Phase Equilibrium Simulator

LLE describes the distribution of components between two immiscible liquid phases. Key concepts include:

• Binodal Curve: Boundary between single-phase and two-phase regions
• Tie Lines: Connect equilibrium compositions in the two phases
• Critical Point: Temperature where the two phases become identical
• Distribution Coefficient: Ratio of component concentrations in the two phases

Applications: Liquid-liquid extraction, solvent recovery, phase separation

Key Equations: NRTL, UNIQUAC, UNIFAC models for activity coefficients

SLE describes the equilibrium between solid and liquid phases. Key concepts include:

• Melting Point Depression: Lowering of melting point by impurities
• Eutectic Point: Composition with lowest melting temperature
• Solid Solution: Homogeneous solid mixture of components
• Phase Diagrams: Temperature-composition diagrams showing solid-liquid regions

Applications: Crystallization, freeze concentration, alloy formation, pharmaceutical purification

Key Equations: Schröder-van Laar equation, regular solution theory

Flash calculations determine the phase distribution when a mixture is partially vaporized or condensed. Key concepts include:

• Vapor Fraction: Fraction of feed that becomes vapor (0 to 1)
• K-values: Equilibrium ratios (y_i/x_i)
• Rachford-Rice Equation: Fundamental equation for flash calculations
• Phase Envelope: Region where two phases coexist

Applications: Separator design, process simulation, reservoir engineering

Key Equations: Rachford-Rice equation, successive substitution, Newton-Raphson method

Vapor-Liquid Equilibrium (VLE) describes the distribution of components between vapor and liquid phases at equilibrium. It is governed by the equality of chemical potentials in both phases.

Liquid-Liquid Equilibrium (LLE) describes the distribution of components between two immiscible liquid phases. This occurs when components have limited mutual solubility.

Key differences:

• VLE involves phase change (vaporization/condensation)
• LLE occurs between two liquid phases without phase change
• VLE is temperature and pressure sensitive
• LLE is more sensitive to composition and temperature
• VLE calculations use vapor pressure data
• LLE calculations use activity coefficient models

NRTL (Non-Random Two-Liquid) and UNIQUAC (UNIversal QUAsiChemical) are both local composition models used for non-ideal mixtures.

Use NRTL when:

• Dealing with polar and non-polar mixtures
• Predicting liquid-liquid equilibrium (LLE)
• Working with systems containing water and organics
• You have experimental binary parameters available

Use UNIQUAC when:

• Working with complex molecular structures
• Dealing with size and shape differences in molecules
• You want a more theoretical basis for calculations
• Extending to group contribution methods (UNIFAC)

Key considerations:

• NRTL has three parameters per binary, UNIQUAC has two
• UNIQUAC requires molecular structural parameters
• NRTL is generally easier to parameterize
• Both models work well for most applications

K-values (equilibrium ratios) are fundamental to phase equilibrium calculations:

K_i = y_i / x_i

Where:

• y_i = mole fraction of component i in vapor phase
• x_i = mole fraction of component i in liquid phase

Interpreting K-values:

• K > 1: Component concentrates in vapor phase (volatile)
• K = 1: Equal distribution between phases (azeotrope)
• K < 1: Component concentrates in liquid phase (heavy)
• K → 0: Component is non-volatile (stays in liquid)
• K → ∞: Component is super-volatile (goes to vapor)

Relative volatility compares separation ease:

α_ij = K_i / K_j

Higher α values indicate easier separation by distillation.

Azeotropes are constant-boiling mixtures where vapor and liquid have identical compositions, creating distillation boundaries.

Causes of azeotrope formation:

• Molecular interactions: Hydrogen bonding, dipole-dipole interactions
• Non-ideal behavior: Deviations from Raoult's Law
• Specific component combinations: Certain pairs form azeotropes naturally

Types of azeotropes:

• Minimum-boiling: Boiling point lower than pure components (e.g., ethanol-water)
• Maximum-boiling: Boiling point higher than pure components (e.g., chloroform-acetone)
• Heterogeneous: Two liquid phases in equilibrium (e.g., water-benzene)

Impact on separation:

• Conventional distillation cannot separate azeotropic mixtures
• Special techniques required: extractive distillation, pressure-swing distillation, or membrane separation
• Azeotropes define distillation boundaries in composition space

Common azeotropic systems:

• Ethanol-Water: 95.6% ethanol at 78.2°C
• Acetone-Chloroform: Maximum-boiling azeotrope
• Benzene-Water: Heterogeneous azeotrope

The accuracy of phase equilibrium calculations depends on several factors:

Factors affecting accuracy:

• Thermodynamic model selection: Appropriate model for the system
• Parameter quality: Accuracy of binary interaction parameters
• Data availability: Experimental data for parameter regression
• System complexity: Number of components and their interactions
• Operating conditions: Temperature and pressure ranges

Typical accuracy ranges:

• Ideal systems: ±1-3% error in composition predictions
• Non-ideal systems with good parameters: ±3-5% error
• Complex systems with limited data: ±5-10% error
• Predictive methods (UNIFAC): ±10-20% error

Improving accuracy:

• Use experimental data to regress model parameters
• Select appropriate thermodynamic model for the system
• Validate predictions with experimental measurements
• Consider uncertainties in input parameters
• Use more sophisticated models for critical applications

Limitations:

• Models are approximations of complex molecular behavior
• Extrapolation beyond parameterization range reduces accuracy
• Association phenomena (e.g., hydrogen bonding) are challenging to model
• High-pressure systems require equations of state with volume translation