Waterhammer Analysis of Oil Transportation Pipeline Using Brunone-Vitkovsky Unsteady Flow Friction Model

Abstract

A transient flow model for heated oil transportation pipeline is built with application of continuity, momentum and energy conservation equations of pipe flow. The transient friction term of the model incorporates both of the steady and unsteady friction and the Brunone-Vitkovsky model is selected to compute unsteady flow friction in pipeline. The method of characteristic, finite-difference scheme and Newton-Raphson method are utilized to solve the model and the computer simulation software is developed on the base of investigation. Ultimately, the hydraulic transient behavior along a heated oil transportation pipeline in the condition of an interim pump station stoppage is simulated. The results show consider the unsteady flow friction is useful to improve the accuracy of water hammer simulation.

Implementation and Validation of a Free Open Source 1D Water Hammer Code

“…In this case the characteristic lines are linear, since it is assumed that a is constant. Approximating Equation (4) with finite differences and integrating along the positive characteristic line and along the negative characteristic line yield Equations (6) and 7, where C p and C m are described with Equations (8) and (9), respectively and B = a gA .…”

“…C m = H B − BQ B + a g J B ∆t + ∆x aA sin(θ)Q B (9) Inserting Equation (6) into Equation (7) and solving for H P yields:…”

“…Equations (6) to (9) are used in a rectangular grid to simulate the water hammer. The friction term J is evaluated explicitly.…”

“…The pressure pulse created is noisy and the pressure pulse may have a magnitude which causes pipe rupture or resulting in other equipment damage. Water hammer may be observed in a variety of applications e.g., in power plant steam generation/cooling systems [1,2], district heating system [3], hydro-power [4], irrigation systems [5,6], domestic plumbing [7], pipeline transport of oil and chemicals [8,9] etc. It is important to be able to accurately model the physical phenomenon for correct dimensioning of pipes, adequate choice of valve closing time etc.…”