Modelagem da Cinética de Secagem de Sementes de Jacaranda Mimosifolia Artigo Científico

Biosystems Engineering 205 2021 234245 Research Paper Modeling drying kinetics of Jacaranda mimosifolia seeds with variable effective diffusivity via diffusion model Marcos P Felizardo a Giovanni RF Merlo b Gustavo D Maia b a Engineering Institute Várzea Grande University Campus Federal University of Mato Grosso Fernando Corrêa da Costa Av 2367 78060900 Cuiabá MT Brazil b Drying Center of Pastes Suspensions and Seeds Chemical Engineering Department Federal University of São Carlos Rod Washington Luiz Km 235 PO Box 676 13565905 São Carlos SP Brazil Jacaranda mimosifolia D Don a tree widely used for afforestation has been studied for different applications due to the composition of its extracts The drying kinetics of J mimosifolia seeds in a thin layer and its process were modelled using an analytical solution of diffusion model first considering the parameter Effective Moisture Diffusivity EMD to be constant For variable EMD a sequential and partial adjustment technique using a classic analytical solution was proposed Thin layer drying kinetics were conducted at temperatures of 40 C and 50 C When EMD was treated as a constant parameter adjustments showed values of R2 0976 and χ2 160 103 but when it was treated as a variable parameter values of R2 0998 and χ2 149 104 were found showing it to be more accurate The proposed sequential fitting method showed good results improving the understanding of diffusive mass transfer mechanisms The technique show promise for applications in process control and product quality in addition to dryer sizing and design 2021 IAgrE Published by Elsevier Ltd All rights reserved 1 Introduction Jacaranda mimosifolia D Don is a species of the family Bignoniaceae native to Argentina Bolivia and Southern Brazil popularly known as Blue Jacaranda or simply Jacaranda Bravo et al 2020 Gentry 1992 It is mainly used for urban afforestation and is planted in cities in countries such as Argentina Brazil South Africa USA Australia New Zealand Italy Portugal Spain and Mexico amongst others Gentry 1992 KuruneriChitepo Shackleton 2011 Muvengwi Kwenda Mbiba Mpindu 2019 In addition to the advantages of providing shade and presenting an ornamental structure studies have also shown that in urban locations its leaves reduce the amount of metal ions in the air Brignole et al 2018 Olowoyo Van Heerden Fischer 2010 Soares et al 2011 showed that from an economic point of view the benefits of the urban planting Jacaranda exceed its costs by four times making the species economically attractive Corresponding author Email address mpfelizardohotmailbr MP Felizardo httpsdoiorg101016jbiosystemseng202103008 15375110 2021 IAgrE Published by Elsevier Ltd All rights reserved Nomenclature Abbreviations EMD Effective moisture diffusivity Symbols ab Parameters Bi Biot number Deff Effective moisture diffusivity m2 s1 Dmr eff Average effective moisture diffusivity m2 s1 Fo Fourier number i Index of observations K Number of observations L Thickness of seed m n Index of summation N Number of terms of series P Total number of unknown parameters R2 Coefficient of determination t Time s T Air temperature C Moisture content of solid kg water kg1 db XI Local moisture ratio X Average moisture ratio of solid X Average moisture content of solid kg water kg1 db z Position in the thickness m Subscripts c Critical db Dry basis e Equilibrium ef Effective est Estimated l Local o Initial obs Observed t Drying time Greek symbols δ Residue values μ Average σ Standard deviation χ2 Chisquared Commercially there are records of using different products from this tree including the application of its fruits in the production of activated carbon having a good response in wastewater treatment TreviñoCordero et al 2013 the leaves and seeds producing extracts with antimicrobial activity Gachet Schühly 2009 and used in the cosmetics industry However considering the presence its exclusive active ingredients Jacaranda is not yet commercialised Bravo et al 2020 Considering its use outside the urban environment Rigal Xu Hu Qiu and Vaast 2020 evaluated the combined cultivation of Jacaranda and coffee They found that Jacaranda shade did not negatively affect coffee production and quality making it possible to use the same area for both coffee cultivation and Jacaranda planting Based on its potential for the pharmaceutical and food industries Van Nieuwenhove et al 2019 considered that essential oils from J mimosifolia seeds have anticarcinogenic potential In addition their indicated that using flour with 05 gg1of seeds to enrich yoghurts showed a significant increase in the nutritional level of these foods They highlighted the importance of researching plants which have medicinal potential to improve the quality of life and health of consumers Despite studies being carried out indicating the importance and relevance of this species and its applications no studies on its processing have been found Thus any commercial application of this kind requires the development of technologies to improve the processing steps ie classification cleaning and drying Goneli Martins Jordan and Geisenhoff 2016 Mujumdar 2006 Onwude Hashim Janius Nawi and Abdan 2016 and Inyang Oboh and Etuk 2018 have shown that knowledge of drying kinetics of materials is essential for the dryer design In modelling the drying of grains and seeds transport parameters are frequently considered constant Bala 2016 Barrozo Mujumdar Freire 2014 Many studies however have pointed that different transport mechanisms occur throughout the process Bejan Dincer Lorente Reis 2004 Belhamri 2003 De Vries 1958 Efremov 1999 Keey 1972 Shen et al 2011 Therefore in the modelling of drying kinetics the hypothesis that the Effective Moisture Diffusivity EMD behaves as a constant parameter often results in periods when the model overestimates the moisture content in the sample followed by periods in which the moisture content is underestimated This has been previously reported by Avhad and Marchetti 2016 Johann da Silva and Pereira 2018 and Torrez Giner 2017 Batista da Rosa and Pinto 2007 describe a significant improvement in the adjustment of the diffusive model when considering EMD as a variable This was observed in the analysis from the shrinkage of chitosan particles during drying when a variable EMD was compared to a constant one Literature research provides a series of approaches along these lines of evidence particularly in the study of thin layer drying which is a wellresearched field De Vries 1958 studied the dependence of this parameter with the diffusion mechanisms in moisture transfer Following this approach subsequent studies about modelling of drying kinetics were reported such as in Chen 2007 Efremov and Kudra 2005 Vagenas and Karathanos 1991 and Parry 1985 These authors studied the variation of EMD in relation to the types of moisture transport mechanisms in biological samples Freire et al 2017 used an adaptive lumper parameter cascade model to study the drying of solid waste from orange juice It consisted in the minimisation of error between the moisture content estimated by the model and the observed values In this way sequential adjustments could be added throughout the process of drying Using this technique parameters as drying kinetic constant overall heat exchange coefficient and rate of heat loss could be estimated Thus the aim of this work was to evaluate the variation of EMD during the drying of J mimosifolia seeds using a diffusive According to Bala 2016 Dincer and Zamfrescu 2016 and Keey 1972 the CD period is characterised by water diffusion mechanisms already in the pendular state During this phase there is a reduction of the liquid film until its depletion where the DE phase begins with a predominance of diffusive mech anisms of the vapour phase In this stage the moisture gradient is formed as a result of evaporation the effects of capillary forces vaporisation and condensation cycles or osmotic effects The combination ofthese mechanisms brings about changes in the coefficient throughout the process This combination of mechanisms was described by De Vries 1958 Fig 3 shows the graphic representation proposed by Pickles 2003 25 Mathematical modelling for drying kinetics e constant parameter Mathematical modelling of drying kinetics can be carried out using various equations as can be seen in Kucuk Kilic and Midilli 2014 where the authors present 60 different equa tions These equations have semiempirical or empirical bases When these equations are used drying kinetics can be more precisely described particularly when more parameters are used Kemp 2011 Theoretical drying models are derived from the laws of transport phenomena such as Newtons law of cooling Fouriers law and Ficks law of diffusion Even empirical models may show better fits but information on the mechanisms of the drying process are limited Barrozo et al 2014 Erbay Icier 2010 Parti 1990 Concerning thin layer drying it can be considered that the seeds is an infinite and isotropic flat plate with constant properties in its thickness including the effective diffusivity of moisture Deff For a system with these characteristics the diffusion model can be written according to Eq 2 vX l vt ¼ Deffv2X vz2l 2 Fig 1 e Schematic design of the experimental unit 1 fan 2 bypass system 3 orifice plate flowmeter 4 electric heater 5 type T thermocouple 6 perforated plate distributor 7 fixed bed 8 data acquisition system 9 heat controller 10 pressure transducer and 11 computer Fig 2 e Typical drying kinetics Bala 2016 Fig 3 e Moisture diffusivity in function of the moisture content Pickles 2003 b i o s y s t e m s e n g i n e e r i n g 2 0 5 2 0 2 1 2 3 4 e2 4 5 237 model with sequential adjustments over the duration of the drying process 2 Materials and methods 21 Seed characterisation and preparation Jacaranda seeds were purchased Arborcenter Birigui SP Brazil who provided a certificate for the species purity The seed dimensions were carried out by image analysis in storage moisture using a digital camera Samsung 13 Mpx resolution Image characterisation technique was used compared to other methods due to the fragility of the Thickness was obtained by analysing the images of this material using a digital calliper with an accuracy of 001 mm taking care not to deform the sample during the procedure To obtain images the seeds were placed on a white background next to a calibrated pattern with an accuracy of 1 mm Measurements were carried out with 165 seeds obtaining a mean and standard deviation to represent the batch The images were analysed using the Image Pro Plus 6 software Media Cybernetics from Rockville WA USA The size parameters determined by the software were the maximum and minimum Feret diameters perimeter and projected area The first two properties approximate to particle length and width values respectively Walton 1948 The seeds were separated into batches of approximately 75 g and were moistened by adding water to a sealed container for 2 d at a temperature of 5 C The amount of water added was such that the final moisture content reached was 1 kg water kg1 dry basis Seeds that with broken skins were excluded from the experimental process to ensure the integrity of the samples Giner Gely 2005 22 Equipment Drying was carried out a speed of approximately 025 m s1 and temperatures of approximately 40 and 50 C of the drying air to control these conditions and to ensure the uniformity of the flow The equipment shown in Fig 1 was used The equipment consisted of a 15 kW power fan 1 that moved air through a 508 mm diameter pipe flow rate was controlled by 508 mm slide valves using a bypass system 2 and measured using an orifice plate 3 air was heated by a system that consisted of two 1000 W power resistors connected in series 4 The system was controlled by a thermostat Flyever model FE50s and the pressure drop across the orifice plate and in the bed was measured by pressure transducers AutoTran Inc from Naples FL USA model 600D21D14 and 600D10 1D14 respectively Five perforated plates 6 were located before the fixed bed and were configured to homogenise air speed profile thus meeting the hypotheses and conditions of the models used There was also a Ttype thermocouple encapsulated in the system to monitor the drying air temperature throughout the experiment 23 Seed drying experiments The drying cell was 508 mm diameter and 10 mm high The seeds were packaged according to the methodology described by Felizardo and Freire 2018 Drying was carried out at constant air velocity and temperature To describe the drying kinetics bed mass data were obtained as a function of drying time The bed mass was measured at the start of the experiment and over time To measure mass the bed was removed from the airflow and weighed on an AD HR120 balance with a precision of 001 g AD HR120 San Jose CA USA The time it taken to weigh the cell was typically 5 s The drying process was continued until the mass variation was less than the precision of the digital balance Gely Giner 2007 After drying the bed seeds were placed in a drying oven Marconi MA0331 from PiracicabaSPBrazil oven at a temperature of 105 3C for 24 h to determine the dry mass Thus the moisture content based on dry basis could be estimated over time The local moisture ratio XI was calculated using the moisture content data on a dry basis at time t Xt at the beginning X0 and at the end of drying Xe which was considered the dynamic equilibrium moisture of the seeds according to Eq 1 XI Xt Xe X0 Xe Dimensionless moisture relates to the amount of water that can still be removed and the amount of total water that can be removed from the solid Barrozo et al 2014 Shen et al 2011 24 Theoretical background Empirical semiempirical and theoretical models are available for modelling grain and drying kinetics of seeds in thin layers Avhad Marchetti 2016 Barrozo et al 2014 Chen 2007 Greig 1970 Johann et al 2018 Mujumdar 2006 By studying a thin layer the behaviour of multiple layers can be estimated during drying making it possible to design equipment with more efficient operational settings for a specific purpose Drying kinetics consists of estimating the moisture content as a function of time as shown in Fig 2 where four main periods that occur during drying can be observed Step AB consists of heating or cooling the material to the wetbulb temperature of air which is generally a quick step compared to the others According to Bala 2016 for agricultural materials there is no constant rate period BC characterised by the constant drying rate and the predominance of convective drying mechanisms From point C when the solid reaches critical moisture Xc there is a predominance of diffusive drying mechanisms for both water in the liquid and vapour phases This decreasing rate period can be divided into two periods which are CD and DE In agricultural materials these steps dominate Bejan Dincer Lorente Reis 2004 Belhamri 2003 Shen et al 2011 For the analytical solution the following boundary conditions can be considered by Eqs 3ab and initial condition by Eq 4 dXlztdzz0 0 t 0 3a XlztzLXeq t 0 3b Xlztt0X0 4 According to Crank 1975 the average dimensionless moisture X can be described as a function of time t as in Eq 5 Xt Xt XeX0 Xe 8π2 n1 to 12n 12 exp2n 12 π2 Fo 5 Thus the Fourier dimensionless number Fo can be calculated by the Effective Moisture Diffusivity Deff drying time t and seed thickness L as described in Eq 6 Fo Deff t L2 6 According to Efremov and Kudra 2005 using 20 terms there is an error of approximately 1 and increasing the number of terms above greatly improves the accuracy of the results The mathematical model from Eq 5 is for a flat plate and there are formulations for cylinders Faggion Tussolini Freire Freire Zanoelo 2016 and spheres Torrez Irigoyen Giner 2017 Parry 1985 presented these models for the three coordinates system for use in modelling the drying of grains in a thin layer showing that the choice of geometry depends on the drying medium examined and the characteristics of the materials 26 Statistical analysis of fitting model The fitting of mathematical models was performed using the least squares method to adjust nonlinear functions Perazzini Freire Freire 2013 Rocha Pohndorf Meneghetti Oliveira Elias 2020 The MatLab nlinfit function R2007b Mathworks was used The residuals δ between the observed Xobs and estimated Xest moisture data were calculated according to Eq 7 δt Xobst Xestt 7 The graphical analysis of the residues with respect to time enabled us to analyse the fitting trends throughout the drying process Thus to indicate that there are no fitting problems through the homogeneity of the residues these residues should have a random distribution Akkoyunlu Pekel Akkoyunlu Pusat 2020 Casciatori Laurentino Zanelato Thoméo 2015 Vásquez Reyes Pailahueque 2019 Using the coefficient of determination R2 and the chisquare test χ2 the quality of the adjustment was evaluated according to Eqs 8 and 9 respectively R2 1 i1 to N δi2 i1 to N Xi X 2 8 χ2 i1 to K δi2 K P 9 where K is the number of observations and P is the number of fitting parameters The better the fit the closer will be the coefficient of determination to unity and the lower the chisquare value Perazzini et al 2013 Rocha et al 2020 27 Effective diffusivity of variable moisture According to De Vries 1958 the sum of the different diffusion mechanisms results in the variation of the effective diffusivity of moisture or total diffusion coefficient In addition other physical mechanisms may be related to these variations such as shrinkage Batista et al 2007 271 Model by Efremov Markowski Białobrzewski Zielinska 2008 Despite their different geometric bases these models carry a hypothesis for their development which is constant properties Thus the EMD is considered constant throughout the drying process which is improper due to the different drying mechanisms shown in Figs 13 Thus to estimate this variable diffusivity the slope method presented in Eq 10 has been used for some time Batista et al 2007 Keey 1972 Vagenas Karathanos 1991 Deff dXdtexp dXdFoTeo 10 For which dXdtexp represents the drying rate obtained by the experimental drying kinetics data and dXdFoTeo represents the slope of the theoretical model obtained by the drying characteristic curve according to Keey 1972 Using these concepts and starting from the Diffusion Model Efremov et al 2008 separated Eq 5 to Fo 008 Eq 11a and 0 Fo 008 Eq 11b Xt 8π2 expπ2 Fo 11a Xt expπ2 bFoa 11b Thus for t 0 Fo 0 Eq 6 and thus for the initial condition Eq 4 we have that X 1 However for Eq 11a this is impossible Thus Eq 11b uses the parameters a and b to correct the sum coefficients these values can be obtained by adjusting the experimental drying kinetics data Thus with the rearrangement of Eqs 8ab substituting Eq 6 Eqs 12ab are obtained For Fo 008 Deff L2 π2 t ln π2 X 8 12a For 0 Fo 008 Deff L2 π2 t lnX1a 1 b 12b The development of these models and the construction of a dependence on diffusivity over time can be seen in Efremov 1999 Efremov et al 2008 and Efremov and Kudra 2005 272 Proposed method To estimate the EMD during drying Eq 4 was fitted sequentially to the experimental drying kinetics data as shown in Fig 4 To do this three different sequential drying times were used and for the initial time t 0 s it was assumed that Deff t 0 s 0 m2 s1 as the drying process had not yet started and for the final time tf kinetics dependent Deff t tf 0 m2 s1 because the diffusive process had ended From the sequential adjustments a 3xK matrix was obtained In this matrix the arithmetic means of the columns were performed for each row obtaining a corresponding matrix for the K observations Methods that divide drying in relative to time were used to optimise the modelling process such as the cascade model presented by Freire et al 2017 In addition the combination of mathematical tools with theoretical modelling for drying has already been used as in Freire Freire Ferreira and Nascimento 2012 Based on these conditions the present work proposes using this sequential adjustment method To validate this proposed method the results will be compared with the model put forward by Efremov et al 2008 Fig 5 a Dimensionless moisture as a function of time and drying rate as a function of b time and c dimensionless moisture for the drying air temperatures of 40 and 50 C Fig 7 a Effective Moisture Diffusivity b coefficient of determination c chisquare and d dimensionless initial moisture as a function of the number of terms in the series in Eq 5 Fig 8 Residues as a function of drying time for drying air temperature of a 40 C and b 50 C for 1 5 10 15 and 20 terms of the series in Eq 5 Fig 9 Residues between observed and estimated data as a function of the Fourier number Fig 10 Comparison of the Effective Moisture Diffusivity as a function of the dimensionless moisture for the different 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