📦 Resource zip

VLE Regression Toolkit (Excel + Python Scripts)

The VLE Regression Toolkit is a computational resource combining Excel-based interfaces and Python scripts to regress vapor–liquid equilibrium (VLE) data for thermodynamic modeling, enabling parameter estimation for equations of state (EoS) and activity coefficient models. It facilitates fitting binary and multicomponent phase equilibrium data to models such as NRTL, UNIQUAC, Peng–Robinson, and Soave–Redlich–Kwong. The toolkit bridges spreadsheet usability with programmatic flexibility for robust, reproducible thermodynamic parameter optimization.

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📖 Overview

Vapor–liquid equilibrium (VLE) regression is essential for designing and simulating separation processes like distillation, extraction, and absorption in chemical engineering. Accurate thermodynamic models require precise interaction parameters—such as binary interaction coefficients (k_ij) in EoS or energy parameters (α_ij, τ_ij) in activity coefficient models—which are determined by minimizing the deviation between experimental VLE data (e.g., T–x–y, P–x–y, or bubble/dew point measurements) and model predictions. The VLE Regression Toolkit integrates Excel for intuitive data input, visualization, and preliminary analysis (e.g., consistency checks via Van Ness test), while Python scripts (using libraries like SciPy, NumPy, and CoolProp) perform nonlinear least-squares optimization, uncertainty quantification, and sensitivity analysis. It supports both local composition models (NRTL, UNIQUAC) for highly non-ideal liquid phases and cubic EoS (PR, SRK) coupled with mixing rules (e.g., van der Waals one-fluid) for high-pressure or supercritical applications. The toolkit emphasizes traceability, reproducibility, and pedagogical clarity—making it valuable for academic instruction, industrial process design, and research validation of new thermodynamic models.

📑 Key Components

1 Excel workbook with interactive VLE data templates and residual plots

2 Python scripts for objective function definition, parameter optimization, and Jacobian computation

3 Thermophysical property backend (e.g., CoolProp or REFPROP integration for pure-component properties)

🎯 Applications

✓ Parameter estimation for activity coefficient models in solvent design
✓ Calibration of cubic equation-of-state parameters for hydrocarbon or CO₂-containing mixtures
✓ Validation and benchmarking of new thermodynamic models against NIST TRC or DDBST experimental databases

📐 Key Formulas

Bubble Pressure (Raoult’s Law Extension)

P = \sum_i x_i \gamma_i P_i^{sat}(T)

Calculates total pressure at bubble point for a liquid-phase mixture using activity coefficients (γ_i) and pure-component saturation pressures (P_i^sat)

Objective Function (Weighted Sum of Squares)

SSE = \sum_{j=1}^{N} w_j \left[ y_j^{exp} - y_j^{calc}(\theta) \right]^2

Minimized residual sum of squares for regression, where y_j^exp are experimental values (e.g., vapor-phase mole fractions), y_j^calc depends on adjustable parameters θ, and w_j are weighting factors

NRTL Activity Coefficient

\ln \gamma_i = \frac{\sum_j x_j G_{ji} \tau_{ji}}{\sum_k x_k G_{ki}} + \sum_j x_j \left[ \frac{G_{ij}}{\sum_k x_k G_{kj}} (\tau_{ij} - \sum_l \frac{x_l G_{lj} \tau_{lj}}{\sum_k x_k G_{kj}}) \right]

Computes activity coefficient γ_i for component i using NRTL model parameters τ_ij (energy interaction) and G_ij (non-randomness factor)

🔗 Related Concepts

Phase Equilibrium Thermodynamics Nonlinear Parameter Estimation Activity Coefficient Models Cubic Equations of State Thermodynamic Consistency Testing

📚 References

DDBST GmbH – Data and Software for Thermodynamic Properties

CoolProp: Open-Source Thermophysical Property Library

NIST ThermoData Engine (TDE): VLE Database and Modeling Tools

#thermodynamics #vle #equation-of-state #parameter-regression #chemical-engineering