Prediction of permeability from NMR response: surface relaxivity heterogeneity

NMR responses are commonly used in reservoir characterization to estimate pore-size information, formation permeability, as well as fluid content and type. Difficulties arise in the interpretation of NMR response as an estimator of permeability due to internal gradients, diffusion coupling, surface-relaxivity heterogeneity, and a possible breakdown of correlations between pore and constriction sizes. Here we consider several scenarios of surface relaxivity heterogeneity for a set of sandstones and a set of carbonate rock in a numerical NMR study based on Xray micro-CT data. We have previously demonstrated the ability to image, visualize, and characterize sedimentary rock in three dimensions (3D) at the pore/grain scale via X-ray microcomputed tomography. We also numerically tested the influence of structure and diffusion-coupling on NMRpermeability correlations. Here we consider surface relaxivity heterogeneities due to pore partitioning, mineralogy, pore size, and saturation history. We partition the pore space and solid phase into regions of pores and grains. These partitions could reflect different mineralogy for weakly coupled pore systems, or differences in mineralogy for the grains. Further, we use a morphological drainage simulation technique to partition the pore space in terms of invasion radius or throat size, reflecting surface relaxivity heterogeneity due to the saturation history of immiscible fluids, which could cause e.g. pressure dependent adsorption on surfaces and/or changes in wettability. Finally, we use the concept of covering radius to assign a surface relaxivity due to pore size. For each sample, four sandstones and three carbonates, we consider distributions of surface relaxivity based on above partitions, keeping the mean surface relaxivity constant, simulate the magnetisation decay, and derive a pore size distribution through an inverse Laplace transform assuming constant surface relaxivity. Further, we test the effect of these heterogeneities on NMR-permeability correlations based on the log-mean of the relaxation time distributions for two frequently used empirical NMR-permeability cross-correlations. At the scales probed here, surface relaxivity heterogeneity changes the prefactor in the equations for sandstones only minimally, while the prefactor is changes orders of magnitudes for carbonates. The influence of surface relaxivity heterogeneity on the quality of the fit for individual samples is small.