STATE ESTIMATION IN THE BATCH DRYING OF FOODS

ABSTRACT

Measurement of material moisture content is necessary for the control of product quality in batch drying. However, this variable cannot be measured on-line, and state estimation techniques are proposed. A non-linear dynamic model is developed for batch drying of foods. Process disturbances and measurement errors are modeled as stochastic processes and a hybrid extended Kalman filter is employed for state estimation. This filter is based on the local linearization of the process model around the suboptimal filter estimates. The moisture estimation approach was applied to experimental points obtained in a laboratory dryer with quite satisfactory results.     

搅拌反应器中反应热的实时监测Ⅱ模拟放热反应过程的状态及参数估计

在自制的５Ｌ规模反应量热实验装置中,以热平衡为基础建立了搅拌反应器的动态热传递模型,应用扩展Ｋａｌｍａｎ参数估计和状态估计的方法在线得到模型参数和模拟反应的放热速率、累积反应热。实验数据和模型估计值比较,预测误差在±７％以内     

ESTIMATION OF FUNCTIONS IN DRYING EQUATIONS

In drying problem, particularly for drying foodstuff, modelling is very difficult. Many physical effects have to be taken into account for mass transfer ; then mass transfer coefficient varies

In different models unknown functions must be estimated. It is particularly the case in simple models of drying using average values of water content, where the mass transfer varies versus mean water content in falling rate period. On the other hand in the “diffusion model” we have the same problem concerning the diffusion coefficient which must be also estimated

The method we propose in this paper for these two models : simple and “diffusion model” of drying consists from measurements of temperature and water content of the product to search a numerical approach of the unknown function. This method uses optimization techniques on computer and least squares criterion between model values and experimental data

Results are given for the “diffusion model” applied to shelled corn drying to find the diffusion coefficient and for a simple 11107 del applied to plum drying to find the mass transfer coefficient.     

MODEL SELECTI0N IN AIR DRYING OF FOODS

The purpose of this investigation is to compare various drying models with respect to (a) the accuracy in calculating the material moisture content and temperature versus time and (b) the computation time required.

Mechanistic as well as phenomenological heat and mass transfer models are considered. The mechanistic models are formulated by considering different combinations of mechanisms between (1) moisture diffusion in the solid towards its external surface (2) vaporization and convective transfer of the vapor into the air stream (3) convective heat transfer from the air to the solid's surface (4) conductive heat transfer within the solid mass. The phenomenological model incorporates the drying constant while the mechanistic models incorporate the mass diffusivity, the mass transfer coefficient in the air boundary layer, the thermal conductivity, and the heat transfer coefficient in the air boundary layer.

The proposed methodology is applied to experimental data of four vegetables, namely, potato, onion, carrot, and green pepper. The experiments involve three thickness levels, five temperatures, three water activities, and three air velocities. The results obtained concern (a) the standard deviations between experimental and calculated values of material moisture content andtemperature, which, in combination with the computation time, are the necessary information for model selection for a special application, and (b) the model parameter estimates which are necessary to use the selected model.     

THERMODYNAMIC ANALYSIS OF DRYING FOODS

Thermodynamic functions computed for food systems showing hysteresis indicate considerable differences. There appears to exist no qualitative agreement between the values obtained. Large differences in values between the adsorption an desorp-tion branches of isotherms make the absolute magnitude of the entropy and enthalpy changes uncertain. The desorption iso-steric heat was found to decrease with temperature while the adsorption branch of the isotherm for a few foods were found to exhibit temperature reversal effect giving higher values at low temperatures. Such trend may indicate either transition in the form of binding energy or the effect of temperature on structural alterations. In designing drying equipment, the isosteric heat of desorption will provide “a worst case” analysis as the true isosteric heat will lie somewhere between the adsorption and desorption isosteric heat. Any overcalculation in designing equipment by using the desorption branch of hysteresis data can only be in favor of increased throughput capability. The use of isosteric heat in freeze drying and in air drying calculations were undertaken and found to rise at a faster rate than the energy expended in moisture removal.     

MODEL SELECTI0N IN AIR DRYING OF FOODS

ABSTRACT

The purpose of this investigation is to compare various drying models with respect to (a) the accuracy in calculating the material moisture content and temperature versus time and (b) the computation time required.

Mechanistic as well as phenomenological heat and mass transfer models are considered. The mechanistic models are formulated by considering different combinations of mechanisms between (1) moisture diffusion in the solid towards its external surface (2) vaporization and convective transfer of the vapor into the air stream (3) convective heat transfer from the air to the solid's surface (4) conductive heat transfer within the solid mass. The phenomenological model incorporates the drying constant while the mechanistic models incorporate the mass diffusivity, the mass transfer coefficient in the air boundary layer, the thermal conductivity, and the heat transfer coefficient in the air boundary layer.

The proposed methodology is applied to experimental data of four vegetables, namely, potato, onion, carrot, and green pepper. The experiments involve three thickness levels, five temperatures, three water activities, and three air velocities. The results obtained concern (a) the standard deviations between experimental and calculated values of material moisture content andtemperature, which, in combination with the computation time, are the necessary information for model selection for a special application, and (b) the model parameter estimates which are necessary to use the selected model.     

THERMODYNAMIC ANALYSIS OF DRYING FOODS

Thermodynamic functions computed for food systems showing hysteresis indicate considerable differences. There appears to exist no qualitative agreement between the values obtained. Large differences in values between the adsorption an desorp-tion branches of isotherms make the absolute magnitude of the entropy and enthalpy changes uncertain. The desorption iso-steric heat was found to decrease with temperature while the adsorption branch of the isotherm for a few foods were found to exhibit temperature reversal effect giving higher values at low temperatures. Such trend may indicate either transition in the form of binding energy or the effect of temperature on structural alterations. In designing drying equipment, the isosteric heat of desorption will provide “a worst case” analysis as the true isosteric heat will lie somewhere between the adsorption and desorption isosteric heat. Any overcalculation in designing equipment by using the desorption branch of hysteresis data can only be in favor of increased throughput capability. The use of isosteric heat in freeze drying and in air drying calculations were undertaken and found to rise at a faster rate than the energy expended in moisture removal.     

MOISTURE DISTRIBUTION IN SPHERICAL FOODS IN MICROWAVE DRYING

Abstract

Moisture distribution in spheres of potato (Solanum tuberosum) and yam (Dioscorea japonica) tubers during microwave drying was investigated. Moisture variation at various locations within the samples was experimentally determined for different drying times. A numerical simulation model was developed based on a modified form of Lambert's law for microwave penetration in spheres and on moisture transfer in both liquid and vapor phases. This model was used to study various factors influencing moisture distribution. Moisture profile during microwave drying was strongly influenced by non-uniform microwave energy distribution within the foods. The core moisture contents were lower than other parts of potato and yam spheres of the various sizes tested in this study (2.6 cm to 6.0 cm diameter). The sphere radius to microwave penetration ratio (2αr_o) was an important parameter affecting the moisture profile in spherical foods. For 2αr_o of less than 2.0, the moisture content in the center of potato and yam spheres was markedly lower than the rest of the food, but for 2αr_o between 2.5 and 4, moisture contents at the center and close to the surface were lower than the average moisture content.     

A STUDY OF THE FREEZE DRYING OF SOME LIQUID FOODS IN VACUO AND AT ATMOSPHERIC PRESSURE

A technique of freeze drying at atmospheric pressure was developed and used to test dry milk, some fruit juices, and solutions of coffee extract. Samples of the same food products were also freeze dried in vacuum. The influence of certain product characteristics, notably dimensions and concentration, on the mechanisms of the freeze drying operations are discussed, comparing the atmospheric technique to the vacuum process.     

SIMULATION OF DRYING IN A BATCH LUMBER KILN FROM SINGLE-BOARD TESTS

ABSTRACT

A deterministic model was developed to perform a board-by-board simulation of a forced convective batch lumber kiln. Individual board properties may be input and dryer operating parameters varied. The drying rates are empirical correlations based on single-board laboratory tests. The model incorporates the thermodynamic properties of the wood and gas, as well as mass and energy balances within the lumber stack. It also accounts for differences in heat and mass transfer resulting from position and changing gas properties throughout the dryer. The rate of drying predicted by the model and the final moisture content distribution were verified by weighing boards in a batch kiln before, during, and after drying. The application of the model is illustrated by simulating four common scenarios.     

SIMULATION OF DRYING IN A BATCH LUMBER KILN FROM SINGLE-BOARD TESTS

A deterministic model was developed to perform a board-by-board simulation of a forced convective batch lumber kiln. Individual board properties may be input and dryer operating parameters varied. The drying rates are empirical correlations based on single-board laboratory tests. The model incorporates the thermodynamic properties of the wood and gas, as well as mass and energy balances within the lumber stack. It also accounts for differences in heat and mass transfer resulting from position and changing gas properties throughout the dryer. The rate of drying predicted by the model and the final moisture content distribution were verified by weighing boards in a batch kiln before, during, and after drying. The application of the model is illustrated by simulating four common scenarios.     

DIELECTRIC DRYING OF PARTICULATE MATERIALS IN A FLUIDIZED STATE

The experimental results of dielectric drying of capillary-porous material with negligible internal resistance to mass flow (alumina) and capillary-colloidal-porous material with significant internal resistance to mass flow (wheat) in a fluidized bed have been presented. The modified adiabatic saturati on equation for radiofrequency and microwave fluidized bed drying has been verified.     

ANALYSIS OF BATCH DRYING DATA USING SAS

An analysis technique is described which uses the nonlinear curve fitting capabilities of the Statistical Analysis System (SAS) to analyze batch drying data. The technique does not require any apriori assumptions about whether a constant rate period exists. Rather, the only assumptions necessary are the possible forms of the equations which can be used to describe the drying phenomenon. The program will then determine, based upon statistical techniques, where each equation should be used during the drying process in order to best describe the overall drying process. Two examples are given; the first analyzes the drying of. sand, a material having a constant rate period; the second analyzes the data describing the drying of French fried potato pieces.     

ANALYSIS OF BATCH DRYING DATA USING SAS

An analysis technique is described which uses the nonlinear curve fitting capabilities of the Statistical Analysis System (SAS) to analyze batch drying data. The technique does not require any apriori assumptions about whether a constant rate period exists. Rather, the only assumptions necessary are the possible forms of the equations which can be used to describe the drying phenomenon. The program will then determine, based upon statistical techniques, where each equation should be used during the drying process in order to best describe the overall drying process. Two examples are given; the first analyzes the drying of. sand, a material having a constant rate period; the second analyzes the data describing the drying of French fried potato pieces.     

DIELECTRIC DRYING OF PARTICULATE MATERIALS IN A FLUIDIZED STATE

The experimental results of dielectric drying of capillary-porous material with negligible internal resistance to mass flow (alumina) and capillary-colloidal-porous material with significant internal resistance to mass flow (wheat) in a fluidized bed have been presented. The modified adiabatic saturati on equation for radiofrequency and microwave fluidized bed drying has been verified.     

BATCH DRYING OF SHELLED CORN IN TWO-DIMENSIONAL SPOUTED BEDS WITH DRAFT PLATES

Geometrically similar spouted beds with draft plates were used to obtain the drying characteristics of freshly harvested shelled corn with 0.28 to 0.31 kg/kg initial moisture content at different air inlet temperatures and bed heights. Thermal equilibrium between air and grains was achieved at minimum spouting conditions. The drying kinetics of shelled corn in a drafted two-dimensional spouted bed was found to be of the "thin layer" type. Expressions for the model parameters in Page's equation accounting for the bed geometry, grain moisture content, and drying conditions were developed.     

BATCH DRYING OF SHELLED CORN IN TWO-DIMENSIONAL SPOUTED BEDS WITH DRAFT PLATES

ABSTRACT

Geometrically similar spouted beds with draft plates were used to obtain the drying characteristics of freshly harvested shelled corn with 0.28 to 0.31 kg/kg initial moisture content at different air inlet temperatures and bed heights. Thermal equilibrium between air and grains was achieved at minimum spouting conditions. The drying kinetics of shelled corn in a drafted two-dimensional spouted bed was found to be of the "thin layer" type. Expressions for the model parameters in Page's equation accounting for the bed geometry, grain moisture content, and drying conditions were developed.     

TOWARD PREDICTION OF POROSITY IN FOODS DURING DRYING: A BRIEF REVIEW

Four generic trends of pore formation during drying are identified from the literature. The present prediction methods are mainly based on empirical correlations. It is common to correlate porosity with water content by quadratic, polynomial, or exponential forms of equations, which do not provide insight into the physics of the process. The glass transition theory is one of the proposed concepts to explain the process of shrinkage and collapse during drying. However, the glass transition theory does not hold true for all products. Other concepts, such as surface tension, structure, environment pressure, and mechanisms of moisture transport also play important roles in explaining the formation of pores. It is hypothesized that as capillary force is the main force responsible for collapse, so counterbalancing this force causes formation of pores and lower shrinkage.