Use of ab initio interaction energies for NRTL to predict Use of ab initio interaction energies for NRTL to predict phase equilibria in the system nitrogen-ethane phase equilibria in the system nitrogen-ethane Gabriele Raabe, Jürgen Köhler Gabriele Raabe, Jürgen Köhler Institut für Thermodynamik, TU Braunschweig, 38106 Braunschweig, Germany Institut für Thermodynamik, TU Braunschweig, 38106 Braunschweig, Germany Motivation Results for the prediction of phase equilibria (VLE and VLLE) Equations of state or activity coefficient models for the determination of phase equilibria usually Predictions of the high-pressure VLE and VLLE were made using the SRK-EOS with ab initio- contain adjustable parameters. These parameters are determined by regressions of experimental data, NRTL in the PSRK-mixing rule. The resulting deviations of the calculated pressures from limiting the models by the availability and accuracy of these data. The present work represents the measurements are shown in the figure below, as well as those from predictions based on first approach to use ab initio interaction energies in activity coefficient models like NRTL to predict UNIFAC: 16 15 UNIFAC phase equilibria in a system with a van der Waals dominated interaction, requiring high level ab initio 14 ab initio NRTLMP4, αij = 0.3 • QCISD(T) yields slightly better results than 13 ab initio NRTLQCISD(T), αij = 0.3 methods to account for electron correlation. 12 exp. data MP4, that tends to overestimate the interaction 11 10 energies Eii, Eij and Ejj. 9 p (MPa) 8 7 • VLE-predictions with ab initio-NRTL and 6 T = 280 K Procedure of calculating interaction energies αij = 0.3 give excellent results for T > 200K. 5 4 3 The calculation of the interaction parameters ∆Eij of NRTL requires the knowledge of the For T < 200K better results are obtained 2 1 T = 220 K interaction energies in dimers of like and unlike molecules Eii, Eij and Ejj, that do not account for using α ij = 0.2. 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 intermolecular orientations and distances. The following is an outline of the steps used for our x'N ,x''N (mol/mol) • Over wide ranges of temperature and 50 2 2 approach to provide unique representative interaction energies Eii, Eij and Ejj: SRK-EOS + PSRK-MR + pressure, the predictions based on ab initio- ab initio-NRTL α12 = 0.2 NRTL are even superior to those using 40 ab initio-NRTL α12 = 0.3 • Construction of dimers (ii, ij, jj) with charac- UNIFAC. UNIFAC teristical different intermolecular orientations. 30 ∆pT= konst. (%) • Only for T < 133 K, ab initio-NRTL is inferior • Optimization of these initial configurations at and further variation of αij is needed to predict 20 the MP2/6-311G(3d,3p)-level. the VLLE correctly (αij = 0.11). 10 • Computation of the interaction energies of the optimized dimers at the MP4 or QCISD(T) / 0 100 120 140 160 180 200 220 240 260 280 300 6-311G(3d,3p) level using the supermolecule T (K) E approach. We used ab initio-NRTLQCISD(T) in different G -mixing rules to predict VLE by the PR- and the SRK-EOS. The comparison with 147 experimental data for T > 200K shows: • Correction of the BSSE by the counterpoise method. ab initio-NRTLQISD(T) SRK PR • Ab initio-NRTL gives good VLE-predictions α (αij = 0.3) used in ∆pm [%] ∆pm [%] • Calculation of the linear mean value of the with different kinds of gE-mixing rules and PSRK pref. = 0 2.62 2.76 energies of the same molecular pairs to obtain with both, the PR- and the SRK-EOS. MHV1 pref. = 0 2.95 2.81 Eii, Eij and Ej. LCVM pref. = - 3.63 3.04 • Best results were obtained with the PSRK- and HVOS pref. = ∞ 4.01 3.36 • Computation of ∆Eij = Eij –Ejj. the MHV1-mixing rule. CHV pref. = ∞ 5.14 4.35 UNIFAC with PSRK 4.57 5.50 Results for the system nitrogen (1) – ethane (2): E11 E22 E12 ∆E12 ∆E21 [J/mol] [J/mol] [J/mol] [J/mol] [J/mol] Discussion MP4 / 6 -311G(3d,3p) -446.510 -3732.673 -1368.956 2363.717 -922.446 Although the results using ab initio-NRTL are encouraging, it has to be mentioned, that QCISD(T) / 6-311G(3d,3p) -247.147 -3654.827 -1178.219 2476.608 -931.072 • the procedures of calculating ∆Eij assumes that the interaction parameters for activity coefficient models can be described as the averaged interaction energies of different minimum-energy configurations of dimers; The ∆Eij are then interpreted as the interaction parameter Cij in NRTL (with αij = 0.2 or 0.3) • restrictions concerning basis sets or cluster size are necessary because of the limitation of ab initio-NRTL currently available computational resources. Using the 6-311G(3d,3p)-basis set, the BSSE is not as small as desired.