SIMULATION OF TRANSPORT DYNAMICS IN FLUIDIZED-BED DRYERS

ABSTRACT

A mathematical model for predicting three-dimensional, two-phase flow, heat and mass transfer inside fluidized-bed dryers has been developed. The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum and energy for both phases inside the dryer, and is coupled with correlations concerning interphase momentum-, heat-, and mass-transfer.

It is shown that the model can predict the most important engineering aspects of a fluidized-bed dryer including pressure drop, particle holdup, temperature distribution in both phases as well as drying efficiency all over the fluidized-bed. Plug-flow conditions are predicted for the gas phase, while back-mixing is predicted for the particles.

The effect of particle mass-flow-rate on fluidized-bed dryer performance is evaluated. It is shown that the lower the particle mass flow-rate, the more intense the horizontal moisture gradients, while the higher the particle rate the more uniform the moisture distribution throughout the bed.     

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.     

STEAM DRYING OF WOOD CHIPS IN PNEUMATIC CONVEYING DRYERS

A model for a pneumatic conveying dryer is presented. Although the main emphasis is put on superheated steam drying of wood chips, it can be used for other porous materials as well

The model includes a comprehensive two-dimensional model for the drying of single wood chips which accounts for the main physical mechanisms occurring in wood during drying. The external drying conditions in a pneumatic conveying dryer were calculated by applying the mass, heat and momentum equations for each incremental step in dryer length. A plug flow assumption was made for the dryer model and the single particle and dryer models were solved in an iterative manner. The non-spherical nature of wood chips were accounted for by measuring the drag and heat transfer coefficients

Model calculations illustrate the complex interactions between steam, particles and walls which occur in a flash dryer. The drying rate varies in a very complex manner through the dryer. The internal resistance to mass transfer becomes very important in The drying of less permeable wood species such as spruce. Two effects were observed as the particle size was increased: firstly the heat transfer rate decreased, and secondly the residence time increased. To some extent, these effects compensate for each other, however, the net result is that larger chips have a higher final moisture content.     

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.     

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.     

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.     

PARAMETERS AFFECTING GRAIN DRYING BY IMMERSION IN A HOT PARTICULATE MEDIUM

High temperature particulate medium conduction grain drying is a very promising technique. However, lack of basic drying characteristic information has resulted in unsuccessful attempts to develop an efficient, economical, continuous flow dryer.

In this study, the effects of initial grain moisture content, initial medium temperature, medium particle size, medium to grain mass ratio, and contact time on the drying of shelled corn immersed in hot sand are evaluated.

Moisture losses ranged between 0.2 and 5.2 percentage points (wb).     

COMPARISON OF SUPERHEATED STEAM AND AIR OPERATED SPRAY DRYERS USING COMPUTATIONAL FLUID DYNAMICS.

In this paper a numerical simulation of a spray dryer using the computational fluid dynamics (CFD) code Fluent is described. This simulation is based on a discrete droplet model and solve the partial differential equations of momentum, heat and mass conservation for both gas and dispersed phase.

The model is used to simulate the behaviour of a pilot scale spray dryer operated with two drying media : superheated steam and air Considering that there is no risk of powder ignition in superheated steam, we choosed a rather high inlet temperature (973 K). For the simulation, drop size spectrum is represented by 6 discrete droplets diameters, fitting to an experimental droplets size distribution and all droplets are injected at the same velocity, equal to the calculated velocity of the liquid sheet at the nozzle orifice.

It is showed that the model can evaluate the most important features of a spray dryer : temperature distribution inside the chamber, velocity of gas, droplets trajectories as well as deposits on the walls. The model predicts a fast down flowing core jet surrounded by a large recirculation zone. Using superheated steam or air as a drying medium shows only slight differences in flow patterns. Except for the recirculation which is tighter in steam.

The general behaviour of droplets in air or steam are quite the same : smallest droplets are entrained by the central core and largest ones are taken into the recirculation zone. In superheated steam, the droplets penetrate to a greater extent in the recirculation zone. Also, they evaporate faster. The contours of gas temperature reflect these differences as these two aspects are strongly coupled. In both air and steam there is a “cool” zone which is narrower in steam than in air. Finally, the panicle deposit problem seems to be more pronounced in air than in steam.

Adding to the inherent interest in using superheated steam as a drying medium, the model predicts attractive behaviour for spray drying with superheated steam. In particular. under the conditions tested with the model, a higher volumetric drying rate is obtained in superheated steam.     

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.     

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.     

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.     

HYDRODYNAMICS OF VIBRO-FLUIDIZED BEDS

Vibro-fluidized bed dryers are being extensively used in the industry to dry granular particles of wide particle size distribution. For drying applications of limited air inlet temperature and hard to dry granules--high diffusion resistance of moisture inside the qranules--baffles are normally provided in these dryers to increase the residence time of particles. The residence time distribution of granules in vibro-fluidized bed dryers is of high importance to successfully model such dryers. There has been some studies reported in the literature for average residence time of granules in vibro-fluidized beds without baffles, but there has been no work reported for average residence time in vibro-fluidized beds with baffles and residence time distribution for beds with or without baffles. Experimental runs were carried out in this study in the 0.93 m2 (10 ft2 ) pilot plant vibro-fluidized bed dryer with baffles to determine the residence time distribution of dry granules and granule height profile through the length of the dryer.

Among all the dryer operating variables considered in this study, vibration amplitude and baffle spacing were identified as most significant. Values of the average residence time and particle diffusivity were obtained for the entire range of the expected operation of the pilot-scale or commercial scale dryers. These values of average residence time and particle diffusivity, along with the appropriate drying rate (kinetic) data, enable full modeling of vibro-fluidized bed dryers.     

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.     

Heat and mass transfer in apple cubes in a microwave-assisted fluidized bed drier

In the present study, a pilot scale microwave assisted fluidized-bed dryer was designed and used to dry apple cubes. A model was developed to describe heat and mass transfer in apple cubes during drying in a combined microwave-assisted fluidized-bed dryer. A numerical solution based on the finite difference method was used to develop the model for moisture distribution and temperature variation of samples. The model was validated using experimental data, including average moisture content, center and surface temperature at various air temperatures and microwave power densities.     

A WASHING THEORY FOR UNSATURATED FILTER CAKES USING THE CAPILLARY MODEL

A rigorous washing theory is developed using the area averaging technique for unsaturated filter cakes. Limiting cases of the resulting equations are investigated. The assumptions used in the modelling are verified.

The mass transfer parameters, which are evaluated by the application of the moment analysis, are shown to be directly proportional with the volumetric flow rate of the wash liquor. Experimental results also indicate that, for a given wash liquor volumetric flow rate, the increase in the cake thickness causes an increase in the mass transfer parameters.

It should be noted that the proposed model is applicable for large particle sizes. As particle size becomes finer and the size distribution becomes wider, the model should be modified by including dead void spaces containing pockets of the mother liquor in the filter cake     

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.     

STEAM DRYLNG OF WOOD FUELS

The objective of this work is to investigate some of the important aspects in the design of a steam band dryer for wood fuels. For this purpose the drying of the material in a bench-scale fixed bed dryer has been studied.

Drying times and thermal efficiencies for experiments conducted under different conditions are compared. The investigated materials are soft-and hardwood chips and softwood bark.

The thermal efficiency, the part of the sensible heat which is used during one passage of the steam through the bed, increases with increasing mass load (mass of dry matter per unit area) and with decreasing steam mass flux. At a mass load of 30 kg/m the thermal efficiency is about 0.85 even at steam mass fluxes as high as 0.6 kg/m² s (1.2 m/s). The thermal efficiency proves to be almost independent of pressure and temperature of the steam.

Due to the very inhomogeneous materials the steam mass flow distribution was uneven. This causes a decreased thermal efficiency. When bark     

HEAT TREATMENT OF CHOPPED ALFALFA IN ROTARY DRUM DRYERS

This paper deals with the heat treatment of alfalfa chops during the high temperature dehydration process. It outlines the dryer characteristics, difficulties and potential errors in measuring temperatures in the dryer, computation techniques, the relationships between moisture and temperature during drying, and the potential effect of dehydration on the destruction of the insect Hessian Fly due to elevated temperatures.

From the analysis based on an existing computer model for dehydration of alfalfa chops, and the available field data, it is shown that the dried chops will attain a temperature of 90°C or higher when the input temperatures are between 500°C and 800°C. These conditions apply to the drying of wet alfalfa (moisture content more than 55 percent wet basis). The plant material loses a large portion of its moisture in the first few seconds in the dryer. The rapid release of moisture may cause the rupture or detachment of particles such as eggs, larva, pupa, and insects from the plant material. These small particles are exposed to an intense heat and rapid dehydration.     

NONDESTRUCTIVE MEASUREMENT OF MOISTURE DIFFUSION COEFFICIENT IN WOOD DRYING

The computer tomography(CT image of wood was analyzed to estimate the moisture content from CT number. Comparing moisture contents, densities and CT numbers, moisture distributions were nondestructively determined by CT numbers detected with the scanner.

By periodically measuring CT images of the same cross section of specimens in drying, change of moisture distribution was computed. The coefficients of moisture movement at given positions inside the specimen were directly calculated from Fick's Law with known values of moisture content change, distance and drying time.

The diffiion coeficient was described as a function of various driving forces of moisture content, partial vapor pressure and chemical potential of moisture in wood. The results were comparable to data in the literature. Furthermore, it is shown that diffusion coefficients based on moisture content varies as a curve with the maximum value at about 15% m.c. during drying, and that the moisture content is actually adaptable to the driving force for moisture movement in wood because of capability over wide moisture content range.     

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.