IMPLEMENTATION OF A MATHEMATICAL MODEL OF NONSTATIONARY GAS MOVEMENT IN A COMPLEX PIPELINE UNDER MIXED BOUNDARY CONDITIONS

Abstract

The study of the movement of real fluid is necessary in the design of not only gas and oil pipelines, but also other hydraulic machines. Mathematical models of the unsteady movement of a liquid or gas are also necessary when solving a number of prob-lems in the operation of pipeline systems. Such tasks can be: pipeline condition monitoring, operating modes optimizing, emergency situations analyzing and others. Attempts to model the dynamics of pressure in pipelines with selection or pumping at given points led to systems of partial differential equations with boundary conditions between the zones of the pipeline section in question. If there are n sampling points (swapping), then we have to solve a system of n + 1 equations. This is due to cumbersome calculations, and sometimes with insurmountable difficulties. Use of the impulse function by Dirac M.A. Huseynzade and his students in oilfield mechanics and in pipe hydraulics made it possible to describe non-stationary processes in complex pipeline systems using a single equation. A section of a pipeline system is usually called «complex» if there are sampling-pumping points, pumping station or different sections of the pipeline have different coefficients of hydraulic resistance or diameters. This article discusses the horizontal section of the pipeline with sampling and pumping points. The problem is solved under mixed boundary conditions using a finite Fourier sine transform. Graphs of pressure dynamics for cases of selection, pumping and without them have been constructed. Special cases are considered. Calculation formulas convenient for practical application are obtained.