The gamma-phi (γ-Φ) or combined method was used for the regression of the measured VLE data. These chemicals are part of the constituent components in the industrial waste streams from petrochemical plants.
Classes of experimental VLE equipment
Static Method
The static-synthetic (non-analytical) method involves preparing a mixture of a certain known concentration and allowing the equilibrium of phases to occur in a cell, usually at isothermal conditions. Since only the measurement of the system pressure is required in the static synthetic or static non-analytical method, the main disadvantage of this method is the problem of complete degassing of the system.
Dew and Bubble Point Method
Dynamic Method
Features of Recirculating Still
For example, the condensate receiver is large and there is no agitation of the condensate (preferably mechanically), the measurement of the equilibrium temperature is unacceptable, regardless of whether the thermometer is located in the vapor phase or in the liquid. There is also the problem of partial vapor condensation on the wall of the boiling flask, which produces non-equilibrium vapors (Raal and Mühlbauer, 1998).
The Gillepsie Design
Modifications to the Gillespie Still
Some modifications to the still have been made in order to minimize some of the errors and limitations of the previous designs. The complexity of the device and its long hours to reach equilibrium are some of its limitations.
The Yerazunis (1964) Still Design
The Malanowski Still Design (1982)
1&2: mixing chamber; 3&4: equilibrium chamber; 5: cooking chamber; 6: vapor sampling point; 7: liquid sample point; 8: thermal well.
Low Pressure VLE still of Raal (Raal and Mühlbauer, 1998)
The problem of partial vapor condensation and heat loss was eliminated by vacuum jacketing the Cottrell tube and balance chamber. The concentric design around the filled section of the balance chamber minimizes the introduction of liquid droplets into the vapor phase and forces the vapor to surround the balance chamber, serving as a thermal barrier.
The VLE still of Joseph (Joseph, 2001)
Still originally designed by Raal, the VLE is capable of measuring isothermal and isobaric data, Joseph (et al., 2001) improved the isothermal operation of the VLE still by manually adjusting the pressure set point on the pressure regulator to achieve the desired temperature. This new design, which enabled both isobaric and isothermal operation of the VLE, was still based on a computer-assisted pulse-width modulation control strategy.
The modified VLE still of Ndlovu (Ndlovu, 2005)
Smooth and fast cooking was also achieved through the integration of internal and external heating elements. During the operation of the still, it was discovered that during the downward passage of vapor in the equilibrium chamber, partial vapor condensation occurred due to contact with the exterior walls.
The modified VLE still of Rinay Bhownath (Bhownath, 2008)
INTRODUCTION
Also, the fugitive coefficient of a saturated liquid or saturated vapor at equilibrium is given as:. Equation (3-8) can be replaced twice by the left side of equation (3-11) and by subtraction we get:. 3-13), where Vi is the molar volume of the liquid phase and is also a very weak function of P at temperatures well below the critical temperature Tc.
Fugacity coefficients from the virial equation of state
Hayden-O’Connell second virial equation of state
The model also accounts for the strong association and solvation effects found in systems containing organic acids. The terms (Bprost - nonpolar)ij and (Bprost - polar)ij refer to the contribution of lone pairs of molecules (nonpolar, non-bonded molecules) and (Bmerljiv)ij, (Brezan)ij and (Bchem)ij consider chemically bonded molecules.
The second virial correlation of Nothnagel et al. (1973)
KA and KB are the chemical equilibrium constant for the dimerization reaction on a pressure basis and are related to the true mole fractions and fugacity coefficients by: . P is the total pressure of the system; zi (i represents A1, A2, B1, B2) is the true species mole fraction; A1 and B1 represent the true mole fractions of monomers, and A2 and B2 are the true mole fractions of dimers.
The Pitzer-Curl correlation for the second virial coefficient
Activity and activity coefficient
The Wilson’s equation
In ASPEN Plus (the process simulator used for the regression of the experimental data in this work), the version of the Wilson model used for the regression of the experimental data does not use molar volumes of liquid. Two important advantages of the Wilson model are; it can be easily generalized to multicomponent systems without introducing parameters other than those for the constituent binary data, and can predict multicomponent properties from binary data.
The NRTL (Non-Random-Two-Liquid) model
Walas (1985) proposed that the non-random parameter values should be set to approximately 0.3 for non-aqueous systems and 0.4 for aqueous organic mixtures. Another advantage of the NRTL equation is that it can be used sufficiently for water systems compared to other models.
The UNIQUAC (Abrams and Prausnitz, 1975) model
This model has some disadvantages, which are: the diversity of the interdependence of the parameters, the concept of choosing a value for the non-random parameter, which can affect the accuracy of the regression. This model has shortcomings in terms of the need for pure component parameters and involves algebraic complexity.
Low pressure VLE data reduction
The combined method (γ-Φ) for VLE data regression
The combined method uses an activity coefficient model (Gibbs excess model) to determine the activity coefficient that accounts for the liquid phase non-idealities and an equation of state to determine the fugacity coefficient that accounts for the non-idealities in the vapor phase. Figures (3-2) and (3-3) illustrate the algorithm used in the γ-Φ method for the regression of isothermal (bubble point pressure) and isobaric (bubble point temperature) VLE data respectively.
Thermodynamic consistency testing
Point Test
The Direct Test
For the direct test, an index of one indicates data of high accuracy while an index of ten indicates poor quality data.
Infinite dilution activity coefficient
Excess Thermodynamic Properties
The molar Gibbs energy (GE) as a function of composition can be calculated from experimental VLE data using the parameters of the appropriate correlation equations. GE = HE - TSE (3-86) This method of estimating excess properties from experimental VLE isothermal data is limited by the accuracy of the measured data, linearity.
Equipment description
- The dynamic VLE recirculating still
- Pressure measurement and control
- Temperature measurement and control
- Sampling and composition analysis
A Pt-100 temperature sensor is placed in a glass tube placed inside the equilibrium chamber and extends to the bottom of the chamber to measure the equilibrium temperature of the mixture. The temperature in the equilibrium chamber was measured with a Pt-100 temperature sensor enclosed in a glass tube extending to the bottom of the chamber to ensure contact with the liquid and vapor phases.
Experimental procedure
Preparation of the VLE still
The presence of leaks at the station or at the node can lead to inaccurate data measurements. The remaining acetone in the kettle was evaporated by operating the still under vacuum at a very low pressure of about 5 kPa.
Temperature, pressure and GC calibration
A Shimadzu 2014 GC with a thermal conductivity detector (TCD) was used for phase composition analyzes in this work. A 4 m × 1/8 in. CRS Porapak Q stainless steel column was used for component separation.
Refractometer operation
Operating procedures
Isobaric operation
This maintains and controls the set pressure in the still using the two solenoid valves at subatmospheric pressure. This should provide sufficient agitation of the component to prevent temperature gradients.
Isothermal operation
Measurements for the second half of the composition range were then taken, repeating the same procedures as the first half. This procedure helps obtain many points in rarefied areas and also verifies the accuracy of the measurement, as the two halves of the phase diagram must meet without discontinuity (Nala, 2012).
Plateau region
The accuracy of the temperature, pressure and composition measurement as well as the purity of the chemicals used have a great influence on the accuracy of the measured experimental data. To ensure correct operation of the still, a test system consisting of cyclohexane (1) + ethanol (2) was therefore measured at 40 kPa and 313 K using the operating procedures described in Chapter 4.
Chemical Purity
The results of all measurements performed in this work are described in detail in this chapter.
Uncertainty measurement
The uncertainty in the measurement of phase composition by the Raal and Mühlbauer method is related to three sources: uncertainty from mass balance, uncertainty in conversion of TCD areas to composition, and uncertainty due to repeatability.
Vapour pressures
Operating conditions for the Shimadzu 2014 gas chromatograph
Binary vapour-liquid equilibrium measurements
Cyclohexane (1) + ethanol system (2)
The GC detector calibration plots, measured experimental data, plots of P-x1-y1 and x1-y1 for each isotherm are presented below. The GC detector calibration plots as well as the experimental data, P-x1-y1 and x1-y1 plots for each isotherm are presented below.
Vapour pressure data regression
This chapter focuses on the discussion and analysis of the experimental data measured in this work, which were presented in Chapter 5. The Antoine equation was chosen for the regression of the vapor pressure data because of its simplicity compared to the Wagner equation.
Refractometer calibration for the test system
Modelling results for the cyclohexane (1) + ethanol (2) system at 313.15 K
The NRTL-HOC model combination was used for the regression of the measured isothermal VLE data. For the NRTL-HOC model combination, the non-randomness parameter α12 for the operation was set to 0.47.
Modelling results for the cyclohexane (1) + ethanol (2) system at 40 kPa
Gas chromatograph calibration for the new systems
VLE data regression
Modelling results for the 1-propanol (1) + 4-methyl-2-pentanone (2) system
When the NRTL activity coefficient model was combined with the HOC and NTH correlations for this isotherm. When the NRTL activity coefficient model was combined with the HOC and NTH correlations, the NRTL-HOC model combination provided the best fit based on ∆y1avg.
Modelling results for the 2-propanol (1) + 4-methyl-2-pentanone (2) system
The P-x-y plots showing the comparison of the activity coefficient models for the three isotherms are shown in Appendix A. The plot also shows that the NRTL-HOC model combination used for the regression of the isothermal VLE data sets was a good fit.
Thermodynamic consistency testing results obtained for the systems measured
Consistency results for the 1-propanol (1) + methyl isobutyl ketone (2) system. 129
The NRTL-HOC model combination also provided the highest value for root mean square deviation at 353.15 K, which is 0.066. Table (6-8) summarizes the analysis obtained for the spot test and direct test for this system.
Consistency results for the 2-pentanone (1) + 2-methyl propan-1-ol (2) system. 131
If the slope of the plot is not linear, Maher and Smith suggest that x1x2/PD. Table (6-11) shows the comparison of the infinite dilution activity coefficient values obtained for the recently measured isothermal VLE data sets.
Excess Thermodynamic Properties
The newly measured isothermal VLE data except for the 2-propanol (1) + 4-methyl-2-pentanone (2) data are concluded to be thermodynamically consistent based on the results of the spot test (Van Ness, 1973 ) and direct test (Van Ness, 1995) performed for the data sets. A new expression for the excess Gibbs energy of partially or completely miscible systems.” American Institute of Chemical Engineers Journal.
