A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

• Published in: Advances in water resources Vol. 96; pp. 354 - 372
• Main Authors: Karimi-Fard, M., Durlofsky, L.J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2016
• Subjects: Discrete feature modeling; Discretization; Dual-continuum model; Finite element method; Finite-volume method; Formations; Fracture mechanics; Fractures; Lists; Mathematical analysis; Mesh generation; Methodology; Modelling; Upscaling; Fractures; Finite-volume method; Dual-continuum model; Mesh generation; Upscaling; Discrete feature modeling
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2016.07.019

•A gridding, discretization and coarsening methodology for fractured formations is proposed.•The gridding technique is based on an approximate representation of fracture intersections.•Coarse models are constructed by the aggregation of fine-grid cells. Fractures and rock regions are aggregated separately providing a dual-continuum representation of the model.•Coarse cell-to-cell transmissibilities are computed using flow-based upscaling procedures.•The accuracy and efficacy of the method is illustrated for gas production from naturally fractured formations and transport through fractured porous media. A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.