Simplified Approach to the Parameterization of the NRTL Model for Partially Miscible Binary Systems: Tττ LLE Methodology

Abstract

A new approach to parameterizing the NRTL model for binary liquid–liquid equilibria (LLE) is presented. It allows for the incorporation of a priori knowledge into the parameterization procedure rather than using the “black box” approach often employed. The method first converts the compositional Txx data to a set of unique binary interaction parameters, Tττ data. Thereafter, the second step improves the parameterization of frequently used temperature-dependent parameters (TDPs) by reducing the traditional nonlinear regression problem to simpler linear regression. This method is less susceptible to poor initial guesses, finding local minima, and significantly reduces computational requirements, with comparable/improved performance to published parameters. A total of 29 binary systems, including upper and/or lower critical solution temperatures, were evaluated using the approach to provide generalized recommendations and understanding of the TDP requirements for each system type. Inclusion of such information and use of the approach will significantly simplify multicomponent LLE model parameterization.

Simplified Approach to Understanding, Evaluating, and Parameterizing the NRTL Model for the Description of Binary VLE: Tττ-VLE Approach

“…The black box parameterization procedure is replaced by an explicit evaluation of each BIP obtained from azeotropic data as a function of temperature, Tτ evaluations. This concept is an extension of previous work on the correlation of binary liquid–liquid equilibrium (LLE) phase behavior (the Tττ-LLE approach) to the correlation of azeotropic VLE data in this work (Tττ-VLE approach). The practical benefits of and insight to be gained from the Tττ-VLE approach are discussed in a case study on the correlation of binary (alcohol + hydrocarbon) systems.…”

“…The most notable difference is the shape of the miscibility boundary. A detailed discussion on such boundaries is presented in recent studies. , Of particular interest is the difference in the shapes of the boundaries between BIPs of −2 to 4, where a protrusion is observed for larger non-randomness parameters. This region is of importance for the prediction of the very common Type II VLE behavior where the predictions in the protrusion account for the increased proportion of Type II azeotropic predictions for α ij = 0.47 in comparison to α i j = 0.20.…”

“…Moreover, due to the proximity of the Type II region on the ττ-plane to the miscibility boundary, the possibility of incorrectly predicting heterogeneous LLE or VLLE behavior is a concern. For example, the default NRTL parameters provided in Aspen Plus V11 process simulator for the completely miscible (water +1-propanol) system incorrectly predict LLE and/or VLLE for lower temperatures (e.g., LLE behavior is predicted at 298.15 K and a heterogeneous minimum boiling azeotrope at 101 kPa). It is thus necessary to either include a restriction in the parameter fitting procedure or to perform a retrospective evaluation of the BIPs, particularly when temperature dependence is incorporated into the BIPs.…”

“…Evaluation of the BIP values as a function of temperature is the cornerstone of the Tττ-approach . It is clear from Figure that the azeotropic BIPs are temperature-dependent, and the correlation thereof may be improved with the incorporation of TDPs.…”

New Empirical Model for the Excess Gibbs Free Energy: Correlation of Liquid–Liquid Equilibrium for Island-Type Ternary Systems

“…Nevertheless, the lack of flexibility of these models for this specific application can only produce rough correlation results in most cases and many uncertainty problems. These difficulties are added to those of a non-linear optimization problem, where some local solutions, with similar estimation of composition, can be found. − Figure shows different possibilities for binary g M curves. Figure a presents a homogeneous (convex in the complete composition range) g M curve.…”