Nuclear magnetic resonance in porous media
[1] This technique allows the determination of characteristics such as the porosity and pore size distribution, the permeability, the water saturation, the wettability, etc.
Microscopically the volume of a single pore in a porous media may be divided into two regions; surface area
This is an effect of paramagnetic centres in the pore wall surface that causes the relaxation time to be faster.
distribution plot reflected by the measured amplitude of the NMR signal is proportional to the total amount of hydrogen nuclei, while the relaxation time depends on the interaction between the nuclear spins and the surroundings.
NMR techniques are typically used to predict permeability for fluid typing and to obtain formation porosity, which is independent of mineralogy.
The former application uses a surface-relaxation mechanism to relate measured relaxation spectra with surface-to-volume ratios of pores, and the latter is used to estimate permeability.
, the bulk relaxation time is small and the equation can be approximated by: Real rocks contain an assembly of interconnected pores of different sizes.
Due to the pore size variations, a non-linear optimization algorithm with multi-exponential terms is used to fit experimental data.
Commonly used NMR permeability correlations as proposed by Dunn et al. are of the form:[6] where
This has given rise to permeability correlations of the form: Standard values for the exponents
Intuitively, correlations of this form are a better model since it incorporates tortuosity information through
affects strongly the NMR signal decay rate and hence the estimated permeability.
Surface relaxivity data are difficult to measure, and most NMR permeability correlations assume a constant
is certainly not constant and surface relaxivity has been reported to increase with higher fractions of microporosity.
In the absence of magnetic field gradients, the equations describing the relaxation are:[8] with the initial condition where
is related to the surface relaxation strength by:[9] If the walker survives, it simply bounces off the interface and its position does not change.
Since the walkers move with equal probability in all directions, the above algorithm is valid as long as there is no magnetic gradient in the system.
When protons are diffusing, the sequence of spin echo amplitudes is affected by inhomogeneities in the permanent magnetic field.
The total magnetization amplitude as a function of time is then given as: The wettability conditions in a porous media containing two or more immiscible fluid phases determine the microscopic fluid distribution in the pore network.
The idea of using NMR as a tool to measure wettability was presented by Brown and Fatt in 1956.
[10] The magnitude of this effect depends upon the wettability characteristics of the solid with respect to the liquid in contact with the surface.
[11] Their theory is based on the hypothesis that molecular movements are slower in the bulk liquid than at the solid-liquid interface.
In this solid-liquid interface the diffusion coefficient is reduced, which correspond to a zone of higher viscosity.
In this higher viscosity zone, the magnetically aligned protons can more easily transfer their energy to their surroundings.
The magnitude of this effect depends upon the wettability characteristics of the solid with respect to the liquid in contact with the surface.
NMR Cryoporometry (NMRC) is a recent technique for measuring total porosity and pore size distributions.
It makes use of the Gibbs-Thomson effect : small crystals of a liquid in the pores melt at a lower temperature than the bulk liquid : The melting point depression is inversely proportional to the pore size.
The technique is closely related to that of the use of gas adsorption to measure pore sizes (Kelvin equation).
Thus it is similar to DSC thermoporosimetry, but has higher resolution, as the signal detection does not rely on transient heat flows, and the measurement can be made arbitrarily slowly.
Nuclear Magnetic Resonance (NMR) may be used as a convenient method of measuring the quantity of liquid that has melted, as a function of temperature, making use of the fact that the
