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Model of gas flow above a bubbling fluidized bed: Prediction of splash zone height
49
Model of Gas Flow above a Bubbling Prediction of Splash Zone Height
Fluidized
Ein Model1 fiir die Gasstriimung ijber einer blasenbildenden Vorausberechnung der Hiihe der Spritzzone
Wirbelschicht:
Bed:
M. SCIAZKO Institute
of Chemical
Processing
of Coal, 41-803 Zabrze
J. RACZEK
and J. BANDROWSKI*
Institute of Kuczewskiego
Chemical Engineering and 7, 44-100 Gliwice (Poland)
(Received
Apparatus
(Poland)
Construction,
Silesian
Technical
University,
April 18, 1988)
Abstract A model of the flow of gas above a bubbling fluidized bed, using the idea of ‘ghost bubble’ motion, has been worked out. The predictions of the model are compared with data from the literature and satisfactory agreement is found. Measurements of particle splash height and model calculations lead to the development of a criterion for the splash zone height. Suitable equations (the first empirical and the second derived from the model) for determination of the splash zone height are proposed. Kurzfassung Ausgehend vom Konzept der ‘ghost-bubble’ Bewegung wurde ein Model1 fur die Gasstriimung im Freiraum einer blasenbildenden Wirbelschicht entwickelt. Ein Vergleich der Voraussagen des Modells mit Literaturdaten ergab eine befriedigende tibereinstimmung. Messungen der Htihe der Partikel-Spritzzone einerseits und die Modellberechnung andererseits ermiiglichten die Angabe eines Kriteriums fiir die Hohe der Spritzzone. Geeignete Gleichungen-eine empirische und eine aus dem Model1 hergeleitete-werden fiir die Bestimmung der Hohe der Spritzzone angegeben.
Synopse Urn den Feststoflaustrag aus FlieJbetten zu begrenzen, werden relativ hohe, oft iiberdimensionierte Freiraumzonen vorgesehen. Wichtig in diesem Zusammenhang ist die sogenannte Spritzzone unmittelbar iiber der Wirbelschicht. Voraussetzung fur die Bestimmung der Spritzhiihe der Partikeln sowie deren Geschwindigkeitsprofil ist die Kenntnis der Gasstriimung im Freiraum. In dieser Arbeit wird ein theoretisches Modellfiir die Gasstriimung in der Spritzzone vorgestellt, welches auf dem Konzept der ‘ghost bubbles’ (unsichtbare BIasen) basiert. Ausgehend von GI. (I) fur die instationtire Bewegung
*To whom correspondence
025%2701/88/$3.50
should be addressed.
einer Blase wurde die Liisung in Gl. (5) bzw. deren vereinfachter Form in Gl. (6), welche den Parameter /3 enthiilt, gewonnen. Em Vergleich zwischen a!er in GI. (7) gegebenen Beziehung fir p und Daten aus Lit. 2Jindet sich in Abb. 2. In Abb. 3 werden die Ergebnisse des vorgesteliten Modells mit anderen experimentellen Daten [2, Abb. 761 verglichen, wobei die Schwankungsgeschwindigkeit V’ aus GI. (8) berechnet wurde. Die Gegeniiberstellung zeigt, daJa die Modellannahmen hinsichtlich der Parameter B und u’ die realen Striimungsverhiiltnisse im Freiraum in befriedigender Weise wiedergeben. Dies wird zusdtzlich bestiitigt durch die dhnlichkeit von GI. (6) und der Beziehung (9) aus Lit. 6, welche den Partikelaustrag im Freiraum beschreibt. Urn die Hiihe der Spritzzone zu bestimmen und eine Verkniipfung zu den o.g. Parametern herzustellen, wurden Versuche an einer absatzweise betriebenen
Chem. Eng. Process., 24 (1988) 49-55
0 Elsevier Sequoia/Printed
in The Netherlands
50
Wirbelschicht durchgefiihrt. Das Kernstiick der Anlage (Abb. 4) ist ein zylindrisches Plexiglasrohr, bestehend aus maximal drei Segmenten zu zweimal 0,6m und einmal 0,8 m mit einem Innendurchmesser von 0,3 m. Die gleichfiirmige Anstriimung des Bettes wurde durch einen Gasverteilerboden in Sandwichbauweise gewahrleistet. Abhangig von der Anzahl der Segmente betrug die Hohe des Gasaustrittsstutzens iiber dem Verteiler 0,75, I,35 bzw. 2,15m. Als Wirbelgas diente Luft. Messungen wurden durchgefiihrt fur Hohen derJuidisierten Schicht von 84,0 &- 3,3mm, 151,O + 3,6mm und 211,l + 9,6mm bei Leerrohrgeschwindigkeiten von U, = O,Sl, U, = 0,81 und IJ, = 1,23m s-‘. Das Anfangsschiittgewicht des Feststoffes wurde so gewiihlt, daJ die o.g. Hohen bei den verschiedenen Gasdurchsiitzen eingehalten wurden. Insgesamt wurden 27 Versuche, d.h. je neun Versuche pro Betthiihe, mit den in Abb. 5 dargestellten Parametern Gasgeschwindigkeit und Hiihe des Austrittsstutzens iiber dem Gasverteilerboden durchgefiihrt. Die Ergebnisse sind in detaillierter Form in Lit. 7 wiedergegeben. Nach Erreichen eines dynamischen Gleichgewichts zwischen den in den Freiraum gelangenden und wieder zuriickfallenden Partikeln wurde die mittlere Schichthiihe sowie die Hohe der Auswurfzone visuell bestimmt. Als Feststofldiente Koks mit der in Tabelle 1 angegebenen Partikeldurchmesserverteilung. Die gemessene Spritzhiihe der Partikeln abziiglich der Betthiihe wurde aufgetragen iiber der UberschuJgasgeschwindigkeit (Abb. 6). Die entsprechende Korrelation in Gl. (IO) ist eine wesentliche Voraussetzung zur Ermittlung der Abhiingigkeit zwischen den Strukturparametern des Modells und der gemessenen Spritzhiihe. Ein Vergleich der experimentellen Ergebnisse mit denen der Modellrechnung fiihrt zu dem SchluJ, dab’ die Hohe der Spritzzone streng mit dem an dieser Stelle bestimmten Volumenanteil der ‘ghost bubbles’ (&) verkniipf ist. Diese Gr6Je ist in Abb. 7als Funktion der UberschuJgasgeschwindigkeit U,, - U,, dargestellt. Fiir die Berechnung der Spritzhiihe wird GI. (I), die aus (6) und (4) abgeleitet wurde, mit 6, z 0,5 empfohlen. Eine wesentlich bessere obereinstimmung mit den MeJwerten, insbesondere fur niedrige Betthiihen, wird erreicht, wenn der Vorfaktor 2 von U,,,, in GI. (1 I) durch 1,8 ersetzt wird (Abb. 8).
1. Introduction In many techniques associated with the chemical processing of coal, contacting of the solid phase with gas, accomplished in fluidized bed systems, plays a significant part. As a rule, the fluidized bed is constituted of a dispersed material, having a wide particle size distribution, and belonging to group B according to Geldart’s classification [ 11. In order to ensure complete fluidization and the required extent of mixing of the bed, it is necessary, therefore, to employ gas velocities which are several times greater than the minimum fluidizing velocity, calculated with respect to the
mean particle size. In consequence, under the conditions of bubbling fluidization, which occur most often in industrial tluidized bed systems, the phenomenon of intensive entrainment of bulk material to the zone situated above the bed surface takes place owing to the eruption of gas bubbles. Larger particles, the terminal velocities of which are larger than the fluidization velocity, will fall back onto the bed if the exit from the vessel is at a sufficient distance from the bed surface. On the other hand, the particles with terminal velocities lower than the fluidization velocity will be entrained with the gas stream outside the apparatus. In order to limit the elutriation in fluidization vessels, very high (often oversized) zones, called disengagement zones, are employed above the bed. Taking into account the costs of the shell, lining and supporting structure of the vessel, it is reasonable to locate the exit of the gas stream at the lowest height possible from a technological viewpoint. In order to realize this task, however, it is necessary to understand the mechanism of entrainment of solid particles from the fluidized bed as well as to estimate the height to which they are transported. From this point of view it is obvious that the most important zone is that situated directly above the bed and remaining under the influence of gas bubbles. However, in order to determine the splash height of the particles and their velocity profiles, knowledge of the gas flow parameters is necessary. In this work a theoretical model of turbulent gas flow in the above-mentioned zone is presented, enabling the gas velocity and the gas velocity fluctuation profile along the freeboard to be determined. The model is based on the concept of ‘ghost bubble’ motion [2].
2. General characteristics of the freeboard In the majority of previous works the problem of the unsteady-state motion of solid particles in the freeboard is considered from the viewpoint of the critical height of entrainment of solids, the so-called ‘transport disengaging height’ (TDH) [3]. This quantity is determined usually by means of empirical correlations. However, the methods based on the TDH do not enable an accurate analysis to be made of the phenomena occurring in the zone under consideration. Horio et al. [4] distinguished three characteristic regions in the freeboard, shown schematically in Fig. 1. At a constant mean velocity of the gas stream the concentration of solid particles and the turbulence intensity are the quantities which characterize the individual regions. The corresponding values are the highest in region I, called the splash zone. For the reason mentioned, this region may in some cases play a decisive role in attaining the required degree. of conversion of solid and gas. Moreover, the height of the splash zone determines the minimal height of the disengagement zone, which
51 Assuming, according to the simplified two-phase theory of gas flow in a fluidized bed 151, that
Height
&t&,, = Qb/A zz u, - u,,,, after integration,
I
u
Diffusion zone
=
0
(‘%I -
x
the following
vO(vbO -
Gf
ub(“O
-
equation
is obtained:
ub)
%O)(“~
-
ub)
ubO(“O- &) +
ln
(4)
ln
+ r”
uO-
~oUm3 ubO
&“d
The above equation, after dropping the first two terms which are usually of minor importance, takes the form of the expression proposed in ref. 2: ub-
Fig.
I.
ub,
mnes of the freeboard.
Characteristic
&I = exp(
Particleconcenhltion
-
- Bz)
in which, assuming expressed by
enables a bed of definite composition to be maintained. In practice, the height of the disengagement zone may be equal to that of the splash zone in the case of combustion of fuels with small contents of N, S and volatiles, drying of bulk materials containing mainly surface moisture, and rapid gas-solid reactions, or for reactors with recirculation of elutriated solid particles. 3. Model of gas in the freeboard A theoretical description of gas flow in the freeboard is based on the idea of Pemberton and Davidson [2] of the motion of a ‘ghost bubble’ leaving the bed. For the sake of simplification it has been assumed that the bubble moves in a solid-free medium and its density is equal to the density of the fluidizing gas. In addition, its motion is determined by the initial conditions, that is, by the velocity of the bubbles and their fraction in the bed, both determined on the bed surface, as well as by the drag reducing the rise velocity. Hence, the unsteady-state motion of a bubble can be described by the following relationship, resulting from the balance of forces:
(6)
uO
/9 = 0.3225/dbo
turbulent
flow, the coefficient p is (7)
These values of /I calculated according to the above relationship are compared with the corresponding experimental values in Fig. 2. In this case, use has been made of data quoted by Pemberton and Davidson [2]. Figure 2 also shows the values of B calculated by these authors from the vortex ring model. Comparison of the data presented shows good agreement between the experimental values and those calculated by means of eqn. (7). In Fig. 3 other experimental data (ref. 2, Fig. 7(b)) are compared with the curves determined on the basis of the model described in this work. Values of the amplitude of the fluctuating velocity were calculated by eqn. (8), expressing the difference between the ‘ghost bubble’ velocity and the velocity of the medium in which the bubble moves:
As Fig. 3 indicates, there is also good agreement between the experimental and the theoretical results. The results of the comparison of the predictions of the mode1 with the experimental data concerning both
(1) Assuming that the fraction of fluidized bed consisting of bubbles, in the given cross-section of the vessel, is equal to 6, the velocities of a bubble and of the medium in which it moves are related to the mean gas velocity by U,(l-6)
+ u,s
= u,
(2)
This fdrmula, together with the equation ity for the bubble phase, 6&, = a,,&,0
z
of continu(3)
enables relationship initial conditions: 7 = 0:
,o 6 -
= 0,
(1) to be solved for the following ub =
ub,
Fig. 2. Comparison of the calculated values of fi with the experimental data of Pemberton and Davidson (ref. 2, Tables 2 and 3): 0, this work, eqn. (7); 0, vortex ring model [2].
52
zone I (Fig. l), which is the subject of the present considerations, is difficult because of the stream of particles entrained from the vessel. In the extreme case, without continuous feeding of the solid material, after the elutriation of the smaller particles it is possible to distinguish the height of ejection of the particles. Employing a material with a wide granulation range and a continuous particle size distribution, the observed maximal ejection height of the clouds of particles corresponds to the height of intense interaction of gas bubbles, the relatively small inertial forces of the particles being neglected. In order to determine the height of the splash zone and to link it with the fluidized bed parameters, batch operation experiments were carried out, the results of which are presented below. 1
2
Z,m
Fig. 3. Comparison of the experimental values of turbulent fluctuations with theoretical models: -----, model of turbulent energy decay(TED)[2];-.-.-.,puffmodel(PM)[2];-p , this work.
p and U’ indicate that the model assumptions approximate fairly well the real conditions of gas flow in the freeboard. Moreover, eqn. (6) is of a form similar to that of eqn. (9), proposed by Wen and Chen [6], which determines the entrainment rate of solids in the freeboard: F-F
A=exp(-OaZ) F,--F, As was shown in their paper, the experimentally determined value of a varies from 3.5 to 6.4mP’, depending on the experimental conditions. This corresponds fairly well with the values of /I predicted by eqn. (7). It would mean that the particle motion is controlled by the gas velocity distribution above the bed and constant a relates directly to constant B. However, to confirm this, further studies are needed. 4. Splash height of gas bubbles
5. Experimental
The experiments were performed in an installation presented schematically in Fig. 4. Its principal element is a cylindrical vessel of diameter 0.3 m, consisting of three segments la, lb, and lc, of heights 0.6 m, 0.6 m and 0.8 m respectively. These segments were made of organic glass which enabled the height of ejection of solid particles from the bed to be measured visually. The apparatus was fitted with a sandwiched gas distributor, made of a perforated plate, mesh wire and cotton fabric, ensuring uniform gas distribution over the cross-section of the vessel. Depending on the number of segments used, the gas exit was located at a height Hi = 0.75 m, Hz = 1.35 m, or H3 = 2.15 m. Air was used as a lluidizing agent.
t Q 2
E
lc
ll
Only one procedure for calculating the particle splash height is known to us; it is based on the results of investigations performed at a relatively low fluidization velocity which does not exceed twice the U,,,, value [4]. Moreover, the gas velocity distribution above the bed was not allowed for, whereas the existence of this profile cannot be called in question nowadays. The solid particles ejected from the fluidized bed are transported upwards by the rising gas stream, the fluctuating velocity component playing a decisive role here. Smaller particles will leave the apparatus, and the remainder will fall back into the bed. In consequence, for definite flow conditions and the solid used, dynamic equilibrium, determining the heights of the individual zones of the freeboard, will be established. In the case of a flow apparatus, however, the discrimination of these zones, and in particular of
set-up
D
II Ilb I
Fig. 4. Experimental set-up: la, lb, lc, vessel segments (organic glass); 2: cyclone; 3, viewing window; 4, container; 5, gas distributor; 6, valve; 7, orifice; 8, blower; A, B, C, D, E, pressure taps.
6. Experimental procedure the materials used
and characteristics
of
The measurements were performed for three fluidized bed heights, 84.0 + 3.3 mm, 151 .O f 3.6 mm and 211.1 k 9.6mm, at superficial gas veloci-
53
ties amounting to U, = 0.51, U, = 0.81 and U, = 1.23 m s- ’ respectively. Practically the same fluidized bed heights, at the various gas velocities, were obtained by using several initial, experimentally determined, masses of solid. Twenty-seven runs were carried out, nine for each bed height (see Table 1). The variables y of Table 1 comprise superficial gas velocities and three heights above the fluidized bed. The detailed results of the experiments are given in ref. 7 (available on request). The solid material was fluidized each time for 40 min; afterwards, no further entrainment was observed. During this period a state of dynamic equilibrium between the number of particles ejected to the freeboard and the number falling back to the bed was established. At equilibrium (which depends on the hydrodynamic conditions and the system geometry) the average bed height and the height of ejection of the clouds of particles were measured directly. After each experiment the particle size distribution of the material remaining in the vessel was determined. Considerable bed fluctuations were allowed for by determining the maximal, minimal and average values of the measured quantity, from which the mean value was calculated. coke breeze of density In the experiments, 1262 kg m-3 and average particle size distribution given in Table 2 was used. TABLE
1. Design of the experiment
HI H2 H3
u,
&
u,
Yll YZI YSI
YIZ Y22 Y32
Y13 Y23 YV
Hf = constant. Y = system response, height. TABLE
2. Particle
No.
i.e. bed height, bed composition,
size distribution
Sieve opening
1
1.200-2.000
2 3 4 5 6
0.750-l 200 0.43wl.750 0.2OwI.430 0.102-0.200 0.08&O. 102
Mean particle
7. Analysis
and splash
diameter
(mm)
C&= I/Z(x/d,),
Mass fraction 0.074 0.345 0.320 0.202 0.037 0.022 = 0.442 mm.
of results
For particles with a continuous size distribution (as in our experiments) the observed particle splash height corresponds to the height of strong bubble activity, here termed the splash zone height. Figure 5 presents the experimentally determined relationship between the particle splash height, re-
1
I 26
-
~=1.215.I12Iu.
- um, I 0
t52.6 =2.4
-
?L
2.2 -
/ &c8
“”
2.0 0
0
‘? @+I/ 0, 00
1.6
0
1.4 - /” 1.2 -
0
1 Fig.
5. Ratio
Hs/Hf
plotted
against
the
velocity
difference
& - urn,.
duced by the bed height, and the difference between the gas velocity and the minimum fluidization velocity. The experimental values obtained were correlated by the relationship, valid in the range studied, H,/Hr=
1.215 + 1.421(Uo - U,,)
(10)
This formula indicates directly that the properties of the bubble phase have a significant effect on the particle splash height. The properties of this phase are expressed by the difference U,, - U,,,, which corresponds (according to the two-phase theory) to the stream of gas flowing through the phase under consideration. Equation (10) was an essential clue in the search for a relation between the structural parameters of the model assumed and the measured height of the splash zone. The minimum fluidization velocity was calculated from the relationship of Babu et al. [8], the bubble size from Mori and Wen [9] and the bubble velocity, as well as the fraction of bubbles in the gas phase, from Kunii and Levenspiel [S]. Comparison of the results of the experiments described with the results of calculations performed according to the proposed model leads to the conclusion that the height of the splash zone of gas bubbles is strictly connected with the volumetric fraction of ‘ghost bubbles’, S,, determined at the splash zone height. Figure 6 presents the variation of this critical value of the fraction of bubbles in the gas phase with the difference between the fluidization velocity and the minimum fluidizing velocity. It may be seen that above the value U, - U,,,, = 0.5 m s’, which corresponds in this case to the ratio U,,JU,,,, > 2,6, assumes a constant value equal to about 0.5. This value is close to the porosity value for theoretically packed spheres, equal to 0.476. In turn, the corresponding gas velocity difference U, - U,,,, is in agreement with the value quoted by Kunii and Levenspiel [5] with respect to the conditions under which the thickness of a cloud sutrounding a bubble may in practice be neglected.
5:.6-, b"
%-
g!!
0.1
t
1.23 m s-’ with those calculated from an equation of the form of (1 l), but with the value of this coefficient reduced from 2 to 1.8. It should be noted that the height of the splash zone of gas bubbles defined in this work is not always equivalent in meaning to the splashing height of the solid. The latter quantity depends strongly on the particle size and in the case of fluidization of monodisperse materials, for instance, none of the particles can reach the height of the splash zone of gas bubbles.
a o---o~-
1”
0.21
I
Fig. 6. Effect of U,, - ci,,,r on the critical bubble fraction S,
When U,lU,,,, < 2 the cloud thickness increases and thus the value of 6,, at which the contact of gas bubbles takes place, is smaller. In consequence, it may be claimed that the splash zone height is determined by conditions at which the extent of packing of the bubbles assumes such a value that they start to interpenetrate and their abrupt coalescence occurs. Consequently, the gas velocity profile tends to become uniform over the whole crosssection of the vessel. Although the residual turbulence shifts to a higher zone, virtually all particles ejected from the bed fall back into it, since the lift required for their further upward motion is lacking. For the calculation of the splash zone height, use can be made of eqn. (1 l), obtained by transforming formula (6), using eqn. (4) and assuming 6, z 0.5: &o-- u0 (11) &- 2Ulllf The above equation, on account of the simplifying assumptions, yields overestimated values of Zfs, in particular for low beds and small fluidization velocities. Much better agreement is obtained when a lower value than 2 is used for the constant coefficient 2.0 in eqn. ( 11). Figure 7 presents a comparison of our own experimental data [7] obtained at U, = 0.81 and Hs=3.1
&In
0.5
E
B 2
8. Conclusions The model of the distribution of gas flow above the bubbling fluidized bed can be applied both to the general characteristic of the freeboard and the detailed analysis of the motion of particles ejected from the bed. In particular, the model was applied to the analysis of the splash zone. The model proposed assumes that the bubbles leaving the bed move upwards in the rising stream of the surrounding gas, practically without changing their size. The bubbles decelerate by loss of momentum owing to the drag force acting on a sphere of bubble diameter in a turbulent flow. The assumption of the unchanging size of ‘ghost bubbles’ was taken from the observations of Pemberton and Davidson 123. These authors come to the conclusion that the puff model would fit the experimental results for small bubble growth in the freeboard. This is in agreement with Moffatt’s [lo] suggestion that ‘ghost bubbles’ above the freely bubbling bed restricted by the vessel are unable to grow as much as a single bubble in an infinite fluid because they compete for the available bulk flow. Experimental investigations and model predictions have made it possible to determine the structural parameters of the splash zone. It was found that at the experimentally determined splash height the volumetric fraction of bubbles in the gas phase corresponds to the value of voidage for packed spheres. Thus, the idea was formulated that at the splash height abrupt coalescence of ‘ghost bubbles’ takes place and ‘two-phase’ gas flow disappears. Obviously, the remaining turbulence is pronounced in the higher zone.
0.L Nomenclature a
0.3
A
2 p
0.2
F”
Fo FCC
0.1
0.1
0.2
0.3
0.L
05
"spmi,m
Fig. 7. Comparison dicted ones.
of experimental
values of H, with the pre-
H
Hr Hs
coefficient, eqn. (9), m-i cross-sectional area, m2 drag coefficient bubble diameter, m diameter of bubble leaving bed, m particle diameter, m total entrainment rate of particles, kg s- ’ total entrainment rate of bed surface, kg s-’ total elutriation rate of particles, kg s-i height above fluidized bed, m fluidized bed height, mm height of splash zone, splash height of particles, m
55
volumetric flow rate of bubble phase, m3 SK’ amplitude of turbulent velocity fluctuation, ms-’ bubble velocity, m s- ’ velocity of bubble leaving bed, m SC’ gas velocity, m s- ’ minimum fluidization velocity, m s-’ superficial gas velocity, m sP 1 height above fluidized bed surface, m coefficient, eqn. (6) m-’ fraction of bubbles in gas phase critical value of 6 initial value of 6 time, s References 1 D. Geldart, 285-292.
Types of gas fluidization,
Powder Technol., 7( 1973)
2 S. T. Pemberton and J. F. Davidson, Turbulence in the freeboard of a gas-fluidised bed. The significance of ghost bubbles, C/rem. Eng. Sci., 39 ( 1984) 829-840. 3 J. F. Davidson, R. Clifi and D. Harrison, Fluidizurion, Academic Press, London, 2nd edn., 1985. 4 M. Horio, T. Shibata and I. Muchi, Design criteria for the fluid&d bed freeboard, in Proc. 4th Int. Fluidization Co&. Kashikojima, Japan, 1983, pp. 4-8-14-8-8. 5 D. Kunii and 0. Levenspiel, Fluidizarion Engineering, Wiley, New York, 1969. 6 C. Y. Wen and L. H. Chen, Fluid&d bed freeboard phenomena: entrainment and elutriation, AIChE J., 28 (1982) 117-128. 7 A. Kustosz and J. Nosek, MSc. Thesis, Silesian Tech. Univ., Gliwice, 1984. 8 S. P. Babu, B. Shah and A. Talwalkar, Fluidization correlation for coal gasification materials-minimum fluidization velocity and fluidized bed expansion ratio, AIChE Symp. Ser., 74 (1978) 176-185. 9 S. Mori and C. Y. Wen, in D. L. Keairns (ed.), Proc. In?. Symp. on Fluidization, Pacific Grove, U.S.A., 1975, p. 179. Cambridge Univ., 10 H. K. Moffatt, Private Communication, U.K. (cited in ref. 2).
Model of Gas Flow above a Bubbling Prediction of Splash Zone Height
Fluidized
Ein Model1 fiir die Gasstriimung ijber einer blasenbildenden Vorausberechnung der Hiihe der Spritzzone
Wirbelschicht:
Bed:
M. SCIAZKO Institute
of Chemical
Processing
of Coal, 41-803 Zabrze
J. RACZEK
and J. BANDROWSKI*
Institute of Kuczewskiego
Chemical Engineering and 7, 44-100 Gliwice (Poland)
(Received
Apparatus
(Poland)
Construction,
Silesian
Technical
University,
April 18, 1988)
Abstract A model of the flow of gas above a bubbling fluidized bed, using the idea of ‘ghost bubble’ motion, has been worked out. The predictions of the model are compared with data from the literature and satisfactory agreement is found. Measurements of particle splash height and model calculations lead to the development of a criterion for the splash zone height. Suitable equations (the first empirical and the second derived from the model) for determination of the splash zone height are proposed. Kurzfassung Ausgehend vom Konzept der ‘ghost-bubble’ Bewegung wurde ein Model1 fur die Gasstriimung im Freiraum einer blasenbildenden Wirbelschicht entwickelt. Ein Vergleich der Voraussagen des Modells mit Literaturdaten ergab eine befriedigende tibereinstimmung. Messungen der Htihe der Partikel-Spritzzone einerseits und die Modellberechnung andererseits ermiiglichten die Angabe eines Kriteriums fiir die Hohe der Spritzzone. Geeignete Gleichungen-eine empirische und eine aus dem Model1 hergeleitete-werden fiir die Bestimmung der Hohe der Spritzzone angegeben.
Synopse Urn den Feststoflaustrag aus FlieJbetten zu begrenzen, werden relativ hohe, oft iiberdimensionierte Freiraumzonen vorgesehen. Wichtig in diesem Zusammenhang ist die sogenannte Spritzzone unmittelbar iiber der Wirbelschicht. Voraussetzung fur die Bestimmung der Spritzhiihe der Partikeln sowie deren Geschwindigkeitsprofil ist die Kenntnis der Gasstriimung im Freiraum. In dieser Arbeit wird ein theoretisches Modellfiir die Gasstriimung in der Spritzzone vorgestellt, welches auf dem Konzept der ‘ghost bubbles’ (unsichtbare BIasen) basiert. Ausgehend von GI. (I) fur die instationtire Bewegung
*To whom correspondence
025%2701/88/$3.50
should be addressed.
einer Blase wurde die Liisung in Gl. (5) bzw. deren vereinfachter Form in Gl. (6), welche den Parameter /3 enthiilt, gewonnen. Em Vergleich zwischen a!er in GI. (7) gegebenen Beziehung fir p und Daten aus Lit. 2Jindet sich in Abb. 2. In Abb. 3 werden die Ergebnisse des vorgesteliten Modells mit anderen experimentellen Daten [2, Abb. 761 verglichen, wobei die Schwankungsgeschwindigkeit V’ aus GI. (8) berechnet wurde. Die Gegeniiberstellung zeigt, daJa die Modellannahmen hinsichtlich der Parameter B und u’ die realen Striimungsverhiiltnisse im Freiraum in befriedigender Weise wiedergeben. Dies wird zusdtzlich bestiitigt durch die dhnlichkeit von GI. (6) und der Beziehung (9) aus Lit. 6, welche den Partikelaustrag im Freiraum beschreibt. Urn die Hiihe der Spritzzone zu bestimmen und eine Verkniipfung zu den o.g. Parametern herzustellen, wurden Versuche an einer absatzweise betriebenen
Chem. Eng. Process., 24 (1988) 49-55
0 Elsevier Sequoia/Printed
in The Netherlands
50
Wirbelschicht durchgefiihrt. Das Kernstiick der Anlage (Abb. 4) ist ein zylindrisches Plexiglasrohr, bestehend aus maximal drei Segmenten zu zweimal 0,6m und einmal 0,8 m mit einem Innendurchmesser von 0,3 m. Die gleichfiirmige Anstriimung des Bettes wurde durch einen Gasverteilerboden in Sandwichbauweise gewahrleistet. Abhangig von der Anzahl der Segmente betrug die Hohe des Gasaustrittsstutzens iiber dem Verteiler 0,75, I,35 bzw. 2,15m. Als Wirbelgas diente Luft. Messungen wurden durchgefiihrt fur Hohen derJuidisierten Schicht von 84,0 &- 3,3mm, 151,O + 3,6mm und 211,l + 9,6mm bei Leerrohrgeschwindigkeiten von U, = O,Sl, U, = 0,81 und IJ, = 1,23m s-‘. Das Anfangsschiittgewicht des Feststoffes wurde so gewiihlt, daJ die o.g. Hohen bei den verschiedenen Gasdurchsiitzen eingehalten wurden. Insgesamt wurden 27 Versuche, d.h. je neun Versuche pro Betthiihe, mit den in Abb. 5 dargestellten Parametern Gasgeschwindigkeit und Hiihe des Austrittsstutzens iiber dem Gasverteilerboden durchgefiihrt. Die Ergebnisse sind in detaillierter Form in Lit. 7 wiedergegeben. Nach Erreichen eines dynamischen Gleichgewichts zwischen den in den Freiraum gelangenden und wieder zuriickfallenden Partikeln wurde die mittlere Schichthiihe sowie die Hohe der Auswurfzone visuell bestimmt. Als Feststofldiente Koks mit der in Tabelle 1 angegebenen Partikeldurchmesserverteilung. Die gemessene Spritzhiihe der Partikeln abziiglich der Betthiihe wurde aufgetragen iiber der UberschuJgasgeschwindigkeit (Abb. 6). Die entsprechende Korrelation in Gl. (IO) ist eine wesentliche Voraussetzung zur Ermittlung der Abhiingigkeit zwischen den Strukturparametern des Modells und der gemessenen Spritzhiihe. Ein Vergleich der experimentellen Ergebnisse mit denen der Modellrechnung fiihrt zu dem SchluJ, dab’ die Hohe der Spritzzone streng mit dem an dieser Stelle bestimmten Volumenanteil der ‘ghost bubbles’ (&) verkniipf ist. Diese Gr6Je ist in Abb. 7als Funktion der UberschuJgasgeschwindigkeit U,, - U,, dargestellt. Fiir die Berechnung der Spritzhiihe wird GI. (I), die aus (6) und (4) abgeleitet wurde, mit 6, z 0,5 empfohlen. Eine wesentlich bessere obereinstimmung mit den MeJwerten, insbesondere fur niedrige Betthiihen, wird erreicht, wenn der Vorfaktor 2 von U,,,, in GI. (1 I) durch 1,8 ersetzt wird (Abb. 8).
1. Introduction In many techniques associated with the chemical processing of coal, contacting of the solid phase with gas, accomplished in fluidized bed systems, plays a significant part. As a rule, the fluidized bed is constituted of a dispersed material, having a wide particle size distribution, and belonging to group B according to Geldart’s classification [ 11. In order to ensure complete fluidization and the required extent of mixing of the bed, it is necessary, therefore, to employ gas velocities which are several times greater than the minimum fluidizing velocity, calculated with respect to the
mean particle size. In consequence, under the conditions of bubbling fluidization, which occur most often in industrial tluidized bed systems, the phenomenon of intensive entrainment of bulk material to the zone situated above the bed surface takes place owing to the eruption of gas bubbles. Larger particles, the terminal velocities of which are larger than the fluidization velocity, will fall back onto the bed if the exit from the vessel is at a sufficient distance from the bed surface. On the other hand, the particles with terminal velocities lower than the fluidization velocity will be entrained with the gas stream outside the apparatus. In order to limit the elutriation in fluidization vessels, very high (often oversized) zones, called disengagement zones, are employed above the bed. Taking into account the costs of the shell, lining and supporting structure of the vessel, it is reasonable to locate the exit of the gas stream at the lowest height possible from a technological viewpoint. In order to realize this task, however, it is necessary to understand the mechanism of entrainment of solid particles from the fluidized bed as well as to estimate the height to which they are transported. From this point of view it is obvious that the most important zone is that situated directly above the bed and remaining under the influence of gas bubbles. However, in order to determine the splash height of the particles and their velocity profiles, knowledge of the gas flow parameters is necessary. In this work a theoretical model of turbulent gas flow in the above-mentioned zone is presented, enabling the gas velocity and the gas velocity fluctuation profile along the freeboard to be determined. The model is based on the concept of ‘ghost bubble’ motion [2].
2. General characteristics of the freeboard In the majority of previous works the problem of the unsteady-state motion of solid particles in the freeboard is considered from the viewpoint of the critical height of entrainment of solids, the so-called ‘transport disengaging height’ (TDH) [3]. This quantity is determined usually by means of empirical correlations. However, the methods based on the TDH do not enable an accurate analysis to be made of the phenomena occurring in the zone under consideration. Horio et al. [4] distinguished three characteristic regions in the freeboard, shown schematically in Fig. 1. At a constant mean velocity of the gas stream the concentration of solid particles and the turbulence intensity are the quantities which characterize the individual regions. The corresponding values are the highest in region I, called the splash zone. For the reason mentioned, this region may in some cases play a decisive role in attaining the required degree. of conversion of solid and gas. Moreover, the height of the splash zone determines the minimal height of the disengagement zone, which
51 Assuming, according to the simplified two-phase theory of gas flow in a fluidized bed 151, that
Height
&t&,, = Qb/A zz u, - u,,,, after integration,
I
u
Diffusion zone
=
0
(‘%I -
x
the following
vO(vbO -
Gf
ub(“O
-
equation
is obtained:
ub)
%O)(“~
-
ub)
ubO(“O- &) +
ln
(4)
ln
+ r”
uO-
~oUm3 ubO
&“d
The above equation, after dropping the first two terms which are usually of minor importance, takes the form of the expression proposed in ref. 2: ub-
Fig.
I.
ub,
mnes of the freeboard.
Characteristic
&I = exp(
Particleconcenhltion
-
- Bz)
in which, assuming expressed by
enables a bed of definite composition to be maintained. In practice, the height of the disengagement zone may be equal to that of the splash zone in the case of combustion of fuels with small contents of N, S and volatiles, drying of bulk materials containing mainly surface moisture, and rapid gas-solid reactions, or for reactors with recirculation of elutriated solid particles. 3. Model of gas in the freeboard A theoretical description of gas flow in the freeboard is based on the idea of Pemberton and Davidson [2] of the motion of a ‘ghost bubble’ leaving the bed. For the sake of simplification it has been assumed that the bubble moves in a solid-free medium and its density is equal to the density of the fluidizing gas. In addition, its motion is determined by the initial conditions, that is, by the velocity of the bubbles and their fraction in the bed, both determined on the bed surface, as well as by the drag reducing the rise velocity. Hence, the unsteady-state motion of a bubble can be described by the following relationship, resulting from the balance of forces:
(6)
uO
/9 = 0.3225/dbo
turbulent
flow, the coefficient p is (7)
These values of /I calculated according to the above relationship are compared with the corresponding experimental values in Fig. 2. In this case, use has been made of data quoted by Pemberton and Davidson [2]. Figure 2 also shows the values of B calculated by these authors from the vortex ring model. Comparison of the data presented shows good agreement between the experimental values and those calculated by means of eqn. (7). In Fig. 3 other experimental data (ref. 2, Fig. 7(b)) are compared with the curves determined on the basis of the model described in this work. Values of the amplitude of the fluctuating velocity were calculated by eqn. (8), expressing the difference between the ‘ghost bubble’ velocity and the velocity of the medium in which the bubble moves:
As Fig. 3 indicates, there is also good agreement between the experimental and the theoretical results. The results of the comparison of the predictions of the mode1 with the experimental data concerning both
(1) Assuming that the fraction of fluidized bed consisting of bubbles, in the given cross-section of the vessel, is equal to 6, the velocities of a bubble and of the medium in which it moves are related to the mean gas velocity by U,(l-6)
+ u,s
= u,
(2)
This fdrmula, together with the equation ity for the bubble phase, 6&, = a,,&,0
z
of continu(3)
enables relationship initial conditions: 7 = 0:
,o 6 -
= 0,
(1) to be solved for the following ub =
ub,
Fig. 2. Comparison of the calculated values of fi with the experimental data of Pemberton and Davidson (ref. 2, Tables 2 and 3): 0, this work, eqn. (7); 0, vortex ring model [2].
52
zone I (Fig. l), which is the subject of the present considerations, is difficult because of the stream of particles entrained from the vessel. In the extreme case, without continuous feeding of the solid material, after the elutriation of the smaller particles it is possible to distinguish the height of ejection of the particles. Employing a material with a wide granulation range and a continuous particle size distribution, the observed maximal ejection height of the clouds of particles corresponds to the height of intense interaction of gas bubbles, the relatively small inertial forces of the particles being neglected. In order to determine the height of the splash zone and to link it with the fluidized bed parameters, batch operation experiments were carried out, the results of which are presented below. 1
2
Z,m
Fig. 3. Comparison of the experimental values of turbulent fluctuations with theoretical models: -----, model of turbulent energy decay(TED)[2];-.-.-.,puffmodel(PM)[2];-p , this work.
p and U’ indicate that the model assumptions approximate fairly well the real conditions of gas flow in the freeboard. Moreover, eqn. (6) is of a form similar to that of eqn. (9), proposed by Wen and Chen [6], which determines the entrainment rate of solids in the freeboard: F-F
A=exp(-OaZ) F,--F, As was shown in their paper, the experimentally determined value of a varies from 3.5 to 6.4mP’, depending on the experimental conditions. This corresponds fairly well with the values of /I predicted by eqn. (7). It would mean that the particle motion is controlled by the gas velocity distribution above the bed and constant a relates directly to constant B. However, to confirm this, further studies are needed. 4. Splash height of gas bubbles
5. Experimental
The experiments were performed in an installation presented schematically in Fig. 4. Its principal element is a cylindrical vessel of diameter 0.3 m, consisting of three segments la, lb, and lc, of heights 0.6 m, 0.6 m and 0.8 m respectively. These segments were made of organic glass which enabled the height of ejection of solid particles from the bed to be measured visually. The apparatus was fitted with a sandwiched gas distributor, made of a perforated plate, mesh wire and cotton fabric, ensuring uniform gas distribution over the cross-section of the vessel. Depending on the number of segments used, the gas exit was located at a height Hi = 0.75 m, Hz = 1.35 m, or H3 = 2.15 m. Air was used as a lluidizing agent.
t Q 2
E
lc
ll
Only one procedure for calculating the particle splash height is known to us; it is based on the results of investigations performed at a relatively low fluidization velocity which does not exceed twice the U,,,, value [4]. Moreover, the gas velocity distribution above the bed was not allowed for, whereas the existence of this profile cannot be called in question nowadays. The solid particles ejected from the fluidized bed are transported upwards by the rising gas stream, the fluctuating velocity component playing a decisive role here. Smaller particles will leave the apparatus, and the remainder will fall back into the bed. In consequence, for definite flow conditions and the solid used, dynamic equilibrium, determining the heights of the individual zones of the freeboard, will be established. In the case of a flow apparatus, however, the discrimination of these zones, and in particular of
set-up
D
II Ilb I
Fig. 4. Experimental set-up: la, lb, lc, vessel segments (organic glass); 2: cyclone; 3, viewing window; 4, container; 5, gas distributor; 6, valve; 7, orifice; 8, blower; A, B, C, D, E, pressure taps.
6. Experimental procedure the materials used
and characteristics
of
The measurements were performed for three fluidized bed heights, 84.0 + 3.3 mm, 151 .O f 3.6 mm and 211.1 k 9.6mm, at superficial gas veloci-
53
ties amounting to U, = 0.51, U, = 0.81 and U, = 1.23 m s- ’ respectively. Practically the same fluidized bed heights, at the various gas velocities, were obtained by using several initial, experimentally determined, masses of solid. Twenty-seven runs were carried out, nine for each bed height (see Table 1). The variables y of Table 1 comprise superficial gas velocities and three heights above the fluidized bed. The detailed results of the experiments are given in ref. 7 (available on request). The solid material was fluidized each time for 40 min; afterwards, no further entrainment was observed. During this period a state of dynamic equilibrium between the number of particles ejected to the freeboard and the number falling back to the bed was established. At equilibrium (which depends on the hydrodynamic conditions and the system geometry) the average bed height and the height of ejection of the clouds of particles were measured directly. After each experiment the particle size distribution of the material remaining in the vessel was determined. Considerable bed fluctuations were allowed for by determining the maximal, minimal and average values of the measured quantity, from which the mean value was calculated. coke breeze of density In the experiments, 1262 kg m-3 and average particle size distribution given in Table 2 was used. TABLE
1. Design of the experiment
HI H2 H3
u,
&
u,
Yll YZI YSI
YIZ Y22 Y32
Y13 Y23 YV
Hf = constant. Y = system response, height. TABLE
2. Particle
No.
i.e. bed height, bed composition,
size distribution
Sieve opening
1
1.200-2.000
2 3 4 5 6
0.750-l 200 0.43wl.750 0.2OwI.430 0.102-0.200 0.08&O. 102
Mean particle
7. Analysis
and splash
diameter
(mm)
C&= I/Z(x/d,),
Mass fraction 0.074 0.345 0.320 0.202 0.037 0.022 = 0.442 mm.
of results
For particles with a continuous size distribution (as in our experiments) the observed particle splash height corresponds to the height of strong bubble activity, here termed the splash zone height. Figure 5 presents the experimentally determined relationship between the particle splash height, re-
1
I 26
-
~=1.215.I12Iu.
- um, I 0
t52.6 =2.4
-
?L
2.2 -
/ &c8
“”
2.0 0
0
‘? @+I/ 0, 00
1.6
0
1.4 - /” 1.2 -
0
1 Fig.
5. Ratio
Hs/Hf
plotted
against
the
velocity
difference
& - urn,.
duced by the bed height, and the difference between the gas velocity and the minimum fluidization velocity. The experimental values obtained were correlated by the relationship, valid in the range studied, H,/Hr=
1.215 + 1.421(Uo - U,,)
(10)
This formula indicates directly that the properties of the bubble phase have a significant effect on the particle splash height. The properties of this phase are expressed by the difference U,, - U,,,, which corresponds (according to the two-phase theory) to the stream of gas flowing through the phase under consideration. Equation (10) was an essential clue in the search for a relation between the structural parameters of the model assumed and the measured height of the splash zone. The minimum fluidization velocity was calculated from the relationship of Babu et al. [8], the bubble size from Mori and Wen [9] and the bubble velocity, as well as the fraction of bubbles in the gas phase, from Kunii and Levenspiel [S]. Comparison of the results of the experiments described with the results of calculations performed according to the proposed model leads to the conclusion that the height of the splash zone of gas bubbles is strictly connected with the volumetric fraction of ‘ghost bubbles’, S,, determined at the splash zone height. Figure 6 presents the variation of this critical value of the fraction of bubbles in the gas phase with the difference between the fluidization velocity and the minimum fluidizing velocity. It may be seen that above the value U, - U,,,, = 0.5 m s’, which corresponds in this case to the ratio U,,JU,,,, > 2,6, assumes a constant value equal to about 0.5. This value is close to the porosity value for theoretically packed spheres, equal to 0.476. In turn, the corresponding gas velocity difference U, - U,,,, is in agreement with the value quoted by Kunii and Levenspiel [5] with respect to the conditions under which the thickness of a cloud sutrounding a bubble may in practice be neglected.
5:.6-, b"
%-
g!!
0.1
t
1.23 m s-’ with those calculated from an equation of the form of (1 l), but with the value of this coefficient reduced from 2 to 1.8. It should be noted that the height of the splash zone of gas bubbles defined in this work is not always equivalent in meaning to the splashing height of the solid. The latter quantity depends strongly on the particle size and in the case of fluidization of monodisperse materials, for instance, none of the particles can reach the height of the splash zone of gas bubbles.
a o---o~-
1”
0.21
I
Fig. 6. Effect of U,, - ci,,,r on the critical bubble fraction S,
When U,lU,,,, < 2 the cloud thickness increases and thus the value of 6,, at which the contact of gas bubbles takes place, is smaller. In consequence, it may be claimed that the splash zone height is determined by conditions at which the extent of packing of the bubbles assumes such a value that they start to interpenetrate and their abrupt coalescence occurs. Consequently, the gas velocity profile tends to become uniform over the whole crosssection of the vessel. Although the residual turbulence shifts to a higher zone, virtually all particles ejected from the bed fall back into it, since the lift required for their further upward motion is lacking. For the calculation of the splash zone height, use can be made of eqn. (1 l), obtained by transforming formula (6), using eqn. (4) and assuming 6, z 0.5: &o-- u0 (11) &- 2Ulllf The above equation, on account of the simplifying assumptions, yields overestimated values of Zfs, in particular for low beds and small fluidization velocities. Much better agreement is obtained when a lower value than 2 is used for the constant coefficient 2.0 in eqn. ( 11). Figure 7 presents a comparison of our own experimental data [7] obtained at U, = 0.81 and Hs=3.1
&In
0.5
E
B 2
8. Conclusions The model of the distribution of gas flow above the bubbling fluidized bed can be applied both to the general characteristic of the freeboard and the detailed analysis of the motion of particles ejected from the bed. In particular, the model was applied to the analysis of the splash zone. The model proposed assumes that the bubbles leaving the bed move upwards in the rising stream of the surrounding gas, practically without changing their size. The bubbles decelerate by loss of momentum owing to the drag force acting on a sphere of bubble diameter in a turbulent flow. The assumption of the unchanging size of ‘ghost bubbles’ was taken from the observations of Pemberton and Davidson 123. These authors come to the conclusion that the puff model would fit the experimental results for small bubble growth in the freeboard. This is in agreement with Moffatt’s [lo] suggestion that ‘ghost bubbles’ above the freely bubbling bed restricted by the vessel are unable to grow as much as a single bubble in an infinite fluid because they compete for the available bulk flow. Experimental investigations and model predictions have made it possible to determine the structural parameters of the splash zone. It was found that at the experimentally determined splash height the volumetric fraction of bubbles in the gas phase corresponds to the value of voidage for packed spheres. Thus, the idea was formulated that at the splash height abrupt coalescence of ‘ghost bubbles’ takes place and ‘two-phase’ gas flow disappears. Obviously, the remaining turbulence is pronounced in the higher zone.
0.L Nomenclature a
0.3
A
2 p
0.2
F”
Fo FCC
0.1
0.1
0.2
0.3
0.L
05
"spmi,m
Fig. 7. Comparison dicted ones.
of experimental
values of H, with the pre-
H
Hr Hs
coefficient, eqn. (9), m-i cross-sectional area, m2 drag coefficient bubble diameter, m diameter of bubble leaving bed, m particle diameter, m total entrainment rate of particles, kg s- ’ total entrainment rate of bed surface, kg s-’ total elutriation rate of particles, kg s-i height above fluidized bed, m fluidized bed height, mm height of splash zone, splash height of particles, m
55
volumetric flow rate of bubble phase, m3 SK’ amplitude of turbulent velocity fluctuation, ms-’ bubble velocity, m s- ’ velocity of bubble leaving bed, m SC’ gas velocity, m s- ’ minimum fluidization velocity, m s-’ superficial gas velocity, m sP 1 height above fluidized bed surface, m coefficient, eqn. (6) m-’ fraction of bubbles in gas phase critical value of 6 initial value of 6 time, s References 1 D. Geldart, 285-292.
Types of gas fluidization,
Powder Technol., 7( 1973)
2 S. T. Pemberton and J. F. Davidson, Turbulence in the freeboard of a gas-fluidised bed. The significance of ghost bubbles, C/rem. Eng. Sci., 39 ( 1984) 829-840. 3 J. F. Davidson, R. Clifi and D. Harrison, Fluidizurion, Academic Press, London, 2nd edn., 1985. 4 M. Horio, T. Shibata and I. Muchi, Design criteria for the fluid&d bed freeboard, in Proc. 4th Int. Fluidization Co&. Kashikojima, Japan, 1983, pp. 4-8-14-8-8. 5 D. Kunii and 0. Levenspiel, Fluidizarion Engineering, Wiley, New York, 1969. 6 C. Y. Wen and L. H. Chen, Fluid&d bed freeboard phenomena: entrainment and elutriation, AIChE J., 28 (1982) 117-128. 7 A. Kustosz and J. Nosek, MSc. Thesis, Silesian Tech. Univ., Gliwice, 1984. 8 S. P. Babu, B. Shah and A. Talwalkar, Fluidization correlation for coal gasification materials-minimum fluidization velocity and fluidized bed expansion ratio, AIChE Symp. Ser., 74 (1978) 176-185. 9 S. Mori and C. Y. Wen, in D. L. Keairns (ed.), Proc. In?. Symp. on Fluidization, Pacific Grove, U.S.A., 1975, p. 179. Cambridge Univ., 10 H. K. Moffatt, Private Communication, U.K. (cited in ref. 2).