Determination of diffusion coefficients from constant volume diffusion tests through numerical simulation

Molecular diffusion is a fundamental mass transport phenomenon crucial to many scientific and industrial fields. Its accurate description relies on diffusion coefficients that can be either experimentally measured or theoretically estimated. The constant volume diffusion (CVD) method is a widely used approach to measure liquid-phase diffusion coefficients at high pressures. However, it requires analytical or numerical solutions to interpret the measured data. In this study, we described in detail a legacy CVD simulation code developed by Michael L. Michelsen and showed how his algorithm can determine constant or composition-dependent diffusion coefficients from the CVD data using the orthogonal collocation method. We further coupled the code with five diffusion coefficient correlations, including the Wilke-Chang (WC), Hayduk-Minhas (HM), extended Sigmund (ES), Riazi-Whitson (RW), and Leahy-Dios-Firoozabadi (LDF), to investigate their performance in terms of predicting and regressing the CVD data for methane-n-alkane and nitrogen-n-alkane systems. We found that the CVD results are insensitive to the gas-phase diffusion coefficients. The simple WC and HM give the closest predictions despite their empirical nature and inherent inconsistency. In contrast, the predictions by LDF under the rigorous Maxwell-Stefan framework are not satisfactory. The regression results using different correlations and a constant liquid-phase diffusion coefficient are almost the same. Different correlations result in different ranges of the regressed coefficients, and those determined using the assumption of constant diffusion coefficients are always within these ranges. We also compared and illustrated the differences in the profiles of diffusion coefficients between these correlations. The study demonstrates that Michelsen's algorithm is an effective tool for processing CVD data, and it also highlights how the interpretation of CVD data depends on the assumed composition-dependence.