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 Wood Particle Motion Through a Concurrent Triple-Pass Rotary Dryer

The retention time of solids in a drum is an important parameter for the design of rotary dryers, since it directly influences the mass and heat transfer rates. If it is too short, the wood particles do not become adequately dried. If it is too long, they become over-dried. Therefore, having an appropriate retention time is useful in terms of both energy and plant capacity. Wood particle mean retention time in a rotary dryer is affected by several variables, such as dryer dimensions, solid characteristics, and operational parameters. The purpose of this work was to simulate the effects of some wood particle characteristics and operational parameters on the mean retention time, drum holdup, and velocity of the wood particles during drying in a pilot-scale, closed-loop, triple-pass rotary dryer by means of a computer code. The simulation results of wood particle motion can be used for modeling, design, and optimization of closed-loop, triple-pass rotary dryers.     

Further Theoretical Studies on Rotary Drying Processes Represented By Distributed Systems

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.     

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.     

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.     

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)     

Flow of slightly settling slurries in a horizontal rotary drum

An experimental study was conducted to examine the flow of slightly settling slurries in a horizontal rotary drum. The effects of the slurry flow rate, feed solids concentration, particle settling velocity and drum rotational speed on the hold-up solids concentration were investigated. At low drum speeds, the hold-up solids concentration was much higher than that of the feed. However, at higher drum speeds, the hold-up solids concentration approached that in the feed. At a given drum speed, the hold-up solids concentration was found to vary linearly with the feed solids concentration. A semi-empirical correlation was developed to predict the hold-up solids concentration using the drum Froude number, the single particle drag coefficient and a dimensionless slurry feed rate.     

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

ABSTRACT

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)     

Mathematical Modeling the Drying of Poplar Wood Particles in a Closed-Loop Triple Pass Rotary Dryer

Closed-loop drying systems are an attractive alternative to conventional drying systems because they provide a wide range of potential advantages. Consequently, type of drying process is attracting increased interest. Rotary drying of wood particles can be assumed as an incorporated process involving fluid–solid interactions and simultaneous heat and mass transfer within and between the particles. Understanding these mechanisms during rotary drying processes may result in determination of the optimum drying parameters and improved dryer design. In this study, due to the complexity and nonlinearity of the momentum, heat, and mass transfer equations, a computerized mathematical model of a closed-loop triple-pass concurrent rotary dryer was developed to simulate the drying behavior of poplar wood particles within the dryer drums. Wood particle moisture content and temperature, drying air temperature, and drying air humidity ratio along the drums lengths can be simulated using this model. The model presented in this work has been shown to successfully predict the steady-state behavior of a concurrent rotary dryer and can be used to analyze the effects of various drying process parameters on the performance of the closed-loop triple-pass rotary dryer to determine the optimum drying parameters. The model was also used to simulate the performance of industrial closed-loop rotary dryers under various operating conditions.     

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

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.     

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.     

SIMULATION AND SCALE-UP OF PNEUMATIC CONVEYING AND CASCADING ROTARY DRYERS

This paper presents a unified model for simulation of cocurrent and countercurrent dispersion-type dryers. The main industrial applications are to pneumatic conveying (flash) dryers and cascading (direct) rotary dryers. The basic model is a one-dimensional incremental (stepwise) simulation, which has been developed over a number of years Equations for particle motion, heat and mass transfer, heat and mass balances and local gas conditions are solved simultaneously over a small increment along the dryer. All workers have previously had considerable difficulty in obtaining a good fit between simulations and actual results from pilot-plants or large-scale industrial dryers. A new “fitting mode” calculation overcomes this by identifying the parameters which need to be adjusted, concentrating on those which cannot be measured accurately. Excellent agreement has been obtained between the model and experimental data by this method. The paper also presents revised formulations for particle motion and heat transfer in rotary dryers. The model has been incorporated into two computer programs for flash and rotary dryers respectively, and results from the former are shown for a case study.     

SIMULATION AND SCALE-UP OF PNEUMATIC CONVEYING AND CASCADING ROTARY DRYERS

ABSTRACT

This paper presents a unified model for simulation of cocurrent and countercurrent dispersion-type dryers. The main industrial applications are to pneumatic conveying (flash) dryers and cascading (direct) rotary dryers. The basic model is a one-dimensional incremental (stepwise) simulation, which has been developed over a number of years Equations for particle motion, heat and mass transfer, heat and mass balances and local gas conditions are solved simultaneously over a small increment along the dryer. All workers have previously had considerable difficulty in obtaining a good fit between simulations and actual results from pilot-plants or large-scale industrial dryers. A new “fitting mode” calculation overcomes this by identifying the parameters which need to be adjusted, concentrating on those which cannot be measured accurately. Excellent agreement has been obtained between the model and experimental data by this method. The paper also presents revised formulations for particle motion and heat transfer in rotary dryers. The model has been incorporated into two computer programs for flash and rotary dryers respectively, and results from the former are shown for a case study.     

Modelling of batch fluidised bed drying of pharmaceutical granules

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control.     

Modeling and simulation of drying characteristics on flexible filamentous particles in rotary dryers

Experiments were conducted to demonstrate the effects of the drum wall temperature on the heat and mass transfer in rotary dryers. The drying characteristics of flexible filamentous particles in rotary dryers were further explored. In addition, the inlet and outlet temperatures and moisture contents of granular particles were measured. As a result, the good agreement between the simulations and experiments verified the rationale and feasibility of the numerical method. Therefore, the approach was adopted to evaluate the temperature and moisture content of wet granular particles in a rotary dryer in different conditions, for instance, drum wall temperature and rotational speed. The results revealed that the higher drum wall temperature led to hotter particles with lower outlet moisture content. Conversely, the higher rotational speed resulted in cooler particles with higher outlet moisture content due to the decrease of residence time in the rotary dryer.     

Modeling of Fertilizer Drying in Roto-Aerated and Conventional Rotary Dryers

Conventional rotary dryers are equipped with flights placed parallel along the length of the shell to promote a rain of solids across the dryer section. In the roto-aerated dryer the hot air flows through the particles that run on the bottom of the drum through a series of mini-pipes and there is no cascading. This study analyzed heat and mass transfer modeling between the air and the fertilizer particles in conventional rotary and roto-aerated dryers, as well as the simulation results with the experimental data. A good agreement between the simulated and experimental results was obtained for the two rotary dryer configurations analyzed.     

Modelling Diffusion-Limited Drying Behaviour in a Batch Fluidized Bed Dryer

Fluidized bed dryers are often used to extract water from granular materials. When the drying process is mainly limited by the resistance against water transport inside the particle the drying behaviour is said to be diffusion-limited. In the literature there are several models that predict this drying process with very diverging results. In this study a model is set up to arrive at a better prediction for this drying process. The heat and mass transfer in the granular material and the drying air is described. The resulting equations are solved numerically. The model must be extended to incorporate the heat capacity of the dryer.