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Mass transfer and bubble size in a bubble column under pressure
Pergamon
MASS
Chnnienl Eq,imei,~
TRANSFER
Department
Sciewe, Vol. 49, N.,. 9, m. 1417-1427, ,994 Copyripht Q 19!34Elsevia S&ma Ltd Printed in Great Britain. All rights rcstrval ooo9-2509f94 s6.03 + 0.m
AND BUBBLE SIZE IN A BUBBLE UNDER PRESSURE
COLUMN
PETER M. WILKINSON’ and HERMAN HARINGA of Chemical Engineering, University of Groningen, 9747 AG Groningen, The Netherlands and LAURENT L. VAN DIERENDONCK DSM Research, PO Box 18, 6160 MD G&en, The Netherlands
(First received
20 August
1991; accepted for publication
in revisedJorm 9 November 1993)
Abstract-The influence of pressure on the gas hold-up in a bubble column is determined for a sodium sulphite solution in combination with the volumetric mass transfer coefficient. Furthermore, for the same conditions the bubble size is also estimated from photos. The results of these experiments show that the interfacial area and the volumetric mass transfer coefficient both increase with pressure, while for design purposes the magnitude of the increase can be safely estimated from the increase in gas hold-up. Finally, the influence of pressure on the Sauter mean bubble size in a number of pure liquids (mono-ethylene glycol, n-heptane and deionized water) is also studied and correlated with a new empirical equation on the basis of photos in combination with literature results.
INTRODUCTION
The mass transfer characteristics (k,a and a) belong to the most important parameters for design and scaleup of bubble columns, and consequently it has been
the subject of much research. In the literature many articles with experimental mass transfer data can be found and a number of empirical equations have been proposed for the estimation of these parameters (Akita and Yoshida, 1974; Hikita et al., 1981; Hammer et al., 1984). A limitation of these articles is that they are virtually all based on atmospheric experimental data in spite of the fact that industrial bubble columns are commonly operated at pressures above atmospheric. Recently, numerous studies have been published (Deckwer et al., 1980; Tarmy et al., 1984; Mochida, 1985; Idogawa et al., 1986, 1987a, b, de Bruijn et al., 1988; Oyevaar, 1989; Clark, 1990; Wilkinson and van Dierendonock, 1990, Oyevaar et al., 1991 and Wilkinson, 1991) which show that gas holdup can increase noticeably if gas density is increased (either by increasing pressure or gas molecular weight). On the basis of these gas hold-up measurements it is also to be expected that the mass transfer characteristics are to be influenced by the value of the gas density. However, papers showing how the interfacial area and/or volumetric mass transfer are influenced by pressure or gas density are far less numerous [e.g. k,a measurement with varying gas density at atmospheric pressure (&tiirk et a[., 1987); k,a measurement at varying pressure (VaFopulos, 1974); ‘Present address: Royal/Shell-Laboratory Amsterdam, PO Box 3003, 1003 AA Amsterdam, The Netherlands.
interfacial area measurement by chemical methods (Oyevaar et a[., 1991)]. Furthermore, the conclusions that can be drawn from these papers with respect to the influence of pressure on bubble size varied from a decrease in bubble size with increasing pressure (Wilkinson and van Dierendonck, 1990) to an increase in bubble size (Oyevaar et al., 1991) with increasing pressure. The aim of this paper is therefore to experimentally determine the influence of pressure on the volumetric mass transfer coefficient (and bubble size) in a bubble column and to explain the apparent discrepancies in the literature regarding the influence of pressure on bubble size. For this purpose the volumetric mass transfer coefficient is determined chemically with a model reaction (the uncatalysed sodium sulphite-water system), while the influence of pressure on bubble size is determined photographically for the sodium sulphite-water system, n-heptane, deionized water and mono-ethylene glycol. DETERMINING
MASS TRANSFER
AT
PRESSURES
ABOVE
ATMOSPHERIC
In principle, the volumetric mass transfer coefficient in a bubble column can be determined in many different ways. The mass transfer rate is often determined by changing the feed gas from nitrogen to oxygen or vice PeTsa, while simultaneously measuring the oxygen concentration change in the liquid with a Clark-type oxygen electrode. For high mass transfer rates (as was expected for high pressure and high gas rates) this procedure, however, requires a very fast response of the oxygen electrode -and a knowledge of the gas
1417
1418
PETER M. WILKINSON er ~1.
residence time distribution during the experiment. Furthermore, at high pressure this procedure is technically relatively complicated. An alternative method that has been developed by Linek et al. (1989) is to make a sudden (small) change in the column pressure and then to determine the resulting change in oxygen concentration in the liquid with a Clark-type oxygen electrode. Although this procedure has the advantage that the mass transfer rate can be evaluated without a knowledge of the gas residence time distribution, it still requires the use of a fast response oxygen electrode. Fast response electrodes do exist for atmospheric conditions; however, for high pressures commercially available oxygen electrodes are either extremely expensive or do not have a sufficiently fast response time [preferably Q l/k,a s (Deckwer, 1985)] to oxygen concentration changes. Alternative procedures to determine the volumetric mass transfer coefficient are usually based on chemical systems, of which a number have been listed by Deckwer (1985) (in combination with guidelines for selecting the appropriate system). In the present study the uncatalysed oxidation of sodium sulphite (Wilkinson et al., 1993) has been chosen as a model reaction to determine the volumetric mass trausfer coefficient. Due to the low solubility of oxygen in water-sodium sulphite solutions, the gas phase conversion remains low, and as a result the oxygen concentration in the gas (and liquid) phase will remain almost constant throughout the bubble column, The main advantage of this is that neither the liquid nor the gas phase mixing have to be known for the evaluation of the volumetric mass transfer coefficient. MASS TRANSFER
EXPERIMENTS
From the literature [e.g. Reilly et al. (1986)] it is known that the influence of the column diameter on gas hold-up (and mass transfer) can be neglected, provided the size of the column is larger than 0.15 m. It is also known that the sparger has virtually no influence on the gas hold-up (and mass transfer), provided the sparger hole-diameters are not too small (as is usually the case for industrial bubble columns). In our study both these conditions were fulfilled: the oxidation rate of sodium sulphite was determined at a constant temperature (20 i O.lOC) in a metal bubble column, with an internal diameter of 0.158 m and the liquid level was 1.5 m. The sparger used was a ring with 19 holes of 10 mm, An additional reason for using such large sparger holes is that the influence of gas density (through its momentum) on the bubble Table
formation process will be minimal if the gas velocity through the sparger holes is not too large. Thus, the use of large sparger holes ensures that any measured influence of pressure (or gas density) is not the result of the gas density on the bubble formation process. At the start of each experiment the column was filled with a 0.8 mol/l sodium sulphite deionized water solution, while the initial pH values were adjusted between pH 6.5 and 8.5 with sulphuric acid (in order to vary the reaction rate). The applied gas was air at pressures between 0.1 and 0.4 MPa and the gas rate was measured with a calibrated gas turbine. The sulphite conversion rate was determined by analysing samples taken from the solution at regular time intervals. All experimental results showed a linear decrease of the sulphite concentration vs time. In addition, for each experiment the gas hold-up was also measured with an overflow technique [as in Wilkinson (1991)]. BUBBLE
CHEMICAL
ABSORPTION
THEORY
The equations necessary for the calculation of the volumetric mass transfer coefficients from the sulphite oxidation experiments can be determined by making
1. Physical properties of liquids used for bubble
n-Heptane Mono-ethylene glycol Water 0.8 M sodium sulphite in water+
SIZE ESTIMATION
In order to determine the bubble size in a bubble column as a function of pressure, a steel vessel was constructed with an internal diameter of 0.25 m equipped with three pairs of 0.15 m sight glasses for pressures up to 1.5 MPa. In this vessel a 0.15 m glass pipe was placed that functioned as the actual bubble column. At the start of an experiment the vessel was filled with liquid in the glass bubble column and in the space surrounding the glass pipe. Due to this arrangement and the absence of a curvature on the sight glass, virtually no optical deformation of the bubbles occurs on the photos. The bubble sizes on the photos were determined with the aid of a Zeiss TGA-10 particle size analyser as described by Kiisters (1976). For the determination of the Sauter mean bubble diameter at least four enlarged photos were used for each condition and between 300 and 500 bubbles. All the photos that were used for the evaluation of the bubble size were taken at the central sight glass 0.6 m above the sparger. The liquids used were n-heptane, mono-ethylene glycol, deionized water and a 0.8 mol/l sodium sulphite deionized water solution (the same as for the mass transfer experiments) at room temperature (Table 1). For most experiments nitrogen was used, while for deionized water a number of other gases were also used (Table 2).
684 1113 998 1086
‘Calculated from the equations of Novoselov
size evaluation
0.020 0.048 0.072 0.075 er al. (1989).
o.Qoc41
0.021 0.0010 0.0015
Mass transfet and bubble size
Table 2. Physical properties of the gases used in the experiments (at 2O”C, 0.1 MPa)
Gas Helium Nitrogen Argon Carbon dioxide Sulphur hexafluoride
105q,, (Pa s)
P# (k&m?
I .94
0.16 1.18 1.69 1.83 6.16
1.75 2.10 1.44 1.51
kla = $$
a number of assumptions for the mixing characteristics of the gas and liquid phase and by using the results of the theory for gas absorption followed by a slow chemical reaction in the liquid, combined with mass balances for the bubble column (that the usage of the theory for a slow chemical reaction is permissible will be demonstrated further on). First of all, from the stoichiometry of the sulphite oxidation it follows that the oxygen conversion rate (Qo,) is
40, = AUACo,.,.,,- co,,,,,,,) = - osr+,
d(c;;:) (1)
whereas the oxygen concentration change in the gas phase of the bubble column is described by
WJ,Co,,,,,) dz
= -
kdm(CO,.l.z
-
mCo,,,)-
(2)
Due to the fact that the gas phase oxygen conversion [calculated from eq. (l)] for all the present experiments in small ( -Z 5%), it can be assumed that the gas flow rate (U,) in eq. (2) remains constant, and, because the oxygen concentration in the gas phase (Co,,,) only changes marginally, the liquid oxygen concentration (Co,,,) will also be almost constant throughout the column. Furthermore, due to the reaction the oxygen concentration in the bulk of the liquid was usually close to zero, which also strengthens the conclusion that the liquid mixing behaviour is of little or no importance. Consequently, in order to simplify the solution of eq. (2) it can be safely assumed that the liquid phase is well mixed, while its value can be calculated (provided the reaction is not chemically enhanced) by krs,
V,&,,,
=
-
O.SV..c,Wso;-1 dt
1419
the average column midpoint pressure) was used for the calculations. With these assumptions eq. (2) is integrated, which leads to
(3)
0.5
“‘“,s,:-)
(kr). i
In order to solve eq. (2) it is assumed that the gas is in in plug Sow. However, again due to the low gas phase oxygen conversion this assumption has little influence on the calculated volumetric mass transfer coefficient. Finally, in order to account for the influence of the change in hydrostatic pressure on the oxygen concentration as well as on the gas flow rate, a constant pressure throughout the column (based on
mco,.,
(5) >’ Co t...-4 - mco2., With the aid of this equation [in combination with eqs. (1) and (4), for the calculation of the oxygen concentrations CO~.~.~~, and Co, ,], the volumetric mass transfer coefficient is calculated. So far, three (implicit) assumptions have been made as regards the oxygen absorption: first of all, it is assumed that the reaction proceeds in the slow reaction regime (the absorption is not chemically enhanced), which implies that the Hatta number (Westerterp et al., 1984) is less than 0.3:
Whether or not this first criterion (Ha < 0.3) holds can be estimated from the experiments by varying the reaction rate constant. If the value of the reaction rate constant has no influence on the calculated volumetric mass transfer coefficient, then this implies that the reaction proceeds in the slow regime (and thus Ha -c 0.3). In our experiments the pseudo-first-order reaction rate constant of the (uncatalysed) sulphite oxidation was varied from k, = 0.5 s ’ to k, = 20 s ’ by adjusting the pH of the sulphite solution with different amounts pseudo-first-order
of sulphuric acid [the values of the reaction rate constant (k,) were
taken from experiments by Wilkinson et al. (1993)]. Secondly, it was assumed that the reaction film volume is small as compared to the bulk volume:
On the basis of (literature) experimental results it is known that k, x=-1 x lo-’ m/s, d, > 2 x lo- 3 m, while Do, = 1.6 x 10e9 m’/s. Using these values for the evaluation of eq. (7) shows that the Hinterland ratio (AI) will be larger than 20 provided the gas hold-up is below 50%. Consequently, the condition described by eq. (7) is fulfilled for the present experiments (as is normally so for bubble columns). Finally, the third condition that should be checked is whether the resistance to gas phase mass transfer is negligible: mK,/k,
and thus
co,, = -
co2.S.i”-
In
S- 1.
(8)
That the gas phase resistance is completely negligible for the sulphite oxidation can be argued on the basis of the k,n and kla measurements of Cho and Wakao (1988) in a bubble column. By combining and reinterpreting their results it is determined that ka AL=2
k
ha
k,
The ratio of the diffusion constants in this equation is for the air [D, = 1.84 x lo- ’ m2/s (Reid et al., 1988)], sulphite [D, = 1.6 x 1O-9 m2/s (Linek and
1420
PETER M. WILKINSON
Mayrhoferova, 1970)] system equal to 1.2 x lo4 at atmospheric pressure. At the highest pressure used in our experiments (P = 0.4 MPa) this ratio is, however, only 3 x lo3 because the gas diffusion constant is inversely proportional to the value of the pressure. This (lowest) estimate of the diffusion coefficient ratio together with the result that the constant c in eq, (9) is never smaller than 0.2 [based on the experimental values of Cho and Wakao (1988)] leads to the conclusion that the gas phase mass transfer coefficient is at least 10 times larger than the liquid phase mass transfer coefficient for the range of conditions in the present experiments. Furthermore, from eq. (8) it can be seen that the resistance to gas phase mass transfer is even further decreased for gases with a low solubility, as is the case for oxygen in a 0.8 mol/l sodium sulphite solution (m = 54).
EXPERIMENTAL
Mass
transfer
RESULTS
and gas hold-up
k,s (81
.Fig. 1. k,a in a 0.8 mol/l sodium sulphite solution vs the superticialgas velocity at 0.1, 0.2, 0.3 and 0.4 MPa.
AND DISCUSSION
in sulphite
solutions
First of all, it was determined that an increase in reaction rate from k, = 0.5 s-’ to k, = 20 s-’ never increased the volumetric mass transfer coefficient calculated from eq. (5) by more than 30%. Obviously, this result indicates that the reaction proceeds in the slow regime (Ha -Z 0.3) for low k, values, whereas the reaction becomes slightly enhanced for the higher k, values. Consequently, in order to prevent chemical enhancement most experiments were done at k, values of 2 and lower. In Fig. 1 the calculated volumetric mass transfer coefficients from these experiments are shown vs the superficial gas velocity at four different pressures, while the gas hold-up for the same conditions is shown in Fig. 2. From these figures it shows that both the gas holdup and the volumetric mass transfer coefficient increase significantly with increasing pressure, especially at high gas velocities. An important consequence of this is that relatively high mass transfer rates are possible at high pressure, despite the use of a sparger with exceptionally large holes (10mm). At low superficial gas velocities (U, < 0.03 m/s) the influence of pressure, however, seems to be relatively small. Presumably, this is the reason why virtually no influence of pressure was observed (Fig. 3) in the only previous work that has dealt with the influence of pressure on the volumetric mass transfer coefficient in bubble columns [Vafopulos (1974) at low superficial gas velocities!]. That the increase of the volumetric mass transfer coefficient with pressure in Fig. 1 resembles the trend by which the gas hold-up increases (Fig. 2) is obviously caused by the fact that the interfacial area is proportional to the gas hold-up through a = 6&,/d,.
et al.
(10)
However, apart from the increase in mass transfer due to the increase in gas hold-up at higher pressures, an additional influence was expected due to the fact that the bubble size (and thus interfacial area) also depends on pressure (Idogawa et al., 1986, 1987a, b;
_..
Fig. 2. Gas hold-up vs superficial gas velocity for the same conditions as in Fig. I.
(m/s1
U,
Fig. 3. k,n in a 0.8 mol/l sodium sulphite solution vs the superficial gas velocity at 0.1,0.2, 0.4,0.6 and 0.8 MPa ob-
tained in a bubble column with a perforated plate with 60 holes of 1 mm [data of Vafopulos (1974); H = 1.46 m, D = 0.4 m-J.
Wilkinson and van Dierendonck, 1990). By dividing the volumetric mass transfer coefficient by the gas hold-up value [eq. (11) J it is possible in combination with eq. (10) to determine to what extent the bubble size (in combination with the liquid mass transfer coefficient) changes with pressure: &,a -=--F.
%
6k, 4
(11)
The value of this ratio is shown in Fig. 4. From this figure it can be seen that the value of k,a/&, increases with an increase in pressure as well as for an increase in superficial gas velocity. The explanation for this increase at higher pressure is obviously a result of the
Mass transfer and bubble size
Fig. 4. k,a/.s, ( = 6k,/d.) vs the superficial gas velocity for the same conditionsas in Fig. 1.
fact that the bubble size (d,) decreases with increasing pressure while the mass transfer coefficient is expected to remain uninfluenced by pressure, because the value of the pressure has a negligible influence on the liquid phase physical properties (IDI, Q, etc.). However, the increase of the value of k,/d, [eq. (1 l)] with increasing pressure cannot be used to calculate the exact magnitude by which the pressure influences the bubble size because the mass transfer coefficient also partly depends on the bubble size. That Fig. 4 shows that the value of k,a/&, also increases with increasing gas velocity is presumably related to the fact that at higher gas velocity the power input to the liquid is greater, which leads to more turbulence. This higher degree of turbulence will promote bubble break-up, while a higher degree of turbulence is also known to lead to higher k, values. Obviously, both these effects contribute to the increased eq. (ll)] at higher gas value of k,a/c, [ = 6k,/d,, velocity. In Fig. 5 the experimental volumetric mass transfer coefficients are shown vs the experimental gas holdup, together with the volumetric mass transfer coefficient predicted from a recent empirical equation by Akita (1989) for water-electrolyte solutions:
1421
Fig. 5. kia vs the gas hold-up for the same conditions as in Fig. 1 in combination with the predicted k,o value from eq. (12).
10
U,
(m/a)
Fig. 6. k,a in xylene vs the superficial gas velocity for hydro-
gen, helium,nitrogen.and air.
k,a = Fig. 7. k,a in xylene vs the gas hold-up for the same conditions as in Fig. 6.
(12) The value of kM in this equation is a function of the type of electrolyte and the electrolyte concentration. For a 0.8 mol/l sodium sulphite solution, a value of 2.4 is calculated (based on data for a 0.8 mol/l sodium sulphate solution). From Fig. 5 it is clear that this empirical equation provides a rather low estimate for all the experimental results. Other empirical equations [e.g. Hikita et al. (1981)], however, usually predict the volumetric mass transfer coefficient as a function of the superficial gas velocity and not as a function of gas hold-up or gas density. Consequently, these other equations do not account for any influence of pressure and are thus even less successful for predicting the mass transfer coefficient at higher pressure. Furthermore, the fact that the experimental volumetric mass
transfer eoetlioients lie virtually on one single line for different pressures is also in agreement with the results of &tiirk et al. (1987) in xylene. &tiirk et al. determined the volumetric mass transfer coefficient as a function of gas density by using different gases at atmospheric pressure (Figs 6 and 7). On the basis of Figs 5 and 7 a procedure is developed to estimate the magnitude by which the volumetric mass transfer coefficient will increase with increasing gas density:
[e]=[E]“,
withn=l.&1.2. (13)
Obviously, it is not possible to apply this equation without a knowledge of the gas hold-up as a function
1422
PETER
M.
WILKINSON
of gas density; the same restriction, however, also holds for eq. (12) of Akita. Furthermore, due to the absence of experimental data on the volumetric mass transfer coefficient at still higher pressure and in different liquids, additional research is certainly desirable. Gas hold-up sures
in sodium
sulphite
solutions
at higher
er al.
0.a $ 0.a
0’
key
P(WmI
t
0.1
‘
0.5
D
1.0
I
pres-
Sodium sulphite solutions with the same composition as for the mass transfer experiments were used in a few experiments to determine the gas hold-up and to estimate the bubble size at still higher pressures. The results of these experiments show (Fig. 8) that the gas hold-up at these high pressures increased more than proportionally with increasing gas veiocity towards gas hold-up values that are much higher than in pure water (Fig. 9). Furthermore, it was seen that numerous small bubbles (approximately 0.5 mm in diameter) accumulate in this aqueous sodium sulphite for low as well as for high pressures. The main visual difference, however, is that at low pressure, in addition to these small bubbles, some large bubbles also occur (typically between 3 and 5 cm, Fig. to), whereas these are not seen at the highest pressure. For the highest pressure, however, a foam-like structure (Fig. 11) develops in the bubble columns when the gas hold-up increases beyond 30-40%, whereas this does not occur at atmospheric pressure. From previous literature results (obtained at atmospheric pressure) it is known that
Fig. 8. The gas hold-up in a 0.8 mol/l sodium sulphite solution vs the superficial gas velocity at O.l,O.S, 1.0, 1.5 and 2.0 MPa.
Fig. 9. The gas hold-up vs the superficialgas velocity at 0.1, 0.5, 1.0, 1.5 and 2.0 MPa (for the same conditions as in Fig. 8, but with deionized water instead of a sodium sulphite solution).
Fig. 10. Photo of bubbles obtained in the bubble column at a gas hold-up of 30% (aqueous 0.8 mot/l sodium sulphite solution, U, = 0.07 m/s, P = 0.1 MPa).
Mass transfer and bubble size
Fig.
1423
11. Photo of the foam structure obtained in the bubble column at a gas hold-up of 40% (aqueous 0.8 mol/l sodium sulphite solution, U, = 0.06 m/s, P = 1.5 MPa).
the addition of sodium sulphite or other electrolytes to water leads to a higher gas hold-up and to smaller bubbles due to the fact that the coalescence rate is reduced in aqueous electrolyte solutions (Zieminski and Whittemore, 1971). The present result indicates that the injluence of electrolyte and the influence ofgas density on gas hold-up are synergistic. The reason for this observation is presumably that both contributions are the result of different mechanisms [the electrolyte hiriders coalescence, whereas a higher gas density promotes bubble break-up (Wilkinson and van Dierendonck, 1990)]. The main practical consequence of these observations is that, although in principle a high pressure will lead to higher (advantageous) volumetric mass transfer rates, in some cases the extremely high gas hold-up values can become a disadvantage: in the case of slow reactions (for which bubble columns are often used) the decrease of the liquid phase reaction volume at higher pressure (due to the higher gas hold-up at high pressure) can lead to a lower overall reaction rate in the bubble column.
Bubble size in (sodium sulphite-) mono-ethylene glycol
water, n-heptane und
During the past few decades techniques have been used and bubble sizes for the estimation Most of these techniques have
different experimental developed to measure of the interfacial area. not only been used at
atmospheric pressure but have (in recent years) also been applied to high-pressure conditions (Table 3). However, in spite of this variety of measuring techniques an accurate estimation of the interfacial area for a large range of conditions remains complicated because each measuring technique has its specific advantages and disadvantages (Table 4). From these different techniques, at present the photographic technique is used most frequently. Presumably, this is mainly due to the fact that photographic bubble size evaluation can be done most easily for a wide range of conditions. Consequently, it is also not surprising that virtually all empirical equations in the literature [e.g. Akita and Yoshida (1974), van Dierendonck (1970) and Kiisters (1976)] for the evaluation of the Sauter mean bubble size or the interfacial area are based on photographically determined bubble sizes. Furthermore, all empirical equations in the literature for the prediction of the Sauter mean bubble diameter are based on atmospheric data and therefore do not incorporate the decrease of bubble size with increasing gas density. In order to quantify the influence of gas density on bubble size the Sauter mean bubble diameter is estimated from photos in mono-ethylene glycol, water and n-heptane at pressures between 0.1 and 1.5 MPa (with different gases, Table 2) and for superficial gas velocities between 0.02 and 0.1 m/s. The results of these experiments, combined with similar atmospheric experiments of Sahabi (1976) in cyc-
1424
PETER M. WLK~NSON
eta/.
Table 3. Studies on the influence of gas density on bubble size in bubble columns Liquid
Gas
Pressure (MPa)
Sparger (m)
Method
Reference
Influence of gas density
NazSO,-water
Air
0.1-10
Ejector
Suction probe
Jekat (1975)
Yes
Cyclohexane
He, N2, Ar, co2
0.1
Sparger cross 24 x 0.5 mm
Photographic
Sahabi (1976)
Yes
Water
Air
0.1-1.0
Perforated 1OOxlmm
Suction probe
Neubauer (1977)
YeS
Water-KC1
Air
0.1-15
Single nozzle d= 1,3or5
Electrical reslstivity probe and photographic
Idogawa (1986)
et al.
Yes
Electrical resistivity probe and photographic
Idogawa (1987a)
et al.
Yf%
plate
Perforated plate 19x1mm Porous plate d = 0.002, d = 0.1 Water-KCI, ethanol, acetone, methanol
Hz, He, air
0.1-5
Perforated 19xImm
Water, methanol, ethanol
HI, He, air
0.1-S
Single orifice d= 1,3or 5
Electrical resistivity probe and photographic
Idogawa (1987b)
et al.
Yes
DEA-water
NtqOz
Perforated plate 21 x0.4 mm Sparger cross 16 x 0.5 mm Porous plate
Chemical
Oyevaar (1991)
et al.
Yes
0.15-g
d =
Table 4. Experimental Experimental
technique
plate
0.03.0.1
techniques
for estimating
the bubble size in bubble columns
Advantage
Disadvantage
Chemical absorption experiment with model reaction
It leads to an integral value of the interfacial area
The use of chemical reaction systems usually influences the hydrodynamics, and the number of mode1 reactions reported in the literature is limited
Suction probe; measurement of bubble volumes sucked from the dispersion
The bubble size can be measured throughout the bubble column, and it is a relatively fast technique
Bubbles larger than the capillary through which the bubbles are sucked are not measured
Electrical resistivity
In addition to local bubble sizes also the local gas hold-up can often be measured simultaneously
Additives are usually required to increase the liquid conductivity, and d, cannot be calculated without making considerable assumptions
Photos can be used bubble size distribution conditions
Only bubbles near the column wall are seen; bubbles more to the centre of the column may be larger but cannot be seen. Furthermore, large, irregular shaped bubbles are difficult to measure
Photographical
probe
technique
to determine the for a wide range of
lohexane with different gases, were correlated (Fig. 12) by regression analysis to a new dimensionless equa-
tion:
(14)
Equation
(14) can be rewritten as
d, = 3g-
0.44~0.34,#.22p;0.4Sp~0.il
u,O.OZ_
(15)
That this correlation shows that the bubble size is proportional to the gas density to the power - 0.11 implies that a tenfold increase in gas density reduces the Sauter mean bubble size by almost 30%. For the
1425
Mass transfer and bubble size 7
.
1
Fig. 12. Predicted [eq. (15)] Sauter mean bubble diameter vs the experimentally determined Sauter mean bubble diameter in four pure liquids.
0.1
-*
Fig. 13. Estimated bubble sizes in a 0.8 mol/l aqueous sodium sulphite solution from photos, in combination with the bubble size predicted from eq. (15) (lines).
same range of conditions, Wilkinson (1991) determined that a tenfold increase of the gas density USUally leads to a (much) larger increase of the gas holdup, especially at high gas velocities. Thus, again, as for the experiments in sodium sulphite, it is to be expected that the interfacial area (6~,/d.) in a bubble column will increase more due to the increase of the gas hold-up than due to the decrease in bubble size with increasing gas density. Finally, it should also be kept in mind that in non-coalescing liquids such as water-sulphite solutions many very small bubbles usually accumulate in the liquid, which leads to a smaller Sauter mean bubble size than is predicted by eq. (15) (Fig. 13). However, it is to he expected that still much more research is needed before these additional effects can be quantified. COMPARISON
WITH LITERATURE
DATA
As has already been shown in Table 3, other authors have previously performed experiments to estimate the bubble size as a function of pressure; it appears, however, that the results obtained in these different references depend partly on the experimental technique by which the results were obtained. For instance, in all cases where the bubble size was determined photographically, it was determined that at higher pressure the average bubble size decreases mainly due to a reduction of the number of large bubbles (which is in accordance with the present re-
sults). The references for which the bubble size is determined with the aid of a suction probe, however, in genera1 observe only a very small influence of both gas density and liquid properties on bubble size. Presumably, this is caused by the fact that the main influence of gas density is to reduce the number of large bubbles, whereas these suction probes are not capable of measuring these large bubbles. Finally, the results of the chemically determined bubble size [C02, aqueous diethanolamine (DEA) (Oyevaar et nl., 1991)] are opposite to the present results. Oyevaar et al. (1991) calculated that the average bubble diameter increased for increasing pressure (while the gas hold-up increased too!). Oyevaar attributed this unlikely increase in bubble size to the fact that the interfacial area is underestimated because many small bubbles accumulate in the bubble column without contributing to mass transfer, and to the presence of a foam layer at the top of the dispersion, which is also less effective for mass transfer. Both these explanations are probable because the overall gas phase conversion for these experiments was very high [up to 99% (Oyevaar, 1989)]. In addition to these reasons, Oyevaar’s results may also be partly explained by the fact that the resistance to gas phase mass transfer [eq. (9)] can become significant at higher pressure (especially for soluble gases such as COz, and because the gas phase diffusion coefficient is inversely proportional to pressure). However, the main implication of this example is that although the interfacial area is expected to increase at higher pressure the advantage of this result may be partly reduced by the increase of the gas phase mass transfer resistance with increasing pressure (especially for soluble gases and at high reaction rates).
CONCLUDING
REMARKS
-An increase in gas density leads to smaller bubbles on average and a higher gas hold-up. -Consequently, the volumetric mass transfer coefficient also increases (substantially) for higher pressures (gas densities). -The uncatalysed sodium sulphite system can be applied as a model reaction for determining the volumetric mass transfer coefficient (of non-coalescing aqueous electrolyte solutions). -The addition of electrolyte increases the gas hold-up, due to its influence on coalescence, at low as well as at high pressure. -A new empirical equation is developed (based on a photographic bubble size evaluation for water, mono-ethylene glycol, cyclohexane and n-heptane) for the estimation of the influence of gas density and liquid properties on bubble size in bubble columns. -Finally, it is also argued that the improved performance of high pressure bubble columns (as compared to atmospheric bubble columns) can, in some cases, be partly limited due to higher gas phase mass transfer resistance at higher pressure or due to a decrease of the liquid reaction phase volume.
PETER M. WILKINSON et nl.
1426 Acknowledgement-The technical and financial Netherlands).
authors gratefully acknowledge the support of the DSM company (The
NOTATION a A Al
interfacial
c
d ds D IID 9 H HU
less gas-side mass transfer coefficient, m/s liquid-side mass transfer coefficient, m/s volumetric mass transfer coefficient, s-l electrolyte specific constant in eq. (12), di-
k, k, kla kM
mensionless first-order reaction rate constant, s - ’ distribution coefficient of oxygen ( = C,/Cr), mol/mol pressure, Pa superficial gas velocity at process conditions, m/s volume of bubble column, m3
k, m P u, K Z
%
m2/m3
cross-sectional area of bubble column, mz Hinterland ratio, dimensionless constant in eq. (9) dimensionless concentration at process conditions, mol/l diameter of sparger holes (Table 3), mm Sauter mean bubble diameter, m diameter of bubble column, m molecular diffusion coefficient, m2/s gravitational acceleration, m/s’ height of gas-liquid dispersion in bubble column, m Hatta number given by eq. (6), dimension-
C
Greek
area,
axial umn,
coordinate m
for
height
in bubble
col-
letters gas hold-up, dimensionless
;02
liquid hold-up, dimensionless liquid viscosity, Pas gas density, kg/m” liquid density, kg/m3 surface tension, N/m Oxygen conversion rate, mol/s
Subscripts b
and superscripts bulk of liquid
9 i
gas
a1 VI PS PI
in
interface conditions at z = 0
1
liquid
02 out
conditions at z = H
oxygen
REFERENCES
Akita, K., 1989, Effect of the electrolyte on the mass transfer characteristics of a bubble column. Int. them. Eagng 29, 127-133. Akita, K. and Yoshida, F., 1974, Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns. Ind. Engng Chem. Process Des. Dev. 13, 84-91. de Bruijn, T. J. W., Chase, J. D. and Dawson, W. H., 1988, Gas holdup in a two-phase vertical tubular reactor at high pressure. Can. .I. them. Engng 66, 330-333.
Cho, J. S. and Wakao, N., 1988, Determination of liquid-side gas-side volumetric mass transfer coefficients in a bubble column. Chew Engng Jpn 21, 576-581. Clark, K. N., 1990, The eliect of high pressure and temperature on phase distribution in a bubble column. Chem. Engng Sci. 45, 23Oll2307. Deckwer, W. D., 1985, Reaktionstechnik in Blasenslulen, in Grundlagen der chemischen Technik. Otto Salle Verlag, Frankfurt am Main, Germany. Deckwer, W. D., Louisi, Y., Zaidi, A. and Ralek, M., 1980, Hydrodynamic properties of the Fischer-Tropsch slurry process. Ind. Enqna Chem. Process Des. Dev. 19.699-708. van Dierendonck. L.-L., 1970, Vergrotingsregels &or gasbelwassers. Ph.D. thesis, Twente, The Netherlands. Hammer, H., Schrag, H., Hektor, K., Schiinau, K., Kiisters, W., Soemamo, A., Sahabi, U. and Napp, W., 1984, New subfunctions on hydrodynamics, heat and mass transfer for gas/liquid and gas/liquid/solid chemical and biochemical reactors. Front. Chem. Engng 464 -474. Hikita, H., Asai, S., Tanigawa, K., Segawa, K. and Kitao. M., 1981, The volumetric liquid-phase mass transfer coellcient in bubble columns. Chem. Engng J. 22, 61-69. Idogawa, K., Ikeda, K., Fukuda, F. and Morooka, S., 1986, Behavior of bubbles of the air-water system in a column under high pressure. Inf. them. Enyny 26, 468-474. Idogawa, K., Ikeda, K., Fukuda, F. and Morooka, S., 1987a, Effect of gas and liquid properties on the behavior of bubbles in a bubble column under high pressure. Inc. them. Engng 27, 93-99. Idogawa. K., Ikeda, K., Fukuda, F. and Morooka, S., 1987b, Formation and flow of gas bubbles in a bubble column with a single orifice or nozzle gas distributor. Cheat. Engng Commun. 59,201-212. Jekat, H., 1975, Messung von Blasengrollenverteilungen in DruckBlasensHulen im bereich von 1 bis 100 bar. Ph.D. thesis, Miinchen, Germany. Kusters, W., 1976, BlasengriiBen-Hauligkeitsverteilungen und Spezifische Phasengrenzfllchen in BlasensiiulenReaktoren. Ph.D. thesis, Aachen, Germany. Linek, V. and Mayrhoferovl, J., 1970, The kinetics of oxidation of aqueous sodium sulfite solution. Chem. Engng Sci. 25, 78-800. Linek, V., Beneg, P. and Vacek, V., 1989, Dynamic pressure method for k,o measurement in large-scale bioreactors. Biorechnol. Bioengng 33, 14061412. Mochida, N., 1985, Direct coal liquefaction. Chemicof Plant Engineering Conference, Tokyo, Japan. Neubauer, G., 1977, Beitrag zur Auslegung von Lochboden fur die Fliissigkeitsbegasung in Blasenslulen unter Hochdruck. Ph.D. thesis, Miinichen, Germany. Novoselov. A. G., Tishin. V. B., Gulvaev. Y. N. and Anisimov, S. A., 1989, Physical properties of aqueous solutions of sodium sulfite. J. appl. Chem. USSR 62, 1069- 1070. Oyevaar, M., 1989, Gas-liquid contacting at elevated pressures. Ph.D. thesis, Twente, The Netherlands. Oyevaar, M. H., Bos, R. and Westerterp, K. R., 1991, Interfacial areas and gas hold-ups in gas-liquid contactors at elevated pressures from 0.1 to 8.0 MPa. Chem. Engng Sci. 46, 1217-1231. &turk, S. S., Schumpe, A. and Deckwer, W. D., 1987, Organic liquids in a bubble column: holdups and mass transfer coefficients, A.1.Ch.E. J. 33, 1473-1480. Reid. R. C.. Prausnitz. J. M. and Poline. B. E.. 1988. The prbpertie~ of gases and liquids in Chymical &ineering Series, 4th Edition. McGraw-Hill, New York. Reillv. 1. G.. Scott. D. S.. de Bruiiin. T.. Jain. A. and Diskorz. J,,-1986, Correlations for gas hold-up in turbulent coalesc: ing bubble columns. Can. .7. them. Engng 64, 705-717. Sahabi, U., 1976, EinRuD der Eigenschaften des Gases auf die BlusengrijBen-HLufigkeitsveGeilung in Cyclohexan. Final Paper, Aachen, Germany. Tarmy, B. L., Chang, M., Coulaloglou, C. A. and Ponzi, P. R., 1984, The three phase hydrodynamic characteristics of
Mass transfer and bubble size the EDS coal liquefaction reactors: their development and and use in reactor scale up. Inst. them. Engng Symp. Ser. 87, 303-3 17. Vafopulos, I., 1974, Der EinfluB des Partialdruckes und der Grcnxilachenspannung auf den Stoffaustausch in Bcgasten Reaktoren. Ph.D. thesis, Grax, Austria. Westerterp, K. R., van Swaaij, W. P. M. and Beerrackers, A. A. C. M., 1984, Chemical Reactor Design and Operation. Wiley, New York. Wilkinson, P. M., 1991, Physical aspects and scale-up of high pressure bubble columns. Ph.D. thesis, University of Groningen, The Netherlands.
1427
Wilkinson, P. M. and van Dierehdonck, L. L., 1990, Pressure and gas density effects on bubble break-up and gas holdup in bubble columns. Chem. Engng. Sci. 45, 23092315. Wilkinson, P. M., Doldersum, B., Cramers, P. and van Dierendonck, L. L., 1993, The kinetics of the uncatalysed sodium sulphite oxidation. Chem. Engng Sci. d&933-941. Zieminski, S. A. and Whittemore, R. C. 1971, Behavior of gas bubbles in aqueous electrolyte solutions. Chem. Engng Sci. 26, 5099520.
MASS
Chnnienl Eq,imei,~
TRANSFER
Department
Sciewe, Vol. 49, N.,. 9, m. 1417-1427, ,994 Copyripht Q 19!34Elsevia S&ma Ltd Printed in Great Britain. All rights rcstrval ooo9-2509f94 s6.03 + 0.m
AND BUBBLE SIZE IN A BUBBLE UNDER PRESSURE
COLUMN
PETER M. WILKINSON’ and HERMAN HARINGA of Chemical Engineering, University of Groningen, 9747 AG Groningen, The Netherlands and LAURENT L. VAN DIERENDONCK DSM Research, PO Box 18, 6160 MD G&en, The Netherlands
(First received
20 August
1991; accepted for publication
in revisedJorm 9 November 1993)
Abstract-The influence of pressure on the gas hold-up in a bubble column is determined for a sodium sulphite solution in combination with the volumetric mass transfer coefficient. Furthermore, for the same conditions the bubble size is also estimated from photos. The results of these experiments show that the interfacial area and the volumetric mass transfer coefficient both increase with pressure, while for design purposes the magnitude of the increase can be safely estimated from the increase in gas hold-up. Finally, the influence of pressure on the Sauter mean bubble size in a number of pure liquids (mono-ethylene glycol, n-heptane and deionized water) is also studied and correlated with a new empirical equation on the basis of photos in combination with literature results.
INTRODUCTION
The mass transfer characteristics (k,a and a) belong to the most important parameters for design and scaleup of bubble columns, and consequently it has been
the subject of much research. In the literature many articles with experimental mass transfer data can be found and a number of empirical equations have been proposed for the estimation of these parameters (Akita and Yoshida, 1974; Hikita et al., 1981; Hammer et al., 1984). A limitation of these articles is that they are virtually all based on atmospheric experimental data in spite of the fact that industrial bubble columns are commonly operated at pressures above atmospheric. Recently, numerous studies have been published (Deckwer et al., 1980; Tarmy et al., 1984; Mochida, 1985; Idogawa et al., 1986, 1987a, b, de Bruijn et al., 1988; Oyevaar, 1989; Clark, 1990; Wilkinson and van Dierendonock, 1990, Oyevaar et al., 1991 and Wilkinson, 1991) which show that gas holdup can increase noticeably if gas density is increased (either by increasing pressure or gas molecular weight). On the basis of these gas hold-up measurements it is also to be expected that the mass transfer characteristics are to be influenced by the value of the gas density. However, papers showing how the interfacial area and/or volumetric mass transfer are influenced by pressure or gas density are far less numerous [e.g. k,a measurement with varying gas density at atmospheric pressure (&tiirk et a[., 1987); k,a measurement at varying pressure (VaFopulos, 1974); ‘Present address: Royal/Shell-Laboratory Amsterdam, PO Box 3003, 1003 AA Amsterdam, The Netherlands.
interfacial area measurement by chemical methods (Oyevaar et a[., 1991)]. Furthermore, the conclusions that can be drawn from these papers with respect to the influence of pressure on bubble size varied from a decrease in bubble size with increasing pressure (Wilkinson and van Dierendonck, 1990) to an increase in bubble size (Oyevaar et al., 1991) with increasing pressure. The aim of this paper is therefore to experimentally determine the influence of pressure on the volumetric mass transfer coefficient (and bubble size) in a bubble column and to explain the apparent discrepancies in the literature regarding the influence of pressure on bubble size. For this purpose the volumetric mass transfer coefficient is determined chemically with a model reaction (the uncatalysed sodium sulphite-water system), while the influence of pressure on bubble size is determined photographically for the sodium sulphite-water system, n-heptane, deionized water and mono-ethylene glycol. DETERMINING
MASS TRANSFER
AT
PRESSURES
ABOVE
ATMOSPHERIC
In principle, the volumetric mass transfer coefficient in a bubble column can be determined in many different ways. The mass transfer rate is often determined by changing the feed gas from nitrogen to oxygen or vice PeTsa, while simultaneously measuring the oxygen concentration change in the liquid with a Clark-type oxygen electrode. For high mass transfer rates (as was expected for high pressure and high gas rates) this procedure, however, requires a very fast response of the oxygen electrode -and a knowledge of the gas
1417
1418
PETER M. WILKINSON er ~1.
residence time distribution during the experiment. Furthermore, at high pressure this procedure is technically relatively complicated. An alternative method that has been developed by Linek et al. (1989) is to make a sudden (small) change in the column pressure and then to determine the resulting change in oxygen concentration in the liquid with a Clark-type oxygen electrode. Although this procedure has the advantage that the mass transfer rate can be evaluated without a knowledge of the gas residence time distribution, it still requires the use of a fast response oxygen electrode. Fast response electrodes do exist for atmospheric conditions; however, for high pressures commercially available oxygen electrodes are either extremely expensive or do not have a sufficiently fast response time [preferably Q l/k,a s (Deckwer, 1985)] to oxygen concentration changes. Alternative procedures to determine the volumetric mass transfer coefficient are usually based on chemical systems, of which a number have been listed by Deckwer (1985) (in combination with guidelines for selecting the appropriate system). In the present study the uncatalysed oxidation of sodium sulphite (Wilkinson et al., 1993) has been chosen as a model reaction to determine the volumetric mass trausfer coefficient. Due to the low solubility of oxygen in water-sodium sulphite solutions, the gas phase conversion remains low, and as a result the oxygen concentration in the gas (and liquid) phase will remain almost constant throughout the bubble column, The main advantage of this is that neither the liquid nor the gas phase mixing have to be known for the evaluation of the volumetric mass transfer coefficient. MASS TRANSFER
EXPERIMENTS
From the literature [e.g. Reilly et al. (1986)] it is known that the influence of the column diameter on gas hold-up (and mass transfer) can be neglected, provided the size of the column is larger than 0.15 m. It is also known that the sparger has virtually no influence on the gas hold-up (and mass transfer), provided the sparger hole-diameters are not too small (as is usually the case for industrial bubble columns). In our study both these conditions were fulfilled: the oxidation rate of sodium sulphite was determined at a constant temperature (20 i O.lOC) in a metal bubble column, with an internal diameter of 0.158 m and the liquid level was 1.5 m. The sparger used was a ring with 19 holes of 10 mm, An additional reason for using such large sparger holes is that the influence of gas density (through its momentum) on the bubble Table
formation process will be minimal if the gas velocity through the sparger holes is not too large. Thus, the use of large sparger holes ensures that any measured influence of pressure (or gas density) is not the result of the gas density on the bubble formation process. At the start of each experiment the column was filled with a 0.8 mol/l sodium sulphite deionized water solution, while the initial pH values were adjusted between pH 6.5 and 8.5 with sulphuric acid (in order to vary the reaction rate). The applied gas was air at pressures between 0.1 and 0.4 MPa and the gas rate was measured with a calibrated gas turbine. The sulphite conversion rate was determined by analysing samples taken from the solution at regular time intervals. All experimental results showed a linear decrease of the sulphite concentration vs time. In addition, for each experiment the gas hold-up was also measured with an overflow technique [as in Wilkinson (1991)]. BUBBLE
CHEMICAL
ABSORPTION
THEORY
The equations necessary for the calculation of the volumetric mass transfer coefficients from the sulphite oxidation experiments can be determined by making
1. Physical properties of liquids used for bubble
n-Heptane Mono-ethylene glycol Water 0.8 M sodium sulphite in water+
SIZE ESTIMATION
In order to determine the bubble size in a bubble column as a function of pressure, a steel vessel was constructed with an internal diameter of 0.25 m equipped with three pairs of 0.15 m sight glasses for pressures up to 1.5 MPa. In this vessel a 0.15 m glass pipe was placed that functioned as the actual bubble column. At the start of an experiment the vessel was filled with liquid in the glass bubble column and in the space surrounding the glass pipe. Due to this arrangement and the absence of a curvature on the sight glass, virtually no optical deformation of the bubbles occurs on the photos. The bubble sizes on the photos were determined with the aid of a Zeiss TGA-10 particle size analyser as described by Kiisters (1976). For the determination of the Sauter mean bubble diameter at least four enlarged photos were used for each condition and between 300 and 500 bubbles. All the photos that were used for the evaluation of the bubble size were taken at the central sight glass 0.6 m above the sparger. The liquids used were n-heptane, mono-ethylene glycol, deionized water and a 0.8 mol/l sodium sulphite deionized water solution (the same as for the mass transfer experiments) at room temperature (Table 1). For most experiments nitrogen was used, while for deionized water a number of other gases were also used (Table 2).
684 1113 998 1086
‘Calculated from the equations of Novoselov
size evaluation
0.020 0.048 0.072 0.075 er al. (1989).
o.Qoc41
0.021 0.0010 0.0015
Mass transfet and bubble size
Table 2. Physical properties of the gases used in the experiments (at 2O”C, 0.1 MPa)
Gas Helium Nitrogen Argon Carbon dioxide Sulphur hexafluoride
105q,, (Pa s)
P# (k&m?
I .94
0.16 1.18 1.69 1.83 6.16
1.75 2.10 1.44 1.51
kla = $$
a number of assumptions for the mixing characteristics of the gas and liquid phase and by using the results of the theory for gas absorption followed by a slow chemical reaction in the liquid, combined with mass balances for the bubble column (that the usage of the theory for a slow chemical reaction is permissible will be demonstrated further on). First of all, from the stoichiometry of the sulphite oxidation it follows that the oxygen conversion rate (Qo,) is
40, = AUACo,.,.,,- co,,,,,,,) = - osr+,
d(c;;:) (1)
whereas the oxygen concentration change in the gas phase of the bubble column is described by
WJ,Co,,,,,) dz
= -
kdm(CO,.l.z
-
mCo,,,)-
(2)
Due to the fact that the gas phase oxygen conversion [calculated from eq. (l)] for all the present experiments in small ( -Z 5%), it can be assumed that the gas flow rate (U,) in eq. (2) remains constant, and, because the oxygen concentration in the gas phase (Co,,,) only changes marginally, the liquid oxygen concentration (Co,,,) will also be almost constant throughout the column. Furthermore, due to the reaction the oxygen concentration in the bulk of the liquid was usually close to zero, which also strengthens the conclusion that the liquid mixing behaviour is of little or no importance. Consequently, in order to simplify the solution of eq. (2) it can be safely assumed that the liquid phase is well mixed, while its value can be calculated (provided the reaction is not chemically enhanced) by krs,
V,&,,,
=
-
O.SV..c,Wso;-1 dt
1419
the average column midpoint pressure) was used for the calculations. With these assumptions eq. (2) is integrated, which leads to
(3)
0.5
“‘“,s,:-)
(kr). i
In order to solve eq. (2) it is assumed that the gas is in in plug Sow. However, again due to the low gas phase oxygen conversion this assumption has little influence on the calculated volumetric mass transfer coefficient. Finally, in order to account for the influence of the change in hydrostatic pressure on the oxygen concentration as well as on the gas flow rate, a constant pressure throughout the column (based on
mco,.,
(5) >’ Co t...-4 - mco2., With the aid of this equation [in combination with eqs. (1) and (4), for the calculation of the oxygen concentrations CO~.~.~~, and Co, ,], the volumetric mass transfer coefficient is calculated. So far, three (implicit) assumptions have been made as regards the oxygen absorption: first of all, it is assumed that the reaction proceeds in the slow reaction regime (the absorption is not chemically enhanced), which implies that the Hatta number (Westerterp et al., 1984) is less than 0.3:
Whether or not this first criterion (Ha < 0.3) holds can be estimated from the experiments by varying the reaction rate constant. If the value of the reaction rate constant has no influence on the calculated volumetric mass transfer coefficient, then this implies that the reaction proceeds in the slow regime (and thus Ha -c 0.3). In our experiments the pseudo-first-order reaction rate constant of the (uncatalysed) sulphite oxidation was varied from k, = 0.5 s ’ to k, = 20 s ’ by adjusting the pH of the sulphite solution with different amounts pseudo-first-order
of sulphuric acid [the values of the reaction rate constant (k,) were
taken from experiments by Wilkinson et al. (1993)]. Secondly, it was assumed that the reaction film volume is small as compared to the bulk volume:
On the basis of (literature) experimental results it is known that k, x=-1 x lo-’ m/s, d, > 2 x lo- 3 m, while Do, = 1.6 x 10e9 m’/s. Using these values for the evaluation of eq. (7) shows that the Hinterland ratio (AI) will be larger than 20 provided the gas hold-up is below 50%. Consequently, the condition described by eq. (7) is fulfilled for the present experiments (as is normally so for bubble columns). Finally, the third condition that should be checked is whether the resistance to gas phase mass transfer is negligible: mK,/k,
and thus
co,, = -
co2.S.i”-
In
S- 1.
(8)
That the gas phase resistance is completely negligible for the sulphite oxidation can be argued on the basis of the k,n and kla measurements of Cho and Wakao (1988) in a bubble column. By combining and reinterpreting their results it is determined that ka AL=2
k
ha
k,
The ratio of the diffusion constants in this equation is for the air [D, = 1.84 x lo- ’ m2/s (Reid et al., 1988)], sulphite [D, = 1.6 x 1O-9 m2/s (Linek and
1420
PETER M. WILKINSON
Mayrhoferova, 1970)] system equal to 1.2 x lo4 at atmospheric pressure. At the highest pressure used in our experiments (P = 0.4 MPa) this ratio is, however, only 3 x lo3 because the gas diffusion constant is inversely proportional to the value of the pressure. This (lowest) estimate of the diffusion coefficient ratio together with the result that the constant c in eq, (9) is never smaller than 0.2 [based on the experimental values of Cho and Wakao (1988)] leads to the conclusion that the gas phase mass transfer coefficient is at least 10 times larger than the liquid phase mass transfer coefficient for the range of conditions in the present experiments. Furthermore, from eq. (8) it can be seen that the resistance to gas phase mass transfer is even further decreased for gases with a low solubility, as is the case for oxygen in a 0.8 mol/l sodium sulphite solution (m = 54).
EXPERIMENTAL
Mass
transfer
RESULTS
and gas hold-up
k,s (81
.Fig. 1. k,a in a 0.8 mol/l sodium sulphite solution vs the superticialgas velocity at 0.1, 0.2, 0.3 and 0.4 MPa.
AND DISCUSSION
in sulphite
solutions
First of all, it was determined that an increase in reaction rate from k, = 0.5 s-’ to k, = 20 s-’ never increased the volumetric mass transfer coefficient calculated from eq. (5) by more than 30%. Obviously, this result indicates that the reaction proceeds in the slow regime (Ha -Z 0.3) for low k, values, whereas the reaction becomes slightly enhanced for the higher k, values. Consequently, in order to prevent chemical enhancement most experiments were done at k, values of 2 and lower. In Fig. 1 the calculated volumetric mass transfer coefficients from these experiments are shown vs the superficial gas velocity at four different pressures, while the gas hold-up for the same conditions is shown in Fig. 2. From these figures it shows that both the gas holdup and the volumetric mass transfer coefficient increase significantly with increasing pressure, especially at high gas velocities. An important consequence of this is that relatively high mass transfer rates are possible at high pressure, despite the use of a sparger with exceptionally large holes (10mm). At low superficial gas velocities (U, < 0.03 m/s) the influence of pressure, however, seems to be relatively small. Presumably, this is the reason why virtually no influence of pressure was observed (Fig. 3) in the only previous work that has dealt with the influence of pressure on the volumetric mass transfer coefficient in bubble columns [Vafopulos (1974) at low superficial gas velocities!]. That the increase of the volumetric mass transfer coefficient with pressure in Fig. 1 resembles the trend by which the gas hold-up increases (Fig. 2) is obviously caused by the fact that the interfacial area is proportional to the gas hold-up through a = 6&,/d,.
et al.
(10)
However, apart from the increase in mass transfer due to the increase in gas hold-up at higher pressures, an additional influence was expected due to the fact that the bubble size (and thus interfacial area) also depends on pressure (Idogawa et al., 1986, 1987a, b;
_..
Fig. 2. Gas hold-up vs superficial gas velocity for the same conditions as in Fig. I.
(m/s1
U,
Fig. 3. k,n in a 0.8 mol/l sodium sulphite solution vs the superficial gas velocity at 0.1,0.2, 0.4,0.6 and 0.8 MPa ob-
tained in a bubble column with a perforated plate with 60 holes of 1 mm [data of Vafopulos (1974); H = 1.46 m, D = 0.4 m-J.
Wilkinson and van Dierendonck, 1990). By dividing the volumetric mass transfer coefficient by the gas hold-up value [eq. (11) J it is possible in combination with eq. (10) to determine to what extent the bubble size (in combination with the liquid mass transfer coefficient) changes with pressure: &,a -=--F.
%
6k, 4
(11)
The value of this ratio is shown in Fig. 4. From this figure it can be seen that the value of k,a/&, increases with an increase in pressure as well as for an increase in superficial gas velocity. The explanation for this increase at higher pressure is obviously a result of the
Mass transfer and bubble size
Fig. 4. k,a/.s, ( = 6k,/d.) vs the superficial gas velocity for the same conditionsas in Fig. 1.
fact that the bubble size (d,) decreases with increasing pressure while the mass transfer coefficient is expected to remain uninfluenced by pressure, because the value of the pressure has a negligible influence on the liquid phase physical properties (IDI, Q, etc.). However, the increase of the value of k,/d, [eq. (1 l)] with increasing pressure cannot be used to calculate the exact magnitude by which the pressure influences the bubble size because the mass transfer coefficient also partly depends on the bubble size. That Fig. 4 shows that the value of k,a/&, also increases with increasing gas velocity is presumably related to the fact that at higher gas velocity the power input to the liquid is greater, which leads to more turbulence. This higher degree of turbulence will promote bubble break-up, while a higher degree of turbulence is also known to lead to higher k, values. Obviously, both these effects contribute to the increased eq. (ll)] at higher gas value of k,a/c, [ = 6k,/d,, velocity. In Fig. 5 the experimental volumetric mass transfer coefficients are shown vs the experimental gas holdup, together with the volumetric mass transfer coefficient predicted from a recent empirical equation by Akita (1989) for water-electrolyte solutions:
1421
Fig. 5. kia vs the gas hold-up for the same conditions as in Fig. 1 in combination with the predicted k,o value from eq. (12).
10
U,
(m/a)
Fig. 6. k,a in xylene vs the superficial gas velocity for hydro-
gen, helium,nitrogen.and air.
k,a = Fig. 7. k,a in xylene vs the gas hold-up for the same conditions as in Fig. 6.
(12) The value of kM in this equation is a function of the type of electrolyte and the electrolyte concentration. For a 0.8 mol/l sodium sulphite solution, a value of 2.4 is calculated (based on data for a 0.8 mol/l sodium sulphate solution). From Fig. 5 it is clear that this empirical equation provides a rather low estimate for all the experimental results. Other empirical equations [e.g. Hikita et al. (1981)], however, usually predict the volumetric mass transfer coefficient as a function of the superficial gas velocity and not as a function of gas hold-up or gas density. Consequently, these other equations do not account for any influence of pressure and are thus even less successful for predicting the mass transfer coefficient at higher pressure. Furthermore, the fact that the experimental volumetric mass
transfer eoetlioients lie virtually on one single line for different pressures is also in agreement with the results of &tiirk et al. (1987) in xylene. &tiirk et al. determined the volumetric mass transfer coefficient as a function of gas density by using different gases at atmospheric pressure (Figs 6 and 7). On the basis of Figs 5 and 7 a procedure is developed to estimate the magnitude by which the volumetric mass transfer coefficient will increase with increasing gas density:
[e]=[E]“,
withn=l.&1.2. (13)
Obviously, it is not possible to apply this equation without a knowledge of the gas hold-up as a function
1422
PETER
M.
WILKINSON
of gas density; the same restriction, however, also holds for eq. (12) of Akita. Furthermore, due to the absence of experimental data on the volumetric mass transfer coefficient at still higher pressure and in different liquids, additional research is certainly desirable. Gas hold-up sures
in sodium
sulphite
solutions
at higher
er al.
0.a $ 0.a
0’
key
P(WmI
t
0.1
‘
0.5
D
1.0
I
pres-
Sodium sulphite solutions with the same composition as for the mass transfer experiments were used in a few experiments to determine the gas hold-up and to estimate the bubble size at still higher pressures. The results of these experiments show (Fig. 8) that the gas hold-up at these high pressures increased more than proportionally with increasing gas veiocity towards gas hold-up values that are much higher than in pure water (Fig. 9). Furthermore, it was seen that numerous small bubbles (approximately 0.5 mm in diameter) accumulate in this aqueous sodium sulphite for low as well as for high pressures. The main visual difference, however, is that at low pressure, in addition to these small bubbles, some large bubbles also occur (typically between 3 and 5 cm, Fig. to), whereas these are not seen at the highest pressure. For the highest pressure, however, a foam-like structure (Fig. 11) develops in the bubble columns when the gas hold-up increases beyond 30-40%, whereas this does not occur at atmospheric pressure. From previous literature results (obtained at atmospheric pressure) it is known that
Fig. 8. The gas hold-up in a 0.8 mol/l sodium sulphite solution vs the superficial gas velocity at O.l,O.S, 1.0, 1.5 and 2.0 MPa.
Fig. 9. The gas hold-up vs the superficialgas velocity at 0.1, 0.5, 1.0, 1.5 and 2.0 MPa (for the same conditions as in Fig. 8, but with deionized water instead of a sodium sulphite solution).
Fig. 10. Photo of bubbles obtained in the bubble column at a gas hold-up of 30% (aqueous 0.8 mot/l sodium sulphite solution, U, = 0.07 m/s, P = 0.1 MPa).
Mass transfer and bubble size
Fig.
1423
11. Photo of the foam structure obtained in the bubble column at a gas hold-up of 40% (aqueous 0.8 mol/l sodium sulphite solution, U, = 0.06 m/s, P = 1.5 MPa).
the addition of sodium sulphite or other electrolytes to water leads to a higher gas hold-up and to smaller bubbles due to the fact that the coalescence rate is reduced in aqueous electrolyte solutions (Zieminski and Whittemore, 1971). The present result indicates that the injluence of electrolyte and the influence ofgas density on gas hold-up are synergistic. The reason for this observation is presumably that both contributions are the result of different mechanisms [the electrolyte hiriders coalescence, whereas a higher gas density promotes bubble break-up (Wilkinson and van Dierendonck, 1990)]. The main practical consequence of these observations is that, although in principle a high pressure will lead to higher (advantageous) volumetric mass transfer rates, in some cases the extremely high gas hold-up values can become a disadvantage: in the case of slow reactions (for which bubble columns are often used) the decrease of the liquid phase reaction volume at higher pressure (due to the higher gas hold-up at high pressure) can lead to a lower overall reaction rate in the bubble column.
Bubble size in (sodium sulphite-) mono-ethylene glycol
water, n-heptane und
During the past few decades techniques have been used and bubble sizes for the estimation Most of these techniques have
different experimental developed to measure of the interfacial area. not only been used at
atmospheric pressure but have (in recent years) also been applied to high-pressure conditions (Table 3). However, in spite of this variety of measuring techniques an accurate estimation of the interfacial area for a large range of conditions remains complicated because each measuring technique has its specific advantages and disadvantages (Table 4). From these different techniques, at present the photographic technique is used most frequently. Presumably, this is mainly due to the fact that photographic bubble size evaluation can be done most easily for a wide range of conditions. Consequently, it is also not surprising that virtually all empirical equations in the literature [e.g. Akita and Yoshida (1974), van Dierendonck (1970) and Kiisters (1976)] for the evaluation of the Sauter mean bubble size or the interfacial area are based on photographically determined bubble sizes. Furthermore, all empirical equations in the literature for the prediction of the Sauter mean bubble diameter are based on atmospheric data and therefore do not incorporate the decrease of bubble size with increasing gas density. In order to quantify the influence of gas density on bubble size the Sauter mean bubble diameter is estimated from photos in mono-ethylene glycol, water and n-heptane at pressures between 0.1 and 1.5 MPa (with different gases, Table 2) and for superficial gas velocities between 0.02 and 0.1 m/s. The results of these experiments, combined with similar atmospheric experiments of Sahabi (1976) in cyc-
1424
PETER M. WLK~NSON
eta/.
Table 3. Studies on the influence of gas density on bubble size in bubble columns Liquid
Gas
Pressure (MPa)
Sparger (m)
Method
Reference
Influence of gas density
NazSO,-water
Air
0.1-10
Ejector
Suction probe
Jekat (1975)
Yes
Cyclohexane
He, N2, Ar, co2
0.1
Sparger cross 24 x 0.5 mm
Photographic
Sahabi (1976)
Yes
Water
Air
0.1-1.0
Perforated 1OOxlmm
Suction probe
Neubauer (1977)
YeS
Water-KC1
Air
0.1-15
Single nozzle d= 1,3or5
Electrical reslstivity probe and photographic
Idogawa (1986)
et al.
Yes
Electrical resistivity probe and photographic
Idogawa (1987a)
et al.
Yf%
plate
Perforated plate 19x1mm Porous plate d = 0.002, d = 0.1 Water-KCI, ethanol, acetone, methanol
Hz, He, air
0.1-5
Perforated 19xImm
Water, methanol, ethanol
HI, He, air
0.1-S
Single orifice d= 1,3or 5
Electrical resistivity probe and photographic
Idogawa (1987b)
et al.
Yes
DEA-water
NtqOz
Perforated plate 21 x0.4 mm Sparger cross 16 x 0.5 mm Porous plate
Chemical
Oyevaar (1991)
et al.
Yes
0.15-g
d =
Table 4. Experimental Experimental
technique
plate
0.03.0.1
techniques
for estimating
the bubble size in bubble columns
Advantage
Disadvantage
Chemical absorption experiment with model reaction
It leads to an integral value of the interfacial area
The use of chemical reaction systems usually influences the hydrodynamics, and the number of mode1 reactions reported in the literature is limited
Suction probe; measurement of bubble volumes sucked from the dispersion
The bubble size can be measured throughout the bubble column, and it is a relatively fast technique
Bubbles larger than the capillary through which the bubbles are sucked are not measured
Electrical resistivity
In addition to local bubble sizes also the local gas hold-up can often be measured simultaneously
Additives are usually required to increase the liquid conductivity, and d, cannot be calculated without making considerable assumptions
Photos can be used bubble size distribution conditions
Only bubbles near the column wall are seen; bubbles more to the centre of the column may be larger but cannot be seen. Furthermore, large, irregular shaped bubbles are difficult to measure
Photographical
probe
technique
to determine the for a wide range of
lohexane with different gases, were correlated (Fig. 12) by regression analysis to a new dimensionless equa-
tion:
(14)
Equation
(14) can be rewritten as
d, = 3g-
0.44~0.34,#.22p;0.4Sp~0.il
u,O.OZ_
(15)
That this correlation shows that the bubble size is proportional to the gas density to the power - 0.11 implies that a tenfold increase in gas density reduces the Sauter mean bubble size by almost 30%. For the
1425
Mass transfer and bubble size 7
.
1
Fig. 12. Predicted [eq. (15)] Sauter mean bubble diameter vs the experimentally determined Sauter mean bubble diameter in four pure liquids.
0.1
-*
Fig. 13. Estimated bubble sizes in a 0.8 mol/l aqueous sodium sulphite solution from photos, in combination with the bubble size predicted from eq. (15) (lines).
same range of conditions, Wilkinson (1991) determined that a tenfold increase of the gas density USUally leads to a (much) larger increase of the gas holdup, especially at high gas velocities. Thus, again, as for the experiments in sodium sulphite, it is to be expected that the interfacial area (6~,/d.) in a bubble column will increase more due to the increase of the gas hold-up than due to the decrease in bubble size with increasing gas density. Finally, it should also be kept in mind that in non-coalescing liquids such as water-sulphite solutions many very small bubbles usually accumulate in the liquid, which leads to a smaller Sauter mean bubble size than is predicted by eq. (15) (Fig. 13). However, it is to he expected that still much more research is needed before these additional effects can be quantified. COMPARISON
WITH LITERATURE
DATA
As has already been shown in Table 3, other authors have previously performed experiments to estimate the bubble size as a function of pressure; it appears, however, that the results obtained in these different references depend partly on the experimental technique by which the results were obtained. For instance, in all cases where the bubble size was determined photographically, it was determined that at higher pressure the average bubble size decreases mainly due to a reduction of the number of large bubbles (which is in accordance with the present re-
sults). The references for which the bubble size is determined with the aid of a suction probe, however, in genera1 observe only a very small influence of both gas density and liquid properties on bubble size. Presumably, this is caused by the fact that the main influence of gas density is to reduce the number of large bubbles, whereas these suction probes are not capable of measuring these large bubbles. Finally, the results of the chemically determined bubble size [C02, aqueous diethanolamine (DEA) (Oyevaar et nl., 1991)] are opposite to the present results. Oyevaar et al. (1991) calculated that the average bubble diameter increased for increasing pressure (while the gas hold-up increased too!). Oyevaar attributed this unlikely increase in bubble size to the fact that the interfacial area is underestimated because many small bubbles accumulate in the bubble column without contributing to mass transfer, and to the presence of a foam layer at the top of the dispersion, which is also less effective for mass transfer. Both these explanations are probable because the overall gas phase conversion for these experiments was very high [up to 99% (Oyevaar, 1989)]. In addition to these reasons, Oyevaar’s results may also be partly explained by the fact that the resistance to gas phase mass transfer [eq. (9)] can become significant at higher pressure (especially for soluble gases such as COz, and because the gas phase diffusion coefficient is inversely proportional to pressure). However, the main implication of this example is that although the interfacial area is expected to increase at higher pressure the advantage of this result may be partly reduced by the increase of the gas phase mass transfer resistance with increasing pressure (especially for soluble gases and at high reaction rates).
CONCLUDING
REMARKS
-An increase in gas density leads to smaller bubbles on average and a higher gas hold-up. -Consequently, the volumetric mass transfer coefficient also increases (substantially) for higher pressures (gas densities). -The uncatalysed sodium sulphite system can be applied as a model reaction for determining the volumetric mass transfer coefficient (of non-coalescing aqueous electrolyte solutions). -The addition of electrolyte increases the gas hold-up, due to its influence on coalescence, at low as well as at high pressure. -A new empirical equation is developed (based on a photographic bubble size evaluation for water, mono-ethylene glycol, cyclohexane and n-heptane) for the estimation of the influence of gas density and liquid properties on bubble size in bubble columns. -Finally, it is also argued that the improved performance of high pressure bubble columns (as compared to atmospheric bubble columns) can, in some cases, be partly limited due to higher gas phase mass transfer resistance at higher pressure or due to a decrease of the liquid reaction phase volume.
PETER M. WILKINSON et nl.
1426 Acknowledgement-The technical and financial Netherlands).
authors gratefully acknowledge the support of the DSM company (The
NOTATION a A Al
interfacial
c
d ds D IID 9 H HU
less gas-side mass transfer coefficient, m/s liquid-side mass transfer coefficient, m/s volumetric mass transfer coefficient, s-l electrolyte specific constant in eq. (12), di-
k, k, kla kM
mensionless first-order reaction rate constant, s - ’ distribution coefficient of oxygen ( = C,/Cr), mol/mol pressure, Pa superficial gas velocity at process conditions, m/s volume of bubble column, m3
k, m P u, K Z
%
m2/m3
cross-sectional area of bubble column, mz Hinterland ratio, dimensionless constant in eq. (9) dimensionless concentration at process conditions, mol/l diameter of sparger holes (Table 3), mm Sauter mean bubble diameter, m diameter of bubble column, m molecular diffusion coefficient, m2/s gravitational acceleration, m/s’ height of gas-liquid dispersion in bubble column, m Hatta number given by eq. (6), dimension-
C
Greek
area,
axial umn,
coordinate m
for
height
in bubble
col-
letters gas hold-up, dimensionless
;02
liquid hold-up, dimensionless liquid viscosity, Pas gas density, kg/m” liquid density, kg/m3 surface tension, N/m Oxygen conversion rate, mol/s
Subscripts b
and superscripts bulk of liquid
9 i
gas
a1 VI PS PI
in
interface conditions at z = 0
1
liquid
02 out
conditions at z = H
oxygen
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