High-Precision Monitoring of Average Molecular Weight of Polyethylene Wax from Waste High-Density Polyethylene
Abstract
:1. Introduction
2. Test Procedure
2.1. Test Platform
2.2. Preparation of Polyethylene Wax
2.3. Characterization of Polyethylene Wax
3. Theoretical Analysis of Pyrolysis Procedure
3.1. Pyrolysis Model
3.2. Theoretical Calculation of Average Carbon-Atom Number of PEW
4. Monitoring Procedure for Average Molecular Weight of Polyethylene Wax
4.1. Arrhenius Equation
4.2. Measure-Point-Independence Verification
4.3. Modified Arrhenius Equation
4.4. Time-Dependent Pyrolysis Temperature
4.5. Inverse Method
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
A1: | the factor before exponent, s−1 |
A2: | the amplitude of temperature fluctuation, K |
b: | the number of not pyrolyzed nodes |
d: | search direction |
E: | activation energy, kJ/mol |
J: | objective function |
k: | reaction rate constant |
l: | the period of temperature fluctuation, s |
m: | carbon-atom number |
M: | the number-average molecular weight of polyethylene wax |
: | the average carbon-atom number of moleculars of polyethylene wax |
n: | screw speed |
n: | the maximum carbon-atom number of moleculars of polyethylene wax |
: | the number of moleculars of polyethylene wax with m carbon atoms |
N: | measure point (a test under a specific process condition) |
o: | the equation order of initial or modified Arrhenius equation |
p: | measure point number |
r: | pyrolysis ratio |
R: | gas constant (8.314 J/(mol·K)) |
T: | temperature, K |
t: | time |
v: | the order of reaction dynamic equation |
Z: | the total number of input measure points |
Greek Symbols | |
: | search step size |
: | the increment of pyrolysis ratio |
: | temperature fluctuation, K |
: | a small positive number |
: | computational domain |
Subscripts | |
cal: | calculated |
m: | melting point |
mea: | measured |
p: | pyrolysis |
v: | evaporation |
Superscripts | |
i, j: | iteration index |
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Screw Speed (rpm) | 2 | 10 | 20 | 30 | 40 |
Pyrolysis Time (s) | 842 | 213 | 179 | 146 | 110 |
Pyrolysis Temperature (K) | 673 | 693 | 713 | 733 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Screw Speed (rpm) | 10 | 2 | 10 | 20 | 30 | 40 | 10 | 20 | 30 | 10 | 20 | 30 |
NAMW of PEW | 4088 | 908 | 3111 | 3649 | 4268 | 5876 | 2919 | 3458 | 4151 | 2075 | 2445 | 3274 |
Measure point | N1 | N2 | N3 | N4 | N5 | N6 | N7 | N8 | N9 | N10 | N11 | N12 |
p = 4 | ✓ | ✓ | ✓ | ✓ | ||||||||
p = 6 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||
p = 8 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Equation Order | Initial or Modified Arrhenius Equation | N4 (%) | N5 (%) | N7 (%) | N11 (%) | Mean (%) |
---|---|---|---|---|---|---|
o = 1 | 5.8 | 10.4 | 8.0 | 8.3 | 8.1 | |
o = 2 | 6.6 | 11.3 | 7.1 | 7.2 | 8.0 | |
o = 3 | 2.2 | 6.7 | 0.8 | 4.7 | 3.6 |
Relative Error (%) | N4 | N5 | N7 | N11 | Mean |
---|---|---|---|---|---|
modified Arrhenius equation (o = 3) | 2.2 | 6.7 | 0.8 | 4.7 | 3.6 |
Inverse method | 0.2 | 4.6 | 0.9 | 6.7 | 3.1 |
Screw-speed-dependent inverse method | 0.6 | 4.8 | 0.2 | 4.5 | 2.5 |
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Guo, Z.; Lan, X.; Xue, P. High-Precision Monitoring of Average Molecular Weight of Polyethylene Wax from Waste High-Density Polyethylene. Polymers 2020, 12, 188. https://doi.org/10.3390/polym12010188
Guo Z, Lan X, Xue P. High-Precision Monitoring of Average Molecular Weight of Polyethylene Wax from Waste High-Density Polyethylene. Polymers. 2020; 12(1):188. https://doi.org/10.3390/polym12010188
Chicago/Turabian StyleGuo, Zhouchao, Xia Lan, and Ping Xue. 2020. "High-Precision Monitoring of Average Molecular Weight of Polyethylene Wax from Waste High-Density Polyethylene" Polymers 12, no. 1: 188. https://doi.org/10.3390/polym12010188