Solution of steady state reactor models using the continuation method and feasible starting point

The solution of steady state chemical reactor models, using classic numerical methods, (like Newton-Raphson, Quasi-Newton, etc.), is often very difficult.

It is proposed to select constraints for the independent variables as the first step of the solution, then to use a combination of the Newton-Raphson and continuation methods, to obtain the solution, starting from a feasible initial guess.

Several methods for the solution of steady reactor models are compared. It is shown that the proposed method is the most reliable and efficient for locating the solution.     

Measurement of nonlinearity in chemical process control systems: The steady state map

Most chemical processes exhibit some degree of nonlinearity, and when selecting an appropriate controller design approach it is important to understand the extent of this nonlinearity. In this paper a quantitative measure of steady-state process nonlinearity is proposed. Drawing from results for nonlinear regression, the curvature is decomposed into tangential and normal components. It is shown that the tangential curvature can be reduced or eliminated by transforming the control inputs, whereas the normal curvature can be reduced or eliminated only by a combination of state feedback and transformations. The problem of scaling is addressed by identifying a “region of interest”, and scale-independent measures of curvature are proposed. Nonlinearity is measured both as root mean squared curvature and directional curvature. The importance of curvature in the foward and inverse steady-state maps is discussed, and a transformation suggested by the curvature arrays is presented. This transformation reduces the static nonlinearity in the process, and can be used to improve the controller performance. Application of the proposed techniques is illustrated using chemical process examples.     

化学反应系统的多稳态分析

描述化学反应系统的方程组具有强非线性,而对于非线性问题一般情况下有多个解,如何求解出这些解是一个研究热点。本文针对这一问题提出了一种扩展的同伦延拓法,并以一个理想反应器体系为例,显示出化学反应器具有的多稳态特性。为了深入了解反应系统的本质特性,文中将稳态解的计算结果转化为参数平面上的空间图像,以进一步分析在单参数连续变化下体系的多稳态解的分布情况。     

人工神经网络在化学工程中的应用

介绍了人工神经网络在化学工程中的应用，讨论了应用中的优点和局限性，预示了其应用的发展前景。     

微型化工设备的研究与应用进展

微型化、集成化是未来科学技术的发展方向,在微化工过程中,微型化工设备的开发和应用为微化工的实现提供了强大的支持。按用途将微型化工设备分为微热交换器、微反应器、微分离器、微混合器等,分别对其特点和研究应用现状进行简单的介绍,并对其前景进行展望,同时指出了未来发展可能会遇到的难题。     

小尺寸稳态实验方法在PE管道中的应用

介绍了小尺寸稳态实验（简称S4）的实验原理，实验装置，温度及管壁厚度等因素对止裂性能的影响。分析认为：S4是模拟聚乙烯压力管道的快速裂纹扩展的一种有效方法。S4的临界压强是衡量管道承受压力的一个标准。实验先将压强确定为0.4MPa，若裂纹快速扩展，则取其一半，若止裂，则取其2倍，反复6次即可得到所需的临界压强值。     

Calculation of multiplicity of steady states in a catalyst pellet by homotopic continuation method

Many exothermic reactions, such as the oxidation of CO in a catalyst pellet may present multiplicity of steady states. Experimental results suggest this behavior in a copper ceria catalyst, and this in turn would indicate that the kinetics should be nonmonotonic with respect to reactants' compositions. The model for the reaction is described by a two‐point boundary value problem that is hard to solve with direct methods, even when seeking a single solution. The aim of this work is to implement a homotopic method to find all the steady states of this kind of problems. The search for solutions is driven by a pseudo arclength continuation. Homotopic curves that passes through all possible solutions are obtained. Also, a study of the dependence of the initial point upon the curve is performed. © 2010 American Institute of Chemical Engineers AIChE J,2011     

卡尔费休法测定水分的发展及其在某些领域中的应用

介绍了卡尔费休容量法和库仑法测定水分的进展的及在实际工作中的应用。     

A general matrix method for the steady state solution of complex distillation assemblies

An algorithm for the solution of El-block band matrices is derived and the number of calculations and the required storage capacity are determined. The algorithm was developed for the solution of multi-column distillation assemblies. The algorithm was applied to a three column, 5 component system in which the three reflux ratios and the three bottom compositions were specified. It was found that convergence was not influenced by the initial composition estimates or the assumed flow rates.     

Role of continuation in engineering analysis

This paper reviews the state of the art of the continuation methods. In particular, a discussion of the tracing of parameter dependent branches of solutions is presented. Basic steps of continuation as predictors, correctors and parametrizations are introduced and their interaction analysed. Such algorithms are emphasized which give rise to reliable general-purpose computer programs and proved to work satisfactorily when applied to nontrivial problems. The review paper includes brief discussion of some topics of most recent interests that are closely related to continuation, as, for instance, stability, branch switching, and tracing of critical boundaries. Several examples illustrate the procedures. Hints on available software complete this paper.     

化工企业的CAD应用工程

介绍了化工企业通过实施国家ＣＡＤ应用工程建立的化工ＣＡＤ系统及其应用效果。     

试论绿色化工技术在化学工程与工艺中的应用

绿色化工技术是基于生态理念基础上产生的新技术,在化工工程生产与工业生产中应用具有重要作用。通过强化绿色化工技术合理应用,能满足化工生产与工艺生产各项要求,对环境污染等各项问题进行有效调控。     

The periodic steady state for cyclic energy storage in paraffin wax

The thermal performance of a latent heat energy storage unit was studied experimentally at the periodic steady state generated by cyclic energy storage and recovery. The periodic steady state was obtained by alternating identical freezing periods with identical melting periods. The storage unit was a cylindrical container of commercial paraffin wax. Energy was transferred to (and from) the wax by temperature controlled water flowing through a submerged helical coil. Measurements were made of the amount of energy stored and recovered as functions of the freezing and melting times, the temperature of water and the geometry of the coil. A simple model was proposed to calculate the energy stored or recovered in the periodic steady state.     

接地故障小电流的稳态分析及应用

分析了小电流接地系统故障特性,指出了经过渡电阻和消弧线圈单相接地时零序电流的特征,并详细阐述了基于时序鉴别法的选线装置的工作原理.长期现场数据和运行结果证明:该选线方法可以准确、可靠地查找配电网单相故障.     

The effect of spiral wound membrane element design characteristics on its performance in steady state desalination — A parametric study

The spiral-wound membrane (SWM) element design variables include retentate- and permeate-spacer characteristics and number of membrane envelopes (or sheet width) for constant total area, in addition to membrane surface properties. The effect of these parameters (varying within realistic ranges) on the operating variables, comprising two-dimensional distribution of permeate flux, trans-membrane pressure (TMP), retentate- and permeate-side pressures and velocities, is systematically assessed. Advanced software is employed, capable of simulating SWM desalination performance with no recourse to empirical parameters. The parametric study involves typical cases of desalinating brackish and sea-water with 2000 mg/L and 40,000 mg/L TDS, respectively, in pressure vessels with seven 8-inch SWM-elements. The results show that low-pressure desalination modules are most sensitive to variations of geometric parameters. The effect of permeate-side fabric is significant, directly affecting TMP and module productivity. In both low- and high-pressure desalination, the effect of retentate-side spacer manifests itself mainly in the pressure drop across the element. The results confirm that the membrane width is very important, with short sheets exhibiting the best overall performance. Noteworthy is the insensitivity of high-pressure SWM-module productivity to significantly different design parameter-values, including envelope width. These results are helpful in guiding SWM element optimization and in setting priorities for related R&D work.     

New optimization method is highly suitable for chemical engineering applications

A new optimization method involving only elementary calculus represents a significant simplification over existing methods. It makes for the easy and rapid solution of many complex problems in chemical engineering. In addition to making use of the first derivative, as in most other methods, the new method also calls for the second derivative of the function to be optimized. When going from one point to another, the method consists essentially in adding simultaneously to each independent variable an increment which, for a given variable, is equal to the negative ratio of the first partial derivative to the second partial derivative, and so on until optimum conditions are reached. A few mathematical examples illustrate the speed of the new method and permit comparisons with other well known methods. Numerical applications pertaining to chemical engineering are also presented.