The correlation of NMR relaxation response and fluid permeability relies on a deterministic relationship between self-diffusion at the 100 micron (individual pore) scale and flux at a significantly larger scale (core plug, whole core). Previous work considered averaging rules for the NMR relaxation response in terms of average relaxation times. In addition to standard assumptions of pore isolation, constant surface relaxivity, and fast diffusion, a permeability averaging rule is implicitly assumed at the finest scale. New developments in MRI adding a Laplace dimension allow characterizing the heterogeneity of V/S. It is then possible to apply the NMR-permeability correlations at different scales and compare permeability estimates based on full scale measurements with upscaled (" averaged") values of local measures. In this work I analyse MRI responses with locally resolved Laplace dimension, numerically derived for a set of Xray-CT images of sandstones and carbonates, and comment on appropriate averaging rules for the different rock classes. It is shown that applying the correct averaging rule reduces the scatter of NMR-permeability correlations. I also apply geostatistical techniques and compare geostatistics of V/S obtained from segmented Xray-CT images with simulated MRI images. The inclusion of MRI data in the NMR interpretation process might increase the predictive power of NMR-permeability correlations by including information about the best averaging rules to use.
In well logging of petroleum reservoirs important physical properties have to be inferred from observable quantities. NMR is used to extract information about transport processes in the rock, and in particular to predict bound water fraction and permeability (Kenyon et al., 1986; Sen et al., 1990; Song et al., 2000). In the petroleum industry, this technique provides the primary well logging tool which holds the promise of an accurate measure of formation permeability. Permeability is derived from empirical relationships between measured transverse relaxation times, T2, and permeability measured on core samples. The relationships are usually expressed as
(mathematical equation)(available in full paper)
where k is the permeability, #x3C6; the NMR measured porosity, T2lm the log-mean of the measured T2 distribution, and a, b, c are constants. The prefactor and exponents on f and T2lm vary considerably between different rocktypes and lithologies, particularly between clean sandstones, vuggy limestones, and fractured porous media (Amabeouku et al., 2001; Ausbrooks et al., 1999; Matteson et al., 1998; Guy et al., 1998) and tool calibration is a major issue in the interpretation of log data. The application and interpretation of NMR measurements rely on an understanding of the rock and fluid properties that cause relaxation (Kenyon, 1997). Brownstein and Tarr (Brownstein and Tarr, 1979) studied the magnetisation evolution of independent pores subject to an external uniform magnetic field B0 to derive a pore size by means of an eigenmode analysis of the diffusion equation. The solution can be expressed by a sum of orthogonal, normalised eigenfunctions #x3C6;n (Lisitza and Song, 2001)
