STATE ESTIMATION IN THE BATCH DRYING OF FOODS

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.     

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.     

DATA-DEPENDENT ESTIMATION OF PREDICTION FUNCTIONS

Abstract. The technique of cross-validation for model selection where the observations have martingale-like structure is developed. It is argued that cross-validation works, unaltered, in this more general setting. The specific example of the stationary Markov process is considered in detail. An estimate of the one-step prediction function of this process is selected from a collection of splines by minimizing the cross-validatory version of the prediction error. Asymptotic optimality of the estimate is established.     

PRESENTATION OF DRYING KINETICS IN A FLUIDIZED BED BY MEANS OF RADIAL BASIS FUNCTIONS

Radial Basis Functions (RBF) have been proposed to describe drying kinetics in a vibro-fluidized bed. Mapping of changes in material moisture content and temperature by means of the RBF has been discussed. The “one step ahead” concept was applied. Results of investigations of agricultural material drying were used for training and testing of artificial neural networks.     

PRESENTATION OF DRYING KINETICS IN A FLUIDIZED BED BY MEANS OF RADIAL BASIS FUNCTIONS

ABSTRACT

Radial Basis Functions (RBF) have been proposed to describe drying kinetics in a vibro-fluidized bed. Mapping of changes in material moisture content and temperature by means of the RBF has been discussed. The “one step ahead” concept was applied. Results of investigations of agricultural material drying were used for training and testing of artificial neural networks.     

REVIEW OF THIN-LAYER DRYING AND WETTING EQUATIONS

Thin-layer equations contribute to the understanding of the heat and mass transfer phenomena in agricultural products and computer simulations for designing new and improving existing commercial drying processes. Many different equations have been developed to represent thin-layer drying behaviour of the grains. Many thin-layer drying and rewetting equations are reviewed and discussed. Some suggestions for future coordinated research work arc given.     

REVIEW OF THIN-LAYER DRYING AND WETTING EQUATIONS

Thin-layer equations contribute to the understanding of the heat and mass transfer phenomena in agricultural products and computer simulations for designing new and improving existing commercial drying processes. Many different equations have been developed to represent thin-layer drying behaviour of the grains. Many thin-layer drying and rewetting equations are reviewed and discussed. Some suggestions for future coordinated research work arc given.     

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.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

ABSTRACT

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.     

ITERATIVE AND RECURSIVE ESTIMATION OF TRANSFER FUNCTIONS

Abstract. A unified treatment of non-linear estimation, pseudolinear regression and stochastic approximation for open-loop transfer function models is provided. Pseudolinear regression techniques are used to derive the recursive non-linear least-squares estimator, avoiding the methodological problems implicit in traditional derivations. Stochastic approximation analysis is used to investigate in a direct manner the conditions of convergence and consistency of both iterative and recursive algorithms. The various methods are compared using data for an industrial process.     

COMPARISON OF TWO METHODS OF SELECTING SMOOTHING SPLINE FUNCTIONS FOR ESTIMATION OF SPECIFIC RATES IN FERMENTATIONS

A new method of selecting smoothing spline functions is presented and used to curve fit experimental fermentation data. From the curves generated, estimates for the specific growth rate, the specific rate of substrate utilization and the biomass energetic yield are made. Selection of the smoothness parameters is based on minimization of a response surface fit to the smoothness parameters used to generate the time profiles of biomass and substrate concentration. The response modelled is the extent of closure of the carbon balance and the available electron balance. Results obtained using cross validation for selection of the smoothness parameter are also presented, and compared to the results calculated using the response surface technique. Estimates made for specific growth rate and biomass energetic yield are used with the covariate adjustment procedure to calculate point and 95% confidence interval estimates for the true biomass energetic yield, η_max, and the maintenance coefficient, m_e. The results show that the spline fit has an effect on the parameter estimates. The newly developed response surface method compares favorably with the cross validation method.     

EVALUATION OF EQUATIONS APPROXIMATING THERMODYNAMIC AND TRANSPORT PROPERTIES OF WATER,STEAM ANDAIR FOR USE IN CAD OF DRYING PROCESSES

Over 70 equations approximating thermodynamic and transport of water and steam at pressure 1 bar and saturated pressure as well as air at pressure 1 bar were tested against reference data. Their accuracy and relative computing time were reported.     

RATE OF DRYING AND STRESSES IN THE FIRST PERIOD OF DRYING

The paper presents a computer simulated processes and illustrate how the drying induced stresses are influenced by the rate of drying. It is shown that the moisture transport coefficient, and thus the rate of drying, depends on the thermal state of the drying material, defined by the wet-bulb temperature. Through these simulated processes one can observe the evolution of the moisture content and stress distributions during drying at constant, but in each process different, wet-bulb temperatures. A convective drying process of a bar with rectangular cross-section is considered as example, and a two-dimensional initial-boundary value problem is solved numerically with the use of the finite element method. The numerical results are visualised in spatial diagrams.     

EVALUATION OF EQUATIONS APPROXIMATING THERMODYNAMIC AND TRANSPORT PROPERTIES OF WATER, STEAM ANDAIR FOR USE IN CAD OF DRYING PROCESSES

Over 70 equations approximating thermodynamic and transport of water and steam at pressure 1 bar and saturated pressure as well as air at pressure 1 bar were tested against reference data. Their accuracy and relative computing time were reported.     

ESTIMATION OF THE EFFECT OF PRODUCT SHRINKAGE ON THE DRYING TIMES,HEAT INPUT AND CONDENSER LOAD OF THE PRIMARY AND SECONDARY DRYING STAGES OF THE LYOPHILIZATION PROCESS IN VIALS

ABSTRACT

The effects of cake shrinkage on the drying times and energy requirements of the primary and secondary drying stages of the freeze drying process involving the drying of a material in a vial, are estimated through the construction and solution of an extended unsteady state and spatially multidimensional model that accounts for the changes introduced by cake shrinkage on the internal and external mass and heat transfer mechanisms of the freeze drying     

EFFECT OF DRYING ON RETENTION OF ETHANOL IN MALTODEXTRIN SOLUTION DURING DRYING OF A SINGLE DROPLET

ABSTRACT

Retention of ethanol in a droplet of maltodextrin solution during drying was studied both theoretically and experimentally under various drying conditions. It was found that a large part of the total amount of ethanol loss occurred in the initial period of drying, and that the final retention of ethanol increased with increasing initial maltodextrin concentration, drying air temperature and velocity, and decreasing of air humidity. Experimental results of the retention of ethanol were in good agreement with theoretical calculations based on so-called selective diffusion theory.     

SIMULATION OF PLUM DRYING IN DEEP BED

Thin layer air drying of plum was studied. The drying conditions in this study are : dry bulb temperature ranging from 60 to 100 °C, air moisture content ranging from 0.008 to 0.089 kg water/kg dry air and air velocity ranging from 0.5 to 2 1x11s. An exponential model was used to describe the drying curve. The heat and moisture balances on the air were used to calculate the outlet air temperature and its moisture content. The heat balance on the product was used to calculate the product temperature. These equations were used to predict the drying of plum in deep bed. A good agreement between the experimental and calculated product moisture content, the product temperature and the outlet air temperature were obtained     

THE USE OF AUXILIARIES IN DRYING TECHNOLOGY

ABSTRACT

In drying technology, the quality characteristics of the solid (its dispersibility, attrition resistance, etc.) are selectively adjusted by the use of auxiliaries. Typical auxiliaries include granulation aids for spray granulation and flow aids for solids with poor flow properties. Such auxiliaries are classified in the first part of this paper according to their mechanisms of action (eg. their adhesive effect, dispersion effect, bursting effect).

In the second part of the paper, an example will be used to illustrate the effect of auxiliaries. The effect of a binder (salt or polymer) on the drying of free-floating suspended droplets is investigated. The fracture resistance of the particles and the required drying time increase as the proportion of dissolved components increases.