Modeling of transition processes during pipeline transportation of real gases
Аннотация
Задачи идентификации утечки, участков накопления высоких напряжений и отклонения функции сети от технологических требований непосредственно связаны переходными процессами. В связи с этим исследование переходных процессов в трубопроводах является актуальным как с теоретической, так и с практической точки зрения. Математическое моделирование переходных процессов в магистральных трубопроводах производится в рамках квазиодномерных уравнений Н.Е. Жуковского с учетом сил трения, гравитации и инерции. Для газовой среды эти уравнения имеют третий порядок относительно неизвестных. Применением способа осреднения типа И.А. Чарного степень уравнений снижается на один порядок. А переход к массовому расходу, аналогу функции тока при решении двумерных уравнений гидродинамики, позволяет получить линейные уравнения относительно массового расхода, в выражении которых фигурирует произведение неизвестных плотности и скорости газа. Относительно массового расхода и давления составлены автономные уравнения, которые представляют тип телеграфного уравнения. С учетом возможных скачкообразных изменений искомых по времени и расстоянию решение ищется в виде функциональных рядов. Наглядность этого метода заключается в том, что выделяются частоты возмущений, свойственные уравнениям параболического и гиперболического типов, и промежуточного варианта. Представляется общий метод решения задач перехода от одного установившегося режима работы участка к другому установившемуся режиму работы. Под установившимся режимом подразумеваются стационарный и периодический режимы работы участка. В этих случая легко определяются производные и в квадратурах вычисляются интегралы, фигурирующие в общем решении задач. Полученные решения легко материализуются в виде программных продуктов и учитывают постоянный уклон оси газопровода, что особенно важно при расчете трубопроводов с большими диаметрами, функционирующих при высоких и сверхвысоких рабочих давлениях.
The problems of identifying gas leak points, high pressure points and other deviations of the pipeline network are directly related to transition processes. Researches in transition processes in pipeline transportation are relevant both from a theoretical and from a practical point of view. Mathematical modeling of transition processes in main pipelines is performed within the framework of quasi-one-dimensional equations of Zhukovsky N.E. taking into account the forces of friction, gravity and inertia. For the gaseous medium, these equations are in the third order with respect to unknowns. By using the method of type averaging, developed by Charny I.A. the degree of equations can be reduced by one order. And the transition to mass flow, analogous to the current function when solving two-dimensional hydrodynamic equations, allows us to obtain linear equations for mass flow, in terms of the product of unknowns of gas density and velocity. Regarding mass flow and pressure, autonomous equations are compiled that represent the type of telegraph equation. Taking into account possible abrupt changes of the unknowns in time and distance, the solution is sought in the form of functional series. The demonstrativeness of this method lies in the fact that the perturbation frequencies relevant to the parabolic and hyperbolic types of equations and the intermediate variant are distinguished. A general method is presented for solving problems of transition from one steady state of operation of a site to another steady state of operation. Under the steady state we refer to the stationary and periodic modes of operation of the site. In these cases, derivatives are easily determined, and the integrals involved in the general solution of problems are calculated with quadrature. The solutions obtained are easily realized in the form of software products and take into account the constant slope of the axis of the gas pipeline, which is especially important when calculating pipelines with large diameters operating at high and ultra-high operating pressures.
The problems of identifying gas leak points, high pressure points and other deviations of the pipeline network are directly related to transition processes. Researches in transition processes in pipeline transportation are relevant both from a theoretical and from a practical point of view. Mathematical modeling of transition processes in main pipelines is performed within the framework of quasi-one-dimensional equations of Zhukovsky N.E. taking into account the forces of friction, gravity and inertia. For the gaseous medium, these equations are in the third order with respect to unknowns. By using the method of type averaging, developed by Charny I.A. the degree of equations can be reduced by one order. And the transition to mass flow, analogous to the current function when solving two-dimensional hydrodynamic equations, allows us to obtain linear equations for mass flow, in terms of the product of unknowns of gas density and velocity. Regarding mass flow and pressure, autonomous equations are compiled that represent the type of telegraph equation. Taking into account possible abrupt changes of the unknowns in time and distance, the solution is sought in the form of functional series. The demonstrativeness of this method lies in the fact that the perturbation frequencies relevant to the parabolic and hyperbolic types of equations and the intermediate variant are distinguished. A general method is presented for solving problems of transition from one steady state of operation of a site to another steady state of operation. Under the steady state we refer to the stationary and periodic modes of operation of the site. In these cases, derivatives are easily determined, and the integrals involved in the general solution of problems are calculated with quadrature. The solutions obtained are easily realized in the form of software products and take into account the constant slope of the axis of the gas pipeline, which is especially important when calculating pipelines with large diameters operating at high and ultra-high operating pressures.