Modeling and Flowsheet Simulation of Vibrated Fluidized Bed Dryers
Abstract
:1. Introduction
1.1. Background on Fluidized Bed Modeling
1.1.1. Modeling of Hydrodynamics
1.1.2. Modeling of Dying Kinetics
1.2. Flowsheet Simulation
2. Model
2.1. Structure and Assumptions
2.2. Hydrodynamics Model
2.3. Thermodynamic Model
2.4. Implementation
3. Materials and Methods
3.1. Materials
3.2. Drying Experiments
4. Results and Discussion
4.1. Validation
4.1.1. Validation for Geldart D Particles
4.1.2. Validation for Geldart B Particles
4.1.3. Validation for Dryer Geometries and Vibration
4.1.4. Validation for Geldart A
4.1.5. Validation of Model Assumptions
4.2. Sensitivity Analysis
4.2.1. Heat Transfer between Particles and Dryer Wall
4.2.2. Number of Transfer Units
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Roman letters | ||
A | transfer surface area | m2 |
amplitude of vibration | m | |
CSTR | continuous stirred tank reactor | - |
CFD | computational fluid dynamics | - |
heat capacity | /kg−1/k−1 | |
d | diameter | m |
DEM | discrete element modeling | - |
activation energy | ||
evaporation enthalpy | /kg−1 | |
f | frequency of vibration | Hz |
FCC | fluid catalytic cracking | - |
g | gravitational acceleration | /s−2 |
h | specific enthalpy | /kg−1 |
H | height | m |
enthalpy flow | W | |
n | number density distribution of residence time | - |
mass flux | /s−1/m−2 | |
M | mass | |
mass flow | /s−1 | |
NCDC | Normalized Characteristic Drying Curve | - |
NTU | number of transfer units | - |
PFTR | plug flow tank reactor | - |
heat flow | W | |
REA | Reaction Engineering Approach | - |
T | temperature | |
u | gas velocity | /s−1 |
VFB | vibrated fluidized bed | - |
X | moisture content of solids | /kg−1 |
Y | gas moisture content | /kg−1 |
Greek symbols | ||
heat transfer coefficient | /kg−1/k−1 | |
mass transfer coefficient | /s−1 | |
bed porosity | - | |
normalized bed height | - | |
vibration intensity | - | |
material specific drying curve | - | |
normalized moisture content | - | |
density | /m−3 | |
residence time | ||
relative humidity | - | |
Subscripts | ||
amb | ambient | |
B | bubble phase | |
d | discretized particle size class | |
cr | critical | |
eq | equilibrium | |
exp | experiment | |
f | discretized particle moisture class | |
fb | fluidized bed under operation conditions | |
G | gas phase | |
in | inlet | |
mf | minimum fluidization | |
max | maximum | |
out | outlet | |
P | particle phase | |
S | suspension phase | |
sim | simulation | |
v | vapor/gaseous | |
W | wall |
Appendix A. Heat and Mass Transfer Streams
Appendix B. Material Properties and Investigated Vibration Parameters
frequency f | [Hz] | 0 | 4 | 6 | 8 | 10 |
amplitude | [mm] | 0 | 5 | 4 | 3.5 | 3 |
vibration intensity | [-] | 0 | 0.32 | 0.59 | 0.9 | 1.21 |
Appendix C. Summary of Experimental and Simulation Results
Exp. Name | [cm] | [cm] | [%] | [K] | [K] | [%] | [kg kg] | [kg kg] | [%] |
---|---|---|---|---|---|---|---|---|---|
GF3_A_01 | 13.0 | 12.4 | 4.47 | 295.60 | 294.95 | 0.22 | 0.170 | 0.144 | 15.16 |
GF3_A_02 | 13.0 | 12.4 | 4.35 | 301.55 | 301.37 | 0.06 | 0.291 | 0.281 | 3.51 |
GF3_A_03 | 13.0 | 12.4 | 4.27 | 308.68 | 314.67 | −1.94 | 0.141 | 0.139 | 1.45 |
GF3_A_04 | 13.0 | 12.4 | 4.32 | 308.02 | 312.53 | −1.47 | 0.172 | 0.182 | −5.68 |
GF3_A_05 | 13.0 | 12.4 | 4.28 | 308.98 | 313.53 | −1.47 | 0.150 | 0.150 | 0.03 |
GF3_A_06 | 8.0 | 7.7 | 4.19 | 307.33 | 318.81 | −3.74 | 0.138 | 0.132 | 4.38 |
GF3_C_01 | 8.1 | 8.2 | −2.20 | 301.62 | 303.56 | −0.64 | 0.087 | 0.060 | 31.23 |
GF3_C_02 | 8.1 | 8.2 | −2.24 | 301.25 | 302.40 | −0.38 | 0.073 | 0.069 | 5.19 |
GF3_C_03 | 7.2 | 7.4 | −3.24 | 306.52 | 311.91 | −1.76 | 0.081 | 0.064 | 21.04 |
GF3_C_04 | 7.2 | 7.4 | −3.24 | 302.91 | 306.55 | −1.20 | 0.124 | 0.092 | 25.45 |
GF3_C_05 | 8.1 | 8.3 | −3.14 | 315.69 | 318.16 | −0.78 | 0.061 | 0.054 | 10.87 |
GF3_C_06 | 8.1 | 8.3 | −3.05 | 311.69 | 312.85 | −0.37 | 0.068 | 0.070 | −3.75 |
GF3_C_07 | 7.2 | 7.4 | −3.84 | 325.43 | 334.32 | −2.73 | 0.046 | 0.046 | −1.05 |
GF3_C_08 | 8.1 | 8.4 | −3.88 | 336.58 | 336.53 | 0.02 | 0.044 | 0.052 | −18.06 |
GF3_C_09 | 8.1 | 8.4 | −3.83 | 326.78 | 330.95 | −1.28 | 0.062 | 0.056 | −8.70 |
VFB_C_01 | 6.8 | 6.4 | 6.06 | 296.79 | 296.60 | −0.12 | 0.104 | 0.114 | −10.17 |
VFB_C_02 | 7.2 | 6.3 | 12.6 | 294.91 | 295.26 | −1.95 | 0.157 | 0.169 | −7.78 |
VFB_C_03 | 6.9 | 7.0 | −0.93 | 307.60 | 313.59 | 0.34 | 0.056 | 0.064 | −13.62 |
VFB_C_04 | 6.9 | 7.0 | −0.56 | 303.90 | 307.04 | −1.03 | 0.081 | 0.090 | −11.82 |
VFB_C_05 | 7.0 | 6.9 | 1.73 | 298.05 | 298.70 | −0.22 | 0.111 | 0.102 | 7.99 |
VFB_C_06 | 7.0 | 7.2 | −2.55 | 303.72 | 306.53 | −0.93 | 0.105 | 0.101 | 3.67 |
VFB_C_07 | 7.0 | 6.9 | 1.81 | 309.55 | 313.03 | −1.12 | 0.063 | 0.070 | −11.33 |
VFB_F_01 | 13.0 | 11.45 | 11.93 | 300.22 | 302.50 | −0.76 | 0.031 | 0.034 | −7.66 |
VFB_F_02 | 13.0 | 11.45 | 11.93 | 303.15 | 302.70 | 0.15 | 0.028 | 0.034 | −21.40 |
VFB_F_03 | 15.0 | 13.96 | 6.94 | 298.32 | 299.21 | −0.30 | 0.037 | 0.041 | −10.96 |
VFB_F_04 | 15.0 | 13.96 | 6.94 | 302.76 | 302.76 | −0.20 | 0.026 | 0.020 | 24.80 |
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Material | Skeletal Density [kg m] | Apparent Density [kg m] | Sauter Diameter [m] | Sphericity [m g] | Specific Surface Area [-] | Geldart Group [-] | * [m s] |
---|---|---|---|---|---|---|---|
- | 3261.2 | 1006.4 | 1701.4 | 0.97 | 206.3 | D | 0.51 |
Cellets 500 | 1464.6 | 1113.6 | 631.8 | 0.85 | 63.6 | B | 0.2 |
FCC catalyst | 2729.2 | 1632.5 | 41.6 | 0.863 | 93.9 | A | 0.015 |
Exp. Name | Dryer | Material | [C] | [m s] | [g s] | [kg kg] | [cm] | [-] | * [g kg] | [C] |
---|---|---|---|---|---|---|---|---|---|---|
GF3_A_01 | GF3 | - | 40 | 1.3 | 1.5 | 0.33 | 12 | 0 | 4.64 | 20 |
GF3_A_02 | GF3 | - | 60 | 1.3 | 2.0 | 0.50 | 12 | 0 | 6.98 | 21 |
GF3_A_03 | GF3 | - | 80 | 1.3 | 1.6 | 0.49 | 12 | 0 | 7.19 | 24 |
GF3_A_04 | GF3 | - | 80 | 1.3 | 1.6 | 0.54 | 12 | 0 | 7.79 | 25 |
GF3_A_05 | GF3 | - | 80 | 1.3 | 1.9 | 0.45 | 12 | 0 | 10.13 | 21 |
GF3_A_06 | GF3 | - | 80 | 1.3 | 1.0 | 0.59 | 7 | 0 | 7.00 | 23 |
GF3_C_01 | GF3 | Cellets | 40 | 1.1 | 0.7 | 0.21 | 12 | 0 | 8.04 | 23 |
GF3_C_02 | GF3 | Cellets | 40 | 1.1 | 0.7 | 0.24 | 12 | 0 | 8.81 | 22 |
GF3_C_03 | GF3 | Cellets | 60 | 0.5 | 0.9 | 0.20 | 12 | 0 | 5.51 | 24 |
GF3_C_04 | GF3 | Cellets | 60 | 0.5 | 1.2 | 0.23 | 12 | 0 | 10.28 | 22 |
GF3_C_05 | GF3 | Cellets | 60 | 1.1 | 1.0 | 0.20 | 12 | 0 | 6.76 | 21 |
GF3_C_06 | GF3 | Cellets | 60 | 1.1 | 1.1 | 0.26 | 12 | 0 | 8.45 | 22 |
GF3_C_07 | GF3 | Cellets | 80 | 0.5 | 0.5 | 0.24 | 12 | 0 | 7.40 | 22 |
GF3_C_08 | GF3 | Cellets | 80 | 1.1 | 0.9 | 0.24 | 12 | 0 | 5.86 | 22 |
GF3_C_09 | GF3 | Cellets | 80 | 1.1 | 1.3 | 0.23 | 12 | 0 | 8.07 | 22 |
VFB_C_01 | VFB | Cellets | 40 | 0.3 | 2.7 | 0.24 | 8 | 0.59 | 7.43 | 22 |
VFB_C_02 | VFB | Cellets | 40 | 0.3 | 5.0 | 0.24 | 8 | 0 | 7.19 | 23 |
VFB_C_03 | VFB | Cellets | 60 | 0.3 | 2.1 | 0.25 | 8 | 0 | 6.77 | 21 |
VFB_C_04 | VFB | Cellets | 60 | 0.3 | 3.3 | 0.25 | 8 | 0 | 8.81 | 21 |
VFB_C_05 | VFB | Cellets | 40 | 0.4 | 3.0 | 0.23 | 8 | 0.59 | 10.58 | 28 |
VFB_C_06 | VFB | Cellets | 60 | 0.4 | 5.3 | 0.23 | 8 | 0 | 10.72 | 28 |
VFB_C_07 | VFB | Cellets | 60 | 0.4 | 3.2 | 0.24 | 8 | 0.59 | 10.48 | 28 |
VFB_F_01 | VFB | FCC | 60 | 0.07 | 0.44 | 0.23 | 16 | 0 | 1.06 | 18 |
VFB_F_02 | VFB | FCC | 60 | 0.07 | 0.43 | 0.24 | 16 | 0 | 1.07 | 18 |
VFB_F_03 | VFB | FCC | 60 | 0.07 | 0.66 | 0.20 | 16 | 0 | 1.02 | 17 |
VFB_F_04 | VFB | FCC | 60 | 0.07 | 0.45 | 0.15 | 16 | 0 | 1.04 | 17 |
Parameter | GF3_A_02 | GF3_C_03 |
---|---|---|
Anderson acceleration factor | 10 | 10 |
Number of height classes | 100 | 100 |
Number of residence time classes | 200 | 200 |
Maximum residence time | 0.95 | 0.95 |
Geldart group | D | B |
[] | 0.53 | 0.2 |
[] | 1.7 | 1.1 |
[] | 2.05 | 1.13 |
[] | 294 | 295 |
[] | 0.50 | 0.26 |
[] | 0.033 | 0.03 |
[] | 333 | 333 |
[] | 6.98 | 8.45 |
[−] | 0 | 0 |
[] | 0.05 | 0.05 |
[] | n.a. | n.a. |
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Lehmann, S.E.; Buchholz, M.; Jongsma, A.; Innings, F.; Heinrich, S. Modeling and Flowsheet Simulation of Vibrated Fluidized Bed Dryers. Processes 2021, 9, 52. https://doi.org/10.3390/pr9010052
Lehmann SE, Buchholz M, Jongsma A, Innings F, Heinrich S. Modeling and Flowsheet Simulation of Vibrated Fluidized Bed Dryers. Processes. 2021; 9(1):52. https://doi.org/10.3390/pr9010052
Chicago/Turabian StyleLehmann, Soeren E., Moritz Buchholz, Alfred Jongsma, Fredrik Innings, and Stefan Heinrich. 2021. "Modeling and Flowsheet Simulation of Vibrated Fluidized Bed Dryers" Processes 9, no. 1: 52. https://doi.org/10.3390/pr9010052
APA StyleLehmann, S. E., Buchholz, M., Jongsma, A., Innings, F., & Heinrich, S. (2021). Modeling and Flowsheet Simulation of Vibrated Fluidized Bed Dryers. Processes, 9(1), 52. https://doi.org/10.3390/pr9010052