From invasion percolation to flow in rock fracture networks

Abstract

The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a general distribution function or are conditioned on measured data from deep geological investigations. We introduce several modifications to the invasion percolation (MIP) to incorporate fracture inclinations, intersection lines, as well as the hydraulic path length inside the fractures. Additionally a trapping algorithm is implemented that forbids any advance of the invading fluid into a region, where the defending fluid is completely encircled by the invader and has no escape route. We study invasion, saturation, and flow through artificial fracture networks, with varying anisotropy and size and finally compare our findings to well studied, conditioned fracture networks.Comment: 18 pages, 10 figure

Multi-scale approach to invasion percolation of rock fracture networks

“…The aim of this work is to improve the trapping MIP of DFNs previously developed by (Wettstein et al, 2012). The DFN construction is explained in detail by Huseby et al (2001) and Khamforoush and Shams (2007).…”

“…The detailed analysis for the effects of anisotropy and fracture density for the DFN model on the number of intersections of fractures is presented by Huseby et al (2001) and Khamforoush et al (2008). For the invaded DFN model, the global system matrix is composed of invaded fractures as elements and the connections as nodes using a simple channel model following Cacas et al (1990) and Wettstein et al (2012). After the DFN is constructed, the invasion of immiscible fluids can be simulated.…”

“…Periodic boundaries are applied on the other four sides. A detailed description of the algorithm can be found in Wettstein et al (2012).…”

“…In fact, this multi-scale analysis is essential due to the strong effects of both scales on the transport properties of fractured rocks (Hamzehpour, et al, 2009;Dreuzy, et al, 2012). In the following, we revisit the previously studied problems of two-phase invasion percolation (IP) in the form of immiscible displacement through isotropic and anisotropic DFNs (Wettstein et al, 2012). In contrast to the previous modifications, fracture intersections are now including the effect fracture orientation, intersection length, as well as the path length along the fractures by using the numerically found scaling relations for B=4.…”

“…The drop of the aperture threshold for each invasion step characterizes the dynamics of the invasion process. The comparison between trapping MIP (C I = 0.5; adjustment parameter for the inclination effect of intersections see (Wettstein et al 2012)) and the newly developed MIP is presented in Figs. 10 and 11.…”