Model to interpret pulsed-field-gradient NMR data including memory and superdispersion effects

Area of Science:

• Geophysics
• Physical Chemistry
• Fluid Dynamics

Background:

• Quantitative interpretation of Nuclear Magnetic Resonance (NMR) velocimetry data is crucial for understanding fluid flow in porous media.
• Existing models may not fully capture complex flow behaviors, including intermittent low velocities and rare high-velocity events.

Purpose of the Study:

• To propose a versatile model for the quantitative interpretation of NMR velocimetry data.
• To incorporate mechanisms of random arrests and long displacements into dispersion theory.
• To provide analytical expressions for NMR signals based on subordinated Lévy processes.

Main Methods:

• Utilized the Lagrangian form of dispersion theory with mobile/immobile tracer particles.
• Incorporated independent random arrests and rare long displacements to simulate complex flow.
• Derived analytical expressions for pulsed-field-gradient NMR signals.
• Applied the model to NMR data from water flow in a homogeneous grain pack column.

Main Results:

• The model provides a framework for quantitative interpretation of NMR velocimetry data.
• Analytical expressions for NMR signals were derived based on subordinated Lévy processes.
• Demonstrated the model's utility in quantifying dispersion for single- and two-phase flow.

Conclusions:

• The proposed model offers a versatile approach for interpreting NMR velocimetry data.
• It effectively quantifies dispersion in porous media by accounting for complex flow dynamics.
• The model is applicable to both single- and two-phase flow conditions.