### Static Behaviour of Natural Gas and its Flow in Pipes [chapter]

Peter Ohirhian
2010 Natural Gas
A general differential equation that governs static and flow behavior of a compressible fluid in horizontal, uphill and downhill inclined pipes is developed. The equation is developed by the combination of Euler equation for the steady flow of any fluid, the Darcy-Weisbach formula for lost head during fluid flow in pipes, the equation of continuity and the Colebrook friction factor equation. The classical fourth order Runge-Kutta numerical algorithm is used to solve to the new differential
more » ... w differential equation. The numerical algorithm is first programmed and applied to a problem of uphill gas flow in a vertical well. The program calculates the flowing bottom hole pressure as 2544.8 psia while the Cullender and Smith method obtains 2544 psia for the 5700 ft (above perforations) deep well Next, the Runge-Kutta solution is transformed to a formula that is suitable for hand calculation of the static or flowing bottom hole pressure of a gas well. The new formula gives close result to that from the computer program, in the case of a flowing gas well. In the static case, the new formula predicts a bottom hole pressure of 2640 psia for the 5790 ft (including perforations) deep well. Ikoku average temperature and deviation factor method obtains 2639 psia while the Cullender and Smith method obtaines 2641 psia for the same well.. The Runge-Kutta algorithm is also used to provide a formula for the direct calculation of the pressure drop during downhill gas flow in a pipe. Comparison of results from the formula with values from a fluid mechanics text book confirmed its accuracy. The direct computation formulas of this work are faster and less tedious than the current methods. They also permit large temperature gradients just as the Cullender and Smith method. Finally, the direct pressure transverse formulas developed in this work are combined wit the Reynolds number and the Colebrook friction factor equation to provide formulas for the direct calculation of the gas volumetric rate 19 www.intechopen.com Natural Gas 436