A study of the dynamic behavior of dispersion-type tubular reactor models

The dynamic behavior of dispersion-type tubular reactors, referred to as finite and truncated models depending on the boundary condition representations at the reactor exit, was investigated through numerical simulations. It was found that the dynamic behavior of the two models can be identical or different depending on how thePéclet number changes.     

Calculation of combustion regimes for a twisted gas flow in a tubular ideal displacement reactor

Using the equations of the hydrodynamics of a twisted flow, we have employed a numerical method to construct the temperature and concentration fields of an exothermically reactive gas. We have analyzed the regimes of combustion and the mechanism involved in the ignition of the flow at various values of the twist parameter.Tomsk. Translated from Fizika Goreniya i Vzryva, No. 2, pp. 89–94, March–April, 1991.     

装填不同填料的管式反应器的微观混合性能

采用碘化物-碘酸盐平行竞争反应为工作体系,以离集指数（X_S）表征微观混合性能,实验考察了Reynolds数Re、物料体积流量比对装填扁环填料和网架填料的管式反应器的微观混合性能的影响及离集指数在管式反应器轴向、径向的分布。结果表明,X_S随着Re的增大而下降,而物料体积流量比的增加会导致X_S增加,相同条件下网架填料的X_S小于扁环填料,离集指数在轴向上呈现先明显降低后基本不变的趋势。在实验研究的基础上,利用团聚模型计算装填网架填料的管式反应器的微观混合时间（t_m）为4.82~2.27 ms。与扁环填料对比,网架填料最小值（2.27 ms）低于扁环填料的最小值（2.73 ms）,同时二者均小于空管的最小值（3.79 ms）,表明装填填料可以改善管式反应器的微观混合性能,网架填料的微观混合性能略优于扁环填料。     

Concentration profiles in laminar-flow tubular reactor with wall injection

The effect of wall injection on the concentration profiles for chemically reacting systems under laminar flow conditions has been analysed. Results indicate significant variation in radial concentrations for second-order reactions, but little effect for zero-order and first-order reactions.     

Regional stability for a tubular reactor with axial mixing

A graphical phase-plane procedure is suggested by which regions of stability can be estimated for a tubular reactor. The technique uses a super-position of limits for primary flow and reaction effects and those arising from secondary axial dispersion. Several detailed numerical tests are reported to substantiate the conjecture.     

Optimization of a tubular nylon 6 reactor with radial gradients

Optimal jacket-fluid temperature profiles for tubular Nylon 6 reactors (in the presence of radial gradients of temperature and concentration) have been obtained using an algorithm based on the continuous minimum principle developed for a distributed parameter system. A gradient search technique has been devised and implemented for obtaining these optimal profiles. The optimal temperature profiles are found to be at the maximum permissible temperature, T_max, at the beginning of the reactor and then slowly decrease to the minimum permissible temperature, T_min, near the end of the reactor. The effect of varying several parameters is also studied. The desired value of the chain length and the reaction time are found to be the parameters which effect the optimal profiles most significantly.     

Numerical simulation of a tubular polymerization reactor

A mathematical model for a tubular emulsion polymerization reactor is developed. The partial differential equations describing the mass balances on initiator, monomer, and number of polymer particles are numerically solved using an implicit–explicit scheme based on the Crank–Nicholson method. The model adequately simulates experimental results reported by Rollin and co-workers and sufficiently explains the unusual behavior of the reactor when operating at relatively low emulsifier concentrations.     

Transient behaviour of a non-ideal tubular reactor

Experimental data are reported for the unsteady state behaviour of a laminar flow reactor with first order homogeneous liquid phase reaction. The data are in agreement with the predictions of the dispersion model, using previously reported reaction-dependent dispersion coefficients which directly gives the bulk mean concentration. The use of proper boundary conditions, ignored in a recent paper on this topic⁽¹⁹⁾, is found to significantly influence the predictions. Unlike the conclusion drawn in⁽¹⁹⁾ it is shown that the Taylor model is unable to correctly predict the reactor length for fast reactions even for high conversions.     

Calcination of limestone in a tubular reactor

Theoretical expressions were developed for the design of a tubular reactor for the calcination of limestone, pneumatically conveyed by flue gas. The total residence time and the length of the reactor are affected in particular by the particle size, the excess thermal capacity of the gas and the heat transfer coefficient. High throughput can be achieved in relatively small reactors. An experimental investigation verified a theoretical prediction, that a considerable part of the decomposition takes place in the first few centimeters of the reactor length. The rate of heat transfer in this section was high, with Nusselt numbers of 9.9 to 31.7.     

Startup of an industrial adiabatic tubular reactor

The dynamic behaviour of an adiabatic tubular plant reactor during the startup is demonstrated, together with the impact of a feed-pump failure of one of the reactants. A dynamic model of the reactor system is presented, and the system response is calculated as a function of experimentally-determined, time-dependent, manipulated variables. The values of model parameters are estimated by using the SimuSolv (1991) computer program. The data set collected during the reactor start-up is used for the parameter estimation procedure. An excellent agreement is obtained between the experimental and the calculated system response. Many continuously-operated commercial reactors require a complete conversion of one of the main reactants at the reactor exit. It is shown that for an industrial tubular reactor a much higher initial reactor temperature is required during the startup, compared to the reactor inlet temperature during normal steady-state operation, to ensure a complete reactant conversion. Much more research is necessary to determine whether this is a generally valid rule.     

Substrate-inhibited enzyme reaction in a tubular reactor with axial dispersion

For a fixed set of physico-chemical parameters, an isothermal substrate-inhibited enzyme reaction in a tubular reactor with axial dispersion can give rise to multiple steady states. Criteria previously developed for non-isothermal reactions are applied to this case to develop analytic conditions which ensure uniqueness of steady states. The criteria compare well with values obtained from exact numerical calculations.     

带芯管的管式反应器中流体力学的实验研究

本文以电石法聚氯乙烯生产流程中的转化器为背景,提出在转化器列管内加入芯管的改进方案,改变管内物料的流动状态及温度分布,以提高反应器的生产能力。通过实验测量反应器入口与各出口流速及压差,计算出空气在其中流动时夹层及开孔处的阻力系数。实验表明在相同的入口流量下,空气进入夹层,分别从芯管和夹层同时流出时,芯管开孔直径越大,芯管与夹层的出口流量比增大;在相同的孔径的条件下,随着入口流量的增加,夹层和芯管的出口流量差值减小。并根据实验数据拟合了空气流经开孔的阻力系数公式。     

Simulation of an industrial nylon 6 tubular reactor

A commonly used energy-efficient nylon 6 reactor is simulated under steady-state conditions. The effects of various operating conditions and parameters, e.g., feed composition, temperature and flow rate, heat transfer coefficients, and reactor dimensions, on the temperature and molecular weight profiles are studied. A temperature maximum is observed in the reactor under usual conditions of operation. The maximum value of the temperature is sensitive to the feed conditions, and one has to ensure that degradation reactions speeded up at high temperatures do not affect product characteristics. The model and the numerical technique used are fairly simple and account for most of the important features of industrial reactors. Hence, these can be used in the development of digital-control algorithms in the future.     

双组水平喷嘴撞击流反应器流场POD分析

利用二维高速粒子图像测速技术研究双组分层水平对置撞击流湍流场,考察了双组喷嘴在不同Re、不同直径及上下径向射流不同工况下的流动结构,对速度场进行POD分解,提取流场中含能大尺度结构。结果表明,低阶本征模态拥有大尺度涡旋结构,流场涡旋结构明显,瞬时流场能量主要集中在一阶模态,易于描述整个流场的流动特征,脉动场的模态重构可以准确还原流场中的涡结构。L=3d工况下,不对称流场能量高于对称流场;低阶模态能量随喷嘴Re的增大而增大,而随喷嘴直径增大呈先递增后递减的趋势,直径d=10 mm的工况下所对应的一阶模态能量最高,涡强最大。     

Coupling of CFD with PBM for a pilot-plant tubular loop polymerization reactor

A computational fluid dynamics model, coupled with population balance model (CFD–PBM), was developed to describe the liquid–solid two-phase flow in a pilot-plant tubular loop propylene polymerization reactor. The model combines the advantage of CFD to calculate the entire flow field and that of PBM to calculate the particle size distribution (PSD). Particle growth, aggregation and breakage were taken into account to describe the evolution of the PSD. The model was first validated by comparing simulation results with the classical calculated data. Furthermore, four cases studies, involving particle aggregation, particle breakage, particle growth or involving particle growth, breakage and aggregation, were designed to identify the model. The entire flow behavior and PSD in the tubular loop reactor, i.e. PSD, solid holdup and liquid phase velocity distribution, were also obtained numerically. The results showed that the model is effective in describing the entire flow behavior and in tracking the evolution of the PSD.     

On modelling and diagnostic checking of vector periodic autoregressive time series models

Abstract.  Vector periodic autoregressive time series models (PVAR) form an important class of time series for modelling data derived from climatology, hydrology, economics and electrical engineering, among others. In this article, we derive the asymptotic distributions of the least squares estimators of the model parameters in PVAR models, allowing the parameters in a given season to satisfy linear constraints. Residual autocorrelations from classical vector autoregressive and moving-average models have been found useful for checking the adequacy of a particular model. In view of this, we obtain the asymptotic distribution of the residual autocovariance matrices in the class of PVAR models, and the asymptotic distribution of the residual autocorrelation matrices is given as a corollary. Portmanteau test statistics designed for diagnosing the adequacy of PVAR models are introduced and we study their asymptotic distributions. The proposed test statistics are illustrated in a small simulation study, and an application with bivariate quarterly West German data is presented.