Znd. Eng. Chem. Res. 1987,26, 2185-2192 q1 = out-leakage, mm3 qz = in-leakage, mm3
Lubrication and Wear, University of Houston, 1963. Hamrock, B. J.; Dowson, D. Trans. ASME, Ser. F 1978, 100, 236-245. Hooke, G. J.; Lines, D. J.; O’Donoghue J. P. “Elastohydrodynamic Lubrication of O-ring Seal”, Proc. Inst. Mech. Eng. 1966, 181, 205-210. Karaszkiewicz, A. Ind. Eng. Chem. Product Res. Deu. 1985, 24, 283-289. Karaszkiwicz, A. “Hydrodynamics of Rubber Seals for Reciprocating Motion-Leakage for 0-seals”, VI11 Internationale Dichtungstagung, Dresden, 1986, Band I, pp D49-64 (in Russian). Karaszkiewicz, A. “Contact Width and Contact Pressure of 0-seals”; Przegl. Mech. 7, 1979, 14-16, 25-26 (in Polish). May, E. M. “Pressure drop across a packing”, Appl. Hydraul. 1957, 1. Muller, H. K. “Hydrodynamics of Flexible Seal.” OelhydrauL Pneumatic 1965, 9(3), 89-93 (in German).
= net-leakage during a double stroke (out and in), mm3 R = cross-sectional radius of the O-ring (R = 0.5d) s = contact width of the ring, mm t = stroke duration of the sealed element, s t = temperature, “C v = velocity, mm/s W = pressure force per unit perimeter of the ring, N/mm x = direction of motion of the sealed element Greek Symbols c = relative squeezing of the 7 = dynamic viscosity, Pes CJ
2185
O-ring, = ( d - g ) / d
= contact pressure of the O-ring, MPa
Literature Cited
Received for review July 1, 1986 Accepted July 8, 1987
Blok H., “Inverse Problems in Hydrodynamic Lubrication and Design Directives for Lubricated Flexible Surfaces”, Symposium on
Measuring the Liquid Circulation Time in a Large Gas-Liquid Contactor by Means of a Radio Pill. 1. Flow Pattern and Mean Circulation Time Jan van Barneveld* and Willem S m i t Akzo Corporate Research Department, P.O. Box 60, 6800 AB Arnhem, The Netherlands
Nico M. G. Oosterhuis Suiker Unie Research, 4709 RA Roosendaal, The Netherlands
H a n s J. Pragt Akzo Engineering bu, 6800 AB Arnhem, The Netherlands
Liquid circulation times have been measured in a 20-m3 stirred tank, provided with two turbines, by means of a radio pill and two aerials. The liquid circulation time can be calculated from the measured radio pill circulation time, taking into consideration the influence of the gas holdup on the falling velocity of the pill. Large differences were observed between the radio pill circulation times measured with the upper and the lower aerial. A flow model comprising the liquid circulation rate and the rate of fall of the pill explains these differences. The observed circulation time of the pill and, consequently, the calculated liquid circulation time are influenced by both the gas flow rate and the distance over which the pill can be detected. 1. Introduction In chemical and microbiological reactions the rate of mass transport often is a limiting factor for the overall reaction rate, particularly in large production reactors. In gas-liquid reactions, e.g., fermentations, one of the mass transport processes is the mixing of the liquid phase. Data on oxygen concentration profiles measured in a production-scale fermentor indicate that in some cases liquid mixing may be relatively slow (Oosterhuis et al., 1983). Here a quantitative knowledge of the liquid circulation time would be very helpful for a better understanding and optimization of the production process. Liquid circulation time in a vessel is defined here as the
* To whom
correspondence should be addressed.
0888-5885/87/2626-2185$01.50/0
time interval between successive passages of a liauid element through the same or a coriespoiding poi& in the vessel. Depending on both the considered process and the type of reactor, the point of reference for the circulation time may be chosen. In a stirred gas-liquid reactor, it is convenient to take the stirrer as this point, starting from the assumption that dissolved gas concentration profiles have an extremum near the stirrer. In practice, passages are not measured at one point but in a zone with finite dimensions. The ratio of the volume of this zone to the total reactor volume has an effect on the observed circulation time. If this ratio approaches zero the circulation time will approach infinity, whereas a ratio of one leads to a circulation time eaual to zero. In a vessel provided with more than one stirrer the value of the circulation time changes with the interpretation of the word 0 1987 American Chemical Society
2186
Ind. Eng. Chem. Res,, Vol. 26, No. 11, 1987
"corresponding" in the definition of circulation time given above. For a two-stirrer vessel three mean circulation times can be given, depending on the assumed equivalence of both stirrers. We are interested in a method of measuring the liquid circulation time distribution in a production-size multistirrer gas-liquid contactor. Use was made of a 20-m3reactor, provided with two Rushton disc turbines and four baffles. The experiments have been carried out in water, applying both ungassed and gassed conditions. We have evaluated the possible methods for the determination of the liquid circulation time distribution, and we have chosen the radio pill method. We used two aerials for our measurements. The obtained circulation time data of the radio pill contain information on the average as well as on the distribution. Here mean liquid circulation time data will be derived from the observed mean circulation times of the pill. In a later paper, the results of the liquid circulation time distribution calculations from these data will be presented. 2. Techniques for Measuring the Liquid Circulation Time 2.1. The most widely used technique to obtain information on the mixing rate and circulation time is the tracer injection method. An amount of tracer is added to the liquid, and the rate at which homogenization takes place is determined. A review of results is given by Brennan and Lehrer (1976). In a more recent paper Einsele and Finn (1980) describe experimental results in a fermentor, obtained by pH-response measurements. Khang and Levenspiel (1976) correlate the decay rate of the fluctuating response of a tracer impulse to a dimensionless mixing number. Data obtained by the tracer injection method may be used for calculating the circulation time. However, no direct information on circulation time distribution is obtained. Moreover, it is nearly impossible to collect reliable information on the tail of the circulation time distribution. 2.2. A rapid way of obtaining information on the liquid circulation time is by means of impeller pumping calculations. The impeller is considered to be a pump, and the volumetric discharge flow from the stirrer is correlated with stirrer speed and stirrer dimensions by eq 1. The diQ, = kND3 (1) mensionless discharge coefficient k is dependent on stirrer type and geometry. In the literature there is quite some variation in the values of k , a review being given by Revill (1982). However, calculation of stirrer pumping capacities in gas-liquid systems is not very accurate. Moreover, no information on circulation time distribution is obtained. 2.3. A more sophisticated way of obtaining information on liquid circulation time distribution is by making a three-dimensional model, comprising direction and magnitude of the liquid velocity anywhere in the vessel. In principle, this can be done by means of a liquid velocity probe (Pitot tube, hot wire anemometer, strain gauge, etc.) by photographic methods (Nagata, 1975) or by sonar. However, it is not easy-if possible at all-to obtain accurate information on liquid flow in a stirred gas-liquid reactor of substantial dimensions. Application of a probe without disturbing the flow pattern will not be an easy task. The other methods are difficult to carry out in a large steel reactor. A principal drawback of all these methods is that, when
Vessel d i a m e t e r Number of impellers Impeller diameter I m p e l l p r b l a d e width Impeller speed B a f f l e width Position of lower impeller P o s i t l o 7 of upper impeller
T
2.
n
i
3,)
m
7
u.32 T
w
0.1 i)
N
- . b
@b
HI, HU
~
,
s
-1
0.39 T
0.35 T 1 . 0 5 'T
Figure 1. Reactor dimensions.
the flow model is assessed, the circulation time distribution has to be calculated instead of being measured directly. 2.4. An attractive method by which direct information on the circulation time distribution is obtained makes use of a flow follower. Mukataka et al. (1980) describe experiments with a magnetic flow follower in vessels up to 30 L. Bryant and Sadeghzadeh (1979) use a flow follower consisting of a small encapsulated radio transmitter, known as a "radio pill". The method has been used by several other workers, even for the determination of the mixing rate in a solids mixer (Cooker et al., 1983). Middleton (1979) reports the measuring of circulation times by means of a radio pill in liquid mixing vessels up to 1.8 m3,with and without gas sparging. A stochastic flow model for the interpretation of flow follower data is given by Mann et al. (1981). The method seems to be rather simple and provides direct information on the mean circulation time and circulation time distribution. The accuracy of the results can be enhanced by increasing the length of time per experiment, which is useful especially for the information dealing with the tail of the distribution. So, we decided to make use of this radio pill technique. 3. Experimental Setup 3.1. Vessel and Medium. All the experiments were
carried out in a dished bottom vessel, T = 2.50 m, provided with four baffles having a width of 0.097'. The vessel was
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2187 polypropylene housing
‘V-ring
Figure 2. Construction of radio pill. Figure 4. Aerial construction.
BO1
I
L Recorder
Figure 5. Squelch circuit. 801
B 01
w a c e l l 10 L 1 ~ 3
R 1
lm
C 1
>GO P
I? 2
15 K
C 2
5G0 P
T U1
Bc 1 4 6 - 3 2
c 3
2 x 2
L 1
bG p f4
- 2
60pH
Figure 3. Common-collector-colpits oscillator.
provided with two central six-blade Rushton disc turbines having a diameter of D = 0.8 m. The stirrer speed was kept constant at N = 2.6 s-l. Gas could be sparged by a star-shaped gas sparger provided with holes 6 mm in diameter. Data on the mixer are given in Figure 1. In all experiments the liquid used was tap water at room temperature. Experiments were performed at a liquid volume of 19 m3 and superficial gas velocities of 0,1.5, and 2.6 cm/s, respectively. Under these conditions gas holdups were, respectively, 2.9%, 9.1% , and 12.5%. One experiment was made at a liquid volume of 11 m3 without gas sparging. In this case only the lower impeller was in contact with the liquid. All the 19 m3 experiments were run for at least 51/2 h, resulting in 2000-10000 passages of the pill along each aerial. 3.2. Radio Pill. The flow follower housing consisted of two hemispheres of polypropylene mounted by means of screws and “0”-rings. This was done to facilitate inspection and battery replacement. The pill was designed to be neutrally buoyant, which limited its total density. It also had to withstand the
impact of the impellers, which means that the construction had to be rather robust. A pill measuring 2 cm in diameter did not meet these requirements, so that a 3-cm pill had to be used. Figure 2 shows the pill construction. The electronics of the pill consist of a so-called “common-collector-colpits” oscillator with a frequency of approximately 1MHz, powered by a silver oxide battery (Duracell 10 L123) (see Figure 3). The frequency is determined by the capacitors C2 and C3 and the coils L1 and L2. These coils are coupled in series and positioned at an angle of 120’ to create an almost spherical electromagnetic field around the pill. The electric power of the circuit is about 7 pW. The operation time of the transmitter is approximately 1200 h, using one battery. The strength of the signal varied slightly in various directions. However, as the pill will spin rather fast under the influence of local velocity gradients, this was considered to be rather unimportant. 3.3. Aerials. Two aerials, each consisting of an isolated steel cable loop, were mounted. Each loop, 1.20 m in diameter, was mounted concentrically around a turbine in the impeller plane. The aerial wires running from the loops to and alongside the vessel wall werre shielded by aluminum tubes. In this way detection of the pill outside the impellar area was prevented. A schematic representation of the configuration is given in Figures 1 and 4. 3.4. Radio Receiver and Data Logger. A radio receiver of Yeusu-musen Co. (Type FRG7) has been used. This receiver is a so-called “general coverage receiver” with a frequency range of 500 kHz up to 29.9 MHz.
2188 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 r -------7
lip
,
I
AERIALS
I
~
1
ANALOG COMPUTER
I 4
-Sum.
DISPLAY
c
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A
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,
I
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i
'
I
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,
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,
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1
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circulation time
;integrated
I
RECElVER
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I CIRCUIT
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Figure 7. Typical signals and circulation times. DISPLAY
off-:lre
Figure 6. Schematic drawing of the signal processing.
With a squelch circuit, given in Figure 5, it is possible to adjust the receiver in such a way that an output signal appears only if the aerial receives a signal greater than an adjusted level. So, the presence of an output signal of the squelch circuit is dependent on the signal strength of the transmitter, i.e., the distance between pill and aerial. The squelch circuit consists of a comparator. The automatic voltage control from the receiver is switched to input 3 of the comparator. This AVC voltage is proportional to the received signal level. Input 2 of the comparator is the switch level. This voltage can be set by the 10-turn potentiometer R1. The comparator only has an output if input 2 is larger than input 3. The output signal of the comparator is fed to the tape recorder and processed off-line with the aid of an hybrid computer. A relationship between the dial set of R1 and the maximum detection distance between the pill and the aerial in water was established. No influence of sparged gas on this relationship was observed. As already mentioned in the Introduction, the volume of the zone in which the presence of the radio pill is detected is important for the circulation time measured. Costes and Couderc (1982) measured velocity profiles in the discharge flow of a Rushton turbine. Their results suggest radial flow over a height of 2 W , measured at a radius of 1.1(0/2). Our aerial has a diameter of 3(0/2), so it seems reasonable to detect the pill over a height larger than 2 W. Moreover, because of existing concentration gradients in the reactor in which we are interested, the circulation time distribution is-in our experiments-related to a volume having a height of 4W. Therefore, most experiments were performed with a detection distance set at 32 cm (=2W). In one experiment this distance was extended to 50 cm.
3.5. Signal Processing. In Figure 6, the general setup of the off-line tape processing is given, while also some schematic outputs at different stages of the processing system have been presented. In the signal processing the playback velocity could be set 8 times higher than the record velocity. With the analog computer the tape signal is preprocessed. Here, filtering of the recorded signal takes place. In principle, the recorded signal possesses two data: one being related to the circulation time and the other to the residence time in the aerial zone. The residence time is equal to the width of the pulses coming from the squelch circuit, while the distance between the pulses is the actual circulation time. Within the analog computer these times can be measure with a so-called "switched integrator". Such an integrator has a constant input signal, and the integrator mode (hold, initial condition, and operate) is controlled by the output of the squelch circuit. In Figure 7 some typical signals are given. From these signals the circulation time was determined as follows. At the trailing edge of the recorded signal the integrator is switched to the operating mode, resulting in a ramp increase of the output owing to the constant input voltage. At the leading edge of the next pulse in the recorded signal the integrator is switched to the hold mode. The output signal of the integrator is then proportional to the distance between the pulses, i.e., the circulating time. As soon as the integrator enters the hold mode the analog to digital convertor is activated and takes over the integrator output to send it to the digital computer where this output value is stored in an array. When this has been completed the ADC-ready signal sets the integrator in the initial condition mode. At the trailing edge of the pulse of the recorded signal the integrator is again switched to the operating mode and the process repeats itself as described above until the array with all integrator hold outputs has been filled up. Simultaneously, the digital computer classifies the numbers entering the array of integrator outputs in 40 classes. The highest class is the time that corresponds with the maximum output of the integrator. The maximum circulation time is determined in such a way that only about 2% of the recorded information is rejected. The building up of the histogram in time can be followed by the visual display unit. If the array is filled up or the process stopped in another way, the histogram is plotted and a statistical program in the digital computer may be started to calculate the mean value and the variance in the mean value of the circulation time, etc. Besides, the statistical variance of the 40 classes can be calculated. Actually, the signals coming from the squelch circuit are not as nicely shaped as mentioned above. Often a pulse consists of a train of fast pulses, which may be caused by
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2189 rotation of the pill or a very turbulent motion at the edges of the aerial zone. Moreover, sometimes very fast pulses with an extremely short pulse width appear. With the aid of digital logic the train of fast pulses is transformed into one pulse having a width of the total duration of the train. Pulses having a width smaller than the ADC-operating time (about 10 ms) are neglected. Possible misinterpretation of the signals has only a slight effect on the observed circulation times of the radio pill. Some work was done on the processing of the residence time of the radio pill in the detection zones around the aerials. As mentioned before, the signals consisted of sequences of short pulses, probably caused by the spinning of the pill. This "spinning frequency" in the aerial zones proved to be constant in all the experiments. As in all the experiments where the stirrer speed was kept constant, this suggests that the spinning is caused by the shear near the impeller. Owing to the relatively small size of the detection zones around the aerials, the residence time of the pill within these zones will be small. So misinterpretation of the obtained radio signals will lead to large mistakes in the observed residence times within the aerial zones. Therefore only qualitative conclusions can be drawn from the results obtained in such residence time measurements. 3.6. Effect of Gas Holdup on the Radio Pill Buoyancy. Our aim is to obtain information on the liquid circulation time distribution (CTD). The experimental results with the radio pill give direct information on its CTD. So, it is essential to know the relationship between the CTD of the liquid and that of the pill. Middleton (1979) made some experiments by observing the movement of small (0.3 mm) flow-following particles and of his radio pill (diameter 2 cm) both in gassed and ungassed systems. The closest agreement between pill and particle velocities was obtained with a pill density equal to that of the dispersion. With our pill, 3 cm in diameter, experiments were performed to investigate the effect of gas sparging on pill movement. A glass cylinder having an internal diameter of 10 cm was provided with a sintered glass bottom. The cylinder was filled with tap water (18 "C),the liquid height being about 1 m. The water was aerated through the sintered glass bottom and the gas holdup was measured. The pill was introduced at the gas-liquid surface, and the rate of fall was measured. The results are given in Figure 8. The rate of fall proved to be somewhat lower than was expected on the basis of pill size and density difference only. This may be caused by gas bubbles sticking to the polypropylene housing of the pill. 4. Interpretation Model of the Radio Pill Data A Rushton turbine i.n a fully baffled tank is known to cause mainly a radial flow. So, a first approximation of the liquid flow in the reactor is made, assuming the presence of five different compartments. Two compartments are situated around the impellers and are, in fact, assumed to be covered by the aerial zones. The remaining three compartments are positioned, respectively, below the lower impeller, above the upper impeller, and in between both impellers. In Figure 1the five compartments are indicated. The liquid flow from compartments 2 and 4 (around the impellers) is expected to be pumped radially to the other compartments; from compartments 1,3, and 5 the liquid is assumed to flow back to 2 and 4. The assumption is made that the liquid flow from an impeller compartment splits up into two equal flows. A further assumption is that the liquid pumping capacity of
/
Z
/
30
/
//
/ /--Calculated, according t o pill diameter and d e n s i t y d i f f e r e n c e
/ /
/ I
I
/
0 1
0
5
10
20
15
25
Gas hold-up l % ~
Figure 8. Rate of fall of the radio pill in aerated water.
the two impellers is not the same. This results in an unequal splitting of the liquid flow leaving compartment 3 in between the two impellers, a fraction m going to compartment 2 and 1- m to compartment 4. The radio pill is assumed to be subject to the liquid flow movement and also to a constant rate of fall, the latter being determined by the gas fraction in the compartment. In consequence, the pill can leave the compartment in two ways: either by the liquid outlet or, alternatively, through the bottom as a result of the downward movement. A relationship between the mean residence time 7 of the pill and of the liquid (q)is derived in the Appendix. The result is eq 2 and 3. If the pill passes n times through a 1 -- -1+
-
71
7
7,
=
1
-
7,
'/H
-
compartment, then a fraction p of n leaves the compartment by falling down to a lower one, while a fraction (1 - p ) of n follows the liquid flow. As p ~ =, (1 - p ) q , it can be concluded from (2) that 7
P'-
(4)
7,
A flow diagram of the radio pill based on the above assumptions is given in Figure 9. For a given mean pill circulation time Ec,p and a known falling probability p in the various compartments, there remain two parameters to be estimated: m and 71. For the experiments using a gas rate of 2.6 cm/s, we calculated 71 values for a number of m values. The best fit was obtained for m = 0.48, indicating equal pumping capacities for both impellers. Therefore, in all further calculations m was assumed to be equal to 0.5. For u, = 0 (gas holdup 2.9%) also the influence of a nonuniform gas distribution (causing different rates of fall for the pill in the various compartments) was investigated. A uniform gas distribution proved to give the best fit.
2190 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 Table I. Calculated a n d Observed Mean Circulation Times liq vol, m3 11 19 superficial gas rate, us, cm/s 0 0 vol gas holdup, 1 - 6, % 2.9 2.9 obsd mean circulation times of the radio pill 1. EC,p2,* s 2.6 4.0 1. tc,p4,9 2. fc,p2+4,C s calcd mean circulation times of the radio pill 1. EC,p", 9 1. tc.p4, s 8.74 2.56 2. tc,p2+4, s calcd mean liq circulation times 1. t,,:, s 3.44 7.45 1. tC,*,s 7.45 2. fC,?+4, s 3.48 liq circulation capacity, Qc,l, m3/s 2.85 2.39
19 0 2.9
19 0 2.9
19 1.5 9.1
19 2.6 12.5
19 2.6 12.5
19 2.6 12.5
3.1 2.3
3.2
3.70 7.45
3.67 31.5
2.41 6.94 6.94 3.24 2.57
6.54 6.54 3.05 2.73
12.1 12.1 5.67 1.48
19 2.6 12.5
2.1" 26.2
8.0
3.83
19 2.6 12.5
11.0" 2.7
3.02 28 2.72
2.64
10.7 10.7 5.02 1.68
10.3 10.3 4.86 1.68
3.08 27.6 10.6 10.6 4.99 1.69
1.60 24.1 1.81
1.26
8.50 8.50 3.58 1.93
5.66 5.66 2.38 2.90
a Aerial threshold value set a t 50 cm; all other experiments 32 cm. * 1. fc,p2(4)= mean time interval between two successive passages of the pill through compartment 2 (4). c2. fc,p.2+4= mean time interval between leaving compartment 2 or 4 and again entering one of these compartments. Mean liquid circulation times are defined in the same way.
U Figure 9. Flow diagram for the radio pill.
5. Results and Discussion
A summary of observed and calculated mean circulation time values is given in Table I. The mean circulation time of the radio pill is dependent on the location of the aerial in the reactor. This is clearly demonstrated by the observed values of fc,p2and fc, * given in Table I. The pill is more frequentfy observed in the lower part of the reactor. For each experiment the observed mean radio pill circulation time with respect to the applied aerial zone is given. The suggested flow model was used to calculate the other two mean pill circulation times. Obviously, the model describes the movement of the pill fairly
correctly, as is suggested by the resemblance between calculated and observed fc,pvalues at gas velocities of 0 as well as 2.6 cm/s. In the experiments with a gas velocity of 2.6 cm/s, the observed circulation time data for a triggering distance of 32 cm fit very well with the model; i.e., fc,p2,fc,p4:and fY,F4 can be explained from the same value for the liquid circulation rate of the turbines and from the experimentally verified rate of fall of the radio pill. This finding as well as the good fit observed under ungassed conditions justifies some confidence in the reliability of the model. The liquid circulation capacities of the impellers, given in Table I, were calculated from the mean liquid residence time and liquid volume within a compartment. The calculated circulation capacities of the impellers in the experiments with unaerated 11- and 19-m3vessels show a close resemblance, as was expected. A mean liquid circulation capacity of 2.64 m3/s is calculated, suggesting a volumetric liquid discharge coefficient k of 1.98. Revill (1982) gives k values of 0.6-0.95; Costes and Couderc (1982) give a k value of 0.97 for a six-bladed Rushton turbine. However, these values are obtained from liquid flow data only over the impeller blade width. Middleton (1979) plots radio pill circulation time data for vessels of 0.18-4.4 m3. He suggests liquid discharge coefficients of 2.79 for the smallest stirrer and k = 1.02 for the biggest one. However, in his experiments the ratio of detection volume to tank volume was
