Composition of LCO in vapor phase (wt%) The effect of applying the minimization of the Gibbs energy with phase stability tests on the prediction of the amount of vaporized middle distillate in presence of hydrogen at hydrotreating (HDT) conditions (70.9 bars and 250-420 degrees C) is studied. The Peng-Robinson (PR) thermodynamic model is used to fit the H-2-pseudocomponents interaction coefficients with experimental data and solving vapor-liquid equilibrium (VLE) by minimizing the Gibbs energy with stability tests. The steepest descent and BFGS (Broyden, Fletcher, Goldfarb, and Shanno) quasi Newton minimization methods are used to solve the VLE with stability test. The optimization of interaction parameters is done by the nonlinear systems Simplex method with a computational tool. The methodology was validated with information reported in the literature of two binary systems: (1) trans-2-hexen-1-ol (C6H12O)/CO2 at 30 degrees C and 65.3-150.0 bars, and (2) H2S/CH4 at -83 degrees C and 40.53 bars. The developed methodology is useful, allows for calculating the VLE through the catalytic bed and the variation in vapor and liquid flows, compositions and thermo physical properties. (C) 2015 Elsevier Ltd. All rights reserved.