Non-linear Forward Model for Gamma Ray Density Prediction
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Solution Overview
Problem
Conventional gamma ray measurement techniques in subterranean formations face limitations due to their assumption of a linear relationship between detector response and formation properties, leading to modest accuracy and computational inefficiencies, particularly in real-time log analysis.
Innovation Solution
A non-linear forward modeling approach is introduced, which calculates the response of a gamma ray measurement tool by assuming a non-linear relationship between properties at multiple spatial locations and the tool's response, using a 2nd-order approximation of sensitivity functions to improve density predictions and computational speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo methods are used for gamma ray measurement analysis, then measurement precision is improved, but productivity deteriorates due to limited computational speed
Solution Approach 1:
The patent creates a simplified copy of the complex Monte Carlo simulation by developing a non-linear forward model that replicates the essential physics of gamma ray interactions. This copy model uses pre-calculated sensitivity functions and non-linear relationships to predict detector responses without requiring full Monte Carlo computations, thereby achieving comparable accuracy at much lower computational cost and enabling real-time log analysis
Solution Approach 2:
The patent transforms the computational approach by changing the mathematical parameters from linear sensitivity functions to non-linear sensitivity functions. This parameter change allows the model to capture the true non-linear relationship between formation properties and detector responses, significantly improving accuracy while maintaining computational efficiency through the use of pre-calculated non-linear sensitivity maps
2Productivity
If linear forward modeling techniques are used, then productivity is improved with sub-second computational speed, but measurement precision deteriorates with modeling errors up to 0.1 g/cc
Solution Approach 1:
The patent fundamentally changes the mathematical parameters from linear sensitivity functions to non-linear sensitivity functions. This parameter transformation allows the model to accurately represent the non-linear physics of gamma ray interactions with formation materials, reducing modeling errors from 0.1 g/cc to significantly lower values while preserving the computational speed advantage of forward modeling techniques
Solution Approach 2:
The patent introduces dynamic non-linear sensitivity functions that adapt to different formation conditions and tool configurations. These dynamic functions are pre-calculated for various scenarios and stored as lookup tables, allowing the model to switch between different non-linear relationships based on the specific measurement conditions, thereby maintaining both high accuracy and computational efficiency
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 method achieves significant improvements in accuracy and versatility, providing accurate density predictions with negligible increase in computational time, capable of handling a wide range of formation densities and drilling conditions, and enabling real-time geosteering in subterranean formations.
Implementation Method 1
By modeling the dominant gamma-ray interactions of Compton scattering and photoelectric absorption
Implementation Method 2
By modeling the dominant gamma-ray interactions of Compton scattering and photoelectric absorption
Data Source
AI summary
Methods and related systems are described for predicting a response of a gamma ray measurement tool located in a borehole surrounded by a subterranean formation. A response of the tool is calculated according to one or more properties at a plurality of spatial locations in relation to the measurement tool using a forward model that assumes a non-linear relationship between the one or more properties at the plurality of spatial locations and the corresponding response of the tool.