Plane-Surface Intersection Algorithm for Geological Formation Modeling

Solution Overview

Problem

Current mathematical models of geological formations for hydrocarbon production lack accuracy in representing surface boundaries and intersections with planes, affecting the estimation of hydrocarbon producibility and related factors such as stress and earthquake likelihood.

Innovation Solution

A computer-implemented method for determining the intersection between a surface boundary representation in an earth formation and a plane, using a processor to accurately handle boundary-plane intersections and calculate surface-plane intersection lines, improving the accuracy of further processing for drilling and hydrocarbon extraction.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional intersection algorithms are used for geological formation modeling, then the computational process is simpler, but the accuracy of surface boundary representation and intersection calculation deteriorates

Engineering Contradiction:

Improveaccuracy of surface boundary representationVSAvoidcomplexity of intersection algorithm

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The boundary is segmented into multiple straight line segments, and the algorithm processes each segment individually to determine its relationship with the cutting plane. This segmentation allows for precise calculation of intersection points while maintaining a systematic and manageable computational approach.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The algorithm performs preliminary classification of boundary segments into three categories (above plane, below plane, intersecting plane) before calculating final intersection points. This preliminary action ensures that only relevant segments are processed in detail, improving both accuracy and computational efficiency.

Inventive Principle:

Principle #10Preliminary action

2Measurement precision

If conventional intersection algorithms are used, then the algorithm implementation is faster, but the accuracy of hydrocarbon producibility estimation deteriorates

Engineering Contradiction:

Improveaccuracy of hydrocarbon producibility estimationVSAvoidcomputation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The algorithm performs preliminary classification of boundary segments into three categories (above plane, below plane, intersecting plane) before calculating final intersection points. This preliminary action ensures that only relevant segments are processed in detail, improving both accuracy and computational efficiency.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The algorithm calculates intersection points only for segments that actually intersect the cutting plane, rather than processing all boundary segments uniformly. This partial action approach reduces unnecessary computations while ensuring accurate results for relevant intersections.

Inventive Principle:

Principle #16Partial or excessive action

3Reliability

If simple boundary intersection methods are used, then the computational complexity is lower, but the reliability of formation model accuracy deteriorates

Engineering Contradiction:

Improvereliability of formation model accuracyVSAvoidcomplexity of boundary handling

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The boundary is segmented into multiple straight line segments, and the algorithm processes each segment individually to determine its relationship with the cutting plane. This segmentation allows for precise calculation of intersection points while maintaining a systematic and manageable computational approach.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The algorithm uses the Z-coordinate values of boundary points relative to the cutting plane as feedback to determine segment classification. This feedback mechanism ensures that each segment is correctly identified and processed according to its spatial relationship with the plane, enhancing model reliability.

Inventive Principle:

Principle #23Feedback

Data Source

PatentEP3208637B1Plane-surface intersection algorithm with consistent boundary support

Publication Date: 2021.11.03 BAKER HUGHES CO

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AI summary

A method (80) for determining an intersection between a polygon representing a boundary (101) of a surface (100) in an earth formation (4) and a plane (102) includes: receiving a polygon representing a boundary of a surface in an earth formation, the polygon having a series of straight segments with a point at each end of each of the segments; overlaying a cutting grid having grid planes over the polygon; identifying a specific pattern of two adjacent segments in the polygon by proceeding from a first segment to a second segment in a selected rotational direction; matching the specific pattern to a reference pattern; categorizing the point between the two adjacent segments as an intersection point (200) or as a non-intersection point based on the reference pattern; the iterating the identifying, matching, and categorizing for each pair of adjacent segments in the polygon such that each point between adjacent segments in the polygon is categorized.