Hydrodynamics of Pulsing Flow in Three-Phase Fixed-Bed Reactor

Mar 25, 2004 - the pressure drop in the bed, as well as the pulse velocity and the frequency of pulsation .... bed of a reactor operating at elevated ...
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Ind. Eng. Chem. Res. 2004, 43, 4511-4521

4511

Hydrodynamics of Pulsing Flow in Three-Phase Fixed-Bed Reactor Operating at an Elevated Pressure Andrzej Burghardt, Graz3 yna Bartelmus,* and Anna Szlemp Institute of Chemical Engineering, Polish Academy of Sciences, Baltycka 5, 44-100 Gliwice, Poland

In the present study, comprehensive investigations of the hydrodynamics of a trickle-bed reactor (TBR) operating in the pulsing flow regime (PF) at an elevated pressure are performed. The transition line between the gas continuous flow (GCF) regime and PF, the liquid hold-up, and the pressure drop in the bed, as well as the pulse velocity and the frequency of pulsation, are estimated experimentally. The influence of the variation of the gas density on the parameters measured is analyzed by using gases of varying molecular mass (helium, argon, nitrogen, air) and increasing the pressure in the reactor. The liquid phase used in the experiments was water and solutions of glycerine and ethylene glycol, the viscosity of which varied in the range (1-5.3) × 10-3 Pa‚s. The mathematical models describing the hydrodynamics of the system considered are verified through the application of our own base of experimental data. The aim of this verification was to choose a model recommended for the calculations of L and ∆P/H in designing the TBR. The measured values of the pulse velocity and frequency of pulsation are expressed in the form of correlation equations. 1. Introduction The phenomena occurring in a three-phase systems [gas-liquid-solid (catalyst)] constitute the basis of many processes in chemical technology. For these reaction systems, the apparatus most frequently used is a fixed-bed reactor with downward flow of the gas and liquid phasessa so-called trickle-bed reactor (TBR). This reactor type is especially widespread in refineries and in the petrochemical industry, where it is commonly used for purification and processing of various fractions of crude oil (hydrodesulfurization, hydrodenitrification, catalytic hydrocracking, and hydrotreating of olefins and aromatic compounds). These reactors also find application in the dynamically developing field of biotechnology, where a bed of immobilized bacteria or enzymes turns out to be very effective in the processes involved in purifying wastewaters and gases polluted with volatile organic compounds. According to Al-Dahhan et al.,1 in the petrochemical industry alone, especially in various hydrotreating processes, the annual throughput of TBRs is estimated at 1.6 billion tons. Such a wide range of application of TBRs in industry fully justifies every effort at improving their operation, leading to an increase in yield and selectivity and, consequently, to both a higher quality of product and more advantageous economic results. Undoubtedly, one of the methods for achieving this goal consists in changing the operating regime in these apparatuses from gas continuous flow (GCF) to pulsing flow (PF). As experiments have revealed,2 the latter regime is quite advantageous for performing processes in which mass transfer of a reactant in the liquid phase is a rate-limiting step (e.g., all hydrotreating processes), because mass-transfer coefficients are considerably higher in this regime than in the GCF regime. As the liquid flow rates are high in the PF regime, we can be certain that the packing is thoroughly wetted by the * To whom correspondence should be addressed. Tel./Fax: +48 32 2310318. E-mail: [email protected].

liquid, thus preventing the occurrence of “hot spots” in the bed. In this case, the heat of reaction generated in the catalyst pores can be easily transported to the liquid phase flowing over the packing. Before the PF regime of operation is applied in industrial reactors, a thorough investigation must be performed in which the basic hydrodynamic and kinetic parameters are determined. Industrial three-phase reactors operate most frequently at an elevated pressure and under conditions such that the physicochemical properties of the liquid phase are different from those of water. Unfortunately, the majority of studies in which the hydrodynamic and transport processes in three-phase reactors have been investigated concern operations carried out at atmospheric pressure and most frequently using the airwater system. These works have been reviewed in the articles of Saroha and Nigam3 and Dudukovic et al.4 The first studies in which experiments were conducted at an elevated pressure have only appeared over the past 10 years1,5-14 and concern mainly the GCF regime. Progress in methods of preparation of very active catalysts will enable the operation of catalytic reactors at high throughputs of both phases, and so an increase in the number of processes conducted in the PF regime can be expected. Therefore, the main goal of this study was to investigate the hydrodynamics of a TBR operating in the PF regime at elevated pressure. As a result of the experiments performed and reported herein, the following hydrodynamic parameters were measured: (i) values of the operating parameters determining the onset of the pulsing flow regime in the reactor; (ii) the hold-up of the liquid and the pressure drop in the bed; and (iii) parameters characterizing the PF regime in the reactor, namely, the pulse velocity and the frequency of pulsation. During the experiments, the physicochemical properties and the flow rates of both phases, as well as the pressure in the reactor, were changed. It should be emphasized that, as a result of the investigations

10.1021/ie030726e CCC: $27.50 © 2004 American Chemical Society Published on Web 03/25/2004

4512 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 Table 1. Physicochemical Properties of the Systems Tested (t ) 20 °C) gas phase

liquid phase

medium

F (kg‚m-3)

µ× (Pa‚s)

aqueous solution (mass percent)

F (kg‚m-3)

µ × 103 (Pa‚s)

σ × 103 (N‚m-1)

nitrogen

1.165

1.744

water glycerine (30%) glycerine (35%) glycerine (47%) ethylene glycol (48%)

998.2 1070.0 1085.5 1118.0 1055.9

1.0 2.5 3.1 5.3 3.3

72.6 74.7 73.0 70.9 60.5

air

1.205

1.805

water glycerine (30%) glycerine (47%)

998.2 1070.0 1118.0

1.0 2.5 5.3

72.6 74.7 70.9

helium

0.164

1.953

water glycerine (47%) ethylene glycol (48%)

998.2 1118.0 1055.9

1.0 5.3 3.3

72.6 70.9 60.5

argon

1.661

2.217

water

998.2

1.0

72.6

105

performed here, the first broad base of experimental data concerning the pulsing flow of fluids through the bed of a reactor operating at elevated pressure was elaborated. 2. Experimental Setup The experiments were carried out in two installations: in an installation operating at near-atmospheric pressure and in a second one designed to operate at pressures up to 5 MPa. The schematic diagrams and modes of operation of both installations are presented in the articles of Burghardt et al.15,16 The main part of both installations was a column packed with glass spheres (3 mm in diameter). The height of the packing was 1.5 m. The column in the atmospheric setup (0.057 m in diameter) was made of transparent vinyl chloride, whereas the column in the installation operating at high pressure (0.05 m in diameter) was made of stainless steel. To enable the observation of the bed during reactor operation, a segment (0.1-m-long) made of transparent polycarbonate was placed 1 m below the top of the column. The physicochemical properties of the media used in the experiments are listed in Table 1. In the atmospheric installation, the gas phase consisted of nitrogen, argon, and helium, whereas in the setup operating under pressure, air was used. The physicochemical properties of the solutions (F, µ, σ) were strictly controlled before and after each measurement. However, the electric conductivity of the solution was monitored continuously by means of an electrode immersed in a tank of liquid and connected to a numerical conductometer. In both installations, the liquid hold-up and the parameters characterizing the pulsing flow were estimated by means of two conductometric cells placed in the bed, which measured the variations of the conductivity of the two-phase gas-liquid mixture flowing through the bed. However, each of the quantities measured by means of this method required a different interpretation of the signals recorded. Therefore, the methods of determining the liquid hold-up and the parameters characterizing the PF are described in the sections concerning these quantities. 3. Change of the Hydrodynamic Regime in the Reactor from GCF to PF Of the various hydrodynamic regimes encountered in three-phase reactors, only two have found practical

application: the gas-continuous flow (GCF) regime reached at relatively low flow rates of both phases and the pulsing flow (PF) regime. The PF regime appears at relatively high flow rates of both phases and is an alternating spatiotemporal flow of “liquid-rich” and “gasrich” portions. Numerous investigations have revealed that the hydrodynamic and kinetic parameters in these two regimes differ considerably, and therefore, they have to be correlated by different relationships.17-20 Thus, for the rigorous design and scaling up of these apparatuses, the correct determination of the hydrodynamic regime prevailing in the reactor is of crucial importance. The experimental data concerning the change of the hydrodynamic regime from GCF to PF are especially abundant for reactors operating at near-atmospheric pressure. These data are collected in review papers.2-4,21 In the literature, only three papers can be found that present the results of experiments conducted in reactors operating at elevated pressure.5,7,22 Hasseni et al.22 determined the transition lines from GCF to PF for the systems nitrogen-water and nitrogen-ethylene glycol up to a pressure of ∼10 MPa. However, Wammes et al.5 did not find the PF regime for pressures exceeding 1.5 MPa for the system nitrogen-water and 2 MPa for the system nitrogen-ethylene glycol (40%). In experiments with helium as the gas phase, the PF regime was observed even at the pressure of 7 MPa.7 In this study, the changeover from GCF to PF was estimated by observing the operation of the bed through a transparent segment of the column. In this way, 103 experimental points were obtained. Upon analysis of the experimental results, the following conclusions can be drawn: (i) An increase in the pressure (gas density) in the reactor shifts the GCF/PF transition line toward higher velocities of the liquid phase (Figure 1). However, analysis of the data obtained in experiments with helium, nitrogen, and argon revealed that the influence of the variation of the gas density on the position of the transition line could be observed only when the gas density, Fg, exceeded ∼3.0 kg‚m-3. This confirms the results of Wammes et al.7 obtained for a TBR operating under pressure with helium and nitrogen as the gas phase. (ii) For liquids of higher viscosity, the PF regime is reached at a lower wetting rate. (iii) Identifying the PF regime was impossible for pressures exceeding 2 MPa for the system airglycerine solution (30%), for pressures exceeding 1.5

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4513

Figure 1. GCF/PF transition lines estimated experimentally. Open points, air-water system, black points, air-glycerine solution (30%) system.

Figure 3. Comparison of the experimental GCF/PF transition lines with those predicted using relations given in the literature. (A) air-water system, (B) air-glycerine (30%) system. 1, Grosser et al.;29 2, Danckworth et al.;30 3, Attou and Ferschneider;31 4, Holub et al.;27 5, Ng.26 a, Pr ) 0.3 MPa; b, Pr ) 0.6 MPa; c, Pr ) 0.9 MPa; d, Pr ) 1.5 MPa; e, Pr ) 2.0 MPa.

Figure 2. Transition points plotted on a Talmor25 diagram.

MPa for the system air-water, and for pressures exceeding 0.9 MPa for the system air-glycerine solution (47%). The results obtained agree with the experiments of Wammes et al.5,7 and indicate that, in the range of flow rates of both phases investigated in this work, the PF regime does not occur for pressures exceeding 2 MPa. There are two methods of correlating the experimental data that determine the operating parameters of the changeover from GCF to PF in the reactor. The first consists in preparing special flow maps; the second is based on the mathematical criteria defining the changeover of the regimes from GCF to PF, derived as a result of the analysis of the hydrodynamic models describing the flow of phases in the reactor.1,23 The experimental results of this study were compared with both the flow maps24,25 and the mathematical criteria26-31 presented in the literature. These comparisons allow us conclude that neither the flow maps (Figure 2) nor the mathematical criteria tested (Figure 3) can be used to estimate the operating parameters of the changeover of the regime from GCF to PF in the reactor. Particularly surprising are the results of the computations performed using the models of Grosser et al.29 and Danckworth et al.30 In both cases, the transition lines between the two regimes shift toward lower wetting rates with increasing pressure, which is incompatible with the experimental results. The computa-

tional results obtained with the criteria of Ng26 and Attou et al.31 agree qualitatively with the experiments (an increase in pressure shifts the transition line between the regimes toward higher liquid flow rates). However, the accuracy of the computational results with respect to the experimental data is not satisfactory. Nevertheless, the computational results obtained do not disqualify the models tested. It can be concluded only that the parameters of the models were probably estimated on the basis of a limited number of experimental results. Finally, following the suggestion of Larachi et al.,10 the Baker coordinates were modified according to our own experimental results, leading to the relation

( )

Ltrλψφ Gtr ) Gtr λ

-1.176

(1)

where

φ)

1 Fg 5.45 + 0.41 FaN

(2)

This relation enables the estimation of the transition line between the GCF and PF regimes with an error not exceeding 10.9% (R ) 0.901) for the systems and the range of pressures investigated in this study (Figure 4). It should be pointed out that the values of the coefficients estimated are similar to those proposed by Larachi et al.10

4514 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 4. Flow map developed on the basis of experimental results of this study. The shaded region is the region covered experimentally in this study.

4. Hydrodynamic Parameters of the Reactor (Liquid Hold-up and Gas Pressure Drop) Literature data concerning the liquid hold-up in TBRs operating at elevated pressure are extremely scarce and include only the GCF regime.6,7,12,32,33 Only in the study of Larachi et al.8 do the authors report that the reactor was operating in the GCF regime as well as in the PF regime; the relationship developed by these authors can be used for the determination of L in both regimes. This relationship is as follows:

SL ) 1 - 10-Γ

(3)

WeL0.15 Γ ) 1.22 0.15 Xg ReL0.20

(4)

where

The second hydrodynamic parameter measured in this research was the pressure drop of the gas in the bed. The value of this parameter is indispensable in designing the system used to pump the media in the installation, and moreover, the variation of ∆P/H influences the change of the liquid hold-up and the parameters connected with it. Thus, the two parameters measured are strictly connected to each other and appear simultaneously in the mass and momentum balances of the fluid flow in the reactor. Analysis of the literature data reveals that only one relationship correlating the experimental results exists; it was developed by Larachi et al.8 and has the form

( )( ) (

)

∆P dhFg 1 17.3 ) 1.5 31.3 + 0.5 H 2G 2 κ κ

(5)

κ ) Xg(ReLWeL)0.25

(6)

where

In this study, the liquid hold-up was determined by measuring the variations of the electric conductivity of

Figure 5. (A) Dynamic liquid hold-up and (B) gas pressure drop for the air-glycerine (30%) system. Pr ) 0.9 MPa.

the two-phase gas-liquid mixture flowing through the bed in gas-rich and liquid-rich portions. For this purpose, a conductometric cell was placed at a distance of 1.0 m from the top of the column. The cell was composed of two electrodes made of platinum wire gauze, each 45 mm in diameter. The electrodes in the cell were supplied with an alternating current of frequency 5 kHz. The signals from the electrodes were sampled with a frequency of 100 Hz and, after amplification, stored in the computer memory at 90-s intervals. In the measurements of the liquid hold-up, the relative value of the conductivity was estimated with respect to the value of the conductivity determined for the one-phase flow of liquid through the flooded bed (SL ) 1, T ) idem). The dynamic calibration of the cell was conducted by means of a liquid draining method. The dynamic component of the liquid hold-up was obtained in the manner described above. The total liquid hold-up was calculated by adding the static component, determined from the correlation suggested by Saez and Carbonell,34 to the measured values of Ld. The pressure drop of the gas in the bed was estimated by means of a differential membrane manometer produced by Omega. The values of L and ∆P/H shown in the diagrams and used in the computations are the time-averaged values of the parameters measured. The experimental values of the liquid hold-up and pressure drop in the bed are presented in Figures 5 and 6 for the system air-30% glycerine solution (which is representative of all of the systems investigated) at two different pressures. It can be seen that, in the PF regime, independent of the pressure in the reactor and

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4515

Figure 6. (A) Dynamic liquid hold-up and (B) gas pressure drop for the air-glycerine (30%) system. Pr ) 1.2 MPa.

the viscosity of the liquid, the dependence of L on the liquid velocity decreases with increasing gas velocity. Simultaneously, the increase in the gas velocity reduces the liquid hold-up in the bed. It should be noted that, at the moment of changeover of the hydrodynamic regime from GCF to PF, a dramatic change in the pressure drop was not observed. The pressure drop of the gas through the bed obviously increases with an increase in the mass velocities of both phases. The influence of the pressure on the parameters measured is shown in Figure 7A and B, whereas Figure 8A and B illustrates the influence of the viscosity of the liquid wetting the bed. As can be seen, the variation of the gas density influences the values of liquid hold-up in the PF regime to a small degree. Comparing the values of ∆P/H at constant gas velocity but at different pressures, it can be observed that the influence of the variation of the gas density is weaker than that of the gas velocity. Both parameters were found to be moderately sensitive to the variation of the liquid viscosity. This seems to indicate that the shear stresses at the gas-liquid and liquid-solid phase boundaries are not large in comparison to the inertial forces. As a result of the investigations performed in this work, a base of about 700 experimental data was created for the PF regime. First, the estimated values of L and ∆P/H were compared with the values computed from the correlation equations of Larachi et al.8 and also with the computational results from the relationship of Ellman et al.,35 which was developed on the basis of ∼5000 data points obtained by different authors. The results of the statistical tests are listed in Table 2.

Figure 7. Effect of pressure on the values of the (A) dynamic liquid hold-up and (B) pressure drop.

As can be seen, the relationship of Larachi et al.8 approximates the values of the liquid hold-up with very good accuracy. The computational results obtained for the pressure drop in the bed are much better upon use of the equation of Ellman et al.35 in the form

( )( )

∆P dhFg ) 6.96(Xgξ1)-2 + 53.27(Xgξ1)-1.5 (7) H 2G 2

where

ξ1 )

ReL0.25WeL0.2 (1 + 3.17ReL1.65WeL1.2)0.1

(8)

The relationship developed by Larachi et al.8 gives considerably lower values of the pressure drop in comparison to the experimental data. It is not the goal of this study to elaborate new equations correlating the results of the investigations. The database obtained was instead applied to verify the models describing the hydrodynamics of the cocurrent flow of liquid and gas through the bed. This enables us to choose a model that describes the hydrodynamics of the system with the highest accuracy (i.e., the values of L and ∆P/H calculated from the model equations should differ to the smallest degree possible from the parameter values determined experimentally). 4.1. Hydrodynamic models of Pulsing Flow and Their Verification. Only three papers have been published (Benkrid et al.,36 Pinna et al.,37 and Fourar et al.38) in which the authors have undertaken an attempt to describe the hydrodynamics of cocurrent gas

4516 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 Table 3. Equations of the Hydrodynamic Models for the PF Regime model Benkrid et al.36

equations B

L )

Awg + wL , w g + wL

( ) -

( )[ 3

E1

or

( ) Pinna et al.37

(T.1)

∆P + FLgˇ ) H  L

-

A ) 0.49, B ) 1

(1 - )2 µLwL + 3dp2 (1 - ) E2 3 FLwL2  dp

0.2

φ*2 )

2.5

FLµL 0.5 1.5 wL aLS, dp C ) 2.35-2.42

(1 - δ˜ ) (1 - δ˜ )

(T.4)

δ˜ 4.8

1 (1 - δ˜ )0.2(1 - δ˜ 2)1.8

(T.5)

al.8

Larachi et Ellman et al.35

8.14 11.84

σst (%) 8.97 8.15

eY (%) 32.87 12.02

(T.8)

(T.9)

where

F/L )

1 , F/g ) SL2 1 ≈ µg (1 - SL ) + 2 SL(1 - SL) µL

σst (%)

2

15.81 9.62

and liquid flow through a bed of solid particles in the pulsing flow regime. In all of these studies, the full coverage of the packing particles with liquid film (because of the relatively high values of the liquid flow rate) and the separate flow of the two phases were assumed. These models were discussed in detail in a paper by Bartelmus and Janecki.39 Therefore, only the equations describing them are listed in Table 3. As mentioned above, the principal assumption of the models discussed is the separated flow of gas and liquid. If this assumption could be accepted for the PF regime, it would be possible to test the hydrodynamic models developed for GCF regime, in which the forces of interaction between phases have been taken into account and ηe ) 1 as well. Obviously, these models should be treated as supplementary models with respect to the averaged operating parameters of the apparatus. Therefore, the models of Grosser et al.,29 Attou et al.,40 and Holub et al.28 with the values of the velocity slip factor (fv) and the shear slip factor (fs) calculated according to Iliuta et al.41 were tested. These models were discussed in the work of Szlemp,42 where the equations associated with the models are also given.

F/gRe] g (1 + F/gRe] g) Ga] g

ΨL ) (Ψ] g - 1)

∆P/H

L eY (%)

(T.7)

F] g FL

Table 2. Mean Relative Errors and Standard Deviations of the Values EL and ∆P/H Calculated from the Correlation Equations Presented in the Available Literature with Respect to the Values Estimated Experimentally in This Study authors of correlation equation

(1 + F/LRe] L)

Ga] L

Ψ] g )

Figure 8. The influence of liquid viscosity on the values of the (A) liquid hold-up and (B) pressure drop. Pr ) 0.6 MPa.

(T.6)

F/LRe] L

ΨL )

(T.3)

2 1.8

SL ) 1 - δ˜ 2 Fourar et al.38

(T.2)

()( )

∆P C + FLgˇ ) H L

χ2 ) R

]

()

1 (1 - SL)2

(T.10)

For the verification of the models presented above and the estimation of their parameters, our own base of about 700 experimental data points was used. The errors in determining the values of ∆P/H and L were estimated by calculating the average relative error (eY) and the standard deviation (σst) of the compared values. First, we tested the proposal of adapting the drift-flux model for the calculation of the liquid hold-up (Benkrid et al.36). As can be seen from Figure 9, the values of JD-F happen to be slightly higher for systems in which the gas phase was helium (Pr ≈ 0.1 MPa) than for the remaining systems investigated. Therefore, separate relationships were developed for correlating the experimental data:

SL )

0.364wg0.805 + wL ; wg + wL

eY ) 4.04%, R ) 0.9

(9)

for 650 experimental points and systems in which the

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4517

Figure 9. Variation of the drift flux with gas superficial velocity. Table 4. Mean Relative Errors (eY) and the Standard Deviations (σst) of the Values EL and ∆P/H Estimated Experimentally and Calculated from the Hydrodynamic Models ∆P/H (Pa‚m-1) model

L

eY (%)

σst (%)

eY (%)

σst (%)

al.36

26.41a

17.58a

4.04

3.18

Pinna et al.37 Fourar et al.38 Fourar et al.38 c Grosser et al.29 Attou et al.40 Holub et al.28 d

25.29b 16.04 45.88 23.63 28.73 17.51 17.35

16.71b 13.64 16.13 14.28 19.44 9.76 10.93

29.03 9.27 6.47 6.59 6.70 7.59

13.38 6.14 4.99 4.74 4.72 5.43

Benkrid et

a ∆P/H by the Ergun approach,  by the drift-flux approach. L ∆P/H by the boundary layer approach, L by the drift-flux approach. c With modified F* functions. d With fs and fv according to Iliuta et al.41

b

gas phase was nitrogen, argon, and air and

SL )

0.487wg0.875 + wL ; wg + w L

eY ) 3.20%, R ) 0.9 (10)

for 65 experimental points, where the gas phase was helium and Pr ≈ 0.1 MPa. If it is necessary to determine only the liquid hold-up values in the reactor, these correlations (eqs 9 and 10) should be applied. The values of L estimated from the above equations were used for the calculation of the gas pressure drop by means of relationships T.2 and T.3 in Table 3. The model of Pinna et al.37 gives considerably lower values of L with respect to the experimental data. Therefore, the coefficient R in this model was estimated on the basis of our own data, yielding R ) 3.55. Unfortunately, this is identical to the value presented by the authors,37 so it was impossible to improve the computational results in this way. The model of Fourar et al.38 gives values that are too low for bothy the pressure drop and the liquid hold-up. Therefore, we tried to verify the relationship defining the F* function of this model. Introduction of the estimated F/R functions into eqs T.7-T.9 of Fourar’s model reduces the average relative error of the calculated values of ∆P/H by one-half; for L, the error is reduced by only 3% (Table 4). The best results were obtained, however, using the model of Attou et al.40 and the full model of Holub et al.28 with the values of the slip coefficients estimated

Figure 10. Comparison of the (A) gas pressure drop and (B) liquid hold-up values obtained experimentally and calculated from the model of Attou et al.40

by Iliuta et al.41 (The Ergun constants were estimated experimentally in this study.) Therefore, these models should be recommended for the calculation of L and ∆P/H in designing TBRs operating in the PF regime (Figures 10A, B and 11A, B). 5. Parameters Characterizing the Pulsing Flow Regime In the majority of experimental studies in which pulsing flow through a bed of solid particles has been investigated, the experimentally estimated quantities such as the pressure drop of the gas, the liquid holdup, the heat- and mass-transfer coefficients, are presented and correlated as time-averaged values. However, for the modeling of pulsing flow, knowledge of the temporal variation of the above-mentioned quantities and the parameters characterizing the pulsing flow is indispensable. The basic parameters of this flow are the velocity of the pulses along the bed and the pulsing frequency.18,20,26,30,43 A pulse is defined as the distance between the fronts of adjacent liquid-rich portions. Therefore, every pulse is composed of both a gas-rich part and a liquid-rich part. A dozen or so studies can be found in the literature

4518 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 12. Variation of the pulse velocity with the real gas and liquid velocities. Air-glycerine (30%) system. Pr ) 0.6 MPa.

Figure 13. Effect of the reactor pressure on the pulse velocity. Air-glycerine (47%) system.

Figure 11. Comparison of the (A) gas pressure drop and (B) liquid hold-up values obtained experimentally and calculated from the model of Holub et al.28 The values of factors fv and fs are from Iliuta et al.41

in which the authors estimated parameters characterizing pulsing flow in a TBR operating at nearly atmospheric pressure. These studies have been reviewed in the papers by Tsochatzidis et al.,44 Bartelmus et al.,45 and Burghardt et al.15 For TBRs operating at elevated pressure and systems with a gas phase of low molecular mass (helium), such experiments have not yet been conducted. Therefore, the subject of this research was to develop the first database for systems in which the gas density is varied over a broad range either by varying the pressure in the reactor or by applying gases of low molecular mass (helium). The velocity of the pulses was measured by two conductometric cells placed in the bed at distances of 0.5 and 0.4 m from the bottom of the column. The structure of the cells, the mode of supplying them with electric current, and the procedure for sampling the signals were described in section 4. The signals from both cells stored in the computer memory were normalized, and then a plot of the cross-correlation function of the two signals was prepared. The time corresponding to a distinct maximum of this function on the plot is the time interval required by the front of a pulse to cover the distance between the conductometric cells.45 As the experiments reveal, similarly to the experiments per-

Figure 14. Influence of the liquid viscosity on the velocity of the pulses. Pr ) 0.9 MPa.

formed at Pr ≈ 0.1 MPa, the values of Vp increase with an increase in velocities of both phases. In the unquestionable majority of the cases investigated, the pulse velocity did not exceed the real velocity of the gas, which can be explained by channelling of the pulses by gas (Figure 12). With an increase in the pressure in the reactor (gas density), a slight drop of the velocity of the pulses is observed at constant vg (Figure 13). Also, an increase in the viscosity of the liquid phase causes the value of Vp to decrease (Figure 14). As a result of the analysis of the experimental data and the comparisons illustrated in the diagrams, it was concluded that the simplest form of the equation correlating the experimentally determined values of Vp is

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4519

Figure 17. Effect of the reactor pressure on the pulsation frequency. Air-water system. Figure 15. Comparison of the experimental and calculated (eq 11) values of the dimensionless modulus Vp/vg.

Figure 16. Variation of the pulsation frequency with the real gas and liquid velocities. Helium-ethylene glycol (48%) system.

Figure 18. Comparison of the experimental and predicted (eq 12) values of the pulsation frequency.

the power-law dependence of the dimensionless modulus (Vp/vg) on the Reynolds numbers of both phases. In the Reynolds numbers, the real velocities of the gas and liquid in the bed are used. The following relationship was obtained for 590 experimental points

be emphasized that, for higher pressures and for all systems investigated, only a few experimental points could be obtained in the range of fixed frequency of pulsation, as the region of pulsing flow vanished. It should also be mentioned that, in the range of linear dependence of the frequency of pulsation on vL, the slope of these straight lines changes slightly with the gas velocity and, above all, with the pressure in the reactor (Figure 17). Variation of the viscosity of the solution does not affect the value of the frequency of pulsation, as its influence is taken into account through the liquid hold-up. To correlate the experimental results, a form of relationship was applied that resulted from the analysis of the experimental data discussed above. For 480 experimental points, the following equation was obtained

( )

Vp Fg ) 3.445 vg FaN

0.352

Reg,r-0.464 ReL,r0.177

(11)

The correlation coefficient of this equation is R ) 0.948, and the mean relative error is 6.6% (Figure 15). To determine the frequency of pulsation, the signal from the upper conductometric cell, placed 0.5 m from the bottom of the bed, was used. This signal, recorded in the computer memory, was analyzed by means of a procedure elaborated and described in detail in the paper by Burghardt et al.15 In this way, the lifetime of a pulse was obtained for each of the 90-s intervals; its reciprocal gives the required value of the frequency of pulsation. The experimental results reveal a distinct increase in the frequency of pulsation with increasing liquid velocity. Moreover, this relationship is linear over a broad range of wetting rates (Figure 16). For the nearatmospheric pressures and for high wetting rates, a stabilization of the frequency of pulsation was observed, i.e., the value of fp did not change as the flow rate of liquid in the reactor was increased. However, it must

fp ) 1 + (51.39 + 8.256 × 10-3Reg,r1.089)vL (12) which correlates the experimental data for all of the systems investigated with a mean relative error not exceeding 14% (R ) 0.93), (Figure 18). This equation correlates the values of fp in the region of operating parameters in which this quantity is a linear function of the wetting rate. However, as has already been noted, in a TBR operating at elevated pressure, this region of variation of fp is the predominant, and often the only, one.

4520 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

6. Conclusions In this paper, results of experiments conducted under the pulsing flow regime in a TBR at elevated pressure are presented. One of the basic problems of this research was to determine whether industrial three-phase reactors can operate under pulsing flow at elevated pressure. The investigations carried out reveal that, in the hydrotreating processes that predominate in processes conducted in TBRs, the possibility exists for the changeover of regimes from GCF to PF. For such processes, the PF regime can be achieved, depending on the liquid viscosity, even at pressures of a dozen or so megapascals. Simultaneously, the correlation equations and hydrodynamic models published by various authors were verified on the basis of our own experimental data (∼700 experimental points). This enabled us to choose the relationships and models that should be recommended for calculating the values of L and ∆P/H in designing TBRs operating under elevated pressure. On the basis of our own database (to the best of our knowledge, the first database of this type), correlation equations were developed for the pulse velocity and the frequency of pulsation. The knowledge of these quantities makes it possible to model the temporal variation of the hydrodynamic and kinetic parameters in the PF regime. Acknowledgment This work is dedicated to Prof. Gerhart Eigenberger on the occasion of his 65th birthday. Nomenclature aLS ) 6(1 - )/dp + 4/D ) specific liquid-solid interfacial area per unit empty bed volume, m-1 D ) column diameter, m dh ) [163/9Π(1 - )2]0.33dp ) hydraulic diameter, m d′h ) 2D/[2 + 3(1 - )(D/dp)] ) hydraulic diameter, m dp ) packing diameter, m E1, E2 ) Ergun constants N eY ) (1/N)∑i)1 |(Yexp,i - Ycalc,i)/Yexp,i| × 100% ) mean relative error, % F/R ) multiplier factor of the superficial velocity in the model of Fourar et al.38 fp ) frequency of pulsation, s-1 fv ) velocity slip factor in the model of Holub et al.28 fs ) shear slip factor in the model of Holub et al.28 G ) superficial mass velocity of the gas phase, kg‚m-2‚s-1 gˇ ) acceleration due to gravity, m‚s-2 H ) column height, m JD-F ) drift flux, m‚s-1 L ) superficial mass velocity of the liquid phase, kg‚m-2‚s-1 M ) molecular mass, kg‚kmol-1 N ) sample size P ˜ ) mean pressure in the reactor, Pa Pr ) inlet pressure in the reactor, Pa ∆P ) pressure drop over the bed, Pa R ) gas constant, J‚kmol-1‚K-1 SL ) liquid-phase saturation T ) temperature, K t ) temperature, °C Vp ) velocity of pulses, m‚s-1 vR ) real velocity of phase R, m‚s-1 wR ) superficial velocity of phase R, m‚s-1 z′ ) compressibility factor

Greek Letters R ) adjustable parameter in the model of Pinna et al.37 Γ ) see eq 4 δ˜ ) δ*/2ω ) dimensionless modulus δ* ) equivalent diameter of the gas channel, m  ) bed porosity L ) total liquid hold-up Ld ) dynamic liquid hold-up ξ1 ) see eq 8 ηe ) external wetting efficiency κ ) see eq 6 λ ) x(Fg/Fa)(FL/Fw) ) flow parameter µ ) dynamic viscosity, Pa‚s µL,g ) µL[(L/G)/(1 + L/G)] + µg[1/(1 + L/G)] ) mean dynamic viscosity of the flowing fluids, Pa‚s F ) density, kg‚m-3 1/FL,g ) (1/FL)[(L/G)/(1 + L/G)] + (1/Fg)[1/(1 + L/G)] ) mean density of the flowing fluids, kg‚m-3 ] Fg ) Pr2/[(z′RT/M)P ˜ ] ) mean density of the gas phase in the reactor, kg‚m-3 σ ) surface tension, N‚m-1 N σst ) x[1/(N-1)]∑i)1 [|(Yexp,i-Ycalc,i)/Yexp,i|-eY]2 × 100% ) standard deviation, % φ ) correction factor in the eq 1 φ* ) x(∆P/H)L,g/(∆P/H)L ) Lockhart-Martinelli parameter χ ) x∆PL/∆Pg ) Lockhart-Martinelli parameter Ψ ) (-∆P/H + Fgˇ )(1/Fgˇ ) ) dimensionless pressure drop ] ˇ + 1 ) dimensionless pressure drop of Ψ] g ) (-∆P/H)/Fg g the gas phase ψ ) (σw/σL)[(µL/µw)(Fw/FL)2]1/3 ) flow parameter ω ) equivalent radius of the interstitial channels, m

Dimensionless Numbers Fr′ ) [(L + G)(1/FL,g)]2/gˇ dh′ ) modified Froude number 2 ˇ d 3/µ 2) ) modified Galileo 3 3 Ga] p L L ) (E2/E1)[ /(1 - ) ](FL g number of the liquid phase 3 3 ˇ d 3/µ 2)[P /(z′RT/M)] ) modiGa] p g r g ) (E2/E1)[ /(1 - ) ](g fied Galileo number of the gas phase Re ) wdpF/µ ) Reynolds number ReR,r ) vRFRdp/µR ) Reynolds number on the real velocity of phase R Re] R ) [E2/E1(1 - )](wRFRdp/µR) ) modified Reynolds number Re′ ) dh′(L + G)/µL,g ) modified Reynolds number We ) dpw2F/σ ) Weber number We′ ) dh′(L + G)2/FL,gσL ) modified Weber number Xg ) (G/L)xFL/Fg ) modified Lockhart-Martinelli parameter Subscripts a ) air calc ) calculated exp ) experimental g ) gas phase i ) gas-liquid interface L ) liquid phase N ) normal condition r ) real tr ) transition w ) water R ) phase R, R ) L, g

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Received for review September 22, 2003 Revised manuscript received January 2, 2004 Accepted January 5, 2004 IE030726E