Borehole Image Reconstruction Using Sparse Transform Inversion
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing borehole imaging tools often produce incomplete images due to tool limitations, leading to inefficient wellbore operations and inadequate formation interpretation.
Innovation Solution
An image generator uses mathematical transformations, such as discrete cosine and Fourier transforms, to generate a complete borehole image from sparse downhole data, filling in missing data and providing 100% azimuthal coverage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If borehole imaging tools are used with limited size or specification, then the tool can be deployed in the borehole, but the generated image is incomplete and insufficient for formation interpretation
Solution Approach 1:
The patent replaces the mechanical limitation of the imaging tool with a mathematical signal processing system. Instead of improving the physical tool specifications, the invention uses discrete cosine transforms and optimization algorithms to reconstruct complete borehole images from incomplete measurements, substituting mechanical complexity with computational processing.
Solution Approach 2:
The invention changes the parameter representation of the borehole image data by transforming it into the discrete cosine transform domain. This parameter transformation allows the system to work with sparse data more effectively and reconstruct complete images by optimizing the representation in the transformed domain rather than working directly with the limited raw measurements.
2Productivity
If sparse downhole data is used, then data acquisition is faster and easier, but the resulting image is incomplete and contains artifacts
Solution Approach 1:
The patent substitutes the physical data collection process with a mathematical reconstruction process. Rather than acquiring more physical measurements, the system uses discrete cosine transforms and Lp-norm optimization to infer missing data, replacing the need for extensive physical measurements with computational inference.
Solution Approach 2:
The discrete cosine transform acts as an intermediary that bridges the gap between sparse measurements and complete images. The transformation domain serves as an intermediate representation where the optimization process can effectively recover missing information before transforming back to the spatial domain to produce the final complete image.
3Loss of information
If traditional interpolation and extrapolation methods are used, then incomplete data can be filled, but artifacts are introduced and minimum sampling density requirements are not met
Solution Approach 1:
The invention fundamentally changes the parameter space by transforming data into the discrete cosine transform domain before processing. This parameter change allows the optimization algorithm to work with the inherent structure of borehole image data, recovering missing information without introducing the artifacts that plague traditional spatial domain interpolation methods.
Solution Approach 2:
The patent replaces traditional interpolation and extrapolation mechanical processes with an optimization-based mathematical approach. Instead of mechanically extending data points, the system uses Lp-norm minimization in the transform domain to infer missing data, achieving superior image quality without the sampling density constraints of traditional methods.
Data Source
AI summary
A system can receive downhole acquisition data relating to a wellbore. The system can pre-process the downhole acquisition data. The system can generate an incomplete borehole image using the downhole acquisition data. The system can determine a sparse representation based on the incomplete borehole image by performing an optimization with respect to the incomplete borehole image. The system can generate a complete borehole image based on an inverse of the sparse representation.