Modeling and simulation of an industrial slurry-phase catalytic olefin polymerization reactor series

In the present study, a comprehensive mathematical model is developed to simulate the dynamic behaviour of an industrial slurry-phase olefin catalytic polymerization loop reactor series. More specifically, the effects of various operating conditions on the dynamic reactor behaviour (i.e., reaction temperature and pressure, inflow rates of catalyst, monomers and diluent, etc.) as well as the on the molecular and rheological polyolefin properties (i.e., M_n, M_w, MWD, complex viscosity, etc.) are fully assessed. According to the proposed modeling approach, each loop reactor (i.e., consisting of the loop reactor and the settling legs) is modeled as an ideal CSTR in series with a semi-continuous product removal unit. Dynamic macroscopic mass species and energy balances are derived to calculate the dynamic evolution of the concentrations of the various molecular species as well as of temperature profiles and heat removal in the two loop reactors. The polymer molecular properties (i.e., number- and weight-average molecular weights and molecular weight distribution) are determined by employing a generalized multi-site, Ziegler–Natta (Z–N) kinetic scheme in conjunction with the well-known method of moments. All the thermodynamic calculations, regarding the equilibrium species concentration in the various phases (i.e., solids and liquid), are carried out using the Sanchez–Lacombe Equation of State (S–L EOS). It is shown that the proposed comprehensive model is capable of simulating the dynamic operation of an industrial slurry-phase cascade-loop reactor series under different plant operating policies (i.e., start-up, grade transition, etc.).     

Modelling of a vacuum residue hydrocracking in an industrial slurry phase reactor

The upgradation of the bottom of the barrel has gained much interest across the refineries due to severe environmental rules, limitations of conventional oil reserves, and its flexibility to produce light end products which benefit end users. Slurry phase hydrocracking is one of the growing technologies to fulfil the increasing demand for light cut. Modelling of an industrial slurry phase reactor (SPR) for vacuum residue hydrocracking using different kinetic models is proposed. The axial dispersion model (ADM) is used for modelling an industrial SPR. The mathematical model of the reactors is incorporated for the three different lump kinetic models. This study deals with the continuous stirred tank reactor (CSTR) and SPR modelling, followed by industrial SPR modelling. The small lab-scale reactor models are validated with the experimental data reported in the literature. The study's objective was to investigate the one-dimensional and two-dimensional concentration dynamics of each lump along the axial and radial positions of industrial SPR. The vacuum residue conversion into the light fractions was obtained by more than 73% in industrial SPR. Also, the yield of vacuum gas oil and resins were evaluated as 49% and 63%, respectively. The sensitivity analysis was performed to explain the effect of process variables. The optimum range was found as a length of 15 m, liquid hourly space velocity (LHSV) of 0.2 h⁻¹, 1% catalyst concentration, and 420°C reaction temperature to enhance the throughput of the reactor.     

乙烯淤浆聚合动态分子量分布模拟计算

以乙烯淤浆聚合反应过程为研究对象,提出动态分子量分布的严格模型的数值计算方法。将动态分子量分布的大规模微分代数混合模型解耦为小规模微分代数方程组动态矩模型与大规模常微分方程组粒数衡算模型,然后通过变量解耦的方法进一步将大规模粒数衡算方程组转换为序贯差分方程组,实现了乙烯动态分子量分布严格模型的数值模拟计算。动态模拟乙烯聚合反应从一个稳态切换到另一个稳态,通过在切换后稳态的分子量分布计算结果与Flory分布计算方法进行比较,两者得到的分子量分布曲线吻合很好,证实了本文提出的动态模拟计算方法的精度和准确度都获得良好的保障。     

Modeling and optimization of a high-pressure ethylene polymerization reactor using gPROMS

A gPROMS implementation of a comprehensive steady-state model of the high-pressure polymerization of ethylene in a tubular reactor is presented. Model outputs along the reactor length include the complete molecular weight distribution and branching indexes, as well as monomer conversion, average molecular weights, reactants’ compositions, and reactor temperature and pressure. A detailed calculation of physical and transport properties, such as the reaction mixture density, heat-transfer capacity, viscosity and global heat-transfer coefficient is also included. The reactor model is included in an optimization framework that is used to determine the best operating conditions for producing a polymer with tailor-made molecular structure in terms of the complete molecular weight distribution, branching and polydispersity.     

Modeling and simulation for an industrial reactor on hydroisomerization of C8-aromatics

将3个二甲苯异构体集总为一个组分,提出一个新的异构化三角反应网络,建立工业异构化反应器模型。基于多组平衡的工业数据,采用传统的优化方法估计动力学参数,然后对不同操作条件下的大量工业数据进行仿真,结果表明模型估计值与观测值相当吻合。与其他模型相比,文中开发的模型在相对误差、相对均方误差和参数估计时间等性能指标上均体现出优越性。     

Modeling, simulation and control of dimethyl ether synthesis in an industrial fixed-bed reactor

Dimethyl ether (DME) as a clean fuel has attracted the interest of many researchers from both industrial communities and academia. The commercially proven process for large scale production of dimethyl ether consists of catalytic dehydration of methanol in an adiabatic fixed-bed reactor. In this study, the industrial reactor of DME synthesis with the accompanying feed preheater has been simulated and controlled in dynamic conditions. The proposed model, consisting of a set of algebraic and partial differential equations, is based on a heterogeneous one-dimensional unsteady state formulation. To verify the proposed model, the simulation results have been compared to available data from an industrial reactor at steady state conditions. A good agreement has been found between the simulation and plant data. A sensitivity analysis has been carried out to evaluate the influence of different possible disturbances on the process. Also, the controllability of the process has been investigated through dynamic simulation of the process under a conventional feedback PID controller. The responses of the system to disturbance and setpoint changes have shown that the control structure can maintain the process at the desired conditions with an appropriate dynamic behavior.     

Digital simulation of an industrial ammonia reactor

A mathematical model for the steady-state simulation of a commercial system formed by a countercurrent tube cooled fixed bed ammonia reactor coupled to a heat exchanger has been developed. The heterogeneous model approximates closely the actual reactor. The results indicate that the phenomenon of multiple steady states occurs. Good agreement was observed between the computer calculated values and the plant data. The model is used to predict a good approximate value for the catalyst activity. The model developed is then used to carry out a parametric study for the converter performance under various conditions.     

Analysis of an industrial continuous slurry reactor for ethylene-butene copolymerization

This work presents the analysis of a slurry polymerization stirred tank reactor for the production of high-density polyethylene. A coordination mechanism is adopted including initiation, propagation, first order deactivation, hydrogen transfer, ethylene transfer, transfer to co-catalyst and β-hydride elimination. Two site types are considered each one with its own kinetic constants. A non-uniform solid phase is considered and in the particle there is a radial distribution of chemical species such as the living and dead polymer chains. In this sense, a general local balance is proposed, providing state equations for the moments of chain length distribution and for the active site concentrations that are treated together with all others modeling scales. The multigrain model approach was adopted, combined with a simulation strategy applying orthogonal collocation. The simulation procedure handles all the equations simultaneously and the model is capable of predicting the behavior of operation variables and variables associated with the polymer properties.     

Multirate multivariable generalized predictive control and its application to a slurry reactor for ethylene polymerization

This study presents closed-loop results regarding the production of high-density polyethylene with Ziegler-Natta and Phillips catalysis. The multivariable control algorithm based on the generalized predictive control approach is adopted. Additional features are employed to consider multiple sampling rates and desired trajectory for the output constraints in the cases of grade transition. Results show a significant improvement in the output profiles such as melt index and density. This work provides an extension in the predictive control practice applied to polymerization reactors and presents a new approach for the generalized predictive control algorithm capable to control outputs measured at different rates.     

Integration of CFD and polymerization for an industrial scale cis-polybutadiene reactor

A computational fluid dynamics (CFD) approach, coupled with anionic polymerization kinetics, was used to investigate the solution polymerization in a 12?m³ industrial scale cis-polybutadiene reactor. The kinetic model with double catalytic active sites was integrated with CFD by a user-defined function. The coupled model was successfully validated by the plant data and then used to investigate the key operating variables. Also, predictions of CFD model were compared with those of continuous stirred tank reactor (CSTR) model. Although the reaction mixture is well mixed in the middle and at the top of the reactor, there exists a poor mixing feeding zone at the bottom, which leads to serious deviations from the ideal CSTR. The polymerization process with nonideal mixing is very sensitive to the inlet temperature and the feeding rate. Enhancing the mixing performance in the feeding zone could be an effective way to improve the product quality.     

Optimization of design and operating policy of an industrial two-bed co-shift reactor

The optimal operating policy for a two-bed adiabatic CO-converter is computed using the Discrete Maximum Principle. The problem is then extended to determine also the optimal design of the system. A sensitivity analysis of the optimal solutions is presented, showing the influence of the principal process parameters. Economical, chemical and physical data have been obtained from an existing CO-converter in a standard 1000 short Tons/day NH₃ plant.     

基于联立法的乙烯淤浆聚合牌号切换过程动态模拟

以乙烯淤浆聚合流程为研究对象,建立了包含动力学和热力学的动态机理模型,采用有限元正交配置法对控制变量和状态变量同步离散化,实现了全联立动态模拟。热力学物性计算采用Kriging函数估计,可适用于多个工况,最大误差不超过2%。利用Aspen Plus 5个牌号工况的数据,进行了模型稳态验证,并实现了牌号切换动态模拟,计算了平均分子量等质量指标,与Aspen Dynamic曲线吻合较好,为牌号切换的优化奠定了基础。     

Multivariable correlation analysis and its application to an industrial polymerization reactor

The correlation analysis (CRA) theory is an important tool in the system identification field. Among its utilities, the correlation analysis enables the mathematical modeling of a process, through the estimate of its impulse response. This model can be used directly, as in some control algorithms, or, at least, can allow the attainment of important preliminary dynamic information that is valuable in constructing a parametric model of the system. This paper presents the mathematical development of the multivariable correlation analysis and its application to simulated and experimental data. Results show that the present method is effective in identifying an industrial polymerization reactor and overperforms the one commonly used, that suggests the use of the monovariable correlation analysis even for multivariable systems. A numeric analysis of the problem is also done and some guidelines are proposed to overcome possible problems.     

Coupled simulation of recirculation zonal firebox model and detailed kinetic reactor model in an industrial ethylene cracking furnace

A coupled system simulating both firebox and reactor is established to study the naphtha pyrolysis in an indus-trial tubular furnace. The firebox model is based on zone method including combustion, radiation, and convection to simulate heat transfer in the furnace. A two-dimensional recirculation model is proposed to estimate the flow field in furnace. The reactor model integrates the feedstock reconstruction model, an auto-generator of detail ki-netic schemes, and the reactor simulation model to simulate the reaction process in the tubular coil. The coupled simulation result is compared with industrial process and shows agreement within short computation time.     

Modeling and optimization of industrial Fischer–Tropsch synthesis with the slurry bubble column reactor and iron-based catalyst

To optimize industrial Fischer–Tropsch(FT) synthesis with the slurry bubble column reactor(SBCR) and ironbased catalyst, a comprehensive process model for FT synthesis that includes a detailed SBCR model, gas liquid separation model, simplified CO_2 removal model and tail gas cycle model was developed. An effective iteration algorithm was proposed to solve this process model, and the model was validated by industrial demonstration experiments data(SBCR with 5.8 m diameter and 30 m height), with a maximum relative error b 10% for predicting the SBCR performances. Subsequently, the proposed model was adopted to optimize the industrial SBCR performances simultaneously considering process and reactor parameters variations. The results show that C_(5+) yield increases as catalyst loading increases within 10–70 ton and syngas H_2/CO value decreases within1.3–1.6, but it doesn't increase obviously when the catalyst loading exceeds 45 ton(about 15 wt% concentration).Higher catalyst loading will result in higher difficulty for wax/catalyst separation and higher catalyst cost. Therefore, the catalyst loading(45 ton) is recommended for the industrial demonstration SBCR operation at syngas H_2/CO = 1.3, and the C_(5+) yield is about 402 ton" per day, which has an about 16% increase than the industrial demonstration run result.     

乙烯气相聚合流化床反应器内Geldart B类和Geldart D类颗粒流动特性的三维数值模拟

乙烯气相聚合流化床反应器的设计、操作和优化依赖于对聚合物颗粒粒径大小和分布、气泡运动特性及聚合反应状况的准确描述。采用Eulerian-Eulerian 双流体模型和群体平衡模型耦合方法对某乙烯气相聚合中试规模的工业流化床反应器分别处于常规聚合工艺(属Geldart B 类颗粒)和免造粒工艺(属Geldart D 类颗粒)时床体的气固流动特征以及不同颗粒类型对反应器操作状态和颗粒运动特性的影响进行了三维数值模拟研究。与传统聚乙烯生产工艺相比,免造粒工艺时的Geldart D 类聚合物颗粒更易聚集于气体入口处区域,而且会产生明显的旋涡并出现较大的气泡。研究结果可为免造粒聚乙烯生产工艺的工业推广应用提供参考。     

Free radical polymerization of methyl methacrylate: Modeling and simulation under semibatch and nonisothermal reactor conditions

For the bulk free radical polymerization of methyl methacrylate (MMA), equations of the material balance can be written that are based on a kinetic diagram that considers initiation by decomposition of an AIBN initiator, propagation, and termination by disproportionation. To quantify the gel and glass effects simple empirical dependences are used between the rate constants of termination and propagation and monomer conversion. Numerical values for the empirical parameters at different temperatures and initiator concentrations are also given. Conversion history and molecular weights are obtained by simulation when an initiator or monomer are added to the reaction mass and the temperature modifies after some reaction has taken place. These intermediate operations are simulated at different moments with respect to the gel and glass effects. The validation of the model for semibatch and nonisothermal conditions are made by comparing the simulation results with literature experimental data. The most important conclusion of the article is that the empirical model proposed for the gel and glass effects can be successfully used under semibatch and nonisothermal reactor conditions. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2561–2570, 1999     

Modeling of molecular weight distribution of propylene slurry phase polymerization on supported metallocene catalysts

A mathematical model of the molecular weight distribution (MWD) based on a particle growth model and the kinetic scheme is developed to simulate the MWD of the slurry phase propylene polymerization on a silica-supported metallocene catalyst by means of the equations of moments. The model is used to predict molecular weight distribution, including the number-average molecular weight, the weight-average molecular weight, and the polydispersity index. The results show that the mass transfer has great influence on the polymerization reaction, and it can broaden the MWD especially; moreover, the MWD can be evaluated by simulation; the average molecular weight increases as pressure or temperature, and MWD shifts to long chain lengths as the effective diffusion coefficient increasing thought the influence is not remarkable; furthermore, the MWD's simulation results are calculated, which fit greatly with the experimental data.     

乙烯氧化反应器数学模拟

针对扬子石化公司乙烯氧化制环氧乙烷工业规模的壁冷式固定床反应器,在YS-6型银催化剂宏观动力学模型的基础上加以修正,获得了YS-7型银催化剂宏观动力学模型,建立了环氧乙烷合成固定床反应器的一维拟均相模型,通过模型计算值与工业生产实际值的比较,两者相差很小,验证了反应器模型和所用的宏观动力学模型的准确性,可用作扬子石化公司环氧乙烷合成反应器的模拟与操作优化。