Feasibility in Chemical Process Design and Simulation

化学工艺设计和模拟的可行性

• 批准号: 9409158
• 负责人: Angelo Lucia
• 金额: $ 13.04万
• 依托单位: Clarkson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-10-01 至 1997-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9409158&HistoricalAwards=false
• 关键词: Feasibility; Chemical; Process; Design; Simulation

Abstract - Lucia - 9409158 Limits of feasibility for mathematical models of many problems in science and engineering are characterized by smooth turning or bifurcation points, which are the singular points of some associated Jacobian matrix. These turning and bifurcation points, as well as the solutions themselves, can be real or complex-valued and many numerical methods for obtaining them can experience periodic, aperiodic or divergent behavior. Accordingly, the PI plans to build a better understanding of the role and utility of singularity in defining and determining limits of feasibility in chemical process design and simulation by: 1. Conducting numerical studies that revolve around the use of (a) nonsingular implicit composite equation systems to define turning and bifurcation points, (b) trust region methods in the complex domain to compute these turning and bifurcation points, and (c) hybrid methods consisting of approximating some of the first partial derivatives of the implicit equations. 2. Developing the necessary mathematical framework for understanding the convergence and rate of convergence of complex domain or extended trust region methods for calculating limits of feasibility. Problem specifications in science and engineering applications always give rise to either feasible or infeasible sets of model equations. Feasible specifications always give rise to zero-valued minima in the two-norm, while infeasible ones correspond to nonzero-valued minima and singular points in the norm. Information regarding feasibility or infeasiblity, whether a priori or concomitant, is important to equation-solving tasks in design and simulation. The PI plans to: 1. Conduct numerical investigations on the use of (a) extended trust region methods for identifying and calculating conditions of feasibility or infeasibility and (b) accelerating convergence to singular points using complex domain quasi-Newton updates to build a quadratic model in the null space. 2. Study t he convergence and rates of convergence of the methods developed above.

摘要 - Lucia - 9409158 科学和工程中许多问题的数学模型的可行性极限都以平滑转折点或分叉点为特征，这些点是某些相关雅可比矩阵的奇异点。 这些转折点和分叉点以及解本身可以是实值或复值，并且许多获得它们的数值方法可以经历周期性、非周期性或发散行为。 因此，PI 计划通过以下方式更好地理解奇异性在定义和确定化学工艺设计和模拟的可行性极限方面的作用和效用： 1. 围绕使用 (a) 非奇异隐式复合方程系统来定义转折点和分叉点，(b) 复杂域中的信任域方法来计算这些转折点和分叉点，以及 (c) 混合进行数值研究 由近似隐式方程的一些一阶偏导数组成的方法。 2. 开发必要的数学框架来理解复杂域的收敛性和收敛速率或计算可行性极限的扩展信任域方法。 科学和工程应用中的问题描述总是会产生可行或不可行的模型方程组。 可行的规范总是会产生二范数中的零值最小值，而不可行的规范则对应于范数中的非零值最小值和奇异点。 有关可行性或不可行性的信息，无论是先验的还是伴随的，对于设计和仿真中的方程求解任务都很重要。 PI 计划： 1. 对使用 (a) 扩展信任域方法来识别和计算可行性或不可行性条件以及 (b) 使用复杂域拟牛顿更新加速收敛到奇点进行数值研究，以在零空间中构建二次模型。 2. 研究上述方法的收敛性和收敛速度。