The interpretation of the Nuclear Magnetic Resonance (NMR) T2 distribution as a pore size distribution assumes homogeneous surface relaxivity, single-phase fluid saturation, and the absence of diffusion of spins across pores. Although these assumptions are true for homogeneous formations with single-phase fluid saturation, they do not hold for heterogeneous formations such as deep-water carbonates, where laminations, vugs, and a mixed solid composition result in non-uniform values of surface relaxivity and diffusion of spins across pores. These spatial heterogeneities in rock formations render the interpretation of NMR logs challenging and non-conclusive. Furthermore, methods to estimate permeability, such as the Timur-Coates and the Schlumberger-Doll-Research (SDR) method assume a single relaxivity value and, thus, cannot be applied to NMR T2 data from formations with non-uniform relaxivity values.
NMR mixing laws describe how to combine data acquired from homogeneous components, thus enabling us to predict the data resulting from a mixture of those homogeneous components. This paper develops a new method to interpret NMR distributions originating from highly heterogeneous formations using mixing laws for T2, T1 — T2, and T2 — D NMR data. This new method allows us to extract the magnetization decay of each homogeneous component from the total magnetization decay of the heterogeneous formation. Decomposing the magnetization decay allows us to estimate the T2 distributions for each individual rock component and use them to obtain improved estimations of petrophysical quantities of interest such as porosity, pore size distribution, and the intrinsic permeability of each homogeneous component.
We show how to use the linear mixing laws in laminated formations to extract the T2 distributions from each individual component of a heterogeneous rock and how to obtain an improved estimation of the permeability of the formation.