As hydrogen is a feed gas and sulphur dioxide a product gas during regeneration, the formation of H:!S, and following CaS. will also depend on fluid bed hydrodynamics.

In the next sulphation cycle the CaS formed will be oxidized to CaO and CaS04 , according to two

simultaneous reactions:

V CaS + 3/2 _{O2 - CaO + S02}

VI CaS + 2 O2 - CaS04

1

('The amount of SO:! formed during oxidation of CaS has been found to be less than 10% of the total CaS convers ion.

~odeling sorbent regeneration

The regeneration process is difficult to model. It is a fast process, which makes it difficult to

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This initial peak is difficult to simulate with existing modeis, and more research has to be done to develop a satisfying regeneration model.

In this design will be worked with the same, steady state, model that was used by van Hout & van

Keep[6). The active surface of a sorbent particle, the Ca surface, will be described as occupied by

caSO., CaO and caS. The surface concentrations are expressed as fractions of the total available Ca surface:

al - surface occupied by caSO. I total Ca surface

a z - surface occupied by CaO I tOtal Ca surface

a) - surface occupied by Cas I total Ca surface

Using these fractions, in combination with the mass balances for CaS04 and CaO and assuming ideal CSTR behaviour and areaction rate flrst order in gas concentrations and extemal surface area of the particles, expressions tor the time average surface occupations can be found:

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where: CH2•3 CH2S•3 kl

k4

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: bulk gas H:! concentration bed 3

: bulk gas H:!S concentration bed 3

: rate constant CaS04 to CaO reaction

: rate constant CaO to CaS reaction

: molar CaO surface concentration

: sorbent residence time in bed 3

Together with the sulphur, oxygen and hydrogen mass balance equations and the equilibrium

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-20-3 INTERCONNECTED FLUIDIZED BED HYDRODYNAMICS

Bed hydrodynamics.

After a couple of decades research and design of tluidized bed reactors, it is still very difficult to pn~dict the tluid dynamic behavior of large scale tluidized bed reactors. There is a large body of experimental data on small beds operated at low velocities with small particles. However there are only a few investigations of somewhat larger laboratory beds, up to about 1 m2 _{cross-section, run}

at ambient temperature and pressure. It is also not clear how results from larger laboratory beds can be applied to commercial beds. Therefore there is a dearth of information currently available for large beds, especially for beds with large particles at elevated temperature and pressure.

Most of the available correlations predicting this dynamic behavior are based on experimental data obtained on fluidized bed column diameters up to about 1 ft. Especially the fluid dynamics of the combustion bed is hard to model because of the disturbing effect of the heat exchange tubes, which are fitted in this bed.

The following section of this paper will discuss the used correlations for this design, given in the order in which the design of the bed has to be made. The motivation of the used correlations and assumptions are discussed in section motivation of the used correlaions and assumptions.

The mini mal fluidization velocity (Umf) - which is the gas flow rate divided by the cross-section of the bed at which the material in the bed begins to fluidize - is calculated by the correlation of Wen and Yu(1):

With Ar:

where: Ar : Archimedes number

ds : diameter of sorbent

g : gravitational constant

Umf : minimal fluidization velocity

7]1 : viscosity of fluidization gas

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When operating at higher fluidization velocities tbe bed will expaod due to a higher bubble fraction. According 10 GeldartlB] tbis bed expansion is predicted by tbe following correlation:

Hp,

- --= _1+---~---

u-u""

H"" U -U"" + 0.71 .

J

god_eq

where: Ah : cross-sectional area of bed

deq : gas bubble diameter

Hh : height of bed

Hmf : height of bed at minimal fluidization

U : gas velocity

Pccal : density of coal <Pecal : coal flow

<P. : sorbent tlow

T : residence time

Witb tbis bed expansion aod tbe known bed voidage at minimal fluidization, tbe bed voidage at tbe chosen gas velocity cao be calculated:

Hmf

e

=

l-(1-e ' 1 .

-mI' H b

where: f : bed voidage

: bed voidage at minimal fluidization

To calculate tbe pressure drop across tbe bed we have to distinguish two different dynamic conditions: bed at minima! fluidization and bed at higher velocities.

At minima! fluidization tbe bed behaves as a packed bed and tberefore tbe correlation of Carman/Ergunl91 cao be used:

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On the other band at bigber velocities the bed does not bebave like a packed bed at all. Therefore another correlation is used:

Segregation of sorbent and ash.

To avoid accumulation of asb in the interconnected fluidized bed, segregation of sorbent and asb, followed by asb removal is necessary. Segregation of particles in a fluidized bed occurs wben particles of different densities and/or different sizes are in the same bed. Althougb segregation of particles on size difference takes place, segregation on density difference is most likely to occur. To predict the segregation, a rather complex empirical correlation is developed[IO.IIJ :

1

M= - - -

= x with z:

z

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with x: X_gem <t> ab

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Finally the height of me top layer consisting of almost pure sorbent:

-I x

I-x

X,. _

H

=

H •

1

+

l-E • . I-x,.

~ b

l-E

P

rrtfr; X C + -I-x P-,

where: D : diameter of bed

Hip : height of top layer

M : mixing index

U

2 : gas velocity in bed two

U

mfe : minimal fluidization velocity of coal

U

mf, : minimal fluidization velocity of sorbent

UT .O : take-over velocity (velocity at which M=O.5)

x : weight fraction of coal in top layer xgem : overall weight fraction of coal

z

: reduced velocity function

Emfe : voidage of bottom layer Emf, : voidage of top layer

(]mfe : shape factor of coal particle (Jmf, : shape factor of sorbent particle

CPab : bottom ash flow

CP. : sorbent flow

With me given expression for calculating Htl, the height of the ash-Iayer is known. By choosing an orifice at two times this ash-Iayer height, the ash fraction in the sorbent will be acceptable low.

Sorbent transport through orifices.

The whole idea of the interconnected fluidized bed reactor is based on particle transport between the four fluidized beds. The transport through the orifices is purely based on density differences of the two connected beds. To predict the solid sorbent flow through the orifices there are again -two different correlations tor the -two different dynamic conditions.

FVO' 3004. KKCI.' _ _ · .... /)eso . . . . .. ti .. ia ~ FIuicIizeoI 8ecI CombllllioD ol Coal

-28-FVO' 3OIM • . . , . . . [)oe • .,... . ;. ~ , .... ~ . . . C-= ... ol CaaI

When neither of the beds is at or beneath minimal fluidization the following correlationl121 _{can be}

used:

àP

=

gop o(H -H )'(E -E)

On & b On 3 2

and

cPLZJ:

where: AoZJ : cross-section of area of orifice Cd : coefficient of discharge

D

oZJ : diameter of orifice H2 : height of bed two

~

: shape factor of particle

~023 : pressure drop over orifice

cPLZJ

: gas leak flow through orifice

. This correlation will be used for calculating the sorbent flow from bed two to bed three.

When one of the two beds is at minimal or beneath minimal fluidization, another - more complex - model has to be usedl6J • Because it is easy to lose track in the following algebraic exercise, a calculation schedule will be given:

First of all the sorbent t10w and a chosen orifice diameter are defined, with which a number of different gas and sorbent flows will be calculated. The gas flows have to be minimized by changing the orifice diameter.

With given cross-section of bed four, the horizontal slip velocity of gas is caleulated with:

FVO' 3OIM, R~ ~ ÎD Iatw

-30-The horizontal partiele veloeity through the orifiee, is determined by the sorbent flow from bed four to bed one (ealculated in the regeneration model):

where: A041

Uahor

q,~l

: surfaee area of orifiee

: horizontal particie velocity through orifiee : sorbent flow through orifiee from bed 4 to bed 1 The sorbent veloeity in bed four is also determined by the sorbent flow:

where: Ab4

U.

: cross-sectional area of bed 4 : sorbent velocity in bed 4

With known U.hot and ~Uhot4h the horizontal gas velocity is calculated:

where: U ghot : horizontal gas velocity

The gas leak: tlow from bed four to bed one is given by:

where: q,lAl : gas leak: from bed 4 to bed 1

The interstitial gas velocity and the sorbent velocity (positive when going down) give the actual gas velocity:

- - - -- - -- -- -- -_ .. -

-FVO' 3004, R~

Der'"

rizróaa ia~" . . . d FIuidizeoI Boel CombuItiaD 0( Coal

-32-Finally the gas velocity needed to achieve minimal fluidization in bed four, corrected for the gas

leak, is calculated:

where: U4 : gas velocity in bed 4

In theory the interconnected fluidized bed can be designed with these correlations. However to intrepid the results of this design, it is derided to know the validity of the used correlations. Referred is therefore to the next section: motivation of the used correlations and assumptions, in which the validity of the used correlations is discussed.

-34-Motivation of the used correlations and assumptions Minima! fluidization velocity

To calculate the minima! fluidization velocity there exist a wide variety of correlations. Babu[7} gives a comprehensive list of published correlations to estimate the minima! fluidization velocity . There are two categories in which these correlations can be divided; Based on the informatioo required:

a) Equations that require the density and viscosity of the fluidizing gas and density and average diameter of the particle.

b) Equations that require the information in a) plus additiona! information such as particle shape factor and the voidage of the bed at minima! fluidization.

Since it is often hard to find this additional information in b), Wen and Yu(1) have fitted an empirical correlatioo based on a wide variety of data. This correlation is therefore used in modelling the IFB. Assumed is by using thiscorrelation that the bed voidage at minimal fluidization (fmI) has a value of 0.4, which is a reasonable value for this type of particles.

For particles which have a wide size distribution and/or a high particle density, this minimum fluidization velocity may be to low. This is also the case for deep beds.

The particle size distribution will, at flrst sight, give some trouble for the combustor bed, because the coal/ash particles will have a wide size distribution. However this coal/ash fraction is very small compared to the sorbent fraction (coal/ash fraction is about 3 % of sorbent fraction), therefore it is assumed that this restriction is no limitation for using the correlation.

The limitation of the particle density will also be no obstruction, because it is fltted up to steel balls. The used particles (sorbent and coal/ash) have a density well below the density of steel. The last restriction, the bed shape, will not be a limiting factor either.The beds are not deep at all.

Bed expansion

The same publication(7) gives a review of published correlations which estimate tluidized bed expansion. The writers of this publication recommend the following correlation, to calculate the bed expansion:

H 14314 ·(U - U )0.738.d 1.006. 0.376

b = 1 + . mI S Ps

H U 0.937 0.126

mi ~ ·PI

Although this correlation is independent of the effect of column diameter and therefore reliable for

scale-up, another correlation is used of calculating this IFB. The reasons for this decision are:

a) The Babu correlation is based on experimental data obtained on t1uidized bed column

FVO , 3004, pe, ooti .. o.-d". . ti 7'~ l'IuicIlz.eO Bed Combuorica ol Coai

6-b) On the other hand, the combustor bed is fitted with heat exchanger tubes, which influence the dynamic fluidization behavior dramatically. According to Glicksman et al. (13) the maximum gas bubble diameter is about 1 to 1.5 times the horizontal pitch (if only a vertically tube configuration is used). With this assumption the maximum bubble diameter will be about 50 to 80 cm (the number of heatexhanger tubes used for recovering the heat, is obtained from van Hout & van Keep(6). Because there is only vertical and no horizontal mixing a the fluidized bed fitted with vertical tubeslI3), the combustor bed can conse-quently be described as a collection of parallelly operated beds with a diameter of about 60 to 100 cm. (assuming the maximum bubble diameter is about 0.8 times the bed diame-ter). By using this assumption the restrietion mentioned in a) is, for the combustor bed, not that limiting any more.

c) Now we have restriction a) and b) contradictory to one another, another criterium for choosing which correlation to use, has to be determined.

The power of the used correlation, mensioned in the section Bed hydrodynamics, lies in using this Glicksman-bubble diameter correlation[l3). Once the number of heat-exchanger tubes is known the dynamie fluidization behavior is predicted by this correlation. And maybe most imported of all this correlation is also tested and fitted on large-scale fluidized beds.

Sel:regation of sorbent and ash

Particle segregation in fluidized beds depend not only on particle density difference andl or

particle size differences, but also the shape of the bed and fluidization velocity influence the degree of segregation. In deep beds two distinctive layers are likely to occur when the density

andl or size differences are large enough. On the other hand in a shallow bed, under the same

conditions, the segregation is not that distinctive at all. Also changes in fluidization velocity are of great importance to the degree of segregation. When operation at the lowest minimal fluidization

velocity, segregation is good. Increasing the velocity will result in a better mixing of the particles.

It is therefore desired to operate around minimal fluidization velocity when segregation is wanted. On the other hand when segregation is not desired the fluidized bed has to be operated at, at leased, 3 times the minimal fluidization velocity .

With these criteria in mind the boudary conditions for the IFB design are easy to determine.

a) The combustor bed has to be weil mixed, therefor high fluidization velocity and a shallow bed are desired.

b) The deep segregation bed has to be operated at minimal fluidization velocity .

The segregation model predicts a sharp boundary between the two particIe layers. This is not very

realistic, but when the height of the orifice is taken 2 to 3 times the height of the boundary, it is assumed that the predicted ash fraction in the toplayer equals the calculated ash fraction (x) in the toplayer.

FVO , 3OCM. RR ... ' _ _ · .... D'>=_'.: 'IIM _ _

-38-FVO' 3004.

a....-m

~ Ïlliala ... FIuioIiDII BM Ca_u

°.

1 ' " CGal

Sorbent transport throueh orifices

Modelling the sorbent transport through orifices is very difficult because a numerous factors are involved. Not on1y the density and pressure differences determine the sorbent flow, but also the size and shape of the orifices and particles influence this transport. Although the correlation used for prediction the sorbent flow from bed two to bed three, uses these factors, the actual value of the particle shape factor and coefficient of discharge have to be determined experimentally.

The correlation used for calculating the sorbent flow from bed four to the combustor bed is based upon another principle. Because bed four is a hopper bed, the sorbent transport from bed four to bed one is not based upon pressure differences. When using the model describing this transport, a couple of important limitatioDS have to be kept in mind. No restriction through the orifices is taken into account (like the Cd-value). By doing so the designer has to be sure that, the orifice used for the particie transport, is large enough and hence the orifice resistance can be neglected. The following limitation makes the use of this model quite difficult:

In the calculation scheme a couple of velocities (U.hor, U. etc.) are determined, with these velocities the gas fluidization velocity in bed four and the gas leak flow are finally calculated. The problem is that what ever these velocities are, there is always a value for the fluidization velocity, which even may seem 'acceptable'. But the gas and sorbent flows in the bed and through the orifice may be enormous to achieve the required sorbent flow. The problem is that there are no distinctive criteria of what is possible and what is not. Chosen is therefore that velocities in the same order of the fluidization velocity are acceptable, when this value is exceeded a larger total orifice area is required.

Because the design of the orifice diameter, by using this correlation, is based upon a maximum sorbent transport at minimal fluidization velocity , the sorbent flow can only be lowered and not increased.

FVO '3004. R~ l)op . . . 'CI '. ia Imoa

-40-FVO , 3OIM.. a.' ... , _ _ O' ... IIriIM;..,

~

4 Mon

RESULTS

Calculating the IFB

The models developed in the chapters 2 and 3, are used to make a preliminary design of a

coal-fed power plant. No attention will be paid to the steam cycle or the different stack cleaning devices necessary to comply to dost emission regulations. These have been treated by van Hout & van Keep[6) in their design of a similar plant. Special attention was paid to use software that is readily transferabie to, and can easily be adapted by other users. For this purpose, the design has been carried out in MathCad 2.52

The design conditions for the power plant are given in table I. These are the same as used by van Hout & van Keep[6).

Table I Design conditions power plant (van Hout & van Keep, 1992)

~ectrical

pow

~

J'~..1.

f'l"\;.J&Y

1!lO-MWê

>

---

---Fuel Coal (polish-5), gas

Sorbent SGC-5oo

Bed temperature 850°C

Number of beds 4

Maximum bed height 4m

maximum SO~ emission 700 mg/Nm3

maximum NOx emission 100 mg/Nm3

()

p

e

~

aJ

;

(J

al

c

(9 (N")+}-(l ( ""'\

~

FVO '3004, Re~ 0 . • .,... iI :' ft ÎII Iuta •• eed Fhaidir.ooi Beo! CombuoIica ol Caal

-42-FVO' 3OOC. R6g r&n ~ .. hII~"I_1III1 ~ ... Cl" ti ., ea.l

The characteristics of the coal and sorbent material used are given in tables II and

m.

Table ll. Characteristics and composition of Polish-5 coal.

Carbon, C weight-% 75.6 Sulphur, S weight-% 0.75 Hydrogen, H weight-% 4.7 Nitrogen, N weight-% 1.3 Oxygen,O weight-% 5.4 Ash weight-% 10.3 fly-ash 80% bottom ash 20% Water weight-% 1.95 Energy content kj/kg 29370

Volatile components weight-% 31.8

Density bottom ash kg/m3 ₂₄₄₈

Diameter bottom ash

mm

2

Table 111. Characteristics of the Sol Gel Condea SGC-5oo sorbent.

Calcium, Ca weight-% 8.91

Po re volume ml/g 0.40

Porosity m3/m3 0.56

Density kg/m3 ₁₄₀₀

FVO , 3004. RRA .... ' _ _

Sulpbation model, Bed 1

NOx emission calculation

cjIsb C{S02,l) C{02.11 L ...•.•...•••.•.. ;' ... NOl tcycle ~sbO ti

Figure 2: Calculation scheme tor sulphation-regeneration

-44-S02 V3 ui u2 u3 , fH2

.

. ·\ ... 1 tcycle Cll Cl2 Cl3 ./

FVO , 3IXM. ~ Daal",," . ti iD beIw $0' FIuidiaol . . c.- ti ol CaaI

This

synthetic sorbent consists of CaO on aporous -y-alumina carrier. This sorbent is made using a sol-gel method in two steps. First an AlOOH-sol is trickted into a two phase system consisting of kerosine floating on a watery NH4

+ solution. In the kerosine phase, the AlOOH forms little

spherical particles whieh, in the NH4+ phase, turn into an alumina-gel. The gelated particles are subsequently dried and caleinated at a temperature of 850°C.

Based on these conditions and the hydrodynamics-, sulphation- and regeneration modeis, a general calculation seheme has been set up, as shown in the figures 2 and~The sulphation-regeneration

scheme can be elarified as follows. (

The eapacity of the power-plant, 100 MWe , in combination with a coal bum-up of 100%

and a 39% thermal yield, fix the coal feed flow into the combustor bed. From this feed, and knowing the composition of the coal, the amount of oxygen needed for complete combustion can be calculated. From this amount of oxygen, the volumetrie air-flow at the reactor temperature can be calculated, which, together with a chosen superficial velocity U I of 3

mis,

fix the combustor bed-area ~.I' When working with a surplus of oxygen, À

larger than 1, the coal feed is decreased to maintain a constant volume throughput of gas. This in order to compare situations with approximately equal superficial gas veloeities.

r

After some preliminary calculations, also a

@

fielght

lSd

s;!:1

fixing the combustor bed volume. The last parameter needed for the sulphation mo êl Is the unreacted core radius

re, which follows from a chosen average degree of CaO convers ion a. The stack

concentrations of sulphur dioxide and oxygen, as weil as the sorbent mass flow are calculated. The incoming sulphur concentration is fixed by the coal and CaS combustion. The amount of CaS depends on the regeneration conditions and thus links, through the sorbent surface concentrations, the calculation of bed one with bed three. To account for a loss of activity of the sorbent, as weil as for attrition, two empirical relations, both functions of cycle time and total residence time, are included. Because the cycle time depends on the other beds as weil, it is estimated for the flrst calculation and used as iteration parameter. The total residence time is fixed at 1500 hours, a time in which the weight of sorbem has decreased 60% and the particles are blown out of the fluidized beds. The output of the combustor bed is used to calculate the NO emission and serves as input for the regeneration model. For the regeneration, both volumetrie gas flow and superflcial gas velocity are set, flxing this bed' s area.' The height of the bed is taken to be equal to that of bed one. The volume fraction hydrogen in the regeneration gas is an input variabie as well and can be used to optimize the regeneration. This entire calculation scheme is iterated until al. a2 and a3 remain constant. The computer program that calculates this

model is given in appendix MathCad Listing of Sulphation-Regeneration model

S ()

t

-be","o

~

s.

f

i

()

(J.)

'B

~d.

h

(i

k.

t

cl

e,tetf/\Ai

vt

e'S

v

0

I

Vt W'tC

~

~

~

re~;

clt

FVO' 3004. R~

1)000...

"

Me • IDa". , ... ~ FIuidizeol BecI CombuoliaD oe Coal % 100% 1 80%

[;]

~RE ., 0,2 0%0 _{1 2 3 4 5 6} 7 8 0

Height bed 1 & bed 3 [mI

Figure 3. Influence of changing bed height on overall performance.

Concentration S02 [mol/m3] alpha1/alpha

[-I

1 . - - - . 0,5 0,8 " . .... 0,4 . ... 0,3 0,4 : ... _ ... . .. , ... 0,2 0,2 ... ' ... ' ... 0,1

°

0 0,02 0,03 0,04 0,05 0,06 0.07 0,08 0.09 0.' 0," 0,'2 0,'3 0, , 4 0, , 5 0,'6 Hydrogen fraction

[-I

Figure 4. Optimal hydrogen content in regeneration bed 3.

-46--C{S02,3} .... a1/a

fVO' 3004. R.,....m ~ .. Inta , I l'haioIDM SM Ca .... _a. el Caal

,,~e.-Based or/ this calculation procedure different IFB configurations have been calculated, and an optiInalfchosen. As expected, and shown in figure 3, an increase in bed height supposes a higher sulphur retention and a higher regeneration efficiency (RE), defined as

4>/,3'CSO~ RE

=

----.,;---=---A.. • fCl 'I'

·actw·--·cx

.r,l M Cl

Because the design should be in physically feasible dimensions, a bed height of 4 meter was chosen. This is the maximum acceptable bed height, and gives acceptable retention as weil as regeneration efficiency values. Another choice that had to be made was the volumetric flow rate of fluidizing gas i~ed three, as weil as the hydrogen content therein. Concerning the hydrogen content, there is

a~

optiïiïi!& as shown in figure 4, around a hydrogen fraction of 0.09. This value was, consequently, chosen. The choice of gas flowrate in bed three follows from the wish to obtain as high a regeneration efficiency and stack S02 concentration as possible. Figure 5 shows that this is achieved with a low flowrate, and thus long gas residence time. However, the flowrate is limited to a minimum to ensure a fluidization velocity larger than the minimal, Umf. From tlgure 6 it can be seen that the choice to operate the combustor bed without a surplus of oxygen seems doubtful. Decreasing the coal-flow, at expense of the power production (!), seems to

decrease S02 emission drastically. From the retention parameter, however, it can be seen that the lower sulphur emission is not due to better capture, but due to a lower amount of sulphur entering the reactor. In any case, emissions are weil below the norms.

X--

'i'l<pl.û,..,.,

Jil"\;o~

~-t' ~d ~!1"

H<.~

Nc

.

R, RE & alphal/alpha [%] U3/Umf3 [-] 100%~~~~~~~~~~---~5 80% 60% Figure 5. -48-2,5 3 3,5 4 4,5 5 5,5

Gas flowrate bed 3 [m3/s]

-R

+RE

-tr alphal/alpha ""'U3/Umf

FVO '3004. RoS'" Mi •• 0 . . ",;' . ,. . . laIea

The hydrodynamic calculation of the commercial IFB coal combustion, is done according to the correlations given in the section F1uidized bed hydrodynamics. Because the sulphation and hydrodynamic models have to be linked, parameters such as mass-flows (coal, sorbent and fluidization gas) and residence time, which are calculated in the S02 model, for bed one and three, are used as input variabie for the hydrodynamic model. Other used parameters like gas velocity or orifice diameter are chosen.

Referred is to the

appen~ix

MathCad Listing of Hydrodynamics model for the used calculation program, and to figure /for the calculation procedure. The assumptions made in this calculation, which were not discussed in chapter 2, will be explained as follows:

Bed one:

Bed two:

Bed three:

With given fluidization gas flow and chosen cross-section area, the superficial gas velocity is set. Chosen is for a high gas velocity (4.5 times the minimal fluidization velo city) to achieve good mixing, although this might cause more attrition.

Because no limitations for this bed were given from the 502 model, most of the used parameters are chosen to achieve good segregation and to optimize the sorbent transport through the orifices. Also a dynamic bed height just below that of the combustor bed is necessary, to make sure the sorbent and bottom ash will flow over the separating wall to the second bed. The residence time has to be large enough to make sure, the sorbent and ash 'have time' to segregate. From Schouten[lOl it was determined that this process will take place within a couple of minutes. Adding a safety factor this will become ten minutes. The bottom ash, removed from this bed, is led into acyclone. The few sorbent particles are removed from this stream and led into bed three. The bottom ash is returned to the combustor bed to make su re a 100 % coal com us Ion talëes pace. Chosen is to use tÏve orifices for the transport of sorbent, in stead of one, although the total orifice cross-sectional area increases with increasing number of holes. Because the gas leaktlow is with five orifices only about 2 % of the total gas tlow in bed three, this will cause no problems. The concentration gradient in bed three will decrease with increasing number of orifices, that is the reason why five orifices are used.

This bed consists only of sorbent particles, which have to be regenerated. From the S02 model, residence time and gas flow are obtained. Therefore only the tluidization velocity is adjustable via the cross-sectional area. But there is another limitation: the bed height, which must be about the same as bed one and two.

Chosen is to set the fluidization velocity at about 2.5 times the minimal fluidi-zation velocity .

H. A. .1P. E H. A. .1P. E Bed 3 Bed 4 :; 'I 11 \) Sorbent Segregation _through orifice

il

$s Sorbem :>< through orifice clIs

Figure 6: Calculating scheme r'or hydrodynamics

-50-Bed four: The sorbent flow through the IFB has to be controlled by this bed. Therefore many parameters are already fixed by the chosen parameter setting of the other beds. One of the few adjustable parameters is the residence time, which is set at ten minutes. From economie point of view, this is very long, because every kilogram ent stored in this bed is a waste of money. But on the other hand it

, \ is, fro process

p

oin

0 vle comfortabie. to have a sorbent buffer, to eliminate,

h~\ f\ ( 'l.e

U"\

or at least mmimizé, c anges in sorbent flow due to small fluctuatioDS in coal flow

~

1

",t\

v.of.

0'"

or fluidization velocity.

1

The fmal design parameters for the IFB coal combustion are presented in the following tabie.

Table IV: Design of the commercial IFB coal combustor

Bed 1 Bed 2 Bed 3 Bed 4

Hb [m] 4 3.9 4 3.5 D [m] 9.8 1.4 1.6 1.4 V [m3_{] 385 8 10 6.5} U [mis] 3.0 0.80 1.56 0.63 e [ -] 0.611 0.46 0.55 0.40 T [sj 26809 780 849 700 cf>r [kg/sj 86 0.5 1.2 0.35 cf>. [kg/sj 7.7 7.7 7.7 7.7 cf>c [kg/sj 8.7 0.179

-

-cf>.o [kg/sj 2.2E-2

-

-

-cf>L [%] 4.5E-2

-

7.5E-2

-SOL [mol/mJ] 7.7E-4

-

0.42

-Do; n [m]; [-]

-

5.0E-2; 5

-

5.0E-2; 5

FVO '3004. R~ [>er'lpbal&ri- .. ~ F1uidizocI BeG Combuoliaa of Coal

~odel Sensltlvlty Analysls. changlng Gas flow. around 4 ml/s PI

-10

-10

X-uls: Rel,Uve oas lIow (I); Y·urs: Relatlve chanoe In bed 3 (lil

Figure 7: Model sensitivity analysis on changes of gas flow in bed 3.

Model Sen.itivity Au&lyei •• changing la.bda. &round 1.1

11

-,

X-a.ais. leh,t.i.,.. l •• kul .. ['I, " •. d ' l aela.ti.,.. ehaD,. I')

Figure 8: Sensitivity analysis on changes in air ratio

-52-10

•

Tau,3 - - H 2.3

•

C{S02.31 - R E

~

~

I

/1

I A I ! 1 1

1

1

f

i

FVO , 3IXM. ae...-.. OeouIpIuarinri. ia ha I cu ... c---.. ol CaaI

Introduction

It is easy to loose track when interpreting data obtained by computer simulations. To avoid generating 'thousaods' of print-outs, it is wise to do a sensitivity aoalysis of the influence of some of the used parameters on the model. By doing so, a better understanding of model aod results cao be achieved. Also knowing which parameters cao be adjusted without influencing the model, can be very useful in up- or downs cal ing. With this knowiedge, final adjustments can be made to the model or its input parameters to optimize the design.

Sulphation and Regeneration

A sensitivity analysis was performed to determine the most important parameters in the combined sulphation-regeneration model. After performing some initial calculations an optimal setting was found, as reported in the previous section. Because of the complex interactions between the different beds, the sensitivity analysis was not performed over the very broad range of possible set-up values, but around this optimal setting. Consequently this analysis serves to visualize the impact of small chaoges in some parameters on the plant performance, once it's operating conditions are set.

As expected, an increase in volumetrie gas flow results in an increase of H2 bypassing the

regeneration bed. Consequently, the sulphur dioxide in the stack gas of bed three decreases, as weU as the regeneration efficiency. Because the gas flow cannot be lowered too much because of the superficial velocity becoming critical, the regenerated bed is operated at 4 m3_{/s. See figure 7.} As can be seen from figure 8, the influence of an oxygen surplus has been calculated. To be able to do this without changing the superficial velocity in bed one, the oxygen surplus was not obtained by increasing the gas flowrate, but by decreasing the amount of coal combusted. This implies that when working with a surplus of oxygen, less than 100 MW power will be produced. As can be seen from tigure 8 the retention in bed improves slightly with increasing air ratio. However, as explained in the Calculating the IFB, this is mainly due to a lower incoming sulphur concentration.

Model Sensltivity Analysls, changlng Sorbent diameter. around 2 mmo 2D

·10

':J

X·aXls: Relal"e Soroent d,anleter {~j; Y·aXls: Relali,e chanqe {II

Figure 9: Model sensitivity analysis on changes in sorbent diameter.

·tO

Model Sensltlvlty Analysi\ :00091n9 gas velocIty, around 0.8 mis \'

i .i..

tO

1'3"\ Re',: '< ",U,dlZat,on 'eloCl', , ." \. Rellt"e cnange IBed 2. Dorf ,013 cm·1 1%1

Figure 10: Model sensitivity analysis on changes in fluidization velocity.

-54-• em!

- e

• Um! 20 - H b • Do • Hb

-

e

dPb - dPo

FVO , JOIM. ae....,av. n .. O!",," . ti. ;. a- ... FIuicIizeol lied c-u-.... ol CoaI

Hydrodynamics

When examining the sensitivity of the model to changes of parameters, it is necessary to make a choice which parameters are being changed and which parameters are held constant. We have chosen to examine changes in sorbent diameter, fluidization velocity , the number of orifices and bubble diameter on the model.

Before calculating the model sensitivity to changes in the sorbent diameter it is predicted that, especially the segregation of ash and sorbent, will become difficult when increasing the sorbent diameter. The. ash fraction in the top layer will consequently increase. Also a strong dependance will be expected on the minimal fluidization velocity .

From figure 9 it can be clearly seen that the minimal fluidization velocity is indeed very sensitive to changes in sorbent diameter. Changing the sorbent diameter by 10 % results in a change of minimal fluidization velocity by 18 %. The same trend is visual for the ash fraction in the top-layer of bed two. The other parameters are not very sensitive to changes in sorbent diameter. Because segregation of ash and sorbent is very important, it is necessary, from hydrodynamic point of view, to chose the sorbent diameter in same order of magnitude as the large ash particles. In a single fluidized bed the bed height and consequently pressure drop over the bed, are presumed to be greatly influenced by changes in fluidization velocity . Because, in this design, the sorbent flow and therefore the bed height etc. is influenced by four beds in stead of one, it is very difficult to predict the sensitivity to changes in fluidization velocity .

Figure 10 shows that the IFB does not react violent to small changes in fluidization velocity ! This means that, when properly designed, the IFB is a --.,;;=;,..,;;.;.;;:;;:;.;;..;;;...;;:.>'

the sorbent flow through the orifices (with in a small range) with great accuracy.

l\-

cl.

0

e.1

~

O~

$ '"

Y

a.",eeJ.t ..

"

"'~

I

~

h

()

t.v

4

,(;\ .... \.

i \,'

~

7

;

6.J

'I

FVO '3004. IbR-'I'S_IIio' ... D=-Iph ri=rim _{ia iDIeI ____ Fluidizooi lIecI Combuoliaa} of Cao!

Model Sensltivity Analysis, changlng number ol orilices, around 3

80

60

-BO

-50

X-axls: Relatlve number of orlflces [~]: Y-axls: Relative change [:Ii]

Fïgure 11: Model sensitivity analysis on changes in number of orifices.

Model Sensitlvity Analysls, cnanglng Bubble diameter, around 0.8 m.

JO :0 10 10 20

[d

Hb

---

0

JO

-...

-20 -10 10 10 ,0

Á-axIS: Relatlve :·_:o,e.) "",eter [%1, Y'aXls Relatlve chanqe [%]

Figure 12: Model sensitivity analysis on changes in bubble diameter.