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. Due to the limited availability of research positions, it is anticipated that the student researcher will be a Hope engineering major in the chemical, biochemical, or environmental engineering emphasis option.
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 Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR). In this work, students will use common equations of state to predict vapor-liquid phase equilibrium or PVT behavior and apply mathematical methods to generate data for physical properties from these equations. Mathematical principles of elementary calculus and elementary statistics may be studied and applied, such as 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; methods for generalizing Antoine vapor pressure constants from the SRK and PR equations; variable transformations which simplify the use of these equations; and an alternative approach to compressibility charts which models the effect of three substance-specific variables with a graphical method which previously modeled only two variables.
Other ongoing or potential projects include 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 Twu-Sim-Tassone (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.
Two students who participated in this research won awards for presenting their work at the national American Institute of Chemical Engineers (AIChE) undergraduate research poster session and competition, in 2008 and 2014.