Multiphase Flow Simulation in Fractured Reservoirs Using Hybrid MFD-SL
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Solution Overview
Problem
Existing methods for simulating multiphase flow in fractured reservoirs are inefficient and lack accuracy, particularly in terms of numerical diffusion error and computational cost, limiting their applicability and effectiveness in reservoir-scale simulations.
Innovation Solution
A hybrid mimetic finite difference and streamline (MFD-SL) approach is employed, where mimetic finite difference is used to discretize the pressure equation and streamline method to solve the saturation equation, applicable to triangular and tetrahedral grids, reducing numerical diffusion error and improving computation efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional numerical methods (Galerkin FE, cell centered FV, control volume FE, mixed FE, boundary element, mimetic finite difference) are used to simulate multi-phase flow in fractured formations, then the simulation can be performed, but the computation cost is high and numerical diffusion error is significant
Solution Approach 1:
The domain is segmented into discrete fracture model (DFM) with explicit representation of fractures and rock-matrix using unstructured grid elements. The pressure equation is discretized separately from the saturation equation, allowing independent optimization of each computational step.
Solution Approach 2:
A streamline-based approach is introduced as an intermediary method to solve the saturation equation. Streamlines serve as computational pathways that trace fluid flow from injection to production wells, enabling accurate saturation calculation without the high computational cost of conventional full-field numerical methods.
Solution Approach 3:
The saturation equation is solved along 1D streamlines rather than in the full 3D domain. This dimensional reduction transforms a complex multi-dimensional problem into a series of simpler one-dimensional problems along flow paths, significantly reducing computational complexity while maintaining accuracy.
2Manufacturing precision
If discrete-fracture model (DFM) with unstructured grid elements is used to explicitly represent fractures and rock-matrix, then detailed characterization is achieved, but the device complexity and computation cost increase
Solution Approach 1:
The fractured formation is segmented into distinct fracture elements and rock-matrix elements within the DFM framework. Each element type can be characterized with appropriate properties and governing equations, allowing detailed representation without requiring a single unified complex model for the entire domain.
Solution Approach 2:
Streamline tracing acts as an intermediary computational approach that simplifies the solution process for complex DFM. By following streamline paths through the unstructured grid, the method handles the complexity of explicit fracture representation without requiring equally complex solution algorithms.
3Measurement precision
If streamline tracing method is implemented on triangular and tetrahedral grids in DFM, then numerical diffusion error is reduced and computation efficiency is improved, but the method complexity increases
Solution Approach 1:
The saturation equation is transformed from a 3D partial differential equation to a series of 1D ordinary differential equations along streamline paths. This dimensional reduction simplifies the mathematical complexity while maintaining the ability to handle complex unstructured triangular and tetrahedral grids used in DFM.
Solution Approach 2:
Streamlines are pre-computed based on the pressure field before solving the saturation equation. This preliminary step establishes the flow paths that will be used for saturation calculation, separating the complexity of flow path determination from the saturation solution process.
Data Source
AI summary
A method for performing fluid extraction from a fractured subsurface formation includes receiving a discrete fracture model representing the fractured subsurface formation and receiving pressure values and saturation values for multiple fluid phases across the discrete fracture model. Based on the pressure values for the multiple fluid phases across the discrete fracture model, face-centroid velocities are generated for the cells and the pressure values for the multiple fluid phases are updated by performing operations including a mimetic finite difference analysis. Based on the generated face-centroid velocities, an exit face and time-of-flight is determined for each cell and the saturation values are updated for the multiple fluid phases across the discrete fracture model based on the exit face and time-of-flight for each cell.