Developing a new algorithm for numerical modeling of discrete fracture network (DFN) for anisotropic rock and percolation properties

Abstract

The role of natural fractures in future reservoir performance is prominent. The fractured porous media is composed of an interconnected network of fractures and blocks of the porous medium where fractures occur in various scales and have a strong influence either when most of the flow is concentrated and them or when they act as barriers. A general numerical model for discrete fracture networks (DFN) is usually employed to handle the observed wide variety of fracture properties and the lack of direct fracture visualization. These models generally use fracture properties’ stochastic distribution based on sparse and seismic data without any physical model constraint. Alternatively, a DFN model includes usual numerical geomechanical approaches like boundary element and finite element. But here, a geostatistical methodology has been used to generate a DFN model. In this paper, an alternative modeling technique is employed to create the realization of an anisotropic fractured rock using simulated annealing (SA) optimization algorithm. There is a notable positive correlation between fracture length and position. There are three principal subjects in a study of fractured rocks. Firstly, the network’s connectivity, secondly, fluid flows through the system, and thirdly, dispersion. Here, connectivity of generated networks is considered. Continuum percolation is the mathematical model to study the geometry of connected components in a random subset of space. Different random realizations from the S.A. algorithm in four different sizes of L = 100, 150, 200, 250 at post-threshold condition are used as disordered media in percolation theory to compute percolation properties using Monte Carlo simulation. The percolation threshold (critical fracture density) and two crucial scaling exponents (β and υ) that dictate the model’s connectivity behavior are estimated to over 200 realizations.