Porous Medium Permeability via Friction Flow Correlations
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Solution Overview
Problem
Current methods for calculating permeability in porous media fail to accurately consider geometric changes and flow region transitions, particularly in hydraulic fractures, leading to inefficiencies and high costs due to the need for numerous tests across varying conditions.
Innovation Solution
A method using hydraulic diameter-friction factor-Reynolds number correlations to predict permeability, incorporating tortuosity and porosity corrections to account for geometric and flow changes, allowing for reduced testing requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If permeability is calculated using traditional Darcy equation and numerous tests under varying flow conditions, then measurement precision is improved, but loss of time and cost increase significantly
Solution Approach 1:
The patent changes the parameter basis from traditional Darcy equation parameters to friction flow characteristic variables (friction factor, Reynolds number, hydraulic diameter). By establishing correlations between these parameters and permeability, the method achieves accurate permeability prediction without requiring numerous tests under varying flow conditions, thus reducing time loss while maintaining measurement precision
Solution Approach 2:
The patent creates a theoretical model (hydraulic diameter-friction factor-Reynolds number correlation) that copies and represents the complex permeability behavior observed in numerous tests. This correlation model serves as a simplified representation that captures essential flow characteristics, allowing permeability calculation without repeating extensive physical tests
2Reliability
If numerous tests are conducted under varying flow conditions and geometric configurations, then reliability of permeability data is improved, but productivity decreases due to extensive testing requirements
Solution Approach 1:
The patent transforms the approach by changing from measuring permeability directly under various conditions to using friction flow characteristic variables that inherently capture the effects of different flow conditions and geometric configurations. The hydraulic diameter-friction factor-Reynolds number correlation reliably represents permeability behavior across varying conditions without requiring separate tests for each scenario, thus improving productivity while maintaining reliability
Solution Approach 2:
The patent develops a universal correlation model that serves multiple functions: it predicts permeability for different flow conditions (laminar and turbulent), accounts for geometric changes (hydraulic diameter variations), and eliminates the need for separate tests under each condition. This multi-functional correlation improves testing efficiency while ensuring reliable permeability data across diverse scenarios
3Device complexity
If traditional permeability calculation methods are used that ignore geometric changes and flow region transitions, then device complexity is reduced, but measurement precision deteriorates
Solution Approach 1:
The patent improves measurement precision by changing the calculation basis from simple Darcy equation parameters to friction flow characteristic variables (friction factor, Reynolds number, hydraulic diameter). These parameters naturally account for geometric changes and flow region transitions, providing accurate permeability predictions without requiring complex additional corrections or multiple separate calculations
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 approach effectively measures permeability variations in porous media due to geometric and flow changes, including hydraulic fracture closure, by using modified friction flow feature variables and similarity features, reducing the need for extensive testing and improving predictive accuracy.
Implementation Method 1
obtaining hydraulic diameters and friction factor-Reynolds number relationships of a plurality of reference porous media
Implementation Method 2
friction factor-Reynolds number relationships
Implementation Method 3
obtaining hydraulic diameters and friction factor-Reynolds number relationships
Implementation Method 4
obtaining a final hydraulic-diameter-based permeability as the permeability of the porous medium to be predicted, by correcting the hydraulic-diameter-based permeability by using laminar tortuosity
Data Source
AI summary
Provided is a method of calculating permeability of a porous medium by using analysis of feature variables of friction flows through the porous medium for laminar and turbulent flows considering a geometric feature and a friction loss feature. A method of calculating permeability of a porous medium, according to an embodiment of the present invention, includes obtaining hydraulic diameters and friction factor-Reynolds number relationships of a plurality of reference porous media, deriving a hydraulic diameter-friction factor-Reynolds number correlation between the hydraulic diameters and the friction factor-Reynolds number relationships, and obtaining permeability of a porous medium to be predicted, by using the hydraulic diameter-friction factor-Reynolds number correlation.