I n d . Eng. C h e m . Res. 1994,33, 519-525
519
Influence of Gas Density on the Hydrodynamics of Cocurrent Gas-Liquid Upflow F,ixed Bed Reactors Faiqal Larachi,’.+ Gabriel Wild$,Andre Laurentt, and Noel Midouxt Laboratoire des Sciences d u Gknie Chimique, CNRS, ENSIC, INPL, 1, Rue Grandville, B P 451, 54001 Nancy Ckdex, France, and Dkpartement de Gknie Chimique, &ole Polytechnique de Montrkal, P.O. Box 6079, Station A , Montrkal, Qukbec, Canada H3C 3A7
The effect of pressure on the frictional two-phase pressure drop and the gas holdup in a flooded fixed bed reactor with cocurrent upflow of gas and liquid is presented. It has been found that pressure and gas molecular weight influence the pressure drop only via gas density. An increase of gas density results in an increase of two-phase pressure drop and gas holdup a t given fluid superficial velocities. Two extrapolation tools for the estimation of pressure drops in pressurized flooded beds exclusively from experiments conducted in nearly atmospheric conditions are proposed. A new two-phase pressure drop correlation based upon more than 1800 measurements (including our data and that from the literature) carried out within broad ranges of gas densities, liquid properties, particle sizes, and column diameters is developed.
Introduction The interest in flooded bed reactors has significantly grown with the numerous potential laboratory-scale applications demonstrated during the past decade in many fields of catalytic and chemical reaction engineering (Mazzarino et al., 1989; Goto and Mabuchi, 1984; van Gelder, 1988;Germain et al., 1979). Existing applications of these reactors can be found in various types of hydrogenation and oligomerizationprocesses (Trambouze, 1991). In addition, flooded reactors with cocurrent gasliquid upflow through a catalyst bed could be more efficient than classical trickle beds, especially from the viewpoint of catalyst wetting, selectivity, liquid distribution, and so forth. Due to their novelty, however, both experimental and theoretical studies are still in the embryonic stage when compared with the overwhelming amount of research dedicated to trickle beds. Evidently, as it is dictated by thermodynamic requirements (e.g., high solubilities),these reactors will be more efficiently operated at elevated pressure. Lack of experimental data at high pressure renders all correlations and models based on data from ambient pressure biased and risky for design purposes. A rather limited number of papers have been devoted to hydrodynamic studies of flooded bed reactors under elevated pressures (Saada, 1975; van Gelder and Westerterp, 1990; Oyevaar et al., 1989; Larachi et al., 1991a). Among these, only Saada (1975) has investigated the pressure drops at elevated pressure (1.36-MPa air-water flooded bed reactor). This author, unfortunately, neither brought out the relationship between pressure and pressure drop nor proposed extrapolation tools to account for the effect of pressure. In this work, the influence of pressure on the frictional two-phase pressure drop and the total gas holdup in a cocurrent gas-liquid flooded bed reactor is presented: experiments were carried out with several different fluids (water and ethylene glycol as liquids and helium, nitrogen, argon, and carbon dioxide as gases) at pressures ranging from 0.3 MPa up to 5.1 MPa and ambient temperature in a 0.395-m-height, 23-mm inner-diameter stainless steel
* To whom correspondence should be addressed. E-mail: larachia ether.chimie.polymtl.ca. + ficole Polytechnique de Montrbal. t CNRS, ENSIC, INPL.
column packed with 3.37-mm hydrophilized nonporous polypropylene extrudates. Most of the experiments were performed in the dispersed bubble flow regime; however, a pulse flow regime was also observed at high gas velocities and low pressures. Two extrapolation techniques which allow for the estimation of pressure drops at high pressure in flooded bed reactors from nearly atmospheric experiments will be discussed. Such techniques have been validated over several systems investigated in the trickleflow operation (Larachi et al., 1991b) and proved true as long as the gas-phase flow is inertia controlled and liquids exhibit at most weak foaming behavior. After establishment of a data base containing more than 1800 two-phase frictional pressure drop data which includes our measurements and those from the literature, a new correlation for the frictional pressure drops in flooded bed reactors is proposed.
Experimental Section A detailed description of the installation and of the measuring technique is available elsewhere (Larachi et al., 1991a). The fluid and packing properties as well as the ranges of the experimental variables investigated are also summarized in the preceding reference. Figure 1 shows a simplified flow sheet of the facility which was designed to withstand pressures as high as 10.0 MPa. The apparatus allows for measurements of the frictional twophase pressure drop and the total gas holdup (part of the bed porosity holding gas) under high-pressure conditions (0.3 IPIMPa I5.1) and ambient temperature (293-298 K). Frictional pressure drop measurements are straightforward and have been obtained by means of a differential pressure transmitter. The experiments were always reproducible within 5 % . Total gas holdups have been determined indirectly by subtracting the measured total liquid holdup from the bed porosity. Liquid holdup experiments have been carried out by injecting imperfect electrolyte tracer pulses and recording on line the timedependent electrical conductivity of liquid measured by means of two probes located at each extremity of the reactor. Gas holdup may then be expressed as a function of the liquid space time 7 (obtained by time domain nonlinear fitting using the axially dispersed plug flow
0888-5885/94/2633-0519$04.50/00 1994 American Chemical Society
520 Ind. Eng. Chem.
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Rea., Vol. 33, No. 3,1994
35
M
A OJMP.
A 1.1 M P . 2.1 MPa
0 5.1 MPa
20 '"PPIY
IS WATER. NITROCEN LIQUID VELOCITY : 12.8 m d s
10
0
I
0.05
0.15
0.1
0.2
, (m/s) 0.2s uc
AOJMP. A 1.1 MP. 2.1 MP. 0 5 . 1 MPs
.
ETHVLENEGLVCOL NITROCEN LIQUID VELOCITY : 11.5 rnds
20
0
Figure 1. F l m h w t of the experimental apparatus
4n
WATER. ARGON L I 12.8 kg m.'. d G = 0.86 kg m". 1.l
.
.
0.05
10
20
30
Time
40
Fimre2. ~entalsystemresponaefortheargon-aratsrsystsm and the beat fit of the PD model.
model) and the distance between the conductivity probee by the following relation:
fo = 6 - ( U L T / Z )
0. I
0.15
,
Ws)
0.2
UG
Figure 3. Influence of operating prassure on the frictional frophaw prssaure drop for the waternitrogen (a, top) and ethylene glycol-nitrogen (b. bottom)systems.
Reduced signa1
P = 2.1 MP.
0.05
(1)
Figure 2 in an example of typical experimental inlet and outletproberesponsesobtainedat 2.1-MPaargonpmure together with the best fit of the axially dispersed plug flow model for the liquid. For the packing size and the column height used in this work, the liquid P k l e t number (based on the bed height) was of the order of 50-100 indicating a nearly pistonlike flow of the liquid. Injection experiments, repeated up to five times, led always to gas holdups reproducible within 5-10s. Results and Discussion When the reador is operating below the critical point of the liquid, pressure exclusively affecta gas-phase p r o p erties (density, diffusivity, viscosity); a t subcritical conditionsfor the gas, dynamicviscositycan safely be assumed
pressure independent, and only density and diffuaivity are functions of pressure. As will be shown below, instead ofusingpressureasavariable,gasdensityis more adequate for the description of the effect of pressure on two-phase pressure drops. Nevertheless, if the same single gas is under consideration, both descriptions are equivalent. Therefore, pressure and gas molecular weight can beviewed as embedded operating parameters contained in a more intrinsic function, the gas density. It should however be mentioned that the attribution of pressure and gas molecular weight hydrodynamic effects in gas-liquid reactors to gas density exclusively is not totally new. Wammes et al. (1991a) found out that gas density-and not pressure or molecular weight-is the exclusive gasphase factor contributing to the pressure drop in trickle beds. Studies on .gas holdups in high-pressure bubble columns with different gases by Wilkinson and van Dierendonck (1990) led also to a similar conclusion. Effect of Gas Density viaPressure. Typical pressure drops and gas holdups versus gas superficial velocities obtained in the experiments, for pressures ranging from 0.3 to 5.1 MPa, are shown in Figures 3 and 4, respectively, for the cocurrent upflow of water and ethylene glycol with gaseous nitrogen. A t a pressure of 5.1 MPa and gas velocities higher than 50 mmls, pressure drops and gas holdups could not be obtained, due to the limited capacity of the gas cylinders used during this work. Pressure drops as well as gas holdups are lees sensitive topressure for low gas superficialvelocities,whereasabove approximately 10-20 mmls, they are increasing functions of the operating pressure. The practical usefulness of the data pertaining to the low gas velocity range is evident since recourse to high-pressure measurements is unnecessary; gas holdups and two-phase pressure drops are fully predictable from atmospheric experiments.
Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994 62 1 A-
APIZ 4 (kPa/m)
WATER. NITROGEN LIQCID VELOCITY : 12.8 mmis
2oY
(mid 0
0.05
0.1
0.15
-H2
,a.
0.2 UG
1.'lll'8!t
0.2t
0.1
0.2
0.3
0.4
predicted
(m/s)
0.5
0.6
0.7
UG
Figure 5. Dependence of the frictional pressure drop on gas molecular weight at constant pressure ( P = 0.3 MPa, U L = 12.8 mm/ 8 ) . Hypothetical hydrogen pressure drop estimated from eq 9.
t
AP/Z (kPdm) ETHYLENEGLYCOL .SITROGEN LIQUID VELOCITY : 11.5mmis
0.05
"
0.05
0.1
0.15
0.2
COCURRENT DOWNFLOW + PROPYLENE CARBONATE
160
.
0 PC He
: 2.1 MPa
+ PC .N2 : 0.3 MPa
uc' COCURRENT UPFLOW A H z 0 . He : 2.1 MPa A H 2 0 . N2 : 0.3 MPa
Figure 4. Influence of operating pressure on the gas holdup for the water-nitrogen (a, top) and ethylene glycol-nitrogen (b, bottom) systems.
Although markedly higher pressure drops are measured with ethylene glycol than with water, antagonistic effects of pressure and liquid viscosity on the gas holdup are evident. Indeed, for the viscous ethylene glycol, the influence of high pressures on nitrogen holdup is less pronounced than in the case of water over a broader gas velocity range. The effect of pressure on gas holdup is damped by liquid viscosity. While the former tends to keep gas holdup high, the latter tends to diminish it by promoting coalescence. In the pressure-insensitive region, the nitrogen holdup and the two-phase pressure drop are steep functions of gas velocity, whereas for larger gas velocities they increase in a less pronounced manner. The pressure independence of gas holdups in flooded bed reactors for the low gas superficial velocity range was also observed by van Gelder and Westerterp (1990) and Oyevaar et al. (1989). Examining the pressure influence of several hydrodynamic parameters in different reactor types shows that the pressure independence at low gas velocities is not only a characteristic of flooded bed reactors. Jiang et al. (1992) found that gas holdup is insensitive to pressure in three-phase fluidized beds. The gas-liquid interfacial areas measured by Oyevaar et al. (1989) in a flooded bed reactor were unaffected by pressure. The pressure is also of minor influence on liquid (or gas) holdups, gas-liquid interfacial areas, volumetric liquidside mass-transfer coefficients, and catalyst wetting in trickle beds (Larachi et al., 1991b;Wammes et al., 1991b; Lara-Marquez et al., 1992; Ring and Missen, 1991). A t higher gas velocities (generally above 10-20 mm/s), the increase of gas holdups with pressure follows qualitatively the trends found in pressurized.bubble columns (De Bruijn et al., 1988; Wilkinson et al., 1992; Wilkinson and van Dierendonck, 1990; Krishna et al., 1991; Oyevaar et al., 19911,three-phase fluidized beds (Jiang et al., 19921, slurry reactors (Tarmy et al., 1984), or trickle beds (Wammesetal., 1991b;Larachietal., 1991b). Theincrease of two-phase pressure drop with pressure was also observed by Enright and Chuang (1978) in countercurrent packed beds and by Wammes et al. (1991b) and Larachi et al. (1991b) in trickle beds.
(mls) 0
0.05
0.1
0.15
0.2
0.25
0.3
uG
Figure 6. Isodensitypressuredrop experimentsusing differentgases in cocurrent upflow and cocurrent downflow.
Effect of Gas Density via Gas Molecular Weight. As shown in Figure 5, at apressure of 0.3 MPa, the pressure drop increases with increasing the gas molecular weight for the same gas superficial velocity (in order of increasing molecular weight: helium, nitrogen, argon, and carbon dioxide were used). The same trend still persists for higher pressure levels. The continuous line drawn below the data corresponding to the water/helium system is the hypothetical pressure drop which would occur in a flooded bed pressurized by pure hydrogen. This line is calculated using the proposed correlation given by eq 9 (see below). Note also the close resemblance between the pressure drop data of Figures 3 and 5. For the low gas superficial velocity regions, neither the pressure nor the gas molecular weight seem to affect the pressure drop, whereas at higher gas velocities, the dependences are quite similar. When helium at 2.1 MPa is used instead of nitrogen at 0.3 MPa, everything else being kept unchanged, the same pressure drops are measured at the same gas densities. This remains true regardless of the flow direction as illustrated by Figure 6 for the systems water-helium and water-nitrogen for the upflow operation and for the systems propylene carbonate-helium and propylene carbonate-nitrogen for the downflow operation. Using different gases means different densities and viscosities. For the gases used in this work, the dynamic viscosities are almost equal. Moreover, dynamic gas viscosities are generally more sensitive to temperature and remain practically pressure independent. For instance, at 250 "C and up to 80 MPa, hydrogen dynamic viscosity corresponds typically to that of nitrogen at 20 OC up to 8 MPa. A t ambient temperature, hydrogen dynamic viscosity is half this value up to 50 MPa. On the basis of this argument, the results shown in Figure 6 simply demonstrate that the
522 Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994
pressure drops in a hydrogen-pressurized flooded bed reactor can be experimentally mimicked in a nearly atmospheric experiment if, instead of hydrogen, a heavier gas is used at the same superficial velocity. The following corresponding density rule can therefore be stated: to evaluate pressure drops in hydrogen pressurized reactors, heavier gases at lower pressures can be used instead with the requirement of equal gas densities and velocities. This can be expressed by the following relation between pressures and molecular weights of both the heavier gas and hydrogen:
where z is the compressibility factor. As an illustration, a 1.6-MPa argon pressure produces an effect equivalent to 40-MPa hydrogen pressure. It is intended that the applicability of the above-mentioned rule is restricted to experimental simulations of gases at ambient temperature. This rule has not yet been proven for the most practical case of high temperature and high pressure since, as far as we know, experiments on twophase pressure drop at high temperature are to date not available. Interpretation of the Gas Density Effect on Gas Holdup and Pressure Drop. At a low gas superficial velocity ( < l e 2 0 mm/s), the single bubbles evolving from the distribution zone ascend individually and follow distinct trajectories through the packing so that their coalescence is prevented. Moreover, considering the low kinetic energy content (or inertia) of the bubbles, no significant breakage will take place during collisions between bubbles and solid particles. Within this gas velocity range, the number of bubbles traversing the bed depends only on gas velocity but not on pressure and so does the gas holdup. The overall frictional two-phase pressure drop is a combination of three types of dissipations: a gas-liquid interfacial dissipation, a liquid-packing dissipation (unaffected by pressure), and a gas-packing dissipation via the liquid (negligible at low gas inertia). The pressure drop does not depend on pressure because neither the gas-liquid interfacial area (or the number of bubbles) nor the liquid-packing drag depends on pressure. At higher gas velocities (>10-20mm/s), the proliferation of bubbles with smaller diameters with increasingpressures is likely responsible for the increase of gas holdups and frictional pressure drops. These tiny bubbles may result from two distinct mechanisms: (i) The first mechanism whereby tiny bubbles may result is by a reduction of their size at their place of birth (the distributor) and an increase of their frequency of liberation at the distributor followed by a coalescence inhibition during their rise in the bed. This scenario has been first proposed by Jiang et al. (1992) to explain the increase of gas holdup with pressure in three-phase fluidized beds. (ii) The second mechanism is by a loss of stability of larger bubbles at high pressure enhancing the bubble breakage during collisions with the packing. The large bubbles may be generated from clusters of small bubbles trapped between the solid particles. This scenario has been originally proposed by Wilkinson and van Dierendonck (1990) to explain the increase of gas holdup with gas density in bubble columns. The simultaneously increasing frictional pressure drops with pressure is due to (i) the proliferation of tiny bubbles which increase both the gas-liquid interfacial area and the gas-liquid interfacial drag and (ii) the increase of the
inertial dissipation of the gas phase (gas-packing drag). The tortuous passages in the porous medium render the gas flow more dissipative at higher momentum flow rates. A Lumped Dimensionless Number Correlating Gas Density Effect on Pressure Drops. Lockhart and Martinelli (1949)first introduced a dimensionless number for characterizing two-phase pressure drop and void fraction in horizontal gas-liquid flow in empty ducts. This number was defined as the square root ratio of the singlephase pressure drops of each fluid flowing alone in the duct at the same operating conditions as in the two-phase flow, and it was defined as
The two-phase separated flow hypothesis assumed by this semiempirical approach considers the pressure drop to be resulting from wall frictions between each of the fluids and the duct, and as a consequence beside viscous and inertial forces,no other forces (gravity, capillary force) are taken into consideration. This ratio was successfully extended by other researchers to atmospheric trickle-flow reactors (Charpentier et al., 1969). In single-phase flow through porous media, pressure drops can be expressed following a Forchheimer-type equation (Forchheimer, 1901) as APJZ = ff,U$L
+ ffip,u,2
U G I Z = aVuGpG+ "~PGUG
(4) 2
(5)
for the liquid and the gas, respectively. aVand ai are constants describing the porous medium for a limiting creeping flow or a limiting inertial flow, respectively. For monodispersed solid particles, parameters avand ai are related to the Blake-Kozeny-Carman hK and the Burke-Plummer hg parameters as
and
Substituting eq 4 and eq 5 into eq 3 and after rearrangement, one obtains
where
Usually typical operating conditions of flooded bed reactors (UG = few cm/s, U L = few mm/s) correspond to bubble flow regime or to the transition between pulsing flow and bubble flow regimes. As will be shown later, experimental evidence does not support the inclusion of a gas Reynolds number in the final dimensionless number (e.g., a friction factor) describing the gas-phase role in the overall mechanical power dissipation. At large gas densities and/or large superficial velocities, the gas flow is either inertia controlled or transitional. A t this level, we state that the gas flow is controlled only by inertia and thus eq 6 can take the following simplified form:
Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994 623 107 -
The difference between eq 6 and eq 7 lies in whether the liquid flows viscously, inertially or transitionally, while the gas flow is always of an inertial type. It is improbable that the liquid will flow turbulently, but instead a viscous or intermediate liquid flow will occur. The confined space offered to the liquid flow and the lower typical liquid throughputs encountered in flooded bed reactors prevents turbulence from developing, and the only inertial effects in the liquid are caused by nonuniform laminar flow. Nevertheless,below the critical point of the liquid, pressure does not affect the liquid properties; hence, without loss of generality and for the sake of simplicity, eq 7 can be simplified further in order to take into account only the influence of gas density on pressure drop. It thus becomes
106 -
A
8 8
A
waterKO2
0 waterlAr
105 104 10’ 102
lo‘
i
-
t
10.)
o 1
o 10
10*
l
Re,
10’
Figure 7. Plot of the dimensionless frictional two-phase pressure drop versus the gas-phase Reynolds number. fLG
107 -
The dimensionless ratio Xi-i (equivalent to the reverse of the flow factor commonly encountered in plate or packed columns, see for example Coulson et al. (1991)) given by eq 8 is a parameter of fundamental importance in the characterization of pressure drops not only in trickle beds but in flooded bed reactors as well. It represents the square root of the ratio of the gas and liquid momentum flow rates. It also represents the asymptotic value of X G for a flow controlled by both gas and liquid inertias. The presence of U L and p~ in eq 8 serve only to render the gas momentum flow rate dimensionless. Figures 7 and 8 show the dimensionless frictional pressure drop fLG as a function respectively of the gas Reynolds number, ReG = pGuGdP/pq,and of the ratio Xi-i for all the gas-liquid systems investigated in this work at a given liquid superficial velocity and at all the pressures. The dimensionless pressure drop has been expressed here as a friction factor fLG given by (p/Z)dh fLG
= 2PGu>
where dh, the Krischer and Kast (1978)hydraulic diameter, is a function which takes into account the geometrical properties of the porous medium and is defined as
Figure 7 indicates that a ReG is not a suitable measure to account for gas density effect on the pressure drop in flooded bed reactors. These results should warn of an unsound use of two-phase pressure drop correlations developed on the basis of a gas-phase Reynolds number. On the contrary, from Figure 8, it can be seen that irrespective of the gas phase, it is possible to predict the value of the dimensionless frictional pressure drop at any pressure level by using only measurements made at atmospheric pressure provided the same liquid and bed are under consideration. For instance, knowing the pressure Pand the gas superficialvelocity UG, one calculates the corresponding momentum flow rate p ~ u ~A2fictitious . gas superficial velocity corresponding to an experiment at atmospheric pressure at the same gas momentum flow rate as at high pressure can then be calculated. Knowing the liquid density and superficial velocity, the associated pressure drop can thus be either measured or estimated. It is evident that this pressure drop corresponds to that
106 . 105 104
10’ 102
101
100
I 10‘’
10”
1
1
10
Xi-i
Figure 8. Plot of the dimensionless frictional two-phase pressure drop versus the inertial Lockhart-Martinelli ratio.
occurring in the actual conditions assumed. Figure 8 also showsthat the pressure drop increaseswith liquidviscosity, meaning that the liquid-side shear stress may not be neglected when compared with the inertial forces. Development of an Empirical Dimensionless Correlation Based on Xi-i. Considering the foregoing analysis, the final quantitative relation between pressure drop and the different involved variables should contain physical properties of the liquid (viscosity,density, surface tension), structural parameters (porosity, shape factor, particle diameter) of the porous medium, fluid velocities, and only gas density. Since it is not always easy to decide which variables should be taken into account in order to get reliable correlations, one should only use correlations within the same range of the variables as that of the data base. The correlation developed here is based on the same dimensional analysis yet carried out on the pressure drop data for the trickle flow operation (Larachi et al., 1991b): a friction factor ~ L G(as defined above) is represented as a function of dimensionless groups which take into account inertial effects in the fluids via the inertial LockhartMartinelli ratio Xi-i (eq 8). The effects of liquid viscosity and surface tension have been accounted for by using a / p ~ a Weber , liquid Reynolds number, ReL = p ~ u ~ c I ~and number, WeL = pLuL2dp/aL. Having determined the relevant variables, a large data base was used in the interest of obtaining the most general, yet accurate correlation possible. Thus, the present correlation is based on data obtained in our team on a high-pressure column (this work) and on two atmospheric columns (Gutache, 1990, LaraMarquez, 1992; Lamine et al., 19921, data from Institut FranGaisdu PBtrole on four atmospheric columns (Barrios,
524 Ind. Eng. Chem. Res., Vol. 33, No. 3, 1994
Table 1. Properties of Materials and Ranges of Experimental Conditions on Which the Present Correlation Is Based. physicalproperties of the fluids gas density dynamic gas viscosity dynamic liquid viscosity liquid density liquid surface tension particle and column characteristics particle diameter bed porosity bed height column diameter operating conditions liquid velocity gas velocity pressure temperature
maximum
max/min
59.4 2.34 X 10-5 0.0189 1113 0.072
180 3 135 2 7.5
0.006
6
0.40 2.15 0.225
1.3 5.5 10
0.06
12
1.8 51 X
323
1800
lo6
51 1.1
liquids: Cd cut, water, water + 10% sucrose, water + 20% sucrose, water + 30%sucrose, water + 40% sucrose, ethylene glycol, cyclohexane, heptane, kerosene, propanol, water + 0.8 M sodium sulfite, water + 1% CMC + 0.8 M sodium sulfite, water+ 1.5 M diethanolamine, water + 1.5 M diethanolamine +40% ethylene glycol, water + 1.5 M diethanolamine + 615% ethylene glycol, ethylene glycol + 0.1 M diethanolamine gases: hydrogen, helium, nitrogen, air, argon, carbon dioxide packings: glass beads, polypropylene extrudates, alumina spheres In SI units. Barrim (1937) t Carnacho (1984,1987)
fLG
4 Gutsebe(19901
-
108
YangW901
0
Lara.Harquez (1992)
A verge1 (199s) Lamine 11992)
0 thiswork
10' lo6 105
10'
-
---
CORRELATIO\
- ._ --_
- - - - :80%
-. -. ..
10'
fLG
= -(45.6 1 X3/2
+ 15.9/X"2)
where
and viscous systems with flow regimes extending from the bubble dispersed flow regime to the pulse flow regime.
Conclusion This study has shown that the frictional two-phase pressure drop and the gas holdup in gas-liquid-solid flooded bed reactors are influenced by pressure. It has been found that it is only the gas density, via the momentum flow rate, which is responsible for that effect on the pressure drop. Two extrapolation techniques which allow for the estimation of pressure drops at high pressure in flooded bed reactors from nearly atmospheric experiments are proposed. The pressure drop in hydrogenpressurized flooded bed reactors can be experimentally mimicked in a nearly atmospheric experiment if, instead of hydrogen, a heavier gas with equal density is used. The inertial Lockhart-Martinelli ratio successfully describes the influence of gas density on pressure drop. A new empirical frictional two-phase pressure drop correlation based on the inertial Lockhart-Martinelli ratio has been developed. All the data presented here were obtained in smallscale and medium-scale columns (0.023 m I column diameter I 0.225 m); experiments in larger reactors are needed to confirm these results. Acknowledgment The authors gratefully acknowledge the financial help received from the Institut FranGais du PBtrole and the Algerian Ministere aux Universith Nomenclature d = particle diameter, mm fLG = friction factor defined with a hydraulic diameter according to Krischer and Kast G = gas mass flux, kgm-2.s-1 h g = Burke-Plummer coefficient h~ = Blake-Kozeny-Carman ccefficient L = liquid mass flux, kgm-2.s-' M = molecular weight, g-mol-' P = operating pressure, MPa hpIZ = pressure drop, Pa.m-1 Re = Reynolds number u = superficial velocity, m-s-1 We = Weber number Xi-i = inertial Lockhart-Martinelli dimensionless ratio z = compressibility factor Z = bed height, m Greek Letters aV = structural parameter in eq 4, m-2 ai = structural parameter in eq 4, m-1 t = bed porosity t~ = gas holdup K = structural parameter in eq 6 A = dimensionless parameter in eq 9 I.L = dynamic viscosity, Pes p = density, kgm3 u = surface tension, N-m-' XG = Lockhart-Martinelli dimensionless ratio T = space time, s Subscripts
Figure 9 shows the prediction of the correlation and its *80 % limits versus experimental data. This correlation is based upon approximately 1800experimental data points (all shown on the figure) and is valid for aqueous coalescence inhibiting, aqueous and organic coalescing,
G = gas GL = gas-liquid h = hydraulic L = liquid p = particle
Ind. Eng. Chem. Res., Vol. 33, No.3, 1994 525
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Received for review June 14, 1993 Revised manuscript received November 29, 1993 Accepted December 14,1993@ Abstract published in Advance ACS Abstracts, February 1, 1994.
