Diffusional Coupling Between Micro And Macroporosity For NMR Relaxation In Sandstones And Grainstones1

Abstract

The interpretation of NMR measurements with fluid saturated rocks assumes that the T 1 or T 2 distribution is directly related to the pore size distribution. In many cases, this assumption is valid. However, the assumption breaks down if the fluid in different sized pores is coupled through diffusion. In such cases, the estimation of formation properties such as permeability and irreducible water saturation using the traditional T 2,cutoff method gives erroneous results. Several techniques like spectral BVI and tapered T 2,cutoff were introduced to take into account the effects of diffusional coupling for better estimation of properties. This paper aims to provide a theoretical and experimental understanding of NMR relaxation in systems with diffusionally coupled micro and macropores. Relaxation is modeled such that the fluid molecules relax at the surface of the micropore and simultaneously diffuse between the two pore types. The T 2 distribution of the pore is a function of several parameters including micropore surface relaxivity, fluid diffusivity and pore geometry. The governing parameters are combined in a single coupling parameter (α) that is defined as the ratio of the characteristic relaxation rate of the coupled pore to the rate of diffusional mixing of magnetization between micro and macropore. Depending on the value of a, the two pore types can communicate through total coupling, intermediate coupling or decoupled regimes. The model is applied to treat diffusional coupling in sandstones with a distribution of macropores lined with clay flakes. Simulations are verified by comparing with experimental results for chlorite-coated, North Burbank sandstone. It is observed that the relaxation time distribution shows a bimodal distribution at 100% water saturation but a unimodal distribution when saturated with hexane. This occurs because the extent of coupling is higher for hexane than for water due to lower relaxivity and higher diffusivity of hexane. The a values indicate intermediate coupling for water and strong coupling for hexane. The model is also applied to explain pore coupling in grainstone carbonates with intra and intergranular porosity. In this case, a is shown to have a quadratic dependence on grain radius and inverse dependence on micropore radius. The theory is experimentally validated on several systems with microporous particles of varying grain diameters and known microporosities. Here too, the T 2 distribution at 100% water saturation varies from bimodal for coarse-grained particles to unimodal for fine-grained particles. The transition from bimodal to unimodal distribution is also predicted theoretically from the values of a.