SOAVE REDLICH KWONG EQUATION OF STATETatiana Caballero1, Ricardo Grandas1

1. Escuela de Ingeniería Química, Universidad Industrial de Santander. Bucaramanga, Colombia

Mixtures separation is a key process in many industries like pharmaceutics, petrochemical and others. Having information about liquid and vaporbehavior is the first step to design operations like distillation in order to obtain more value product from raw materials like plants, and heavyhydrocarbons. Cubic equations of state are widely used in process simulation and calculations of vapor-liquid equilibrium, and have been applied tothe representation of properties of pure compounds and mixtures. The Soave-Redlich-Kwong (SRK) [Soave, 1972; Redlich and Kwong, 1949] and thePeng-Robinson (PR) [Peng and Robinson, 1976] equations of state are well known. This job presents a review of the SRK equations and itsadvantages and limitiations.

SOAVE REDLICH KWONG EQUATION OF STATE

INTRODUCTION

Chemical engineers from petroleum companies widely use cubicequation of state and especially the one proposed by soave (SRK).This equation of state directly stem from the Van der Waals theoryand can be written for a given mixture under the general form:

Mixtures:

𝒂 = 𝑗 𝑖 𝑋𝑖𝑋𝑗𝑎𝑖𝑗 = 𝑗 𝑖 𝑋𝑖𝑋𝑗 (1 − 𝑘𝑖) 𝑎𝑖𝑎𝑗 b= 𝑗 𝑋𝑖𝑏𝑖

𝑷 =𝑅𝑇

𝑣 − 𝑏−

𝑎(𝑇)

𝑣(𝑣 + 𝑏)

𝒃 = 𝑏𝐶 = 0.08664𝑅𝑇𝐶𝑃𝐶

𝒂 𝑻 = 𝛼 𝑇 ∗ 0.42748𝑅2𝑇𝐶

2

𝑃𝐶

𝜶 𝑻 = 1 +𝑚 1 −𝑇

𝑇𝐶

1 22

𝒎 = 0.480 + 1.574𝜔 + 0.176𝜔2

𝑻: Absolute Temperature

𝑷: Pressure

𝒗: Specific volumen

𝑻𝑪: Critical temperatura

𝑷𝑪: Critical pressure

𝝎: Acentric factor

𝒂: Intermolecular attraction forces

𝒃: Volume occupied by molecules;

𝒌𝒊: Binary interaction parameter

𝜶 𝑻 : Dimensionless coefficient

Where:

ADVANTAGESThe advantages of this equation are that it can accurately and easilyrepresent the relation among temperature, pressure, and phasecompositions in binary and multicomponent systems. SRK onlyrequire the critical properties and acentric factor for the generalizedparameters. Little computer time is required and good phaseequilibrium correlations can be obtained.

LIMITATIONSThe SRK equation cannot be applied at temperatures below –143°С and pressures above 350 bar, and it cannot be used for describing systems with methanol and glycols and for calculating vapor–liquid–liquid equilibrium.In addition, it cannot be used for calculations near the critical point of a mixture.

CALCULATE THE BINARY INTERACTION PARAMETER ki

Fig 2. Temperature dependence of estimated binary interaction parameters (𝑘𝑖𝑗)

Fig. 6. Deviation on vaporpressure vs. temperature,SRK and PR EoS

Fig. 7. Relative errors forvapor pressure vs.Temperature, SRK and PR EoS

REFERENCES1. LEIBOVICI F., NICHITA V. Fluid Phase Equilibria 2013; 356:371-3732. AKBEROV R. Theorical Foundations of Chemical Engineering 2011; Vol 45-3:312-3183. JAUBERT JN., PRIVAT R. Fluid Phase Equilibria 2010; 295:26-374. SHAAN C. Chemical Engineering Research and Design 2013: 91;1163-11695. NASRI Z,. BINOUS H. National Institute of Applied Sciences and Technology 2007; Vol 40-

6:534-538

𝛼𝑖 𝑇 = [1 + 𝐶1,𝑖 1 − 𝑇𝑟0.5 + 𝐶2,𝑖(1 − 𝑇𝑟

0.5)2+𝐶3,𝑖(1 − 𝑇𝑟0.5)3]2

𝐶𝑗,𝑖 = Pure fluid parameters

PREDICTIVE SOAVE REDLICH KWONG EoS

Fig 8. Experimental and predicted liquid-phase compositions of CO2 and toluene.

Fig 9. Experimental and predicted volumeexpansion ratios of CO2 and toluene.

SRK UNCERTAINTY

CONCLUSIONSSRK can give a satisfactory description of the vapor–liquid-equilibrium(VLE) behavior of systems formed by hydrocarbons and relatedCompounds.Some modification based on improvement Soave's function can bedone in order to improve the poor performance of SRK EoS whenmodeling some heavy and polar substances.SRK model can predict the different kij trends commonlyencountered.

VAPOR-LIQUID EQUILIBRIUM (VLE) DIAGRAM

Fig 3. Ethane-Benzene at 298,15 K Fig 4. Ethane-Benzene at 448,15 K

Fig 1. SRK algorithm

Fig 5. Experimental,and SRK(----),PR( ) equation of state for thesystem CO2 – Iso-Pentanol.

PRSRK