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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

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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

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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

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Overall Modeling

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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

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Model ValidationNO removal efficiency

Mean error PF 9.7% Mean error DC 15.5%

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Model ValidationSO2 removal efficiency

Mean error PF 4.9% Mean error DC 5.2%

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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

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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%

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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%

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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.

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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.

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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

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Thank you for your attention!