A New Approach for Generalizing Phase Behavior Models

Accurate predictions of phase equilibria of pure-fluids and mixtures are essential for designing and optimizing separation processes and numerous other unit operations in the chemical and energy sectors.

At the heart of equilibrium phase behavior modeling is accounting the non-ideal solution behavior of fluids involved. In general, the non-ideality of the fluid behavior is evaluated using the fugacity coefficient (ϕ) for both liquid and vapor phases and alternatively the activity coefficient (γ) for the liquid phase and the fugacity coefficient for the vapor phase. Thus, within the Gibbsian framework, vapor-liquid equilibrium (VLE) calculations are commonly performed by employing either the symmetric (ϕ−ϕ) or the split (γ−ϕ) approach. Many equations of state (EOS) and activity coefficient models (ACM) have being used in industry to determine the equilibrium properties of numerous fluid mixtures. Our work focuses on a comprehensive assessment of the representation and predictive capabilities models and methods in current use.

Typically, the ϕ−ϕ approach is applied for high-pressure systems following careful selection of an applicable EOS and suitable mixing rules. In contrast, the γ−ϕ approach is used for low-pressure vapor-liquid equilibrium systems involving mixtures containing a variety of chemical structures, including both polar and non-polar components. The precision and accuracy of aforementioned approaches is dependent on the EOS and ACM employed. The Peng−Robinson (PR) EOS [1], the nonrandom two liquid (NRTL) [2] and the universal quasichemical (UNIQUAC) [3] activity coefficient models, are among the most widely used models in industry. The common facet among these models is the need for binary interaction parameters.

In general, reliable experimental vapor-liquid equilibrium data (which are both time consuming and expensive) are used to regress binary interaction parameters. However, when such data are lacking, generalized model parameters are employed relying mainly on group-contribution methods, such as UNIFAC [4] used for predicting activity coefficients. As such, a need still exists for accurate, reliable models that can provide a priori predictions of equilibrium properties of pure fluids and of mixtures without the need for extensive experimentation.

To meet this need, we have sought to develop improved methods and algorithms for non-linear, quantitative structure-property relationship (QSPR) modeling that can provide reliable predictions for thermodynamic properties of interest in the chemical and energy sectors. Specifically, we have developed generalized theory-framed QSPR (TF-QSPR) models to predict a priori important pure-fluid physical and saturation properties and the phase behavior of multicomponent, multiphase equilibrium systems. In this approach, the behavior models used are based on theory, and the model substance-specific parameters are generalized using QSPR technique aided with artificial neural networks (ANNs). In these modeling efforts  [see, e.g., 5-11], we demonstrate that TF-QSPR modeling overcomes the current limitation in applying QSPR modeling to temperature- and composition-dependent properties; and as such, we realize the full benefit of structure-based property generalizations.

In this study, and as a follow up to our model parameter generalization efforts, a comprehensive assessment of the representation and predictive capability of these two approaches, γ−ϕ and ϕ−ϕ, utilizing the UNIQUAC model to determine the activity coefficients and the Peng−Robinson (PR) EOS to calculate the fugacity coefficients are presented. The assessment was completed using a comprehensive and diverse binary vapor-liquid equilibrium database consisting of 916 binary systems involving 140 compounds belonging to 31 chemical classes. Both the overall results and the results addressing highly non-ideal systems and for aqueous systems are presented.

Specifically, regressed and generalized parameters are utilized in model internal and external consistency tests to evaluate, respectively, the model representation and generalized predictions. Further, the phase behavior of sample systems was analyzed using Danner’s molecular classification [12] method based on the mNRTL1 parameter and GE/RT values [9]. 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 (K), respectively. In comparison, the ϕ−ϕ approach regression results are, on average, within 3 times the error of the γ−ϕ approach. A similar trend was observed for the QSPR 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 K, respectively. The ϕ−ϕ approach generalized predictions produced on average twice the error obtained from the γ−ϕ approach.

The phase behavior results based on Danner’s molecular classification (1) confirm that abilities of the γ−ϕ approach in handling the vast majority of the systems consider irrespective of their classifications, and (2) demonstrate that the quality of the representations for the ϕ−ϕ approach are generally good (within twice the experimental uncertainties) for most system classifications, with the exception of some strongly polar−strongly polar and aqueous−strongly polar systems. We believe the scope of this assessment should prove useful in demonstrating the merits of applying the γ−ϕ and ϕ−ϕ approaches for different types of mixtures.

In closing, we believe our recent model generalizations [see, e.g., 5-11] will have a significant impact on phase behavior modeling. Specifically, they:

1. Demonstrate the efficacy of the theory-framed QSPR methodology in parameter generalization and point the way for similar development in thermos-physical property modeling.
2. Provide useful model parameter generalizations, which produce predications within three-times the experimental uncertainties. Thus, a reliable predictive capability superior to current literature generalizations and a wealth of knowledge on mixture phase behavior are gained without the need for experimentation.
3. Provide a comprehensive assessment for two widely used approaches for calculating equilibrium properties.

References:

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