{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T06:32:42Z","timestamp":1762929162229,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,29]],"date-time":"2025-03-29T00:00:00Z","timestamp":1743206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Navigator Company, Portugal"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Processes"],"abstract":"<jats:p>This paper presents a study on the ring formation phenomenon in lime kilns using simulation. The research focuses on the chemical recovery cycle integrated into the pulp production process at a pulp mill, with particular emphasis on the calcium cycle within the lime kilns. Lime kilns are critical components, as their unavailability can significantly impact the overall cost-effectiveness of the facility. The calcination of lime sludge occurs in a rotary kiln, where calcium carbonate in the lime sludge is converted into calcium oxide (lime). Under certain conditions, material can progressively accumulate, leading to ring formation and eventual kiln clogging, resulting in operational downtime. To investigate this issue, the authors developed a physics-based model using a finite-dimensional, one-dimensional approach that considers only longitudinal variation. Several approximations were made to maintain a reasonable simulation time without compromising accuracy. Simulations based on real operational data identified fluctuations in fuel flow rate and sulfur content from non-condensable gases as key contributors to ring formation. The results showed that these fluctuations caused instability in the temperature profiles of the solids and gas beds, leading to periods of cooling before the lime sludge reaches the outlet to the coolers. This cooling promotes the recarbonation of lime and, consequently, the formation of rings. The findings highlight that stabilizing fuel flow and managing sulfur content could mitigate ring formation and improve kiln efficiency. The developed model provides a valuable tool for predictive analysis and process optimization, potentially supporting the development of a digital twin to enhance real-time monitoring and operational control.<\/jats:p>","DOI":"10.3390\/pr13041022","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T01:59:36Z","timestamp":1743386376000},"page":"1022","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modeling and Simulation of a Real Lime Kiln Plant to Understand Ring Formation Phenomena"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1338-0287","authenticated-orcid":false,"given":"Rui","family":"Neves-Silva","sequence":"first","affiliation":[{"name":"School of Science and Technology and Uninova CTS, NOVA University of Lisbon, Campus de Caparica, 2829-516 Caparica, Portugal"}]},{"given":"Paulo","family":"Pina","sequence":"additional","affiliation":[{"name":"inknow solutions, 1600-312 Lisboa, Portugal"}]},{"given":"Joaquim","family":"Belfo","sequence":"additional","affiliation":[{"name":"The Navigator Company, 2901-861 Set\u00fabal, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.32964\/TJ19.7.345","article-title":"Combatting lime kiln ringing problems at the Arauco Constituci\u00f3n mill","volume":"19","author":"Keim","year":"2020","journal-title":"TAPPI J."},{"key":"ref_2","first-page":"131","article-title":"An overview of ring formation in lime kilns","volume":"74","author":"Tran","year":"1991","journal-title":"TAPPI J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"205","DOI":"10.32964\/TJ15.3.205","article-title":"Ring removal in rotary kilns used by the pulp and paper industry","volume":"15","author":"Gorog","year":"2016","journal-title":"TAPPI J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"301","DOI":"10.32964\/TJ21.6.301","article-title":"Effects of rings on flow and temperature in lime kilns","volume":"21","author":"Gareau","year":"2022","journal-title":"TAPPI J."},{"key":"ref_5","first-page":"23","article-title":"Detection and Diagnosis of Ring Formation in Rotary Lime Kilns","volume":"1","author":"Rippon","year":"2021","journal-title":"CSChE Syst. 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