Peng-Robinson Equation of State Formula
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| \( p \;=\; \dfrac{ R \cdot T }{ V - b } - \dfrac{ a \cdot \alpha }{ V \cdot (V + b ) + b \cdot (V - b ) } \) | ||
| Symbol | English | Metric |
| \( p \) = Fluid Pressure | \(lbf \;/\; in^2\) | \(Pa\) |
| \( R \) = Universal Gas Constant | \(lbf-ft\;/\;lbmol-R\) | \(J\;/\;kmol-K\) |
| \( T \) = System Temperature | \(^\circ F\) | \(^\circ K\) |
| \( V \) = Fluid Molar Volume | \(in^3\) | \(mm^3\) |
| \( b \) = Parameters Specific to the Fluid, known as the Peng-Robinson Parameters | \(in^3\) | \(mm^3\) |
| \( a \) = Parameters Specific to the Fluid, known as the Peng-Robinson Parameters | \(in^3\) | \(mm^3\) |
Peng–Robinson equation of state is a cubic thermodynamic model used to describe the pressure–volume–temperature (PVT) behavior of real fluids, especially hydrocarbons and other non-ideal gases. It improves upon earlier cubic equations of state by providing more accurate predictions of both vapor-phase properties and liquid densities near the critical point. The equation relates pressure, temperature, and molar volume through parameters that account for intermolecular attractive forces and the finite size of molecules, with these parameters being functions of critical properties and the acentric factor of the substance. Because it balances reasonable accuracy with mathematical simplicity, the Peng–Robinson equation of state is widely used in chemical engineering, petroleum engineering, and process simulation for phase-equilibrium calculations such as vapor–liquid equilibrium, compressibility, and fugacity of real fluids.
Peng-Robinson Equation of State Formula
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\( b \;=\; 0.07780 \cdot \dfrac{ R \cdot T_c }{ P_c } \) \( a \;=\; 0.45724 \cdot \dfrac{ R^2 \cdot T_c^2 }{ P_c } \) \( \alpha \;=\; [ \; 1 + k \cdot ( \;1 - \sqrt{ T_r } \; ) \; ]^2 \) \( k \;=\; 0.37464 + 1.54226 \cdot \omega - 0.26992 \cdot \omega^2 \) \( T_r \;=\; \frac{ T }{ T_c } \) |
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| Symbol | English | Metric |
| \( b \) = Volume (Molecular Size) | - | \(m^3\;/\;mol\) |
| \( a \) = Attractive Force | - | \(Pa \cdot m^6 \cdot K^{0.5} \;/\;mol^2\) |
| \( R \) = Universal Gas Constant | - | \(J\;/\;kmol-K\) |
| \( T_c \) = Critical Temperature | - | \(^\circ K\) |
| \( P_c \) = Critical Pressure | - | \(Pa\) |
| \( \alpha \) (Greek Symbol alpha) = Temperature Dependent Correction Factor | - | \(dimensionless\) |
| \( k \) = Function of the Acentric Factor | - | \(dimensionless\) |
| \( T \) = System Temperature | - | \(^\circ K\) |
| \( T_r \) = Reduced Temperature | - | \(^\circ K\) |
| \( \omega \) (Greek Symbol omega) = Acentric Factor | - | \(dimensionless\) |