Polytropic Flow Of Natural Gas In Vertical Pipes

A method is presented for calculating the flowing bottom hole pressure in natural gas wells using a polytropic equation of state. The polytropic equation is based on an empirical exponent and is determined by using the point functions of pressure P, temperature T and compressibility factor Z at the terminals of the vertical flow string. A comparison of calculated and field measured results were made on gas well data presented in the literature. The average percent deviation between the calculated and observed flowing bottom hole pressures was 0.416. The polytropic method may use any compressibility factor correlation applicable to the fluid under study, which is important when the amount of inerts is appreciable. An example demonstrating the polytropic method is presented-using friction factor correlations which are based on an absolute pipe roughness of 0.0006 in.