Mean Regression Function for Permeability Prediction
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Solution Overview
Problem
Current methods for determining permeability in oilfield operations often underestimate permeability due to biases in regression methods used with transformation functions, leading to inaccurate predictions.
Innovation Solution
The method computes quantile regression functions (Q10, Q50, Q90) from porosity data, combining them with coefficients to produce a combined mean regression function that predicts mean permeability, using a logarithmic transformation and least squares regression techniques to improve accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional regression methods with transformation functions are used to determine permeability, then the calculation process is simple, but the permeability prediction accuracy deteriorates due to underestimation bias
Solution Approach 1:
The patent segments the regression process into multiple quantile regression functions (Q10, Q50, Q90) that operate on different portions of the data distribution. Each quantile function addresses specific bias issues in different regions, with Q10 correcting underestimation in lower ranges, Q50 handling the median, and Q90 addressing upper range variations. This segmentation resolves the contradiction by improving accuracy through specialized sub-functions rather than a single biased regression.
Solution Approach 2:
The patent changes the regression approach from traditional single-parameter regression to multi-quantile regression with different weighting parameters. By applying different coefficients to different quantile functions (0.25×Q10 + 0.50×Q50 + 0.25×Q90), the method transforms the regression process to eliminate systematic underestimation bias while maintaining computational feasibility through parameter optimization.
2Measurement precision
If quantile regression functions are combined to produce mean regression, then permeability prediction accuracy improves, but the calculation complexity increases
Solution Approach 1:
The patent performs preliminary calculations by pre-computing the three quantile regression functions (Q10, Q50, Q90) from the training data before actual permeability prediction is needed. These quantile functions are stored and can be quickly combined using the weighted formula during production, eliminating the need for real-time complex iterations and reducing calculation time while maintaining accuracy.
Solution Approach 2:
The patent optimizes the computational efficiency by changing the approach from iterative complex regression to a straightforward weighted summation of pre-computed quantile functions. The fixed coefficients (0.25, 0.50, 0.25) are determined in advance, allowing rapid calculation during actual permeability assessment without repeated complex computations.
Data Source
AI summary
A method having obtaining one or more porosity data of a subsurface of the Earth using a data acquisition tool; computing one or more permeability data from the porosity data using a transformation function; computing a first quantile regression function and a second quantile regression function of the one or more permeability data; producing a combined mean regression function of the one or more permeability data by summing the first quantile regression function and the second quantile regression function, wherein the first quantile regression function is multiplied by a first coefficient and the second quantile regression function is multiplied by a second coefficient; and using the combined mean regression function to predict a mean permeability of the subsurface.