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A New Hard Sphere Cubic Equation of State for Predicting Fluids’ Properties and Vapor-Liquid Phase Equilibrium Calculations

  • Basic and Applied Research
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Abstract

In this study, a new cubic hard sphere equation of state (EOS) was developed from standard classical thermodynamics. The new equation is applied to calculate properties of fluids and vapor-liquid phase equilibrium calculations. The derived equation is a simplified expression of the hard sphere equation which yields satisfactory agreement with the molecular simulation of hard molecule data. The EOS is written in a cubic form by combining the derived repulsive hard spheres with Redlich-Kwong (RK) empirical attractive term. Satisfactory calculated results for the saturated properties of pure fluids for temperature ranges from 303 to 523 K and pressure ranges from 50 to 5000 psi are obtained. Simplicity and generality of this equation combined with reasonable accuracy makes it a useable EOS for almost all areas of equipment design for separation processes and production operations including refinery and petroleum reservoir industries. The accuracy of the predicted properties from the developed EOS are greater than of other commonly used two parameter cubic equations of state, RK and Pang-Robinson (PR).

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Abbreviations

AAD:

Average absolute deviation

BIAS:

Bias

RMS:

Root mean square

a :

Attractive parameter

b :

Repulsive parameter

d :

Error

f :

Fugacity

K :

Boltzmann’s constant

m, n :

Constants in Eq 28 and 29

n :

Number of points

N :

Number of molecules

P :

Pressure

Q :

Partition function

R :

Universal gas constant

T :

Absolute temperature

v :

Molar volume

V :

Total volume

Z :

Compressibility factor

α,  β:

Dimensionless functions

ɛ,  γ,  λ:

Constants in Eq 12

η:

Packing fraction

ρ:

Density

ω:

Acentric factor

att:

Attraction

cal:

Calculated property

exp:

Experimental

rep:

Repulsion

c:

Critical property

f:

Free

hs:

Hard sphere

l:

Liquid

r:

Reduced property

tr:

Translational

v:

Vapor

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Acknowledgment

The authors are grateful to the Oil and Gas Center of Excellence, department of Chemical Engineering, University of Tehran.

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Authors and Affiliations

  1. Oil and Gas Center of Excellence, Department of Chemical Engineering, University of Tehran, Enghlab Ave., Tehran, 1944874, Islamic Republic of Iran

    S. Hajipour & M. Edalat

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  1. S. Hajipour
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  2. M. Edalat
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Correspondence to M. Edalat.

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Hajipour, S., Edalat, M. A New Hard Sphere Cubic Equation of State for Predicting Fluids’ Properties and Vapor-Liquid Phase Equilibrium Calculations. J Phs Eqil and Diff 29, 322–332 (2008). https://doi.org/10.1007/s11669-008-9317-9

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  • DOI: https://doi.org/10.1007/s11669-008-9317-9

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