Estimating the Permeability of Rocks by Principal Component Regressions of NMR and MICP Data

The estimation of continuous downhole permeability is widely performed by nuclear magnetic resonance (NMR) using the classical Seevers-Kenyon and Timur-Coates models. The first approach uses an average of the relaxation times, whereas the latter approach is based on the fractional fluid content computed from a relaxation time distribution cutoff. However, several case studies in the literature reported that these models might fail, especially when applied to complex carbonate rocks in which permeability is often less correlated to porosity, irreducible water saturation, and relaxation times. This study develops and evaluates perm-estimators that use multiple relaxation times, proving that they are a general case of the classical models. The so-called multivariate estimators are calibrated with core permeability using principal component regression, which describes NMR variables in a simple and linear-independent space according to data variance. An important feature of the multivariate approach is the possibility of simultaneously using longitudinal T1 and transverse T2 relaxation times or simply using a specific segment of their distribution. Moreover, the multivariate estimators can also be applied to size-scaled T1,2 distributions for cases in which relaxation times are less sensitive to permeability, such as the carbonate rocks studied in this work. By employing mercury injection capillary pressure (MICP) data for the NMR size scaling, permeability estimates are improved considerably compared to the nonscaled estimates. The superior results achieved with the novel multivariate estimators over the classical models indicate that core and NMR well-logging data should be better explored to improve the accuracy of permeability estimates.