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Precise identification of the end of the gas maldistribution in bubble columns equipped with perforated plate gas distributors
Accepted Manuscript Precise Identification of the End of the Gas Maldistribution in Bubble Columns Equipped with Perforated Plate Gas Distributors Stoyan Nedeltchev PII: DOI: Reference:
S1385-8947(19)30893-9 https://doi.org/10.1016/j.cej.2019.04.115 CEJ 21535
To appear in:
Chemical Engineering Journal
Received Date: Revised Date: Accepted Date:
1 November 2018 24 March 2019 17 April 2019
Please cite this article as: S. Nedeltchev, Precise Identification of the End of the Gas Maldistribution in Bubble Columns Equipped with Perforated Plate Gas Distributors, Chemical Engineering Journal (2019), doi: https:// doi.org/10.1016/j.cej.2019.04.115
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To be considered for the GLS14 Special Issue
Precise Identification of the End of the Gas Maldistribution in Bubble Columns Equipped with Perforated Plate Gas Distributors Stoyan NEDELTCHEV1,2 1
Sofia University “Kliment Ohridski”, Department of Chemical Engineering and Pharmacy, 1164 Sofia, Bulgaria 2
Consulting firm “CRED” (Chemical Reactor Engineering & Development), 1618 Sofia, Bulgaria Email address: [email protected]
Abstract The gas maldistribution in bubble columns (BCs) is detrimental to their performance. In the literature hitherto, there is no any systematic studies about this practical problem. In this work, for the first time the upper boundary of the gas maldistribution has been identified based on different entropies (total and maximum information as well as Shannon) extracted from various time series. In addition, three other parameters (maximum number of visits in a region, number of crossings of the mean and modified average absolute deviation) have been introduced for successful identification of the range of gas maldistribution. Different BCs equipped with various types of perforated plate (PP) gas distributors have been used. Both shallow and deep bubble beds have been studied. Water and organic liquids have been investigated. It has been found that when the hole diameter (of the PP gas distributor) is between Ø 0.5×10-3 m and Ø 1.32×10-3 m, the gas maldistribution is stable up to superficial gas velocity Ug of 0.02 m/s. In the case of nitrogen-ethanol system, the transition velocity has occurred at much lower Ug (0.0062 m/s). Only when the hole diameter is as large as
Ø 4.0×10-3 m, then the upper boundary of the gas maldistribution shifts to somewhat higher Ug value (0.034 m/s). Keywords: Bubble columns; Gas maldistribution; Entropy analysis; Pressure fluctuations; Wire-mesh sensor; Tomographic techniques 1. Introduction Bubble columns (BC) are frequently used as gas-liquid contactors in both chemical and biochemical industries. They are utilized as absorbers, fermenters, flotation columns, etc. due to their excellent mass and heat transfer rates as well as intensive mixing. BCs are also used frequently for chemical reactions that require suspended catalyst particles. For instance, biochemical reactions, hydrogenation of liquid petroleum fractions and coal liquefaction. Although BCs are simple in construction and operation, their hydrodynamics are complex and a strong function of operating conditions (e.g. pressure and gas velocity), physical properties (e.g. liquid viscosity, surface tension) and scale (column diameter, bed height). The BC operation is strongly dependent on the bubble characteristics (bubble size, bubble rise velocity and bubble wake phenomena). These parameters determine the gas holdup, the interfacial area, the gas residence time and also the liquid mixing. Due to the complex BC hydrodynamics, multiple flow regimes are being formed as the superficial gas velocity Ug increases. The main three flow regimes are as follows: homogeneous (bubbly flow), transition and heterogeneous (churn-turbulent) [1-2]. In the available flow regime maps [1-3] the gas maldistribution is not included, which is 2
one of their drawbacks. Yamashita and Inoue [4] were the only ones who have measured the gas holdup under non-uniform inlet gas distribution conditions. In this article for the first time scientific parameters (instead of visual observations) will be used to identify the upper boundary (or the end) of the gas maldistribution regime. Some of these parameters are new (number of visits per region, total or maximum information entropy and modified average absolute deviation and Shannon entropy). The work is original since the gas maldistribution is not studied well in the literature hitherto and it is not included in the classical flow regime map [1]. A new database with transition velocities will be presented.
1.1. Description of gas maldistribution The hydrodynamics and flow patterns in BCs are complex phenomena, which makes both the design and scale-up of BCs a difficult task. The gas distributor design affects the flow patterns in the bubble bed and very often leads to non-uniform velocity profiles, short circuiting, bypassing and channeling, gas velocity fluctuations and backflow of fluid due to velocity differences between phases. The gas maldistribution leads to non-uniformities in the radial gas holdup profiles and it causes gas channeling and a significant lowering of the gas holdup. The gas maldistribution causes observable overall liquid circulation and leads to a smaller bed expansion for a given gas flow rate than for a uniform distribution of both fluids. It is worth noting that gas maldistribution can result not only from partial hole blockage but also from premixing of gas and liquid below the distributor plate.
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In general, the poor gas distribution occurs always at low Ug values when a perforated plate (PP) gas distributor or ring and cross spargers are used. This regime is detrimental to the BC performance and it should be avoided. Good knowledge of the extent of gas maldistribution is essential to the modelling, design and optimization of BCs. The use of PP gas distributors (or ring and cross spargers) generates preferentially aerated regions with enhanced liquid turbulence and dead zones in the bubble bed. Especially the existence of dead zones in the reactor’s volume substantially reduces the overall mass transfer efficiency. The factors (for instance the hole diameter or number of openings), which lead to the formation of gas maldistribution should be carefully studied. The gas maldistribution can influence heat and mass transfer rates as well as mixing and flow patterns of both the gas and liquid. According to Wilkinson et al. [5] the influence of the sparger design on gas holdup is negligible (for various liquids and at various pressures) provided that the sparger hole diameters are larger than approximately 1-2×10-3 m (and care is taken to avoid the gas maldistribution at the sparger). It is worth noting that in industry usually less effective gas spargers are used. They have larger hole diameters that are less sensitive to fouling. The influence of the gas sparger on flow patterns and gas holdup usually diminishes in tall BCs due to the ongoing process of bubble coalescence. In short BCs (bed aspect ratio<3) the liquid circulation patterns are not fully developed and they do not affect the gas holdup. Wilkinson et al. [5] argue that the flow patterns and the gas holdup are virtually
4
independent of the column dimensions and sparger layout (for low as well as high pressures) provided that the following three criteria are fulfilled: - the column diameter has to be larger than 0.15 m; - the column height to diameter ratio has to be in excess of 5; - the hole diameter of the gas sparger has to be larger than 1-2×10-3 m. There are no generally accepted procedures for the proper design of a gas distributor. In addition to the lack of design criteria, there is little appreciation of the consequences of gas maldistribution, e.g. caused by faultry design, fouling or hole blockage. The initial gas-liquid flow maldistribution has an influence on the gas holdup behavior. A bed contraction occurs when the gas and liquid are distributed non-uniformly. The gas distributors with the worst gas maldistribution generally give the greatest reduction in gas holdup. The gas maldistribution is associated with more vigorous liquid circulation patterns leading to consistently lower gas holdups. It is expected that the bubbling through a reduced number of orifices would increase the initial bubble size or at least channel the gas, leading to a reduction in gas holdup. In the case of gas maldistribution, the gas distributor appears to push the gas towards the column walls. It is essential to identify correctly the nature of the gas-liquid flow for every gas distributor. Gas and liquid maldistribution occur due to partial blockage of the gas distributor. Liquid circulation arises from the gas maldistribution. The gas holdup and overall bed expansion generally decrease as a result of gas maldistribution.
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It has been found that a uniform gas distributor leads to a higher overall gas holdup than a non-uniform one. A good gas distributor should introduce fine bubbles and distribute them (as well as the liquid) uniformly over the entire cross-section and minimize the pressure drop. The distributor hole blockage can also change the bubble size at the bottom of the column and this can also affect the gas holdups. The hole blockage leads to an increase in the gas distributor pressure drop and thus a deterioration in the gas distributor’s performance. Under some conditions a smaller area available for gas entry leads to higher orifice velocities and smaller bubbles, which could counterbalance the effect of spatial gas maldistribution. Gas maldistribution at the distributor causes a significant drop in the overall gas holdup. Maintaining a uniform spatial distribution of gas and liquid entry is clearly essential to ensure uniform motion and maximum fluid holdups in BCs.
1.2. Description of main hydrodynamic regimes Three different flow regimes (homogeneous, transition and heterogeneous) are usually observed in the BC operation. However, at very low Ug values chain bubbling regime might be observed [6-8]. The mechanisms governing both the homogeneous and heterogeneous regimes are different. In general, the global and local flow properties in BCs are related to the prevailing flow regime. The transitions between the different flow regimes depend on the operating mode, design parameters and the physicochemical properties of the phases. For instance, in viscous liquids (such as mono-ethylene glycol) the transition to the churn-turbulent regime occurs at a very 6
low Ug value [5]. In liquids with lower surface tension (for example, n-heptane) the transition to the churn-turbulent regime is delayed and it corresponds to higher transitional gas holdup [5]. It has been reported that the increase of gas density (or operating pressure) shifts the main transition velocity to higher Ug values. In order to understand the gas maldistribution better, one should know the main characteristics of both homogeneous (bubbly flow) and transition flow regimes, which follow after the gas maldistribution. The homogeneous regime is characterized by a narrow bubble size distribution (BSD). According to Leonard et al. [2] two sub-regimes can be distinguished depending on the span of the BSD. In the case of a narrow BSD the flow is called “perfect bubbly”. The “imperfect bubbly flow” is characterized with a larger BSD. Guédon et al. [9] have also distinguished “pure homogeneous”
(or
“mono-dispersed
homogeneous”)
sub-regime
and
“pseudo-homogeneous” (or “poly-dispersed homogeneous”) sub-regime. The latter is characterized by the presence of large bubbles whose lift coefficient is negative. In the homogeneous regime there is no bubble coalescence. The flow pattern is primarily determined by the primary bubble size formed at the gas distributor. The turbulence is mainly attributed to bubble drag, resulting in a liquid microcirculation. There is a gentle agitation of the gas-liquid dispersion and uniform gas holdup profile. The transition between the homogeneous and heterogeneous regimes is a gradual process. The transition between both main flow regimes is caused by the formation of large fast-rising bubbles. The formation of the first large bubbles can be delayed to a higher Ug value when the coalescence rate is reduced by the addition of an electrolyte. 7
In the transition flow regime a macro-circulation occurs [2,10]. There is a widened BSD. The formation of first large (coalesced) bubbles is observed. The critical velocity between the homogeneous and heterogeneous regimes can be affected by various parameters (column diameter, liquid viscosity, presence of surfactants, temperature, pressure, etc.). The transition flow regime has been subdivided into first and second sub-regimes [11,12]. Chen et al. [13] has subdivided the heterogeneous regime into several sub-regimes. In most of the publications on BCs the gas maldistribution has not been studied. For the first time, Nedeltchev et al. [10,14] have identified clearly the upper boundary of the gas maldistribution. At high Ug values, the fully developed heterogeneous (churn-turbulent) flow regime is established. It is associated with high coalescence and break-up rates and a wide variety of bubble sizes. León-Becerril et al. [15] have reported that for an air-water system the transition between homogeneous and heterogeneous regimes occurs at Ug value between 0.04 and 0.05 m/s. Zahradník and Fialová [16] have reported a transition velocity of 0.04 m/s for an air-water BC (0.14 m in ID) equipped with a PP gas distributor (hole diameter: Ø 0.5×10-3 m). Leonard et al. [2] also argues that for an air-water system the transition velocity appears at 0.04 m/s depending on both the gas distributor and column design. Therefore, the gas maldistribution should disappear below this critical velocity. The main objective of this work is to identify the upper boundary of the gas maldistribution based on efficient novel methods for flow regime identification. The 8
new identification methods will be applied to various time series obtained by modern measurement techniques. Newly identified transition velocities in several BCs equipped with different PP gas distributors will be reported. Both water and organic liquids will be used.
2. Identification methods In this work, the upper boundary of the gas maldistribution will be identified based on different entropies and other statistical parameters extracted from various time series. The following entropies will be used:
2.1. Modified information entropy and Shannon entropy derived from gauge pressure fluctuations The time series (10,000 points) of gauge pressure (GP) fluctuations have been divided into 10 intervals (1000 points). For each of them, the average absolute deviation (AAD) [17] has been calculated. Then, the information entropy (IE) algorithm developed by Nedeltchev et al. [18] has been applied. As a first step, the sum of all ten AAD has been calculated. Each particular probability has been estimated as a ratio between the local AAD for that interval and the sum of all AAD. Then the local information amount and IE (product of the probability and the information amount) have been calculated. According to the algorithm, the total IE is a sum of all local IE. The modified Shannon entropy (SE) has been calculated from the same ten AAD values at each run based on the SE algorithm proposed by Nedeltchev et al. [19]. The
9
local SE for each interval has been calculated based on the above-mentioned definition of probability. The total SE is a sum of all local SE values.
2.2. Maximum and total information entropy derived from photon counts and differential pressure fluctuations These two parameters have been introduced by Nedeltchev and Shaikh [18]. The range of various signals has been divided into different regions (with predetermined height) between the minimum and maximum values of the fluctuations. The number of visits of the signal into each of these regions has been counted. Then, the classical IE theory has been applied. As a unit height has been used the height of the smallest region [18]. The total IE is a sum of the products of the probability, information amount and dimensionless height of each visited region. This parameter gives the total information that could be obtained from a fluctuating signal, which visits multiple regions. The maximum information entropy IEmax represents the highest IE among all regions. This parameter gives the maximum information that could be obtained from a single region (which usually is the most frequently visited one). Three other statistical parameters (maximum number of visits in a region, number of crossings of the mean and modified average absolute deviation) will be explained briefly in section 4. In Table 1 are summarized the scientific parameters used to identify the end of the gas maldistribution in different BCs.
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Table 1. Summary of the scientific parameters applied to various signals. Gas distributor Perforated plate (PP) 121 holes, Ø 1.32×10-3 m Perforated plate (PP) 241 holes, Ø 3.0×10-3 m Perforated plate (PP) 19 holes, Ø 1.0×10-3 m Perforated plate (PP) 14 holes, Ø 4.0×10-3 m Perforated plate (PP) 101 holes, Ø 4.0×10-3 m Perforated plate (PP) 163 holes, 1.32×10-3 m Perforated plate (PP) 64 holes, 1.32×10-3 m Perforated plate (PP) 55 holes, 0.5×10-3 m
Column diameter 0.14 m
Recorded signal
Parameter used AAD and NC
0.162 m
Gauge pressure (GP) fluctuations Gauge pressure (GP) fluctuations Differential pressure (DP) fluctuations Gas holdup fluctuations Gas holdup fluctuations Photon counts
0.1 m
Photon counts
0.1 m
Pixel values (X-ray scans)
0.45 m 0.102 m 0.15 m 0.40 m
Total IE and SE Max # of visits Total IE Maximum number of visits in a region Maximum number of visits in a region Maximum information entropy Maximum information entropy Modified AAD
3. Experimental setups and measurement techniques 3.1. Gauge pressure (GP) fluctuations in bubble columns The GP fluctuations (10 000 points) have been recorded (at a sampling frequency of 67 Hz) in two air-tap water BCs (0.14 m and 0.45 m in ID) by means of GP transducer PX409 (Omega Inc., USA) . They have been installed at an axial height z of about 1 m above the gas distributor. The raw data have been low-pass filtered in order to eliminate or minimize the noise. The small BC (0.14 m in ID) has been equipped with a PP gas distributor (121 holes, Ø 1.32 × 10-3 m, open area (OA)=1.08 %). The large BC (0.45 m in ID) has been also equipped with a PP gas distributor, however, with larger number of holes (241 holes, Ø 3.0 × 10-3 m, OA=1.07 %). Two different clear liquid heights (1.33 and 0.4 m) have been tested in the small BC and two deeper clear liquid heights (1.91 and 11
2.67 m) have been tested in the large BC. The bed aspect ratios in the smaller column have been fixed at 9.5 and 2.86, respectively. In the bigger column the bed aspect ratios have been fixed at 4.24 and 5.93. It is worth noting that only the hole diameter and the column diameter as well as one of the clear liquid heights in both columns have satisfied the scale-up criteria of Wilkinson et al. [5]. The pressure transducers PX409 have been always connected to OMB-DAQ-56 (Omega Inc., USA) data acquisition board.
3.2. Differential pressure (DP) fluctuations in a bubble column The DP fluctuations (10 000 points) have been measured (at a sampling frequency of 100 Hz) in a stainless steel BC (0.102 m in ID) by means of DP transducers (LABOM GmbH, Germany). The raw data have been low-pass filtered in order to eliminate or minimize the noise. One end of the transducers has been connected to a certain axial position z (0, 0.65 or 1.2 m), while the other end has been connected to the top of the column. The BC has been equipped with a PP gas distributor (19 holes, Ø 1.0 × 10-3 m, OA=0.19 %). The clear liquid height has been set at 1.3 m, i.e. the bed aspect ratio has been fixed at 12.75. As a gas phase has been used nitrogen, whereas as a liquid phase has been used both tap water and ethanol (96 %). It is worth noting that only the hole diameter and the bed aspect ratio have satisfied the scale-up criteria of Wilkinson et al. [5].
3.3. Gas holdup fluctuations measured by a wire-mesh sensor A new statistical parameter has been extracted from gas holdup fluctuations (60 000 points) recorded (at a sampling frequency of 2000 Hz) by means of a wire-mesh 12
sensor in two air-water BCs (0.15 m and 0.4 m in ID) operated with different PP gas distributors (the orifice diameter was kept constant at Ø 4.0×10-3 m). The raw data have been low-pass filtered in order to eliminate or minimize the noise. The PP gas distributor in the smaller column has consisted of 14 holes, whereas 101 holes have been available on the gas sparger in the bigger column. In such a way, the OA has been kept constant at 1 %. Both BCs have been operated with an air-deionized water system at ambient conditions. The clear liquid height in both columns have been adjusted at 2.0 m. The bed aspect ratio in the smaller column has been fixed at 13.33, whereas the one in the bigger column has been set at 5. It is worth noting that in the case of these measurements all three scale-up criteria of Wilkinson et al. [5] have been satisfied. The conductivity wire-mesh sensors have consisted of 2 electrode planes each with 24 (in the case of the small BC) or 64 (in the case of the large BC) stainless-steel wires of 0.2×10-3 m and 6.125×10-3 m distance between the wires. The distance between the planes has been set at 4.0×10-3 m and the wires from different planes have crossed each other at right angles. This arrangement has consisted of 576 (in the small BC) or 4096 (in the large BC) crossing points, 78 % thereof inside the circular cross-sections of both columns. One plane of the electrodes has acted as a transmitter, while the other plane has acted as a receiver. More details about the wire-mesh sensors are available in Nedeltchev et al. [10]. The conductivity wire-mesh sensors have been always installed at an axial height of 1.3 m above the gas distributor.
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3.4. Photon count fluctuations recorded by computed tomography (CT) and nuclear gauge densitometry (NGD) in bubble columns Photon counts (10 000 points) have been also used for identification of the end of the gas maldistribution. They have been measured (at a sampling frequency of 20 Hz) by means of Computed Tomography (CT). The raw data have been low-pass filtered in order to eliminate or minimize the noise. The setup has consisted of an array of 5 scintillation detectors (SD) with an opposing radioactive source. Both the detectors and the source have rotated together around the BC. The CT scanner has used a Cesium (Cs-137) encapsulated gamma-ray source with an activity of about 85 mCi. The array of 5 SD and the source have been mounted on a gantry, which has been able to rotate 360o around the BC. The SD have been made of NaI. Each detector has consisted of a cylindrical 0.0510.051 m NaI crystal, a photo multiplicator and electronics, forming a 0.0540.26 m cylindrical assembly. In each view, every detector has acquired 7 projections, covering a total angular span of 2.72o of the detector face. A total of 99 views have been acquired, with 3.6o of angular shift after every view. The gas holdup distribution at each cross-sectional plane have been obtained from 3465 projections (5799). All CT scans have been performed at a dimensionless axial height of 5.5, which means that the measurements have been recorded at z=0.89 m above the gas sparger. The aerated liquid height has been fixed at 1.8 m, which corresponded to a bed aspect ratio of 11.11. More details about the CT setup can be found in Nedeltchev et al. [18,20,21]. The CT scans have been performed in a BC (0.162 m in ID, total height=2.5 m) 14
operated with an air-therminol LT system. The BC has been equipped with a PP gas distributor (163 holes, 1.3210-3 m, OA=1.08 %). It is worth noting that all three scale-up criteria of Wilkinson et al. [5] have been satisfied. The existing CT setup has been converted into Nuclear Gauge Densitometry (NGD) by placing a detector in front of an encapsulated gamma-ray Cs-137 source (about 100 mCi). A collimator (0.160.4810-2 m) has been placed in front of the detector. A focused beam of radiation has been transmitted from the source through the column and the gas-liquid dispersion to the SD. As the density of the material in the column has changed, the amount of radiation reaching the detector has varied. It is generally believed that the amount of radiation is reflective of its flow behavior and properties. The main advantages of both CT and NGD techniques are that they are nonintrusive-the sources and detectors are mounted externally from the column and thus they are completely unaffected by the conditions inside it. The NGD scans have been performed at a sampling frequency of 50 Hz in an air-water BC (0.1 m in ID, aerated liquid height=1.2 m) equipped with a PP gas distributor (64 holes, 1.3210-3 m, OA=1.09 %). The detector has recorded the photon counts (10 000 points) at an axial height of 0.89 m. More details about the NGD setup can be found in Nedeltchev et al. [20]. It is worth noting that only the hole diameter and the bed aspect ratio (12) have satisfied the scale-up criteria of Wilkinson et al. [5].
3.4. X-ray fluctuations recorded by ultrafast X-ray tomography The tomographic X-ray facility has not employed rotating objects or source-detector compounds. An electron beam (of up to 10 kW power) has been 15
sharply focused on a circular tungsten target and has been at the same time periodically deflected with a high frequency in order to generate a moving focal spot on the target and thus an X-ray source rotating around the column. This X-ray source has irradiated the column from different viewing angles. X-rays have been produced in the beam’s focal spot. Rapid deflection by means of electron optics has allowed a fast circulation of the focal spot around the column. A static detector ring surrounding the column has measured the radiation passing the column at a high frequency synchronized with the beam deflection. X-rays passing the BC have been recorded by a very fast multi-pixel X-ray arc detector co-aligned with the target. From the projected data set of one revolution of the electron beam a non-superimposed cross-sectional image of the density distribution within the column can be reconstructed. A snapshot of the in-house developed ultrafast electron beam X-ray tomographic facility is available in Nedeltchev et al. [22]. This nonintrusive measurement technique could be used to visualize stacks of cross-sectional images of the flow structure inside the BC. The X-ray scans have been performed in an air-water BC (0.1 m in ID) at z=0.5 m above the PP gas distributor (55 holes, 0.510-3 m, OA=0.14 %). The clear liquid height has been fixed at 0.66 m, which corresponded to a bed aspect ratio of 6.6. It is worth noting that only the hole diameter and the bed aspect ratio have satisfied the scale-up criteria of Wilkinson et al. [5]. The time series (29 000 points) have been recorded at a sampling frequency of 1000 Hz (i.e. 1000 cross-sectional images per second) at a spatial resolution of 110-3
16
m. The raw data have been low-pass filtered in order to eliminate or minimize the noise. More details are available in Nedeltchev et al. [22]. In Table 2 are summarized both the experimental facilities and measurement techniques used. Table 2. Summary of the experimental facilities and measurement techniques used. Gas distributor Perforated plate (PP) 121 holes, Ø 1.32×10-3 m Perforated plate (PP) 241 holes, Ø 3.0×10-3 m Perforated plate (PP) 19 holes, Ø 1.0×10-3 m Perforated plate (PP) 14 holes, Ø 4.0×10-3 m Perforated plate (PP) 101 holes, Ø 4.0×10-3 m Perforated plate (PP) 163 holes, 1.32×10-3 m Perforated plate (PP) 64 holes, 1.32×10-3 m Perforated plate (PP) 55 holes, 0.5×10-3 m
Column diameter 0.14 m
Clear liquid height 0.4, 0.65, 1.33 m
0.45 m
1.91 m, 2.67 m
0.102 m
1.3 m
0.14 m
2.0 m
0.40 m
2.0 m
0.162 m
1.8 m (aerated) 1.2 m (aerated) 0.66 m
0.1 m 0.1 m
Measurement method Gauge pressure (GP) transducer Gauge pressure (GP) transducer Differential pressure (DP) transducer Wire-mesh sensor (conductivity) Wire-mesh sensor (conductivity) Computed tomography (photon counts) Nuclear gauge densitometry (photons) X-ray tomography (pixel values)
4. Results and Discussion 4.1. Identification of the end of the gas maldistribution based on GP fluctuations In the case of a bigger (0.45 m in ID) BC equipped with a PP gas distributor (241 holes, Ø 3.0×10-3 m, OA=1.07 %) and operated with an air-tap water system, the end of the gas maldistribution was identified at Ug = 0.018 m/s. Figures 1a-b show that at this Ug value and z=1.05 m the total IE and SE exhibit a well-pronounced local minimum. Figures 2a-b show photos, which clearly demonstrate the gas maldistribution effect on the flow structure. At Ug = 0.016 m/s (see Fig. 2a) the right 17
part of the BC is still not well aerated. At Ug = 0.026 m/s (see Fig. 2b) almost every opening of the gas distributor forms bubbles.
(a)
(b) Fig. 1. Total IE and SE profiles as a function of Ug in an air-water BC (0.45 m in ID). Axial position z=1.05 m. Clear liquid height=1.91 m.
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(a)
(b) Fig. 2. Gas maldistribution in a BC (0.45 m in ID) operated at: (a) Ug=0.016 m/s; (b) Ug=0.026 m/s. Clear liquid height=1.91 m. Fig. 3 shows the profile of a parameter called maximum number of visits in a single region Nvmax. The algorithm for its calculation is explained in Nedeltchev et al. [10]. Both the minimum and maximum values of every signal are determined and then it is divided into multiple regions. The smallest region is with a height of 0.0005 and the other regions are proportional (2, 3, 4 and 5 times) to the lowest height. The parameter Nvmax corresponds to the maximum number of visits in one of these regions. 19
Fig. 3 shows that in a deeper bubble bed (clear liquid height=2.67 m) and at a higher axial position (z=1.41 m) the end of the gas maldistribution occurs at somewhat lower Ug value (0.015 m/s). A well-pronounced local minimum in the Nvmax profile distinguishes the onset of the bubbly flow regime.
Fig. 3. Nvmax profile as a function of Ug in an air-water BC (0.45 m in ID). Axial position z=1.41 m. Clear liquid height=2.67 m.
Fig. 4 shows that in a small BC (0.14 m in ID) equipped with a PP gas distributor (121 holes, Ø 1.32 × 10-3 m, OA=1.08 %) at an axial position z=1 m above the gas distributor, the transition velocity occurs at somewhat higher Ug value (0.02 m/s). There is a well-pronounced local minimum in the AAD profile.
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Fig. 4. AAD profile as a function of Ug in an air-water BC (0.14 m in ID). Axial position z=1.0 m. Clear liquid height=1.33 m. Almost identical transition velocity (Ug=0.021 m/s) has been identified in the same BC at z=0.25 m and clear liquid height=0.65 m. Figure 5 shows that the AAD profile has a well-pronounced local minimum at the end of the gas maldistribution.
Fig. 5. AAD profile as a function of Ug in an air-water BC (0.14 m in ID). Axial position z=0.25 m. Clear liquid height=0.65 m. 21
Figure 6 exhibits that the parameter “number of crossings” NC of the mean of the signal can be used for flow regime identification. In a shallow bubble bed (clear liquid height=0.4 m) the range of the gas maldistribution is narrower and thus its transition to bubbly flow regime occurs earlier. At Ug=0.016 m/s the NC profile exhibits a very well-pronounced local minimum. Below this critical Ug value the NC values monotonously decrease, while beyond the transition velocity the NC values start to increase again.
Fig. 6. NC profile as a function of Ug in an air-water BC (0.14 m in ID). Axial position z=0.12 m. Clear liquid height=0.4 m. 4.2. Identification of the end of the gas maldistribution based on gas holdup fluctuations recorded by a wire-mesh sensor Nedeltchev et al. [10] has defined a new parameter called maximum number of visits in a single region Nvmax. It has been extracted from gas holdup fluctuations recorded in two BCs by a wire-mesh sensor at an axial height of 1.3 m. All the details about the division of the signals between their minimum and maximum values are provided in [10]. Fig. 7 shows that in a small BC (0.15 m in ID) equipped with a PP 22
gas distributor (14 holes, 4.010-3 m, OA=1.14 %) this parameter is capable of identifying the end of the gas maldistribution and the formation of the transition flow regime. At Ug=0.034 m/s the Nvmax profile exhibits a well-pronounced minimum. Figs. 8a-c clearly demonstrate the existence of the gas maldistribution at Ug=0.01, 0.02 and 0.03 m/s, respectively. Figure 8d shows that at Ug=0.045 m/s every opening of the gas distributor generates bubbles.
Fig. 7. Profile of Nvmax as a function of Ug in an air-water BC (0.15 m in ID). Axial position z=0.5 m. Clear liquid height=2.0 m.
(a) 23
(b)
(c)
(d) Fig. 8. Gas maldistribution in a BC (0.15 m in ID) operated at: (a) Ug=0.012 m/s, (b) Ug=0.022 m/s, (b) Ug=0.034 m/s, (d) Ug=0.045 m/s, Clear liquid height=2.0 m. 24
Fig. 9 exhibits that in a larger BC (0.4 m in ID) equipped with a PP gas distributor (101 holes, 4.010-3 m, OA=1.01 %) the gas maldistribution is stable up to Ug=0.034 m/s. At this critical velocity a well-pronounced local minimum in the Nvmax profile occurs, which marks the onset of the transition flow regime. Figs. 10a-d clearly demonstrate that the gas maldistribution do exist.
Fig. 9. Profile of Nvmax as a function of Ug in an air-water BC (0.4 m in ID). Axial position z=0.5 m. Clear liquid height=2.0 m.
(a) 25
(b)
(c)
(d) Fig. 10. Gas maldistribution in a BC (0.40 m in ID) operated at: (a) Ug=0.011 m/s, (b) Ug=0.023 m/s, (b) Ug=0.034 m/s, 26
(d) Ug=0.045 m/s, Clear liquid height=2.0 m. 4.3. Identification of the end of the gas maldistribution based on photon counts recorded by a computed tomography Nedeltchev and Shaikh [18] has demonstrated that a gas maldistribution also exists in a BC (0.162 m in ID) equipped with a PP gas distributor (163 holes, 1.3210-3 m, OA=1.08 %) and operated with an air-therminol LT system at ambient conditions. The aerated liquid height has been fixed at 1.8 m. Photon counts have been recorded by five different scintillation detectors (SD). Fig. 11a-d show that the maximum information entropy (IEmax) extracted from the readings of detectors 1, 2, 4 and 5 is capable of identifying the end of the gas maldistribution. At Ug=0.02 m/s the IEmax profile suddenly drops, which indicates the upper limit of the gas maldistribution and its transformation into transition flow regime.
(a)
27
(b)
(c)
28
(d) Fig. 11. Profile of IEmax as a function of Ug in the case of: (a) SD I, (b) SD II, (c) SD IV and (d) SD V. The photon counts have been also recorded by means of a NGD in an air-tap water BC (0.1 m in ID, 1.2 m in height) equipped with a PP gas distributor (64 holes, 1.3210-3 m, OA=1.12 %). Fig. 12 shows that the IEmax profile is capable of identifying the end of the gas maldistribution at Ug=0.02 m/s. Beyond this critical velocity the IEmax values monotonously increase up to Ug=0.035 m/s and then the trend reverses again.
29
Fig. 12. Profile of IEmax as a function of Ug based on photon counts recorded by nuclear gauge densitometry in a BC (0.1 m in ID). 4.4. Identification of the end of the gas maldistribution based on ultrafast X-ray tomography When the time series are divided into 289 vector pairs (each vector consisting of 50 elements) and the distance between each vector pair is estimated (based on the maximum norm definition), then the modified average absolute deviation (AAD) can be used to identify the end of the gas maldistribution. Only the repeating cases with distance smaller than the cut-off length (=3AAD) have been taken into account. It has been counted how many times the consecutive vector pairs repeat twice, three times, four times, etc. Then, based on the distribution of these numbers the AAD definition has been applied. The new parameter is called modified AAD since it is applied to reconstructed data. Fig. 13 shows that in an air-water BC (0.1 m in ID, clear liquid height=0.66 m) equipped with a PP gas distributor (55 holes, 0.510-3 m, OA=0.14 %) the modified AAD exhibits a local minimum at Ug=0.02 m/s. This 30
critical gas velocity distinguishes the end of the gas maldistribution and the onset of the bubbly flow regime. This result is similar with the results in Figs. 4, 5 and 11.
Fig. 13. Profile of modified AAD as a function of Ug in air-water BC (0.1 m in ID). Fig. 14 shows that the photos for Ug=0.01 and 0.02 m/s confirm the existence of gas maldistribution in the case of PP gas distributor. All openings of the gas distributor begin to form bubbles at Ug=0.04 m/s.
Fig. 14. Photographic evidence for the existence of gas maldistribution in an air-water BC (0.1 m in ID) equipped with a perforated plate (PP) gas distributor. 4.5. Identification of the end of the gas maldistribution based on DP fluctuations It has been found that when the total IE algorithm developed by Nedeltchev and Shaikh [18] is applied to differential pressure (DP) fluctuations, then the end of the 31
gas maldistribution can be identified in a straightforward manner. In every signal the difference between the minimum and maximum values has been determined and then the fluctuations have been divided into various regions with different heights (the smallest height has been set at 0.5 mbar and every other height has been increased with this value). The number of visits of the signal in the different regions has been used to calculate the local probability, information amount and IE. All heights have been taken into account in the algorithm. The total IE has been calculated as a sum of all local IE values. Fig. 15a shows that in the vicinity (z=0 m) of the PP gas distributor (19 holes, Ø 1.0×10-3 m, OA=0.19 %) the end of the gas maldistribution regime occurs at Ug = 0.014 m/s in a BC (0.102 m in ID, clear liquid height=1.3 m) operated with a nitrogen–tap water system. The total IE exhibits a local minimum at this particular Ug value. When the axial position z is located in the upper zone of the column, then the end of the gas maldistribution is shifted to higher Ug value (0.021 m/s). In other words, the effect of the gas maldistribution is more pronounced in the upper zone of the column. At z=0.65 m the transition flow regime begins at Ug = 0.01 m/s.
32
(a)
(b) Fig. 15. Profile of total IE as a function of Ug in a N2-tap water BC (0.102 m in ID): (a) at z=0 m; (b) at z=1.2 m. In the case of nitrogen–ethanol (96 %) system in the same BC (0.102 m in ID), the total IE profile (see Fig. 16a-c) is capable of identifying the end of the gas maldistribution regime at Ug=0.0062 m/s. At all three axial positions z a well 33
pronounced local minimum in the total IE profile at Ug=0.0062 m/s is observed. This is a much lower transition velocity than the one in a N2-tap water system. The main reason is the smaller mean bubble diameter (and thus lower degree of liquid turbulence) in the N2-ethanol system. Beyond this critical velocity the total IE profile monotonously increases, which implies that the behavior of the system becomes more predictable (more information is gained).
(a)
34
(b)
(c) Fig. 16. Profile of total IE as a function of Ug in a N2-ethanol BC (0.102 m in ID): (a) at z=0 m; (b) at z=0.65 m and (c) at z=1.2 m. The results from this study are summarized in Table 3. It is clear that for most of the PP gas distributor types, the end of the gas maldistribution occurs at Ug = 0.02 m/s.
35
Only when the distributor holes have a diameter 4.010-3 m, then the range of the gas maldistribution extends to Ug = 0.034 m/s. Table 3. Effect of the PP gas distributor characteristics on the end of the gas maldistribution. Type of gas distr.
Open area
Column
Liquid height
Gas-liquid system
End of gas maldistr.
diam.
241 holes, Ø 3.0×10-3 m
1.07 %
0.45 m
1.91 m
Air-tap water
Ug = 0.018 m/s
241 holes, Ø 3.0×10-3 m
1.07 %
0.45 m
2.67 m
Air-tap water
Ug = 0.015 m/s
121 holes, Ø 1.32×10-3 m 121 holes, Ø 1.32×10-3 m 121 holes, Ø 1.32×10-3 m 14 holes, 4.010-3 m 101 holes, 4.010-3 m 163 holes, 1.3210-3 m 64 holes, 1.3210-3 m 55 holes, 0.510-3 m 19 holes, 1.010-3 m
1.08 %
0.14 m
1.33 m
Air-tap water
Ug = 0.02 m/s
1.08 %
0.14 m
0.65 m
Air-tap water
Ug = 0.021 m/s
1.08 %
0.14 m
0.4 m
Air-tap water
Ug = 0.016 m/s
1.14 %
0.15 m
2.0 m
Air-tap water
Ug = 0.034 m/s
1.01 %
0.40 m
2.0 m
Air-tap water
Ug = 0.034 m/s
1.08 %
0.162 m
Air-therminol
Ug = 0.02 m/s
1.12 %
0.1 m
Air-tap water
Ug = 0.02 m/s
0.14 %
0.1 m
1.8 m (aerated) 1.2 m (aerated) 0.66 m
Air-tap water
Ug = 0.02 m/s
0.19 %
0.1 m
1.3 m
N2-tap water
Ug = 0.014 m/s Ug = 0.021 m/s
19 holes, 1.010-3 m
0.19 %
0.1 m
1.3 m
N2-ethanol
Ug = 0.006 m/s
In Fig. 16 are shown the gas maldistribution conditions for air-water system (see the black circles) from Table 3, which are plotted on the famous flow regime map of Shah et al. [1]. It is obvious that the hole diameter of the PP gas distributor plays an 36
important role on the end of the gas maldistribution. The flow regime map does not take into account this factor and this is one of its serious drawbacks. For hole diameters, which do not exceed 3.010-3 m the end of the gas maldistribution regime occurs at Ug ≤ 0.021 m/s (with some exceptions). When the hole diameters become as large as 4.010-3 m, then the range of the gas maldistribution widens and it is becomes stable up to Ug =0.034 m/s.
Hole diam.: 4 mm Hole diam.: ≤ 3 mm
Fig. 16. Correction for the gas maldistribution on the classical flow regime map [1]. The results reported in this work can be used in industry since most of the industrial BCs are equipped with similar PP gas distributors. In such a way the danger of fouling (due to the presence of impurities) is eliminated. The article reports the existence of gas maldistribution in relatively large BCs (column diameters=0.4 and 0.45 m) and deep BCs (clear liquid heights=1.91, 2.0 and 2.67 m). These conditions 37
are very close to the industrial operating conditions. In addition, the results in this work will help the industrial engineers to design well those industrial BCs, which should operate in the homogeneous regime (mostly in the field of biotechnology and waste water treatment) and the existence of gas maldistribution should be avoided.
5. Conclusions For the first time a systematic study on the determination of the end (so-called upper boundary) of the gas maldistribution has been performed. For this purpose, many different parameters (total information entropy, maximum information entropy, modified Shannon entropy and AAD, number of crossings of the mean and maximum number of visits in a single region) have been employed. All these parameters have exhibited a well-pronounced local minimum, which identified the upper limit of the gas maldistribution. It has been found that in most of the cases examined the end of the gas maldistribution occurs at Ug=0.02 m/s (with some exceptions, see Table 3). Therefore, this Ug range should be avoided since the gas maldistribution is detrimental to the BC performance. Only when the hole diameter is equal to 4.010-3 m, then the gas maldistribution becomes more stable and its upper boundary shifts to Ug=0.034 m/s. The information (on gas maldistribution) reported in this article will help to improve the design procedures for BCs. Transition velocities in organic liquids (therminol LT and ethanol) have been also reported.
38
Acknowledgments Dr. Stoyan Nedeltchev expresses his gratitude to both the Alexander von Humboldt Foundation (Germany) and the European Commission (Marie Curie Outgoing International Fellowship) for sponsoring this important research.
Nomenclature DC
column diameter (m)
IEmax
maximum information entropy (bits)
Nvmax
maximum number of visits in a single region (-)
Ug
superficial gas velocity (m/s)
z
axial height above the gas sparger (m)
Abbreviations AAD
average absolute deviation
BC
bubble column
BSD
bubble size distribution
CT
computed tomography
DP
differential pressure
GP
gauge pressure
ID
inner diameter
IE
information entropy
NC
number of crossings
NGD
nuclear gauge densitometry
OA
open area 39
PP
perforated plate
SD
scintillation detector
SE
(modified) Shannon entropy
References [1] Y. T. Shah, B. G. Kelkar, S. P. Godbole, W.-D. Deckwer, Design parameters estimations for bubble column reactors, AIChE Journal 28 (1982) 353-379. [2] C. Leonard, J.-H. Ferrasse, O. Boutin, S. Lefevre, A. Viand, Bubble column reactors for high pressures and high temperatures operation. Chemical Engineering Research and Design 100 (2015) 391-421. http://dx.doi.org/10.1016/j.cherd.2015.05.013. [3] T. Maruyama, S. Yoshida, T. Mizushina, The flow transition in a bubble column, Journal of Chemical Engineering of Japan 14 (1981) 352-357. [4] F. Yamashita, H. Inoue, Gas holdup in bubble columns, J. Chem. Eng. Japan 8 (1975) 334-336. [5] P. M. Wilkinson, A. P. Spek, L. L. Van Dierendonck, Design parameters estimation for scale-up of high-pressure bubble columns. AIChE Journal 38 (1992) 544-554. [6] D. N. Miller, Scale-up of agitated vessels gas-liquid mass transfer, AIChE Journal 20 (1974) 445-453. [7] E. Camarasa, C. Vial, S. Poncin, G. Wild, N. Midoux, J. Bouillard, Influence of the coalescence behavior of the liquid and of the gas sparging on hydrodynamics and bubble characteristics in a bubble column, Chemical Engineering and Processing 38 (1999) 329-344. [8] M. Liu, Z. Hu, Studies on the hydrodynamics of chaotic bubbling in a gas-liquid bubble column with a single nozzle, Chemical Engineering & Technology 27 (2004) 537-547. https://doi.org/10.1002/ceat.200401935. [9] G. R. Guédon, G. Besagni, F. Inzoli, Prediction of gas-liquid flow in an annular gap bubble column using a bi-dispersed Eulerian model. Chemical Engineering Science 161 (2017) 138-150. [10] S. Nedeltchev, S. Rabha, U. Hampel, M. Schubert, A new statistical parameter for identifying the main transition velocities in bubble columns, Chemical Engineering & Technology 38 (2015) 1940-1946. DOI: 10.1002/ceat.201400728. [11] E. Olmos, C. Gentric, S. Poncin, N. Midoux, Description of flow regime transitions in bubble columns via laser Doppler anemometry signals processing, Chemical Engineering Science 58 (2003) 1731-1742. 40
[12] E. Olmos, C. Gentric, N. Midoux, Numerical description of flow regime transitions in bubble column reactors by a multiple gas phase model. Chemical Engineering Science 58 (2003) 2113-2121. [13] R. C. Chen, J. Reese, L.-S. Fan, Flow structure in a three-dimensional bubble column and three-phase fluidized bed. AIChE Journal 40 (1994) 1093-1104. [14] S. Nedeltchev, S. Aradhya, F. Zaid, M. Al-Dahhan, Flow regime identification in three multiphase reactors based on Kolmogorov entropies derived from gauge pressure fluctuations, Journal of Chemical Engineering of Japan 45 (2012) 757-764. [15] E. León-Becerril, A. Cockx, A. Liné, Effect of bubble deformation on stability and mixing in bubble columns, Chemical Engineering Science 57 (2002) 3283-3297. [16] J. Zahradník, M. Fialová, The effect of bubbling regime on gas and liquid phase mixing in bubble column reactors, Chemical Engineering Science 51 (1996) 2491-2500. [17] S. Nedeltchev, A. Shaikh, M. Al-Dahhan, Flow regime identification in a bubble column based on both statistical and chaotic parameters applied to computed tomography data. Chemical Engineering & Technology 29 (2006) 1054-1060. DOI: 10.1002/ceat.200600162. [18] S. Nedeltchev, A. Shaikh, A new method for identification of the main transition velocities in multiphase reactors based on information entropy theory, Chemical Engineering Science 100 (2013) 2-14. http://dx.doi.org/10.1016/j.ces.2013.03.039. [19] S. Nedeltchev, U. Hampel, M. Schubert, Investigation of the radial effect on the transition velocities in a bubble column based on the modified Shannon entropy, Chemical Engineering Research and Design 115 (2016) 303-309. http://dx.doi.org/10.1016/j.cherd.2016.08.011. [20] S. Nedeltchev, A. Shaikh, M. Al-Dahhan, Flow regime identification in a bubble column via nuclear gauge densitometry and chaos analysis, Chemical Engineering & Technology 34 (2011) 225-233. DOI: 10.1002/ceat.201000308. [21] S. Nedeltchev, New methods for flow regime identification in bubble columns and fluidized beds, Chemical Engineering Science 137 (2015) 436-446. http://dx.doi.org/10.1016/j.ces.2015.06.054. [22] S. Nedeltchev, U. Hampel, M. Schubert, Extraction of information and reconstruction entropies from ultrafast X-ray tomography data in a bubble column, Chemical Engineering Science 170 (2017) 225-233. http://dx.doi.org/10.1016/j.ces.2017.03.020.
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S1385-8947(19)30893-9 https://doi.org/10.1016/j.cej.2019.04.115 CEJ 21535
To appear in:
Chemical Engineering Journal
Received Date: Revised Date: Accepted Date:
1 November 2018 24 March 2019 17 April 2019
Please cite this article as: S. Nedeltchev, Precise Identification of the End of the Gas Maldistribution in Bubble Columns Equipped with Perforated Plate Gas Distributors, Chemical Engineering Journal (2019), doi: https:// doi.org/10.1016/j.cej.2019.04.115
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To be considered for the GLS14 Special Issue
Precise Identification of the End of the Gas Maldistribution in Bubble Columns Equipped with Perforated Plate Gas Distributors Stoyan NEDELTCHEV1,2 1
Sofia University “Kliment Ohridski”, Department of Chemical Engineering and Pharmacy, 1164 Sofia, Bulgaria 2
Consulting firm “CRED” (Chemical Reactor Engineering & Development), 1618 Sofia, Bulgaria Email address: [email protected]
Abstract The gas maldistribution in bubble columns (BCs) is detrimental to their performance. In the literature hitherto, there is no any systematic studies about this practical problem. In this work, for the first time the upper boundary of the gas maldistribution has been identified based on different entropies (total and maximum information as well as Shannon) extracted from various time series. In addition, three other parameters (maximum number of visits in a region, number of crossings of the mean and modified average absolute deviation) have been introduced for successful identification of the range of gas maldistribution. Different BCs equipped with various types of perforated plate (PP) gas distributors have been used. Both shallow and deep bubble beds have been studied. Water and organic liquids have been investigated. It has been found that when the hole diameter (of the PP gas distributor) is between Ø 0.5×10-3 m and Ø 1.32×10-3 m, the gas maldistribution is stable up to superficial gas velocity Ug of 0.02 m/s. In the case of nitrogen-ethanol system, the transition velocity has occurred at much lower Ug (0.0062 m/s). Only when the hole diameter is as large as
Ø 4.0×10-3 m, then the upper boundary of the gas maldistribution shifts to somewhat higher Ug value (0.034 m/s). Keywords: Bubble columns; Gas maldistribution; Entropy analysis; Pressure fluctuations; Wire-mesh sensor; Tomographic techniques 1. Introduction Bubble columns (BC) are frequently used as gas-liquid contactors in both chemical and biochemical industries. They are utilized as absorbers, fermenters, flotation columns, etc. due to their excellent mass and heat transfer rates as well as intensive mixing. BCs are also used frequently for chemical reactions that require suspended catalyst particles. For instance, biochemical reactions, hydrogenation of liquid petroleum fractions and coal liquefaction. Although BCs are simple in construction and operation, their hydrodynamics are complex and a strong function of operating conditions (e.g. pressure and gas velocity), physical properties (e.g. liquid viscosity, surface tension) and scale (column diameter, bed height). The BC operation is strongly dependent on the bubble characteristics (bubble size, bubble rise velocity and bubble wake phenomena). These parameters determine the gas holdup, the interfacial area, the gas residence time and also the liquid mixing. Due to the complex BC hydrodynamics, multiple flow regimes are being formed as the superficial gas velocity Ug increases. The main three flow regimes are as follows: homogeneous (bubbly flow), transition and heterogeneous (churn-turbulent) [1-2]. In the available flow regime maps [1-3] the gas maldistribution is not included, which is 2
one of their drawbacks. Yamashita and Inoue [4] were the only ones who have measured the gas holdup under non-uniform inlet gas distribution conditions. In this article for the first time scientific parameters (instead of visual observations) will be used to identify the upper boundary (or the end) of the gas maldistribution regime. Some of these parameters are new (number of visits per region, total or maximum information entropy and modified average absolute deviation and Shannon entropy). The work is original since the gas maldistribution is not studied well in the literature hitherto and it is not included in the classical flow regime map [1]. A new database with transition velocities will be presented.
1.1. Description of gas maldistribution The hydrodynamics and flow patterns in BCs are complex phenomena, which makes both the design and scale-up of BCs a difficult task. The gas distributor design affects the flow patterns in the bubble bed and very often leads to non-uniform velocity profiles, short circuiting, bypassing and channeling, gas velocity fluctuations and backflow of fluid due to velocity differences between phases. The gas maldistribution leads to non-uniformities in the radial gas holdup profiles and it causes gas channeling and a significant lowering of the gas holdup. The gas maldistribution causes observable overall liquid circulation and leads to a smaller bed expansion for a given gas flow rate than for a uniform distribution of both fluids. It is worth noting that gas maldistribution can result not only from partial hole blockage but also from premixing of gas and liquid below the distributor plate.
3
In general, the poor gas distribution occurs always at low Ug values when a perforated plate (PP) gas distributor or ring and cross spargers are used. This regime is detrimental to the BC performance and it should be avoided. Good knowledge of the extent of gas maldistribution is essential to the modelling, design and optimization of BCs. The use of PP gas distributors (or ring and cross spargers) generates preferentially aerated regions with enhanced liquid turbulence and dead zones in the bubble bed. Especially the existence of dead zones in the reactor’s volume substantially reduces the overall mass transfer efficiency. The factors (for instance the hole diameter or number of openings), which lead to the formation of gas maldistribution should be carefully studied. The gas maldistribution can influence heat and mass transfer rates as well as mixing and flow patterns of both the gas and liquid. According to Wilkinson et al. [5] the influence of the sparger design on gas holdup is negligible (for various liquids and at various pressures) provided that the sparger hole diameters are larger than approximately 1-2×10-3 m (and care is taken to avoid the gas maldistribution at the sparger). It is worth noting that in industry usually less effective gas spargers are used. They have larger hole diameters that are less sensitive to fouling. The influence of the gas sparger on flow patterns and gas holdup usually diminishes in tall BCs due to the ongoing process of bubble coalescence. In short BCs (bed aspect ratio<3) the liquid circulation patterns are not fully developed and they do not affect the gas holdup. Wilkinson et al. [5] argue that the flow patterns and the gas holdup are virtually
4
independent of the column dimensions and sparger layout (for low as well as high pressures) provided that the following three criteria are fulfilled: - the column diameter has to be larger than 0.15 m; - the column height to diameter ratio has to be in excess of 5; - the hole diameter of the gas sparger has to be larger than 1-2×10-3 m. There are no generally accepted procedures for the proper design of a gas distributor. In addition to the lack of design criteria, there is little appreciation of the consequences of gas maldistribution, e.g. caused by faultry design, fouling or hole blockage. The initial gas-liquid flow maldistribution has an influence on the gas holdup behavior. A bed contraction occurs when the gas and liquid are distributed non-uniformly. The gas distributors with the worst gas maldistribution generally give the greatest reduction in gas holdup. The gas maldistribution is associated with more vigorous liquid circulation patterns leading to consistently lower gas holdups. It is expected that the bubbling through a reduced number of orifices would increase the initial bubble size or at least channel the gas, leading to a reduction in gas holdup. In the case of gas maldistribution, the gas distributor appears to push the gas towards the column walls. It is essential to identify correctly the nature of the gas-liquid flow for every gas distributor. Gas and liquid maldistribution occur due to partial blockage of the gas distributor. Liquid circulation arises from the gas maldistribution. The gas holdup and overall bed expansion generally decrease as a result of gas maldistribution.
5
It has been found that a uniform gas distributor leads to a higher overall gas holdup than a non-uniform one. A good gas distributor should introduce fine bubbles and distribute them (as well as the liquid) uniformly over the entire cross-section and minimize the pressure drop. The distributor hole blockage can also change the bubble size at the bottom of the column and this can also affect the gas holdups. The hole blockage leads to an increase in the gas distributor pressure drop and thus a deterioration in the gas distributor’s performance. Under some conditions a smaller area available for gas entry leads to higher orifice velocities and smaller bubbles, which could counterbalance the effect of spatial gas maldistribution. Gas maldistribution at the distributor causes a significant drop in the overall gas holdup. Maintaining a uniform spatial distribution of gas and liquid entry is clearly essential to ensure uniform motion and maximum fluid holdups in BCs.
1.2. Description of main hydrodynamic regimes Three different flow regimes (homogeneous, transition and heterogeneous) are usually observed in the BC operation. However, at very low Ug values chain bubbling regime might be observed [6-8]. The mechanisms governing both the homogeneous and heterogeneous regimes are different. In general, the global and local flow properties in BCs are related to the prevailing flow regime. The transitions between the different flow regimes depend on the operating mode, design parameters and the physicochemical properties of the phases. For instance, in viscous liquids (such as mono-ethylene glycol) the transition to the churn-turbulent regime occurs at a very 6
low Ug value [5]. In liquids with lower surface tension (for example, n-heptane) the transition to the churn-turbulent regime is delayed and it corresponds to higher transitional gas holdup [5]. It has been reported that the increase of gas density (or operating pressure) shifts the main transition velocity to higher Ug values. In order to understand the gas maldistribution better, one should know the main characteristics of both homogeneous (bubbly flow) and transition flow regimes, which follow after the gas maldistribution. The homogeneous regime is characterized by a narrow bubble size distribution (BSD). According to Leonard et al. [2] two sub-regimes can be distinguished depending on the span of the BSD. In the case of a narrow BSD the flow is called “perfect bubbly”. The “imperfect bubbly flow” is characterized with a larger BSD. Guédon et al. [9] have also distinguished “pure homogeneous”
(or
“mono-dispersed
homogeneous”)
sub-regime
and
“pseudo-homogeneous” (or “poly-dispersed homogeneous”) sub-regime. The latter is characterized by the presence of large bubbles whose lift coefficient is negative. In the homogeneous regime there is no bubble coalescence. The flow pattern is primarily determined by the primary bubble size formed at the gas distributor. The turbulence is mainly attributed to bubble drag, resulting in a liquid microcirculation. There is a gentle agitation of the gas-liquid dispersion and uniform gas holdup profile. The transition between the homogeneous and heterogeneous regimes is a gradual process. The transition between both main flow regimes is caused by the formation of large fast-rising bubbles. The formation of the first large bubbles can be delayed to a higher Ug value when the coalescence rate is reduced by the addition of an electrolyte. 7
In the transition flow regime a macro-circulation occurs [2,10]. There is a widened BSD. The formation of first large (coalesced) bubbles is observed. The critical velocity between the homogeneous and heterogeneous regimes can be affected by various parameters (column diameter, liquid viscosity, presence of surfactants, temperature, pressure, etc.). The transition flow regime has been subdivided into first and second sub-regimes [11,12]. Chen et al. [13] has subdivided the heterogeneous regime into several sub-regimes. In most of the publications on BCs the gas maldistribution has not been studied. For the first time, Nedeltchev et al. [10,14] have identified clearly the upper boundary of the gas maldistribution. At high Ug values, the fully developed heterogeneous (churn-turbulent) flow regime is established. It is associated with high coalescence and break-up rates and a wide variety of bubble sizes. León-Becerril et al. [15] have reported that for an air-water system the transition between homogeneous and heterogeneous regimes occurs at Ug value between 0.04 and 0.05 m/s. Zahradník and Fialová [16] have reported a transition velocity of 0.04 m/s for an air-water BC (0.14 m in ID) equipped with a PP gas distributor (hole diameter: Ø 0.5×10-3 m). Leonard et al. [2] also argues that for an air-water system the transition velocity appears at 0.04 m/s depending on both the gas distributor and column design. Therefore, the gas maldistribution should disappear below this critical velocity. The main objective of this work is to identify the upper boundary of the gas maldistribution based on efficient novel methods for flow regime identification. The 8
new identification methods will be applied to various time series obtained by modern measurement techniques. Newly identified transition velocities in several BCs equipped with different PP gas distributors will be reported. Both water and organic liquids will be used.
2. Identification methods In this work, the upper boundary of the gas maldistribution will be identified based on different entropies and other statistical parameters extracted from various time series. The following entropies will be used:
2.1. Modified information entropy and Shannon entropy derived from gauge pressure fluctuations The time series (10,000 points) of gauge pressure (GP) fluctuations have been divided into 10 intervals (1000 points). For each of them, the average absolute deviation (AAD) [17] has been calculated. Then, the information entropy (IE) algorithm developed by Nedeltchev et al. [18] has been applied. As a first step, the sum of all ten AAD has been calculated. Each particular probability has been estimated as a ratio between the local AAD for that interval and the sum of all AAD. Then the local information amount and IE (product of the probability and the information amount) have been calculated. According to the algorithm, the total IE is a sum of all local IE. The modified Shannon entropy (SE) has been calculated from the same ten AAD values at each run based on the SE algorithm proposed by Nedeltchev et al. [19]. The
9
local SE for each interval has been calculated based on the above-mentioned definition of probability. The total SE is a sum of all local SE values.
2.2. Maximum and total information entropy derived from photon counts and differential pressure fluctuations These two parameters have been introduced by Nedeltchev and Shaikh [18]. The range of various signals has been divided into different regions (with predetermined height) between the minimum and maximum values of the fluctuations. The number of visits of the signal into each of these regions has been counted. Then, the classical IE theory has been applied. As a unit height has been used the height of the smallest region [18]. The total IE is a sum of the products of the probability, information amount and dimensionless height of each visited region. This parameter gives the total information that could be obtained from a fluctuating signal, which visits multiple regions. The maximum information entropy IEmax represents the highest IE among all regions. This parameter gives the maximum information that could be obtained from a single region (which usually is the most frequently visited one). Three other statistical parameters (maximum number of visits in a region, number of crossings of the mean and modified average absolute deviation) will be explained briefly in section 4. In Table 1 are summarized the scientific parameters used to identify the end of the gas maldistribution in different BCs.
10
Table 1. Summary of the scientific parameters applied to various signals. Gas distributor Perforated plate (PP) 121 holes, Ø 1.32×10-3 m Perforated plate (PP) 241 holes, Ø 3.0×10-3 m Perforated plate (PP) 19 holes, Ø 1.0×10-3 m Perforated plate (PP) 14 holes, Ø 4.0×10-3 m Perforated plate (PP) 101 holes, Ø 4.0×10-3 m Perforated plate (PP) 163 holes, 1.32×10-3 m Perforated plate (PP) 64 holes, 1.32×10-3 m Perforated plate (PP) 55 holes, 0.5×10-3 m
Column diameter 0.14 m
Recorded signal
Parameter used AAD and NC
0.162 m
Gauge pressure (GP) fluctuations Gauge pressure (GP) fluctuations Differential pressure (DP) fluctuations Gas holdup fluctuations Gas holdup fluctuations Photon counts
0.1 m
Photon counts
0.1 m
Pixel values (X-ray scans)
0.45 m 0.102 m 0.15 m 0.40 m
Total IE and SE Max # of visits Total IE Maximum number of visits in a region Maximum number of visits in a region Maximum information entropy Maximum information entropy Modified AAD
3. Experimental setups and measurement techniques 3.1. Gauge pressure (GP) fluctuations in bubble columns The GP fluctuations (10 000 points) have been recorded (at a sampling frequency of 67 Hz) in two air-tap water BCs (0.14 m and 0.45 m in ID) by means of GP transducer PX409 (Omega Inc., USA) . They have been installed at an axial height z of about 1 m above the gas distributor. The raw data have been low-pass filtered in order to eliminate or minimize the noise. The small BC (0.14 m in ID) has been equipped with a PP gas distributor (121 holes, Ø 1.32 × 10-3 m, open area (OA)=1.08 %). The large BC (0.45 m in ID) has been also equipped with a PP gas distributor, however, with larger number of holes (241 holes, Ø 3.0 × 10-3 m, OA=1.07 %). Two different clear liquid heights (1.33 and 0.4 m) have been tested in the small BC and two deeper clear liquid heights (1.91 and 11
2.67 m) have been tested in the large BC. The bed aspect ratios in the smaller column have been fixed at 9.5 and 2.86, respectively. In the bigger column the bed aspect ratios have been fixed at 4.24 and 5.93. It is worth noting that only the hole diameter and the column diameter as well as one of the clear liquid heights in both columns have satisfied the scale-up criteria of Wilkinson et al. [5]. The pressure transducers PX409 have been always connected to OMB-DAQ-56 (Omega Inc., USA) data acquisition board.
3.2. Differential pressure (DP) fluctuations in a bubble column The DP fluctuations (10 000 points) have been measured (at a sampling frequency of 100 Hz) in a stainless steel BC (0.102 m in ID) by means of DP transducers (LABOM GmbH, Germany). The raw data have been low-pass filtered in order to eliminate or minimize the noise. One end of the transducers has been connected to a certain axial position z (0, 0.65 or 1.2 m), while the other end has been connected to the top of the column. The BC has been equipped with a PP gas distributor (19 holes, Ø 1.0 × 10-3 m, OA=0.19 %). The clear liquid height has been set at 1.3 m, i.e. the bed aspect ratio has been fixed at 12.75. As a gas phase has been used nitrogen, whereas as a liquid phase has been used both tap water and ethanol (96 %). It is worth noting that only the hole diameter and the bed aspect ratio have satisfied the scale-up criteria of Wilkinson et al. [5].
3.3. Gas holdup fluctuations measured by a wire-mesh sensor A new statistical parameter has been extracted from gas holdup fluctuations (60 000 points) recorded (at a sampling frequency of 2000 Hz) by means of a wire-mesh 12
sensor in two air-water BCs (0.15 m and 0.4 m in ID) operated with different PP gas distributors (the orifice diameter was kept constant at Ø 4.0×10-3 m). The raw data have been low-pass filtered in order to eliminate or minimize the noise. The PP gas distributor in the smaller column has consisted of 14 holes, whereas 101 holes have been available on the gas sparger in the bigger column. In such a way, the OA has been kept constant at 1 %. Both BCs have been operated with an air-deionized water system at ambient conditions. The clear liquid height in both columns have been adjusted at 2.0 m. The bed aspect ratio in the smaller column has been fixed at 13.33, whereas the one in the bigger column has been set at 5. It is worth noting that in the case of these measurements all three scale-up criteria of Wilkinson et al. [5] have been satisfied. The conductivity wire-mesh sensors have consisted of 2 electrode planes each with 24 (in the case of the small BC) or 64 (in the case of the large BC) stainless-steel wires of 0.2×10-3 m and 6.125×10-3 m distance between the wires. The distance between the planes has been set at 4.0×10-3 m and the wires from different planes have crossed each other at right angles. This arrangement has consisted of 576 (in the small BC) or 4096 (in the large BC) crossing points, 78 % thereof inside the circular cross-sections of both columns. One plane of the electrodes has acted as a transmitter, while the other plane has acted as a receiver. More details about the wire-mesh sensors are available in Nedeltchev et al. [10]. The conductivity wire-mesh sensors have been always installed at an axial height of 1.3 m above the gas distributor.
13
3.4. Photon count fluctuations recorded by computed tomography (CT) and nuclear gauge densitometry (NGD) in bubble columns Photon counts (10 000 points) have been also used for identification of the end of the gas maldistribution. They have been measured (at a sampling frequency of 20 Hz) by means of Computed Tomography (CT). The raw data have been low-pass filtered in order to eliminate or minimize the noise. The setup has consisted of an array of 5 scintillation detectors (SD) with an opposing radioactive source. Both the detectors and the source have rotated together around the BC. The CT scanner has used a Cesium (Cs-137) encapsulated gamma-ray source with an activity of about 85 mCi. The array of 5 SD and the source have been mounted on a gantry, which has been able to rotate 360o around the BC. The SD have been made of NaI. Each detector has consisted of a cylindrical 0.0510.051 m NaI crystal, a photo multiplicator and electronics, forming a 0.0540.26 m cylindrical assembly. In each view, every detector has acquired 7 projections, covering a total angular span of 2.72o of the detector face. A total of 99 views have been acquired, with 3.6o of angular shift after every view. The gas holdup distribution at each cross-sectional plane have been obtained from 3465 projections (5799). All CT scans have been performed at a dimensionless axial height of 5.5, which means that the measurements have been recorded at z=0.89 m above the gas sparger. The aerated liquid height has been fixed at 1.8 m, which corresponded to a bed aspect ratio of 11.11. More details about the CT setup can be found in Nedeltchev et al. [18,20,21]. The CT scans have been performed in a BC (0.162 m in ID, total height=2.5 m) 14
operated with an air-therminol LT system. The BC has been equipped with a PP gas distributor (163 holes, 1.3210-3 m, OA=1.08 %). It is worth noting that all three scale-up criteria of Wilkinson et al. [5] have been satisfied. The existing CT setup has been converted into Nuclear Gauge Densitometry (NGD) by placing a detector in front of an encapsulated gamma-ray Cs-137 source (about 100 mCi). A collimator (0.160.4810-2 m) has been placed in front of the detector. A focused beam of radiation has been transmitted from the source through the column and the gas-liquid dispersion to the SD. As the density of the material in the column has changed, the amount of radiation reaching the detector has varied. It is generally believed that the amount of radiation is reflective of its flow behavior and properties. The main advantages of both CT and NGD techniques are that they are nonintrusive-the sources and detectors are mounted externally from the column and thus they are completely unaffected by the conditions inside it. The NGD scans have been performed at a sampling frequency of 50 Hz in an air-water BC (0.1 m in ID, aerated liquid height=1.2 m) equipped with a PP gas distributor (64 holes, 1.3210-3 m, OA=1.09 %). The detector has recorded the photon counts (10 000 points) at an axial height of 0.89 m. More details about the NGD setup can be found in Nedeltchev et al. [20]. It is worth noting that only the hole diameter and the bed aspect ratio (12) have satisfied the scale-up criteria of Wilkinson et al. [5].
3.4. X-ray fluctuations recorded by ultrafast X-ray tomography The tomographic X-ray facility has not employed rotating objects or source-detector compounds. An electron beam (of up to 10 kW power) has been 15
sharply focused on a circular tungsten target and has been at the same time periodically deflected with a high frequency in order to generate a moving focal spot on the target and thus an X-ray source rotating around the column. This X-ray source has irradiated the column from different viewing angles. X-rays have been produced in the beam’s focal spot. Rapid deflection by means of electron optics has allowed a fast circulation of the focal spot around the column. A static detector ring surrounding the column has measured the radiation passing the column at a high frequency synchronized with the beam deflection. X-rays passing the BC have been recorded by a very fast multi-pixel X-ray arc detector co-aligned with the target. From the projected data set of one revolution of the electron beam a non-superimposed cross-sectional image of the density distribution within the column can be reconstructed. A snapshot of the in-house developed ultrafast electron beam X-ray tomographic facility is available in Nedeltchev et al. [22]. This nonintrusive measurement technique could be used to visualize stacks of cross-sectional images of the flow structure inside the BC. The X-ray scans have been performed in an air-water BC (0.1 m in ID) at z=0.5 m above the PP gas distributor (55 holes, 0.510-3 m, OA=0.14 %). The clear liquid height has been fixed at 0.66 m, which corresponded to a bed aspect ratio of 6.6. It is worth noting that only the hole diameter and the bed aspect ratio have satisfied the scale-up criteria of Wilkinson et al. [5]. The time series (29 000 points) have been recorded at a sampling frequency of 1000 Hz (i.e. 1000 cross-sectional images per second) at a spatial resolution of 110-3
16
m. The raw data have been low-pass filtered in order to eliminate or minimize the noise. More details are available in Nedeltchev et al. [22]. In Table 2 are summarized both the experimental facilities and measurement techniques used. Table 2. Summary of the experimental facilities and measurement techniques used. Gas distributor Perforated plate (PP) 121 holes, Ø 1.32×10-3 m Perforated plate (PP) 241 holes, Ø 3.0×10-3 m Perforated plate (PP) 19 holes, Ø 1.0×10-3 m Perforated plate (PP) 14 holes, Ø 4.0×10-3 m Perforated plate (PP) 101 holes, Ø 4.0×10-3 m Perforated plate (PP) 163 holes, 1.32×10-3 m Perforated plate (PP) 64 holes, 1.32×10-3 m Perforated plate (PP) 55 holes, 0.5×10-3 m
Column diameter 0.14 m
Clear liquid height 0.4, 0.65, 1.33 m
0.45 m
1.91 m, 2.67 m
0.102 m
1.3 m
0.14 m
2.0 m
0.40 m
2.0 m
0.162 m
1.8 m (aerated) 1.2 m (aerated) 0.66 m
0.1 m 0.1 m
Measurement method Gauge pressure (GP) transducer Gauge pressure (GP) transducer Differential pressure (DP) transducer Wire-mesh sensor (conductivity) Wire-mesh sensor (conductivity) Computed tomography (photon counts) Nuclear gauge densitometry (photons) X-ray tomography (pixel values)
4. Results and Discussion 4.1. Identification of the end of the gas maldistribution based on GP fluctuations In the case of a bigger (0.45 m in ID) BC equipped with a PP gas distributor (241 holes, Ø 3.0×10-3 m, OA=1.07 %) and operated with an air-tap water system, the end of the gas maldistribution was identified at Ug = 0.018 m/s. Figures 1a-b show that at this Ug value and z=1.05 m the total IE and SE exhibit a well-pronounced local minimum. Figures 2a-b show photos, which clearly demonstrate the gas maldistribution effect on the flow structure. At Ug = 0.016 m/s (see Fig. 2a) the right 17
part of the BC is still not well aerated. At Ug = 0.026 m/s (see Fig. 2b) almost every opening of the gas distributor forms bubbles.
(a)
(b) Fig. 1. Total IE and SE profiles as a function of Ug in an air-water BC (0.45 m in ID). Axial position z=1.05 m. Clear liquid height=1.91 m.
18
(a)
(b) Fig. 2. Gas maldistribution in a BC (0.45 m in ID) operated at: (a) Ug=0.016 m/s; (b) Ug=0.026 m/s. Clear liquid height=1.91 m. Fig. 3 shows the profile of a parameter called maximum number of visits in a single region Nvmax. The algorithm for its calculation is explained in Nedeltchev et al. [10]. Both the minimum and maximum values of every signal are determined and then it is divided into multiple regions. The smallest region is with a height of 0.0005 and the other regions are proportional (2, 3, 4 and 5 times) to the lowest height. The parameter Nvmax corresponds to the maximum number of visits in one of these regions. 19
Fig. 3 shows that in a deeper bubble bed (clear liquid height=2.67 m) and at a higher axial position (z=1.41 m) the end of the gas maldistribution occurs at somewhat lower Ug value (0.015 m/s). A well-pronounced local minimum in the Nvmax profile distinguishes the onset of the bubbly flow regime.
Fig. 3. Nvmax profile as a function of Ug in an air-water BC (0.45 m in ID). Axial position z=1.41 m. Clear liquid height=2.67 m.
Fig. 4 shows that in a small BC (0.14 m in ID) equipped with a PP gas distributor (121 holes, Ø 1.32 × 10-3 m, OA=1.08 %) at an axial position z=1 m above the gas distributor, the transition velocity occurs at somewhat higher Ug value (0.02 m/s). There is a well-pronounced local minimum in the AAD profile.
20
Fig. 4. AAD profile as a function of Ug in an air-water BC (0.14 m in ID). Axial position z=1.0 m. Clear liquid height=1.33 m. Almost identical transition velocity (Ug=0.021 m/s) has been identified in the same BC at z=0.25 m and clear liquid height=0.65 m. Figure 5 shows that the AAD profile has a well-pronounced local minimum at the end of the gas maldistribution.
Fig. 5. AAD profile as a function of Ug in an air-water BC (0.14 m in ID). Axial position z=0.25 m. Clear liquid height=0.65 m. 21
Figure 6 exhibits that the parameter “number of crossings” NC of the mean of the signal can be used for flow regime identification. In a shallow bubble bed (clear liquid height=0.4 m) the range of the gas maldistribution is narrower and thus its transition to bubbly flow regime occurs earlier. At Ug=0.016 m/s the NC profile exhibits a very well-pronounced local minimum. Below this critical Ug value the NC values monotonously decrease, while beyond the transition velocity the NC values start to increase again.
Fig. 6. NC profile as a function of Ug in an air-water BC (0.14 m in ID). Axial position z=0.12 m. Clear liquid height=0.4 m. 4.2. Identification of the end of the gas maldistribution based on gas holdup fluctuations recorded by a wire-mesh sensor Nedeltchev et al. [10] has defined a new parameter called maximum number of visits in a single region Nvmax. It has been extracted from gas holdup fluctuations recorded in two BCs by a wire-mesh sensor at an axial height of 1.3 m. All the details about the division of the signals between their minimum and maximum values are provided in [10]. Fig. 7 shows that in a small BC (0.15 m in ID) equipped with a PP 22
gas distributor (14 holes, 4.010-3 m, OA=1.14 %) this parameter is capable of identifying the end of the gas maldistribution and the formation of the transition flow regime. At Ug=0.034 m/s the Nvmax profile exhibits a well-pronounced minimum. Figs. 8a-c clearly demonstrate the existence of the gas maldistribution at Ug=0.01, 0.02 and 0.03 m/s, respectively. Figure 8d shows that at Ug=0.045 m/s every opening of the gas distributor generates bubbles.
Fig. 7. Profile of Nvmax as a function of Ug in an air-water BC (0.15 m in ID). Axial position z=0.5 m. Clear liquid height=2.0 m.
(a) 23
(b)
(c)
(d) Fig. 8. Gas maldistribution in a BC (0.15 m in ID) operated at: (a) Ug=0.012 m/s, (b) Ug=0.022 m/s, (b) Ug=0.034 m/s, (d) Ug=0.045 m/s, Clear liquid height=2.0 m. 24
Fig. 9 exhibits that in a larger BC (0.4 m in ID) equipped with a PP gas distributor (101 holes, 4.010-3 m, OA=1.01 %) the gas maldistribution is stable up to Ug=0.034 m/s. At this critical velocity a well-pronounced local minimum in the Nvmax profile occurs, which marks the onset of the transition flow regime. Figs. 10a-d clearly demonstrate that the gas maldistribution do exist.
Fig. 9. Profile of Nvmax as a function of Ug in an air-water BC (0.4 m in ID). Axial position z=0.5 m. Clear liquid height=2.0 m.
(a) 25
(b)
(c)
(d) Fig. 10. Gas maldistribution in a BC (0.40 m in ID) operated at: (a) Ug=0.011 m/s, (b) Ug=0.023 m/s, (b) Ug=0.034 m/s, 26
(d) Ug=0.045 m/s, Clear liquid height=2.0 m. 4.3. Identification of the end of the gas maldistribution based on photon counts recorded by a computed tomography Nedeltchev and Shaikh [18] has demonstrated that a gas maldistribution also exists in a BC (0.162 m in ID) equipped with a PP gas distributor (163 holes, 1.3210-3 m, OA=1.08 %) and operated with an air-therminol LT system at ambient conditions. The aerated liquid height has been fixed at 1.8 m. Photon counts have been recorded by five different scintillation detectors (SD). Fig. 11a-d show that the maximum information entropy (IEmax) extracted from the readings of detectors 1, 2, 4 and 5 is capable of identifying the end of the gas maldistribution. At Ug=0.02 m/s the IEmax profile suddenly drops, which indicates the upper limit of the gas maldistribution and its transformation into transition flow regime.
(a)
27
(b)
(c)
28
(d) Fig. 11. Profile of IEmax as a function of Ug in the case of: (a) SD I, (b) SD II, (c) SD IV and (d) SD V. The photon counts have been also recorded by means of a NGD in an air-tap water BC (0.1 m in ID, 1.2 m in height) equipped with a PP gas distributor (64 holes, 1.3210-3 m, OA=1.12 %). Fig. 12 shows that the IEmax profile is capable of identifying the end of the gas maldistribution at Ug=0.02 m/s. Beyond this critical velocity the IEmax values monotonously increase up to Ug=0.035 m/s and then the trend reverses again.
29
Fig. 12. Profile of IEmax as a function of Ug based on photon counts recorded by nuclear gauge densitometry in a BC (0.1 m in ID). 4.4. Identification of the end of the gas maldistribution based on ultrafast X-ray tomography When the time series are divided into 289 vector pairs (each vector consisting of 50 elements) and the distance between each vector pair is estimated (based on the maximum norm definition), then the modified average absolute deviation (AAD) can be used to identify the end of the gas maldistribution. Only the repeating cases with distance smaller than the cut-off length (=3AAD) have been taken into account. It has been counted how many times the consecutive vector pairs repeat twice, three times, four times, etc. Then, based on the distribution of these numbers the AAD definition has been applied. The new parameter is called modified AAD since it is applied to reconstructed data. Fig. 13 shows that in an air-water BC (0.1 m in ID, clear liquid height=0.66 m) equipped with a PP gas distributor (55 holes, 0.510-3 m, OA=0.14 %) the modified AAD exhibits a local minimum at Ug=0.02 m/s. This 30
critical gas velocity distinguishes the end of the gas maldistribution and the onset of the bubbly flow regime. This result is similar with the results in Figs. 4, 5 and 11.
Fig. 13. Profile of modified AAD as a function of Ug in air-water BC (0.1 m in ID). Fig. 14 shows that the photos for Ug=0.01 and 0.02 m/s confirm the existence of gas maldistribution in the case of PP gas distributor. All openings of the gas distributor begin to form bubbles at Ug=0.04 m/s.
Fig. 14. Photographic evidence for the existence of gas maldistribution in an air-water BC (0.1 m in ID) equipped with a perforated plate (PP) gas distributor. 4.5. Identification of the end of the gas maldistribution based on DP fluctuations It has been found that when the total IE algorithm developed by Nedeltchev and Shaikh [18] is applied to differential pressure (DP) fluctuations, then the end of the 31
gas maldistribution can be identified in a straightforward manner. In every signal the difference between the minimum and maximum values has been determined and then the fluctuations have been divided into various regions with different heights (the smallest height has been set at 0.5 mbar and every other height has been increased with this value). The number of visits of the signal in the different regions has been used to calculate the local probability, information amount and IE. All heights have been taken into account in the algorithm. The total IE has been calculated as a sum of all local IE values. Fig. 15a shows that in the vicinity (z=0 m) of the PP gas distributor (19 holes, Ø 1.0×10-3 m, OA=0.19 %) the end of the gas maldistribution regime occurs at Ug = 0.014 m/s in a BC (0.102 m in ID, clear liquid height=1.3 m) operated with a nitrogen–tap water system. The total IE exhibits a local minimum at this particular Ug value. When the axial position z is located in the upper zone of the column, then the end of the gas maldistribution is shifted to higher Ug value (0.021 m/s). In other words, the effect of the gas maldistribution is more pronounced in the upper zone of the column. At z=0.65 m the transition flow regime begins at Ug = 0.01 m/s.
32
(a)
(b) Fig. 15. Profile of total IE as a function of Ug in a N2-tap water BC (0.102 m in ID): (a) at z=0 m; (b) at z=1.2 m. In the case of nitrogen–ethanol (96 %) system in the same BC (0.102 m in ID), the total IE profile (see Fig. 16a-c) is capable of identifying the end of the gas maldistribution regime at Ug=0.0062 m/s. At all three axial positions z a well 33
pronounced local minimum in the total IE profile at Ug=0.0062 m/s is observed. This is a much lower transition velocity than the one in a N2-tap water system. The main reason is the smaller mean bubble diameter (and thus lower degree of liquid turbulence) in the N2-ethanol system. Beyond this critical velocity the total IE profile monotonously increases, which implies that the behavior of the system becomes more predictable (more information is gained).
(a)
34
(b)
(c) Fig. 16. Profile of total IE as a function of Ug in a N2-ethanol BC (0.102 m in ID): (a) at z=0 m; (b) at z=0.65 m and (c) at z=1.2 m. The results from this study are summarized in Table 3. It is clear that for most of the PP gas distributor types, the end of the gas maldistribution occurs at Ug = 0.02 m/s.
35
Only when the distributor holes have a diameter 4.010-3 m, then the range of the gas maldistribution extends to Ug = 0.034 m/s. Table 3. Effect of the PP gas distributor characteristics on the end of the gas maldistribution. Type of gas distr.
Open area
Column
Liquid height
Gas-liquid system
End of gas maldistr.
diam.
241 holes, Ø 3.0×10-3 m
1.07 %
0.45 m
1.91 m
Air-tap water
Ug = 0.018 m/s
241 holes, Ø 3.0×10-3 m
1.07 %
0.45 m
2.67 m
Air-tap water
Ug = 0.015 m/s
121 holes, Ø 1.32×10-3 m 121 holes, Ø 1.32×10-3 m 121 holes, Ø 1.32×10-3 m 14 holes, 4.010-3 m 101 holes, 4.010-3 m 163 holes, 1.3210-3 m 64 holes, 1.3210-3 m 55 holes, 0.510-3 m 19 holes, 1.010-3 m
1.08 %
0.14 m
1.33 m
Air-tap water
Ug = 0.02 m/s
1.08 %
0.14 m
0.65 m
Air-tap water
Ug = 0.021 m/s
1.08 %
0.14 m
0.4 m
Air-tap water
Ug = 0.016 m/s
1.14 %
0.15 m
2.0 m
Air-tap water
Ug = 0.034 m/s
1.01 %
0.40 m
2.0 m
Air-tap water
Ug = 0.034 m/s
1.08 %
0.162 m
Air-therminol
Ug = 0.02 m/s
1.12 %
0.1 m
Air-tap water
Ug = 0.02 m/s
0.14 %
0.1 m
1.8 m (aerated) 1.2 m (aerated) 0.66 m
Air-tap water
Ug = 0.02 m/s
0.19 %
0.1 m
1.3 m
N2-tap water
Ug = 0.014 m/s Ug = 0.021 m/s
19 holes, 1.010-3 m
0.19 %
0.1 m
1.3 m
N2-ethanol
Ug = 0.006 m/s
In Fig. 16 are shown the gas maldistribution conditions for air-water system (see the black circles) from Table 3, which are plotted on the famous flow regime map of Shah et al. [1]. It is obvious that the hole diameter of the PP gas distributor plays an 36
important role on the end of the gas maldistribution. The flow regime map does not take into account this factor and this is one of its serious drawbacks. For hole diameters, which do not exceed 3.010-3 m the end of the gas maldistribution regime occurs at Ug ≤ 0.021 m/s (with some exceptions). When the hole diameters become as large as 4.010-3 m, then the range of the gas maldistribution widens and it is becomes stable up to Ug =0.034 m/s.
Hole diam.: 4 mm Hole diam.: ≤ 3 mm
Fig. 16. Correction for the gas maldistribution on the classical flow regime map [1]. The results reported in this work can be used in industry since most of the industrial BCs are equipped with similar PP gas distributors. In such a way the danger of fouling (due to the presence of impurities) is eliminated. The article reports the existence of gas maldistribution in relatively large BCs (column diameters=0.4 and 0.45 m) and deep BCs (clear liquid heights=1.91, 2.0 and 2.67 m). These conditions 37
are very close to the industrial operating conditions. In addition, the results in this work will help the industrial engineers to design well those industrial BCs, which should operate in the homogeneous regime (mostly in the field of biotechnology and waste water treatment) and the existence of gas maldistribution should be avoided.
5. Conclusions For the first time a systematic study on the determination of the end (so-called upper boundary) of the gas maldistribution has been performed. For this purpose, many different parameters (total information entropy, maximum information entropy, modified Shannon entropy and AAD, number of crossings of the mean and maximum number of visits in a single region) have been employed. All these parameters have exhibited a well-pronounced local minimum, which identified the upper limit of the gas maldistribution. It has been found that in most of the cases examined the end of the gas maldistribution occurs at Ug=0.02 m/s (with some exceptions, see Table 3). Therefore, this Ug range should be avoided since the gas maldistribution is detrimental to the BC performance. Only when the hole diameter is equal to 4.010-3 m, then the gas maldistribution becomes more stable and its upper boundary shifts to Ug=0.034 m/s. The information (on gas maldistribution) reported in this article will help to improve the design procedures for BCs. Transition velocities in organic liquids (therminol LT and ethanol) have been also reported.
38
Acknowledgments Dr. Stoyan Nedeltchev expresses his gratitude to both the Alexander von Humboldt Foundation (Germany) and the European Commission (Marie Curie Outgoing International Fellowship) for sponsoring this important research.
Nomenclature DC
column diameter (m)
IEmax
maximum information entropy (bits)
Nvmax
maximum number of visits in a single region (-)
Ug
superficial gas velocity (m/s)
z
axial height above the gas sparger (m)
Abbreviations AAD
average absolute deviation
BC
bubble column
BSD
bubble size distribution
CT
computed tomography
DP
differential pressure
GP
gauge pressure
ID
inner diameter
IE
information entropy
NC
number of crossings
NGD
nuclear gauge densitometry
OA
open area 39
PP
perforated plate
SD
scintillation detector
SE
(modified) Shannon entropy
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