Analytical Steady-State Model of the Pipeline Flow Process

The paper addresses the issue of modeling the flow process in transmission pipelines. A base model used for numerical simulation is introduced. Under certain assumptions concerning steady state analysis, the differential equations describing the process are solved analytically for two cases: zero and nonzero inclination angle $\alpha$. These equations describe a constant flow rate and a corresponding distribution of the pressure along the considered pipeline for both cases. The pipe length at which the pipeline is choking (the mass flow is equal zero) for given boundary pressures and inclination angle, is also derived. Convergence of the proposed solution for inclination angle $\alpha\rightarrow 0$ to the zero tilt solution, is proved. An exemplary practical relationship based on obtained equations is provided as a 3D chart. A test pipeline with adjustable inclination angles of its selected parts is considered. The analytic solution for the effective angle is compared with numerical solutions, which show relevant discrepancies between the results obtained for nonzero angles. Clearly, the numerical solution for a straight pipeline (with the increasing number of segments) is convergent to the analytic solution. Moreover, up to 16°, the analytic approximation (using an effective inclination angle) is sufficient, and produces similar results as the numerical simulation.