Modeling Gas‐Solid Reactions in the Bed of a Rotary Kiln

When dealing with gas‐solid reactions in rotary kilns, it is necessary to realize that the total particle surface within the granular bed can be much larger than the outer surface of the bed. Depending on the reaction conditions this inner surface can contribute considerably to the chemical conversion in the kiln. In this paper, a model is presented, which describes the reaction within the bed for the case of bed movement according to the cascade mode. In this case, gas is drawn into the rotating bed together with the particles. As a key quantity, an effectiveness factor η of the bed is defined. It is the ratio of the actual conversion to the conversion that would occur if the concentration of the reacting component remained unchanged throughout the bed, i.e. at its entrance concentration. An evaluation for reactions of order mshows this factor to be more than 25 % when the Damköhler number is smaller than 2. It approaches 100 % as the Damköhler number approaches 0. The Damköhler number used in this paper contains the void fraction of the particle bed in its denominator.     

Numerical Simulation of Open‐Circuit Continuous Mills Using a Non‐Linear Population Balance Framework: Incorporation of Non‐First‐Order Effects

Population balance modeling has been used as a tool for simulating, optimizing, and designing various particulate processes, including milling. A fundamental tenet of the traditional models for milling processes is the first‐order breakage kinetics. Ample data obtained from batch milling studies show that this assumption is not necessarily valid for certain milling systems. In the present theoretical investigation, an attempt has been made to incorporate these experimentally observed non‐first‐order effects into continuous mill models within the context of a novel non‐linear population balance framework. In view of two idealized flow regimes, i.e., perfect mixing and plug‐flow, continuous mills operating in the open‐circuit mode are numerically simulated. The simulations indicate that not only does the product size distribution depend on the degree of mixedness in a continuous mill, but also on the non‐first‐order effects arising from multi‐particle interactions.     

Steady‐State Modeling and Simulation of an Axial‐Radial Ammonia Synthesis Reactor

A two‐dimensional model was developed for an axial‐radial ammonia synthesis reactor of the Shiraz petrochemical plant. In this model, momentum and continuity equations as well as mass and energy balance equations are solved simultaneously by orthogonal collocation on the finite element method to obtain pressure, velocity, concentration and temperature profiles in both axial and radial directions. For the catalyst particle, the effectiveness factor is calculated by solving a two‐point boundary value differential equation. The boundary conditions for the Navier‐Stokes and continuity equations are obtained by using equations representing the phenomena of gases splitting or joining in different streams and going through holes in a thin wall. The results of the mathematical model have been compared with the plant data and a good agreement is obtained.     

Modeling of Caked Contacts in DEMs

When modeling the caking properties of bulk solids, it is not only necessary to incorporate the yield properties of individual particle contacts, but also to extend them to a many‐particle system. To accomplish this by means of Distinct Element Method (DEM) simulations a contact model for (spherical) particles, including a yield criterion for combined load is proposed. An application to the simulation of a caking test is presented and compared to experiments.     

高温萤石粉稀相气力输送工程设计分析

通过工程实践，证实了稀相正压气力输送系统用于短距离高温萤石粉输送是可行的，对系统运行中出现的料气混合比偏高、料斗侧壁积料以及部分设备和弯管磨损严重等问题进行了分析，并提出了解决措施。     

中低压稀相气力输送在PVC工程中的应用

结合PVC树脂粉料气力输送工程的实例，分析了系统设计方案，确定采用中低压稀相气力输送。介绍了PVC粉料气力输送系统工艺流程、主要技术参数和试车情况，认为可在扩建、新建PVC工程中推广应用。     

Model for Gas‐Liquid Flow through Wet Porous Medium

A method involving bubbling of air through a fibrous filter immersed in water has recently been investigated (Agranovski et al. [1]). Experimental results showed that the removal efficiency for ultra‐fine aerosols by such filters was greatly increased compared to dry filters. Nuclear Magnetic Resonance (NMR) imaging was used to examine the wet filter and to determine the nature of the gas flow inside the filter (Agranovski et al. [2]). It was found that tortuous preferential pathways (or flow tubes) develop within the filter through which the air flows and the distribution of air and water inside the porous medium has been investigated. The aim of this paper is to investigate the geometry of the pathways and to make estimates of the flow velocities and particle removal efficiency in such pathways. A mathematical model of the flow of air along the preferred pathways has been developed and verified experimentally. Even for the highest realistic gas velocity the flow field was essentially laminar (Re ≈ 250). We solved Laplace's equation for stream function to map trajectories of particles and gas molecules to investigate the possibility of their removal from the carrier.     

Modeling of Nitrogen and Carbon Dioxide Solubility in Alternative Fuels at High Pressures Using the Soave‐Redlich‐Kwong Equation of State

In this paper, the Soave‐Redlich‐Kwong equation of state with quadratic mixing rule has been tested for correlation of vapor‐liquid equilibria (VLE) at high pressures in the binary nitrogen + dimethyl ether, dimethyl ether + methanol, nitrogen + methanol, carbon dioxide + dimethyl ether and carbon dioxide + methanol systems. The interaction parameters k_ij were evaluated for each binary pair and used for prediction of VLE in the ternary nitrogen + dimethyl ether + methanol and carbon dioxide + dimethyl ether + methanol systems at high pressures. The results of correlation and prediction are discussed.     

Mass Transfer Mechanisms in the Fixed‐Bed Ion‐exchange Process for Dilute Colloidal Silica Manufacture

The ion exchange behavior of the H⁺ form C‐100 Purolite resin for the production of colloidal silica from dilute sodium silicate solutions has been investigated. The exchange isotherm has been found to be almost irreversible. The effective resin diffusion coefficient has been found to be 2.84 × 10^–10 m² s^–1 using a shrinking core model for the batch uptake experiments. Fixed bed experiments for different column heights and feed flow rates were performed. Numerical solution of the governing equations showed that the process is initially controlled by film diffusion and consequently by resin diffusion. Axial dispersion had to be taken into account. A simple power law correlation has been determined that relates the fluid Peclet number to the Reynolds number. It is presumed that some sort of resin ‘deactivation’ due to intraparticle microgel formation is responsible for the sluggish end part of the breakthrough curves.     

垂直管栓流密相气力输送的参数模拟

通过建立对气体流动及粉体颗粒与颗粒之间相互作用的计算模型,在不同空隙率、粒子速度及管壁的剪应力的情况下,利用离散理论对栓流密相输送系统进行三维模拟,并将模拟结果与实际实验数据进行了比较。由于该模型建模简单、计算量小,模拟结果与实验数据相符,比较容易被工厂采用,以便指导生产。     

Modeling of Particle Layer Detachment under Consideration of Transient Kinetic Effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the device running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely nonstationary concerning place and time, primarily due to changing conditions for the forces on the one hand and changes in the particle layer morphology on the other. This paper describes a model and a simulation considering such transient kinetic effects on filter cake detachment. Diverse computing results are presented and discussed.     

Engineering Model of Friction of Gas‐Solids Flow in a Jet Mill Nozzle

In this study we develop a model for estimating particle friction against the wall of a jet mill nozzle. The computation is reduced to a definition of conventional force acting on particles in a polydispersed stream. It is assumed that energy losses due to friction are caused by multiple particle collisions against the nozzle walls. The proposed model is oriented to calculating jet mill nozzles and is much simpler than previously applied methods. A parametric study of the proposed model was carried out and the effect of particle friction on particle and gas velocities was derived.     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.     

气力输送装置设计

简要介绍粉料气力运送装置的设计与计算方法,利用该方法可以确定某些工艺参数,为设计提供依据。     

Numerical Calculations of Spray Roasting Reactors of the Steel Industry with Special Emphasis on Fe2O3‐Particle Formation

This work presents numerical calculations for the lay‐out of spray roasting reactors for the steel industry. In these reactors, a pickling liquor based on water and HCl containing FeCl₂ is regenerated in a combustor leading to the formation of Fe₂O₃ particles. For the lay‐out of these reactors, detailed knowledge of the flow and temperature field, the associated gas phase reactions, and especially, of the formation of the Fe₂O₃ particles is required. An extended particle formation model is presented which is based on earlier work. Finally, results for an industrial spray roasting reactor are given showing the potential of the numerical tools developed for the improvement of the technical lay‐out of such thermal reactors.