Bernstein copula modeling for 2D discrete fracture network simulations

Abstract

In many naturally fractured reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependence relationships that may exist between geometric properties of fractures (direction, length, aperture), that is, each property is simulated independently.In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented.The application of this method is illustrated in an example which shows high agreement between data and simulation, both graphically and in its descriptive statistics, both marginally and jointly, and in the DFN as a whole.