Monotone embedded discrete fractures method for flows in porous media

Abstract We propose a new method for modeling of flows in fractured media which preserves non-negativity of the solution or satisfies the discrete maximum principle. The method consists in coupling of the embedded discrete fracture method (EDFM) with two nonlinear schemes: monotone two-point flux approximation and compact multi-point flux approximation with the discrete maximum principle. The resulting monotone EDFM (mEDFM) combines effectiveness and simplicity of standard EDFM approach with accuracy and physical relevance of the nonlinear FV schemes on non-orthogonal grids and anisotropic media.

[1]  Hadi Hajibeygi,et al.  Projection-based Embedded Discrete Fracture Model (pEDFM) , 2017 .

[2]  Bradley T. Mallison,et al.  A compact multipoint flux approximation method with improved robustness , 2008 .

[3]  D. Waldren,et al.  A Multicomponent Isothermal System for Efficient Reservoir Simulation , 1983 .

[4]  Nonlinear finite volume method with discrete maximum principle for the two-phase flow model , 2016 .

[5]  L. Durlofsky,et al.  An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators , 2004 .

[6]  Bradley T. Mallison,et al.  Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem , 2017, J. Comput. Phys..

[7]  G. I. Barenblatt,et al.  Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata] , 1960 .

[8]  J. J. Walsh,et al.  Measurement and characterisation of spatial distributions of fractures , 1993 .

[9]  Yuri V. Vassilevski,et al.  A monotone nonlinear finite volume method for diffusion equations and multiphase flows , 2014, Computational Geosciences.

[10]  Patrick Jenny,et al.  A hierarchical fracture model for the iterative multiscale finite volume method , 2011, J. Comput. Phys..

[11]  J. E. Warren,et al.  The Behavior of Naturally Fractured Reservoirs , 1963 .

[12]  Daniil Svyatskiy,et al.  Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes , 2009, J. Comput. Phys..

[13]  L. Durlofsky,et al.  Upscaling Discrete Fracture Characterizations to Dual-Porosity, Dual-Permeability Models for Efficient Simulation of Flow With Strong Gravitational Effects , 2008 .

[14]  Daniil Svyatskiy,et al.  Minimal stencil finite volume scheme with the discrete maximum principle , 2012 .

[15]  Seong H. Lee,et al.  Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media , 2008 .

[16]  Kamy Sepehrnoori,et al.  Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs , 2014 .

[17]  N. P. Christensen,et al.  Variations in fracture system geometry and their implications for fluid flow in fractures hydrocarbon reservoirs , 1999, Petroleum Geoscience.

[18]  Kamy Sepehrnoori,et al.  Development of a Coupled Dual Continuum and Discrete Fracture Model for the Simulation of Unconventional Reservoirs , 2013, ANSS 2013.

[19]  Alessio Fumagalli,et al.  Benchmarks for single-phase flow in fractured porous media , 2017, ArXiv.

[20]  M. F. Lough,et al.  Hierarchical modeling of flow in naturally fractured formations with multiple length scales , 2001 .

[21]  Yu. V. Vassilevski,et al.  A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes , 2009 .

[22]  Jiamin Jiang,et al.  An improved projection-based embedded discrete fracture model (pEDFM) for multiphase flow in fractured reservoirs , 2017 .

[23]  H. Kazemi,et al.  NUMERICAL SIMULATION OF WATER-OIL FLOW IN NATURALLY FRACTURED RESERVOIRS , 1976 .

[24]  Milind Deo,et al.  Finite element, discrete‐fracture model for multiphase flow in porous media , 2000 .

[25]  A. Firoozabadi,et al.  Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media , 2004 .