Chemical Engineering Journal 288 (2016) 489–504
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Global and local hydrodynamics of bubble columns – Effect of gas distributor Safa Sharaf a, Maria Zednikova b, Marek C. Ruzicka b, Barry J. Azzopardi a,⇑ a b
Manufacturing and Process Technologies Research Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom Department of Multiphase Reactors, Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Rozvojova 135, Prague 6 165 02, Czech Republic
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Global and local hydrodynamics of
Time history of phase across a diameter of the bubble column blue is liquid, red is gas. Earliest time at top, later time below.
bubble columns: level swell and WMS. Flow regimes in bubble column and their transitions: effect of gas distributor. Critical review of current modelling strategies. New data on gas–liquid interfacial area.
0.013 0.053 Superficial gas velocities (m/s)
a r t i c l e
i n f o
Article history: Received 22 July 2015 Received in revised form 22 October 2015 Accepted 21 November 2015 Available online 12 December 2015 Keywords: Bubble columns Wire mesh sensor Gas holdup Bubble size Flow regimes Modelling
0.079
0.105
0.145
a b s t r a c t Global (level swell) and local (WMS – Wire Mesh Sensor) measurements were made on waters of different purities and air, in a cylindrical laboratory bubble column (2 m tall, 0.127 m dia) using two different gas distributors: a perforated plate (to produce homogeneous flow) and a spider sparger (to produce heterogeneous flow). The level swell method provided the steady space-averaged gas holdup/gas flow rate data. The WMS method provided the actual gas holdups and bubble sizes resolved in time and space at one cross-sectional horizontal plane (1 m above distributor), whose integration yields the timeaveraged data. The following results were obtained: The global and local data agree relatively well; there are distinct differences between the radial profiles and bubble size distributions between the two main flow regimes; the local information identifies why the predictions of published models, which account for the smaller and larger bubbles in the flow, may not perform well; the modelling approaches based on the hindrance and enhancement concepts prove to be suitable for the flow regime identification and description, including the transition range between the homogeneous and heterogeneous flows; based on the hydrodynamics, the specific interfacial area is obtained, together with the mass transfer coefficient. Ó 2015 Published by Elsevier B.V.
1. Introduction In this section, two aspects of bubble columns are considered: (i) the experimental findings regarding the key features of the ⇑ Corresponding author. E-mail address:
[email protected] (B.J. Azzopardi). http://dx.doi.org/10.1016/j.cej.2015.11.106 1385-8947/Ó 2015 Published by Elsevier B.V.
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columns behaviour relevant to the present study, and (ii) the mathematical modelling especially related to the description and interpretation of the measured data. The formulas introduced in here below (Section 1.2) are then applied to the present data (Section 3.4).
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Nomenclature a a0 C0 C1 C2 DB D32 g Hf Hi j k kL kLa n p u ud ugs uTr uo
constant in Eq. (5) specific interfacial area (m2/m3) term accounting for profile effects critical point marking end of homogeneous regime critical point marking boundary between transition and heterogeneous regimes large bubble size (m) Sauter mean diameter of bubbles (m) gravitational acceleration (m2/s) height of aerated column (m) initial or clear height of liquid (m) drift flux (m3/m2 s) constant in Eq. (4) liquid side mass transfer coefficient (m/s) volumetric liquid side mass transfer coefficient (1/s) power in Richardson and Zaki relationship, Eq. (4) weighting function bubble velocity (m/s) drift velocity (m/s) superficial gas velocity (m/s) velocity at upper boundary of homogeneous flow constant in Eq. (5)
1.1. Experimental findings Bubble columns are gas/liquid contactors which are often used as chemical reactors. They do not employ moving parts to produce mixing but achieve this purely by the hydrodynamics. Their background, geometries and characteristics are described in texts [1–4]. However, in spite of the plentiful literature on the topic there is still a need for improved understanding. In their simplest form, bubble columns are cylindrical vessels which can sometimes contain tube banks or coils for heat transfer control. There can be more complicated versions with internal or external down-comers to provide recirculation of the liquid and hence a larger liquid residence time. Here consideration will be focused on the simplest type without any inserts. Many of the equations published for bubble column design are empirical correlations and, therefore, their applications should be limited to interpolation. For the important parameter of gas holdup (also called: voidage, porosity, void fraction, etc.), published correlations have been reviewed by Ribeiro and Lang [5]. They found 37 sources, most with many empirical constants. Computational Fluid Dynamics has been applied to bubble columns and can give good results. Though, in expert hands they can give valuable information, they are not so useful for initial, first-design calculations. For such applications, simpler models with a sound physical basis are much more appropriate. However, the current versions of these models need to be strengthened and improved. Important geometric parameters in the design of a bubble column are column height, diameter, and the distribution, type and size of holes in the gas injector. These need to be considered along with the gas and liquid densities, the liquid viscosity and the presence and concentration of chemicals particularly those which can inhibit bubble coalescence, e.g., salts, alcohols and other surfactants. In simple bubble columns and bubbly flows, the following basic flow regimes have been identified: homogeneous or bubble flow; heterogeneous or churn-turbulent flow, and slug flow [6]. At low gas flow rates, with carefully designed ‘fine’ gas distributors, homogeneous flow is produced. This takes the form of small bubbles that are uniformly dispersed within the column. At higher gas velocities, when it transits into the heterogeneous flow, larger
Vg Vl
Deg/DDB eg hegi eB eTr
ql
volume of gas in aerated column (m3) volume of liquid in aerated column (m3)
gas holdup volume average gas holdup gas holdup in large bubbles gas holdup at upper boundary of homogeneous flow liquid density (kg/m3)
Subscripts He heterogeneous Ho homogeneous 1 at boundary between homogeneous and transition 2 at boundary between transition and heterogeneous Abbreviations ECT Electrical Capacitance Tomography EIT Electrical Impedance Tomography MRI Magnetic Resonance Imaging WMS Wire Mesh Sensor
bubbles appear that are interspersed between the small ones. With ‘coarse’ distributors, heterogeneous flow is produced at all gas inputs. In small diameter columns (6100 mm), at higher gas velocities, the large bubbles are stabilised by the column walls and the flow becomes slug flow. Mudde et al. [7] noted that a majority of industrial bubble columns operate in the heterogeneous flow regime region. In lab scale columns, we can typically have the three following flow regimes: homogeneous, heterogeneous, transition, which are also considered in this study. An important parameter in bubble column design is the gas holdup as, together with bubble size, it determines the gas–liquid interfacial area, which is crucial for mass transfer between the phases [4]. The volumetric gas holdup, eg, is defined as the ratio of the volume of the gas phase V g to the total volume of the dispersion ðV g þ V l Þ. The volume averaged gas holdup, hegi, can be calculated using ‘‘level swell”, i.e., the relative difference between the aerated liquid height, Hf, and its unaerated height, Hi, and is given by hegi = (Hf Hi)/Hf. From experiments on columns with diameters of 0.15, 0.225 and 0.4 m, Groen [8] showed that there is little effect of the column diameter on the overall gas holdup/superficial gas velocity relationship. The clear liquid height was shown [9] to decrease the gas holdup as the height of the two-phase mixture increased. In contrast, in the heterogeneous regime, little difference is seen between the data of Letzel et al. [10] (1.2 m tall bubble column with 200 0.5 mm diameter holes) and that of Cheng et al. [11] (10 m high column with measurements made at the 5 m level and having 6 mm diameter holes for air entry). It is generally agreed that the main effect of increasing liquid viscosity is to reduce the gas holdup [12]. However, in some cases, particularly in the homogeneous regime, a ‘dual effect’ of the viscosity can occasionally be reported: first to enhance the holdup and then to reduce it, with a maximum occurring somewhere within 1– 10 mPa s, say (e.g. Ruzicka et al. [13], Olivieri et al. [14]). Anderson and Quinn [15] measured the gas holdup in a bubble column with water at different levels of purity. Impurities suppress bubble coalescence and hence increase its gas holdup. As tap water has more impurities than deionised or distilled water, it is not surprising that its gas holdup was higher than that in the other two. In a similar
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experiment [16] the concentration of salt in the water was varied and resulted in an increase in gas holdup as the salt concentration is increased. However, when the salt content is further increased, a drop in the gas holdup was observed [17]. Thus surfactants can affect the gas holdup in two ways – ‘dual effect’. Note that salts (electrolytes) can produce the Marangoni phenomena in a similar way as organic substances and thus deserve the name ‘surfactants’. Similarly, these different ‘dual’ effects were observed to also occur when solid particles were present, i.e., in slurry bubble columns (e.g. Mena et al. [18], Rabha et al. [19]). Similar homogeneous injectors to the one used in the present research have been investigated in the past [20,21]. More recent work on a similar sized bubble column and a multiple needle injector (559 0.8 mm diameter needles) has been reported [22]. Mudde et al. [7] shows a comparison of gas holdups obtained with the multiple needle distributor [22] against data for a porous plate [8] and perforated plate distributors with two pore sizes [23]. It is interesting to note that it was found that injectors with 0.5 mm holes produced homogeneous flow, whereas injectors with 1.6 mm holes only produced a heterogeneous flow with a central peak in the radial gas holdup distribution [19,21]. Wall peaks in the radial profiles of gas holdup in homogeneous flow have been reported [7,22], for example, at a gas holdup of 6.1% and a superficial gas velocity of 0.015 m/s. Wall peaking was found to occur when there was a co-flowing liquid [22]. Experiments using a distributor with 61 holes of 0.4 mm in diameter showed [24] the radial profiles to be constant at low superficial gas velocities i.e. a homogeneous regime with a uniform value of gas holdup across the centre of the column and peaks in gas holdup near the pipe wall. The gas holdup distribution showed a centre peak at higher gas velocities i.e. a heterogeneous regime, as a consequence of the bubbles being concentrated and rising more rapidly in the centre of the pipe. There is a tendency for the peakiness of the radial gas holdup distribution to increase as the superficial gas velocity is increased. Some of the experimental methods for the determination of the detailed behaviour of gas–liquid flows in bubble columns provide data that is resolved in time but localised in space whilst others provide spatial information but are averaged in time. There are some techniques which can provide data resolved in both time and space. Local methods, which can give information which is time resolved, include needle probes which can give local phase (from which gas holdup can be extracted) and bubble size and velocity (if more than one needle is used simultaneously). There have been many papers published in this area [24,25]. Laser Doppler anemometry has been employed to measure local liquid velocity by Harteveld et al. [26] amongst others. Space resolved, though time averaged methods for gas holdup were pioneered by the group of Dudukovic, e.g., Kumar et al. [27]. Methods which can give information resolved in time and space usually depend on a form of fast tomography. They can be based on X-rays [28], Magnetic Resonance Imaging (MRI) [29,30] or electrical methods. The latter can be with external electrodes using capacitance (Electrical Capacitance Tomography, ECT) [31] or flush mounted electrodes using impedance (Electrical Impedance Tomography, EIT) [32]. The Wire Mesh Sensor (WMS) system is intrusive by having very fine wires stretched along chords. It was originally developed on the basis of conductance [33] and later extended to employ capacitance [34]. Bubble size information can be extracted from the WMS output [35]. The WMS technique has been applied to bubble column studies [36]. The tomographic methods, fast X-ray, MRI, ECT, EIT, WMS, are very powerful and can give prodigious quantities of information. They each have their particular strength and weaknesses. For example, ECT is non-intrusive but has a lower spatial resolution than other methods. However, it can be used with pairs of planes, one downstream of the other, and so provide velocity information.
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This, as well as the WMS, can handle column diameters up to large values and are fairly portable. In contrast, fast X-ray and MRI are not portable and currently limited to smaller column diameters. However, they do have excellent spatial resolution; the former can give 3D information by use of several axially spaced planes, the MRI provides it intrinsically. In this paper the application of global methods, monitoring liquid column expansion due to aeration, and more detailed interrogation, applying the WMS measuring technique, are presented and the results discussed to obtain understanding of the behaviour of bubble columns. The detailed information is used to test global methods which are based on a physical concept rather that purely empirical correlations. 1.2. Modelling approaches There have been a large number of equations to predict gas holdup in bubble columns. Many of these are empirical and take no account of the flow regime which is present. Three of the methods are based on simple models of the flow and correspond to the three regimes. In the first, for the homogeneous regime Wallis [37] suggested that the gas holdup could be determined from the ratio of superficial gas velocity, ugs, and the actual rise velocity of the bubbles u, i.e., eg = ugs/u. It is realised that at higher concentration the presence of other bubbles would hinder the rise of bubbles, whence u depends on eg. The hindered settling approach [38] has been employed to account for this effect. Those authors proposed a correction factor to the isolated bubble terminal velocity u0 in the form of u = u0(1 eg)n, where the value of n depends on a Reynolds number based on the diameter and terminal rise velocity of the bubble. This results in an implicit equation for gas holdup which has to be solved iteratively. In the second, the heterogeneous regime, the gas holdup can be calculated from the ratio of superficial gas velocity to the actual velocity of the bubbles using the equation proposed by Zuber and Findlay [39]:
eg ¼
ugs C 0 ugs þ ud
ð1Þ
where C0 is a term to account for radial profile effects about the cross-section and ud is the drift velocity, the typical velocity of bubbles. In the third, the duality of the two regimes and their transition, where the holdup passes through a maxima at increasing gas input, was a challenge [21]. Krishna and his group [40] adopted an older concept of ‘small-and-large’ bubbles and inferred the proportions of large and small bubbles from the results of dynamic gas disengagement experiments, which was designed for this purpose. They illustrated a typical experimental result for air/tetradecane in a 0.1 m diameter column with an initial clear height of 1.2 m, showing the transition when holdup passes through a peak, as it should. Beyond the peak they recall that large bubbles began to make a significant contribution to the gas holdup. The gas holdup contained in small bubbles became independent of the gas flow rate at values higher than the critical. To encompass the homogeneous and the heterogeneous regions [41,42], they started by identifying a transition point. Equations for the gas velocity and gas holdup at transition have been proposed [43,44]. The Krishna group assumed that part of the flow, whose flow rate corresponds to the transition value, flows as small bubbles. Any gas flow rate beyond this value flows as large bubbles. They consider that these larger bubbles were formed by coalescence of smaller ones. Letzel et al. [10] provided an empirical correlation to predict the gas holdup of large bubbles directly and a means of combining the small bubble and large bubble gas holdups. In contrast, Krishna et al. [41] calculated
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the rise velocity of large bubble from the methods of Collins [45] which allowed for the effect of the column walls. They provided an empirical equation to specify the large bubble diameter:
DB ¼ 0:069ðugs uTr Þ0:376
ð2Þ
The large bubble gas holdup, eB, was determined from the superficial gas velocity above transition (ugs uTr) divided by the large bubble velocity, uB. The total gas holdup was calculated from:
eg ¼ eB þ eTr ð1 eB Þ:
ð3Þ
However, this concept cannot recover the peak that is typical for the transition region, and their holdup graph is a monotonously increasing function. The relevant forces which affect the size of bubbles formed at orifices have been identified [46]. These were modelled for the cases where each of three forces (inertia, surface tension and liquid viscosity) was dominant. This resulted in rather cumbersome methodology to predict bubble sizes and so a relatively simple explicit equation was developed which gave a good fit to those models. This equation was shown to give reasonable predictions of the mean bubble size for bubble columns [47]. More recent work [22] has also confirmed the ability of the equation of Gaddis and Vogelpohl [46] to predict bubble sizes. Others [48,49] have published alternative equations for bubble sizes. The methods which have been employed to analyse the present experimental data (Section 3.4), i.e., to identify the flow regime and to quantify the empirical parameters which define the characterising equations for each regime, are presented here. This starts from arrays of measured mean (space–time averaged) gas holdups, eg, for each gas flow rate, defined through the superficial gas velocity, ugs. It is noted that the simple basic relation eg = ugs/u, where u is the actual gas velocity of the bubbly mixture, is not a definition of eg nor a hypothesis or an experimental finding. It is the steady-state mass balance of the gas phase in the column. It holds generally, regardless of the flow regime present. If the gas velocity, u, is its terminal speed u0, which has a fixed value, then the graph of eg versus ugs is a straight line with tangent (1/u0). Deviations from linearity are indicative of the flow regimes. In the homogeneous regime, u < u0 due to the hindrance effect on bubble rise and the plot of eg against ugs is convex. In the heterogeneous regime, u > u0 due to the enhancement effect caused by liquid circulations increasing the rise velocity of the bubbles, and the plot is concave. The borderline case u u0 does not mean the absence of the gas–liquid phase coupling but marks the end of one regime and beginning of the other. It is noted that this methodology is not subjective because it reflects the reality of the prevailing character of the force interactions between the gas and liquid phases in the mixture. The flow regime discrimination based on the geometry of the graph eg = eg(ugs) is not a result of the free-will choice of the observer but is the direct manifestation of the underlying physics of the phase coupling. The simple models listed below provide a useful insight into the interpretation of the eg ugs data by classifying them with help of the two extreme and well-defined flow situations: homogeneous and heterogeneous. These two limits differ in their flow and transport features and most of the real flows are somewhere in between these two idealised cases. The models enable us to assess the degree to which a given flow approaches the either limit. 1.2.1. Pure heterogeneous regime The easiest case to treat is the pure heterogeneous regime. Plots of gas holdup against superficial gas velocity are typically concave because of the enhancement effect. Eq. (1) usually produces a good fit. The two parameters, ud and C0, can be determined by linear regression and can be assigned certain physical meaning, i.e., ud
is the terminal bubble speed u0, C0 is the radial profile factor, the strength of the gas–liquid inter-phase coupling. The gas holdup increases almost linearly at low gas inputs and asymptotes to a limiting value at large superficial gas velocities. This regime can typically be obtained with coarse spargers in viscous liquids and those in which bubbles coalesce easily. 1.2.2. Homogeneous regime Here, the gas holdup graph eg(ugs) is typically convex due to the hindrance effect and can be fitted empirically by a power-law with exponent >1. A more soundly-based approach uses a hindrance function, e.g., that proposed by Richardson and Zaki [38] which is widely employed and considered a very effective description,
u ¼ kð1 eg Þn
ð4Þ
Here k is expected to be close to the bubble terminal speed u0 (which is often, but not always, the case). Values of the exponents n, which are found to be >0, indicate the strength of the hindrance effect. Typical values are of order of unity. Amongst the many other hindrance formulae, the following
u ¼ u0 ð1 aeg =ð1 eg ÞÞ:
ð5Þ
Has two parameters with clear physical meaning (a – coefficient of Darwin hydrodynamic drift) and will also be used below [50]. If ugs and eg are measured and u is obtained from u = ugs/eg, the hindrance parameters (k, n and u0, a) can be found by fitting the data with the above equations. The homogeneous gas holdup is then be described by an implicit relation e.g. in the form:
eg ¼ ugs =uðeg Þ;
ð6Þ
closed by Eqs. (4) or (5). As the gas flow rate is increased, liquid circulations develop and the homogeneous regime loses stability at the first critical point, ugs1, where it changes into the transition regime. This point is marked by a balance between the hindrance and enhancement effects and the data start to deviate from the hindrance equations. Alternatively, the drift-flux plot proposed by Wallis [37] can be employed. It is re-phrasing the reality of the hindrance phenomenon using a different coordinate system. The flux j = j(eg) can be expressed in two equivalent forms: j = eg(1 eg)u and j = (1 – eg)ugs. The former expression is used for drawing the theoretical line with its typical dome shape, where a suitable closure is used for the hindrance u(eg). The latter expression is used for plotting the ‘experimental line’, where the measured data are shown. The data depart from the model at ugs1. Beyond the first critical point C1 at ugs1, the gas holdup/superficial gas velocity plot passes through a maximum, where the convex branch turns into the concave branch within the range of the transition regime. At the second critical point C2 at ugs2 > ugs1, the transition is completed, and the stable heterogeneous regime sets in. The uniform regime with transition can typically be obtained with fine spargers in non-coalescent liquids of low viscosity. 1.2.3. Heterogeneous regime resulting from transition The heterogeneous regime resulting from the transition starts at ugs2 and can be taken as identical to the pure heterogeneous regime, which is described by Eq. (1). Fitting of parameters for this equation (u0, C0) is carried out starting from large ugs where we can assume the heterogeneity is fully developed. Several data points are taken from this range and fitted to Eq. (1). These should give an excellent fit, identified by a value of the correlation coefficient close to 1. Further points are then included into this process decreasing the values of superficial gas velocity included until the correlation coefficient decreases to below a pre-set limit. There, the point ugs2 has been reached [50].
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1.2.4. Transition regime There are not many studies dealing with simple physical modelling of the transition regime in bubble columns, which is a bridge between the uniform and non-uniform flow modes. One approach [50] is based on the simple and natural assumption that the transition regime can be described as a properly weighted sum of both of its ingredients, homogeneous, egHo, and heterogeneous, egHe. These can be any relevant quantities used for the weighting, for instance, the gas holdup,
egTr ¼ ð1 pÞegHo þ pegHe ;
ð7Þ
here p is a suitable ‘bridging’ function whose values will be in the range 0–1. The parameter p is also called the intermittency factor, since the both flow regimes, homogeneous and heterogeneous, coexist in the column, in varying proportion, in space and time (analogy with laminar-turbulent transition). The requirements of the function p(ugs) are that it starts from 0 at the first critical point, ugs1, and achieves the value of 1 at the second critical point, ugs2. This functional parameter must be extracted from experimental data. By re-arranging Eq. (7) to yield a formula explicit in p,
p¼
ðegTr egHo Þ ðegHe egHo Þ
ð8Þ
is obtained. The bridging function p(ugs) is obtained from the data as a table of several discrete values, [ugsi, pi], i = 1, 2, ... , N, where N is a number of experimental points within the transition region. This data sets can then be fitted with an empirical function to obtain a closed formula, suitable for practical modelling. Other than the above physically based semi-empirical practical models designed for the respective flow regimes, an ideal target would be to compare the experimental data with the results of the rigorous stability analysis of the fundamental multiphase flow equations in their full 3-D version. However, this is beyond the scope of current modelling knowledge. Instead, approximations have been developed (one or two-dimensional models), where a direct link to the present data is not obvious. Also attempts employing Computational Fluid Dynamics are ongoing aimed at identification of the flow structures numerically. 2. Experimental arrangements In this section, the experiments are described, regarding the apparatus and the data acquisition and treatment. One bubble column with two different gas distributors yielded the three flow
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regimes. Two measurement methods provided the global and local data. The water purity was also tested.
2.1. Bubble column, distributors, and phases The present experiments were conducted in a bubble column made from acrylic resin pipe with an internal diameter of 0.127 m and height of 2 m and open at the top. Two different distributors were used. These are illustrated in Fig. 1. The first distributor was the perforated plate (‘fine’ sparger) and was designed to produce smaller bubbles and generate stable homogeneous flow at low gas inputs. It consists of a brass plate 2 mm thick with 121 holes of 0.5 mm diameter, uniformly distributed about the column cross-section. This gave an open area, i.e., the sum of the area of all the holes divided by the cross-sectional area of the column, of 0.19%. The second distributor was the spider sparger (‘coarse’ sparger), with six pipes of 5 mm external diameter and 1 mm wall thickness emerging horizontally from a central boss of 50 mm diameter. There were six 2 mm diameter holes spaced at 5 mm intervals along each pipe resulting in an open area of 0.89%. Care was taken to ensure that the bubble column was strictly vertical and always clean, to minimise any contamination that might affect the results. Any foaming was disregarded. A high-speed video camera capable of >1000 frames per second, a Phantom V7 Camera (manufactured by Vision Research Inc.) was also used to record images for both types of injectors. The level swell for global measurements was noted visually throughout these experiments. A 32 32 Wire Mesh Sensor for local measurements was installed at a height of 1 m above the gas distributor. The gas employed was air provided by the laboratory compressed air main at 6 bar. The system provided filtered air with minimal moisture. The flow was metered by a calibrated variable area meter which could be read to a precision of 0.0013 m/s. The liquid employed was water. Four different purities were used: distilled water, deionised water; Nottingham tap water and a 0.5% aqueous solution of butanol. The electrical conductivity of the liquids was determined after the experiments at each gas flow rate by a WTW LF 340 conductivity meter. The average values for each liquid were: 45, 1.8, and 0.3 mS/m for the tap, deionised and distilled water and 0.1 mS/m for the solution of butanol in distilled water. The experiments were carried out at laboratory ambient temperature. The temperature of the liquid was monitored throughout the experiments using calibrated thermocouple. The temperatures varied only between 17 and 22 °C for the entire series of tests. For
Fig. 1. The two gas distributors employed: (a) Perforated plate (fine sparger, homogeneous regime) showing the 121 holes of 0.5 mm diameter; (b) spider sparger (coarse sparger, heterogeneous regime) showing the six pipes each with six holes of 2 mm diameter.
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each individual set of experiments the variation in temperature was <1 °C. The level swell method was simple and reliable, with good reproducibility since the bubble bed was in the steady state (at fixed gas input). The overall error in the gas holdup data was estimated up to 5%. At large gas flow rates, the surface oscillated but the mean value of holdup was reproducible.
2.2. Wire mesh sensor The WMS system uses two arrays of wires positioned along chords of the pipe cross-section. The two arrays are axially displaced by 2 mm and are orthogonal to each other. One wire of one array is activated and the signals received by all the wires of the other set are monitored. The process is then repeated for all wires of the transmitter array. This is carried out using measurements of either conductance or capacitance of the system [33,34]. The system is calibrated by taking measurements in air and with the Sensor completely immersed in liquid. During the measurements the conductance or capacitance at each crossing point is taken. This is converted to local gas holdup. Post processing of the data can then yield time-averaged radial gas holdup distributions, and information about the sizes of bubbles present. The former is achieved by considering each crossing point as a square ‘‘pixel” and then defining annular rings. The data from each pixel is allocated, whole or in part to each ring. The average value for each ring gives the gas holdup for that radial position. Bubble size information for bubbles greater than the wire spacing, 4 mm, can be extracted using the method proposed by Prasser et al. [33,35]. This involves sorting information from all the crossing points on any one time frame and using a logic system to identify each bubble and it extent about the column cross section. For the sensor used in the present work, the two arrays were each made of 32 wires of 0.1 mm diameter and made of stainless steel which were stretched across chords of the pipe. The WMS instrumentation has been tested by making simultaneous measurements with Electrical Capacitance Tomography (ECT) [51] and c-ray absorption [52]. Good agreement between the instruments was achieved in both cases, usually within 2% variance in the holdup values. The comparisons with ECT were for cases with zero net liquid flow and excellent agreement was achieved between the two methods in both the overall (crosssection and time-averaged) gas holdup and the time-varying time series of cross-sectionally averaged gas holdup. Most recently [28], simultaneous measurements have been made using a WMS device placed 8 mm downstream of a plane at which an ultrafast X-ray tomography system was operating. For bubbly flow, they showed good agreement in the bubble size distribution from the two measurement techniques. As part of the preparation for the present experiments, measurements were made with the WMS whilst the level swell was recorded simultaneously. The capacitance approach was employed for the lower conductivity liquid, e.g., distilled water, and the conductance approach was utilised for the higher conductivity tap water. When they were applied to the same liquid, there was good agreement between the methods. It is noted that when the flow was in the heterogeneous regime, there was considerable fluctuation of the position of the top surface of the bubbly liquid producing an uncertainty in Hf. It might be considered that the mesh inserted in the bubble column could affect the behaviour of the flow within the column. The wires of the mesh can break up larger bubbles into smaller ones. This does occur. Carefully set up experiments using high-speed video showed that bubbles were indeed cut up by the mesh but the bubbles reformed very quickly. Another effect of the wire mesh
is to produce a slight slowing down of bubbles at the mesh which might encourage coalescence and hence the production of larger bubbles. It has been reported that small bubbles might adhere to the wires of the mesh. The column on which the WMS was inserted was constructed of transparent material. No evidence was seen of bubbles remaining attached to the wires. At higher gas flow rates, the mesh was not visible because of the presence of other bubbles. However, the higher the gas flow rate the less likely bubbles are to adhere to the wires, see also Prasser et al. [33,35]. In the WMS tests data was taken over either 30 or 60 s at a sampling frequency of 1000 cross-sections per second. In all cases the level swell was also measured. Repeat experiments were carried out with WMS which showed good reproducibility of the temporally and spatially (over radial coordinate) averaged gas holdup showing errors of about 2%. 2.3. Types of measurements Two types of measurements were carried out: global and local, to see the difference in their outputs, consistency and complementarity. The global data were measured by the level-swell method where the overall space-averaged mean holdup within the column is obtained, under steady conditions. These data are easy to interpret: the total gas phase fraction in the mixture. From these data the prevailing flow regime can be determined, even without knowing the details about bubble sizes and holdup profiles, thanks to the physical robustness of the hindrance and enhancement concepts. The local data were measured by the wire-mesh sensor (WMS) where the detailed information about the actual and time-averaged holdup structure at one horizontal cross-section is obtained. For the comparison with the global data, the time- and cross-sectional-averaged WMS measurements were used. The sensor senses the presence or absence of the liquid. The bubble size distributions are not a primary result of this measurement technique but require post-processing of the data obtained. The approach adopted is that the locations of those wire cross-over locations which are in gas together with those similar ones in contact with it and those surrounding ones which are in liquid for each time step are identified. Those only partially in one phase are identified by a local gas holdup. The sum of these areas gives the bubble area in the cross-section at that time step. This is repeated over successive time steps to provide a volume for each bubble. Obviously, a velocity has to be provided to convert the time axis to distance. By employing appropriate software, the method is able to identify more than one bubble per cross-section. Note that it is tacitly assumed that the time-average at one position by WMS equals the space-average over the whole column by level swell. This is however not proved and can therefore only be used as a practical ‘working hypothesis’ The global measurements (level swell) were carried out during the commissioning of the bubble column with the two distributors, involving water at different purities. The perforated plate was used with deionised water, tap water, and 0.5% butanol at clear liquid height of 0.9 m. The spider sparger was used with distilled water and tap water at clear liquid height of 1.2 m. The local measurements (WMS) were carried out in two Series, A and B: Series A: the (fine) perforated plate distributor, air/tap water, clear liquid height 1.1 m, conduction electronics for WMS, superficial gas velocities within 0.02–0.145 m/s. Series B: the (coarse) spider sparger, air/distilled water, clear liquid height 1.2 m, capacitance electronics for WMS, superficial gas velocities within 0.014–0.171 m/s.
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The lower value of the gas input was selected as one for which most holes were bubbling, the upper value was one that was well into the heterogeneous regime. 3. Results and discussion In this section the obtained results are presented and discussed in a logical order, along two lines: global and local measurements. First, the gas holdup data are shown and from their character the prevailing flow regime is assessed, including the effect of water purity. Then the local data are analysed in detail since much information can be retrieve from them: radial holdup profiles, bubble size distribution, time–space patterns of holdup dynamics. The present results are compared with published data to show that even the established references may not be valid universally. Effort is spent on proper mathematical modelling of the gross flow structure in the column, with the focus on the flow regimes. Based on the hydrodynamic data, an attempt is made to quantify the key mass transport parameters: the interfacial area and the transfer coefficient, to close the result section. 3.1. Global measurement (level swell) 3.1.1. Gas holdup and flow regimes The results obtained with the perforated plate are shown in Fig. 2a and illustrate that the more contaminated the water, the
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higher the gas holdup and the higher the gas velocity at which deviations from homogeneous flow occur. The data show the transition region with gas holdup passing through the maximum, then decreasing with increasing superficial gas velocity, and then the heterogeneous region when gas holdup once again increases with superficial gas velocity. The results obtained with the spider sparger are shown in Fig. 2b. In both cases the gas holdup data showed the characteristics of the heterogeneous flow – concave graphs and a little difference between the two liquids used.
3.2. Local measurements (WMS) 3.2.1. Gas holdup and flow regimes Series A. For the tap water and perforated plate, the effect of superficial gas velocity on the gas holdup is shown in Fig. 2c. This shows the characteristic homogeneous, transition, heterogeneous behaviour. Also shown are the gas holdups obtained simultaneously from the level swell. There is reasonable agreement between the results of the two measurements particularly considering that they are not measuring exactly the same thing (local vs. global data). The gas holdups obtained were lower than those shown in Fig. 2a. The reason can be seen in slightly varying the experimental conditions, namely the clear liquid height was 0.88 m for the data in Fig. 2a and 0.98 m for those in Fig. 2c, which corresponds to the lower gas holdup in the latter case. A secondary effect could be caused by the small difference in the temperature between
Fig. 2. Gas holdup data. Effect of measuring method, gas distributor, and water purity: (a) Global measurements by level swell, perforated plate, three water purities, homogeneous regime and transition; (b) global measurements by level swell, spider sparger, two water purities, pure heterogeneous regime; (c) Series A. Comparison of global (level swell) and local (WMS) measurements, perforated plate, tap water, homogeneous regime and transition; (d) Series B. Comparison of global (level swell) and local (WMS) measurements, spider sparger, distilled water, pure heterogeneous regime. Uncertainty band of ±5 cm due to the surface fluctuations at large gas inputs. WMS data were averaged over time and cross-section.
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the two sets of experiments, which results in an increase of the liquid viscosity of 8% between the cases illustrated in Fig. 2a and c. Series B. For the distilled water and spider sparger, the results are shown in Fig. 2d. These exhibit typical heterogeneous flow behaviour. Again there was reasonable agreement between WMS and level swell results, particularly at low gas flow rates. Much better agreement can be seen when the (overall) level swell results are corrected for the effect of hydrostatic pressure, i.e. bubbles are compressed and so the gas holdup is diminished, to give values more equivalent to the local WMS sensor values. Though there are differences at high gas rates, it is noted that the position of the top interface fluctuates significantly with an amplitude order 0.1 m for an aerated depth of 1.5 m. When a variation of ±50 mm is included in the plot, it is seen that the difference between the methods is within the uncertainty of the level swell data. 3.2.2. Radial profiles of gas holdup and bubble sizes Time-averaged, radial profiles of gas holdup can be extracted from the WMS data. These can be thought of as annuli; measuring the gas holdup all around the pipe, starting in the centre and working outwards to the circumference. In addition, starting from the WMS data, bubble size distributions can be extracted. A particular strength of WMS over other sensors in this area is that it measures the bubble size distribution across the whole cross-section as opposed to taking point measurements. Bubble size distributions based on the volumes of each bubble are determined using the approach proposed by Prasser et al. [33,35]. The distribution of volumetric gas holdups per bubble diameter will be used here identified as Deg =DDd and expressed as %/mm (the portion of the gas holdup carried by bubbles of a given size class). This expression is suitable for the present application, because the area under the curve is the time and cross-sectional average gas holdup.
Series A data are shown in Fig. 3a. They exhibit the almost flat radial profiles of gas holdup and single peaked bubble sized distributions (small bubbles) at the lowest gas velocities, in the homogeneous regime. At the higher gas velocities, it changes to the parabolic gas holdup profile and an increasingly larger second peak at larger bubble sizes, which is the flow regime transition region. Further on, very large bubbles prevail at the highest gas velocities, in the heterogeneous regime. Series B data are in Fig. 3b, where the basically bi-modal distribution (smaller and bigger bubbles) clearly indicates the heterogeneous flow. The bubble size distribution shows larger bubbles than at the lowest gas flow rate. Bubbles of these larger sizes, >50 mm diameter, have been reported from experiments with X-ray tomography [19]. The occurrence of peaks, both at the wall and in the centre of the column are similar to those reported in the literature [19,21,22,24] as discussed in Section 1.1. The gas holdup of gas carried in small bubbles, i.e., those relating to the distributor prior their further coalescence in the bulk, were obtained from the bubbles size distributions, by fitting a Gaussian distribution to the peaks at lower bubble sizes. This has been carried out for the data from the Series A and B experiments and the results are shown in Fig. 4. For the Series A runs, it is clear that the small bubble gas holdup constitutes almost the entirety of the overall gas holdup for superficial gas velocities to the upper limit of the transition regime. The vertical lines indicate the boundaries between the homogeneous and the transition regimes and the transition and heterogeneous regimes. These were determined using the methods described below. It is only when the gas flow rate has risen to levels where the heterogeneous regime occurs that there is a significant decrease in the small bubble gas holdup. This is an indication that small bubbles are coalescing into larger ones. In the case of the Series B data, there is a point at which the overall gas holdup is seen to deviate from the small bubble gas holdup at a much lower gas flow rate probably by the increase
Fig. 3. Local measurements by WMS: radial profiles and bubble sizes (1 m above gas distributor): (a) Series A (perforated plate, tap water). Radial profiles of directly measured holdup evolve from flat (and very slightly wall-peaked) into parabolic and centre-peaked shape, indicating the homogeneous–heterogeneous regime transition at increasing gas input (top diagram). Indirectly calculated bubble size distributions with small bubbles in the homogeneous regime and with growing population of larger bubbles during the regime transition (bottom diagram). (b) Series B (spider sparger, distilled water). Radial profiles of holdup quickly take pronounced parabolic shapes, witnessing the pure heterogeneous regime (top diagram). Bubble size distribution shows the simultaneous presence of two peaks, smaller and bigger bubbles, shifting to larger sizes with rising gas input (bottom diagram).
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experimental data from other research groups. Such a brief comparative study is useful because it shows that the published and established models, commonly used in the multiphase community, can work well in some situations but perform less than satisfactory in others.
Fig. 4. Effect of gas flow rate and gas distributor on overall gas holdup and gas holdup carried by the small bubbles. Closed symbols – data of Series A (perforated plate, homogeneous regime and transition – demarcated by two vertical lines). Open symbols – data of Series B (spider sparger, heterogeneous regime).
in coalescence. From that point onwards the residual gas holdup in small bubbles increases very slowly with increase in gas flow rate. 3.2.3. Spatio-temporal dynamics of gas holdup The WMS output provides information about the distribution of the phases about the cross-section and with time. Different views can be extracted. In Fig. 5a and b the void distribution across a diameter is shown for a series of sequential times for a number of superficial gas velocities. These have been chosen to be as near as possible the same for the two Series of experiments shown in these figures. Examination of these images confirmed the results presented in Fig. 4 that for the Series A results there are only smaller bubbles present until the superficial gas velocity reaches 0.086 m/s. In contrast, in the Series B images larger bubbles are visible by a superficial gas velocity of 0.053 m/s. 3.3. Comparison of present data with published results Before comparing the present data with the predictions of models, it is instructive to make comparisons with relevant
3.3.1. Gas holdup data Here the data obtained with water using the perforated plate distributor and the spider sparger distributor are examined. If the perforated plate distributor is considered, comparisons can be made with the data of Vandu and Krishna [53] from columns of 0.1, 0.15 and 0.38 m diameter all filled to a clear liquid height of 1.6 m, compared to a height of 0.9 m used in the present work. As with the present work, the gas distributors used by Vandu and Krishna have holes of 0.5 mm diameter; the open areas were 0.19% for the present work and 0.49%, 0.69% and 0.48% for the three columns of Vandu and Krishna. As can be seen in Fig. 6a, there is agreement between all four data sets at the lower gas flow rates. The data of Vandu and Krishna do not show the pronounced ‘homogeneous’ peak seen in the data from the present work, possibly because their open area is about three times larger than that of the Series A experiments. A second reason for the differences between the present data and that of Vandu and Krishna is the different initial liquid heights. A third reason, which might account for the difference in the position of the peak in gas holdup, is the properties of the water employed. Vandu and Krishna do not give details of the properties of their water. The results from the present work (Series A) were carried out with Nottingham tap water which is particularly hard, conductivity 45 mS/m. As was noted in the Introduction, increasing the initial height decreased the gas holdup as seen in the peak values on Fig. 6a. Also, the number of orifices is larger, their spacing is reduced and the bubbles can coalesce right at the plate. Also, the stable plate operation (all orifices bubbling) is reached at higher gas input [54]. These two conditions promote the heterogeneity of the bubbly mixture near the plate. At the higher gas flow rates, there is a distinct effect of column diameter with the Series A data (0.127 m) lying between the 0.1 and 0.15 m data of Vandu and Krishna. This decrease in gas holdup in wider columns agrees with literature [8]. For the spider sparger cases, comparison has been
Fig. 5. Local measurements by WMS: spatio-temporal dynamics of gas holdup. Time sequences of holdup distribution across the column diameter for several gas velocities. Blue colour indicates water and red colour indicates air (gas holdup). (a) Series A. The perforated plate generates the homogeneous regime and its transition starting at about 0.046 m/s (cf. Fig. 4). No large red patches are seen at low gas input. (b) Series B. The spider sparger produces the stable pure heterogeneous regime. Big air pockets occur even at low gas inputs. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. Comparison of present gas holdup data with the published holdup data: (a) Series A. Perforated plate, tap water, homogeneous regime and transition. In all cases the diameters of the holes were 0.5 mm. The open areas were 0.19% for present data, and 0.49%, 0.69%, 0.48% for the published results (Vandu and Krishna [53]) from columns with diameters of 0.1, 0.15, 0.38 m respectively. (b) Series B. Spider sparger, distilled water, pure heterogeneous regime. The hole diameter was 2 mm for present data, and 2.5 mm for Vandu and Krishna [53], and 3 mm for Pioli et al. [55]. The corresponding open areas were 0.89%, 1.09% and 0.1% respectively.
made of the Series B data from the present work [column diameter = 0.127 m, hole diameter = 2 mm, open area = 0.89%] with the data of Pioli et al. [55] [column diameter = 0.24 m, hole diameter = 3 mm, open area = 1.09%] and Vandu and Krishna [column diameter = 0.63 m, hole diameter = 2.5 mm, open area = 0.1%]. As can be seen in Fig. 6b, all three data sets lie on the same curve with the monotonically rising shape characteristic of heterogeneous flows. The clear liquid heights were 1.2 m for the present work, 1.6–4.6 m for the data of Pioli et al. and 2.18 m for Vandu and Krishna. Given the fact that the data reported by Pioli et al. was from a range of clear liquid heights and that the all lay on the same curve, it can be deduced that the clear height is not important for this type of distributer. Not surprisingly data from the three sources are similar in spite of the different clear heights. Given the difference between the open area in the Vandu and Krishna case and the other two data sets, it is not the open area that pushes the flow into heterogeneous flow but it is the size of the holes that is a more controlling factor as was confirmed by Drahos et al. [20]. 3.3.2. Bubble sizes The bubble size distributions presented in Fig. 3a and b shows a peak in the region of 8 mm. For Series A at the lowest gas flow rates studied, there is just a single peak which can be taken to be the bubbles formed at the orifices. At higher flow rates larger bubbles can be seen to occur. It is reasonable to assume that these are due to coalescence. Bubbles of the smaller size can be seen at all flow rates for this series, implying that some of the bubbles created at the orifices persist even when there is coalescence occurring. For the Series B data similar trends are present. However, it is only at the lowest flow rates that there is only a single peak. From the bubble size distribution data shown in Fig. 3a and b, the sizes of ‘‘small” and ‘‘large” bubbles have been identified. These are taken to correspond to the sizes at which there are peaks in the distribution. They are plotted in Fig. 7a and b. If the smaller bubbles are considered first, the sizes are compared with those predicted by published equations [46,48,49] in those figures. There is reasonable agreement but the Gaddis and Vogelpohl equation shows the correct trend and has absolute values nearest to the experimental data. Considering the size of the large bubbles it is seen that they are about an order of magnitude bigger than the small bubbles. For the Series A data the large bubbles do not appear until a superficial gas velocity of 0.07 m/s. For Series B they appear at a much smaller velocity. The sizes of these larger bubbles are compared against the prediction of the fully empirical equation proposed by Krishna et al. [41], Eq. (2), in Fig. 7a and b. The agreement is not good. The reason is that the three model parameters
(0.069, 0.376, uTr = 0.034) are not universal but strongly depend on the particular data. For instance, if it is possible to select alternative constants which are shown in Eq. (9a)
DB ¼ 0:278ðugs uTr Þ0:49 ;
ð9aÞ
where uTr was taken as 0.07 m/s. This gives a good fit to the present data as shown in Fig. 7a. However, good agreement can also be obtained by other types of equations, for example, the rational function can be used to have the concave shape of the data, e.g.,
DB ¼
0:093ðugs uTr Þ : ð0:0225 uTr Þ
ð9bÞ
Again uTr was taken as 0.07 m/s. If the data pass through an inflection point, as they can when the big-bubble population develops slowly, the following more elaborate equation can be provided,
DB ¼ ½0:075 tanhð40ugs 3Þ þ 1ðugs uTr Þ0:376 ;
ð9cÞ
where the original numerical factor (0.069) in Eq. (2) was replaced with an empirical function. For Series B, Eq. (2) can be used with parameters (0.2, 0.48, uTr = 0.034), as seen in Fig. 7b and denoted as ‘Eq. (2) with alternative constants’. 3.3.3. Present data and published models Comparisons have been made between the data reported above and models/correlations published by other authors. These consider average gas holdup, radial variation of gas holdup and bubble sizes. The performance of methods to predict gas holdup has been tested against the data for Series A and B. Shown in Fig. 8a and b are the predictions of: The homogeneous model using the hindered rise factor of Richardson and Zaki [38]. The drift flux equation, Eq. (1), using the simplest possible parameters (C0 = 2, ud = 0.3 m/s for water). Note, these drift flux constants for water were originally suggested by Zahradnik and Kastanek [56]. The transition conditions of Reilly et al.[44]. The model of Krishna et al. [41,42]. This is an extension of that of Krishna and Ellenberger [40] and Letzel et al. [10] which assumed that beyond transition all extra gas goes into the larger bubbles. They provide an equation for the large bubble gas holdup together with a method of combining the small and large bubble gas holdups. Krishna et al. [41] calculate the large bubble size from an empirical equation. It then determines the large bubble velocity using a method which allows for the effect of the column walls taken from the work of Collins [45]. The
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Fig. 7. Comparison of present bubble size data with the published results: data and models. New equations proposed in the text are also shown: Eqs. (9a)–(9c) for Series A and modified Eq. (2) for Series B: (a) Series A. Perforated plate, tap water, homogeneous regime and transition. Data denoted as WMS 1st and 2nd peaks are taken from Fig. 3a (bottom). (b) Series B. Spider sparger, distilled water, pure heterogeneous regime. Data denoted as WMS 1st and 2nd peaks are taken from Fig. 3b (bottom).
Fig. 8. Comparison of different published models applied to present gas holdup data. (a) Series A. Perforated plate, tap water, homogeneous regime and transition (data from Fig. 2c). (b) Series B. Spider sparger, distilled water, pure heterogeneous regime (data from Fig. 2d).
large bubble gas holdup is then calculated from the ratio of the difference between the superficial gas velocity and the superficial gas velocity at the transition from homogeneous flow as given by the equation of Reilly et al. [44] and the large bubble velocity. Also shown for the Series A case are the predictions in which the large bubble velocity are calculated using Eq. (9). The concept of the existence of three regimes: homogeneous, transition and heterogeneous flows. Instead of taking the equations with given constants, e.g., the hindered rise equation of Richardson and Zaki [38] for homogeneous regime and the drift flux equation for the heterogeneous regime, these equations are used to extract the optimal values of the constants, A bridging function is employed to fit the transition regime as described above. For the Series A data, Fig. 8a, it can be seen that the homogeneous curve has the correct trend at the lower gas flow rates. However, the absolute values are higher than those measured. The conditions of the homogeneous transition are reasonably predicted by the equations of Reilly et al. [44]. The predictions of the method Krishna et al. [41] are in good agreement at the highest gas flow rates but do not reproduce the peak in the transition region. Even utilising the new equation for the sizes of large bubbles does not bring the predictions of the Krishna et al. model anywhere near the measured values of gas holdup. For the experiments with the spider sparger, Series B, the predictions for the homogeneous model and the transition point to heterogeneous flow as proposed by Reilly et al. are significantly
higher than the experimental values. The method Krishna et al. [41,42] also predicts gas holdups higher that those measured as shown in Fig. 8b. Again, the predictions of the drift flux methods are also high. Obviously, the modified drift flux equation produced following the methods presented above gives a very good fit. For this case the constants are C0 = 1.25 and ud = 0.48 m/s, c.f., the values of 2 and 0.3 were proposed by Zahradnik and Kastanek [56]. For Series B values of C0 and ud noted above gave much better agreement with the experimental data. The equation is in line with the results shown in Fig. 4 and the images illustrated in Fig. 5a. The reasons for the poor predictions of the model of Krishna et al. [41] can be clearly seen in Fig. 4. The assumption of the model is that, at low gas rates, the gas holdup increases by there being cumulatively more small bubbles until the gas flow rate that is the transition from homogeneous flow; for higher gas flow rate the gas holdup corresponding to small bubbles remained constant and increases in gas holdup were taken to be due to large bubbles. In contrast, the experimental data show that the gas holdup held in small bubbles continues to increase well into the transition regime and that the processes of coalescence moving all the gas into large bubbles only occurs at the transition to the heterogeneous regime. Even for the data obtained when injecting gas through the spider sparger, the gas holdup in small bubbles continues to increase beyond the transition from the homogeneous regime. It is interesting to note that Krishna et al. [41] show a similar increase in the small bubble gas holdup beyond the transition point in their Fig. 5(c).
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3.4. Present modelling strategy: flow regimes determination and description The level swell data, i.e., global gas holdup, eg, versus gas flow rate, ugs, reported in this paper have been processed utilising the methods described in Section 1.2. It is shown that this methodology is robust and can give a useful insight into the character of the experimental data identifying the flow regime present. Note also, that this simple physical modelling of the whole regime transition process has only rarely been applied. It is probably the first case where recent matching methodology based on the ‘bridging function’ has been applied to a broader range of data. Typically, perforated plate distributors with small holes with low viscosity liquids (such as water) produce homogeneous flow and then, at higher flow rates, heterogeneous flow (Series A). With distributors with larger holes, only the pure heterogeneous regime occurs for all liquids (Series B). The data in Fig. 2a and c (Series A) exhibit the flow regime transition, marked with the typical maxima in the eg(ugs) graph. The other data, Fig. 2b and d (Series B) display characteristics of the pure heterogeneous regime. The critical point No. 1 is denoted as C1 = [ugs1, eg1], which is the end of homogeneous regime and the start of the transition regime. The critical point No. 2 is denoted as C2 = [ugs2, eg2], which is the end of transition regime and the start of the heterogeneous regime. The transition regime is located between C1 and C2. The values of all parameters derived in this Section are tabulated in Table 1.
3.4.1. Fig. 2a. Perforated plate distributor. Butanol solution data This data set covers the range of homogeneous regime and the very beginning of the transition regime. The convex shape is rather obvious. These gas holdup data are higher than the water data as butanol in water acts as a surfactant and can suppress the coalescence by slowing the liquid film drainage due to Marangoni effects. The population of small bubbles thus survives until larger gas inputs, i.e., the flow regime transition is delayed and the homogeneous regime is stabilized. The data were fitted with the Eqs. (5) and (6) and are shown in Fig. 9a.
3.4.2. Tap water data This covers all three flow regimes and smoothly changes from the convex to the concave shape. It is a copybook example of well measured data. The data lie within butanol and other water data. Tap water contains relatively large amount of inorganic salts – electrolytes, which also exert surface effects. Unlike the common organic surfactants, which attract to surface and strongly reduce its tension, the electrolytes often repel from the surface and weakly enhance its tension [57,58]. The homogeneous regime data fitted by Eqs. (5) and (6) are shown in Fig. 9a. The heterogeneous regime data resulting from the regime transition and fitted by Eq. (1) are shown in Fig. 9b. The transition regime data was also analysed and model fitted, as discussed below.
3.4.3. Deionized water data The data set also covers the three regimes. The deionization process reduces the salt content and so places these data below tap water. There is a maximum, typical for the regime transition, but less pronounced. However, the homogeneous regime data are not convex. It means that there is no hindrance effect and the hindrance closures Eqs. (4) and (5) do not apply. The collective bubble speed (the speed of the swarm of bubbles) u(eg) is either constant or decreases with the bubble concentration, which is atypical. The flows of bubbly mixtures are very complex and sensitive to many influences, not all are fully understood. Occasionally, some unusual behaviour may be seen, when the system behaves in a different way. An example of this can be seen in the deionized water data. The point C1 cannot be extracted with methods based on the hindrance phenomenon. For this data set, the speed of the bubble swarm is nearly constant at 0.24 m/s and the fitted value of n is 0. The homogeneous regime data can be well fitted with a straight line, eg = 4.166 ugs. This is not unexpected as eg is always = ugs/u. The heterogeneous regime data after transition fitted with Eq. (1) are shown in Fig. 9b. It was not possible to analyse the transition regime branch. 3.4.4. Fig. 2b. Spider sparger distributor. Tap and distilled water data The data show the pure heterogeneous regime, which is typical for the non-uniform flows generated by coarse gas distributors. heterogeneous regime is highly turbulent and robustly stable. There is no apparent ‘order’ that could break. Therefore, all the data are visually almost identical: distilled and tap waters in Fig. 2b and the Series B data in Fig. 2d. Here, Eq. (1) applies but the fitting parameter ud does not reflect the terminal bubble speed u0, since its values are rather large. The fit is shown in Fig. 8b. Despite the similarity of the data their fitting parameters may differ slightly (see Table 1). 3.4.5. Fig. 2c. Series A. Perforated plate and tap water The data appear sensible. They cover the three flow regimes and display the maxima over the transition range. The global data (by level swell) are convex in the homogeneous regime. The heterogeneous regime data after transition and predictions from Eq. (1) are shown in Fig. 9b. 3.4.6. Fig. 2d. Series B. Spider sparger and distilled water These data show pure heterogeneous regime, because the holes in the gas distributor are larger. They and their fit to Eq. (1) are shown in Fig. 8b. 3.4.7. Fig. 2a. Flow regime transition – tap water data The data cover the three flow regimes, homogeneous regime ? transition regime ? heterogeneous regime, and can be modelled by smooth matching the uniform and non-uniform branches via a suitable bringing function p(ugs) over the transient region between the points C1 and C2. The uniform branch up C1 to was
Table 1 Parameters of models in Section 1.2 determined from data analysis. Distributor
Liquid
Perforated plate, data in Fig. 2a Perforated plate, Fig. 2a Perforated plate, Fig. 2a Perforated plate, Fig. 2c, Ser. A Spider sparger, Fig. 2d, Ser. B Spider sparger, Fig. 2b
Aqueous butanol solution Tap water Deionised water Tap water Distilled water Tap water
Transition 1, crit. point C1
Transition 2, crit. point C2
ugs1 (m/s)
eg1
0.053 0.053 0.052 0.046
0.28 0.26 0.21 0.25
ugs2 (m/s) 0.131 0.118 0.086
Eqs. (5) and (6) flow in HoR
Eq. (1) flow in HeR
eg2
u0 (m/s)
a
C0
ud (m/s)
0.3 0.26 0.18
0.238 0.26 0.24 0.22
0.531 0.73 0 0.5
1.5 1.6 3.54 1.25 1.94
0.26 0.28 0.175 0.48 0.37
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501
Fig. 9. Modelling strategy suitable for all three flow regimes: homogeneous, heterogeneous, transient: (a) Homogeneous regime can be fitted (lines) with Eqs. (5) and (6). The data (marks) are taken from Fig. 2a for tap water and butanol solutions, from the convex homogeneous branch before the instability threshold (before point C1 in Table 1). (b) Heterogeneous regime resulting from the transition can be fitted (lines) with Eq. (1). The data (marks) are taken from Fig. 2a for tap water and deionised water, and from Fig. 2c for tap water by level swell, from the concave heterogeneous branch after the transition completed (beyond point C2 in Table 1). (c) Homogeneous–heterogeneous regime transition can be fitted (lines) with Eqs. (1), (5), (6) and (8), where Eqs. (5) and (6) describe the homogeneous branch till the point C1, and Eq. (1) describes the heterogeneous branch after the point C2, and the bridging function p = p(ugs) by Eq. (8) glues these two branches together over the transient region between C1 and C2 (the sigmoidal S-shaped dotted line running from 0 to 1 with the ordinate on the right). The data (marks) are taken from the Fig. 2a for the tap water.
modelled with Eqs. (5) and (6). The non-uniform branch beyond C2 was modelled with Eq. (1). The matching was performed with help of Eq. (7), where instead of the gas holdup eg, the weighted quantity was the liquid-phase velocity, as suggested previously [50]. The numerical values of the parameter p(ugs) were obtained from the data with help of a formula similar to Eq. (8) and were approximated with a sigmoid function, as suggested recently [59]. The following parameter values were employed for the two separate regimes (see Table 1): homogeneous regime, u0 = 0.26 m/s, drift coefficient a = 0.73; heterogeneous regime, u02 = 0.26 m/s, C0 = 1.5. Within the transition region, between 0.053 and 0.13 m/ s, the two main regimes were combined with the sigmoid:
pðugs Þ ¼ h
1 þ exp
1
ðugs 0:09Þ 0:014
i
ð10Þ
which is shown in Fig. 9c. 3.4.8. Fig. 2c. Series A. Flow regime transition – tap water data These data are also amenable to the full treatment, bridging over the transition region. The following parameter values were employed for the two separate regimes (see Table 1): homogeneous regime, u0 = 0.22 m/s, drift coefficient a = 0.5; heterogeneous regime, u02 = 0.175 m/s, C0 = 3.54. Within the transition region, between 0.046 and 0.086 m/s, the two regimes were glued with the sigmoid:
pðugs Þ ¼ h
1 þ exp
1
i :
ðugs 0:0715Þ 0:0089
ð11Þ
The final result is seen in Fig. 8a. As mentioned at the end of Section 1.2.4, the experimentally obtained instability threshold (critical value C1) should be compared with predictive results of a stability theory for bubble columns. To our knowledge, there is no such theory suitable. There are several 1-D theories where the instability mechanism typically precedes via longitudinal gas holdup waves, as the first modes excited from the uniform base state: this usually applies to bubbly flows in long pipes. In bubble columns, the instability is of the convective nature where large-scale circulations gradually develop; therefore at least 2-D models are needed. However, there are not many [60–63]. The earliest [60] yields an explicit stability criterion, which was compared with data [43] with moderate agreement. Some [60,61] consider the effect of bubble deformation, whilst others [61] focus on the change of sign of the coefficient of the lift force on stability. The study by Monahan and Fox [64] that does not yield an explicit criterion and still requires direct testing against data. We are not aware of a full 3-D mathematical stability theory for bubble columns. One attempt at the 3-D case is a simple physically based stability concept [65] in which an explicit criterion for the onset of circulations in bubbly layers is suggested. The critical gas holdup predicted by their convective theory for the experimental case similar to that in this study can be taken from their Fig. 4a (line) and is about eg1 0.19, which is lower than the values 0.25 and 0.26 in Table 1. The second attempt is the highly simplified stability model [59] that yields the criterion in the form: eg1 = 1/ (1 + n) where n is the Richardson–Zaki exponent from Eq. (4). It is notable that this criterion can be obtained as the limit case of the rigorous theory. For the present values of the critical gas
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holdup, eg1 = 0.21 and 0.28 in Table 1, we have the corresponding values of n = 3.76 and 2.57, which are not unusual for bubbly flows. To conclude, it is noted that the flow regimes can also be approached from the numerical side [66]. 3.5. Interface areas and mass transport coefficients The specific interfacial area is the interfacial area per unit volume which is determined from 6eg/D32 after the work of Mandal [67], where D32 is the Sauter-mean diameter. This can be considered at different levels. The information can be examined as averaged in time but resolved in bubble size. For Series A, Fig. 10a, tap water with the perforated plate distributor, the bulk of the area at the lowest gas flow rate arises from bubbles whose sizes are dictated by the size of the holes of the distributor. In contrast, at the highest gas flow rate there are 29% of the bubbles in sizes comparable with that of the column. However it is noted that these bubbles only contribute 10% of the specific interfacial area. The largest fraction of area is in bubbles about twice as large as those created at the orifices, i.e., 17 mm diameter. For the spider sparger with water, Series B, Fig. 10b, the distribution of specific interfacial area at the lowest gas flow rate is similar to those of Series A. Similarly, at the highest gas flow rate, as with Series A, there is a second peak with about 10% of the area. Fig. 11a shows the overall specific interfacial area, averaged over time integrated over the whole range of bubble sizes. The data is presented according the power per unit volume. Here, this parameter was calculated from the simple equation proposed by
Bouaifi et al. [68] (=qlgugs), where ql is the liquid density and g the gravitational acceleration. For water, Series A, B, the specific interfacial area from the perforated plate distributor (A) is much greater, particularly at the peak gas holdup where it is approximately three times the value for the spider sparger. However, at the higher superficial gas velocities the data from the two distributors converge which is not surprising as both are in the heterogeneous regime. Moreover, they seem to be asymptoting to a constant value. Data obtained by Bouaifi et al. for an air-water system from a column diameter (0.15 m) similar to that used in the present work is also presented, denoted as M1 and PP1 in Fig. 11a. It is limited to the lower end of the gas flow rates employed here because of the experimental technique they utilised. However, within their rage of power per unit volume, it shows good agreement with the Series A data, which is the most similar of the present experiments to their work. The information in Fig. 11a has been used to examine how the mass transfer coefficient, kL, varies with superficial gas velocity. Though mass transfer data was not taken in the present work, the measurements of Vandu and Krishna [53] can be used. These were taken in a column of similar diameter to that used in the present work. They report data for kLa. If this is combined with the data for specific interfacial area a0 reported in Fig. 11a, the results plotted in Fig. 11b are obtained. These indicate that at higher gas flow rates, in the heterogeneous regime, the mass transfer coefficient increases with increase of superficial gas velocity. This is in contrast to the much smaller increasing specific interfacial area with gas flow rate. Thus it could be argued that pushing up the
Fig. 10. Local measurements by WMS: specific interfacial area. The gas–liquid contact area is averaged over time but resolved by bubble size, for two gas inputs. ‘Low’ refers to the lowest superficial gas velocity, ‘High’ to the highest. (a) Series A. Perforated plate, tap water, homogeneous regime and transition. (b) Series B. Spider sparger, distilled water, pure heterogeneous regime.
Fig. 11. Mass transport: energy spent on making contact area and mass transfer coefficient kL. (a) Specific interfacial area averaged over time and integrated across all bubble sizes plotted against power per unit volume. The present data for Series A and B are labelled ‘A’ and ‘B’. The data taken from the work of Bouaifi et al. [68] are from a 0.15 m diameter bubble column utilising air and water. That labelled ‘M1’ employed a membrane gas distributor with initially 0.5 mm diameter orifices, and ‘PP1’ was a perforated plate with 2.5 mm diameter orifices. (b) The relation between the mass transfer coefficient kL and the gas input was obtained by taking the former as the specific value kLa0 from the literature (Vandu and Krishna [53]) and combining it with the present data on the specific area a0 from Fig. 11a, for Series A and B.
S. Sharaf et al. / Chemical Engineering Journal 288 (2016) 489–504
gas flow rate with its price of increased power input, mainly through pressure loss, does not give more interfacial area but could improve the mass transfer possibly by increased turbulence at the bubble surface. Results for this separation of kL and a’ have been reported recently [69] in experiments using chemical systems. They worked at low gas flow rates, in the homogeneous regime, and reported trends similar to those in Fig. 11a and b at gas superficial velocities up to 0.02 m/s. It is noted by Vandu and Krishna [53] that the ratio of volumetric mass transfer coefficient (kLa) to gas holdup has a constant value once a minimum value of velocity is reached.
F016050/1). The financial support by the MSMT-Ministry of the Czech Republic (Project No. LD-13018) is gratefully acknowledged. References [1] [2] [3] [4]
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4. Conclusions
[7] [8]
From a study of the effect of gas flow rate, gas distributor, and water purity, using both global and local (spatially and temporally resolved) approaches on the hydrodynamics of a bubble column the following conclusions can be drawn: Overall gas holdup results from the perforated plate (fine distributor) with the uniformly spaced small diameter holes show distinct homogeneous, transition and heterogeneous behaviour in the gas holdup/superficial gas velocity plots. The spider sparger (coarse distributor) generates only the pure heterogeneous regime. Generally, the global (level swell) and the time- and cross-sectional-averaged local (WMS) data agree both qualitatively and quantitatively. The water contamination increases the gas holdup and stabilize the homogeneous regime by suppressing the bubble coalescence due to the Marangoni stresses. The radial profile of gas holdup, directly measured by WMS, shows wall peaks in the homogeneous regime and a central peak in the heterogeneous flow regime. The bubble size distribution, indirectly reconstructed from the WMS signals, shows a single peak (small bubbles) in the homogeneous regime. The simultaneous presence of two peaks (small and large bubbles) is typical for the heterogeneous regime. The small bubble sizes are well described by the equation of Gaddis and Vogelpohl [46]. The very big ‘bubbles’ of 5–10 cm are interpreted as coalescing holdup clusters or deficiencies in the algorithms employed. The spatio-temporal patterns of gas holdup obtained by WMS give very instructive insight into the interior dynamics within the bulk of the bubbly mixture. The critical comparison of the present data with the established literature results indicates that not always these results correspond well and therefore cannot be taken as ‘universal’. The applied modelling strategies for the overall gas holdup results proved the robustness of the physically based hindrance and enhancement concepts. The former well reflects the flow reality of the homogeneous regime, while the latter (formally equivalent with the drift flux approach) applies to the heterogeneous regimes. A suitable combination of the models for the respective regimes (via the bridging function) can be used for fitting also the transition data. As the last point, the interfacial area was extracted from the measured data and the mass transfer coefficient was calculated, which is valuable for practical use.
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