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)     

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)     

Effects of sudden pressure changes in the surrounding gas phase on flow properties of bulk solids

The variation in the behaviour of bulk solids as a result of sudden pressure changes in the surrounding gas phase is of interest in the application of lock hoppers for transfer of bulk solids into pressure vessels. By using such sluice systems, problems occur due to consolidation of the pressurized bulk solids. This paper presents the results of experimental and theoretical research, which allow to describe the influence of several parameters on pressure compensation and the degree of consolidation. With reference to the forces and mechanisms responsible for consolidation, it is possible to describe the different consolidation behaviour of incompressible (limestone) and compressible (hard coal) bulk solids.     

Gasification of coal-derived chars in synthesis gas mixtures under intraparticle mass-transfer-controlled conditions

A model has been formulated to describe the quasi-steady-state gasification of coal-derived chars in gas mixtures where both the reactants carbon dioxide and steam, and the gasification products carbon monoxide and hydrogen are present. As such, these conditions reflect the situation found in most practical gasification systems.The model presented is applied under conditions where intraparticle mass transfer is rate-controlling. Intraparticle heat transfer is neglected. In view of the non-equimolar gasification reactions, the mass flux equations are derived from the continuum limit of the dusty gas model. These flux equations are combined with strongly non-linear Langmuir-Hinshelwood kinetics for the gasification reactions. The model accounts for local variations of the diffusive and convective permeability parameters, as well as variations in the reactive surface area, during burnoff of a char particle.The impact of the various relevant mass-transfer parameters, the gasification temperature and pressure, and the char particle size on the gasification behaviour is discussed. A comparison is made between the present model and existing models, and various modelling approaches are critically reviewed.     

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.     

Numerical Simulations of the Effect of Conical Dimension on the Hydrodynamic Behaviour in Spouted Beds

The flow behaviours of gas‐solids were predicted by means of a hydrodynamic model of dense gas‐solid flow in spouted beds. Constitutive equations describing the particulate solids pressure and viscosity were implemented into a hydrodynamic simulation computer program. The effect of operating conditions (inclined angle and gas spouting velocity) on particle velocity and concentration in the spout, annulus and fountain regions were numerical studied. Both vertical and horizontal particle velocities increased with increasing spouting gas velocity. The diameter of the spout increases with decreasing the inclination angle. As the inclination angle is set greater than 60°, the spout cross‐section starts becoming bottlenecked, limiting the upwards flow of solids.     

固体氧化物燃料电池中的阳极电化学过程数学模拟研究

在质量守恒、动量守恒和能量守恒定律及Butler-Voulmer方程组的基础上,加上边界条件和初始条件,通过数学模型对SOFC中的阳极催化层内部的燃料反应气体的气相扩散及产物的气相扩散的基本动态规律进行了描述。其偏微分方程只能通过数值计算求解,而无法得到解析解。增大阳极孔隙率ε可提高多孔电极中的有效气体扩散系数。当阳极较薄时,阳极的总极化电阻与单位体积内的电化学活性区的面积A成反比,增大阳极的电化学活性区的面积有利于降低其总极化电阻。该数学推演结论对阳极的优化制备具有重要的参考价值。     

Mixing dynamics in bubbling fluidized beds

Solids mixing affects thermal and concentration gradients in fluidized bed reactors and is, therefore, critical to their performance. Despite substantial effort over the past decades, understanding of solids mixing continues to be lacking because of technical limitations of diagnostics in large pilot and commercial‐scale reactors. This study is focused on investigating mixing dynamics and their dependence on operating conditions using computational fluid dynamics simulations. Toward this end, fine‐grid 3D simulations are conducted for the bubbling fluidization of three distinct Geldart B particles (1.15 mm LLDPE, 0.50 mm glass, and 0.29 mm alumina) at superficial gas velocities U/Umf = 2–4 in a pilot‐scale 50 cm diameter bed. The Two‐Fluid Model (TFM) is employed to describe the solids motion efficiently while bubbles are detected and tracked using MS3DATA. Detailed statistics of the flow‐field in and around bubbles are computed and used to describe bubble‐induced solids micromixing: solids upflow driven in the nose and wake regions while downflow along the bubble walls. Further, within these regions, the hydrodynamics are dependent only on particle and bubble characteristics, and relatively independent of the global operating conditions. Based on this finding, a predictive mechanistic, analytical model is developed which integrates bubble‐induced micromixing contributions over their size and spatial distributions to describe the gross solids circulation within the fluidized bed. Finally, it is shown that solids mixing is affected adversely in the presence of gas bypass, or throughflow, particularly in the fluidization of heavier particles. This is because of inefficient gas solids contacting as 30–50% of the superficial gas flow escapes with 2–3× shorter residence time through the bed. This is one of the first large‐scale studies where both the gas (bubble) and solids motion, and their interaction, are investigated in detail and the developed framework is useful for predicting solids mixing in large‐scale reactors as well as for analyzing mixing dynamics in complex reactive particulate systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4316–4328, 2017     

A Sedimentation-Dispersion Model for both Non-attached and Attached Particles in Three-Phase Batchwise Fluidized Beds

The axial concentration distribution of both particles with better wetting (forming non-attached system) and poorer wetting (forming attached system) was investigated in a vertical gas-liquid-solid fluidized bed of 4.2 cm in diameter and 130 cm in height with the solids holdup less than 0.05. The one-dimensional sedimentation-dispersion model could be used satisfactorily to describe the axial distribution of solids holdup by modifying only a model parameter, i.e. by means of the terminal settling velocity minus a certain value, which is a function of gas velocity and considers the effect of an additional drag force resulted from attached rising bubbles. The axial profiles of solid concentration predicted are in good agreement with experimental results. This model also explains reasonably the different axial distributions of solid concentration, i.e. the solids holdup decreases as the axial height increases in non-attached system, but increases with the axial height in attached system at a given gas veloc     

Experimental and analytical study of the solids circulation loop of a compartmented fluidized bed

Experiments were conducted to identify the necessary conditions for achieving stable operation and identify the operational range of a novel fluidized solids circulation system using a compartmented fluidized bed and vertical transport line (VTL). The VTL has allowed the conveying of relatively fine particles (Group B — near the transition from Group A to B) under a wide range of experimental conditions. It was also demonstrated that the nozzle geometric configuration can alter the entrainment behaviour of the motive gas jet quite significantly by altering the flow patterns in the vicinity of the jet. Of all the geometric modifications studied, the inclined plate and the shroud were shown to have the most favourable impact on the entrainment rate.A CO₂ tracer study quantified the amount of fluidization gas entrained into the VTL riser for the closed loop configuration. It was discovered that a significant amount of gas leaked back out into the fluidized bed from the motive gas jet. An empirical model was derived in order to further characterize the system behaviour. For fully developed flow, the main resistive forces in the riser for a given solids holdup were the solids weight and solids-wall friction, however, the pressure drop from the nozzle tip to the riser inlet is significant and affects the solids flow rate and pattern. Specifically, it was shown that the solids entrainment into the riser is highly dependent upon the system pressure balance when comparing a solids circulation loop with an open configuration to one that was closed.     

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.     

Modeling of an internally circulating fluidized bed reactor for thermal treatment of industrial solid wastes

A predictive mathematical model is developed to describe and characterize the key design variables of a novel Internal Circulating Fluidized Bed Combustor. The model is based on fundamental principles of heat transfer, mass transfer, hydrodynamics and reaction kinetics. Under justifiable assumptions unsteady state mathematical equations are written and solved. The input parameters of the model are gas and solid flowrates, solid circulation flux, as well as physical properties of gas and solids. The model allows to predict and to investigate the temperature, the combustible conversion, the oxygen concentration, the residence time, the voidage and the solid velocity in the riser. Experiments with spent foundry sand are undertaken in order to assess the validity of the model. The predictions for the transition period of heating clean sand and the treatment of waste compare satisfactorily to the experimental data.     

Gas Adsorption on Structurally Heterogeneous Microporous Solids

Abstract

Isotherm equations for gas adsorption on microporous adsorbents are derived for four distribution functions that characterize the structural heterogeneity of the solids. Since these functions represent the size distributions of micropores, they are physically meaningful for describing gas adsorption on heterogeneous microporous solids. Presentation of relationships between the distribution functions describing either structural or energetic heterogeneity of a solid increases the utility of previous distribution functions for characterization of microporous adsorbents.     

Zur Verfestigung von Schüttgütern – Mikroprozesse und Kinetikmodelle

Storage tanks are important elements of a self-operating closed processing system. The reliability and availability of storage equipment essentially depends on the flow behaviour of particulate solids in storage containers. A wide residence time distribution (i.e. too long a storage time at rest) in silos, bunkers or transportation containers, respectively, can lead to the hazardous problem of so-called “time consolidation” of particulate solids. During this hardening process, solid bridges are forming with resulting solidification and solid properties of bulk material. In principle, there are four main physico-chemical effects in bulk materials storing and handling which can produce solid briding between the particle contacts due to crystallisation, chemical reactions, solidification of high-viscous bonding agents and sintering. Generally, new adhesion force based models are presented to describe the consolidation kinetics of particulate solids. Preliminary solutions of kinetic model equations are discussed and compared with new test results and practical conclusions are drawn concerning the reliable processing, storage and transportation of bulk materials.     

CFD SIMULATION OF THE GAS-SOLID FLOW IN THE RISER OF A CIRCULATING FLUIDIZED BED WITH SECONDARY AIR INJECTION

A comprehensive investigation was carried out to study hydrodynamics aspects of secondary air injection in circulating fluidized beds. This article presents modeling and results of computational fluid dynamics simulations of gas-solid flow in the riser section of a laboratory-scale (ID = 0.23 m, height = 7.6 m) circulating fluidized bed with a radial secondary air injector. The gas-solid flow model is based on the two-fluid (Eulerian-Eulerian) approach, where both gas and solids phases are treated as interpenetrating continua. A granular kinetic theory model is used to describe the solids phase stresses. The simulation results are compared with measured pressure drop and axial particle velocity profiles; reasonable agreement is obtained. Qualitatively, excellent agreement is obtained in predicting the increase in solids volume fraction below secondary air ports, the accumulation of solids around the center of the riser due to momentum of secondary air jets, and the absence of the solids down-flow near the wall above the secondary air injection ports, which are the prominent features of secondary air injection observed in the experiments.     

CFD SIMULATION OF THE GAS-SOLID FLOW IN THE RISER OF A CIRCULATING FLUIDIZED BED WITH SECONDARY AIR INJECTION

A comprehensive investigation was carried out to study hydrodynamics aspects of secondary air injection in circulating fluidized beds. This article presents modeling and results of computational fluid dynamics simulations of gas-solid flow in the riser section of a laboratory-scale (ID = 0.23 m, height = 7.6 m) circulating fluidized bed with a radial secondary air injector. The gas-solid flow model is based on the two-fluid (Eulerian-Eulerian) approach, where both gas and solids phases are treated as interpenetrating continua. A granular kinetic theory model is used to describe the solids phase stresses. The simulation results are compared with measured pressure drop and axial particle velocity profiles; reasonable agreement is obtained. Qualitatively, excellent agreement is obtained in predicting the increase in solids volume fraction below secondary air ports, the accumulation of solids around the center of the riser due to momentum of secondary air jets, and the absence of the solids down-flow near the wall above the secondary air injection ports, which are the prominent features of secondary air injection observed in the experiments.     

Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

Fluid mechanics of circulating fluidized beds

A fluid mechanical model of segregated vertical gas-solids flow has been developed. Mass and force balances were set up with the aid of this model and, finally, a dimensionless state and pressure drop diagram was calculated. In this diagram, the pressure gradient caused by the solids transport is plotted in dimensionaless form versus the superficial gas velocity in the form of a particle Froude number. Parameter is the ratio of the solids volumetric flow rate at minimum fluidization to the gas volumetric flow rate. The state and pressure drop diagram is valid for a given gas-solids system, i.e. for a given Archimedes number and given minimum fluidization porosity. The fluid mechanical behaviour of different types of circulating fluidized beds can be explained with the aid of the state and pressure drop diagram for segregated vertical gas-solids flow. As an example, the operating behaviour of circulating fluidized bed with a syphon in the solids downcomer is discussed. Measurements of the circulating solids mass flow rates are compared with calculation results.     

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

ABSTRACT

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.