DYNAMICS OF GROWING INTERFACES FROM THE SIMULATION OF UNSTABLE FLOW IN RANDOM-MEDIA

Viscous fingering in random porous media is encountered in many applic ations of two-phase flow, where the interface is unstable because the ratio of the viscosity of the displaced fluid to that of the injected fluid is large. In these applications, including enhanced oil recovery , characterization of the width of the interface is an important conce rn. In the limit of stable flow, the interfacial width had been found to grow as w almost-equal-to t(beta), where beta almost-equal-to 0.66, approximately independent of capillary number. To study the same beha vior for the unstable case, we have simulated flow in two-dimensional random porous media using a standard model with different viscosity ra tios and zero capillary pressure. When the injected fluid has zero vis cosity, viscosity ratio M = infinity, the interfacial width has the ex pected self-similar diffusion-limited-aggregation-like behavior. For s maller viscosity ratios, the flow is self-affine with beta = 0.66 +/- 0.04, which is the same value that had been observed in studies of sta ble flow. Furthermore, the crossover from self-similar fractal flow to self-affine fractal flow is observed to scale with the same ''charact eristic'' time, tau = M0.17, that had been found to scale the average interface position. This ''fractal'' scaling of the crossover leads to definite predictions about the viscosity-ratio dependence of the ampl itudes associated with interfacial position and interfacial width.