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liquid flow
Chemical Engineering and Processing, 31 (1992) 87-96
Measuring
device for gas/liquid flow
MeI3werterfassungssystem Bernd
Genenger*
Institut ftir Therm&he
Dedicated
to Prof.
87
fiir Gas/Fliissig-Striimungen
and Burkhard Verfahrenstechnik
Dr.-Ing.
Lohrengel
der Technischen
A. Vogelpohl
Universitiit
on the occasion
Clausthal,
Leibnizstr.
15, 3392 ClausthaI-Zellerfeld
(Germany)
of his 6l?th birthday
(Received October 21, 1991; in final form December 5, 1991)
Abstract For the design and scale-up of gas/liquid contact apparatus, the bubble size distribution, the gas hold-up and the residence time behaviour of the liquid phase must be known. A purely theoretical prediction of these hydrodynamic parameters is not possible because of the complex relationships between the fluid dynamics and the properties of the phases, as well as the geometrical and operating parameters. Therefore, a fully automatic measuring device was developed at the Mass Transfer Laboratories of the Technical University of Clausthal, which enables the bubble size distribution to be determined experimentally with a photoelectric suction probe, the gas hold-up with the differential pressure method and the residence time behaviour by measuring the conductivity. Some results of the measurements carried out in a jet-driven loop reactor are presented and discussed to demonstrate the practical application of the measuring device.
Kurzfassung Zur Auslegung und MaBstabsvergrSBerung von Gas/Fliissig-Kontaktapparaten miissen die Blasengriige, der Gasgehalt und das Vermischungsverhalten der fliissigen Phase bekannt sein. Da eine Vorausberechnung aufgrund der komplexen Zusammenhange zwischen den Geometrie- und Betriebsparametern sowie den Stoffdaten einerseits und der Fluiddynamik andererseits nicht moglich ist, wurde am Institut fur Thermische Verfahrenstechnik der TU Clausthal ein MeDwerterfassungssystem entwickelt. Mit diesem Mebwerterfassungssystem kann die Blasengrdge mit der fotoelektrischen Absaugsonde, der Gasgehalt mit der Differenzdruckmethode und das Vermischungsverhdlten mit einer Leitfahigkeitsmessung bestimmt werden. Die Anwendung des Megwerterfassungssystems wird am Beispiel eines strahlgetriebenen Schlaufenreaktors erllutert. Einige Ergebnisse der Messungen an diesem Apparat werden diskutiert.
Synopse
Die volumenbezogene Phasengrenzjltiche in Gas/Flussig-Kontaktapparaten ist durch den Gasgehalt und die BlasengroJe bestimmt. Der Umsatz einer chemischen Reaktion wird vom Vermischungsverhalten der fltissigen Phase beeinfl@t. Die Blasengriipe, der Gasgehalt und das Vermischungsverhalten der fltissigen Phase miissen deshalb fur die Auslegung und die MaJstabsvergroJerung von GaslFliissig-Kontaktapparaten bekannt sein. Da die GroJen nur selten theoretisch vorausberechnet werden kiinnen, wurde am Institut fur Thermische Verfahrenstechnik der TU Clausthal ein MeJwerterfassungssystem endwickelt. Mit diesem Mefiwerterfassungssystem werden
*Author
to whom correspondence
0255-2701/92/$5.00
should be addressed.
die BlasengriJe mit der fotoelektrischen Absaugsonde, der Gasgehalt mit der Dtflerenzdruckmethode und das Vermischungsverhalten durch Leitfahigkeitsmessungen ermittelt. Zur Bestimmung der BlasengriiJBenverteilung wird die in Abb. 1 dargestellte fotoelektrische Absaugsonde eingesetzt. Ein Teil des Zweiphasengemisches wird aus dem Apparat abgesaugt. Die Blasen werden in einer Glaskapillare zu zylindrischen Pfropfen verformt, deren Lange und Geschwindigkeit mit der MeJsonde erfa& werden. Aus den in Abb. 2 gezeigten MeJsignalen wird der Durchmesser der volumengleichen Kugel berechnet. Die Signale von bis zu ftinf Sonden werden automatisch erfaj’t, ausgewertet und wiihrend der Messung auf Fehler iiberpriift. Das Ergebnis einer Messung sind die Anzahl-, die Oberfiichenund die Volumendichteverteilung der Blasen .
0
1992 -
Elsevier Sequoia.
All rights reserved
88 Zur Bestimmung des Vermischungsverhaltens stehen zwei Methoden zur Verftigung, die 1 -MeJ’stellen - und die Z-MeJstellen-Methode. Mit der 1 -MeJstellen-Methode wird die Verweilzeitdichtekurve eines Reaktors gemessen. Der Tracer ist in Form eines Dirac-Impulses am Fliissigkeitseintritt aufzugeben. Diese Methode eignet sich fur Apparate, deren Vermischungsverhalten dem eines Riihrkessels nahe kommt. Sol1 aus der Verweilzeitdichtekurve auf die Striimung im Apparat geschlossen werden, so ist die Verweilzeitdichtekurve mit einem geeigneten Model1 fir das Verweilzeitverhalten zu vergleichen. Das Vermischungsverhalten von Rohrreaktoren wird in vielen Fdllen durch das eindimensionale Dispersionsmodell wiedergegeben. Zur Bestimmung der beiden Parameter des Dispersionsmodells, der Stromungsgeschwindigkeit und des Dispersionskoefhzienten, wird am Fliissigkeitseintritt in den Reaktor ein Salz-Tracer injiziert. Im Apparat wird die Leitfahigkeit der Jliissigen Phase, wie in Abb. 3 gezeigt, mit zwei Leitjshigkeitssonden am gemessen. Aus dem Signal der Leitf~higkeitssonde Eintritt in die Mefjstrecke wird das Signal der zweiten Elektrode mit Hilfe der iibertragungsfunktion (Gl. 5) und des Faltungsintegrals (Gl. 6) berechnet. Die Parameter des eindimensionalen Dispersionsmodells werden mit Hilfe einer Anpassungsrechnung solange variiert, bis das Ausgangssignal mit einer miiglichst kleinen Abweichung aus dem Eingangssignal berechnet werden kann. Der Gasgehalt wird mit der in Abb. 4 gezeigten Dtyerenzdruckmethode bestimmt. Die Signale des elektronischen Dtflierenzdruckuufnehmers werden digital erfapt und mit Gl. 8 in den Gasgehult umgerechnet. Die Einsatzfiihigkeit des MeJwerterfassungssystems wird anhand von MeJwerten demonstriert, die an einem strahlgetriebenen Schlaufenreaktor uufgenommen wurden, der in Abb. 5 dargestellt ist. Ergebnisse der Gasgehaltsmessungen an diesem Reaktor sind in Abb. 7 aufgetragen. Abb. 10 zeigt BlasengroJenverteilungen, die an verschiedenen Orten im Ringraum des Schlaufenreaktors gemessen wurden. Der im Reaktor umlaufende Fliissigkeitsvolumenstrom wurde mit der 1 -MeJstellenund der 2-MeJstellenMethode bestimmt. Bei den Messungen mit der 2MeJstellen-Methode wurden zwei Leitftihigkeitssonden im Ringraum des Reaktors installiert. Zur Bestimmung des umlaufenden Fliissigkeitsvolumenstroms mit der IMeJstellen-Methode wurde die Leitfiihigkeit im Fliissigkeitsablauf des Apparats gemessen und in die Verweilzeitdichtekurve umgerechnet. Die Verweilzeitdichtekurve wurde mit dem in Abb. 11 dargestellten Model1 fur das Verweilzeitverhalten des strahlgetriebenen Schlaufenreaktors verglichen. Einer der Parameter dieses Modells ist der im Reaktor umlaufende Fliissigkeitsvolumenstrom. Die Ergebnisse der Messungen mit der I-MeJstellen13 und der 2-MeBstellen-Methode sind in Abb.
dargestellt. Beide Methoden liefern iibereinstimmende Werte ftir den umlaufenden Fliissigkeitsvolumenstrom.
1. Introduction For the design and scale-up of gas/liquid contact apparatus, the bubble size distribution, the gas hold-up and the residence time behaviour of both phases must be known. In most cases, the purely theoretical prediction of these parameters is not possible because of the complex relationships between the properties of the phases and the fluid dynamics, as well as the geometrical and operating parameters. Therefore, the fluiddynamic parameters of interest have to be measured. At the Mass Transfer Laboratories of the Technical University of Clausthal a fully automatic measuring device was developed to determine experimentally the bubble size distribution, the gas hold-up and the residence time behaviour of the liquid phase in several types of gas/liquid contact apparatus. The measured values are recorded by a personal computer and then processed using computer programs based on mathematical models. To demonstrate the practical application of the measuring device, some results of the measurements carried out in a jet-driven loop reactor are presented and discussed.
2. Bubble size distribution The bubble size distribution is measured with the photoelectric suction probe, the principle of which is given in Fig. 1 [l-3]. A sample from the gas/liquid contact apparatus is sucked through a glass capillary at a controlled flow rate. One end of the capillary is funnel-shaped. The bubbles, which are sucked along together with the continuous phase, are transformed into cylindrical slugs inside the capillary. The velocity and length of these slugs are measured with the measuring probe, which encloses the capillary. The measuring probe consists of two light barriers, made up of an incandescent lamp and a phototransistor. The light barriers are placed 2 mm apart at an angle of 90” relative to each other. The electrical resistance of the phototransistor and the corresponding light intensity are dependent on the refractive index of the medium between the incandescent lamp and the transistor. A signal from the photoelectric suction probe is shown in Fig. 2. The measured signal must be triggered for further processing. For this purpose a triggering threshold is fixed, so that the beginning and end of a slug can be detected when the threshold is exceeded.
89
are calculated. If the whole cross-section lary is covered by the slug, the diameter sponding sphere can be calculated from
of the capilof the corre-
l/3
d,r=
(3)
During the measurement the recorded data are checked on-line for their correctness. Incorrect data are marked and not used for further processing. The number of wrong measurements and the kind of error are registered in the record so that the quality of the measurement can be assessed. For plotting the bubble size distribution and calculating the mean bubble diameter only those data are used which fulfil the following criteria. (1) None of the times t, to t4 is negative. Negative times are obtained if a very small bubble does not move along the axis of the capillary or if the bubble measured at each light barrier is not the same one. (2) The difference between the velocities of the slugs inside the capillary calculated from t, and t, must be less than 15%. This value was estimated experimentally
Fig. 1. Photoelectric suction probe.
real signal
-light barner
; dkap21 ( >
1
111. light barrier
(3) The lengths of the slugs calculated from t, and t, differ from each other by less than half the capillary diameter [ 11. (4) The velocity of the slugs inside the capillary must be in a range determined by the physical properties of the two phases. For a water/air system the velocity of the slugs must be in the range 1.3-1.7 m/s. Jf the velocity is too small, the probe signals cannot be processed, because oscillations in the signals are induced when the beginning or end of a slug passes the light barriers. If the velocity inside the capillary is too high, the slugs will be slashed inside the capillary. (5) Large slugs, which are longer than 150 mm, cannot be sucked through without destroying the bubble. Such values for the length are determined when the end of a slug is not detected correctly. (6) The diameter of a bubble must be greater than the bubble size half cannotthe becapillary measureddiameter. reliably, Otherwise,
2
&iggmg_
-___~--__
triggering
---
threshold
triggered signal
Fig. 2. Processing of the probe signals.
The triggered signals of both light barriers are then processed electronically. From the measured times t, to t, the velocity of the slugs in the capillary wG = a/t, = a/t,
(1)
and the length of the slugs I= w,t, = MjC,t2
(2)
The diameter of the capillary is chosen according to the last two criteria. Capillaries with an inner diameter between 0.4 and 2.2 mm are used [4]. With these capillaries, bubble diameters between 0.2 and 11 mm can be measured. Bubble diameters in this range can be evaluated with a maximum deviation of + 10%. This deviation results from the film of the continuous phase between the bubble and the capillary wall. Because of this film, the length of the cylindrical slugs in the capillary is increased and too large a diameter is calculated for the corresponding sphere. If the deviation is too large, the photoelectric suction probe must be calibrated with bubbles of known diameter [4].
90
To apply the photoelectric suction probe in a two- or three-phase flow the following criteria must be fulfilled. (1) Light from the incandescent lamp must reach the phototransistor. This criterion is fulfilled in transparent liquids and fermentation broths up to a concentration of 10 g/l of biomass. (2) The velocity inside the capillary must be higher than the velocity of the liquid flow near the funnelshaped end of the glass capillary. If the flow velocity is higher the bubbles cannot be sucked out. (3) The gas hold-up must be smaller than about 25%. If the gas hold-up is higher, coalescence of the bubbles occurs at the funnel-shaped end of the capillary. (4) Solid particles in a three-phase flow must be smaller in diameter than the inner diameter of the capillary. Otherwise, the capillary is blocked by solid particles.
second
measuring
pod
-Ll
first
measuring
point
--El
flow
dlrectmn
Fig. 3. Two measuring points method.
3. Residence time behaviour 3.1. One measuring point method
To determine the residence time behaviour with the one measuring point method, a salt tracer is added at the inlet of the liquid. The salt tracer must be injected in such a way that the signal at the inlet has the shape of a Dirac function. The conductivity of the liquid at the outlet is measured with a conductivity probe. From this probe’s signal, the residence time density function is calculated. This method is used to determine the residence time behaviour of apparatus in which the residence time behaviour is close to that of a stirred tank reactor. If further information about the flow structure inside the apparatus is required, the residence time density function has to be compared with that obtained from a model for the residence time behaviour. 3.2. Two measuring points method The residence time behaviour of tubular reactors can usually be described by the one-dimensional dispersion model. This model is based on the idea that the idealized behaviour of the flow is superposed by a stochastic fluid motion. This model, analogous to Fick’s law of diffusion, is described by the material balance for the tracer [5,61:
6c St-
-
6C -ws;+“;$
-2
(4)
To estimate the two parameters of the dispersion model, the flow velocity and the dispersion coefficient, a salt tracer is injected at the inlet of the reactor. The conductivity of the liquid is then measured with two conductivity probes installed at a known distance inside the apparatus. The set-up for the measurements is given in Fig. 3.
From the signal of the probe at the inlet of the measuring section the signal of the second probe is calculated using the transfer function g(t) = i (-$$J’* and the convolution
c,,,(t) =
exp( -(L~~z~t)2) integral
c,“(t)) g(t - t’) dt’
(6)
a
The flow velocity and the dispersion coefficient are varied until the signal at the outlet can be calculated from the signal at the inlet of the measuring section with a minimum deviation [6]. Equation (5) is bound by the following conditions [ 71: ~ the liquid phase is totally mixed in the radial direction; _ the mixing parameters are constant; _ the liquid and the tracer exhibit the same flow behaviour; ~ the apparatus is a long one-dimensional reactor; _ there is no chemical reaction producing or consuming the tracer; - the concentration of the tracer can be measured easily and reliably. In a multiphase flow, mixing is induced mainly by the dispersed phase carrying the continuous phase through the apparatus. Thus, the mixing in a multiphase flow depends on other mechanisms than those described by the one-dimensional dispersion model. Therefore, the results of the measurements in a multiphase flow based on the one-dimensional dispersion model have to be used carefully.
4. Gas hold-up
To measure the gas hold-up, two methods were used. For calculating the gas hold-up with the first method, the difference between the height of the two-phase mixture during operation and the height of the pure water after turning off the reactor pump is measured: E = Ah/H,
(7)
The second method is the differential pressure method. According to this method, the pressure difference between two measuring points is measured with a differential pressure meter. The experimental set-up for a vertical tube is given in Fig. 4. The two pipes which connect the apparatus and the differential pressure meter are filled with pure liquid. The gas hold-up can be calculated from the pressure difference between the two measuring points,
H7
h
, ti
(8) when the pressure drop due to friction and acceleration is negligible [6]. If the differential pressure is measured with an electronic device, the signals of this device can be recorded and then processed by a personal computer.
5. Application
of the measuring
device
The measuring device for the determination of the hydrodynamic parameters was used successfully in investigating a jet-driven loop reactor [8]. During these investigations, the gas hold-up, the bubble size distribution and the liquid recycle rate were estimated. To
flow direction
Fig. 4.
Differential
pressure
method.
Fig. 5. Compact reactor.
evaluate the liquid recycle rate, the residence time density function was measured. The data were collected with the computer-supported measuring device, developed at the Mass Transfer Laboratories of the Technical University of Clausthal, and further processed using computer programs based on mathematical models. 5.1. Compact reactor The compact reactor is a jet-driven loop reactor aerated at the top. This reactor is shown in Fig. 5. The gas and the liquid are fed through a two-phase nozzle at the top of the apparatus. This nozzle can be used as an injector where the gas is fed under pressure, or as an ejector where the gas is sucked from the environment under the influence of the vacuum induced inside the nozzle [g- lo]. The two-phase mixture flows downwards through the draft tube driven by the liquid jet. At the bottom of the reactor, a part of the liquid is sucked out at a point under a baffle plate. The other part is diverted, together with the gas, into the annular space and flows to the top of the reactor. At the top, a part of the gas leaves the apparatus. The other part is directed, together with the liquid, into the draft tube and starts another circulation through the reactor. The buoyancy force of the bubbles inside the draft tube is opposite to the flow direction. Therefore the gas accumulates inside the draft tube. In the annular space, the direction of the buoyancy force of the bubbles is the same as the flow direction. Therefore the bubbles move fast to the top of the reactor. The gas hold-up in the
92 compressed
Fig. 6. Experimental
air
set-up.
annular space is always smaller than in the draft tube. The result is a difference in the values of the gas hold-up between the annular space and the draft tube. For the design and scale-up of the compact reactor, the flow rate of the gas sucked from the environment using the nozzle as an ejector, the liquid recycle rate, the gas hold-up and the bubble size distribution must be known. These parameters determine the mass transfer from the gas to the liquid phase and the residence time behaviour of the apparatus. 5.2. Experimental set -up The experimental set-up is given in Fig. 6. The main part of the set-up is the compact reactor (CR) with a volume of 120 1. For the measurements, an air/water system was used. The air was sucked from the environment, that is* the two-phase nozzle was used as an ejector. The flow rate of the air through the nozzle was measured with the caloric flowmeter (DM), which induces a very small pressure drop. So the flow rate of the air sucked from the environment was not influenced by the measuring device [9]. The mean gas hold-up was determined by measuring the difference between the height of the two-phase mixture during operation and the height of the pure liquid after turning off the reactor pump. The gas hold-up in the annular space was measured using an electronic differential pressure meter (DP). The bubble size distribution was measured at three points in the annular space with the photoelectric suction probe (BSD). The liquid recycle rate was evaluated with both the one measuring point and the two measuring points method. For each method, a salt tracer was injected into the liquid near the two-phase nozzle. For that
purpose, a tank made of steel was filled with a solution of NaCl in tap water. The concentration of the salt solution was 300 g/l. The steel tank was put under pressure with air taken from the compressed air mains. The pressure inside the steel tank was about 2 bar higher than the pressure in the liquid near the twophase nozzle. An electromagnetic valve is installed at the bottom of the steel tank. This was opened and closed by a computer. To determine the liquid recycle rate with the two measuring points method, the conductivity of the liquid was measured at two points in the annular space. The signals from the two probes (CP) were then processed with a computer program based on the one-dimensional dispersion model. The dispersion coefficient and the flow velocity in the annular space were calculated using a mathematical optimization procedure. The liquid flow rate in the annular space was then calculated from the flow velocity, the cross-sectional area of the annular space and the gas hold-up inside the annular space. During the measurements with the two measuring points method, the plant was operated in a small closed loop. Salt, sucked from the bottom of the reactor and recycled through the nozzle, did not affect the measurements The water was pumped from the bottom of the reactor through the heat exchanger (HE), the mohno pump (MP) and the flowmeter (FM) to the two-phase nozzle. The heat exchanger was used to set the temperature of the water at 20 “C. The liquid flow rate was varied by means of the mohno pump by changing the number of revolutions per minute and measured by the flowmeter. During the measurements with the one measuring point method, the conductivity was measured at the outlet of the reactor (CP). The plant was operated in a large loop. The residence time density function of the compact reactor was measured. Therefore, it was not allowed to recycle the salt sucked off at the bottom of the reactor. The water from the reactor flowed into one of the tanks (T) and the pump sucked pure water from the other tank. Thus, during the measurement of the residence time density function, no salt was recycled into the reactor. The measured residence time density function was compared with an appropriate mathematical model for the residence time behaviour. One of the parameters of this mathematical model is the liquid recycle rate. 5.3. Gas hold-up The gas hold-up in the annular space, measured with the differential pressure method, is plotted against the volumetric power input in Fig. 7 for two diameters of the draft tube. The volumetric power input is the kinetic power of the liquid jet related to the volume of the reactor.
93
2.0
2.5
3.0
(t/Vl/kWm-'
Fig. 7. Gas hold-up power inputs.
0.
in the annular
Du/OR=0.60
Dpld,= l&S
space for various
AT/A&-
volumetric
1.2
0.6
0
0
0.5
10
Fig. 8. Air flow rate for various
1.5
2.0
volumetric
3.0 2.5 (i/V)/ kWm-'
power
inputs.
The gas hold-up increases with increasing power input and decreasing diameter of the draft tube. The increase of the gas hold-up with increasing power input is induced by the higher flow rate of the air sucked from the environment. The air flow rate for various volumetric power inputs is shown in Fig. 8. With increasing volumetric power input, the liquid flow rate through the nozzle increases. Therefore, air at a higher flow rate can be sucked from the environment and transported through the draft tube to the bottom of the reactor. Because of the increase in liquid velocity inside the draft tube with decreasing diameter of the draft tube, the air flow rate inside the draft tube with the smaller diameter is higher. During operation with the draft tube with the diameter ratio, D,/D, = 0.60, the flow rate of the air sucked from the environment is limited by the air transport from the top to the bottom of the reactor. The maximum air flow rate can be calculated with a mathematical model describing the fluid-dynamics of the compact reactor [ 111. 5.4. Bubble size The computer program calculates the density distribution of the bubble number, the bubble surface and
the bubble volume, and gives information about the velocity inside the capillary, the total number of bubbles sucked from the apparatus and the kinds of error during the measurements. Theoretical density functions are fitted to the measured distributions. For example, the results of a bubble size distribution measurement are given in Fig. 9. Figure 9 shows the measured qo, q2 and q3 distributions, the calculated logarithmic normal distribution using a mathematical optimization procedure and the mean values of the three bubble size distributions. Figure 10 shows three density distributions of the bubble volume measured at the same time in the annular space of the compact reactor. The distance between the measuring points and the bottom of the reactor increases from the bottom to the top of the Figure. The shape of the distributions does not change inside the annular space. The increase in the mean value of the distributions is induced by the change in the static pressure. Therefore, coalescence or dispersion of bubbles does not occur or compensate each other. 5.5. Liquid recycle rate To get information about the flow inside the compact reactor from the measured residence time density functions, an appropriate mathematical model was developed for the residence time behaviour of the compact reactor. The model is shown in Fig. 11. The residence time behaviour of the draft tube and the annular space is given by the residence time behaviour of a cascade of stirred tank reactors. The two cascades are connected by the liquid recycle rate [8, 121. The material balance for the tracer was solved with the Laplace transformation. The number of tanks in the draft tube, the number of tanks in the annular space and the liquid recycle rate are the parameters of the mathematical model. These parameters can be calculated from the measured residence time density function by fitting the theoretical density function to the measured density function. A measured and a calculated residence time density function are given in Fig. 12. The results of the curve fitting, the number of tanks in the draft tube and in the annular space as well as the liquid recycle rate are given in the Figure. The residence time behaviour of the compact reactor can be described with the above model. The measured and calculated residence time distributions agree with one another particularly well at small values of the time. This good agreement occurs because the values of the density function are identified as more significant for short times. The liquid recycle rate depends on the time differences between the relative maxima of the density curve. These maxima can be identified clearly only for short times because of the relatively high salt concentration in the outlet of the reactor. If the
, o=L.2L mm LllwL
0.2
0.2
1.6
3.2
46
6.L /“6k0 d
1.6
3.2
L.0
6.1.
8.0 d/mm
Fig. 9. Bubble size distribution at one measuring point in the annular space of the compact reactor
0.L 0.3 0.2 0.1
0.0
vT
0.4
Fig. 1 I. Model reactor.
0.3
for the residence
time behaviour
of the compact
0.2
0.1 0.0
0.0 1.0 2.0 30
L.0 5.0 6.0 70 dv/
Fig. 10. Bubble
size distributions
8.0 9.0 10.0
mm
in the annular
space.
gas hold-up inside the apparatus is very high, the relative maxima cannot be identified for longer times, because the liquid phase inside the reactor is well mixed.
The liquid recycle rate is plotted against the volumetric power input in Fig. 13 for one diameter of the draft tube and for one geometry of the two-phase nozzle. In this figure the recycle rates measured with both the one measuring point method and.the two measuring points method are given. The liquid recycle rate is nearly independent of the volumetric power input. The liquid recycle rates measured with both methods agree well. If the gas hold-up is higher than lo%, the liquid recycle rate cannot be measured with the two measuring points method. Because of the high gas hold-up, the signals of
95 l.ZOr
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
@I-
Fig. 12. Measured
and calculated
residence
time density functions.
ti/V)lkWm-’
Fig. 13. Liquid
recycle rate
for various volumetric power inputs.
the probes are disturbed and cannot be processed further with the one-dimensional dispersion model. The pressure drop of the two-phase flow through the compact reactor is given by the pressure drop induced by the difference between the gas hold-up inside the annular space and that inside the draft tube and the pressure drop caused by friction. The flow rate of air sucked from the environment increases with increasing power input. Therefore, the gas hold-up increases and the difference between the gas hold-up in the annular space and that in the draft tube rises. This means, that the pressure drop induced by the difference between the gas hold-ups increases at higher volumetric power input. So the power input by the liquid jet, which can be used to compensate the pressure drop caused by friction, is nearly constant. Therefore, the liquid recycle rate must be nearly independent of the volumetric power input.
6. Conclusions At the Mass Transfer Laboratories of the Technical University of Clausthal a measuring device was developed for the determination of the bubble size distribu-
tion, the gas hold-up and the residence time behaviour of the liquid in gas/liquid contact apparatus. The data are recorded by a personal computer and further processed with computer programs based on mathematical models. The bubble size distribution is measured with the photoelectric suction probe. The measuring device offers the possibility of determining bubble size distributions simultaneously at five measuring points. Errors during the measurements are recorded to show the reliability of the collected data. The gas hold-up is measured with the differential pressure method. For the determination of the residence time behaviour, two methods are available, the one measuring point and the two measuring points method. For both methods a salt tracer is used and the conductivity of the liquid is measured with conductivity probes. The two measuring points method is used in long one-dimensional apparatus and yields the parameters of the one-dimensional dispersion model, the flow velocity and the dispersion coefficient. The residence time density function is measured with the one measuring point method. If a mathematical model for the residence time behaviour of the apparatus is available, the parameters of this model can be calculated from the residence time density function. To demonstrate the applicability of the measuring device, some experimental results in a jet-driven loop reactor are presented and discussed.
Nomenclature
A a 6 DZ d d 1.0 d 1.* d I, 3 i g g(t) H Ah L I n AP 4
cross-sectional area, m2 distance between two light barriers, m tracer concentration, kg/m3 diameter, m dispersion coefficient, m*/s diameter, m mean diameter of density distribution, of bubble number, m mean diameter of density distribution of bubble surface, m mean diameter of density distribution of bubble volume, m power input, W gravitational acceleration, m/s2 transfer function, s-’ Height, m difference between height of two-phase mixture and pure liquid, m length, m length of slug, m number of stirred tanks pressure drop, Pa density distribution, m- ’
96 t t t’
V P W Z
E 8 P
References
time, s mean residence time, s time, s volume of reactor, m3 flow rate, m3/s velocity, m/s axial coordinate, m gas hold-up = t/t dimensionless density, kg/m3
time
Zndices B G
in kap L M t; out R RR T U
urn ; 0 2 3
19 . . . 94
bottom of reactor gas, aeration tube inlet into measuring section capillary liquid measuring section, measuring mixture total mass related to liquid reactor outlet of measuring section reactor annular space liquid jet, liquid jet nozzle draft tube recycle corresponding sphere two-phase mixture bubble number bubble surface bubble volume counter
point volume
inside
1 E. Aufderheide, D. Niebuhr and A. Vogelpohl, Die Messung von TropfengrBBen in pulsierten Siebboden-Extraktionskolonnen mit der Absaugsonde, Tech. Messen, 50 (1983) 237-241. 2 T. Pilhofer, H. Jekat, H.-D. Miller and J. H. Miiller, Messung der GrijBenverteilung fluider Partikeln in Blasenslulen und Spriihkolonnen, Chem:Ing.-Tech., 46 (1974) 913. 3 D. Rauen, E. Aufderheide and A. Vogelpohl, Automatischer Abgleich der Absaugsonde zur Tropfengr%enmessung, Techn. Messen, 51 (1984) 409-412. 4 B. Genenger, B. Lohrengel, M. Lorenz and A. Vogelpohl, MeDsystem zur Bestimmung hydrodynamischer Parameter in Mehrphasenstriimungen: Fotoelektrische Absaugsonde Chem.Ing.-Tech., 62 (1990) 862-863. 5 0. Levenspiel, Chemical Reaction Engineering, Wiley, New York, 2nd edn., 1972. 6 M. Lorenz, Untersuchungen zum fluiddynamischen Verhalten von pulsierten Siebboden-Extraktionskolonnen, Ph.D. Thesis, Tech. Univ. Clausthal, 1990. 7 K. Bauckhage, H.-D. Bauermann, E. BlaI3, H. Sauer, M. Stiilting, J. Tenhumberg and H. Wagner, Zur Auslegung von Apparaten der Fliissig/Fliissig-Extraktion, Chem.-Ing.-Tech., 47 (1975) 169-182. 8 B. Lohrengel, Untersuchungen zur Fluiddynamik zwei- und dreiphasig betriebener Schlaufenreaktoren, Ph.D. Thesis, Tech. Univ. Clausthal, 1991. 9 B. Lohrengel and A. Vogelpohl, Auslegung einer im Ejektorbetrieb arbeitenden Zweistoffdiise, Chem.-lng.-Tech., 62 (1990) 338-339. 10 U. Wachsmann, Zur Hydrodynamik strahlgetriebener Schlaufenreaktoren, Ph.D. Thesis, Tech. Univ. Clausthal, 1986. 11 B. Genenger and A. Vogelpohl, Scale-up eines strahlgetriebenen Schlaufenreaktors, Lecture presented at GVC-FachausschuJsitzung “Bioverfahrenstechnik” and DECHEMA Arbeitsausschu&irzung “Technik biologischer Prozesse”, Liineburg, Germany, May 1991. 12 C. G. Sinclair and K. J. McNaughton, The residence time probability density of complex flow systems, Chem. Eng., 20 (1965) 261-264.
Measuring
device for gas/liquid flow
MeI3werterfassungssystem Bernd
Genenger*
Institut ftir Therm&he
Dedicated
to Prof.
87
fiir Gas/Fliissig-Striimungen
and Burkhard Verfahrenstechnik
Dr.-Ing.
Lohrengel
der Technischen
A. Vogelpohl
Universitiit
on the occasion
Clausthal,
Leibnizstr.
15, 3392 ClausthaI-Zellerfeld
(Germany)
of his 6l?th birthday
(Received October 21, 1991; in final form December 5, 1991)
Abstract For the design and scale-up of gas/liquid contact apparatus, the bubble size distribution, the gas hold-up and the residence time behaviour of the liquid phase must be known. A purely theoretical prediction of these hydrodynamic parameters is not possible because of the complex relationships between the fluid dynamics and the properties of the phases, as well as the geometrical and operating parameters. Therefore, a fully automatic measuring device was developed at the Mass Transfer Laboratories of the Technical University of Clausthal, which enables the bubble size distribution to be determined experimentally with a photoelectric suction probe, the gas hold-up with the differential pressure method and the residence time behaviour by measuring the conductivity. Some results of the measurements carried out in a jet-driven loop reactor are presented and discussed to demonstrate the practical application of the measuring device.
Kurzfassung Zur Auslegung und MaBstabsvergrSBerung von Gas/Fliissig-Kontaktapparaten miissen die Blasengriige, der Gasgehalt und das Vermischungsverhalten der fliissigen Phase bekannt sein. Da eine Vorausberechnung aufgrund der komplexen Zusammenhange zwischen den Geometrie- und Betriebsparametern sowie den Stoffdaten einerseits und der Fluiddynamik andererseits nicht moglich ist, wurde am Institut fur Thermische Verfahrenstechnik der TU Clausthal ein MeDwerterfassungssystem entwickelt. Mit diesem Mebwerterfassungssystem kann die Blasengrdge mit der fotoelektrischen Absaugsonde, der Gasgehalt mit der Differenzdruckmethode und das Vermischungsverhdlten mit einer Leitfahigkeitsmessung bestimmt werden. Die Anwendung des Megwerterfassungssystems wird am Beispiel eines strahlgetriebenen Schlaufenreaktors erllutert. Einige Ergebnisse der Messungen an diesem Apparat werden diskutiert.
Synopse
Die volumenbezogene Phasengrenzjltiche in Gas/Flussig-Kontaktapparaten ist durch den Gasgehalt und die BlasengroJe bestimmt. Der Umsatz einer chemischen Reaktion wird vom Vermischungsverhalten der fltissigen Phase beeinfl@t. Die Blasengriipe, der Gasgehalt und das Vermischungsverhalten der fltissigen Phase miissen deshalb fur die Auslegung und die MaJstabsvergroJerung von GaslFliissig-Kontaktapparaten bekannt sein. Da die GroJen nur selten theoretisch vorausberechnet werden kiinnen, wurde am Institut fur Thermische Verfahrenstechnik der TU Clausthal ein MeJwerterfassungssystem endwickelt. Mit diesem Mefiwerterfassungssystem werden
*Author
to whom correspondence
0255-2701/92/$5.00
should be addressed.
die BlasengriJe mit der fotoelektrischen Absaugsonde, der Gasgehalt mit der Dtflerenzdruckmethode und das Vermischungsverhalten durch Leitfahigkeitsmessungen ermittelt. Zur Bestimmung der BlasengriiJBenverteilung wird die in Abb. 1 dargestellte fotoelektrische Absaugsonde eingesetzt. Ein Teil des Zweiphasengemisches wird aus dem Apparat abgesaugt. Die Blasen werden in einer Glaskapillare zu zylindrischen Pfropfen verformt, deren Lange und Geschwindigkeit mit der MeJsonde erfa& werden. Aus den in Abb. 2 gezeigten MeJsignalen wird der Durchmesser der volumengleichen Kugel berechnet. Die Signale von bis zu ftinf Sonden werden automatisch erfaj’t, ausgewertet und wiihrend der Messung auf Fehler iiberpriift. Das Ergebnis einer Messung sind die Anzahl-, die Oberfiichenund die Volumendichteverteilung der Blasen .
0
1992 -
Elsevier Sequoia.
All rights reserved
88 Zur Bestimmung des Vermischungsverhaltens stehen zwei Methoden zur Verftigung, die 1 -MeJ’stellen - und die Z-MeJstellen-Methode. Mit der 1 -MeJstellen-Methode wird die Verweilzeitdichtekurve eines Reaktors gemessen. Der Tracer ist in Form eines Dirac-Impulses am Fliissigkeitseintritt aufzugeben. Diese Methode eignet sich fur Apparate, deren Vermischungsverhalten dem eines Riihrkessels nahe kommt. Sol1 aus der Verweilzeitdichtekurve auf die Striimung im Apparat geschlossen werden, so ist die Verweilzeitdichtekurve mit einem geeigneten Model1 fir das Verweilzeitverhalten zu vergleichen. Das Vermischungsverhalten von Rohrreaktoren wird in vielen Fdllen durch das eindimensionale Dispersionsmodell wiedergegeben. Zur Bestimmung der beiden Parameter des Dispersionsmodells, der Stromungsgeschwindigkeit und des Dispersionskoefhzienten, wird am Fliissigkeitseintritt in den Reaktor ein Salz-Tracer injiziert. Im Apparat wird die Leitfahigkeit der Jliissigen Phase, wie in Abb. 3 gezeigt, mit zwei Leitjshigkeitssonden am gemessen. Aus dem Signal der Leitf~higkeitssonde Eintritt in die Mefjstrecke wird das Signal der zweiten Elektrode mit Hilfe der iibertragungsfunktion (Gl. 5) und des Faltungsintegrals (Gl. 6) berechnet. Die Parameter des eindimensionalen Dispersionsmodells werden mit Hilfe einer Anpassungsrechnung solange variiert, bis das Ausgangssignal mit einer miiglichst kleinen Abweichung aus dem Eingangssignal berechnet werden kann. Der Gasgehalt wird mit der in Abb. 4 gezeigten Dtyerenzdruckmethode bestimmt. Die Signale des elektronischen Dtflierenzdruckuufnehmers werden digital erfapt und mit Gl. 8 in den Gasgehult umgerechnet. Die Einsatzfiihigkeit des MeJwerterfassungssystems wird anhand von MeJwerten demonstriert, die an einem strahlgetriebenen Schlaufenreaktor uufgenommen wurden, der in Abb. 5 dargestellt ist. Ergebnisse der Gasgehaltsmessungen an diesem Reaktor sind in Abb. 7 aufgetragen. Abb. 10 zeigt BlasengroJenverteilungen, die an verschiedenen Orten im Ringraum des Schlaufenreaktors gemessen wurden. Der im Reaktor umlaufende Fliissigkeitsvolumenstrom wurde mit der 1 -MeJstellenund der 2-MeJstellenMethode bestimmt. Bei den Messungen mit der 2MeJstellen-Methode wurden zwei Leitftihigkeitssonden im Ringraum des Reaktors installiert. Zur Bestimmung des umlaufenden Fliissigkeitsvolumenstroms mit der IMeJstellen-Methode wurde die Leitfiihigkeit im Fliissigkeitsablauf des Apparats gemessen und in die Verweilzeitdichtekurve umgerechnet. Die Verweilzeitdichtekurve wurde mit dem in Abb. 11 dargestellten Model1 fur das Verweilzeitverhalten des strahlgetriebenen Schlaufenreaktors verglichen. Einer der Parameter dieses Modells ist der im Reaktor umlaufende Fliissigkeitsvolumenstrom. Die Ergebnisse der Messungen mit der I-MeJstellen13 und der 2-MeBstellen-Methode sind in Abb.
dargestellt. Beide Methoden liefern iibereinstimmende Werte ftir den umlaufenden Fliissigkeitsvolumenstrom.
1. Introduction For the design and scale-up of gas/liquid contact apparatus, the bubble size distribution, the gas hold-up and the residence time behaviour of both phases must be known. In most cases, the purely theoretical prediction of these parameters is not possible because of the complex relationships between the properties of the phases and the fluid dynamics, as well as the geometrical and operating parameters. Therefore, the fluiddynamic parameters of interest have to be measured. At the Mass Transfer Laboratories of the Technical University of Clausthal a fully automatic measuring device was developed to determine experimentally the bubble size distribution, the gas hold-up and the residence time behaviour of the liquid phase in several types of gas/liquid contact apparatus. The measured values are recorded by a personal computer and then processed using computer programs based on mathematical models. To demonstrate the practical application of the measuring device, some results of the measurements carried out in a jet-driven loop reactor are presented and discussed.
2. Bubble size distribution The bubble size distribution is measured with the photoelectric suction probe, the principle of which is given in Fig. 1 [l-3]. A sample from the gas/liquid contact apparatus is sucked through a glass capillary at a controlled flow rate. One end of the capillary is funnel-shaped. The bubbles, which are sucked along together with the continuous phase, are transformed into cylindrical slugs inside the capillary. The velocity and length of these slugs are measured with the measuring probe, which encloses the capillary. The measuring probe consists of two light barriers, made up of an incandescent lamp and a phototransistor. The light barriers are placed 2 mm apart at an angle of 90” relative to each other. The electrical resistance of the phototransistor and the corresponding light intensity are dependent on the refractive index of the medium between the incandescent lamp and the transistor. A signal from the photoelectric suction probe is shown in Fig. 2. The measured signal must be triggered for further processing. For this purpose a triggering threshold is fixed, so that the beginning and end of a slug can be detected when the threshold is exceeded.
89
are calculated. If the whole cross-section lary is covered by the slug, the diameter sponding sphere can be calculated from
of the capilof the corre-
l/3
d,r=
(3)
During the measurement the recorded data are checked on-line for their correctness. Incorrect data are marked and not used for further processing. The number of wrong measurements and the kind of error are registered in the record so that the quality of the measurement can be assessed. For plotting the bubble size distribution and calculating the mean bubble diameter only those data are used which fulfil the following criteria. (1) None of the times t, to t4 is negative. Negative times are obtained if a very small bubble does not move along the axis of the capillary or if the bubble measured at each light barrier is not the same one. (2) The difference between the velocities of the slugs inside the capillary calculated from t, and t, must be less than 15%. This value was estimated experimentally
Fig. 1. Photoelectric suction probe.
real signal
-light barner
; dkap21 ( >
1
111. light barrier
(3) The lengths of the slugs calculated from t, and t, differ from each other by less than half the capillary diameter [ 11. (4) The velocity of the slugs inside the capillary must be in a range determined by the physical properties of the two phases. For a water/air system the velocity of the slugs must be in the range 1.3-1.7 m/s. Jf the velocity is too small, the probe signals cannot be processed, because oscillations in the signals are induced when the beginning or end of a slug passes the light barriers. If the velocity inside the capillary is too high, the slugs will be slashed inside the capillary. (5) Large slugs, which are longer than 150 mm, cannot be sucked through without destroying the bubble. Such values for the length are determined when the end of a slug is not detected correctly. (6) The diameter of a bubble must be greater than the bubble size half cannotthe becapillary measureddiameter. reliably, Otherwise,
2
&iggmg_
-___~--__
triggering
---
threshold
triggered signal
Fig. 2. Processing of the probe signals.
The triggered signals of both light barriers are then processed electronically. From the measured times t, to t, the velocity of the slugs in the capillary wG = a/t, = a/t,
(1)
and the length of the slugs I= w,t, = MjC,t2
(2)
The diameter of the capillary is chosen according to the last two criteria. Capillaries with an inner diameter between 0.4 and 2.2 mm are used [4]. With these capillaries, bubble diameters between 0.2 and 11 mm can be measured. Bubble diameters in this range can be evaluated with a maximum deviation of + 10%. This deviation results from the film of the continuous phase between the bubble and the capillary wall. Because of this film, the length of the cylindrical slugs in the capillary is increased and too large a diameter is calculated for the corresponding sphere. If the deviation is too large, the photoelectric suction probe must be calibrated with bubbles of known diameter [4].
90
To apply the photoelectric suction probe in a two- or three-phase flow the following criteria must be fulfilled. (1) Light from the incandescent lamp must reach the phototransistor. This criterion is fulfilled in transparent liquids and fermentation broths up to a concentration of 10 g/l of biomass. (2) The velocity inside the capillary must be higher than the velocity of the liquid flow near the funnelshaped end of the glass capillary. If the flow velocity is higher the bubbles cannot be sucked out. (3) The gas hold-up must be smaller than about 25%. If the gas hold-up is higher, coalescence of the bubbles occurs at the funnel-shaped end of the capillary. (4) Solid particles in a three-phase flow must be smaller in diameter than the inner diameter of the capillary. Otherwise, the capillary is blocked by solid particles.
second
measuring
pod
-Ll
first
measuring
point
--El
flow
dlrectmn
Fig. 3. Two measuring points method.
3. Residence time behaviour 3.1. One measuring point method
To determine the residence time behaviour with the one measuring point method, a salt tracer is added at the inlet of the liquid. The salt tracer must be injected in such a way that the signal at the inlet has the shape of a Dirac function. The conductivity of the liquid at the outlet is measured with a conductivity probe. From this probe’s signal, the residence time density function is calculated. This method is used to determine the residence time behaviour of apparatus in which the residence time behaviour is close to that of a stirred tank reactor. If further information about the flow structure inside the apparatus is required, the residence time density function has to be compared with that obtained from a model for the residence time behaviour. 3.2. Two measuring points method The residence time behaviour of tubular reactors can usually be described by the one-dimensional dispersion model. This model is based on the idea that the idealized behaviour of the flow is superposed by a stochastic fluid motion. This model, analogous to Fick’s law of diffusion, is described by the material balance for the tracer [5,61:
6c St-
-
6C -ws;+“;$
-2
(4)
To estimate the two parameters of the dispersion model, the flow velocity and the dispersion coefficient, a salt tracer is injected at the inlet of the reactor. The conductivity of the liquid is then measured with two conductivity probes installed at a known distance inside the apparatus. The set-up for the measurements is given in Fig. 3.
From the signal of the probe at the inlet of the measuring section the signal of the second probe is calculated using the transfer function g(t) = i (-$$J’* and the convolution
c,,,(t) =
exp( -(L~~z~t)2) integral
c,“(t)) g(t - t’) dt’
(6)
a
The flow velocity and the dispersion coefficient are varied until the signal at the outlet can be calculated from the signal at the inlet of the measuring section with a minimum deviation [6]. Equation (5) is bound by the following conditions [ 71: ~ the liquid phase is totally mixed in the radial direction; _ the mixing parameters are constant; _ the liquid and the tracer exhibit the same flow behaviour; ~ the apparatus is a long one-dimensional reactor; _ there is no chemical reaction producing or consuming the tracer; - the concentration of the tracer can be measured easily and reliably. In a multiphase flow, mixing is induced mainly by the dispersed phase carrying the continuous phase through the apparatus. Thus, the mixing in a multiphase flow depends on other mechanisms than those described by the one-dimensional dispersion model. Therefore, the results of the measurements in a multiphase flow based on the one-dimensional dispersion model have to be used carefully.
4. Gas hold-up
To measure the gas hold-up, two methods were used. For calculating the gas hold-up with the first method, the difference between the height of the two-phase mixture during operation and the height of the pure water after turning off the reactor pump is measured: E = Ah/H,
(7)
The second method is the differential pressure method. According to this method, the pressure difference between two measuring points is measured with a differential pressure meter. The experimental set-up for a vertical tube is given in Fig. 4. The two pipes which connect the apparatus and the differential pressure meter are filled with pure liquid. The gas hold-up can be calculated from the pressure difference between the two measuring points,
H7
h
, ti
(8) when the pressure drop due to friction and acceleration is negligible [6]. If the differential pressure is measured with an electronic device, the signals of this device can be recorded and then processed by a personal computer.
5. Application
of the measuring
device
The measuring device for the determination of the hydrodynamic parameters was used successfully in investigating a jet-driven loop reactor [8]. During these investigations, the gas hold-up, the bubble size distribution and the liquid recycle rate were estimated. To
flow direction
Fig. 4.
Differential
pressure
method.
Fig. 5. Compact reactor.
evaluate the liquid recycle rate, the residence time density function was measured. The data were collected with the computer-supported measuring device, developed at the Mass Transfer Laboratories of the Technical University of Clausthal, and further processed using computer programs based on mathematical models. 5.1. Compact reactor The compact reactor is a jet-driven loop reactor aerated at the top. This reactor is shown in Fig. 5. The gas and the liquid are fed through a two-phase nozzle at the top of the apparatus. This nozzle can be used as an injector where the gas is fed under pressure, or as an ejector where the gas is sucked from the environment under the influence of the vacuum induced inside the nozzle [g- lo]. The two-phase mixture flows downwards through the draft tube driven by the liquid jet. At the bottom of the reactor, a part of the liquid is sucked out at a point under a baffle plate. The other part is diverted, together with the gas, into the annular space and flows to the top of the reactor. At the top, a part of the gas leaves the apparatus. The other part is directed, together with the liquid, into the draft tube and starts another circulation through the reactor. The buoyancy force of the bubbles inside the draft tube is opposite to the flow direction. Therefore the gas accumulates inside the draft tube. In the annular space, the direction of the buoyancy force of the bubbles is the same as the flow direction. Therefore the bubbles move fast to the top of the reactor. The gas hold-up in the
92 compressed
Fig. 6. Experimental
air
set-up.
annular space is always smaller than in the draft tube. The result is a difference in the values of the gas hold-up between the annular space and the draft tube. For the design and scale-up of the compact reactor, the flow rate of the gas sucked from the environment using the nozzle as an ejector, the liquid recycle rate, the gas hold-up and the bubble size distribution must be known. These parameters determine the mass transfer from the gas to the liquid phase and the residence time behaviour of the apparatus. 5.2. Experimental set -up The experimental set-up is given in Fig. 6. The main part of the set-up is the compact reactor (CR) with a volume of 120 1. For the measurements, an air/water system was used. The air was sucked from the environment, that is* the two-phase nozzle was used as an ejector. The flow rate of the air through the nozzle was measured with the caloric flowmeter (DM), which induces a very small pressure drop. So the flow rate of the air sucked from the environment was not influenced by the measuring device [9]. The mean gas hold-up was determined by measuring the difference between the height of the two-phase mixture during operation and the height of the pure liquid after turning off the reactor pump. The gas hold-up in the annular space was measured using an electronic differential pressure meter (DP). The bubble size distribution was measured at three points in the annular space with the photoelectric suction probe (BSD). The liquid recycle rate was evaluated with both the one measuring point and the two measuring points method. For each method, a salt tracer was injected into the liquid near the two-phase nozzle. For that
purpose, a tank made of steel was filled with a solution of NaCl in tap water. The concentration of the salt solution was 300 g/l. The steel tank was put under pressure with air taken from the compressed air mains. The pressure inside the steel tank was about 2 bar higher than the pressure in the liquid near the twophase nozzle. An electromagnetic valve is installed at the bottom of the steel tank. This was opened and closed by a computer. To determine the liquid recycle rate with the two measuring points method, the conductivity of the liquid was measured at two points in the annular space. The signals from the two probes (CP) were then processed with a computer program based on the one-dimensional dispersion model. The dispersion coefficient and the flow velocity in the annular space were calculated using a mathematical optimization procedure. The liquid flow rate in the annular space was then calculated from the flow velocity, the cross-sectional area of the annular space and the gas hold-up inside the annular space. During the measurements with the two measuring points method, the plant was operated in a small closed loop. Salt, sucked from the bottom of the reactor and recycled through the nozzle, did not affect the measurements The water was pumped from the bottom of the reactor through the heat exchanger (HE), the mohno pump (MP) and the flowmeter (FM) to the two-phase nozzle. The heat exchanger was used to set the temperature of the water at 20 “C. The liquid flow rate was varied by means of the mohno pump by changing the number of revolutions per minute and measured by the flowmeter. During the measurements with the one measuring point method, the conductivity was measured at the outlet of the reactor (CP). The plant was operated in a large loop. The residence time density function of the compact reactor was measured. Therefore, it was not allowed to recycle the salt sucked off at the bottom of the reactor. The water from the reactor flowed into one of the tanks (T) and the pump sucked pure water from the other tank. Thus, during the measurement of the residence time density function, no salt was recycled into the reactor. The measured residence time density function was compared with an appropriate mathematical model for the residence time behaviour. One of the parameters of this mathematical model is the liquid recycle rate. 5.3. Gas hold-up The gas hold-up in the annular space, measured with the differential pressure method, is plotted against the volumetric power input in Fig. 7 for two diameters of the draft tube. The volumetric power input is the kinetic power of the liquid jet related to the volume of the reactor.
93
2.0
2.5
3.0
(t/Vl/kWm-'
Fig. 7. Gas hold-up power inputs.
0.
in the annular
Du/OR=0.60
Dpld,= l&S
space for various
AT/A&-
volumetric
1.2
0.6
0
0
0.5
10
Fig. 8. Air flow rate for various
1.5
2.0
volumetric
3.0 2.5 (i/V)/ kWm-'
power
inputs.
The gas hold-up increases with increasing power input and decreasing diameter of the draft tube. The increase of the gas hold-up with increasing power input is induced by the higher flow rate of the air sucked from the environment. The air flow rate for various volumetric power inputs is shown in Fig. 8. With increasing volumetric power input, the liquid flow rate through the nozzle increases. Therefore, air at a higher flow rate can be sucked from the environment and transported through the draft tube to the bottom of the reactor. Because of the increase in liquid velocity inside the draft tube with decreasing diameter of the draft tube, the air flow rate inside the draft tube with the smaller diameter is higher. During operation with the draft tube with the diameter ratio, D,/D, = 0.60, the flow rate of the air sucked from the environment is limited by the air transport from the top to the bottom of the reactor. The maximum air flow rate can be calculated with a mathematical model describing the fluid-dynamics of the compact reactor [ 111. 5.4. Bubble size The computer program calculates the density distribution of the bubble number, the bubble surface and
the bubble volume, and gives information about the velocity inside the capillary, the total number of bubbles sucked from the apparatus and the kinds of error during the measurements. Theoretical density functions are fitted to the measured distributions. For example, the results of a bubble size distribution measurement are given in Fig. 9. Figure 9 shows the measured qo, q2 and q3 distributions, the calculated logarithmic normal distribution using a mathematical optimization procedure and the mean values of the three bubble size distributions. Figure 10 shows three density distributions of the bubble volume measured at the same time in the annular space of the compact reactor. The distance between the measuring points and the bottom of the reactor increases from the bottom to the top of the Figure. The shape of the distributions does not change inside the annular space. The increase in the mean value of the distributions is induced by the change in the static pressure. Therefore, coalescence or dispersion of bubbles does not occur or compensate each other. 5.5. Liquid recycle rate To get information about the flow inside the compact reactor from the measured residence time density functions, an appropriate mathematical model was developed for the residence time behaviour of the compact reactor. The model is shown in Fig. 11. The residence time behaviour of the draft tube and the annular space is given by the residence time behaviour of a cascade of stirred tank reactors. The two cascades are connected by the liquid recycle rate [8, 121. The material balance for the tracer was solved with the Laplace transformation. The number of tanks in the draft tube, the number of tanks in the annular space and the liquid recycle rate are the parameters of the mathematical model. These parameters can be calculated from the measured residence time density function by fitting the theoretical density function to the measured density function. A measured and a calculated residence time density function are given in Fig. 12. The results of the curve fitting, the number of tanks in the draft tube and in the annular space as well as the liquid recycle rate are given in the Figure. The residence time behaviour of the compact reactor can be described with the above model. The measured and calculated residence time distributions agree with one another particularly well at small values of the time. This good agreement occurs because the values of the density function are identified as more significant for short times. The liquid recycle rate depends on the time differences between the relative maxima of the density curve. These maxima can be identified clearly only for short times because of the relatively high salt concentration in the outlet of the reactor. If the
, o=L.2L mm LllwL
0.2
0.2
1.6
3.2
46
6.L /“6k0 d
1.6
3.2
L.0
6.1.
8.0 d/mm
Fig. 9. Bubble size distribution at one measuring point in the annular space of the compact reactor
0.L 0.3 0.2 0.1
0.0
vT
0.4
Fig. 1 I. Model reactor.
0.3
for the residence
time behaviour
of the compact
0.2
0.1 0.0
0.0 1.0 2.0 30
L.0 5.0 6.0 70 dv/
Fig. 10. Bubble
size distributions
8.0 9.0 10.0
mm
in the annular
space.
gas hold-up inside the apparatus is very high, the relative maxima cannot be identified for longer times, because the liquid phase inside the reactor is well mixed.
The liquid recycle rate is plotted against the volumetric power input in Fig. 13 for one diameter of the draft tube and for one geometry of the two-phase nozzle. In this figure the recycle rates measured with both the one measuring point method and.the two measuring points method are given. The liquid recycle rate is nearly independent of the volumetric power input. The liquid recycle rates measured with both methods agree well. If the gas hold-up is higher than lo%, the liquid recycle rate cannot be measured with the two measuring points method. Because of the high gas hold-up, the signals of
95 l.ZOr
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
@I-
Fig. 12. Measured
and calculated
residence
time density functions.
ti/V)lkWm-’
Fig. 13. Liquid
recycle rate
for various volumetric power inputs.
the probes are disturbed and cannot be processed further with the one-dimensional dispersion model. The pressure drop of the two-phase flow through the compact reactor is given by the pressure drop induced by the difference between the gas hold-up inside the annular space and that inside the draft tube and the pressure drop caused by friction. The flow rate of air sucked from the environment increases with increasing power input. Therefore, the gas hold-up increases and the difference between the gas hold-up in the annular space and that in the draft tube rises. This means, that the pressure drop induced by the difference between the gas hold-ups increases at higher volumetric power input. So the power input by the liquid jet, which can be used to compensate the pressure drop caused by friction, is nearly constant. Therefore, the liquid recycle rate must be nearly independent of the volumetric power input.
6. Conclusions At the Mass Transfer Laboratories of the Technical University of Clausthal a measuring device was developed for the determination of the bubble size distribu-
tion, the gas hold-up and the residence time behaviour of the liquid in gas/liquid contact apparatus. The data are recorded by a personal computer and further processed with computer programs based on mathematical models. The bubble size distribution is measured with the photoelectric suction probe. The measuring device offers the possibility of determining bubble size distributions simultaneously at five measuring points. Errors during the measurements are recorded to show the reliability of the collected data. The gas hold-up is measured with the differential pressure method. For the determination of the residence time behaviour, two methods are available, the one measuring point and the two measuring points method. For both methods a salt tracer is used and the conductivity of the liquid is measured with conductivity probes. The two measuring points method is used in long one-dimensional apparatus and yields the parameters of the one-dimensional dispersion model, the flow velocity and the dispersion coefficient. The residence time density function is measured with the one measuring point method. If a mathematical model for the residence time behaviour of the apparatus is available, the parameters of this model can be calculated from the residence time density function. To demonstrate the applicability of the measuring device, some experimental results in a jet-driven loop reactor are presented and discussed.
Nomenclature
A a 6 DZ d d 1.0 d 1.* d I, 3 i g g(t) H Ah L I n AP 4
cross-sectional area, m2 distance between two light barriers, m tracer concentration, kg/m3 diameter, m dispersion coefficient, m*/s diameter, m mean diameter of density distribution, of bubble number, m mean diameter of density distribution of bubble surface, m mean diameter of density distribution of bubble volume, m power input, W gravitational acceleration, m/s2 transfer function, s-’ Height, m difference between height of two-phase mixture and pure liquid, m length, m length of slug, m number of stirred tanks pressure drop, Pa density distribution, m- ’
96 t t t’
V P W Z
E 8 P
References
time, s mean residence time, s time, s volume of reactor, m3 flow rate, m3/s velocity, m/s axial coordinate, m gas hold-up = t/t dimensionless density, kg/m3
time
Zndices B G
in kap L M t; out R RR T U
urn ; 0 2 3
19 . . . 94
bottom of reactor gas, aeration tube inlet into measuring section capillary liquid measuring section, measuring mixture total mass related to liquid reactor outlet of measuring section reactor annular space liquid jet, liquid jet nozzle draft tube recycle corresponding sphere two-phase mixture bubble number bubble surface bubble volume counter
point volume
inside
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