Porosity Prediction via Variable Compression Index
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Solution Overview
Problem
Existing models for estimating porosity in marine sediments are limited by their reliance on a single constant for compaction, which is only applicable over a small range of void ratios, leading to inaccurate predictions and potential for physically impossible negative void ratios.
Innovation Solution
An empirical model expressing void ratio as a fraction of the difference between depositional maximum and minimum residual porosity, with the compression index represented as the square root of the proportional void ratio, allowing for a single model to span the full range of compaction and avoiding negative void ratios.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a single constant compression index is used for porosity estimation, then the model is simple to implement, but the prediction accuracy deteriorates outside a small range of void ratios and can produce physically impossible negative values
Solution Approach 1:
The compression index is transformed from a static constant to a dynamic variable that changes with void ratio. The patent implements this by defining the compression index as a function of the current void ratio relative to minimum and maximum void ratios, allowing the model to adapt its compaction behavior across different porosity states and avoid the limitations of a fixed constant approach
Solution Approach 2:
The patent changes the parameter representation from a single constant compression index to a variable compression index that depends on the current void ratio. This is achieved by introducing minimum and maximum void ratio parameters and expressing the compression index as a function of the proportional void ratio, thereby expanding the model's applicability range while maintaining physical realism
2Measurement precision
If the compression index is made variable based on void ratio, then the porosity prediction accuracy improves across the full compaction range, but the model complexity increases
Solution Approach 1:
The patent segments the compaction process into distinct phases by identifying minimum and maximum void ratio boundaries. The compression index is then expressed as a function of the current void ratio's position within this segmented range (proportional void ratio), allowing different compaction behaviors to be captured in different segments while maintaining a unified mathematical framework
Solution Approach 2:
The patent creates a universal porosity model that can handle the full range of compaction conditions using a single unified equation. The variable compression index formulation allows the same model structure to accurately represent both early-stage and late-stage compaction, as well as predict porosity under future stress conditions, without requiring separate empirical relationships for different regimes
Data Source
AI summary
Systems and methods relate to generating a self-consistent sediment model. Initially, void ratio extrema are determined for each sediment layer in a sediment column based on historical data or a direct measurement of the sediment column. Initial stress is determined for each sediment layer based on the void ratio extrema. A porosity model is generated for each sediment layer based on the void ratio extrema and the initial stress. At this stage, measured data is obtained for each sediment layer from a data collection device positioned at or near a geographic location of the sediment column. The porosity model of each of the sediment layer is combined with the measured data of the sediment layer to generate the self-consistent sediment model for each sediment layer. The porosity model and the self-consistent sediment model of each sediment layer is updated based on updated measured data obtained from the data collection device.