A DYNAMIC MODEL WITH ON-LINE IDENTIFICATION FOR ROTARY SUGAR DRYING PROCESSES

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to replace the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.     

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.     

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.     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

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.     

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.     

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.     

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.     

HYBRID NEURAL APPROACHES FOR MODELLING DRYING PROCESSES FOR PARTICULATE SOLIDS

This work presents methods for synthesizing drying process models for particulate solids that combine prior knowledge with artificial neural networks. The inclusion of prior knowledge is investigated by developing two applications with the data from two indirect rotary steam dryers. The first application consisted in the modelling of the drying process of soya meal in a batch indirect rotary dryer, The external and internal mass transfer resistances were associated in the hidden layer of the network to linear and sigmoidal nodes, respectively. The second application consisted in the modelling of the drying process of soya meal in a continuos indirect rotary dryer. The model was constructed using the Semi-parametric Design Approach. The model predicts the evolution of solid moisture content and temperature as a function of the solid position in the dryer. The results show that the hybrid model performs better than the pure “ black box” neural network and default models. They also shows that prior knowledge enhances the extrapolation capabilities of a neural network model,     

HYBRID NEURAL APPROACHES FOR MODELLING DRYING PROCESSES FOR PARTICULATE SOLIDS

ABSTRACT

This work presents methods for synthesizing drying process models for particulate solids that combine prior knowledge with artificial neural networks. The inclusion of prior knowledge is investigated by developing two applications with the data from two indirect rotary steam dryers. The first application consisted in the modelling of the drying process of soya meal in a batch indirect rotary dryer, The external and internal mass transfer resistances were associated in the hidden layer of the network to linear and sigmoidal nodes, respectively. The second application consisted in the modelling of the drying process of soya meal in a continuos indirect rotary dryer. The model was constructed using the Semi-parametric Design Approach. The model predicts the evolution of solid moisture content and temperature as a function of the solid position in the dryer. The results show that the hybrid model performs better than the pure “ black box” neural network and default models. They also shows that prior knowledge enhances the extrapolation capabilities of a neural network model,     

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.     

Adaptive linear quadratic gaussian (LQG) control of a bioreactor

The paper deals with the modelling and adaptive control of a continuous-flow fermentation process for the production of alcohol. The fermenter model has been developed from mass balance and leads to nonlinear differential equations. In practice, control strategies are difficult to derive using this non-linear model. The dilution rate and the substrate concentration have been considered as control and controlled variables, respectively. The adaptive control algorithm implemented is based on the linear quadratic control approach, where the associated Riccati equation is iterated until the system closed-loop poles belong to a restricted stability domain which is included in the unit circle. A single input/output model is used for control purposes. The model parameters are estimated on-line using a robust identification algorithm which includes: data normalization, time-varying forgetting factor, covariance matrix factorization, etc. Experimental results show the performance of this adaptive scheme and its ability to control biotechnological processes.     

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.     

Rotary Dryer Control Using a Grey-Box Neural Model Scheme

The application of a Grey-box Neural Model (GNM) in a nonlinear model predictive control scheme (NMPC) of a direct rotary dyer is presented in this work. The GNM, which is based on the combination of phenomenological models and empirical artificial neural network (ANN) models, was properly developed and validated by using experimental fish-meal rotary drying information. The GNM was created by combining the rotary dryer mass and energy balances and a feed forward neural network (FFNN), trained off-line to estimate the drying rate and the volumetric heat transfer coefficient. The GNM results allowed us to obtain the relation between the controlled variable (solid moisture content) and the manipulated variable (gas phase entrance temperature) used in the predictive control strategy. Two NMPC control strategies, one with a fixed extended prediction horizon and another with an extended range prediction horizon, were applied to a simulated industrial fish-meal drying process. The results showed that a correct rotary dryer representation can be obtained by using a GNM approach. Due to the representation capability of the GNM approach, excellent control performances of the NMPCs were observed when the process variables were subject to disturbances. As analyzed in this work, the fixed extended prediction horizon MPC surpassed recognized control methodologies (quadratic dynamic matrix control).     

Modelling low-temperature carbonisation of solid fuels in a heated rotary kiln for clean fuel production

A numerical simulation of the physico-chemical processes occurring inside a heated rotary kiln reactor, where coal, lignite or biomass are treated in vacuum for the production of clean solid fuel, has been performed with FLUENT6 Computational Fluid Dynamics (CFD) code. The model accounts for the rotation of the kiln walls and mixing blades, multiphase flow modelling of the solid (fuel) and gaseous (mixture of gases) phases, heat transfer between phases and the heated kiln walls and mass transfer due to chemical reaction between species of different (heterogeneous) phases. The objective is to contribute towards a reliable numerical methodology as a design tool with reference to the fuel feed properties (e.g. solids size, volatile, carbon and moisture content, feed rate) and process requirements (e.g. desired residence time). Kiln wall erosion is also assessed.     

Modelling and Simulation of a Direct Contact Rotary Dryer

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.     

Mathematical Modeling of Rotary Drying of Woody Biomass

Woody biomass in the form of forestry industry residues has been recognized as a promising resource for renewable energy and liquid fuels. Drying of the woody biomass is one of the key operations in development of the energy conversion technologies. Rotary drying is an effective method due to the enhanced contact between the solids and the drying medium (hot air). In this work, a mathematical model was developed to simulate the drying of the woody biomass as chips in a rotary dryer, based on energy and mass balance and transfer, experimental drying kinetics of the wood chips, and using literature correlations for the residence time. A new correlation between the theoretical maximum drying rate and the actual constant drying rate for the wood chips was obtained from the drying experiments, which was incorporated in the drying model. The model was applied both for cocurrent and countercurrent rotary dryers, and the simulation results are consistent with the observed trend. However, the accuracy of the model needs to be further investigated through experimental validation of the residence time correlation.     

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.     

MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.     

Bibliography on Mathematical Models of Drying and Dryers

Mathematical modelling of drying processes as well as dryers has become an active and challenging area of research internationally. Despite the volume of literature published and continuing to appear on this subject, much remains to be accomplished in view of the intrinsic complexities associated with coupled heat, mass and momentum transfer with or without phase change occurring in porous media which are often deformable as well. Characterization of the solid media is still a major obstacle to modelling of drying. Since industrial drying is increasingly carried out using several modes of heat transfer (e.g. convection coupled wih conduction or microwave or infrared heating modelling of drying or dryers will remain an important research area in the years to come.

We hope that this bibliography will serve as a useful tool for both the novice as well as the experienced researcher in the subject area in locating appropriate literature for a critical evaluation.