First of all I would like to thank Dr. Walter Wukovits for his guidance throughout the project, great help and valuable suggestions for my work. Second, I want to thank Professor Anton Friedl for giving me the opportunity to work at TU Wien and collaborate with him and his group on this project. Also, I would like to thank for his willingness to help and support Professor Epaminondas Voutsas, who gave me the opportunity to realize this thesis at TU Wien, as well as for his valuable suggestions and recommendations throughout the experimental work and calculations.
In addition, I would like to thank everyone in the office and laboratory at TU Wien for their understanding and selfless help with everything I needed. And finally, I would like to thank my family and friends for their endless support and for the inspiration and encouragement to pursue my goals and dreams.
Introduction
The composition of the liquid will be determined by the mole fraction of the most volatile component (lowest boiling point). The parameters specifically defined for binary vapor-liquid equilibrium systems are temperature, pressure, and compositions of the constituent phases.
Vapor-Liquid Equilibrium
- Raoult’s Law
- Ideal mixtures
- Non-ideal mixtures
- Vapor pressure / composition diagrams
- Dalton’s Law
- Antoine Equation
- Deviations from Raoult’s Law – Non-ideal Systems
With vapor-liquid equilibrium, the standard state is almost always the pure component at the temperature and pressure of the mixture. It states that the partial vapor pressure of each component in an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. In this equation, pA and pB are the partial vapor pressures of components A and B.
The total vapor pressure of the mixture is equal to the sum of the values for A and B together at each composition. The August equation describes a linear relationship between the logarithm of the pressure and the reciprocal of the temperature.
Activity Coefficients
Activity Coefficient Models
- Van Laar equation
- Margules equation
- Wilson equation
- NRTL equation
- UNIQUAC equation
- UNIFAC equation
The estimation of the parameters in the equations of van Laar and Margules naturally requires experimental activity coefficients for the given binary system. For this purpose, regression analysis is made for all data to get the values of the parameters that give better fit. It is of course possible that the values of the parameters result from some experimental activity coefficients, by solving a system of two equations with two unknowns.
Margules and Van Laar equations fit multiple points, requiring regression of the parameters to optimize the fit. The main disadvantage of the NRTL model is the strong correlation between the two parameters of the model [27].
Effect of temperature on Vapor-Liquid Equilibria
Complete implementations of the UNIFAC method with a large number of functional groups are typically available in chemical engineering process design software. An inspection of the values of L at infinite dilution, calculated from the heat of mixing liquids in the International Critical Tables, reveals values as high as 2000 calories/mol for mixtures of organic liquids. To give an idea of the order of magnitude of the change in the activity coefficient with temperature, a 6 percent change in the activity coefficient results from a 30 oC change in temperature with L = 500 calories/mol.
If the left side of the various equations is written RT In γ instead of log γ, and the resulting parameters are considered independent of temperature, the activity coefficients will approach unity as the temperature increases, which corresponds to the general rule for organic liquids. Unfortunately, most of the available data on L have been measured only at room temperature, and there are indications that L changes rapidly with temperature [17].
Activity Coefficients at Infinite Dilution
The work of calculating the effect of temperature on the x-y diagram is significantly reduced when the activity coefficient curves can be fitted with van Laar or Margules equations. These equations are written in the form that the constants are terminal values of log γ. Activity coefficients for systems of organic liquids that have either positive or negative deviations from Raoult's law approach unity as temperature increases, thus approaching Raoult's law as a limit.
Sandler discusses theoretical and practical applications of infinite dilution activity coefficient (IDAC) values in chemical and environmental engineering. Addition of water to selective solvents (e.g. NMP + water) often increases the selectivity of the solvents used [5].
Methods for Determination of VLE
- Dynamic equilibrium stills
- Static VLE apparatus
- Composition determination
- Thermodynamic Consistency Test
- The Interdependence of Activity Coefficients
- Area Consistency Test
The composition of the boiling liquid and the vapor changes with time until a steady state is reached [17]. One challenge that should be mentioned in the use of the automated apparatus is the possible need to adjust the heat input to the Cottrell pump. Another disadvantage of this type of apparatus is the time required to produce an isotherm and calibrate the analyzer.
The static analysis method is the most common of the static methods for VLE measurements. The contents of the equilibrium cell are stirred to promote contact between the phases, thereby shortening the time it takes to reach equilibrium.
Experimental Measurement of VLE
- Setup for the determination of VLE
- Procedure for measuring a binary system at ambient pressure
- Calibration for the operation of the apparatus
- Temperature calibration
- Reproducibility of Results
The operating procedure is based on the principle of the circulation method (Dynamic VLE Still). Part of the liquid mixture is evaporated by an electric immersion heater (7) installed in the glass apparatus. The composition of the mixtures is obtained from the refractive indices of the samples or from GC analysis.
The refractive index is a function of temperature, the wavelength of the light source and the substance being examined. At the beginning, the ventilation of the apparatus is checked by opening valves and 20. The VLE apparatus is first filled with approximately 110 ml of the lower boiling substance (via the feed opening).
The liquid level in the reboiler has a great influence on the operation of the device and must be approximately 2 cm above the immersion heater. The measured liquid and vapor chamber compositions are identical and do not represent equilibrium. Then some liquid must be removed through the boiler vent valve (v. 21).
First, the binary Ethanol-Water system is being measured to determine the operating conditions of the VLE 602 apparatus. At 20% heating power and the liquid level is approximately half the distance between the immersion heater and the column. There is a constant flow of waste, however, the boil is still not calm.
Experimental Measurement of Phase Equilibrium Data
Experimental results
- Binary system Ethanol – Butan-2-ol
- Binary system Methanol – Ethanol
- Binary system Methanol – 2-Butanol
- Binary system Ethanol – Water
- Binary system Methanol – Water
- Binary system Acetone – Ethanol
- Binary system Acetone – Buta-2-nol
Since molecules in the binary system are similar, the vapor-liquid equilibrium can be represented by the Van Laar activity coefficient model. The reason for this behavior may be the fact that samples for refractometer analysis are analyzed immediately after collection. Although dependent on the chosen dataset, the interaction parameters (Table 4) obtained from datasets generated by measuring the refractive index are close to the values from the literature and give good accuracy with respect to the xy plot and the literature curve ( Figure 15). ).
Surprisingly, data obtained from GC analysis also give reasonable results for interaction parameters (Table 5) and the equilibrium plot (Figure 16). This may be due to the mentioned problem of evaporation of the samples during the period of refrigeration, although the results fit well in light of the poor experimental data from GC analysis. In Table 7, one of the interaction parameters is not negative as it was assumed to be according to the literature and which applies to the Van Laar model, indicating thermodynamic inconsistencies, although experimental ELO data fit well with the literature.
The interaction parameters obtained from infinite dilution (refractive index) differ greatly from literature values. The obtained values for interaction parameters of infinite dilution based on GC data (Table 9) were positively calculated in contrast to literature data. Although it is an aqueous mixture, the Van Laar model can accurately predict the behavior of the system.
However, surprisingly, the values calculated with the Van Laar activity coefficient model predict the xy data with excellent fit to the literature. There is not much literature data for the acetone-butan-2-ol system and the system has not yet been extensively investigated. This is the reason why no literature interaction parameters were found for the Van Laar activity coefficient model.
Consistency results
However, the Van Laar activity coefficient model fails to accurately calculate mixture activity coefficients.
Summary and Outlook
Vapor-liquid equilibrium measurements are time-consuming and require careful operation of the apparatus. The instrumentation is dependent on the temperature in the laboratory environment, and the cold days condense less steam than warmer days. For better and more accurate results, the apparatus should also run at least one round without taking measurements the day before performing the experiment.
Additionally, small amounts of mixture must be added and extracted during the experiment to maintain equilibrium in the separation chamber and to collect sufficient data points. In summary, the results show that the device and the proposed procedure allow a satisfactory determination of the vapor-liquid equilibrium of binary organic and aqueous systems. Van Laar's activity coefficient model – despite its simplicity – allows a good reproduction of x-y plots of the investigated systems based on regressive interaction parameters.
Both parts – device and model – are thus suitable to be used for educational and research purposes in the chemical engineering laboratory at TU Wien.
Nomenclature
Objective function analysis in minimizing binary VLE data for asymmetric mixtures at high pressure. Phase behavior of supercritical CO2 + ionic liquid mixture: thermodynamic consistency test of experimental data. An analysis of the industrial use of a phase equilibrium prediction model based on thermodynamic perturbation theory.
Web address (accessed 3 February 2016) http://www.eng.umd.edu/~nsw/chbe446/ThermoModels-ElliotLira.pdf.
Ethanol – Butan-2-ol
Methanol – Ethanol
Methanol – Butan-2-ol
Ethanol – Water
Methanol - Water
Acetone - Ethanol
Acetone – Butan-2-ol