Kinetic Analysis of Reduction Reaction of MnO from High Carbon Ferromanganese Slag using Fractional Differential Equations (FDE)

Kinetic Analysis of Reduction Reaction of MnO from High Carbon Ferromanganese Slag using Fractional Differential Equations (FDE) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Kinetic Analysis of Reduction Reaction of MnO from High Carbon Ferromanganese Slag using Fractional Differential Equations (FDE) Kim UnDok, Kim MyongJae, Ju IlChol This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5855473/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, a kinetic model for the reduction process by solid carbon of MnO in high-carbon ferromanganese slags using fractional differential equations(FDE) was developed, the relationship between fractional order, fractional rate constant and temperature was determined, and the accuracy of the fractional order model was verified. The fractional order q is 0.892, 0.808, and 0.522, at 1,450 ℃, 1,500 ℃, and 1,600 ℃respectively, and the fractional rate constant k q 1.176E-03, 2.856E-03, and 3.477E-02. A linear relationship exists between the fractional order and the temperature, and an exponential relationship exists with the fractional rate constant. Comparing the conversion factors calculated from the FDE and previous model with the experimental values, the RMSE were 0.005 and 0.029, respectively, and the r 2 0.999 and 0.980. This means the FDE model is more accurate. The apparent activation energy of the MnO reduction process calculated using the model was 181.1 kJ/mol. fractional differential equation(FDE) fractional rate constant MnO reduction kinetics conversion factor Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5855473","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":408385931,"identity":"5849e7c2-0732-444b-82ff-efb9762b1874","order_by":0,"name":"Kim UnDok","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Kim","middleName":"","lastName":"UnDok","suffix":""},{"id":408385932,"identity":"65506c6e-8ee8-43db-b460-de09c5836573","order_by":1,"name":"Kim MyongJae","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIie3PsQrCQAyA4ZSD63I4X6lUH+GKL5Qi2KXdO3QQhEzi6CLoWzhfKXSqT9ClUPAZOjhYF9dmFLx/ypAPEgCX6wfTAFi/TBlJ/2DZJOlV0WwWqkE2EUa1IrnqbM0jwdk+dUAyJcgAxuI+T8IQdzqmZU7wsN6x7eZJ9CEJyZy8EwqPuKQikUqhDI9Mh23jfStQSi4JLpgMUDQxKYkV6xfdZViDKVer21D1Y8EgAAq/o+XsT/ncRZfL5frb3p/6OSCiCsDCAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Kim","middleName":"","lastName":"MyongJae","suffix":""},{"id":408385933,"identity":"c6da48b6-0a22-494c-9bf1-ca1663846194","order_by":2,"name":"Ju IlChol","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Ju","middleName":"","lastName":"IlChol","suffix":""}],"badges":[],"createdAt":"2025-01-18 13:53:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5855473/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5855473/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":75064991,"identity":"2b594828-baa7-4d5d-9f9b-576b54fb73ca","added_by":"auto","created_at":"2025-01-30 05:29:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":505638,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5855473/v1_covered_183753b4-a405-43b4-ab47-283058f80aac.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Kinetic Analysis of Reduction Reaction of MnO from High Carbon Ferromanganese Slag using Fractional Differential Equations (FDE)","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"fractional differential equation(FDE), fractional rate constant, MnO reduction, kinetics, conversion factor","lastPublishedDoi":"10.21203/rs.3.rs-5855473/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5855473/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, a kinetic model for the reduction process by solid carbon of MnO in high-carbon ferromanganese slags using fractional differential equations(FDE) was developed, the relationship between fractional order, fractional rate constant and temperature was determined, and the accuracy of the fractional order model was verified. The fractional order \u003cem\u003eq\u003c/em\u003e is 0.892, 0.808, and 0.522, at 1,450 ℃, 1,500 ℃, and 1,600 ℃respectively, and the fractional rate constant \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eq\u003c/em\u003e\u003c/sub\u003e \u0026nbsp;1.176E-03, 2.856E-03, and 3.477E-02. A linear relationship exists between the fractional order and the temperature, and an exponential relationship exists with the fractional rate constant. Comparing the conversion factors calculated from the FDE and previous model with the experimental values, the RMSE were 0.005 and 0.029, respectively, and the \u003cem\u003er\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e 0.999 and 0.980. This means the FDE model is more accurate. The apparent activation energy of the MnO reduction process calculated using the model was 181.1 kJ/mol.\u003c/p\u003e","manuscriptTitle":"Kinetic Analysis of Reduction Reaction of MnO from High Carbon Ferromanganese Slag using Fractional Differential Equations (FDE)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-30 04:57:20","doi":"10.21203/rs.3.rs-5855473/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"70bfb4be-a137-4296-a0ce-2667f052549a","owner":[],"postedDate":"January 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-30T04:57:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-30 04:57:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5855473","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5855473","identity":"rs-5855473","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}