Hybrid TPFA-MFD Projection Embedded Discrete Fracture Model
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Solution Overview
Problem
Current reservoir numerical simulation technologies lack an efficient and robust projection-based embedded discrete fracture model (pEDFM) capable of handling general anisotropic two-phase flow scenarios, particularly with complex fracture geometries and low-conductivity fractures, leading to increased computational costs and reduced accuracy.
Innovation Solution
A novel projection-based embedded discrete fracture model using a hybrid of two-point flux approximation (TPFA) and mimetic finite difference (MFD) methods, which constructs suitable treatments for low-conductivity fractures and calculates numerical fluxes on both K-orthogonal and non-K-orthogonal grids, improving computational efficiency and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If MFD method is used to construct EDFM for full permeability tensors, then manufacturing precision is improved, but device complexity increases and productivity decreases
Solution Approach 1:
The patent segments the computational domain into matrix blocks and fracture grids, applying different numerical methods to each. TPFA is used for matrix blocks where K-orthogonality holds, while MFD is applied only where needed for non-K-orthogonal grids or fracture regions, reducing overall Jacobian density while maintaining accuracy where required.
Solution Approach 2:
The patent applies local quality by using MFD method specifically in regions with non-K-orthogonal grids or complex fracture geometries, while using simpler TPFA in regular matrix regions. This localized application of MFD maintains calculation accuracy in critical areas while avoiding unnecessary computational overhead in other regions.
2Adaptability or versatility
If generic pEDFM workflow is applied to wide range of flow scenarios, then adaptability is improved, but device complexity increases due to complex inter-grid connections and low-conductivity fracture treatment
Solution Approach 1:
The patent creates a universal pEDFM framework that handles multiple flow scenarios (single-phase, two-phase, anisotropic, low-conductivity fractures) through a unified algorithmic structure. The hybrid TPFA-MFD approach and automated projection configuration work across different flow types without requiring scenario-specific modifications, achieving multi-functionality.
Solution Approach 2:
The patent implements self-service through automated algorithms that construct fracture projection configurations and inter-grid connections without manual intervention. The system automatically identifies K-orthogonal vs non-K-orthogonal grids, configures appropriate numerical methods, and handles low-conductivity fracture treatments, eliminating the need for manual setup while maintaining adaptability.
3Manufacturing precision
If MFD method is used instead of TPFA, then manufacturing precision is improved, but productivity decreases due to increased computational cost
Solution Approach 1:
The patent segments the computational domain to apply MFD only where necessary (non-K-orthogonal grids, fracture regions) while using TPFA in regular matrix blocks. This segmentation maintains high flux calculation accuracy in critical areas while preserving computational efficiency in larger regular regions.
Solution Approach 2:
The patent changes the numerical method parameter dynamically based on grid properties. For K-orthogonal grids, TPFA is used for efficiency; for non-K-orthogonal grids or fracture regions, MFD is applied for accuracy. This parameter change strategy optimizes the balance between computational cost and accuracy.
Data Source
AI summary
This invention presents a projection embedded discrete fracture model integrating a TPFA and MFD hybrid approach, creating a pEDFM framework for various anisotropic two-phase flow situations. It specifies the distribution of extra pressure freedoms on matrix grids for MFD implementation, maintains f-f connections in TPFA through a standard pEDFM workflow, and introduces a low-conductivity fracture treatment for MFD. It also outlines the derivation of numerical flux calculation formulas for effective m-m and m-f connections. The mixed TPFA-MFD design applies to numerical flux estimation across both K-orthogonal and non-K-orthogonal grids, enhancing computational efficiency and facilitating the spatial discretization of continuity equations for matrix and fracture grids under anisotropic permeability conditions. A global equation system is formulated based on the continuity of effective connections, with time discretization via the implicit backward Euler method and pressure and water saturation distributions determined by a Newton-Raphson based nonlinear solver.