A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

A nonequilibrium distributed parameter model for rotary drying and cooling processes described by a set of partial differitial equations with nonlinear algebraic constraints is developed in this work. These equations arise from the multi-phase heat and mass balances on a typical rotary dryer. A computational algorithm is devekped by employing a polynonial approximation ( orthogonal collocation) with a glotal splinc technique leading to a differential-algebraic equation ( DAE) system. The numerical solution is carried out by using a standard DAE solver.

The two- phase-flow heat transfer coelficient is computed by introducing a correction factor to the commonly accepted correlations. Since interaction between the falling particles are considered in the correction factor,the results are more reliable than those computed by assuming that heat transfer between a single falling particle and the drying air is unaffected by other particles. The heat transfer computations can be further justified via a study on the analogies between heat and mass transfer.

The general model devloped in this work is mathematically more ritorous yet more flexible that the lumped parameter models established by one of the authors (Douglas et al., (1993)). The three major assumptions of an equilibrium operation, perfect mixing and constant drying raic, are removed in the distributed parameter model.

The simulation results are compared with the operational data from an industrial sugar dryer and predictions from earlier models. The model and algorithm successfully predict the steady state behaviour of rotary dryers and collers. The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

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.     

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.     

THE FLOODING CAPACITY OF PERFORATED PLATES IN ROTATING LIQUID-LIQUID-SYSTEMS†

Centrifugal extractors found wide applications in the industry, but up to now very little is known about what happens inside and how to calculate fluid-dynamic and mass transfer. For the basic research of dispersed liquid-liquid-systems in centrifugal fields a model centrifuge was built which is resistant to the high loads produced by rotation and which enabled us to observe the flow mechanism at the flooding points.

The processes inside have been measured and photographed by a high-speed-camera.

The calculation of centrifugal extractors is based mainly on the contact surfaces of the phases and the contact times. The maximum flow or flooding capacity is determined by three limits. Two of them are determined by the interface locations inside, controlled from the back pressure. The third limit is given by the maximum combined flow. This limit is dependent on the set of internals, the rotor speed and the physical properties of the liquid system. The experimental results will be shown and compared with new theories for the flooding capacities of perforated cylindrical plates in rotating liquid-liquid-systems.

The results predicted using the mathematical model for calculating the capacities are in fair agreement with the measurements.     

Welding Mechanisms of Plastics: A Review

Strength of welded joints is a function of technological parameters of the production process. The type of function is dependent on the welding mechanism. Different mechanisms were found under various welding conditions. The processes included in the plastic welding mechanism are divided into two groups:

1) Processes which realize the joining of the parts.

2) Processes which create conditions for the first group to proceed. The first series of processes includes:

a) diffusion of macroradicals, molecular segments or molecules of the polymer which can be either in a solid, melted or dissolved state.

b) convective mass transfer.

c) recombination of macroradicals across the contact surface.

d) physical (surface) interaction.

e) any combination of processes described above.

The second group contains:

a) formation of the real contact surface.

b) formation of the macroradicals.

c) destruction and removal of inert layers which prevent real contact of active material.

Each process and the conditions of its proceeding are discussed individually.     

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.     

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     

MULTI-STAGE SPRAY DRYING METHOD IN MANUFACTURING HEAVY DUTY DETERGENTS

Collision of droplets; counter-current spray dryer; drying rate; heat transfer; nonphosphated detergent; spray drying

The spray drying method of non-phosphated granular detergents is studied to decrease the amount of agglomerate particles. The formation of agglomerates is mainly influenced by the concentration of droplets in spray cloud and the water content of droplets at the time of collision. The overlaps of different spray clouds should be de- creased.

The drying rate near the nozzle zone is considerably faster than that calculated by Ranz-Marshal's equation. According to these phenomena, “Multi-stage spray drying” is developed, which is characterized by in stalling plural spraying stages in a spray dryer.

Consequently, non-phosphated detergents are manufactured with the same powder properties and productivity as phosphated detergents.     

SCALE-UP OF CONTACT DRYERS

The scale-up of contact dryers is still based on experimental drying curves. In order to keep the effort to a minimum the drying curve is determined using a small laboratory or pilot dryer of similar geometry to the production dryer.

This paper introduces a new scale -up method for contact dryers. The new scale-up method is based on the assumption that heat transfer is the controlling mechanism. The scale-up method is derived from the material balance, the energy balance, the kinetic equation of heat transfer and thermodynamic equilibrium. The scale up method can be used to convert the drying time required to achieve a certain residual moisture content from the laboratory or pilot dryer to the production dryer and/or different drying conditions.

The scale-up method was verified by drying test with four different products in conical mixer dryers of 1, 60, 250, 1000 I volume. Two products were free flowing and two products were non free flowing in the wet state. The products can be considered non-hygroscopic in the moisture range investigated.     

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.     

UNSTEADY, TWO-DIMENSIONAL HEAT AND MASS TRANSFER IN A PACKED BED OF FINE PARTICLES WITH AN ENDOTHERMIC PROCESS

The basic differential equations controlling the temperature and concentration field in a single packed bed of fine particles were derived and solved for the general case in which unsteady, two-dimensional heat and mass transfer lakes place with an endothermic process.

The time-change of particle- and fluid-temperature and concentration of water vapor (humidity) were calculated by a numerical method which assumed that the rate of the endothermic process can be expressed by a first-order rate equation and that the fluid flowing through the bed is of the piston flow type.

The experiments were conducted for the drying of silica-gel and the two-stage dehydration reaction of natural gypsum to demonstrate the applicability of the present theoretical analysis.

It has been found that the calculated results show satisfactory agreement with the measured data within the range of the experimental conditions employed.     

Steam Drying - Modelling and Applications

The concept of steam drying originates from the mid of the last century. However, a broad industrial acceptance of the technique has so far not taken place. The paper deals with modelling the steam drying process and applications of steam drying with in certain industrial sectors where the technique has been deemed to hove special opponunities.

In the modelling scction the mass and heat transfer proceases are described along with equilibrium, capillarity and sorption phenomena occurring in porous materials during the steam drying process. In addition existing models in the literslure are presented.

The applications discussed involve drying of fuels with high moisture contcna, cattle feed exemplified by sugar beet pulp. lumber. paper pulp. paper and sludges.

Steam drying is compared to flue gas drying of biofuels prior to combustion in a boiler. With reference to a current insrallation in Sweden. the exergy losses. as manifested by loss of co-generation cupacity. are discussed. The energy saving potentid when using steam drying of sugar beet pulp as compared to other possible plant configurations is demonstrated.

Mechanical vapour recompression applied to steam drying is analysed with reference to reponed dau from industriul plsnts. Finally. environmcntul advantages when using steam drying are presented.     

VACUUM CONTACT DRYING OF SELECTED BIOTECHNOLOGY PRODUCTS

The paper is mainly concentrated on investigations of the vacuum contact drying of the following biomaterials: (1) beer yeast, (2) whey and its components: proteinaceous liquid, lactose, post-lactose liquid, (3) saturated solution of the citric acid, (4) post-fermentation broth of the fodder antibiotic bacitracin. The investigations of vacuum contact drying process in which dried material adheres closely to a hot surface were performed. In order to make possible the determination of optimal process parameters the measurements were performed for various constant temperatures of the hot surface, total pressures in vacuum chamber and layer thickness of biomaterials.

The effective thermal properties for dry layers of selected biomaterials depending on temperature and total pressure were also experimentally determined.

A mathematical model of the vacuum contact drying for most intensive regime of its performance i.e. boiling one was presented. It will enable the process simulation and estimation of the dryers efficiency depending on process parameters.

In addition, investigations of beer yeast viability depending on the hot surface temperature and the total pressure were performed.     

HIGH INTENSITY DRYING

A mathematical model simulating the heat and mass transfer process during high intensity drying of paper and board has been developed. The model is successful in predicting the vapor pressure developments, pressure driven bulk flow of liquid and vapor, and increased drying rates during high-intensity drying, closely matching the experimental determination.

The model predicts substantial amounts of water removal in the liquid form during high-intensity drying being pushed out of the web by pressurized vapor zone. Water removal by pressure flow of liquid could account for as much as one-third of the total water removed.

Similar to drying under conventional conditions, the existence of a dry zone, wet zone and an intermediate zone with accompanying advancing heat pipe has also been shown for drying under high intensity conditions.     

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.     

Uneven Ink Absorption and Its Relation to Drying of Coated Papers

The aim of this work was to study mottling in offset printing. The papers studied were coated and princed LWC-papers.The base paper was obtained from a commercial source. Both macroscopic and microscopic analyses were performed.The conventional macroscopic methods take into account variations in nm-cm scale while the microscopic methods consider the nm-pm scale.

The used conventional methods could not emplain mottling. Microscopic studies, however, revealed that mottling could be a problem caused by varying coat weight and surface structure.

The influence of different drying strategies was also studied. The beet print result was obtained on paper where the drying was relativeiy intense in the beginning of the process and mild during the coating color immobilization stage. Uneven binder migration was not found in these samples.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

CONTRIBUTION TO THE ANALYSIS OF THE SELECTIVITY OF GAS-LIQUID REACTIONS PART II: COMPARISON OF EXPERIMENTAL RESULTS WITH MODEL PREDICTIONS

The chlorination of paracresol is used in an experimental study of selectivity in gas-liquid contactors.

Experiments in a batch reactor show the influence on selectivity of the dimensionless numbers presented in Part I and involving competition between mass transfer and chemical reaction together with the hydrodynamics.

The extension of open reactor model presented in Part 1 to the batch reactor permits a comparison between theory and experiments and shows a good agreement     

HEAT AND MASS TRANSFER IN THE SHORT-TERM CONTACT OF THE MOIST MATERIALS WITH THE HEATING SURFACE

Abstract

Compounded boundary-valued problem of the diffusion-filtering heat and mass transfer with arbitrary dimensions of the transfer potential vector was raised and solved based on the theory of short-term contact between the moist material and heat-transfer surface.

The boundary lines of the application of the short-term contact models were established.

The solution of the problem allows to select the directions of the intensification of the drying processes with short-term contact of the phases and to calculate various technological characteristics of the drying processes.     

FRUIT AND VEGETABLE POWDERS PRODUCTION TECHNOLOGY ON THE BASES OF SPRAY AND CONVECTIVE DRYING METHODS

The peculiarities of fruit and vegetable powders production technology based on spray & convective drying methods are shown.

The experimental data related to the drying kinetics of apple juice droplets as well as the production flow diagrams and the performance of a spray dryer intended for the treatment of hygroscopic pasty products are presented.