Fracture modelling based on the stochastic extended finite element method

Abstract

Because a large number of oil and gas reservoirs are naturally fractured, they play an important role in hydrocarbon exploration and production. To fully extract and model the fracture system features of reservoirs, a new fracture modelling method, called the stochastic extended finite element (SEFE) method, is presented in this paper. This method couples fracture mechanics and the kriging method with a multi-field trend in an attempt to benefit from the advantages of each method: compliance with fracture mechanics equations and the reproduction of the fracture’s observed data, respectively. Based on the SEFE simulation method, we wrote a fracture modelling system software and built a fracture propagation model and a fracture distribution model of the Upper Cretaceous Formation in the Daqingzi region. A parallel study was performed to verify the fracture propagation pattern and boundary conditions in the proposed model based on a geomechanical analogue experiment. The results of these studies demonstrate that fracture modelling based on the SEFE method may improve the precise characterization of fractured reservoirs.

An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties

“…The XFEM was combined with random field theory and Monte Carlo simulations in Reference 20 to model hydraulic fracturing under material heterogeneity. Stochastic fracture propagation simulation was coupled with discrete fracture network simulation in Reference 21. The XFEM was coupled with Monte Carlo approach to quantify the uncertainty in the effective homogenized material properties of multiphase materials in 22 .…”