Inhomogeneous diffusion-limited aggregation

In order to simulate viscous fingering in a porous medium with inhomogeneous permeability, we make use of a generalization of the diffusion-limited aggregation (DLA) model. In this generalized DLA, the randomly diffusing particles have transition probabilities which depend on the local permeability values of the underlying medium. This method is applied to the simulation of unstable two-fluid displacement in two-dimensional disordered pore-pipe networks. We show that the model may only be used to simulate flow in media which have inhomogeneous permeability and homogeneous porosity. We explore the combined effects of two types of noise: noise in the growth process, and disorder in the permeability of the medium; we find a morphology phase diagram which shows that both types of noise strongly affect morphology selection. In addition, we perform an analysis of DLA with noise reduction and find that the magnitude of interface velocity fluctuations is proportional to 1/√s , where s is the noise-reduction parameter. We show that these fluctuations are ‘‘multiplicative’’ in character and vanish in the large-noise-reduction limit. Finally, we address the potential application of this model to petroleum reservoir simulation.