Abstracts Engineering

NMR oil well logging: Diffusional coupling and internal gradients in porous media

by Vivek Anand

The default assumptions used for interpreting Nuclear Magnetic Resonance (NMR) measurements with reservoir rocks fail for many sandstone and carbonate formations. This study provides quantitative understanding of the mechanisms governing NMR relaxation of formation fluids for two important cases in which default assumptions are not valid. The first is diffusional coupling between micro and macropore, the second is susceptibility-induced magnetic field inhomogeneities. Understanding of governing mechanisms can aid in better estimation of formation properties such as pore size distribution and irreducible water saturation. The assumption of direct correspondence between relaxation time and pore size distribution of a rock fails if fluid in different sized pores is coupled by diffusion. Pore scale simulations of relaxation in coupled micro and macropores are done to analyze the effect of governing parameters such as surface relaxivity, pore geometry and fluid diffusivity. A new coupling parameter (alpha) is introduced which quantifies the extent of coupling by comparing the rate of relaxation in a coupled pore to the rate of diffusional transport. Depending on alpha, the pores can communicate through total, intermediate or decoupled regimes of coupling. This work also develops a new technique for accurate estimation of irreducible saturation, an approach that is applicable in all coupling regimes. The theory is validated for representative cases of pore coupling in sandstone and carbonate formations. Another assumption used in NMR formation evaluation is that the magnetic field distribution in the pores corresponds to the externally applied field. However, strong field inhomogeneities can be induced in presence of paramagnetic minerals such as iron on pore surfaces of sedimentary rocks. A generalized relaxation theory is proposed which identifies three asymptotic relaxation regimes of motionally averaging, localization and free diffusion. The relaxation characteristics of the asymptotic regimes such as T 1/T2 ratio and echo spacing dependence are quantitatively illustrated by random walk simulations and experiments with paramagnetic particles of several sizes. The theory can aid in better interpretation of diffusion measurements in porous media as well as imaging experiments in Magnetic Resonance Imaging (MRI).