{"title":"Numerical analysis of equilibrium control in various isothermal adsorption modes: criteria for effective equilibrium determination","authors":"Chenghao Liu, Qingquan Liu, Biao Lv, Peizhuang Han, Yuanping Cheng, Liang Wang","doi":"10.1007/s10450-024-00586-0","DOIUrl":null,"url":null,"abstract":"<div><p>Adsorption is the process of enriching or depleting components at the interface of phases, and isothermal adsorption experiments are key to studying the adsorption capacity of coal-rock porous media. These experiments reveal that coal-rock samples require significant time to reach adsorption equilibrium, often lasting several tens of days, and the efficiency of various adsorption modes remains unclear. This paper introduces a mathematical model for gas isothermal adsorption at constant volume and varying pressure. It establishes numerical models based on three common adsorption modes and validates them against experimental results. Methane is initially adsorbed on the coal surface until uniform pressure is reached, after which it gradually penetrates the coal. Achieving uniform adsorption can take over 1000 h. By comparison, the time required for different adsorption modes to reach equilibrium for gas in coal under certain conditions was determined as follows: keeping the connecting valve open reduces time by 41.47% compared to keeping it closed at the same initial pressure, while closing the valve at the same equilibrium pressure shortens the time by 41.56% compared to keeping it open, and by 58.84% compared to constant pressure adsorption. Additionally, the paper discusses an equilibrium determination method based on pressure accuracy (Δ<i>p</i>) and determination duration (Δ<i>t</i>), emphasizing the need to avoid lower accuracy equipment and shorter durations in long adsorption processes. This research aids in selecting optimal experimental methods for time-consuming isothermal adsorption experiments and establishes criteria for determining adsorption equilibrium.</p></div>","PeriodicalId":458,"journal":{"name":"Adsorption","volume":"31 2","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Adsorption","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10450-024-00586-0","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Adsorption is the process of enriching or depleting components at the interface of phases, and isothermal adsorption experiments are key to studying the adsorption capacity of coal-rock porous media. These experiments reveal that coal-rock samples require significant time to reach adsorption equilibrium, often lasting several tens of days, and the efficiency of various adsorption modes remains unclear. This paper introduces a mathematical model for gas isothermal adsorption at constant volume and varying pressure. It establishes numerical models based on three common adsorption modes and validates them against experimental results. Methane is initially adsorbed on the coal surface until uniform pressure is reached, after which it gradually penetrates the coal. Achieving uniform adsorption can take over 1000 h. By comparison, the time required for different adsorption modes to reach equilibrium for gas in coal under certain conditions was determined as follows: keeping the connecting valve open reduces time by 41.47% compared to keeping it closed at the same initial pressure, while closing the valve at the same equilibrium pressure shortens the time by 41.56% compared to keeping it open, and by 58.84% compared to constant pressure adsorption. Additionally, the paper discusses an equilibrium determination method based on pressure accuracy (Δp) and determination duration (Δt), emphasizing the need to avoid lower accuracy equipment and shorter durations in long adsorption processes. This research aids in selecting optimal experimental methods for time-consuming isothermal adsorption experiments and establishes criteria for determining adsorption equilibrium.
期刊介绍：
The journal Adsorption provides authoritative information on adsorption and allied fields to scientists, engineers, and technologists throughout the world. The information takes the form of peer-reviewed articles, R&D notes, topical review papers, tutorial papers, book reviews, meeting announcements, and news.
Coverage includes fundamental and practical aspects of adsorption: mathematics, thermodynamics, chemistry, and physics, as well as processes, applications, models engineering, and equipment design.
Among the topics are Adsorbents: new materials, new synthesis techniques, characterization of structure and properties, and applications; Equilibria: novel theories or semi-empirical models, experimental data, and new measurement methods; Kinetics: new models, experimental data, and measurement methods. Processes: chemical, biochemical, environmental, and other applications, purification or bulk separation, fixed bed or moving bed systems, simulations, experiments, and design procedures.
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