An experimental investigation of the relationship between borehole-NMR derived effective diffusion in unconsolidated media and hydraulic conductivity

Abstract:

A staple in the oilfield--borehole NMR measurements are increasingly being relied upon for hydrologic characterization. Most tool designs utilize strong permanent magnets in order to achieve sufficient S/N, this has the side effect that the measured NMR phenomenon occur in the presence of a constant static-field gradient $\left( \nabla \mathbf{B}_0 \right)$. The gradient can be exploited, using enhanced diffusion methods (EDM), in order to measure the temperature-dependent effective diffusion ($D_{\mathit{eff}}(T)$) constant of the investigated fluids. EDM have proven to be powerful and reliable techniques for fluid-type discrimination.In water-only samples deviation of the apparent diffusion from the intrinsic molecular diffusion coefficient of water $(D_w(T))$ is primarily controlled by restricted diffusion--the physical obstruction of spins which impedes free diffusion within the gradient.

The ability to relate hydraulic conductivity to NMR measurements is of fundamental interest in hydrogeophysics. Commonly, NMR relaxation and recovery time constants $\left(T_{1,2}\right)$ are used for this purpose. A growing body of work has highlighted the complicated nature of these relationships, particularity in unconsolidated high-porosity media. Furthermore, these relationships are dependent on the
surface relaxivity ($\rho_{N}$) and micro-porosity of the media.

$D_{\mathit{eff}}$ is intrinsically linked to the mobility of spins within a sample, has been related to pore geometry, and intriguingly shares units with transmissivity. The short-time behavior of $D_{\mathit{eff}}$ is independent of $\rho_N$ while full records can be used to yield estimates of relaxivity. In this study we compare data collected from laboratory and borehole NMR instruments with laboratory permeameter measurements for unconsolidated mixtures of sands, silt, and fine gravels. A 2D inversion for $T_2$ and $D_{\mathit{eff}}$ was developed under the assumption that all diffusion-related signal attenuation occurs in the motional averaging regime. Correlation between $T_2$, $D_0$, and hydraulic conductivity is then investigated as well as limitations of the approaches. We find that the addition of $D_{\mathit{eff}}$ information yields valuable additional information for NMR hydraulic studies.