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Isothermal (vapor + liquid) equilibria for the binary mixtures of (propylene oxide +
ethanol) and (propylene oxide + 1-propanol) at several temperatures
An analysis of experimental design and calculations used
Dhruv JainSaumil KothariVignesh ShekarVijey Raghavan Lakshmi NarasimhanYash Patankar
INTRODUCTION Potential applications. Experimental apparatus and procedure. Data Generated. Mathematical models used to predict similar
systems. Experimental vs. Calculated values. Applicability of models to binary
component systems.
Potential Applications Propylene oxide is commonly used in production of
polymers
Generally combined with alcohols for catalytic reaction into esters
Reactions are carried out at isothermal conditions
Reaction vessels usually kept a pressure and temp at which a liquid-vapor system is generated
Experimental Setup
Systems is allowed to equilibrate at isothermPressure is read directly from vesselMole fraction in liquid is determined by Gas Chromatography
Calculations performed on data
Data was interpreted with:• Peng-Robertson-Stryjek-Vera Equation of
state. (PRSV)• Wong Sadler mixing rule
Then correlated to models: Non-Random Two Liquid (NRTL) Universal Quasi-chemical (UNIQUAC) Wilson Model
Peng-Robinson-Stryjek-Vera EOS Background
Developed in order to satisfy these goals: Parameters should be expressible in terms of the critical
properties and the acentric factor. Should provide reasonable accuracy near the critical
point, particularly for calculations of the compressibility factor and density.
Single binary interaction parameter, independent of temperature pressure and composition.
The equation should be applicable to all calculations of all fluid properties in natural gas processes.
Drawbacks Not accurate enough, in general, for phase
equilibrium calculations. The highly non-linear behavior of phase-equilibrium calculation methods tends to amplify what would otherwise be acceptably small errors.
In the PSRV equation, the parameter fit is done in a particular temperature range below the critical temperature. Above the critical temperature, the PRSV alpha function diverges and become arbitrarily large instead of tending towards 0.
Wong-Sadler Background
• Thermodynamic mixing rule used for vapor–liquid equilibrium calculations
• Developed for cubic equations of state equates the excess Helmholtz free energy at infinite pressure from an equation of state to that from an activity coefficient model. Use of the Helmholtz free energy insures that the second virial coefficient calculated from the equation of state has composition dependence, as required by statistical mechanics. Consequently, this mixing rule produces the correct low- and high-density limits without being density-dependent.
Wong-Sadler Background• Equally applicable and accurate for simple mixtures
containing hydrocarbons and inorganic gases and mixtures containing polar, aromatic and associating species over a wide range of pressures.
• Makes it possible to use a single equation of state model with equal accuracy for mixtures usually described by equations of state and for those traditionally described by activity coefficient models. It is the correct bridge between these two classes of models.
NRTL BackgroundThe concept of NRTL is based on the hypothesis
of Wilson that the local concentration around a molecule is different from the bulk concentration.
This difference is due to a difference between the interaction energy of the central molecule with the molecules of its own kind and that with the molecules of the other kind .
The NRTL equation was derived by Renon in 1968. It is applicable to partially miscible and completely systems.
= x1x2( +
Where τ12 = ; =
G12 = exp(-α12τ12); G21= exp(-α12τ12) τ12 and τ21 are the dimensionless interaction parameters. Gij is similar to ʎij in Wilson’s equation. Gij is an energy parameter characteristic of the i-j interaction. The α12 parameter is related to the non-randomness in mixture, at zero value the mixture is completely random. It is often set arbitrarily to α12= 0.3.
The activity coefficients are,
lnγ1 =
lnγ2 =
The main disadvantage of the NRTL model is the strong correlation between the two parameters[(τ21
τ12) & (G12 and G21)] of the model.
UNIQUAC Background
UNIQUAC ( UNIversalQUAsiChemical) is an activity coefficient model used in descriptionModels such as UNIQUAC allow chemical engineers to predict the phase behavior of multicomponent chemical mixtures. of phase equilibria.
The UNIQUAC method equation for gE is
residual
has two parts:
1. A combinatorial part which attempts to describe the dominant entropic contribution
= x1 + x2 +
The combinatorial part is determined by the composition and the sizes and shapes of molecules only.
2. A residual part for intermolecular forces that are responsible for the enthalpy of mixing
residual = - x1τ21) – x2ln(τ12)
The residual part depends on intermolecular forces.
Where
Θ and ϕ are segment and area fractions Parameters q and q’ are pure components molecular structure
constants. τ12 and τ21 are the two adjustable parameters.
Wilson Background Wilson, NRTL, and UNIQUAC equations are proposed for the relationship
between activity coefficients and mole fractions.
In 1964 Wilson presented the expression for excess Gibbs energy of a binary solution.
And the activity coefficients derived from this equation are:
Wilson Background
Gibbs energy in Wilson’s equation is defined with reference to an ideal solution. The equation follows the boundary condition that gE disappears as either x1 or x2 goes to zero.
Wilson’s equation has two adjustable parameters (Λ12, Ʌ21). They are related to the pure component molar volumes.
Results and DiscussionData showed good correlation with predictive models.
Results and DiscussionDeviation from all 3 models was experimentally acceptable.
Critiqueo Authors did not explain rationale for selecting coefficients
in the models.i. UNIQUAC Coordination number ii. NRTL Non-randomness valueiii. Values selected were “commonly used” values, not
necessarily specific to this system.
o Substitution of Gibbs Free energy for Helmholtz energy in modelsi. Authors assert that these values are interchangeable at
experimental conditionsii. Reduces applicability to other systems.
CONCLUSION Experimental data proved to be a good fit with all
3 models
Assumptions made appear to be applicable to the system studies.
Further work should include justification of assumptions, and additional isothermal temperatures.
REFERENCES1. "Helmholtz and Gibbs Free Energies." Hyeprphysics. Georgia State University, n.d.
Web. 29 Apr. 2015. <http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Fthermo%2Fhelmholtz.html>.
2. Kim, Hwayong, and Et Al. "The Journal of Chemical Thermodynamics." The Journal of Chemical Thermodynamics 86 (2015): 1-5. Web.
3. "Non-random Two-liquid Model." Wikipedia. Wikimedia Foundation, n.d. Web. 23 Apr. 2015. <http://en.wikipedia.org/wiki/Non-random_two-liquid_model>.
4. Prausnitz, J. M., R. N. Lichtenthader, and E. G. DeAzevedo. Molecular Thermodynamics of Fluid-phase Equilibria. 3rd ed. Upper Saddle River, N.J: Prentice Hall PTR, 1999. Print.
5. Proust, P., and J. H. Vera. "PRSV: The Stryjek-vera Modification of the Peng-Robinson Equation of State. Parameters for Other Pure Compounds of Industrial Interest." The Canadian Journal of Chemical Engineering 67.1 (1989): 170-73. Web.
6. "UNIQUAC." Wikipedia. Wikimedia Foundation, n.d. Web. 23 Apr. 2015. <http://en.wikipedia.org/wiki/UNIQUAC>.