The NMR relaxation response of porous reservoir rock is frequently used to gain length scale estimates of pore morphology. These pore size distributions are often anchored by experiments like mercury intrusion capillary pressure. In practice this means that a constant surface relaxivity is found such that the pore size distribution from NMR overlaps the "pore size" distribution from mercury intrusion. There are three types of problems associated with this approach:
Physical interpretation: mercury intrusion really measures pore space accessibility at a given pressure and does not represent pore body size.
Parameters: The surface relaxivity which leads to a match between a NMR pore size distribution and a surface area reference measurement is a fitting parameter. It depends, apart from mineralogy, on surface area homogeneity and the resolution of the surface area reference measurement. Bulk relaxation effects might be ignored and the NMR response shifted to regions where no structural length scales are measurable by NMR.
Signal processing issues: the ill-conditioning of the inverse Laplace transform leads to an unavoidable loss of information associated with the smooth multi-exponential decay kernel.
In this paper we ignore mineralogy effects and use a combination of Xray-CT and other methods to characterize the pore structure in 3D from nanometers to centimeters. This addresses the first issue, since a partitioning of the pore space gives an excellent pore size distribution standard. The second issue we approach by numerically modeling the NMR relaxation response and comparing to experiment for a set of carbonate rock. In previous Xray-CT based simulations, a surface relaxivity was set to match experiment and could take very high values (up to 50 micron/s) because the surface area measured from Xray-CT significantly underestimated the surface area reference measurement used to derive experimental surface relaxivities. In this work we reduce the influence of the surface relaxivity parameter by a) having a much better discretisation, leading to a smaller surface relaxivity in the simulations and b) by separately calculating the internal field at very high resolution. The latter allows us to model the dephasing explicitely based on structure and susceptibility contrast alone. Thus, a coarse scale voxel in a simplistic NMR simulation is replaced with a high-resolution model of structure, and the dependence on surface relaxivity is reduced since two fine-scale mechanisms contribute to the previously used coarse scale surface relaxivity.
The NMR relaxation response of porous rock is often used in the characterization of reservoir rock to provide a length scale for the estimation of permeability (Wayne and Cotts, 1966; Brownstein and Tarr, 1979; Kenyon et al., 1986; Kenyon et al., 1988; Kenyon, 1992; Song et al., 2000). Assumptions typically made in such an interpretation include constant surface relaxivity, weak coupling between pores, and fast diffusion within pores.
