Formation Top Estimation Using Gridded Delaunay Interpolation
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Solution Overview
Problem
Existing methods for estimating formation tops in drilling wells face challenges due to missing well logs, subjective manual processes, and the requirement for standardized digital well logs, which are often unavailable, and interpolation methods lack easy application of Delaunay's triangulation.
Innovation Solution
A method utilizing a stacked and gridded interpolation approach, involving grid construction from offset wells, Delaunay triangulation, and applying interpolation methods like linear, cubic, or spline to estimate formation tops in proposed drilling wells.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If manual interpretation of well logs is used to estimate formation tops, then flexibility in handling incomplete data is improved, but subjectivity and time consumption increase
Solution Approach 1:
The patent segments the formation top estimation process into discrete computational steps: grid construction from available well data, Delaunay triangulation of the grid points, and interpolation calculations. This segmentation allows automated processing of incomplete data through systematic handling of missing wells or intervals, while eliminating manual subjectivity and reducing time consumption through algorithmic execution.
Solution Approach 2:
The patent introduces Delaunay triangulation as an intermediary geometric structure between the discrete well data points and the continuous formation top surface. This intermediary allows automated interpolation to handle incomplete data flexibly by constructing triangles from available points, while the computational nature of the triangulation process eliminates manual subjectivity and accelerates the estimation process.
2Loss of time
If automated warping algorithms are used to estimate formation tops, then time consumption is reduced, but requirements for standardized digital well logs increase complexity
Solution Approach 1:
The patent changes the parameter representation from requiring standardized digital well logs to using flexible grid coordinates derived from available well data. By constructing grids from actual measured points and using Delaunay triangulation, the method accepts various data formats and completeness levels, reducing the complexity requirement while maintaining automated processing speed.
Solution Approach 2:
The patent segments the data processing into grid construction from available wells, triangulation of grid points, and interpolation steps. This segmentation allows the system to process incomplete or non-standardized data by working only with available well locations, eliminating the need for complete standardized logs while maintaining automated efficiency.
3Measurement precision
If Delaunay triangulation is applied to formation top estimation, then interpolation accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent segments the computational domain into triangular elements through Delaunay triangulation of grid points. This segmentation improves interpolation accuracy by creating optimal triangular meshes that maximize minimum angles, while the systematic algorithmic approach to triangulation keeps computational complexity manageable through efficient geometric algorithms.
Solution Approach 2:
The patent uses Delaunay triangulation to transform the 2D grid of well locations into a 3D interpolation framework by creating tetrahedral elements. This dimensional transformation improves accuracy by providing a more robust geometric basis for interpolation, while the structured nature of the triangulation maintains computational efficiency.
Data Source
AI summary
System and methods are disclosed relating to estimating formation tops for a proposed drilling well ahead of its drilling by taking known depths for each formation from offset wells, converting these known depths to a gridded set of points, forming a polygon, and then evaluating the depth of a new point in the polygon by using any of the linear, cubic, Akima, or spline interpolation methods. Performing this for all the formation tops creates a stack of grids, and the stacked grids are solved recursively to generate a complete formation tops profile for a proposed drilling well.