Vapor–Liquid Equilibria of Mixtures Containing Ethanol, Oxygen, and Nitrogen at Elevated Pressure and Temperature, Measured with In Situ Raman Spectroscopy in Microcapillaries

Ethanol and oxygen containing gases are mixed in a T-junction at elevated pressure and then passed into a fused silica microcapillary, located in a heating block. Inside the microcapillary a Taylor flow of alternating liquid and vapor segments is formed. The thermodynamic equilibrium composition of the liquid and vapor segment depends on pressure and temperature. Their compositions are measured inside the microcapillary using in situ Raman spectroscopy. The main results obtained therefrom are temperature–composition (Tx) diagrams at conditions relevant for combustion engines [p = (3 to 8) MPa; T = (303 to 473) K]. Isothermal vapor–liquid equilibria (VLE) data are derived and given in pressure–composition (px) diagrams. The investigation of different gas mixtures containing oxygen and nitrogen allows furthermore the illustration of VLE data at constant pressure and temperature in ternary diagrams. The obtained results are compared to scarce literature data. An equation of state (Peng–Robinson EOS) is furthermore adjusted to the measured results.


I -Calibration results
The calibration results are given in detail in Table S1: for given pressure and temperature the set molar ratios of ethanol to nitrogen ( ), ethanol to oxygen ( ) and oxygen to nitrogen ( ), as well as the respective measured signal ratios ( , and ), and the respective standard uncertainties of the mean ( ( ), ( ) and ( )), calculated as the standard deviations of the measured signal ratios that were obtained by the 32 single spectra each.

II -Fitting of binary interaction parameters
The binary interaction parameters of the Peng-Robinson-EOS for ethanol/oxygen ( ) and ethanol/nitrogen ( ) were fitted by a least square approach (Levenberg-Marquardt algorithm) in the temperature range of = {303 to 463}K in steps of ∆ = 10 K, minimizing the error ( . ) of the objective function (S1) for each temperature. This function describes the deviation between the experimental pressure ( ) of the isothermal px-data points, given in supporting information B, and the respective calculated pressure obtained by the px-cycle of the PR-EOS, as shown in Figure S2. The results are given in Figure S1 and were fitted by straight lines (coefficients given in main manuscript). Figure S1 -fitting of binary interaction parameters ( ) of the Peng-Robinson-EOS by least square minimization of objective function (S1); an outlier at 443 K for ethanol/nitrogen was not considered for the linear fit

III -Modelling of VLE data with Peng-Robinson-EOS
The flowchart that describes the applied modelling of the Peng-Robinson-EOS is shown in Figure S2. Initial parameters are pressure ( ) and vapor phase mole fractions ( ), while fixing the temperature ( ) and liquid phase mole fractions ( ). Input parameters for the px-and Tx-cycle are hereby the acentric factors ( ), binary interaction parameters ( ), as well as critical temperatures ( , ) and pressures ( , ), to calculate phase-independent pure parameters ( , , ) and mixture parameters ( ), as well as phasedependent mixture parameters ( , ), fugacity coefficients ( ) and molar volumes ( ). In the ternary calculation cycle the liquid phase mole fraction of ethanol ( ) is iterated for a given liquid phase oxygen/nitrogen molar ratio ( ), in order to find the matching ternary (isothermal and isobaric) compositions for given temperature and pressure ( ). are termination criteria to either check isofugacity or the deviations between calculated and goal pressures in the Tx-and ternary cycles.

V -Henry's law coefficients
The Henry's law coefficients obtained in this study by the Peng-Robinson-EOS ( ) are given in

VI -Average percentage errors
The average percentage errors of pressure (∆ . ) and vapor phase composition (∆ , ) are calculated with the following equations (S3) and (S4) for each temperature for the number of available experimental points (np). The corresponding calculated values are obtained by the px-cycle of the Peng-Robinson-EOS (compare Figure S2). The results are given in Table S3 for the system ethanol/oxygen.

VII -VLE data
The VLE data (ordered isothermally) are given in the Tables S4, S5 and S6. The necessary data of Klima (ethanol/nitrogen) that has been used for the Peng-Robinson-EOS and the illustration of ternary VLE data are given in Table S7. The standard uncertainty of the mean mole fraction ( ) is calculated as the standard deviation of 32 mole fractions obtained by 32 single Raman spectra. As stated in the calibration section, the standard uncertainty in terms of pressure is 0.2 MPa and in terms of temperature is 0.3 K. All data are furthermore ordered as ternary VLE data in Table S8.  Table S5 -VLE data of the system ethanol/gas mix 1; ( ) = ( ) and ( ) = ( )  Table S6 -VLE data of the system ethanol/gas mix 2; ( ) = ( ) and ( ) = ( )