Chemical Process Simulation in Singular Regions

将开发稳健和快速的算法来求解与化工过程模拟相关的方程。奇点经常出现在化工过程模型中。这些奇点可以极大地改变化学过程模拟中常用的方程求解方法的性能。目前许多基于牛顿方法的模拟在奇异区域都失败了，必须重新开始。这项研究将解决奇点对重要的方程求解方面的影响，如可靠性、收敛速度和计算效率。这项工作致力于开发一种新的、智能的复域方法，用于奇异区域的过程模拟，其核心是一个统一的理论和计算框架，用于(1)识别奇异区域，(2)使用二次逼近收敛到奇异点，(3)确定过程模型方程的一个或多个解。该方法能够从给定的奇点找到路径不连通的解，并且计算效率很高。将证明为路径存在提供严格的理论保证、将初值放置在给定的吸引盆中以及全局收敛的定理。理论和算法体系结构将同步开发，将处理所有类型的奇点，并将作为一组可移植的Fortan 77程序实现。模拟问题，如蒸馏，反应工程，和一般流程的例子，将被用来验证所有的理论发展。所开发的算法可能会应用于改进化工过程的模拟。

Robust and rapid algorithms for solving equations relevant to chemical process simulation will be developed. Singularities frequently occur in chemical process models. These singularities can dramatically alter the performance of equation-solving methods commonly used in chemical process simulation. Many current simulations based on Newton's method fail in singular regions and must be restarted. This study will address the effects of singular points on important equation-solving aspects such as reliability, rates of convergence, and computational efficiency. This work is concerned with the development of a novel and intelligent complex domain methodology for process simulation in singular regions centered around a unified theoretical and computational framework for (1) identifying singular regions, (2) converging to singular points using quadratic approximation, and (3) determining one or more solutions to process model equations. The proposed approach is capable of finding path-disconnected solutions from a given singular point and is computationally efficient. Theorems that provide rigorous theoretical guarantees of a path existence, placing initial values in a given basin of attraction, and global convergence will be proved. The theoretical and algorithmic architectures will be developed in tandem, will address all types of singular points, and will be implemented as a set of portable Fortan 77 programs. Simulation problems such as distillation, reaction engineering, and general process flowsheet examples will be used to verify all theoretical developments. The algorithms developed may have application to improving chemical process simulations.