大型射流流化床气化炉的数学模拟Ⅰ.模型的建立

本文是在充分考虑了流动特性、质量平衡、能量平衡和动量平衡以后，建立了一个基于大型射流流化床气化炉（直径大于１米）的模型。通过与实验结果比较、证明该模型可用于大型气化炉的模拟工作。     

Analysis of the combustion reaction of carbon and lignite char with ignition and extinction phenomena: Shrinking sphere model

Single‐particle combustion of carbon and lignite char is analyzed in the present work using a generalized shrinking sphere model. Finite volume method (FVM), which was earlier employed by the authors in solving such moving boundary problems involving single particle analysis of general fluid–solid noncatalytic reactions, has been used in this work to solve the transient mass and energy balance equations. The computed results are compared with published experimental data of fluidized‐bed combustion of lignite char. The effects of various parameters like bulk temperature, initial particle temperature, initial particle radius, etc. are examined on the dynamics of combustion of carbon and lignite char. The phenomena of ignition and extinction are also investigated. The importance of nonequimolar diffusion in the combustion reaction has also been analyzed. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 307–319, 2007     

气固流化床内射流特性的研究

采用Brandani等的数学模型模拟了中心射流宽度为0.01m的二维气固流化床(高1.6m、宽0.3m)内鼓泡和射流的瞬态及时均流体动力学特性。一种典型的Geldart B颗粒――砂子(粒径为500mm、密度为2660kg/m3)作为研究的模拟物料。瞬态结果表明，床内射流产生和发展、射流崩塌后所形成气泡尺寸以及全床内的气体速度场和空隙率均存在明显的非对称性，但是由压力信号功率谱密度得到的时均压力特性则有较好的对称性。因此，对于商业化稳定运转的射流床，可以用半床模拟结果近似解释整床特性；然而，在考察射流床的瞬态特性时，半床模拟结果与整床结果存在明显偏差。     

气-固流化床反应器内双流体力学模型及其验证 Ⅱ.单组分两维射流床内流场特性分析

由以质量、动量和能量三大守恒定律为基础的湍流两相流理论出发,建立了描述气固流化床内两相流动的数学模型;在微型计算机上编写了相应的数值计算和图形处理程序;为了验证模型的可靠性,本文着手模拟与分析了单组分颗粒体系两维射流流化床内气、固相速度场、空隙度和压力场随时间、空间变化规律;得到了与前人实验结果相吻合的结论。     

Mean residence time of Markov processes for particle transport in fludized bed reactors

A new approach for studying the particle dynamics and RTD (residence time distribution) in processes is to formulate stochastic models. A common question to all models for RTD is whether Danckwerts’ law for mean residence time holds. In this paper we revisit a Markov process that has been proposed by Dehling et al. (1999) as a stochastic model for particle transport in fluidized bed reactors. Under the volumetric flow balance conditions, we deduce different boundary conditions at the entrance and the exit of the reactor, and in both discrete model and continuous model we show that processes satisfy Danckwerts’ law, stating that the mean residence time of particle transport in fluidized bed reactors equals V/v, where V denotes the volume of the reactor occupied by the fluid and v the volumetric inflow rate.     

New algorithms for the computation of column dynamics of multicomponent liquid phase adsorption

New and efficient numerical algorithms were developed for simulating column dynamics of multicomponent liquid phase adsorption. Simple and realistic models are used for the simulation. Langmuir form of isotherm and linear driving force rate expressions are employed in the model equations. Algorithms were formulated for three different rate control mechanisms, namely, film diffusion control, particle diffusion control and combined film and particle diffusion control. The algorithms derived are explicit with the exception of the requirement of solving a nonlinear equation in one single variable which is the concentration of a reference species. Thus the tedious iterative calculation procedure for solving simultaneous nonlinear equations in a multicomponent fixed bed system is avoided. Example calculations indicated very good numerical accuracy as verified from an independent check by means of an overall mass balance.     

Geldart B 类颗粒气固流化床内的压力波动特性(英文)

采用多通道压力采集系统测量了Geldart B类颗粒（树脂）矩形流化床(2.000m×0.300m×0.025m)内的压力波动,探索了流化床内的压力波动特征;同时采用标准方差、自相关和互相关函数分析了表观气速和静床高度对压力波动、压力波速度和压力波主频的影响。结果表明,气泡行为（如：气泡的形成、发展、聚并和破碎）是影响流化床内压力波动的主要因素;密相和稀相界面处的压力波动幅值主要由气泡崩塌决定;压力波在流化床内进行传播,并且具有明显的周期性特征;此外,压力波动、压力波速度和压力波主频均与表观气速和静床高度密切相关。     

Dynamic behavior of interfaces: Modeling with nonequilibrium thermodynamics

In multiphase systems the transfer of mass, heat, and momentum, both along and across phase interfaces, has an important impact on the overall dynamics of the system. Familiar examples are the effects of surface diffusion on foam drainage (Marangoni effect), or the effect of surface elasticities on the deformation of vesicles or red blood cells in an arterial flow. In this paper we will review recent work on modeling transfer processes associated with interfaces in the context of nonequilibrium thermodynamics (NET). The focus will be on NET frameworks employing the Gibbs dividing surface model, in which the interface is modeled as a two-dimensional plane. This plane has excess variables associated with it, such as a surface mass density, a surface momentum density, a surface energy density, and a surface entropy density. We will review a number of NET frameworks which can be used to derive balance equations and constitutive models for the time rate of change of these excess variables, as a result of in-plane (tangential) transfer processes, and exchange with the adjoining bulk phases. These balance equations must be solved together with mass, momentum, and energy balances for the bulk phases, and a set of boundary conditions coupling the set of bulk and interface equations. This entire set of equations constitutes a comprehensive continuum model for a multiphase system, and allows us to examine the role of the interfacial dynamics on the overall dynamics of the system. With respect to the constitutive equations we will focus primarily on equations for the surface extra stress tensor.     

Dynamics of adsorption by zeolites from the liquid phase, simulated using data on adsorption statics

A mathematical model for calculation of the dynamics of liquid-phase adsorption in a fixed sorbent bed is constructed on the basis of material balance equations solved by numerical integration on the assumption of a constant mass-transfer coefficient and a limiting inner-diffusion resistance.     

Kinetic modeling of industrial steam cracker

A comprehensive mathematical model is a very useful tool for the selection of feedstock, optimized cracker product mix, downstream production planning, and optimized plant performance. As a part of achieving this prime objective, a mathematical model has been developed for the simulation of the radiation section of a steam cracker unit. The model involves solving differential component, energy, and momentum balance equations numerically to generate temperature, concentration, and pressure profiles along the length of the reactor tube. The model has been developed in FORTRAN using the lSODE solver. The model considers 19 free radicals and 35 molecules connected over 433 reactions. The model was used to simulate the performance of propane and ethane cracking. The model predicted propane conversion is 95.55 against the plant data of 95% at a coil outlet temperature of 845 ​°C and the corresponding predicted ethylene and propylene yield is 34.49 and 11.53% respectively. The model has been validated for ethane cracking performance. The model predicted ethylene yield is in good agreement with that of plant values for ethane cracking. The model provides a basis for the optimization of process parameters for the given geometry. The model is useful to answer what-if questions and to investigate operational strategies.     

Structure of mass, momentum, and energy transfer equations under highly nonequilibrium conditions

The structure of mass, momentum, and energy transfer equations under highly non-equilibrium conditions is considered when the traditional assumption of nonequilibrium thermodynamics (the local equilibrium condition) is violated. The derived transfer equations based on particle mass, momentum, and the law of energy conservation are related to heterogeneous systems with arbitrary density, i.e., for three aggregate states and their interfaces. Fluxes of the mentioned properties are described at the atomic-molecular level by nonequilibrium discrete unary and binary distribution functions (in the lattice gas model) with regard to interparticle potential interactions of system components. It is found that the total set of local transfer equations consists of five modified mass, momentum, and energy transfer equations for each of the system sites, and of 15 new equations describing the correlated characteristics of the density, rate, and temperature for the sites of a pair. The relationship between the derived equations and previous theories is discussed.     

Analysis of constant permeate flow filtration using dead-end hollow fiber membranes

Dead-end filtration of colloids using hollow fibers has been analysed theoretically and experimentally. A mathematical model for constant flux filtration using dead-end hollow fiber membranes has been developed by combining the Hagen–Poiseuille equation, the (standard) filtration equation, and cake filtration theory of Petsev et al. [D.N. Petsev, V.M. Starov, I.B. Ivanov, Concentrated dispersions of charged colloidal particles: sedimentation, ultrafiltration and diffusion, Colloid Surf. A: Physicochem. Eng. Aspects, 81 (1993) 65–81.] to describe the time dependence of the filtration behavior of hollow fiber membranes experiencing particle deposition on their surface. Instead of using traditional constitutive equations, the resistance of the cake layer formed by the deposited colloids has been directly correlated to the cake structure. This structure is determined by application of a force balance on a particle in the cake layer combined with the assumption that an electrostatically stable cake layer of mono-sized particles would be ordered in a regular packing geometry of minimum energy. The developed model has been used to identify the relationship between the filtration behavior of the hollow fiber membrane and the particle properties, fiber size, and imposed average flux. Filtration experiments using polystyrene latex particles of relatively narrow size distribution with a single dead-end hollow fiber membrane demonstrate good consistency between experimental results and model prediction. The developed model has been used to simulate the distribution of the cake resistance, transmembrane pressure, and flux along the hollow fiber membrane and used to assess the effect of fiber size, particle size, zeta potential, and the average imposed flux on the suction pressure-time profiles, flux, and cake resistance distributions. These results provide new insights into the filtration behavior of the hollow fiber membrane under constant flux conditions.     

Influence of particle diameter distribution on protein recovery in the expanded bed adsorption process

The General Rate model has been developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial and local variation of particle size distribution (PSD), external and intra-particle mass transfer resistances, and dispersion in liquid phase. The influence of PSD on breakthrough profiles has been analysed. The simulation results show that for a significantly high expanded bed the lower part of the breakthrough curve profiles, calculated for local particle size distribution (LPSD) and for axial average particle size distribution (APSD) are very similar. However, the upper part of breakthrough profiles calculated for LPSD approaches inlet concentration much more slowly than those calculated for APSD. The retention times of the lower part of uptake curves calculated with average particle diameter are constantly shorter than those obtained from LPSD. For the calculation of the dynamic capacity (DC), the LPSD can be replaced by APSD for large expanded bed heights. Using breakthrough profiles calculated for average particle size, DC values are constantly underestimated.     

煤在热载体流化床中的热解模型

煤粒在热载体流化床中的热解规律对于设计煤气、热、电三联产的关键装置－热载体流化床干馏炉是十分重要的。本文建立了煤粒在热载体流化床中的传热和热解反应的微分方程，并对其进行了数值求解，得到了煤粒度、热载体流化床操作速度、热载体流化床床层温度、热载体颗粒粒径等对煤气产率的影响规律，为热载体流化床干馏炉的设计提供了计算方法和理论依据。     

A model for the characterization of supported catalysts by temperature-programmed desorption with readsorption and heterogeneity

A model has been developed in which the thermogram is the net balance of the overall desorption-adsorption process. The equations necessary for its application are proposed and the model is tested using a simulation program.     

煤中氮热解析出转化的颗粒模型研究

采用数值模型，研究了煤热解、燃烧过程中挥发分氮的析出、中间含氮产物HCN的生成以及转变为NO的过程。应用有限体积法对质量、化学组分、动量和热量守恒方程进行离散求解，并与试验结果进行了比较。研究结果揭示了炉膛温度、颗粒直径以及氧浓度等参数对煤中挥发分氮的析出和进一步转化为NO过程的影响。     

Modeling and experimental studies on combustion characteristics of porous coal char: Volume reaction model

A generalized single‐particle model for the prediction of combustion dynamics of a porous coal char in a fluidized bed is analyzed in the present work using a volume reaction model (VRM). A fully transient nonisothermal model involving both heterogeneous and homogeneous chemical reactions, multicomponent mass transfer, heat transfer with intraparticle resistances, as well as char structure evolution is developed. The model takes into account convection and diffusion inside the particle pores, as well as in the boundary layer. By addressing the Stefan flow originated due to nonequimolar mass transfer and chemical reactions, this work enables a more realistic analysis of the combustion process. The model, characterized by a set of partial differential equations coupled with nonlinear boundary conditions, is solved numerically using the implicit finite volume method (FVM) with a FORTRAN code developed in‐house. The use of a FVM for solving such an elaborate char combustion model, based on the VRM, was not reported earlier. Experiments consisting of fluidized‐bed combustion of a single char particle were carried out to determine the internal surface area of a partially burned char particle and to enable model validation. Predicted results are found to compare well with the reported experimental results for porous coal char combustion. The effects of various parameters (i.e., bulk temperature and initial particle radius) are examined on the dynamics of combustion of coal char. The phenomena of ignition and extinction are also investigated. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 299–315, 2010     

Drying and pyrolysis of wood particles: experiments and simulation

The objective of this study is to develop a flexible and stable numerical method to predict the thermal decomposition of large wood particles due to drying and pyrolysis. At a later stage, this model is applied to each particle of a packed bed and thus, forms the entire packed bed process as a sum of individual particle processes. Therefore, this approach can deal with particles of different sizes, shapes and properties. A general formulation of the conservation equations allows the geometry of a fuel particle to be treated as a plate, cylinder or sphere. The various processes such as heat-up, drying and pyrolysis are described by a set of one-dimensional and transient conservation equations for mass and energy. This allows for simultaneous processes e.g. reactions in time and covers the entire range between transport-limited (shrinking core) and kinetically limited (reacting core) reaction regimes. The particles interact with a gas phase by heat and mass transfer taking into account the Stefan correction due to the gas outflow during conversion. Experiments carried out span a temperature range between T=300 and 900 °C for particle sizes varying between 8 and 17 mm. A comparison between measurements and predictions of drying models yielded satisfactory agreement only for the constant evaporation temperature model and thus, indicating, that the drying process is transport limited by heat transfer for large wood particles. Likewise, predicted results of pyrolysis for the above-mentioned range of temperatures and sizes agreed satisfactorily with measurements.     

Measurements and particle resolved modelling of the thermo- and fluid dynamics of a packed bed

The objective of this study is to investigate experimentally and numerically into heat-up, drying and pyrolysis of a packed bed consisting of large single particles. The novelty of the current approach is that the numerical model contrary to continuum mechanic approaches considers a packed bed as an ensemble of a finite number of particles, which may have different material properties or sizes. The heat-up, drying and pyrolysis process of each particle is described sufficiently accurate by a set of one-dimensional and transient differential conservation equations for mass and energy. Applying this model to all particles, including interactions between them, of a packed bed forms the entire backed bed process as a sum of individual particle processes. The arrangement of particles within a bed defines a void space between the particles. The flow through the void space of a packed bed is modelled as a flow through a porous media taking into account interaction between the solid and the gaseous phase by heat and mass transfer. Experiments for drying and pyrolysis of a packed bed were carried out for validation in a temperature range of T=120–530 °C. The temperatures and the mass loss due to drying and pyrolysis were recorded during the experiments. The measured mass loss of the packed bed due to drying were well predicted by the constant evaporation temperature model of the particles and thus, indicating, that the drying process is transport limited by heat transfer for large wood particles in a temperature range of T=120–530 °C. A comparison between experiments and predictions of pyrolysis yielded reasonable agreement for temperatures above T=300 °C. For temperatures of T≈200 °C the deviations were not acceptable. However, the results show, that a particle resolved approach is well suited to describe packed bed processes.