# Emerging challenges in phase behavior modeling of reservoir fluids at high-pressure high-temperature (HPHT) conditions

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## Abstract

Global energy demand is driving the oil and gas industry to explore uncharted areas leading to unconventional reservoirs at extreme temperature (T > 420 K) and pressure (P > 68 MPa) conditions where widely used equations of state (EOS) models fail to accurately predict properties of reservoir fluids and model their phase behavior. This work compares promising and adaptable EOS models for HPHT systems, highlighting their concomitant shortfalls in specified scenarios which need to be addressed by researchers in the quest for accurate predictive tools at extreme T and P reservoir conditions. Five EOS models were used for density prediction for n-heptane at 323 K and 423 K over a pressure range of 28–270 MPa where PC SAFT emerged the overall best. At 520 K however, VT PR-EOS and VT SRK-EOS performed better. For a binary system of C3/nC10, PC SAFT, which was highly promising, began to drop in accuracy with increase in temperature from 277 to 510 K. Furthermore, four EOS were tested for volume and z-factor prediction of pure systems (C1–C6) and their binaries. While PC SAFT is most promising, significant drawbacks are evident when applied to binary systems and are expected to worsen with increase in number of constituents. It was made clear that a pressure-dependent correction factor will significantly improve the accuracy of the PC-SAFT model. Suggestions on novel alternative routes for EOS model development and improvement are also given.

## Keywords

Equation of state Reservoir Modeling HPHT## List of symbols

- \( A \)
Constant for fitted HPHT volume-translation term, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- \( a \)
Attractive force term, \( \frac{{{\text{m}}\; {\text{L}}^{5} }}{\text{mol}} \), \( \frac{{ {\text{m}}^{6} \; {\text{Pa}}}}{\text{mol}} \)

- \( B \)
Constant for for fitted HPHT volume-translation term, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- b
Effective molecular volume repulsion term, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{B} \)
Correlation for BWRS equation of state \( \frac{{{\text{L}}^{3} }}{\text{mol}} \), \( \frac{{ {\text{m}}^{3} }}{\text{mol}} \)

- \( c \)
Systematic volume deviation, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{D} \)
Correlation for BWRS equation of state, \( \left( {\frac{{{\text{L}}^{3} }}{\text{mol}}} \right)^{4} \), \( \left( {\frac{{ {\text{m}}^{3} }}{\text{mol}}} \right)^{4} \)

- \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{E} \)
Correlation for BWRS equation of state, \( \left( {\frac{{{\text{L}}^{3} }}{\text{mol}}} \right)^{2} \), \( \left( {\frac{{ {\text{m}}^{3} }}{\text{mol}}} \right)^{2} \)

- \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} \)
Correlation for BWRS equation of state, \( \left( {\frac{{{\text{L}}^{3} }}{\text{mol}}} \right)^{2} \), \( \left( {\frac{{ {\text{m}}^{3} }}{\text{mol}}} \right)^{2} \)

- \( M \)
Molecular weight, \( \frac{\text{mol}}{{{\text{L}}^{3} }} \), \( \frac{\text{mol}}{{{\text{M}}^{3} }} \)

- \( P \)
Gas pressure, liquid pressure, \( \frac{\text{M}}{{{\text{L}}\; {\text{t}}^{2} }} \), \( {\text{MPa}} \)

- \( P_{c} \)
Critical pressure, \( \frac{\text{M}}{{{\text{L}}\; {\text{t}}^{2} }} \), \( {\text{MPa}} \)

- R
Universal gas constant, \( \frac{{{\text{ML}}^{2} {\text{T}}^{2}\uptheta}}{\text{mol}} \), \( \frac{{{\text{m}}^{3} \;{\text{Pa}}}}{{{\text{K}}\; {\text{mol}}}} \)

- T
Temperature, \( \uptheta \), \( {\text{K }} \)

- \( T_{c} \)
Critical temperature, \( \uptheta \), \( {\text{K }} \)

- \( T_{r} \)
Reduced temperature

- \( V \)
Gas volume, liquid volume, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- \( V_{EOS} \)
Volume predicted by equation of state, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- \( V_{EXP} \)
Volume obtained from experiment, \( {\text{L}}^{3} \), \( {\text{m}}^{3} \)

- \( u \)
Constant for generalized equation of state for PR and SRK

- \( w \)
Constant for generalized equation of state for PR and SRK

- \( Z \)
Compressibility factor

- \( Z_{hc} \)
Hard-chain contribution for the repulsive molecular interactions

- \( Z_{disp} \)
Attractive Term

- \( \alpha \)
Correlation for \( T_{c} \;and\; \omega \)

- \( \rho \)
Molar density, \( \frac{\text{mol}}{{{\text{L}}^{3} }} \), \( \frac{\text{mol}}{{{\text{M}}^{3} }} \)

- \( \omega \)
Acentric factor

## Notes

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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