What is the NRTL equation?

The NRTL equation can be used to determine the properties of multicomponent solutions based on binary data. Its main advantage is that it can be applied to partially miscible systems, making it particularly suitable for calculating liquid-liquid stratified systems; it is a three-parameter equation

The calculation methods for vapor-liquid equilibrium can be summarized into two categories: the single-equation method (both the vapor and liquid phases’ fugacities are expressed using fugacity coefficients)； Multi-equation method (the vapor phase fugacity is expressed using a fugacity coefficient, while the liquid phase fugacity is expressed using an activity coefficient). 3 The single-equation method, namely the equation of state method: it uses only one equation of state to calculate the fugacities of both the vapor and liquid phases simultaneously. Equation of state further includes cubic equation of state and multiparameter equation of state. 3.1 Cubic equation of state The cubic equation of state can be expanded as a cube of volume (or density). Such equations have few parameters, offer great flexibility, and can also be solved manually. Their common feature is the ability to express pressure as two components: a repulsive term and an attractive term. Abott generalized existing cubic equation of state into a universal form: 3.1.1 Two-parameter equation of state. Early examples of such equations include the van der Waals equation, which, although not very accurate, has a simple form. The modern development of cubic equation of state began with the RK equation, which is applicable to gaseous phases. It offers significantly higher accuracy when calculating non-polar and weakly polar compounds compared to the vdW equation, but it still exhibits considerable errors for most strongly polar compounds. The SRK equation, derived by modifying the RK equation using Soave’s method, is suitable for calculations involving two-phase systems of vapor and liquid. It provides high accuracy in determining the vapor-liquid equilibrium of pure hydrocarbons or hydrocarbon mixtures, which is why it is widely used in industry. West and Erbar tested its application to light hydrocarbon systems and reported that this equation is quite accurate for vapor-liquid equilibrium. Like the SRK equation, another equation commonly used in engineering phase equilibrium calculations is the PR equation. The latter is superior in predicting the molar volume of liquids. Later, Stryjek and Vera made two further revisions to the PR equation, naming them PRSV and PRSV2 respectively. They offer improved computational accuracy compared to the original PR equation. Twu also proposed the RK-Twu and PR-Twu equations for the RK and PR equations, which offer significantly improved accuracy in calculating vapor pressures compared to the PR and PRSV equations. 3.1.2 Three-parameter equation of state The three-parameter equation of state includes the PT equation proposed by Patel and Teja, the Harmens-Knapp equation, the Lee-Erbar-Edmister equation, and others. The PT equation is used to calculate the saturated gas and liquid densities of some polar and non-polar pure substances, with relatively small average deviations; it also yields good results for calculating the vapor-liquid equilibrium of systems such as light hydrocarbons and alcohol-water mixtures. Three-parameter equations can yield a critical compressibility factor related to the material; the presence of multiple parameters helps improve the accuracy of the equation, but it also reduces its simplicity and ease of calculation. Over the past 20-odd years, improvements to cubic equation of state models have intensified, with significant progress made in both the attractive and repulsive terms; however, these two aspects should not be treated separately. Guo Tianmin and others have commented that \"it is insufficient to improve only the van der Waals repulsive term – corresponding improvements are also needed for the attractive term.\" It is generally believed that higher-order state equations with more equation parameters have a wider range of applicability and higher accuracy. But the computational load and complexity often increase as well. In today’s era of highly advanced computer technology, the practical application and research of multi-parameter equations have received significant attention. 3.2 Multiparameter state equations: The virial equation has a solid theoretical foundation. It is generally expressed using its two-term truncated form at T

It’s explained in great detail; I’ve learned from it. My previous understanding of this method wasn’t very accurate

During simulation calculations, it is necessary to choose a thermodynamic method. When dealing with different material compositions, it can be difficult to decide which method to use; especially for similar situations (such as non-ideal solutions), there are several thermodynamic methods available. Yet the gas-liquid equilibrium data obtained using these methods still differ to some extent. It’s not clear whether such differences represent acceptable errors, and this makes it even harder to decide which method to select.

NRTL is an abbreviation for Non-Random Two Liquids, meaning non-random two-phase liquids; as the name suggests, it is applicable to systems in which the liquid phases are not completely miscible

Good things keep it ~~

Reply to 3# Wanderer in the Far Lands: What a great post! I’ve learned something from it; I support you!

Thank you!

The fugacity of the components in a mixture is calculated from the activity coefficient model; the NRTL equation is applicable to systems with incompletely miscible liquid phases!