NMR Inversion Model for Internal Gradients and Restricted Diffusion
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Solution Overview
Problem
Current NMR measurement techniques for boreholes fail to accurately account for internal magnetic field gradients and restricted diffusion effects, leading to overestimation of diffusivity in fluid typing applications, particularly in sedimentary rocks with varying paramagnetic material distributions.
Innovation Solution
A method and apparatus that incorporate internal gradient and restricted diffusion effects into the data inversion process using a model defining the measured relaxation rate as a function of diffusivity, intrinsic transverse relaxation time, and magnetic susceptibility contrast, involving a logging tool with a magnet to generate an internal magnetic field gradient and a processor to estimate diffusion properties from NMR signals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional free diffusion models are used for NMR data interpretation, then the measurement process is simple and fast, but the diffusion property estimation becomes inaccurate due to unaccounted internal gradients and restricted diffusion effects
Solution Approach 1:
The patent transforms the NMR data interpretation problem by changing the mathematical parameters in the inversion model. It incorporates internal gradient effects and restricted diffusion effects by modifying the relaxation rate equation to include additional parameters: magnetic susceptibility contrast (Δχ), pore radius (a), and diffusion coefficient (D). This allows the model to account for the complex physical phenomena while maintaining a systematic approach to parameter estimation.
Solution Approach 2:
The patent introduces an intermediary approach by using a simplified analytical model that bridges the gap between complex numerical simulations and simple free diffusion models. The model uses closed-form expressions for the relaxation rate that incorporate the effects of internal gradients and restricted diffusion, providing an intermediate level of complexity that improves accuracy without requiring full numerical inversion.
2Measurement precision
If internal gradient effects are incorporated into the NMR model, then diffusion property estimation accuracy improves, but the computational complexity of data inversion increases
Solution Approach 1:
The patent changes the mathematical formulation by introducing dimensionless parameters that simplify the computational burden. By defining dimensionless diffusion coefficient (D*) and using normalized time variables, the patent reduces the computational complexity of inverting data that includes internal gradient effects, making the process more efficient while maintaining accuracy.
Solution Approach 2:
The patent applies local quality by making the model adaptable to different measurement conditions. The inversion process can selectively incorporate internal gradient effects when the magnetic susceptibility contrast is significant, while using simpler models when appropriate, thus optimizing processing time based on the specific geological context.
3Reliability
If restricted diffusion effects are accounted for in the inversion model, then the reliability of reservoir evaluation improves, but the difficulty of detecting and measuring increases
Solution Approach 1:
The patent transforms the difficult-to-measure restricted diffusion effects into measurable parameters by changing the mathematical representation. It introduces the pore radius (a) as an explicit parameter in the relaxation rate equation, which can be estimated from the NMR data along with the diffusion coefficient. This parameter transformation makes the restricted diffusion effects detectable and measurable through standard NMR logging techniques.
Solution Approach 2:
The patent segments the complex relaxation process into distinct components: bulk relaxation, surface relaxation, internal gradient effects, and restricted diffusion effects. By separating these contributions in the inversion model, each parameter can be determined more reliably through multi-parameter fitting of the NMR echo train data.
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 significantly improves the accuracy of diffusion property estimation by accounting for internal gradients, reducing errors in fluid typing and reservoir evaluation, and providing more precise data interpretation compared to traditional free diffusion models.
Implementation Method 1
using a magnet on the logging tool for applying a magnetic field to polarize nuclei in a pore space of a region of examination in the earth formation, the applied magnetic field generating an internal magnetic field gradient in the pore spaces
Implementation Method 2
applying a radio frequency (RF) field to excite the nuclei; receiving nuclear magnetic resonance (NMR) signals from the excited nuclei
Implementation Method 3
The problem of diffusive motion under constraints of pore boundaries has many implications... the exact influence of the internal gradient with restricted diffusion effect is unknown
Implementation Method 4
the internal gradient is mainly produced by paramagnetic ions... magnetic susceptibility contrast between a fluid in the pore spaces and a material of a matrix of the earth formation
Data Source
AI summary
Pulse sequences are applied to a fluid in an earth formation with an external static magnetic field and NMR spin echo signals are obtained. The received NMR signals are affected by internal field gradients due to a contrast in magnetic susceptibility between the grains of the formation matrix and the fluid in the pore space. Processing of the data gives the relaxation time and diffusivity of the fluid.