The Use of Departure Functions to Estimate Deviation of a Real Gas from the Ideal Gas Model

In many practical applications of thermodynamics, the use of simplified relationships of the ideal-gas model over a more accurate but more complex real gas model, is a critical decision to make. Thermodynamic departure functions provide screening criteria to evaluate whether the ideal-gas model can accurately represent a gas behavior. This paper reports several departure functions to evaluate deviation of a real gas from the ideal-gas model. Included in this paper is the derivation of departure functions based on isothermal compressibility, isobaric expansivity, isochoric change of pressure with temperature, isochoric change of internal energy with pressure, sonic speed, and heat capacities difference. The description of each of these departure functions is accompanied by a numerical example. Departure functions defined in this paper have led to improved representation of deviation from the ideal-gas model across a range of 2% deviation of the specific volume departure (also known as the compressibility factor, Z) for a typical gas mixture encountered in natural gas processing. The limitations involved in using the compressibility factor, Z, to evaluate departure from the ideal-gas model is highlighted. It is shown that even as the compressibility factor, Z, approaches unity at certain thermodynamic conditions, other departure functions exhibit considerable deviations from the ideal-gas model. It is concluded that the compressibility factor, Z, should not be used as "the only criterion" to evaluate conformance to the ideal-gas model. This paper also explains the physical significance of Schultz compressibility functions X, Y, and L [3] by introducing departure functions based on isothermal compressibility and isobaric expansivity.