Developing a Molecular Model to Predict Equations of States from Computational Quantum Chemistry and Machine Learning

Computational models can allow engineers to design advanced transportation engines that operate at significantly high pressures. In order to improve fuel-air mixing in the engines and increase efficiency, chemical engineers need to understand the thermodynamic properties of the mixture under these conditions. An equation of state (EOS), which represents a mathematical relation of volume of a mixture to temperature and pressure, offers a valuable tool for understanding important properties of mixtures such as vapor-liquid equilibria and other thermodynamic quantities. For example, important fluid properties such as compressibility factor, flow density and critical conditions of hydrocarbon mixtures can be derived from the EOS to predict the condensation of gas mixtures in pipelines.

Given that EOS is valuable in deriving essential thermodynamic properties, the challenge of current technology is the ability to predict the EOS for hydrocarbon mixtures at these high pressures with better accuracy. The current method of empirically determining accurate EOS through laboratory measurements is problematic because it requires too much time and many experiments. In addition, the number of transportation fuels is constantly increasing. Biofuels, such as alcohols, ethers and ketones also behave differently from more traditional petroleum-derived alkanes due to their chemical bonding and molecular structures. Consequently, there is an increasing demand for EOS for new mixtures and the ability to accurately predict the EOS for any mixture of interest. Therefore, designing a better approach for applying EOS to an arbitrary mixture would represent a significant scientific achievement that would result in major breakthroughs in designing advanced engines.

The goal of this project is to examine the practicability of predicting equations of state, focusing on a specific class of EOS known as the virial equation of state. Theoretically, important properties of mixtures can be accurately determined from the virial EOS. However, the lack of accurate parameters limits our ability to accurately predict intermolecular interactions. I will apply computational quantum chemistry to produce these parameters. In this project, I will employ a two-step method in this project. First, I will identify the coordinate system and the degrees of freedom of the system. This process will produce a mathematical description of a multi-dimensional function of intermolecular potential. Second, the Electronic Structure Method will be employed to sample values of intermolecular potential to solve for the second virial coefficient. The Monte Carlo Integration method can be used to estimate integrals that cannot be evaluated analytically, such as the intermolecular potential function in this model. Further, I can apply my method to study the contribution of chemical functional groups in more complicated molecular system and calculate the third virial coefficient. By the end of the project, I will have developed a high-performance computational model to compute pairwise potential, enabling chemical engineers to simulate and design their processes with greater efficiency.