5 – phase equilibria in fluid systems


Textbook Examples:

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05.01 Poynting factor for Ethanol and Water at Various Pressure
Differences (p. 188)


05.02 Fugacity coefficients and Real Gas Factor for the System
Ethanol-Water Using the Virial Equation (p. 188)


05.03 Activity Coefficients from Experimental xyPT-Data (p. 192)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.04 Construct a Diagram with gE, hE and –TsE (p. 197)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.05 Temperature Dependence of the Activity Coefficients (p. 199)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.06 Activity Coefficients at Infinite Dilution at Different Temperatures Using the Partial Molar Excess Enthalpy at Infinite Dilution (p. 200)


05.07 Excess Volume of the Liquid Mixture Ethanol – Water (p. 201)


05.08 Activity Coefficient of the Monomer in a Polymer Using the Athermal Flory-Huggins Equation (p. 205)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.09 Compare Experimental VLE to Wilson Equation Results (p. 207)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.10 Thermodynamic Consistency Using the Area Test (p. 219)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.11 VLE of N2 – CH4 Using SRK (p. 238)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.12 Azeotropic Points of the System Acetone – Methanol (p. 245)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.13 Estimate the Temperature Dependence of the Azeotropic Composition
Using the Heat of Vaporization (p. 247)


05.14 Henry Constant for CO2 from Phase Equilibrium Data (p. 260)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS



05.16 Henry Constant for Methane in Benzene at 60 °C with the Help of the Soave-Redlich-Kwong Equation of State (p. 262)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.17 Henry Constant for Methane in Benzene at 60 °C Using the Method
of Prausnitz and Shair (p. 264)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.18 VLLE of n-Butanol – Water at 50°C Using UNIQUAC (p. 271)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


05.19 Liquid-Liquid Equilibrium for the System Water – Ethanol – Benzene – K-Factor Method UNIQUAC (p. 275)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS



05.21 VLE of Hexane-Butanone-2 Via UNIFAC (p. 286)
Mathcad (2001) – Solution (zip) – step by step
Mathcad (2001) – Solution as XPS- step by step

Mathcad (2001) – Solution (zip) – as function
Mathcad (2001) – Solution as XPS – as function


05.22 Liquid-Liquid Solubility for Alkane-Water from Empirical Correlation (p. 302)


Additional Problems:

P05.01 VLE Calculation For the System Ethanol – Water Using Wilson, NRTL and
UNIQUAC
Calculate the pressure and the vapor phase mole fraction for the
system ethanol (1)- water (2) at 70°C with the help of the different gE-models
(Wilson, NRTL, UNIQUAC) for an ethanol mole fraction of 0.2152 using the
interaction parameters, auxiliary parameters and Antoine constants given
in Fig. 5.30 and assuming ideal vapor phase behavior. Besides total and
partial pressures and vapor phase composition, calculate also K-factors
and separation factors. Repeat the calculation using the real gas
factors φ1=0.9955 and φ2=1.0068.

Mathcad (2001) – Solution (zip) (Wilson)
Mathcad (2001) – Solution as XPS

Mathcad (2001) – Solution (zip) (NRTL)
Mathcad (2001) – Solution as XPS

Mathcad (2001) – Solution (zip) (UNIQUAC)
Mathcad (2001) – Solution as XPS


P05.02 Regression of UNIQUAC Parameters to Binary VLE Data For the Mixture Ethanol – Water
Regress the binary interaction parameters of the UNIQUAC model to the isobaric VLE data measured by Kojima et al. at 1 atm and listed below. As objective function, use:
a) relative quadratic deviation in the activity coefficients
b) quadratic deviation in boiling temperatures
c) relative quadratic deviation in vapor phase compositions
d) relative deviation in separation factors
Adjust the vapor pressure curves using a constant factor to exactly match the author’s pure component vapor pressures.

Reference: Kojima K., Tochigi K., Seki H., Watase K., Kagaku Kogaku, 32, p149-153, 1968

Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.03 Experimental VLE Data and Modified UNIFAC and VTPR Predictions for the Mixture Ethanol – Water
Compare the experimental data for the system ethanol – water measured at 70°C (see
Fig. 5.30 and below) with the results of the group contribution method modified UNIFAC and the group contribution equation of state VTPR.
Reference: Mertl I., Collect.Czech.Chem.Commun., 37(2), 366-374, 1972

Modified UNIFAC:

Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS

VTPR:
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.04 VLE Calculation For the System Ethanol – Benzene Using the Wilson Model

Calculate the Pxy-diagram at 70°C for the system ethanol (1) – benzene (2) assuming ideal vapor phase behavior using the Wilson equation. The binary Wilson parameters Λ12 and
Λ21 should be derived from the activity coefficients at infinite dilution (see Table 5.6). Experimentally the following activity coefficients at infinite dilution were determined at this temperature: (see solution file)

Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.05 Azeotropic Composition of Homogeneous Binary Mixtures Using
Modified UNIFAC
Determine the azeotropic composition of the following homogeneous
binary systems
a) acetone – water
b) ethanol – 1,4-dioxane
c) acetone – methanol
at 50, 100, and 150°C using the group contribution method modified UNIFAC.
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.06 Discontinuous Distillation of Ethanol – Water Contaminated with Methanol
In the manual of a home glass distillery (s. Fig. 1) the following recommendation is given: “After some time liquid will drip out of the cooler. You are kindly requested to collect the first small quantity and not to use it, as first a methanol enrichment takes place.” Does this recommendation make sense? The purpose of the glass distillery is to enrich ethanol. Consider the wine to be distilled as a mixture of ethanol (10 wt.-%), methanol (200 wt.-ppm) and water. The one stage distillation takes place at atmospheric pressure.

Calculate the percentages of methanol and ethanol removed from 200 g feed, when 10 g of the distillate is withdrawn. For the calculation the modified UNIFAC method should be applied. The constants for the Antoine equation for ethanol and water can directly be taken from Fig. 5.30. For methanol the vapor pressure constants and molar mass are given in Appendix A. For the calculation ideal vapor phase should be assumed.
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.07 VLE Behavior, hE data, Azeotropic Data and Activity Coefficients at Infinite Dilution for Pentane – Acetone Using Modified UNIFAC
Calculate the VLE behavior, hE data, azeotropic data and activity coefficients at infinite dilution for the system pentane-acetone at 373K, 398K and 423K using modified UNIFAC. The results are shown graphically in Fig. 5.103.
The vapor pressure constants are given in Appendix A. Experimental data can be downloaded from the textbook page on http://www.ddbst.com. For the calculation by modified UNIFAC ideal vapor phase behavior should be assumed.
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.08 Mixture Data For the System Acetone – Hexane Using DDBSP
Using the free Explorer Version of DDB/DDBSP, search for mixture data for the system acetone – hexane.
a) Plot the experimental pressure as function of liquid and vapor phase composition
together with the predictions from UNIFAC, mod. UNIFAC and PSRK for the data sets at 318 K and 338 K.
b) How large are the differences in the azeotropic composition as shown in the plot of
separation factor vs. composition?
c) Plot the experimental heat of mixing data as function of liquid phase composition together with the predictions from UNIFAC, mod. UNIFAC and PSRK for the data sets at 243 K, 253 K, and 298 K. Interpret the linear part in some of the calculated heat of mixing curves.
d) Plot the experimental LLE data together with the results from UNIFAC and mod.
UNIFAC. What led to the improved results in case of mod. UNIFAC?
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.09 Experimental and Predicted VLE Data For the Systems CO2 – n-Hexane and CO2 – Hexadecane Using DDBSP
Using the free Explorer Version of DDB/DDBSP, search for mixture data for the systems
CO2 – n-hexane and CO2 – hexadecane. Plot the experimental high pressure VLE data (HPV) together with the predictions from PSRK. Compare the results to those of VTPR (Fig. 5.99-d) and examine the results for SLE in the binary mixture CO2 – n-hexane.
DDB Explorer Version demonstration video

P05.10 Regression of Isobaric VLE Data for the System Methanol –
Toluene
Calculate the activity coefficients in the system methanol (1)–toluene (2) from the data measured by Ocon J., Tojo G., Espada L., Anal.Quim., 65, 641-648, 1969 at atmospheric pressure assuming ideal vapor phase behavior. Try to fit the untypical behavior of the activity coefficients of methanol as function of composition using temperature independent gE-model parameters (Wilson, NRTL, UNIQUAC). Explain why the activity coefficients of methanol show a maximum at high toluene concentration.

The vapor pressure constants are given in Appendix A. Experimental data as well as molar volumes, r and q values can be downloaded from the textbook page on http://www.ddbst.com. For the calculation, ideal vapor phase behavior should be assumed.
auxiliary data download (xlsx)
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.11 Prediction of Henry Constants for Different Gases in Methanol Using PSRK and VTPR

Predict the Henry constants of methane, carbon dioxide and hydrogen sulfide in methanol in the temperature range -50 – 200 °C with the help of the group contribution methods PSRK and VTPR.
Compare the predicted Henry constants with experimental values from the textbook page on www.ddbst.com.

auxiliary data download
Math
cad (2001) – Solution
(zip)
Mathcad (2001) – Solution as XPS


P05.12 Prediction of Solubilities at Different Partial Pressures and for Different Gases in Methanol Using PSRK and VTPR
Predict the solubility of methane, carbon dioxide and hydrogen sulfide in methanol at a temperature of ­30°C for a partial pressure of 5, 10 and 20 bar using the PSRK and VTPR group contribution equations of state. Compare the results with the solubility obtained using Henry’s law and the Henry constants predicted in problem P05.11.
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS


P05.13 Retrieval, Visualization, Prediction and Regression of Data For
Subsystems of the System Methanol – Methane – Carbon Dioxide Using DDBSP
In the free DDBSP Explorer Edition, search for data for all
subsystems of the system methanol – methane – carbon dioxide.
a) Compare the available gas solubility data with the results of the PSRK method via the data prediction option in DDBSP.
b) Plot the available high pressure VLE data (HPV) for the system methanol – carbon dioxide together with the predicted curve using the PSRK method. Examine and familiarize yourself with the different graphical representations.
c) Regress the dataset 2256 using the Soave-Redlich-Kwong equation of state with the quadratic mixing rule and a gE mixing rule with activity coefficient calculation via the UNIQUAC model. Explain the differences.
DDB Explorer Version demonstration video


P05.14 Solubility of Benzene in Water from LLE Data and
Activity Coefficients at Infinite Dilution Using DDBSP
In the free DDBSP Explorer Edition, search for all mixture data
for the system benzene – water. Calculate the solubility of benzene in
water from the experimental activity coefficients at infinite dilution
and compare the results to the experimental LLE data.
DDB Explorer Version demonstration video


P05.15 Azeotropic Points in Binary Systems Using the Regular
Solution Theory, UNIFAC and Modified UNIFAC
Examine with the help of the regular solution theory, UNIFAC and
modified UNIFAC if the binary systems benzene – cyclohexane and benzene
– n-hexane show an azeotropic point at 80 °C. In case of the regular
solution theory, calculate the solubility parameter from the saturated
liquid density and the heat of vaporization using Eq. 5.70. All required
data are given in Appendix A, H and I.
Mathcad (2001) – Solution (zip)
Mathcad (2001) – Solution as XPS