STATIONARY MODE OF FLUID FLOW IN THE PIPELINE IN THE PRESENCE OF ASSOCIATED SAMPLING AND PUMPING

Abstract

Pipeline transportation of oil and petroleum products plays a significant role in the transport system of the Russian Federation. When operating oil pipelines, reliability and energy efficiency are the most important criteria. To achieve these indicators, it is necessary to perform optimal technological modes. When constructing models of technological regimes, a methodology is used in which the movement of oil and petroleum products is considered as steady. Based on this assumption, the throughput, pump operating modes, strength characteristics and other parameters are determined. During the operation of the equipment, almost every day it is necessary to switch from one mode to another, which entails unsteady fluid movement for some time. At the same time, the unsteady mode makes up a small part of the total operating time of the system.The beginning of studies of unsteady fluid processes in pipes dates back to the last quarter of the 19th century. N. E. Zhukovsky made a fundamental contribution to the study of this problem. His classic work on water hammer in water pipes was the beginning for the creation of a large number of works in pipe hydraulics. The problem was solved for an ideal elastic fluid, i.e. without taking into account the friction forces against the pipe walls. The resulting formula, according to which the pressure increment is proportional to the velocity, has received numerous experimental confirmations for cases when it is possible to neglect pressure losses to overcome hydraulic resistances. N. E. Zhukovsky also obtained a formula for determining the sound velocity of a liquid droplet in a pipe with elastic walls. It is proved that this speed depends on the pipe material and its thickness.In the future, a large number of works were carried out to study the flow of liquid and gas in round pipes. The fundamental works of I. A. Charny, who obtained a mathematical model in the form of a system of partial differential equations of hyperbolic type, proved fruitful in this direction. Linearization of the equation, taking into account viscosity and hydraulic resistance allowed the researcher to obtain solutions to a number of engineering problems.The introduction of the Dirac function in the description of selectionpumping at specified points made it possible to describe processes in complex pipelines with one partial differential equation.This article discusses a horizontal section of the pipeline with sampling and pumping points. A stationary process for a drip liquid is considered. The problem is solved using the sine-Fourier transform.