Nonrandom two‐liquid activity coefficient model with association theory

Abstract

Considered one of the most versatile and widely used classical thermodynamic models to correlate phase equilibria behavior of nonideal systems, the nonrandom two‐liquid (NRTL) theory does not explicitly account for specific chemical associations such as hydrogen bonding. This deficiency has been recognized as the cause for unsatisfactory representation of association systems like methanol–alkanes binaries. This work presents a practical approach to integrate Wertheim's perturbation theory for association contribution with the classical NRTL model. Specifically, the association contribution is calculated from pre‐determined molecule‐specific association strengths while the physical interaction contribution is captured with NRTL binary interaction parameters. The resulting association NRTL model correlates fluid phase equilibria of association systems with few adjustable parameters and offers improved predictive capability for higher order systems.

Association‐based activity coefficient model for electrolyte solutions

“…28 The association theory has been successfully applied to NRTL-SAC and NRTL activity coefficient models to describe the nonideality due to the hydrogen bonding between molecules in nonelectrolyte systems and showed a remarkably better representation of phase equilibria for association systems. 29,30 In this work, the association theory is applied to calculate the nonideality resulted from the self-association of water and crossassociation of water-ion and cation-anion in aqueous electrolyte solutions using a generalized formulation with two association site types including the electron acceptor and the electron donor. The model formulation can be directly applied to mixed-salt and mixedsolvent systems that involve complex multicomponent associations.…”

“…The r i is specified as 0.76 for water 30 and is assumed to be constants at 0.76 for all the ions studied in this work because the regression results are insensitive to the r i of ions.…”

Thermodynamics of solvent-driven water extraction from hypersaline brines using dimethyl ether

“…Coupled with an energy-efficient solvent regeneration system, DME-driven SDWE has several practical applications ranging from hypersaline brine desalination for the concentration of industrial wastewater to fractional precipitation for the enhanced recovery and recycling of critical energy materials. At the molecular scale, further research is required to understand the fluid phase equilibrium behavior of a broader range of aqueous-organicelectrolyte mixtures, including multi-electrolyte mixtures [70,[111][112][113]. In particular, a combined experimental and theoretical approach is needed to study the solvation of highly concentrated electrolytes in multi-solvent solutions [114].…”

Modeling Phase Equilibrium of Common Sugars Glucose, Fructose, and Sucrose in Mixed Solvents

“…The NRTL model has been further improved to better describe highly associating systems with the addition of an association term . The activity coefficient of component i in the aNRTL model is described by the equation: The residual term, ln γ i Resid , is calculated with the original NRTL equation (eq ).…”

“…The combinatorial term, ln γ i Comb , uses a modified Flory–Huggins expression: where φ i ’ is the modified volume fraction: and r i is the molecular van der Waals volume that may be calculated from Bondi’s group-contribution method . The association term, ln γ i Assoc was derived by Ferreira et al , from Wertheim’s theory: where: Here ν i A is the number of sites of type A in component i ; X A and X i A are the unbounded site fractions of type A in the solution and in pure component i , respectively; and ρ A and ρ i A are the dimensionless molar density of site type A in the solution and in pure component i . The index B in eqs and refers to the sites which associate with sites of Type A , so the definitions of ρ B , ρ i B , and v i B are analogous to those of ρ A , ρ i A , and v i A .…”