Non-uniform NMR Pulse Sequences for Fluid Property Estimation
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Solution Overview
Problem
Traditional NMR well-logging methods for estimating fluid properties are hindered by the ill-conditioned nature of inverse Laplace transforms, leading to errors in relaxation and diffusion distributions, which propagate into inaccuracies in petrophysical and hydrocarbon property estimation.
Innovation Solution
A method involving non-uniformly spaced pulse sequences that directly measure moments of relaxation or diffusion distributions, allowing for direct computation of fluid properties like average chain length and viscosity, bypassing the need for inverse Laplace transforms and reducing estimation errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional uniformly spaced pulse sequences are used for NMR measurements, then the measurement process is simple and straightforward, but the estimation of fluid properties suffers from high errors due to the ill-conditioned nature of inverse Laplace transforms
Solution Approach 1:
The patent changes the temporal spacing parameter of the pulse sequence from uniform to non-uniform intervals. Specifically, the measurement times are selected according to a power law distribution rather than uniform spacing, which transforms the ill-conditioned inverse Laplace transform problem into a well-conditioned moment estimation problem, thereby significantly improving measurement precision
Solution Approach 2:
The patent replaces the traditional mechanical/mathematical approach of uniform sampling with inverse Laplace transform with a new approach based on non-uniform sampling and direct moment calculation. This substitution eliminates the need for ill-conditioned mathematical transformations and directly yields accurate fluid property estimates through simpler moment-based calculations
2Measurement precision
If non-uniformly spaced pulse sequences are used to directly measure moments, then the accuracy of fluid property estimation is improved, but the complexity of determining optimal measurement intervals increases
Solution Approach 1:
The patent applies power law spacing to the measurement intervals, where the time between successive measurements follows a power law distribution. This parameter transformation simplifies the determination of optimal intervals by providing a clear mathematical formula based on the desired moment order, eliminating the need for complex optimization procedures
Solution Approach 2:
The patent performs preliminary determination of the power law exponent based on the specific moment to be measured. By pre-calculating the appropriate spacing parameters before measurement, the system eliminates the need for complex real-time optimization during the measurement process, making the procedure straightforward while maintaining high accuracy
3Reliability
If traditional inverse Laplace transform methods are used, then the measurement process is straightforward, but errors in relaxation and diffusion distributions propagate into inaccuracies in petrophysical and hydrocarbon property estimation
Solution Approach 1:
The patent extracts and directly measures the moments of relaxation and diffusion distributions through non-uniformly spaced pulse sequences, bypassing the need for full distribution reconstruction via inverse Laplace transform. This extraction approach eliminates error propagation to petrophysical properties while maintaining computational efficiency through direct moment calculation
Solution Approach 2:
Instead of using inverse Laplace transform to reconstruct distributions from uniformly spaced data, the patent inverts the approach by using non-uniformly spaced measurements to directly obtain moments. This inversion strategy transforms a computationally intensive and error-prone process into a simple and reliable moment estimation procedure
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 faster and more accurate estimation of fluid properties with lower error bars, improving the reliability of petrophysical and hydrocarbon property assessments.
Implementation Method 1
Nuclear Magnetic Resonance (NMR) are obtained by study of longitudinal or transverse relaxation or diffusion measurements
Implementation Method 2
The multi-exponential time-decay of NMR magnetization is characterized by relaxation time constants T1, T2
Data Source
AI summary
Methods and related systems are described for estimating fluid or rock properties from NMR measurements. A modified pulse sequence is provided that can directly provide moments of relaxation-time or diffusion distributions. This pulse sequence can be adapted to the desired moment of relaxation-time or diffusion coefficient. The data from this pulse sequence provides direct estimates of fluid properties such as average chain length and viscosity of a hydrocarbon. In comparison to the uniformly-spaced pulse sequence, these pulse sequences are faster and have a lower error bar in computing the fluid properties.