Borehole Shape Determination Using Probability Functions
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Solution Overview
Problem
Current methods for determining the shape of a borehole in a subsurface formation are complex and require multi-variate optimization processes, making them inefficient for accurate and rapid shape assessment, which is crucial for hydrocarbon extraction and well completion.
Innovation Solution
The use of probability functions, such as probability density functions and cumulative distribution functions, to determine the semimajor and semiminor axes of a borehole shape based on apparent diameters measured by ultrasonic calipers, reducing computational complexity and enabling efficient shape determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-variate optimization processes are used to determine borehole shape, then measurement precision is improved, but device complexity and processing time increase
Solution Approach 1:
The patent extracts only the essential parameters needed for borehole shape determination (standoff measurements and apparent diameters) and applies probability functions specifically tailored for ellipse parameter estimation. This selective approach removes unnecessary computational complexity while preserving measurement precision by focusing only on the critical variables: semimajor axis, semiminor axis, and orientation.
Solution Approach 2:
The patent transforms the complex multi-variate optimization problem into a simpler parameter estimation problem by changing the mathematical approach from general optimization to probability-based estimation. By using probability density functions and cumulative distribution functions, the method converts multiple interdependent variables into a framework that directly estimates ellipse parameters, significantly reducing computational complexity while maintaining accuracy.
2Measurement precision
If multi-variate optimization processes are used to determine borehole shape, then measurement precision is improved, but processing time increases
Solution Approach 1:
The patent extracts and focuses exclusively on the essential measurements (standoff and apparent diameter) required for borehole shape determination, eliminating time-consuming computations of unnecessary parameters. By applying probability functions that directly estimate ellipse parameters from these extracted measurements, the method achieves rapid processing while maintaining measurement precision.
Solution Approach 2:
The patent changes the computational paradigm from iterative multi-variate optimization to direct probability-based parameter estimation. This parameter transformation allows the system to calculate borehole shape parameters (semimajor axis, semiminor axis, orientation) in a single computational pass using probability density and cumulative distribution functions, dramatically reducing processing time while preserving accuracy.
3Productivity
If simple methods are used to determine borehole shape, then processing time is reduced, but measurement precision deteriorates
Solution Approach 1:
The patent replaces complex mechanical optimization processes with a mathematical probability-based system. Instead of using iterative mechanical adjustment and optimization algorithms, the invention uses probability density functions and cumulative distribution functions to directly calculate borehole parameters from measurements, achieving both simplicity and precision simultaneously.
Solution Approach 2:
The patent transforms the measurement and analysis approach by changing from direct geometric measurement to probability-based parameter estimation. This parameter transformation enables the system to derive accurate borehole shape parameters (semimajor axis, semiminor axis, orientation) through statistical functions, maintaining high precision while achieving rapid processing suitable for real-time drilling operations.
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 simplifies the determination of borehole shape by identifying semimajor and semiminor axes through probability functions, reducing processing time and allowing for accurate borehole shape assessment without the need for complex multi-variate optimization, facilitating efficient hydrocarbon extraction and well completion.
Implementation Method 1
A logging while drilling (LWD) tool having an ultrasonic caliper is inserted into the borehole. The ultrasonic caliper transmits ultrasonic waves and receives reflections from the borehole wall at different rotational angles of the tool.
Implementation Method 2
The shape of the borehole can be determined based on a diameter of the tool and a travel time of the ultrasonic waves from the tool to a wall of the borehole and back to the tool.
Data Source
AI summary
A method includes positioning a downhole tool in a borehole formed in a subsurface formation, wherein the downhole tool comprises a plurality of calipers arranged around a circumference of the downhole tool. The method includes detecting, using the plurality of calipers, a plurality of standoff measurements at different rotation angles and determining a plurality of apparent diameters of the borehole for the different rotation angles of the downhole tool based on the plurality of standoff measurements and at least one of a radius and a diameter of the downhole tool. The method includes determining a probability function based on the plurality of apparent diameters and determining a shape of the borehole based on the probability function.