The increase in energy consumption, along with an increase in human population and industrial activities after the industrial revolution, has caused to increase in the consumption of fossil fuels. Carbon dioxide from fossil fuels has the most significant effect on the production of greenhouse gases and global warming. The absorption of CO2 emitted into the atmosphere is the most crucial method to reduce carbon dioxide in the air. Recently, a new solvent has been developed to absorb greenhouse gases under the name of deep eutectic solvents (DES). These solvents are biodegradable, non-toxic, or low-toxic compounds that are easily obtained. A mathematical model based on the Peng–Robinson (PR) equation of state (EOS) with three different mixing rules Modified van der Waal's (M1), Quadratic (M2) and Wong Sandler (M3) was developed to correlate the CO2 solubility in six types of DESs. The model was validated and compare with the obtained experimental data reported in the literature at temperatures (293.15 – 333.15) K and pressure (0.405 – 30.408) bar. The experimental and calculated data of PR EOS with three mixing rules were generally in a good agreement by obtaining % AARD a round (0.08 – 8.08), (0.05 – 7.58) and (0.09 – 6.56) for M1, M2 and M3 respectively, and the best results with less %AARD was obtained from Wong-Sandler mixing rule in the most of cases.

In this study, Peng-Robinson equations of state associated with three different mixing rules used to predict the experimental solubility data of two acid gases, carbon dioxide and hydrogen sulfide in seven ionic liquids. The solubility data were obtained from different literature in pressure range (0.119 – 65.2) bar and verity range of temperatures (298.2 – 353) K. Mixing rules, used the modified Van der Waal (MR1), the Quadratic (MR2) and the Wong Sandler (MR3). The ionic liquids critical properties were correlated by modified Lydersen-Joback-Reid technique. The Average Absolute Relative Deviation (%AARD) was applied to compare the experimental data and that obtained from the model. The evaluated critical properties give a very close result with the literature. The mathematical model in almost systems using the three mixing rule gives good agreement with experimental data only in H2S - ILs systems gives very high deviation from the experimental data when use MR3. Quadratic mixing rule (MR2) was the best comparing with MR1 and MR3, give the lowest range %AARD 0.9 to 21.