Permeability Prediction via Anisotropic Concentric Annulus Model
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Solution Overview
Problem
Current methods for predicting permeability in porous media are limited by the complexity of internal structures and the lack of precise internal information, leading to inaccurate flow theories and definitions of state variables.
Innovation Solution
A method based on an anisotropic flow model, which involves establishing a concentric annulus flow model, calculating interstitial flow velocity, hydraulic tortuosity, and hydraulic diameter, and using these parameters to predict permeability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional flow theories (Darcy's equation, Kozeny's equation, Kozeny-Carman equation) are used for permeability prediction, then the theoretical framework is simple and well-established, but the prediction accuracy is limited due to the complex internal structure of porous media and lack of precise internal information
Solution Approach 1:
The patent segments the porous medium into concentric annular elements, transforming the complex three-dimensional pore structure into a series of simplified two-dimensional annular flow paths. This segmentation allows the application of classical flow equations to each annular element while capturing the overall anisotropic flow behavior through integration, thereby improving permeability prediction accuracy without requiring complex 3D internal structure data
Solution Approach 2:
The patent introduces anisotropic permeability parameters (k_r for radial direction, k_a for axial direction) that change according to the flow direction and pore structure characteristics. By incorporating direction-dependent permeability parameters and anisotropic tortuosity factors into the flow model, the system accurately reflects the directional flow properties of porous media while maintaining a manageable mathematical framework
2Reliability
If the internal structure of porous media is observed in detail to improve flow theory, then the measurement precision of flow properties improves, but the difficulty of detecting and measuring internal pathways increases due to microscopic and nanoscopic scales and opacity
Solution Approach 1:
The patent creates a simplified two-dimensional concentric annular copy of the three-dimensional porous medium structure. This copy captures the essential flow characteristics (porosity, tortuosity, permeability) in an analytically tractable form, allowing rigorous flow theory development without requiring direct observation of the complex microscopic pore network. The annular model serves as a representative simplified geometry that preserves key flow physics
Solution Approach 2:
The patent introduces effective medium parameters (effective permeability, effective tortuosity, hydraulic radius) as intermediaries that bridge the gap between microscopic pore-scale phenomena and macroscopic flow observations. These intermediary parameters allow the formulation of rigorous flow equations at the macroscopic level without requiring direct measurement or detailed knowledge of microscopic pore pathways
3Measurement precision
If anisotropic flow model with concentric annulus is used, then the correlation between hydraulic tortuosity and permeability improves, but the calculation complexity increases
Solution Approach 1:
The patent applies different flow properties and parameters to different regions of the porous medium represented by concentric annular elements. Each annular element has its own local porosity, tortuosity, and permeability characteristics that reflect the radial variation in pore structure. This local quality approach allows accurate representation of anisotropic flow without requiring a fully complex three-dimensional model
Solution Approach 2:
The patent transforms the three-dimensional porous medium problem into a two-dimensional concentric annular problem by integrating flow properties over the radial dimension. This dimensionality reduction simplifies the mathematical formulation while preserving the essential anisotropic flow characteristics through the use of radial and axial permeability components and effective tortuosity factors
Data Source
AI summary
Provided a method of predicting permeability of porous material based on anisotropic flow model. The method of predicting permeability of porous material based on anisotropic flow model comprises: providing a porous medium; establishing a concentric annulus flow model for the porous medium; calculating a concentric annulus cylinder interstitial flow velocity, a concentric annulus cylinder hydraulic tortuosity, and a concentric annulus cylinder hydraulic diameter using the concentric annulus flow model; and predicting a permeability for the porous medium using the concentric annulus cylinder hydraulic tortuosity and the concentric annulus cylinder hydraulic diameter.