Natural gas systems are becoming more and more complex as the usage of this energy source increase. Mathematical models are used to design, optimize, and operate increasingly complex natural gas pipeline systems. Researchers continue to develop unsteady mathematical models that focus on the unsteady nature of these systems. Many related design problems, however, could be solved using steady-state modeling. Several investigators have studied the problem of compressible fluid flow through pipelines and have developed various numerical schemes, which include the method of characteristics, finite element methods, and explicit and implicit finite difference methods. The choice partly depends on the individual requirements of the system under investigation. In this work, the fully implicit finite difference method was used to solve the continuity, momentum, energy, and equations of state for flow within a gas pipeline system. The particular solution method described in this paper does not neglect the inertia term in the conservation of momentum equation. It also considered the compressibility factor as a function of temperature and pressure, and the friction factor as a function of the Reynolds number. the fully implicit method representation of the equations offer the advantage of guaranteed stability for a large time step, which is very useful for the gas industry. The results show that the effect of treating the gas in a non-isothermal manner is extremely necessary for pipeline flow calculation accuracies, especially for rapid transient processes. The results indicate that the inertia term plays an important role in the gas flow analysis and cannot be neglected from the calculation.

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