{"id":"https://openalex.org/W7203464458","doi":"https://doi.org/10.3390/c12030065","title":"Mathematical Modeling of Biochar Pore Descriptors from Pyrolysis Temperature: Semi-Empirical Correlations for BET Surface Area, Total Pore Volume, and Mean Pore Diameter of Lignocellulosic Feedstocks","display_name":"Mathematical Modeling of Biochar Pore Descriptors from Pyrolysis Temperature: Semi-Empirical Correlations for BET Surface Area, Total Pore Volume, and Mean Pore Diameter of Lignocellulosic Feedstocks","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7203464458","doi":"https://doi.org/10.3390/c12030065"},"language":"en","primary_location":{"id":"doi:10.3390/c12030065","doi":"https://doi.org/10.3390/c12030065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/c12030065","pdf_url":null,"source":{"id":"https://openalex.org/S4210233808","display_name":"C \u2013 Journal of Carbon Research","issn_l":"2311-5629","issn":["2311-5629"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"C","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/c12030065","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045955492","display_name":"Jes\u00fas David Rhenals Julio","orcid":"https://orcid.org/0000-0002-8975-8584","observed_orcids":["https://orcid.org/0000-0002-8975-8584"]},"institutions":[{"id":"https://openalex.org/I142879360","display_name":"Universidad del Norte","ror":"https://ror.org/031e6xm45","country_code":"CO","type":"education","lineage":["https://openalex.org/I142879360"]},{"id":"https://openalex.org/I324290372","display_name":"University of C\u00f3rdoba","ror":"https://ror.org/04nmbd607","country_code":"CO","type":"education","lineage":["https://openalex.org/I324290372"]}],"countries":["CO"],"is_corresponding":true,"raw_author_name":"Jes\u00fas D. Rhenals-Julio","raw_affiliation_strings":["Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia","Department of Mechanical Engineering, Universidad del Norte, Km. 5 V\u00eda Puerto Colombia, Barranquilla 081007, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-8975-8584","affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia","institution_ids":["https://openalex.org/I324290372"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Universidad del Norte, Km. 5 V\u00eda Puerto Colombia, Barranquilla 081007, Colombia","institution_ids":["https://openalex.org/I142879360"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044508965","display_name":"Jorge Mario Mendoza Fandi\u00f1o","orcid":"https://orcid.org/0000-0001-5349-9958","observed_orcids":["https://orcid.org/0000-0001-5349-9958"]},"institutions":[{"id":"https://openalex.org/I324290372","display_name":"University of C\u00f3rdoba","ror":"https://ror.org/04nmbd607","country_code":"CO","type":"education","lineage":["https://openalex.org/I324290372"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Jorge M. Mendoza","raw_affiliation_strings":["Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-5515-5814","affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia","institution_ids":["https://openalex.org/I324290372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071359111","display_name":"Andr\u00e9s Felipe Jaramillo","orcid":"https://orcid.org/0000-0002-0466-8353","observed_orcids":["https://orcid.org/0000-0002-0466-8353"]},"institutions":[{"id":"https://openalex.org/I11944219","display_name":"Universidad de La Frontera","ror":"https://ror.org/04v0snf24","country_code":"CL","type":"education","lineage":["https://openalex.org/I11944219"]},{"id":"https://openalex.org/I324290372","display_name":"University of C\u00f3rdoba","ror":"https://ror.org/04nmbd607","country_code":"CO","type":"education","lineage":["https://openalex.org/I324290372"]}],"countries":["CL","CO"],"is_corresponding":false,"raw_author_name":"Andr\u00e9s F. Jaramillo","raw_affiliation_strings":["Centro de Manejo de Residuos y Bioenerg\u00eda, BIOREN, Universidad de La Frontera, 01145 Francisco Salazar, Temuco 4780000, Chile","Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-0466-8353","affiliations":[{"raw_affiliation_string":"Centro de Manejo de Residuos y Bioenerg\u00eda, BIOREN, Universidad de La Frontera, 01145 Francisco Salazar, Temuco 4780000, Chile","institution_ids":["https://openalex.org/I11944219"]},{"raw_affiliation_string":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia","institution_ids":["https://openalex.org/I324290372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092985196","display_name":"Calixto Rhenals","orcid":"https://orcid.org/0000-0002-7674-6998","observed_orcids":["https://orcid.org/0000-0002-7674-6998"]},"institutions":[{"id":"https://openalex.org/I324290372","display_name":"University of C\u00f3rdoba","ror":"https://ror.org/04nmbd607","country_code":"CO","type":"education","lineage":["https://openalex.org/I324290372"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Calixto Jos\u00e9 Rhenals","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-7674-6998","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de C\u00f3rdoba, Cr 6 #76-103, Monter\u00eda 230002, Colombia","institution_ids":["https://openalex.org/I324290372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089535968","display_name":"Antonio Bula","orcid":"https://orcid.org/0000-0002-3816-6423","observed_orcids":["https://orcid.org/0000-0002-3816-6423"]},"institutions":[{"id":"https://openalex.org/I142879360","display_name":"Universidad del Norte","ror":"https://ror.org/031e6xm45","country_code":"CO","type":"education","lineage":["https://openalex.org/I142879360"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Antonio Bula Silvera","raw_affiliation_strings":["Department of Mechanical Engineering, Universidad del Norte, Km. 5 V\u00eda Puerto Colombia, Barranquilla 081007, Colombia"],"raw_orcid":"https://orcid.org/0000-0002-3816-6423","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Universidad del Norte, Km. 5 V\u00eda Puerto Colombia, Barranquilla 081007, Colombia","institution_ids":["https://openalex.org/I142879360"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045955492"],"corresponding_institution_ids":["https://openalex.org/I142879360","https://openalex.org/I324290372"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1930},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1930},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.56182639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"3","first_page":"65","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10088","display_name":"Thermochemical Biomass Conversion Processes","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10088","display_name":"Thermochemical Biomass Conversion Processes","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10016","display_name":"Adsorption and biosorption for pollutant removal","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10004","display_name":"Soil Carbon and Nitrogen Dynamics","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/1111","display_name":"Soil Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/biochar","display_name":"biochar","score":0.7749999761581421},{"id":"https://openalex.org/keywords/pore-structure","display_name":"pore structure","score":0.8019999861717224},{"id":"https://openalex.org/keywords/pyrolysis-temperature","display_name":"pyrolysis temperature","score":0.9710000157356262},{"id":"https://openalex.org/keywords/lignocellulosic-feedstock","display_name":"lignocellulosic feedstock","score":0.9629999995231628},{"id":"https://openalex.org/keywords/bet-surface-area","display_name":"BET surface area","score":0.9350000023841858},{"id":"https://openalex.org/keywords/pore-volume","display_name":"pore volume","score":0.9520000219345093},{"id":"https://openalex.org/keywords/mean-pore-diameter","display_name":"mean pore diameter","score":0.9980000257492065},{"id":"https://openalex.org/keywords/arrhenius-correlation","display_name":"Arrhenius correlation","score":0.8080000281333923},{"id":"https://openalex.org/keywords/power-law-correlations","display_name":"power-law correlations","score":0.949999988079071},{"id":"https://openalex.org/keywords/semi-empirical-correlation","display_name":"semi-empirical correlation","score":0.7910000085830688},{"id":"https://openalex.org/keywords/feedstock-effects","display_name":"feedstock effects","score":0.699999988079071},{"id":"https://openalex.org/keywords/cross-validation","display_name":"cross-validation","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.7551000118255615},{"id":"https://openalex.org/C206139338","wikidata":"https://www.wikidata.org/wiki/Q192355","display_name":"Raw material","level":2,"score":0.6848000288009644},{"id":"https://openalex.org/C36759035","wikidata":"https://www.wikidata.org/wiki/Q176848","display_name":"Pyrolysis","level":2,"score":0.6759999990463257},{"id":"https://openalex.org/C56085101","wikidata":"https://www.wikidata.org/wiki/Q905495","display_name":"Biochar","level":3,"score":0.6191999912261963},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5091999769210815},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.5060999989509583},{"id":"https://openalex.org/C86183883","wikidata":"https://www.wikidata.org/wiki/Q507505","display_name":"Arrhenius equation","level":3,"score":0.4943999946117401},{"id":"https://openalex.org/C115540264","wikidata":"https://www.wikidata.org/wiki/Q2945560","display_name":"Biomass (ecology)","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.4417000114917755},{"id":"https://openalex.org/C2983524802","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic model","level":3,"score":0.3982999920845032},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.3862999975681305},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3677999973297119},{"id":"https://openalex.org/C27923307","wikidata":"https://www.wikidata.org/wiki/Q795838","display_name":"BET theory","level":3,"score":0.3668000102043152},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C55037315","wikidata":"https://www.wikidata.org/wiki/Q5421151","display_name":"Experimental data","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C21880701","wikidata":"https://www.wikidata.org/wiki/Q2144042","display_name":"Process engineering","level":1,"score":0.3174999952316284},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C169258074","wikidata":"https://www.wikidata.org/wiki/Q245748","display_name":"Random forest","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C199289684","wikidata":"https://www.wikidata.org/wiki/Q83353","display_name":"Mineralogy","level":1,"score":0.2912999987602234},{"id":"https://openalex.org/C132964779","wikidata":"https://www.wikidata.org/wiki/Q2110223","display_name":"Raw data","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C2778234585","wikidata":"https://www.wikidata.org/wiki/Q508355","display_name":"Lignocellulosic biomass","level":3,"score":0.27790001034736633},{"id":"https://openalex.org/C150077022","wikidata":"https://www.wikidata.org/wiki/Q3136137","display_name":"Response surface methodology","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C128990827","wikidata":"https://www.wikidata.org/wiki/Q192830","display_name":"Coefficient of determination","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C150581940","wikidata":"https://www.wikidata.org/wiki/Q622205","display_name":"Specific surface area","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C528095902","wikidata":"https://www.wikidata.org/wiki/Q2283886","display_name":"Pulp and paper industry","level":1,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/c12030065","doi":"https://doi.org/10.3390/c12030065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/c12030065","pdf_url":null,"source":{"id":"https://openalex.org/S4210233808","display_name":"C \u2013 Journal of Carbon Research","issn_l":"2311-5629","issn":["2311-5629"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"C","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2b8ede64dc4a4615914d82334b522803","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/2b8ede64dc4a4615914d82334b522803","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"C, Vol 12, Iss 3, p 65 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/c12030065","doi":"https://doi.org/10.3390/c12030065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/c12030065","pdf_url":null,"source":{"id":"https://openalex.org/S4210233808","display_name":"C \u2013 Journal of Carbon Research","issn_l":"2311-5629","issn":["2311-5629"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"C","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Life on land","id":"https://metadata.un.org/sdg/15","score":0.5169370770454407}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W843007777","https://openalex.org/W1914914878","https://openalex.org/W1963614168","https://openalex.org/W1975849292","https://openalex.org/W1992469412","https://openalex.org/W1995945562","https://openalex.org/W2011254969","https://openalex.org/W2016210396","https://openalex.org/W2050695214","https://openalex.org/W2070779353","https://openalex.org/W2097457893","https://openalex.org/W2130881995","https://openalex.org/W2137737658","https://openalex.org/W2312199777","https://openalex.org/W2560399683","https://openalex.org/W2763682599","https://openalex.org/W2939177051","https://openalex.org/W3030765964","https://openalex.org/W3034115121","https://openalex.org/W3114007253","https://openalex.org/W3134724538","https://openalex.org/W4214824118","https://openalex.org/W4309573079","https://openalex.org/W4311401295"],"related_works":[],"abstract_inverted_index":{"Predicting":[0],"the":[1,103,134],"pore":[2],"structure":[3],"of":[4],"lignocellulosic":[5],"biochar":[6],"from":[7,41,90],"pyrolysis":[8,26],"conditions":[9],"without":[10],"exhaustive":[11],"experimental":[12],"characterization":[13],"remains":[14],"an":[15],"open":[16,43],"challenge.":[17],"We":[18],"fit":[19,171],"semi-empirical":[20],"Arrhenius-type":[21],"and":[22,31,96,116,161],"power-law":[23,97],"correlations":[24,139],"linking":[25],"temperature":[27,58],"to":[28],"SBET,":[29],"VT,":[30],"d\u00afp":[32],"by":[33],"nonlinear":[34],"least":[35],"squares,":[36],"using":[37],"45":[38],"literature":[39],"records":[40],"seven":[42],"access":[44],"studies":[45],"(12":[46],"feedstocks,":[47],"300\u2013800":[48],"\u00b0C).":[49],"The":[50,94,138],"central":[51],"finding":[52],"is":[53,106],"that":[54,127,166],"feedstock":[55,136],"category,":[56],"not":[57,148,173],"alone,":[59],"dominates":[60],"variance":[61],"in":[62],"SBET:":[63],"pooled":[64],"calibration":[65,131,146],"explains":[66],"only":[67],"R2=0.199":[68],"(RMSE":[69,121],"=":[70,81,122],"183":[71],"m2":[72,83,124],"g\u22121),":[73],"whereas":[74],"feedstock-stratified":[75],"fitting":[76],"recovers":[77],"accuracy":[78],"(e.g.,":[79],"RMSE":[80],"43.6":[82],"g\u22121":[84],"for":[85,108],"grasses,":[86],"a":[87,91,157],"within-study":[88],"estimate":[89],"single":[92],"source).":[93],"Arrhenius":[95,104],"forms":[98],"are":[99,140],"statistically":[100],"indistinguishable":[101],"(\u0394AIC<2);":[102],"form":[105],"adopted":[107],"physical":[109],"interpretability.":[110],"Pooled":[111],"fits":[112],"reach":[113],"R2=0.691":[114],"(VT)":[115],"0.563":[117],"(d\u00afp).":[118],"Leave-one-study-out":[119],"cross-validation":[120],"184":[123],"g\u22121)":[125],"confirms":[126,165],"reliable":[128],"prediction":[129],"requires":[130],"data":[132],"within":[133,144],"target":[135],"category.":[137],"descriptive":[141],"tools":[142],"valid":[143],"their":[145],"envelope,":[147],"general":[149],"predictive":[150],"models.":[151],"Estimation":[152],"uses":[153],"no":[154],"machine":[155],"learning;":[156],"benchmark":[158],"against":[159],"OLS":[160],"random":[162],"forest":[163],"models":[164],"greater":[167],"flexibility":[168],"improves":[169],"in-sample":[170],"but":[172],"out-of-sample":[174],"generalization.":[175]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2026-08-15T00:00:00"}
