![سامانه مدیریت نشریات علمی دانشگاه سمنان](./data/logo.png)
تعداد نشریات | 21 |
تعداد شمارهها | 573 |
تعداد مقالات | 8,591 |
تعداد مشاهده مقاله | 66,294,039 |
تعداد دریافت فایل اصل مقاله | 6,827,801 |
Estimation of Parameters and Selection of Models Applied to Population Balance Dynamics via Approximate Bayesian Computational | ||
Journal of Heat and Mass Transfer Research | ||
دوره 9، شماره 1 - شماره پیاپی 17، مرداد 2022، صفحه 53-64 اصل مقاله (2.34 M) | ||
نوع مقاله: Full Length Research Article | ||
شناسه دیجیتال (DOI): 10.22075/jhmtr.2022.25186.1361 | ||
نویسندگان | ||
Carlos Henrique Moura1؛ Bruno Marques Viegas2؛ Maria Tavares3؛ Emanuel Macedo2؛ Diego Cardoso Estumano* 4 | ||
1Graduate Program in Chemical Engineering | ||
2Federal University of Para | ||
3University Federal of Para | ||
4University of Para | ||
تاریخ دریافت: 18 آبان 1400، تاریخ بازنگری: 29 خرداد 1401، تاریخ پذیرش: 29 خرداد 1401 | ||
چکیده | ||
Population balance models mathematically describe the particle size distribution based on modeling physical phenomena that influence the distribution, such as aggregation, growth, and breakage. Due to the wide range of mechanisms present, several models are presented in the literature since several hypotheses are considered. In the current work, the Approximate Bayesian Computational statistical technique was used to select four different models of population balance and estimate their parameters. Three strategies were applied to the drawing of parameters, evaluating the correlation between the parameters of the models. An adaptive tolerance in each population and a stopping criterion, based on Morozov's uncertainty principle, were used for the algorithm. The technique obtained reasonable estimates for the phenomenological rates of the models. The algorithm correctly selected the model used for generating measurements, and the three draw strategies demonstrated good applicability. The results obtained showed that the algorithm presented accuracy and precision in estimating the parameters and properly selected the models analyzed. | ||
کلیدواژهها | ||
Particulate systems؛ Population balance؛ Bayesian Statistics؛ Approximate Bayesian Computational | ||
مراجع | ||
[1] Naimi, L. J., Sokhansanj, S., Womac, A. R., Bi, X., Lim, C. J., Igathinathane, C., Lau, A. K., Sowlati, T., Melin, S., Emami, M. and Afzal, M., 2011. Development of a Population Balance Model to Simulate Fractionation of Ground Switchgrass. Transactions of the ASABE, 54(1), pp.219-227.
[2] Hosseini, S. and Shah, N., 2011. Modelling enzymatic hydrolysis of cellulose part I: Population balance modelling of hydrolysis by endoglucanase. Biomass and Bioenergy, 35(9), pp.3841-3848.
[3] Santos, T.C.S.S., Almeida, A.C.M., Pinheiro, D.R., Costa, C.M.L., Estumano, D.C., Ribeiro, N.F.P., Synthesis and Characterization of Colouful Aluminates Based on Nickel and Zinc, Journal of Alloys and Compounds, 2020, 815,152477.
Sajjadi, B., Raman, A., Ibrahim, S. and Shah, R., 2012. Review on gas-liquid mixing analysis in multiscale stirred vessel using CFD. Reviews in Chemical Engineering, 28(2-3).
[4] Singh, M. and Ramkrishna, D., 2013. A Comprehensive Approach to Predicting Crystal Morphology Distributions with Population Balances. Crystal Growth & Design, 13(4), pp.1397-1411.
[5] Flood, A. and Wantha, L., 2013. Population balance modeling of the solution mediated transformation of polymorphs: Limitations and future trends. Journal of Crystal Growth, 373, pp.7-12.
[6] Fernandes, R., Carlquist, M., Lundin, L., Heins, A., Dutta, A., Sørensen, S., Jensen, A., Nopens, I., Lantz, A. and Gernaey, K., 2012. Cell mass and cell cycle dynamics of an asynchronous budding yeast population: Experimental observations, flow cytometry data analysis, and multi-scale modeling. Biotechnology and Bioengineering, 110(3), pp.812-826.
[7] Ramkrishna, D., 2000. Population Balances. Burlington: Elsevier.
[8] Pinar, Z., Dutta, A., Bény, G. and Öziş, T., 2014. Analytical solution of population balance equation involving aggregation and breakage in terms of auxiliary equation method. Pramana, 84(1), pp.9-21.
[9] Dutta, A., Pınar, Z., Constales, D. and Öziş, T., 2018. Population Balances Involving Aggregation and Breakage Through Homotopy Approaches. International Journal of Chemical Reactor Engineering, 16(6).
[10] Randolph, A. and Larson, M., 1988. Theory of particulate processes. New York: Academic Press.
[11] Cryer, S., 1999. Modeling agglomeration processes in fluid-bed granulation. AIChE Journal, 45(10), pp.2069-2078.
[12] Rigopoulos, S. and Jones, A., 2003. Finite-element scheme for solution of the dynamic population balance equation. AIChE Journal, 49(5), pp.1127-1139.
[13] Hede, P.D., 2006. Modelling Batch Systems Using Population Balances. Bookboon, London, UK.
[14] Kumar, J., Peglow, M., Warnecke, G. and Heinrich, S., 2008. An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation. Powder Technology, 182(1), pp.81-104.
[15] Shiea, M., Buffo, A., Vanni, M. and Marchisio, D., 2020. Numerical Methods for the Solution of Population Balance Equations Coupled with Computational Fluid Dynamics. Annual Review of Chemical and Biomolecular Engineering, 11(1), pp.339-366.
[16] Rigopoulos, S., 2010. Population balance modelling of polydispersed particles in reactive flows. Progress in Energy and Combustion Science, 36(4), pp.412-443.
[17] Marchisio, D. and Fox, R., 2005. Solution of population balance equations using the direct quadrature method of moments. Journal of Aerosol Science, 36(1), pp.43-73.
[18] Kiparissides, C., Krallis, A., Meimaroglou, D., Pladis, P. and Baltsas, A., 2010. From Molecular to Plant-Scale Modeling of Polymerization Processes: A Digital High-Pressure Low-Density Polyethylene Production Paradigm. Chemical Engineering & Technology, 33(11), pp.1754-1766.
[19] Omar, H. and Rohani, S., 2017. Crystal Population Balance Formulation and Solution Methods: A Review. Crystal Growth & Design, 17(7), pp.4028-4041.
[20] Naveira-Cotta, C., Cotta, R. and Orlande, H., 2010. Inverse analysis of forced convection in micro-channels with slip flow via integral transforms and Bayesian inference. International Journal of Thermal Sciences, 49(6), pp.879-888.
[21] Naveira-Cotta, C., Cotta, R. and Orlande, H., 2011. Inverse analysis with integral transformed temperature fields: Identification of thermophysical properties in heterogeneous media. International Journal of Heat and Mass Transfer, 54(7-8), pp.1506-1519.
[22] Moreira, P., van Genuchten, M., Orlande, H. and Cotta, R., 2016. Bayesian estimation of the hydraulic and solute transport properties of a small-scale unsaturated soil column. Journal of Hydrology and Hydromechanics, 64(1), pp.30-44.
[23] Costa, J. and Naveira-Cotta, C., 2019. Estimation of kinetic coefficients in micro-reactors for biodiesel synthesis: Bayesian inference with reduced mass transfer model. Chemical Engineering Research and Design, 141, pp.550-565.
[24] Knupp, D., Naveira-Cotta, C., Ayres, J., Orlande, H. and Cotta, R., 2012. Space-variable thermophysical properties identification in nanocomposites via integral transforms, Bayesian inference and infrared thermography. Inverse Problems in Science and Engineering, 20(5), pp.609-637.
[25] Brock, J., Derjaguin, B., Drake, R., Hidy, G. and Yalamov, Y., 1971. Topics in current aerosol research. Oxford, New York: Pergamon Press.
[26] Ramabhadran, T., Peterson, T. and Seinfeld, J., 1976. Dynamics of aerosol coagulation and condensation. AIChE Journal, 22(5), pp.840-851.
[27] Gelbard, F. and Seinfeld, J., 1978. Numerical solution of the dynamic equation for particulate systems. Journal of Computational Physics, 28(3), pp.357-375.
[28] Peterson, T., Gelbard, F. and Seinfeld, J., 1978. Dynamics of source-reinforced, coagulating, and condensing aerosols. Journal of Colloid and Interface Science, 63(3), pp.426-445.
[29] Smoluchowski, M.V., 1916. Drei Vortrage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen. Zeitschrift für Physik, 17, pp. 557-585.
[30] Ilievski, D., 2001. Development and application of a constant supersaturation, semi-batch crystalliser for investigating gibbsite agglomeration. Journal of Crystal Growth, 233(4), pp.846-862.
[31] Bekker, A. and Livk, I., 2011. Agglomeration Process Modeling Based on a PDE Approximation of the Safronov Agglomeration Equation. Industrial & Engineering Chemistry Research, 50(6), pp.3464-3474.
[32] Barrasso, D., El Hagrasy, A., Litster, J. and Ramachandran, R., 2015. Multi-dimensional population balance model development and validation for a twin screw granulation process. Powder Technology, 270, pp.612-621.
[33] Chaudhury, A., Tamrakar, A., Schöngut, M., Smrčka, D., Štěpánek, F. and Ramachandran, R., 2015. Multidimensional Population Balance Model Development and Validation of a Reactive Detergent Granulation Process. Industrial & Engineering Chemistry Research, 54(3), pp.842-857.
[34] Kapur, P. and Fuerstenau, D., 1969. Coalescence Model for Granulation. Industrial & Engineering Chemistry Process Design and Development, 8(1), pp.56-62.
[35] Scott, W., 1968. Analytic Studies of Cloud Droplet Coalescence I. Journal of the Atmospheric Sciences, 25(1), pp.54-65.
[36] Salman, A., Hounslow, M. and Seville, J., 2006. Granulation, Volume 11. Burlington: Elsevier.
[37] Golovin, A. M., 1963. The Solution of the Coagulation Equation for Raindrops. Taking Condensation into Account. Soviet Physics Doklady, 8, pp. 191-193.
[38] Hidy, G. and Brock, J., 1970. International review in aerosol physics and chemistry. Oxford; New York; Toronto: Pergamon Press.
[39] Slama, M., Shaker, M., Aly, R. and Sirwah, M., 2014. Applications of aerosol model in the reactor containment. Journal of Radiation Research and Applied Sciences, 7(4), pp.499-505.
[40] Tarantola, A., 2014. Inverse Problem Theory. Amsterdam: Elsevier Science.
[41] Orlande, H., Colaço, M. and Dulikravich, G., 2008. Approximation of the likelihood function in the Bayesian technique for the solution of inverse problems. Inverse Problems in Science and Engineering, 16(6), pp.677-692.
[42] Estumano, D.C., Hamilton, F.C., Colaço, M.J., Leiroz, A.J., Orlande, H.R., Carvalho, R.N., & Dulikravich, G.S., 2014. Bayesian estimate of mass fraction of burned fuel in internal combustion engines using pressure measurements. Engineering Optimization IV - Proceedings of the 4th International Conference on Engineering Optimization, pp. 997–1004
[43] Pasqualette, M., Estumano, D., Hamilton, F., Colaço, M., Leiroz, A., Orlande, H., Carvalho, R. and Dulikravich, G., 2016. Bayesian estimate of pre-mixed and diffusive rate of heat release phases in marine diesel engines. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(5), pp.1835-1844.
[44] Moura, C.H.R., Viegas, B.M., Tavares, M.R.M., Macêdo, E.N., Estumano D.C., Quaresma J.N.N.,2021. Parameter estimation in population balance through Bayesian technique Markov Chain Monte Carlo, J. Appl. Comput. Mech., 7(2), pp. 890– 901.
[45] Nunes, K., Dávila, I., Amador, I., Estumano, D. and Féris, L., 2021. Evaluation of zinc adsorption through batch and continuous scale applying Bayesian technique for estimate parameters and select model. Journal of Environmental Science and Health, Part A, 56(11), pp.1228-1242.
[46] Oliveira, R., Nunes, K., Jurado, I., Amador, I., Estumano, D. and Féris, L., 2020. Cr (VI) adsorption in batch and continuous scale: A mathematical and experimental approach for operational parameters prediction. Environmental Technology & Innovation, 20, p.101092.
[47] Pritchard, J., Seielstad, M., Perez-Lezaun, A. and Feldman, M., 1999. Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Molecular Biology and Evolution, 16(12), pp.1791-1798.
[48] Marjoram, P., Molitor, J., Plagnol, V. and Tavaré, S., 2003. Markov chain Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences, 100(26), pp.15324-15328.
[49] Sisson, S., Fan, Y. and Tanaka, M., 2007. Sequential Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences, 104(6), pp.1760-1765.
[50] Toni, T., Welch, D., Strelkowa, N., Ipsen, A. and Stumpf, M., 2008. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of The Royal Society Interface, 6(31), pp.187-202.
[51] Beaumont, M., Cornuet, J., Marin, J. and Robert, C., 2009. Adaptive approximate Bayesian computation. Biometrika, 96(4), pp.983-990.
[52] Tavaré, S., Balding, D., Griffiths, R. and Donnelly, P., 1997. Inferring Coalescence Times From, DNA Sequence Data. Genetics, 145(2), pp.505-518.
[53] Beaumont, M., Zhang, W. and Balding, D., 2002. Approximate Bayesian Computation in Population Genetics. Genetics, 162(4), pp.2025-2035.
[54] Lenormand, M., Jabot, F. and Deffuant, G., 2013. Adaptive approximate Bayesian computation for complex models. Computational Statistics, 28(6), pp.2777-2796.
[55] Amador, I.C.B., Nunes, K.G.P., De Franco, M.A.E, Viegas, B.M., Macêdo, E.N., Féris, L.A., Estumano, D.C., 2022. Application of Approximate Bayesian Computational Technique to Characterize the Breakthrough of Paracetamol Adsorption in Fixed Bed Column. International Communication in Heat and Mass Transfer 132, pp.105917.
[56] Toni, T. and Stumpf, M., 2009. Simulation-based model selection for dynamical systems in systems and population biology. Bioinformatics, 26(1), pp.104-110.
[57] Toni, T., Stumpf, M., 2009. Tutorial on ABC rejection and ABC SMC for parameter estimation and model selection.
[58] Morozov, V.A., 1966. On the solution of functional equations by the method of regularization. Soviet Mathematics Doklady, 7, pp. 414-417
[59] Toni, T., 2010. Approximate Bayesian computation for parameter inference and model selection in systems biology. Imperial College London (University of London).
[60] Mukaka, M.M., 2012. Statistics corner: A guide to appropriate use of correlation coefficient in medical research. Malawi Medical Journal, 24, pp. 69-71.
[61] Ilievski, D. and White, E., 1994. Agglomeration during precipitation: agglomeration mechanism identification for Al(OH)3 crystals in stirred caustic aluminate solutions. Chemical Engineering Science, 49(19), pp.3227-3239. | ||
آمار تعداد مشاهده مقاله: 338 تعداد دریافت فایل اصل مقاله: 246 |