Moving Least Squares Design Space Construction

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Solution Overview

Problem

Current methods for constructing a continuous design space from a faulted subsurface reservoir are inefficient, cumbersome, and introduce significant volumetric distortion, making it difficult to model and modify geological concepts in hydrocarbon prospecting and reservoir management.

Innovation Solution

The method employs moving least squares transformation to map a faulted subsurface region to a continuous design space, minimizing objective functions and using decaying weights to control deformation, allowing for efficient and geologically plausible modeling without requiring a grid, thus enabling easy modification and accurate representation of material properties.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Stability of the object's composition

If traditional fault restoration methods are used to construct design space, then the continuous depositional space can be achieved, but the process becomes cumbersome and requires building the geologic model from scratch when modifications are needed

Engineering Contradiction:

Improvecontinuity of design spaceVSAvoidcomplexity of geologic model construction

Core Design Contradiction:

Stability of the object's compositionVSDevice complexity

Solution Approach 1:

The patent creates a continuous design space by copying and transforming the faulted physical space through a mathematical transformation framework. Instead of restoring faults to their pre-fault state, the method copies the faulted geometry and applies a continuous transformation that removes discontinuities, allowing the design space to be populated and modified without rebuilding the entire model.

Inventive Principle:

Principle #26Copying

Solution Approach 2:

The patent transforms the faulted subsurface model into a continuous design space by changing the spatial parameters through a mathematical transformation. The transformation modifies the coordinate system and geometric parameters to eliminate fault discontinuities while preserving the essential geological relationships, enabling continuous property population and easier model modification.

Inventive Principle:

Principle #35Parameter changes

2Stability of the object's composition

If fault restoration techniques are applied to remove discontinuities, then continuous design space is achieved, but significant volumetric distortion is introduced

Engineering Contradiction:

Improvecontinuity of design spaceVSAvoidvolumetric distortion

Core Design Contradiction:

Stability of the object's compositionVSManufacturing precision

Solution Approach 1:

The patent employs a mathematical transformation that changes the spatial parameters to achieve continuity while minimizing volumetric distortion. The transformation framework adjusts coordinate parameters and scaling factors to maintain volume relationships as much as possible while removing fault discontinuities, thereby reducing artificial distortion compared to traditional restoration methods.

Inventive Principle:

Principle #35Parameter changes

3Stability of the object's composition

If grid-based methods are used for transformation, then structured data organization is achieved, but computational complexity and time consumption increase

Engineering Contradiction:

Improvedata organizationVSAvoidcomputational efficiency

Core Design Contradiction:

Stability of the object's compositionVSProductivity

Solution Approach 1:

The patent replaces the mechanical grid-based transformation approach with a mathematical field-based transformation. Instead of discretizing space into grid cells and transforming each cell individually, the method uses continuous mathematical functions to define the transformation, significantly reducing computational complexity and execution time while maintaining data organization.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Measurement precision

If the geologic model is modified with new data, then updated accuracy is achieved, but the entire model must be rebuilt from scratch

Engineering Contradiction:

Improvemodel accuracyVSAvoidtime to rebuild model

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent performs preliminary action by creating the continuous design space transformation framework upfront. Once the transformation is established, new data can be integrated and the model can be updated by applying changes within the existing continuous framework rather than rebuilding the entire model, significantly reducing the time required for model updates while maintaining accuracy.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS11409023B2Methods to handle discontinuity in constructing design space using moving least squares

Publication Date: 2022.08.09 EXXONMOBIL UPSTREAM RESEARCH COMPANY(US)

AI summary

Method for constructing a continuous design space for generating a physical property model in a faulted subsurface medium. The matching relationship of the fault traces on the two sides of each fault is used in a systematic way to determine the location of the fault traces in the design space. The location of any other point in the design space may then be determined by interpolation of the locations of fault traces. The fault traces are thus used as control points for the mapping. The method involves: (a) identifying the control points and determining their location in both physical and design space and (b) using selected control points, mapping any point from physical space to design space, preferably using the moving least squares method.