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.     

气流干燥含湿氧化铝颗粒传热传质数值模拟

基于二相流理论,提出了一个描述含湿氧化铝颗粒气流干燥过程的一维数学模型。模型考虑了干燥管内气固二相间的传热传质和动量传递、含水质量分数和气固二相温度的变化。根据B ird所提出的努赛尔数经验公式,利用标准四阶龙格-库塔法对由非线性常微分方程组成的气流干燥耦合模型进行计算,得到了含湿氧化铝颗粒在不同气流干燥条件的干燥曲线。整个干燥过程中数值计算结果与试验实测数据吻合得很好,可以用来预测含湿氧化铝颗粒的干燥含水质量分数。     

A Quasi‐Steady State Shell and Shrinking Core Approach to the Drying of Porous Particles and an Example of Parameter Identification

A quasi‐steady state shell and shrinking core approach which recognizes heat and mass transfer resistances in both the gas and particle phases for drying of a porous particle is proposed. A mean field model (constant properties) using this approach was embedded in a spreadsheet combined with a genetic algorithm for parameter identification to provide an easy means of characterizing the drying process from drying data. In drying, assuming a mean field, four major parameters are typically unknown: two related to the process (heat and mass transfer coefficients) and two which incorporate porous particle properties (shell thermal conductivity and vapour diffusivity). It is shown how these four parameters may be determined from experimental drying data. The model was applied to data for spouted bed drying of rice. For the particular case studied, external heat transfer was found to be the controlling mode, although resistance to moisture diffusion within the particle is important. The approach presented admits of future refinements to improve its scope and utility.     

Numerical Study of Two-Stage Horizontal Spray Dryers Using Computational Fluid Dynamics

This article presents the findings of a numerical simulation model of the spray-drying process in a two-stage horizontal chamber design with the aid of a computational fluid dynamic (CFD) model. The model describes heat, mass, and momentum transfer between two phases; namely, a continuous gas phase and a discrete phase of droplets (or particles), using the finite volume method. In this study, a new two-dimensional horizontal spray dryer (HSD) geometry is considered as a pilot study into the spray-drying process in this novel chamber configuration. The tested model is able to predict some important features of the spray-drying process, such as air flow patterns indicating recirculation zones and particle trajectory plots. Some performance parameters for spray drying, such as the rate of evaporation, average volumetric heat and mass transfer rates, etc., are calculated and discussed. This two-stage drying process especially applicable for the horizontal spray dryer (HSD) model is investigated and modeled. The bottom wall of the HSD is assumed to be a shallow fluid bed used for second stage drying. In this article, the fluid bed drying conditions are changed and compared. The drying within the fluid bed itself is not modeled in this study, however. It is shown that the particle residence time is higher when the fluid bed is included. The drying performance of this two-stage horizontal spray dryer is expected to be better than that of a single-stage dryer.     

Numerical Study of Two-Stage Horizontal Spray Dryers Using Computational Fluid Dynamics

This article presents the findings of a numerical simulation model of the spray-drying process in a two-stage horizontal chamber design with the aid of a computational fluid dynamic (CFD) model. The model describes heat, mass, and momentum transfer between two phases; namely, a continuous gas phase and a discrete phase of droplets (or particles), using the finite volume method. In this study, a new two-dimensional horizontal spray dryer (HSD) geometry is considered as a pilot study into the spray-drying process in this novel chamber configuration. The tested model is able to predict some important features of the spray-drying process, such as air flow patterns indicating recirculation zones and particle trajectory plots. Some performance parameters for spray drying, such as the rate of evaporation, average volumetric heat and mass transfer rates, etc., are calculated and discussed. This two-stage drying process especially applicable for the horizontal spray dryer (HSD) model is investigated and modeled. The bottom wall of the HSD is assumed to be a shallow fluid bed used for second stage drying. In this article, the fluid bed drying conditions are changed and compared. The drying within the fluid bed itself is not modeled in this study, however. It is shown that the particle residence time is higher when the fluid bed is included. The drying performance of this two-stage horizontal spray dryer is expected to be better than that of a single-stage dryer.     

Two-Fluid, Two-Dimensional Model for Pneumatic Drying

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

Two-Fluid,Two-Dimensional Model for Pneumatic Drying

Abstract

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

RADIO FREQUENCY VACUUM DRYING OF WOOD. I. MATHEMATICAL MODEL

A one-dimensional mathematical model to describe the transport phenomena during continuous radio frequency/vacuum (RF/V) drying of thick lumber was developed from general conservation equations. When drying at temperatures near the boiling point, as in RF/V drying, the effect of the gas phase pressure gradient on moisture transfer within the solid can be very important. The controlling resistances and transport mechanisms are discussed in detail. In addition, capillary transport in RF/V drying is discussed and its effect is compared with convective drying. The model provides a relatively fast and efficient way to simulate vacuum drying behavior assisted by dielectric heating. As an example, the governing heat and mass transfer equations, including consideration of internal heat generation and the effect of gas phase pressure gradient, are derived and solved in a one-dimensional system using a finite volume method. The effect of changes of the most important parameters on the predictions of the model is also presented.     

用多粒模型模拟丁二烯气相聚合的颗粒增长

Gas phase polymerization of butadiene by neodymium catalyst was modeled. The effects of mass and heat transfer resistances in the external boundary layer and within particles, sorption of butadiene in polybutadiene,and deactivation of active sites on polymer particle growth and morphology were studied. Simulation results show that the effects of intraparticle mass and heat transfer resistances on the growth rate of polymer particles are insignificant, and that there is no significant effect of mass transfer resistance on the morphology of polymer particles.The simulation results were compared with the experimental results.     

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.     

Modelling wood combustion under fixed bed conditions

A computer model describing the conversion of wood under packed-bed conditions is presented. The packed bed is considered to be an arrangement of a finite number of particles, typically sized between 5 and 25 mm, with a void space left between them. Each particle is undergoing a thermal conversion process, which is described by a one-dimensional and transient model.Within the single-particle model, heating, drying, pyrolysis, gasification and combustion are considered, whereby each particle exchanges energy due to conduction and radiation with its neighbours. Because of the one-dimensional discretization of the particles, heat transfer and mass transfer is taken into account explicitly. Therefore, no macrokinetic data are needed within the model. For ease of implementation and access, kinetic data and property data are stored in a database. The global conversion of the packed bed is represented by the contributions of single particles, where each particle is coupled to the surrounding gas phase by heat and mass transfer. For gas phase flow through the porous bed, the conservation equations for mass, momentum and energy are solved on a Cartesian mesh by a Finite Volume method.Experiments have been performed to validate the single particle model for the conversion of beech wood during pyrolysis and char combustion. Agreement between experimental and predictions obtained by the model is very satisfactory. However, for wet wood, changes in structure seem to enhance the heat transfer to the solid which is not yet covered in the model.     

A theoretical and experimental study of simultaneous heat and mass transport resistances in a shallow fluidized bed dryer of mate leaves

A theoretical and a semi-theoretical modeling approach were applied in order to predict drying kinetics of mate leaves in a shallow fluidized bed dryer. The first procedure involves an internal diffusive mechanism of mass transport (Fick's second law), while the second one assumes that the resistance for water transport is represented by an apparent convective term analogous to the Newton's law of cooling (Lewis model). Since heat and mass transfer occurs at the same time, an energy equation assuming negligible internal conduction was written to the solid phase and it was coupled to the mass balance representing the mechanism of mass transfer. Model parameters were simultaneously tuned on experimental transient moisture content and on temperature profiles of mate leaves, which were obtained by varying the equivalent particle diameter approximately from 5.2 × 10⁻³ to 1.1 × 10⁻² m at the drying temperatures of 52 and 101 °C. A regression analysis based on the uncertainties in the calculated parameters as well as on the identification of possible tendencies in residuals corroborates the assumption of negligible internal heat transfer conduction and evidences that the semi-theoretical model of Lewis describes better than the purely diffusive model the transport of water over the whole period of drying. The estimated Biot number (0 < Bi < 100) reveals that both internal and external mass transport resistances play an important role for mate leaves drying and demonstrates that the single parameter of the Lewis model represents an effective coefficient that takes into accounts both diffusion and convection. A significant effect of the equivalent particle diameter and temperature on the drying constant and on the external heat transfer coefficient is also evidenced.     

气流干燥过程的数学模拟

针对颗粒和空气在干燥管内的相互作用和传质传热机理,首先建立了直管式气流干燥数学模型,然后通过分析脉冲式气流干燥器的结构特点,求出了管径变化的微分方程,将其和直管式气流干燥的五个常微分方程耦合在一起,构成了脉冲式气流干燥的传质传热数学模型。根据模型方程的特点,运用四阶龙格-库塔法对其进行了数值求解。通过实验结果验证,该模型正确可靠。     

Heat transfer of dry granular materials in a bladed mixer: Effect of thermal properties and agitation rate

Agitated drying of pharmaceuticals remains a challenging manufacturing step due to the simultaneous heat transfer, mass transfer, and physicochemical changes occurring during the process. This work focuses on the heat transfer component by implementing the discrete element method to model dry particles in a heated bladed mixer. Simulations varying material conductivities and impeller agitation rates were conducted to evaluate the influence on the mean bed temperature and distribution. The results indicated that increasing the agitation rate generally improved heat transfer up until a critical agitation rate where the rate of heat transfer plateaued. The magnitude of this improvement in heat transfer depended on the material's thermal properties. We observed three regimes: a conduction-dominated regime where particles heated quickly but with an annular temperature gradient, a granular convection-dominated regime where particles heated slowly but uniformly, and an intermediate regime. The results were nondimensionalized to enable predictions and help inform drying protocols.     

BOUND MOISTURE REMOVAL: HEAT AND MASS TRANSFER IN CONTACT DRYING

Coupled heat and mass transfer in short-term contact of the moist material and the heating surface (the physical model of drying with agitation) is examined. Technological characteristics of the drying process: heating rate and drying rate, heat transfer coefficient, etc. have been determined based on solutions of the diffusion and diffusion-filtration heat and mass transfer. The usage of non-field method of determination of mass and heat fluxes on the phase interface allows calculation of the drying equipment efficiency without preliminary determination of the fields of required quantities. The results may be used for estimation of the influence of drying conditions and material properties on the moisture removal process.     

Lumped heat and mass transfer coefficient for simulation of a pressure swing adsorption process

The practical implications of replacing various individual transport resistances such as gas-solid mass and heat transfer, and gas phase axial dispersions of mass and heat in a numerical model of a pressure swing adsorption (PSA) process by a single, empirical, lumped, effective mass transport coefficient were evaluated. A non-isothermal, adiabatic, four-step Skarstrom-like PSA process for production of pure helium from a binary helium-nitrogen mixture using 5A zeolite adsorbent was considered. It was found that the above-described model simplification was adequate to describe key process performances such as the bed size factor and the product recovery vis-a-vis a detailed model where the effects of all individual resistances were explicitly included.     

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.     

CFD analysis of the dispersed phase behavior for micropowders production via spray drying and ultrasonic atomization

Abstract

This work is devoted to the use of modern computer simulation tools based on the principles and methods of computational fluid dynamics that are applied to develop processes and equipment for producing spray dried micropowders. The feed solution was atomized into small droplets using an ultrasonic nozzle that exploits the principle of liquid disintegration caused by impact of high-frequency wave oscillations. The use of this device for spraying a liquid allowed obtaining spherical particles with diameters less than 20?μm and with a narrow size distribution. The process development is based on a mathematical model incorporating the hydrodynamics, heat and mass transfer mechanisms, which has been formulated to numerically predict particles trajectories and temporal changes of their mass and temperatures. The generated data were used to analyze the trajectories of discrete phase particles considering various process parameters and to estimate adhesion of wet particles to the drying chamber and nozzle. Also, predicted were the degree of particles deposition and precipitation in a cyclone, since these are useful for selection of process parameters to ensure maximum quality of particles and maximum attainable efficiency of the system collecting finished products.     

CFD modeling of a pilot-scale countercurrent spray drying tower for the manufacture of detergent powder

A steady-state, three-dimensional, multiphase computational fluid dynamics (CFD) modeling of a pilot-plant countercurrent spray drying tower is carried out to study the drying behavior of detergent slurry droplets. The software package ANSYS Fluent is employed to solve the heat, mass, and momentum transfer between the hot gas and the polydispersed droplets/particles using the Eulerian–Lagrangian approach. The continuous-phase turbulence is modeled using the differential Reynolds stress model. The drying kinetics is modeled using a single-droplet drying model, which is incorporated into the CFD code using user-defined functions (UDFs). Heat loss from the insulated tower wall to the surrounding is modeled by considering thermal resistances due to deposits on the inside surface, wall, insulation, and outside convective film. For the particle–wall interaction, the restitution coefficient is specified as a constant value as well as a function of particle moisture content. It is found that the variation in the value of restitution coefficient with moisture causes significant changes in the velocity, temperature, and moisture profiles of the gas as well as the particles. Overall, a reasonably good agreement is obtained between the measured and predicted powder temperature, moisture content, and gas temperature at the bottom and top outlets of the tower; considering the complexity of the spray drying process, simplifying assumptions made in both the CFD and droplet drying models and the errors associated with the measurements.     

Towards a Complete Population Balance Model for Fluidized-Bed Spray Agglomeration

This article concerns the simultaneous processes of agglomeration and drying. In order to predict temperatures and moisture content in gas and particle phase, heat and mass transfer mechanism and particle size enlargement has been considered in one model. The model takes heat and mass transfer phenomena between particle phase, suspension gas, and bypass gas into account. The disperse phase is modeled by a three-dimensional population balance (PBE), which can be reduced to a set of three one-dimensional PBEs. The latter are coupled with heat and mass transfer balances of the gas phase. Furthermore, some simulation and experimental results are presented.