# Equation of State Modeling

An equation of state is a function that relates the properties pressure ($$p$$), volume ($$V$$), temperature ($$T$$) and molar amount ($$n$$). These properties define the field of research which is often referred to as PVT. Typically, the volume and molar amount are merged into a molar volume ($$v=V/n$$). Some examples of EOS models are the ideal gas law, the real gas law, Benedict-Webb-Rubin (BWR) EOS models and cubic EOS models.

The most used EOS model for petroleum modeling are the BWR EOS models for non-ideal gases (e.g. the Hall-Yarbrough real gas correlation1), while cubic EOS models like the Peng-Robinson2 and Soave-Redlich-Kwong3 EOS are used for two-phase fluid modeling. There are also other types of EOS models, e.g. the generalized polynomial EOS models (typically referred to as virial equations) and other more exotic EOS models which are not related to petroleum engineering.

The role of an EOS model is to predict the phase behavior of a fluid system and to give the foundation for other calculations like reservoir simulations, surface processing, fluid mapping and many more applications. Cubic EOS models can be used to generate black-oil tables given that the EOS model is properly tuned to PVT-data. A tuned EOS model can be a valuable tool for many reservoir and process engineering tasks.

One of the main calculation that makes an accurate EOS model so valuable is the isothermal flash calculation. This is a key part of most PVT calculations. There are a range of software's that offer PVT simulations to estimate the result of traditional PVT experiments like constant composition expansion and separator testing. To name a few software's that offer such PVT calculations are PhazeComp, PVTx, PVTp, PVTi and PVTsim. All these PVT simulators have an option to use a cubic EOS to calculate different PVT results.

1. K. R. Hall and L. Yarborough. A new equation of state for z-factor calculations. Oil Gas J, 71:82, 1973.

2. D. B. Robinson and D. Y. Peng. The characterization of the heptanes and heavier fractions for the GPA Peng-Robinson programs. Gas processors association, 1978.

3. G. Soave. Equilibrium constants from a modified redlich-kwong equation of state. Chemical engineering science, 27:1197–1203, 1972. doi:https://doi.org/10.1016/0009-2509$72$80096-4