Fundamentals of Fluid Flow in Porous Media

 

Chapter 3

Diffusion Coefficient: Measurement Techniques

NMR Method: Principles of NMR and Processing

Tipping Process

After exposing the protons to the net static magnetic field ( B₀ ), apply an oscillating magnetic field (B₁) perpendicular to B₀, therefore, the magnetization M will precess farther and farther away from the z-axis. This process is called ‘Tipping’. According to the quantum mechanics point of view, if a proton is at the low-energy state (its processional axes are parallel to the net magnetic field), it may absorb energy provided by B₁ and jump to the high-energy state. The application of B₁ also causes the protons to precess in phase with one another. This change in energy state and in-phase precession caused by B₁ is called nuclear magnetic resonance.

Figure 3-11: Polarization / Relaxation Curve

The magnetization vector M can be thought of as having a component M_Z along the z-axis (direction of B₀), which called longitudinal magnetization, and a component M_xy perpendicular to the field named transverse magnetization. At equilibrium M_xy = 0 and M_Z = M. when the protons are exposed to the oscillating magnetic field B₁, M_Z decreases and M_xy increases. The angle of deflection or rotation of sample’s net magnetization depends primarily on the product of amplitude (energy) of the B₁ and the length of time that B₁ is applied:

Where,

θ = Tip angle,

B₁ = Amplitude (energy) of the oscillating field,

τ = Time over which the oscillating field (B₁) is applied

γ = The gyromagnetic ratio (measure of the strength of the nuclear magnetism)

Each nucleus has a fixed γ value. For hydrogen: γ / 2π = 42.58 MHz/tesla.

Angular pulse terms such as π pulse (180° pulse) or a π / 2 pulse (90° pulse), refer to the angle through which magnetization is tipped by B₁ (Figure 3‑12).

Figure 3-12: The Tipping Process