Determination of Acoustic Velocities for Natural Gas

Abstract

Acoustic velocities for natural gas are calculated as a function of temperature, pressure, and gas gravity. The method is based on a generalized equation of state for natural gas that may also be used to calculate a number of thermodynamic properties such as specific internal energy and isentropic expansion. Introduction Some uses of acoustic velocities for natural gas are to determine liquid levels in gas wells and to locate hydrate freezes, lost ‘pigs’, or other obstructions in gas pipelines. These distances can be calculated from well defined acoustic records (Fig. 1a) by associating the number of pipe sections with their corresponding lengths. If, however, an uninterpretable acoustic record (Fig. 1b) is obtained, or if the lengths of the pipe sections of a given flow string are unknown, pipe sections of a given flow string are unknown, distance between the shot deflection and the reflecting surface can be obtained by integrating the relationship between velocity distance and time (1) The utility of this technique depends upon one's ability to calculate acoustic velocities and to measure system variables such as gas gravity or composition, temperature, temperature gradient and pressure. In the past, acoustic velocities have been calculated from an approximate relationship involving atmospheric heat capacity ratios rather than ratios that are a function of pressure. As has been pointed out, this approximate relationship provides a good working equation for calculating acoustic velocities at low pressure ranges but should not be used at higher pressures. The purpose of this work is to present a method for rigorously calculating acoustic velocities for natural gas over a broad range of temperatures, pressures and gas gravities. Calculation of Acoustic Velocity Starting from the equation for the speed of sound in a compressible fluid (2) it is possible to derive the following equation for a real gas (see Appendix). (3) Eq. 3 can also be expressed in terms of the isentropic expansion coefficient, n, since (4) Making this substitution yields (5) To compute the velocity of sound in a real gas from either Eq. 3 or Eq. 5, it is necessary to know the PVT behavior of the gas and the variation of the beat capacity ratio with temperature and pressure. To accomplish this, an equation of state for natural gas was developed. JPT P. 889