DIFFUSIONAL COUPLING BETWEEN MICRO AND MACROPOROSITY FOR NMR RELAXATION IN SANDSTONES AND GRAINSTONES

摘要

Pore structure analysis by NMR relaxation assumes that the T1 or T2 distribution is directly related to the pore size distribution. This 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 T2,cutoff method would give erroneous results. Several techniques like "spectral" BVI and tapered T2,cutoff have been introduced to take into account the effects of diffusional coupling for better estimation of properties. In this paper, we aim 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 micropores and simultaneously diffuse between the two pore types. The T2 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) which is defined as the ratio of the characteristic relaxation rate of the pore system to the rate of diffusional mixing of fluid molecules between microand macropores. It is shown that depending on the value of α, the two pore types can communicate through total, intermediate or decoupled regimes of coupling. 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 T1 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 α values indicate intermediate coupling for water and strong coupling for hexane. The model is also applied to grainstone carbonates with intra and intergranular porosity. In this case, α is found 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 T2 distribution at 100% water saturation varies from bimodal for coarsegrained particles to unimodal for fine-grained particles. The transition from bimodal to unimodal distribution is also predicted theoretically from the values of α.