ESTIMATING THE PERMEABILITY OF CARBONATE ROCKS BY PRINCIPAL COMPONENT REGRESSIONS OF NMR AND MICP DATA

摘要

The estimation of continuous downhole permeability is widely performed by nuclear magnetic resonance (NMR) using the classical approaches of Seevers-Kenyon and Timur-Coates. 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 estimators might fail when applied to carbonate rocks in which permeability is often less correlated to porosity, irreducible water content and relaxation times. Furthermore, carbonate rocks may have more complex pore body and throat size distributions (e.g., bimodal distributions) that may be poorly described by a single parameter of the NMR distribution (i.e., the average or the cutoff).This study develops an estimator that uses multiple NMR distribution bins, representing a general case of the classical estimators. This multivariate approach evaluates the size information encoded in each relaxation time bin to estimate permeability. The multivariate estimators are calibrated with absolute permeability using principal component regression (PCR), whereas classical estimators uses standard multiple linear regression. PCR reliably describes relaxation time distributions in a simple and linear-independent manner according to data variance and is a potentially suitable tool for this multivariate calibration task. The performance of the classical and multivariate estimators are compared after undergoing full cross-validationAn important feature of the novel multivariate approach is the possibility of simultaneously using longitudinal (T_1) and transverse (T_2) relaxation times or simply using a specific segment of the T_(1,2) distribution. Both situations could be highly useful for well logging because NMR activations can either simultaneously acquire complete T_1 and T_2 data or can emphasize certain components (e.g., the irreducible fluid signal). Moreover, the multivariate estimators can also be applied to size-scaled T_(1,2) distributions for cases in which relaxation times are less sensitive to permeability, which may occur in many carbonates. By employing mercury injection capillary pressure (MICP) data for NMR size scaling, permeability estimates are improved considerably compared to the non-scaled estimates. The superior results achieved with the novel multivariate estimators over the classical estimators indicate that NMR well logging data should be further explored to improve the accuracy of permeability estimates.