In their paper titled "Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh," authors Jeffrey D. Hyman, Matthew R. Sweeney, Carl W. Gable, Daniil Svyatsky, Konstantin Lipnikov, and J. David Moulton present a comprehensive workflow for simulating single-phase flow and transport in fractured porous media utilizing the discrete fracture matrix approach. The <kw1>workflow</kw1> consists of three primary components: (1) a method for generating conforming meshes around a complex three-dimensional fracture network, (2) the discretization of governing equations through a second-order mimetic finite difference method, and (3) the implementation of numerical methods tailored for high-performance computing environments. The authors introduce a technique to create a conforming Delaunay tetrahedralization surrounding the fracture network, where triangular cells within the fracture mesh serve as faces in the volume mesh. This addresses common issues that arise and compromise mesh quality. Their open-source subsurface simulator employs a hierarchy of process kernels—one per physical process—allowing for both strong and weak coupling of the fracture and matrix domains. Verification tests based on analytic solutions for flow and transport are provided alongside demonstrations of numerical convergence. The authors showcase the method's robustness by exploring scenarios where the fracture network acts as a flow barrier, primary pathway, or offers resistance similar to the surrounding matrix. Furthermore, they present multiple applications of their method in complex fracture networks. In one example, they demonstrate robustness through two scenarios involving different behaviors of the fracture network in relation to flow dynamics. In another test case, they illustrate flow and transport through a stochastically generated three-dimensional network containing 257 fractures. Overall, this work contributes significantly to advancing our understanding of flow and transport phenomena in fractured porous media by providing an innovative workflow that combines advanced mesh generation techniques with efficient numerical methods tailored for high-performance computing environments.
- Authors present a comprehensive workflow for simulating single-phase flow and transport in fractured porous media utilizing the discrete fracture matrix approach
- Method for generating conforming meshes around a complex three-dimensional fracture network
- Discretization of governing equations through a second-order mimetic finite difference method
- Implementation of numerical methods tailored for high-performance computing environments
- Technique introduced to create a conforming Delaunay tetrahedralization surrounding the fracture network, addressing common mesh quality issues
- Open-source subsurface simulator employs a hierarchy of process kernels allowing for strong and weak coupling of fracture and matrix domains
- Verification tests based on analytic solutions provided alongside demonstrations of numerical convergence
- Authors showcase method's robustness by exploring scenarios where fracture network acts as flow barrier, primary pathway, or offers resistance similar to surrounding matrix
- Multiple applications demonstrated in complex fracture networks, including scenarios involving different behaviors of the fracture network in relation to flow dynamics
SummaryAuthors explain how to model fluid movement in rocks with cracks using a special method. The method has three main parts: making detailed 3D models of the cracks, solving equations with a specific math technique, and using computer programs for fast calculations. They also show a new way to create good quality models around the cracks. A free software tool is used that can handle different types of connections between the cracks and rock. The authors test their method by trying different situations where the cracks can either block, guide, or slow down the flow of fluids.
Definitions
- Authors: People who write books or papers.
- Workflow: A series of steps to complete a task.
- Fracture: A crack or break in something solid like rocks.
- Porous media: Materials with small holes that liquids or gases can pass through.
- Discrete: Separate or distinct.
- Matrix: An arrangement of elements into rows and columns.
- Conforming meshes: Detailed structures that fit together perfectly.
- Governing equations: Mathematical rules that describe how things change over time.
- Mimetic finite difference method: A specific mathematical technique for solving problems accurately.
- Numerical methods: Techniques used in mathematics to solve problems on computers.
- High-performance computing environments: Powerful systems for running complex calculations quickly.
- Delaunay tetrahedralization: Creating 3D shapes from points in space according to certain rules.
- Subsurface simulator: Software that models processes happening below the surface of Earth or other
Introduction
The study of flow and transport in fractured porous media is crucial for understanding various natural processes such as groundwater flow, contaminant transport, and oil and gas production. However, simulating these phenomena accurately can be challenging due to the complex nature of fractured networks. In their paper titled "Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh," authors Jeffrey D. Hyman, Matthew R. Sweeney, Carl W. Gable, Daniil Svyatsky, Konstantin Lipnikov, and J. David Moulton present a comprehensive workflow for simulating single-phase flow and transport in fractured porous media utilizing the discrete fracture matrix approach.
The Workflow
The workflow presented by the authors consists of three primary components: (1) a method for generating conforming meshes around a complex three-dimensional fracture network, (2) the discretization of governing equations through a second-order mimetic finite difference method, and (3) the implementation of numerical methods tailored for high-performance computing environments.
Mesh Generation
One of the key challenges in simulating flow and transport in fractured porous media is creating an accurate mesh that captures the complexity of the fracture network while maintaining good quality elements. The authors address this issue by introducing a technique to create a conforming Delaunay tetrahedralization surrounding the fracture network.
This method involves first generating triangular cells within the fracture mesh that serve as faces in the volume mesh. This ensures that all fractures are captured within individual cells without intersecting each other or neighboring cells. The resulting volume mesh is then used to discretize both fractures and matrix domains separately.
Mimetic Finite Difference Method
To discretize governing equations efficiently on this conforming multi-dimensional mesh, the authors utilize a second-order mimetic finite difference method. This approach ensures that the discrete equations satisfy key properties of the continuous equations, such as conservation laws and symmetry.
The authors also employ a hierarchy of process kernels—one per physical process—allowing for both strong and weak coupling of the fracture and matrix domains. This allows for accurate representation of complex flow and transport phenomena in fractured porous media.
High-Performance Computing
To make their workflow suitable for high-performance computing environments, the authors implement efficient numerical methods tailored specifically for this purpose. These methods include parallelization techniques to distribute computational tasks among multiple processors, resulting in faster simulations.
Verification Tests
To validate their workflow, the authors provide verification tests based on analytic solutions for flow and transport. These tests demonstrate the accuracy and convergence of their method compared to theoretical solutions.
Applications
The robustness and versatility of this workflow are demonstrated through various applications in complex fracture networks. In one example, the authors showcase how their method can accurately simulate scenarios where the fracture network acts as a flow barrier or primary pathway for fluid flow. In another test case, they illustrate flow and transport through a stochastically generated three-dimensional network containing 257 fractures.
Overall, these applications highlight the effectiveness of this workflow in capturing different behaviors of fractured networks and simulating them accurately.
Conclusion
In conclusion, Hyman et al.'s paper presents an innovative workflow that combines advanced mesh generation techniques with efficient numerical methods tailored for high-performance computing environments to simulate single-phase flow and transport in fractured porous media using discrete fracture matrix models. The use of conforming meshes surrounding complex three-dimensional fracture networks addresses common issues with mesh quality while maintaining accuracy. Verification tests show good agreement with analytical solutions, further validating this approach's effectiveness. Multiple applications demonstrate its robustness in capturing different behaviors of fractured networks accurately. Overall, this work significantly contributes to advancing our understanding of flow and transport phenomena in fractured porous media.
