A New Approach to Contact Drying Modelling

ABSTRACT

This paper deals with contact drying modelling. The more general models of granular material contact dryers are based on assumptions proposed by Schlunder and al. (1.21. In this paper, a sensitivity study of the models is presented in order to find and to explain the influence of the different arameters.

A new approach, based on the same Schlunder's assumptions, but with less restrictive hypothesis, which can be applied to drying in the presence of an inert gas as well as vacuum drying and which take into account phenomena which were ignored untill now such as the local grain dehydration kinetics or the vapour diffusion inside the bed has been developped.

This new model has been compared uith some experimental results found in the litterature. A good agreement between the calculated and the experimental results has been observed. Moreover, this model is able to justify some assumptions made by Schlunder, which have not been so untill now.     

Image Analysis, Homogenization, Numerical Simulation and Experiment as Complementary Tools to Enlighten the Relationship between Wood Anatomy and Drying Behavior

This paper has been written for a special issue devoted to the works done in France in the field of drying. Therefore, it aims, through numerous examples, to show the spirit which initiates and guides the research work of the Forest Products Unit at ENGREF : how more and more microscopic information can be included in the study of the drying process ?

Two steps are involved :

•microscopic observation and experiments to predict the macroscopic properties

•use of the macroscopic properties (the previous step + experiments carried our at the macroscopic scale) to predict the drying behavior.

In this approach, each prediction comes from a model, that means assumptions, formulations, calculations and then validation.

Several tools (image analysis, homogenization, measurement of microscopic and macroscopic properties, numerical simulation of heat and mass transfer, refined drying experiments) are used to study the drying of wood.     

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 IN THE SHORT-TERM CONTACT OF THE MOIST MATERIALS WITH THE HEATING SURFACE

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.     

CONVECTIVE DRYING OF PAPER CALCULATED WITH A NEW MODEL OF THE PAPER STRUCTURE

Paper drying models are based on the assumption of a rigid solid matrix. Because of the interaction of water molecules and paper fibre the dimensions of the sheet are changing, especially the thickness. These changes influence the moisture transport within the material. A model of the paper structure has been developed taking into account different kinds of pores in the paper.

By the assistance of this model the dependence between water content and thickness or transport parameters as permeability and thermal conductivity can be predicted. The only informations which are needed are sorption isotherms, apparent paper density and permeability of the single phase flow. Further informations as the pore size distribution are useful but not necessary.

The transport parameters are generated in the suggested way for wood pulp. It is shown that in the case of convective drying, the agreement between experimental results and model simulations is good.     

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.     

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.     

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.     

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.     

KINETICS OF THE CLAY ROOFING TILE CONVECTION DRYING

Kinetics of the convection drying process of flat tile has been investigated experimentally in an industrial tunnel dryer. Several velocities of wet tile movement through the dryer were tested to obtain maximum allowable drying rate curve. As there are various models to describe the kinetics of convection drying, finding a model that would fairly well approximate the kinetics of the whole drying process was part of the research. Especially the polynomial and exponential models were tested.

It was found that exponential model of the type: B(t) = (a-B_e. EXP(-bt²) +B_et (-dB(t)/dt) = 2bt(B(t)-B_e significantly correlates the kinetics of the whole tile drying process.

Applying the maximum allowable drying rate curve obtained for flat tile in the first period of drying, a grapho-analytic model for the optimal conducting of the process has been developed.     

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.     

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.     

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.     

AUTOMATIC CONTROL OF COMMERCIAL CROSSFLOW GRAIN DRYERS

An unsteady state model of crossflow grain drying has been developed. The model has been used to develop several empirical models as process models for a feedforward dryer control system.

The control system consists of an empirical drying model, an on-line moisture meter, a tachometer, data acquisition software, a microcomputer, and the feedforward/feedback control software. It has been tested on several commercial crossflow maize (corn) dryers. With the inlet grain moisture content varying between 16.1% to 34.3% (w.b.), the new control system controlled the outlet grain moisture content to + 0.6% of the set point.     

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.     

AN APPLICATION OF SIMULTANEOUS HEAT AND MASS TRANSFER IN A CYLINDER USING THE FINITE-DIFFERENCE METHOD

A study of simultaneous heat and mass transfer during drying an infinite cylinder shape material (twigs of ilex paraguayenais saint hilaire) was carried out. The finite-difference method was used to solve the drying model and a simultaneous heat and mass balance in each node was made. Models with different assumptions were tested and the external mass transfer coefficient was used as a parameter to fit the model to experimental data. The thickness of the node and the time step were selected considering the system stability.

Drying temperature, twig diameter and air velocity were selected as study variables. The models results were in good agreement with experimental measurements giving mass coefficient values between 1.97 10^-4and 9.55 10^-4 Kg/m² s.     

CONTACT DRYIXG OF WOOD VENEER

A model for contact drying of wood veneer is presented and compared with experimental results. The model is and-dimensional and assumes that convective transport of liquid and vapor is dominant for the drying conditions examined. Model results are in good agreement with the experimental data.

A parameter study indicates that total drying time is a strong function of platen temperature and veneer thickness. The model indicates that the spacing of ventilation grooves does not affect drying rate significantly, but has a large effect on pressure buildup in the veneer. Veneer permeability shoved a similar effect--with lover permeabilities resulting in slightly slower drying, but significantly higher internal pressure.     

THE INFLUENCE OF PRESSURE AND TEMPERATURE ON THE KINETICS OF VACUUM DRYING OF KETOPROFEN

This paper explores the influence of temperature and pressure on drying kinetics of 2-(3-benzoylphenil propionic acid) ketoprofen, in a vacuum dryer on laboratory scale, Experimentally determined relations between moisture content and drying rate vs time, were approximated with an exponential model. Model parameters were correlated with drying conditions (temperature, pressure) and defined by functions of their potentions.

From an energy balance of the process, a mathematical model for simulating dependence of sample temperature vs drying time, and moisture content of material, has been developed.

Simulation of the drying kinetics and sample temperature, by use of those functional dependencies shows good agreement with experimental results.     

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.