Analysis and Modernization of Mixture Critical Point Calculation Methods

Abstract

Critical point calculations are a topic of great importance and a fundamental part of classical thermodynamics. While the basis of this field is hundreds of years old, the effective handling of complex, multicomponent fluid mixtures has been an ongoing area of study over the past 50 years. Two major critical point formulations exist (i.e., the root-finding method and the optimization method), each with many modifications and improvements. Despite this, mixture critical point calculation algorithms can be difficult to implement, unreliable, and slow. In recent years, the development of machine learning and modern computer science theory has led to many computational techniques that have the capacity to improve and streamline the mixture critical point calculations. This work investigates the application of modern computational techniques to both root-finding-based and optimization-based mixture critical point calculations. Firstly, we apply the automatic differentiation (AD) technique to both methods. We demonstrate the effectiveness of AD in calculating the thermodynamic derivatives that are involved in critical point calculations. Next, we compare the root-finding methods and the optimization methods in terms of their robustness and accuracy. We find that the root-finding methods are more robust and accurate for simple mixtures. Meanwhile, the global optimization methods are effective in computing the critical points of large, complex mixtures. Finally, we develop a novel procedure that utilizes deep learning models to create predictions of mixture critical points; this procedure can be used to initialize critical point calculations. Our procedure, when implemented into both the root-finding and the global optimization methods, leads to speed and robustness improvements in mixture critical point calculations.