Exploring cluster formation in CO₂ + hydrocarbon mixtures: From binary to ternary systems

This study aims to investigate clustering phenomena at infinite dilution in supercritical CO₂-rich mixtures with n-heptane ( n -C₇) and n-dodecane ( n -C₁₂), in both binary and ternary systems. The main objective is to understand how the individual clustering behaviors of the solutes combine in the ternary mixture, and whether this combination follows an additive rule. To this end, density measurements were carried out at 313.15 K and 323.15 K over a pressure range of (10 to 70) MPa, enabling the determination of partial molar volumes as indicators of clustering. The results reveal a pronounced clustering effect at low pressures (below 20 MPa) for both binary and ternary systems, as evidenced by strongly negative partial molar volumes, which indicate the formation of compact solvation clusters around the solutes. In the ternary mixture, the clustering behavior was found to follow a nearly linear combination, based on the mole fractions of the clusters observed in the binary systems. This suggests that clustering in CO₂ + multi-solute systems may be predicted from binary behavior. Two SAFT-type equations of state (PC-SAFT and SAFT-VR Mie) were employed to evaluate their ability to model the transition from binary to ternary systems. While both captured the non-ideal volumetric behavior, SAFT-VR Mie demonstrated better quantitative agreement. These findings improve our understanding of solute–solvent interactions in CO₂-rich environments and support enhanced modeling of processes such as supercritical extraction, carbon capture and storage (CCUS), and enhanced oil recovery (EOR). Cluster size of binary and ternary systems, where ● ; (binary CO 2 -C 7 and CO 2 -C 12 systems), × ; (ternary CO 2 -C 7 -C 12 system) and ̶; (linear correlation). • New density data in CO 2 + n-C 7 , CO 2 + n-C 12 binary systems. • Density data in CO 2 + n-C 7 + n-C 12 ternary system. • Derivations of partial molar volume at infinite dilution. • Determination of clustering effect in binary and ternary systems. • Combining rule for clustering effect with multi solutes in CO 2 .