MASS TRANSFER MODELING FOR VIRGINIA TOBACCO CURING

Four mathematical models, describing the moisture transfer during Virginia tobacco curing under varying air-temperature and humidity were tested using experimental data from an industrial dryer.

The model, based on the assumption that the major resistance to moisture transfer is at the air boundary layer and that the driving force is the water activity difference, was found to be the most accurate. The appropriate mass transfer coefficient was determined.

An empirical equation, predicting the equilibrium moisture content of Virginia tobacco as a function of temperature and water activity of the surrounding air, was proposed and experimentally tested.     

DRYING KINETICS FOR SOME FRUITS: PREDICTING OF POROSITY AND COLOR DURING DEHYDRATION.

Drying kinetics of four fruits (prune, quince, fig and strawberry) were studied by using a simple mass transfer mathematical model involving a characteristic parameter (K) as a function of process variables. The model was tested with data produced in a laboratory air dryer, using non-linear regression analysis. The investigation involved three values of sample thickness (5, 10, 15mm) and three different air temperatures (50, 60, 70 °C).

The parameters of the model were found to be greatly affected by sample thickness and air temperature. The effect of moisture content on the porosity of three fruits (namely avocado, prune and strawberry) was also investigated. A simple mathematical model was used to correlate porosity with moisture content. It was found that porosity increased with decreasing moisture content.

Samples of three fruits (avocado, prune and strawberry) were investigated to estimate color changes during conventional drying at 70 °C. A first order kinetic model was fitted to experimental data with great success. It is found that the color of avocado and strawberry change while the color of prune remains the same.

Furthermore, the water sorption isotherms of three fruits (avocado, prune and strawberry) at 25° temperature were determined experimentally and the parameters at the GAB equation were evaluated by means of non-linear regression analysis. The use of the above equation produced a very good fit.     

Drying Sawdust in a Pulsed Fluidized Bed

The objective of this work was the experimental and theoretical study of sawdust drying, in batch and continuous experiences, using a pulsed fluidized bed dryer.

In the batch experiences, a 2³ factorial design was used to determine the kinetics of drying, the critical moisture content, and the effective coefficients of both diffusivity and heat transfer, all of them as a function of the velocity and temperature of the air, the speed of turning of the slotted plate that generates the air pulses in the dryer, using sawdust with 65% moisture in each run.

In the continuous operation, a 2³ factorial design was used to study the effect of the solid flow and the velocity and temperature of the air on both the product moisture and the distribution of residence times. In order to determine these last ones, digital image processing was used, utilizing sawdust colored by a solution of methylene blue as tracer.

The statistically significant factors were the velocity and the temperature of the heating air, for both the continuous and batch operations. Although the speed of turn of the slotted plate was not significant, it was observed that the air pulses increased the movement of particles, facilitating its fluidization, especially at the beginning of drying.

The heat transfer coefficients were adjusted according to the equation Nu = 0.0014 Re_p^1.52, whose standard deviation of fit is 0.145.

The period of decreasing rate was adjusted to several diffusivity models, giving the best fit the simplified variable diffusivity model (SVDM). The curve of distribution of residence times was adjusted using the model of tanks in series, with values between 2.6 and 5 tanks.     

HEAT AND MASS TRANSFER DURING SAPWOOD DRYING ABOVE THE FIBRE SATURATION POINT

Pine sapwood was dried in an air convection kiln at temperatures between 60-80 °C. Temperature and weight measurements were used to calculate the position of the evaporation front beneath the surface. It was assumed that the drying during a first regime is controlled by the heat transfer to the evaporation front until irreducible saturation occurs. Comparisons were made with CT-scanned density pictures of the dry shell formation during initial stages of drying of boards.

The results indicate a receding evaporation front behaviour for sapwood above approximately 40-50% MC when the moisture flux is heat transfer controlled. After that we finally reach a period where bound water diffusion is assumed to control the drying rate.

The heat transfer from the circulating air to the evaporation front controls the migration flux. In many industrial kilns the heating coils therefore have too small heat transfer rates for batches of thin boards and boards with high sapwood content.     

Determination of Spray-Drying Kinetics in a Small Scale

The main aim of the study presented in this article was to develop and test a method to determine spray-drying kinetics in a laboratory scale. A special measuring tunnel to obtain evaporation rate similar to the conditions observed in a spray-drying column was designed, built and tested.

Extensive studies of drying kinetics for maltodextrin were performed for different air flow rates and air temperatures. Test runs to determine repeatability of this technique showed satisfactory agreement between subsequent measurements, which confirms accuracy of the developed measuring method.

An effect of the initial moisture content on the critical moisture content was observed which is related to a decrease of the equilibrium vapor pressure over the solution and a decrease of the driving force of evaporation and drying rate of the process.

Results of the experiments proved that the generalized drying curve obtained from small-scale experiments could be used to describe spray-drying kinetics if the critical moisture content of the material is known.     

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.     

CHANGE IN VIABILITY OF MAIZE DURING HIGH-TEMPERATURE DRYING

Germination and moisture content loss data were collected of maize with a moisture content ranging from 15 to 32% (w.b.), an air temperature from 40 to 75°C, and an exposure time from 0.5 to 180 minutes.

A germination-retention model was developed based on the normally distributed death-rate theory (NDD). The NDD model was combined with a concurrent-flow (CCF) dryer model, and tested against viability data of maize dried in a commercial two-stage CCF dryer. Acceptable agreement between the predicted and experimental viabilities was obtained.

The effect of the CCF dryer design, and of several operating parameters, on the loss of maize-seed viability was analyzed. Simulation with the NDD-CCF dryer model shows that high quality seed can be produced by drying at air temperatures well above 100°C.     

ATMOSPHERIC CONTACT DRYING OF GRANULAR BEDS WETTED WITH A BINARY MIXTURE

When regarding the atmospheric contact drying of granular beds wetted with a liquid mixture, both the drying rate and the selectivity of the process, i.e. the change of moisture composition, are of interest. The batch drying of a free flowing ceramic substance, wetted with a 2-propanol-water mixture, is investigated in a rotary dryer with heated wall and air flow.

The theoretical analysis is based on physical models for heat and mass transfer, moisture migration and particle transport, which are presented in examples.

The experimental and theoretical results show that higher selectivities can be achieved by reducing the particle size because of the lower liquid-phase mass-transfer resistance. An increase of the rotational speed leads to a higher drying rate with slightly decreased selectivity if the particles are sufficiently small, since contact heat transfer is enhanced.     

MEASUREMENT OF INTERFACIAL AREA AND MASS TRANSFER COEFFICIENTS BY CHEMICAL METHOD OF C02 ABSORPTION INTO AQUEOUS SOLUTIONS OF NaOH IN A MODEL COLUMN WITH EXPANDED METAL SHEET PACKING

The theory of gas absorption accompanied by fast pseudo-fast order reaction which considered dependences of diffusivity, kinetic constant and Henry's law constant on absolute temperature and ionic strength was used to obtain values of effective interfacial areas and mass transfer coefficients in gas and liquid phase.

Experimental measurement of carbon dioxide absorption from mixture with air was performed in a pilot-plant column with expanded metal sheet packing irrigated with sodium hydroxide solution.

Resulting liquid and gas-side mass transfer coefficients are compared with values obtained from physical Absorption measurement of carbon dioxide into water and with measurement of gas-side mass transfer coefficient for sulphur dioxide in the same column.

The differences between determined values are discussed.     

Drying of Transformer Board

The internal insulation in shell type power transforms is usually ensured by the stacking of plates of board impregnated with oil. A board is in equilibrium with the atmosphere at a moisture content varying from seven to eight percent by weight, but, when the insulating function is required, the water content must be lower than 0.5 %. The aim of the present work is the understanding and the modelling of transformer boards drying.

The first part of this work presents experimental studies showing that the drying of transform board follows two regimes :

- a fast regime in the fim period

- a slow regime, up to 99 percent of dryness.

The effect of heating and the influence of the board thickness on the drying rate also studied. In the second part of this paper, we presnt a model capable to represent the observed kinetics of transformer board drying. This model is based on the diffusion of water vapour in the gaseous phases combined with the transfer of water vapor from the fibres to the -us phase. The due of the average global transfer coefficient can be deduced from the slope of the curve 1 f(drying time), where x     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

DEVELOPMENT AND VALIDATION OF A PROCESS SIMULATOR FOR DRYING SUBBITUMINOUS COAL

Drying subbituminous coal has never been practiced commercially. The commercial dryers built to date have been designed for drying surface moisture in conjunction with upstream coal preparation facilities. This type of drying is mainly controlled by input energy and the basis of the design is an energy balance. In drying inherent moisture from subbituminous coal, the thermal conductivity of the coal and the diffusion of molecular water within coal particles impose limitations on the process conditions. Energy input and solids residence time in the dryer have to be controlled properly for simultaneously balancing the heat and mass transfer within the coal particles. Improper control of either parameter can cause fires and explosions during the key steps of the drying process—drying and cooling

In parallel to the Anaconda coal drying pilot plant program, a cross-flow, fluid-bed coal drying/cooling process simulator was developed for: (1) understanding the drying phenomena on an individual particle basis; (2) analyzing potential risks and safety limits, and (3) designing the Anaconda pilot plant program

The development of the process simulator was based on both first principles and laboratory data and can be divided into two phases:

1 Development of a semi-mechanistic drying model for Powder River Basin subbituminous coal employing an analytical solution of the diffusion equation

2.Formulation of a fluid-bed cross-bed cross-flow dryer/cooler simulator employing simultaneous heat and mass transfer

This model was validated against process variables data taken on a 4 tph pilot plant. An operable range, or process envelope, has been developed through the pilot plant experience and the process simulation study. Based on the model predictions, an uncertainly range was defined in the design recommendations of a pioneer coal drying plant in scale-up.     

DRYING OF GRANULAR PARTICLES IN A MULTISTAGE INCLINED FLUIDIZED BED WITH MECHANICAL VIBRATION

A mathematical model for the drying rate of granular particles in a multistage inclined fluidized bed(IFB) is presented from the standpoint of simultaneous heat and mass transfer, with taking the effect of mechanical vibration added vertically into consideration.

Steady-state distributions for the temperatures and concentrations of the particles and the heating gas, and for the moisture content of the particles are numerically calculated based on the present model. The calculated results show fairly good agreement with the experimental data, which were obtained from the drying experiments of brick particles in a three-stage IFB using comparatively low temperature air(40-60°C) as the heating gas.

It has been found within the range of the experimental conditions employed that, the mechanical vibration added vertically enhances the over-all drying rate of the particles and its effect can be considered equivalent to an increase in the air velocity.     

Factors affecting the resistance of moisture transfer during drying of cut grass

Measurements have been made of the drying rate of thin layers of cut grass, with forced convection of air at 250c and 50% relative humidity. From measurements of the exposed surface areas of the grass and the evaporation rates measured during drying, estimates have been made of the grasses' resistance to moisture transfer.

Some of the grasses had been mechanically treated, by conventional agricultural mower conditioners, to improve the drying rates. An expression has been derived relating resistance to moisture transfer to the conditioning treatment and physical characteristics of the grass.     

IMPINGING JET DRYER

In coating and gravure printing, an impinging jet nozzle with high thermal efficiency for drying of coated film was developed.

Trial production 0f 40 kinds of nozzle enables to develop a high-performance impinging jet nozzle with heat transfer coefficient 1.5 times larger than that of current slit nozzle, through measurement of heat transfer coefficient, visualizations of air flow and heat transfer, and measuremenu of jet velocity and turbulence distribution. The purpose of the trial production was to expand a range of high heat transfer and promote turbulence compared with the current nozzle.

Paying attention to mass transfer within gravure ink coated film, drying characteristic of the film was analyzed by numerical solution of a set of equations governing the drying process in which concentration dependencies 0f the diffusion coefficient and the equilibrium vapor pressure were considered.

Applying these analyses. an industrial scale dryer with excellent drying efficiency has finally been developed.     

MASS TRANSFER AND DIFFUSION COEFFICIENT DETERMINATION IN THE WET AND DRY SALTING OF MEAT

Dehydrated salted meat is widely used in Brazil as a very important source of animal protein. The main objective of this kind of processing is water removal. initially by osmotic pressure changes and then by drying, resulting in a product with intermediate moisture levels.

In this work, mass transfer and salt diffusion in pieces of meat submitted to wet and dry salting were studied. Slabs of beef m. trapezius with an infinite plate geometry were salted in a NaCl saturated solution or in a dry salt bed, at two temperatures (10 and 20°C) and different time exposures (120 min and 96 hours). Equilibration studies were extended up to six days.

It was observed that water loss increased with salt uptake, for increasing periods of times. At 20°C the moisture loss was higher than it was at 10°C in both salting processes. On the other hand, the kinetics of salt uptake and moisture loss were of greater importance in the process of dry salting than in that of wet salting.

The salt diffusion coefficient for wet salting was 0.26 × 10^-10m²/s at20°C and 0.25 × 10^-10 m²/s at 10°C and for the dry salting the values were 19.37 × 10^-10 m²/s at 20°C and 17.21 × 10^-10 m²/s at 10°C.     

HEAT AND MOISTURE TRANSFER IN CAPILLARY-POROUS BODIES SOME EXPERIMENTAL METHODS OF INVESTIGATION

This paper presents a synthesis of our scientific activity in the area of heat and moisture transfers in capillary-porous bodies. The materials which have been under investigation are essentially in the field of Civil Engineering but our ways of experimentation may be generalized.

Transfers may be characterized by two independent variables : temperature and water content. We have been concerned by the achievement of measurement technics of these quantities and of perturbation technics of materials at equilibrium.

When comparing a fitting model and the temperature or water content response to such perturbations, it is possible to infer the values of parameters which are significant. Then, the experimental results must be compared with results obtained by other authors or by means of different methods.

In the future, the assumption of an unstrained porous skeleton will not be kept any longer and the coupling of transfers with mechanical phenomena will be considered.     

A COMPARTMENTAL MODEL OF THIN-LAYER DRYING KINETICS OF ROUGH RICE

Rough rice at about 21% (wet basis) was dried at various conditions of temperatures and evaporating capacities of air. The influence of both parameters on drying rate has been studied. At high temperatures, high drying rates can be achieved with low evaporating capacities. In addition, desorption isotherms of rough rice were measured at 35, 60 and 85°C and the experimental isotherms data were fitted using a modified Pfost equation.

A compartmental model was developed to simulate the grain moisture content. Heat and mass transfer coefficients were optimized using a Nelder & Mead method. Internal mass transfer coefficient was written as an exponential function of the average moisture content and temperature of the grain and the external mass transfer coefficient as a function of air temperature. The compartmental approach predicts very well the average moisture content with a mean error of about 5% in static and dynamic conditions.     

MULTIPHASE HYDRODYNAMICS AND SOLID-LIQUID MASS TRANSPORT IN AN EXTERNAL-LOOP AIRLIFT REACTOR—A COMPARATIVE STUDY

The solid-solid mass transfer performance of an external-loop airlift reactor was measured by dissolution of benzoic acid coated on nylon-6 particles, and the hydrodynamics of the gas-liquid-solid multiphase system in the airlift reactor were investigated. The solid-liquid system was designed to simulate the micro-carrier culture of animal cells, and some typical suspensions of immobilized enzyme particles.

The solid-liquid mass transfer coefficient remained constant below a superficial air velocity of 0.04 ms^-1 for the particles examined, but increased rapidly with further increase in gas velocity. Solids loading (0.3-3.5% w/w) did not affect the mass transfer coefficient in turbulent flow.

The mass transfer coefficient was correlated with energy dissipation rate in the airlift reactor. The mass transfer coefficient in stirred vessels, bubble columns, fluidized beds, and airlift reactors was compared.

Over an energy dissipation Reynolds number of 4-400, the solid-liquid mass transfer coefficient in the airlift device was comparable to that obtainable in fluidized beds. The performance of the airlift was distinctly superior to that of bubble columns and stirred tanks.     

DETERMINATION OF MOISTURE DIFFUSIVITY OF PINE NUT SEEDS

The mechanism of drying and the diffusion of water in fresh pine nut seeds (2.5-2.62mm diameter) were successfully interpreted and modeled by using Fick's law. The initial moisture content of fresh pine nut seed was 23-24% and drying temperatures (45-60°C) were varied, but the drying air was kept at constant velocity and humidity.

The effective diffusivity was estimated from drying rate curves and expressed by an Arhenius relation. In addition, the absorption, and desorption-isotherms for fresh pine nuts were estimated at 20°C at water activity of 0.15-1.00. The isotherms of the fresh pine nuts were estimated in experimental runs.