A COMPREHENSIVE MATHEMATICAL MODEL FOR A MULTIZONE TUBULAR HIGH PRESSURE LDPE REACTOR

In this study a comprehensive mathematical model of high pressure tubular ethylene polymerization reactors is presented. A fairly general reaction mechanism is employed to describe the complex kinetics of ethylene polymerization. To determine the variation of molecular properties along the reactor length the method of moments is applied to the infinite set of species balance equations to transform it into a low order system of differential equations in terms of the leading moments of the number chain length distribution. Detailed algebraic equations are given describing the variation of kinetic rate constants, thermodynamic and transport properties of the reaction mixture with temperature, pressure and composition. A new correlation is derived to describe the change of reaction viscosity with reactor operating conditions. The model permits a realistic calculation of temperature and pressure profiles, monomer and initiator concentrations, molecular properties of LDPE (i.e. M_n, M_m, LCB and SCB) as well as the variation of inside film heat transfer coefficient with respect to the reactor length. Simulation results are presented illustrating the effects of initiator concentration, inlet pressure, chain transfer concentration and wall fouling on the polymer quality and reactor operation. The present model predictions are in good agreement with experimental observations in industrial high pressure tubular LDPE reactors.     

Mathematical modeling of endothermic reactions in the catalyst unit with structured catalytic beds

A mathematical model was developed and numerical modeling of a heat transfer process in a set of plane-parallel plates was performed. Basic conditions were defined, at which a non-stationary process of heat transfer proceeds as dissipating heat waves. The influence of chemical reaction (the endothermic processes of cyclic hydrocarbons dehydrogenation, conversion of methane and decomposition of ammonia) on the wave mode of heat distribution in the catalyst unit was investigated. The optimal values of some parameters influencing the process of heat transfer were defined.     

塑料挤出吹塑冷却阶段温度场的有限元分析

挤出吹塑中冷却与固化阶段温度场的演化对制品的最终性能有很大的影响。首先,建立塑料挤出吹塑制品冷却过程热传递问题的教学模型；然后,利用有限元软体POLYFLOW求解数学模型获得制品冷却过程的温度场；最后,在有限元模型基础上分析了不同内冷方式、制品壁厚以及初始温度对制品温度场的影响。     

玻璃熔制过程三维数学模拟的运用

采用所建立的玻璃的熔制过程的三维数值模型对彩色显微管玻璃熔窑进行模拟,详细研究了不同壁面散热和两通道引出量不对称条件对玻璃熔制过程的影响。三维数值模拟的结果可以真实地反映玻璃熔池实际运行过程,有助于加深对玻璃熔制机理的认识和指导实际生产。     

乙烯氧氯化工业反应器的模型化

针对乙烯氧氯化反应过程所用的挡板流化床反应器的结构和操作特点，建立了一个比较完整和实用的能反映中、高气速下，较大开孔率挡板流化床的气固流动的多釜串联模型，并进行了模型的数学推导和求解。该模型能较好地模拟工业反应器内轴向的气体浓度分布和床层温度分布规律。研究结果表明，在本反应体系中，因乙烯和氧的过量，导致反应过程的后期ＨＣｌ转化率为相间传质控制，强化相间传质效果是保证ＨＣｌ高转化率的有效手段。     

Dissolution of Polydisperse Silica Grains in Glass Melts–Analysis

By combining population balance with mass-transfer-controlled dissolution, a formulation is developed to analyze the dissolution of polydisperse silica grains in glass furnaces. For an initial lognormal distriution of particle sizes, the change in the distribution with respect to a modified time scale is expressed analytically. This paper shows how the formulation can be combined with time-temperature data along various flow path lines in a glass melter to calculate the extent of dissolution in the melter. Calculated results are presented on the dissolution of polydisperse silica grains in a glass melter for which the information on path lines was obtained by using a three-dimensional mathematical model for flow and heat transfer. The effects of maximum particle size of a truncated distribution and the standard deviation on the extent of dissolution are examined.     

多孔材料中甲烷水合物生成的传热数值模拟研究

水合物储运(NGH)是近几年发展起来的天然气储运技术,已具备实现工业化的潜力。但水合物的生长是传质传热控制的反应,因此在放大实验中存在诸多不确定因素。针对该问题,对水合物反应器中多孔材料内甲烷水合物生成传热过程建立了基于化学反应动力学和多孔材料内传质传热的甲烷水合物生成传热数学模型,可用于计算反应器内水合物生成分布和热量分布,指导水合反应器的设计和优化。通过模拟与实验数据对比验证了该模型的可靠性,并对使用了不同热导率填料的水合反应过程进行数值模拟。结果显示,模拟值与实验值的绝对平均相对误差小于6%,生成传热模型准确性高;在水合反应过程中,热量传递是影响水合物生成速率的关键因素之一。导热不良时,易在水合物生成中心部分形成局部过热,对水合物生长造成热抑制。在进行水合物生成放大实验时,应特别注意反应器内部的热量控制。     

多孔材料中甲烷水合物生成的传热数值模拟研究

水合物储运(NGH)是近几年发展起来的天然气储运技术,已具备实现工业化的潜力。但水合物的生长是传质传热控制的反应,因此在放大实验中存在诸多不确定因素。针对该问题,对水合物反应器中多孔材料内甲烷水合物生成传热过程建立了基于化学反应动力学和多孔材料内传质传热的甲烷水合物生成传热数学模型,可用于计算反应器内水合物生成分布和热量分布,指导水合反应器的设计和优化。通过模拟与实验数据对比验证了该模型的可靠性,并对使用了不同热导率填料的水合反应过程进行数值模拟。结果显示,模拟值与实验值的绝对平均相对误差小于6%,生成传热模型准确性高;在水合反应过程中,热量传递是影响水合物生成速率的关键因素之一。导热不良时,易在水合物生成中心部分形成局部过热,对水合物生长造成热抑制。在进行水合物生成放大实验时,应特别注意反应器内部的热量控制。     

Modeling batch melting: Roles of heat transfer and reaction kinetics

Development of mathematical models of heat and mass transfer in glass-melting furnaces began in the 1970s and progressed rapidly with advances in sophisticated experimental/numerical techniques and increasing computational power. Today, practically all newly built or rebuilt furnaces are optimized with these models to meet stringent quality requirements, reduce the unit costs of manufacturing, or control emissions. One remaining hurdle is to model the batch-to-glass conversion accurately enough to reliably assess the glass production rate. This article summarizes two key aspects of the batch-conversion modeling—the heat transfer and the kinetics of conversion—and reviews the current state-of-the-art approaches to simulating them. We critically examine the advantages of the commonly used heat transfer approach, but also explain that its predictive capabilities are significantly restricted by the dependence of batch thermal properties on the time-temperature history. We argue that kinetic approaches to the batch-conversion modeling would offer a significant improvement when coupled with the heat transfer approach. Finally, we summarize key areas requiring further research on the way toward a realistic model of the batch blanket.     

CFD analysis of a symmetrical planar SOFC with heterogeneous electrode properties

A comprehensive 2-D CFD model is developed to investigate bi-electrode supported cell (BSC) performance. The model takes into account the coupled complex transport phenomena of mass/heat transfer, charge (electron/ion) transport, and electrochemical reactions. The uniqueness of this modeling work is that heterogeneous electrode properties are taken into account, which includes not only linear functionally graded porosity distribution but also various nonlinear distributions in a general sense according to porous electrode features in BSC design. Extensive numerical analysis is performed to elucidate various heterogeneous porous electrode property effects on cell performance. Results indicate that cell performance is strongly dependent on porous microstructure distributions of electrodes. Among the various porosity distributions, inverse parabolic porosity distribution shows promising effects on cell performance. For a given porosity distribution of electrodes, cell performance is also dependent on operating conditions, typically fuel/gas pressure losses across the electrodes. The mathematical model developed in this paper can be utilized for high performance BSC SOFC design and optimization.     

Experimental and numerical investigation on the pyrolysis of single coarse lignite particles

This paper reports on the mathematical modeling of the pyrolysis of single coarse lignite particles using a kinetics model coupled with a heat transfer model. The parallel reaction kinetics model of the lignite pyrolysis makes no assumptions about the activation energy distribution and the conversion of sub-reactions. The pyrolysis kinetics parameters were obtained on the basis of experimental data from thermogravimetric analysis (TGA) tests. The heat transfer model includes diffusive, convective and radiative heat transfer modes. The experimental investigations were carried out for single lignite particles in an electrically heated reactor. Measurements of the temperature and mass loss were performed during the pyrolysis in a nitrogen atmosphere. The model predictions for the temperature and mass loss histories agree well with the experimental data, verifying that the mathematical model accurately evaluates the pyrolysis of lignite particles. The effects of temperature and particle size on the pyrolysis time and final residual mass fraction were evaluated using the numerical model.     

TPA和EG连续生产PET的第一酯化反应器操作模拟

对乙二醇(EG)和对苯二甲酸(TPA)连续生产对苯二甲酸乙二酯(PET)的第一酯化反应器进行了数学模拟。数学模型中包括了反应动力学方程、气液平衡和气液传质方程,使模拟结果接近于工厂实践。此外对不同停留时间、不同的反应器操作温度及压力、不同的进料 EG/TPA 的 mol比,进行了模拟计算,得出了反应器出口各种产物的组成随操作参数的变化,并对各操作参数的范围和对反应的影响进行了评述。     

管式炉传热数学模型

本文研究了管式炉辐射传热,提出了焰墙黑度ε_gω新概念,从而导出了新的传热数学模型 q=4.96ε_0 F_c/(F_c)〔（T_g/100）~4-（T_c/100）~4〕+a_k（T_g-T_c）上述模型可以计算近代生产乙烯裂解管式炉。对于箱式加热管式炉和圆筒加热管式炉的传热计算,也提出了相应的数学模型。 用本文提出的方法和另外两种通用的方法进行了6种裂解管式炉的计算。计算结果表明,此法计算简单,计算值与实际值符合得很好。     

Coupled simulation of combustion with heat transfer and cracking reaction in SL-Ⅱ industrial ethylene pyrolyzer

采用计算流体力学(CFD)方法对SL-Ⅱ型工业乙烯裂解炉辐射段炉膛内的燃烧传热及管内石脑油裂解反应过程进行耦合模拟,建模及耦合求解在CFX中完成。计算时采用标准k-ε双方程湍流模型、旋涡耗散/有限化学速率(EDM/FRC)燃烧模型和离散传播(DT)辐射模型,其中介质辐射特性采用多灰气加权模型;石脑油裂解反应采用Kumar分子反应模型,流体流动方程组由全隐式的耦合算法求解。模拟结果与工业数据吻合良好,验证了模型的可靠性。结果表明,管内裂解产物丙烯和丁烯收率先增后减,甲烷和乙烯收率一直增大;出口管外壁温度沿管长分布因侧壁烧嘴的加入而更加均匀;炉膛中部的回流区使该区温度更加均匀;裂解炉结构的非对称性引起烟气流速分布不对称,进而导致后墙上侧壁烧嘴的供热效率相对前墙侧较低,本文模拟结果为裂解炉进一步设计与改造提供理论指导。     

Investigation of radiative heat transfer in fixed bed biomass furnaces

This paper presents an investigation of the radiative heat transfer process in two fixed bed furnaces firing biomass fuels and the performance of several widely used models for calculation of radiative heat transfer in the free-room of fixed bed furnaces. The simple optically thin (OT) model, the spherical harmonic P₁-approximation model, the grey gas model based on finite volume discretization (FGG), and the more accurate but time consuming spectral line weighted-sum-of-grey-gases (SLW) model are investigated. The effective mean grey gas absorption coefficients are calculated using an optimised version of the exponential wide band model (EWBM) based on an optical mean beam length. Fly-ash and char particles are taken into account using Mie scattering. In the investigated updraft small-scale fixed bed furnace radiative transfer carries heat from the bed to the free-room, whereas in the cross-current bed large-scale industry furnace, radiative transfer brings heat from the hot zones in the free-room to the drying zone of the bed. Not all the investigated models can predict these heat transfer trends, and the sensitivity of results to model parameters is fairly different in the two furnaces. In the small-scale furnace, the gas absorption coefficient predicted by using different optical lengths has great impact on the predicted temperature field. In the large-scale furnaces, the predicted temperature field is less sensitive to the optical length. In both furnaces, with the same radiative properties, the low-computational-cost P₁ model predicts a temperature field in the free-room similar to that by the more time consuming SLW model. In general, the radiative heat transfer rates to the fuel bed are not very sensitive to the radiative properties, but they are sensitive to the different radiative heat transfer models. For a realistic prediction of the radiative heat transfer rate to the fuel bed or to the walls, more computationally demanding models such as the FGG or SLW models should be used.     

SL-Ⅱ型工业乙烯裂解炉内燃烧传热与裂解反应的耦合模拟

采用计算流体力学(CFD)方法对SL-Ⅱ型工业乙烯裂解炉辐射段炉膛内的燃烧传热及管内石脑油裂解反应过程进行耦合模拟,建模及耦合求解在CFX中完成.计算时采用标准k-ε双方程湍流模型、旋涡耗散/有限化学速率(EDM/FRC)燃烧模型和离散传播(DT)辐射模型,其中介质辐射特性采用多灰气加权模型;石脑油裂解反应采用Kuma...     

Ultrapyrolysis of n-hexadecane in a novel micro-reactor

A novel reaction system, which provides better control compared with the tubular flow reactors of previous researchers, was employed to study the ultrapyrolysis kinetics of n-hexadecane, a gas oil model compound. Ultrapyrolysis, or ultra rapid pyrolysis, refers to thermal cracking under conditions of high temperature, very short reaction time, high heating rate and rapid product quench. Modern-day ‘millisecond’ furnaces, operating under such conditions, have demonstrated significantly higher ethylene yields due to improved selectivity. The automated micro-reaction system employed a Curie point pyrolyser to rapidly heat microgram n-hexadecane samples to high temperature. The Curie point phenomenon ensured that a reproducible and well-defined temperature was attained. A rapid direct quench system was used to stop the reactions and transfer the products to the analyser. n-Hexadecane was pyrolysed at 576–842 °C for 100–3200 ms. Peak ethylene production (28 wt%) was exhibited at ultrapyrolytic conditions of 842 °C and 500 ms. A first-order kinetic analysis performed on the pyrolysis data yielded an activation energy of 39.4 kcal mol⁻¹.     

在方箱炉、圆筒炉中区域法计算辐射传热的数学模型及其应用

本文叙述了以区域法计算辐射传热的数学模型。在区域法中,系统被分为表面区和气体区,区域数取决于所要求的结果精度和计算时间。炉子的温度分布可通过解每区的能量平衡而得。作为Hottel和Cohen的原始开发,直接交换面积限于立方体和正方形;本文给出了在方箱炉、圆筒炉中任何两区之间直接交换面积方程式的推导。这些方程式可适用于任何大小的矩形、共轴圆筒壁、炉底环形区和其他形状。 本文提供了一个关于烃类一段蒸汽转化炉和圆筒炉的设计方法。计及反应动力学、对流传热、管内压降,采用区域法计算这些炉子的温度分布,从而预言工艺气、烟气、管表面和耐火墙表面的温度分布。计算结果与工厂实测数据相吻合。     

热管式生物质气化炉的模拟

从化学反应和传热两个方面考虑,建立了生物质间接供热气化模型,包括化学反应和传热两个子模型。化学反应子模型可以预测产气主要成分以及气化反应需要的热量,而传热子模型则可以估算热管的总热阻和传热功率。在模型分析基础上,开发设计了热管式生物质气化炉,并对化学反应子模型进行了验证。结果表明生物质间接供热气化模型成功地预测了产气主要成分,在利用热管间接供热的生物质气化产气中氢气含量在50%～60%之间,并且气体热值较高,可达10 MJ·m^-3