Generalized Interaction Parameter for the Modified Nonrandom Two-Liquid (NRTL) Activity Coefficient Model

Activity coefficients are used in phase equilibria calculations to account for the nonideal behavior of liquids in a mixture. In our previous work, we proposed a modification to the widely used nonrandom two liquid (NRTL) activity coefficient model that reduced the number of parameters from two to one. The current work is an extension to the previous work, and it focuses on generalizing the parameter of the modified NRTL (mNRTL1) model using a theory-framed quantitative structure–property relationship (QSPR) modeling approach, where the mNRTL1 model was used as a theoretical framework to develop the behavior model, and QSPR was used to generalize the substance-specific parameter of the model. In this work, a VLE database consisting of 916 binary systems with a wide range of functional-group interactions was assembled. Data regression analyses were performed to determine the parameter of the mNRTL1 model. The structural descriptors of the molecules were used as inputs in the QSPR model to predict the regressed parameter. The generalized QSPR model produced equilibrium property predictions within two times the errors obtained through regression of the experimental data. The newly developed QSPR model resulted in comparable phase equilibria predictions to that of the group-contribution method, UNIFAC. In comparison, the QSPR model has less than 10% of the number of parameters used by UNIFAC and is applicable to a wider range of systems

Generalized Nonrandom Two-Liquid (NRTL) Interaction Model Parameters for Predicting Liquid–Liquid Equilibrium Behavior

The nonrandom two-liquid (NRTL) model is an activity coefficient model used widely in phase equilibria calculations. The NRTL model has three adjustable parameters that are determined through regression of experimental data for a specific system. A generalization for the model parameters would reduce the time, money and effort expended on the collection of experimental data. This work focuses on the application of a theory-framed quantitative structure–property relationship (QSPR) modeling approach for the estimation of NRTL parameters. A database of 342 low-temperature binary (10–40 °C) liquid–liquid equilibria (LLE) systems was employed in this work. Data regression analyses were performed to determine the NRTL model parameters. Structural descriptors of the molecules were generated and used in developing a QSPR model to estimate the regressed NRTL parameters. The newly developed QSPR model uses 30 significant descriptors as inputs. The model yielded binary predictions with 8, 38, 51 and 44% absolute average deviation for the mole fractions (<i>x</i>₁ in 1-rich phase and <i>x</i>₁ in 2-rich phase) and partition coefficients (<i>K</i>₁ and <i>K</i>₂), respectively. These errors are approximately 3 to 4 times the errors found from the regression analyses. Further, we observed an 11% prediction failure rate, in which cases the model fails to converge to an equilibrium solution. The application of the popular and often employed UNIFAC-1981-LLE model resulted in 3 to 7 times the errors obtained through regression analyses and a prediction failure rate of 36%. These results demonstrate the efficacy of our QSPR model in providing improved predictions and an increased range of applicability when compared to the UNIFAC-1981-LLE model for LLE systems

A Comparative Study of QSPR Generalized Activity Coefficient Model Parameters for Vapor–Liquid Equilibrium Mixtures

Generalized activity coefficient models are often essential for predicting the extent of liquid nonideality in a mixture in the absence of experimental data. This work is focused on generalizing the interaction parameters of three widely used activity coefficient models, nonrandom two-liquid (NRTL), universal quasi-chemical (UNIQUAC), and Wilson. Specifically, we applied a theory-framed quantitative structure–property relationship (TF-QSPR) modeling approach for the purpose of generalization. In this modeling approach, theoretical frameworks, such as the NRTL model, are used to describe the phase behavior properties, and QSPR methodology is used to generalize the binary interaction parameters of the models. In this study, a binary VLE database consisting of 916 systems was compiled and employed to develop the QSPR models. Interaction parameters of the NRTL, UNIQUAC, and Wilson models were determined by performing data regression analyses. QSPR models were developed to predict the interaction parameters found in the regression analyses. The structural descriptors of the molecules were used as inputs in the QSPR models. The phase equilibria properties estimated using the generalized QSPR models resulted in about 2 times the error as compared to the results found in the data regression analyses. Overall, the quality of property predictions from the QSPR models is comparable to those of the UNIFAC-2006 group-contribution model when all of its group-interaction parameters are available; however, the UNIFAC model produced worse predictions when such parameters are lacking. Thus, our methodology offers a viable complement when UNIFAC parameters are missing

Application of Modified NRTL Models for Binary LLE Phase Characterization

Phase characterization of liquid–liquid mixtures is required in numerous chemical process calculations. The original nonrandom two-liquid (NRTL) model is used widely in describing liquid–liquid equilibria (LLE). Application of this model, however, is affected by (a) lack of reliable parameters, (b) a wide range of acceptable parameter values, and (c) highly correlated parameters. Recent modifications of the NRTL model, the two-parameter modified NRTL, “mNRTL2”, and the one-parameter NRTL, “mNRTL1”, address these issues and show promising results for characterizing LLE systems. The accuracy of these two modifications was tested in our previous studies using a comprehensive vapor–liquid equilibria (VLE) experimental database and a representative LLE database. In the current study, the efficacy of these modified NRTL models is assessed for the proper characterization of LLE phase conditions and attributes, including phase stability, miscibility, and consolute point coordinates. For the systems considered, the modified NRTL models produce acceptable LLE characterization results in comparison to those of the original NRTL; albeit, the results from the mNRTL2 model are more precise than those of the mNRTL1 model

Representation and Prediction of Vapor–Liquid Equilibrium Using the Peng–Robinson Equation of State and UNIQUAC Activity Coefficient Model

Many important processes in the oil and gas industry (e.g., distillation, absorption, extraction) involve contact between liquid and vapor phases. The reliable design of these industrial processes requires accurate thermodynamic models to describe the vapor–liquid equilibrium (VLE) of the mixtures of interest. Two common approaches, γ–ϕ and ϕ–ϕ, are utilized to describe such VLE behavior. In this study, we present a comprehensive assessment of the representation and predictive capability of these two approaches, utilizing the UNIQUAC model to determine the activity coefficients and the Peng–Robinson (PR) equation of state to calculate the fugacity coefficients. The assessment was completed using a diverse binary VLE database consisting of 916 binary systems involving 140 compounds belonging to 31 chemical classes. Both the overall results and the results categorized for highly nonideal systems and for aqueous systems are presented within the context of internal and external consistency tests. Specifically, regressed and generalized parameters are utilized in internal and external consistency tests, respectively. Further, the phase behavior of sample systems was analyzed using Danner’s molecular classification method based on the mNRTL1 parameter and <i>G</i>^E<i>/<i>RT</i></i> values. For the systems considered, the regression results show that the γ–ϕ approach represents the VLE behavior more precisely compared to the ϕ–ϕ approach. The overall results using the γ–ϕ approach exhibit an absolute average deviation (% AAD) of 1.6, 0.1, 4.5, and 5.7 for the pressure, temperature, mole fraction, and equilibrium constant (<i>K</i>), respectively. The ϕ–ϕ approach regression results are within 3 times the error of the γ–ϕ approach. A similar trend was observed for the quantitative structure–property relationship generalized predictions. The γ–ϕ approach predicts the VLE behavior more accurately compared to the ϕ–ϕ approach. The overall results based on the γ–ϕ approach exhibit % AADs of 5.1, 0.4, 5.9, and 8.1 for the pressure, temperature, mole fraction, and <i>K</i>, respectively. The ϕ–ϕ approach generalized predictions are within 2 times the error obtained from the γ–ϕ approach. The results of Danner’s molecular classification of the phase behavior indicated that systems with similar components are more likely to produce nearly ideal mixture behavior and systems involving dissimilar components are more likely to produce nonideal mixture behavior. Further, the quality of the representations for the ϕ–ϕ approach are generally good for most system classifications with the exception of adequate or poor fits observed for strongly polar–strongly polar and aqueous–strongly polar systems