THE DEVELOPMENT AND VALIDATION OF A SYSTEM MODEL FOR A COUNTERCURRENT CASCADING ROTARY DRYER

An overall system model for a countercurrent rotary dryer has been developed with the ullimale aim of assessing controller pairings in these dryers. This model is based on heat and mass balances within dryer regions combined with two subsidiary models, one describing the equipment (which determines particle transport and heat transfer)and the other describing the behaviour of the material (the drying kinetics). Six partial differential equations have been set up to evaluate six state variables: solids moisture content, solids temperature, gas humidity, gas temperature, solids holdup and gas holdup as functions of time and rotary dryer length. A control-volume method has been used to reduce the six partial differential equations with respect to time and the length of the rotary dryer to six ordinary differential equations in time.

The drying model has been implemented in the SPEEDUP flowsheeting package (with FORTRAN subroutines) The model has been validated by fifteen experiments-in a pilot scale countercurrent-flow rotary dryer (0.2m in diameter and 2m in length)     

INDIRECT THERMAL DRYING OF LIGNITE: DESIGN ASPECTS OF A ROTARY DRYER

ABSTRACT

An investigation of the thermal drying of lignite has been carried out, by using an indirect heat pilot rotary drum. The process aims at the production of dry lignite and clean steam as part of a gasification procedure. Both flighted and bare drum modes have been employed. Temperature profiles along the dryer length, the amount of evaporation (moisture conversion) and the solids residence time distribution (RTD) were measured. A non-isothermal model was tested under three different regimes of solids flow. Model integration, by taking account of experimental amount of evaporation at dryer exit and temperature profiles along the dryer length, has been utilized in the validation of drying kinetics and heat transfer correlations. Model predictions compare satisfactorily with the operating data of an indirect heat industrial lignite dryer. Overall heat transfer coefficients of the pilot rotary dryer were found to agree well with those reported for direct heat dryers.     

A Funtadamental Study on Particle Transport Through Rotary Dryers for Flight Design and System Optimisation

ABSTRACT

A model for particle transport in a flighted horizontal rotary dryer is developed in this paper. Mathematical principles applied to the current study are in the areas of differential calculus and analytical geomentry. In contrast to the conventional approaches which are either based on mpirical/semi-empirical correlations or obtained from the investieation of single particle trajectories, this paper develops rigorous mathematical analysis of the transport of bulk solids. A variety of important issues in rotary drying, such as axial flowrate of solids, retention time distribution and solid holdup are addressed and treated by using non-traditional methods. Since the model takes dimension, number and geometry of flights into account, it possesses the following two haracteristics : (1) it is not only useful in the study of rotary drying dynamics, but lso applicable to other processes employing flighted rotating cylinders (such as granulation drumsand crushers) and (2) based on the model, an optimal drum configuration can be designed by using optimisation techniques. The model can be incorporated within a distributed arameter dryer model developed previously to form a more rigorous integrated dynamic model. A heoretical foundation for optimal flight design by using the current model is explained.

A pilot scale perspex rotary dryer equipped with a video camera has been constructed and used for model validation. Raw sugar was handled in the experiments. Particle transport was observed and measured by using a flow visualisation technique supplemented with traditional sampling methods. A significant model quality improvement has been observed through a comparative study between the newly developed model and conventional ones.     

SOLIDS TRANSPORTATION MODEL OF AN INDUSTRIAL ROTARY DRYER

ABSTRACT

A complete simulation model has been developed for an industrial rotary dryer to account for the heat and mass exchange between the solids and the gas. This simulator is mainly composed of three models: solids transportation model, furnace model, and gas model. The solids transportation model is the modified Cholette-Cloutier model It consists of a series of interactive reservoirs which are subdivided into an active and a dead compartments to account for the characteristic extended tail of the residence time distribution (RTD) curves observed in industrial dryers.

To expand the validity of the model, experiments have been performed in an industrial rotary dryer to obtain RTD curves under different mineral concentrate and gas flow rates. This paper describes these experiments and presents the variation of the average residence time and model parameters as function of solids and gas flow rates.     

A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

ABSTRACT

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.     

INDIRECT THERMAL DRYING OF LIGNITE: DESIGN ASPECTS OF A ROTARY DRYER

An investigation of the thermal drying of lignite has been carried out, by using an indirect heat pilot rotary drum. The process aims at the production of dry lignite and clean steam as part of a gasification procedure. Both flighted and bare drum modes have been employed. Temperature profiles along the dryer length, the amount of evaporation (moisture conversion) and the solids residence time distribution (RTD) were measured. A non-isothermal model was tested under three different regimes of solids flow. Model integration, by taking account of experimental amount of evaporation at dryer exit and temperature profiles along the dryer length, has been utilized in the validation of drying kinetics and heat transfer correlations. Model predictions compare satisfactorily with the operating data of an indirect heat industrial lignite dryer. Overall heat transfer coefficients of the pilot rotary dryer were found to agree well with those reported for direct heat dryers.     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

ABSTRACT

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

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.     

Dynamic Characteristics of Solids Transportation in Rotary Dryers

Abstract

An original method was proposed for the determination of the mean residence time in a continuous dryer, based on the step-change in the solids feed rate. The method has been validated through experiments performed in a pilot-scale rotary dryer. The effect of the solids flow rate, gas flow rate, dryer rotation speed, and dryer slope was quantified. Several design correlations to predict the residence time in rotary dryers were critically evaluated, and a new, more accurate correlation was derived.     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

ABSTRACT

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

COMPARISON OF RESIDENCE TIME MODELS FOR CASCADING ROTARY DRYERS

ABSTRACT

The predictions of the models of Matchett and Baker (1988) Saeman and Mitchell (1954) and Friedman and Marshall (1949) for the solids residence time in rotary dryers have been compared with both pilot-scale and industrial-scale data. A countercurrent pilot-scale dryer of 0.2m diameter and 2m long has been used with air velocities up to 1.5 ms^?1 to measure the residence times of sorghum grain, The average discrepancy for the solids residence time between the predictions and the experiments that were carried out in the pilot-scale rotary dryer is — 10.4% Compared with the models of Friedman and Marshall (1949) and Saeman and Mitchell (1954) for the pilot-scale data obtained here, the Matchett and Baker model is more satisfactory for predicting the solids residence time in this pilot-scale dryer. It has also been found that the model of Matchett and Baker describes the industrial data of Saeman and Mitchell (1954) than the correlation of Friedman and Marshall (1949).     

PNEUMATIC DRYING OF MEALS: APPLICATION OF THE VARIABLE DIFFUSIV1TY MODEL

ABSTRACT

The superficial and bound moisture removal from soya meal was studied in a pneumatic dryer. The effect of external condition over the effective diffusivity in drying kinetics prediction has been demonstrated and a model that considers time variable diffusion coefficient was developed and correlated with gas temperature and velocities. A simple experimental technique using a pulse injection of humected solid was utilized to determine real drying kinetics under steady state operation with solids recycling. The model fitted the experimental data well over a gas temperature range between 100° C and 300° C and gas velocities of 3.5 m/ s and 20 m/ s.     

SIMULATION OF FORESTRY BIOMASS DRYING IN A ROTARY DRYER

ABSTRACT

Drying of forestry biomass in a rotary dryer has been performed. The raw material used was Erica Arborea belonging to the ever-green, broad leaves ecosystem which covers Central Greece and other Mediterranean countries. The study was part of a project concerning a Greek biomass pyrolysis demonstration plant where drying of biomass is very important in the contribution to the global energy balance and product yields of pyrolysis.

The study includes two parts. First, the experimental part concerns the influence of air flowrate, temperature, rotation speed and inclination of a laboratory rotary dryer to biomass residence time and biomass outlet moisture content. The second part concerns the development of a mathematical model for biomass drying in a rotary dryer. Experimental measurements in a rotary dryer were compared to the data from the model, in order to check the validity of the model.     

Further Theoretical Studies on Rotary Drying Processes Represented By Distributed Systems

ABSTRACT

Mathematical tools for studying panicle transpon in rotary drying and cooling processes are developed in this paper. In contrast to conventional approaches aimed at deriving empirical or xmi-empirical correlations, a rigorous mathematical analysis which employs dilferential calculus and analytical geometry is emphasis4 in the current research. These developments allow accurale computations of solid flowrate, retention time and particle holdup in rotary dryers with arbilrary flight configurations. Consequently, optimal dryer configuration design in terms of drum dimension, flight number and geometry can be achieved through a better understanding of the mathematical insight of rotary drum performance.

Techniques developed using this method are applied to the distributed parameter model eslablished earlier by the authors (Wang el al., 1993) to replace out-dated correlations for the determination of retention Lime and solid holdup. As a result of the new developments, the distributed parameter approach to the dynamics of rotary drying processes becomes more general and more reliable.     

SIMULATION OF DEEP BED DRYING OF HAZELNUTS

Abstract

The deep bed drying modelling of hazelnut (Corylus avellana L.) have been studied by considering the deep bed as a series of thin layers. A partial differential equations model has been developed to simulate heat and mass transfer in fixed deep bed hazelnut dryers. The computer program developed permits the calculation of temperature and moisture content profiles along the dryer. As a process of validation of the model, the predicted and experimental results of average moisture content of the whole bed were compared. It has been observed that the simulation results agreed quite well with experimental data.     

A Funtadamental Study on Particle Transport Through Rotary Dryers for Flight Design and System Optimisation

A model for particle transport in a flighted horizontal rotary dryer is developed in this paper. Mathematical principles applied to the current study are in the areas of differential calculus and analytical geomentry. In contrast to the conventional approaches which are either based on mpirical/semi-empirical correlations or obtained from the investieation of single particle trajectories, this paper develops rigorous mathematical analysis of the transport of bulk solids. A variety of important issues in rotary drying, such as axial flowrate of solids, retention time distribution and solid holdup are addressed and treated by using non-traditional methods. Since the model takes dimension, number and geometry of flights into account, it possesses the following two haracteristics : (1) it is not only useful in the study of rotary drying dynamics, but lso applicable to other processes employing flighted rotating cylinders (such as granulation drumsand crushers) and (2) based on the model, an optimal drum configuration can be designed by using optimisation techniques. The model can be incorporated within a distributed arameter dryer model developed previously to form a more rigorous integrated dynamic model. A heoretical foundation for optimal flight design by using the current model is explained.

A pilot scale perspex rotary dryer equipped with a video camera has been constructed and used for model validation. Raw sugar was handled in the experiments. Particle transport was observed and measured by using a flow visualisation technique supplemented with traditional sampling methods. A significant model quality improvement has been observed through a comparative study between the newly developed model and conventional ones.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

STEAM DRYING OF WOOD CHIPS IN PNEUMATIC CONVEYING DRYERS

ABSTRACT

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.     

Modelling and Simulation of a Direct Contact Rotary Dryer

ABSTRACT

A mathematical model able to predict solid and drying gas temperature and moisture content axial profiles along a direct contact rotary dryer was developed. The study was focused on the drying kinetics based on phenomenological models. Two different drying mechanisms in the decreasing drying rate period were tested: proponional to the unbound moisture content and moisture diffusion inside the particle. Experimental data collected in a pilot-scale direct contact rotary dryer was used to validate the model. Soya and fish meals were used as drying material.     

INFLUENCE OF SOLIDS MOISTURE CONTENT ON THE AVERAGE RESIDENCE TIME IN A ROTARY DRYER

The solids mean residence time in a rotary dryer is influenced by several variables such as dryer dimensions and solids characteristics. One of these characteristics, usually not taken into account in correlations proposed to estimate the mean residence time, is the solids feed moisture content. Although it is well known that the solids moisture content has a major impact on the ability of the solids to move along the rotary dryer, it does not enter as a parameter in available correlations. In this investigation, numerous experiments were performed in a pilot-scale rotary dryer to study the influence of solids moisture content and drying gas temperature on the mean residence time. Sand employed in cement makeup was used to perform these experiments. Results show that the mean residence time for a moisture content in the range of 8% to 12% is four times higher than for dry solids. The moisture content and the drying gas temperature influence significantly the shape of the residence time distribution curve.