Accuracy of simulation of transient response of liquid pipelines can be improved by using a more accurate equation of state. A new equation of state intended for the above application is presented in this paper. The proposed equation is based on a limited number of experimental measurements, selected correlations published by the American Petroleum Institute, (API), and general principles of thermodynamics.


Continuing growth o f the oil and natural gas industries resulted in an increased demand for more accurate equations of state. Equation of state in general describes a relationship between the most commonly used intensive thermodynamic properties of pressure and temperature and the three most commonly used extensive thermodynamic properties of density, enthalpy and entropy. Historically equations of state used by the oil arid natural gas industry have been developed as a surface fitting to a set of experimental measurements. Both experiments and subsequent development of the correlations were designed to meet the specific end objectives. The most common end applications of the equations of state were phase equilibrium calculations and mass or volume computations related to custody transfer of natural gas, crude oil or refined products. Equations of state developed for the above end applications have been used extensively by the industry with continually improved accuracy. Various authors who have developed transient modeling software relied on the above mentioned equations of state to obtain required correlation between density, (and for some cases a form of energy related property or properties) pressure and temperature. Application o f the transient modeling into the domain of real time demonstrated that the existing equations of state do not describe the relationship between pressure and density with the degree of accuracy required to model transient response of some of the liquid pipelines, particularly in Real Time Applications.


The efforts described in this paper were directed to development of an equation of state which will improve the accuracy of transient modeling of liquid pipelines. The following reasons were considered as justifying the above specifications:

  • the operating range of pressures and temperatures encountered in the liquid lines is relatively narrow and concentrating on such a narrow range of applications allows to achieve better accuracy and simpler correlations.

  • Minimum density of 600 kg/m3 excludes some of the lighter hydrocarbons transported through pipelines like NGL, ethane, propane and ethylene for which the existing equation of state based on product composition (BWR, Peng-Robinson, etc) give good results.

  • Selection of the bulk input parameters rather than the composition of the product was made as the above parameters are more readily available and much easier to define with a good degree of reliability.

  • Special emphasis has been put on accurate modeling of the effects of pressure on density as this function defines the speed of propagation of transient effects in the line. Significant difficulties are encountered in real time modeling of liquid lines if erroneous correlation between pressure and density is relied upon.

This content is only available via PDF.
You can access this article if you purchase or spend a download.