The research, carried out by Omar M. Basha and Nour M. Basha of ONB Engineering Research and Technical Services, focuses on the workhorses of process simulation: the Peng-Robinson and Soave-Redlich-Kwong cubic equations of state. These equations strike a pragmatic balance between accuracy and computational speed, and they are already built into commercial simulators such as Aspen Plus and Aspen HYSYS. But when applied to mixtures, they demand binary interaction parameters — empirical correction terms known as k-ij and l-ij — that tune how the two components of a mixture interact. For gas-ionic-liquid pairs, those parameters were scattered across decades of fragmented literature, each fitted to a single system with no consistent methodology, which made plant-scale screening of candidate solvents nearly impossible.

To fix this, the authors compiled experimental solubility data for 22 carbon dioxide-ionic-liquid systems and 15 hydrogen sulfide systems, encompassing 2,236 data points for CO2 spanning 278 to 413 kelvin and pressures up to nearly 200 bar, and 685 data points for H2S between 303 and 403 kelvin. Treating each ionic liquid as a nonvolatile pseudo-component with estimated critical properties, they regressed k-ij and l-ij for both equations of state using a two-stage optimization: a Nelder-Mead simplex algorithm to find a robust starting point, followed by Marquardt refinement. The objective function minimized the average absolute deviation between measured and calculated liquid-phase gas mole fractions, with a stringent convergence tolerance of 10 to the power of minus 8.

A crucial and technically sophisticated step followed. Rather than leaving the fitted parameters as isolated numbers, the team correlated each one with temperature using parsimonious three-term expressions of the form k(T) = k1 + k2·T + k3/T, and similarly for l-ij. These functions can be typed directly into process simulators, making them immediately usable by engineers. The correlations achieved overall absolute average relative errors of 7.6 percent for CO2 and 12.0 percent for H2S with the Peng-Robinson equation, and slightly better with Soave-Redlich-Kwong. Because such fitting risks over-parameterization, the authors compressed roughly two parameters per isotherm into just six coefficients per system, sharply reducing the model’s degrees of freedom.

To prove the temperature correlations genuinely interpolate rather than merely memorize, the researchers deployed leave-one-temperature-out cross-validation. For every system with at least four measured temperatures, the correlation was refitted without one temperature and then asked to predict the held-out values. The median errors were impressively small: 0.014 for k-ij and 0.007 for l-ij in CO2 systems, and 0.013 and 0.005 respectively for H2S, using Peng-Robinson. The 90th-percentile errors flagged sparse or curved datasets where extrapolation would be dangerous, and the authors are explicit that these correlations must never be pushed outside their experimental temperature windows.

But what about the ionic liquids nobody has measured yet? That is where the study makes its most forward-looking contribution: two generalized estimators that predict interaction parameters without any solubility data at all. The first is a property-based ridge regression that uses reduced temperature, molecular weight, critical pressure, and acentric factor — the classic corresponding-states descriptors of classical thermodynamics. The second, and more striking, is a cation-and-anion fragment model that needs only the identity of the ionic liquid and the temperature, combining low-order temperature terms with additive contributions from each ionic head group relative to a reference pair.

The validation scheme here was deliberately brutal. In leave-one-ionic-liquid-out cross-validation, every data point for an entire ionic liquid — all temperatures, all pressures — was withheld, and the model had to predict its parameters from chemistry alone. For CO2 with the Peng-Robinson equation, the fragment estimator cut the root-mean-square error for k-ij from 0.093 with the property-based approach to 0.062 across all liquids, and down to 0.042 when both the cation and anion appeared elsewhere in the training set. For H2S, the improvement was even more dramatic: from 0.218 to 0.099, and to 0.058 for interpolation-only cases. Clustered bootstrap resampling of whole ionic liquids, 2,000 replicates at a time, provided 95 percent confidence intervals on those errors, ensuring that no information leaked from the test systems into training.

Parameter errors mean little to a plant designer, though, so the team went one level deeper by propagating the generalized estimates through full vapor-liquid equilibrium calculations and comparing the predicted gas solubilities against a fitted-parameter baseline. The results are striking. For CO2 at 10 bar with Peng-Robinson, the fragment-based estimator produced a median solubility deviation of just 4.3 percent, with a 90th percentile of 15.5 percent — compared with 18.9 percent for the property-based correlation and a hefty 32.4 percent for the common shortcut of setting l-ij to zero. That last finding carries a practical warning: the co-volume interaction term is not a cosmetic refinement, and ignoring it can more than quadruple the typical solubility error. The analysis also revealed that k-ij and l-ij are strongly coupled, with median correlation coefficients of 0.93 for CO2 systems and 0.99 for H2S, which is precisely why the authors lean on out-of-sample validation rather than single-isotherm statistics to assess uncertainty.

The study is candid about its limits. The fragment library covers only the cations and anions present in the compiled database, so novel fluorinated anions or exotic cation families fall outside its domain and should receive only rough initial guesses pending new measurements. Because ionic liquids decompose far below any true critical point, their pseudo-critical properties are estimation-method-dependent, and the authors note that refitting the full database under alternative property correlations remains a priority for future work, along with direct validation against raw experimental solubility data rather than the fitted-parameter baseline.

Even so, the combined deliverables — the curated database, temperature correlations, two cross-validated generalized estimators, machine-readable supplementary tables, and a fully reproducible Python workflow — form a coherent toolbox for screening ionic liquid solvents, initializing regressions in commercial simulators, and refining models as new data arrive. As industries racing toward decarbonization and cleaner natural gas weigh the cost of amine solvents against next-generation alternatives, this work quietly transforms ionic liquids from a laboratory curiosity into a computable engineering option, one validated interaction parameter at a time.

Subject of Research: Thermodynamic modeling of CO2 and H2S solubility in ionic liquids using cubic equations of state

Article Title: Temperature dependent binary interaction parameters and generalized estimators for carbon dioxide and hydrogen sulfide solubility in ionic liquids

Article References: Basha, O. M., & Basha, N. M. (2026). Temperature dependent binary interaction parameters and generalized estimators for carbon dioxide and hydrogen sulfide solubility in ionic liquids. Discover Chemistry, 3(1), Article 538. https://doi.org/10.1007/s44371-026-00970-5

Image Credits: AI Generated

DOI: 10.1007/s44371-026-00970-5

Keywords: ionic liquids, carbon capture, hydrogen sulfide, binary interaction parameters, Peng-Robinson equation, Soave-Redlich-Kwong equation, gas solubility, cross-validation, process simulation, acid gas removal, thermodynamic modeling, Temperature