Separation operations are generally the most expensive components of chemical processes. Therefore, it is especially important to optimize separations to accelerate the concept-to-implementation timeline of a project. Designing these operations requires accurate and flexible thermodynamic models, but existing tools often fall short when applied to systems with polar components. The hydrogen bonding (or association) which occurs between these components has a dramatic effect on chemical properties and the phenomenon is poorly represented in traditional models. This work aims to address this limitation by:
- Developing a thermodynamic model which incorporates a statistical mechanics approach (Wertheim’s perturbation theory) to calculate the extent and effects of association.
- Evaluating parameters for the model by leveraging a combination of IR and NMR spectroscopy as well as molecular and quantum simulations. Each tool will serve to reduce the liabilities of another.
- Delivering the resulting model as a commercial tool (an Aspen Plus user model) to be utilized by industrial partners and the broader engineering community
Activity Coefficient Modeling via the Wertheim Approach
This project integrates the Wertheim approach into an activity coefficient model. Activity coefficient models permit accurate fitting of pure component vapor pressures independently of mixture parameters, but traditionally the models don't represent association effects of hydrogen bonding. Adding the Wertheim association term addresses the deficiency. The approach adds the association term to the typical residual and combinitorial terms,
ln γ = ln γres + ln γcomb + ln γassoc
The figure shows the improvement for the methanol + cyclohexane system compared to other models. The cubic plus assiciation (CPA) fit is from literature. The Scatchard-Hildebrand model uses only two adjustable parameters, but is unable to accurately represent the assymetry of the LLE. The NRTL model includes the Flory equation with the Staverman-Guggenheim correction in addition to the Wertheim term.
Aspen User Model
We have developed an Aspen user model that is publicly available for download, click here.
Spectroscopic Determination of Association
We are using IR and NMR to determine association constants. On the right is the IR spectra of 10 mol% butanol in cyclohexane at 70 C. We are interpreting the spectra in terms of the Wertheim model.
IR absorbance is due to vibrational modes, not species. As shown below, the peak at 3630 cm-1 represents free hydrogens of the alpha and beta classes. The peak can be fitted with two Lorentzian-Gaussian peaks shown by the black and blue peaks. At the illustrated mole fraction of 10 mol%, significant absorption also occurs due to the gamma bonds shown by the red peak.
Free hydrogens can be calculated by the Werthiem model. The fraction of hydrogen sites free is represented by XD which is calculated via
XD = 2/(1+sqrt(1+4xbutanolρΔ))
where ρ is molar density, and Δ is the temperature-dependent Wertheim association constant. The absorprtion in the free-hydrogen region is proportional to the concentration of free donor sites.
Quantum Mechanics to Guide Spectroscopy
A unique feature of the MSU associating fluid project is the incorporation of quantum calculations to guide interpretation of the spectra. In literature, the peak at 3630 cm-1 has been speculated to be both alpha and beta hydroxyls. Our calculations confirm the empirical assumptions used previously. Our dedicated 28 supercomputer cores with 512 GB RAM on the MSU Institute for Cyber-Enabled Computing permit us to run quantum calculations on medium-sized clusters. We also have shared access to the other 15,000 processers of the ICER facility.
In our approach, we run molecular simulations to generate realistic molecular environments and save frames. We analyze the frames to locate hydroxyls and characterize them as alphas, beta, and gammas. After classifying species, we capture the surrounding molecules to create a realistic cluster. We pass the cluster to Gaussian. We minimize the hydroxyl using PM6 and then run minimization and frequency calculations at the B3LYP/6-31G* level of theory on the H, O, C and H atoms bonded to the carbon. Finally, we verify the classification of the hydroxyl after the quantum calculations because the classification sometimes changes during the quantum calculations.
The histograms show nomalized number counts of the species collected from runs of 10 and 50 mol% n-butanol in cyclohexane. The results here result from over 1200 clusters. We show that the free hydroxyl peak includes both alpha and beta hydroxyls. The broad band at 3550 cm-1 is due to the gammas. Note that dimer gammas vibrate at higher frequencies than the oligomer gammas. The delta bonds vibrate at lower wavenumbers (not shown).
Collaborators
We are collaborating with Dow Chemical and NIST to implement enhanced versions of the model.
Funding
This material is based upon work supported by the National Science Foundation under Grant No. 1603705. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
This work was supported in part by Michigan State University through computational resources provided by the Institute for Cyber-Enabled Research