«Automation and Informatization of the fuel and energy complex»

Models of isothermal non-barotropic flow in pipelines

UDC: 004.942
DOI: -

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: mathematical modeling of pipelines transport, sequential pumping, transport equation, non-barotropic flow

Annotation:

A mathematical model of fluid isothermal flow in a pipeline section under conditions of variable density and viscosity is obtained. The model accounts for non-barotropic properties of liquid. In addition to the classical mass and momentum conservation equations, the nominal volume conservation equation is deduced. It is shown that the density advection equation in the absence of diffusion can be deduced as a consequence of the nominal volume and mass conservation laws or directly in the Lagrangian coordinate system. The conditions of quasi-stationary assumptions are formulated. Taking into account the introduced assumptions, estimates of the equations members of the non-stationary flow model were obtained. On the basis of the estimates, members of equations insignificant for quasi-stationary conditions were discarded. The obtained equations allow performing hydraulic calculations of quasi-stationary flows taking into account chaotic changes of the pumped liquid’s characteristics at the pipeline inlet. It is noted that generally accepted assertion of the consistency of nominal volume flow rate along the pipeline in quasi-stationary mode, strictly speaking, is not observed. The value of the error introduced by this factor requires additional verification with account for the real quasi-stationary dynamics.

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