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Chamcd Engmemng Scmcc 1577 Vol 32 PP 229-232 Per@moo Press Pnnted m Great Bntam

INTERFACIAL AREA IN THREE-PHASE

FLUIDIZED BEDS

CZESJ LAW STRUMI LCO and TADEUSZ KUDRAL6dz Techmcal Umverslty, Institute of Chemical Engmeenng, Poland

(Received 14 anuary 1976, accepted 20 July 1976)

Abstract--On the basis of mass transfer models and the results of our previous mvestmtions, Danckwerts’pseudo-first order reaction method was adapted for the determmation of mterfacml area m a three-phase flmtid

bed The results of our expenmental mvesttgattons on the absorption of carbon &oxlde UI aqueous sodturn hydroxtde

are presented The works of other authors are analysed

Turbulent bed contactors have been the SubJeCt of

numerous mvestigations[1-4] One of the essential

parameters for the correct design of such an apparatus IS

the lnterfaclal area&71 Analysis of such data shows

considerable dlscrepancles m results obtamed by each of

the authors both m the character of changes and the

values of mterfaclal area These drscrepancles, amongother thmgs, m&t be produced by mcorrect mterpreta-

bon of expenmental data caused by neglectmg the

different hydrodynanuc condltlons of two-phase gas-

hquld systems, mto which movable packmg elements are

mtroduced

For the correct mterp retatton of experunental results

on heat and mass transfer m three-phase fluidlzed beds,

the phenomena at the Interface, mam ly surface renewal

rate, are of basic unportance

In tbs paper the mves@a tion has been concerned with

the determma tion of the mterfacml area m the turbulent

bed contactor, takmg mto account the hydrodynanuc

characterrstlcs of three-phase flmdlzed beds

Danckw erts’ pseudo-fist order reaction method [S, 91

which enables the independent d etermmation of mterfa-

cml area and mass transfer coefficient, was adop ted

When a first or pseudo-first order lrreverstble reaction

with a rate constant k, occurs, the solution of the dtiuslon

equation on the basis of Danckw erts’ model[8] leads to

R = acd/(Dk , + s)) (1)

or

xzQ2k+Qzs

c*D 1 (2)

The absorption rate IS a hnear function of kl If al l

remammg parameters are constant the plot of expresslon

(2) agamst k, should gwe a stratght hne of slope a2 an d

mtercept Q’S

In this method the correct results are obtamed when the

chemical reactton rate constant IS of the same ord er as the

interfacial surface renewal rate Takmg m to account the

bh turbulence of the fhud stream m a three-phase

flmdlzed bed, carbon dloxlde-so&urn hydroxide was

chosen as a test system Thus system ought to fulfil the

condltlons of apphcabtilty of Danckw erts’ method

-AL-o0

The scheme of exp ertmental eq mpm ent IS shown m Fe

1 The construction parameters of the movm g bed column

(such as free cross section of the turbognd plate, he&t of

measunng sectron and the method of hqntd dlstrrbution)

were accepted on the basis of our earher stu&es and the

hterature dataThe mam part of the column-measurm g section was a

glass pipe 0 085 m m ner diameter and 0 5 m he&t

At the column bottom, the turbognd plate was placed

with free cross section equal to 0 65 and slot width equal

to 2 mm On the bottom plate the layer of packmg

elements with a height of Ii&, was placed

The exp erunents were carried out by carbon &oxtde

absorption m the cuculatmg sodium hydroxide solution

from an au mixture

One experunental pomt was obtamed dunng absorption

of COz m NaOH solution with constant hydrodynam ic

con&tlons of the three-phase Amtied bed, and with

Fig 1 The scheme of expenmental eqtupment 1 Section V&I

movmg bed, 2 Cuculatmg tank, 3 Demster, 4 Turbomd plate, 5Elements of packmg, 6 Spray, 7 Elecplc heater, 8 W ater coohng,9 Sturer, 10 Onfice meter, 11 Sensor of termoanemometer, 12Blower, 13 Gauqe, 14 Carbon &oxide flask, 15 Carbon Qoxlde

rotameter, 16 Liqrud pump, 17 Tank, 18 Pressure pulsation

electromc system, 19 Llqmd rotameter

229



230 C ZESZA W STRUMIEZO and TADEUSZ UDRA

constant concentration of CO2 m air Due to CO,

absorption, the hydroxyl Ion concentration changed

durmg the course of the experiment

The concentration of the absorbmg solution was

determined by potentlometic tltratlon of solution sam-

ples taken at regular intervals of 10 or 5 mm

Constant hqud and gas temperatures were mamtamed

by an automatic temperature regulation system

Gas flow rate was measured by or&e plate and

thermo-anemometer ZBS 11 The hquld rate was deter-mined by rotameter The pressure at several pomts of the

apparatus was measured by means of an electromc

system

The absorption rate was determined from the relation

The condltlons of experunent were as follows

packmg elements, diameters d, = 10 0, 7 5 and 5 0 mm

packing elements, density pW= lOSOkg/m’

static bed hewht H,, = 26160 mm

hquld flow rate L = 33-l 10 m3/mz h

superfacial gas flow rate uo = 0 5-3 5 m/s

CO2 concentration m the a=

at inlet (constant m

absorption runs) c = 34% vol

OH- concentration in solution

before absorption COH- = 2-3 g ion/l

overall hquld volume v=181

gas temperature To = 303°K

liquid temperature T L = 303°K

The liquid analysis was carried out by a standard

potentlomemc tltratlon[lO] The gas analysis was per-

formed by automatic analyser INFR ALYT T

TREATMENTOFDATA

When the gas side resistance 1s neglwble, the basic

equation of Danckwerts’ pseudo-first order reaction

method of determination mterfaclal area 1s

y= R2 = a%1 + u*sp =H2D

The necessary quantities reqmred for Danckwerts’ plot

were calculated as follows

(4)

The experunental pomts descrlbmg the dependence of

NaOH concentration m the absorbing solution on tune

were approxunated by a polynomial of second order On

the basis of the prehmmary experiments, the lmear

change of solution volume, resulting from the waterevaporation and hquld drop entramment, was taken mto

account

The physical solublllties of CO1 in hydroxide and

bicarbonate solutions were calculated by Van Krevelen

and HoftlJ zer [ 111

log (H/H,..) = - 2 KJ

usmg the values of K c and H , given by

The dlffuslvltles were estnnated by

relation

I , T = const (6)

(5)

Barrett[l2]

means of the

where a has been taken as 0 85 (after[l3])

The equation aven by Barrett[ 121 were used to

calculate viscosity of solution, dtiuslvlty of CO* m water

and pseudo-first order reaction rate constant

Pa~Qal pressure of COz was calculated as the anthmetlc

mean value of mlet and outlet

RESULTS

Durmg our expenments a constant change Wlfh time of

hydroxide ion concentration m the absorbmg solution was

observed The relation between hydroxide ion concentra-

tion and tune for some of the test series 1s shown m Fig 2

The polynomial coefficient a, by means of which

experimental points were described for all series was of

the order of 10-5-10” gmolell mm* The correlation error

did not exceed 1% It allows us to state that If the

conversion of NaOH does not exceed 30%, the change m

concentration of hydroxide ion with tune may be

described with sufficient accuracy by a straight line The

6

a

oa

I I I T’ I I I I I Itr,._r I

Fe 2 The concentrationof hydrovlde ion vs absorption tune



Intmfaclal area m three-phase fluldmzxi beds 231

results confum those of Kosew ef al [S] and Porter et

al [14], who observed a sun&r linear relation for the

COrNaOH system

A plot after Danckwerts’ IS shown as an example m

Fig 3 In all the test series, the experunental points

on Danckwerts’ plot lay on a straight line with a mean

devlatlon of 2% It shows the apphcabrllty of Danckwerts’

model m descnbmg mass transfer m a three-phase

fludlzed bed Also It ndicates that the mterfacral area and

mass transfer coefficient might be determinable by

Danckwerts’ method

It was found, that the surface renewal rate m the

three-phase flmdlzed bed I S of the order of 103-lo5 s-’

Because the range of pseudo-first order reaction rate

constant was of the order 104, he observed results can be

treated as correct The CO,NaOH system has been used

by many workers, because the reaction hnetlcs are well

known In these studies the reaction between carbon

dloxlde and hydroxide ions was treated as mstantaneous

The rightness of such an assumption arose from the fact

of very small surface renewal rate m comparison wtth the

absorption rate constant In such case the equation

N = (c, - cr) d/(Dls + k,) (7)

sunphfies to the form

N = (c, - C,)V/(Dkl) (8)

which 1s vahd for absorption with a very fast chemical

reaction

In this paper It has been shown, that the surface

renewal rate 1s comparable quantltatlvely urlth the

chemical reaction rate constant, so that 111 bs case It 1s

not only the speed of chemical reactron which controls thetotal mass transfer rate According to eqn (7) the mass

transfer coefficient for the absorption of CO* m NaOH

solution m a turbulent bed contractor should be calculated

from the equation

k= = d(Dls + k,) (9)

The analysis of the results of works by Kosew et al I S]

Gelperm et al [71 and Woimak and Bstergaard [6], carried

0 t 2 3 4 5 6 7 8

Fig 3 Danckwerts’plot

out on the absorption of CO, m NaOH solutions m

columns with moving beds, showed that they applied the

method of determination of mterfaclal area for sieve

plates

Consequently, for calculating the hqud phase mass

transfer coeficlent they used the equation

(10)

We found [151on the basis of the analysis of the relations

between parameters E, E , and M (fully discussed by

Danckwertstg]) that the method of determination of

mterfaclal area used m[S-71 1s not appropnate and could

lead to erroneous estlmatlon of this important parameter

Moreover, It was found that they used m their

calculations the reaction rate constant values gven by

Nllsmg et al [ 131 However, the work by Pohoreclu[16]

shows that the reaction rate constant, data of NiJ smg

tiers from the values obtamed by others authors by

about 40%

So, the values of interfacial area obtained m the

work 15-71 can not be treated as completely

unquestionable

The change of mterfaclal area w&h some parameters of

turbulent bed contactor performance obtamed from the

basis of the present mvestlgations I S shown by way of

example m Figs 4 and 5

It 1s to be seen from the figures that an mcrease 111 as

velocltles and static bed height up to a certam value leads

to an increase m the mterfaclal area At higher values of

those parameters the interfacial area decreases It has

been stated on the basis of pressure osclllatlon[17], that m

this range of gas velocity and static bed he&t, the

homogemety of the floatmg bed was disturbed

The results of our own experiments up to the maximumvalue A(u, s 3 m/s, H,, s 120 mm) were correlated by

the empmcal relationship

A = 2 15Y~“~L”~H~~~‘~;;O~, m2/m2 (11)

The eqn (11) was obtained on the basis of statistical

t505 75 10

A ~r&n? d,lmm

/

0 I I L /mJ/m*h j50 80 110

Fig 4 Dataof mterfaczal area measurements



232 CZ~WAW STRUMIUOand TADEUSZKUDRA

150 20 LO 60 80 10 0 120 IL0 I60

A Im2/m3 J~rrn7rnl

0 c.@n/sI

0 05 10 r5 20 25 3,0 35

Fig 5 Data of mterfacml area measurements

methods, using multiple regressron[l81 For the level of

slgmficance equal to 0 05, the correlation coefficient wasequal to 0 945 In the range of 95% of confidence mterval

were 93% of expernnental pomts

It seems, that the proposed method of determmmg the

mterfaclal area 111 hree-phase fluldued beds could help m

obtammg a better understandmg of the heat and mass

transfer mechamsm m a turbulent bed contactor and

permit the correct design of such eqmpment

mterfaclal area per unit volume of floating bed

NtYI’ATlON

mterfacial area per umt cross section of column

concentratton of carbon dtoxlde at interface

dtiuslvlty of carbon dloxlde m hqmdsolubfllty of carbon dioxide m liquid

iomc strength

pseudo-fist order reaction rate constant

solubdlty factor

rate of mass transfer

parttal pressure

rate of absorption of carbon dloxlde per umt

absorbing volume

surface renewal rate

tune

volume of absorbent m the column

stolchlometic coefficient of reaction

Greek symbol

7 vlscosrty of hquld

I ndices

1 instantaneous value

W water

dc,- rate of absorbent

dt change

active part concentration

It lmmmJcEs

[l] MIodzmskl B and Warych I, Nowa Technrka WNT,

Warszawa 1973

[2] Koch R and Kuhsa R, Kokumny polkowe z warstwu

[3 1

c4 1

ISI

161

[7 1

181

191

WI

Cl11

WI

1131

r141

WI

[161

1171

ruchomego wypeln#enur Prace naukowe Inst Lnz Chem I

Urzadzen Cleplnych P W . Wrociaw 1973

Stumdlo Cz , Adarmec J &d Kudra T , Ch& tucky’ Prrimysl

1974 24 85

Strumdlo Cz , Adamlec J and Kudra T ,Znt Chem Engng

1974 14 652

Kosew A, Peev G and Elenkow D , Verfohrenstechnlk 19715 340

Wozmak M and Ostergaard K , A report on mass transfer

rnuestrgutlons m a turbulent bed contactor Techmcal

Unrverslty of Denmark, Department of Chemlcat Engmeer-

mg, Lyngby. Denmark 1972

Gelpenn N I , Grlszko W Z ,MlchaJ low W A and Sokolow

W I, CHZSA 72

Danckwerts P V , Gus-Lrquul Reuctrons McGraw-Hill,

New York 1970

Danckwerts P V , Kennedy A M and Roberts D , Chem

Chemiczne] PL

Engng Scr 1963 18 63

Ewmg G W , I nstrumental Methods of Chemical Analysrs,

McGraw-Hdl, New York 1960

Van Kreveien D W and HofQzer 0 I, Chum Znd Congris

I nternational de Chemle Zndustnelle 1948 168

Barrett P V L, Ph D Thesis, Umverslty of Cambrrdge

(1966)

NIJ S~II~ A T D , Hendrlksz R H , Kramers H , Chem

Engng Scr 1959 10 88

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Engrs 1966 44 274

Kudra T , Ph D Thesis, Technical Umverslty, Lodz (1975)

Pohoreclu R , Prace Nuukowe Pohtechmka Warszawska.

Chenua nr 5, 1970

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[IS] Volk W, Applred Staflstrcs for Engmeers, McGraw-H&

New York 1969

[19] Danckwerts P V and Sharma M M , I Chem E Review

Senes No 2 The Chemical Engmeer, CE 244, 1966

APPJmDlx

COINaOH reachon takmg place m ths system wdl be of

pseudo-fist order d the mequahty aven by Danckwerts’ and

Sharma[l9]

&s)J( 1k, ,COH_

?r -zc (12)

IS fulfilled

Under the experunental conditions, takmgD = 153 X o-’ cm*/s

k, = 5 51 x lo4 s-‘. H = 146 x lo-’ mole/cm3 at, z = 2, s =

1 34 x l(r s-‘, p = 2 76 x 10m2at, con- = 2 mole/I, we have found

the nght-hand side of the relation (12) lo3 times of the left side

The temperature rise near the Interface. calculated accordmg to

Danckwerts[l] was about 10-4”C, thus satisfying the Isothermalabsorption assumption

The error Introduced by neglectmg the gas-side mass transfer

resistance was estunated on the basis of experunents with

absorption of pure carbon &oxlde m sodium hydroxide solution

This resistance was found to be less than 3%[15] The error m

evaluatron of rnterfacml area by eqn (3) does not exceed 5% (on

the basis of error analysts)

The experlmental matenal and the calculation of the results as

well as the mterpretatlon of the theoretlcal and expenmental data

is given in[15]

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