Coupling granule properties and granulation rates in high-shear granulation

It is possible to link granulation rates to granule properties. The linkage is by multiple dimension population balance equations that, by means of simplifying assumptions, can be reduced to multiple one-dimensional (1-D) population balance equations (PBEs). Using simple physically based models, this paper demonstrates how multiple one-dimensional population balance equations can describe the results of high-shear granulation experiments of two different materials, calcium carbonate and lactose. Good agreement between experimental and simulated results was achieved enabling the granulation rates to be defined by two model parameters: the critical binder volume fraction and the aggregation rate constant. The modelling framework presented in this paper also provides a basis for the kinetic analysis of granulation experiments so that with further work, it is possible to determine the effect of process conditions and material properties on the model parameters.     

EXPERIMENTAL STUDY OF A COMPLEX CATALYTIC REACTION NETWORK IN A TRICKLE-BED REACTOR

In the present report a relatively complex reaction system including several side reactions to the desired main reaction has been studied in a trickle-bed reactor. In addition the experimental part—which showed very good reproducibility of the results—an attempt to a reasonable modelling of the reactor was tried. The starting point was the differential equation system describing the kinetics of the reactions as well as the corresponding kinetic parameters, which had been established earlier in a slurry-reactor. It was possible to demonstrate that the behaviour of a trickle-bed reactor can be simulated by a relatively simple approach containing the basic kinetic equations, the wetting efficiency of the catalyst particles and a one-dimensional, pseudohomogeneous reactor model, the cell model. The so calculated concentration curves of the different reactants and products fitted the experimental values very closely. For those reasons, and especially for the reasonable effort needed for very satisfactory modeling, the results and proceeding steps outlined here might be of particular interest for further applications of trickle-bed reactors.     

Simplified flocculation model for inorganic and polymer flocculants

Simulation of the flocculation process using both inorganic and polymer flocculants is very difficult because there are many factors that influence the process. In this study, a model that enables the visual understanding of the qualitative trends of the flocculation system using both inorganic and polymer flocculants is proposed. It is a simplified one-dimensional model that expresses flocculation under various additive manners of the flocculant. Various kinds of thought experiments as well as experimental runs with model flocculants were carried out based on the model; the results demonstrate that the model can express many empirical qualitative trends of flocculation.     

Application of a simple enthalpy‐based pyrolysis model in numerical simulations of pyrolysis of charring materials

A new, simple pyrolysis model for charring materials is applied to several numerical and experimental test cases with variable externally imposed heat fluxes. The model is based on enthalpy. A piecewise linear temperature field representation is adopted, in combination with an estimate for the pyrolysis front position. Chemical kinetics are not accounted for: the pyrolysis process takes place in an infinitely thin front, at the ‘pyrolysis temperature’. The evolution in time of pyrolysis gases mass flow rates and surface temperatures is discussed. The presented model is able to reproduce numerical reference results, which were obtained with the more complex moving mesh model. It performs better than the integral model. We illustrate good agreement with numerical reference results for variable thickness and boundary conditions. This reveals that the model provides good results for the entire range of thermally thin and thermally thick materials. It also shows that possible interruption of the pyrolysis process, due to excessive heat losses, is automatically predicted with the present approach. Finally, an experimental test case is considered. Copyright © 2009 John Wiley & Sons, Ltd.     

On the implementation of membrane models in computational fluid dynamics calculations of polymer electrolyte membrane fuel cells

The implementation of phenomenological membrane models within computational fluid dynamics (CFD) codes requires coupling of the conservation equation for water content within the membrane to the conservation equations for species mass outside the membrane. It is common practice to treat water and current transport within the membrane as one-dimensional (1D), i.e., normal to the membrane surface only. The purpose of this study is to investigate the accuracy and efficiency of various strategies of implementing a phenomenological membrane model within the framework of a two-dimensional (2D) CFD code. Springer's membrane model was compared against two other models available from the literature, and the accuracy of each model was assessed by comparing predicted results against experimental data. Results appear to indicate that the Springer model and the Nguyen and White model over-predict the drying of the membrane, while the Fuller and Newman model provides the best match with experimental data. Following these studies, three strategies for implementation of the membrane model were investigated: (1) 2D transport in membrane, (2) 1D transport in membrane and (3) 1D transport with approximate transport properties. Fuller and Newman's membrane model was used for these studies. The results obtained using the three approaches were found to be within 4% of each other, while there was no significant difference in the computational time required by the three models, indicating that an analytical 1D transport model for the membrane that uses approximate properties is adequate for describing transport through it.     

水平管段塞流气弹区液膜特性研究

为了研究气液段塞流相界面的结构特征,采用了双平行电导探针技术对水平管内段塞流气弹区的液膜特性进行了实验测量,并基于一维双流体模型导出液膜厚度的控制方程,该方程对液膜厚度的预测结果与实验结果吻合良好。结合液膜厚度计算模型提出了计算段塞流的机理模型,该段塞流机理模型的计算结果表明对于液相表观速度较高而气相表观速度较低的段塞流,机理模型中忽略液膜非平衡性时得到的平均液膜厚度和气弹区长度明显偏低。     

Kinetics of Isothermal Crystallization of Hydrogenated Castor Oil-in-Water Emulsions

Kinetics of isothermal crystallization of hydrogenated castor oil in water emulsions exhibiting multiple crystal morphologies have been studied experimentally by DSC and polarized light microscopy. The induction time of nucleation increases with the increase of the isothermal temperature under which crystallization occurred. Crystal growth has been observed by microscopy showing that both crystal morphologies, fibers and rosettes, grow linearly at the initial stage of crystallization and then slow down to reach a plateau value. The Avrami model, which has been widely used in kinetics studies of triacylglycerol systems, was employed to fit experimental results at different isothermal temperatures. It was found that experimental trends could be captured by introducing the volume fraction of each type of morphology into three-dimensional and one-dimensional full Avrami models.     

PET固相缩聚反应器动态模型

PET固相缩聚过程涉及反应固体颗粒和反应器床层两个空间尺度的传质,是一个复杂的多维多相对象。以反应过程控制为目标,在已有的反应动力学模型基础上,同时考虑可逆化学反应和小分子产物内外扩散两个控制因素,并借用固定床拟均相模型的建模思想,将小分子产物在颗粒内外扩散形成的浓度梯度用一个有效系数来表示,从而建立了简化的PET固相缩聚反应器一维动态模型。在相关文献的实验条件下求解分布参数模型的数值解,并进行启动过程仿真和过程动态分析,计算反应器出口质量指标,与文献曲线和数据对照,验证了模型的正确性。     

Modeling hydrogen fluoride adsorption by sodium fluoride

In the current study, hydrogen fluoride (HF) adsorption onto the sodium fluoride pellets is modeled. For this purpose a two-dimensional, non-isothermal model was developed and the governing equations were solved numerically. The contributions of diffusion transport in axial and radial directions also were considered in mathematical formulations. The model results of effluent concentration and breakthrough curves of HF were compared with the experimental data obtained in a lab-scale adsorption unit, reported in our previous work [1]. The results indicate while the feed gas velocity decreases, the HF adsorption capacity on NaF is significantly enhanced and there is a delay in breakthrough time. The adsorption capacity of HF on NaF decreases slightly when inlet HF concentration increases. Moreover, the model results were compared with the obtained results from a one-dimension model. This comparison indicates that one-dimensional model can well predict the HF dynamic adsorption behavior for lab-scale fixed beds. Comparing the experimental breakthrough curves of HF adsorption on NaF pellets with the model results shows the ability and accuracy of the model with maximum 7.82% errors.     

A one-dimensional plug-flow model of a counter-current spray drying tower

A one-dimensional numerical model for a detergent slurry drying process in a counter-current spray drying tower is developed for the prediction of the gas and droplet/particle temperature profiles within the tower. The model accommodates droplets/particles over a range of sizes. A semi-empirical slurry droplet drying model is integrated with a counter-current tower simulation based on mass, energy and particulate phase momentum balances in order to calculate the drying rate and the particle residence time within the tower. The coupled first order ordinary differential equations for the two phases are solved numerically using the iterative shooting method in an algorithm developed within MATLAB. The predictions of the numerical model are compared with industrial pilot plant data. The results are found to vary significantly with the specified size distribution of the droplets. Despite the simplicity of the model in ignoring the coalescence, agglomeration, wall deposition and re-entrainment, the model gives reasonable agreement with the experimental data.     

Intrinsic Reaction and Self-Diffusion Kinetics for Silicon Carbide Synthesis by Rapid Carbothermal Reduction

A one-dimensional nonisothermal model has been developed for the "rapid carbothermal reduction" synthesis of fine silicon carbide powders. Intrinsic reaction and self-diffusion kinetics are identified through simulation of the model and comparison to experimental results. The reaction rate follows a shrinking-core mechanism and is described by the relation [formula omitted] The self-diffusion coefficient for SiC in the aerosol flow reactor is described by the relation The self-diffusion coefficient for SiC in the aerosol flow reactor is described by the relation      

A two-dimensional model of second order rapid reactions in turbulent tubular reactors

Previous studies of second order rapid reactions in turbulent tubular reactors have been analyzed in terms of a one-dimensional model. Deviations between theory and experiment have been interpreted in terms of diffusion limited reaction rates. In this paper the experimental results are re-analyzed in terms of a two-dimensional model leading to the conclusion that mixing and entrance region effects are responsible for the deviations between the experimental results and one-dimensional theory. A new upper bound for the Damköhler number associated with diffusion controlled reaction rates is suggested.     

A mathematical model for drum drying of black liquor slurry using superheated steam impinging jets

A mathematical model is developed and tested for drum drying of an aqueous slurry subjected to impinging jets of superheated steam. The heat and mass transfer within the slurry film was modeled as a one dimensional, pseudo unsteady diffusion problem while the external convective heat transfer rate was obtained by solving the steady full conservation equations of mass, momentum and energy numerically in two and three dimensions. A modified low Reynolds number version of the k-? turbulence model was selected after a careful evaluation of the predictive performance of various k-? models for impingement flow and heat transfer. The computed heat transfer one-dimensional diffusion model for the slurry film. Agreement between experimental data obtained using a black liquor slurry and results of the model was found to be satisfactory.     

一维变压压榨脱水理论研究

介绍分析了压榨脱水的现状;在建立一维变压压榨原理模型的基础上,通过合理的基本假设,结合渗流理论,推导出了一维变压压榨基本方程;给出符合实际的初始、边界条件,并经过奇次化,求出了压榨基本方程理论解的脱水速率全新表达式,为一维变压榨实验研究奠定了理论基础。     

生物质流化床空气-水蒸气气化模型研究

根据流化床反应器特点,结合生物质气化动力学反应机理,建立了生物质在流化床内气化的等温稳态、一维二相动力学模型。该模型所做的主要假定如下:流化床分为气泡相和乳相,在气泡相和乳相内均存在化学反应,考虑二相内的轴向气体扩散,生物质热解过程瞬时完成,主要考虑焦碳以及CO,CO2,H2,H2O,CH4等在流化床内发生的8个主要化学反应。数学模型属于常微分方程组边值问题,利用数值计算软件M atlab7.0进行编程求解。以木粉为原料,将模型结果与实验结果进行了对比,模拟结果与试验数据符合良好,在一定程度上证明了模型的有效性和可靠性。     

苯酚在活性炭上吸附平衡模型的研究

本文研究了苯酚在活性炭上的吸附特性,并发现在低pH,低温度下有利于活性炭吸附苯,研究表明Freundlich模型能较好描述吸附过程,并得到了在考虑温度,pH值影响情况下苯酚的Freundlich模型表达式。     

Potential and concentration gradients in a hybrid ion-exchange/electrodialysis cell

The regeneration of 2, 4 and 8% cross-linked ion-exchange resins in the nickel-form was carried out in a three-compartment hybrid ion-exchange/electrodialysis cell. During the process the potential and nickel concentration profiles in the bed were measured. The experimental results are compared to results from a one-dimensional transport model able to simulate the development of potential and concentration gradients during the process; the amount of nickel transported out of the ion-exchange bed to the cathode, or concentrate, compartment was also reasonably well predicted. Differences between the model and experimental results are also discussed. It was found that under extreme conditions (i.e., high bed voltage), the formation of metallic nickel was observed in the central ion-exchange compartment.     

有限体积法解多场耦合下散射性非灰介质内的辐射换热

将有限体积法与谱带模型结合 ,求解了吸收、散射性非灰介质内的耦合换热 .经与光线踪迹法、离散传递法的计算结果比较表明 :提出的数值方法具有较高的精度 ;有限体积法适合辐射导热的多场耦合计算 ;对非灰介质建议选用谱带模型 ;并应考虑折射率对传热的影响     

快速流化床一维轴向稳态流动模型

本文对稳态操作的快速流化床气固两相流动进行了分析,表明颗粒在床内的加速运动对床层各项参数有显著影响。考虑了颗粒加速作用以及由于颗粒聚集使气固两相相互作用力减小的事实后,可采用一维轴向稳态流动模型获得截面平均颗粒速度、空隙率以及曳力系数等参数及其轴向分布规律。模型预测与实验直接测定结果吻合很好。     

Estimation of the pseudohomogeneous one-dimensional heat transfer coefficient in a fixed bed

A critical analysis of the methods used to determine the overall heat transfer coefficient is carried out. The measurement of the axis temperature is recommended for the evaluation of the local value of the coefficient; an asymptotic value is obtained for bed lengths greater than a certain minimum. The different relationships that can be established between the heat transfer parameter of the pseudohomogeneous one-dimensional model and the basic parameters are established. The best agreement with numerical simulations is obtained for the equation derived via the heterogeneous one-dimensional model. A comparison with experimental results validates both the equation proposed and the correlations used for the evaluation of the basic parameters.