A practical model for fluid flow in discrete-fracture porous media by using the numerical manifold method |
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| Institution: | 1. College of Civil and Transportation Engineering, Hohai University, Nanjing, 210098, China;2. Energy Geosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;1. Department of Civil Engineering, University of Siegen, 57068 Siegen, Germany;2. Department of Earth Sciences, Utrecht University, 3508TA Utrecht, The Netherlands;1. Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Chemical Engineering, South Kensington Campus, Imperial College London, London SW7 2AZ, UK;2. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK;1. Department of Geoscience & Engineering, Delft University, Delft, Netherlands;2. Technical University of Denmark, The Danish Hydrocarbon Research and Technology Centre, Copenhagen, Denmark;1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;2. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China;3. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;2. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China |
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| Abstract: | In this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix. |
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