Abstract

The mesh-free Lagrangian Smoothed Particle Hydrodynamics (SPH) method is used to simulate the problem of viscous fingering in Hele-Shaw geometry. Viscous fingering occurs when a lower-viscosity fluid displaces a higher-viscosity fluid in a narrow channel, and is a major concern in the removal of drilling mud’s from oil well bores and in secondary and tertiary oil recovery. The flow field was modelled using two sets of particles with different properties, initially placed in the left half and in the right half of the channel, respectively; in particular, the two fluids had the same density and a viscosity ratio of 1:10. Results show that SPH can reproduce the formation of a low-viscosity finger penetrating into the higher-viscosity fluid during displacement. Because of its intrinsically Lagrangian, mesh-free nature, SPH is a promising method to simulate viscous fingering in complex geometries; in addition, it can easily incorporate non-Newtonian constitutive equations to account for shear-thinning and/or viscoplastic behaviours.