Generalization of the Riemann method for the trunk gas pipelines considering the quadratic law of resistance

Ismatulla Khujayev,Аlisher Ismailov,S Akhmadjonov

doi:10.1051/e3sconf/202126401013

Abstract

A mathematical model of the problem of pulse propagation in a semi-infinite gas pipeline was developed by expressing the pressure drop by the quadratic law of resistance and the local component of the gas inertia force by the law of conservation of momentum, using the law of conservation of mass in a one-dimensional statement. The model repeats the Riemann problem but takes into account the frictional resistance force. Using an auxiliary function in the form of the natural logarithm of the reduced density, and gauge functions, and certain simplifications, an equation for the reference solution of the problem in terms of gas velocity was derived and solved. For the analytical solution of the problem on gas velocity, the Riemann solution was used, and a refined analytical solution was obtained considering the quadratic law of resistance for the calculation of the perturbed and non-perturbed subdomains.

Highlights

Trunk gas pipelines are the main part of the gas transportation system [1]
The greater share of energy costs in pipeline gas transportation falls on this part of the system
The conditions for the uniqueness of the solution to the problem for the gas velocity are taken in the form of one boundary and two initial conditions

Summary

Introduction

Trunk gas pipelines are the main part of the gas transportation system [1]. The greater share of energy costs in pipeline gas transportation falls on this part of the system. The characteristics of the pipeline network and the set technological tasks are the determining factors for the operating mode of other equipment of the system. In this regard, it is important to ensure the ability to calculate the operating mode of the trunk gas pipeline with a sufficient degree of accuracy. Despite the seeming simplicity of the gas pipeline design, complex processes of motion, friction, interaction with gravity forces, internal and external heat transfer take place in it. These processes, as a rule, change over time; that is, they are non-stationary processes

Methods

Results

Conclusion