Modelling Diffusion-Limited Drying Behaviour in a Batch Fluidized Bed Dryer

ABSTRACT

Fluidized bed dryers are often used to extract water from granular materials. When the drying process is mainly limited by the resistance against water transport inside the particle the drying behaviour is said to be diffusion-limited. In the literature there are several models that predict this drying process with very diverging results. In this study a model is set up to arrive at a better prediction for this drying process. The heat and mass transfer in the granular material and the drying air is described. The resulting equations are solved numerically. The model must be extended to incorporate the heat capacity of the dryer.     

Heating/Drying Using Particulate Medium : A Review Part I. General and Heat transfer parameters

This paper presents an Overview of particulate medium drying and heat treating of cereal grains. While the conventional air drying of grains is well documented, studies on the drying of grains using heated granular medium do not appear to exist. The scientific study of the different aspects of drying with a heated granular medium began in the early 1970's. Progress on the utilization of particle-to-particle heat transfer was slow as evidenced by the fact that there is no commercial dryer using the method as of today.

The first section of this paper deals with conduction heating and how it led to the use of granular medium in heating the grain. Starting with the earliest work on conduction heating reported by Kelly ( 1939), the developments in the heating of grain using granular media is discussed. For decades since Kelly's report, work in the subject area dealt mostly with the theoretical aspects of solid-to-solid heat transfer. Thus, in the succeeding section of the paper, heat transfer parameters and mechanisms involved in the process are thoroughly investigated.     

Measurement and simulation of the contact drying of sewage sludge in a Nara-type paddle dryer

Contact drying experiments were carried out in a Nara-type paddle dryer to study the drying kinetics of sewage sludge in the presence of air. In order to have a better understanding of the sewage sludge drying mechanism, a penetration model developed by Tsotsas and Schlünder is used to simulate the drying kinetics of the pasty, lumpy and granular phase which the sludge experiences during the drying process. The pasty phase is assumed to be a saturated particulate phase, and the granular phase is considered as a mono-dispersed particulate phase whose diameter was experimentally determined. In the lumpy phase, a sludge wall sticking still to the paddle-shaft surface was formed, and the heat transfer resistance from the sludge wall is considered during the model calculation. The influence of the drying parameters (temperature, stirrer speed and air flowrate) on the drying process is investigated experimentally and theoretically. The result indicates that the penetration theory is able to describe the sludge drying kinetics of the three distinct phases. Experimental and calculated drying kinetics are in satisfactory agreement for different drying parameters.     

Heating/Drying Using Particulate Medium : A Review Part I. General and Heat transfer parameters

ABSTRACT

This paper presents an Overview of particulate medium drying and heat treating of cereal grains. While the conventional air drying of grains is well documented, studies on the drying of grains using heated granular medium do not appear to exist. The scientific study of the different aspects of drying with a heated granular medium began in the early 1970's. Progress on the utilization of particle-to-particle heat transfer was slow as evidenced by the fact that there is no commercial dryer using the method as of today.

The first section of this paper deals with conduction heating and how it led to the use of granular medium in heating the grain. Starting with the earliest work on conduction heating reported by Kelly ( 1939), the developments in the heating of grain using granular media is discussed. For decades since Kelly's report, work in the subject area dealt mostly with the theoretical aspects of solid-to-solid heat transfer. Thus, in the succeeding section of the paper, heat transfer parameters and mechanisms involved in the process are thoroughly investigated.     

A comprehensive review on modeling of pneumatic and flash drying

Pneumatic conveying drying (PCD) is a widely used process in the industries and is a combination of heat and mass transfer and pneumatic handling technology. Drying processes consume large amounts of energy and, therefore, reduction in operating cost will be extremely beneficial for the industry. Many studies have been conducted to model and optimize the pneumatic drying. This review article focuses on the different strategies used in the literature to model pneumatic drying processes. An analysis is provided for the different mathematical modeling and its components such as balance and complementary equations and modeling assumptions. Two-fluid theory, Eulerian granular, and the discrete element method are reviewed as well as gas–solid flow modeling methods. In addition, the numerical methods and the main studied parameters in the field of pneumatic drying are investigated. To this end, heat and mass transfer coefficients, gas and dispersed phase properties are reviewed.     

水循环式热泵干燥装置的性能分析

水循环式热泵干燥装置是指热泵和干燥部分通过水循环耦合而成的热泵干燥系统，是一种中小型热泵干燥装置的结构型式。对水循环式热泵干燥装置的开机过程、调控特性、能源效率进行了分析，相关结论可为推广应用提供参考。     

THE INFLUENCE OF THE DRYING MEDIUM ON HIGH TEMPERATURE CONVECTIVE DRYING OF SINGLE WOOD CHIPS

High temperature convective drying of single wood chips with air and superheated steam respectively is studied theoretically. The two-dimensional model presented describes the coupled transport of water, vapour, air and heat. Transport mechanisms included are the convection of gas and liquid, intergas as well as bound water diffusion. In the initial part of the drying process, moisture is transported to the surface mainly due to capillary forces in the transversal direction where evaporation occurs, As the surface becomes dry, the drying front moves towards the centre of the particle and an overpressure is simultaneously built up which affects the drying process

The differences between drying in air and steam respectively can be assigned to the physical properties of the drying medium. The period of constant drying rate which does not exist (or is very short) in air drying becomes more significant with decreasing amounts of air in the drying medium and is clearly visible in Dure superheated steam drying. The maximal drying rate is larger in air drying, and shorter drying times are obtained since the heat flux to the wood chip particle increases with increasing amounts of air in the drying medium. The period of falling drying rate can be divided into two parts: in the first, the drying rate is dependent upon the humidity of the drying medium whereas in the second, there is no such correlation.     

对撞流干燥的实验与理论研究

The experiments of one-stage semi-circular and two-stage semi-circular impinging stream drying as well as the vertical and semi-cricular combined impinging stream drying were carried out.The velocity distribution and the mean residence time of particles,and the influence of various factors on drying characteristics were studied.A mathematical model of granular material drying in a semi-circular impinging stream dryer was proposed,in which the flow characteristics as well as the heat and mass transfer mechanisms were considered.Reasonable numerical methods were used to solve the equations.Under various conditons,the calculated results of drying rate and moisture content versus time were obtained.The results indicate that constant drying rate period does not exist in a semi-circular impinging stream dryer.Appropriate semi-cricular stage number and curvature radius,flow-rate ratio,air velocity,and higher inlet air temperature should be used for enhancing the drying process.     

不同加热功率下含油污泥的干燥

辽河油田的含油污泥含有大量的水分,为了更有效地进行油泥热解和减少热解过程中的能耗,需运用干燥技术处理油泥。实验考察了不同干燥功率对油泥干燥速率、湿分比的影响。实验结果表明:油泥干燥可以分成3个阶段,即恒速干燥阶段、第1降速干燥阶段和第2降速干燥阶段;加热功率越大,达到平衡含水质量分数所用的时间越短,恒速干燥速率越大。然后运用干燥方程求得干燥时间。最后运用热分析动力学对实验数据进行处理,得到干燥动力学的数学模型。模拟结果表明修正Page模型符合油泥干燥过程。     

AN ANALYTICAL SOLUTION OF THE GRANULAR PRODUCT IN DEEP-BED FALLING RATE DRYING PROCESS

Abstract

According to analysis of drying characteristics of granular product, the paper describes analytical solutions on a single grain with two falling rale drying stages during corresponding period of deep-bed drying process. Changes of drying and physical parameters and their correlation were discussed. A mathematical model was developed and solved numerically. The application of this analytical solution is also given.     

离心流化床干燥过程中传热传质的数值模拟

通过对典型的多孔湿物料在离心流化床中干燥过程的理论分析和实验研究 ,首次将含湿多孔介质传热传质过程和物料与气流之间的外部传递过程相耦合 ,导出了离心流化床的理论模型和控制方程组 ,对于离心流化床中湿物料的干燥过程引进了数值模拟 ,结果表明增加气体表观流速、控制入口气体的温度和相对湿度以及加大床体转速均对干燥有不同的影响     

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.     

THE INFLUENCE OF THE DRYING MEDIUM ON HIGH TEMPERATURE CONVECTIVE DRYING OF SINGLE WOOD CHIPS

ABSTRACT

High temperature convective drying of single wood chips with air and superheated steam respectively is studied theoretically. The two-dimensional model presented describes the coupled transport of water, vapour, air and heat. Transport mechanisms included are the convection of gas and liquid, intergas as well as bound water diffusion. In the initial part of the drying process, moisture is transported to the surface mainly due to capillary forces in the transversal direction where evaporation occurs, As the surface becomes dry, the drying front moves towards the centre of the particle and an overpressure is simultaneously built up which affects the drying process

The differences between drying in air and steam respectively can be assigned to the physical properties of the drying medium. The period of constant drying rate which does not exist (or is very short) in air drying becomes more significant with decreasing amounts of air in the drying medium and is clearly visible in Dure superheated steam drying. The maximal drying rate is larger in air drying, and shorter drying times are obtained since the heat flux to the wood chip particle increases with increasing amounts of air in the drying medium. The period of falling drying rate can be divided into two parts: in the first, the drying rate is dependent upon the humidity of the drying medium whereas in the second, there is no such correlation.     

Modeling coupled heat and mass transfer during drying in tape casting with a simple ceramics–water system

In many industrial processes such as in tape casting for electronics or in the food industry, drying is one of the determining physical phenomena. In this study, the evaporation of water from a ceramic–water mixture is investigated with the purpose of understanding the drying rate in the drying process of thin sheets produced by the tape casting process. The rate of mass loss in the drying process is a key factor that often is of interest, as it affects the final properties of the tapes. The 1D heat conduction equation is solved numerically to obtain the temperature field in a ceramic sheet. The change in the concentration of the water content is then used as the driving force for diffusive mass transport of the water. Mass–averaged thermal properties are assumed for the ceramic–water mixture in the initial stage. As the water evaporates, the thermal properties of the solid ceramic become more dominant since the fraction of water approaches zero. The developed model is used to simulate a simple test for the drying process. The drying rate is simply calculated by examining the water content in each time step. It is found that the mass loss due to the evaporation is increasing close to linearly with the drying time corresponding to an almost constant drying rate. However, the rate starts to decrease after some time in the simulation. It is also shown that too extensive surface drying results in a slow diffusion rate from the bottom, which in turn reduces the drying rate in general and hence is not favorable from a process viewpoint.     

COMBINED MICROWAVE AND CONVECTIVE DRYING OF A POROUS MATERIAL

A model is formulated to describe the drying of a slab of porous material in a combined microwave and convective environment. The model describes the evolution of temperature, pressure, moisture and power distributions that occur during the drying process. The microwave internal heat source is calculated from electromagnetic theory with varying dielectric properties. The inclusion of pressure in the model allows the physical phenomena of “water pumping”, often observed in microwave drying systems, to be accounted for. The influence of sample size; on the drying kinetics 1s examined and found to be an important parameter during the drying process. In particular the effect of resonance on the moisture and temperature profiles and the need for careful consideration of surface mass transfer coefficients are investigated. Simulation results are presented for the combined microwave and convective drying of a homogeneous, isotropic porous material.     

Ultrasonic Convective Drying Kinetics of Clipfish During the Initial Drying Period

A hybrid drying system for high-intensity airborne ultrasound applied in convective drying was investigated for the drying of salted codfish (clipfish). Convective drying with ultrasonic assistance at 10, 20, and 30°C was compared to the same process without ultrasound. The Weibull model was used to model and investigate the drying behavior, and the effective diffusion in Fick's law was determined. The ultrasound decreased the drying time more at lower drying temperatures. The drying time was reduced by over 90% at a drying temperature of 10°C. For an industrial drying process at a temperature of 20°C, the drying time was reduced by 32.2%. The ultrasonic, convective drying of clipfish at a temperature of 20°C was faster than the same process without ultrasound at 30°C. The investigations showed a thermal effect for all products when ultrasound was applied. The specific moisture extraction ratio (SMER) in the investigated system was improved by 0.2 kg_water kWh^?1. The heat transfer coefficient in the system used was increased by 32.6% for a heating process in a separate investigation, whereas for a cooling process no increased heat transfer coefficient was determined. The thermal effect might (at least partially) explain the faster drying of ultrasonic-assisted convective drying. The results obtained demonstrate the potential of airborne ultrasound in convective drying with regard to drying time, energy consumption, and product quality. Documentation of the thermal effect should be included in future R&D on this topic.     

关于水系流延过程中膜带干燥的若干问题研究

水基流延成型的膜带在干燥技术的许多方面存在着“知其然而不知其所以然”,其干燥过程在固体介质中同时发生热量、质量和动量的传递,用数学对其进行描述存在着相当的困难性和无效性.可以将流延膜的干燥过程分为恒定速率阶段和蒸发速率下降两个阶段.过去由于实验技术条件的限制使人们对一些干燥机理没有充分的认识,就是研究较多的干燥动力学,也存在禁地和误区.由于干燥机理复杂,目前研究得不够充分,关于干燥的动力学数据多取自试验测定值.通过结构与性能关联的研究可拓展人们对于燥过程的认识:通过电子显微镜对膜带的表征,可深入研究其显微结构及湿组份在膜带内的运动机理；通过热重分析技术将膜带的湿度变化与其温度变化相关联,可为设计干燥工艺提供合理的依据；通过固相核磁共振技术,测量湿组份中水分子层的质子自旋松弛时间,可用来半定量计算膜带中的可除去结合水和自由水及不可除去结合水的比例.     

DEVELOPMENT AND VALIDATION OF A PROCESS SIMULATOR FOR DRYING SUBBITUMINOUS COAL

Drying subbituminous coal has never been practiced commercially. The commercial dryers built to date have been designed for drying surface moisture in conjunction with upstream coal preparation facilities. This type of drying is mainly controlled by input energy and the basis of the design is an energy balance. In drying inherent moisture from subbituminous coal, the thermal conductivity of the coal and the diffusion of molecular water within coal particles impose limitations on the process conditions. Energy input and solids residence time in the dryer have to be controlled properly for simultaneously balancing the heat and mass transfer within the coal particles. Improper control of either parameter can cause fires and explosions during the key steps of the drying process—drying and cooling

In parallel to the Anaconda coal drying pilot plant program, a cross-flow, fluid-bed coal drying/cooling process simulator was developed for: (1) understanding the drying phenomena on an individual particle basis; (2) analyzing potential risks and safety limits, and (3) designing the Anaconda pilot plant program

The development of the process simulator was based on both first principles and laboratory data and can be divided into two phases:

1 Development of a semi-mechanistic drying model for Powder River Basin subbituminous coal employing an analytical solution of the diffusion equation

2.Formulation of a fluid-bed cross-bed cross-flow dryer/cooler simulator employing simultaneous heat and mass transfer

This model was validated against process variables data taken on a 4 tph pilot plant. An operable range, or process envelope, has been developed through the pilot plant experience and the process simulation study. Based on the model predictions, an uncertainly range was defined in the design recommendations of a pioneer coal drying plant in scale-up.     

Numerical analysis and differential push-flow structure optimization of vacuum disc drying process

The drying characteristics of sludge in a uniaxial vacuum disc dryer are numerically studied in the present study, and the results showed that the drying process of sludge includes three stages: the viscous stage, the sticky stage, and the granular stage. The influence of main parameters such as sludge feeding rate, heat source temperature, and rotating speed of the shaft on the drying process of sludge in the uniaxial vacuum disc dryer is analyzed. In order to optimize the drying efficiency of the dryer, a differential push-flow structure is proposed in this study, which provides different propulsion effects for the sludge in different drying stages. The differential push-flow is achieved by changing the number and angle of the push-flow blades on the discs. Compared with the dryer before optimization, the dryer with optimized differential push-flow structure has better performance.