Multi-thread Band Matrix Solver for Subterranean Fluid Flow
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Solution Overview
Problem
Current methods for simulating fluid flow in subterranean fracture networks are computationally intensive due to complex solid-fluid interactions and multi-dimensional flow phenomena, making real-time simulations challenging and resource-intensive.
Innovation Solution
The approach involves dividing the simulation into multiple subsystem models connected by junction models, allowing for parallel processing and internal elimination to represent internal variables in terms of junction variables, using sparse matrices and banded linear systems to reduce computational complexity, and employing parallel algorithms like two-thread or multi-thread methods for efficient solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional flow models are used to simulate fluid flow in fracture networks, then simulation accuracy is maintained, but computational resources and time requirements increase significantly
Solution Approach 1:
The fracture network is divided into multiple subsystems, each representing a portion of the network. Each subsystem is solved independently using local elimination techniques, reducing the overall computational burden while maintaining simulation accuracy through proper coupling at junction points.
Solution Approach 2:
The problem is transformed from solving a single large-scale system of equations to solving multiple smaller subsystems in parallel. This dimensional transformation in the solution space enables significant computational speedup while preserving the accuracy of the original flow model.
2Reliability
If complex solid-fluid interactions and multi-dimensional flow phenomena are modeled, then simulation realism is improved, but computational complexity increases
Solution Approach 1:
Complex solid-fluid interactions and multi-dimensional flow phenomena are decomposed into separate subsystems. Each subsystem handles specific physical processes, allowing for specialized numerical treatments that reduce overall computational complexity while maintaining realism through proper coupling of subsystem solutions.
Solution Approach 2:
Different numerical methods and levels of complexity are applied to different subsystems based on their specific physical characteristics. This allows realistic modeling of complex phenomena where needed while using simplified approaches in regions where full complexity is not required, optimizing the balance between realism and computational cost.
Data Source
AI summary
In some aspects, techniques and systems for operating a subterranean region model are described. A band matrix that represents well system fluid flow in a subterranean region is accessed. The band matrix includes flow variable coefficients based on governing flow equations for the well system fluid flow. A first elimination is performed on an upper part of the band matrix. The upper part of the band matrix includes a first subset of the flow variable coefficients corresponding to a first subset of flow variables. In parallel with the first elimination, a second elimination is performed on a lower part of the band matrix. The lower part of the band matrix includes a second subset of flow variable coefficients corresponding to a second subset of the flow variables. An intermediate part of the band matrix can be solved. The intermediate part of the band matrix includes other flow variable coefficients.