Nuclear magnetic resonance (NMR) has been used to estimate the permeability of water-saturated rocks with uniform grain-surface composition. Geologic formations, however, usually consist of layers of rocks with different grain-surface compositions. In the absence of water diffusional coupling between adjacent layers, the NMR T2 distribution measured by a borehole logging tool is a weighted average (i.e., it obeys a linear mixing law) of the T2 distributions of each layer. However, when the layers are very thin (compared with the self-diffusion length of water) or the different grain types form a dispersed mixture (i.e., they are finely mixed), the resultant T2 distribution does not obey a linear mixing law anymore. The question arises as to whether it is possible to differentiate between dispersed and layered formations using mixing laws. We have developed a nonlinear mixing law to calculate the NMR T2 distribution of a water-saturated sample composed of a fine mixture of two different grain types from the T2 distributions of the water-saturated samples for each grain type. Water-saturated mixtures of crushed Texas Cream limestone and white silica sand were prepared in different volume ratios; we used the new nonlinear mixing law to compute the T2 distribution of the mixtures using the T2 distributions of the pure water-saturated samples and their volume fractions. Conversely, we also applied the nonlinear mixing law to the mixture to calculate the volume fractions of pure components using the T2 distributions of the pure components and the mixtures. Our results indicate that enough differences exist between the nonlinear and linear NMR mixing laws predictions that they can be used to establish whether in a given rock formation with two different grain types the pure components form layers or they are present in dispersed form.

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