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The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

THE REPRESENTATION AND APPROXIMATION OF THE DYNAMICS OF A CLASS OF HIGH ORDER DISTRIBUTED PARAMETER PROCESSES

The dynamic behavior of process models consisting of higher order sets of linear coupled hyperbolic partial differential equations is considered. The formalism of the Riemann representation of the solution to second order hyperbolic equations is extended to problems of any order. The general time domain solution can then be written in terms of integrals of disturbance functions weighted with generalized Riemann matrices. If the solution for the Riemann matrix is approximated, a common approximation method serves to obtain the complete solution for all state variables subject to all disturbances. The approach is demonstrated on two examples, a double pipe heat exchanger and a nonisothermal packed bed reactor.     

THE REPRESENTATION AND APPROXIMATION OF THE DYNAMICS OF A CLASS OF HIGH ORDER DISTRIBUTED PARAMETER PROCESSES

The dynamic behavior of process models consisting of higher order sets of linear coupled hyperbolic partial differential equations is considered. The formalism of the Riemann representation of the solution to second order hyperbolic equations is extended to problems of any order. The general time domain solution can then be written in terms of integrals of disturbance functions weighted with generalized Riemann matrices. If the solution for the Riemann matrix is approximated, a common approximation method serves to obtain the complete solution for all state variables subject to all disturbances. The approach is demonstrated on two examples, a double pipe heat exchanger and a nonisothermal packed bed reactor.     

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.     

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.     

A SYSTEMATIC APPROACH FOR INVESTIGATION OF SPRAY DRYING PROCESSES

Abstract

A systematic approach is developed for investigation of spray drying processes for chemical and biological systems. The approach involves an in-depth study of atomizer performance, spray dryer parametric sensitivity, spray-dried powder properties, thermal inactivation and post-drying properties. The approach helps considerably in rational design of spray drying experiments and in investigation and optimization of various process aspects of spray drying of chemical and biological systems, leading to large savings in labor, cost and time.     

A SYSTEMATIC APPROACH FOR INVESTIGATION OF SPRAY DRYING PROCESSES

A systematic approach is developed for investigation of spray drying processes for chemical and biological systems. The approach involves an in-depth study of atomizer performance, spray dryer parametric sensitivity, spray-dried powder properties, thermal inactivation and post-drying properties. The approach helps considerably in rational design of spray drying experiments and in investigation and optimization of various process aspects of spray drying of chemical and biological systems, leading to large savings in labor, cost and time.     

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.     

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 STOCHASTIC APPROACH TO THE DRYING OF SOLIDS IN A MULTI-STAGE FLUIDIZED BED

The residence times of solids flowing through a fluidized bed dryer exhibit dispersion about the mean. In this paper, expressions for the probability density functions of solids moisture content in the various stages of a multi-stage dryer are derived. A simple recurrence relationship for the moments of the distribution is also presented. The analysis is applied to the drying of cereal grains, and it is shown that the degree of drying increases with the number of stages in the dryer. Probability density functions of the moisture content are presented.     

PROCESSES RELATED TO DRYING: PART I,THEORETICAL MODEL

The aim of this paper is to summarize ten years of work in order to model the drying of solids. Nowadays there is a general agreement amongst the various researchers worldwide. If the porous medium is viewed at the so-called “macroscopic” scale (that is to say when it is viewed as a continuous and homogeneous equivalent medium) a set of three partial derivative equations is derived, three state variables being necessary to thermodynamically describe the medium (temperature, moisture content and total pressure in the gaseous phase for example).

After a short historical survey of the modeling of drying, we want to obtain this set of equations drawing the readers attention to three particular points : the importance of the air mass balance, the right way to write the energy equation (and the associated boundary conditions) and the taking into account of the adsorbed water.

A second part of this article [I] will be devoted to the numerical solution of this problem and will illustrate these points.     

A STOCHASTIC APPROACH TO THE DRYING OF SOLIDS IN A MULTI-STAGE FLUIDIZED BED

The residence times of solids flowing through a fluidized bed dryer exhibit dispersion about the mean. In this paper, expressions for the probability density functions of solids moisture content in the various stages of a multi-stage dryer are derived. A simple recurrence relationship for the moments of the distribution is also presented. The analysis is applied to the drying of cereal grains, and it is shown that the degree of drying increases with the number of stages in the dryer. Probability density functions of the moisture content are presented.     

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.     

A SEMI-EMPIRICAL APPROACH TO OPTIMISE THE QUANTITY OF DRYING AIDS REQUIRED TO SPRAY DRY SUGAR-RICH FOODS

A semi-empirical linear equation has been developed to optimise the amount of maltodextrin additive (DE 6) required to successfully spray dry a sugar-rich product on the basis of its composition. Based on spray drying experiments, drying index values for individual sugars (sucrose, glucose, fructose) and citric acid were determined, and using these index values an equation for model mixtures of these components was established. This equation has been tested with two sugar-rich natural products, pineapple juice and honey. The relationship was found to be valid for these products.     

A SEMI-EMPIRICAL APPROACH TO OPTIMISE THE QUANTITY OF DRYING AIDS REQUIRED TO SPRAY DRY SUGAR-RICH FOODS

ABSTRACT

A semi-empirical linear equation has been developed to optimise the amount of maltodextrin additive (DE 6) required to successfully spray dry a sugar-rich product on the basis of its composition. Based on spray drying experiments, drying index values for individual sugars (sucrose, glucose, fructose) and citric acid were determined, and using these index values an equation for model mixtures of these components was established. This equation has been tested with two sugar-rich natural products, pineapple juice and honey. The relationship was found to be valid for these products.     

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.     

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.     

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)