Transition from viscous fingers to foam during drainage in heterogeneous porous media

Abstract

We investigate the behavior of drainage displacements in heterogeneous porous media finding a transition from viscous fingering to foam-like region. A pore network model incorporating the formation of blobs is adopted to study this phenomenon. By imposing a pressure difference between the inlet and outlet, we observe that the displacement pattern undergoes a significant transition from a continuous front of growing viscous fingers to the emergence of foam, which develops and propagates until breakthrough. This transition occurs at a specific distance from the inlet, which we measure and analyze as a function of the viscosity ratio and the capillary number, demonstrating that it follows a non-trivial power-law decay with both the parameters. Moreover, we discuss the relationship between the evolution of the total flow rate and the local pressure drop, showing that the foam developed reduces global mobility. We observe that foam is formed from the fragmentation of viscous fingers beneath the front, and this instability mechanism is connected with fluctuations of the local flow rate, which we analyze both in the viscous fingering region and in the foam region.