A simple method for regime identification and flow characterisation in bubble columns and airlift reactors

A simple method for regime identification and flow characterisation in bubble columns and airlift reactors

Chemical Engineering and Processing 40 (2001) 135– 151 www.elsevier.com/locate/cep A simple method for regime identification and flow characterisatio...

334KB Sizes 2 Downloads 216 Views

Chemical Engineering and Processing 40 (2001) 135– 151 www.elsevier.com/locate/cep

A simple method for regime identification and flow characterisation in bubble columns and airlift reactors Christophe Vial, Souhila Poncin *, Gabriel Wild, Noe¨l Midoux Laboratoire des Sciences du Ge´nie Chimique CNRS-ENSIC-INPL 1, rue Grand6ille, BP 451, F-54001 Nancy, Cedex, France Received 20 October 1999; received in revised form 15 March 2000; accepted 31 May 2000

Abstract A new diagnosis method for regime identification in bubble columns and airlift reactors based on a theoretical analysis of the auto-correlation function (ACF) of wall pressure fluctuations is proposed. It yields quantitative information, such as a characteristic time and a characteristic frequency of the two-phase flow, which are closely related to the flow structure in the prevailing regime. This method is shown to be simple, low-cost, reliable and efficient and has been applied successfully to a bubble column and an external loop airlift reactor. Experimental data on both reactors are shown to be in good agreement with theoretically predicted values. The order of magnitude of the characteristic time can be used for regime identification. Combined with an analysis of the cross-correlation function (CCF) of two signals recorded simultaneously, the method is also able to yield an estimate of the axial dimension of the flow structures. This analysis is, therefore, promising for regime identification and flow structure characterisation in industrial equipment. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Bubble column; Airlift reactor; Hydrodynamic regime; Coherent structures; Pressure fluctuations

1. Introduction Numerous industrial gas – liquid reactions are conducted in bubble columns in which the gas is dispersed in a liquid. These contactors are widely used in chemical and biotechnological industry to carry out slow reactions such as oxidations and chlorinations [1]. They offer many advantages over other multiphase reactors — simple construction, no mechanically moving parts, good mass transfer properties, high thermal stability, low energy supply and hence low construction and operation costs [2]. Airlift reactors are an important class of modified bubble columns and are preferentially used for biotechnological applications [3]. However, only a few parameters like gas and liquid flow rates, geometry or type and construction of the distributor (porous plate, nozzle, …) can be controlled by design and operation of these reactors. The decisive parameAbbre6iations: ACF, auto-correlation function; CCF, cross-correlation function; PSDF, power-spectral density function. * Corresponding author. Tel.: + 33-3-83175223; fax: +33-383322975. E-mail address: [email protected] (S. Poncin).

ters like gas hold-up, interfacial area or heat and mass transfer coefficients are not directly adjustable. Consequently, design and scale-up of bubble columns are still a difficult task, as the influence of operating conditions, reactor geometry and physico-chemical properties of the phases on the hydrodynamics is not yet fully understood.

1.1. Hydrodynamic regime Bubble column hydrodynamics is characterised by different flow patterns depending on the gas flow rate — homogeneous (bubbly flow), transition and heterogeneous (churn-turbulent flow) regimes. Another regime, namely slug flow, is also observed in small diameter laboratory columns when the large bubbles are stabilised by the column wall. This regime does not occur in industrial reactors. The homogeneous regime is encountered at low gas velocity and is characterised by a narrow bubble size distribution, a radially uniform gas hold-up and a minor bubble –bubble interaction. Coalescence and break-up phenomena can be neglected and there is no large-scale liquid circulation in the bed. In batch bubble columns equipped with an efficient gas

0255-2701/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S0255-2701(00)00133-1

136

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

distributor, it is well known that homogeneous conditions are generally present up to 3 cm s − 1 with the air – water system. In loop reactors, the homogeneous regime can be extended up to higher superficial gas velocities because of the effect of the liquid velocity on the stability of the flow. Consequently, the differences between regimes are less apparent in airlift reactors as compared with bubble columns. At higher gas velocity, the flow becomes unstable and the homogeneous regime cannot be maintained. Large bubbles are formed by coalescence, which move with higher rise velocity than smaller bubbles. This flow pattern is referred to as heterogeneous regime and is characterised by a wide bubble size distribution and a marked radial gas hold-up profile. Both local and gross liquid circulations appear and macro-scale liquid circulation is induced by the voidage profile. These two patterns are separated by the transition regime that corresponds to the development of local liquid circulation pattern in the column [4]. When a poorly efficient gas distributor is used, heterogeneous conditions prevail at all gas flow rate.

1.2. Regime and flow structure The description of the local liquid circulation pattern has been the aim of numerous studies in bubble columns and many theoretical descriptions of the flow structure have been proposed [5 – 13]. Some of them assume the existence of a global circulation pattern in the column. They are based on experimental evidence that the liquid phase flows upwards in the centre of the column and downwards near the wall. The calculation of the time averaged liquid velocity profile is possible, but experimental radial gas hold-up profiles are required and a fitting parameter in the momentum equations is needed, which is generally the eddy viscosity. Variations of these models have been proposed depending on the input and fitting parameters [5 – 7]. The

second class of flow description assumes the existence of local macro-circulation cells. Idealised flow structures proposed by some of the models of this class are described on Fig. 1. Joshi and Sharma [8] suggested a multiple-circulation cell pattern (Fig. 1b), based on an extension of the early inviscid model of Freedman and Davidson [9] for bubble columns with Hc = Dc (Fig. 1a). These authors conclude that cells of height equal to column diameter are present. Van den Akker and Rietema [10] modified this model, as it is physically impossible for streamlines of adjacent cells to have opposite directions. Their new model predicts, however, an alternatively positive and negative axial centreline velocity, which has never been observed experimentally (Fig. 1c). Then Joshi and Sharma [11] proposed a modified version of their previous model by incorporating the cells into an overall circulation pattern (Fig. 1e). Another description of the flow, based on multiple cells, has been proposed by Zehner [12] and is referred to as Zehner’s vortex cell model (Fig. 1d). All the previous models suppose that the axial dimension of the cells is the column diameter. Finally, it appears that it is commonly admitted in bubble columns that the axial characteristic dimension of the flow is the bubble size when homogeneous conditions prevail, whereas it is the column diameter when heterogeneous regime occurs [4]. This assumption has been taken into account to propose a new description of turbulence in both homogeneous and heterogeneous regimes [13]. However, there is no experimental proof of this assumption. The recent works using PIV on a 2-D bubble column are promising for a better description of the flow structure [14], but definitive evidence has not yet been provided. Contrary to bubble columns, there is a lack of theoretical and experimental studies, which are aimed at exploring the flow structure in airlift reactors; this structure differs from that in a bubble column as the global liquid recirculation in the downcomer stabilises

Fig. 1. Liquid circulation models in bubble columns.

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

137

Fig. 2. Determination of regime transitions in bubble columns.

the flow. In the heterogeneous regime, a local circulation pattern has been reported, but it is dampened by the global liquid flow [15]. This local recirculation refers to local circulation cells within the riser and should not be mistaken with the global liquid circulation. Both phenomena are superimposed in heterogeneous conditions. Net liquid flow delays cell formation and transition to heterogeneous regime, which appear consequently at far higher gas velocities than in bubble columns. A view of the differences between the local recirculating patterns in airlift reactors and bubble columns based on visual observations is well illustrated by Merchuk [15].

1.3. Interest of the work Hydrodynamic parameters, phase mixing and mass transfer are strongly dependent on the flow structure and the corresponding flow patterns [4]. Identification of the nature of the dispersion is, therefore, essential for proper design and modelling of the reactor. Numerous studies have investigated flow regime transitions and have tried to describe flow characteristics under the different regimes. In the last decade, many original methods based on recorded signal analysis have been proposed in order to allow a regime identification better than classical techniques like drift-flux analysis [16,17]. These methods have provided a deeper insight into the complex hydrodynamics of the gas – liquid system [18,19]. Several processing techniques have been used to extract information about flow regimes from recorded signals [20 –22]. Despite these attempts to quantify flow regime transitions, firmly established criteria are not yet available. Furthermore, these works are always conducted in a simple bubble column and there is a lack of data for airlift reactors. The present work proposes a new method based on a theoretical analysis of the auto-correlation function (ACF) of wall pressure fluctuations. It allows the pre-

diction of characteristic parameters of the flow, the order of magnitude of which strongly depends on the flow structure and the prevailing regime. Experiments are performed both in a liquid batch operating bubble column and in an external loop airlift reactor in order to confirm the validity of this analysis.

2. Methods for regime identification

2.1. Classical methods Historically, flow regimes used to be distinguished by visual observation. As it was necessary to quantify transitions, several empirical methods have been proposed. The first experimental way to identify the flow pattern consists in measuring the evolution with UG of the mean value of a parameter closely related to the flow structure. This parameter must exhibit an extremum or a significant ‘break-up’ when transition occurs. In bubble columns, average gas hold-up measurement is the preferred way to characterise the dispersion [4]. Fig. 2a illustrates schematically mG versus UG data obtained in a bubble column. The homogeneous region is characterised by the linearity of the mG versus UG curve. The fully developed heterogeneous regime is observed at higher UG, starting from the point when the gas holdup exhibits a minimum. A pronounced maximum is observed in the transition region reflecting the development of the liquid macro-scale circulation. However, such a clear view of the transition is not always obtained. It is, for instance, more difficult to determine regime limits in airlift reactors because no maximum is generally observed even when transition occurs [3]. In bubble columns, transitions depend strongly on the gas sparging device. When an efficient gas distributor (e.g. a porous plate) is used, the typical behaviour shown on Fig. 2a is observed. When a poor distributor is used, like a single-orifice nozzle, no maximum is observed, as

138

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

the heterogeneous regime prevails even at the lowest gas flow rate generally used in these reactors [23]. Another way to describe regime limits with mG measurements is provided by the classical drift-flux analysis of Zuber and Findlay [24]. This approach is, however, more efficient in airlift reactors than in bubble columns. It consists in plotting UG/mG against UG +UL. A change in flow pattern is indicated by a change of the slope of this curve. Zuber and Findlay derived the following expression relating the two previous quantities: UG = C0(UG + UL)+C1 mG

(1)

where C0 is the distribution parameter that takes the radial profiles of velocity and hold-up in the column into account. When these profiles are flatter, C0 is closer to unity. This parameter can be used to quantify the degree of flow uniformity. This justifies that driftflux analysis is superior to mG versus UG analysis. C1 is a constant that represents the gas velocity relative to the velocity of the mixture. Zuber and Findlay model is still recommended for prediction of gas hold-up in heterogeneous bubble beds [4]. In batch bubble columns, it is preferable to use the approach proposed by Wallis [16], which consists in plotting UG/mG versus mG. Although this method provides generally a better view of regime transitions, it has the same drawback as mG versus UG analysis. Both suffer from a lack of accuracy due to the smallish difference between slopes when transition occurs. A last empirical method for regime identification is the dynamic gas disengagement technique (DGD), introduced first by Sriram and Mann [25]. It involves following the dispersion height after the gas feed has been shut off. The height of the dispersion was initially determined by visual observations. This has been replaced by the use of a pressure transducer located a few centimetres below the non-aerated liquid height [26]. This procedure does not require a transparent column and may be applied in industrial reactors. The measured disengagement profile enables the estimation of the hold-up structure and allows the evaluation of the rise velocities of bubbles in the dispersion prior to gas flow interruption. Main assumptions of DGD analysis and problems associated with the deviations from these assumptions in coalescing systems at high gas flow rate have been already discussed [27,28]. The classical analysis of DGD assumes one dominant bubble size in the homogeneous regime and two in the heterogeneous one. The method is able to provide mean rise velocity and the fractional hold-up of the small and the large bubble classes. Typical curves obtained in the bubble column are plotted in Fig. 2b. The presence of large bubbles is an evidence of churn-turbulent flow and can be used for regime discrimination. DGD does not provide a better view of transition than former meth-

ods. However, it is a good tool to analyse simultaneously the hydrodynamic regime and the flow structure of the gas phase. The typical behaviour of DGD curves has been used by Krishna et al. [29] to develop a bimodal bubble size class model. However, the DGD technique is not applicable in airlift reactors as the gas shut-off stops the liquid circulation.

2.2. Recent methods The main drawback of previous techniques for regime identification is their lack of generality as their ability to detect transitions depends on the reactor. This is the reason why a second class of more general methods, based on the study of dynamic fluctuations of a signal related to the flow pattern, has been proposed to improve the accuracy of the determination of the limits between regimes. These methods have been applied on many two and three-phase flows to discriminate regimes in pipes [20], packed bed reactors [30], trickle-bed reactors [31] and fluidised bed reactors [32]. The analysis of several signals has been explored for this purpose, wall pressure fluctuations [18]; local gas hold-up fluctuations with optical probes [21]; chordal void fraction fluctuations with absorption techniques [22]; wall mass transfer fluctuations using electrochemical probes [30,31]; local gas hold-up fluctuations with resistive probes [32]; temperature fluctuations [33]; and acoustic measurements [34]. Numerous processing techniques have been proposed in order to unravel the flow regime characteristics from the selected signal, statistical analysis [19]; stochastic modelling [35]; parametric modelling of time series [18,36]; spectral analysis [18,37]; fractal analysis [32,38]; chaotic dynamics diagnosis [19,39]; time-frequency analysis [21,37]. A comparison of these techniques has been proposed recently [40]. Among the different signals available, pressure signal is the most attractive option to study hydrodynamics in bubble columns. The measuring technique is simple, robust and relatively cheap. Sensors are non-intrusive and can be applied in opaque reactors in a large range of operating conditions of pressure and temperature, which can be of interest for industrial applications. However, the main problem is that pressure is an energetic parameter whose relation with the flow structure is not direct, since it results from numerous phenomena such as bubble passage and flow circulation. Most of the different processing techniques have been explored with pressure transducers in batch bubble columns. Only limited statistical and spectral approaches have been adopted by Glasgow [36] to analyse the dynamic behaviour of airlift reactors. The aim of the present work is, therefore, to propose a new simple and efficient method for regime identification in gas – liquid contactors using wall pressure transducers. ‘Sim-

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

ple’ means that the method should require only easy and rapid calculations. Simultaneously, the method should be ‘efficient’ by allowing a good determination of regime limits both in a bubble column and in an airlift reactor. These objectives have been reached using an analysis of the ACF of the pressure signal.

3. Experimental set-up The bubble column (Fig. 3a) is a cylindrical semibatch one with an inside diameter of 0.10 m and a height of 2 m. Two spargers are used, “ a multiple-orifice sparger (62 holes of 1 mm uniformly spaced), which produces a uniform gas distribution and which can be considered as an efficient gas sparger; “ a single-orifice nozzle with a 5-mm orifice, which produces a non-uniform gas distribution and which is not an efficient gas distributor. The superficial gas velocity is varied from 6 mm s − 1 up to 15 cm s − 1 and is controlled by two rotameters. The dimensions of the external loop airlift reactor (Fig. 3b) are 10-cm riser diameter, 6-cm downcomer diameter and 2.75-m height. Gas can be fed with the two spargers described previously. The superficial gas velocity is

139

varied from 1 to 24 cm s − 1 by means of a mass flow controller. All experiments are carried out with tap water at room temperature and atmospheric pressure. In both reactors, the average gas hold-up is measured by the usual manometric method [41]. Pressure measurements are performed with piezo-resistive sensors imbedded in the wall (Keller PR25/8797.1; 0–150 or 0–500 mbar) with accuracy of 0.02% of the full scale. Pressure signals are sampled with a 12 bit RTI 815 A/D acquisition card and stored in a PC computer. The software TestPoint™ is used to control the data acquisition. For static hold-up measurements, signals are recorded at a frequency of 10 Hz during 100 s. Dynamic pressure measurements are performed at frequencies of 50–500 Hz with one or two probes located at different heights, far enough from the distributor and the liquid level to avoid end effects. The total acquisition length is 10 000 or 20 000 points for each experiment in order to minimise statistical error. In the external loop airlift reactor, the flow rate of the liquid phase in the downcomer is determined by a tracer technique. A pulse of 4 ml of saturated NaCl solution is injected at the top of the downcomer. The conductivity is followed at downstream locations by two probes placed 1.76 m apart in the downcomer. The signals are recorded simultaneously at a frequency of 10

Fig. 3. Experimental set-up.

140

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

Fig. 4. Gas hold-up data in the bubble column and in the airlift reactor.

Hz. As the liquid phase is in plug flow in the downcomer, the two conductivity signals can be fitted with a normal function by means of the least square method. From the difference between the first moments of the normal distributions, the liquid velocity in the downcomer can be deduced.

4. Preliminary regime identification Regimes and transitions were first determined in both reactors using classical methods. Knowing the transition points is necessary to validate the results of the new approach. Fig. 4 shows the evolution of gas holdup versus gas flow rate in the bubble column and the external loop airlift reactor. In the bubble column (Fig. 4a), the typical behaviour of Fig. 2a is observed with the multiple-orifice sparger. The limit of the linear region, corresponding to the end of the homogeneous region, is reached at a superficial gas velocity of 3 cm s − 1. The heterogeneous regime begins when UG value is higher than 9 cm s − 1 when the curve exhibits a minimum. These results are confirmed by Wallis’ drift-flux analysis (Fig. 5a). With the single-orifice nozzle, no maximum is observed and the column always operates in the heterogeneous regime. In the airlift reactor equipped with the multipleorifice sparger, transitions take place at higher gas velocities due to the presence of the global liquid circulation. Consequently, the limit of the homogeneous region is reached at a gas flow rate value of about 5 cm s − 1 (Fig. 4b). A maximum of gas hold-up is not observed. The transition region corresponds to a flatter zone where the slope of the curve is smaller than in the homogeneous and the heterogeneous regimes. When this region is large, it may be a plateau-like zone [3]. Heterogeneous conditions seem to prevail when UG is larger than 15 cm s − 1. An accurate determination of

this transition is rather difficult, due to the smallish slope evolution when the transition occurs. A better view of transitions is obtained using the Zuber and Findlay model. However, this requires liquid velocity measurements (Fig. 6). The curve in Fig. 5b features three linear sections corresponding, respectively, to the passage from homogeneous to transition regime and to the passage from transition to heterogeneous regime. When the value of UG + UL in the riser is smaller than 0.37 m s − 1, the slope C0 (Eq. (1)) equals 1.02, which is characteristic of the homogeneous regime. When UG + UL is higher than 0.57 m s − 1, the heterogeneous regime prevails and C0 = 1.53. In the transition region, C0 = 1.98. These results are in agreement with those of Zahradnı´k et al. [4] who find, respectively, C0 =1.08 in the homogeneous regime and C0 = 1.52 in the heterogeneous one. The superficial gas velocities corresponding to the two transitions are deduced from Fig. 5b and are, respectively, UG = 6 and 16 cm s − 1. When the reactor is equipped with the single-orifice nozzle, the UG versus UG + UL curve features only one linear section with C0 = 1.52. This proves that heterogeneous conditions prevail at all gas flow rate.

5. Theoretical analysis of frequency spectra and ACF shape

5.1. Spectral analysis Spectral analysis by Fourier transform is now a very simple tool for flow regime analysis as Fast Fourier Transform algorithm implementations are currently available in most mathematical libraries. The Fourier transform F of a times series x(t) is defined as: F(x)=

&

+



x(t) exp(− j 2yft) dt

(2)

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

141

Fig. 5. Characterisation of regime transitions with the drift-flux model.

The Power spectral density function (PSDF) of a time series is, therefore, easily obtained using the following relation: PSDF(x)= F(x 2) = F(Cxx )

(3)

where Cxx is the ACF of x. This function is defined as: Cxx (~)= limT “

1 T

&

T

x(t)x(t − ~) dt

(4)

0

Characteristic frequencies of gas – liquid flows can then be extracted from a pressure signal. Drahosˇ et al. [18] have applied this approach in a bubble column and have shown that the interesting frequencies range from 0 to 20 Hz for bubble columns with such sensors. This has been confirmed by measurements performed at a frequency of 500 Hz on both reactors. An example of PSDF of a pressure signal obtained at this frequency in the bubble column is shown on Fig. 7. For pressure fluctuation measurements, a sampling frequency of 50 Hz has been finally retained. The signal is first filtered using a digital low pass filter with a cut-off frequency of 25 Hz to reduce aliasing. The PSDF of the fluctuating part of the pressure signal is then estimated on time series of 20 000 points, divided in segments of 512 points each, using an overlap of 10% of this block length and a Hanning windowing to further decrease the influence of aliasing. A block length of 512 points has been chosen because it appeared that the use of larger segments of 1024, 2048 or 4096 points do not affect significantly the shape of the PSDF. This value is, however, a minimum as this corresponds to about 10 s, which is almost the order of magnitude of the longterm processes observed by several authors [18,42,43]. Larger blocks are not needed here, because only a qualitative interpretation of the PSDF will be used in this study, which does not require a very accurate estimation of the frequency spectrum. The orders of

magnitude of the characteristic frequencies of the main phenomena occurring in the bubble bed have been reported by Letzel et al. [19] and are shown on Fig. 8. ACF is closely related to PSDF as it can be obtained from the inverse Fourier transform of the PSDF (Eq. (3)). But this function can also be evaluated directly from the averaged product of data values of the fluctuating part of the pressure signal (Eq. (4)), using the following approximation: Cxx (~):

1 T

&

T

x(t)x(t −~) dt

(5)

0

provided the length of the time series T is long enough. Since ACF connects x(t) with x(t− ~), it shows how x(t) is influenced by its past and consequently, it is able to detect hidden periodicity. But ACF is not often applied for flow pattern identification because PSDF is easier to interpret. Max [44] suggests that Eq. (5) is accurate only when ~5 T/40. In this study, this way is used to estimate Cxx. As a good precision is required for the ACF, this function is calculated only on the

Fig. 6. Liquid superficial velocity in the riser of the airlift reactor.

142

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

Fig. 7. Typical frequency spectrum in the airlift.

time interval 0B ~5 2 s, which is quite sufficient for the following calculations and fulfils the condition suggested by Max [44]. Typical spectra for the bubble column and the airlift reactor equipped with the multiple-orifice sparger are shown in Fig. 9a and b. In both reactors, the PSDF exhibits two main frequency bands at 0.1 and 3 –5 Hz. In the homogeneous regime, the low frequency band dominates the spectrum. In the heterogeneous regime, the PSDF exhibits a broader peak in the range 3 –5 Hz. The transition region is characterised by the simultaneous presence of both peaks. The evolution of the shape of the PSDF is roughly similar in the airlift reactor. However, the peak, which appears when transition occurs is closer to 3 Hz in the bubble column, whereas it is almost 4 or 5 Hz in the airlift reactor. When both reactors are equipped with the singleorifice nozzle, two cases can be distinguished. With the airlift reactor, a single peak at 3 – 5 Hz dominates at all gas flow rate. The low frequency band is never observed, which is in agreement with results obtained in heterogeneous regime with the other gas distributor. With the bubble column, a far different behaviour is observed. At low gas flow rate, a peak appears in the 10 – 20 Hz frequency band. At increasing gas velocity, the peak at 3–5 Hz, which characterises the heterogeneous regime, develops and finally overshadows higher frequencies (Fig. 9c).

Fig. 8. Order of magnitude of the main characteristic frequencies of the pressure signal in bubble columns [19].

Fig. 10 shows typical ACF curves of the pressure signal observed in the homogeneous and heterogeneous regimes for the airlift reactor. It appears clearly that ACF presents an exponentially decreasing shape in the homogeneous regime. In the heterogeneous regime, a periodic behaviour is superimposed on the exponential shape. Similar curves are obtained in the bubble column as the PSDF presents similar trends in both reactors. The shape of the PSDF results from the combination of random and quasi-periodic processes. Among them, the main processes are liquid level oscillations, bubble formation, bubble passage, bubble rupture and coalescence, and liquid eddy movement. They can be divided into two classes. The first one corresponds to processes, which occur in the vicinity of the sensor, generally due to bubbles or liquid circulation. The second class is formed by processes, which occur far from the sensor, in the distributor region like bubble formation, or at the top of the column where gas disengages and induces dispersion level oscillations. Since the sensors are located in the wall region far enough from the distributor, the influence of bubble formation phenomena can be neglected with a uniform gas distribution. Typical spectra in the distributor region show the presence of characteristic frequencies between 10 and 20 Hz, which are not observed in Fig. 9a and b. In the homogeneous regime, bubble coalescence and rupture are also negligible and there is no marked liquid circulation pattern. The only characteristic frequency found in the PSDF is of the order of magnitude of 10 − 1 Hz. This frequency cannot be attributed to bubble passage whose main frequency would be several hertz. As there are only limited bubble –bubble interactions, bubble behaviour is mainly stochastic and does not induce a detectable characteristic frequency. On the contrary, liquid level oscillations can be visually observed and their frequency corresponds approximately to the one of the peaks in the PSDF plot. This is in accordance with previous results of Drahosˇ et al. [18]. When the heterogeneous regime prevails, the existence of a local liquid circulation pattern is established, but bubble aggregates or bubble clusters have also been reported [14,45]. This regime is thus characterised by the presence of macrostructures in both phases, the behaviour of which is, of course, closely linked. In the wall region, it can be visually observed in the bubble column that groups of bubble move alternatively upwards and downwards. This behaviour has been confirmed experimentally by local optical probe experiments performed by Groen et al. [46]. This corresponds to a quasi-periodic phenomenon that induces higher pressure fluctuations in the wall region and produce new characteristic frequencies in the spectrum of the pressure signal. It explains the peak observed at 3–5 Hz in Fig. 9. Even if bubble coalescence and break-up occur in this regime, it is

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

143

Fig. 9. PSDF in both reactors at different UG.

probable that the intensity of these phenomena, which occur stochastically, is far lower than that of the previous processes. In the transition region, the existence of the two peaks comes from the development of the quasi-periodical processes, which gradually overshadow the dominant sources of pressure fluctuations of the homogeneous regime. This interpretation can be extended in a first approximation to airlift reactors, with the restrictions mentioned previously in Section 1.2. With a non-uniform gas distribution, the difference observed between the bubble column and the airlift reactor comes from the respective influence of the distributor in both reactors. In the bubble column, the

single-orifice nozzle always operates in the jet regime. At low gas flow rate, the influence of the nozzle persists far from the distributor, as a large part of the column is partially aerated (Fig. 11a). This explains why the typical frequencies measured near the distributor (Fig. 12) are found in Fig. 9c and are dominant. A low-frequency band, corresponding to the slow oscillations of the bubble plume could also be expected. However, it may be assumed that this contribution is overshadowed by that of the phenomena occurring in the plume. This may be justified by the fact that the low-frequency band does not appear in the sparger region even if it is clearly observed that the bubble jet oscillates there (Fig. 12).

144

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

Fig. 10. Typical ACF curves in the homogeneous and heterogeneous regimes.

This is also in a qualitative agreement with the results obtained with a uniform aeration: the intensity of the low-frequency peak seems to be generally very weak (see Fig. 9a and b) and is probably far lower than that of the peak of the 10 – 20 Hz frequency band in Fig. 9c. It is also important to note that the relation between the flow structure and pressure may not be so straightforward as with local gas hold-up or local liquid velocity, as already mentioned in Section 2.2. Consequently, pressure is more difficult to interpret. This limitation has been already emphasised by Drahosˇ and Cerma´k [20]. At higher gas flow rate, the influence of the sparger disappears because the column is almost completely aerated in the region of the pressure sensor (Fig. 11b) and the flow is dominated by the presence of the macro-structures of the heterogeneous regime. In the airlift reactor, the 10 – 20 Hz frequency band never appears because the liquid circulation induces a rapid gas dispersion as it is obtained at high gas flow rate in the bubble column (Fig. 9b). This is the reason why the frequency band of the macro-structures always dominates the spectra.

sents the time during which events are correlated, it can be evaluated as follows: ~0 =

1 Cxx (0)

&

T

Cxx (~) d~

(6)

0

This time corresponds to the characteristic time of the structures of flow. As Cxx presents theoretically an exponentially decreasing shape, it can be approximated by the expression:

 

Cxx (~) ~ = exp − Cxx (0) ~0

(7)

In heterogeneous conditions, ACF is characterised by an oscillating component superimposed on random processes. This shape is less classical and requires a special treatment. The frequency f0 of the oscillations should correspond to the frequency of the peak in the PSDF. ACF can then be expressed as by Yutani et al. [34] in three-phase fluidised bed reactors to interpret the signal of micro-resistive probes:

5.2. ACF analysis PSDF shapes have been theoretically explained in the previous section. Spectral analysis of pressure fluctuations is able to distinguish regimes and to give information about characteristic frequencies of the phenomena in the respective regime. However, it does not provide a good determination of regime limits. ACF analysis seems far more promising. ACF evolution with gas velocity can be easily understood using PSDF behaviour. The time-domain representation differs, however, from the PSDF. Long-term periodic processes (10 − 1 Hz) do not appear in the ACF curve because the amplitude of the periodic oscillation they would induce is very weak, as can be deduced from the peak intensity in the PSDF (Fig. 9). This result justifies why the ACF may be evaluated only on the interval of 0 – 2 s without loosing information even at low UG values. In the homogeneous regime, ACF shape reflects typically classical random processes. A characteristic time ~0 repre-

Fig. 11. Influence of gas flow rate on aeration in the bubble column equipped with the single-orifice nozzle.

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

145

and Sharma [11] and the model of Zehner [12]. Zehner suggests the following relation for the vortex velocity: 6xy =



1 z L − zG gDcUG 2.3 zL

n

1/3

(10)

Joshi and Sharma proposed another formulation for the circulation rate: 6xy = 1.31[gDc(UG − mG6b )]1/3

Fig. 12. PSDF in the sparger region of the bubble column equipped with the single-orifice nozzle.

 

Cxx (~) ~ =cos (2yf0~)exp − Cxx (0) ~0

(8)

Experimental ACF curves can then be analysed using either Eq. (7) or Eq. (8), depending on their shape. This analysis finally yields a characteristic time ~0 and the dominant frequency f0 of the flow structure near the wall in both regimes.

5.3. Prediction of theoretical ~0 6alues Assuming the axial dimension of the flow structure is the bubble size (about 5 mm) in the homogeneous regime and the column diameter (10 cm) in the heterogeneous regime, ~0 can be estimated using the mean liquid circulation velocity near the wall 6xy. This quantity must be estimated. In bubble columns, two cases can be distinguished. In the homogeneous regime, 6xy is low. Measurements performed recently by Mudde et al. [42] report a downward velocity of 2 – 5 cm s − 1. The theoretical characteristic time is then evaluated as follows: ~0 =

D 6xy

(9)

where D is the dimension of the flow structure. In the homogeneous regime, D is in the order of magnitude of the bubble diameter (about 5 mm) as we have already said in Section 1.2. ~0 is between 0.05 and 0.1 s. In the heterogeneous regime, 6xy can be estimated using one of the models previously described in Section 1.2. We have retained two of them: the models proposed by Joshi

(11)

where 6b is the stationary rise velocity of individual bubbles. This model has the disadvantage to require the average gas hold-up to predict the circulation velocity. However, it is able to incorporate the influence of liquid velocity in gas –liquid co-current and counter-current flows when the liquid phase throughput is continuous. In the range of gas flow rate used, the two models give values of 6xy between 20 and 50 cm s − 1. The value of ~0 is then deduced using a value of the axial D:Dc (10 cm). It is found that ~0 is about 0.2 –0.5 s. It appears that the model predicts a value ~0 twice to ten times higher in the heterogeneous regime than in homogeneous conditions. ~0 could, therefore, be used to determine the regime transition in bubble columns. In airlift reactors, 6xy is easier to estimate. In the homogeneous regime, the velocity profile is flat [47] and 6xy is about the average liquid velocity in the riser ULR. Many correlations can be used to estimate ULR. In the homogeneous regime, we have used the correlation of Dhaouadi [48]. ULR is evaluated at about 10–20 cm s − 1. As a consequence, ~0 is between 0.025 and 0.05 s. In the heterogeneous regime, the velocity profile is almost parabolic, but near the wall, the mean liquid velocity in the riser ULR can also be used as a first approximation of 6xy. ULR is between 20 and 40 cm s − 1 using correlations reported by Joshi et al. [3]. The value of ~0 is then estimated using Dc = 10 cm and is about 0.2 –0.5 s. It appears that ~0 is a criterion, which should be able to detect the beginning of transition in airlift reactors. Table 1 summarises the theoretical values of ~0. The difference in ~0 values depending on the hydrodynamic regime can be interpreted in the following way. In the homogeneous regime, the characteristic time is small because there are little interactions between bubbles and ~0 is related to the flow and the bubble behaviour near the sensor. In the transition region and the heterogeneous regime, the presence of a

Table 1 Characteristic time and frequency values Reactor

Regime

Theoretical, ~0 (s)

~0 From ACF (s)

f0 From ACF (Hz)

Bubble column Bubble column Airlift reactor Airlift reactor

Homogeneous Heterogeneous Homogeneous Heterogeneous

0.05–0.1 0.2–0.5 0.02–0.05 0.25–0.5

0.05 (Eq. (7)) 0.25 (Eq. (8)) 0.02 (Eq. (7)) 0.4 (Eq. (8))

:0 2–5 :0 2–5

(Eq. (Eq. (Eq. (Eq.

(7)) (8)) (7)) (8))

146

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

Fig. 13. Comparison of ACF calculated from data and model.

macro-scale circulation of the liquid phase induces longer time scale processes.

6. Analysis of the characteristic time and frequency ACF curves, evaluated from experimental data, fit with Eq. (7) or Eq. (8) depending on its shape by means of the least-square method optimising on f0 and ~0. Fig. 13 illustrates the fitting of an ACF of the pressure signal based on Eq. (8). The characteristic frequency f0 is always found to be between 3 and 5 Hz and corre-

sponds to the frequency of the peak observed in the PSDF. Fig. 14 shows the evolution with UG of the characteristic time ~0 in the bubble column and the airlift reactor. In the homogeneous regime, ~0 is almost constant — in the bubble column equipped with the multiple-orifice sparger, it is about 0.05 s. Transition between regimes is accompanied by a steep increase in ~0. In the heterogeneous regime, it is about 0.3 s. The values of ~0 from Eqs. (7) and (8) have to be compared with the theoretically predicted values. Table 1 confirms that the agreement is very good. There is a factor 6 between ~0 in both regimes. The characteristic frequency f0 is near 0 in the homogeneous regime whereas it is 3 Hz in the heterogeneous regime. Regime limits obtained by this method are in good agreement with those obtained in Section 4 by more classical ways. As a consequence, the method is able to determine accurately the prevailing regime in a semi-batch bubble column from the knowledge of ~0 and f0. When the single-orifice sparger is used, ~0 rises continuously with UG, whereas f0 decreases continuously with UG from 5 to 3 Hz. It is remarkable that ~0 values obtained in the transition region with a uniform gas distribution are larger than ~0 values measured in the heterogeneous regime with a non-uniform gas distribution. This result is in agreement with the decrease of ~0 observed previ-

Fig. 14. Evolution of ~0 with UG in both reactors.

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

ously when the heterogeneous regime is reached and proves that the flow is more structured in the transition region than in the heterogeneous regime. In the airlift reactor equipped with the multipleorifice sparger, a shape similar to that of the bubble column is obtained for ~0 and f0, but the values of ~0 in both regimes are different and f0 is nearly 3 Hz even in the transition region. In the homogeneous regime, ~0 is about 0.03, whereas ~0 is about 0.5 in heterogeneous conditions. ~0 Decreases when fully established heterogeneous regime is reached, but less than in the bubble column. The study of the evolutions of ~0 and f0 with UG is shown to be a good criterion to detect regime transitions in external loop airlift reactors. The good agreement between these values and the theoretical value of ~0 is shown on Table 1. The regime limits are also in good agreement with the values obtained in Section 4. When the airlift reactor is equipped with the single-orifice nozzle, the results are similar to that of the bubble column and identical conclusions can be deduced. As a conclusion, the theoretical analysis proposed in the previous section has been validated on two different gas – liquid reactors — a bubble column and an airlift reactor. The ability of the method to detect regime limits is confirmed. The order of magnitude of ~0 and f0 from experiments is able to show if the reactor operates in the homogeneous regime. The evolution of the ~0 value in the three flow patterns shows that the first transition corresponds to the development of a macrocirculation structure, whereas the transition to the fully established heterogeneous regime corresponds to an alteration of this structure and a more chaotic flow.

7. Model improvement: estimation of the axial size of flow structures Up to now, we used correlations and theoretical considerations to predict theoretically the characteristic time. This value was compared with the value of ~0 obtained from the ACF analysis described in Section 6. We propose now to measure the liquid velocity near the wall, as this has already been done by several authors [20,46]. This velocity can be estimated using the transit velocity 6xy of the pressure signal between two sensors in the bubble column and the airlift reactor. 6xy can then be used to evaluate the axial dimension of the flow structure near the wall. The advantage of this method is that it provides both the characteristic time and the axial dimension of the flow structures from experiments. This can be useful for theoretical analysis and comprehension of the flow behaviour. However, this is not necessary when the objective is only the discrimination between regimes. In our case, the determination of the characteristic size of the flow structure in the axial

147

Fig. 15. Example of a CCF in the bubble column (distance between sensors: 10 cm).

direction will also be used to validate the hypothesis that D: Db in the homogeneous regime and D:Dc in the heterogeneous one. The transit velocity near the wall can be measured with the same pressure transducers we used previously. It requires, however, the simultaneous measurement of the pressure signal at two different heights and the evaluation of the cross-correlation function (CCF) between these signals. CCF of the two times series x(t) and y(t) is defined as follows: Cxy (~)= limT “

1 T

&

T

x(t)y(t−~) dt

(12)

0

The ACF is the limiting case when y= x. The CCF is able to detect if two signals are correlated. When x(t) and y(t) are coherent, the CCF exhibits a peak at ~"0, which corresponds to the mean time delay between the signals. In the bubble column, sensors have been located 10, 20 or 30 cm apart, depending on the gas flow rate. Fig. 15 shows a typical CCF with the three peaks commonly observed [46]. The sharp peak at ~= 0 corresponds to the phenomena occurring, simultaneously, near both sensors, such as bubble coalescence and break-up, or liquid level oscillations. The peak at ~B0 is due to the predominant liquid downward flow near the wall. The third peak at ~\ 0 is a consequence of ascending liquid velocity due to bubble passage near the wall. It confirms the fact that both positive and negative liquid velocity values coexist in the wall region in an unsteady manner [46]. However, the determination of the transit time can also be done accurately by another equivalent method proposed by Drahosˇ and Cerma´k [20]. It consists in evaluating the phase angle of the ‘cross spectral density function’ qxy, which is the Fourier transform of the CCF. The transit time function ~xy ( f ) is then deduced from the relation: qxy = − 2yf~xy ( f )

(13)

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

148

This method also gives additional information about frequency dependence of the transit time. ~xy has to be evaluated, simultaneously, with the coherence function, which indicates how both signals are correlated at a particular frequency. The coherence function is defined as: [Coherence( f )]2 =

F(Cxy ) 2 F(Cxx )F(Cyy )

(14)

A value of unity means coherent signals at a frequency f, whereas a value of zero means uncorrelated signals at this frequency. This method corresponds also to a linear fit of the phase angle qxy of the Cross-Spectral Density Function versus f, weighting it with the coherence function. Fig. 16 gives an example of the phase angle, coherence and the transit time functions (on Fig. 16, ~xy is between −0.25 and − 0.3 s when 05 f5 0.4 Hz). The peak of coherence between 3 and 5 Hz is not retained because it is due to bubble processes that occur simultaneously and give values of the transit time close to zero. For both methods, circulation velocity near the wall is then calculated using the transit time related to liquid downward circulation and the distance L between the sensors. 6xy =

L ~

With the single-orifice sparger, D increases more progressively because there is no break-up due to regime transition. Consequently, at a same gas velocity, D is higher with an efficient sparger than with a poor sparger in the range of UG corresponding to the transition region. Similar values of D are obtained only when the column operates in the heterogeneous regime with both spargers. In the airlift reactor, the mean liquid velocity ULR in the riser (obtained from the value of the liquid velocity measured in the downcomer by the tracer technique)

(15)

Fig. 17 presents the evolution of the measured liquid circulation velocity with UG in the bubble column. The values are compared with experimental values of Groen et al. [46] obtained in a 10-cm diameter column and with the values estimated using the models of Joshi and Sharma [11] and of Zehner [12]. The experimental values of 6xy are shown to be between the theoretical values. A good agreement is also obtained with the measurements of Groen et al. [46]. A rough estimation of the axial dimension of macrostructures for the bubble column is obtained from Eq. (9). The evolution of D versus UG in the bubble column is reported in Fig. 18a. D increases steeply when transition begins. With the multiple-orifice sparger, D is approximately 1 cm at the end of the homogeneous regime, whereas D is about 15 cm in the transition region and the heterogeneous regime within the accuracy of the measurements. This confirms the assumption that the scale of structure is of the order of the bubble size in the homogeneous regime and of the order of column diameter in heterogeneous conditions with a uniform gas distribution. The precision of the method is, however, limited by the accuracy of the liquid velocity measurement near the wall. As it is not possible to obtain good measurements when these velocities are too low or too high, precise measurements cannot be reached in fully established homogeneous or heterogeneous regimes. The influence of the sparger appears clearly when UG is between 3 and 9 cm s − 1.

Fig. 16. Example of phase, transit time and coherence functions.

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

149

8. Summary and conclusions

Fig. 17. Liquid circulation velocity near the wall.

can be used to estimate the transit velocity of the signal, as we assumed in Section 1.1. The evolution of D versus UG is shown in Fig. 18b. With the multiple-orifice sparger, D is found to be 5 – 10 mm at low gas velocity and 10–15 cm in the transition region and the fully established heterogeneous regime. D is shown to increase steeply at the beginning of the transition region. Results are more accurate than in the bubble column because a good estimation of the liquid velocity near the wall can be reached in all regimes. In both reactors, the scale dimensions found by this method are also in accordance with visual observation. As a conclusion, this method, based on the combined analysis of the ACF and CCF, gives a satisfactory estimation of the scale of the structures in the axial direction in accordance with the literature. The assumptions used for the theoretical prediction of ~0 are also confirmed. With the single-orifice nozzle, the evolution of D is more progressive. The influence of the sparger is similar to that observed in the bubble column. As a conclusion, D can be estimated successfully both in bubble columns and external loop airlift reactors equipped with an efficient gas sparger or a non-efficient one.

A model has been proposed to interpret pressure fluctuations near the wall both in a bubble column and an external loop airlift reactor. It is based on the analysis of ACF of the pressure signal. The model finally gives a characteristic time of the flow based on the pressure signal. This time is shown to be strongly dependent on the hydrodynamic regime. The evolution of ~0 and f0 versus UG provides a good determination of regime transitions. Combined to the analysis of CCF between the signals of two sensors, the method can be improved by measuring experimentally the liquid velocity near the wall 6xy. As a consequence, the axial dimension of flow structure D can also be estimated from experiments. The values of 6xy and D have been shown to be in agreement with literature data. These results also validate the theoretical estimation of ~0. Finally, this time-domain approach is shown to be useful for a better theoretical flow understanding. The evolution of D with UG shows that the flow is more structured in the transition region than in the heterogeneous regime. This result is in good agreement with the work of Letzel et al. based on chaos analysis [19]. The strong influence of the sparger on the flow structure has been highlighted by the evolutions of ~0, f0 and D. Many differences between the batch bubble column and the external loop airlift reactor have also been evidenced, especially when a non-uniform gas distribution is produced by the sparger. As a conclusion, the proposed method is shown to be reliable and efficient for regime discrimination and for a quantitative characterisation of the flow. This method has also a wide range of potential applications, “ it can be applied in industrial conditions because it is hopeful that the evolutions of ~0 and D are qualitatively similar in larger columns, even if scale effects affect the values of D and ~0; “ the validity of the method with non-coalescing media has still to be proved, but there is no a priori limitation due to the coalescence behaviour of the gas –liquid system.

Fig. 18. Evolution of the axial dimension of the flow structures with UG in both reactors.

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

150

We hope, therefore, that this method will be helpful for a better regime identification. The estimation of the characteristic time and size of the flow structures is also very important for flow comprehension and modelling. The importance of the coherent structures of the flow on reactor performance has been reminded recently [49]. Flow structures are not yet fully understood in bubble columns despite the recent progresses in measuring techniques [42,43]. The comprehension of the behaviour of these structures is, however, needed by the CFD approach, which has been developed recently [45,50]. We hope this method will also be helpful for further works in these fields.

Appendix A. Notations

C0, C1 Cxx, Cxy D Dc F(x) f f0 Hc L t T UG ULR 6b 6xy x, y

drift flux parameters in Eq. (1) correlation functions axial dimension of structures (m) column/riser diameter (m) Fourier transform of x frequency (Hz) characteristic frequency (Hz) height of the reactor (m) distance between sensors (m) time (s) length of a time series (s) superficial gas velocity (m s−1) superficial liquid velocity in the riser of the airlift reactor (m s−1) stationary rise velocity of a single bubble (m s−1) transit velocity (m s−1) time series

Greek letters mG average gas hold-up qxy phase angle of the cross spectral density function (rad) v average value of a time series (Pa) ~ time lag (s) ~0 characteristic time (s) ~xy transit time of the signal (s)

References [1] Y.T. Shah, B.G. Kelkar, S.P. Godbole, W.-D. Deckwer, Design parameters estimations for bubble columns reactors, Am. Inst. Chem. Eng. J. 28 (1982) 353–379. [2] W.-D. Deckwer, Bubble Column Reactors, Wiley, Chichester, UK, 1992.

[3] J.B. Joshi, V. Ranade, S.D. Gharat, S.S. Lele, Sparged loop reactors, Can. J. Chem. Eng. 68 (1990) 705– 741. [4] J. Zahradnı´k, M. Fialova, M. Ruzicka, J. Drahosˇ, F. Kasˇta´nek, N.H. Thomas, Duality of the gas– liquid flow regimes in bubble column reactors, Chem. Eng. Sci. 52 (1997) 3811– 3826. [5] K. Ueyama, T. Miyauchi, Properties of recirculating turbulent two-phase flow in gas bubble columns, Am. Inst. Chem. Eng. J. 25 (1979) 258– 266. [6] J.F. Walter, W. Blanch, Liquid circulation patterns and their effect on gas hold-up and axial mixing in bubble columns, Chem. Eng. Commun. 19 (1983) 243– 262. [7] Z. Yang, U. Rustermeyer, R. Buchholz, U. Onken, Profile of liquid flow in bubble columns, Chem. Eng. Commun. 49 (1986) 51 – 67. [8] J.B. Joshi, M.M. Sharma, A circulation cell model for bubbles columns, Trans. Inst. Chem. Eng. 57 (1979) 244– 251. [9] W. Freedman, J.F. Davidson, Holdup and liquid circulation in bubble columns, Trans. Inst. Chem. Eng. 47 (1969) T251–T262. [10] H.E.A. Van den Akker, K. Rietema, Comments on paper by Joshi and Sharma, Trans. Inst. Chem. Eng. 57 (1980) (1979) 1255– 1256. [11] J.B. Joshi, M.M. Sharma, Axial mixing in multiphase reactors: a unified correlation, Trans. Inst. Chem. Eng. 58 (1980) 155–165. [12] P. Zehner, Impuls-, Stoff- und Wa¨rmetransport in Bla¨sena¨ulen, Chem. Ing. Tech. 54 (1982) 248. [13] L.F. Burns, R.G. Rice, Circulation in bubble columns, Am. Inst. Chem. Eng. J. 43 (1997) 1390– 1401. [14] T.J. Lin, J. Reese, T. Hong, L.S. Fan, Quantitative analysis and computation of two-dimensional bubble columns, Am. Inst. Chem. Eng. J. 42 (1996) 301– 318. [15] J.C. Merchuk, Hydrodynamics and hold-up in air-lift reactors, in: N. Cheremisinoff (Ed.), Encyclopedia of Fluid Mechanics, Gulf Publishing, Houston, USA, 1993, pp. 1495– 1511. [16] G.B. Wallis, One-Dimensional Two-Phase Flow, Mc Graw-Hill, New York, 1969. [17] N. Bendjaballah, H. Dhaouadi, S. Poncin, N. Midoux, J.M. Hornut, G. Wild, Hydrodynamics and flow regimes in an external loop airlift reactor, Chem. Eng. Sci. 54 (1999) 5211–5221. [18] J. Drahosˇ, J. Zahradnı´k, M. Puncocha´r, M. Fialova´, F. Bradka, Effect of operating conditions on the characteristics of pressure fluctuations in a bubble column, Chem. Eng. Process. 29 (1991) 107– 115. [19] H.M. Letzel, J.C. Schouten, R. Krishna, C.M. van den Bleek, Characterisation of regimes and regime transitions in bubble columns by chaos analysis of pressure signals, Chem. Eng. Sci. 52 (1997) 4447– 4459. [20] J. Drahosˇ, J. Cerma´k, Diagnostics of gas– liquid patterns in chemical engineering systems, Chem. Eng. Process. 26 (1989) 147– 164. [21] B.R. Bakshi, H. Zhong, P. Jiang, L.-S. Fan, Analysis of flow in gas– liquid bubble columns using multi-resolution methods, Trans. Inst. Chem. Eng. 73 (1995) 608– 614. [22] R. Kikuchi, T. Yano, A. Tsutsumi, K. Yoshida, M. Punchocar, J. Drahosˇ, Diagnosis of chaotic dynamics of bubble motion in a bubble column, Chem. Eng. Sci. 52 (1997) 3741– 3745. [23] E. Camarasa, C. Vial, S. Poncin, G. Wild, N. Midoux, J. Bouillard, Influence of coalescence behaviour of the liquid and of gas sparging on hydrodynamics in a bubble characteristics in a bubble column, Chem. Eng. Process. (1999), 329– 344. [24] N. Zuber, J.A. Findlay, Average volumetric concentration in two-phase flow systems, J. Heat Transfer Trans. ASME 87 (1965) 453– 468. [25] K. Sriram, R. Mann, Dynamic gas disengagement: a new technique for assessing the behaviour of bubble columns, Chem. Eng. Sci. 32 (1976) 571– 580. [26] J.G. Daly, S.A. Patel, D.B. Bukur, Measurement of gas holdups and sauter mean bubble diameters in bubble column reactors by

C. Vial et al. / Chemical Engineering and Processing 40 (2001) 135–151

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35] [36]

[37]

dynamic gas disengagement method, Chem. Eng. Sci. 47 (1992) 3647– 3654. A. Schumpe, G. Grund, The gas disengagement technique for studying gas holdup structure in bubble columns, Can. J. Chem. Eng. 64 (1986) 891–896. N.S. Deshpande, M. Dinkar, J.B. Joshi, Disengagement of the gas phase in bubble columns, Int. J. Multiphase Flow 21 (1990) 1191– 1201. R. Krishna, P.M. Wilkinson, L.L. Van Dierendonck, A model for gas holdup in bubble columns incorporating the influence of gas density on flow regimes transitions, Chem. Eng. Sci. 10 (1991) 2491– 2496. M.A. Latifi, N. Midoux, A. Storck, J.N. Gence, The use of micro-electrodes in the study of flow regimes in a packed bed reactor with a single phase liquid flow, Chem. Eng. Sci. 44 (1989) 2501– 2508. M.A. Latifi, S. Rode, N. Midoux, A. Storck, The use of microelectrodes in the study of flow regimes in a trickle-bed reactor, Chem. Eng. Sci. 47 (1992) 1955–1961. L.A. Briens, C.L. Briens, A. Margaritis, J. Hay, Minimum liquid fluidization velocity in gas–liquid–solid fluidized bed of lowdensity particles, Chem. Eng. Sci. 52 (1997) 4231–4238. P.R. Thimmapuram, N.S. Rao, S.C. Saxena, Characterization of hydrodynamic regimes in a bubble column, Chem. Eng. Sci. 47 (1992) 3355– 3362. L.A. Glasgow, J. Hua, T.-Y. Yiin, L.E. Erikson, Acoustic studies of interfacial effects in airlift reactors, Chem. Eng. Commun. 113 (1992) 151– 181. N. Yutani, L.T. Fan, J.R. Too, Behavior of particles in liquid– solids fluidized bed, Am. Inst. Chem. Eng. J. 29 (1983) 101– 106. L.A. Glasgow, L.E. Erikson, C.H. Lee, S.A. Patel, Wall pressure fluctuations and bubble size distributions at several positions of an airlift fermentor, Chem. Eng. Commmun. 29 (1984) 331– 336. K. Tsuchiya, Y. Irahara, T. Tsubone, T. Tomida, Time-frequency analysis of local fluctuations induced by bubble flow, Fourth Japanese/German Symposium, Bubble Columns, Kyoto, Japan, Soc. Chem. Eng., 1997.

.

151

[38] J. Drahosˇ, F. Bradka, M. Puncocha´r, Fractal behaviour of pressure fluctuations in a bubble column, Chem. Eng. Sci. 47 (1992) 4069– 4075. [39] W. Luewisutthichat, A. Tsutsumi, K. Yoshida, Chaotic hydrodynamics of continuous single-bubble flow systems, Chem. Eng. Sci. 21 (1997) 3685– 3691. [40] C. Vial, E. Camarasa, S. Poncin, N. Midoux, G. Wild, N. Midoux, J. Bouillard, Study of the hydrodynamic behaviour in bubble columns and external loop airlift reactors through analysis of pressure fluctuations, Chem. Eng. Sci. 55 (2000) 2957– 2973. [41] R. Nottenka¨mper, A. Steiff, P.-M. Weinspach, Experimental investigation of hydrodynamics of bubble columns, Ger. Chem. Eng. 6 (1983) 147– 155. [42] R.F. Mudde, D.J. Lee, J. Reese, L.-S. Fan, Role of coherent structures on Reynolds stresses in a 2-D bubble column, Am. Inst. Chem. Eng. J. 43 (1998) 913– 926. [43] R.F. Mudde, J.S. Groen, H.E.A. van den Akker, Liquid velocity field in a bubble column: LDA experiments, Chem. Eng. Sci. 52 (1997) 4217– 4224. [44] J. Max, Me´thodes et techniques de traitement du signal et applications aux mesures physiques, vol. I, Masson et Cie Editeurs, Paris, France, 1972. [45] A. Lapin, A. Lu¨bbert, Numerical simulation of the dynamics of two-phase gas– liquid flows in bubble columns, Chem. Eng. Sci. 49 (1994) 3661– 3674. [46] J.S. Groen, R.F. Mudde, H.E.A. Van den Akker, Time dependent behaviour of the flow in bubble column, Trans. Inst. Chem. Eng. 73 (1995) 615– 621. [47] M.A. Young, G.R. Carbonell, D.F. Ollis, Airlift biorecators: analysis of the local two-phase hydrodynamics, Am. Inst. Chem. Eng. J. 37 (1991) 403– 428. [48] H. Dhaouadi, Etude d’un Re´acteur a` gazosiphon a` Recirculation externe, Doctoral thesis, INPL-Nancy, France, 1997. [49] H.E.A. Van den Akker, Coherent structures of multiphase-flows, Powder Technol. 100 (1998) 123– 136. [50] A. Sokolichin, G. Eigenberger, Gas– liquid flow in bubble columns and loop reactors: part I. Detailed modeling and numerical simulation, Chem. Eng. Sci. 49 (1994) 5747– 5762.