Prediction of critical fluidization velocity and maximum bed pressure drop for binary mixture of regular particles in gas–solid tapered fluidized beds

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Chemical Engineering and Processing 47 (2008) 2114–2120

Prediction of critical fluidization velocity and maximum bed pressure drop for binary mixture of regular particles in gas–solid tapered fluidized beds D.C. Sau a , S. Mohanty b,∗ , K.C. Biswal c a

Department of Chemical Engineering, Indira Gandhi Institute of Technology, Sarang 759146, India b Institute of Minerals & Materials Technology, Bhubaneswar 751013, India c Department of Chemical Engineering, National Institute of Technology, Rourkela 769008, India Received 2 April 2007; received in revised form 22 October 2007; accepted 28 October 2007 Available online 4 November 2007

Abstract The problems associated with conventional (cylindrical) fluidized beds, viz., fluidization of wider size range of particles, entrainment of particles and limitation of fluidization velocity could be overcome by using tapered fluidized beds. Limited work has been carried out to study the hydrodynamics of single materials with uniform size particles in tapered beds. In the present work, an attempt has been made to study the hydrodynamic characteristics of binary mixtures of homogeneous and heterogeneous regular particles (glass bead and sago) in tapered fluidized beds having different tapered angles. Correlations have been developed for critical fluidization velocity and maximum bed pressure drop for gas–solid tapered fluidized beds for binary mixtures of regular particles. Model predictions were compared with experimental data, which were in good agreement. © 2007 Elsevier B.V. All rights reserved. Keywords: Gas–solid fluidization; Critical fluidization velocity; Maximum bed pressure drop; Tapered fluidized beds; Binary mixture

1. Introduction Fluidization in cylindrical columns is an important operation in process industries. Generally, the particles are of non-uniform size due to size reduction during chemical reactions (combustion or gasification) and attrition. Reduction in particle size results in entrainment, slugging and non-uniform fluidization in cylindrical fluidized beds. These disadvantages can be overcome by the use of tapered fluidized beds, where there is a gradual decrease in the superficial gas velocity with increasing cross sectional area and height. Tapered fluidized beds have therefore found wide applications in many industrial processes such as biological treatment of waste water, immobilized biofilm reaction, incineration of waste materials, coating of nuclear fuel particles, crystallization, coal gasification, roasting of sulfide ores [1] and food processing [2]. They are also useful for fluidization of materials with wide particle size distribution and for exothermic reactions [3]. Tapered beds can also reduce back mixing of particles [4].

∗

Corresponding author. E-mail address: [email protected] (S. Mohanty).

0255-2701/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2007.10.022

Some of the previous investigations include development of a model for maximum pressure drop at incipient fluidization condition of a tapered fluidized bed [5], development of an analytical expression for critical fluidization velocity as well as pressure drop in a packed bed of spherical particles for gas–solid system in conical vessels by Biswal et al. [6,7] and correlation for calculation of maximum pressure drop in conical spouted bed by Olazer et al. [8]. Later, Peng and Fan [1] made an in-depth study of the hydrodynamic characteristics of solid–liquid fluidization in tapered beds and derived a theoretical model based on dynamic balance of forces exerted on the particle for the prediction of critical fluidization velocity and maximum bed pressure drop. Jing et al. [9] and Shan et al. [10] developed a model for gas–solid conical fluidized bed for spherical coarse and fine particles, respectively, based on Peng and Fan model [1], but neglected the pressure drop due to kinetic change in the bed. Recently, Sau et al. [11] have developed empirical correlations for minimum fluidization velocities and maximum bed pressure drops for gas–solid tapered fluidized beds. All these studies were carried out for a single material of uniform particle size. A number of studies have been carried out on the hydrodynamic characteristics of binary mixtures of particles in

D.C. Sau et al. / Chemical Engineering and Processing 47 (2008) 2114–2120

conventional (cylindrical) fluidized bed [12–15]. Studies have also been carried out for multi-component systems in cylindrical bed [16]. However, in general, the particles are of non-uniform size in the feed itself and there may be particle size reduction during operation in fluidized beds, which can cause high elutriation loss, defluidization, segregation in size, and inhomogeneous residence time in the bed [3]. Little work has been reported in the literature for hydrodynamic characteristics of binary mixtures in conical fluidized beds [17,18]. Therefore, it was felt necessary to develop correlations for the calculation of critical fluidization velocity and maximum bed pressure drop in tapered fluidized beds, which are important characteristics of gas–solid fluidization. In this study, empirical dimensionless correlations have been developed for predicting the critical fluidization velocity and maximum bed pressure drop for binary mixtures of regular particles for gas–solid systems. 2. Experimental details 2.1. Apparatus Fig. 1 shows the schematic diagram of the experimental set-up used in this study. Three fluidized beds made up of transparent Perspex sheets with tapered angle of 4.61◦ , 7.47◦ and 9.52◦ were used in this study. The diameters at the bottom were 48 mm, 42 mm and 50 mm; and the diameters at the top were

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Fig. 1. Experimental set-up: 1, compressor; 2, receiver; 3, silica gel tower; 4, bypass valve; 5, control valve; 6, rotameter; 7, bed materials; 8, fluidizer; and 9 pressure tapping to manometer.

132 mm, 174 mm and 212 mm, respectively. The bed heights were 520 mm, 504 mm and 483 mm, respectively. A 60 mesh screen at the bottom served as the support as well as the distributor. The calming section of the bed was filled with glass beads for uniform distribution of fluid. Two pressure taps, one at the entrance (just above the distributor) and the other at the exit section of the bed were provided to record the pressure drops. Pressure drop was measured with a 1 m long manometer. Carbon tetrachloride (density = 1594 kg m−3 ) was used as the manometric fluid. Air at a temperature of 301 K (ρf = 1.17 kg m−3 and μf = 1.83 × 10−5 kg m−1 s−1 ), used as the fluidizing medium, was passed through a receiver and a silica gel tower to dry and

Table 1 Comparison of critical fluidization velocities with experimental data Materials

Composition (wt%)

Hs (m)

α (◦ )

Uc (exp.) (m s−1 )

Uc (predicted value) (m s−1 )

Absolute error (%)

GB1 + GB2

50 + 50

0.096 0.11 0.121

4.61 4.61 4.61

1.84 1.84 1.84

2.139 2.139 2.139

16.25 16.25 16.25

S1 + S2

50 + 50

0.072 0.103 0.131

4.61 4.61 4.61

1.23 1.23 1.23

1.31 1.31 1.31

6.50 6.50 6.50

GB1 + GB2

50 + 50

0.105 0.125 0.143

7.47 7.47 7.47

2.41 2.41 2.41

2.578 2.578 2.578

6.97 6.97 6.97

S1 + S2

50 + 50

0.098 0.116 0.132

7.47 7.47 7.47

1.604 1.604 1.604

1.579 1.579 1.579

1.56 1.56 1.56

GB1 + GB2

50 + 50

0.11 0.125 0.14

9.52 9.52 9.52

1.981 1.981 1.981

2.126 2.126 2.126

7.32 7.32 7.32

S1 + S2

50 + 50

0.105 0.135 0.16

9.52 9.52 9.52

1.132 1.132 1.132

1.302 1.302 1.302

15.02 15.02 15.02

0.06 0.09 0.118 0.086 0.107 0.126 0.095 0.123 0.141

4.61 4.61 4.61 7.47 7.47 7.47 9.52 9.52 9.52

1.84 1.84 1.84 2.41 2.41 2.41 1.981 1.981 1.981

1.716 1.716 1.716 2.068 2.068 2.068 1.705 1.705 1.705

6.74 6.74 6.74 14.19 14.19 14.19 13.93 13.93 13.93

50 + 50

GB1 + S1

50 + 50

50 + 50

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control the air flow before being sent through the tapered column. Two rotameters, one for the lower range (0–10 m3 h−1 ) and the other for the higher range (10–120 m3 h−1 ) were used to measure the air-flow rates. 2.2. Procedure The experiments were carried out in tapered columns having tapered angles of 4.61◦ , 7.47◦ and 9.52◦ . Two types of materials viz. glass beads (density = 2600 kg m−3 ) and sago (white colored spherical cereal, density = 1303 kg m−3 ) were used for the investigation. All experimental runs were performed at a temperature of around 301 K and atmospheric pressure of 101.3 kPa. The mean diameter of the spherical particles (glass bead (2608 ␮m, 2215 ␮m and 3676 ␮m) and sago (2608 ␮m, 2215 ␮m and 3676 ␮m)) was determined by randomly selecting sample particles; measuring the diameters of individual particles by a vernier caliper; and averaging the measurements. The density of the particles was obtained by dividing the weight of the particles by the volume of the water displaced when the particles were placed in a cylindrical column filled with water. The weighed quantity of the mixture was charged into the fluidization column. Prior to recording any data, the charge was vigorously fluidized with air at a velocity at which no entrainment was observed. After a certain time, the air flow was suddenly stopped to obtain a mixed packed bed/segregation bed with which the experiments were carried out. To determine

the critical fluidization velocity and maximum pressure drop, the procedure followed by Li et al. [19] was followed. The initial stagnant bed height was recorded. The velocity of the air was increased incrementally allowing sufficient time to reach a steady state. The rotameter and manometer readings were noted for each increment in flow rate and the pressure drop and the superficial velocity calculated. The velocity at which the pressure drop was maximum was taken as the critical fluidization velocity. The same process was repeated for different stagnant bed heights, different mixture of particles and different tapered angles of the tapered beds. 3. Development of models Based on the experimental results obtained (Tables 1 and 2) in the present study, for different mixtures of the materials, correlations have been obtained by carrying out dimensionless analysis and estimating the constant coefficients by non-linear regression. For critical fluidization velocity in tapered fluidized beds, a correlation similar to that of Thonglimp et al. (minimum fluidization velocity of binary mixture in cylindrical bed) [15] and for maximum pressure drop a correlation similar to that of Olazer et al. (maximum pressure drop in conical spouted bed) [8] have been proposed. The effect of tapered angle, which is an important parameter in tapered fluidized bed hydrodynamics [3], has been included in the correlations. The proposed correlations are applicable over a wide range of geometric factors of the bed

Table 2 Comparison of maximum bed pressure drops with experimental data Materials

Composition (wt%)

Hs (m)

α (◦ )

Pmax (exp.) (Pa)

Pmax (predicted value) (Pa)

GB1 + GB2

50 + 50

0.096 0.11 0.121

4.61 4.61 4.61

1515.26 1905.79 2108.86

1650.42 1831.89 1970.69

8.92 3.88 6.55

S1 + S2

50 + 50

0.072 0.103 0.131

4.61 4.61 4.61

570.18 593.6 796.68

539.80 710.23 853.94

5.33 19.65 7.19

GB1 + GB2

50 + 50

0.105 0.125 0.143

7.47 7.47 7.47

2015.14 2671.23 2874.44

2063.18 2358.10 2614.17

2.38 11.72 9.05

S1 + S2

50 + 50

0.098 0.116 0.132

7.47 7.47 7.47

843.54 890.41 1312.18

797.92 907.49 1002.49

5.41 1.92 23.60

GB1 + GB2

50 + 50

0.11 0.125 0.14

9.52 9.52 9.52

2725.24 2872.44 3025.32

2439.66 2690.75 2934.87

10.48 6.33 2.99

S1 + S2

50 + 50

0.105 0.135 0.16

9.52 9.52 9.52

908.73 1112.35 1350.87

959.91 1163.77 1325.59

5.63 4.62 1.87

50 + 50

0.06 0.09 0.118 0.086 0.107 0.126 0.095 0.123 0.141

4.61 4.61 4.61 7.47 7.47 7.47 9.52 9.52 9.52

656.09 952.89 1030.99 1077.86 1405.15 1437.15 1015.38 1351.23 1890.17

707.86 965.79 1189.59 1088.62 1287.02 1458.76 1340.63 1634.08 1814.37

7.89 1.35 15.38 0.99 8.41 1.50 32.03 20.93 4.01

GB1 + S1

Absolute error (%)

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(tapered angle, gas inlet diameter) and experimental conditions (particle size, particle density, stagnant bed height). The dimensionless correlation for critical fluidization velocity is given in Eq. (1) and for maximum pressure drop in Eq. (2).  Rec = 16.364(Ar)0.1969

ρ ρf

0.3154 

dpm D0

1.1854 (Sin α)0.0585 (1)

 −0.2337 Pmax Hs = 0.081(Ar)0.1493 (Sin ␣)0.3826 gρsm Hs D0

(2)

In order to develop correlations for binary systems, it is necessary to define the particle diameter and the density of the binary

Fig. 2. Effect of superficial gas velocity on pressure drop of GB1 + GB2 mixture (stagnant bed height = 0.14 m, tapered angle = 9.52◦ ).

Fig. 3. Comparison of critical fluidization velocity (predicted) with experimental results.

Fig. 4. (a) Comparison of maximum pressure drop (predicted) with experimental results (tapered angle = 4.61◦ ). (b) Comparison of maximum pressure drop (predicted) with experimental results (tapered angle = 7.47◦ ). (c) Comparison of maximum pressure drop (predicted) with experimental results (tapered angle = 9.52◦ ).

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systems. In this study, these are defined as [20]. 1 wl wh = + ρsm ρsl ρsh

(3)

1 wl wh = + dpm ρsm dpl ρsl dph ρsh

(4)

4. Results and discussion The hydrodynamic behavior of a tapered fluidized bed is best described by the plot of pressure drop across the bed versus superficial velocity of the fluid, based on the bottom diameter of the bed. One such plot is shown in Fig. 2. From point A to point B, the pressure drop increases with the increase of superficial gas velocity. The transition from fixed bed to partially fluidized bed occurs at point B. From point B, the pressure drop decreases with the increase in superficial gas velocity and from point C it remains constant. Point B to point C is called partially fluidized bed and thereafter it is known as fully fluidized bed. The hydrodynamic characteristics associated with the phenomenon are critical fluidization velocity, maximum pressure drop, minimum velocity for full fluidization, pressure drop at full fluidization, maximum velocity for full defluidization and hysteresis. The details and the significance of each of the characteristics are explained by Peng and Fan [1]. The velocity at point B is called critical fluidization velocity or minimum velocity for partial fluidization. At this point the pressure drop is maximum. The critical fluidization velocity and maximum bed pressure drop were calculated using Eqs. (1) and (2), respectively, for binary mixture of regular particles in gas–solid system and compared with experimental results. In relation to binary systems, it should be noted that the mixture of GB1 + GB2 and S1 + S2 were completely mixed and homogeneous as the diam-

eter ratio was low. These mixtures behave like mono component. In contrast, the mixture of GB1 + S1 was completely segregated because the density ratio was nearly 2. The critical fluidization velocity is strongly dependent upon the ratio of (dpm /D0 ) compared to other parameters whereas the maximum pressure drop is strongly dependent upon bed aspect ratio (Hs /D0 ). This can also be seen in Tables 1 and 2. The comparison of predicted critical fluidization velocities and maximum bed pressure drops with experimental results are shown in Figs. 3 and 4(a–c), respectively. A fairly good agreement with the experimental results can be seen from these figures. The average absolute percentage errors for critical fluidization velocity and maximum bed pressure drop for all the experimental conditions are within 10%. In addition, the mean, standard deviation and coefficient of variation of the predicted values from the corresponding experimental ones have been obtained as 7.81, 6.08 and 77.87, respectively, for critical fluidization velocities and 14.84, 10.61 and 71.53, respectively, for maximum pressure drops (Tables 3 and 4) of other sets (those are not being used to develop the correlations). Therefore, the critical fluidization velocity and maximum pressure drop for binary mixture of regular solids in tapered fluidized bed can be estimated satisfactorily by the correlations given in Eqs. (1) and (2), respectively. Comparison of calculated critical fluidization velocity and maximum bed pressure drop with experimental data as absolute error (%) are also shown in Tables 1 and 2, respectively. To assess the true potential of the correlations, other sets of experimental data with different compositions and different diameters were obtained. The experimental data compared well with the predicted values (Tables 3 and 4). These experimental data were not included during the development of the correlations. The statistical analyses of the error between the experimental and calculated critical fluidization velocity as well

Table 3 Comparison of test set of experimental data (different compositions) for critical fluidization velocities with predicted values from developed correlation Materials

Composition (wt%)

Hs (m)

α (◦ )

Uc (exp.) (m s−1 )

Uc (predicted value) (m s−1 )

GB2 + GB1

25 + 75 75 + 25

0.071 0.073

4.61 4.61

2.149 1.996

2.208 2.138

2.79 7.14

S2 + S3

25 + 75 75 + 25

0.075 0.08

4.61 4.61

1.535 1.23

1.623 1.337

5.72 8.71

S1 + GB1

25 + 75 75 + 25

0.09 0.121

4.61 4.61

1.996 1.535

1.951 1.538

2.23 0.22

GB2 + GB1

25 + 75 75 + 25

0.076 0.077

7.47 7.47

2.61 2.41

2.662 2.577

2.00 6.95

S2 + S1

25 + 75 75 + 25

0.078 0.077

7.47 7.47

1.805 1.404

1.631 1.531

9.65 9.06

S3 + GB3

25 + 75 75 + 25

0.093 0.117

7.47 7.47

3.21 2.21

3.07 2.419

4.36 9.50

GB2 + GB1

25 + 75 75 + 25

0.067 0.068

9.52 9.52

2.264 1.84

2.195 2.126

3.02 15.53

S2 + S3

25 + 75 75 + 25

0.066 0.067

9.52 9.52

1.27 0.99

1.345 1.263

5.90 27.55

S3 + GB3

25 + 75 75 + 25

0.082 0.103

9.52 9.52

2.264 1.84

2.532 1.996

11.83 8.47

Absolute error (%)

D.C. Sau et al. / Chemical Engineering and Processing 47 (2008) 2114–2120

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Table 4 Comparison of test set of experimental data (different compositions) for maximum bed pressure drops with predicted values from developed correlation Materials

Composition (wt%)

Hs (m)

α (◦ )

Pmax (exp.) (Pa)

Pmax (predicted value) (Pa)

Absolute error (%)

GB2 + GB1

25 + 75 75 + 25

0.071 0.073

4.61 4.61

1312.18 1187.21

1334.48 1337.86

1.70 12.69

S2 + S3

25 + 75 75 + 25

0.075 0.08

4.61 4.61

593.61 577.98

630.23 592.15

6.17 2.45

S1 + GB1

25 + 75 75 + 25

0.09 0.121

4.61 4.61

1202.83 1312.18

1222.82 992.42

1.66 24.37

GB2 + GB1

25 + 75 75 + 25

0.076 0.077

7.47 7.47

1390.28 1327.8

1640.89 1626.74

18.03 22.51

S2 + S1

25 + 75 75 + 25

0.078 0.077

7.47 7.47

624.85 609.23

682.51 651.62

9.23 6.96

S3 + GB3

25 + 75 75 + 25

0.093 0.117

7.47 7.47

1452.77 1577.74

1706.72 1316.42

17.48 16.56

GB2 + GB1

25 + 75 75 + 25

0.067 0.068

9.52 9.52

1202.83 1327.8

1699.98 1687.57

41.53 27.09

S2 + S3

25 + 75 75 + 25

0.066 0.067

9.52 9.52

609.23 546.74

685.21 668.36

12.47 22.24

S3 + GB3

25 + 75 75 + 25

0.082 0.103

9.52 9.52

1437.15 1374.67

1768.39 1362.36

23.05 0.89

as maximum bed pressure drop were carried out. Replicates for all the experimental data were not available. The mean, standard deviation and the coefficient of variation of the absolute percentage error for critical fluidization velocity were, 9.83%, 4.8% and 48.8%, respectively. For the maximum bed pressure drop, the mean, standard deviation and the coefficient of variation of the percentage absolute error were, 8.52%, 7.53% and 88.34%, respectively. For the test data set, the mean, standard deviation and coefficient of variation of the percentage absolute error for critical fluidization velocity were, 7.81%, 6.08% and 77.87%, respectively. The mean, standard deviation and coefficient of variation of the percentage absolute error for maximum bed pressure drop for the test data set were, 14.84%, 10.61% and 71.53%, respectively. It was also experimentally seen that the Uc was not a function of stagnant bed height in tapered bed. This phenomenon was also observed by Povrenovic et al. [21] and Caicedo et al. [22]. 5. Conclusion The hydrodynamic characteristics of the tapered fluidized bed are quite different from those of the columnar fluidized bed; therefore, the known correlations for the columnar bed cannot be used for the tapered bed. Experiments were carried out with a number of binary mixtures of regular particles in tapered fluidized beds. Dimensionless empirical correlations have been developed for the calculation of critical fluidization velocity and maximum bed pressure drop for binary mixture of regular particles in gas–solid system in tapered beds. The constant coefficients for these correlations were obtained by non-linear regression analysis. The experimental values for gas–solid systems in tapered beds were found to fit well with the proposed model correlations. This indicates that these correlations are

valid and are of practical use in the range of present system variables. The developed empirical correlations can be used widely for analyzing the hydrodynamic characteristics of binary mixture of regular particles in tapered beds over a good range of the variables. The present study could provide some insight into the behavior of binary mixture of particles in gas–solid systems in tapered beds. The proposed correlations could also find practical utility in designing and operation of tapered fluidized beds for binary mixture of gas– solid systems. Appendix A

Nomenclature 3 ρ2 /μ2 ) Ar Archimedes number (= gdpm sm f D0 bottom diameter of tapered bed (m) dpm diameter of binary mixture (m) dpl diameter of light particle (m) dph diameter of heavy particle (m) g acceleration due to gravity (m s−2 ) Hs initial stagnant height of the particle bed (m) Pmax maximum pressure drop through the particle bed (Pa) Rec Reynolds number at Uc (= dpm Uc ρf /μf ) Uc critical fluidization velocity based on the bottom diameter of the bed (m s−1 ) wl weight fraction of light (or small) particle wh weight fraction of heavy (or big) particle Greek letters α tapered angle (◦ ) fluid viscosity (kg m−1 s−1 ) μf ρsm density of binary mixture (kg m−3 ) ρsl density of light (small) particle (kg m−3 )

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ρsh ρf ρ

D.C. Sau et al. / Chemical Engineering and Processing 47 (2008) 2114–2120

density of heavy (big) particle (kg m−3 ) fluid density (kg m−3 ) (ρsm − ρf ) (kg m−3 )

Subscript exp. experimental value GB1 glass bead of size 2608 ␮m GB2 glass bead of size 2215 ␮m GB3 glass bead of size 3676 ␮m S1 sago of size 2608 ␮m S2 sago of size 2215 ␮m S3 sago of size 3676 ␮m References [1] Y. Peng, L.T. Fan, Hydrodynamic characteristics of fluidization in liquid–solid tapered beds, Chem. Eng. Sci. 52 (14) (1997) 2277–2290. [2] F. Depypere, J.G. Pieters, K. Dewettinck, Expanded bed height determination in a tapered fluidized bed reactor, J. Food Eng. 67 (2005) 353–359. [3] H.G. Kim, I.O. Lee, U.C. Chung, Y.H. Kim, Fluidization characteristics of iron ore fines of wide size distribution in a cold tapered gas–solid fluidized bed, ISIJ Int. 40 (2000) 16–22. [4] R.K. Singh, A. Suryanarayana, G.K. Roy, Prediction of minimum velocity and minimum bed pressure drop for gas–solid fluidization in conical conduits, Can. J. Chem. Eng. 70 (1992) 185–189. [5] Y.F. Shi, Y.S. Yu, L.T. Fan, Incipient fluidization condition for a tapered fluidized bed, Ind. Eng. Chem. Fundam. 23 (1984) 484–489. [6] K.C. Biswal, T. Bhowmik, G.K. Roy, Prediction of minimum fluidization velocity for gas–solid fluidization of regular particles in conical vessels, Chem. Eng. J. 30 (1985) 57–62. [7] K.C. Biswal, T. Bhowmik, G.K. Roy, Prediction of pressure drop for a conical fixed bed of spherical particles in gas–solid systems, Chem. Eng. J. 29 (1984) 47–50. [8] M. Olazer, M.J. San Jose, A.T. Aguayo, J.M. Arandes, J. Bilbao, Pressure drop in conical spouted beds, Chem. Eng. J. 51 (1993) 53–60.

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