Hydrodynamics and heat transfer in packed bed with cocurrent upflow

Hydrodynamics and heat transfer in packed bed with cocurrent upflow

Chemicd Engineering Scienrr. Printed in Great Britain. Vol. 47, No. 13/14. pp. 3493-3500. 1992. Q HYDRODYNAMICS A.S. AND HEAT TRANSFER IN WIT...

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Chemicd Engineering Scienrr. Printed in Great Britain.

Vol.

47,

No.

13/14.

pp.

3493-3500.

1992. Q

HYDRODYNAMICS A.S.

AND HEAT TRANSFER IN WITH COCURRENT UPFLOW

LAMINE,

M.T.

COLLI

SERRANO,

PACKED

OCHW--2509/92 $S.OO+O.CUl 1992 Pergamon Prers hi

BED

G. WILD

Laboratoire des Sciences du Genie Chimique - CNRS - ENSIC - INPL NANCY, B.P. 451, l.rue Grandville, F-54001 Nancy C&dex, FRANCE

The authors investigate radial heat transfer in packed columns with cocunent upflow of gas and liquid. The experiments are performed in a packed bed electrically heated through its wall, with flow of water and saturated nitrogen The packing diameter has been varied from 1 to 6 mm, and the reactor inner diameter is either 50 or 1OOmm. Radial and axial temperature profiles are measured inside the ckedbed.ThelXat transfer parameters of the packed bed are obtained by fitting the parameters o p”a two-dimensional, homogeneous model to the measured profiXes: the radial effective thermal conductivity of the packed bed (Ar). and the wall heat transfer coefficient (aw). The liquid holdup is measured by conductimetric probes, using a salt tracer technique. The heat transfer in the packed bed strongly depends on the flow regimes. A discussion on the flow regimes and on liquid holdup estimation is first presented and then heat transfer flow, bubble flow and pulsed flow. results and comlaricms are proposed for each fIow regime : scpamd KEYWORDS

Gas-liquid-solid reactor. packed bed; hydrodynamics; wall heat transfer coefficient.

liquid holdup; beat transfer. thermal conductivity;

INTRODUCI’lON Packed bed reactors with cocurrent upflow or downflow of gas and liquid are often used in chemical and petrochemical industry, for heterogeneous catalytic reachons. If the reaction is exothermic (such as hydrogenation reactions), the heat of maction has to be removed, by cooling the walls. in order to avoid hot spots. production of undesired species or catalyst desactivation. Cocunent packed bed reactors are usually operated in dowflow (trickle bed reactors). Although the upflow reactor implies higher pressure drop, it has several advantages compared to the downtlow reactor : better wetting of the catalyst. higher liquid holdup and better heat transfer performance. The resulting improved higher efficiency and lifetime of the catalyst are of great industrial interest. As in all gas-liquid-solid reactors, the heat transfer strongly depends on hydrodynamics and especially on flow regimes. That these flow regimes are not very well known makes it important to mea~su{~&ineously hydrodynamics and heat transfer parameters and to be able to predict them by accumte Most of heat transfer studies in packed bed with cocurrent flow of gas and liquid have been performed in downflow reactors (Weekman and Meyers, 1965 ; Hashlmoto ctd., 1977 ; Specchla et uJ.. 1979 ; Chu and Ng. 1985). Some studies have also been carried out in upflow but their authors proposed correXations valid in specific flow regimes only : Nalcamura et ol. (1981) in pulsed flow. Sokolov et al.(1983) in bubble flow, Gutsche et ol. (1989) in separated flow. EXPERIMENTALEQUIPMENT Figure 1 shows the experimental equipment. It mainly consists in a ICKhnm ID packed column, of 2.7 meter height. The column is made of glass, except for the heating section. The gas is saturate! with water vapor in

a packed bed before entering the reactor.

CES 47:13/14-v

3493

A. S. LAMINE et al.

3494

Gas (nittogen) and liquid (water) ate supplied at the bottom of the column. They first flow through a calming section of one meter length which allows a uniform temperature of the fluids in the bed at the entrance of the heating section. The latter consists in a brass tube electrically heated with a constant heat flux. It is one meter long and made of four cylindrical pieces separatedby insulating joints: in order to limit axial heat conduction in the wall. Tbe superlicial velocity of the liquid is in the range of 0.02 to 1.5 cm/s and for gas. it is of 0 to lm/s. The packing is made of glass spheres (diameter 1,2,4 or 6mm). Some results have also been obtained in a smaller colutnn (SOmm ID), with similar packings and fluid velocities.

c2

1 1 heating section

2 calming section 3 flowmeters 2 ~xifugal pump 6 conductimetric woks 7 visualization se&ion

In both columns, temperatures profiles in the were measured at different levels in the bed. In the 1OOmm ID column, twenty thermocouples are placed at different axial and __ _radial positions __ _ in the bed _. _ and at me watt (two axtat ana ten raaial Fig. 1. Experimental equipment positions). ln the SOmm ID column, eighteen thermocouples are placed at different axial and radial positions in the bed and at the wall (eight axial and four radial positions). The wall thermocouples are soldered into holes (drilled in the tube wall) and the inner surface of the tube has been polii thereafter. The thermocouples in the bed are set in a comb, the support tube is of 6mm outer diameter and the thermocouples are of type K and protected by an stainless steel tube of lmm outer diameter. The measurements are made in stationnary regime and each temperatun profite is measured ten times and averaged.

bed and wall temperatures

The hydrodynamics are investigated by using a salt tracer technique. A small amount of IM KCl solution is injected at the bottom of the column. The transient mean salt conCent.ration on two cross sections of the column (inlet and outlet of the heating section) are measured by conduaimetric proks. HYDRODYNAMICS pvdrodvmunics

AND HEAT TRANSFER MODELS

: plue flow model with a-

The response curYe (mean outlet concentration) is well represented by the plug flow model with axial dispersion. The parameters of the model. the mean residence time of the liquid and the axial dispersion P&let number, am obtained by minimization of the difference behveen the calculated and the experimental response curves (using the classical imperfect pulse technique. see e.g. Villetmaux. 1982).

Heat transfer in a packed bed reactor can be described by homogeoneous or heterogeneous models. The hetero eneous model considers separately the tempetiUute of each phase as well as the bea! transfer between the difpkrent phases but, for practical purposes, leads to a far too complicated descripion of the phenomena. In case of slow, not highly cxothermic reactions, the difference between these temperatures is low enough to allow the use of a homogeneous model, with yields much simpler equations. The results were represented therefore by using a two-parameters homogeneous model, assuming plug flow of fluid and considering the packed bed as an equivalent quasihomogeneous medium ; the parameters are the bed effective radial conductivity hr and the wall heat transfer coefficient aw. The latter parameter allows to take into account a supplementary heat transfer resistance at the wall, due to a lower radial dispersion of the fluid. For a cylindrical packed bed, in steady statecondition. the heat balance gives :

with

Cpg* = AH*/cr,,t-Tin)

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Packed

bed with

comment

upflow

3495

Cpg* is the equivalent heat capacity of saturated gas and allows to take an evaporation of liquid during the flow through the column into account_ AH* is the increase of specific enthalpy of the gas between the outlet and the inlet of the heating section. It is assumed that the gas is always saturated with liquid vapor. The axial second derivative of the heat balance equation is assumed to be very small compared to the other terms. This assumption has been checked by severals authors (e.g. Dixon, 1985). The boundaty conditions am constantheatfhrxatthewauandcylindricalsymmetry: Ar($)=qw

for r=R

alXI

I=0

for r=O

(3)

The solution of this equation, given by Carslaw and Jaeger (1959) is then used to fit the computed temperature profiles to the experimental ones, and to determine the heat transfer parameters Ar and aw. The heat transfer coefficient verifies the following equation, Tw beii measured. and TeR being extrapolated from the computed profiles : qw = aw ( Tw - TeR ).A detailed description of this classical fitting technique may be found in Gutsche (199Ob) This procedure leads to a satisfactory fitting of the temperatureprofiles. HYDRODYNAMICS

The flow in the reactor is represented by the plug flow model with axial dispersion, and the heat transfer is described by a homogeneous model assuming plug flow. The axial dispersion coefficient Dx has thus to be small enough, which is considered to be verified when the axial dispersion -let number PEx = uolH,!Da is higher than hundred (H being the height of measuring section). For L>lkg/rn%. PEx>lCKl and the plug flow assumption is justified, but for U 1kg,@& axial dispersion may be important,

For smaller particles (1 and 2 mm) neither bubbles nor pulses are observed but separated flow in the pores (called single-phase pore-flow by Saada. 1974). For bigger particles (4 and 6 mm) bubbling flow is observed at small gas velocities and pulsing flow at higher gas velocities. Comparison with existing flow maps (as weLl as comparison between them!) is rather disappointing. Nevettheless, as to the transitionfrom bubble flow to pulsed flow in upflow reactor, satisfactory agreement is found between different studies : in this study the transition is observed for G = 0.1 too.15 kg/m~,Nakamura(198l)mentionnedG=O.11 to 0.17 and Sokolov (1983) G - 0.17 kg/m%. PI L(kg/m* rbdtmm) =

The liquid holdup & is defined by the ratio of bed ,,8 void volume occupied by liquid. Figure 2 shows Bl as a function of gas velocity, for different particle sizes and for different liquid flow rates 0.6 (all packings are non-porous). - the liquid holdup decreases with gas velocity (first strongly and then slowly, at higher gas flow 0.4

l

- the liquid holdup @creases with liqui.d velocity. E fg bAggGf=zles (4 or 6mm) hqmd flow o.2 -

__

_

__

_

__

__ _

__

l-l

A 5.9-1

0

0.1

0.2

0.3

11-l

0

1-4

A

5.9-q

0

11.3-4

G (kg/m* s)

- at given fluid velocities, the liquid floldup Fig. 2. Dependance of the liquid holdup to packing incteases with particle diameter. diameter, gas and liquid mass flow rates . . n wtth coComparison with correlations proposed for trickle flow (Guts&e, 1990 ; ElIman, 1988 has correlated data from different authors) shows that the liquid holdup is higher in upflow than in downflow. Achwal and Stepanek (1976) worked in upflow and proposed the following correlation: @1= I- ( 1 + 0.59 uol9.13 Llog’o~~63 )”

(4)

The experimental results obtained in both columns and with the different sixes of packing have been compared to this correlation. The agreement is of flO% for 4 and 6mm (except for liquid superficial velocities lower than lmm/s). For smaller particles, the liquid holdup becomes smaller and the correlation overestimates the result of 15 to 20%. The correlation, which has been obtained for 6mm packing. has thus

cz

A. S. LAMINE et al.

3496

and 2mm) and we propose to use (with an agreement of f109b to

for smaller particles (d-l the experimental results, see figure 3a) :

to be corrected

B1= 1-( 1.3 + 0.3 uolOJ3 uog-0.563 )-I T+

E$s:

(5)

between small and large packing. is not sur~xising, it is to be +ated to the different fIow rem separated flow. at same gas and hquld velocrues. the gas occupres more space than m bubble

~erence .

drift flux approach (delined by Saberian et crl., 1984) gives another way to correlate liquid holdup. A drift velocity vgl of the gas is defirnzd as the difference between the linear gas velocity and the mean linear velocity of the gas-Liquidmixture:

The

flux of the gas ugl is the conesponcllng aupcrfrcial velocity ; ugl = es - pl (kg + u& and it is WSilyshoWnthatthe fO~OwingfO~ulationOf~~iStquiValenttothisdefiniti~:~~=(~+ Ud>/(~g+U,&. The main interest of this approach is that in many cases, ugl is found to be independant of the liquid velocity and approximatl proportional to the gas velocity. This was shown by Larachi et al. (1991) in cocurrent upflow or dow nfYow fixed bed reactor (in high interaction regime) and by Nacef et al. (1988) in fluidixed bed reactors in coalesced bubble flow. Tbe drift

Present exIxzirnentaI results yield ugl - 0.5 uog for d= 1 and 2mm (in separated flow) and u - 0.6 uog for d= 4 and 6 mm (in bubble flow) ; this is valid for uog 2 O.Scm/s and ~012 O.IcnUs (as saiJVle fore. plug flow is not verified for uol 5 O.lcm/s and furthermore, at very low liquid velocities, the gas phase may become continuous in some cases). These results correspond to a simple conelation of Iiquid holdup : a UOE+

~01 a = 0.5 in separated flow : a = 0.6 in bubble flow ; for uog 2 O.Scm/, ~12O,Icm./s (7) uo1 In its range of application, this correlation represents the liquid holdup to flO% (figure 3b). Althrough its range of validity is smaller than Achwal and Stepanek’s correlation (valid at any gas and liquid velocity), this approach has the great advantage to yield a very simple mlation and to be based on a physical phenomenon. Pl=

uog+

Another author (Yang, 1990) proposed a correlation based on this kind of approach: gl = 1- k uog / (WA+ proposed k=0,16/& for non-foaming systems and set the condition of validity as: uog / (u~l+ wg) S 0.93. This relation, represents our results to f25%.

uog ) and

cl-lmm

A

A d-2mm 0.6

d-4mm

l

d-6mm

0

d-4

-

corr.(5)

l

d-6

-.

cotr.(4)

0 0

2

4

6

6

10

12

14

16

18

A d-l 0.6

0

uo

p.13w9-0.563

A d-2

0 0

0.1

0.2

0.3

0,4

0.5

0.6

0.7

0.8

0.9

1

',*xP.

Fig. 3. Liquid holdup correlations. a : Achwal and Stepanek. 1976 (45) : b: drift flux approach (7) HEATTRANSFER In case of two phase tlow, the thermal hehaviour strongIy depends on the flow regime. With smaller particles (1 and 2 mm) and moderate flow rate of liquid (i.e. I? our range of experimental conditions) separated flow in the pores is observed. whereas for larger parucles (4 and 6 mm) bubble flow is first observed and then puIsed flow, with increasing flow rate.

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upflow

3497

For smaller particles.in the [email protected] of separaredflow, & is an increasingfunctionof both gas and liquid flow rates. For larger panicles. AZincressessuonglywiththegas~wrateinbubMtflowanddecneasesin pulsed flow regime. The increase of Ar with gas flow rate ban IX e~plainea by the tillowing physical phwnnef~ : - Decxeasing liquid holdup leads to a higher liquid velocity and thus to a hater radial mixing of the liquid; - The presence of gas flowing through the packing increases the mixing length of the liquid and thus the dispersion. Astothedeawse of conductivity in pulsed flow, it can be observed gas flow rates gas bubbles coalesce and gas continuous - At hi zones. !Puch conditions are less ppicious to radial mixing of liquid ;pdquid holdup is also smaller for bigger particles (compared

that : zone altemate with liquid umtinuous ;

to the case of small ones) at high gas

.

For small particles, an extension of the single-phase flow model (due to Schliinder, 1966 and Bauer, 1983) 40,0,, represents well our experimental results. This extension our team by Gutsche. 1989 confirmed by and measurements) is ba following assumptions : - The presence of gas accelerates the ‘O ’O’ liquid and the liquid velocity has to be divided by the liquid holdup; - The gas contribution to radial ’’” ’ dispersion can be evaluated in the same manner as the liquid one since both phases are nearly wntinuous ; 200 150 100 50 0 - The mixing length has to be it is smaller than in singlecorrected, phase flow since the presence of gas Fig. 4. Bed conductivity, in separated flow, corr.(8) Interrupts the liquid flow, the proposed value being x=0.9 d ; - The thermal resistance of both phases are assumed to be pamuel. The effective thermal conductivity is thus the sum of the conuibutions liquid and is estimated by the following equation : Ar =&$o+

250

of the stagnant bed. the gas and the

0.9 L CD1 d + 0.9 G C&

d

(8) ScMlI g Bl Figure 4 shows the comparison of calculated and experimental radial conductivity in the case of 2 mm particles, the liquid holdup being estimated by equation (5). The agreement between this simple model and our experiments is quite satisfactory. The experimental data obtained with particles of 1 to 2 mm and reactors of 50 and 1OOmm ID are also successiUy rrpresglud by the model. However, it fails to m the heat transfer for larger particles. But since the flow regime also changes, it is not su~rising. ‘Ihe move of gas bubbles further increases the mixing and therfore the heat transfer. This should at least be taken into account by an addtionnal term, depending on both gas and liquid velocities. vclareeres. (4 and 6 mti Depending on the fluid flow rates, two different flow regimes are observed : bubble flow and pulsed flow. Since the heat transfer strongly depends on the hydrodynamics. no general correlation can be expected. We propose two empirical correlations, one for each regime. flow

a

In this case, the liquid is the continuous phase and the gas the dispersed one. Therefore. we assume th+ the term due to the liquid is the same as measured in single-phase liquid flow, Provided the liquid velocity is divided by the liquid holdup. Then the additional term due to the &as is emprically determintd ; the liquid holdup is estimated by Achwslr and Stepanek correlation (4); the proposed com?lation is the following :

A. S. LAMINE et al.

3498

hr _ bo+ 0,055 L ($1 d ti ti As shown in figure 5 this-equation represents satisfactory the expefimeiual reesults ; it was also tested for 6mm glass beads. For both packings, the agreement is of LU%. For mea~umment~ canied in the smaller mactor CSOmmXD)the agreement is of &30%. In this flow regime, completely different from the preceding ones, the conductivity dectwrscs withgaS flow rate. Tht experimental results are well represented by Nakamura’s correlation @btkamura, 1981) who alsowo~inup~owandwithncariythcsamesizeofpackings(~4md6.6mmIna57mmIDluwxor): & - = a,Relb Regc ti

with 22.5 s a I; 26.9 O.SS 5 b 5 057 and c=-O.3

(10)

oUr~~~~~alsoprwedthat,atgiVenRe~~Re*,thebedconductivity increascswithpanicle diameter and deneases with column diameter. lherefom, we propoSe the following modit5ed equa&m ; (11) This correlation has been compared to heat transfer m easumment in both reactors (1Oomm and 5omm LD) and with NV0Si=S of packing (4 and 6 mm) and alsO to Nakamurp’s experimental m~ults (57 ID reactor, 4 and 6.6 mm packing). The fitting is better than 25% (figure 6)cxccpt in a few casts for the Xkmn reactor and 6mm packing. But in this reactor, the lower number of thermocouples (three instead of &ne in the core of the bed) induces a less precise measurement. hr/ LI 60 50

40

30

20

10

0

Pel/B, Fig. 5. Correlation of bed conductivity in bubble flow regime (9). 0

100

50

150

200

250

300

350

400

450

d(mm)lD(mm)

0 Fig.

1

2

3

4

5

6

II

7

6. Correlation of bed conductivity in pulsed flow regime (11).

~

Comparison of experimental results to correlations established in down flow studies does not yield good agreement (as already shown by Gutsche, 1990) ; comparison of re~uh~ in bubble flow re8ime to results

Of

Hashimoto (1976) shows a systematic higher conduchvity in upflow. This confirms that the heat transfer and thus the thermal stability is better in upflow reactors than in trickle bed reactors in c&e of moderate gqS velocities (in bubble flow regime). Compatison to Sokolov’s correlation, established in bubble upflow IS rather satisfactory (20 to 50%) but the discrepancy is increaSing with liquid flow rate.

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Packed

bed with cocurrent

upflow

3499

In some cases, for big particles (4 and 6 mm) and very low liquid flow rates (0.15 to I kg/m&). measured temperature profiles are neariy flat (figure 7). and the obtainad value of equivalent bed conductivity is very high. The conductivity comes back to usual values for high gas flow rate. This high radial mixing can first be explained by low Iiquid holdup @I = 0.1 to 0.4 for d=6mm and L=O_%g/m*s) and thus by a high liquid linear velocity. Furthermore, rxcirculating flow probably occurS in the bed. This assumption seems to be which wem slightly higher confirmed by some temperature values in centre snd in upper part of the mr than at the wall in some cases (L4),5kg/m2s and OcGS0,1kg/m2s). ‘Ibis phenomena are enhanced by a greater porn dimension (they do not occur for d-l and 2mm and am stronger for d=6 than for d=4mm). 16

T-Tin(W)

T-Tin(%)

14

G(km’

=I

-0

t

1 0

0.004

*

0.006

0

0.025

A 0.097

. _.

Id-5mm

0 0.01

0

0.02

Fig.

: L-0.5Wm2 _ 0.04

0.03

r(m)

sl

I

0.05

r(m)

7. Temperature profiles at low (Js0.S)

and ordii

(lsS.9

k&m%)liquid flow

rate.

Wall > transfercoefficient (1.VI(W/m

*K)

10000

1000~

100 7 0.001

0.01

G (Kg/m

*s)

0.1

0.001

0.01

0.1

‘G

(Kg/m

2

S)

10

Fig. 8. Wall heat tmnsfer coefficient : a : smaller packings ; b = larger packings. The wall heat transfer coefftcient increases with liquid velocity. Like the bed thermal conductivity. aw depends on hydrodynamics. For smaller packings (in separated flow), aw is nearly constant ; for larger packings, this coefficient increases in bubble flow and decmases in pulsed fIow (figure 8). At given values of gas and liquid velocities. aw increases with packing diameter, this means that the wall heat transfer resistance is stronger for smaller particles. For gas and liquid flaw rates higher than 0.05 and 1 kg/m%, the Biot number roughly tends to a constant value, with Bi- aw d/Ar (BirO.2 for d-l ; Bid.4 for d=2 and Bi-0.6 for d=4 and 6mm). The wall heat resistance is thus never negligible in two-phase flow. CONCLUSION The heat transfer in tubuIar packed bed reactors with cocurrent upflow has been studied : it is quite well represented by the homogeneous model, except for very low liquid velocities wher the temperatureproiles tend to &come flat. Heat uansfer parameters have been shown to be strongly dependent on hydrodynamics. The flow regime depends on gas and liquid flow rates. and also on particle diameter. Adequate correlations have to be used for each case : - for smaller packings (d=l and 2mm) 0.9 L CD1 d + 0.9 G C&d separatedflowinthepolrts: Ar=&+

8 81

8 U-$II

3500

c2

A. S. LAMINE et al.

-.for larger

packings (d=4 and 6mm) : Ar

inbubbleflow.

* -=-+ h

x,

0.055L Cnl d

h

Xl Bl

NOMENCLATURE

Cpr

cpl* d D Ds G H * ; 5 qw

Heat capacity of liquid (J/kgK) Heat capacity of sammted gas (aq.2) (JlkgK) Packing particle diameter (m) Reactor diameter (m) Axial dispersion coefficient (m2/s) Gas mass flow rate (kg/m%) Height of measuring 2one (m) Specific enthalpy of saturated gas (J/kg) Inner diameter (m) Liquid mass flow rate (kg’m%) Axial dispersion P6clet number (I&-I/D& (-) Prandtl number of the fluid (= pt Ct.,&) (-) Wall heat flux density (W/m2)

Radial coordinate

Wall heat transfer coefficient (WIm2K) Liquid holdup (-) Bed void fraction (-) Liquid them& conductivity (W/inK) Bed radial conductivity (W/mK) Bed conductivity without liquid flow (W/mK)

Bed axial conductivity (W/mK) Gas viscosity (Pa s) Liquid viscosity (Pa s) Gas density -3) Liquid density -3)

(m) Reynolds mmber of thegas (G d /pg) (-) Reyr~~ldsnumber of the liquid (L d / cy) (-) Entrance (of he;lting sectiat) fluid temperam=(K) Outlet (of heating section) liquid tanpcmmm(K) Drift flux of the gas (m/s) Gas supetIi15al velocity (m/s) Liquid superficial velocity (m/s) Axif coordinate (m) Mixinglength

REFERENCES Achwal S.K.and Stepanek J.B. (1976). Holdup profiles in packed beds, Clrrm. Eng. J., J2,, 69-75 Bauer R.( 1977). Effektive radiale WiSnneleitigkeit gasdtuchstt0mter Schttttungen mit Pamkeln unterschiedlicher Form und GrCIj3envetteilung, VDI-Forsch.-H4ft 582, Wsseldorf Carslaw H.S. and J.C. Jaeger (1959) Conduction of hear in solti, Oxford University Rcss. Dixon A.G. (3985). The length effect on packed bed effective heat tmnsfer parameters, Ghan. Engl., 31. 163-173 Elhnan.M.J.. N. Midoux, G.Wild, A, Laurent and J.C. Chatpentier (1990). A new. improved liquid holdup cotrelation for trickle-bed teactots, Chem. Eng. Sci., 45. 1677-1684 Gutsche S. (1990). Tran$ert de chalew dans un reactew & litd cocour4~ ascen&znt & gaz et de &q&e, PhD thesis, Institut National Polyttchnique de Lorraine, Nancy Gutsche S.. 0. Wild, C. Roixard. N. Midoux, J.C. Chsrpentier (1989). Heat transfer phenomena in packed bed reactors with cocunent upflow of a gas and a liquid, Pruce&gs qfthc 5rh Coti Applied Chem. Unit Operations and Processes, Vesxptim, Hungary, 402408. Hashimoto,K, K. Muroyama, K. Fujiyosh, S. Nagata (1976). Effective radial themtal ccmductivity in ctxmmnt flow of a gas and liquid through a packed bed. I#. Chem.Eng, J&720-727 Nakamura.M., T. Tanahashi. D.Takada, K. Ohsasa and S. Sugiyama (1981). , Heat transfer in a packed bed with gas-liquid cocurrent upflow. Heat Transfer : Japanese Research. JO, 92-99 Saada MY. (1974). Fluid mechanics of co-current two-phase flow in packed beds : pressure dtop and liquid holdup studies, Per. PO&. Chem. Eng.. 19. 317-337. SchlUnder E.U. (1966). W&me- und StoffIibertragung zwischen dutchst&mten Schiittungen tmd datin eingebetteten Einxelk&pem. Chem.-lng.-Techn., 38 ,967-979. Soko1ov.V.N. and M.A. Yablokova (1983). Thermal conductivity of a stationary granular bed with upward gas-liquid flow, J. Appld. Chem. USSR (2%. Prikl. Khim.). 56 ,551~553 Villennaux I. (1982) G&tie de ka r&action chimique. Conception etfonctionnement de r&actews, Technitltte et documentation, Lavoisier. Pans. Yang.X.L.. G. Wild, J.P. Euzen (1989). Etude de la *tention liquide dans les r&cteurs P lit f=e aver Ccoulement ascendant de gaz et de liquid, Entropie, J50,17-28