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NanoParticle Flow Reactor (NanoPFR): a tested model for simulating carbon nanoparticle formation in flow reactors

  • Neil A. Juan , Ali Naseri , M. Reza Kholghy and Murray J. Thomson EMAIL logo
Published/Copyright: August 31, 2022

Abstract

Flow reactors are widely used to study the formation of various nanoparticles, such as carbon black, soot, nickel, titania, and silica. Such reactors provide well-controlled conditions, making them a favored laboratory tool to investigate the details of particle formation. Here we present NanoParticle Flow Reactor (NanoPFR), a detailed model to simulate nanoparticle synthesis in flow reactors. The model predicts the agglomerate fractal-like morphology and size distribution with a 2-variable sectional population balance model coupled with gas-phase chemistry. The particle formation processes employed in the code are tested using detailed discrete element modeling simulations and then used to predict carbon black formation from ethylene pyrolysis experiments from the literature. The code is a robust flow reactor predictive tool with a strong foundation that can serve as a basis for further development, including the simulation of other nanoparticles formation.


Corresponding author: Murray J. Thomson, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, M5S 3G8, Toronto, ON, Canada, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

Abid, A. D., N. Heinz, E. D. Tolmachoff, D. J. Phares, C. S. Campbell, and H. Wang. 2008. “On Evolution of Particle Size Distribution Functions of Incipient Soot in Premixed Ethylene–Oxygen–Argon Flames.” Combustion and Flame 154 (4): 775–88.10.1016/j.combustflame.2008.06.009Search in Google Scholar

Akhtar, M. K., Y. Xiong, and S. E. Pratsinis. 1991. “Vapor Synthesis of Titania Powder by Titanium Tetrachloride Oxidation.” AIChE Journal 37 (10): 1561–70.10.1002/aic.690371013Search in Google Scholar

Appel, J., H. Bockhorn, and M. Frenklach. 2000. “Kinetic Modeling of Soot Formation with Detailed Chemistry and Physics: Laminar Premixed Flames of C2 Hydrocarbons.” Combustion and Flame 121 (1–2): 122–36.10.1016/S0010-2180(99)00135-2Search in Google Scholar

Appel, J., H. Bockhorn, and M. Wulkow. 2001. “A Detailed Numerical Study of the Evolution of Soot Particle Size Distributions in Laminar Premixed Flames.” Chemosphere 42 (5): 635–45, https://doi.org/10.1016/S0045-6535(00)00237-X.Search in Google Scholar

Araki, Y., Y. Matsukawa, Y. Saito, Y. Matsushita, H. Aoki, K. Era, and T. Aoki. 2021. “Effects of Carrier Gas on the Properties of Soot Produced by Ethylene Pyrolysis.” Fuel Processing Technology 213: 106673.10.1016/j.fuproc.2020.106673Search in Google Scholar

Balthasar, M., and M. Kraft. 2003. “A Stochastic Approach to Calculate the Particle Size Distribution Function of Soot Particles in Laminar Premixed Flames.” Combustion and Flame 133 (3): 289–98.10.1016/S0010-2180(03)00003-8Search in Google Scholar

Blanquart, G., and H. Pitsch. 2009. “Analyzing the Effects of Temperature on Soot Formation with a Joint Volume-Surface-Hydrogen Model.” Combustion and Flame 156 (8): 1614–26, https://doi.org/10.1016/j.combustflame.2009.04.010.Search in Google Scholar

Blanquart, G., P. Pepiot-Desjardins, and H. Pitsch. 2009. “Chemical Mechanism for High Temperature Combustion of Engine Relevant Fuels with Emphasis on Soot Precursors.” Combustion and Flame 156 (3): 588–607.10.1016/j.combustflame.2008.12.007Search in Google Scholar

Camacho, J., C. Liu, C. Gu, H. Lin, Z. Huang, Q. Tang, X. You, C. Saggese, Y. Li, H. Jung. 2015. “Mobility Size and Mass of Nascent Soot Particles in a Benchmark Premixed Ethylene Flame.” Combustion and Flame 162 (10): 3810–22.10.1016/j.combustflame.2015.07.018Search in Google Scholar

D’Alessio, A., A. Barone, R. Cau, A. D’Anna, and P. Minutolo. 2005. “Surface Deposition and Coagulation Efficiency of Combustion Generated Nanoparticles in the Size Range from 1 to 10 Nm.” Proceedings of the Combustion Institute 30 (2): 2595–603.10.1016/j.proci.2004.08.267Search in Google Scholar

Dewa, K., K. Ono, A. Watanabe, K. Takahashi, Y. Matsukawa, Y. Saito, Y. Matsushita, H. Aoki, K. Era, T. Aoki. 2016. “Evolution of Size Distribution and Morphology of Carbon Nanoparticles during Ethylene Pyrolysis.” Combustion and Flame 163: 115–21.10.1016/j.combustflame.2015.09.007Search in Google Scholar

Donnet, J. B. 1993. Carbon Black: Sci. and Technol. CRC Press.Search in Google Scholar

Dworkin, S. B. 2009. “Serial and distributed-memory parallel Computation of Sooting, Steady and Time-dependent, Laminar Flames Using a modified Vorticity-Velocity Formulation.” PhD. thesis, Yale University.Search in Google Scholar

Eaves, N. A., S. B. Dworkin, and M. J. Thomson. 2015. “The Importance of Reversibility in Modeling Soot Nucleation and Condensation Processes.” Proceedings of the Combustion Institute 35 (2): 1787–94.10.1016/j.proci.2014.05.036Search in Google Scholar

Eaves, N. A., S. B. Dworkin, and M. J. Thomson. 2017. “Assessing Relative Contributions of PAHs to Soot Mass by Reversible Heterogeneous Nucleation and Condensation.” Proceedings of the Combustion Institute 36 (1): 935–45, https://doi.org/10.1016/j.proci.2016.06.051.Search in Google Scholar

EPA. 2020. Integrated Science Assessment (Isa) for Particulate Matter (Final Report, 2019), Tech. Rep., U.S. Environmental Protection Agency. Also Available at: https://cfpub.epa.gov/ncea/isa/recordisplay.cfm?deid=347534.Search in Google Scholar

Eveleigh, A., N. Ladommatos, and R. Balachandran. 2015. “Gas and Particulate Matter Products Formed in a Laminar Flow Reactor: Pyrolysis of Single-Component C2 Fuels.” Energy Procedia 66: 41–4.10.1016/j.egypro.2015.02.022Search in Google Scholar

Frenklach, M., and S. J. Harris. 1987. “Aerosol Dynamics Modeling Using the Method of Moments.” Journal of Colloid and Interface Science 118 (1): 252–61.10.1016/0021-9797(87)90454-1Search in Google Scholar

Frenklach, M., and H. Wang. 1994. “Detailed Mechanism and Modeling of Soot Particle Formation.” In Soot Form in Combust., p. 165–92. Berlin, Heidelberg: Springer.10.1007/978-3-642-85167-4_10Search in Google Scholar

Frenklach, M., W. Gardiner, S. Stein, D. Clary, and T. Yuan. 1986. “Mechanism of Soot Formation in Acetylene-Oxygen Mixtures.” Combustion Science and Technology 50 (1–3): 79–115, https://doi.org/10.1080/00102208608923927.Search in Google Scholar

Frenklach, M. 2002. “Reaction Mechanism of Soot Formation in Flames.” Physical Chemistry 4 (11): 2028–37.10.1039/b110045aSearch in Google Scholar

Fuchs, N. A., R. E. Daisley, M. Fuchs, C. N. Davies, and M. E. Straumanis. 1965. “The Mechanics of Aerosols.” Physics Today 18: 73.10.1063/1.3047354Search in Google Scholar

Goudeli, E., M. L. Eggersdorfer, and S. E. Pratsinis. 2015. “Coagulation–agglomeration of Fractal-like Particles: Structure and Self-Preserving Size Distribution.” Langmuir 31 (4): 1320–7.10.1021/la504296zSearch in Google Scholar PubMed

Hou, D., C. S. Lindberg, M. Y. Manuputty, X. You, and M. Kraft. 2019. “Modelling Soot Formation in a Benchmark Ethylene Stagnation Flame with a New Detailed Population Balance Model.” Combustion and Flame 203: 56–71.10.1016/j.combustflame.2019.01.035Search in Google Scholar

Javadi, M., and M. Moghiman. 2010. “Hydrogen and Carbon Black Production from Thermal Decomposition of Sub-quality Natural Gas.” International Journal of Spray and Combustion Dynamics 2 (1): 85–101, https://doi.org/10.1260/1756-8277.2.1.85.Search in Google Scholar

Jiang, X., L. Zhang, F. Wang, Y. Liu, Q. Guo, and C. Wang. 2016. “Investigation of Carbon Black Production from Coal Tar via Chemical Looping Pyrolysis.” Energy and Fuels 30 (4): 3535–40, https://doi.org/10.1021/acs.energyfuels.5b02915.Search in Google Scholar

Juan, N. A., N. A. Eaves, and M. J. Thomson. 2022. “The Effect of Radial Diffusion on Nanoparticle Formation in Laminar Flow Reactors.” Combustion and Flame 236: 111757.10.1016/j.combustflame.2021.111757Search in Google Scholar

Kee, R. J., F. M. Rupley, and J. A. Miller. 1989. “Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-phase Chemical Kinetics.”Tech. Rep., Livermore, CA (USA): Sandia National Labs.10.2172/5681118Search in Google Scholar

Kelesidis, G. A., E. Goudeli, and S. E. Pratsinis. 2017. “Flame Synthesis of Functional Nanostructured Materials and Devices: Surface Growth and Aggregation.” Proceedings of the Combustion Institute 36 (1): 29–50.10.1016/j.proci.2016.08.078Search in Google Scholar

Kelesidis, G. A., M. R. Kholghy, J. Zuercher, J. Robertz, M. Allemann, A. Duric, and S. E. Pratsinis. 2020. “Light Scattering from Nanoparticle Agglomerates.” Powder Technology 365: 52–9.10.1016/j.powtec.2019.02.003Search in Google Scholar

Kholghy, M. R., and G. A. Kelesidis. 2020. “Free Molecular Coagulation dynamics of agglomerates at High Concentrations by a Monodisperse Model.” Journal of Aerosol Science (2020 submitted) manuscript number: JAEROSCI–D–20–00195.Search in Google Scholar

Kholghy, M. R., and G. A. Kelesidis. 2021. “Surface Growth, Coagulation and Oxidation of Soot by a Monodisperse Population Balance Model.” Combustion and Flame 227: 456–63.10.1016/j.combustflame.2021.01.010Search in Google Scholar

Kholghy, M. R., A. Veshkini, and M. J. Thomson. 2016. “The Core–Shell Internal Nanostructure of Soot–A Criterion to Model Soot Maturity.” Carbon 100: 508–36.10.1016/j.carbon.2016.01.022Search in Google Scholar

Kholghy, M. R., G. A. Kelesidis, and S. E. Pratsinis. 2018. “Reactive Polycyclic Aromatic Hydrocarbon Dimerization Drives Soot Nucleation.” Physical Chemistry Chemical Physics 20 (16): 10926–38, https://doi.org/10.1039/C7CP07803J.Search in Google Scholar

Lindstedt, R. P., and B. B. O. Waldheim. 2013. “Modeling of Soot Particle Size Distributions in Premixed Stagnation Flow Flames.” Proceedings of the Combustion Institute 34 (1): 1861–8, https://doi.org/10.1016/j.proci.2012.05.047.Search in Google Scholar

Maag, G., G. Zanganeh, and A. Steinfeld. 2009. “Solar Thermal Cracking of Methane in a Particle-Flow Reactor for the Co-production of Hydrogen and Carbon.” International Journal of Hydrogen Energy 34 (18): 7676–85.10.1016/j.ijhydene.2009.07.037Search in Google Scholar

McIlroy, A., G. McRae, V. Sick, D. L. Siebers, C. K. Westbrook, P. J. Smith, C. Taatjes, A. Trouve, A. F. Wagner, E. Rohlfing. 2006. “Basic Research Needs for Clean and Efficient Combustion of 21st Century Transportation Fuels.” Tech. Rep., Washington, D. C.: USDOE Office of Science (SC).10.2172/935428Search in Google Scholar

Mei, J., M. Wang, X. You, and C. K. Law. 2019. “Quantitative Measurement of Particle Size Distributions of Carbonaceous Nanoparticles during Ethylene Pyrolysis in a Laminar Flow Reactor.” Combustion and Flame 200: 15–22.10.1016/j.combustflame.2018.11.010Search in Google Scholar

Melchior, T., C. Perkins, P. Lichty, A. W. Weimer, and A. Steinfeld. 2009. “Solar-driven Biochar Gasification in a Particle-Flow Reactor.” Chemical Engineering and Processing: Process Intensification 48 (8): 1279–87.10.1016/j.cep.2009.05.006Search in Google Scholar

Morgan, N., M. Kraft, M. Balthasar, D. Wong, M. Frenklach, and P. Mitchell. 2007. “Numerical Simulations of Soot Aggregation in Premixed Laminar Flames.” Proceedings of the Combustion Institute 31 (1): 693–700.10.1016/j.proci.2006.08.021Search in Google Scholar

Naseri, A., and M. J. Thomson. 2019. “Development of a Numerical Model to Simulate Carbon Black Synthesis and Predict the Aggregate Structure in Flow Reactors.” Combustion and Flame 207: 314–26. doi:https://doi.org/10.1016/j.combustflame.2019.06.001.Search in Google Scholar

Naseri, A., A. Veshkini, and M. J. Thomson. 2017. “Detailed Modeling of CO2 Addition Effects on the Evolution of Soot Particle Size Distribution Functions in Premixed Laminar Ethylene Flames.” Combustion and Flame 183: 75–87.10.1016/j.combustflame.2017.04.028Search in Google Scholar

Neoh, K. G., J. B. Howard, and A. F. Sarofim. 1981. “Soot Oxidation in Flames.” In Part. Carbon, p. 261–82. Boston, MA: Springer.10.1007/978-1-4757-6137-5_9Search in Google Scholar

Norinaga, K., V. M. Janardhanan, and O. Deutschmann. 2008. “Detailed Chemical Kinetic Modeling of Pyrolysis of Ethylene, Acetylene, and Propylene at 1073–1373 K with a Plug-Flow Reactor Model.” International Journal of Chemical Kinetics 40 (4): 199–208. https://doi.org/10.1002/kin.20302.Search in Google Scholar

Ono, K., M. Yanaka, S. Tanaka, Y. Saito, H. Aoki, O. Fukuda, T. Aoki, and T. Yamaguchi. 2012. “Influence of Furnace Temperature and Residence Time on Configurations of Carbon Black.” Chemical Engineering Journal 200: 541–8.10.1016/j.cej.2012.06.061Search in Google Scholar

Ono, K., A. Watanabe, K. Dewa, Y. Matsukawa, Y. Saito, Y. Matsushita, H. Aoki, O. Fukuda, T. Aoki, and T. Yamaguchi. 2014. “Detailed Kinetic Analysis of the Impact of Nucleation Behavior and Particle Size Distribution on the Configurations of Carbon Black.” Journal of Nanoparticle Research 16 (7): 2519.10.1007/s11051-014-2519-7Search in Google Scholar

Panda, S., and S. E. Pratsinis. 1995. “Modeling the Synthesis of Aluminum Particles by Evaporation-Condensation in an Aerosol Flow Reactor.” Nanostructured Materials 5 (7–8): 755–67.10.1016/0965-9773(95)00292-MSearch in Google Scholar

Park, S. H., and S. N. Rogak. 2004. “A Novel Fixed-Sectional Model for the Formation and Growth of Aerosol Agglomerates.” Journal of Aerosol Science 35 (11): 1385–404.10.1016/j.jaerosci.2004.05.010Search in Google Scholar

Park, S. H., S. N. Rogak, W. K. Bushe, Z. Wen, and M. J. Thomson. 2004. “An Aerosol Model to Predict Size and Structure of Soot Particles.” Journal of Aerosol Science 35: S825–S826.10.1016/S0021-8502(19)30158-2Search in Google Scholar

Park, S. H., S. N. Rogak, W. K. Bushe, J. Z. Wen, and M. J. Thomson. 2005. “An Aerosol Model to Predict Size and Structure of Soot Particles.” Combustion Theory and Modelling 9 (3): 499–513.10.1080/13647830500195005Search in Google Scholar

Petzold, L. R. 1982. “Description of Dassl: a Differential/algebraic System Solver.” Tech. Rep., Livermore, CA (USA): Sandia National Labs.Search in Google Scholar

Quan, Y., Q. Liu, S. Zhang, and S. Zhang. 2018. “Comparison of the Morphology, Chemical Composition and Microstructure of Cryptocrystalline Graphite and Carbon Black.” Applied Surface Science 445: 335–41, https://doi.org/10.1016/J.APSUSC.2018.03.182.Search in Google Scholar

Ranzi, E., A. Frassoldati, R. Grana, A. Cuoci, T. Faravelli, A. Kelley, and C. Law. 2012. “Hierarchical and Comparative Kinetic Modeling of Laminar Flame Speeds of Hydrocarbon and Oxygenated Fuels.” Progress in Energy and Combustion Science 38 (4): 468–501, https://doi.org/10.1016/j.pecs.2012.03.004.Search in Google Scholar

Ruiz, M. P., R. Guzmán de Villoria, Á. Millera, M. U. Alzueta, and R. Bilbao. 2007. “Influence of Different Operation Conditions on Soot Formation from C2h2 Pyrolysis.” Industrial & Engineering Chemistry Research 46 (23): 7550–60.10.1021/ie070008iSearch in Google Scholar

Saggese, C., A. Cuoci, A. Frassoldati, S. Ferrario, J. Camacho, H. Wang, and T. Faravelli. 2016. “Probe Effects in Soot Sampling from a Burner-Stabilized Stagnation Flame.” Combustion and Flame 167: 184–97. https://doi.org/10.1016/j.combustflame.2016.02.013.Search in Google Scholar

Sanchez, N. E., A. Callejas, A. Millera, R. Bilbao, and M. U. Alzueta. 2012. “Polycyclic Aromatic Hydrocarbon (PAH) and Soot Formation in the Pyrolysis of Acetylene and Ethylene: Effect of the Reaction Temperature.” Energy and Fuels 26 (8): 4823–9.10.1021/ef300749qSearch in Google Scholar

Sediako, A. D., C. Soong, J. Y. Howe, M. R. Kholghy, and M. J. Thomson. 2017. “Real-time Observation of Soot Aggregate Oxidation in an Environmental Transmission Electron Microscope.” Proceedings of the Combustion Institute 36 (1): 841–51.10.1016/j.proci.2016.07.048Search in Google Scholar

Singh, J., M. Balthasar, M. Kraft, and W. Wagner. 2005. “Stochastic Modeling of Soot Particle Size and Age Distributions in Laminar Premixed Flames.” Proceedings of the Combustion Institute 30 (1): 1457–65, https://doi.org/10.1016/j.proci.2004.08.120.Search in Google Scholar

Singh, J., R. I. A. Patterson, M. Kraft, and H. Wang. 2006. “Numerical Simulation and Sensitivity Analysis of Detailed Soot Particle Size Distribution in Laminar Premixed Ethylene Flames.” Combustion and Flame 145 (1): 117–27, https://doi.org/10.1016/j.combustflame.2005.11.003.Search in Google Scholar

Skjøth-Rasmussen, M. S., P. Glarborg, M. Østberg, J. T. Johannessen, H. Livbjerg, A. D. Jensen, and T. S. Christensen. 2004. “Formation of Polycyclic Aromatic Hydrocarbons and Soot in Fuel-Rich Oxidation of Methane in a Laminar Flow Reactor.” Combustion and Flame 136 (1–2): 91–128, https://doi.org/10.1016/J.COMBUSTFLAME.2003.09.011.Search in Google Scholar

Smooke, M. D., C. S. McEnally, L. D. Pfefferle, R. J. Hall, and M. B. Colket. 1999. “Computational and Experimental Study of Soot Formation in a Coflow, Laminar Diffusion Flame.” Combustion and Flame 117 (1–2): 117–39.10.1016/S0010-2180(98)00096-0Search in Google Scholar

Smooke, M. D., M. B. Long, B. C. Connelly, M. B. Colket, and R. J. Hall. 2005. “Soot Formation in Laminar Diffusion Flames.” Combustion and Flame 143 (4): 613–28, https://doi.org/10.1016/j.combustflame.2005.08.028.Search in Google Scholar

S. N. Laboratories, U. S. D. of Energy, U. S. D. of Energy. Office of Scientific, T. Information. 1996. PLUG: A FORTRAN Program For the Analysis Of PLUG Flow Reactors With Gas-phase and Surface Chemistry. United States: Department of Energy.Search in Google Scholar

Veshkini, A., N. A. Eaves, S. B. Dworkin, and M. J. Thomson. 2016. “Application of Pah-Condensation Reversibility in Modeling Soot Growth in Laminar Premixed and Nonpremixed Flames.” Combustion and Flame 167: 335–52, https://doi.org/10.1016/j.combustflame.2016.02.024.Search in Google Scholar

Von, M. 1917. “Smoluchowski, versuch einer mathematischen theorie der koagulationskinetic kolloider lösunger.” Zeitschrift fuer Physikalische Chemie 92: 129–68.10.1515/zpch-1918-9209Search in Google Scholar

Wang, G. M., and C. M. Sorensen. 1999. “Diffusive Mobility of Fractal Aggregates over the Entire Knudsen Number Range.” Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 60 (3): 3036.10.1103/PhysRevE.60.3036Search in Google Scholar PubMed

Wen, J. Z., M. J. Thomson, S. H. Park, S. N. Rogak, and M. F. Lightstone. 2005. “Study of Soot Growth in a Plug Flow Reactor Using a Moving Sectional Model.” Proceedings of the Combustion Institute 30 (1): 1477–84.10.1016/j.proci.2004.08.178Search in Google Scholar

Wen, J. Z., M. J. Thomson, M. F. Lightstone, and S. N. Rogak. 2006. “Detailed Kinetic Modeling of Carbonaceous Nanoparticle Inception and Surface Growth during the Pyrolysis of C6H6 behind Shock Waves.” Energy and Fuels 20 (2): 547–59.10.1021/ef050081qSearch in Google Scholar

Zhang, Q., M. J. Thomson, H. Guo, F. Liu, and G. J. Smallwood. 2010. “Modeling of Oxidation-Driven Soot Aggregate Fragmentation in a Laminar Coflow Diffusion Flame.” Combustion Science and Technology 182 (4–6): 491–504, https://doi.org/10.1080/00102200903463050.Search in Google Scholar


Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/ijcre-2021-0258).


Received: 2021-10-18
Accepted: 2022-08-07
Published Online: 2022-08-31

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