The Effect of Spatial Correlation on Viscous Fingering in a Dynamic Pore-Network Model with Delaunay Tessellated Structure

Abstract

The formation of viscous fingers is a well known and often unwanted (e.g. in oil recovery) effect in porous systems with fluids of different viscosities. In this study viscous fingering is studied with a dynamic pore-network model using Delaunay tessellated networks. The pore size distribution is modeled as a correlated random field with varying correlation length. We focus on the effect of correlation length on viscous fingering. The topologically disordered networks are generated using a network generator which is developed in this work. The parameters are based on a Berea sandstone sample network. Analysis on the produced networks found that they are roughly in agreement with input parameters, and that they are statistically similar. Because of the stochastic nature of the network generation, three network realizations were produced for four different correlation lengths for the simulations, so that averaging can be applied. Using these networks drainage simulations were performed, with a viscosity ratio M = 0.1 to allow viscous fingering. We found that viscous fingering effects increased with increasing correlation length. This was most apparent at the initial stages of the simulations, at low global saturations. The fingering zone is suggested to be affected by correlation length, i.e., the correlation length is suggested to correlate inversely with the amount of fingers and the density of the invading fluid in the fingering zone, and positively with finger length and the size of the fingering zone. These effects cause a reversal in the order of the tails of the saturation profiles at higher global saturations. Additionally, breakthrough profiles were constructed, which provide more evidence on enhanced viscous fingering with increasing correlation length. However, at large correlation lengths results start to act erratic. Fingering patterns were also visualized; the evolution in fingering patterns suggest that fingers travel through preferential pathways by means of pore size heterogeneities. These heterogeneities may act as zones of high or low permeability. For various correlation lengths the appearance of long dominant fingers can be observed.