气液平衡

Vapor-liquid equilibrium (VLE) is a state where a pure component or mixture exists in both liquid and vapor phases at equilibrium, with no changes in macroscopic properties over time. VLE is essential to the design, operation, and analysis of many engineering processes, particularly separations like distillation, where understanding component distribution between phases enables engineers to optimize process efficiency and reduce operating costs.

In a heated mixture at equilibrium, the substance with the lower boiling point concentrates in the vapor phase while the substance with the higher boiling point remains predominantly in the liquid phase. Engineers express this using mole fractions: xi for the liquid phase and yi for the vapor phase. This compositional difference is depicted on an xy curve, which illustrates the relationship between component concentrations in each phase.

The activity coefficient (gamma) relates a component's fugacity in an actual mixture to the fugacity of an ideal solution with the same composition. It quantifies deviations from ideality and is calculated by measuring temperature, pressure, and the compositions of vapor and liquid phases in equilibrium. Activity coefficients are essential for predicting how mixtures will behave and for correlating experimental VLE data to thermodynamic models.

The Antoine equation calculates saturation vapor pressure using species-specific constants (A, B, and C) found in literature. Combined with measured temperature and liquid and vapor mole fractions, the Antoine equation allows engineers to directly calculate activity coefficients. This relationship, known as Raoult's law, simplifies VLE calculations by connecting saturation vapor pressure to equilibrium compositions.

Various compositions of methanol, isopropyl alcohol, and water are boiled in a VLE apparatus. Lower boiling point components vaporize and are collected separately while liquid gathers in the initial vessel. Once equilibrium is reached, both liquid and condensed vapor fractions are analyzed using gas chromatography to determine their compositions, enabling calculation of activity coefficients for the mixture.

Distillation columns separate mixtures based on component volatility, with different compositions in liquid and vapor phases on each tray. The more volatile component vaporizes and is collected at the column top, while the less volatile component remains liquid and drains to the bottom. VLE data determines the number of trays needed to achieve desired separation, helping engineers optimize the process while keeping operating costs low.

Flash separation exploits the principle that a liquid at or above its bubble point pressure partially evaporates when pressure is reduced. The preheated feed enters the separator as a mixture of liquid and vapor in equilibrium. The degree of vaporization and solute distribution between phases depends on the initial feed state, making VLE data critical for predicting separation outcomes and optimizing flash separator design.