NMR Echo Train Inversion Using Nonlinear Equality Constraint

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Solution Overview

Problem

Conventional NMR inversion methods for estimating properties of subterranean formations, such as porosity and fluid saturation, are inaccurate due to incorrect selection of the smoothing factor, which is sensitive to noise assumptions that do not hold in downhole applications.

Innovation Solution

A method and system that calculate a T2 distribution using a nonlinear equality constraint and a new smoothing factor defined as the ratio of the L2-norm of measured noise to the L2-norm of the solution, minimizing the objective function and optimizing the solution for the T2 distribution, thereby reducing noise sensitivity.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional NMR inversion methods are used with traditional smoothing factor selection, then the inversion process is computationally simpler, but the estimation accuracy of formation properties deteriorates due to noise sensitivity

Engineering Contradiction:

Improveestimation accuracy of formation propertiesVSAvoidinversion method complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent changes the parameter selection criterion from conventional smoothing factor methods to a new approach based on the L2-norm of measured noise and the L2-norm of the solution. This parameter change enables accurate noise characterization while maintaining inversion accuracy, directly resolving the contradiction between measurement precision and method complexity.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the conventional mechanical/smoothness-based smoothing factor selection with a noise-based L2-norm optimization approach. This substitution allows the inversion to explicitly account for measured noise characteristics, improving estimation accuracy without proportionally increasing computational complexity.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If a new smoothing factor based on L2-norm ratio is used, then noise sensitivity is reduced and estimation accuracy improves, but computational cost increases

Engineering Contradiction:

Improverobustness to noiseVSAvoidcomputational cost

Core Design Contradiction:

ReliabilityVSUse of energy by moving object

Solution Approach 1:

The patent extracts and utilizes the measured noise component separately from the echo train signal. By calculating the L2-norm of the measured noise and using it in the smoothing factor determination, the method explicitly separates noise characterization from signal processing, improving robustness while keeping computational overhead manageable.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent performs preliminary noise measurement and characterization before the inversion process. By pre-calculating the L2-norm of measured noise and using it to determine the smoothing factor in advance, the method reduces noise sensitivity without requiring iterative computational adjustments during the inversion, thereby controlling computational cost.

Inventive Principle:

Principle #10Preliminary action

3Productivity

If conventional smoothing factor selection is used, then the inversion process is faster, but the fitting error between measured and modeled echo trains increases

Engineering Contradiction:

Improveinversion processing speedVSAvoidfitting error between echo trains

Core Design Contradiction:

ProductivityVSManufacturing precision

Solution Approach 1:

The patent implements feedback by using the measured noise information to adjust and optimize the smoothing factor selection. The L2-norm of measured noise provides feedback on the actual noise level present in the data, allowing the inversion to adaptively select appropriate smoothing that minimizes fitting error while maintaining processing efficiency.

Inventive Principle:

Principle #23Feedback

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 approach provides a more accurate and robust estimation of formation properties with reduced computational cost, effectively addressing the limitations of conventional techniques by accounting for noise in echo trains.

Implementation Method 1

Nuclear Magnetic Resonance (NMR) is a technique that is used in the energy industry to estimate properties of subterranean formations. NMR typically involves applying a constant magnetic field and an oscillating magnetic field to a formation region, and detecting NMR signals due to voltage induced in a detector by precession of the nuclear spins of atomic nuclei in the region.

Methodology Applied

Scientific EffectNuclear Magnetic Resonance:

Data Source

PatentUS11231474B2Inversion of NMR echo trains using a supplementary nonlinear equality constraint

Publication Date: 2022.01.25 BAKER HUGHES OILFIELD OPERATIONS LLC

AI summary

A method of estimating properties of a resource bearing formation includes receiving, by a processor, a measured echo train generated by a nuclear magnetic resonance (NMR) measurement device deployed in a region of interest, and a measured noise of the measured echo train, and calculating a T2 distribution subject to a nonlinear equality constraint, the nonlinear equality constraint dependent on the measured noise and a fitting error between the measured echo train and a modeled echo train. Calculating the T2 distribution includes estimating a solution for the T2 distribution that is closest to satisfying the nonlinear equality constraint.