## PC-SAFT: The next generation EOS?

For more than 30 years, cubic equations of state have been the standard tool in the oil industry for modeling of PVT behavior. As the oil industry is facing still more challenging problems, there is a need for more sophisticated models. There is, for example a need to model gas injection in heavily under-saturated reservoirs, asphaltene precipitation, and phase behavior of complex mixtures of hydrocarbons and polar components. The PC-SAFT equation (Perturbed Chain Statistical Association Fluid Theory) is one of the most promising alternatives to the cubic equations. Calsep is working towards full integration of the PC-SAFT equation in PVTsim.

Some of the appealing features of the PC-SAFT equation are better predictions of important derivative properties (including compressibility and speed of sound) while absolute densities and phase equilibria are still matched well. If an association term is included, the equation can be used for equilibrium calculations of mixtures of polar and non-polar components without the need for complex mixing rules.

The basic form of PC-SAFT utilizes 3 component specific model parameters (segment number, m, segment diameter, σ, and energy parameter, ε). If the mixture contains components that can form hydrogen bonds or associate, a term with two additional component specific parameters (association energy εAiBi and association volume κAiBi) can be included.

Calsep has already developed a PC-SAFT characterization procedure for heavy hydrocarbons (Pedersen et al., 2012) and verified that the equation is capable of modeling standard and EOR PVT data (Leekumjorn and Krejberg (2012) and Pedersen et al. (2012)).

The current activities include

- Implementation and testing of an association term for aqueous mixtures (and asphaltenes)
- Improved modeling of asphaltenes
- Investigating limitations in the PC-SAFT equation

The association term allows complex mixtures of hydrocarbons and aqueous components (including hydrate inhibitors) to be modeled without having to use complex mixing rules (as for example Huron-Vidal). Physical properties (density, compressibility, speed of sound) of a water phase with significant amounts of hydrate inhibitors can be modeled better with PC-SAFT than with the classical equations.

The PC-SAFT equation has shown good results for asphaltene modeling, which is primarily thanks to a good description of the pressure derivative of the volume. Assigning model parameters to asphaltenes is not straightforward. High energy (attraction) parameters may be needed to match measured asphaltene onset pressures, but very high energy parameters have turned out to introduce incorrect behavior at lower temperatures. Asphaltene molecules are believed to self-associate and cross-associate with aromatic constituents in the oil. Therefore the problems may be overcome by including the association term in the asphaltene modeling.

Although the PC-SAFT model has many positive features, it also has limitations. Some of the weaknesses of the model that Calsep would like to address in the R&D work are

- Poor match of critical point for pure components
- Calculation speed is lower than for cubic equations
- False liquid roots may exist at low temperatures

### REFERENCES

Leekumjorn, S. and Krejbjerg, K., “Phase Behavior of Reservoir Fluids: Comparisons of PC-SAFT and Cubic Equation of State Simulations”, Fluid Phase Equilibria 359, 2013, pp. 17-23.

Pedersen, K.S., Leekumjorn, S., Krejbjerg, K. and Azeem, J., “Modeling of EOR PVT data using PC-SAFT equation”, SPE-162346-PP , Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 11–14 November, 2012.

## Asphaltene Gravity Segregation and Tar Mats

A considerable compositional variation with depth is seen in asphaltene rich oil reservoirs. That is for example the case with the Carito-Mulata field in Venezuela (Figura et al., 2010). Over a depth interval of 3,000 ft the fluid changes from a gas condensate, to become a volatile oil, and end up as an undersaturated black oil. While the asphaltene content is less than 0.1 weight% at the top, it has increased to more than 20 weight% 3,000 ft further down.

In a newly started R&D project Calsep is modeling the variation in asphaltene concentration with depth considering gravity and temperature segregation. As can be seen from the below plot, it was possible to match the steep increase in the asphaltenes concentration with depth observed in the Carito-Mulata field in Venezuela.

Calsep has taken the asphaltene segregation modeling one step further and developed a procedure for detecting the depth in which an asphaltene tar mat will occur. With the asphaltene concentration increasing with depth the asphaltene onset pressure will also increase. If the asphaltene onset pressure in a certain depth becomes equal to the reservoir pressure, an asphaltene phase, known as a tar mat has been encounted, which will extend from the depth and downwards.

REFERENCES

Figuera, L., Marin, M., Lopez, L., Marin, E., Gammiero, A., and Granado, C., “Characterization and Modelling of Asphaltene Precipitation and Deposition in a Compositional Reservoir”, SPE 133180, Sep. 2010.

Nagineni, V. , Leekumjorn, S. and Agger, C., "Modeling of Asphaltene Component Segregation and Tar Mat Formation", 37th International Symposium on the Application of Computers and Operations Research in the Mineral Industry, Fairbanks, Alaska, 2015. (Abstract accepted)