INTERNATIONAL YOUTH SCIENCE FORUM ”LITTERIS ET ARTIBUS”, 26–28 NOVEMBER 2015, LVIV, UKRAINE 192 Determining of Volume of Natural Gas Losses Caused by Damages of Distribution Networks Viktor Dzhyhyrei, Fedir Matiko, Dmytro Klymkovskyi Department of Automation of Heat and Chemical Processes, Lviv Polytechnic National University, UKRAINE, Lviv, S. Bandery street, 12, E-mail: dv-@ukr.net Abstract – The algorithm of calculation of gas volume losses caused by damages of above-grounded pipelines is proposed in this paper. The mathematical model of natural gas movement in the pipeline is developed for the implementation of the algorithm. The model is used to determine the parameters of the gas flow at the leakage point. The equation for calculation gas flowrate through the holes in the pipeline wall is developed on the basis of the formula of Saint-Venant-Wentzel. The equation is valid for subcritical and critical regime of gas flow. The equation for determining discharge coefficient of the holes in the pipeline wall for gas pressure up to 1.2 MPa is proposed. Key words – pipeline, damage, mathematical model, gas leakage rate, gas losses. I. Introduction Losses of natural gas occur during the operation of gas distribution networks (GDN). They are the result of the constant leakage of gas through pipelines and equipment tightness and of equipment damages. The methods for determining the losses of gas at suppositive normative tightness of the GDN elements are presented in the existing Ukrainian normative documents for determining the technological losses of natural gas, particularly in [1]. However there is no method for determining volume losses of natural gas caused by pipelines damages. Therefore developing the mathematical model of gas losses from the pipelines and equipment caused by their damages is an urgent task. II. Determining the Volume Gas Losses The problem of determining the parameters of natural gas at the damage point and the gas flowrate through the damage arises during the modeling the process of gas leakage through the holes in pipelines. Differential equation of changes of gas pressure along the length of the tilted section of pipeline is obtained from the equation system that contains the equation of saving of mechanical energy of isothermal gas flow [2], the flow continuity equation and the equation of state of real gas 2 0; 2 ; . x m dv dp gdy gdh q vF const R p z T M (1) where is the linear velocity of natural gas in the pipeline; g is gravity acceleration; dy is change of the height of vertical marks of pipeline; dh x is the pressure loss along the length of the pipeline (friction loss); q m is mass flowrate of gas; F is the line flow area of the pipeline; p, T, , z, M are pressure, temperature, density, compressibility factor and molar mass of natural gas; R is universal gas constant. The differential equation of change of the gas temperature along the long tilted pipeline is obtained from the heat balance equation of the pipeline section. Thus mathematical model of natural gas movement in pipeline is a system of differential equations of changes in pressure and temperature of gas along the pipeline, which is completed with the equation of state of real gas [3]: 2 2 2 2 2 2 5 /( ) 8 ; 16 ; , , , ; , , m gr p а y c m i t z m p q zRT p gM y zRT L M D dp dx q zRT p pM dT dp g y T T D dx dx cL k D qc z f p D Tx x (2) where Т gr is the absolute temperature of the soil; Δy is the difference between the final and the initial heights of pipeline location; L is the length of the pipeline section; λ is the coefficient of hydraulic resistance; D i is Joule- Thomson coefficient; c p is isobar heat capacity of natural gas; k t is the coefficient of heat transfer from the gas to the soil; D z , D are the outer and the inner diameters of pipeline; ρ с is the gas density at standard conditions. The example of application model (2) to build gas pressure distributions along the damaged pipeline is presented in Figure 1. Fig. 1. Pressure distribution along the length of the pipeline: without leakage (line 1), with leakage 0.1q 1 - (2), 0.2q 1 - (3), 0.3q 1 - (4) Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua