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1
Introduction to mathematical modeling of physical and chemical
processes in the EBFGT
Drd. MSc Valentina GogulanceaProf. dr. eng. Ioan Calinescu
Prof. dr. eng. Vasile Lavric
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The installation of EBFGT
Irradiation Reactor
Electron Beam System
Water Spray Tower
Flue Gas
Electrostatic precipitator
Fertilizer
Stack
Clean gas
Ammonia injection system
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Historical Developments1. Nishimura, K. & Suzuki, N. 1981. Radiation Treatment of Exhaust Gases - Analysis of NO Oxidation and
Decomposition in Dry and Moist NO-O2-N2 Mixtures by Computer Simulation. Journal of Nuclear Science and Technology, 18, 878-886.
2. Mätzing, H. 1991. Chemical Kinetics of Flue Gas Cleaning by Irradiation with Electrons. Advances in Chemical Physics, volume 80, Ed I Prigogine & S. Rice. John Wiley & Sons, Inc.
3. Paur, H. R. & Matzing, H. 1993. Electron-Beam-Induced Purification of Dilute Off Gases from Industrial-Processes and Automobile Tunnels. Radiation Physics and Chemistry, 42, 719-722.
4. Matzing, H., Namba, H. & Tokunaga, O. 1993. Kinetics of SO2 Removal from Flue-Gas by Electron-Beam Technique. Radiation Physics and Chemistry, 42, 673-677.
5. Penetrante, B. M. 1996. Flue Gas Dry Scrubbing Using Pulsed Electron Beams. Second International Symposium on Environmental Applications of Advanced oxidation Technologies. San Francisco, CA.
6. Penetrante, B. M. 1997. Fundamental limits on NOx reduction by plasma. Technical report – SAE Publications Group7. Penetrante, B. M. 1997. Kinetic Analysis of Non-Thermal Plasmas Used for Pollution Control, Japanese Journal of
Applied Physics, 36, pp 5007-50178. Gerasimov, G. Y., Gerasimova, T. S., Makarov, V. N. & Fadeev, S. A. 1996. Homogeneous and heterogeneous radiation
induced NO and SO2 removal from power plants flue gases - Modeling study. Radiation Physics and Chemistry, 48, 763-769.
9. Li, R. N., Yan, K. P., Miao, J. S. & Wu, X. L. 1998. Heterogeneous reactions in non-thermal plasma flue gas desulfurization. Chemical Engineering Science, 53, 1529-1540.
10. Zhang, J., Sun, J., Gong, Y., Wang, D., Ma, T. & Liu, Y. 2009. A scheme for solving strongly coupled chemical reaction equations appearing in the removal of SO2 and NOx from flue gases. Vacuum, 83, 133-137.
11. Schmitt, K. L., Murray, D. M. & Dibble, T. S. 2009. Towards a Consistent Chemical Kinetic Model of Electron Beam Irradiation of Humid Air. Plasma Chemistry and Plasma Processing, 29, 347-362.
12. Schmitt, K. L. & Dibble, T. S. 2011. Understanding OH Yields in Electron Beam Irradiation of Humid N(2). Plasma Chemistry and Plasma Processing, 31, 41-50.
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Gas Phase Modeling
Ionization
Excitation
Dissociation
Charge transfer Radical reactions
Ion – ion recombination
Radical – neutralMolecularreactions
Primary Processes Secondary Processes
Hypothesis Ideal gas behaviorEvenly distributed dose inside the chamber
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
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Gas Phase Modeling
Dose dependency
2 2 42 24.14 N 0.885 N D 0.295 N P 1.87 N P 2.27 N 0.69 N 2.96 e
12 25.3 O 2.98 O 2.25 O D 2.07 O 1.23 O 3.3e
32 2 26.7 H O 0.51 H 4.25 OH 4.15 H 0.46 O P 1.99 H O 1.99e
2 27.54 CO 4.72 CO 5.16 O 2.24 CO 0.51 CO 0.07 O 2.82e
Radiochemical yields (G values) – Willis and Boyd (1976) & Matzing (1991)
Absorbed
Referance
( ) ( )
G value
G value
Absorbed Dose kGyReference Dose kGy
Reference Dose= 8 kGray
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
Kim K-J, Kim J, Son Y-S, Chung S-G, Kim J-C (2012) Advanced oxidation of aromatic VOCs using a pilot system with electron beam–catalyst coupling. Radiation Physics and Chemistry 81 (5):561-565.
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Gas Phase Modeling
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Early stages
5 10 15 20 25 30 35 40 45 50 550
10
20
30
40
50
60
70
80
90
100
100 ppm
150 ppm
200 ppm
250 ppm
350 ppm
500 ppm
Dose (kGy)
NO
Effi
cien
cy (%
)
Using Zhang & al. modelNo ammonia addition & no nitrate formation
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
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Early stages
5 10 15 20 25 30 35 40 45 50 550
10
20
30
40
50
60
70
80
90
100
100 ppm
150 ppm
200 ppm
250 ppm
350 ppm
500 ppm
Dose (kGy)
SO2
Effici
ency
(%)
Using Zhang & al. modelNo ammonia addition & no sulphate formation
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Early stagesAmmonia addition
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
100
100 ppm150 ppm200 ppm250 ppm350 ppm500 ppm
Dose (kGy)
NO
Effi
cien
cy (%
)
Considering lumped reactions for the thermal
pathway
SO2 + 2NH3 → (NH4)2SO4, k = 1.52*10-30 exp(9000/T)
SO2 + 2NH3 → (NH4)2SO3, k = 1.01*10-31 exp(9000/T)
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Early stages
0 1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
100 ppm150 ppm200 ppm250 ppm350 ppm500 ppm
Dose (kGy)
Effici
ency
SO
2 (%
)
Improving Zhang & al.’s model
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Gas Phase ModelingThermo-Chemical Pathway*
1 SO2 + NH3 → NH3SO22∙10-18
2 NH3SO2+ NH3 →(NH3)2SO26.8∙10-17
3 (NH3)2SO2 + 0.5 O2 → NH4SO3NH23.24168∙10-18
4 (NH3)2SO2 + H2O → (NH4)2SO35.49221∙10-23
5 NH4SO3NH2 + H2O→ (NH4)2SO42.5053∙10-18
1 SO2 + NH3 → NH3SO2 5.1∙10-16
2 NH3SO2 + NH3 → (NH3)2SO2 5.1∙10-12
3 (NH3)2SO2 + 0.5 O2 →NH4SO3NH2 5.1∙10-8
4 (NH3)2SO2 + H2O → (NH4)2SO3 5.1∙10-17
5 NH4SO3NH2 + H2O→ (NH4)2SO4 5.1∙10-16
Experimental removal efficiencies for SO2 at zero irradiation + operating conditions
Model only consisting of the thermal reactions
Genetic Algorithm Optimization
Repeated until the value of the objective function was sufficiently low
*Bulearca, A. M., Călinescu, I. & Lavric, V. 2010. Model studies of NOx and Sox reactions in flue gas treatment by electron beam. U.P.B. Sci.Bull., Series B, 72, 101-112.
Over-estimation of SO2 removal rate
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Liquid Phase Modeling
Hypothesis
Nucleation of H2O and H2SO4 accounted for
Instant thermodynamic equilibrium between gas & liquid
No mass transfer resistances
Coagulation and sulfuric acid condensation are neglected
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
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Liquid Phase ModelingModeling nucleation phenomena
Empirical Semi-empirical Nucleation theory
Vehkamaki, H., Kulmala, M. & Lehtinen, K. E. J. 2003. Modelling Binary Homogeneous Nucleation of Water-Sulfuric Acid Vapours: Parameterisation for High Temperature Emissions. Environ. Sci. Technol, 37, 3392-3398.
Composition of the nucleated dropletsRadius of the dropletsSeinfeld JH, Lurmann FW, Roth PM (1998)
Grid-based aerosol modeling: a tutorial.
Nucleation rate Computationally exhausting
2 4
exp 7 64.24 4.7 (6.13 1.95 ) log[ ]gnuclJ RH RH H SO
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
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Absorption Phenomena
Henry Law
• Valid for infinite dilutions (almost pure solutions)
• Henry Constants are affected by the presence of hydrogen ions
Solubility Coefficients
• Values influenced by the liquid phase composition
• Can be used even for more concentrated solutions
1t tH nG L gas nLL
ngas H L
k N V K N
K k V
2
2max
,, ,
H O
H O Lj L j G
CC C
C
2
2
max ,H O
jj G
j jH O
C M
M sC
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
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Dissociation in Liquid Phase
Reaction Equilibrium constant
H2SO4 ↔ HSO4- + H+ 1000
HSO4- ↔ SO4
2- + H+ 0.0266
SO2 H∙ 2O ↔ HSO3- + H+ 2.4554 10∙ -2
HSO3- ↔ SO3
2- + H+ 3.8944 10∙ -8
HNO3 ↔ H+ + NO3- 7.1596 10∙ -1
HNO2 ↔ NO2- + H+ 7.9538 10∙ -4
NH3 H∙ 2O ↔ NH4+ + OH- 3.8502 10∙ -6
H2O ↔ OH- + H+ 10-14
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
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Dissociation in Liquid Phase[SO2]in =[SO2]+ [SO3
2-] + [HSO3-]
[NH3 H∙ 2O]in = [NH3 H∙ 2O] + [NH4+]
[H2SO4]in = [H2SO4] + [HSO4-] + [SO4
2-]
[HNO3]in = [HNO3] + [NO3-]
[HNO2]in = [HNO2] + [NO2-]
[H2O]i = [H2O] + [OH-]
+ -
a
[H ] [A ]K =
[HA]
[H+] + [NH4+] = [HSO3
-] + 2 [SO32-] + [HO-] + [HSO4
-] + 2 [SO42-] + [NO3
-] + [NO2-]
Charge Balance
Mass Balance
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
10 soluble species, 15 mass & charge balance equations => system of linear and non-linear algebraic equations
17
Liquid Phase Reactions
2 2 2 24.1 H O 2.7OH 0.6H 0.45H 0.7 H O 2.6 H 2.6 e
Radiolysis Phenomena Dose distributed between the liquid and gas phase
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
18
Gas & Liquid Kinetic System
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Reactor ConfigurationDiscontinuous Approach
Plug Flow Approach
* (1 ) (1 )
G i i L G G LN D G X rate of formation dV f N dN rate of decomposition dV f
* (1 )
GG i i
L
dND G X rate of formation rate of decomposition
f dV
* LL i i
L
dND G X rate of formation rate of decomposition
f dV
3
*
3
100
G
ii i
t
L
molecules of gasN V m
seV kg
Dkg s m
molecules moleculesG X
eV molecules
f liquid fraction
* i ii i iD G X rate of formation dt N dN rate of decomposition dtN
20
Overall Modeling
21
Model validation Chmielewski, A. G., Tyminski, B., Dobrowolski, A., Iller, E., Zimek, Z. & Licki, J. 2000. Empirical models for NOx and SO2 removal in a double stage flue gas irradiation process. Radiation Physics and Chemistry, 57, 527-530.
Experimental conditions Removal efficiencies
Experiment # Temperature (⁰C) Humidity (%) Dose (kGy) Residence time (s) [NO]initial (ppm) [SO2]initial (ppm) NH3 ratio NO (%) SO2 (%)
1 58.6 12.0 10.0 14.43 127 383 0.92 77.9 93.22 59.2 10.7 10.0 14.36 171 364 0.89 72.5 99.23 60.4 8.6 10.2 4.11 161 673 0.89 82.1 81.04 54.9 8.2 10.0 13.4 129 359 0.88 81.0 98.65 60.3 7.7 10.1 4.05 196 467 0.88 74.0 74.16 78.8 6.9 10.1 6.02 216 430 0.9 74.1 67.77 55.1 7.9 12.5 3.56 157 465 0.91 73.9 89.28 55.8 8.0 12.7 3.63 159 484 0.88 77.3 81.09 78.8 6.7 10.1 5.99 216 421 0.91 74.1 74.3
10 61.2 8.1 7.1 4.37 181 427 0.87 74.6 84.811 62.3 7.8 5.1 4.41 186 515 0.91 65.6 85.412 59.8 7.8 2.8 4.22 182 510 0.87 47.3 89.013 59.1 9.0 8.0 4.03 146 462 0.93 63.7 77.914 59.3 8.0 10.4 4.13 158 624 0.91 75.1 84.615 60.9 8.2 10.2 4.11 194 443 0.89 79.4 74.316 60.8 9.8 10.1 11.94 175 314 0.91 80.8 93.317 59.0 12.4 11.4 13.78 181 358 0.9 74.6 97.418 60.6 10.7 12.1 14.36 168 377 0.87 76.7 99.319 59.8 7.7 12.1 4.08 190 386 0.9 86.8 73.620 61.8 7.7 10.2 4.13 185 398 0.9 83.2 78.6
22
Model ValidationNO removal efficiency
Mean error PF 9.7% Mean error DC 15.5%
23
Model ValidationSO2 removal efficiency
Mean error PF 4.9% Mean error DC 5.2%
24
Validation– Discontinuous Approach
0 1 2 3 4 5 6 7 8 9 1060
70
80
90
100
Using Henry's Coefficients
ExperimentalModel
Experiment #
Rem
oval
Effi
cienc
y SO
2(%
)
0 1 2 3 4 5 6 7 8 9 1065
75
85
95
Using Solubility Coefficients
ExperimentalModel
Experiment #
Rem
oval
Effi
cienc
y SO
2(%
)
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
25
Model results – Discontinuous Approach
SO2 & NH3 profiles – Discontinuous Approach*
Experiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
SO2 model – 95.2%SO2 exp – 97.4%
26
Model results – Discontinuous Approach
Nitrogen dioxide & nitric oxide profiles – Discontinuous Approach*
Experiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
NO model – 70.2%NO exp – 74.6%
27
Model results – Discontinuous ApproachMain oxidizing species gas phase profiles
Experiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
28
Model results – Discontinuous Approach
Nitric & nitrous acid gas phase profilesExperiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
29
Model results – Discontinuous Approach
Ammonia nitrate and sulfate profiles Experiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
30
Model results – Discontinuous Approach
Nitrous oxide & Dinitrogen pentoxide gas phase profilesExperiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
31
Model results – Discontinuous Approach
Main sulfur containing compounds’ gas phase profiles
Experiment #17
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
32
Model results – Discontinuous Approach
Experiment #17 Nucleation Rate
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
33
Model results – Discontinuous Approach
Experiment #17 Liquid phase profiles for the bisulfate & sulfate anions
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
34
Model results – Discontinuous Approach
Experiment #17
Liquid phase profiles for the nitric oxide & sulphur dioxide
*Gogulancea, V. & Lavric, V. 2014. A Mathematical Modeling Study for the Flue Gas Removal of SO2 and NOx Using High Energy Electron Beams. Plasma Chemistry and Plasma Processing. DOI: 10.1007/s11090-014-9579-4
35
Sensitivity Analysis
Full three level factorial design – parameters corresponding to experiment #3
Box – Wilson central composite factorial design
Operating Parameters
Variation
Dose 8.2 – 12.2 kGy
Humidity 6.8 – 10.3 %
NO 129 – 193 ppm
Gogulancea, V. & Lavric, V. 2014. Flue gas cleaning by high energy electron beam – Modeling and sensitivity analysis. Applied Thermal Engineering, 70, 1253-1261.
36
Sensitivity Analysis
Gogulancea, V. & Lavric, V. 2014. Flue gas cleaning by high energy electron beam – Modeling and sensitivity analysis. Applied Thermal Engineering, 70, 1253-1261.
37
Sensitivity Analysis
Gogulancea, V. & Lavric, V. 2014. Flue gas cleaning by high energy electron beam – Modeling and sensitivity analysis. Applied Thermal Engineering, 70, 1253-1261.
38
Perspectives
•Fine water droplet addition
•Optimization – response surface using ANN
•Cost analysis
•Relax the hypothesis of uniform dose distribution
•Influence of axial dispersion – reactor configuration
Introduction to mathematical modeling of physical and chemical processes in the EBFGT
39
Thank you for your attention!