Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
357
REVIEW
Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels Klaas Van’t Riet
Ind. Eng. Chem. Proc. Des. Dev. 1979.18:357-364. Downloaded from pubs.acs.org by UNIV OF BRITISH COLUMBIA on 01/04/19. For personal use only.
Gist-Brocades N.V., Research and Development, 2600 MA Delft, The Netherlands
A search has been made for relations between published results about gas-liquid mass transfer in stirred vessels filled with water. The dynamic gassing-out method, the sulfite method, the separate determinations of A and kL as well as a number of other experimental methods were judged on their own merits. Most methods appear to be of limited applicability, and the sulfite method is even more restricted in this respect. Correlation of the various reports on mass transfer is possible with power per unit volume and gas superficial velocity. This requires a rigid differentiation between water without and water with ions in solution. Among the equipment variables it is in particular the position of the sparger which appears to be of influence.
Introduction Stirred vessels
The purpose of this article is to review the relations between kGA and the chief parameters from the literature. In this connection, the various experimental methods are examined for reliability, the results for khA are presented, and finally the influence of a number of vessel geometry parameters is dealt with. Discussions are restricted to aqueous systems, and the aim is to comment on as many features of these systems as possible rather than summarize all relevant publications.
frequently employed to achieve a large contact area between a gas and a liquid. If, for example, oxygen is the reactant to be transferred in these agitated gas-liquid dispersions, the oxygen transfer rate {OTR) is determined by the specific contact area A, the of mass transfer coefficient kL {l/kL provides a measure resistance), and the driving force CG/H CL, according to are
-
OTR
=
khA
Measuring Methods Dynamic Gassing-Out Method.
(1)
The underlying principle is that after a given liquid has been deoxygenated by passing, for example, nitrogen through it, the dissolved oxygen concentration profile is monitored following the start of the air inflow. As a rule, a polarographic electrode (the Clark cell) is used. It follows from the mass balance equation for oxygen between tx and t2 that
where CG = the 02 concentration in the gas phase, CL = = the 02 concentration in the liquid phase, and the constant. Henry The resistance in the gas phase, /eG_1, has been neglected, which is nearly always permitted (Calderbank, 1959; Schaftlein and Russell, 1968; Joshi and Sharma, 1976). Equation 1 is valid for the local CG and CL values. Normally CG and CL are assumed unvariable throughout the vessel. This means that both the gas phase and the liquid phase need to be well mixed. The last assumption is unnecessary if kLA is constant throughout the vessel. This is reasonably acceptable for low viscous systems, in contrast to highly viscous systems (Steel and Maxon, 1966). Notably the assumption of a well mixed gas phase can be dangerous in vessels with a tank height Ht vs. diameter T ratio HJT » 1. For these vessels plug flow for the gas phase is a more accurate model. Different models are given by Schaftlein and Russell (1968). At first sight, there is not much consistency in the literature about mass transfer. One can assign various reasons for this. Thus, there is a large variety of methods to determine khA, some of which occasionally yield incorrect values. In addition, both kh and A can be affected in several ways. Among the most important variables are power consumption, gas superficial velocity, and liquid phase properties such as ionic strength, surface tension, and viscosity. Inasmuch as these variables are not always selected in a consistent manner or may be latently present, different values can be found for fcLA under seemingly identical conditions. 0019-7882/79/1118-0357$01.00/0
Cn/H-Cdh) Cg/H
-
CL(t2)
kGA as 1951, Wise indicated the underlying principles of this method. This method seems to be an ideal one but one should not overlook a few restrictions on its applicability. Thus, problems occur where as a result of rapid changes in dissolved oxygen concentration with time, a response lag arises and the probe output is not directly related to the instantaneous value of that concentration. The response lag itself is mainly due to diffusion through the membrane. In principle, the probe response time, rp (the time needed to record 63% of a stepwise change), would have to be much smaller than the mass transfer response time of system: 1 /khA. In practice, this is seldom the case, and therefore many models have been designed to calculate kLA from the probe response all the same. These range from one for first order response (Van de Sande, 1974) to
As early
©
1979 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
complicated models for diffusion (Heineken, 1970, 1971; Linek, 1972, and Linek et al., 1973). It is pertinent to ask whether one really has to perform all these extensive procedures. Van’t Riet (1975) has demonstrated that in Van de Sande’s model the ultimate error in khA
(s-1)
(8)
for pure water; volume measured up to 2600 L; 500 < P/V < 10000 (W/m3). The correlation is shown in Figures 1-3 as broken lines and is accurate within approximately 20-40%. Measurements in Water with Ions. The addition of ions to water is known to reduce average bubble size markedly. As demonstrated by Lessard and Zieminski (1971) and Marucci and Nicodemo (1967) in model experiments and by Koetsier and Thoenes (1972) in a stirred vessel, it is especially the frequency of bubble coalescence that decreases rapidly as the ion concentration increases. Reith and Beek (1970) have examined gas phase mixing, which also appears to be complete for ionic solutions at a sufficiently high stirrer speed, indicating some coalescing mechanism. This, however, is in particular due to the impeller coalescence with the cavity behind the stirrer blade, which, as shown by Van’t Riet et al. (1976), is also very intensive in ionic solutions. The increase in A as a result of the decrease in bubble diameter is further enhanced by the tendency of the holdup itself to become larger. Under differing conditions, Machón et al. (1977) have measured an increase by a factor
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
361
a comparable geometry. The results of Smith et al. (1977) are only shown for the P/V range in which the gas holdup cannot be of influence.
in
In most
sulfite method utilizes 10-100 g of a high ion concentration. Therefore, the results obtained by this method are included in this section. It is a safe generalization to say that pertinent reports are scarce. Most measurements for the determination of the kLA for physically controlled mass transfer must be excluded because reaction kinetics have been very inadequately checked, if at all. Eventually, the results of Reith and Beek (1968) prove the most reliable. Converted on the basis of kh = 4 X 10“4, they are shown in Figure 4. It should be noted that the measurements made by Lee yield values that are larger than those produced by the dynamic gassing-out method. This discrepancy may quite well have been caused by the experimental method. They themselves report to have measured in a region where the interfacial area was mainly larger than the average one. If this appears to be true, the measuring results of the various authors agree rather well. The superficial gas velocity has little influence in this respect. Westerterp et al. (1963) and also Reith and Beek (1968) claim that at us >0.5 the superficial gas velocity exerts only a slight influence. Zlokarnik (1970) has found a slightly better correlation with vs0·2 than with us°. Robinson and Wilke (1974) have found a us°·36 dependence at vs < 0.005. Also the results of Lee and Meyrick (1970) indicate a slight os dependence. It may be expected that there exists a very limited influence which, on simple linear regression of a large number of measurements, disappears as a result of the dependence of P/ V7. No author has applied partial regression techniques. When the us°·2 is taken into account, one obtains from Figure 4 ( P\0.7 cases, the
sulfite/L, which implies
Figure 4. Literature data and correlation equation in ionic solutions.
of 2. Lee and Meyrick (1970) have demonstrated by means of the light transmission method that at higher ion concentrations A may be increased up to 10 times. Yoshida and Miura (1963) have reported measurements showing a much smaller variation, but they used a stirrer tip velocity of 0.4-1.7 m/s, which is by no means sufficient to
ensure proper dispersion (according to a rough-and-ready rule, that stirrer tip velocity has to be > 2-2.5 m/s). The value of kh is likewise affected by the addition of ions —both direct by the presence of ions on the bubble surface and indirect by changes in the bubble diameter. The direct influence is probably small. Lessard and Zieminski (1971) and Raymond and Zieminski (1976) report an increase and also a decrease by ca. 10-20% in the presence of ions and a greater increase in aluminum salt concentrations. Various authors (Calderbank, 1959; Calderbank and Moo-Young, 1961; Linek et al., 1970; Li et al., 1965; Lessard and Zieminski, 1971; Yoshida and Miura, 1963; Topiwala and Hamer, 1974) have discussed the influence of the bubble diameter on kL. Most of them make mention of a decrease in kL, due to changes in hydrodynamics as the bubble diameter becomes smaller. Yet there are a few workers who claim the opposite. At any rate, kL 1-4 X lCT4, which implies that it will not become lower by a factor in excess of 1-4. Bearing in mind the influence of ions on kL and A, one may expect the product of kL and A to increase 2-10 times, which, indeed, has been found by, in particular, Zlokarnik (1975). The results mentioned in the literature (with the exception of those obtained by the sulfite method) have been measured by Topiwala and Hamer (1973), Robinson and Wilke (1973, 1974), and Smith et al. (1977) using the dynamic gassing-out method, while Lee and Meyrick (1970) have applied the light transmission technique to establish A values. The results in question are depicted in Figure 4. The conversion of A values obtained by Lee, into kLA is based on kL 4 X 4, which, considering the literature, is an arbitrary but also the best possible estimate. For that matter, Reith and Beek (1968) have determined this value =
=
/eLA
=
2.0X10-3^-j
vs°·2
(9)
where 500 < P/V < 10,000 W/m3; 2 < V < 4400 L; strong ionic solutions; accurate for 20-40%. On comparison with eq 8 for pure water, it will be found that a and ß differ markedly, as can also be seen in Figure 5, where ionic and pure water results are given. Conclusions for kLA. On the condition that an accuracy of, say, 20-40% is regarded as acceptable, it may be said that the results presented in the literature show much agreement. A distinction between water with and water without ions is, however, essential. By raising the ion concentration in solution, kLA is increased considerably. Once a limit of, for example, ca. 10 g of NaCl/L has been reached, the increase is much smaller. The distinction depends on P/V and ¿;s. It increases at higher P/ V values; hence, the fcLA’s for ionic solutions are more dependent on P¡ V than those for pure water. The formulas presented predict a kLA with an accuracy of 20-40%. For a given determination to be more accurate, the kLA in vessel and fluid concerned should be measured as exactly as possible. The question is whether this can be achieved with the limitations of the experimental methods and it might be better to be content with this
margin. Vessel Geometry Parameters Influence of Stirrer Type and Number. In the discussion of kL values in pure water and ionic solutions, no mention was made of the type of stirrer. It is, however, immaterial what sort of stirrer is employed because nearly all authors agree that this does not affect any correlation of kLA with P/V. A large variety of stirrers such as
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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
bubbles enter the vessel by way of the cavity. Bruijn et al. (1974) have demonstrated that this diminishes dispersion and leads to a relatively higher value of power consumption. It may be expected that, as a consequence, mass transfer conditions become less favorable. Indeed, data of Oldshue and Conelly (1977) show that spargers
larger in diameter than stirrers are less suitable. Karwat (1959) describes a situation in which the sparger is placed on the bottom. Bubbles from an open pipe then can miss the stirrer and cannot be dispersed. This causes a difference in kLA between an open pipe and a sintered sparger. At higher power values, the difference becomes smaller under the influence of an increasing circulation capacity. Results of Reith and Beek (1968), indeed, point that way, and Karwat has observed virtually no difference at ca. 5000 W/m3. There are more authors who have found differences such as those outlined above. The reported stirrer tip velocities are, however, much lower and, therefore the results of, for example, Bartholomew et al. (1950), Miller (1974), and Paca and Gregr (1976) are not representative of stirred vessels.
Influence of Fluid Height. No direct correlations with P/ V have so far been reported. Although Westerterp et al. (1963) have not worked with P/V, the finding that at
given stirrer speed (and, in this connection, a practically constant P) khA + T/H; i.e., + l/V confirms the P/V relation. Mehta and Sharma (1971) have observed a linearly decreasing relation with H/T. Within the limits set, this can, however, be described with the same degree of accuracy as linearly increasing with T/H. The influence of the fluid height can be described in terms of P/ V, yet only within a defined region, as it assumes a well mixed gas phase and invariable kLA over the content of the vessel. At extremely high H/T ratios and one stirrer near the bottom the contents of a vessel can be more properly described as a well-stirred area in the lower part along with a bubble column in the upper part. Eventually, the mass transfer in the bubble column will be hardly dependent on P/V dissipated in the well-stirred a
Figure 5. Correlation equations at several superficial gas velocities for pure water and ionic solutions.
turbines, paddles, propellers, lochscheiben, rods, and self-sucking agitators, has been used (Judat, 1976; Topiwala and Hamer, 1973; Valentin and Preen, 1962; Karwat, 1959; Van’t Riet, 1975; Zlokarnik, 1975; Smith et al., 1977). Several authors have not correlated khA with P/V but with various N,D combinations. On evaluation of their results, it becomes clear that P/V correlation is not affected by the choice of stirrer (Westerterp et al., 1963; Mehta and Sharma, 1971; Friedman and Lightfoot, 1957). Where it is unimportant which type of stirrer is used and only the power dissipated in the fluid is essential, it may be expected that the number of stirrers is also immaterial, as, indeed, is confirmed in the articles by Rushton et al. (1956), Moritz et al. (1974), and Oldshue (1966). It must be added here that on some occasions a fluctuating difference (up to 40%) in the amount of mass transfer occurs but this may be related to experimental accuracy. For calculation of kLA for vessels with many stirrers at large Ht/T ratios the introductory reservations concerning gas phase plug flow must be taken into account. Exceptions to the above have in particular been reported by Steel (1962) and Westerterp et al. (1963), who found a difference by a factor of 10 at variations oiD/T (T = tank diameter) of 0.20-0.60. This does not seem plausible in the light of the findings outlined above. The role of flooding, surface air entrainment, and differences in sulfite kinetics (see Reith, 1973) may well prove responsible. Influence of Type of Sparger. Frequently, a sparger is used under the stirrer. Examples are a ring sparger and an open pipe. Van’t Riet (1975) and Bruijn et al. (1974) have demonstrated that bubbles from the sparger come under the stirrer and are invariably dispersed via the cavity. The choice of sparger then has little effect on the mass transfer. Data obtained by Smith et al. (1977) and Oldshue and Conelly (1977) point that way. As the diameter of the sparger relative to that of the stirrer becomes greater, the mechanism of dispersion undergoes more changes; thus, in the case of ring spargers having a diameter larger than that of the stirrer, fewer
area.
Influence of Stirrer Position. As stated above, neither the fluid height nor the type and number of stirrers have any influence on feLA vs. P/ V. It may thus be said that the stirrer position is also of no importance. With regard to the stirrer position, two complications may occur. (1) If the distance between stirrer and bottom is too small, i.e., smaller than the stirrer diameter, dissipated power decreases. This, as demonstrated by Mehta and Sharma (1971) and Karwat (1959), diminishes mass transfer but data on any correlation with Pj V are, unfortunately, lacking in their publications. (2) If the stirrer is positioned close to the surface, air can be entrained. At the same time, power consumption decreases. This probably explains the reduced feLA, as found by Karwat under such circumstances. He reports to have observed no differences within the whole range, i.e., between 0.2 T < hR < 0.75T, but the stirrer speed proved sufficient to bring about recirculation. Where the stirrer speed is too low and, as a result, recirculation does not take place, difficulties may arise (Nienow and Wisdom, 1976).
Surface Air Entrainment. This subject has been dealt with above. Basically, it will not affect mass transfer, provided that the superficial velocity of both sparged gas and entrained gas is adequate. Under extreme circumstances this is also the case with a self-sucking stirrer where no sparged gas is present. This is exemplified by Figure
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
the data of Topiwala et al. (1973). on the extent of entrainment has been Van Dierendonck (1970), Biesecker (1972), and reported by Mehta and Sharma (1971). In general, the Fronde number is an important feature. The stirrer tip speed shows little variation during scaling-up on gas dispersion, which, roughly speaking, means that Fr + N+ 1 ¡D. This explains why in larger vessels —especially those >1 m3 —surface air entrainment seldom occurs nowadays. In addition, the effect of entrainment decreases rapidly with increasing vs because the fluid surface becomes quieter. Impeller location near the liquid surface will give surface air entrainment even in large scale equipment. The superficial velocities of sparged and entrained gas together determine the khA value again when the gas phase is well mixed. Sparged Gas Energy. At high gas inflow rates, energy supplied by gas could be of great importance. Only a few authors (Karwat, 1959; Smith et al., 1977) have recognized this. At low power values (103 W/m3). Flooding. By flooding is meant that the gas handling capacity of the stirrer becomes smaller than the amount of gas introduced. In extreme cases, the gas will bubble up around the stirrer and along its shaft. Circulation then shows just an opposite pattern, the dispersing power of the stirrer decreasing and khA being lower than may be predicted on the basis of correlations. The deviation of khA curves at lower power consumption values largely involves flooding. In case of flooding, A is little dependent, if at all, on power consumption values. Flooding is a rather complicated problem, and an extensive discussion would lie outside the scope of this review. For more information, see Judat (1976), Biesecker (1962), Rushton and Bimbinet (1968), Zwietering (1963), Nienow and Wisdom (1976), Van’t Riet (1975), and John (1971). Conclusions for Vessel Geometry Parameters. On correlation with P/V, there is no influence of stirrer geometry and number of stirrers on mass transfer in non4 showing
Information
viscous systems. In the event of full recirculation, the stirrer position is rather immaterial. By placing the stirrer between the middle of the vessel and one stirrer diameter away from the bottom, an optimal power consumption value and mass transfer are ensured. At a fluid height in the range of 0.5 < T/ < 1.5, P/V appears to be a variable with which khA can be correlated. The sparger may not be fitted at a distance from the center larger than the stirrer radius. It may be useful to correlate with the sum of power introduced by the stirrer and gas. In general, it may be concluded that on condition that the vessel is properly stirred (which means absence of flooding or surface air entrainment and the presence of a suitable gas sparger) and allowance is made for the ions in the solution, P/V and vs are sufficient to describe kLA.
Nomenclature A
= =
Cg CL
D
db
= =
= =
Ht
= =
/iR
K
kG
constant
= = =
kn
specific contact area, m2/m3 02 concentration in the gas phase, mol/m3 02 concentration in the liquid phase, mol/m3 stirrer diameter, m bubble diameter, m Henry coefficient tank height, m distance between stirrer and bottom, m
=
transfer coefficient in the gas phase, m/s transfer coefficient in the liquid phase, m/s reaction rate constant mass
mass
363
N
= stirrer speed, 1/s OTR = oxygen transfer rate, mol/m3 P = stirrer power consumption, W T tank diameter, m
s
-
t
time,
=
V
s
fluid volume,
=
m3
superficial velocity, m/s exponent ß exponent € fractional gas hold-up probe response time, s tp gas phase residence time, s tg l>s a =
=
gas
=
=
=
=
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Van't Riet,
Boom, J. M., Smith, J. M., Trans. Inst. Chem. Eng., 54. 124 (1976). Votruba, J., Sobotka, M., Biotechnol. Bioeng., 18, 1815 (1976). Votruba, J., Sobotka, M., Prokop, A., Biotechnol. Bioeng., 19, 435 (1977). Westerterp, K. R., Van Dierendonck, L. L, De Kraa, J. A., Chem. Eng. Sci., 18, 157 (1963). Wise, W. S„ J. Gen. Microbiol., 5, 167 (1951). Yoshida, F., Miura, Y., Ind. Eng. Chem. Process Des. Dev., 2, 263 (1963). Zlokarnik, M„ Chem. Ing. Tech., 42, 1310 (1970).
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Received for review June 26, 1978 Accepted December 20, 1978
Part of this article was presented as a paper at the Engineering Foundation “Mixing” Conference, August 1977, Rindge, N. H.
ARTICLES
Simulation of Ammonia Synthesis Reactors Chandra P. P. Singh and Deokl N. Saraf* Department of Chemical Engineering, Indian Institute of Technology, Kanpur-208016, India
A workable method to calculate diffusion effects within pores of a catalyst pellet, for a complex reaction, has been developed. Suitable rate equations have been selected to describe the rate of ammonia synthesis reaction over catalysts of different make. This, in conjunction with the method developed to calculate the effectiveness factor, has been used to obtain a mathematical model for ammonia synthesis reactors. Reactors having ‘adiabatic catalyst beds with interstage cooling as well as autothermal reactors have been considered. Plant data and simulation results are, generally, in very good agreement.
A mathematical model considering all physical and chemical processes in the reactor has been described in this paper. A method to solve transport equations to evaluate the effectiveness factor, up to the desired accuracy, is developed and used in the model calculations.
Introduction Synthesis of ammonia from hydrogen and nitrogen is one of the simplest kinetic reactions. The synthesis is straightforward, there is no side reaction, and the product is stable. The physical and thermodynamic properties of the reactants and products are well known (Gillespie and Beattie, 1930). However, the mechanism of this reaction over the synthesis catalyst (iron catalyst) is not well rate equations, all understood. This has led to numerous of which are of complex order. Because of the complexity of these rate equations it is difficult to account for the diffusional resistances to the transport of reactants and product in catalyst pores. This, in addition to limited reliability of rate equation, makes it difficult to have a mathematical description of the processes taking place inside an ammonia synthesis reactor. Major changes have taken place in the design of ammonia synthesis reactors since the first commercial production started in 1925 (Johansen, 1970). Most of these changes have been based on historical plant data rather than an insight into the physical and chemical processes taking place in the reactors. However, the use of computers in design, optimization, and control made it necessary to have a mathematical description of the process. Simulation models for ammonia synthesis converters of different types have been developed for design, optimi-
Rate Expressions The literature contains innumerable rate expressions. Those reported until the early thirties have been summarized by Frankenburg (1933) and Emmett (1932,1940). In 1940 Temkin and Pyzhev developed a rate equation which offered a satisfactory kinetic approach to the synthesis and decomposition of ammonia over doubly promoted iron catalysts. Since then this rate equation as such or in modified forms has been most extensively used,
some doubts about the generality of the equation have been raised (Adams and Comings, 1953; Emmett and Kummer, 1943; Hays et al., 1964). The modified form of the Temkin equation (Dyson and Simon, 1968) used in this
although
work, is
follows
·~-'[*'·"-( )'(^)
“
reaction rate, kg-mol of NH3/(h m3 of catvelocity constant of the reverse reaction, kg-mol/(h m3), /N¡¡, /Ha, /nh3 = fugacities of nitrogen, hydrogen, and ammonia, respectively, ka = equilibrium constant of the reaction: 1.5H2 + 0.5N2 NH3, and a = = a 0.5 for all iron to some workers constant. According catalysts (Morozov et al., 1965; Temkin and Pyzhev, 1940; Temkin et al., 1963) whereas others obtained values ranging from 0.4 to 0.8 (Anderson, 1960; Bokhoven et al., 1955; Bokhoven and Van Raayen, 1954; Brill, 1951; Buzzi where
rNH3
alyst), K2
zation (Murase et al., 1970; Singh, 1975), and control (Shah, 1967; Shah and Weisenfelder, 1969) purposes. To describe the reactor operating conditions as accurately as possible, the simulation model should take into consideration all the physical and chemical processes taking place in the reactor. In order to avoid the complexity resulting from such a consideration, earlier workers have attempted only approximate simulations.
0019-7882/79/1118-0364S01.00/0
as
=
=
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©
1979 American Chemical Society
