Residence time distribution studies of high pressure fluidized bed of microparticles

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J. of Supercritical Fluids 44 (2008) 433–440

Residence time distribution studies of high pressure fluidized bed of microparticles S. Rodr´ıguez-Rojo, N. L´opez-Valdezate, M.J. Cocero ∗ High Pressure Processes Group, Department of Chemical Engineering and Environmental Technology, University of Valladolid, Prado de la Magdalena s/n, 47011 Valladolid, Spain Received 2 March 2007; received in revised form 3 September 2007; accepted 11 September 2007

Abstract Fluidized bed coating with supercritical carbon dioxide (SC-CO2 ) is a promising technology for processing microparticles of high added value. Up to now, mainly particles with sizes higher than 100 ␮m have been used. The main challenge is to be able to uniformly coat particles with smaller sizes. The key point is to get a good mixing of both, solids and supercritical fluid. The quality of the liquid mixing has been analyzed by means of residence time distribution studies of fluidized Geldart type A glass beads (dp,s = 65 ␮m; dp,s = 176 ␮m) at pressures from 8 to 14 MPa and temperatures from 35 up to 50 ◦ C. Experimental results have been correlated satisfactorily with a one-parameter model (N tanks in series) and show that the mixing is acceptable with two or three tanks in series, with the exception of experiments at fluid velocities below twice the minimum fluidization velocity and small initial volume of solids where the mixing is worse. © 2007 Elsevier B.V. All rights reserved. Keywords: High pressure fluidized bed; Flow pattern; Mixing; RTD studies

1. Introduction Fluidized bed technology is widely used in different industrial processes for reactions, drying, coating and combustion. This technology was developed in the 1920s for combustion applications; hence, it is a broadly studied process also because of its good mixing properties, low thermal gradients and low agglomeration tendency. However, there are some limitations concerning nanoparticles and microparticles with sizes smaller than 100 ␮m due to cohesive forces [1]. There are two main fluidization patterns: homogeneous or particulate and heterogeneous or aggregative. The particulate regime has been typically associated with liquid fluidization and the aggregative one to gas fluidization. However, several authors have shown that the fluidized state change progressively from one to the other by changes in fluid density or operating velocity. This means that an infinite number of intermediate states exist in between [2]. There are different criteria to predict whether the fluidization is homogeneous [2–4]. Some of them are summarized in Table 1. A drawback

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of most of these criteria is that they are only applicable to the onset of fluidization, so it is not possible to predict when the minimum bubbling fluidization velocity is achieved, which denotes the change from particulate to aggregative fluidization pattern. This is the normal behavior of Geldart B and A particles in SC-CO2 bed contactors found by different authors for particles ranging from 7 to 250 ␮m and operating pressures from 2 to 28 MPa at temperatures between 35 and 55 ◦ C [11,12]. However, Tanneur et al. [13], found that particles of 71 ␮m were not fluidized in a pressure range from 7.5 to 12 MPa and temperatures of 40 and 50 ◦ C, at gas velocities higher than the minimum fluidization velocity. To test this hypothesis, this work proposes a method to study the global fluid mixing quality, which is one of the main advantages offered by fluidized bed contactors, through residence time distribution curves (RTD). This is a simple and non intrusive method, compared with other methods employed to measured the radial distribution of voidage at a certain level of the bed, such us electrical capacitance tomography [12,14], or the heat transfer coefficient between the bed and an immersed surface [15] or to follow the path of the particles by means of radioactive tracer particles [16]. These techniques give information about the transition from homogenous to bubbling fluidization regimes, hence, about mixing.

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2. Experimental Nomenclature Ar

Archimedes number; Ar =

d(3,2)3 ρCO2 (ρp −ρCO2 )g μ2CO 2

C(t)

concentration of tracer at outlet expressed in absorbance units E(t) external residence time distribution curve, according to Eq. (2) (min−1 ) d(1,0) mean diameter (␮m) d(3,0) volume mean diameter (␮m) d(3,2) = dp,s surface/volume mean diameter. Sauter mean diameter (␮m) dv,10 fractional volume diameter: 10% of particles have a bigger diameter (␮m) g gravitational acceleration (m/s2 ) H0 total height of the fluidization bed vessel (mm) %M.A.D.mean absolute deviation; M.A.D. (%) =   E(t)experimental −E(t)model  × 100 n n number of experimental data N number of tanks in the residence distribution time curve model Remf Reynolds number for minimum fluidization conu d(3,2)ρ ditions; Remf = mf μCO CO2 2

S tm,exp tn tp,mod tp,theo Tr u V VF wtbed

cross sectional area of the bed (m2 ) mean residence time of each fluid element calculated according to Eq. (6), Appendix A (min) mixing time in each one of the tanks in the residence distribution time model (min) piston time in the residence distribution time model (min) piston time calculated theoretically from the volume of pipes (min) g1/2 d

3/2

(ρ −ρ)

p p transition number; Tr = μ fluid velocity (m/s) volume of the analyzed system (m3 ) volumetric gas flow rate (m3 /min) bed weight. Apparent weight of the particles compensated by buoyancy, expressed in pressure units m g(ρ −ρ) (Pa); wtbed = p ρSp

Greek symbols −P measured pressure drop along the fluidized bed (Pa) Φ sphericity of solid particles μ viscosity (Pa s) ρ density (kg/m3 ) τ exp space–time variable calculated, Eq. (7), Appendix A (min) τ theo space–time variable, τ = V(m3 )/VF (m3 /s) (min) Subscripts mb minimum bubbling mf minimum fluidization t terminal or free-falling

The experimental setup is shown in Fig. 1. It consists on (a) CO2 cylinder, (b) cryostat, (c) high pressure membrane pump (LEWA GmbH; 30 MPa; 2–40 L/h), (d) thermostatic bath, (e) 1/16 in. two-position, six-port switching valve (Rheodyne 7010, 30 MPa) for introducing the tracer, (f) pressure jacket vessel, (g) filter, (h) U.V. online analyzer (HP 1100) and (i) backpressure valve (GO regulator) to control the pressure in the fluidized bed. The flow through the U.V analyzer was 1 mL/min and it was controlled by a gas rotameter at the outlet of the flow line. The maximum absolute uncertainties in the measured values of pressure, temperature and flow are, respectively, 0.10 MPa, 0.8 ◦ C and 0.8 kg/h for high CO2 flows (around 33 kg/h) and 0.18 kg/h for low flows (7 kg/h). A stainless steel basket (V = 0.582 L; D = 40.9 mm), with porous plates at bottom and top, is used to introduce the particles inside the vessel and to make their handling easier. The fluidized state was assured by means of pressure drop across the bed measurements that were carried out with a (j) differential pressure meter (Fisher-Rosemunt 1151HP) by means of two concentrical tubes of 1/8 and 1/4 in. inside the bed. Experiments were repeated with and without this device to test reproducibility of results and to guarantee that it had no influence on the mixing performance of the fluid. 2.1. Materials The carbon dioxide was of 99.5% purity and was provided by S.E. Carburos Met´alicos S.A. (Spain). The particles used to analyze the flow pattern were glass beads of two different sizes so that results could be compared. Their physical and morphological characteristics are given in Table 2. Glass beads (GB) were chosen because they are commonly used as model particles in many works due to their sphericity (φ ≈ 1) and smooth surface [11,17,18]. As tracer, acetone was selected because of its high absorptivity (εmax = 15848 L/mol/cm) and because it is totally soluble in SC-CO2 in the whole range of operation conditions (P = 8–14 MPa; T = 35–50 ◦ C) [19]. Acetone of technical grade (99%) supplied by Cofarcas S.A. (Spain) was employed. The U.V. spectra was taken from NIST data base [20] and also confirmed (HITACHI U-2000 Spectrophotometer) to assure that λmax (265 nm) was not influenced by possible impurities in the solvent. 2.2. Methods The stimulus–response method was used to determine the residence time distribution curves. This method uses the introduction of a tracer in the flow stream before it enters into the system and the analysis of its concentration profile at the outlet. There are two main ways to introduce the tracer: step mode and pulse mode. One of the main requirements of a tracer is that it should introduce as small a disturbance as possible and its physical properties (ρ, μ) should be similar to those of the bulk fluid. However, the density of CO2 in the range of the experimental conditions varies in a drastic way, from 275 to 720 kg/m3 , so it

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Table 1 Criteria for particulate–aggregative fluidization transition (adapted from ref. [2]) Criterion

Formula Ar ρp −ρf Remf ρf

Discrimination number

Dn =

ue ; uz

uz = 0.56n(1 − εb )0.5 εn−1 b , 



Nf ; (Nf ) cr ; (Nf ) Ntr R De dp

Froude number



cr



Nf = Ar ρρa , (Nf ) cr f 0.5 ρ −ρ p f Ntr = (gdp3 ) μ ρp −ρf Hmf R = Frmf Remf ρ DT f



De dp

= 71.3

Frmf =



μ2 gdp ρf2





ue = =

(gdp )0.5 Ut



1.5 mf ) 128 (1−ε , ε2mf (3−εmf )

(ρp /(ρp −ρf ))−εmf 1−εmf

  

ρp −ρf ρp

Aggregative

Reference

Dn < 104

Dn > 106

Lui et al. (1996) [2]

0.5 uz < ue 

(Nf )

1+

Particulate

cr

=

gdp3 ρf (ρp −ρf ) 54μ2

1.5 mf ) 640 (1−ε ε2mf (3−εmf )

0.5

2 −1

u2mf gdp

uz > ue 

Nf < (Nf ) cr

Nf > (Nf )

Ntr < 50

Ntr > 5000

Verloop and Heertjes (1970) [7]

R < 100

R > 100

Romero and Johanson (1962) [8]

De dp

De dp

Harrison et al. (1961) [9]

<1

Frmf < 0.13

is not possible to find a tracer with the same properties. Consequently, the tracer was introduced in the pulse mode. Moreover, the step mode was tested in previous experiments for 1 wt% of ethyl acetate showing that the experiments were not reproducible [21]. Introducing a perfect impulse input is difficult, even more so at high pressure conditions. The most adequate way is to use a 1/16 in. two-position, six-port switching valve (Rheodyne 7010, 30 MPa), typically employed in chromatographic analyses [22]. The loading of the loop with tracer was made at atmospheric conditions. The loop volume was set by trial and error, taking into account that the operational flow rates were in the range of preparative chromatography, where the loop size varies from 0.5 to 20 mL. The selected volume of the loop was 1 mL for glass beads type III (GB III). The loop was constructed with 1/8 in. tubing to avoid large pressure drops at the mass flow rates employed (6–9 kg/h). Another key aspect to get good analyses is that the system has to be closed, which means there should not be axial dispersion neither at the inlet nor the outlet of the tracer [23]. Otherwise, the mathematical analysis of the curves (Appendix A) would be not possible.

Foscolo and Gibilaro (1984) [5] 

> 10

Frmf > 1.3

cr

Doichev (1974) [6]

Wilhelm and Kwauk (1948) [10]

Nine experiments were programmed (Table 3) to be performed with GB III (d(3,2) = 65 ␮m) to analyze the variation of pressure (P), temperature (T), CO2 flow rate, the ratio of mass flow (G) to minimum fluidization mass flow (Gmf ) and the initial volume of particles in the bed. The minimum fluidization velocity (umf ) for GB I and GB III was measured in a previous work [24] and also by other authors [12] in this range of conditions. It was shown (Fig. 2) that umf , can be predicted by the Wen and Yu equation [25], although for the smallest particles (GB III) it is advisable to have an excess of CO2 of 14.5%: Remf = (33.72 + 0.0408Ar)

0.5

− 33.7

(1)

3. Results and discussion A typical output signal for a pulse input (C(t)) is depicted in Fig. 3. The model tested is plug flow (P.F.) followed by N tanks in series. The plug flow model represents the delay time from the inlet of the tracer to the fluidized bed and from the outlet to the U.V. analyzer (Fig. 1) and the number of tanks provides the

Fig. 1. Experimental setup.

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Table 2 Physical characteristic and size distribution parameters of the glass beads (GB) Material

Supplier

ρs (kg/m3 )

d(1,0) (␮m)

d(3,0) (␮m)

d(3,2) (␮m)

dv10 (␮m)

dv50 (␮m)

dv90 (␮m)

Φ

GB I GB III

Sigma–Aldrich Abrasivos y Maquinaria S.A. (Spain)

2500 2500

173 48

175 58

176 65

157 9

172 58

191 72

0.99 0.89

Fig. 2. Experimental data of minimum fluidization velocity for different size of glass beds (GB I: dps = 176 ␮m; GB II: dps = 103 ␮m; GB III: dps = 65 ␮m) correlated by Wen–Yu equation [25].

degree of mixing. A small number of tanks means good mixing. As shown in Fig. 4, the agreement between the model and the experimental data is excellent with a maximum percentage mean absolute deviation (%M.A.D.) of 2.5% (Table 4). Fig. 5 shows the variation of the number of tanks with pressure (Fig. 5a), temperature (Fig. 5b), flow rate (Fig. 5c) and solids initial volume (Fig. 5d). The initial volume of solids is represented as mass of particles, and it can be directly related to the height of the vessel (H0 = 445 mm) by a ratio of 1/5, 1/10 and 3/10, respectively. It can be noticed that, even if the ideal model of complete mixing (N = 1) has not been achieved, in general the mixing is good (2 and 3 tanks). Fig. 5a, c and d show consistent tendencies: the degree of mixing enhances increasing pressure [21], gas flow rate and initial volume of solids. How-

Fig. 4. External residence time distribution curve for glass beads type III: comparison of experimental and model results. Experiment 5: P = 10.0 MPa; T = 49 ◦ C and G/Gmf = 2.

ever, the degree of mixing becomes better when the temperature is increased, which was not expected due to its reducing effect on CO2 density, for this range of conditions. Nevertheless, increasing the flow rate above twice umf is not worthwhile because the degree of mixing does not increase (Fig. 5c). These results agree with the experimental conditions for microparticles (dp ≈ 180 ␮m) coating in SC-CO2 fluidized bed used by other authors [18]. Since pressure and temperature were found to enhance the fluidization quality, a new experiment at higher pressure, 14 MPa, was performed. However, the complete mixing of the fluid (N = 1) was not reached (Fig. 6). Regarding temperature, no experiments at higher temperatures were made because the final application of this fluidized bed process is the coating of thermolabile compounds, such as proteins and carbohydrates. To test if the fluidization for larger particles was better, some experiments were made with glass spheres of larger Table 3 Programmed experiments with glass beads type III

Fig. 3. Response curve for a pulse input (C(t)) for glass beads type III. Experiment 1: P = 8 MPa, T = 40 ◦ C and G/Gmf = 2.

Number of experiment

T (◦ C)

P (MPa)

G/Gmf

mp (g)

ρ (kg/m3 )

1 2 3 4 5 6 7 8 9

40 40 40 35 50 40 40 40 40

80 100 120 100 100 100 100 100 100

2 2 2 2 2 1.5 2.5 2 2

150 150 150 150 150 150 150 75 225

278 629 718 713 384 629 629 629 629

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Fig. 5. Number of tanks for different experimental conditions with glass beads type III. (a) Number of tanks at T = 40 ◦ C, u/umf = 2 and different pressures. (b) Number of tanks at P = 10 MPa, u/umf = 2 and different temperatures. (c) Number of tanks at T = 40 ◦ C, P = 10 MPa and different u/umf ratios. (d) Number of tanks at T = 40 ◦ C, P = 10 MPa, u/umf = 2 and different initial volumen of solids, expressed as mass of solids.

Fig. 6. Variation of experimental number of tanks for glass beads type III at different pressures at T = 40 ◦ C and u/umf = 2.

diameters (GB I) whose fluidization in supercritical CO2 has been assessed by several authors [12,26]. Fig. 7a and b shows similar mixing behavior for both kind of particles at the same operating conditions. Moreover, the increase in mixing quality when increasing temperature is demonstrated. The complete data for these experiments are summarized in Table 5. An attempt to relate the dynamic response observed in the RTD and the flow pattern of the fluidization was carried out. First of all, the minimum bubbling velocity (umb ) for both kind of particles was predicted following the method of Vogt et al. [12] for fluidization at supercritical conditions (Appendix B). The results of umb are shown in Tables 6 and 7 for GB III and GB I, respectively, as umb /umf ratios. In Table 6, experiments 8 and 9 have been excluded because they were used to investigate

Fig. 7. Comparison of mixing behaviour for glass beads type III (GB III) and glass beads type I (GB I). (a) Number of tanks at T = 40 ◦ C, u/umf = 2 and different pressures. (b) Number of tanks at P = 10 MPa, u/umf = 2 and different temperatures.

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Table 4 Experimental and model data for RTD experiments with glass beads type III Number of experiment

1

2

3

4

5

6

7

8

9

10

P (MPa) T (◦ C) G (kg/h) u/umf ρ (kg/m3 ) mp (g) −P/wtbed tm,exp (min) τ exp (min) τ theo (min) tp,theo (min)

8.1 39.3 7.2 1.93 302 150 1.00 3.21 3.12 2.38 0.92

10.1 38.9 6.8 2.13 658 150 0.95 6.03 5.85 5.07 1.67

12.1 40.5 6.0 2.02 715 150 0.89 9.54 9.41 6.08 1.88

10.0 35.8 6.0 1.99 703 150 0.85 7.42 7.26 5.96 1.86

10.0 49.4 7.6 2.00 405 150 0.87 3.29 3.20 2.84 0.93

10.1 40.0 5.0 1.52 632 150 0.65 7.53 7.38 6.22 1.79

10.0 41.5 8.1 2.38 600 150 1.05 4.71 4.63 4.02 1.44

10.1 40.7 7.0 2.12 622 75 0.93 4.81 4.73 4.64 1.56

10.1 40.6 6.5 1.95 620 225 0.85 4.26 4.18 4.40 1.59

14.0 41.0 5.3 1.93 759 150 1.05 7.26 6.58 7.06 2.09

3 1.75 1.30

3 2.00 1.17

2 1.65 0.82

5 2.9 0.42

2 1.83 1.23

7 2.00 1.24

3 1.95 1.17

12 0 2.46

2 1.3 1.94

2 2.00 1.75

N tanks tp,model %M.A.D.

Table 5 Experimental and model data for RTD experiments with glass beads type I Number of experiment

1

2

3

4

5

6

P (MPa) T (◦ C) G (kg/h) u/umf ρ (kg/m3 ) mp (g) −P/wtbed tm,exp (min) τ exp (min) τ theo (min) tp,theo (min)

8.3 31.8 32.9 1.98 683 150 0.85 2.26 2.12 2.01 1.29

10.0 42.6 36.2 2.03 567 150 0.91 2.03 1.92 1.60 1.06

12.0 42.0 33.0 2.02 696 150 0.87 2.68 2.59 2.04 1.31

10.1 33.2 33.8 2.16 738 150 0.99 2.39 2.31 2.26 1.50

10.2 39.3 35.4 2.09 655 150 0.92 2.56 2.36 2.47 1.70

10.1 43.9 36.2 2.00 537 150 1.03 1.83 1.75 1.52 1.00

3 0.5 2.00

2 0.99 3.47

2 1.50 1.50

7 0.77 1.56

5 0.90 2.00

3 0.83 1.51

N tanks tp,model %M.A.D.

Table 6 Data for fluidization regime investigation with glass beads type III Number of experiment

1

2

3

10

4

5

6

7

P (MPa) T (◦ C) ρ (kg/m3 ) u/umf umf /umb Fr(u) Dn(umf )

8.1 39.3 302 1.93 3.75 0.040 5605

10.1 38.9 658 2.13 7.53 0.007 1914

12.1 40.5 715 2.02 8.63 0.005 1798

10.0 41.0 759 1.93 9.71 0.004 1661

10.0 35.8 703 1.99 8.37 0.005 1876

10.0 49.4 405 2.00 4.53 0.025 3821

10.1 40.0 632 1.52 7.1 0.004 2847

10.0 41.5 600 2.38 6.62 0.013 1945

N tanks

3

3

2

2

5

2

7

3

Table 7 Data for fluidization regime investigation with glass beads type I Number of experiment

7

1

2

3

4

5

6

P (MPa) T (◦ C) ρ (kg/m3 ) u/umf umb /umf Fr(u) Dn(umf )

10.0 40.5 617 1.46 1.83 0.045 6064

8.3 31.8 683 1.98 2.00 0.061 5131

10.0 42.6 567 2.03 1.71 0.107 6929

12.0 42.0 696 2.032 2.05 0.059 4960

10.1 33.2 738 2.16 2.17 0.055 4497

10.2 39.3 655 2.09 1.93 0.077 5492

10.1 43.9 537 2.00 1.64 0.120 7553

N tanks

2

3

2

2

7

5

3

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the effect of the initial amount of solids, and this variable cannot be analyzed regarding flow patterns. Two criteria for particulate–aggregative fluidization transition from Table 1 were employed, the “discrimination number (Dn)” and the “Froude number (Fr)”. The main conclusions that can be extracted from Tables 6 and 7, is that while the flow regime for experiments with GB III particles is particulate, as expected, the flow regimen for GB I, is just in the transition from particle to aggregative regime. However, a clear relationship cannot be found between the values of the different flow criteria (Dn and Fr) and the quality of the mixing expressed as number of tanks. 4. Conclusions A non-intrusive stimulus–response method was used to determine the degree of fluid mixing in a high-pressure fluidized bed of Geldart type A (dp,s = 65 ␮m) and type B (dp,s = 176 ␮m) spherical glass particles. The tracer, acetone, was introduced in pulse mode and its concentration at the outlet of the fluidized bed was determined by an U.V. on-line detector. The experimental curves were successfully adjusted to a one-parameter model (N tanks in series) (%M.A.D. ≤ 2.5). The results show that the mixing is very good, but not complete. The influence of the operation conditions – pressure, temperature, initial volume of solids and flow rate – is clearly demonstrated in the selected operation range for each variable. It is noticeable that the behavior was independent on the particle size for the two tested types of particles. However, results do not show a correlation between the mixing quality, expressed as number of tanks, and the values of the flow pattern criteria. These experiments are useful to set the experimental conditions for coating experiments to obtain the best possible mixing (N = 2): P ≥ 10 MPa, T ≥ 40 ◦ C and u/umf = 2 for a fixed bed to total equipment height ratio of at least 1/5. The RTD analysis is useful to assess the mixing quality in reaction, extraction and coating processes, and is very simple to implement. Acknowledgements

439

External residence time distribution curve : C(t) C(t) E(t) = o = ∞ C tm 0 C(t) dt

(2)

The RTD curve according to plug flow followed by N tanks in series model is: E(t) = 0; E(t) =

(3)

t < tp

(t − tp )N−1 e(t−tp )/tn ; tnN (N − 1)!

t ≥ tp

(4)

The main condition for this analysis to be true is that the system (from the inlet of the tracer to the analysis equipment) has to be a closed system: there should not exit dispersion flow in these borders. The condition that characterizes closed systems is: tm = τ,

(5)

where tm is the mean residence time of each fluid element and τ is the space–time variable or hydraulic residence time. They are calculated as follows:  ∞ tE(t) dt (6) Mean residence time : tm = 0

Espace-time or hydraulic residence time :  ∞ τ= (1 − F (t)) dt

(7)

0

Accumulated residence time distribution curve :  F (t) = E(t) dt

(8)

Appendix B The steps followed to calculate the minimum fluidization velocity (umb ) according to ref. [12] are: - Estimation of εmb from Creasy’s [27] criterion: log(Tr) = 4.0 + 3.7εmb − 1.4εmf

(9)

where the transition number, expressed in C.G.S. units, is 3/2

The authors acknowledge the financial support of this research provided by the Spanish Ministry of Education and Science (MEC) project CTQ 2006-02099. Soraya Rodr´ıguezRojo thanks the MEC for her grant from the F.P.U. Program and Noem´ı L´opez-Valdezate is grateful to University of Valladolid for her collaboration grant. Appendix A The treatment of experimental data to get the curve represented in Fig. 2 and the parameters of Table 3 is as follows [20]:

Tr =

g1/2 dp (ρp − ρ) μ

(10)

- Calculation of umb from a modified Richardson–Zaki equation:

εmb n umb = umf (11) εmf where n = 11.8Re−0.23 t Ret =

ut dp ρ μ

(12) (13)

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The terminal free-fall velocity (ut ) was calculated using the approximation for direct evaluation suggested by Haider and Levenspiel [28]: −1  18 0.591 ∗ + , Φs ≈ 1 (14) ut = (dp∗ )2 (dp∗ )0.5 dp∗ = dp u∗t = ut





ρ(ρs − ρ)g μ2 ρ2 μ(ρs − ρ)g

1/3 = Ar 1/3

(15)

Ret Ar 1/3

(16)

1/3 =

Since the εmf was not experimentally determined and its value is barely affected by pressure, it was theoretically calculated from the following correlation [29], expressed in C.G.S. units: φ2

ε3mf 0.14 = 1 − εmf Re0.063 mf

(17)

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