# THE MATHEMATICAL MODELLING METHODS APPLYING TO ESTIMATE THE PIPELINES TECHNICAL STATE AND ENVIRONMENT SITUATION

## Authors

• A. P. Oliinyk IFNTUOG; 76019, Ivano-Frankivsk, Karpatska str., 15
• G. V. Grigorchuk IFNTUOG; 76019, Ivano-Frankivsk, Karpatska str., 15
• R. M. Govdyak MASHEXPORT ENGINEERING COMPANY 04655, Kyiv, Shevchenkivskyi raion, Uzviz Kudryavsky, house 7

## Keywords:

pipeline, stress-deformed state, leakage current, diffusion, harmful substances distribution

## Abstract

In the context of providing trouble-free operation of oil and gas pipelines and preventing possible negative impacts on the environment, the issues of constructing an integrated mathematical model for assessing the technical condition of pipelines and the impact of emergency situations on the state of the environment in the course of hydrocarbon leakage are considered. The model of the evaluation of the stress-strain state of the pipeline according to the data on the displacement of surface points for the above ground and underground sections is given by constructing the law of motion of the site by known displacements of a certain set of surface points using assumptions about the type of deformation of the sections and reproduction of the deformations and stresses tensors components   on the basis of different models of deformed solid body.

The specified model does not require information on the whole complex of forces and loads acting on the investigated object during operation. The flow model has been refined in a pipeline with a violation of its tightness by recording a special type of boundary conditions for a Navier-Stokes equation system in a two-dimensional formulation and developing an original method for its solution on the basis of the finite difference method. In the article the stability conditions of the proposed numerical schemes on basis of the spectral sign of stability are presented. In order to assess possible negative impacts on the environment, a model of propagation of matter at its leakage from the pipeline was developed by solving two-dimensional diffusion equations taking into account the variables and different types of boundary conditions that take into account the number of sources of pollution and their intensity. The results of computations based on computational algorithms implemented by these models and graphic material illustrating these calculations are presented, peculiarities of distribution of harmful substances in the environment near the pipeline are analyzed. Directions of further researches for successful practical realization of the offered models are established.

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2019-06-27

## How to Cite

Oliinyk, A. P., Grigorchuk, G. V., & Govdyak, R. M. (2019). THE MATHEMATICAL MODELLING METHODS APPLYING TO ESTIMATE THE PIPELINES TECHNICAL STATE AND ENVIRONMENT SITUATION. METHODS AND DEVICES OF QUALITY CONTROL, (1(42), 97–103. https://doi.org/10.31471/1993-9981-2019-1(42)-97-103

## Section

AUTOMATION AND COMPUTER-INTEGRATED NON-DESTRUCTIVE TESTING TECHNOLOGIES