Local solid—liquid mass transfer coefficients in a three-phase fixed bed reactor

111

Local Solid-Liquid Mass Transfer Coefficients in a Three-Phase Fixed Bed Reactor GRAPYNA

BARTELMUS

Institute of Chemical Engineering, Polish Academy 44-100 Gliwice (Poland) Dedicated

to Prof. Dr.-kg.

(Received

March

Dr. h.c./INPL

of Sciences, ul. Baltycka

E. U. Schhkder

5,

on the occasion of his 6iBh birth&y

30, 1989)

Abstract Experimental data are presented concerning the local solid-liquid mass transfer coefficients in a packed column operated with a cocurrent downflow of gas and liquid. The experiments were carried out for two diameters of spherical particles, with the flow rates of both phases and the physicochemical properties of the liquid varied over a wide range. The experimental results are correlated and compared with the appropriate literature data.

1. Introduction The term ‘trickle bed’ is generally used to describe reactors in which gas and liquid flow cocurrently down a solid bed of catalyst particles. The studies on trickle bed reactors have been initiated quite recently, stimulated by the development of the petrochemical industry, where they are most widely used (hydrogenation of lubricating oils, hydrodesulphurization or hydrocracking of heavy oil residues); such reactors are also employed for oxidizing organic components in waste waters (trickling filters). One of the main advantages of the cocurrent operation is the possibility of using high flow rates of the media without flooding. The mechanism of the cocurrent flow of gas and liquid along a solid bed is, however, more complex than that for a countercurrent flow and results from the changes of the velocities of both phases, their physicochemical properties, the geometry of the bed, etc. At low flow rates of the phases the liquid flows down as a laminar film or trickles over the surface of the bed, whereas the gas passes as a continuous stream through the free volume of the reactor. This regime corresponds to a large extent to the conditions prevailing in countercurrent apparatus below the flooding point and is usually called the ‘gas continuous flow regime’. Charpentier and Favier [l] term it the ‘poor interaction regime’ because, as they show, the two cocurrently flowing phases do not affect each other. With the increase of the velocities of the phases, pulsation appears at the bottom of the column, whose point of inception moves rapidly upwards 0252701/89/$3.50

Chem.

Eng. Process.,

26 (1989)

with further increase of the gas or liquid flow rate. The liquid-rich portions flow down with a given velocity [2], and the phenomenon recurs with frequency l-10 Hz. The whole liquid flowing in excess of the amount corresponding to the limiting velocity of transition from the gas continuous to pulsed flow is transported through the bed as liquid-rich ‘plugs’, in which the liquid hold-up is about 1.6 times higher than in the region between consecutive pulses. This regime, regarded by many authors as a cocurrent equivalent of flooding, is very profitable from the point of view of mass transfer for, as the experiments show, the corresponding mass transfer coefficients are much higher than those in the gas continuotis flow regime. Another advantage, found by a number of investigators [3-S], is the complete wetting of the packing by the liquid, which is particularly important in reactors with catalyst particles as a bed. The review presented above mentions only two hydrodynamic regimes in trickle bed reactors, as industrial apparatus of this type usually operate under conditions corresponding to either of them. Thus, for design purposes, it is necessary to know the relations defining the pressure drops and the heat or mass transfer coefficients in both these regimes. If the process should give high conversion of a component present in only small amounts in the liquid phase (e.g. organic compounds of sulphur and nitrogen in petroleum processing), the rate of transport of this component to the catalyst surface becomes a rate-limiting step for the whole process. Experimental determination of the local solidliquid mass transfer coefficients was based initially on measurements of the rate of dissolution of the packing particles made of benzoic acid, naphthalene, 11 I-120

0

Elsevier Sequoia/Printed

in The Netherlands

112 etc., in water flowing through [3, 4,6-lo]. Later, the chemical [8, 11) and electrochemical [S, 12-141 methods were developed. A review of these methods is given by Shah in his monograph [IS] and by Ramachandran and Chaudhari [ 161. Discussion of the literature data available leads to the conclusion that, in spite of a rather limited number of experimental techniques employed, the results are often divergent, even in a qualitative interpretation of the phenomenon. Excluding the rather surprising findings of Specchia et al. [3] and Sylvester and Pitayagulsarn [7j it seems that other investigators agree only about the fact that in trickle bed reactors the increase in the mass velocity of the liquid produces the increase in the mass transfer coefficients kLs under all hydrodynamic conditions of operation. There is much controversy, however, concerning the effect of the gas-phase velocity on kLp, especially in the gas continuous flow regime, where the increase of the gas flow rate is accompanied-until a certain point-by the increase of the effective liquid-solid contact area (increase of the wetting efficiency). It should also be noted that in the experiments mentioned the liquid used was usually water or aqueous electrolyte solutions with physicochemical parameters similar to those for pure water. Consequently, the correlation equations do not show the effect of the physicochemical properties of the liquid on the mass transfer coefficients.

1

Thus, experiments were carried out in the present work concerning not only the effect of the flow rates of the phases and the size of the packing elements on the solid-liquid mass transfer coefficients kLs, but also the influence of the physicochemical properties of the liquid under all basic hydrodynamic conditions of operation. The liquids employed were an aqueous electrolyte solution and glycerol solutions of viscosities much higher than those reported in the previous works. The experiments were performed using the electrochemical method, whose principles are given by Mizushina [ 171. The values of the mass transfer coefficients have been obtained for: - downflow for a flooded bed (i.e. for a column totally filled with the liquid phase); - free flow of liquid over the packing (wp = 0); - the gas continuous flow regime; - the pulsed flow regime. The coefficients are described using appropriate correlation equations and are compared with the literature data.

2. Experimental details The experimental set-up is shown in Fig. 1. Its main part consisted of a Plexiglas column of inner diameter 7.5 x lo-’ m, packed with spheres made of

3 12

c

f

nitrogen exit; 11. bottle; layer2,ofliquid small tank; spheres; 3, 4,12,heating nitrogencoil; 5, liquid pump; 6, rotameter; 7, gas-liquid Fig. distributor; 1. Scheme 8, packed of experimental zone; 9, anode; set-up:10,I, gas humidifier; 13, gas-liquid separator.

113 vitreous crystalline material called Agalit. The diameter of the spheres, porosity and specific surface area of the packing were, respectively, dp = 6.32 x 1O-3 and 3.86 x lop3 m, E = 0.4 and 0.38, a = 569.5 and 961 m2/m3. The total bed height was 0.75 m. The upper part of the packing was additionally covered with a 5 x lo-‘rn layer of small spheres (d, G 2 x lop3 m) ensuring good mixing of both phases. The aqueous electrolyte solutions were employed as liquids, containing both oxidized and reduced forms of the reactant in the following concentrations: 0.01 mol 1-l of potassium ferricyanide, K, Fe( CN,); 0.05 mol l- ’ of potassium ferrocyanide, K4 Fe( CN), . Sodium hydroxide in the concentration 0.5 mol l- ’ was used as a current carrier; in solutions whose viscosities were increased with glycerol it was replaced by potassium chloride. All measurements were carried out at gas (nitrogen) and liquid temperatures equal to 300.3 k 0.1 K. Diffusivities of the ferricyanide ions in the solutions employed in this work were taken from ref. 18, where they were determined using a rotating disc method. The liquid viscosity was varied in the range (1.1-6.35) x 1O-3 Pa s, leading to diffusivities changing from 7.06 x lo-” to 1 3 x lo-” m* s-‘. In order to perform the-experiments the cathodic reduction of potassium ferricyanide was utilized upon the surface of a platinum electrode (cathode), formed by five spheres of diameters equal to that of the inert packing and placed along the axis of the column at 0.1 m intervals, starting 0.25 m below the top. The anode was a segment of a tube (9 in Fig. 1) covered with platinum foil, through which the electrolyte flowed out of the column and whose area was 200 times higher than that of the cathode. The electrochemical determination of the mass transfer coefficient kLs requires the density of the limiting current (which is a cathodic response to changes occurring at its surface) to be estimated when the rate of diffusion of the reacting ions to the surface of the electrode limits the overall rate of the process. Under such conditions the limiting current Z, does not change with changing cathode potential (Fig. 2) and the value of the liquid-solid mass transfer coefficient k,, may be calculated from the relation kLP= Z,JnFC

(1)

Thus, the main quantity evaluated in the experiments was the polarization curve for each of the five electrodes placed along the bed. After the region of the limiting current had been determined, the current was transformed into a voltage signal and then, using an analogutiigital converter, into a numerical form transmitted further to a microcomputer which, upon analysing the signal, calculated the timeaveraged value of the diffusion current density. The signal was analysed with frequency 50 Hz and the average was found using at least 5000 of its instantaneous values.

/

{/-f Cathode

overpotential,

volts

Fig. 2. Typical limiting current-potential

curve.

The value of kLsr calculated from (1) and representing a single experimental point, is an arithmetic mean of the local values of this coefficient obtained by the analysis of the signals generated by the five electrodes disposed along the bed. Prior to each experiment the density, viscosity and composition of the solution were determined and the electrodes weri cleaned and depolarized. After filling up the column with the packing and, subsequently, with the liquid phase, the slow upward flow of liquid was maintained for about half an hour to ensure the thorough wetting of the bed surface. 3. Experimental results 3. I. Flooded bed The initial measurements, carried out for a flooded bed, were designed to test the accuracy of the experimental technique employed. Thus, not only the liquid flow rate but also its composition were varied in the experiments (i.e. the concentration of the current carrier from 0.5 to 0.1 mol l-l, and of potassium ferricyanide from 0.01 to 0.005 mol 1-l). Moreover, the maldistribution of liquid over the packing elements, leading to incomplete wetting of their surface and commonly encountered in the operation of spray columns, was eliminated under flooding conditions. The results obtained for a flooded bed are usually correlated [6,8, 191 as a relation between the dimensionless group Sh/Sc0.33 and the liquid Reynolds number. If the measurements are carried out for more than one packing size this group is supplemented with the coefficient E. Unfortunately, E is nearly constant and does not represent the real effect of the size, but allows only for the changes of porosity owing to the maldistribution of particles near the column walls, often occurring in experimental situations (small diameters of columns). In the present measurements the Schmidt number varied from 1560 to about 42 000, thus enabling the exponent of this number to be determined. The calculations yielded the same value as that generally assumed in this case and equal to 0.33; the interpolation curve for 140 experiments is given by ESh = 0.798 x Re,O,‘* SCO.‘~

(2)

114

at

m SC

I 3

iIO L

a 6

4

2

6

Fig. 3. Diagram

a

10

of the relation

20

40

&Sh/Sco-33 = f(Re,)

60

for a flooded

a0

100

‘JO

Re L

column.

The experimental results are shown in Fig. 3 as a function e Sh/Sc0.33 = f( Re,); the solid line represents the correlation equation (2). As may be seen, the discrepancy between the measured values and those evaluated from eqn. (2) does not exceed a few per cent. Figure 4 presents the values of sSh/Sc”.33 calculated using correlations of several investigators. It should be noted, however, that only the equations of Hirose et al. [8] and Satterfield et al. [6] were obtained for the range of Re, corresponding to the present experiments, and it is these correlations that best agree with our results. This agreement becomes even more satisfactory if we take into account that

the relationships of Hirose et al. [8] and Satterfleld et al. [6] represent the average values of the mass transfer coefficients, whereas our measurements gave the local values which were assumed to hold for the whole volume of the bed. If the mass exchange takes place in the whole bed, then the effective driving force of the process is somewhat lower (owing to the different concentration profiles in the apparatus) than for a single active element placed in an inert bed. Consequently, one might expect that the measurements of the local values of k,, should yield slightly higher results than those obtained from the measurements of the average kLs. It is difficult,

a

6

2

1,

6

a

10

20

40

60

80 100

Re

200 L

Fig. 4. Comparison

of mass transfer

correlations

obtained

by different

authors

for a flooded

column.

115 however, to explain the considerable discrepancies between our results and those of Barthole [ 141 and Latifi et al. [ 131. While in ref. 13 the viscosity of the solution was raised to 4 x lop3 Pa s using an organic compound DMSO (dimethyl sulphoxide) and the disagreement may have been produced by the presence of this component, the liquid employed in ref. 14 was a typical aqueous electrolyte solution, with its physicochemical properties similar to those of pure water; moreover, the experimental technique resembled the procedures used in other investigations [5, 191 and in the present work. 3.2. Free Jlow of liquid (w, = 0) and gas continuous jlow regime In analysing the results obtained for the free flow of liquid over the bed and for the gas continuous flow regime it is important to take into account an additional parameter, the fraction of the wetted area, 4, which, in spite of numerous attempts, remains difficult to determine. It should be remembered that in trickle bed reactors the packing forms a catalytic bed; therefore, incomplete wetting of its external surface has a crucial effect on the rate of the process by changing the conditions of transfer of reactants to the active bed surface where chemical reactions take place. Hofmann [20] carried out a review of the studies concerning the relation between the fraction of the wetted area and the flow rates of the phases or the packing size. Unfortunately, the results of these studies differ considerably from each other and do not provide a reliable basis for calculating a value of the liquid flow rate for which 4, representing the fraction of the external surface of the packing covered by liquid, approaches unity. This fact is reflected in the correlation equations in which the Sherwood number is supplemented by 4. It is not the object of this work to determine the coefficient 4 under various operating conditions. As in the experiments the value of Z., (which depends directly on the wetted surface area of the electrode) is evaluated for five separate points along the column, it may be assumed that if the bed (and, consequently, the electrodes) is not properly wetted, the refilling of the column carried out prior to each experiment should produce different limiting current densities for individual electrodes. Thus, the following procedure was employed: using at least three diffusion current profiles along the column, determined for a given liquid flow rate, the average value (Zd),” was calculated. If the local value of the current density for each of the five electrodes did not differ by more than + 10% from (I&, it was assumed that the bed was probably uniformly wetted by the liquid flowing down. The experiments led to the conclusion that the liquid mass velocities for which, according to this procedure, the effective wetting of the packing may be assumed are surprisingly high: for the smaller of the two packings investigated (d, = 3.87 x 10m3 m)

the above conditions were satisfied only for velocities as high as 7.5-8 kg m-2 s-‘; for the larger one the velocity was about 6 kg mm2 s-i. It is difficult to say whether these findings, based upon the results obtained for single electrodes placed along the axis of the column, may be extended to the whole bed. Until now it has been assumed [21] that non-uniform distribution of liquid over the crosssection of a column manifests itself by the flow of considerable amounts of the liquid towards the walls; thus, the probes arranged along the axis should be the first to be affected by the poor wetting. The results of Weekman and Myers [22] contradict, however, the above conclusions. These authors, investigating the radial distribution of the phases, found that the liquid flow tended to concentrate not only near the wall of the column, but also at the centre of the bed. Increasing the gas flow rate had the general effect of giving a more uniform radial liquid distribution. Consequently, the most favourable (or, at least, the same as in the whole bed [23]) wetting conditions should prevail along the axis of the apparatus. The results of our experiments suggest that the gas, flowing cocurrently with the liquid, has little effect on the mass transfer at the liquid-solid interface (Fig. 5); obviously, this conclusion is valid only in the region where the thorough wetting of the electrodes may be assumed. For very low liquid flow rates the influence of this parameter reported in refs. 6, 9 and 24 is probably due to the increase in the effective contact area between the liquid and the solid surface, as this area increases with the liquid as well as the gas flow rate. In Fig. 6 the experimental results are shown as a function Sh/Sc0.33= f(Re,) both for the free flow of liquid and for the gas continuous flow regime. The scatter of the experimental points reflects the effect of the changes in the physicochemical properties of the liquid and in the diameter of the packing elements. Thus, if we assume that the gas continuous flow regime is, as Charpentier and Favier [ 1] defined it, a region of weak interactions, experimental results obtained for the free flow of liquid (wp = 0) and for the

Fig. 5. Effect of gas flow rate on the mass transfer in the gas continuous flow regime.

116 I

$z 40 30

20

I

= P 0 v A 1.163 1363 2.23 3.36 3.96

10

v

Fig. 6. Results of liquid-solid continuous flow regime.

mass transfer

experiments

and

Re, = wplap

(3)

On the one hand, such forms take better account of the variable physicochemical properties of the liquid; on the other hand, by eliminating the diameter of the packing elements from the Reynolds and Sherwood numbers, it becomes possible to make a direct comparison of the results of the authors who performed their experiments for packings other than spheres [9,241. Based on the calculations carried out for 236 experimental data the following correlation has been derived: Sh,/Sc0.33 = ( 1.19 + 0.0072 Re,) x ( Re,,)0.494Ga-o-22

5.60

in a fixed bed: open symbols,

gas continuous flow regime should be represented by a single relationship which, at the same time, would take into account an increase of a few per cent in the mass transfer coefficient (see Fig. 5) due to the effect of the gas phase. As the experiments discussed above are a typical case of the liquid flowing down the surface of the packing, it has been decided to return to the forms of the dimensionless numbers generally employed in this case: Sh, = k,,9,/D

3.86 6.32 -u-(I-,I -

I.’ (4)

which is presented in Fig. 7 together with the experimental results (the mean deviation between the experimental points and the correlating curve is about 8%). Comparison of the empirical data obtained in this work with other studies is difficult for several reasons. First, the experimental material presented in the literature is very limited; many authors performed their measurements for two liquid flow rates only

- 1, -

free flow of liquid (ws = 0); closed symbols,

gas

[9,24], the lower of which does not seem to ensure the effective wetting of the packing. Second, most of the investigations were carried out for systems whose physicochemical properties did not differ much from those of pure water (constant Galileo number); the results of Latifi et al. [ 131 and Gambitto and Lemcoff [12], concerning nonNewtonian liquids, are surprisingly low, even for a flooded column (cf. $3.1). It should be noted, however (Fig. 8A), that owing to the particular form of the correlation equation proposed, the results obtained by Barthole [14] (,uL g 1 x 10m3 Pa s) and Latifi et al. [ 131 (fiL s 4 x lop3 Pa s), apparently using the same experimental apparatus, lie along a single straight line. This means that they may be described by an equation of the form of eqn. (3), although with a much lower value for the constant coefficient. Third, the authors differ as to the effect of the gas phase on the values of the mass transfer coefficients; this is shown in Fig. 8B. While Hirose et al. [8] assume that this effect manifests itself only for high liquid Reynolds numbers (although not strongly enough to justify its inclusion in the correlation equations), Rao and Drinkenburg [24] find an opposite tendency-in their experiments, for higher liquid Reynolds numbers, the transfer coefficients seem to be independent of the gas flow rate. Fourth, only a single work is available where the experiments were performed for the packing whose shape (and, more important, porosity) differed considerably from those generally used, that is, spheres or granules. This is a study by Ruether et al. [9], who employed Berl saddles. Unfortunately, comparison of their results with those of other authors is rather difficult, as in the gas continuous flow regime they change the gas Reynolds number over the range 17-101 which, for other packing geometries, corre-

117 10 8

6

. R i

T

v

1.163

3.86 6.32

A 1.163 a

2.23

I,

o

3.38

II

m 3.96 * 5.88

II Ii

I

8

Fig. 7. Our experimental

results correlated

using eqn. (4). Symbols as in Fig. 6.

sponds to the regime of a fully developed pulsed flow. Thus, Fig. 9 shows the line representing the results of Ruether et al. only for the lowest value of Re,; the literature data and the correlation curve described by eqn. (4) are also compared in this

Figure. It may be seen that refs. 5 and 8-10 give slightly lower results than those obtained in this work (by less than 17%) which, taking into account all the limitations listed above, seems to be quite satisfactory.

x 181 v A H A

8. A

G+2+

rI31 091 bOJ b41

Re,,

e 151 . L81

/’

1

--I5

o k4](dp=6mn) 5 -17 ._ Q [24](d,=3m-n! 5 -34 M r91 17 -101 # -

[lOI this work

O-036 3 -15

L 1

Fig. 8. Comparison

2

of experimental

1

35 -- -‘

4

6

8

IO

J 20

R%L

40

results obtained by different authors: A, free flow of liquid (w, = 0); B, gas continuous

flow regime.

118

Fig. 9. Gas continuous

3.3. Pulsed flow

flow regime: experimental

results of several authors

regime

A transition from the gas continuous to the pulsed flow regime depends not only on the flow rates of the phases, but also on the particle size and shape and on the physicochemical properties of the liquid. According to Blok et al. [25] the transition occurs at a constant value of the Froude number, whose limiting value decreases with increasing viscosity (thus, for higher liquid viscosities the pulsed flow regime should appear for lower flow rates of this phase). The boundary dividing the regimes was determined by Charpentier and Favier [l] as a function of the so-called ‘flow parameters’, (L/G)@ = f(G/A). This relationship was therefore employed in calculating the operating conditions for individual measurement points. It is not easy to correlate the experimental data for the pulsed flow regime by an equation describing the effect of the operating parameters, physicochemical properties of the liquid and the packing size on the mass transfer coefficients kLs. Hence, a number of different relationships are proposed which approximate the experimental results more or less accurately. A detailed review of these studies is given in ref. 26 where it is shown that one of the reasons for large discrepancies between the various literature data may have been the incorrect positioning of the test sections, leading to the low values of kLs obtained in refs. 3, 6 and 7 and, partly, in ref. 8. According to Blok et al. [2, 271, it is only about 0.2 m below the top of the column that the pulsed flow may be regarded as fully developed. In refs. 8 and 24 the authors, analysing the mass transfer experiments for the pulsed flow, presented the results as a correlation between Sh/Sc0.33 (or, directly, kLs) and the parameter called the ‘energy of dissipation’. Such an interpretation of the results has a serious disadvantage, as all the hydrodynamic characteristics of the system are lumped into a single parameter (not to mention the difficulty in determining the value of this parameter). Another form of the correlation was originally proposed by Ruether et al. [9] and then modified by Rao and Drinkenburg [24], who described their own

using eqn. (4). Symbols as in Fig. 8B.

experimental results as well as those of other authors [4, 5,9] by the following equation: sSh/Sc”.33 = 0.58( Re;)0.52

(5)

with an accuracy of +20%. The approach of Ruether et al. [9] requires, however, an appropriate formula to determine the liquid hold-up, necessary to calculate the modified liquid Reynolds number (Re; = ReJhr). Rao and Drinkenburg [ 241 suggest a simple relationship, derived in ref. 28 and expressing the liquid hold-up only as a function of the gas Reynolds number and the specific surface area of the packing. It should be stressed, however, that this relationship is based on the experiments performed exclusively for the airwater system and for the packing consisting of spheres or Raschig rings; its application to systems with different physicochemical properties or packing geometries (e.g. Berl saddles) does not appear possible. Consequently, it seems that at this stage of research attempts should be made to find the relation between the mass transfer coefficients and the external well-known parameters, such as fluid flow rates, packing characteristics, etc. Although such an approach, like the ones described above, does not reflect the whole complexity of the process, it enables incorporation of intermediate quantities into the correlation equation to be avoided; these quantities would have to be calculated using some additional relationships, often burdened with substantial error. Based on the calculations performed for 207 experimental points the following formula has been obtained: Sh,/Sc0.33 = 2.269( Re,,)0.4g4( Re,)0~‘78Ga-0~276

(6)

which approximates the results of all the experiments, with a mean deviation of less than a few per cent (Fig. 10). Despite the complexity of the processes involved, the comparison of our data with those of other authors (Fig. 11) reveals a highly satisfactory agreement, especially with the results of Chou et al. [S] and Rao and Drinkenburg [24]; the findings of

119

d, lo3 ).I ’ IO3 [Pas] Cm3

v

1.163

3.86 6.32

* 1.163 + 2.23 0

3.36

A 6.32

Fig. 10. Experimental

results on liquid-solid

mass transfer in the pulsed flow regime. The full line represents the correlation

equation (6).

R%

2 .-

28 - 56 10.5 - 79 22 - 56 . [Zb](d,-6mn) 25 - 66 -3 [24] (dPdmml 12 - 35 w [91 18 -102 7 this work 0 - LO

1 --

10

20

40

60

a0

100

Fig. 11. Pulsed flow regime: results of several investigators

200

correlated using eqn. (6).

Lemay et al. [4] show a very strong dependence on the gas Reynolds number (exponent equal to about 0.42), while Ruether et al. [9] suggest the influence of this parameter to be weak as it is in the gas continuous flow regime. All in all, there is an urgent need to formulate a model of mass transfer in the pulsed flow regime which would describe all the phenomena occurring in the system, its complex hydrodynamic characteristics included. It should be remembered that the mass transfer coefficients are evaluated using an average value of the diffusion current which fluctuates with the changes taking place around a test element. The changes of the gas and liquid flow rates modify both the frequency and the amplitude of the signal, thus reflecting the variation in frequency and height of the liquid ‘pulses’ forming in the column. 4. Concluding

remarks

In the present work the local solid-liquid

RezL

mass

transfer coefficients have been determined for a cocurrent downflow of gas and liquid through a bed of spherical particles, using an electrochemical method. The measurement data obtained for solutions of different viscosities (from 1.1 x 10e3 to 6.35 x lop3 Pas) and for two packing sixes (3.87 x 10M3 and 6.32 x 10m3 m) have been correlated by means of eqns. (2), (4) and (6). The discussion of both the experimental results and the literature data leads to the following conclusions. (1) In the gas continuous flow regime the method for correlating experimental results does not seem to raise any doubts. Unfortunately, as long as the problem of the effective wetting of the bed remains unsolved, some discrepancies may appear in the empirical data obtained by different authors. (2) In the pulsed flow regime a form of correlation should be attempted which would link, to some extent at least, the mass transfer process with the complex hydrodynamic characteristics of the flow.

120

Nomenclature a

C

Re, Re, ReL Ret ReZL SC Sh Sh, wg, WL

external surface area of packing per unit column volume, m2/m3 concentration of potassium ferricyanide, mol m-’ diffusion coefficient in liquid phase, m2 s-l packing diameter, m Faraday’s constant, C mol-’ superficial gas flow rate, kg/m2 s = dv3pL2g/pL2, Galileo number acceleration due to gravity, m sp2 total liquid hold-up limiting current density, A m-’ liquid-particle mass transfer coefficient, ms-’ superficial liquid flow rate, kg/m2 s number of electrons reducing one oxidized particle = dPwgpg/pg, Reynolds number for gas modified Reynolds number for = w,p,lap,, gas = dpwLpL/pL, Reynolds number for liquid Re, /hL , modified Reynolds number = Re,/h,, modified Reynolds number = p/D, Schmidt number = k,,d,/D, Sherwood number = kLs 9,JD, modified Sherwood number superficial velocity of gas and liquid phase, ms-’ packing porosity, m3 void/m3 column film thickness, m = (PL2kPL2> “3, equivalent = [(PLlPw)(PglPair)l l/2> flow parameter viscosity of gas and liquid phase, Pa s viscosity of water, Pa s density of gas and liquid phase, kg m-’ density of water, kg rnp3 surface tension of liquid phase and water, Nm-’ fraction of wetted area para= (0 I~LWLIPWXP wlP37 1’39 flow mete:

References .I. C. Charpentier and M. Favier, Some liquid holdup experimental data in trickle-bed reactors for foaming and nonfoaming hydrocarbons, AIChE J., 21 (1975) 1213. J. R. Blok and A. A. H. Drinkenburg, Hydrodynamic properties of pulses in two-phase downflow operated packed columns, Chem. Eng. J., 25 (1982) 89. V. Specchia, G. Baldi and A. Gianetto, Solid-liquid mass transfer in cocurrent two-phase flow through packed beds, Ind. Eng. Chem., Process Des. Dev., 17 (1978) 362. Y. Lemay, G. Pineault and J. Ruether, Particle-liquid mass transfer in a three-phase fixed-bed reactor with cocurrent flow in the pulsing regime, Ind. Eng. Chem., Process Des. Dev., 14 (1975) 280.

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