NMR T2-Diffusion Probability Density Estimation

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Solution Overview

Problem

Existing methods for characterizing fluid types in geological formations using NMR diffusion modulated amplitude data face challenges in computational intensity and loss of original data during compression, limited to zero-order regularization, and inability to independently regularize transverse relaxation time and diffusion distributions.

Innovation Solution

Computing apparent and intrinsic probability density functions from NMR measurements by partitioning variables, using regularization parameters to improve solution smoothness, and reducing the problem space through T2 and D inversions to efficiently estimate fluid types and distributions, allowing for accurate fluid typing and well completion decisions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If data compression algorithms are applied to reduce computational intensity, then processing speed is improved, but original data values are lost

Engineering Contradiction:

Improvecomputational intensityVSAvoidoriginal data values

Core Design Contradiction:

ProductivityVSLoss of information

Solution Approach 1:

The patent segments the probability density function estimation into multiple discrete bins along the T2 and diffusion axes. By dividing the continuous parameter space into discrete segments, the method enables accurate reconstruction of original data values from compressed measurements, resolving the contradiction between computational efficiency and data integrity.

Inventive Principle:

Principle #1Segmentation

2Device complexity

If zero-order regularization matrix is used for probability density function, then computational simplicity is maintained, but independent regularization of T2 and diffusion distributions is not possible

Engineering Contradiction:

Improveregularization matrix complexityVSAvoidindependent regularization capability

Core Design Contradiction:

Device complexityVSAdaptability or versatility

Solution Approach 1:

The patent transitions from zero-order (0th derivative) regularization to second-order regularization by incorporating the second derivative of the probability density function. This dimensional change in the regularization order enables independent control of smoothness for both T2 and diffusion distributions while maintaining computational tractability through the discrete binning approach.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Data Source

PatentUS8044662B2Estimating T2-diffusion probability density functions from nuclear magnetic resonance diffusion modulated amplitude measurements

Publication Date: 2011.10.25 HALLIBURTON ENERGY SERVICES INC

AI summary

In some embodiments, apparatus and systems, as well as methods, may operate to acquire data representing a plurality of nuclear magnetic resonance (NMR) echo trains associated with a material, such as a geological formation. Additional operations may include inverting a model of at least one of the plurality of NMR echo trains to provide an estimated distribution of transverse relaxation time constants, inverting models of selected ones of the plurality of NMR echo trains using the estimated distribution of transverse relaxation time constants to provide an estimated diffusion distribution, and inverting a model of selected ones of the plurality of NMR echo trains, using the estimated distributions of transverse relaxation time constants and diffusion, to provide an apparent and an intrinsic probability density function to identify fluid types in the material.