Korean3~Chem.Eng., 16(3),292-297(1999)



## Effect of Initial Droplet Size Distribution on Sulfur Removal Efficiency in FGD/SDA

Eui-Kyung Oh,Gi-HuneJung,Sun-GeonKim*,Hyung-KeunLee* andIn-Won Kim** Department ofChemical Engineering, Chung Ang University, 221, Huksuk-Dong, Dongjak-Ku, Seoul 156-756, Korea

*Energy and Environmental Research Department, Korea Institute ofEnergy Research,

71-2, Jang-Doug, Yusong-Ku, Taejon 305-343, Korea **Department ofChemical Engineering, Kon Kuk Umvel-sity, 93-1, Mojin-Dong, Kwangjin-Ku, Seoul 143-701, Korea (Received 5August 1998 9 accepted 22 February 1999)

Abstract Dry scrubbing with lime slurryin a spray dryer [spray dryer absorber (SDA)] has been an important technologyfor flue gas desulfi~ization (FGD). Mathematical models based on theheat andmass balances are used to predict SO2removal in the SDA as a function ofilfitial size distribution of slurry di-oplets. Since the existence ofmois~re inthe droplets appreciably enhances the SO~removal,itsremoval efficiencydepends onthe rate ofdrying as well as that of SO~removal itself, both depending on droplet diameter. With the increase in the geometric standard deviation (GSD) ofthe initial droplet size distribution, the efficiencyof SO2removal first increases and then decreases, showing a maximum at a certain value ofGSD. Tiffstrend is altered bytile sorbent content ofthe droplets, expressed as stoichiometric ratio (SR).The decrease in SRmakesthemaximummovetohigher GSD andreduces thevariation inthe efficiency withrespect to GSD. For SR<0.73, a minimumefficiency also appears, ahead of themaximum. Tileresults are well ~,r bythe spedficrates ofboth drying and SO2removalofthedroplets. Keywords:FlueGasDestflfmization, SprayDryerAbsorber, Modeling, Droplet SizeDistribution, Drying, SO2Removal



### INTRODUCTION

In semi-@ FGD processes, the slurry droplets containing sorbent particles are sprayed to reactively absorb SO2 in flue gas while drying by sensible heat of the gas. Dry and spent sorbent particles are either disposed of or recovered. Without a doubt, tile initial size distribution oftile droplets plays
a very important role inthe series ofprocesses described above and consequently in SO2 removal [Kliugspor et al., 1983]. Although many types of spray have been developed, producing quite different size distribution of droplets, there have been very few studies on their size effect. Jozewicz and Rochelle [1984] calculated the time needed to evaporate 99% of the polydisperse spray. They showed the time does not differ significantly from that needed for evaporating monodispel-se sprays for low values of standard deviation, but the time rises dramatically for a standard deviation (expressed in In o-a)larger than 1.0 (or o'a>2.72). They also calculated SO2 removal as a fimction ofthe approachtemperature to saturation for different lime stoictfiomeby,wtfichis defined as tile ratio oftile total moles ofCa(OH)2 to the moles of SO2 inthe flue gas. Allthe results were obtained for the spray of a standard deviation (in o'a)of 1.56 (which can be converted to ~ 4.76, an uncommonly large value) assuming an infinite rate of Ca(OH)2 dissolution. At stoichiometry>1.5 the removal of SQ was the same as predicted by a simple concurrent model without size distribution. At low stoichiometry and close approach to the satorationtenlperature, all oftile Ca(OH)2 was utilized. Their results

WowhomconespoMenceshouldbeaddiessed. E-raail :sgkfln@cattac.ta are, however, too qualitative and unrealistic to generalize and applypractically. In order to get a clear idea ofthe droplet size effect onthe SDA performance, we quantitatively investigated the effect of polydispersity on the evaporation of water, removal efficiency of SO2,and thus sorbent utilization in SDA, modifyingthe previous model [Jang et al., 1996].


### FUNDAMENTAL EQUATIONS AND NUMERICAL 

### APPROACH

292 In our model, tile sluily droplets containing Ca(OH)2 as sotbent particles are sprayed in the top ofthe SDA and the flue gas consisting ofnitrogen, water vapor and SO2 is introduced above tile spray. Since tile sprayed droplets injected radially lose their velocities in an extremely short period oftime, the flow ofboth the gas and droplets is assumed concurrent and plug flow. We also assume there is neither circulationnor tempem~re distribution in a droplet andneglectheat loss across the SDAwall. Tile size disliibution funcgonoftile sprayed droplets, fide)is assumedlognormal, whose applicability hasbeenproven:

f (ln_d~-ln_d~ 

## l__!__exp (1)

2(ln ff~): 

## f(d~) 2J~-a

## (~

where fie is tile geometric standard deviation, ctdtile droplet diameter and cletile geometric mean diameter of droplets. All tile assumptions above are tile same as those of Partridge, 1987; Shih, 1989; Kolluri, 1991 and Yuan, 1990. 

### 1.Rate of SO: Removal The rate of SO: removal by di-oplets can be expressed asEffectofInitial Droplet Size Disbibulionon Sulfur RemovalEfficiencyin FGD/SDA 293

[Kolluri, 1991]:

m~- 1 1 t~d~Sa~ (2) --+ q--

where Qc and Ca, are the concentrations ofsorbent and SQ in liquid and gas phases, respectively,DI,,and Dz~are the diffusion coefficients of SO2 and sorbent in the liquid phase, respectively ; H is the HerLry's law constant ; k~, and k~, are the mass transfer coefficients of SO2 in liquid and gas phases, respectively; S the hypothetical thickness ofthe liquid film sur-rounding the sorbent particle ;RL is the fraction ofthe sorbent ura-eacted inthe sorbentparticle andNp is the number of sorbentparticles in a droplet. Eq. (2) canbeused only it"the moisture content (X) of the droplet exceeds a certain value, X~, while for X <X~,the rate of SQ removal is calculatedby gas-solidreaction, m, k,C~, where k~ is the constant ofthe gas-solid reaction. The threshold moisture content, X; is estimated by X~= 6.1*RH*X~ [Shih, 1989], where RH is the relative humidity of outlet fluegas and X~is the equilibrium moisture content ofthe sorbentparticle. 

### 2. Governing Equations The structure ofthe governing equations is almost unchanged compared with those appearing in our previous publication [Jang et al., 1996]. The droplet-phase variables in the gasphase balance equations are, however, expressed in the forms integrated with respect to the diameter ofthe droplets. The balance for the mass of the sorbent Ca(OH)2 (m~) in
a droplet with a diameter ofde is : dr~(d~) .m0(d~) (3) dt i~ where i~is the stoichiometric ratio of SO2 to Ca(OH)2 based
on mass. The balance for the mass of water (m~) in a droplet with
a diameter ofdeis : dm~(c!~) .m~(ctd)row(d9 (4) dt i~ where i~ is the stoichiometric ratio of SO2 to water based on mass, and nb is the &ying rate ofwater. The rate is expressed according to the types of drying-rate period~ respectively, as [Partridge, 1987] : m~(d~)=2~rC,d~D~hll Y~w for constant drying-rate period(5)

1-y,,~


### m~(d~)=2~rC,

d~D~hl y~X X~ 1-y,,~X~.- X. for falling chying-rate period 

### (6) where Ct is the total molar concentration of the gas phase, y~ and y,,~are the mole fractions ofwater vapor in bulk gas and at the surface ofthe droplet, respectively, and De~ is the diffi~sion coefficient ofwater vapor in the gas phase. The Wansition from the constant drying-rate period to the falling drying-rate period occurs atthe critical moisture content, Xc. The energy balance for a slurry droplet with a diameter of d~consisting of sensible heat supply from the gas phase, latent and sensible heat consumption by water evaporation, and heat effect from dissolution ofgaseous SQ into the droplet, is : d[m~(d~)%'~(dDT~(d~)] m~.(d~)Ib +m~(d~)h= dt +~d~h,(G)[T~-TZG)] (7) where md, %d and Te are the mass, specific heat and teraperature ofthe droplet with a diameter of de, respectively, 1%and t~ are the specific enthalpies of water vapor and gas-phase SO2, respectively, ht the heat transfer coefficient in the gas phase, and T~the gas temperature. The SO2 mass balance in the gas phase is:
dxn~,~ dt NicTic~ f(dd)ddd (8)
where m~, is the mass flow rate of SQ in the flue gas, N the total number flowrate of droplets (number of droplets/see) and the integral term represents the mean rate of SQ removal over the whole spectrum of droplet size. On the other hand, the humidity (Y~) balance in the flue gas gives: dH m~ =Ni~nb(de)f(dd)ddd (9)
where ma is the mass flow rate of dry flue gas. The integral term again represents the mean rate of drying over the whole spec~ama of droplet size. The energy balance equation in the gas phase, cansistiig of sensible heat supply out ofthe flue gas, and latent and sensible heat effects arising from water evaporation, is: d(m % T ) ~-~t '~ ~ =NI= [m~(d~)H~ /rddl~(dd)[T~ Td(dD] m~(dDH=]f(dDddd (10) where rn~and %~ are the flow rate and constant-pressure specific heat of total gas, respectively. The right-hand side term also contains an integral form over the whole size spectrum. 

### 3. Numerical Scheme The whole spectlxnn of droplet size approximately in the range of in d~+3 in G is divided equally in logarithmic scale into 11 classes. For Eqs. (3), (4) and (7), each class of sizehas corresponding expressions to yield a total of 3• ordinary dig ferential equations. For Eqs. (8), (9) and (10) for the flue gas, the integral tenns in the right-trand side are calculated numerically. All the equations are rewritten in terms ofvertical distance instead oftime by the following relationship : dz dt=-- (11) Ud(dd) where Ue is the &oplet velocity. As proved in ora-previous study [Jang et al., 1996], the dropletvelocity is assumed equal to the gas velocity U~, which is recalculated at each iteration. 

### KoreanJ. Chem.Eng~0fol.16,No. 3)E.-K. Oh et al.

145 ~ 5% 913 ppm

11~

1 15.2 sec 82pm 37.8~ 1.25pm 29.2 %

6% Parameters Base-line value

0 E p}
g "6 

### g

LL Inlet gastemperature % water vapor in inlet gas In let SO2concentration in the gas Approachtemperature to saturation Stoichiometric ratio Residence time Inlet droplet diameter Inlet droplet temperature Inlet sorbent particle diameter Critical moisture content Equilibrium moisture content 1.0

(18

O = ' ,

"6 (1'* g . ~ . . . , & - - ' ~ ~l'-----~'&---'-- SR=I.0 * ~--~g=l.0
ii --&-- ~g=20

I I I I O~Qon Q2 Q4 Q6 Q8 1.0 Z Fig. 2.Variation in droplet size distribution with respect to dimensionless axial length, Z (SR=I.0, o'F2.0).

The axial distance isthen normalized bythe total SDA length.

The thirty-six ordinary differential equations are then solved by LSODE package, one ofthe initial-value ODE solvers. The sorbent particles in our study are monodisperse and their size is fixed, as shown in Table 1. Their number in each droplet is proportional to its volume (d~) forthe given SR.

The SDA data used in this study are Partridge'sbaseline conditions, which have been quoted by many authors [Partridge, 1987; Shih, 1989; Yuan, 1990]. Partridge's apparatus has a diameter of2.13 m, a length of2.5 m. Table 1 shows the baseline condition set up by Partridge.

The initial droplet diameter shown in Table 1 is used as the geometric mean diameter dg. The geometric standard deviations range from 1.00001 (close to monodispersity)to 2.0. The variables in Table 1 are all set to their baseline values except the stoichiometric ratio (SR) which is the most significant variable for the SO2 removal [Jang et al., 1996]. SR varies from 0.6 to 2.0.

RESULTS AND DISCUSSION

Fig. 1 shows the initial size distributions ofdroplets forthree different values ofGSD (a~).The geometric mean diameter of the droplets fixed at 82• 6m is the same as the diameter of monodisperse droplets (a~-l.0). For a~-l.2, the droplet size

25 294
Table 1. Baseline condition

~%:1.2

1.0 

### g
as 4=

(10= *,

. . 105 104 103 dd, m Fig. l.Variation in droplet size distribution with respect to dimensionless axial length, Z (SR=I.0, o'g=1.35). May, 1999 1.0

Q8

06

Q4

02

no

QO Q2 Q4 Q6 Q8 1.0 Z Fig.3.Effect of initial geometric standard deviation of droplet size distribution, ag on exit flue-gas humidity.

ranges from 50• 6 m to 140• 

## 6m,for az-l.4, from 30• 6
m to 250• 

## 6m, and for az-2.0, from 10• 6 m to 650• 6
m. Figs. 2 and 3 show the axial distributions ofthe fraction of sulfur removal in the flue gas, as a parameter ofGSD, for SR1.0 and SR-0.6, respectively. Formonodisperse droplets, the variations in both cease very close to the inlet, but the increase in GSD spreads out their variations further towards the SDA outlet. The figures also show that the fraction for SR-1.0 and az1.35 exceeds that for monodisperse droplets around the middle ofthe SDA while the fraction for SR-0.6 and az-l.80 does
nearthe outlet ofthe SDA. The reasons why will be explained later. 1.The Effect of Size Distribution of Slurry Droplets on Their Drying

Fig. 4 shows the variation in droplet size distribution along the SDA axis forthe initial a~-1.35. Since, as shown in Eqs. (5) and (6), the rate ofdrying per unit droplet is proportional to d~, the corresponding specific rate (rate per mass ofdroplet) is inversely proportional to d~.Therefore, the smaller the droplets, the earlier they dry up. As a result, alongthe axis, the size distribution ofthe droplets becomes, in turn, skewed with long head (Z-0.01), symmetrical (lognormal) but broader than the initial one (Z-0.05), and skewed with long tail (Z-0.1, 0.5). Finally the lognormal distribution with the initial broadness is recovered (Z-1.0), as all the droplets dry up. In Fig. 5 fortheEffectofInitial Droplet Size Distribution on Sulfur RemovalEfficiencyin FGD/SDA 295

1.4

"O~'1= 1.2 ~" 1.o -% "o (18 _c
-o (16

~
,1= a2 "o (10 106 1135 164 103 da, m Fig. 4. Effect of initial geometric standard deviation of droplet size distribution, % on exit flue-gas temperature. 70oE 4~

1.0 20 % Fig. 7. Variation in sorbent conversion of droplets with different sizes along SDA axis (SR=I.0, o'g=2.0).

Q7

"xD __c v,?,
,4= v "10 [ ~z=0 i.--o..-z=0.0. 05 [~ z=0.0~ I"A --z=Q1 I-'- z=o5 Q4 I""-V"" z=l.0

a2

Ol
(10 .

10-6 105 10"4 10 -3 

### dd, m Fig. 5. Effect of initial geometric standard deviation of droplet sizedistributionon sulfurremovalefficiencyas a parameter of SR.

distribution of a~-2.0, similar trends are observed. However, the large droplets in the broadened distribution do not dry completely even at the outlet and the distribution ends up with a long tail.

Fig. 6 shows the effect of droplet size distribution on the flue gas humidity at the SDA outlet, as a parameter of SR. The distribution effect is hardly observed forthe systems with ~<1.4, where most droplets dry up within SDA. However, for ~>1.4, the humidity decreases appreciably with ~ due to the incomplete drying, as described above. For the systems with narrower distribution (a~<l.4), the increase in the sorbent
mass (SR) slightly decreases the humidity since the sorbent needs more equilibrium moisture which cannot eventually evaporate from the droplets. It is suggested that the effect is obscured for the systems with broader distribution, due to the incomplete drying. The effect of size distribution on the flue gas temperature, shown in Fig. 7, is reversed, since the gas humidity increases at the expense ofthe sensible heat ofthe gas. 2.The Effect ofSizeDistribution on SO2 Removal Efficiency

Fig. 8 shows the conversion ofsorbent particles in each class of droplets along the SDA axis for the system with SR-1 and the initial ~-1.35. As shown in Eq. (2), the rate of SO2 removal per unit droplet is proportional to d~rwhen the third term in the denominator in right-hand side (sorbent dissolution term) is neglected. Ifthe term is dominant, the SO2 removal is proportional to d,~,since Nj, is proportional to d~;.The corresponding specific rates (rates per mass of droplet) are, therefore, inversely proportional to d,~(n_<1). Due to higher size-dependence ofdrying (inversely proportional to d,2~)than SO2 removal, the drying of smaller droplets occurs much faster than their SO2 removal (thus, their sorbent conversion) does. As described in a previous paper [Jang et al., 1996], the SO2 removal is appreciable only for the droplets having free toolsQ074

Q072

Q070

I % Fig. 6.Variation in sorbent conversion of droplets with different sizes along SDA axis (SR=I.0, GF1.35). 1.0

--n-- z=0,01 I /~ 08 --o-- z=0.~ I O~ --V-- z=-Q5 I ~O 06 --,11~ z=1.0 I r "6

'-O 02

QO i i ~1= 9 9 = = i , , , ,

105 104 103 dd, m Fig. 8.Variation in sorbent conversion of droplets with different sizes along SDA axis (SR=I.0, o'71.35).
Korean J. Chem. Eng.(Vol. 16, No. 3)296 E.-K. Oh et al.
1.0 SR=l.0,cg=21 --9 08 --e--z=O.05 --&-- z'=OI --V-- z=-O5 --4,~ z=l.0

9 ~ 114

O a2

00~

10

`5 10 4 10 `3 rid, rn Fig. 9. Variation in sorbent conversion of droplets with different sizes along SDA axis (SR=I.0, 

## O'g=2.0). 0.75

0.70' --~==~1~-4~~ I~&-- SR=0.9 ~oE ~ .~--~---.~= I-~ sR-~.0 o,66,- _ _ ~ I+SR=!5

0.60 60 '~ 0.55 r'- o , o 0.50 9 LL 0.45 1.0 1.2 1.4 1.6 1.8 2.0 Og Fig. lO.Effect of initial geometric standard deviation of droplet size distribution on sulfur removal efficiency as a parameter of SR.

ture. Therefore, the smaller droplets have higher conversion
as far as the moisture is retained in them, but their conversion is almost frozen as soon as their drying ends up. On the other hand, larger droplets retain moisture much longer than smaller ones and have more opportunity to enhance their conversion by the reaction with SO> As shown in the figure, the droplet size showing maximum conversion, therefore, moves to the larger one along the SDA axis and, at the outlet, the largest droplet has the highest conversion, since it has almost dried up (Fig. 4). Fig. 9 shows the results for %-2.0. Compared to Fig. 8, the conversions for the droplets in the lower part of the broadened distribution are frozen at lower values due to their increased drying rates. On the other hand, since the droplets in the upper part of the distribution are not completely dried (Fig. 5), their conversions decrease with the diameter ofthe droplets, as described above. Therefore, the largest droplets do not have the highest conversion even at the exit ofthe SDA.

The broadening effect ofthe droplet size distribution on the overall SO2 removal efficiency, therefore, appears somewhat complicated. It depends on whether the loss of SO2 removal capacity in the smaller droplets can be recovered by its gain in the larger droplets or not. Fig. 10 shows the effect of size distribution on SO2 removal efficiency as a parameter of SR. For SR>0.73, the efficiency increases with GSD (%) up to a maximum and then greatly decreases to a much lower value than the monodisperse (c~z-1) efficiency. For SR>I.0, the SO2 removal efficiency ranges from 50 to 70 %. It is suggested that the slight broadening ofthe size distribution increases the time of water retention in larger droplets, which leads to a greater chance for SO2 removal as a whole, and makes the gain in larger-sized droplets exceed the loss in lower-sized
ones more and more. However, with further increase in %, the overall removal efficiency declines since the gain is substantially reduced and cannot recover the loss due to the reduction in the rate ofSO2 removal, as described before (inverselyproportional to d,~,where n<l).

With the reduction of sorbent content (SR), the GSD showing the maximum efficiency (c~ma,)moves to a higher value. It is suggested that the decrease in SR reduces the rate of SO2 removal, due to the decrease in both the number (Nj,)and liquid-phase concentrations (Qc) of sorbent particles [Eq. (2)], and makes the removal rate more controlled by sorbent dissolution. Therefore, SO2 removal depends less on the droplet diameter, since n decreases from unity in the size dependence of its specific rate, d,r As a result, for lower SR the decline ofthe efficiency begins at higher GSD. Further reduction in SR below 0.73 shows a minimum efficiency at a certain value of %<%

...... This implies that such a small increase in broadness is not sumcient forthe positive effect on the SO2 removal in the upper part of the distribution to exceed the negative effect in the lower part, due to much lowered rate of SO2 removal. This and the lowered dependence on the diameter make the efficiency variation with respectto GSD appreciably reduced. For example, for SR-0.6, the SO2 removal efficiency decreases upto o-~-1.2,then increasesto a maximum at %-1.8 and finally decreases afterwards, and the efficiency varies only between 46 and 53 %.
CONCLUSION

We have numerically investigated the effect of the droplet size distribution on the SO2removal efficiency of the spray dryer absorber (SDA). In general, the size distribution affects the efficiencythrough the variation in both the moisture-retention ability and SO2 removal rate ofthe droplets.
1.The size distribution of droplets becomes distorted and broader until their drying is completed.

2.High polydispersity makes the exit gas humidity fall and the exit gas temperature rise.

3.The droplets, which are about to dry up, have the highest conversion. The size of the droplets with maximum conversion becomes larger along the SDA axis.

4.The effect of size distribution on SO2 removal efficiency becomes significant with the stoichiometric ratio of sorbent to SO> For SR>0.73, the slight broadening in the distribution enhances the SO2 removal efficiency, while a further increase in % significantly lowers the efficiency. The maximum efficiency
moves to higher % with the reduction in SR.

5.For SR<0.73, the droplet size distribution affects the reMay, 1999Effect ofInitial I~@ct Size Distribution on Sulfur Removal Efficiency in FGD/SDA 297

moval efficiency less, though showing both the minimum and maximum efficiencies with respect to the standard geometric deviation ofdroplet size distribution.

ACKNOWLEDGEMENT
This work was supportedby Electrical Engineering mid Science Research Institute in SeoulNational University (96-050).

REFERENCES Jang, S.H., Oh, E.K., Lee, H.K. and Kim, S.G., ~Model Development of SprayDryerAbsorber FGD Process" 

### Clean Technology (Korean), 2, 80 (1996). Joze~vicz,W. and Rochelle, G.T., ~Modeling of SO~ Removed by SprayDryers~'Proc. FirstAnnual Pittsbmgh Coal Conf., Sept. 17-21, 663 (1984). Klingspor, J., Karlsson, H.T. and Bjerle, I., ~A Kinetic Studyof the Dry SO2-Limestone Reaction at LowTemperature," 

### Chem. Eng. Commun., 22, 81 (1983). Kolluri, R., Hatcher, Jr., W.J. and Jefcoat, L.A., ~Simulation of Spray Drying with Reaction :Absoiption of Hydi~gm Sulfide in Ammoniacal Solution ofZinc Chlofide~'

### Drying Technology, 9, 367 (1991). Partridge, G.P., Jr., 

### '% Mechanistic Spray Dryer Mathematical Model Based onFilm Theoryto Predict Sulfur-DioxideAb-sorpfion and Reactionby a Calcium Hydroxide Slurry inthe ConstiltRatePeliod," PhD.Dissertation,TennesseeUniv.,Kiloxville, U.S.A. (1987). Shill, H. 8., "Silllulation ofSulfur-Dioxide RemovalviaHydrated Lime Slurries in a Spray Dryer Absorber Flue-Gas Desulfurizafion Systen~' Ph.D. Dissertation, AlabamaUniv., Tuscaloosa, U.S.A. (1989). Yuan, C. S., "Simultaneous Collection of SO2 and NO~via Spray Drying:Using Sodium Based and Calcium Based Sorbents with Select Additives"Ph.D. Dissertation, Univ. of Illinois at Urbana-Champalgn, U.S.A. (1990).

Korean J. Chem. Eng~(Vol. 16,No. 3)