Dynamic Navier-Stokes Flow Transition Modeling
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Solution Overview
Problem
Existing numerical simulation techniques for hydraulic fracturing struggle to accurately model fluid flow in variable environments, relying on a single type of simplified Navier-Stokes equation, which is not ideal for simulating fluid flow in dynamic conditions.
Innovation Solution
An algorithmic approach that automatically switches between different types of Navier-Stokes equations, such as Darcy flow and Poiseuille flow, based on the specific conditions of each layer in a variable geological or physical environment, to improve simulation accuracy and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a single type of simplified Navier-Stokes equation is used for fluid flow modeling, then computational efficiency is improved, but simulation accuracy deteriorates in variable environments
Solution Approach 1:
The patent applies dynamics by making the flow regime selection dynamic rather than static. The system automatically transitions between Darcy flow and Poiseuille flow models based on real-time aperture conditions, allowing the simulation to adapt to changing environmental variables during the hydraulic fracturing process
Solution Approach 2:
The patent implements parameter changes by switching between different mathematical models (Darcy vs. Poiseuille flow equations) based on the aperture parameter. When the aperture exceeds a threshold, the system transitions from Darcy flow to Poiseuille flow, and vice versa, optimizing both accuracy and computational efficiency
2Measurement precision
If different fluid analysis techniques are used for different layers, then simulation accuracy is improved, but device complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the geological formation into multiple layers, each capable of having different fluid analysis techniques assigned. This allows the system to handle heterogeneity in the subsurface environment while maintaining a structured, manageable model framework
Solution Approach 2:
The patent implements universality by creating a unified modeling framework that can accommodate multiple fluid analysis techniques (Darcy flow, Poiseuille flow, and transitional flow) within a single system. The same cohesive element framework handles all flow types, reducing overall system complexity despite the diversity of physical processes
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method allows for more accurate and computationally efficient modeling of fluid flow in hydraulic fracturing and other applications by systematically handling transitions between flow regimes, ensuring the most efficient numerical flow solution is used while maintaining necessary accuracy.
Implementation Method 1
The one or more fluid analysis techniques used to model the flow of fluid in the given layer may include Darcy flow and Poiseuille flow
Implementation Method 2
The one or more fluid analysis techniques used to model the flow of fluid in the given layer may include Darcy flow and Poiseuille flow
Implementation Method 3
An algorithmic approach that automatically switches between different types of Navier-Stokes equations, such as Darcy flow and Poiseuille flow
Data Source
AI summary
Embodiments provide methods and systems for modeling the flow of fluid in variable physical and geological environments using dynamically determined Navier-Stokes equations (NSE), such as Darcy Flow and Poiseuille flow.