CPMG relaxation by diffusion with constant magnetic field gradient in a restricted geometry: numerical simulation and...

Area of Science:

• Geophysics
• Nuclear Magnetic Resonance Spectroscopy
• Petroleum Engineering

Background:

• Carr-Purcell-Meiboom-Gill (CPMG) measurements are vital for nuclear magnetic resonance (NMR) well logging and laboratory analysis of reservoir properties.
• Accurate interpretation of spin-spin relaxation time (T(2)) distributions is essential for estimating bulk volume irreducible (BVI), permeability, and fluid types.
• Diffusion in inhomogeneous fields and restricted geometries complicates T(2) interpretation, especially for non-wetting fluids like oil and gas.

Purpose of the Study:

• To numerically evaluate the impact of field gradient, diffusion, and restricted geometry on CPMG relaxation.
• To reduce the complex parameter space to two dimensionless groups, D* and tau*, for analyzing relaxation regimes.
• To compare numerical simulation results with analytical solutions and refine the understanding of relaxation boundaries.

Main Methods:

• Employed a numerical method to simulate spin diffusion under varying system parameters, neglecting surface relaxation for non-wetting fluids.
• Reduced the relaxation process parameter space to dimensionless groups D* and tau*.
• Identified three distinct relaxation regimes: free diffusion, localization, and motionally averaging, within the (log(10)D*, log(10)tau*) domain.

Main Results:

• The normalized magnetization, M*, was found to relax as a single exponential with a constant dimensionless relaxation time, T*(2), across most of the parameter space.
• Numerical simulations and analytical solutions showed discrepancies in regime boundary locations when based on equal length scales.
• Adjusting boundaries by equalizing T*(2) led to excellent agreement between numerical and analytical results for all identified relaxation regimes.

Conclusions:

• The study successfully identified and characterized three distinct relaxation regimes in CPMG NMR measurements using numerical simulations.
• Refined understanding of relaxation regime boundaries by equalizing T*(2) improves the accuracy of analytical solutions.
• Fluid diffusivity and pore length can be reliably estimated from analytical solutions in the free diffusion and motionally averaging regimes, respectively, with numerical simulations aiding estimations near boundaries.