A SIMPLIFIED MODEL FOR DETERMINATION OF MOISTURE DIFFUSIVITY OF DATE FROM EXPERIMENTAL DRYING CURVES

Experimental drying curves for Tunisia Deglet Nour dates were obtained in a laboratory dryer under different drying conditions The air temperature was varied from 30 to 69^°C, relative humidity from 11.6 to 47.1 % and air velocity from 0.9 to 2.7 m/s. A numerical method to obtain a solution of a diffusion equation in which the diffusivity depends upon temperature and moisture content has been proposed to investigate the moisture movement in a date by assuming the sample to be a homogenous infinite cylinder. To rind the fitting moisture and temperature dependent diffusivity, the calculated drying curves are compared with the observed drying curves and an empirical equation for the moisture diffusivity of the date has presented as a function of temperature and moisture. It has been shown that the moisture distribution in the date during drying can be obtained by using the empirical equation presented.     

A SIMPLIFIED MODEL FOR DETERMINATION OF MOISTURE DIFFUSIVITY OF DATE FROM EXPERIMENTAL DRYING CURVES

ABSTRACT

Experimental drying curves for Tunisia Deglet Nour dates were obtained in a laboratory dryer under different drying conditions The air temperature was varied from 30 to 69^°C, relative humidity from 11.6 to 47.1 % and air velocity from 0.9 to 2.7 m/s. A numerical method to obtain a solution of a diffusion equation in which the diffusivity depends upon temperature and moisture content has been proposed to investigate the moisture movement in a date by assuming the sample to be a homogenous infinite cylinder. To rind the fitting moisture and temperature dependent diffusivity, the calculated drying curves are compared with the observed drying curves and an empirical equation for the moisture diffusivity of the date has presented as a function of temperature and moisture. It has been shown that the moisture distribution in the date during drying can be obtained by using the empirical equation presented.     

MEASUREMENT ERRORS PROCESSING BY COVARIANCE ANALYSIS FOR AN IMPROVED ESTIMATION OF DRYING CHARACTERISTIC CURVE PARAMETERS

ABSTRACT

The aim of this paper is to show the interest of the covariance analysis applied to measurement error in the particular case of the identification of a drying characteristic curve from experimental drying data. The modelisation of drying by use of the Drying Characteristic Curve (DCC) method is first presented with usual specifications (power function, critical moisture content …). The experimental procedure used to obtain drying curves and the data processing are detailled and analysed. Measurements errors are identified at the first step of the procedure and their effects on the estimation error of the exponent α of the power function are estimated. Three different methods for estimating α are presented under their matrix form: the least square method and two methods based on the «Gauss–Markov» or «Maximum likelihood» theorem, firstly under a simplified form suited if the estimation errors are uncorrelated and secondly under a complete form suited even if the estimation errors are correlated. These three methods are applied to experimental results obtained with ginger roots drying. The value of the exponent α of the power function and then the distances between the three corresponding theoretical drying curves (representing product water content vs. time) and the experimental points are studied. It is shown that in this particular application, the complete Gauss–Markov method leads to the better fitting and that the simplified Gauss–Markov method, since it is a priori non appliable in this case where errors are correlated, gives quite better results than the oridnary least squares method. The covariance matrices of the estimation errors of reduced water content, reduced drying rate and exponent α are also presented in order to show the correlations existing between the measurement errors of each variable during a drying cycle.     

Analysis of the Drying Kinetics of Brachiaria brizantha (Hochst. Stapf) Grass Seeds at Different Drying Modes

Forage grass seeds have a high economical importance in the Brazilian bovine cattle breeding and seed drying is a fundamental stage of processing to guarantee their stability and allow their storage for long periods. In this context, the objective of this work was to develop a pilot-scale belt dryer, which operates also as a fixed and fluidized bed. Brachiaria brizantha seeds dehydration was analyzed under different air velocities and temperatures. Experimental data of moisture content variation along the drying time was successfully fit to a one-term exponential model. The experimental drying rate points were calculated by approximating the derivatives to finite differences. Its behavior was accomplished fitting curves of the drying rate versus water content and time. Finally, fissure, germination, and vigor rates were analyzed as a function of the drying conditions so that the experimental conditions combine the best process efficiency with the best physiological quality maintenance.     

Investigation of moisture transport properties of cementitious materials

This paper is focused on two ways to enhance our understanding of moisture transport properties of cementitious materials. The first one utilizes a multi-phasic moisture transport model to adjust the permeability through the fitting of measured mass loss curves during a drying experiment. In the second one, measured apparent diffusion coefficient curves vs. relative humidity (RH) are fitted by a general expression which includes both liquid transport and vapour diffusion. Due to different RH ranges of predominance of liquid and vapour transport, the permeability and vapour diffusion coefficient can be determined separately. Three cement pastes, whose properties are collected from the literature, are analysed by means of those two methods. Discussions on relative permeability and Knudsen diffusion show a significant influence on the modelling of moisture transport. A further comparison with measured permeability data found in the literature is able to provide a deeper understanding of moisture transport properties.     

Analysis of the Drying Kinetics of Brachiaria brizantha (Hochst. Stapf) Grass Seeds at Different Drying Modes

Forage grass seeds have a high economical importance in the Brazilian bovine cattle breeding and seed drying is a fundamental stage of processing to guarantee their stability and allow their storage for long periods. In this context, the objective of this work was to develop a pilot-scale belt dryer, which operates also as a fixed and fluidized bed. Brachiaria brizantha seeds dehydration was analyzed under different air velocities and temperatures. Experimental data of moisture content variation along the drying time was successfully fit to a one-term exponential model. The experimental drying rate points were calculated by approximating the derivatives to finite differences. Its behavior was accomplished fitting curves of the drying rate versus water content and time. Finally, fissure, germination, and vigor rates were analyzed as a function of the drying conditions so that the experimental conditions combine the best process efficiency with the best physiological quality maintenance.     

Drying Kinetics of Instant Asian Noodles Processed in Superheated Steam

The objective for this work was to develop a novel technique for creating instant noodles by determining the drying kinetics of noodles undergoing simultaneous drying and processing using superheated steam. The mathematical model of moisture ratio was differentiated to determine the drying rates of noodles during processing. There was a constant rate drying period for all temperatures at a steam velocity of 1.5 m/s but there was no constant rate drying period at a steam velocity of 0.5 m/s. The constant rate drying period suggested by measurement of internal noodle temperature is much longer and well defined for all processing conditions than from the drying curves. The constant drying rate period, was nearly 200 s at 110°C but decreased to 50 s at 150°C. Equilibrium moisture content isobars were determined from mass changes during superheated steam processing. It was determined that isotherm equations for equilibrium moisture content in hot air systems may be utilized to model isobars in superheated steam systems.     

COMBINED CONVECTIVE-MICROWAVE DRYING OF AGAR GELS: INFLUENCE OF MICROWAVE POWER ON DRYING KINETICS

The use of microwave energy in the drying of deformable material such as gel considerably reduces drying time and enables the control of retraction in the sample. A further advantage is that no hot spots are produced, allowing a dry product of superior quality to be obtained.The aim of this work has been to determine the kinetics of the convective-microwave drying process of agar gel plates. For this purpose, we developed a pilot closed loop, computer-controlled apparatus of convective-microwave drying, that enables the drying air conditions to be changed and the microwave power to be supplied over a wide value range. The equipment also records the sample surface temperature by means of an infrared thermometer. The drying curves obtained for plane geometry present four different drying phases: an initial phase where a rapid increase in the drying rate and in the surface temperature can be observed, as well as a constant rate phase that ends in the so-called convective critical moisture content, a first falling rate phase that concludes in the microwave critical moisture point, and finally a second falling rate phase. Combined convective-microwave drying enables a considerable reduction in drying time compared to convective drying, the time required being inversely proportional to the microwave power supplied. The empirical equation that best represents the kinetics is of the Page type. The absorbed volumetric power in terms of the moisture content was experimentally estimated, with the experimental data fitting an empirical equation.     

Prediction of moisture content in pre-osmosed and ultrasounded dried banana using genetic algorithm and neural network

In this study, application of a versatile approach for estimation moisture content of dried banana using neural network and genetic algorithm has been presented. The banana samples were dehydrated using two non-thermal processes namely osmotic and ultrasound pretreatments, at different solution concentrations and dehydration times and were then subjected to air drying at 60 and 80 °C for 4, 5 and 6 h. The processing conditions were considered as inputs of neural network to predict final moisture content of banana. Network structure and learning parameters were optimized using genetic algorithm. It was found that the designed networks containing 7 and 10 neurons in first and second hidden layers, respectively, give the best fitting to experimental data. This configuration could predict moisture content of dried banana with correlation coefficient of 0.94. In addition, sensitivity analysis showed that the two most sensitive input variables towards such prediction were drying time and temperature.     

MVR空心桨叶干燥污泥的特性及动力学

基于空心桨叶干燥机建立了一套机械蒸汽再压缩式热泵干燥系统,将相同质量的污泥(100±0.1)kg,在真空压力约为95kPa、压缩机出口蒸汽温度为95~115℃进行恒温干燥实验,从而得到污泥干燥过程中含水率以及干燥速率等变化曲线,压缩机出口蒸汽温度为95~115℃,污泥临界湿含量从0.22增加到0.34。引入5种常用的污泥干燥模型,利用Origin软件对实验数据进行分段拟合分析,得到污泥加速阶段和降速阶段的干燥动力学模型MR=exp(-ktⁿ)。以分段函数形式表示的干燥方程分别为:MR=exp[-(2.78×10^-4T-0.01896)t^1.596],(加速阶段);MR=0.894-0.564(1.737×10^-4T-8.05×10^-3)t(恒速阶段);MR=exp[-(2.26×10^-4T-0.01365)t^1.984](降速阶段)。对实验得到的干燥模型进行验证,计算得到各干燥阶段污泥湿含量平均相对误差,并将实验所得干燥曲线和干燥速率曲线与模型计算值进行比较,可以看出分段处理能较好的描述污泥干燥规律。     

Heat of sorption: A comparison between isotherm models and calorimeter measurements of wood pulp

This article introduces a method to validate heat of sorption measurements from isotherms by comparing them to direct measurements using reaction calorimetry. We have evaluated some frequently used single-temperature isotherm models (BET, GAB) as well as two multi-temperature isotherm equations (Anderson, Heikkilä). It turned out that the isotherm models with better isotherm curve fitting characteristics did not deliver the best results for the heat of sorption. Multi-temperature isotherm models such as the Heikkilä equation are able to deliver good results in terms of modelling the isotherm data and determining the heat of sorption. Single-temperature models fit the isotherm data better than multi-temperature models, but failed to deliver correct values for the heat of sorption. We specifically investigated the heat of sorption at very low moisture content, which is most relevant for paper drying. The resulting heat of sorption curves were analyzed with respect to their saturation behavior, which is expected to occur below BET monolayer moisture. The heat of sorption from the Heikkilä’s model was the only one to show the expected saturation at very low moisture content.     

Effective Moisture Diffusivity Estimation from Drying Data. A Comparison Between Various Methods of Analysis

Moisture diffusivity is the most crucial property in drying calculations. Literature data are scarce due to the variation of both experimental measurement techniques and methods of analysis. The effect of using different methods of analysis on the same experimental drying data is examined in this work. Detailed and simplified mathematical models, incorporating moisture diffusivity as model parameter, are applied. It is proved, that significant differences in the calculated values of moisture diffusivity result when different models are used, and probably these differences explain the variation in literature data. Thus, the adoption of a standardised methodology will be of great importance in moisture diffusivity evaluation.

The above findings resulted from the application of four alternative models on the drying data of three common food materials, potato, carrot and apple. A typical pilot plant scale dryer with controlled drying air conditions was used for the experiments. The moisture content dependence of the diffusion coefficient was proved significant at the last drying stage, while the temperature dependence followed the well known Arrhenius relation. The effects of considering external mass transfer and volume shrinkage during drying, were also investigated.     

RELATIVE IMPORTANCE OF VAPOUR DIFFUSION AND CONVECTTVE FLOW IN MODELLING OF SOFTWOOD DRYING

The influence of vapour diffusion on the drying rate of a softwood board has been examined for drying temperatures varying from 60°C to 140°C. It is found that for very low temperature drying a model which considers both vapour convective and diffusion in wood predicts dry-rate curves matching the experimental data closely. For high temperature drying, both of the above drying model and a drying model which considers only vapour convective flow give predictions in agreement with the observed data. This illustrates that the diffusion of vapour and air is important in low temperature drying panicularly during the late stages of drying. However, for high temperature drying, the convective flow of moisture vapour is dominant and the diffusion component is negligible. The observation provides evidence for simplifying a drying model for high temperature drying without reducing its credibility in predicting drying rate curves.     

Effective Moisture Diffusivity Estimation from Drying Data. A Comparison Between Various Methods of Analysis

ABSTRACT

Moisture diffusivity is the most crucial property in drying calculations. Literature data are scarce due to the variation of both experimental measurement techniques and methods of analysis. The effect of using different methods of analysis on the same experimental drying data is examined in this work. Detailed and simplified mathematical models, incorporating moisture diffusivity as model parameter, are applied. It is proved, that significant differences in the calculated values of moisture diffusivity result when different models are used, and probably these differences explain the variation in literature data. Thus, the adoption of a standardised methodology will be of great importance in moisture diffusivity evaluation.

The above findings resulted from the application of four alternative models on the drying data of three common food materials, potato, carrot and apple. A typical pilot plant scale dryer with controlled drying air conditions was used for the experiments. The moisture content dependence of the diffusion coefficient was proved significant at the last drying stage, while the temperature dependence followed the well known Arrhenius relation. The effects of considering external mass transfer and volume shrinkage during drying, were also investigated.     

RELATIVE IMPORTANCE OF VAPOUR DIFFUSION AND CONVECTTVE FLOW IN MODELLING OF SOFTWOOD DRYING

ABSTRACT

The influence of vapour diffusion on the drying rate of a softwood board has been examined for drying temperatures varying from 60°C to 140°C. It is found that for very low temperature drying a model which considers both vapour convective and diffusion in wood predicts dry-rate curves matching the experimental data closely. For high temperature drying, both of the above drying model and a drying model which considers only vapour convective flow give predictions in agreement with the observed data. This illustrates that the diffusion of vapour and air is important in low temperature drying panicularly during the late stages of drying. However, for high temperature drying, the convective flow of moisture vapour is dominant and the diffusion component is negligible. The observation provides evidence for simplifying a drying model for high temperature drying without reducing its credibility in predicting drying rate curves.     

不同形貌氢氧化镁微纳米结构的干燥动力学研究

采用沉淀转化法制备出两种氢氧化镁纳米片;采用直接沉淀法合成出氢氧化镁微米颗粒。通过干燥动力学实验得到三种形貌氢氧化镁的干燥曲线和干燥速率曲线;测定出三种形貌氢氧化镁在12℃下的平衡水分吸附等温线。研究结果表明,三种形貌氢氧化镁滤饼的初始含水量,纳米片的高于微米颗粒;它们的干燥速率曲线形状相似,但氢氧化镁纳米片的恒速段干燥速率曲线略有下降趋势;在相同的空气相时湿度下,纳米片的平衡含水量高于微米颗粒。     

Drying with Chemical Reaction in Cocoa Beans

Desirable flavor qualities of cocoa are dependent on how the cocoa beans are fermented, dried, and roasted. During fermentation and drying, polyphenols such as leucocyanidin and apecatechin are oxidized by polyphenols oxidase to form o-quinone, which later react nonenzymatically with a hydroquinone in a condensation reaction to form browning products and moisture. The objective of this article is to model the cocoa beans drying together with the browning reaction. A Luikov drying model for the moisture and a simple Fick's law diffusion model combined with first-order reactions for both the enzymatic oxidation and nonenzymatic condensation reactions were constructed. Both models were used to identify moisture diffusivity coefficient and total polyphenols diffusivity in cocoa beans from experimental drying and polyphenols degradation data and published kinetic data of the reactions. The theoretical drying model fitted the experimental cocoa bean drying curves with low mean square of residuals. The polyphenols diffusion and reaction model also fitted the experimental polyphenols degradation curves with minimum mean residual squares. The rate of polyphenols degradation in the cocoa beans increases at higher temperature and higher relative humidity. This is because the increasing reaction rate of polyphenols oxidation reaction as well as higher moisture diffusion at higher relative humidity and temperature. The effective moisture diffusivity in cocoa beans is estimated to be between 8.194 × 10^-9 and 8.542 × 10^-9 m²·s^-1, which is of the same order of magnitude as published data. The effective total polyphenols diffusivity is estimated to be between 8.333 × 10^-12 to 1.000 × 10^-11 m²·s^-1 with minimum mean residual squares. It is three orders of magnitude less than the estimated moisture diffusivity because of the larger polyphenols molecules. The estimated polyphenols diffusivity is very close to those published in the literature for sorption and ultrafiltration processes.     

Generalized drying curves for porous solids

The purpose of this study is to obtain generalized drying curves which can be used in the prediction of drying times of porous solids in the falling-rate period. The drying model introduced assumes that the movement of moisture in the solid body is by capillary motion, and that the major resistance to heat and mass transfer lies on the boundary layer at the solid surface. It has been applied to the drying of gypsum particles of various sizes in a rotary dryer at different feed rates and gas temperatures. The results show that the deviation between the experimental data and the ones predicted from theory is very small. The deviation increases at low moisture concentrations which may indicate that internal resistance to moisture flow starts to dominate the drying phenomena.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical curve is governed by the constant diffusivity Fick's taw diffusion equation (the constraint). Although the estimation of Fick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Fick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Fick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms The drying of oil palm kernels are used as a case study. Ii is found that the estimated diffusivities of moisture in oil palm kernels range from 0 5 to 5.0 × 10^-10 m²sol;s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.     

棒状MgCO3·3H2O的干燥动力学研究

以六水氯化镁为原料,碳酸氢铵为沉淀剂,采用直接沉淀法,制备出长约为80μm,直径为5～10μm的棒状三水碳酸镁;通过不同热空气温度及不同湿物料层厚度下的干燥动力学实验,获得棒状三水碳酸镁的干燥曲线和干燥速率曲线。采用相变动力学理论,对干燥动力学实验数据进行拟合分析,得到棒状三水碳酸镁的干燥方程、干燥速率方程及干燥动力学参数。