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

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

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

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" 1964. 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), 116 128, 1975 Margules Van Laar Wilson NRTL UNIQUAC Developed by Johannes van Laar in 1910-1913. 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.135 144, 1968

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

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

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

Antoine Etanol Iso amyl A 8.204 7.334 B 1642.890 1353.300 C 230.300 172.190 log P sat = A + B C + T/ Before Optimization A12 0.5 A21 0.21 P 101.3 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 1 1.0000 0.0000 1.0000 0.0000 78.3000 101.2228 11.3785 1.0008 1.0000 1.2337 101.2228 0.0772 2 0.9513 0.0487 0.9955 0.0045 79.3000 105.3110 11.9555 1.0066 0.7833 0.9999 1.2687 100.9115 0.3885 3 0.8751 0.1249 0.9918 0.0082 81.2000 113.4594 13.1195 1.0119 0.5082 0.9999 1.3248 101.4482 0.1482 4 0.6169 0.3831 0.9412 0.0588 88.4000 149.2769 18.4281 1.0352 0.8444 1.0211 1.5020 104.6381 3.3381 5 0.4716 0.5284 0.8518 0.1482 93.4000 179.3157 23.0806 1.0203 1.2311 1.0653 1.5409 108.8791 7.5791 6 0.3896 0.6104 0.8319 0.1681 96.7000 201.7611 26.6553 1.0721 1.0467 1.1075 1.5762 112.6967 11.3967 7 0.2619 0.7381 0.6855 0.3145 105.2000 270.4739 38.0194 0.9804 1.1352 1.2088 1.5086 127.9590 26.6590 8 0.0967 0.9033 0.3964 0.6036 122.3000 467.3119 72.9951 0.8889 0.9273 1.4366 1.3395 153.2211 51.9211 9 0.0215 0.9785 0.1479 0.8521 127.4000 544.5513 87.4022 1.2784 1.0094 1.5948 1.2491 125.5093 24.2093 10 0.0000 1.0000 0.0000 1.0000 131.7000 617.4413 101.2604 1.0004 1.6487 1.2337 124.9228 23.6228 OF (ΣΔP) 149.3399

Antoine Etanol Iso amyl A 8.204 7.334 B 1642.890 1353.300 C 230.300 172.190 log P sat = A + B C + T/ After Optimization A12 0.029962097 A21 0.043072889 P 101.3 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 1 1.0000 0.0000 1.0000 0.0000 78.3000 101.2228 11.3785 1.0008 1.0000 1.0440 101.2228 0.0772 2 0.9513 0.0487 0.9955 0.0045 79.3000 105.3110 11.9555 1.0066 0.7833 1.0001 1.0427 100.8053 0.4947 3 0.8751 0.1249 0.9918 0.0082 81.2000 113.4594 13.1195 1.0119 0.5082 1.0008 1.0407 101.0763 0.2237 4 0.6169 0.3831 0.9412 0.0588 88.4000 149.2769 18.4281 1.0352 0.8444 1.0068 1.0348 100.0238 1.2762 5 0.4716 0.5284 0.8518 0.1482 93.4000 179.3157 23.0806 1.0203 1.2311 1.0119 1.0336 98.1779 3.1221 6 0.3896 0.6104 0.8319 0.1681 96.7000 201.7611 26.6553 1.0721 1.0467 1.0151 1.0325 96.5855 4.7145 7 0.2619 0.7381 0.6855 0.3145 105.2000 270.4739 38.0194 0.9804 1.1352 1.0203 1.0346 101.2997 0.0003 8 0.0967 0.9033 0.3964 0.6036 122.3000 467.3119 72.9951 0.8889 0.9273 1.0269 1.0401 114.9717 13.6717 9 0.0215 0.9785 0.1479 0.8521 127.4000 544.5513 87.4022 1.2784 1.0094 1.0297 1.0434 101.2998 0.0002 10 0.0000 1.0000 0.0000 1.0000 131.7000 617.4413 101.2604 1.0004 1.0304 1.0440 105.7173 4.4173 OF (ΣΔP) 27.9980

No x1 y1-exp y 1 -calc 1 1.000 1.000 1.001 2 0.951 0.996 1.000 3 0.875 0.992 0.994 4 0.617 0.941 0.953 5 0.472 0.852 0.879 6 0.390 0.832 0.872 7 0.262 0.686 0.686 8 0.097 0.396 0.349 9 0.022 0.148 0.148 10 0.000 0.000 0.000 Calculate y1 using Parameter obtained by Margules Minimization

T/ C Coefficient Activity Model 140 VLE data of Etanol + Isoamyl Alcohol at 101,33 kpa 130 120 110 x y- exp y- calc 100 90 80 70 0.0 0.2 0.4 0.6 0.8 1.0 x 1 (etanol mol fraction)