Journal on Processing and Energy in Agriculture 26 (2022) 1 1 Biblid: 1821-4487 (2022) 26; 1; p 1 - 7 Original Scientific Paper UDK: 634.14 Originalni naučni rad DOI: 10.5937/jpea%v-36839 REVIEW MODELS OF SORPTION ISOTHERMS PREGLED MODELA SORPCIONIH IZOTERMI Vangelce MITREVSKI * , Cvetanka MITREVSKA ** , Ljupco TRAJCEVSKI * , Borce MITREVSKI *** * Faculty of Technical Sciences, Bitola, Makedonska Falanga 33, North Macedonia ** Faculty for Safety Engineering, Sveti Nikole, North Macedonia *** Center for Energy Efficiency “Bobi Turs”, Bitola, North Macedonia e-mail: vangelce.mitrevski@uklo.edu.mk ABSTRACT Numerous mathematical models for approximation of sorption data of food and agriculture materials are available in the referent scientific and engineering literature. Depending on the number of parameters included in the model for approximation of moisture sorption data, the models may be one, two, three, four, five or more parametric. Also the sorption models may be included or not the temperature as a parameter into the equation. The objectives of the presented article was a review of one hundred seventy-two sorption no temperature dependent sorption isotherm models which used to for approximation equilibrium moisture data of food materials. For statistics evaluation of those models the equilibrium moisture data of quince were used. The value on coefficient of determination the root mean squared error, the mean relative deviation and graphical evaluation of the residual randomness were the main assessment criterions for statistical evaluation of the sorption isotherms model. Based on the performed statistical analysis it was concluded that the model of Popovski&Mitrevski i.e. M161 has the best statistical performances. Key words: models of sorption isotherms, statistical evaluation, quince. REZIME Krive sorpcije i desorpcije su veoma važne pri definisanju ravnotežne vlažnosti prehra mbenih i poljoprivrednih proizvoda. Predviđanje promena ovih veličina u zavisnosti od stanja okolnog vazduha su veoma važne za procese sušenja i skladištenja. Za aproksimaciju sorpcionih podataka prehrambenih materijala u referentnoj naučnoj i inženjerskoj literaturi dostupni su brojni matematički modeli. Zavisno od broja parametara, modeli mogu biti jedno, dvo, tro, cetvoro, peto ili više parametarski. Sa druge strane, ovi modeli mogu biti zavisni ili nezavisni od temperature okolnog vazduha. U radu je prikazana statistička ocena sto sedamdeset i dva temperaturno nezavisnih sorpcionih modela koji su korišćeni za aproksimaciju ravnotežne vlažnosti dunje. Na osnovu dobijenih rezultata može se zaključiti da model Popovski & Mitrevski t.e. model sa referentnim brojem M161 ima najbolje statističke performanse. Glavni kriterijumi statističke ocene bili su koeficijent determinacije, kvadratni koren srednje kvadratne greške, srednja relativna devijacija kako i grafička prezentacija slučajnih ostataka regresione analize. Vrednosti statističkih parametara modela Popovski & Mitrevski procenjene su salaganjem sa eksperimentalnim podacima ravnotežne vlažnosti dunje sa procenjenim vrednostima dobijenim korišćenjem Quasi-Newton metodom procene koji minimizira greške sume kvadrata. Ključne reči: modeli izotermi sorpcije, statistička ocena, dunja. INTRODUCTION In the reference scientific and engineering literature in the last few years have an increasing number of articles in which was research sorption isotherm problems of food materials. These articles includes the methods for determination of sorption or desorption isotherms (Mitrevski et al., 2015; Mitrevski et al., 2018), temperature dependence of sorption isotherms (Popovski&Mitrevski, 2004), determination of heat of sorption and development of mathematical models for approximation of moisture sorption data (Mitrevski et al., 2012; Mitrevski et al., 2015a). In the previously article (Mitrevski et al., 2019, Mitrevski et al., 2020) it was concluded that in depending on the number of parameters which are included in the mathematical model for approximation of moisture sorption data, the models may be one, two, three, four, five or more parametric. The objectives of the presented article is a review of sorption isotherm models and statistical evaluation of one hundred seventy two sorption isotherm models for approximation of equilibrium moisture data. The statistically performance of those models were tested on the equilibrium moisture data of quince. From the performed statistical analyze it was concluded that the model of Popovski&Mitrevski i.e. the model M161 (Popovski&Mitrevski, 2005), has the best statistical performances. NOMENCLATURE: A, B, C, D, E - parameters a w (-) - water activity MRD (-) - mean relative deviation R 2 (-) - coefficient of determination RMSE (-) - the root mean squared error X eq (kg/kg) - equilibrium moisture content MATERIAL AND METHODS The equilibrium moisture content of quince was determined at temperatures of 15, 30, 45 and 60 o C using static gravimetric method (Mitrevski et al., 2018). Ten saturated salt solutions L i Cl, CH 3 COOK, MgCl, K 2 CO 3 , Mg(NO 3 ) 2 , NaBr, SrCl 2 , NaCl, KCl and BaCl 2 were used to give defined constant equilibrium relative humidity in the glass jars from 0.110 to 0.920 (Mitrevski et al., 2018). Three replications were made at each temperature and equilibrium relative humidity in the glass jars, using two samples per replication, and the average values of the equilibrium moisture content were calculated (Mitrevski et al., 2019).