Mathematical Apparatus for Detecting Leakage in Gas Pipelines

Estimation of possibilities of calculations based on simplified models of the leak location in gas pipelines

“…The adequacy of the stationary mathematical model (1)−( 4), as noted, depends on the choice of the variables λ, β, c p and on the choice of the type of dependence Z(p, T ) of the compressibility coefficient in the investigated range of pressure, temperature and flow changes. The system of equations (1)−( 4) is supplemented by the boundary condition z = 0 : p = P(0), T = T (0), (5) where P(0), T (0) are dimensional pressure and temperature at the gas pipeline inlet. The solution of the system of equations (1)−(4) under the boundary condition (5) exists and is unique in a wide range of Q 0 , P(0), T (0), R and L. The numerical solution can be obtained with high accuracy, for example, by the Runge−Kutta method.…”

“…Expression (9) for the variable c p includes the values of temperature and pressure at the outlet. These variables either are measured experimentally or can be calculated using the system of equations (1)−( 4) with boundary condition (5). In the second case, the variable c p is calculated iteratively.…”

“…The solution of the problem of calculating the coordinates of the gas leak according to model (1)−( 4) is given in [5]. The analysis of these calculations showed that there is a range of parameters Q 0 , P(0), T (0), R, L, β, λ, T * change, in which, with an acceptable accuracy, it is possible to calculate the pressure and temperature distributions in the gas flow using simplified models.…”

“…Numerous publications have been devoted to calculations of the leak location in gas pipelines and wells based on a mathematical model of gas flow, starting with the fundamental work of Vasiliev, Bondarev, Voevodin and Kanibolotsky [1], up to the present, for example, papers [2][3][4][5]. Success in solving this problem is impossible without creating an adequate mathematical model of gas flow under the conditions under study.…”

“…Paper [9] also presents a solution of the problem of calculating the coordinates of a stationary gas leak by iteration using quasilinearization for superhigh pressures (under the assumption of a stable flow pattern both before the leak and some time after its occurrence). The solution of the similar problem for medium pressures is given in [5]. In this paper we consider the admissibility of using relatively simple models for calculating the coordinate of the stationary leak in gas pipelines, the pressure in which does not exceed 100 atm.…”