Agung Ari Wibowo, S.T, M.Sc THERMODYNAMICS MODEL

Transcription

1 Agung Ari Wibowo, S.T, M.Sc THERMODYNAMICS MODEL

2 THERMODYNAMICS MODEL For the description of phase equilibria today modern thermodynamic models are available. For vapor-liquid equilibria it can bedistinguished between two different methods. One method only requires fugacity coefficients φi and the other require coefficient activity (ɣ) for the liquid (L) and the vapor (V) phase: Or

3 Thermodynamic model for the excess Gibbs free energy of a liquid mixture Introduced in 1895 by Max Margules Published by Grant M. Wilson as "Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing" Abrams D.S., Prausnitz J.M., Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems, AIChE J., 21(1), , 1975 Margules Van Laar Wilson NRTL UNIQUAC Developed by Johannes van Laar in The equation was derived from the Van der Waals. Renon H., Prausnitz J. M., "Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures", AIChE J., 14(1), S , 1968

4 Both methods mentioned above have different advantages and disadvantages. They have in common that phase equilibria of multicomponent mixtures can be calculated using binary data alone. This is most important since nearly no data are available for multicomponent systems. But for fitting the required binary parameters reliable phase equilibrium information for the whole concentration and a large temperature range is required. For actual problems often at least a part of the required binary data is missing. This means that in many cases the methods mentioned above cannot directly be applied

5 Margules Model Roult Modification The activity coefficient of component i is found by differentiation of the excess Gibbs energy towards xi In here A 12 and A 21 are binary interaction parameter

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7 Data Fitting to get binary interaction parameter VLE data of Etanol + Isoamil Alkohol at 101,33 kpa How to perform data fitting? Calculate P sat of each component at given experimental T, using Antoine Equation Calculate γ 1 and γ 2 of experimental data using Roult Modified Equation Calculate γ 1 and γ 2 using Margules Model, by Guessing any Value of A12 and A21 Evaluate the new value of P total using P = x1* γ 1 * P 1 sat + x2* γ 2 * P 2 sat Calculate ΔP = abs (P exp P calc) Sum all ΔP and perform minimization of total ΔP using Solver by changing the value of A12 and A21

8 Antoine Etanol Iso amyl A B C log P sat = A + B C + T/ Before Optimization A A P kpa Fraksi etanol No x1 x2 y1 y2 T Exp P1 sat (kpa) P2 sat (kpa) gamma 1 exp gamma 2 exp gamma 1 cal gamma 2 cal P cal delta P OF (ΣΔP)

9 Antoine Etanol Iso amyl A B C log P sat = A + B C + T/ After Optimization A A P kpa Fraksi etanol No x1 x2 y1 y2 T Exp P1 sat (kpa) P2 sat (kpa) gamma 1 exp gamma 2 exp gamma 1 cal gamma 2 cal P cal delta P OF (ΣΔP)

10 No x1 y1-exp y 1 -calc Calculate y1 using Parameter obtained by Margules Minimization

11 T/ C Coefficient Activity Model 140 VLE data of Etanol + Isoamyl Alcohol at 101,33 kpa x y- exp y- calc x 1 (etanol mol fraction)