An Implicit Method for Transient Flow in Pipe Networks.

Virtual Pipeline System Testbed to Optimize the U.S. Natural Gas Transmission Pipeline System

“…The results that were obtained were compared with those reported by Kiuchi (1994), who used the fully implicit method for an isothermal solution. The results show that modeling gas in a nonisothermal manner provides accurate pipeline flow calculations, and is extremely necessary for rapid transient processes.…”

“…Maddox and Zhou (1983) used steady-state friction loss calculation techniques applied in real time to determine the unsteady state behavior of pipeline systems from pressure drop and material balance relationships. Kiuchi (1994) described a fully implicit finite difference method for solving isothermal unsteady compressible flow. A Von Neumann stability analysis on the finite difference equations of a pipe (after neglecting the inertia term in the momentum equation) showed that the equations are unconditionally stable.…”

“…A Von Neumann stability analysis on the finite difference equations of a pipe (after neglecting the inertia term in the momentum equation) showed that the equations are unconditionally stable. Kiuchi (1994) compared this method with other methods such as the method of characteristics, Lax-Wendroff method, Guys method and the Crank-Nicolson method and showed that fully implicit methods are very accurate for a small number of sections and a large time step, which is very useful for industrial gas pipelines because of the savings in computation time. Luongo (1986) presented an isothermal solution for gas pipelines using the Crank-Nicolson method for solving equations.…”

“…The method of solution is the fully implicit finite difference method, which is very suitable for gas pipeline simulation because of its large step time and low computation time [Thorley and Tiley (1987), Kiuchi (1994)]. The algorithm to solve the nonlinear finite-difference equations of a pipe is based on the Newton-Raphson Method.…”

“…This method is unconditionally stable. Mohitpour et al (1996) and Kiuchi (1994) used this method to solve the continuity and momentum equations for a gas pipeline network. This method is very accurate for the gas pipeline industry because their problems usually involve relativity slow transients, and rapidly occurring phenomena are of far less importance than long-term transients (Kiuchi, 1994).…”