Numerical simulation of the thermodynamic and hydrodynamic effects on viscous fingering in partially miscible systems

The displacement of a more viscous fluid by a less viscous fluid in porous media or Hele–Shaw cells exhibits fingerlike interfacial patterns known as viscous fingering (VF). Classically, VF dynamics are divided into two categories depending on whether the fluids are fully miscible or immiscible. Recently, attention has been drawn to a third category, namely, VF in partially miscible systems. Our previous numerical study showed that, in such systems, VF patterns can transition to multiple droplet patterns with certain values of parameters. In the present work, we numerically investigate the effects of seven key parameters on partially miscible VF dynamics: (i) Péclet number, (ii) log-mobility ratio, (iii) Korteweg force, (iv) interfacial energy, (v) and (vi) two transport parameters governing mass transfer, and (vii) a parameter for the bulk free energy. We find that fingering patterns are primarily governed by the hydrodynamic parameters (i) and (ii) and the chemical–thermodynamic parameters (iii) and (iv), whereas droplet patterns are mainly controlled by the chemical–thermodynamic parameters (v), (vi), and (vii). This parametric study contributes to improved prediction and control of processes such as enhanced oil recovery and CO2 sequestration, where partially miscible systems arise under high temperature and pressure.