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Parameter Estimation in Mass Balance Model Applied in Fixed Bed Adsorption using the Markov Chain Monte Carlo Method | ||
| Journal of Heat and Mass Transfer Research | ||
| مقاله 11، دوره 9، شماره 2 - شماره پیاپی 18، بهمن 2022، صفحه 219-232 اصل مقاله (1.27 M) | ||
| نوع مقاله: Full Length Research Article | ||
| شناسه دیجیتال (DOI): 10.22075/jhmtr.2023.28050.1389 | ||
| نویسندگان | ||
| Rhaisa Tavares1؛ Camila Santana Dias2؛ Carlos Henrique Rodrigues Moura2؛ Emerson Cardoso Rodrigues3؛ Bruno Viegas4؛ Emanuel Macedo3؛ Diego Cardoso Estumano* 4 | ||
| 1Graduate Program in Process Engineering, Federal University of Pará, Pará, Brazil | ||
| 2Graduate Program in Natural Resource in the Amazon, Federal University of Pará, Pará, Brazil | ||
| 3Faculty of Chemical Engineering, Federal University of Pará, Pará, Brazil | ||
| 4Faculty of Biotechnology, Federal University of Pará, Pará, Brazil | ||
| تاریخ دریافت: 19 مرداد 1401، تاریخ بازنگری: 26 بهمن 1401، تاریخ پذیرش: 02 اسفند 1401 | ||
| چکیده | ||
| In this work, a mathematical model is adopted to predict the breakthrough curve in a fixed bed adsorption process, neglecting radial dispersion effects in the bed, with properties such as interstitial velocity and porosity being constant, linear adsorption kinetics and equilibrium relationship represented by the Langmuir isotherm. The resulting partial differential equation is numerically solved by the Method of Lines (MOL), while the Markov Chain Monte Carlo method is employed to estimate the model parameters, using simulated measures and a priori Gaussian probability distribution for the parameters, varying the mean and standard deviation. A convergence analysis was performed to look for numerical convergence between the number of nodes (N) used and the computational cost (CPU time) and it was observed that N = 100 obtained the lowest computational cost (less than 0.2 s). The estimated values of Peclet's number (Pe) and Langmuir's constant (KL) showed deviations of 7% and 0.01%, respectively, compared to their exact value which shows that the estimates were accurate, i.e., the parameters are close to the exact value. Also, the estimated values were within the credibility interval of 99 % established, which shows precise estimates. The information taken from these estimates has become of fundamental importance in predicting the behavior of the breakthrough curve at different points in the bed, showing that the MOL in combination with the MCMC are efficient tools in the direct and inverse analysis of models of breakthrough curves. | ||
| کلیدواژه‌ها | ||
| Adsorption؛ Breakthrough curve؛ MCMC؛ Parameter estimation؛ Convergence analysis | ||
| مراجع | ||
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[1] PEREIRA, A. M., SILVA, L. J., LARANJEIRO, C. S., MEISEL, L. M., LINO, C. M., PENA, A. Human pharmaceuticals in Portuguese rivers: The impact of water scarcity in the environmental risk. Science of the Total Environment, v. 609, p. 1182-1191, 2017.
[2] SOUZA, F. S., SILVA, V. V., JANK, L., ROSIN, C. K., HAINZENREDER, L., ARENZON, A., PIZZOLATO, T., FERIS, L.A., Determination of pharmaceutical compounds in hospital wastewater and their elimination by advanced oxidation processes. Journal of environmental science and health part a-toxic/hazardous substances & environmental Engineering, p. 1-9, 2017.
[3] SOUZA, F.S., SILVA, V.V., ROSIN, C. K., HAINZENREDER, L., ARENZON, A. FÉRIS, L.A., Comparison of different advanced oxidation processes for the removal of amoxicillin in aqueous solution. Environmental Technology, 39:5, 549-557, 2018.
[4] ZOUMPOULI, G. A., SIQUEIRA SOUZA, F., PETRIE, B., FÉRIS, L. A., KASPRZYK-HORDERN, B., WENK, J., Simultaneous ozonation of 90 organic micropollutants including illicit drugs and their metabolites in different water matrices. Environmental Science: Water Research and Technology, 6(9), 2020.
[5] DÁVILA, I. V. J., HÜBNER, J. V. M., NUNES, K. G. P., & FÉRIS, L. A., Caffeine Removal by Adsorption: Kinetics, Equilibrium Thermodynamic and Regeneration Studies. The Journal of Solid Waste Technology and Management, 47(1), 95-103, 2021. https://doi.org/10.5276/JSWTM/2021.95.
[6] ROSSET, M., SFREDDO, L. W., PEREZ-LOPEZ, O. W., & FÉRIS, L. A, Effect of concentration in the equilibrium and kinetics of adsorption of acetylsalicylic acid on ZnAl layered double hydroxide. Journal of Environmental Chemical Engineering, 8(4), 103991, 2020. https://doi.org/10.1016/j.jece.2020.103991.
[7] COSTA, L. R. D. C., FÉRIS, L. A., Use of functionalized adsorbents for tetracycline removal in wastewater: adsorption mechanism and comparison with activated carbon. Journal of Environmental Science and Health, Part A, 55(14), 1604-1614, 2020.
[8] HARO, N. K., DÁVILA, I. V. J., NUNES, K. G. P., DE FRANCO, M. A. E., MARCILIO, N. R., & FÉRIS, L. A.,Kinetic, equilibrium and thermodynamic studies of the adsorption of paracetamol in activated carbon in batch model and fixed-bed column. Applied Water Science, 11(2), 2021. https://doi.org/10.1007/s13201-020-01346-5.
[9] SANTOS, T. C.S., ALMEIDA, A. C. M., do Rosario Pinheiro, D., COSTA, C. M. L., ESTUMANO, D. C., & da Paixao Ribeiro, N. F. (2020). Synthesis and characterization of colourful aluminates based on nickel and zinc. Journal of Alloys and Compounds, 815, 152477.
[10] BARROCAS, B., NEVES, M. C., OLIVEIRA, M. C., MONTEIRO, O. C. Enhanced photocatalytic degradation of psychoactive substances using amine-modified elongated titanate nanostructures. Environmental Science: Nano, v. 5, n. 2, p. 350-361, 2018. https://doi.org/10.1039/C7EN00882A.
[11] KIM, S., CHU, K. H., AL-HAMADANI, Y. A., PARK, C. M., JANG, M., KIM, D. H., YOON, Y. Removal of contaminants of emerging concern by membranes in water and wastewater: a review. Chemical Engineering Journal, v. 335, p. 896-914, 2018. https://doi.org/10.1016/j.cej.2017.11.044.
[12] LIU, C., LI, P., TANG, X., KORSHIN, G. V. Ozonation effects on emerging micropollutants and effluent organic matter in wastewater: characterization using changes of three-dimensional HP-SEC and EEM fluorescence data. Environmental Science and Pollution Research, v. 23, n. 20, p. 20567-20579, 2016. https://doi.org/10.1007/s11356-016-7287-8.
[13] OLLER, I.; MALATO, S. Photo-Fenton applied to the removal of pharmaceutical and other pollutants of emerging concern. Current Opinion in Green and Sustainable Chemistry, p. 100458, 2021. https://doi.org/10.1016/j.cogsc.2021.100458.
[14] HU, Y.; BOYER, T. H. Removal of multiple drinking water contaminants by combined ion exchange resin in a completely mixed flow reactor. Journal of Water Supply: Research and Technology-Aqua, v. 67, n. 7, p. 659-672, 2018. https://doi.org/10.2166/aqua.2018.101.
[15] LV, Y., LIANG, Z., LI, Y., CHEN, Y., LIU, K., YANG, G., LIU, M. Efficient adsorption of diclofenac sodium in water by a novel functionalized cellulose aerogel. Environmental Research, v. 194, p. 110652, 2021.
[16] TATARCHUK, T., MYSLIN, M., LAPCHUK, I., SHYICHUK, A., MURTHY, A. P., GARGULA, R., PĘDZIWIATR, A. T. Magnesium-zinc ferrites as magnetic adsorbents for Cr (VI) and Ni (II) ions removal: cation distribution and antistructure modeling. Chemosphere, v. 270, p. 129414, 2021. https://doi.org/10.1016/j.chemosphere.2020.129414.
[17] SHARAFEE, M. S., AZHA, S. F., BADAWI, M., BONILLA-PETRICIOLET, A. Performance and interactions of diclofenac adsorption using Alginate/Carbon-based Films: Experimental investigation and statistical physics modelling. Chemical Engineering Journal, p. 131929, 2021. https://doi.org/10.1016/j.cej.2021.131929.
[18] RUTHVEN, D. M. Principles of adsorption and adsorption processes. John Wiley & Sons, 1984.
[19] TIEN, C. Introduction to adsorption: Basics, analysis, and applications. Elsevier, 2018. https://doi.org/10.1016/C2018-0-00297-2.
[20] DOTTO, G.L., MCKAY, G. Current scenario and challenges in adsorption for water treatment, Journal of Environmental Chemical Engineering, 8(4), 103988, 2020. https://doi.org/10.1016/j.jece.2020.103988.
[21] AKSU, Z., GÖNEN, F., Binary biosorption of phenol and chromium (VI) onto immobilized activated sludge in a packed bed: prediction of kinetic parameters and breakthrough curves, Separation and Purification Technology, 49(3), 205-216, 2006.
[22] PATEL, H., Fixed-bed column adsorption study: a comprehensive review, Applied Water Science, 9(3), 1-17, 2019. https://doi.org/10.1007/s13201-019-0927-7
[23] XU, Z., CAI, J. G., PAN,B.C., Mathematically modeling fixed-bed adsorption in aqueous systems, Journal of Zhejiang University SCIENCE A, 14(3), 155-176, 2013.
[24] VERA, M., JUELA, D. M., CRUZAT, C., & VANEGAS, E., Modeling and computational fluid dynamic simulation of acetaminophen adsorption using sugarcane bagasse, Journal of Environmental Chemical Engineering, 9(2), 105056, 2021.
[25] THOMAS, H. C. The kinetics of fixed-bed ion exchange. Ion Exchange, FC Nachod, ed, 29,1949.
[26] YOON, Y. H., NELSON, J. H., Application of gas adsorption kinetics I. A theoretical model for respirator cartridge service life, American Industrial Hygiene Association Journal, 45(8), 509-516, 1984.
[27] CLARK, R. M., Evaluating the cost and performance of field-scale granular activated carbon systems. Environmental science & technology, 21(6), 573-580, 1987.
[28] WOLBORSKA, A., Adsorption on activated carbon of p-nitrophenol from aqueous solution. Water research, 23(1), 85-91, 1989.
[29] DANISH, M., ANSARI, K. B., DANISH, M., KHATOON, A., RAO, R. A. K., ZAIDI, S., & AFTAB, R. A. , 2022. A comprehensive investigation of external mass transfer and intraparticle diffusion for batch and continuous adsorption of heavy metals using pore volume and surface diffusion model. Separation and Purification Technology, 292, 120996.
[30] DORADO, A. D., GAMISANS, X., VALDERRAMA, C., SOLÉ, M., LAO, C., Cr (III) removal from aqueous solutions: a straightforward model approaching of the adsorption in a fixed-bed column. Journal of Environmental Science and Health, Part A, 49(2), 179-186, 2014.
[31] SCHEUFELE, F.B., A.N. MÓDENES,C.E. BORBA, RIBEIRO, C. ESPINOZA-QUIÑONES, F.R. BERGAMASCO, R. N. PEREIRA, C. Monolayer–multilayer adsorption phenomenological model: kinetics, equilibrium and thermodynamics, Chem. Eng. J., 284,1328–1341, 2016.
[32] JARIA, G., CALISTO, V., SILVA, C.P., GIL, M.V., OTERO, M., ESTEVES, V.I., Fixed-bed performance of a waste-derived granular activated carbon for the removal of micropollutants from municipal wastewater, Sci. Total Environ, 683, 699-708., 2019. https://doi.org/10.1016/ j.scitotenv.2019.05.198. [33] LI, H., HE, J., CHEN, K., SHI, Z., LI, M., GUO, P., WU, L., Dynamic adsorption of sulfamethoxazole from aqueous solution by lignite activated coke, Materials 13, 1785, 2020. https://doi.org/ 10.3390/ma13071785. [34] JUELA, D., VERA, M., CRUZAT, C., ALVAREZ, X., VANEGAS, E., Mathematical modeling and numerical simulation of sulfamethoxazole adsorption onto sugarcane bagasse in a fixed-bed column. Chemosphere, 280, 130687, 2021. https://doi.org/10.1016/j.chemosphere.2021.130687.
[35] YAMAMOTO, Y., YAJIMA, T., & KAWAJIRI, Y., Uncertainty Quantification for Chromatography Model Parameters by Bayesian Inference using Sequential Monte Carlo Method, Chemical Engineering Research and Design, 2021.
[36] DAS, L., SENGUPTA, S., DAS, P., BHOWAL, A., BHATTACHARJEE, C. Experimental and Numerical modeling on dye adsorption using pyrolyzed mesoporous biochar in Batch and fixed-bed column reactor: Isotherm, Thermodynamics, Mass transfer, Kinetic analysis. Surfaces and Interfaces, v. 23, p. 100985.
[37] IHEANACHO, O. C., NWABANNE, J. T., OBI, C. C., ONU, C. E. Packed bed column adsorption of phenol onto corn cob activated carbon: linear and nonlinear kinetics modeling. South African Journal of Chemical Engineering, v. 36, p. 80-93, 2021.
[38] MÓDENES, A. N., BAZARIN, G., BORBA, C. E., LOCATELLI, P. P. P., BORSATO, F. P., PAGNO, V., SCHEUFELE, F. B. Tetracycline adsorption by tilapia fish bone-based biochar: Mass transfer assessment and fixed-bed data prediction by hybrid statistical-phenomenological modeling. Journal of Cleaner Production, v. 279, p. 123775, 2021. https://doi.org/10.1016/j.jclepro.2020.123775.
[39] FEIZI, F., SARMAH, A. K., RANGSIVEK, R. Adsorption of pharmaceuticals in a fixed-bed column using tyre-based activated carbon: Experimental investigations and numerical modelling. Journal of Hazardous Materials, v. 417, p. 126010, 2021.
[40] ÖZIŞIK, M. N., ORLANDE, H. R., COLACO, M. J., Cotta, R. M. Finite difference methods in heat transfer. CRC press, 2017. https://doi.org/10.1201/9781315121475.
[41] KAIPIO, J., SOMERSALO, E., Statistical and Computational Inverse Problems, Springer, New York, NY, 2004. https://doi.org/10.1007 /b138659. [42] MOURA, C. H.R., VIEGAS, B. M., TAVARES, M., MACEDO, E., & ESTUMANO, D. C., (2022). Estimation Of Parameters And Selection Of Models Applied To Population Balance Dynamics Via Approximate Bayesian Computational. Journal of Heat and Mass Transfer Research. 10.22075/JHMTR.2022.25186.1361.
[43] PASQUALETTE, M.A., ESTUMANO, D.C., HAMILTON, F.C. . Bayesian estimate of pre-mixed and diffusive rate of heat release phases in marine diesel engines. J Braz. Soc. Mech. Sci. Eng. 39, 1835–1844, 2017. http://dx.doi.org/10.1007/ s40430-016-0649-9. [44] VIEGAS, B. M., MAGALHÃES, E. M., ORLANDE, H. R. B., ESTUMANO, D. C., & MACÊDO, E. N. (2022). Experimental study and mathematical modelling of red mud leaching: application of Bayesian techniques. International Journal of Environmental Science and Technology, 1-14. https://doi.org/10.1007/s13762-022-04346-x
[45] 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., 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 (2022) 105917, https://doi.org/10.1016/ j.icheatmasstransfer.2022.105917. [46] 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, ENGOPT 2014, 2014, pp. 997–1004. http://dx.doi.org/10.1201/ b17488-181. [47] OLIVEIRA, R. F., NUNES, K. G. P., JURADO, I. V., AMADOR, I. C. B., ESTUMANO, D. C., & FÉRIS, L. A., Cr (VI) adsorption in batch and continuous scale: A mathematical and experimental approach for operational parameters prediction, Environmental Technology & Innovation, 20, 1092-1105, 2020. https://doi.org/10.1016/ j.eti.2020.101092. [48] MOURA C.H.R., VIEGAS B.M., TAVARES M.R.M., MACÊDO E.N., ESTUMANO D.C., QUARESMA J.N.N. Parameter estimation in population balance through Bayesian technique Markov Chain Monte Carlo, J. Appl. Comput. Mech., 7(2), 2021, 890– 901. https://doi.org/10.22055/JACM.2021.35741.2725.
[49] NUNES, K. G. P., DÁVILA, I. V. J., AMADOR, I. C. B., ESTUMANO, D. C., & FÉRIS, L. A. (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, 1-15. https://doi.org/10.1080/10934529.2021.1977059.
[50] NUNES, K. G. P., DAVILA, I. V. J., ARNOLD, D., MOURA, C. H. R., ESTUMANO, D. C., & FÉRIS, L. A. (2022). Kinetics and Thermodynamic Study of Laponite Application in Caffeine Removal by Adsorption. Environmental Processes, 9(3), 47.
[51] GELMAN A, SIMPSON D, BETANCOURT M. The Prior Can Often Only Be Understood in the Context of the Likelihood, Entropy, 19(10), 555, 2017. https://doi.org/10.3390/e19100555. | ||
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