Modelling and Simulation of Momentum, Heat, and Mass Transfer in a Deep-Bed Grain Dryer

This article concerns the modelling and simulation of a deep-bed grain dryer in a large diameter-column. Two-dimensional (2D) models of deep-bed grain dryers were built by considering simultaneously momentum, heat, and mass transfer in the drying phase together with coupled heat and mass balance in the grain phase. The dynamic equations are solved numerically by using finite difference method. The momentum equations are applied to simulate pressure drop and velocity field of the drying air across the bed. The mass and heat balance in the two phases determine the profile of temperature and moisture content in both phases. Further, drying rate curves for various temperature of inlet drying gas together with moisture content of grain were simulated. The simulated profiles are in close agreement with experimental data.     

Coupled Heat and Mass Transfer in a Solar Grain Dryer

This paper presents the analysis of a coupled heat and mass transfer process in a fixed-bed solar grain dryer. Measurements of moisture concentration and air humidity along with temperature measurements were carried out in a solar grain dryer located in Port Harcourt, Nigeria, at the latitude of 4.858°N and longitude of 8.372°E. The process was also modelled, mathematically, by a set of partial differential equations that were coupled within the grain and through the grain boundary with the hot drying air. A finite difference scheme was used to obtain the moisture concentration and air humidity, and temperature fields within the grain and drying air. There was good agreement between the theoretical and experimental results at specified Biot and Posnov numbers, and varying Fourier number. The effects of time, space, and key model parameters such as the Biot and Posnov numbers and the initial conditions of the grains and drying air were simulated and discussed. The results from this study can be used to specify the design parameters for solar grain dryers.     

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.     

Modelling and Simulation of Batch and Continuous Fluidized Bed Dryers

The performance of batch and continuous fluidized solids dryers has been modeled, with allowance for diffusional moisture transport in the dense phase particles and for interstitial gas-to-particle mass transfer within the dense phase, as well as for interphase exchange resistance between gas bubbles and the dense phase. Two types of boundary conditions are employed. Variations of the bed temperature and product moisture content in the bed with time are predicted numerically under various batch drying conditions. Exit product moisture contents, bed temperatures and outlet air humidities are also predicted for continuous drying at various mean residence times. The model can be used for homogeneous as well as bubbling fluidized bed drying. It can be used for a wide range of materials, including cereal grains and granular synthetic polymeric materials.     

DYNAMIC SIMULATION AND CONTROL OF CONVEYOR-BELT DRYERS

Abstract

The dynamic behavior of conveyor-belt dryers involving externally controlled heat and mass transfer phenomena has been studied via digital simulation. The investigation concerned an industrial dryer used for the moisture removal from wet raisins. The dryer consisted of three drying chambers and a cooling section, all involving the same conveyor belt. For each chamber, perfect temperature control was assumed for the drying air temperature, while its humidity was left uncontrolled. The effect of material temperature and moisture content at the entrance of the dryer and the drying air temperature on material temperature and moisture content at the exit of the dryer and the corresponding drying air humidity, have been explored by step forcing the disturbance and manipulated variables in the non-linear dryer model simulator. Results showed that material moisture content at the exit of the dryer is greatly affected by material moisture content at the entrance as well as by the drying air temperature. Reliable transfer functions for each process module were obtained by fitting several transfer function models on the simulated data using a least-squares approach. It was found that when input material moisture content could be instantly measured, the system responded slowly enough so that excellent control could be achieved for material moisture content at the exit of each chamber. In this case a Pi-feedback cascade temperature controller was used. When a 15 sec delay measuring sensor was introduced, poor performance was observed. A simplified lead-lag feedforward controller, added to the system, in conjunction with the primary Pi-feedback cascade controller, resulted in good control performance of the delay sensor system.     

DYNAMIC SIMULATION AND CONTROL OF CONVEYOR-BELT DRYERS

The dynamic behavior of conveyor-belt dryers involving externally controlled heat and mass transfer phenomena has been studied via digital simulation. The investigation concerned an industrial dryer used for the moisture removal from wet raisins. The dryer consisted of three drying chambers and a cooling section, all involving the same conveyor belt. For each chamber, perfect temperature control was assumed for the drying air temperature, while its humidity was left uncontrolled. The effect of material temperature and moisture content at the entrance of the dryer and the drying air temperature on material temperature and moisture content at the exit of the dryer and the corresponding drying air humidity, have been explored by step forcing the disturbance and manipulated variables in the non-linear dryer model simulator. Results showed that material moisture content at the exit of the dryer is greatly affected by material moisture content at the entrance as well as by the drying air temperature. Reliable transfer functions for each process module were obtained by fitting several transfer function models on the simulated data using a least-squares approach. It was found that when input material moisture content could be instantly measured, the system responded slowly enough so that excellent control could be achieved for material moisture content at the exit of each chamber. In this case a Pi-feedback cascade temperature controller was used. When a 15 sec delay measuring sensor was introduced, poor performance was observed. A simplified lead-lag feedforward controller, added to the system, in conjunction with the primary Pi-feedback cascade controller, resulted in good control performance of the delay sensor system.     

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)     

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.     

COMPUTER SIMULATION ON INTERMITTENT DRYING OF ROUGH RICE

This study applied a partial differential equation model with newly-developed thin layer equations to simulate batch re-circulating dryers under different drying conditions, which are combinations of four parameters: drying air temperature, drying air absolute humidity, drying period duration, and tempering period duration. The moisture change and the drying rate, which were of particular concern with respect to the simulated data, were investigated. Validation drying tests were carried out in a lab scale re-circulating rice dryer. Two sets of experiment were performed involving different drying parameters to simulate re-circulating rice dryers which are extensively used in Asian countries. Comparing these two experimental data with two simulated drying curves respectively, it revealed they are quite consist with each other under the same drying conditions. Drying air temperature, drying air humidity, drying period duration and tempering period duration significantly influenced the drying rate. Under the same drying condition, the tempering period duration effect was insignificant to the drying rate in drying zone as the drying air humidity or temperature increased. And, a higher initial moisture content obtained higher time and energy efficiency for the re-circulating rice dryers.     

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)     

A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

Drying of Soybean Seeds in a Concurrent Moving Bed: Heat and Mass Transfer and Quality Analysis

The purpose of the present work is to study the simultaneous heat and mass transfer between air and soybean seeds in a concurrent moving bed dryer, based on the application of a two-phase model to the drying process. The numerical solution of the model is obtained by using a computational code based on BDF methods (Backwards Differentials Formulas). The experimental data of air humidity and temperature and of seed moisture content and temperature at the dryer outlet are compared to the simulated values, showing a good agreement. This work also analyzes the effect of the main process variables (drying air temperature, air relative humidity, air velocity and solids flow rate) on the soybean seeds quality during drying. Empirical equations fitted to the experimental data are proposed for predicting the soybean seed quality (germination, vigor and fissures) as a function of the investigated variables.     

Comparison of Moving Bed Dryers of Solids Operating in Parallel and Counterflow Modes

The drying rates in moving bed dryers are compared. The gas and the solids to be dried are in parallel flow or counterflow. A new simplified method to simulate the drying in parallel and counterflow moving beds is developed. This model is based on the solution of arbitrary experimental or theoretical drying rate Equations of single solid particles (or thin-layer drying rate equation) coupled with heat and mass conservation Equations of the dryer. The solution is presented in an integral form of the drying equation showing the relation between time or location in the dryer and degree of drying. The method allows rapid calculation of the moisture, vapor mass fraction, and temperature distributions along the dryer in drying with moist air or steam. The model is demonstrated by using a result based on the receding front evaporation model as the specific thin-layer drying equation in the moving bed model. Wood chips are chosen as an example of the substance to be dried, but the method applies also for other medium, if the dependence of the drying rate on moisture and ambient temperature and humidity (thin layer drying rate) is known. The size of the dryer needed to reach the same degree of drying operating in the parallel mode is much greater than that of counterflow type, when the drying medium is air or flue gases. The reason for the poorer drying in parallel flow is mainly the unfavorable distribution of the evaporation temperature. In steam drying, the difference in the size is not so great, since the evaporation takes place approximately at constant temperature.     

Comparison of Moving Bed Dryers of Solids Operating in Parallel and Counterflow Modes

Abstract

The drying rates in moving bed dryers are compared. The gas and the solids to be dried are in parallel flow or counterflow. A new simplified method to simulate the drying in parallel and counterflow moving beds is developed. This model is based on the solution of arbitrary experimental or theoretical drying rate Equations of single solid particles (or thin-layer drying rate equation) coupled with heat and mass conservation Equations of the dryer. The solution is presented in an integral form of the drying equation showing the relation between time or location in the dryer and degree of drying. The method allows rapid calculation of the moisture, vapor mass fraction, and temperature distributions along the dryer in drying with moist air or steam. The model is demonstrated by using a result based on the receding front evaporation model as the specific thin-layer drying equation in the moving bed model. Wood chips are chosen as an example of the substance to be dried, but the method applies also for other medium, if the dependence of the drying rate on moisture and ambient temperature and humidity (thin layer drying rate) is known. The size of the dryer needed to reach the same degree of drying operating in the parallel mode is much greater than that of counterflow type, when the drying medium is air or flue gases. The reason for the poorer drying in parallel flow is mainly the unfavorable distribution of the evaporation temperature. In steam drying, the difference in the size is not so great, since the evaporation takes place approximately at constant temperature.     

A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

ABSTRACT

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

Dynamic Modeling and a Parametric Study of an Indirect Solar Cabinet Dryer

A dynamic mathematical model for drying of agricultural products in an indirect cabinet solar dryer is presented. This model describes the heat and mass transfer in the drying chamber and also considers the heat transfer and temperature distribution in a solar collector under transient conditions. For this purpose, using conservation laws of heat and mass transfer and considering the physical phenomena occurring in a solar dryer, the governing equations are derived and solved numerically. The model solution provides an effective tool to study the variation of temperature and humidity of the drying air, drying material temperature, and its moisture content on each tray. The predicted results are compared with available experimental data. It is shown that the model can predict the performance of the cabinet solar dryer in unsteady-state operating conditions well. Furthermore, the effect of some operating parameters on the performance and efficiency of dryer is investigated and compared with selected published data.     

Mathematical Model for Batch Drying in an Inert Medium Fluidized Bed

A modified three-phase model is proposed for batch drying of fine powders in an inert medium fluidized bed. The overall heat and mass transfer coefficients between the interstitial gas and solid phases have been determined by the proposed surface-stripping model in which the Biot number is a governing parameter. The effects of gas velocity, inlet gas temperature and mass ratio of starch to inert particles on the drying characteristics of starch in a 0.083 m ID × 0.80 m high medium fluidized bed have been determined. Based on the proposed model, the internal resistance of mass transfer at the powder is equal to the external resistance. The model predicts well the bed temperature, humidity of outlet gas, moisture content of solid particles, heat and mass transfer in an inert medium fluidized bed.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

THE DRYING OF SOYBEAN SEEDS IN COUNTERCURRENT AND CONCURRENT MOVING BED DRYERS

The aim of this work was to analyze the simultaneous heat and mass transfer between air and soybean seeds in countercurrent and concurrent moving bed dryers by simulation. The technique chosen was based on modeling from mass and energy conservation equations for the fluid and particulate phases. The equilibrium, heat transfer and mass transfer equations were taken from specific studies. The equation representing drying kinetics was obtained by means of a thin-layer study, whereas the equilibrium equations was chosen from rival model discrimination, based on nonlinearity measures. Hence, the model parameters were defined by the respectives studies. The profiles for temperature and humidity of the fluid and the temperature and moisture of the seeds were obtained by numerical solution of the model. This model consisted of ordinary differential equations and the solution was obtained by a specific code. The simulated results indicated a significant.