Homogeneous Fluidization of Geldart D Particles in a Gas–Solid

Article pubs.acs.org/IECR

Homogeneous Fluidization of Geldart D Particles in a Gas−Solid Fluidized Bed with a Frame Impeller Ying Han,† Jia-Jun Wang,*,† Xue-Ping Gu,† Lian-Fang Feng,† and Guo-Hua Hu‡,§ †

State Key Laboratory of Chemical Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China ‡ Laboratory of Reactions and Process Engineering, CNRSUniversity of Lorraine, ENSIC, 1 rue Grandville, BP 20451, 54001 Nancy, France § Institut Universitaire de France, Maison des Universitiés, 103 Boulevard Saint-Michel, 75005 Paris, France S Supporting Information *

ABSTRACT: The influence of agitation of a frame impeller on the fluidization performance of Geldart D particles is experimentally and numerically studied in a gas−solid stirred fluidized bed, using a three-dimensional (3D) unsteady computational fluid dynamics (CFD) simulation. The bed pressure drops obtained from simulations are in reasonable agreement with those measured with pressure transducers, which validates the CFD models. The experimental results of the pressure fluctuation and the simulated ones of the solid volume fraction distribution show that Geldart D particles can perform homogeneous fluidization in the presence of the impeller. The homogeneous fluidization regime expands as the minimum bubbling velocity increases with the agitation speed while the minimum fluidizing velocity remains unaffected. In addition, the uniformity of particle velocities that are distributed in the entire fluidized bed is also improved by the agitation of the frame impeller. agitator.15,16 Although mechanical agitation can improve fluidization, it is uncertain how, and to what extent, it affects hydrodynamics and bubble behaviors. For the industrial Hypol process, agitators that are capable of covering the entire reactor volume, such as the frame impeller, are preferred in order to scrape the adhesive polymer particles from the reactor wall. We conducted experimental and numerical studies on the effect of agitation of a frame-type impeller on the fluidization quality in a stirred fluidized bed. A three-dimensional (3D) unsteady computational fluid dynamics (CFD) simulation is implemented based on the Eulerian− Eulerian frame coupled with the kinetic theory of granular flow (KTGF) for the solid phase. The multiple reference frame (MRF) approach is incorporated to address the rotation of the impeller. The numerical model is validated by the experimentally measured pressure drop. The fluidization performance at different agitation speeds of the frame impeller and superficial gas velocities is discussed.

1. INTRODUCTION In a gas−solid fluidized bed polymerization reactor,1,2 the monomer in the gas phase is polymerized with a co-monomer and hydrogen under a specific catalyst in the solid phase. The polymer accumulates in the reactor and is fluidized with the gas flow. However, adverse fluidization phenomena (e.g., particle agglomeration, bridging, and channeling) are also frequently encountered. The bypassing of fluidizing gas is detrimental to efficient gas−solid contacting. To improve fluidization in industrial processes, mechanical agitation has been applied,2 such as the frame impeller for the Himont process and Hypol process, and the ribbon agitator for the Innovene process. Work on the effect of agitation of fluidized beds started in the 1950s. Reed and Fenske3 used an oscillating stirrer to increase the heat transfer between air and the extended surface in contact with fluidized beds in a small rectangular vessel. Subsequently various types of blades were used in gas−solid fluidized beds to meet the needs of different experimental and industrial processes, such as control of granule diameter in granulation,4,5 increase in drying rate,6 acceleration of the crystallization rate,7 disruption of bakers’ yeast cells,8 and separation of flotsam and jetsam particles.9 The pressure drop, bed expansion, and power requirement were found to be closely related to the fixation and speed of blades in a laboratory-scale fluidized bed.10−12 Godard and Richardson13 found that their agitating stirrer was able to destroy channels and the minimum bubbling velocity for Geldart A particles was sensitive to the presence of the stirrer. The fluidization quality of waste-wood particles, which belonged to Geldart C particles and presented an unstable hydrodynamic behavior, was improved using a semi-inverted-anchor type of agitator.14 Fluidization of phosphor particles was smoothed using an © 2012 American Chemical Society

2. EXPERIMENTAL SECTION Experimental work was implemented in a plexiglas column with an inner diameter of 0.188 m. A frame-type impeller, 0.182 and 0.390 m in diameter and height, respectively, was located just above a perforated plate gas distributor. The impeller had four blades, of which the cross sections in the horizontal and vertical directions were right-angled trapezoid and rectangle, respecReceived: Revised: Accepted: Published: 16482

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The multiple reference frame (MRF) model was incorporated to address the rotating frame impeller in the gas−solid fluidized bed. The computational domain is divided into two cell zones, separated by interfacial boundaries. Zones containing the moving components were solved using the rotating reference frame equations, whereas others with the stationary ones. The local frame transformation was performed at the interfaces between the cell zones to enable flow variables in one zone to be used to calculate the flux at the boundary with the adjacent zone. The interface treatment applies to the velocity and its gradient, since the vector quantities change with a change in the reference frame.21 Considering a coordinate system which is rotating steadily with an angular velocity (ϖ⃗ ) relative to a stationary reference frame, an arbitrary point in the CFD domain is located by a position vector (r)⃗ from the origin of the rotating frame. The velocity and its gradient are converted by the following equations when it is transferred from the rotating reference to the stationary one:

tively. The pressure probes were mounted along the bed elevation (H), with a height of 0.035, 0.150, 0.265, and 0.380 m with respect to the gas distributor, respectively. The pressure signals were obtained by pressure transducers (KYBD14, Advantech) with a data sampling rate of 200 Hz. The detailed information is given in Figure 1.

υ ⃗ = υr⃗ + (ϖ⃗ × r ⃗) + υt⃗

(1)

∇υ ⃗ = ∇υr⃗ + ∇(ϖ⃗ × r ⃗)

(2)

where υ⃗r and υ⃗t are the relative velocity (the velocity viewed from the rotating frame) and the translational one, respectively. Although it is a steady-state approximation, an unsteady flow can also be solved with reasonable accuracy, requiring a small amount of computational effort. The operation conditions in the numerical work were consistent with those in the experiments, in addition to the particle size polydisperse of the system. The simulated particle diameter is considered as the average diameter used in the experiments (i.e., 1.130 mm). The fluidizing gas was treated as an ideal gas. The computational domain contained 145 000 tetrahedral meshes generated with the Gambit 2.2.30 software, which were refined in the impeller blades and the gap between blades and bed wall. The sensitivity of the grid size was tested to reach independence. The three-dimensional (3D) unsteady numerical models were solved by a commercial CFD code, Fluent 6.3.26 (Ansys, Inc.). The turbulence in the fluidized bed was described by the dispersed k−ε model. An implicit integration method was employed because it has the advantage of being more stable for solving a stiff equation. No-slip boundary condition for both phases was employed. Phase-coupled SIMPLE algorithm was adopted for the pressure and velocity coupling, and the firstorder upwind discretization was applied to discretize the computational domain for its stability.31 The numerical model has been tested by comparing the pressure drop with the experimental data. The pressure drop was slightly underestimated with an average relative error of 5%. Further model validation could refer to our previous work.22

Figure 1. Schematic representation of the experimental setup of a fluidized bed with a frame impeller.

Polypropylene particles (Sinopec, China), which belonged to the Geldart D group, were employed in this work. They had an average diameter of 1.130 mm and a density of 997.9 kg/m3. The fluidized bed was operated with a static bed height of 0.4 m. Compressed air was used as the fluidizing gas. The superficial gas velocity was in the range of 0−0.9 m/s and was measured by a standard orifice flow meter. The minimum fluidizing velocity (Umf) was determined experimentally by the classical method (pressure drop across the bed versus superficial gas velocity). The value of Umf was found to be 0.428, 0.424, 0.431, 0.423, and 0.431 m/s, corresponding to 0, 10, 20, 30, and 45 rpm (revolutions per minute), respectively. Those values were very close to each other, indicating that the agitation speed had little effect on Umf.

3. NUMERICAL MODELS The simulations were carried out in the Eulerian−Eulerian frame, using the two-fluid model. The gas and solid phases were assumed to be two interpenetrating continua with their own volumes, velocities, and pressures. Their lift and virtual mass forces as well as the mass transfer between them were neglected in the momentum equations. To close the momentum equations, constitutive equations derived from the kinetic theory of granular flow (KTGF) were used. The transport equation of the granular temperature, which describes the kinetic energy of moving particles, is given by Ding and Gidaspow.17 The coefficients of restitution (0.8−0.95), ess, was set to 0.95. The interphase drag force model employed in this work is derived from Gidaspow,18 which combines the Wen− Yu model19 and Ergun equation.20 The governing and constitutive equations are summarized in Table S1 in the Supporting Information.

4. RESULTS AND DISCUSSION 4.1. Pressure Fluctuation. Pressure fluctuation is closely associated with the bubble behavior in gas−solid fluidized beds.23 The standard deviation of pressure fluctuation (σP) during steady fluidization is always employed to qualitatively estimate the bubble size. The fluidization is more homogeneous with smaller bubbles. Accordingly, σP is lower. Figure 2 illustrates the experimental results for the standard deviation of pressure fluctuation at the bed elevation of 0.035 m for various operating conditions. For a given agitation speed, 16483

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Umb and Umf, three fluidization regimes can be identified: fixed bed, homogeneous fluidization, and bubbling fluidization. An increase in the agitation speed enlarges the homogeneous fluidization regime to an extent that is common to, which usually happens in liquid−solid fluidized beds, gas−solid fluidized beds with Geldart A particles or high operating pressure.27−29 4.2. Solid Volume Fraction Distribution. It is difficult to obtain information in the impeller region by experiments because probes cannot be inserted inside it. Instead, computational fluid dynamics (CFD) simulation is a useful tool to provide flow field, solid volume fraction and other detailed information. Typical features of homogeneous fluidization for Geldart A particles such as homogeneous expansion and gross particle circulation in the absence of bubbles can be described by CFD using the discrete particle model (DPM)30−32 and the Eulerian−Eulerian method.33,34 In this section, the two-fluid model is used to investigate the fluidization performance for Geldart D particles at different agitation speeds. As the minimum fluidizing velocity is measured to be ∼0.43 m/s, all numerical simulations are carried out with superficial gas velocities of at least 0.5 m/s, to ensure complete fluidization. In a gas−solid fluidized bed, it is difficult to define what a bubble really means for such a system, because there is no sharp boundary between a bubble and solid particles. Wang et al.34 defined that there is no bubble when the solid volume fraction is larger than 0.2 and bubbles exist when it is smaller than 0.15. The minimum bubbling velocity is defined as the superficial gas velocity when the first bubble appears. Figure 4 shows the solid volume fraction distributions at a physical fluidization time of 10 s for different agitation speeds and superficial gas velocities. The holes denote regions where bubbles exist with a solid volume fraction smaller than 0.15. When the agitation speed of the frame impeller is 10 rpm, the fluidization performance in the stirred fluidized bed is very close to that in a classical one (0 rpm). Bubbles split and coalesce continuously as the fluidization proceeds.35 The particles exhibit aggregative fluidization for the entire range of the superficial gas velocity, and the bubble size increases with increasing superficial gas velocity. However, the agitation of the frame impeller seems to have little effect on the fluidization quality and its inefficiency may be attributed to the fact that its speed is low. By CFD, Shi et al.36 also found that the fluidization quality in a stirred fluidized bed for olefin polymerization was somewhat worsened, with an agitation speed of 10 rpm. When the agitation speed exceeds 20 rpm, the fluidization performance is much improved. At low superficial gas velocity, bubbles do not exist in the bed and the Geldart D particles exhibit homogeneous fluidization. As the superficial gas velocity increases, the fluidized bed goes from bubbleless fluidization to bubbling fluidization. At high superficial gas velocity, an increase in the agitation speed brings about a decrease in the bubble size, because the agitation of the frame impeller forces particles to enter the bubbles. When bubbles shrink or vanish completely, the fluidization undergoes a transition from aggregative fluidization to homogeneous fluidization. In addition, an increase in the agitation speed increases the upper limit of the gas velocity for homogeneous fluidization, which is in agreement with the result from the fluidization regime diagram (see Figure 3).

Figure 2. Experimentally obtained standard deviation of pressure fluctuation as a function of the superficial gas velocity at the bed elevation of 0.035 m for various agitation speeds. (Symbols represent experiments; line represents linear fitting.)

the standard deviation increases linearly with the superficial gas velocity, indicating a more heterogeneous fluidization because of an increase in the bubble size. The corresponding regression lines for different agitation speeds are more or less parallel to each other. For a given gas velocity, although the pressure drop is independent of the rotation of the frame impeller,22 an increase in the agitation speed improves the fluidization performance with a lower σP. The agitation of the frame impeller reduces the bubble size by breaking up big bubbles or preventing bubbles from coalescing. Since σP is closely associated with the bubble behavior, the intersection of the regression line with the gas-velocity axis corresponds to the case in which no bubbles are generated. Accordingly, it would be considered as the minimum bubbling velocity (Umb). Davies et al.24,25 also believed that the Umb could be measured with application of the bed pressure drop fluctuation. Therefore, the method proposed by Puncochar et al.,26 which is based on the relationship between the gas velocity and standard deviation of pressure fluctuation, is used to estimate Umb in our work. Figure 3 shows the regime diagram of fluidization performance, according to the relationship of Umb obtained by the

Figure 3. Fluidization regime diagram. (Symbols represent experiments; curves represent fitting.)

Puncochar method and Umf measured by the pressure drop plot versus the agitation speed. The Umf and Umb at the agitation speed of 0 rpm are 0.428 and 0.426 m/s, respectively. The fact that the discrepancy between them is very small validates the Puncochar method. The Umb is greater than Umf when the frame impeller is rotating. While Umf remains almost unchanged, Umb clearly increases with the agitation speed. It is important to point out that the transition from aggregative fluidization to homogeneous fluidization for Geldart D particles is achieved by the agitation of the frame impeller. According to the fitted lines for 16484

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Figure 4. Solid volume fraction distribution of steady fluidization at the physical fluidization time of 10 s for different superficial gas velocities and agitation speeds. (The holes denote the regions where bubbles exist with a solid volume fraction smaller than 0.15.)

The fluidization performance is quantified by the timeaveraged standard deviation of voidage (σεg) in Figure 5. An

gas velocity weakens the positive effect of the agitation of the frame impeller on the fluidization performance. CFD can reveal phenomena like the onset of homogeneous fluidization and the expansion of the homogeneous regime with increasing agitation speed of the impeller. However, it should be mentioned that there is a discrepancy in the minimum bubbling velocity between the predictions and those determined by experiments. 4.3. Particle Velocity Distribution. The time-averaged distributions of particle velocity (24−25 s) in the entire fluidized bed reactor at a gas velocity of 0.85 m/s are illustrated in Figure 6. A higher agitation speed decreases the proportion of small particle velocity and yields a shift of the peak to higher particle velocity. It may be attributed to the fact that the agitation appends a component of tangential velocity to the particles. The proportion of particle velocity larger than 0.3 m/s is also reduced with the increasing agitation speed of frame impeller. It seems that the particle velocity shows a normal distribution, and it tends to be more uniform due to more homogeneous fluidization with smaller bubble.

Figure 5. Simulation results for the time-averaged standard deviation of voidage under different operating conditions.

increase in the superficial gas velocity brings about an increase in σεg, indicating that the fluidization performance is worsened. At 10 rpm, agitation does not have a positive effect on the fluidization performance, which is in agreement with the above discussion. When its speed exceeds 20 rpm and the superficial gas velocity is smaller than 0.65 m/s, the value of σεg is very low and remains unchanged with the superficial gas velocity, corresponding to the homogeneous fluidization regime. The aggregative fluidization appears as the superficial gas velocity is higher and the corresponding σεg becomes larger. However, the latter is still much smaller than those at 0 and 10 rpm. A high

5. CONCLUSIONS We performed experimental work and numerical simulations in order to investigate the fluidization performance in a stirred gas−solid fluidized bed filled with Geldart D particles. The three-dimensional (3D) unsteady computational fluid dynamics (CFD) model, which incorporates the two-fluid model kinetic 16485

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ACKNOWLEDGMENTS

This work was supported financially by the National Natural Science Foundation of China (No. 21276222), the National High Technology Research and Development Program of China (No. 2012AA040305), and the Fundamental Research Funds for the Central Universities (No. 2012FZA4024).

■ Figure 6. Time-averaged distributions of particle velocity (24 to 25 s) in the entire fluidized bed reactor at a gas velocity of 0.85 m/s.

NOMENCLATURE ess = particle−particle restitution coefficient, dimensionless H = bed elevation, m N = agitation speed, revolutions/min (rpm) P = pressure, Pa t = physical fluidization time, s Ug = superficial gas velocity, m/s

Greek Letters

ε = volume fraction, dimensionless σP = standard deviation of pressure fluctuation, Pa σεg = standard deviation of voidage, dimensionless

theory of granular flow and multiple reference frame model, is validated with experimental data, with respect to the bed pressure drop. As expected, the agitation of frame impeller improves the fluidization performance and solids mixing in the gas−solid fluidized bed. Furthermore, the transition from aggregative fluidization to homogeneous fluidization for Geldart D particles is observed. As is well-known, a regime of homogeneous fluidization commonly exists in the liquid−solid fluidized bed, the gas−solid fluidized bed with Geldart A particles or with high operating pressure. In addition, the homogeneous fluidization regime can also be predicted and illustrated by the simulated solid volume fraction distribution for the cases of agitation speed exceeding 20 rpm. The particles are forced to break into bubbles by the agitation of impeller, while the bubbles shrink and finally vanish, and homogeneous fluidization presents. Three fluidization regimes are formed according to different operating conditions: fixed bed, homogeneous fluidization, bubbling fluidization. The minimum bubbling velocity increases with the agitation speed of frame impeller, while the minimum fluidizing velocity is independent of agitation. Therefore, the homogeneous fluidization regime is extended with the increase of agitation speed, while CFD simulation also illustrates that the bubbleless fluidization can be formed at higher superficial gas velocity. The particle velocity tends to resemble a normal distribution when the agitation speed increases. Both the proportions of small particle velocity and large particle velocity decrease. The uniformity of particle velocities that are distributed in the entire fluidized bed can be attributed to homogeneous fluidization.

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Subscripts

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The governing and constitutive equations are summarized in Table S1. This information is available free of charge via the Internet at http://pubs.acs.org/.

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g = gas phase mb = minimum bubbling mf = minimum fluidization s = solid (granular) phase

AUTHOR INFORMATION

Corresponding Author

*Tel.: +8657187951307. Fax: +8657187951612. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 16486

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