Theoretical and Experimental Study of Multiplicity Features of Distributed Parameter Chemically Reacting Systems

所提出的工作是该PI先前在分析非线性化学反应系统的多重特征方面的工作的逻辑扩展。他之前的工作涉及集中参数系统，而在这个项目中，他计划使用最近开发的数学技术来研究更复杂的分布参数问题。与稳态多重性相关的问题主要在用于进行放热化学反应的催化反应器中遇到。工业反应器的有效利用、运行和控制需要了解其所有行为特征，例如所有可能的稳态。提出的分析将提供一种系统的方法来发现分布参数系统的所有定性特征，其中分散和化学动力学之间的相互作用可能导致多个稳态。这可以指导实验者寻找新的和更有利可图的状态，并使合理的发展或更可靠和安全的控制和启动政策。在这项工作中开发的方法也将用于扩散和化学动力学之间的相互作用可能导致稳态多样性的其他领域，如燃烧，化学气相沉积，高性能陶瓷材料和耐腐蚀合金的设计。许多化学和物理系统在相同的操作条件下可能达到不同的稳态。所有这些系统的一个共同特点是出现非线性的流-力关系和一些反馈（通信）机制。化学系统中的反馈可能是由自加速或自抑制反应步骤引起的，或者反馈是由于物理性质或反应速率随转化率的变化引起的。分析和预测几个反应同时发生的实际系统的多重特性的主要困难是控制方程是高度非线性的，并且包含非常多的参数。因此，在没有合适的理论指导的情况下，从多维参数空间的参数研究中确定多重性特征是极其困难的，而且往往实际上是不可能的。这些数学上的困难使大多数研究局限于只发生单一反应的情况，尽管大多数与稳态多重性有关的实际问题都是在几个反应同时发生的系统中遇到的。并且是由于被不想要的反应“接管”。理论工作将围绕单个催化剂颗粒的内部和内部温度梯度建模（从而引入分布式参数分析）以及填充床管式反应器的多重特征建模。实验工作将用于验证这些模型。这些信息将使控制和启动政策的设计更安全、更可靠。PI是这个领域的领导者之一，设施非常好。建议连续三年的奖助金为86财政年度基金中的73,340美元、87财政年度基金中的70,537美元及88财政年度基金中的69,966美元。

The proposed work is the logical extension of this PI's previous work on analyzing multiplicity features in nonlinear chemically reacting systems. His previous work dealt with lumped parameter systems whereas in this project he is planning to use recently developed mathematical techniques to look at more complex distributed parameter problems. Problems associated with steady-state multiplicity are encountered mainly in catalytic reactors used to carry out exothermic chemical reactions. The efficient utilization, operation and control of industrial reactors requires knowledge of all their behavioral features, such as all the possible steady states. The proposed analysis will provide a systematic approach to finding all the qualitative features of distributed parameter systems in which the interaction between the dispersion and chemical kinetics may lead to multiple steady state. This could guide the experimentalist in finding new and more profitable states and eneable the rational development or more reliable and safe control and start-up policies. The methodology developed in this work will be useful also in other areas in which the interaction between diffusion and chemical kinetics can lead to steady-state multiplicity such as combusion, chemical vapor deposition, high performance ceramic materials and design of corrosion resistant alloys. Many chemical and physical systems may reach different steady states under the sam operating conditions. A common feature of all these systems is the occurence of nonlinear flux-force relations and some feedback (communication) mechanism. The feedback in chemical systems may be caused by an auto- accelerating or self-inhibitory reaction step or feedback is due to changes in either the physical properties or reaction rate with conversion. The main difficulty in analyzing and predicting the multiplicity features of practical systems, in which several reactions occur simultaneously, is that the governing equations are highly nonlinear and contain a very large number of parameters. Thus, it is extremely difficult, and often practically impossible, to determine the multiplicity features from a parametric study in the multi-dimensional parameter space, without having suitable theoretical guidance. These mathematical difficulties have restricted most studies to limiting cases in which only a single reaction occurs, even though most practical problems associated with steady-state multiplicity are encountered in systems in which several reactions occur simultaneously, and are due to the "taking over" by an unwanted reaction. The theoretical work will center around modeling intra - as well as interpractical temperature gradients in individual catalyst pellets (thus introducing distributed parameter analysis) as well as modeling of the multiplicity features of packed bed tubular reactors. The experimental work will be used to verify these models. This information will enable a safer and more reliable design of control and start-up policies. The PI is one of the leaders in this area and the facilities are excellent. A three year continuous grant is recommended at $73,340 out of FY 86 $70,537 out of FY 87 funds, and $69,966 out of FY 88 funds.