A Theoretical Analysis of Un-steady State Gas Flow in Pige Line

Abstract

The gas flow in pipe line under steady state has been described by various anthers. But when we draw up the plan of instantaneous flow control by process computer, the theory of gas flow under un-steady state should be needed. In this paper, the anther sets up a simultaneous partial differential equations of un-steady state gas flow in pipe line (Eq. 11 & 18), based on the equation of motion (Eq. 1) and the equation of continuity (Eq. 9). Subsequently, he expands these equation to simultaneous difference equations (Eq. 26 27), and simultates real gas flow. The simulator starts with random noise, caused by the changes of pressure or flow rate at either end point in pipe line (the unit), in which gas flow has been under steady state, and traces the changes of pressure and flow rate of any place in the unit with time. At the starting time, we can put any value of pressure and flow rate at any place in the unit, which is first condition of simultaneous difference equation (Eq. 26 & 27). But in the next time-step, the pressure or flow rate of end point in the unit, which is boundry condition of the simultaneous equation, can not be difined from solving the Eq. 26 & 27. The auther notices that if we select the point enough close by end point in the unit, the gas flow between them changes instantly to steady state. So he applies this conception to calculation of next time-step boundry condition in the unit, such as Eq. 30 & 31. Setting up data and giving selected noises to the simulator, sufficient results are obtained as shown Fig. 5-12.