Equation of State (EOS) modelling has become a very important part of reservoir fluid analysis. EOS modelling is used as an adjunct for experimental analysis in the capacity of quality control and quality assurance. It is also used by oilfield practitioners to assess what type of compositional trends they can expect as a function of time. Still other applications include full compositional simulation where the EOS approximates the compositions of the phases in situ.
The science of EOS modelling is well documented in the literature. There have been a number of good publications including text books and papers that outlined the basis for EOS applications and the origin of such analysis in terms of theoretical constructs. However, the art of EOS modelling has been less extensively reported in the literature and it seems that experience often means the difference between obtaining a representative EOS model and not. Indeed, the approach to obtaining a good EOS model appears to be very subjective.
This paper presents an approach to EOS modelling involving a specific protocol. This protocol can be used every time and should result in abbreviating the path to a representative EOS model. To put EOS modelling into perspective, this paper begins with a discussion of the five areas of empiricism associated with the EOS. A brief discussion of the two main types of application\ follows and then the technique proposed for practical EOS modelling is described.
The protocol suggested is:
Define the use of the EOS model. Is it going to be used for volatility- or extraction-based systems?
Acquire experimental data that represent the application.
Determine the number of components required.
De-couple the different areas of the data and associate them with their respective VLE parameters in the EOS.
Tune the constitutive relations to the data that are de-coupled from the VLE computations.
The equation at the heart of EOS modelling is
Equation (Available In Full Paper)
The necessary condition for the computation of phase equilibrium is equality of component fugacity, fi, phase to phase. The sufficient condition is the minimization of free energy, which can also be expressed as a molar-weighted average of the component fugacities across all phases [Equation (2)]. Equation (Available In Full Paper)
No matter what the numerical engine for the computations, the calculation of fugacity or chemical potential must occur. The great breakthrough provided by the EOS is that the integral in Equation (1) can be readily and easily computed, over and over in the iterative sequence of the solution of the nonlinear equations(1–3).
It should be remembered that Equation (1) is perfect. There are no simplifying assumptions, and if the parameters in Equation (1) are known with a high degree of accuracy, then the computation of fugacity will be accurate. Therefore, the more accurate the EOS, the better the fugacities and the more representative the phase behaviour predictions.
