Steady state adiabatic compression and one-dimensional generalized gas flow is analyzed using governing conservation laws and Redlich-Kwong-Soave (R-K-S) equation of state applied to a representative mixture of natural gas. The objective of this work is to obtain the state properties of the natural gas considered as an open thermodynamic system at compressor and gas pipeline exits, then the compressor power and energy auto-consumptions for a few diameters and pipe line lengths configurations. The adiabatic, irreversible compression process is analyzed with formal state property definitions where departures from ideal gas properties are obtained using R-K-S equation of state. The one-dimensional generalized gas flow problem is analyzed with continuity, momentum and energy equations, combined with the equation of state; Reynolds analogy between heat transfer and flow friction is adopted. This problem is thus defined with four non linear coupled differential equations; the variables to be determined are pressure, temperature, specific volume and velocity at the gas pipeline exit. The adopted calculation procedure to obtain the gas properties is iterative. It assumes pressure and temperature initial values, solves the equation of state for the specific volume and the continuity equation for the velocity, then corrects for pressure and temperature with integrated values to be used with the next iteration from a solution of the differential equations of motion and energy. This procedure is applied to a few gas pipeline configurations of pipe diameters sections and number of boosting compressor stations for a gas pipeline capacity of 13.5 billions standard cubic meters per year to be delivered to a natural gas liquefaction plant located at a sea port at a distance of some 350 miles.
A conservative implicit scheme for steady state solutions of diatomic gas flow in all flow regimes