This project will incorporate concepts from the disciplines of engineering, physics, chemistry, mathematics, and computer science. However the project is specifically housed within the Hope College Department of Engineering and the mentor is an Engineering faculty member. Students majoring in other disciplines have successfully participated in previous years and are welcome to apply.
In chemical process design, engineers need general methods for predicting physical properties of various substances as both liquids and vapors. Chemical engineers commonly use cubic equations of state such as SoaveRedlichKwong (SRK) and PengRobinson (PR). In this work, students will use common equations of state to predict vaporliquid phase equilibrium and apply mathematical methods to generate data for physical properties from these equations. Mathematical principles of elementary calculus and elementary statistics will be studied and applied; specifically, multivariable series expansions and linear/nonlinear least squares regression. Students participating in the research will be expected to have taken one year of calculus; other coursework in math, chemistry, engineering, or computer science may be helpful but is not required of applicants. The goal of this work will be to generate relatively simple, yet general, equations to accurately predict physical properties.
Recent results have included series approximations for the vapor pressure, phase densities, and volume change and enthalpy change of vaporization predicted by the SRK and PR equations at moderate to high pressures; a method for estimating vapor pressures and liquid densities based upon a low temperature limit; and methods for generalizing Antoine vapor pressure constants from the SRK and PR equations.
Some current and upcoming research includes applying these methods to more complex cubic equations used in practice and simulation software, such as the Stryjek/Vidal variant of the PR equation or the TwuSimTassone (TST) equation; generalization or improvement of simple estimation methods like Watson's correlation for heat of vaporization or the Rackett equation for liquid density; investigating approaches for applying these methods or alternative methods with techniques like volume translation or lattice fluid equations that show proper scaling behavior at the critical point; and a generalization of these methods for predicting phase behavior of mixtures.
