炼油工艺过程数学模型及其基于模型一般概念的定性分析

Serhii Polozhaenko, F. Garaschenko, L. Prokofieva
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引用次数: 0

摘要

推导并证明了原油预处理过程和装置的广义数学模型的微分方程系统决策的存在唯一性定理。泛化在开发一类粗烃预处理过程(装置)数学模型的数值实现方法时提供了应用统一和类型化原理的机会,而相应定理的证明(本质-定性分析)提供了在所研究过程(装置)数学建模应用问题中应用泛化模型的正确性。公式化定理的证明是严格的,逻辑上是正确的,并且在泛函分析的范围内一致地执行。决策的存在性和唯一性定理作为定性分析的组成部分的实际适用性,是通过对所研究的一类过程(设备)的数学建模的算法手段的充分性的基础上的研究的可能性来确定的。
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Mathematical Models of Technological Processes of Oil Refining and Their Qualitative Analysis Based on the General Concept Of Models
Theorems of existence and uniqueness of the decision of system of the equations in the private derivatives, representing the generalized mathematical model of processes and devices of preprocessing of crude hydrocarbons are formulated and proved. Generalization gives the chance to apply the principle of unification and typification when de-veloping a method of numerical realization of mathematical models of a class of processes (devices) of preprocessing of crude hydrocarbons, and the proof of the corresponding theorems (an essence —the qua-litative analysis) provides a correctness of application of the generalized model in applied problems of mathematical modeling of studied pro-cesses (devices). Proofs of the formulated theorems are strict, logically true and are consistently executed within terms of the functional ana-lysis. Practical applicability of theorems of existence and uniqueness of the decision as component of the qualitative analysis, is defined by pos-sibility of research on their basis of adequacy of algorithmic means of mathematical modeling of a studied class of processes (devices).
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