Application of parametric sensitivity to batch process safety: Theoretical and experimental studies

The generalised thermal parametric sensitivity criterion is applied to the thermal behaviour of the esterification of 2-butanol with propionic anhydride in a batch reactor under isoperibolic conditions. The reaction is catalysed by sulphuric acid, and the study covered the effects of both catalyst concentration and, in the absence of catalyst, jacket temperature. The experimental location of regions of parametric sensitivity agreed well with theoretical predictions. However, the process conditions that meet conventional standards for safe process design fall into the supercritical sensitivity region of the parametric model. This apparently contradictory result is discussed. The usefulness of the parametric sensitivity approach is illustrated by practical examples of scale-up and heat transfer in reactions prone to thermal runaway.     

Experimental and theoretical investigation of parametric sensitivity and dynamics of a continuous stirred tank reactor for acid catalyzed hydrolysis of acetic anhydride

The continuous stirred tank reactor is a dynamic system exhibiting nonlinear behavior such as multiplicity and oscillations and, in certain range of operating conditions, may exhibit a parametric sensitivity where small changes in one or more of the input parameters lead to large changes in the output variable. In the present work, hydrolysis of acetic anhydride reaction system was used to demonstrate the existence of parametric sensitivity with respect to the input parameter, the cooling water flow rate. The applications of parametric sensitivity analysis were used for detection of parametric sensitivity in a continuous stirred tank reactor using catalyses hydrolysis of acetic anhydride reaction system. Also, theoretical investigation revealed that the effect of wall capacitance has definite influence on the dynamics of continuous stirred tank reactor. The continuous stirred tank reactor showed parametric sensitivity both in the regions of uniqueness and multiplicity, and a mathematical model was developed for the reactor. The numerically simulated results are in satisfactory agreement with the experimental data.     

Parametric sensitivity of a CSTR

It is shown that the generalized sensitivity criterion recently developed in the context of thermal explosions and tubular reactors can be easily applied in the case of a CSTR as well. An illustrative example concerning sensitivity analysis of a single nth order irreversible exothermic reaction in a nonadiabatic CSTR is presented. A generalized region of parametric sensitivity is identified where the reactor temperature is parametrically sensitive simultaneously to all the input parameters. Asymptotic analysis for large heats of reaction is performed to investigate limiting behaviour, which leads to the classical Semenov limit in the case of large activation energies. It is shown that parametric sensitivity can occur even when unique steady states exist for all Damköhler number (Da) values. Furthermore, if operating conditions are chosen so as to avoid completely the possibility of parametric sensitivity for all Da, then the possibility of steady-state multiplicity is automatically avoided.     

Analysis of a CFSTR with two consecutive reactions in transient states

The sensitivity of a chemical reactor is defined by the matrix which relates the steady state gain of output variables to unit step changes in input variables. This definition proves applicable to reactors with arbitrary residence time distributions. The sensitivity calculation is illustrated by treating a specific example. Three ordinary differential equations which govern (he transient behavior of a CFSTR with two consecutive reactions are numerically solved to demonstrate the parametric sensitivity and temperature runaway phenomena for some parameters such as the feed temperature, the feed concentration, the heat transfer coefficient and the wall temperature. The estimation of the regions of parametric sensitivity is briefly discussed.     

间歇放热反应系统热失控参数敏感性研究

以参数敏感性定义作为理论基础和数学依据,证明了一级间歇放热反应系统操作曲线与温度最大点曲线的拐点轨迹相切的点是反应系统热失控的参数敏感点,从理论上给出了反应系统的安全操作所允许的温度上限。利用敏感点和超临界操作曲线的拐点关系,推导出反应系统安全操作的临界判据。将该临界判据与Adler和Enig、van Welsenaere和Froment以及Wu等的经典判据进行比较,结果与文献值基本一致。将该临界判据和经典判据与Allen和Rice的实验结果进行对比,该标准也能很好地预测出偶氮甲烷分解爆炸的压力。     

非绝热式固定床反应器的参数敏感性及热失控临界参数

寻找安全有效的反应条件一直是绿色化工的重要研究内容之一。采用邻二甲苯氧化的反应动力学模型,分析了非绝热式固定床反应器的参数灵敏性和热失控行为,考察了非绝热式固定床反应器温度对冷却介质流量、进料温度和初始压力的敏感性。模拟计算结果表明,当反应进入敏感性区域后,反应器对冷却介质流量、进料温度和初始压力的改变极其敏感。采用系统散度判据（div>0）计算该反应的热失控临界操作参数,计算结果与文献中的判据进行了分析比较,得到类似的结果,但计算更简单。考虑冷却介质的影响,修正了div判据,得到更准确的热失控临界操作参数。研究结果表明,此判据能为反应器的设计及过程控制提供重要的参考依据。     

A GENERAL RUNAWAY CRITERION FOR FIXED-BED REACTORS

The safe design and operation of fixed bed reactors require the consideration of potential runaways. The steep temperature rise may affect the selectivity, activity and stability of catalysts and in certain cases the reactor safety.

Mathematical models simulate the runaway conditions. Such simulations require extensive calculations to define the range of safe operation. A new runaway criterion was developed to replace the need to solve the differential reactor balances. The criterion is simple, defined by one algebraic equation. It can be applied to any kinetic expression. Extensive testing shows an excellent agreement between the runaway criterion and the two-dimensional model predictions. It also predicts the runaway conditions in agreement with experimental data.     

Nonlinear control of polymerization reactor

In this work, nonlinear model based control was applied to the free radical solution polymerization of styrene in a jacketted batch reactor and its performance was examined to reach the required monomer conversion and molecular weight. Optimal temperature profiles for the properties of polymer quality were evaluated using the Hamiltonian optimization method. Total simulation program having mass and energy balances of the jacketed polymerization reactor was used to calculate the optimal trajectories. For control purposes, several experimental and theoretical dynamic studies have been made to observe the validity of simulation program. Experimental and theoretical nonlinear model based control have been investigated to track the temperature at the optimal trajectory Two types of parametric and nonparametric models were evaluated to achieve the temperature control. For this purpose, reaction curve was obtained to calculate the system dynamic matrix as a nonparametric model. In all control work, heat input to the reactor was chosen as a manipulated variable. Nonlinear auto regressive moving average exogenous (NARMAX) giving a relation between heat input and reactor temperature was chosen to represent the system dynamic and this model was used to describe the related control system as a parametric model. NARMAX model parameters were determined by using Levenberg Marquard algorithm. A pseudo random binary sequence (P.R.B.S.) signal was employed to disturb the system. Total simulation program was used to calculate the system and control parameters. Several types and orders were used to construct the NARMAX models. The efficiency and the performance of the nonlinear model based control with the NARMAX model and dynamic matrix were tested to calculate the best model. Nonlinear model based control system was used to control the reactor temperature at desired temperature trajectory experimentally and theoretically. Theoretical simulation results were compared with experimental control data. It was concluded that the control simulation program represents the behavior of the controlled reactor temperature well. In addition, nonlinear model based control keeps the reactor temperature of optimal trajectory satisfactorily.     

间歇反应器的热参数敏感性及其临界判据(Ⅰ)

以参数敏感性定义作为理论基础和数学依据,证明了间歇反应器操作曲线与温度最大点曲线的拐点轨迹相切的点是反应系统的参数敏感点,从理论上给出了间歇反应器中进行一级反应时,反应系统安全操作所允许的温度上限,并利用临界操作曲线温度最大点和超临界操作曲线的拐点关系,推导出反应系统安全操作的临界判据.将该临界判据用于冷却介质温度与物料入口温度相等的反应系统,并与Adler和Enig,van Welsenaere和Froment以及Wu,Morbidelli和Varma的经典判据进行了比较.该临界判据与Allen和Rice的实验结果吻合良好.     

Parametric sensitivity in co-currently cooled tubular reactors

An intrinsic criterion was derived for parametric sensitivity and runaway in co-currently cooled tubular reactors. It is essentially based on the approach of Van Welsenaere and Froment (1970) developed for the constant wall temperature case and which makes use of fundamental properties of the trajectory in the temperature vs. partial pressure plane. The criterion limits the maximum allowable temperature on an objective basis and permits the calculation of the corresponding critical inlet values for the operating variables, like partial pressure of the reactant, temperature of the reactor fluid, temperature of the cooling medium, coolant flow rate, reactor throughput ... . In addition to the rigorous treatment, a simple extrapolation procedure is presented, which proves to be very useful and accurate, provided the conditions are not too severe.     

CFD modelling of stirred tank chemical reactors: homogeneous and heterogeneous reaction systems

The presented work is a part of studies carried out to develop a practical method to prevent runaway events in chemical reactors. The use of computational fluid dynamics (CFD) techniques is proposed here to indicate in advance the local hot-spots in the reaction mixture, so as to elaborate an efficient and sensitive method for early warning detection of runaway. The CFD method has been chosen to support, elaborated by Bosch et al. (Comput. Chem. Eng. 28 (2004) 527), the on-line runaway detection method in batch reactors, which is based on the divergence criterion. Series of CFD simulations have been executed for two exothermic reactions, being the esterification reaction of the 2-butanol and the propionic anhydrite catalysed by the sulphuric acid (homogeneous system) and the hydrolysis of the propionic anhydrite catalysed by the sulphuric acid (heterogeneous system). For both the considered reactions the results of calculations have been verified with the results of experimental measurements performed in a bench scale RC1 Mettler-Toledo reaction calorimeter. The elaborated conclusions can be further employed in the parametric sensitivity analysis (Comput. Chem. Eng. 28 (2004) 527; Am. Inst. Chem. Eng. J. 45 (1999) 2429) to indicate a number of temperature sensors and their location inside the reactor, which will help to apply efficiently the divergence criterion method.     

Study of parametric sensitivity in an autothermal nylon 6 reactor

The parametric sensitivity of an industrial autothermal nylon 6 reactor was studied. The sensitivities of the temperature maxima with respect to various parameters of the model are computed numerically. The sensitivity peaks were found to occur (almost) at the same value of the input parameter, thus confirming the generalized nature of the thermal parametric sensitivity criterion. It is shown that this criterion can easily be used to find safer regions of operation of the reactor. The variation of the number‐average chain length of the product, μ_nf, with the variation of input parameter, W₀, was also studied. A methodology was suggested to obtain the desired ranges of operation of the reactor which represent an optimal balance between the thermal sensitivity and the sensitivity of μ_nf. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 333–343, 1999     

Selective Hydrogenation of Acetylene in an Ethylene Stream in an Adiabatic Reactor

In earlier studies the behavior of single catalyst pellets of Pd on alumina has been investigated for the reaction of acetylene in an ethylene stream with hydrogen. Particle runaway, temperature over‐ and undershoots and chemically induced temperature oscillations have been observed. After that, the steady state and dynamic behavior of an adiabatic packed bed reactor has been studied experimentally. Temperature profiles of both the gas and solid phase as well as local temperature differences between the two phases were measured. Also here the temperature in the reaction zone exhibited oscillatory behavior. On addition of CO, the oscillations disappeared and the selectivity improved. For a given set of operating conditions, there existed a relatively small range of CO contents with good selectivity and satisfactory conversion. This range depends strongly on the inlet temperature. The dynamic response of the reactor to changes in the CO content showed a considerable wrong‐way behavior. This high sensitivity to fluctuations in the CO content, found for our experimental reactor, indicates a probable cause for a thermal runaway in industrial practice. Recommendations for a stable reactor operation are given.     

Erweiterung des Semenov‐Kriteriums auf konzentrationsabhängige Reaktionen

Exothermic reactions in liquid phase are often performed in a batch reactor with cooling. To avoid runaway, suitable conditions of the reaction and its performance must be selected. It is shown that in the case of liquid phase reactions these conditions should not be determined by the Semenov criterion but by its extension, the sensitivity, which regards the concentration dependency of the reaction. The theoretical relationships are derived on the basis of the heat and mass balances. The results are illustrated by numerical calculations.     

搅拌槽中酯化反应热失控的CFD模拟

热失控是化工过程中常见的安全风险之一。在间歇釜式反应器中,桨叶的机械转动可以增强流体的循环流动、湍流强度、混合程度以及传热,进而有效防范热失控。防控效果与反应器结构和搅拌桨型密切相关。针对丙酸异丙酯酯化反应,采用计算流体力学模拟研究了桨型(Rushton桨、30o PBT桨及60o PBT桨)、转动方向和挡板对釜式反应器内温度演化的影响,从流动结构方面分析了原因。基于散度的失控判据比较了三种搅拌桨抑制热失控的能力,抑制能力为Rushton桨＞30° PBTD桨＞60° PBTD桨。本研究可为搅拌反应器热失控的优化设计提供一定的理论依据。     

BEHAVIOUR OF AN ADIABATIC PACKED BED REACTOR PART 1: EXPERIMENTAL STUDY

The steady state and dynamic behaviour of an adiabatic packed bed reactor for the selective hydrogenation of ethyne and ethene mixtures was studied experimentally. Different methods to achieve adiabatic conditions on a laboratory scale were tested. Temperature profiles of both the gas and solid phase as well as local temperature differences between the two phases were measured. For hydrogenation in the absence of carbon monoxide the selectivity was always poor. Also, in that case, the temperature in the reaction zone exhibited oscillatory behaviour. On addition of CO, the oscillations disappeared and the selectivity improved. For a given set of operating conditions there existed a relatively small range of CO contents with good selectivity and satisfactory conversion. This range depends strongly on the inlet temperature. The dynamic response of the reactor to changes in the CO content showed a considerable wrong-way behaviour. This high sensitivity to fluctuations in the CO content, found for our experimental reactor, indicates a probable cause for a thermal runaway in industrial practice.     

乙氧基化管式反应器的数学模拟

建立了乙氧基化管式反应器的数学模型,考察了各参数对反应器温度分布的影响,认为反应器具有较强的参数敏感性,冷却剂进口温度是影响反应器温度分布的主导因素。分析了反应器的参数敏感性,得到了反应器的安全操作区域,对放大和生产操作提供了理论指导。     

Studies on parametric sensitivity and safe operation criteria of batch processes

Heat accumulation in batch reactors may eventually lead to a temperature runaway. Critical values of process parameters were used to investigate process safety. Parameter sensitivity is discussed for a wide range of operating conditions. Two criteria for safe operation are presented, based on critical values of process parameters.     

间歇反应器的热参数敏感性及其临界判据(Ⅱ)

根据间歇反应器出现热参数敏感性的理论依据和数学特征,证明了n级间歇反应器操作曲线与温度最大点曲线的拐点轨迹相切的点是反应系统的参数敏感点,从理论上给出了间歇反应器中进行n级反应时,反应系统安全操作所允许的温度上限,并运用小参数扰动法,给出了n级间歇反应系统的安全操作温度上限的简洁渐进表达式.利用临界操作曲线温度最大点和超临界操作曲线的拐点关系,推导出反应系统安全操作的临界判据通式,并将该临界判据与AE以及WMV经典判据进行了比较.比较发现,在反应热参数B值的某个范围内,两个经典判据比本文推导的判据保守,大于该值时,则本文推导的判据比经典判据保守,但当B趋向无穷大时,新判据与经典判据之间的差值趋于某一恒定值.     

A study of chain addition polymerizations with temperature variations: II. Thermal runaway and instability—a computer study

A computer study was made to determine the thermal ignition criteria and ignition boundaries for chain-addition polymerization in a well-mixed batch system using a simple kinetic model. The occurrence of thermal runaway was shown to be a function of initiator type, feed conditions, and heat transport parameters. It was found that thermal runaway does not occur early with respect to monomer and initiator conversions and that for strongly dead-ending systems, the sensitivity characteristic of ignition disappears. The role of various dimensionless parameters in characterizing reaction behavior is also discussed.