Study of gas-liquid stirred reactor stability taking into account the temperature influence on gas solubility

The paper is devoted to the dynamic behavior and stability of gas-liquid stirred reactor taking into account the temperature influence on gas solubility. Since the rate of gas-liquid processes is very sensitive to concentration of gas reactant dissolved in liquid, even weak fluctuations of temperature can significantly influence on process pass. There are two cases of temperature influence on gas solubility are possible: (1) the solubility decreases with increasing temperature; (2) the solubility grows with increasing temperature. The first case is typical for majority of gases. The second case occurs more rarely but has a great practical importance. It takes place, for example, for the hydrogenation of many compounds in organic solvents (such as benzene, toluene, isopropyl alcohol and others). A model of gas-liquid process has been developed to demonstrate the stability of gas-liquid reactor. It has been shown that the gas solubility behavior has an influence on the form of heat production curve and therefore on the multiplicity of the steady states. The areas of multiplicity and limit cycles were found and the phenomenon of hysteresis in the reactor was shown. A criterion to determine whether the multiplicity is possible under the given conditions was found. By means of an analysis of a mathematical model the stability of steady states of the reactor was studied.     

具有随机时延和丢包的网络化离散系统的动态输出反馈H_∞控制

针对前向通道和反馈通道均存在随机时延和丢包现象的网络控制系统(NCSs),研究了关于离散时域下鲁棒H∞控制器的设计问题。采用伯努利分布描述随机时延和丢包现象,将闭环NCSs建模为随机参数系统。根据Lyapunov稳定性理论和增广状态空间法,得到闭环NCSs均方指数稳定的H∞性能判据;利用LMI技术和锥补线性化算法,给出动态输出反馈控制器的设计方法。最后,把这种方法应用于搅拌斧反应器中,仿真验证了所提控制器设计方法的有效性。     

Tuning of multivariate PID controllers based on characteristic matrix eigenvalues, Lyapunov functions and robustness criteria

A tuning criterion for multiple input-multiple output (MIMO) PID controllers based on characteristic matrix eigenvalues and Lyapunov functions was suggested. In this method, the tuning problem is stated as an optimization one in which the Lyapunov quadratic index variation with respect to dynamic parameters was minimized with constrains in eigenvalues. Proposed criterion was applied to the multivariate controls of a distillation column, and a nonlinear biochemical reactor.     

Parametric sensitivity of a fixed bed catalytic reactor: Cooling fluid flow influence

Temperature variation in a cocurrent cooling medium and its influence on the operation of a fixed bed catalytic reactor of the type used for orthoxylen oxydation is examined. Two characteristic regimes are found: a first regime where temperature shows a maximum at a finite axial reactor position (MFARP and a second regime where temperature is always increasing with the axial reactor coordinate: pseudoakiabatic operation (PO). The relative importance o ach operating mode may be observed by modifying the cooling flow. Two equations are derived from these findings. One of them estimates the limiting condition between MFARP temperature curves and PO curves. The other equation establishes an a prioi run away criterion for hot spot operation, being an extension of a previous formula derived by Van Welsenaere and Froment.     

固定床反应器的飞温和参数敏感性

以参数敏感性定义作为理论基础和数学依据,证明了热点轨迹拐点是反应系统的参数敏感点,从理论上给出了固定床反应器采用一维拟均相模型,进行一级反应,冷却介质温度不变,且与物料入口温度相等时,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热点和超临界操作曲线拐点之间的关系,推导出反应系统安全操作的临界判据,该关联式与El-Swai等人的实验结果吻合很好.     

固定床反应器的飞温和参数敏感性

以参数敏感性定义作为理论基础和数学依据,证明了热点轨迹拐点是反应系统的参数敏感点,从理论上给出了固定床反应器采用一维拟均相模型,进行一级反应,冷却介质温度不变,且与物料入口温度相等时,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热点和超临界操作曲线拐点之间的关系,推导出反应系统安全操作的临界判据,该关联式与El-Swai等人的实验结果吻合很好.     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.     

Biotechnological Process Dynamics under the Conditions of Multiplicity of Steady States

The dynamics of cultivation of aerobic microorganisms in a well-stirred reactor is studied. The character and degree of stability of steady states by the first Lyapunov method are determined. The phase portrait of the system, which reflects the process dynamics, is constructed.     

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.     

An application of Routh stability criterion to derive the necessary conditions for multiplicity of a CSTR

It is well known that the Routh stability criterion (RSC) is a powerful method for analyzing control system stability. A new RSC finding that can aid the tangent analysis method (TAM) to determine the necessary conditions for multiplicity is presented. Adding RSC to TAM can find the bifurcation start point which cannot be obtained using TAM alone. To the author's knowledge, the above new RSC application has not been discussed in past literatures. Our results are helpful for chemical reactor design. We used two examples of the binary reaction in a non‐adiabatic CSTR to demonstrate the merit of our methods.     

Thermal runaway analysis of a three-phase reactor for LCO hydrotreatment

Safety is a high-priority topic for the chemical industry to minimize the frequency and severity of accidents while keeping the productivity and quality of the production. The processes that may undergo thermal runaways due to exothermic reactions are at the heart of the risks of accidents. The study of such highly reactive systems is essential to achieve a safe and productive operation of existing processes and to ensure inherently safe new designs. It is well known that the stationary analysis with the van Heerden criterion must be satisfied, however, this is not sufficient to ensure reactor stability. Only dynamic analysis can provide an accurate answer concerning the safe operation of the reactor. Most of the reported stability studies are carried out for relatively simple systems (pseudo-homogeneous models, simple reaction schemes). This work presents the dynamic thermal stability study of a refining process (hydrotreatment of light cycle oils) carried out with real gasoils at industrial operating conditions. A 1D dynamic model that accurately represents the reactive system (gas–liquid–solid) was developed and validated with experimental pilot plant data. This mathematical model was used to perform the thermal stability analysis of the dynamic system using a perturbation method. The effect of the variation of the heat transfer coefficient on the thermal stability is presented. The spectral analysis of the eigenvalues indicating the stable/unstable behavior of the reactive system was compared with dynamic simulations. An excellent agreement was found between the simulations and the stability analysis. The case of oscillating behavior is also described. The frequencies of oscillation determined by the stability analysis are compared to the frequencies calculated by Fourier transform applied to the simulated signal. The reactor behavior and the oscillations features are accurately predicted with this stability analysis method.     

A study on polymer blending microrheology

In this paper it is shown that the formation and subsequent breakup of threadlike particles are important disperging mechanisms and largely govern the morphology resulting from a polymer blending process. Experiments on the breakup of Newtonian threads surrounded by a second Newtonian fluid have been carried out and good agreement with Tomotika's theory is achieved. Experiments on the breakup of viscoelastic fluid threads showed the influence of shear thinning and stretch thickening effects of the fluids used. To investigate the influence of non-Newtonian behavior of molten polymers on capillary instabilities, experiments were carried out on the breakup of molten polymer threads embedded in a second polymer melt. Surprisingly an absence of shear thinning and stretch thickening effects was noticed and good agreement with Tomotika's theory was obtained. Finally, the stability of threads of fluids exhibiting a yield stress was studied. A criterion predicting the stability of such threads was established and verified experimentally. On the basis of this criterion a possible explanation is given for the stability of a certain class of co-continuous morphologies.     

The stability of fixed bed catalytic reactors

A proper control design for safe and economic operation of industrial catalytic reactors requires a detailed study of transient and steady state behaviour. The present paper discusses contributions in this area with an emphasis on the stability problem. In addition, an attempt has been made to relate the stability of a fixed bed catalytic reactor to that of individual catalyst particles. Sufficient conditions for local stability of a two-dimensional and a one dimensional model for the reactor are obtained using the extension of Lyapunov stability theory to distributed parameter systems. For the two-dimensional model, the sufficient conditions are in the form of inequalities which require steady-state information. For the one dimensional model, the reactor is locally stable if and only if the slope of the heat removal line is greater than the slope of the heat generation curve at the steady state for small perturbations in temperature and concentration.     

A combined method for stability analysis of linear time invariant control systems based on Hermite-Fujiwara matrix and Cholesky decomposition

In this paper, we have developed an integrative method for checking the stability of linear time-invariant (LTI) systems as well as nonlinear continuous-time ones. In our method, we first apply the iterative Faddeev–Leverrier algorithm to obtain the characteristic polynomial of the LTI system. Subsequently, the associated Hermite-Fujiwara matrix will be evaluated by a particularly efficient technique for the calculation of the Bézoutian matrices. The positive-definiteness of the Hermite-Fujiwara form, as the stability criterion, is next tested by performing the Cholesky decomposition. Our method is extended to assess the local stability of nonlinear continuous-time systems with the help of the Jacobian matrix concept. The proposed method is demonstrated to approximately be 2.2 times faster than the classical Hurwitz algorithm in average, at least for matrices with dimensions less than 40, according to a performed central processing unit (CPU) time analysis. For the sake of illustration, four numerical examples are given, including dynamical models for a real-world hydrolysis reactor and a well-mixed bioreactor.     

Extremum‐seeking control of retention for a microparticulate system

The operation of a paper machine relies on the close monitoring and control of several integrated units to ensure a high quality paper with the required specifications. In this paper, the retention control system in the wet‐end of a paper machine is considered. The control objective is to maximize the retention of fines and fibres in the paper sheet to prevent the accumulation of micro particles in the water system. We present an adaptive extremum‐seeking scheme for the optimization and control of retention in the wet‐end of a paper machine. An adaptive learning technique is introduced to construct an algorithm that drives the system to the optimal retention value. Lyapunov's stability theory is used in the design of the extremum‐seeking controller structure and the development of the parameter learning laws. The performance of the technique is illustrated via simulations based on a first‐principles dynamic model developed previously for a micro‐particulate system.     

Compressible and incompressible 1‐D linear wave propagation assessment in fast fluidized beds

We propose two equivalent 1‐D perturbation models for a fast fluidized bed considering compressibility effects. The first model is the explicit summation of incompressible and compressible terms. All compressible terms appear multiplied by the inverse squared gas sound propagation speed, s. In the second model, a lumped waving structure is presented, with just one term corresponding to each wave hierarchy. In both proposed models, the incompressible part was retrieved in the limit s → ∞. The Liu's linear stability analysis, based on Whitham's, was extended to estimate the compressibility contribution. Stability conditions on the propagation speeds and a criterion on the wave number were developed. This method was applied to two physical systems whose solid properties differ widely. It was shown that the effect of the fluid compressibility is at least as important as the effect of the solid compressibility modulus. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues

Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues is proposed. It is showed that this tuning criterion is equivalent to H_∞ optimal control. Under the proposed criterion, the tuning problem is stated as an optimization problem, in which the complex/real ratio of the characteristic matrix eigenvalues, a Lyapunov quadratic index, and the spectral abscissa were simultaneously minimized. Proposed criterion was applied to the multivariate controls of a distillation column, and a non-linear chemical reactor, both reported in the literature.     

The use of krasovskii's stability technique for control strategy evaluation and system design

Krasovskii's stability method for generating Lyapunov functions for the prediction of regions of asymptotic stability (RAS) is applied to a second-order chemical reaction in an adiabatic CSTR. Three conclusions are drawn from this study. Firstly, that the stability areas predicted by the method are too conservative for use as criteria for control system design. Secondly, that the method fails to predict valid regions of asymptotic stability under some circumstances. Thirdly the results are shown to be sensitive to changes in system parameter values.