Jimena B. Dima, Mariano A. Ferrari, Noemi Zaritzky
{"title":"Mathematical modeling of breakthrough curves in dynamic column adsorption: analytical solutions and validation","authors":"Jimena B. Dima, Mariano A. Ferrari, Noemi Zaritzky","doi":"10.1007/s10665-024-10375-x","DOIUrl":null,"url":null,"abstract":"<p>Water pollution is a critical global problem. The fixed- bed continuous adsorption column provides the most practical application in the industry for wastewater treatment. The mass transfer process in the column can be described using a mass balance differential equation, and a sorbate–adsorbent interaction rate equation. The objective of this work was to describe the mass transfer in an adsorption column, analyzing the differential equations of the process and their analytical solutions. A general rate equation with four parameters was proposed, adding a zero-order parameter. The general model was solved using Laplace Transform method. The model proposed was applied to describe the adsorption of hexavalent chromium on chitosan biopolymer. The theoretical solution found was satisfactory to estimate the experimental breakthrough curves, and the estimated parameters allowed to predict other curves with different operational conditions. The zero-order parameter added relates to the baseline height of the breakthrough curve. The general model proposed generalizes already known plug flow models based on a single rate equation. The present model uses the information obtained from the column and from the equilibrium batch isotherm, which constitutes a useful tool for describing the dynamic adsorption process and to make decisions on column design.</p>","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Engineering Mathematics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s10665-024-10375-x","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Water pollution is a critical global problem. The fixed- bed continuous adsorption column provides the most practical application in the industry for wastewater treatment. The mass transfer process in the column can be described using a mass balance differential equation, and a sorbate–adsorbent interaction rate equation. The objective of this work was to describe the mass transfer in an adsorption column, analyzing the differential equations of the process and their analytical solutions. A general rate equation with four parameters was proposed, adding a zero-order parameter. The general model was solved using Laplace Transform method. The model proposed was applied to describe the adsorption of hexavalent chromium on chitosan biopolymer. The theoretical solution found was satisfactory to estimate the experimental breakthrough curves, and the estimated parameters allowed to predict other curves with different operational conditions. The zero-order parameter added relates to the baseline height of the breakthrough curve. The general model proposed generalizes already known plug flow models based on a single rate equation. The present model uses the information obtained from the column and from the equilibrium batch isotherm, which constitutes a useful tool for describing the dynamic adsorption process and to make decisions on column design.
期刊介绍：
The aim of this journal is to promote the application of mathematics to problems from engineering and the applied sciences. It also aims to emphasize the intrinsic unity, through mathematics, of the fundamental problems of applied and engineering science. The scope of the journal includes the following:
• Mathematics: Ordinary and partial differential equations, Integral equations, Asymptotics, Variational and functional−analytic methods, Numerical analysis, Computational methods.
• Applied Fields: Continuum mechanics, Stability theory, Wave propagation, Diffusion, Heat and mass transfer, Free−boundary problems; Fluid mechanics: Aero− and hydrodynamics, Boundary layers, Shock waves, Fluid machinery, Fluid−structure interactions, Convection, Combustion, Acoustics, Multi−phase flows, Transition and turbulence, Creeping flow, Rheology, Porous−media flows, Ocean engineering, Atmospheric engineering, Non-Newtonian flows, Ship hydrodynamics; Solid mechanics: Elasticity, Classical mechanics, Nonlinear mechanics, Vibrations, Plates and shells, Fracture mechanics; Biomedical engineering, Geophysical engineering, Reaction−diffusion problems; and related areas.
The Journal also publishes occasional invited ''Perspectives'' articles by distinguished researchers reviewing and bringing their authoritative overview to recent developments in topics of current interest in their area of expertise. Authors wishing to suggest topics for such articles should contact the Editors-in-Chief directly.
Prospective authors are encouraged to consult recent issues of the journal in order to judge whether or not their manuscript is consistent with the style and content of published papers.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
