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 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 a series approximation for the vapor pressure and phase densities predicted by the PR equation at moderate to high pressures; a series approximation for volume change and enthalpy change of vaporization predicted by the SRK and PR equations from low to high pressures; an improved approach for vapor pressures predicted by the SRK equation at moderate 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 equation.
Some current and upcoming research includes developing a technique for "tuning" the series method to converge well in a specific temperature range; applying the method 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 the series method 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 the series method for predicting phase behavior of mixtures. |
