Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern

[EN] Adsorption kinetics are commonly modeled using pseudo-first order (PFO) and pseudo-second order (PSO) rate laws. Both models are formulated via differential equations whose coefficients are commonly treated as deterministic quantities, which are calculated from experimental data using regressio...

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Autores: Cortés, J.-C.|||0000-0002-6528-2155, Sferle, Sorina Madalina|||0000-0002-2028-1191, Navarro-Quiles, A., Santonja, F.-J
Tipo de documento: artigo
Data de publicação:2023
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositório:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglês
OAI Identifier:oai:riunet.upv.es:10251/204660
Acesso em linha:https://riunet.upv.es/handle/10251/204660
Access Level:Acceso aberto
Palavra-chave:Pseudo-first order random kinetic model
Pseudo-second order random kinetic model
Probability density function
Random variable transformation technique
Real data
Estimation parameter techniques
MATEMATICA APLICADA
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repository_id_str
spelling Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fernCortés, J.-C.|||0000-0002-6528-2155Sferle, Sorina Madalina|||0000-0002-2028-1191Navarro-Quiles, A.Santonja, F.-JPseudo-first order random kinetic modelPseudo-second order random kinetic modelProbability density functionRandom variable transformation techniqueReal dataEstimation parameter techniquesMATEMATICA APLICADA[EN] Adsorption kinetics are commonly modeled using pseudo-first order (PFO) and pseudo-second order (PSO) rate laws. Both models are formulated via differential equations whose coefficients are commonly treated as deterministic quantities, which are calculated from experimental data using regression techniques. In this paper, we propose a full randomization of both models by assuming that all the parameters of the PFO and PSO models are random variables with arbitrary densities. Then, we probabilistically solve both models by determining semi-explicit expressions of the first probability density functions of the corresponding solution stochastic processes, as well as the densities of the time until a fixed adsorbed amount of reactant has been reached for each model too. The analysis is conducted under very general assumptions and is based on extensive application of the so-called Random Variable Transformation (RVT) technique. Finally, we apply all the aforementioned theoretical findings to model the adsorption of cadmium ions onto tree fern, using real data. We compare the results obtained by the randomized PFO and PSO models, using a Bayesian and a randomized version of the least mean square method to assign reasonable densities to model parameters. After comparing the results, the PSO model is selected, and, we then show how the RVT technique can be applied to obtain further key information, such as the second probability density function, of the solution and the covariance function.This work has been supported by the grant PID2020-115270GB- I00 granted by MCIN/AEI/10.13039/501100011033 and the grant PRE2021-101090, granted by MCIN/AEI/10.13039/501100011033 and by FSE+. We thank the two anonymous reviewers for their comments that have helped us to improve the paper.ElsevierFacultad de Administración y Dirección de EmpresasDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarEuropean Social FundAGENCIA ESTATAL DE INVESTIGACIONUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-09-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/204660reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-115270GB-I00 ECUACIONES DIFERENCIALES ALEATORIAS. CUANTIFICACION DE LA INCERTIDUMBRE Y APLICACIONESEuropean Science Foundation https://doi.org/10.13039/501100000782 PRE2021-101090open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2046602026-06-13T07:49:27Z
dc.title.none.fl_str_mv Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
title Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
spellingShingle Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
Cortés, J.-C.|||0000-0002-6528-2155
Pseudo-first order random kinetic model
Pseudo-second order random kinetic model
Probability density function
Random variable transformation technique
Real data
Estimation parameter techniques
MATEMATICA APLICADA
title_short Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
title_full Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
title_fullStr Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
title_full_unstemmed Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
title_sort Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern
dc.creator.none.fl_str_mv Cortés, J.-C.|||0000-0002-6528-2155
Sferle, Sorina Madalina|||0000-0002-2028-1191
Navarro-Quiles, A.
Santonja, F.-J
author Cortés, J.-C.|||0000-0002-6528-2155
author_facet Cortés, J.-C.|||0000-0002-6528-2155
Sferle, Sorina Madalina|||0000-0002-2028-1191
Navarro-Quiles, A.
Santonja, F.-J
author_role author
author2 Sferle, Sorina Madalina|||0000-0002-2028-1191
Navarro-Quiles, A.
Santonja, F.-J
author2_role author
author
author
dc.contributor.none.fl_str_mv Facultad de Administración y Dirección de Empresas
Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
European Social Fund
AGENCIA ESTATAL DE INVESTIGACION
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Pseudo-first order random kinetic model
Pseudo-second order random kinetic model
Probability density function
Random variable transformation technique
Real data
Estimation parameter techniques
MATEMATICA APLICADA
topic Pseudo-first order random kinetic model
Pseudo-second order random kinetic model
Probability density function
Random variable transformation technique
Real data
Estimation parameter techniques
MATEMATICA APLICADA
description [EN] Adsorption kinetics are commonly modeled using pseudo-first order (PFO) and pseudo-second order (PSO) rate laws. Both models are formulated via differential equations whose coefficients are commonly treated as deterministic quantities, which are calculated from experimental data using regression techniques. In this paper, we propose a full randomization of both models by assuming that all the parameters of the PFO and PSO models are random variables with arbitrary densities. Then, we probabilistically solve both models by determining semi-explicit expressions of the first probability density functions of the corresponding solution stochastic processes, as well as the densities of the time until a fixed adsorbed amount of reactant has been reached for each model too. The analysis is conducted under very general assumptions and is based on extensive application of the so-called Random Variable Transformation (RVT) technique. Finally, we apply all the aforementioned theoretical findings to model the adsorption of cadmium ions onto tree fern, using real data. We compare the results obtained by the randomized PFO and PSO models, using a Bayesian and a randomized version of the least mean square method to assign reasonable densities to model parameters. After comparing the results, the PSO model is selected, and, we then show how the RVT technique can be applied to obtain further key information, such as the second probability density function, of the solution and the covariance function.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-09-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/204660
url https://riunet.upv.es/handle/10251/204660
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-115270GB-I00 ECUACIONES DIFERENCIALES ALEATORIAS. CUANTIFICACION DE LA INCERTIDUMBRE Y APLICACIONES
European Science Foundation https://doi.org/10.13039/501100000782 PRE2021-101090
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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