trickle bed wettingfactorsfrom pressure ...fs.teledos.gr:2206/>research...

TRICKLEBEDWETTINGFACTORSFROMPRESSUREDROPANDLIQUIDHOLDUPMEASUREMENTS

YANINALUCIANIDOSINDAGONZA¤ LEZ-MENDIZABAL

Departamento deTermodina¤ mica y Feno¤ menos deTransferencia, Universidad Simo¤ n Bol|¤ var, Sartenejas,Caracas,Venezuela

FILIPPOPIRONTI

Inelectra S.A., Edif. Oficentro, San Luis, Caracas,Venezuela

In this work, solid-liquid wetting factors were determined from liquid holdup

and pressure drop measurements according to the model proposed by Pironti

et al. for different air-liquid systems: distilled water and CMC solutions at

viscosity values of 3, 6, 9, and 12mPa . s. The experiments were carried out at

atmospheric conditions in a column of 10.2 cm internal diameter and 2m

high, packed with a cylindrical material. The superficial mass velocities varied

from 0.67 to 18.6 kg=m2s for liquid flow and from 0.024 to 0.31 kg/m2s for gas

flow. Under these operating conditions, regime of continuous gas flow was

observed. The wetting factors obtained were in agreement with those reported

by other methods, which allow us to confirm that the model used in this work

is applicable to fluids of different properties at low gas velocities.

Keywords: Wetting factor; Wetting efficiency; Trickle bed reactor; Pressure

drop; Liquid holdup; Shear stress

Received 3 August 2000; in final form 30 May 2001.

Address correspondence to Dosinda Gonz�aalez-Mendizabal, Departamento de Termo-

din�aamica y Fen�oomenos de Transferencia, Universidad Sim�oon Bol|´ var, Sartenejas, ApartadoPostal 89000, Caracas 1080-A, Venezuela. E-mail: [email protected]

Chem. Eng. Comm., 189: 1653�1670, 2002Copyright # 2002 Taylor & Francis

0098-6445/02 $12.00 + .00

DOI: 10.1080/00986440290013022

1653

INTRODUCTION

A trickle bed reactor (TBR) is a system in which two phases, one liquidand the other gas, flow in a descending and concurrent way through afixed packed bed, usually filled with catalysts or reactant solids. Thesereactors are extremely important, judging by the tons of material that areannually processed through them. They are widely used in the oilindustry in hydrodesulfuration processes, residual oil hydrocracking,lubricating oils’ hydrotreatment, demetallization, etc. They are also fre-quently used in chemical processes such as the hydrogenation of glucoseto sorbitol and treatments for the control of water and air pollutionthrough bacteriological processes, in addition to also being used in bio-logical, agricultural, and pharmaceutical processes.

Different flow regimes can be found in these reactors depending onthe physical properties of the fluids involved (density, viscosity, surfacetension), the characteristics of the packed bed (porosity, size and shape ofthe particles), and the dimensions of the reactor and the superficial massvelocities of both phases. The design and scaleup parameters are affectedin a different manner in each flow regime as the hydrodynamics changefrom one to the other. In the low interaction regime the gas has practi-cally no effect on the fluidodynamic behavior of the fluid; however, theproblem of incomplete wetting of the solid surface presents itself due tothe low velocities of the liquid being used. In porous particles, the wetarea or solid-liquid contact surface can be external or internal. However,it has been shown that even at very low liquid velocities, in the order of0.05 cm=s, the internal wetting of the porous particles is total, probablyby the capillary phenomenon (Colombo et al., 1976; Al-Dahhan andDudukovic, 1995; Llano et al., 1997). Schwartz et al. (1976) reported thatthe internal wetting factor is constant and equal to 0.92. For this reason,the internal wetting fraction can be taken as 1 for practical effect.However, this assumption is not always valid when the reactions arestrongly exothermic (Mills and Dudukovic, 1993). In contrast, the effi-ciency or external wetting factor f increases with the liquid and gasspeeds, and equals 1 only at high liquid velocity. The knowledge of thisfactor is essential for the design and scaling of the reactors, since it allowsthe calculation of the utilization degree.

From the literature data f has been obtained either with a chemicalmethod—comparison of reaction rates in a two-phase operation and in areactor completely filled with the liquid—or with physical techniques.The physical tracer method is based on the analysis of the reactorbehavior after a step change perturbation in the tracer concentration iscarried out at the entrance, obtaining as a result a kinetic constant or anapparent interparticle diffusivity. It has been shown that the wettingfactor is proportional to the ratio of these apparent values with those

1654 Y. LUCIANI ET AL.

obtained in experiments when the particles are totally wetted. Modelswidely used in the literature for wetting efficiency are summarized inTable I.

The external fraction of wetted area f has been correlated basically asa function of dimensionless numbers that include physical properties andoperative parameters. Some of the oldest expressions are the onesreported by Onda et al. (1967) and Puranik and Vogelpohl (1974). A briefsummary of proposed correlations to estimate wetting efficiencies in TBRis included in Table II.

It should be noted that Equation (11) leads asymptotically to phy-sically bounded values of wetting factor approaching unity. In effect,substituting Equations (12) and (13) into Equation (11) and simplifyingyields:

f ¼eLeB þ

DP2�phase�DPgas�filledLgðrL�rGÞ

1þ DPliquid�full bed�DPgas�filledLgðrL�rGÞ

ð16Þ

eL=eB is lower or equal to one, since the liquid holdup is always less thanvoid fraction; it will be one if no gas is present. On the other hand, two-phase pressure drop is also lower than liquid full-bed pressure drop underthe assumption that pressure drop is due only to frictional losses. Soaccording to Equation (16), f is bounded to a maximum value of one,excluding of course experimental errors that may lead to inaccuracies ondetermined variables. If two-phase pressure drop increases in lieu of alarge gas velocity or a high pressure (gas density), both liquid holdup andliquid thickness will decrease and induce liquid separation from solidsurface. Under these circumstances nonfrictional losses will become

Table I Wetting Efficiency Models

Satterfield (1975), Scwhartz et al.

(1976)

f ¼ðKAÞapparent

ðKAÞliquid�full bed(1)

Colombo et al. (1976) f ¼ðDeffÞ2�phase

ðDeffÞliquid�filled(2)

Dudukov|´ c (1977), Mills andDudukov|´ c (1981), Al-Dahhan andDudukov|´ c (1995, 1996)

f ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDeffÞ2�phase

ðDeffÞliquid�filled

s(3)

Lakota and Levec (1990),

Gonz�aalez-Mendizabal et al.

(1998)

f ¼ðKS � aLSÞ2�phaseðKS � aÞliquid�filled

At the same v�L (4)

Pironti et al. (1999) f ¼ðtLS � aLSÞ2�phase

ðtLS � aÞliquid�full bedAt the same v�L and v

�G (5)

TRICKLE BED WETTING FACTORS 1655

Table

IIWettingEfficiency

ModelsandCorrelations

MillsandDudukovic

(1981)

f¼

tgh

0:664

r LvLdp

m L

�� 0:3

33

v2 La

g�� 0:1

95

r Lv2 L

sa

�� 0

:171

ad2 p

e2 B ! �0

:0615

2 43 5

(6)

El-Hisnawiet

al.(1982)

f¼

1:617Re0 L�� 0:14

61Ga0 L

�� 0:

0711orf¼

b Ld

ðÞ0

:224

(7)

Alicilaret

al.(1994)

f¼

1�

25:626

Re0 L�� 0:96

35<

Re0 L

<180

(8)

Al-DahhanandDudukovic

(1995)

f¼

1:104Re1

=3

L1þ½ðD

P=LÞ=r L

g

GaL

� 1=9

(9)

Gonz� aalez-Mendizabalet

al.(1998)

f¼

1�exp�4:265�10�2Re0

:745

LRe0

:079

G

��

6:71�

Re L

�117:90and32:00�

Re G

�204:19

(10)

Pirontiet

al.(1999)

f¼

gr L

e Lþr G

ðeB�e LÞ

½

þ

e BDP2�phase

L�ðt

GS�aÞ g

as�

filled

ðtLS�aÞ li

quid�filled

bed�ðt

GS�aÞ g

as�

filled

(11)

ðtLS�aÞ li

quid�fullbed

¼e BðD

PÞ li

quid�fullbed

Lþe Br L

g(12)

ðtGS�aÞ g

as�

filled

¼e BðD

PÞ g

as�

filled

Lþe Br G

g(13)

Double-SlitModel,Iliuta

etal.(2000)

f¼

f2

2E1

e L e B�� 2

CL�1þr G rL

�� G

aL

Re L

f s

þf2

2E1

e L e B�� 2

CL�1þr G rL

�� G

aL

Re L

f s

"# 2 �

O

8 < :9 = ;1=

2(14)

O¼

f2

E1

e L e B�� 2

CL�1þr G rL

�� G

aL

Re L

f sþ2f2

3E1

e L e B�� 3 C

LGaL

Re L

(15)

1656

predominant, and this model is not applicable since wetting factorsgreater than one will be obtained.

Recently, Iliuta and Larachi (1999) proposed a generalized slit modelfor the prediction of frictional two-phase pressure drop, external liquidholdup, gas-liquid interfacial area, and wetting efficiencies in TBR. Thewetting factor may be calculated from the relationship in Equation (14),shown in Table II, knowing the velocities and properties of each fluid,Ergun’s constants (E1, E2), and the shear and velocity slip factors (Iliutaet al., 2000).

The applicability of the empirical correlations that have beendeveloped to determine the degree of wetting of the packing as a functionof the liquid and gas velocities, the physical and chemical properties ofthe liquid, and the size of the packing is questionable, as it requires theperformance of experiments under conditions corresponding to suchoperations (Satterfield, 1975). In this work the solid-liquid wetting factorwas experimentally determined using the model proposed by Pironti et al.(1999). This model was validated with experimental data reported byAl-Dahhan and Dudukovic (1994) and data obtained by same authorsfor the air-water system. The main objective of this work is to determineif the model applies to different air-Newtonian liquid systems.

EXPERIMENTAL

The experimental facility, bench scale, used to measure pressure dropsand liquid holdup for both single-phase and trickle-bed operation isshown in Figure 1. This facility consists of a trickle-bed reactor setup, thegas and liquid delivery systems, and data acquisition system. The reactorwas made of a 10.16 cm internal diameter and 2m high carbon steel tubewith four 0.635 cm pressure taps, each one separated 0.6m. The columnhas a thick optically clear acrylic window to observe the behavior of thetwo-phase flow near the wall surface. The gas-liquid distributor designedis similar to the one used by Herskowitz and Mosseri (1983) to ensureuniform liquid and gas distribution at the bed inlet.

The liquid phase from its storage in a 200L reservoir was pumpedthrough a rotameter up to the top of the column. The flow was regulatedmanually by needle valves. Distilled water and four aqueous solutions ofCMC in different concentrations were used as liquid substances. In orderto characterize the substances being used, the densities of the fluids weremeasured utilizing pycnometers, a Brookfield viscosimeter to measure theviscosities, and the pendant drop method (L�oopez de Ramos et al., 1993)to measure the surface tension. These properties are summarized inTable III. The steady shear stress-rate data obtained for the aqueoussolutions of CMC was shown to be linear, so Newtonian behavior wasassumed to prevail for the range used in this work. Additionally, during


the course of experiments, periodical measurements of rheologicalproperties were done to ensure that no mechanical degradations of CMCaqueous solutions may have occurred.

Compressed air, regulated to a fixed pressure of 515 kPa, was driventhrough gas rotameters and introduced to the top of the column at agiven flow manually fixed by a needle valve. For all the experimentalruns, the liquid and gas phases were at ambient conditions (25�C andatmospheric pressure). The column is packed with cylindrical extrudedcatalyst material with 3.19mm mean diameter and 5.33mm mean height.The characteristics of the column and bed properties are shown in

Figure 1. Schematic diagram of the experimental setup. B1: pump; D: distributor; PT: pres-

sure transducer; R: reactor; R1, R2, R3, R4: rotameters; S1, S2: solenoid valves; St: terminal

section; V1 to V9: valves.

Table III Characteristics of Fluids Employed

Fluid Air Water CMC-3 CMC-6 CMC-9 CMC-12

Density (kg=m3) 1.184 997 1001.3 1002.2 1002.3 1002.4

Viscosity (mPa.s) 0.0182 1 3 6 9 12

Surface tension (mN=m) � 70.8 55.8 54.9 53.3 53.0


Table IV. The column to particle diameter ratio is about 26, enough toavoid channeling and to ensure a uniform distribution of liquid throughthe packing (Al-Dahhan and Dudukovic, 1996).

On the top and at the bottom of the column there are two solenoidvalves connected to a switch that suddenly and simultaneously interruptsthe entrance and the exit of fluids to the column and thus allows themeasurement of external liquid holdup. The exit valve of the column isopened, allowing the liquid to drain for at least 30min. After thatthe liquid collected is weighted. Then the dynamic liquid holdup iscalculated by:

eLd ¼WLrLV

ð17Þ

Pressure drops across the particle bed were measured with pressuretransducers connected to the top and bottom of the reactor bed. Then thesignal was recorded by a data acquisition system. For each gas and liquidflow rate, a minimum of 20min was allowed for the pressure drop andliquid holdup measurements to ensure the data reflected true steady state(Holub et al., 1993). The mass flux range adopted in this work variedfrom 0.67 to 18.6 kg=m2s for liquid flow and varied from 0.024 to 0.31 kg/m2s for gas flow. Under these operating conditions, visual observationthrough the acrylic window indicated the existence of continuous gas flowregime in the column. This was corroborated by stable and steadypressure drop measurements.

To determine the wetting factor, according to the model employed inthis work (Equations (11)�(13), Table II), single-phase pressure dropsare needed as well for different gas and liquid flows under two-phaseflow, and liquid holdup for two-phase runs. To predict pressure dropwhen only one-phase experiments are carried out through the column,Ergun’s equation can be used (Ergun, 1952). The Ergun constants E1 andE2 were determined for the packed bed using only gas flow on drypacking. The values obtained were E1¼ 150 and E2¼ 1.8 (Pironti et al.,1999). Previous to each two-phase flow experiment the packing bed wasextensively prewetted by flooding the bed, then the exit valve of the

Table IV Characteristics of Solids and Column

Column diameter 10.16 cm

Column volume 16.86L

Void fraction of the bed (eB) 0.41±0.01Static holdup (eLS) 0.036±0.001Mean equivalent diameter of the particles 3.68±0.01mm


column was opened, allowing the liquid to drain. This procedure assureda uniform liquid-gas distribution and prevented hysteresis effects inmeasured pressure drop.

RESULTSANDDISCUSSION

A total of 125 experimental tests were performed with varying flow ratesof both phases. For each fixed liquid flow rate, different air Reynoldsnumbers were operated: 34, 52, 71, 89, and 107. In Figure 2, the effect ofthe liquid phase properties over the dynamic retention of a liquid for aconstant gas velocity (ReG¼ 34 and 107) is shown. It is clearly observedthat the holdup increases at a higher viscosity and at a lower surfacetension. This behavior coincides with that reported by Ellman et al.(1990). Wammnes et al. (1990) indicated that surface tension of the liquidhas no drastic influence on the dynamic holdup unless the working sys-tem is of the foaming type. For this reason, in this work we can attributethe augmentation of the holdup, in a larger degree, to the increase of theviscosity in the CMC solutions, and not to the decrease of the surfacetension of the solutions. Iliuta et al. (1996) found that dynamic liquidholdup increased with increasing CMC concentration, as a result oflarger liquid phase stresses in the gas-liquid and solid-liquid interphases.

Basically, all correlations reported in the literature for the calcu-lation of the dynamic liquid holdup show a direct power dependencyupon liquid superficial velocity or liquid Reynolds number, with anexponent according to the movement of the liquid through the bed(laminar film, turbulent films, or spray) and the particle texture.Generally the values of this exponent oscillate between 1/3 for laminarfilms and 0.5�0.6 for turbulent films (Wammes et al., 1990). However,contradictory results have been found, for instance, Goto and Smith(1975) reported a 1/3 power for lower liquid Reynolds numbers, whileKohler and Richarz (1984) related the liquid dynamic holdup, eLd,with a 0.53 power for very low ReL (0.1�5). In this work, the expo-nents obtained for all the liquids used are around 0.3, which is anindication that the flow regime is laminar film, where the energy lossof the fluid is mainly due to the viscous effects between the liquid andthe packing (Wammes et al., 1990). Regarding the effect of the gasupon the liquid holdup, Shah (1979) and Ramachandran andChaudhari (1983) reported that at atmospheric pressure it was notconsiderable. Their results are in agreement with those obtained in thiswork. However, at high pressure, the gas flow reduces the liquidholdup notably due to the increase of the drag force in the liquid-gasinterface.

Figure 3 shows the effect of the liquid properties on the pressuregradient throughout the packed bed for ReG¼ 34 and 107. As was


expected, a larger pressure drop is produced with substances that have ahigher viscosity due to the fact that the shear stresses of the liquid sideincrease at the gas-liquid and liquid-solid interfaces (Iliuta et al., 1996).Furthermore, it is observed in this same figure that for all liquids used,pressure drop increases with liquid and gas flow rates.

Figure 2. Dynamic liquid holdup vs. superficial liquid mass velocity for ReG¼ 34 andReG¼ 107.


Shear stress for liquid- and gas-full bed was calculated from theErgun equation with the constants determined by measured single-phasepressure drops. The shear stress for two-phase operation together withthe liquid-full bed results for air-CMC-3 are shown in Figure 4 as afunction of modified liquid Reynolds numbers (ReL*¼ReL�eB=eLd) for

Figure 3. Pressure drop for two-phase flow vs. superficial liquid mass velocity for ReG¼ 34and ReG¼ 107.


several gas Reynolds numbers. The same behavior predicted by Lakotaand Levec (1990), Gonz�aalez-Mendizabal et al. (1998), and Pironti et al.(1999) is clearly observed from this figure. As the gas and liquid flowincreases, the wetting factor should come closer to unity, since the shearstress for two-phase operation is approaching the liquid-full bed values,even more if the Reynolds number is based on the intrinsic liquid velocityover the particles.

The wetting factors were calculated by the model of Pironti et al.(1999), showing that the wetting efficiency increases monotonically to onewith the liquid mass velocity and gas Reynolds numbers. Figure 5 showsthe effect of liquid properties over the wetting factor for ReG¼ 34 and107. As can be observed, the wetting factor increases as the viscosity ofthe liquid solutions increases and the surface tension decreases. As sur-face tension decreases, the contact angle between the fluids and solidsdecreases, favoring the wetting of the packed bed. Additionally, as theviscosity increases, so does the liquid’s holdup, favoring an increase inthe wetting factor. However, the results do not allow the decoupling ofthe influences of each isolated property.

In Figure 6, all wetting factor values obtained in this work are showntogether with some literature data and correlation reported by Gonz�aalez-Mendizabal et al. (1998) for ReG¼ 107. As can be observed, the values off follow similar tendencies as those found in the diverse literaturecited. Furthermore, when compared with the correlation proposedby El-Hisnawi et al. (1982) and the mechanistic model proposed byAl-Dahhan and Dudukovic (1995), a maximum divergence of 25% wasfound (Figures 7 and 8). Additionally, in Figure 9, our results are

Figure 4. Liquid-solid shear stresses as a function of modified Reynolds number for two-

phase and single-phase (liquid-full bed) flow. System: air-CMC-3.


compared with those obtained using the Double-Slit Model (Iliuta et al.,2000), and the average deviation was 35%. These results confirm thatthe model and experimental methodology employed in this work areadequate to calculate solid-liquid wetting factors in three-phase columns

Figure 5. Solid-liquid wetting factors as a function of superficial liquid mass velocity for

ReG¼ 34 and ReG¼ 107.


Figure 6. Wetting factors as a function of superficial liquid mass velocity. Comparison be-

tween data obtained and values reported in the literature.

Figure 7. Parity plot of experimental wetting factors obtained in this work and values cal-

culated from model proposed by El-Hisnawi et al. (1982).


with a fixed packed bed in a continuous gas regime, for Newtonianliquids with different properties at low air velocities. For large gasvelocities at fixed liquid rate, pressure drop increases. This incrementimproves liquid film spreading, making the external area wetter. However,the model proposed by Pironti et al. (1999) fails to take into account thegas-liquid turbulent stresses now present.

Finally, it can be inferred from Figure 6 that the measurementmethod does not affect the f values, since data obtained from physicaltechniques were compared with values recollected through physical andchemical methods, and no striking difference was observed. This beha-vior is contradictory to that reported by Llano et al. (1997), who foundthat their wetting factor values obtained through chemical method werebelow those calculated through physical techniques, especially at lowliquid velocities. To our knowledge, no other investigator has reportedthis result explicitly. In fact, other authors (i.e., Mills and Dudukovic,1981) have used the data originating from chemical and physical tech-niques without distinguishing them and have even related them with thesame empirical expression. Gianetto and Specchia (1992) also reporteda graph comparing a large number of data regarding f obtained throughboth methods, concluding that there exists no evident effect of the


culated from model proposed by Al-Dahhan and Dudukovic (1995).


measurement technique on the results. Additionally, it was concludedthat the divergence of the f values is due to the characteristics of theparticles used by each researcher (form, size, wettability), and that manydid not consider the effects of the gas stream. This effect could be con-sidered if working with the modified Reynolds number instead of thetraditional one, as was done during this work.

CONCLUSIONS

Solid-liquid wetting factors were calculated through a physical non-intrusive method, in continuous gas regime, from liquid holdup andpressure drop measurements. A direct dependency of the wetting fractionwith the liquid and gas flows was verified. It was shown that wettingfactor increases as the viscosity of the liquid solutions increases and thesurface tension decreases; however, these two variables were not studiedseparately. The experimental values were contrasted against thosereported in the literature, and it was found that they are within the ampleband of values proposed by other authors for the same liquid and gasflows combination.


culated from model proposed by Iliuta et al. (2000).


When establishing a comparison between the values of f obtained inthis work against those found in diverse literature, there was no evidencethat the measurement technique (physical or chemical) could affect theresults.

ACKNOWLEDGMENTS

The authors acknowledge financial support from Secci�oon de Fen�oomenosde Transporte, Laboratorio ‘‘A,’’ Universidad Sim�oon Bol|´ var. Specialthanks to Javier Fuentes for his measurement of surface tension.

NOTATION

a effective interfacial area of particles per unit volume of bed, m71

A column cross-section, m2

de average equivalent particle diameter defined as six times the volume-to-surface ra-

tio, m

dp particle diameter, m

Deff intraparticle effective diffusivity

E1, E2 Ergun constants for the single-phase flow on the packing (describes bed tortuosity

and roughness)

f wetting factor

fs interfacial friction factor

Ga Galileo number, Ga ¼ r2gd3em2

e3Bð1� eBÞ3

Ga0 modified Galileo number, Ga ¼ r2gd3em2

ks.a volumetric liquid-solid mass transfer coefficient without reaction, s71

KA adsorption equilibrium constant

L superficial liquid mass velocity, kg .m72 . s71

Q volumetric flow, m3 . s71

Re Reynolds number, Re¼ (Q=AeB)(r=m)de(eB=(17 eB))ReL* modified liquid Reynolds number, ReL*¼ReLeB=eLdRe0L modified liquid Reynolds number, Re

0L ¼

QrdeAm

v superficial velocity, m . s71

vG* intrinsic gas velocity, vG*¼QG=(A (eB7 eL))vL* intrinsic liquid velocity, vL*¼QL=(A eLd)V column volume, m3

WL weight of the liquid, kg

Greek lettersbLd dynamic liquid saturation (liquid volume per void volume), bLd¼ eLd=eBeB packed-bed void per reactor volume (bed porosity)eL total external liquid holdup per reactor volume (eL¼ eLdþ eLS)eLd dynamic liquid holdup per reactor volumeeLS static liquid holdup per reactor volumef sphericity factorm viscosity, kg .m71 . s71

r density, kg .m73

s liquid surface tension, N .m71


t shear stress, PaDP=L pressure drop per unit of length, Pa .m71

CL dimensionless body force on liquid phase, CL ¼DP=LrLg

CG dimensionless body force on gas phase, CG ¼DP=LrGg

SubscriptsG referred to gas phase

GS referred to gas-solid phases

L referred to liquid phase

LS referred to liquid-solid phases

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