Mathematical Models of Technological Processes of Oil Refining and Their Qualitative Analysis Based on the General Concept Of Models

Abstract

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).