1-s2.0-0255270194040028-main

E L S E V I E R Chemical Engineering and Processing 34 (1995) 157-172

Chemic al Engine r,ng

a n a . Processing

Heat transfer in two- and three-phase bubble column reactors with internals

S. Schlfiter ~'*, A. Steiff ~, P.-M. Weinspach b aInstitut fih Umwelt-, Sicherheits- und Energietechnik (UMSICHT), OsterfelderstraJ3e 3, D-46047 Oberhausen, Germany

bLehrstuhl fiir Thermische Verfahrenstechnik und Wiirme- und Stoffaustausch, Fachbereich Chemietechnik der Universitgit Dortmund, D-44221 Dortmund, Germany

Dedicated to Prof. Dr. Dietmar Werner on the occasion o f his 60th birthday

Abstract

Indirect and direct heat transfer is an important aspect in the design of bubble column reactors used for many industrial organic and inorganic processes. Longitudinal flow or cross-flow tube-bundle heat-exchangers, jacket cooling, direct evaporative cooling or circulation cooling are possible methods for this purpose. The existing physical and empirical models describing heat transfer in bubble columns are reviewed. The results of experimental investigations of longitudinal-flow and cross-flow tube-bundle heat-exchangers in bubble columns are presented and compared with empirica ! and semi-theoretical correlations.

In the second part of the article the governing equations describing heat transfer in gas/liquid bubble column reactors are derived under the assumptions of the axial dispersion model and the cell model with backflow. For steady-state conditions, the axial dispersion model leads to a boundary value problem consisting of non-linear ordinary differential equations, whereas the c~I1 model with backflow can be represented by a system of non-linear algebraic equations. Both equation systems include strong non-linearities and can be solved only by special numerical methods.

As an example of the use of heat-transfer correlations in modelling bubble columns, the wet air oxidation of municipal sewage sludge carried out in a three-phase bubble column reactor (18 m in height, 2 m in diameter) is simulated considering different heat-removal methods. The simulation runs were carried out with the BCR program, which was developed at the University of Dortmund and the UMSICHT institute for the simulation of bubble column reactors operated under industrial conditions.

Keywords: Heat transfer; Bubble column reactors; Tube-bundie heat-exchangers; Longitudinal flow; Cross flow; AxiaI dispersion model

1. Introduction

Many gas-liquid and gas-l iquid-solid reactions are connected with heat production. Some processes which are representative of industrial two- and three-phase reactions carried out in bubble columns are listed in Table 1. In addition, reaction enthalpies and significant operating conditions are also given. In the case of exothermic reactions, as presented in Table 1, the removal of the heat of reaction is an important aspect in the design of bubble column reactors in order to ensure safe process operation.

* Corresponding author.

Basically there are two different methods for remov- ing energy from a multiphase reaction system: (i) direct heat transfer and (ii) indirect heat transfer. Direct heat removal is realized by vaporization of a solvent or a liquid reactant and is the most effective way of heat transfer. Direct heat removal is especially suitable for emergency cooling where a lot of energy must be re- moved in a short time. Investigations in this field have already been carried out at the University of Dortmund [1-3]. However, in this paper only indirect heat transfer is discussed. Indirect heat transfer is very important for industrial practice since it can be applied in most cases. Figure 1 shows some examples of indirect heat transfer in bubble column reactors.

158 S. Schliiter et al./ Chemical Engineerhlg and Processing 34 (1995) 157-I72

Table 1 Industrial two- and three-phase reactions carried out in bubble column reactors [.9,10]

Main products Chemical reactants Heat of Operation Operation reaction pressure temperature (kJ mol- i) (bar) (oC)

acetaldehyde ethylene, oxygen -243 acetone propylene, oxygen -255 ethyl benzene benzene, ethylene - 113 benzoic acid toluene, oxygen -628 n-, iso-butyraldehyde propene, hydrogen, - 118,

carbon monoxide cumene benzene, propene - 113 cyclohexane benzene, hydrogen -214 cyclohexanol cyclohexane, air -294 1,2-dicloroethane ethylene, chlorine -239

ethylene, hydrogen - 80 chloride, oxygen

acetic acid acetaldehyde, -294 oxygen

acetic acid, n-butane, air -176 methyl ethyl ketone

vinyl acetate ethylene, acetic acid, -176 oxygen

wet air oxidation sewage sludge, air -435 of sewage sludge

Fischer-Tropsch hydrogen, carbon -210 synthesis monoxide

methanol (slurry hydrogen, carbon -91 phase process) monoxide

-147

3 120-130 t0-14 110-120 2-4 125-140 2-3 110-120 7-25 90-120

7 35-70 50 200-225

8-15 125-165 15-20 170-185 4-5 40-70

2.3-2,5 50-70

15-20 170-190

30-40 I10-130

50-150 200-300

12-15 250-290

50-100 220-270

Large specific-heat-exchanging surfaces can be installed by using tube bundles. In the case of highly exothermic reactions, longitudinal flow tube bundles

are suitable for producing high-pressure steam. Ac- count must be taken of the fact that installations change the fluid dynamics of a bubble column. Hence,

2,er 2,er

gos liquid

external heat

exchanger

-•- liquid

. - - = > ==>-

heat carrier

heat carrier

, -<:= liquid

jacket heat

exchanger

gas

ca; er

~ d - liquid , ~ --~ -==~

heat carrier

heat carrier

_-q= liquKl

coil

heal carrier =:b- <=-

<#= liquid

cross

flow tube bundle

liquid

longitudinal flow

tube bundle

Fig. I. Indirect heat transfer in bubble column reactors.

S. Schliiter et al./ Chemical Engineering and Processing 34 (I995) I57-172 I59

correlations describing heat-transfer coefficients obtained by measurements in columns without installations cannot be applied in every case.

This paper presents measurements of heat-.transfer coefficients in columns with longitudinal flow and cross- flow tube bundles and their correlations. First the basic approaches described in the literature towards heat transfer in bubble columns with and without installations need to be summarized. In the second part of the paper, the governing equations for modelling heat transfer in two-phase and slurry bubble columns are derived and some ideas of solution methods presented.

2. Basic approaches

Investigations on heat transfer in bubble columns were first carried out by K61bel and coworkers [4]. The authors presented their results in the form of art empirical correlation, i.e.

Nu = aRe~ (1)

with a and b as empirical constants. Kast [5] developed a simple model by analyzing the motion of fluid elements around an ascending gas bubble near the column wall. According to Kast's model, heat transfer is deter- mined by the radial components of the induced liquid velocity. In front of the bubble, fluid eleme, nts are displaced and receive a radial velocity towards the heat-exchanging surface. On the other hand, these fluid elements are sucked into the region at the rear of the bubble. Assuming that for the flow around ascending bubbles mass, viscosity and gravitational forces are decisive, Kast proposed the following dimensionless relation,

~W ~ Uo,OLCp,L or S t - C~w UG PL Cp,L - - - f { R e o Fr~ PrL a}

(2)

which does not include a characteristic length. Starting from Kast's model, Deckwer [6] has em-

ployed Higbie's surface renewal theory of interphase mass transfer [7]. Deckwer assumed that there is a steady flow of fluid elements from the bulk of the fluid to the wall surface and vice versa. The fluid elements reside for a finite time (the contact time) at the surface until they return to the bulk. If the surface renewal theory is linked with Kolmogoroff's theory of isotropic turbulence [4], a relation for the contact time can be derived:

~ (3)

In two-phase bubble columns, the energy dissipation rate per unit mass can be calculated from

g = uog (4)

From these assumptions, Deckwer has derived a dimensionless equation,

St = 0.1 (Reo Fro Pr 2) - 0.2s (5)

which corresponds to Eq. (2) proposed by Kast. Joshi and Sharma [8] regard heat transfer in bubble

columns as being similar to heat transfer in mechani- cally agitated contactors. The heat-transfer coefficient can be calculated from

~wDa (DRVcIOL~2/3(I~LCp,L~I/3( /~L ~0.14 7.--7 - 0.4 (6) \ 'L / k 2L / \rlLw/

if the following expression for the liquid circulation velocity in bubble columns is used:

3 v c = 1.31 ~x/gDr<(uc - eGVB~ ) (7)

In a similar manner to the approach of Joshi and Sharma, Zehner [11-t3] assumed that the circulation velocity of large fluid eddies is a determining property of heat transfer in bubble columns. In contrast to Kast and Deckwer, however, Zehner's model is based on the existence of a boundary layer. Zehner derived his model from the heat transfer of single-phase flow over a flat surface by introducing the liquid circulation velocity as the characteristic velocity and the average distance of the bubbles as the characteristic length. The liquid circulation velocity as given by Zehner is

Vc = 37~-.-.~ (PLp?G)gDauo (8)

On the assumption that the heat-transfer coefficient of the two-phase system is proportional to the fractional liquid phase hold-up, Zehner proposed the following equation:

CZw = 0.18(1 I- eo) ~/22PL 7,r Cp,L lB v----L with IB = du 6eo

(9)

At the University of Dortmund, investigations on heat transfer in bubble columns with longitudinal flow tube bundles have been carried out by Westermeyer [14]. Westermeyer developed a model to describe heat transfer in columns with installations similar to Zeh- ner's model. In contrast to Zehner, however, Wester- meyer used only simple measurable physical quantities. He assumed that the boundary layer on the heat-exchange surface will be destroyed by gas bubbles which are moved by liquid circulation eddies. The disturbed boundary layer is then filled by liquid flowing with a local liquid velocity 1 given by

~ Measurements of this quantity are available from the work of Bernemann [15] and Korte [i0].

160 S. Schliiter et al. / Cllemical Enghleerhlg and Processhlg 34 (1995) I57-172

10000

W m2K

d 5000

0J , m

1..)

8 b co c- 2

"5 2000 t-

1000 0,002

KSlbel

J o s h i / S h o ~

;t ::: i[ / ~ Zehner s tern ter / L ~'L Pq.

, ~ [",Oeckwer kg/m a mPos d/lkgg} W/linK} 1 - -

" \ Kost 1000 1 4182 0.60L 7

column diameter DR=O,2m

0.005 0,01 0,02 0,05 0,1 0,2 rn/s 0,5

superficial gas velocity Voo =

Fig. 2. Comparison of different approaches to correlate the heat-transfer coefficient for the air-water system,

"DR

He = 2tR

DR -- da

( 1 - 2"'~ ~

7 fiGUS . . VL,loc= ~ f ia~LguGH e or VL,loc = 8L PL 8L PL g!AG/'/e

(io)

Here He is the height of liquid circulation eddies and ~' is a parameter describing the energy distribution given by Westermeyer [14] as follows:

for columns without tube bundles

:GL,OL'~ for \ g'-~L; < 106

\ gr/4L J I> 10 6

~ = 1 7 0 M o ~ 8 ( l + 7 . 8 5 x 1 0 - 4 D ~ 3 G-3x/~LMOI.

[ 10-8]'~ x exp~ - ~o-~%j, )

From the measured data, Westermeyer finally derived the following dimensionless equation for the local heat-transfer coefficient:

2L / ~ VL ~/ 2L VIL,W/

dRJ (ii)

Here the mean thickness of the boundary layer, 3"L, is given by:

fit. = 2.32 /dB~ (12) "~/ PC,loc

In Fig. 2, some known correlations for the estimation of heat-transfer coefficients in bubble column reactors for systems with low liquid viscosities are compared. Their mathematical representation is given amongst others in Table 2.

3. Results of experimental investigations

As shown in Fig. 3, the heat-transfer coefficient increases with the superficial gas velocity. In highly viscous liquids, the heat-transfer coefficient reaches a limiting value. In these liquids the coefficient is also much smaller than in liquids with low viscosity. The tube pitch has only a small effect in the case of highly viscous liquids. Figure 4 shows that only in low viscosity liquids does the heat-transfer coefficient increase with the reactor diameter. Otherwise the coefficient is

S. Schliiter et al. I Chemical Engineering and Processing 34 (1995) 157-I72

Table 2 Correlations for the estimation of heat-transfer coefficients in bubble column reactors

i6I

Authors Correlation

K6Ibel et aI. [4]

Fair et al. [16]

Kast [5,17]

K61beI and Langemann [18]

Shaykhutdinov et al. [I9]

Burkel [20]

Nishikawa et aI. [21]

Louisi [22] Deckwer et al. [6,9,23]

Joshi and Sharma [8]

Zehner [11-13]

Wendt [24]

Micheal [25]

Korte [I0]

Westermeyer [14]

NU(dR) = 34.7 m,0.22 for > 150 ~'O,dR ReO,dR Nu(aR) = 22.4 m,0.36 for < 150 ~'G,de. eeG,da

~w = 8850u~ 22

St = 0. i 0 [(Re o Fr o Pr[) 1/3] - 2/3 __ 2.5 1/3--0.66 Stsu~- 0.124[(R%,s~FroPrs~) ]

St = 0.11 x 1.25[(Reo Fro PrZu "~) i/3] -0.667

St = 0.11 [(Re o Fr o Pr~48) 1/3] -0.69

St = 0.418(Reo w" --<O---LJ D'2'--I/3"'I/4(PL--fl~G~II3( "G /7"~L ~ -0"05 \ Pu J V/t~.w/

I St = 0.30(Reo Fro Pr 2)- t/3 _ _ _ _ \ PL J \r/L,WJ

(,oL_,ooT, ( \ PL ) \1'] L,W/

St = O. 136 [(Reo Fro prrl "94) 1/3] - 0.81

St = 0.10[(Re o Fr o Pr~f/3] -o.75 S ts~ = 0.10[(Reo,s~ Fro PrZ~s) 1/3]- 0.75

At. \ ~TL / V/L,w/

v c = 1.3I[gDR (u o -- e o vs~. )]1/3

2 L \ V L / \ 2t- /

3/1

IB = dB 37-~ec,

St = 0.037I Re~°'t7Fr~°'32pr~ -°'46

St = 0.1 l[Reo Fro pr2) U3] -0.75 S ts~ ~ = 0.12[(Re a ,su~ Fro pr2us) m] - 0.75

(DR~0.,5( /~t- ~0.30 St = 0.120[(Re o Fr o Pr~2) 1/3] -0.83

\ d a / \r/L,W/ V 1/2 t/3 0.23 6~ c~dB 0664(c,l<,jB / (r/LCp,L~ (r/L "] (1'4-L /

zL ' \ vt- J t ~L J V1L,wJ \ dR/

VC'Ioc=7(C'oPo-b6LPL-kesPS) g D R u G \ '%PL

(I COO = 7, (1) n = 0.75 li-@--4~es, ( /= 170 MoU s 1 + 7.85 x 10 .4 ~ exp[-~--~%f)

nea r ly i n d e p e n d e n t o f the g e o m e t r i c d imens ions . M e a -

sured N u s s e l t n u m b e r s are c o m p a r e d wi th va lues pre-

d ic ted by Eq . (11) in Fig . 5. I t c an be seen tha t the re is

a c o r r e s p o n d e n c e to w i t h i n 15%.

F i g u r e s 6 a n d 7 s h o w m e a s u r e d d a t a o b t a i n e d by

K o r t e [10] in b u b b l e c o l u m n s w i t h c ross - f low tube

bundles . T h e p l o t t e d cu rves are s imi la r to those s h o w n

in Fig. 3 desp i te the fac t t ha t c ross - f low a n d long i tud i -

162 S. SchhTter et al./ Ckemical Enghwerhlg and Processhtg 34 (1995) 157-172

(3)

~J

0 c j

C 0

_C.

10 ~

W m2K

5

10 3

5

S ...m ev~/--'~

column DR : 029m , HR : t, 27m .gos....._sp~__..rger_._ sieve lroy , dL=2mm

mlernols : Iongi tudinol flow lube bundle, da --25rnrn

s.uper f iciol l iquid veloci ly~ vt. o -- 1orals

D

At (%1 97,0

tR [ram] 120

12

tube O arrongemenl

72.5

t,0

13

® 90,3

70

1/.

@ g/,,8

120

15

0

I

,0 ,I,I, m, T. - i I , -

12 13 1L .15 12 13 lb 15

woter propylene glycol

di, . ' m / Y _ ~ I • - - A~.~ . ~

IrIJi ,,~- symbol tube

orrongement

liquid

"ilL[ toPos] 1,0 Z,6,3

3.10 2 t I 1 I I 1

0 0,1 0,2 02 0,4 0,5 0,6 .~- 0,7

s u p e r f i c i a l gas v e l o c i t y Voo

Fig. 3. Influence of superficial gas velocity and tube pitch on heat transfer in bubble columns (longitudinal-flow tube bundle).

hal-flow tube bundles cause different flow conditions. In contrast to longitudinal flow tubes, there is a significant effect of superficial liquid velocity on heat transfer. Large superficial liquid velocities increase the heat- transfer coefficient. A smaller tube pitch increases this effect. A comparison between Figs. 6 and 7 shows the influence of liquid viscosity. In the case of highly viscous liquids, the heat transfer decreases.

Heat-transfer coefficients in bubble columns with cross-flow tube bundles can be estimated by a correlation given by Korte [10]:

St = Stlph + C" St2p h (13)

where Stlp h and St2p h describe the heat transfer for single phase flow conditions and the additional effect of the second phase on the heat transfer in bubble columns with a single tube, respectively. The second term can be predicted from data measured by Korte [1o]:

fn \o.ts/, \0.30 St2p h = 0 .120(ReGFroPr~2)_0 .277 (~_~_a) ( '/L ) (14)

\ a a / \r/L,W/

The adjusting factor C in Eq. (13) is given by

c = 10.2 Re -°29PrE°"N? ° ' 4 \aRJ (15)

As shown in Fig. 8, experimental data can be predicted by Eq. (13) with a mean deviation of +20%.

4. Modelling heat transfer in bubble column reactors

To set up the energy balance, it is assumed that mass and energy dispersion can be coupled in accordance with the Lewis analogy". By analogy to Fourier's law of heat conduction in solids, the heat dispersion flow is given by

< ) Qdi,p{X} - -2=rrAr~ ~ with 2~rr-D~frcpp (16)

Thus the law of energy conservation written for a differential element in the bubble column consisting of phases m = 1, 2 can be represented as follows:

2 Badura et al. [26] and Wendt [24] have investigated mass and heat dispersion in bubble columns. Their experimental results show a correspondence between the dimensionless concentration and temperature distributions over the reaction height. Hence it seems to be possible to put the effective heat conduction coefficient equal to the overall mass dispersion coefficient by using Lewis' analogy a~rr = 2ar/ (pcp)= Dcrr.

S. Schliiter et al. I Chemical Engineering and Processing 34 (1995) I57-172 163

W rn2K

symbol

lube arrangement

liquids

O z~, [3 2 13 19

water ' t:f" 2 19

propylene glycol

"qL [toPos ] 1,0 22,6

. gas_._Sl~o._rger~ sieve troy, dL= 2ram internals: Iongttudmol flow

tube bundle ; d n =25ram s, uperficiol liquid velocit y~ vLo =lcm/s

1 <D U

©

u~ C O

3

I ~ - -E ] , - - - - - - - - - m " - ' - ' - ' " [3 " - - -

l o < - _ _/c .~._n~--n~ o - _0_% .~'e~o__ _o_----o-

5 7D/'%<'~ ~ O

DR [ ram] 100

tR /d:R {11 1,5 2

tube arrangement @

290 450 1,6 .1,6

13

® 19

0 ,i

[- I [ I I I I r I f

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 m 1,0 S

superficial gas velocity Voo -----,-- Fig. 4. Influence of superficial gas velocity and reactor diameter on heat transfer in bubble columns (longitudinal-flow tube bundle).

2 (U+Ekin+Epot) 8H a(pV)_ E (p,.lP,.h,. {T(~)}) (x)

8t 8T 8t m = 2 2

= E (Pml )m(Um- ' i - ek in ,m+epot ,m) ) 0~) -- E (Pro ~'mh'n {T(x+dx) })(x+dx) in= 1 In = 1

-- E (PmI)m(Um+eki . . . . + pot,m]/ , ~ = ~ , ~ = , \axJ)

- Z + Z )

2 ( ¢8T'~'~ °':+d':) d0+d~" (17) -1L m~= 1 /~el:l',m A R ~m k ~ X ) ) - -

The overall power term d W is equal to the sum of the technical power d I4zt and the flow displacement power:

2 dI~=dl~t+ 2 ( ( V ' m - p ) ( x ) - - ( ~ n P ) (x+dx)) (18)

m= 1

After introducing the system enthalpy via the definition

H H - U + p V and h - (19)

M

the energy conservation law can be written as

- d O + d I~ t (20)

The enthalpy H is a function of temperature, pressure and the molar composition of the system. The total differential of H is given by

d. (d 0

+i~=t -~ i r , ; ,~i \ at ] (21)

The term (SH/ST);,Ni is equivalent to the expression (pVcp). The term (SH/OP)r, Ne can be neglected for liquids in most cases, for ideal gases it disappears

164 S. Schliiter et al. I Chemical Engineering and Processbig 34 (1995) 157-172

10 2

Z

DR single IR r ~Os,v dR rn tube mm ' ~ '%~"e ' T

~0 70 120 0015 / / / ' / / / 0,190 n + m + ~> -- 0,421÷0,8A 2 0-15 0:025 ../Z /

0 . ; ~ - + o ,'-o +o0.308-0.92t. 0 0.025, /~:/"

1 o" i i " -~ //..+7

101 . /,/~Y'~ model

i symbol operolion Pr L

/ / c ~ + 2-phose / r.J--~ , 7

+150/0/¢, / ' / ,> 3-p~e - - ' , / 9 / / ~, 2-p~,o 275 ///<,-lSOio

10 0 i I I I I ) i l l i I I i I ! I 10 0 101

0,66,. ~ (l+-~r)) Fig. 5. Comparison between measured Nusselt numbers and values predicted by Eq. (11).

1

10 2

totally 3. The term (SHISN~)~°N... is the partial molar enthalpy ~ of component t m the mixture. By definition, the system enthalpy H can be expressed as

H: :vh= £ N,~= v :~ c,Z. i=l i~ l

and Eq. (21) simplifies to

dH ~ dNz

i ~ l

(22)

(23)

For two-phase flow conditions, the enthalpy H of the system can be composed, for example, of the enthalpies of the gas and liquid phase:

d g dHa d i l l dT dt - ~ + T = ( ' o G V o C p ' G - ] - f l L VLCp'L)--~

" (~ dY,,o dX,;L~ + 2m \ " O dt +/~''L dt ] (24)

3 Thermodynamic considerations show the validity of the folloMng expression:

When introducing the equation of state for an ideal gas, the right- hand expression is equivalent to zero.

Equation (24) has to be completed by the mass-balance equations for the bubble column reactor:

dNi, G dt = ( I';'G Ci,o)('~) -- ( f>'O <t,G )¢x + d.~)

- @ ~°~°'.° (d<<°'?: t, Tx );'

- (kLa),,.b, lbt (~:~Cj, o -- <i,t.)Ai~ dx

+ (ko.),,v.. (c,,L_ ) %

\to" Cf, o_Ar~ dx (25)

dN,.,i. d t = (I;"LC';L)("O- (I?LCi'L)(X+dX)

/ /dcl, L'~\(x) / (dqL\\(~+d'')

+ (kL a)l,.b: ~'l (tc'ici, o -- qL)AR dx

- ( k o a ) ~ , v . ~ ( c ~ j . _ \ tc~' Cf.o)AR dx

w +eLAR dx y" Vi, kRk (26)

k--1

The mass-transfer rates due to absorption and evaporation given above are described later [see Eqs. (45) and (46) for explanations]. Defining the heat of reaction as

S. Schliiter et al . / Chemical Engineering and Processing 34 (1995) 157-I 72 I65

6

0

ul C

2

@ t-

W m2K

1600(

I sy~bo, o 110 3~0 v L__9_,O 1,0 cm/s

I~ 32 mm

I

• 11o 3[0 1.0

6A

/ 0 1 /

12000 / '° '°

M / _ _ , '-- 8000 2 ~...., - ~ - - ~ - ' o V

i x ~ E l l I 0 0 , , - O - -

4000' {

¢

V i

0 0 10 20

Fig. 6. Influence of superficial gas and liquid velocity on heat

_system: water l a i r , "qt .= lmPas

column : OR=0196rn, HR = 6,81m .gas sparger~ sieve tray d~=3mm internals: 3 tube rows . . . ~ 7 ~

.probe posi t ion:h/HR=0.5,r lR~0

, , I , I , I 30 AO 50 60 70 80 cm/s 100 t10

superficial gas velocity Yea

transfer in bubble columns with cross-flow tube bundles.

A£.~= ~, ~,.~{r} (27) i~I

the energy change of the system due to chemical reactions can be considered without defining any heat source terms. Considering Eq. (16), the energy dispersion by backflow, i.e.

(l~ {T}AReDefr{dci~ (28) i=t \dxl] is equivalent to the effective overall heat dispersion in the system:

~(~{T}ApsDe~:¢dci)~ (dT) ~= ~ \ dx J ] - AR s2~ -~x (29)

The heat of absorption and the heat of evaporation can be defined as

A]~abs,i ~ (]~',G {T} -- ~',L { T})abs

and

Ai~vap#" ~ (~/ ,o {T} - ~,L { T } ) v a p (30)

Neglecting mixing effects, Affab s and Ah'va p can be calculated from the molar enthalpy differences of the pure compounds, given as the molar heat of absorption or evaporation in chemical engineering data collections. Heat flows added or withdrawn from the system by indirect heat transfer are given by:

f~ d Q = d Q w = ~ C~w,~aw,o~Aadx(T-Tw,o)) (31)

c o ~ l

with the volumetric heat transfer surface area aw,~ defined by:

( d A w q aw,~ = aw,~ {x} - \ ~ ] (32)

Generally the heat-transfer coefficients C~w and the surface temperatures Tw depend on each other and must be calculated iteratively by numerical procedures. Using a Taylor expansion around (x) for the quantities at differential position (x+dx), a non-linear ordinary differential equation is obtained for the axial temperature of the multiphase system in the bubble column:

d2T (SG2eff, G "-~ 8L.~eff, L + (SL Jr- 8S)2eff, S ) dx2

dT = (b/G/gG CP'G + ULPL Cp'L -/I- (UL -- 8L/')S)DS Cp'S) "~X

-- ~ (kLa)i, abs @i (KI'Ci, G -- Ci, L)(A~abs, i) i= l

+ i ) ,=, \ 4 ' c,,o (AL~p,;) tp

-8~ 2 R~(-A#r,k) k=l

+ 2 C~w,~aw,~(T- Tw,~) (33) (0=•

166 S. Schliiter et al. / Chemical Engbmerhlg and Processhlg 34 (I995) I57-172

.j

8

C e

"5 c"

] .T_ W ._system propylene glycol / a i r . l l t :55 rnPos

m2K

2400

2000

1600

column : On:O,lg6m , HR = 6 81m .gas sporger sieve tray d L : 3ram internals' 3 tube rows

_probe posit ion: hlHl~ :0.5. rlR:O ".M ~

~ ~ <

1200 I

k A..~v-*

y _,Co*O-- 400~ i°'°

O L Q

0 10

.V I ~ 1 ' '

------'1 , O ~ ~ O, 0 ,0

32 64

= ~ ~ £

20 30 40 50 60 70 80 crn/s 100 superficial gas velocity %0

Fig. 7. Heat transfer in bubble columns with cross-flow

110

tube bundles in the case of highly viscous liquids,

In Eq. (33), the energy content of a dispersed solid particle phase is considered by introducing its molar heat capacity and rise velocity.

An alternative approach for modelling heat transfer in bubble columns is the 'Cell Model with Backflow' (CMB). Here the multiphase flow is simplified to a cascade of ideally mixed tank reactors in series (see Figs. 9 and 10) with a single tank volume of

V , LR Tic = £ with Nc = ~ (34)

For characterizing the degree of back-mixing in the partially mixed system, a backflow circulating between neighbouring cells is used. Assuming equidistant cell heights, the backflow ratio, defined as the backflow related to the overall convective volumetric flow rate, can be coupled mathematically with the lumped axial dispersion coefficient of the axial dispersion model:

[?G,b = uGLR _ ; Nc 1 with B a t - (35) VG,fee d Boc 2 ecD~m t

t~,b Nc 1 UL LR Y = I?L,,'e~d BOL 2 with Boi. -= eLD~r,L (36)

Considering the energy flows given in Figs. 9 and 10 for cocurrent gas-liquid flow, the following algebraic equation system can be set up for modelling heat transfer and energy distribution in a bubble column reactor:

j = 1:

( cp.c AR 0c) (r~¢ -- (uc Pc Cp,t at)(1)

- ((ut)")[@ t cp,c Or):' - Co t cp.t Oo):'-)]

_}_ ( M L h L ) freed) (ULPLhL)(1) - - (yUL) (1) Aa

× [(pLhD m - (pLhL)c2)]

~:~/~bs .~ yap 4 ~ =0

AR AR AR AR

1 < j < N c :

(uo Po %0 0c )u- :) _ (uc Pc Cp,c 0c )u~

- @c)v?[Coo cp.c OG)v? _ @ t ep,t a t ) v + :)]

+ ((Ut)q- :)[(P C Cp,t Oa)~- '} -- GOt %,t at)u~]

+ (ULPLhL)U-- l) _ (ULPLhL)O?

+ (YUL)0'--D[COLhL)O-D_ (pLhU~]

_ (7UL)O?[(pL hL)O? _ (puhL)0 + I)]

A~. AR AR Ar<

(37)

(38)

S. Schliiter et aL / Chemical Engineering and Processing 34 (I995) I57-172 167

t z

100(

50(

vL ° / c._gm_ 10 12.0 26.0

Voo/ c.~_ 0,7; 5,5 ~ 15,0 ;50.0

internals: 3;5~11 tube rows

20(

/

(>

[] ;

5/

f / /

]

/ p - glycol

Pr L = 519

&

4 ° /

2"/

/" o / O

/

liquids

p- glycol glycerol / water water

PrL= 105 PrL =61 Pr L ; 7

0 [] o 100V" / ~ I

100 200 500 1000

NUcolculoted - - D , -

Fig. 8. Comparison between measured Nusselt numbers and values predicted by Eq. (I3).

j = N c :

(u~ PG Cp,G 0~)(Nc - t) _ (UG PO Cp,G 00)(Nc)

+ (~'UG)(N C -- 1)[(/gG Cp,G t9 G )(N C -- 1) - - (PG Cp,G 0G) (NC)]

+ (ULPLhL) (Nc- ~) __ (ULPLhL)(NC)

+ (TUL) (Nc- ~)[(p~ hL)(Xc-~) __ (pL hL)0V~)]

Q~Nc) ~(~C) f) (Nc) 0 (Nc) + - - { Zabs :r-,va.__.....~p = 0 (39)

AR Aa AR Aa

The system (37)-(39) must be solved in paralM with the mass balances for the gas and liquid phase (overall and component-wise) leading to a temperature distribution T{x} over the column height. For mathematical and numerical reasons, the single cell height should not be higher than the reactor diameter. So the number of equidistant cells Nc should be at least

LR Nc/> (40)

Da

Good results should be obtained with Nc = 2La ~DR in most cases. The heat source and heat-transfer terms of a cell (/) can be written as follows:

0 ~ = H~c ~ AR Z C~w(r- Tw) (41) CO=[ CO

Qr ~ = H°c ? AR(1 - e~) 2 R~?( - hh~~) (42) k = l

Q~s H°c ? AR ~ Ck a ~ ,/,o)Oc' - c ~o)AE ~ \ L )i,absg'i \ iCi, G i,L) abs,i i=1

(43)

"~ Hc AR ~ (kGa);,vap --ci, G Q vap = (J) Q') ~i'L A]~v(J,)ap,i (44) i=1 \ K i

In Eqs. (43) and (44), the volumetric mass-transfer coefficients for absorption and evaporation of component i in the cell (/) are given by:

1 1 (K'(/)? 3 k a~0~ ( / L a ) ? + - -

L J,,abs (riGa)? ?

and

1 1 1 k a ~ = (/~Ga)? ~- (~"pLa)?~ (45)

G ]i, vap

The special thermodynamic conditions for absorption and evaporation of components in the gas-liquid multiphase system are considered by the gas-liquid distribution parameters ~c'~ and ~c i . Phase equilibrium expressions using rational Henry's law (absorption) or liquid-phase activity coefficients (evaporation) lead to

168 S. Schliiter et a l . / Chemical Engineerhtg and Processing 34 (1995) 157-172

t (/x_: 0 '(~':-~)

• 0 JNc) (X~5.~ ~)

t :~ (~:) <- - - -dA~)

t ;

t~,v~) ~'~,,~ ~) t ~, ~) ~'~,,c ~)

t t cell (/)

t t z¢. 0 x(l-~) , ,~ ,9-x): 0 41-~) ~ , . o o) u o) ~,oo~,.~ o) (¢-j'-"(oo%:of

M<;' '0 ,0) • fi) l) • (1) ~)

t t ;

t Fig. 9. Gas-phase energy flow rates in the cell model with backflow.

~;- -:;-- = \~r ~e / C i,O (abs)

and

~ ; - ~ = o

The algebraic system (37)-(39) must be solved in parallel with the mass balances for the gas and liquid phase (overall and component-wise) and the static pressure drop. Due to the strong non-linearities involved in coupling highly non-linear mass and energy rate equations, this is not an easy job and can be done only by special numerical techniques like the NLEQ family solvers or the ALCON family solvers developed at the Konrad-Zuse-Zentrum, Berlin.

5. Simulation of heat transfer in bubble column reactors

To give an example of the use of correlations for predicting heat-transfer coefficients, a computer simula-

,,.J

(,~.IL j No)

t cdl (No)

t t (:~d'o-o (r~j'o"(oL1d,o-,,

.< ~N:)

d~'~. )

(:,~d,o-M.i,j,,,ol

d__2, ~1 r

I

t t ; cell (I) L ~O/t.

t t ,I (~,,,.)'-" (~,a y-"co,.,,,.),J-" (,,a Y"(,,,.,,,.)<'~

t t ,l,

t Fig. lO. Liquid-phase energy flow rates in the cell model with backflow.

tion of the wet air oxidation of municipal sewage sludge in the slurry phase will be presented. The BCR program developed at the University of Dortmund and the UMSICHT institute in Oberhausen considers the specific flow conditions and simultaneous heat and mass transfer in connection with chemical reaction processes in bubble column reactors [27-29]. It is based on the cell model with backflow and solves the numerical problem by several modified Newton methods (NLEQ family) and special continuation techniques (ALCON family) developed at the Konrad-Zuse-Zentrum in Berlin.

Already in 1911, a process to oxidize waste sulphite liquor from pulp production in autoc!aves at a temperature of ca. 180 °C had been patented. In the mid- 1960s, a number of wet air oxidation plants for the treatment of municipal sewage sludge were installed in the USA by the ZIMPRO Corporation. Ploos van Amstel and Rietema [30,31] investigated the kinetics of the wet air oxidation of municipal sewage sludges in

S. Schliiter et al./ Chemical Eng#wering and Processing 34 (1995) 157-I72 169

laboratory scale. They suggested that the sludge components should be divided into three main reactivity categories: (i) easily oxidable components (component class A); (ii) difficultly oxidable components (component class B); and (iii) very difficultly or not oxidable components (component class C). For the oxidable component classes A and B, Ploos van Am~tel and Rietema [31] proposed the following second-order reaction kinetic expressions:

-~COD,A = ]CA CCOD,A 002,L

and (47)

RCOD,B : kB CCOD,B Co 2,L

In the classical Zimmermann process the reactor temperature is controlled only by the feed sludge temperature without any additional heat removal installations. Heat exchange is therefore limited to the mass flows leaving the bubble column reactor. With regard to process temperature control and energy recovery, two other methods for reaction heat removal [A/)'r 450 kJ (mol 02) -1] may be mentioned: (a) jacket cooling over the reactor wall; and (b) internal tube bundle heat exchanger, longitudinal-flow or cross-flow. Jacket cooling over the reactor wall, however, cannot be rec- ommended for the process conditions of wet air oxidation. A wall thickness of ca. 100 mm and above causes a relatively high heat transport resistance at the reactor wall which dominates the overall heat-transfer coefficient. As a result, either the amount of energy trans- ferred to the cooling fluid is low or the outlet temperature of the cooling medium is relatively low which prevents effective heat recovery.

The internal tube-bundle heat-exchanger raakes it possible to use larger specific-heat transfer surfaces and results in high overall heat-transfer coefficients. Thus it is possible to remove reaction heat by producing high- pressure steam at temperatures above 250 °C and to control the process temperature safely at very high levels. In addition, the reactor can be preheated by steam condensing in the tubes during the start-up phase.

The basis of the mathematical model is a set of balance equations arising from mass and energy balances for the column and its surroundings. The size and mathematical type of the resulting non-linear equation system depend strongly on the number of reacting components which are to be balanced in the gas and liquid phase, and from the basis type of the model. For wet air oxidation of sewage sludge in the bubble column reactor, the axial dispersion model leads to a boundary value problem which is set up by three first-order differential equations [27,28]:

1. hydrostatic pressure drop, gas-liquid mixture 2. overall mass balance, gas phase 3. overall mass balance, liquid phase

and seven second-order non-linear differential equations:

4. mass balance 02, gas phase 5. mass balance 02, liquid phase 6. mass balance C Q , gas phase 7. mass balance CO2, liquid phase 8. mass balance easily oxidable component class A,

liquid phase 9. mass balance difficultly oxidable component class

B, liquid phase 10. energy balance, gas-liquid mixture

For the cell model with backflow, the model equations listed above must be set up for each single cell in the balanced reactor volume, resulting in 10 algebraic equations per celt. To give an example, for a 90-cell representation of a 18 m height bubble column reactor, this method leads to an algebraic system of 900 non- linear equations with 900 unknown quantities. Addi- tionally, a large number of dependent parameter vari- ables (gas hold-up, heat-transfer coefficients, etc.) need to be solved simultaneously. The results described be- low have been computed with the BCR program using the basic data record in Table 3 for the wet air oxidation of municipal sewage sludge suspensions.

The axial temperature profile for the bubble column reactor with external (suspension feed temperature --- 190 °C) or internal (steam temperature -- 280 °C) heat-exchangers is demonstrated in Figs. 11 and 12. The curve parameters are the inner reactor diameter or the suspension feed temperature, respectively. The reactor without an internal cooling tube bundle shows a temperature increase of ca. 50 K up to an outlet temperature above 300 °C, whereas the temperature increase in the reactor with an internal tube-bundle heat-exchanger is limited to about 8 K over the temperature range 280-288 °C. For optimal process control, the reactor cooled with an internal tube-bundle heat-exchanger is superior to the classical method of heat-exchange between fluids entering and leaving the reactor.

A considerable amount of reaction heat can be recovered as high-pressure steam by installing an internal tube-bundle heat-exchanger. In addition, the amount of energy recovered by preheating the entering feed sludge is considerably higher in the case of internal heat

Table 3 Basic data for the wet air oxidation of municipal sewage sludge

Simulation parameter Quantity Unit

column diameter 2.0 m column height 18.0 m reactor operating pressure (head) 125.0 bar suspension feed temperature 190.0 °C steam temperature (tube) 280.0 °C superficial gas velocity (bottom) 2.25 cm s - superficial liquid velocity 0.85 cm s-

170 S. Schliiter et al. / Chemical Enghwerhtg and Processing 34 (1995) 157-I72

320 °C

310 E 3oo I

280 / J column diometer : _ _ o 3.0m / b 2,5m

270 / c 2,Ore

cl 1,5m 260,.. e 1,Ore

250 0 2 z, 6 8 10 12 1/-, 16 m 18

reQctor height

Fig. 1I. Axial temperature plots for the reactor with an external heat-exchanger.

290 [~----i--~ - -

0 2 /. 6

o 220°c d 250~c F---~-- ~ b 230°c ~ 26o°c1 [

10 12 % 15 m 18 reoctor height =

Fig. 12. Axial temperature plots for the reactor with an internal longitudinal-flow tube-bundle heat-exchanger.

removal because of the higher feed sludge temperatures necessary for the best process operation. Further numerical simulations showed that an increase of the feed sludge temperature caused an increase of the energy-recovery potential of both internal steam generation and feed preheating. However, a simultaneous decrease in the temperature difference between feed and outlet flow increased the technical need for feed preheating. Hence an optimum solution has to be found taking account of the effective costs for feed preheating, the profit from high-pressure steam generation and better process temperature control.

Nomenclature

A, B AR Aw aw

sludge reactivity categories A and B cross-sectional area, m 2 heat-transfer surface area, m 2 volumetric heat-transfer surface area, m 2

COD C

CCOD

CG c ;

CL c*

Cp,°

Cp,L

¢p,S Dr{ Deft

Derr, i

ekin Epot

epot g H

H o r-&

h AE~u~

K

Eo

go He kA, kB (koa)~.p

(kLa)abs

LR

&

M

n n

P

chemical oxygen demand, tool 02 molar concentration, tool m -3 corresponding concentration of chemical oxygen demand, COD m -3 molar gas-phase concentration, mol m -3 molar gas-phase concentration at interphase, mol m -3 molar liquid-phase concentration, mol m -3 molar liquid-phase concentration at interphase, mol m -3 gas heat capacity, J kg-~K - liquid heat capacity, J kg-z K-i heat capacity of solids, J kg-1 K- reactor diameter, m axial dispersion coefficient, m z s- axial gas-phase dispersion coefficient, m'-s -~ axial liquid-phase dispersion coefficient, m 2 s-1

bubble Sauter diameter, m tube diameter, m kinetic energy, J specific kinetic energy, J kg-i potential energy, J specific potential energy, J kg- gravitational acceleration, m s -2 enthalpy, J cell height, m gas enthalpy, J liquid enthalpy, J specific enthalpy, J kg- molar heat of absorption, J kg-I molar heat of reaction, J kg-1 molar heat of evaporation, J kg- partial molar enthalpy, J mol- partial molar gas cnthalpy, J mol- partial molar liquid enthalpy, J tool- height of liquid circulation eddies, m Henry's law constant, Pa reaction rate constants, m 3 ( m o l Q ) -1 s -~ overall volumetric mass-transfer coefficient for evaporation, s- overall volumetric mass-transfer coefficient for absorption, s- length of reactor, m

3 3 / ~ ' = dB x / ~ = mean bubble distance, m

mass, kg gas-phase mass flow rate, kg s- liquid phase mass flow rate, kg s- number of cells, - number of moles in gas phase, tool number of moles in liquid phase, tool number of tubes, - numerical parameters, - number of components, - pressure, Pa

S. Schliiter et al./ Chemical Engineering and Processing 34 (1995) 157-i 72 171

Psat 0 Qabs Q" disp Qr

vap 0w R RcoD

T rw tR U

UG UL V

vo VL V

Vo,u

gG,feed

VE,b gL,feed t~Boz

~)L,loc VS

X

~W

t%Ga

f ie a

g

bE es

s°t

7

~L ~L,W

/C /

saturation pressure, Pa ~c" heat flow rate, W production rate of heat of absorption, W 2L heat dispersion flow rate, W 2e~ production rate of heat of reaction, W v production rate of heat of evaporation, W VL indirect heat transfer flow rate, W reaction rate, mol m -3 s - I ~G

corresponding reaction rate, COD m -3 s -1 ¢, radial position, m ¢, temperature, K Pc wall temperature, K PG tube pitch, m PL internal energy, J /~L specific internal energy, J kg -~ Ps superficial gas velocity, m s-~ #5 superficial liquid velocity, m s -~ ~7 L volume, m 3 r cell volume, m 3 ~' gas volume, m 3

liquid volume, m 3 volumetric flow rate, m 3 s -1

volumetric gas flow rate, m 3 s- volumetric gas backflow rate, m 3 S-1

volumetric gas feed flow rate, m 3 s -1

volumetric liquid flow rate, m 3 s-~ BoG volumetric liquid backflow rate, m 3 s -1

volumetric liquid feed flow rate, m 3 s-~ BOL terminal rise velocity of a bubble, m s- liquid circulation velocity, m s-1 FrG local liquid velocity, m s-~ GaL hindered settling velocity of solid particles, MoE m s -1 Nu power, W NuB technical power, W PrL axial coordinate, m ReG

heat-transfer coefficient, W m-2 K - t ReE ReL,loc

volumetric mass-transfer coefficient, s-1 St

volumetric mass-transfer coefficient, s -~ Stlph

= 2 . 3 2 d B / ~ (see Westermeye:c [14]) St2p h = mean thickness of the boundary layer, m

energy dissipation rate per unit mass, m 2 s -3 volumetric gas hold-up volumetric liquid-phase hold-up volumetric solid-phase hold-up fugacity coefficient fugactiy coefficient of pure component at saturation liquid backflow ratio activity coefficient rational activity coefficient liquid dynamic viscosity, Pa s liquid dynamic viscosity at wall temperature, Pa s gas/liquid distribution parameter, - [see Eq. (47)]

gas/liquid distribution parameter, - [see Eq. (47)] liquid thermal conductivity, W m - 1 K - effective thermal conductivity, W m -1 K -I stoichiometric coefficient, - liquid kinematic viscosity, m 2 s -I energy distribution parameter, - gas temperature, °C energy dissipation function, - enhancement factor, - gas density, kg m -3 molar gas density, tool m -3 liquid density, kg m -3 molar liquid density, mol m -3 solid density, kg m -3 mean density of multiphase system, kg m -3 liquid surface tension, N m -1 contact time, s gas backflow ratio number of reactions number of heat-transfer surfaces

Dimens ionless quanti t ies

= u~La/(eGDerc, G) = Bodenstein number gas phase = ULLR/@LDeff, L ) = Bodenstein number liq-

uid phase = u ~ / ( g D R ) = Froude number = D ~ g / v 2 = Galilei number = ;7~g/(G3/)L) = Morton number = c~wDa/2 E = Nusselt number 1 = c~wdB/2 E = Nusselt number 2 = ~IL Cp,L/2L = Prandtl number = u c D a / v E = Reynolds number 1 = ULda/v E = Reynolds number 2 = vL,~oo dB ~rE = Reynolds number 3 = ~w/(PLCp,LU~) = Stanton number 1 = Cqph/(pECp,LUG) = Stanton number 2 = ~2ph/(DLCp,LUG) ---- Stanton number 3

References

[I] M. Nitsche, Zur W~irmetibertragung bei der Verdampfung yon Tropfenschw~rmen in fliissigem Kontinuum, Thesis, University of Dortmund, I989.

[2] M. Song and A. Steiff, Simulation of vaporization height with considering size distribution of drobbles in drobble columns, Chem. Eng. Process., 34 (1995) 87-95.

[3] J. Steiner, Zur direkten Wfirme(ibertragung bei der Verdampfung eines KNtmittels in eiem mit diesem nicht mischbaren flfissigen Kontinuum, Thesis, University of Dortmund, 1993.

[4] H. K6IbeI, W. Siemens, R. Maas and K. Mtiller, W/irmeiibergang in Blasens~iulen, Chem.-Ing.-Tech., 30 (1958) 400-404.

[5] W. Kaste, Analyse des W/irmeiibergangs in Blasens~iulen, Int. J. Heat Mass Transfer, 5 (1962) 329-336.

172 S. Schl,'iter et al./ Chemical Engineering and Processing 34 (I995) 157-172

[6] W.-D. Deckwer, On the mechanism of heat transfer in bubble column reactors, Cf, em. Eng. Sci., 35 (1980) 1341-1346.

[7] R. Higbie, The rate of absorption of a pure gas into a still liquid during short periods of exposure, Trans. Am. Inst. Chem. Eng., 35 (1935) 365-389.

[8] J.B. Joshi and M.M. Sharma, Heat transfer in multiphase contactors, Chem. Eng. Commun., 6 (1980) 257-271.

[9] W.-D. Deckwer, Rea&tionstechnik in Blasens~ulen, Verlag Sauer- I/inder & Salle, Frankfurt/M., 1985.

[I0] H.J. Korte, W~rmeiibergang in Blasens/iulen mit und ohne Ein- bauten, Tt, esis, University of Dortmund, 1987.

[i 1] P. Zehner, Impuls-, Stoff- und W~.rmetransport in Blasens~.ulen. Teil 1. Str6mungsmodell der Blasens~.ule und Phasenge- sehwindigkeiten, Verfahrenstechnik (Mainz), 16 (1982) 347-351.

[12] P. Zehner, Impuls-, Stoff- und W~.rmetransport in Blasens~ulen. Teil 2. Axiale Durchmischung und WS.rmeiibergang, Verfahrens- technik (Mainz), 16 (1982) 514-517.

[13] P. Zehner, Impuls-, Stoff- und WS.rrnetransport in Blasens~ulen, Chem.-Ing.-Tech., 54 (1982) 248-251.

[14] H. Westermeyer, WfirmeO.bergang und Gasgehalt in zwei- und dreiphasig betriebenen Blasens~.ulen mit l~.ngseingebauten Rohren, Thesis, University of Dortmund, 1992.

[15] K. Bernemann, Zur Fluiddynamik und zum Vermischungsver- halten der flfissigen Phase in Blasens~.ulen mit lfingsangestr6mten Rohrbfindeln, Thesis, University of Dortmund, 1989.

[16] J.R. Fair, A.J. Lambright and J.W. Andersen, Heat transfer and gas hold-up in a sparged contactor, Ind. Eng. Chem., Process Des. Dev., 1 (1962) 33-36.

[I7] W. Kast, Untersuchungen zum W~.rmefibergang in Blasens~.ulen, Chem.-Ing.-Tech., 35 (1963) 785-788.

[18] H. K61beI and H. Langemann, W~.rme/ibergang in Blasens/iulen, Erd61-Z., 80 (1964) 265.

[19] A.G. Shaykhutdinov, N.U. Bakirov and A.G. Usmanov, Deter- mination and mathematical correlation of heat coefficients under

conditions of bubble flow, cellular and turbulent foam, htdian Chem. Eng., I1 (1971) 641.

[20] W. Burkel, Auslegung yon Gasvcrteilern und Gasgehalt in Blasens~.ulen, Thesis, Technical University of Munich, 1974.

[21] M. Nishikawa, H. Kato and K. Hasimoto, Heat transfer in aerated tower filled with non-Newtonian liquid, htd, Eng. Chem., Process Des. Dev., I6 (1977) 133-137.

[22] Y. Louisi, Ermitthmg yon fluiddynamisehen Kenngr613en fur die Fischer-Tropsch-Synthese in Blasens~ulenreaktoren, Thesis, Technical University of Berlin, 1979.

[23] W.-D. Deckwer, Y. Louisi, A. Zaidi and M. Ralek, Hydrody- namic properties of the Fischer-Tropsch slurry process, hzd. Eng. Chem., Process Des. Dee., I9 (1980) 699-708.

[24] R. Wendt, Untersuchungen zum Wfirmefibergang an Einzel- rohren und querangestrSmten Rohrbfindelw~irmeaustauschern in Blasensfiulenreaktoren, Thesis, University of Dortmund, 1983.

[25] R. Michael, Polymerisation yon Ethylen im Blasens~ulenreaktor, Thesis, Technical University of Berlin, 1983.

[26] R. Badura, W.-D. Deckwer, H.J. Warnecke and H. Langemann, Durchmischung in Blasens~ulen, Chem..htg.-Tech., 46(1974) 399.

[27] S. Schl)?ter, Modellierung und Simulation yon Blasens,'iulenreak- toren, Thesis, University of Dortmund, 1992.

[28] S. Schlfiter, A. Steiff and P.-M. Weinspach, Modelling and simulation of bubble column reactors, Chore. Eng. Process., 31 (1992) 97-117.

[29] S. Schlfiter, Simulation of bubble column reactors with the BCR computer code, Chem. Eng. Process., 34 (1995) 127-136.

[30] J.J.A. Ploos van Amstel and K. Rietema, Nagoxidation von Abwassersehlamm. Teil 1. Oxidation yon Glucose als ModeHsub- stanz, Chem,-Ing.-Tech., 42 (1970) 981-990.

[31] J.J.A. Ploos von Amstel and K. Rietema, Wet air oxidation of sewage sludge. Part 2. The oxidation of real sludges, Chem..Ing.- Tech., 45 (1973) 1205-1211.

Documents

1-s2.0-0255270194040028-main