The 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 like permeability and irreducible volume saturations 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 magnetization relaxes at the surface of micropores and simultaneously diffuses 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(P which is defined as the ratio of the characteristic relaxation rate of the pore system to the rate of diffusional mixing of magnetization between micro- and macropores. It is shown that depending on the value of P, 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 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 is because the extent of coupling is higher for hexane than for water due to lower relaxivity and higher diffusivity of hexane. The values of P indicate intermediate coupling for water and strong coupling for hexane. The model is also applied to grainstone carbonates with intra and inter-granular porosity. In this case, P is found to have a quadratic dependence on grain radius and inverse dependence on micropore radius. The theory is validated by experiments with water-saturated silica gels of varying grain diameters and known microporosities. The relaxation characteristics of the silica gels are analogous to those of the microporous grainstones. Here too, the T2 distribution varies from bimodal for coarse-grained silica gel to unimodal for fine-grained silica gel. The transition from bimodal to unimodal distribution is also predicted theoretically from the values of P.
Diffusional coupling between micro and macroporosity for NMR relaxation in sandstones and carbonates
Anand, Vivek, and George J. Hirasaki. "Diffusional coupling between micro and macroporosity for NMR relaxation in sandstones and carbonates." Paper presented at the SPWLA 46th Annual Logging Symposium, New Orleans, Louisiana, June 2005.
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