Radial flows in heterogeneous porous media with a linear injection scheme

•Highly accurate numerical simulations for complex flow patterns of viscous fingering in a heterogeneous porous medium.•Comprehensive investigations of both miscible and immiscible interfaces.•Verifications of applicability for controlling the fingering instability by a linear injection scheme.

A robust diffuse-interface formulation is applied to simulate miscible and immiscible radial flows in heterogeneous porous media, in which the permeability is characterized by a log Gaussian distribution. The stabilizing effects of linear injection scheme, determined by the fingering interfacial length, are investigated to verify its applicability in various conditions of miscibility and permeability heterogeneity. For fully miscible conditions, the linear injection scheme shows destabilizing effects both in homogeneous and heterogeneous media. On the other hand, even the immiscible fingering instability in a homogenous medium can be suppressed effectively by applying the linear injection scheme, the stabilizing effect on such a linear injection scheme is insignificant in a heterogeneous medium.