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.     

Gas—particle heat transfer in a crossflow moving packed bed heat exchanger

A programme of work on a moving packed bed heat exchanger, whereby a gas is blown vertically upwards through a horizontally moving packed bed of particles, is described in this paper. Such a device can be used for the process heating or cooling of particulate solids. In the work rigorous and simplified analyses to describe the process of gas—particle heat transfer in the system were developed and the application of these analyses demonstrated by a series of experiments on a small-scale unit.     

Mathematical modeling of a moving bed reactor for post‐combustion CO2 capture

A mathematical model for a moving bed reactor with embedded heat exchanger has been developed for application to solid sorbent‐based capture of carbon dioxide from flue gas emitted by coal‐fired power plants. The reactor model is one‐dimensional, non‐isothermal, and pressure‐driven. The two‐phase (gas and solids) model includes rigorous kinetics and heat and mass transfer between the two phases. Flow characteristics of the gas and solids in the moving bed are obtained by analogy with correlations for fixed and fluidized bed systems. From the steady‐state perspective, this work presents the impact of key design variables that can be used for optimization. From the dynamic perspective, the article shows transient profiles of key outputs that should be taken into account while designing an effective control system. In addition, the article also presents performance of a model predictive controller for the moving bed regenerator under process constraints. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3899–3914, 2016     

Monitoring the particle-wall contact in a gas fluidized bed by RPT

Particle-wall contact behavior of the solids in a gas-solid fluidized bed was experimentally studied using the radioactive particle tracking (RPT) technique in which the position of a radioactive tracer is monitored when moving freely in the bed. The solids were sand particles, fluidized by air at room temperature and atmospheric pressure at various superficial velocities, covering both bubbling and turbulent regimes of fluidization. The motion of individual particles near the wall of the bed was studied based on the position of the tracer. The contact time, contact distance and contact frequency of the particles at the wall were evaluated. It was found that the distribution functions of these three parameters become wider by increasing the superficial gas velocity. Axial profiles of contact time and contact distance were also studied in this work. Axial profiles of the overall heat transfer coefficient in the fluidized bed were estimated based on the formulas reported in the literature and the experimental particle-wall contact time evaluated in the present study. Based on such profiles, in order to benefit from the maximum heat transfer coefficient along the bed, it is recommended to place the heat exchanging surface in the middle of the bed, i.e., not very close to the gas distributor as well as far from the top of the dense bed.     

Transient heating and cooling of cocurrent three-phase fluidized beds

The thermal transient behaviour of three-phase fluidized beds have been investigated for a liquid viscosity ranging from 35 to 75 mPa · s. For the operating conditions used in this study, a 6 mm glass particle bed was found to have a thermal response similar to that of a fixed bed. The transient responses, which were not significantly affected by gas sparging, were, however, faster for heating than for cooling. This result has been analyzed from a model assuming liquid plug flow through stationary particles using combined free and forced convection correlations for heat transfer around the particles. Different correlations are then proposed to predict the contribution of natural convection to the liquid-to-particle heat transfer in heating and cooling modes. The effect of gas sparging was found to strongly affect The 2.0 mm particle bed responses but only moderately the 3.9 mm bed responses. These responses were analyzed using axial dispersion models for the liquid and solid phases. For the 3.9 mm particle bed, the axial dispersion coefficient of the solids, E_ZS, was found to be of the same order of magnitude as that of the liquid coefficient, E_ZL. However, the value of E_zs for the 2 mm particle bed was found to be five times that of E_ZL.     

气固循环流化床提升管环核区颗粒质量传递系数的估计

Based on analysis of energy dissipation in the core region of gas-solid fluidized bed risers,a simplified model for determination of core-annulus solids mass transfer coefficient was developed according to turbulent diffu- sion mechanism of particles.The simulation results are consistent with published experimental data.Core-annulus solids mass transfer coefficient decreases with increasing particle size,particle density and solids circulation rate, but generally increases with increasing superficial gas velocity and riser diameter.In the upper dilute region of gas-solid fiuidized bed risers,core-annulus solids mass transfer coefficient was found to change little with the axial coordinate in the bed.     

Heat transfer in a fluidized bed. Part II. Interpretation of the heat transfer coefficient on the basis of solids movement

In Part I the influence of the thermal driving force on the coefficient for heat exchange with a fluidized bed was described.The extent of this was clearly related to the kind of powder fluidized, i.e. powders which exhibited dense phase expansion were strongly influenced as opposed to those which did not exhibit dense phase expansion. The latter yielded heat transfer coefficients which could be reasonably predicted by a theoretical model based on a combination of solids movement and unsteady-state heat conduction, using well-known models from the literature. The slight influence of the driving force on the experimentally determined heat transfer coefficients could also be anticipated when accounting for the temperature-dependent thermal properties of gas and solids.For powders exhibiting dense phase expansion, prediction with the proposed model proved to be impossible. Here, the solids behaviour seems to be governed by random movements which are difficult to relate to fluidizing parameters. Tentative calculations suggested that the bubble frequency may be a useful correlating parameter.     

BUBBLE DYNAMICS AND ELUTRIATION STUDIES IN GAS-FLUID1ZED BEDS

In order to adequately interpret the heat and mass transfer data taken in a gas-fluidized bed, it is essential to know the bubble dynamics and solids movement in the bed, and solids elutriation from the bed. To generate information on these aspects, an experimental facility has been designed, fabricated and successfully tested. This consists of a two-dimensional fluidized bed with its gas supply and cleanup system. The bubble dynamics and solids projection from the bed are recorded by a high-speed movie camera. The films are analyzed on a photo-optical data analyser and digitizer provided with an electronic graphics calculator connected to tape printer and a Teletype terminal interfaced with a computer. The analysis of recorded bed dynamics suggests that for large particles the bubbles grow to be non-spherical and these rise almost above the bed surface before bursting when the wake remains intact while the solids bulge at the bubble nose ruptures to release the bubble gas. It is concluded unambiguously that the solids projected in the freeboard originate from the bubble bulge, and not from the bubble wake as commonly believed. A series of experiments is proposed which will facilitate the development of a general quantitative theory for solids elutriation from industrial fluidized beds.

In addition, a fairly complete review of the work done on bubble dynamics, solids movement in the bed, and solids projection from the bed surface in two- and three-dimensional fluidized beds is presented. Thus, on the whole the present work reviews the state-of-the-art of these three different fluid-bed aspects, and reports new data.     

A Cross-Flow Model for Continuous Plug Flow Fluidized-Bed Cross-Flow Dryers

Plug flow fluidized bed cross-flow dryers have been used in drying of particulate solids such as paddy and other grains for many years. However, simulation of the performance of any particular design of the dryer has always been problematic due to the inadequate overall empirical models used that are too inflexible and too specific to the particular design. In addition, previous theoretical models of the plug flow fluidized bed cross-flow dryer did not model the gas cross flow properly and had difficulty in modeling the moving solid bed. A new steady-state cross-flow model of the dryer that models the gas cross-flow is proposed. The profiles for the solids and air moisture contents and temperatures were found to be dependent on the gas-solid flow ratio, G/F, the specific heat demand, C_PY(T_I - T_A)/(Y_E - Y_I), the total number of a transfer units, N_T = Gε/KφaSL and the specific drying load, (X_I - X_P)/ (Y_E - Y_I). The model was validated by comparing the simulated data with experimental data that were obtained by drying paddy in a plug flow fluidized bed cross-flow dryer pilot plant. The model was found to estimate very well the solids moisture content and temperature, the gas moisture content and temperature profiles, and the driving force profile.     

A CFD model for predicting the heat transfer in the industrial scale packed bed

Compared to the traditional lumped-parameter model,computational fluid dynamics (CFD) attracted more attentions due to facilitating more accurate reactor design and optimization methods when analyzing the heat transfer in the industrial packed bed.Here,a model was developed based on the CFD theory,in which the heterogeneous fluid flow was resolved by considering the oscillatory behavior of voidage and the effective fluid viscosity.The energy transports in packed bed were calculated by the convection and diffusion incorporated with gaseous dispersion in fluid and the contacting thermal conductivity of packed particles in solids.The heat transfer coefficient between fluid and wall was evaluated by considering the turbulence due to the packed particles adjacent to the wall.Thus,the heat transfer in packed bed can be predicted without using any adjustable semi-empirical effective thermal conductivity coefficient.The experimental results from the literature were employed to validate this model.     

移动颗粒床中高温气体渗流传热数值计算

针对移动颗粒床中物料层内的高温气体渗流传热现象 ,考虑渗流与传热的相互作用 ,采用局部非热平衡假设建立了多孔介质渗流传热物理数学模型并进行了数值计算 .研究了不同情况下床内填充多孔介质中的流速、气固温度和床层压力损失 .计算结果表明 ,高温热气对移动床颗粒料层的热渗透主要发生在渗流入口端区域 ,增大入口渗流速度以及减小床层物料下移速度将导致物料温度沿床高慢速下降 ,热渗透深度扩大 ,热渗透作用区域内的物料温度水平提高 .在热渗透作用区域 ,孔隙率对流场和压力损失有很大的影响 .研究结果对于移动颗粒床反应器的设计与运行具有一定的参考作用     

Computational fluid dynamics simulations of interphase heat transfer in a bubbling fluidized bed

Numerical simulations based on the Eulerian-Eulerian approach have been performed in the study of interphase heat transfer in a gas solid fluidized bed. The kinetic theory of granular flow (KTGF) has been used to describe the solid phase rheology. An assessment of drag models in the prediction of heat transfer coefficients shows that no major difference is observed in the choice of the drag model used. Fluctuations of the interphase heat transfer coefficient have been found to be closely related to the bubble motion in the bed. Effects of the wall boundary condition, inlet gas velocity, initial bed height and particle size on the predicted heat transfer coefficient have also been investigated. Typical temperature profiles in the bed show that thermal saturation is attained instantaneously close to the gas distributor. Simulated results of the coefficients are in fair agreement with those reported in literature.     

Rubber heat engines,analyses and theory

It has long been known that elastomeric solids could be used as the working “fluid” in engines designed to convert heat into mechanical work. In the past rubber heat engine cycles were not given serious consideration since energy alternatives were not in demand and a majority of the scientific community is unaware of their gas-like thermodynamic behavior. Consequently, past work has dealt with the subject primarily as a novelty or as a demonstrative proof of thermodynamic behavior. This paper provides an idealized mechanical and thermodynamic analysis of the rubber cycle and compares it to an equivalent cycle wherein a gas is the working fluid. Experimental data on a small rubber fiber engine is included which confirms the high power potential of these engines when they are designed using modern elastomeric fibers. These materials have remarkable properties and can respond rapidly to cyclic thermal disturbances. Power densities of roughly one watt/g of rubber have been attained using only a 30°C difference between the heat source and heat sink. Engine speeds well over 1000 RPM have also been attained when atmospheric pressure steam was used as the heat source. The analyses demonstrate that elastomers are ideally suited for energy conversion when only small temperature differences are available.     

气体流动条件下钴基催化剂固定床的传热

在气体流量4~8 Nm3/h、气体分布器进口温度190~210℃、加热管壁温约240℃的条件下,对气体流动时活性组分呈蛋壳型分布的钴基催化剂固定床的传热进行了实验研究,建立了二维拟均相传热模型,利用正交配置法和Levenberg-Marquardt法对其求解,得到了钴基催化剂床层径向有效导热系数及壁给热系数的关联式,并将传热参数与由气体处于静态时固定床的有效导热系数计算而得的固定床传热参数值进行了比较,在气体入口温度范围内考察了其对固定床传热参数的影响. 结果表明,实验所得传热参数与文献值的最大偏差绝对值均在15%以内.     

竖直管气固鼓泡流化床传热机理的CPFD模拟

针对细颗粒气固鼓泡流化床中床料与竖直传热管壁面间的传热行为,在前期实验的基础上,采用计算颗粒流体力学(CPFD)方法从颗粒在传热壁面更新的角度,深入分析了传热特性与壁面气固流动行为之间的关联性。结果表明,模拟得到的传热管壁面颗粒更新通量和基于颗粒团更新模型的颗粒团平均停留时间均能很好解释实验测得的传热系数变化规律,这证实颗粒团更新是影响传热过程的控制性因素。模拟还发现随加热管从床层中心向边壁的移动,加热管周向方向上颗粒更新通量和传热系数的不均匀性都呈增大趋势。随着表观气速的增大,气泡行为导致床层颗粒内循环流率增大,这是导致颗粒团在加热管壁面上的更新频率增大以及床层与壁面间传热系数增大的根源。     

Heat transfer to submerged surfaces in coarse-grained pressurized fluidized beds and fixed beds

This contribution reports on the theory underlying a uniform representation of heat transfer to submerged surfaces in fixed bed reactors and of gas convective part of heat transfer in fluidized beds with coarse-grained bulk solids and/or at elevated pressure. Based on an analysis of the pressure drop behaviour of fixed bed percolation at different gas pressures and with different bulk solids, a new dimensionless pressure drop parameter was developed. Fixed bed heat transfer data are very well correlated by this new dimensionless number. As soon as fluid throughput is in excess of minimum fluidization velocity, the pressure drop parameter transforms into the well-known Archimedes number. These two dimensionless numbers are connected by the condition of equilibrium for pressure drop and mass of practices in a fluidized bed. This equilibrium is fulfilled as soon as fluidization commences. Up to now, the Archimedes number has been generally accepted as the significant parameter, determining the gas convective part of heat transfer in fluidized beds; however, without any physical interpretation of this parameter. Introduction of the pressure drop number, which is consistent with the Archimedes number, reduces the heat transfer behaviour to pressure drop characteristics. The usefulness of this concept is proven by the comparison of experimental results and prediction.     

BUBBLE DYNAMICS AND ELUTRIATION STUDIES IN GAS-FLUID1ZED BEDS

In order to adequately interpret the heat and mass transfer data taken in a gas-fluidized bed, it is essential to know the bubble dynamics and solids movement in the bed, and solids elutriation from the bed. To generate information on these aspects, an experimental facility has been designed, fabricated and successfully tested. This consists of a two-dimensional fluidized bed with its gas supply and cleanup system. The bubble dynamics and solids projection from the bed are recorded by a high-speed movie camera. The films are analyzed on a photo-optical data analyser and digitizer provided with an electronic graphics calculator connected to tape printer and a Teletype terminal interfaced with a computer. The analysis of recorded bed dynamics suggests that for large particles the bubbles grow to be non-spherical and these rise almost above the bed surface before bursting when the wake remains intact while the solids bulge at the bubble nose ruptures to release the bubble gas. It is concluded unambiguously that the solids projected in the freeboard originate from the bubble bulge, and not from the bubble wake as commonly believed. A series of experiments is proposed which will facilitate the development of a general quantitative theory for solids elutriation from industrial fluidized beds.

In addition, a fairly complete review of the work done on bubble dynamics, solids movement in the bed, and solids projection from the bed surface in two- and three-dimensional fluidized beds is presented. Thus, on the whole the present work reviews the state-of-the-art of these three different fluid-bed aspects, and reports new data.     

流化床中气固均匀分布的失稳现象

流化床因其均匀且剧烈的气固相互作用保证了其优异的流动和传递性能,因而广泛应用于化学工业中。因此,构建定量计算气固均匀分布的失稳临界点既是重要的学术问题又具有工程意义。本文分别使用气相和固体颗粒相的质量分数表示气固分布状态;引入颗粒床层压力载荷（Φ _T）描述分布器输入的规则负熵和固体颗粒床层自身混沌熵产生之间相互作用;由于密相颗粒床层远离平衡态且具有强非线性耗散项,因此需基于普利高津最小超量熵增原理给出气固密相流在并联系统均布状态的失稳临界点（Φ _Tc）：分布器和固体颗粒床层总熵增在气固均布和气固非均布情况下相等;由于并联系统的对称性,可将N单元路径并联系统气固均布稳定性分析简化为判断单元路径压降二阶导数正负;在此基础上讨论了操作参数、固体颗粒性质和分布器结构参数对气固密相床层均布稳定性的影响。此外,通过气体示踪和压力脉动频谱分析在直径为300mm冷模实验验证了颗粒床层压力载荷（Φ _T）对密相气固均布稳定性的影响;同时应用该方法论计算了工业流化床反应器临界床层高度、临界表观气速以及分布器临界阻力系数,指导了操作工况的调整和分布器结构设计,对比分析了改造前后的反应情况。     

Particle-fluid heat transfer and dispersion in fluidised beds

The dynamic response of a gas fluidised bed has been measured for a range of particle sizes of lead glass ballotini and a range of particle Reynolds numbers. A dispersion model has been formulated that includes the effects of gas and particle mixing, fluid-to-particle heat transfer and intraparticle thermal conductivity, and the dynamic thermal response in theory has been found by solving the partial differential equations in the Laplace transform domain. The coefficient of thermal dispersion, the particle-to-fluid heat transfer coefficient and the intraparticle thermal conductivity have been found for the experimental response by non-linear regression. The coefficient of axial dispersion was found to be large and the particle to fluid heat transfer coefficients agreed with an established correlation for fixed and fluidised beds. The intraparticle thermal conductivity agreed with literature values for lead glass, the estimates showed no trend with flowrate, and the standard deviation of the estimate was three times smaller than the deviation found from similar experiments in fixed beds.     

A Numerical Study of Heat Transfer Mechanisms in Gas–Solids Flows Through Pipes Using a Coupled CFD and DEM Model

Abstract

A two dimensional numerical model has been developed to simulate heat transfer in gas–solids flows through pipes, in which the gas phase is modelled as a continuum using the Computational Fluid Dynamics (CFD) approach and the solids phase is modelled by the Discrete Element Method (DEM). This allows interactions between gas, particles, and pipe wall to be accounted at the scale of individual particles and convective and conductive heat transfers to be calculated using local gas and solids parameters. The predicted changes to the flow structures and the various heat transfer mechanisms due to the presence of particles were analyzed and compared with other workers' findings. This study has quantitatively demonstrated the crucial effect of particle transverse motion on heat transfers due firstly to the thermal energy transport by rebounding particles and secondly to the modification of the fluid thermal boundary layer characteristics.