Local Gas Holdup Measurement in Sparged and Aerated Tanks by γ

In the present work, a γ-ray attenuation technique was used to measure gas holdup distribution in stirred tanks. Measurements have been carried out i...
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Ind. Eng. Chem. Res. 2004, 43, 5389-5399

5389

Local Gas Holdup Measurement in Sparged and Aerated Tanks by γ-Ray Attenuation Technique A. R. Thatte,† R. S. Ghadge,† A. W. Patwardhan,*,† J. B. Joshi,† and G. Singh‡ Institute of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India, and Isotopes Application Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India

In the present work, a γ-ray attenuation technique was used to measure gas holdup distribution in stirred tanks. Measurements have been carried out in a 0.57-m-i.d. tank agitated by a pitched blade downflow turbine (PBTD45°) and a disk turbine under two different conditions, namely, surface aeration and sparger aeration beneath the impeller. The measurements have been made at various operating speeds. In both the cases, the average gas holdup calculated by integration of the local gas holdup was found to match well with those obtained by visual observations based on volume expansion. The gas holdup profiles also enable identification of speeds of regime transition. This technique appears to be promising for the characterization of industrial stirred reactors. Introduction For rational design of gas-liquid stirred reactors, it is vital to understand the effect of various operating parameters on the regime of operation. The nature of flow in stirred tanks is complex; it also depends on various operating conditions and geometry. Moreover, the quantities such as overall gas holdup and overall mass transfer coefficients give only the global picture. Local information on hydrodynamics of two-phase flow is required for reliable design. One of the important aspects is the local value of the fractional gas holdup. Such information can be ultimately used for process optimization and process intensification. In the literature, various methods of local gas holdup measurement have been reported. Calderbank1 was the first to address the problem of local gas holdup measurement. A capillary suction method was used for measurements with an air-water system in a 0.5-m-diameter tank equipped with a six-bladed radial flow impeller. Barigou and Greaves2 employed conductivity probes in a 1-mdiameter vessel agitated by a 0.33-m standard Rushton turbine. Nagase and Yasui3 used a resistivity probe inside a tube to sample the two-phase flow within the vessel. They used a 0.25-m fully baffled vessel equipped with a disk turbine (0.125-m diameter) and a vane disk turbine (0.108-m diameter). Nienow et al.4 employed the suction method (using a peristaltic pump) to withdraw air-water dispersions from a 0.29-mdiameter vessel. Mishra and Joshi5 developed a procedure for local gas holdup measurement using LDAgenerated velocity (liquid and gas)-time data. Takenaka and Takahashi6 used an electrical conductivity probe in a 0.29-m-diameter fully baffled vessel equipped with a Rushton turbine. Gas dispersion by the impeller is an important part of operations involving gas-liquid contact in stirred vessels. The gas dispersion in a stirred tank is extremely complex with the possibility of several dispersion regimes (flooding, loading, complete dispersion, recircula* To whom correspondence should be addressed. Phone: 9122-414 5616. Fax: 91-22-414 5614. E-mail: [email protected]. † University of Mumbai. ‡ Bhabha Atomic Research Centre.

tion of gas-liquid mixture) depending upon the type of impeller, speed of agitation, superficial gas velocity, sparger size, type, and location. The complete dispersion of gas is the most desirable and important requirement for any mechanically agitated contactor. The flooding phenomenon, being undesirable, forms an important limit to the gas-handling capacity of a given impeller and hence must be avoided in gas-liquid operations. Flooding of the impeller makes it difficult to disperse the gas; the gas passes through the reactor without being dispersed thereby reducing the effectiveness of the stirrer and causing a significant reduction in the gas holdup and gas-liquid interfacial area. For an industrial reactor, the identification of flow regimes would therefore give valuable insight into its operation. The flooding-loading transition for a Rushton turbine impeller was originally defined by Nienow et al.4 as the beginning of the radial pumping action of the impeller. They concluded that the transition from flooding to loading can be characterized by a linear relationship between the impeller Froude number and the gas flow number.4 Over the years, a number of researchers have investigated the flooding-loading, loading-complete dispersion, and dispersion-recirculation transitions for a variety of impellers. The successive stages between the flooded and dispersed conditions very often appear to be continuous. The transition between impeller flooding and loading can be detected in a number of ways: (i) visual observation;4 (ii) with the help of a power curve, (PG/Po) plotted as a function of impeller speed;7,8 (iii) shaft torque variance as a function of impeller speed;8 (iv) spectra of pressure/sound fluctuations near the impeller blade;9 (v) time series analysis of conductance fluctuations along the cross section of the vessel.10 However, such methods cannot be used for industrial-scale reactors for a number of reasons, such as opaque nature, inability to vary speed, and inability to install probes at various locations inside the reactor. It would therefore be highly desirable to make measurements of the local gas holdup within the reactor and thereby determine the operating regime of the stirred tank. In view of this, the aim of the present work was to test the applicability of the γ-ray attenuation technique to measure the local gas holdup distribution and

10.1021/ie049816p CCC: $27.50 © 2004 American Chemical Society Published on Web 07/13/2004

5390 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

thereby get information about the operating regime and the hydrodynamics of stirred tanks. Previous Work Since the evolution of process tomography during the mid 1980s, computerized tomography has been a useful tool for multiphase flow measurement in systems such as bubble columns, packed beds, gas-solid fluidized beds, and trickle bed reactors. Tomographic technique involves acquisition of measurement signals from the sensors located on the periphery of process vessels. A variety of sensors such as ultrasound (ultrasonic tomography), electrical (electrical resistance tomography and electrical capacitance tomography), nucleonic (X-ray or γ-ray tomography), and optical (optical tomography) can be used. Process tomography gives information on cross-sectional profiles of the distribution of phases in process equipment or pipelines, thus giving more insight into the operation. Ultrasound computerized tomography has long been used to understand the hydrodynamics of multiphase systems. Dispersed-phase holdups are measured by noting the change in velocity of ultrasound in dispersions. The time shift difference and the energy attenuation of the ultrasound pulses propagating through a two-phase medium are used to obtain the local phase holdups. Ultrasound computerized tomography has been used to measure gas holdups,11 bubble velocities, bubble diameters,11 and specific interfacial areas.12 Supardan et al.13 have used this technique using a combination of the ultrasonic technique and neural networks for measuring local gas holdup in a dispersion system of air-water and air-glycerol solution in a bubble column. Results obtained from the proposed technique showed good agreement with the experimental data. Xu et al.14 developed an ultrasound computerized tomography system for monitoring/imaging gas-liquid flow using a fast binary back-projection image reconstruction algorithm. The system was utilized for flow regime identification. A Perspex pipe of inner diameter 0.187 m, 0.22 m long, and 0.007 m thick was used. The ultrasound array consisted of six half-cylindrical transducers and 36 rectangular transducers mounted along the periphery of the pipe. Both parallel and fan beam scanning were employed. The multiple tomographic images generated were used to understand the different two-phase flow patterns in pipe flow. Electrical tomography techniques are based on imaging the distribution of an electrical property within a medium for capacitance (ECT) and resistivity (ERT). The difference between these two electrical tomography techniques lies in the electrical property whose distribution is being imaged, the way the electrodes are assembled, and the type of object material to be scanned. In electrical capacitance tomography, electrodes are voltage excited one by one and the capacitance values between the excited electrode and the remaining ones are measured using capacitance-sensing probes installed in a noninvasive way. Electrical capacitance tomography is suitable for electrically insulating (nonconducting) multiphase systems (gas-liquid systems, insulating liquids). Electrical resistance tomography, on the other hand, is suitable for electrically conductive fluids and when the electrodes can be placed in contact with the process fluid without altering the flow patterns. The bulk phase must be electrically conducting and must make contact with the electrodes. It involves

passing electric current through the two electrodes and recording the voltage/potential difference between the remaining electrodes. Resistivity sensing probes are small in size, usually kept in contact with the media. Hence, unlike capacitance probes, which are noninvasive, resistance sensing probes are invasive but nonintrusive in operation. Electrical tomography techniques have been applied for imaging gas holdup distribution in two-phase bubble columns,15,16 investigation of liquid-liquid mixing processes in stirred tanks,17,18,19,20 to obtain gas holdups in gas-liquid-solid systems,21 and gas holdup as well as solids fraction in three-phase fluidized beds.15 Mann et al.17,18,20 and Holden et al.19 carried out a considerable amount of work on the application of electrical resistance tomography to understand gas-liquid and liquidliquid mixing processes in stirred tanks. Mann et al.18 have shown that the networks of zones model can provide a simplified but practical basis for detection and quantification of the nonuniformities in gas holdups. This technique provides a detailed map of the local gas flow rates throughout the network, overall gas recirculation ratio, and gas split ratio. However, the gas holdup distribution and the overall gas holdup calculation is based on the assumption of a uniform bubble size and bubble velocity throughout the vessel, which may not be the case in practice. Mann et al.17 have used an ERT system to visualize the different gas-liquid flow characteristics in a stirred tank that provide a qualitative picture of the holdup distribution. However, only the overall profiles have been depicted, and the absolute values of gas holdups encountered in gas-liquid stirred tanks have not been provided. Further, attempts have not been made to investigate the gas dispersion characteristics, namely, regimes of operation observed with different spargers and different types of impellers. The soft field effect is encountered in both electrical capacitance tomography and electrical resistance tomography. The electric field applied in electrical capacitance tomography and electrical resistance tomography is called “soft” as it is easily distorted and changes both in magnitude and in direction due to contact with the material present. Moreover, the electric field applied along a straight line changes not only with the phases present along the line but also with the phase distribution within the column. Such an electric field due to its easy susceptibility to distortion by contact with the material present is known as a soft field. Due to the nonstationary and transient nature of the fields of density, concentration, and void fraction, the tomographic measurement techniques need to have a high time and spatial resolution. Hence, a need arises for scanning the field for every smallest possible area (high spatial resolution) in the least possible time, meaning more scans per second (high time resolution). However, a high spatial resolution means a same sized field being divided into a larger number of scanning areas, thereby requiring more time, and hence resulting in low spatial resolution and vice versa, for example, a time resolution of up to 100 image frames/s (electrical tomographic measurement) results in a low spatial resolution equivalent to 10% of the cross-sectional diameter. Hence, there is a need to strike a balance with a proper combination of spatial and time resolution while selecting a tomography technique for a particular application. Although the electrical tomography techniques have the advantage of being capable of time-resolved measurements,

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5391

Figure 1. Schematic diagram of experimental setup for an aerated stirred tank. Key: A, shaft torque sensor for power measurement; B, impeller; C, gas sparger; D, scintillation detector; E, personal computer; F, multicounter; G, data acquisition facility; S, radioactive source.

the soft field effect and the limited possible number of independent measurements significantly limit the spatial resolution (1 × 2.54 mm2 for a 32-electrode system) compared to X-ray (0.25 × 2 mm2) or γ-ray tomography (1 × 1 cm2) and hence require advanced image reconstruction methods. In addition, imaging different sections of the flow is quite cumbersome since the electrodes are integrated into the wall of the test section. Hence, other tomography techniques (X-ray tomography and γ-ray tomography) involving a hard field sensor system are well suited for imaging gas holdup distribution in multiphase systems. A hard field sensor system generates a uniform narrow field wherein the variation of counts along a path is independent of the distribution of the property (density, concentration, etc.) in the region other than the path; for example, the attenuation of the radiation beam in a measurement plane is only dependent on the density changes encountered by the radiation beam on the straight path from the source to the detector. Such a field is hard enough to be affected by the properties or changes in properties of the material present and hence is known as a hard field. X-Ray tomography has been used to study the flow patterns and holdup distributions inside fluidized beds22,23 and trickle bed reactors23,24 and to determine the flow regime, the time behavior of the two-phase flow, and the void fraction distribution in bubble columns.25 X-Ray tomography allows a better spatial resolution because of the small size of the detectors and is safe compared to other nuclear radiography techniques, i.e., the γ-ray attenuation technique. However, it is not suited to the study of large test sections. In such cases, more penetrative γ-rays are preferred. The γ-ray attenuation technique has been used for void fraction or phase concentration distribution measurements in twophase flow systems such as two-phase horizontal pipe flows,26,27 trickle bed reactors,28 bubble columns,29 and fluidized beds.30 It is observed that the different tomography techniques (ultrasound computed tomography, electrical tomography, X-ray tomography) are well suited and widely used for phase holdup distribution in pipelines, fluidized beds, bubble columns and trickle bed reactors. However, their applicability for local gas holdup measurement in gas-liquid stirred tanks has not been studied. The γ-ray attenuation technique has also still not been applied for gas holdup measurements in stirred

tanks. In view of this, the objectives of the present work were the following: (i) Standardize the γ-ray attenuation technique for gas-liquid stirred tank reactors, such that the results are accurate and reproducible. (ii) Measure the gas holdup distribution in stirred tanks for different impeller and sparger combinations. (iii) Use the gas holdup measurements to get more insight into the hydrodynamics such as regime of operation. (iv) Apply the γ-ray attenuation technique to surface aeration and get more insight into the hydrodynamics of stirred tanks under surface aeration conditions. Experimental Section Equipment. Experiments were carried out in a transparent, flat-bottom, cylindrical tank of 0.57-m internal diameter equipped with four baffles each 0.057 m in width. Liquid height was maintained equal to the tank diameter. Air and tap water were used as the working fluids. The schematic diagram of the experimental setup for sparged reactors is shown in Figure 1. A similar setup with slight modifications (absence of gas sparger) was used for surface aeration experiments. Measurements have been carried out for two different conditions, namely, air sparging through the sparger and surface aeration. The impeller rotational speed, the impeller power consumption, and the air flow rate were measured with an rpm sensor, a shaft torque sensor, and a gas rotameter, respectively. Two types of impellers, namely, pitched blade downflow turbine (PBTD45°) and disk turbine (DT) were employed. Ring spargers of 0.19 and 0.41m in diameter were employed for gas sparging. The ratio of the impeller diameter to the tank diameter (D/T) and the ratio of impeller clearance from the tank bottom to the tank diameter (C/T) were kept equal to 1/3. The ratio of impeller blade width to impeller diameter (W/D) was fixed at 0.3 for pitched blade turbine and 0.2 for disk turbine. For the purpose of validation of the γ-ray attenuation measurements, the average fractional gas holdup was measured visually by noting the height in the presence and absence of gas sparging. Visual observations of different flow regimes were also made to facilitate the identification of regime transitions and regime transition speeds. Power measurements in the presence and absence of gas were done using a shaft torque sensor to generate a power curve (PG/Po vs N), the shape of which

5392 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 Table 1. Summary of Experimental Conditions (with Gas Sparging) impeller studied PBTD45 PBTD45 DT

details

sparger details

parameters studied

C/T ) D/T ) 1/3, W/D ) 0.3 C/T ) D/T ) 1/3, W/D ) 0.3, C/T ) D/T ) 1/3, W/D ) 0.2,

0.19-m-diameter ring sparger 0.095 m from the bottom of the tank. 0.41-m-diameter ring sparger 0.095 m from the bottom of the tank. 0.19-m-diameter ring sparger 0.095 m from the bottom of the tank.

VG ) 0.01 m/s N ) 1.67, 3.33, 5, and 6.67 rps VG ) 0.02 m/s N ) 1.67, 3.33, 5, and 6.67 rps VG ) 0.01 m/s N ) 1.67, 3.33, 5, and 6.67 rps

Table 2. Summary of Experimental Conditions (Surface Aeration) impeller studied PBTD45 DT

details

parameters varied

submergence ) 0.38 m, D/T ) 1/3, W/D ) 0.3 submergence ) 0.38 m, D/T ) 1/3, W/D ) 0.2

N ) 8.33, 10, and 11.67 rps N ) 5, 6.67, and 8.33 rps

would help in identifying the different regime transition speeds. Tables 1 and 2 summarize the experimental conditions for the two cases, namely, air sparging through the sparger and surface aeration, respectively. The experimental setup for the measurement of gas holdup using a γ-ray attenuation technique is also shown in Figure 1. It consists of a 67.5 µC 137Cs γ-source (disk source of 0.02-m diameter), sodium iodide with thallium-activated scintillation detectors (Bicron), photomultiplier tube, preamplifier, multichannel (5 channels) analyzer, data acquisition system, and related hardware and software.31 The source collimator slit was 3 cm long and 3 mm in thickness. Collimators for the detectors are cylindrical, 8.7 cm in diameter and 10.3 cm long. The collimator slit was 3.5 cm in length and 4 mm in width. Parallel beam scanning was employed and tomography scans were carried out at different axial (0.12, 0.22, 0.32, 0.42, and 0.54 m from the bottom of the tank) locations and radial positions. Dwell time, obviously, has an effect on the gas holdup accuracy. The selection of an appropriate dwell time would depend on the instabilities involved in the process under consideration, the desired temporal resolution, and the actual temporal variations inherent in the void fraction. Trial runs indicated that a dwell time of roughly 50 s was necessary to satisfactorily capture the temporal variations in void fraction and the steady-state dynamic behavior of flow patterns prevailing in a stirred tank. Hence, a dwell time of 50 s was used in the experiments after analyzing different combinations of dwell time and number of events. The two-phase counts were checked with the background counts. Based on these preliminary results, the number of events and dwell time were fixed at 20 and 50 s, respectively. The total acquisition time for each line plane (chord) measurement was 1000 s. There are advantages of moving to faster data acquisition. However, these are dependent on many factors such as the source strength, source and detector collimator dimensions, distance between the source and the object to be scanned. Use of a higher strength source can definitely allow faster data acquisition and would significantly reduce the total scan time. But due to safety considerations and other disadvantages such as high noise and background scatter associated with a higher source strength, a 137Cs source of 67 µC strength was used in the present work and was found to give satisfactory results. The reproducibility of measurements was also within (10%. Every measurement yielded the value of chordal gas holdup.

The objective of the present work was to develop a γ-ray attenuation technique to generate gas holdup profiles in stirred tanks, which would be useful in identifying different flow regimes of operation in a stirred tank: flooding, loading, complete dispersion, and recirculation. Each flow regime, depending on the distribution of gas, results in varying gradients of axial, radial, and tangential gas fractions. In a stirred tank, the axial and radial gradients of gas fractions are large compared to the tangential gradient of gas fractions. Further, Lo32 has reported the gas holdup profiles for a horizontal plane below the impeller for a Rushton turbine agitated stirred tank obtained through CFD simulation. It can be seen from their results that tangential asymmetry in gas holdup profiles exists only near the baffle region. Elsewhere the profiles were quite symmetric. Ranade and Van den Akker33 depicted contour plots of gas holdups obtained through CFD simulation for a horizontal plane just below the impeller center plane for a standard six-bladed disk turbine agitated stirred tank. These contour plots show that the gas holdup distribution is not symmetric only between the impeller blades, but quite symmetric outside the impeller region. Therefore, in the present work, the emphasis was kept on measuring the axial and radial gradients of gas fraction, and as a first step, tangential symmetry was assumed. In view of this, the Abel transform method,34 presented below, has been used for the estimation of local gas holdups. Estimation of Local Gas Holdup. Reconstruction has been done using the Abel transform.34 f (r, R) is a function of radial position within a circle of radius R given as

f (r,R) ) -

1 π

∫rR

(dφ/dx)

xx2 - r2

dx

(1)

Inversion of f (r, R) in terms of φ using the inverse Abel formula, given by Bracewell,35 is as follows:

φ(x,R) ) 2

∫xR

f (r,R)r

xr2 - x2

dr

(2)

which is a line integral along the projection in the y-direction at x. The projection (chord) is a line integral of f, given by

ψ(x,R) )

φ(x,R) 2xR2 - x2

(3)

which is a line integral of f along the ray at x divided by the path length. Both the functions f and ψ are interrelated, and if one is an even polynomial then the other is also a polynomial of the same degree. Expression for f and ψ were assumed to be of the form

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5393 N

∑ am(r/R)2m m)0

f (r,R) )

(4)

N

ψ(x,R) )

bn(x/R)2n ∑ n)0

(5)

Shollenberger et al.34 derived the reconstruction relation as N

am )

∑

n)0

cmnbn

(6)

dnmam

(7)

N

bn )

∑

m)0

where,

[

[

cmn ) -

][

2m + 1 22n(2n - 2m - 1)

0,

[

[

](

2n - 2m 2m , m en n-m m m>n (8)

]( )

22n 2n - 2m / 2m , n e m 2m + 1 n - m m 0, n>m

dnm ) -

]

Figure 2. Power curve for PBTD45STD with a 0.19-m-diameter ring sparger, VG ) 10 mm/s.

)( )

]

(9)

Results and Discussion Power Consumption. Power measurements in the presence and absence of gas sparging at a constant air flow rate with increasing impeller speeds gives rise to a power curve (PG/Po vs N rps). Figure 2 shows the power curve for a stirred tank agitated by a pitched blade downflow turbine (PBTD45°), aerated by a ring sparger below the impeller. At low impeller speeds, the gas bubbles generated by the sparger rise vertically through the impeller without any hindrance. The impeller action is in the direction opposite to the gas flow and hence PG/Po is higher than unity. Under such conditions, the impeller is said to be flooded with gas and region AC is called flooding region. At impeller speed corresponding to point B, cavity formation begins and the cavity size increases with an increase in impeller speed. At point C, the cavity size is maximum. Cavity formation decreases the intensity of eddy motion behind the impeller and causes a reduction in the drag on the impeller blades. Hence, the impeller power consumption and power number decreases along the line AC. Cavity breakage starts at point C. As the impeller speed increases along the line CD, the cavity breakage increases and the power number continuously increases. At impeller speed exceeding point C, the gas bubbles penetrate into the region below the impeller and the impeller action dominates over the action of gas sparging. Point D, at which impeller action dominates, is termed as critical impeller speed for gas dispersion. At impeller speeds beyond point E, gas recirculation begins, resulting in a reduction in the power number. This regime is called recirculation region. Figure 3 depicts the power curve for a stirred tank agitated by a pitched blade downflow turbine (PBTD45°), aerated by a large 0.41-m-diameter ring sparger situated below the impeller. The gas bubbles generated at the sparger rise vertically at low impeller speeds, and

Figure 3. Power curve for PBTD45 with a 0.41m diameter ring sparger, VG ) 20 mm/s.

the impeller is still unexposed to the gas. So the impeller is flooded with gas, and hence, PG/Po decreases along the curve ABC. With an increase in speed, the impeller action becomes strong enough to disperse the gas. The gas starts penetrating in the region below the sparger and gas dispersion begins. Point D indicates the critical impeller speed for complete dispersion. The ratio PG/Po increases up to the point E. Beyond point E, the recirculation regime starts and the PG/Po ratio decreases. Figure 4 depicts the power curve for a stirred tank agitated by a disk turbine, aerated by a 0.19-m-diameter ring sparger situated below the impeller. The impeller remains completely flooded until the speed increases to 4.33 rps (corresponding to the minimum point C). The upward flow of the sparged gas remains unobstructed by the impeller action. The gassed power (PG) up to this point decreases more rapidly than ungassed power Po, and hence, the PG/Po ratio decreases with increasing N at constant VG. Beyond point C, the impeller pumping action increases with speed and the impeller starts dispersing the gas radially outward. The impeller enters the dispersion mode. The PG/Po ratio increases as N increases until maximum (point E) is reached. Beyond point E, dispersion with recirculation regime begins and the PG/Po ratio decreases.

5394 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

Figure 4. Power curve for DT with a 0.19-m-diameter ring sparger, VG ) 10 mm/s.

Figure 6. Contours/gas holdup profiles for vessel agitated by PBTD45. T ) 0.57m, D ) 0.19 m, VG ) 0.02 m/s. (A) N ) 1.67 rps; (B) N ) 3.33 rps; (C) N ) 5 rps; (D) N ) 6.67 rps. Key: dark blue, 0.00-0.05; medium blue, 0.05-0.10; light blue, 0.10-0.15; green, 0.15-0.20; yellow, 0.20-0.25; light orange, 0.25-0.30; dark orange, 0.30-0.35; red, 0.35-0.40; black, 0.40-0.45.

Figure 5. Contours/gas holdup profiles for vessel agitated by PBTD45STD. T ) 0.57 m, D ) 0.19 m, VG ) 0.01 m/s. (A) N ) 1.67 rps; (B) N ) 3.33 rps; (C) N ) 5 rps; (D) N ) 6.67 rps. Key: dark blue, 0.00-0.05; medium blue, 0.05-0.10; light blue, 0.100.15; green, 0.15-0.20; yellow, 0.20-0.25; light orange, 0.25-0.30; dark orange, 0.30-0.35; red, 0.35-0.40.

Gas Holdup Profiles. Figures 5A-D and 6A-D depict the gas holdup profiles in the form of contours generated using the γ-ray attenuation technique for stirred tanks agitated by pitched blade downflow turbine (PBTD45°), aerated by 0.19- and 0.41-m ring spargers, respectively. Gas holdup profiles, in the form of contours, generated using the γ-ray attenuation technique for stirred tank agitated by a disk turbine and aerated by a 0.19-m ring sparger are shown in Figure 7. These gas holdup profiles clearly depict the flow patterns prevailing in the stirred vessel. A pitched blade downflow turbine (PBTD45°) at different impeller speeds generates widely different gas holdup profiles. At a low speed of 1.67 rps (Figure 5A)

Figure 7. Contours/gas holdup profiles for vessel agitated by DT. T ) 0.57 m, D ) 0.19 m, VG ) 0.01 m/s. (A) N ) 1.67 rps; (B) N ) 3.33 rps; (C) N ) 5 rps; (D) N ) 6.67 rps. Key: dark blue, 0.000.03; medium blue, 0.03-0.06; light blue, 0.06-0.09; yellow, 0.090.12; light orange, 0.12-0.15; dark orange, 0.15-0.18; red, 0.180.21.

gas is present in a zone vertically above the sparger. Highest gas holdups (0.35-0.4) near the impeller were

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5395

observed with progressively decreasing holdups toward the top liquid surface. Most of the sparged gas passes through the impeller without being dispersed. At low speeds, there is very low holdup, 0.05 near the walls and in the vicinity of the tank bottom. With a gradual increase in speed to 3.33 rps (Figure 5B), the sparged gas starts spreading radially outward. As a result, the region near the wall, especially near the top liquid surface, shows slightly increased (0.05-0.1) holdup values. Also owing to the onset of radial dispersion of the gas, the zone of high gas holdup around the impeller enlarges in the radial direction and shrinks in height. Since the impeller is a downflow type, the location of the highest gas holdup shifts closer to the impeller. As the impeller speed is further increased to 5 rps (Figure 5C), the gas is dispersed even below the impeller. The zone of holdup around the impeller is spread over a larger volume and holdup is now higher (0.05-0.1) near the walls. The point of highest gas holdup shifts further below the impeller. Also, a greater number of gas bubbles enter the region below the sparger thereby increasing the holdup. At an even higher agitation speed of 6.67 rps (Figure 5D), more and more gas is transported toward the bottom of the vessel due to increased downward liquid pumping. The zone of holdup formed around the impeller is compressed. This results in higher gas holdups (0.05-0.1) in the wall regions and near the top liquid surface. Further G reaches a value as high as 0.2-0.3 in the impeller plane. Sparging the gas through a larger diameter (0.41 m) sparger into a vessel agitated by a 0.19-m-diameter pitched blade downflow turbine causes the gas to be pulled toward the impeller due to the low-pressure region generated around the impeller blades (Figure 6A). This zone, however, is restricted to a smaller region around the impeller as compared to Figure 5A. This is because the sparger is larger in diameter (two times the impeller diameter), so most of the sparged gas escapes the action of the impeller and reaches the top. Since the sparger holes are nearer to the wall, even a slight increase in speed starts the radial dispersion of the gas as seen in Figure 6B. This is, however, not seen in the case of a smaller sparger (Figure 5B). With an increase in speed (Figure 6C), the central zone of high holdups begins to enlarge or spread along the shaft toward the top surface. The gas reaching the top liquid surface gets pulled downward near the walls, and the gas immediately above the impeller gets pulled downward. This results in high gas holdup near and below the impeller, moderately low gas holdup above the impeller, and again higher gas holdup in the corner annulated region between the walls and the top liquid surface. An increase in the impeller speed to 6.67 rps expands the zone of holdups above the impeller radially and along the shaft. As can be seen from Figure 6D, the holdup along the shaft varies in the range of 0.15-0.25, while holdup along the wall is uniform (0.05-0.1). However, the region below the sparger remains devoid of the gas and very low holdups (0-0.05) are observed all along the bottom surface. For a disk turbine agitated vessel sparged by a 0.19m-diameter ring sparger, Figure 7 shows a completely different picture as compared to the axial impeller (Figures 5 and 6). Operation at low impeller speeds (Figure 7A) shows the formation of a central zone of higher holdups (0.25-0.4) around the impeller. The radial action generated by the impeller causes gas

Table 3. Comparison of Flooding-Loading Transition Speeds NFL (rps) experimental details PBTD45, VG ) 0.01 m/s, d ) 0.19 m, D ) 0.19 m, Z ) 0.095 m, T ) 0.57m PBTD45, VG ) 0.02 m/s, d ) 0.41 m, D ) 0.19 m, Z ) 0.095 m, T ) 0.57 m DT, VG ) 0.01 m/s, d ) 0.19 m, D ) 0.19 m, Z ) 0.095 m, T ) 0.57 m

power visual curve

contours

3.33

3

3.33-5

3

2.67

1.67-3.33

2.67

3.33

1.67-3.33

Table 4. Comparison of Complete Dispersion Transition Speeds NCD (rps) experimental details

visual

power curve

contours

PBTD45, VG ) 0.01 m/s, d ) 0.19 m, D ) 0.19 m, Z ) 0.095 m, T ) 0.57 m PBTD45, VG ) 0.02 m/s, d ) 0.41 m, D ) 0.19 m, Z ) 0.095 m, T ) 0.57 m DT, VG ) 0.01 m/s, d ) 0.19 m, D ) 0.19 m, Z ) 0.095 m, T ) 0.57 m

5.83

5.33

5-6.67

5

4.67

5-6.67

5.67

4.67

5-6.67

bubbles to travel slightly more toward the wall, but since the speed is low, these bubbles rise vertically upward. At an equal speed of 1.67 rps, a disk turbine counters the gas influx into the impeller zone more efficiently than a pitched blade downflow turbine by radially dispersing the gas thereby showing comparatively higher gas holdups near the wall region than seen in Figure 5A and B. With a further increase in speed, bubbles start spreading radially outward very quickly as compared to that seen in Figure 5A and B. As the impeller speed increases, the action of the impeller disperses the bubbles radially outward with the impeller discharge stream. In the impeller discharge stream, the holdup increases considerably away from the agitator. The central zone formed just around the impeller shrinks in size and elongates along the shaft with more and more gas reaching the top surface with holdups varying in the range of 0.15-0.25. At still higher speeds (3.33 rps, Figure 7B), the gas reaching the wall is dispersed both ways along the wall. Most of the bulk of the vessel is filled with gas and the central zone is spread. Hence, holdup is uniform (0.2-0.25) in the bulk of the vessel. The lower part of the vessel shows low holdups (0-0.05). All these trends observed for a stirred vessel agitated by a pitched blade downflow turbine (PBTD45°) and by a Rushton turbine are similar to those reported in the literature by Rewatkar et al.36 Regime Transition Identification. The gas holdup profiles obtained using the γ-ray attenuation technique were used to identify regimes of operation and hence the regime transition speeds. To validate the measurements, transition speeds were also determined visually and from power curve. Tables 3 and 4 compare the transition speeds obtained by visual observation, power curve analysis, and observation of gas holdup profiles for the experiments under consideration. For example, for operation with a pitched blade downflow turbine (PBTD45°) with gas sparging through a ring sparger of 0.19-m diameter, contours are as

5396 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

shown in Figure 5A and B. As seen from the figure, radial pumping action of the impeller starts between 3.33 and 5 rps. Therefore, it may be concluded that the flooding-loading transition occurs between 3.33 and 5 rps, as indicated by radial dispersion of the gas with progressively increasing holdup (0.05) near the wall. The flooding-loading transition speed from the power curve (Figure 2) comes out to be 3 rps (point B) whereas visually it is observed to be 3.33 rps. The critical impeller speed for complete dispersion lies somewhere between 5 and 6.67 rps. The substantial portion of the gas going below the impeller is seen in the contours as the holdup change in the region below the impeller. Point D (5.33 rps) in the power curve (Figure 2) indicates the critical impeller speed for complete dispersion, which was visually observed to be 5.84 rps. Beyond point E (5.84 rps) in the power curve, gas recirculation sets in. Gas is dispersed in the entire vessel and the power number decreases continuously. Similar observation of other contours yields the range of transition speeds for the other cases as well. The contours provide a fairly good picture of the different flow regimes, flooding (undesirable phenomenon), and complete dispersion (most important requirement) and a rough but fairly accurate estimate of the different regime transition speeds. It can thus be concluded that the γ-ray attenuation technique offers a way of measuring the hydrodynamic behavior of gas-liquid stirred tanks. This could especially be useful in industrial stirred reactors; for example, one could measure the gas holdup distribution for an industrial stirred reactor operating at a particular speed. If the gas holdup profiles show a pattern similar to that seen in Figure 5A, we would be sure that the impeller is flooded. However if the holdup profiles are similar to those seen in Figure 5D, we could confidently say that the impeller is able to disperse the gas properly and is doing the job it is supposed to do. Overall Gas Holdup. Chordal gas holdups at every radial location (10 in total) for each axial location (5 in total) and for every impeller speed were obtained by γ-ray attenuation measurements. The local gas holdup profiles show variation in gas holdup with respect to r as well as z. The overall gas holdup was calculated by taking a volume average of all the gas holdup values (50 points). The average gas holdup was estimated using the following equation

∫0H ∫0R 2πrG dr dz jG ) ∫0H ∫0R 2πr dr dz

(10)

Overall gas holdup was measured visually at different impeller speeds by noting the clear liquid height and the height of dispersion. The experimentally measured mean gas holdups (obtained using eq 10) were compared with those reported by Rewatkar et al.,36

(DT)

G ) 3.54

2.08

(Fr)0.51(Flg)0.43

(11)

and Smith et al.37

G ) 0.85(Re.Fr.Flg)0.35(D/T)1.25

(12)

The range of variables (PTD, H ) T, T ) 0.57, 1, and 1.5 m, D/T ) 0.3-0.5, C/T ) 1/3, N ) 0.4-10.5 rps, QG

Figure 8. Overall gas holdup comparison for vessel agitated by PBTD45STD. T ) 0.57 m, D ) 0.19 m, VG ) 0.01 m/s. Key: 2, visual; 4, γ-ray measurements; ], ref 36.

Figure 9. Overall gas holdup comparison for vessel agitated by PBTD45. T ) 0.57 m, D ) 0.19 m, VG ) 0.02 m/s. Key: 2, visual; 4, γ-ray measurements; ], ref 36.

) 8.93 × 10-4-5.3 × 10-4 m3/s) over which the correlation of Rewatkar et al.36 has been developed compares well with our experimental conditions and hence this correlation has been selected. For DT, the correlation of Smith et al.37 has been chosen for comparison since it has been shown to be valid over a wide range of scales of operation and operating conditions for disk turbine impellers. These comparisons have been shown in Figures 8-10. The visual observation method of gas holdup measurement has been used in the development of these correlations; therefore, they would have an inherent error of ∼10%. Although the visual method of gas holdup measurement is low cost and safe, it does not provide the value of local gas holdup, which is possible by γ-ray attenuation technique in a noninvasive way making it applicable to industrial stirred tanks. It can be seen from the figures that the gas holdup values obtained by γ-ray attenuation technique are found to be in good agreement with those obtained from previous literature. Surface Aeration. Figures 11 and 12 show gas holdup profiles for vessels agitated by pitched blade downflow turbine (PBTD45°) and a disk turbine, respectively. For a vessel agitated by a downflow turbine (located at a distance of 2D from the top liquid surface) at low impeller speeds, the liquid surface was totally free of ripples and there were no bubbles. Even at a speed of 6.67 rps there was no entrainment at the

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5397

Figure 10. Overall gas holdup comparison for vessel agitated by DT T ) 0.57 m, D ) 0.19 m, VG ) 0.01 m/s. Key: 2, visual; 4, γ-ray measurements; ], ref 37.

Figure 12. Contours/gas holdup profiles for vessel agitated by DT under surface aeration conditions. T ) 0.57 m. (A) N ) 5 rps; (B) N ) 6.67 rps; (C) N ) 8.33 rps. Key: dark blue, 0.00-0.03; medium blue, 0.03-0.06; light blue, 0.06-0.09; yellow, 0.09-0.12; light orange, 0.12-0.15; dark orange, 0.15-0.18; red, 0.18-0.21.

Figure 11. Contours/gas holdup profiles for vessel agitated by PBTD45STD under surface aeration conditions. T ) 0.57 m. (A) N ) 8.33 rps; (B) N ) 10 rps; (C) N ) 11.67 rps. Key: dark blue, 0.00-0.03; medium blue, 0.03-0.06; light blue, 0.06-0.09; yellow, 0.09-0.12; light orange, 0.12-0.15; dark orange, 0.15-0.18; red, 0.18-0.21.

surface. This was due to the high submergence of the impeller. Visual observation of the flow patterns with gradual increase in impeller speed from 6.67 to 8.33 rps allowed determination of NCSA, the critical impeller speed for complete surface aeration at which the reactor was entirely filled with gas bubbles. NCSA was found to be 7.5 rps. Hence, measurements were carried out at impeller speeds higher than 7.5 rps. Surface aeration occurs from the top liquid surface showing high gas holdup near the surface. The impeller employed being a downflow impeller, the gas bubbles are dragged down into the central region and further because the impeller pulls down the bubbles. Due to the low-pressure region behind the impeller blades, high gas holdup is seen near the impeller (Figure 11A), as the

impeller is able to distribute the gas bubbles even below the blades. These bubbles rise along the walls, thus showing high holdup near the walls. Two circulation loops with very low holdups are formed in the region between the impeller and the top surface. As the impeller speed increases further, more gas is drawn along the impeller shaft into the impeller zone. Hence, the holdup region near the impeller enlarges. Holdup near the impeller blades and the walls also increases. The extent of surface aeration at the top surface increases, thereby increasing the holdup near the top surface. The low holdup regions between the impeller and the top surface diminish in size as seen in Figure 11B. With further increase in impeller speed, the high holdup region at the top surface increases in size (Figure 11C). Also, most of the region between the impeller and the top surface shows increased holdup and the low holdup region further diminishes in size. However, low holdups are observed in the region below the impeller. In the case of a vessel agitated by a disk turbine, at an impeller speed of 5 rps, the gas is sucked into the liquid at approximately midway between the shaft and the wall just below the liquid surface as seen in Figure 12A. Two characteristic loops due to radial pumping action of the impeller are formed around the impeller blades and in the region between the impeller and the top surface. These regions show high gas holdups. Gas holdup is very low near the vessel bottom and at the walls. At a higher speed (6.67 rps, Figure 12B), the circulation loops formed around the impeller blades and in the upper region increase in size with high holdup near the top surface. Gas reaches the walls, and the low holdup regions near the wall diminish in size. At an impeller speed of 8.33 rps as seen in Figure 12C, the loop around the impeller increases in size in both the

5398 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

valuable for understanding the hydrodynamics of industrial-scale stirred reactors. Acknowledgment The authors acknowledge financial support in the form of a research grant and fellowship from the Department of Atomic Energy (DAE), India (Project 47.01). Nomenclature

Figure 13. Overall gas holdup comparison for aerated vessel agitated by PBTD45STD. T ) 0.57 m. Key: 2, visual; 4, γ-ray measurements.

Figure 14. Overall gas holdup comparison for aerated vessel agitated by DTSTD. T ) 0.57 m. Key: 2, visual; 4, γ-ray measurements.

directions (axial and radial). Due to internal circulation within the loop, holdup in the loops around the impeller increases and the two loops merge. The low holdup regions also diminish in size. However, the region below the impeller still shows low values of holdups. The overall gas holdup values obtained by visual observation and by γ-ray attenuation technique for surface aerated reactors have been compared in Figures 13 and 14 for vessels agitated by pitched blade downflow turbine (PBTD45°) and a disk turbine, respectively, and found to be in good agreement with each other.

am ) constant in eq 6 bn ) constant in eq 7 cmn ) Abel inversion transform coefficient C ) clearance of the impeller from the tank bottom, m d ) sparger diameter, m dnm ) forward Abel transform coefficient D ) impeller diameter, m f (r,R) ) gas holdup radial variation, dimensionless Flg ) gassed flow number, (QG/ND3) Fr ) Froude number, (N2D/g) H ) liquid height, m m ) row number n ) column number N ) impeller speed, rps NCD ) complete dispersion transition speed, rps NCSA ) critical impeller speed for complete surface aeration, rps NFL ) flooding-loading transition speed, rps PG ) impeller gassed power, W Po ) impeller ungassed power, W QG ) volumetric gas flow rate, m3/s r ) radial position in the column, m R ) radius of the column, m Re ) Reynolds number based on impeller speed, (ND2F/µ) T ) tank diameter, m VG ) superficial gas velocity, m/s W ) impeller blade width, m X ) horizontal position, m z ) axial position, m Z ) sparger clearance from bottom of the tank, m Greek Letters G ) local gas holdup, dimensionless jG ) average gas holdup, dimensionless φ(x,R) ) Abel transform function Ψ ) ray averaged gas holdup, dimensionless

Literature Cited Conclusion γ-Ray attenuation technique has been applied to stirred tanks, and gas holdup profiles have been measured for a wide variety of situations; different speeds, different spargers, impellers, etc. Validation of the technique has been confirmed by comparing the regime transition speeds obtained from power curves and visual observations. The average gas holdup values calculated by integration of the local holdups were found to match very well with those obtained by visual observations. The γ-ray attenuation technique was developed as an effective and reliable tool for local gas holdup measurements in sparged vessels that can be effectively applied for the characterization of prevailing dispersion regime. The knowledge of holdup profiles is expected to be very

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Received for review March 6, 2004 Revised manuscript received May 26, 2004 Accepted June 8, 2004 IE049816P