VLE Consistency Test Workbook (Gibbs-Duhem Numerical Validation)
The VLE Consistency Test Workbook is an Excel-based computational tool that implements the Gibbs-Duhem equation numerically to validate the thermodynamic consistency of experimentally measured or simulated vapor-liquid equilibrium (VLE) data. It checks whether a given set of P–x–y or T–x–y data satisfies the fundamental constraint imposed by the second law of thermodynamics on activity coefficients. A consistent dataset yields a near-zero integrated Gibbs-Duhem residual across the composition range.
📖 Overview
📑 Key Components
🎯 Applications
- ✓ Validation of laboratory VLE measurements prior to parameter regression
- ✓ Quality control of published binary/multicomponent VLE datasets
- ✓ Educational demonstration of thermodynamic consistency principles in undergraduate/graduate courses
📐 Key Formulas
Gibbs-Duhem Equation (activity coefficient form)
x_1 \frac{d \ln \gamma_1}{dx_1} + x_2 \frac{d \ln \gamma_2}{dx_1} = 0
Ensures thermodynamic consistency of activity coefficients γ₁ and γ₂ in a binary mixture at constant T and P
Activity Coefficient Estimation (binary, low-P)
\gamma_i = \frac{y_i P}{x_i P_i^{sat}(T)}
Computes γᵢ from experimental vapor-phase mole fraction yᵢ, total pressure P, liquid-phase mole fraction xᵢ, and pure-component saturation pressure Pᵢ^sat(T)
Consistency Integral (Van Ness criterion)
I = \left| \int_{0}^{1} \left( x_1 \frac{d \ln \gamma_1}{dx_1} + x_2 \frac{d \ln \gamma_2}{dx_1} \right) dx_1 \right|
Quantifies deviation from consistency; I < 0.02 generally accepted as consistent