Calculating absolute permeability using nuclear magnetic resonance models

Abstract

1D transverse relaxation measurements were made on fully cylindrical cores of sandstone sediments with varying values of porosity, pore size and magnetic susceptibility. Porosity calculated from amplitudes of transverse relaxation measurements agrees well with porosity determined by independent method. Transverse relaxation measurements within the homogeneous magnetic field can be used for permeability prediction. In the case of sandstone samples with high porosity, a standard calculation scheme from NMR logging in the oil industry yields good results. However, standard SDR (Schlumberger Doll Research) model based on the T2LM cannot be applied for an accurate permeability prediction for samples with low porosity, small pore sizes, clay filling pores, and presence of iron minerals and associated with high internal magnetic field gradients. Therefore, a model theory was developed physically based on Kozeny-Carman equation, which describes the pore radius dependence of the surface relaxivity ρ as both an analytical and a more practicable empirical equation was applied. Regarding corrected ρ values, permeability can be predicted more accurately from the physically based Kozeny-Carman equation than from the logarithmic mean of the T2 distribution. From the relaxation measurements new empirical models with high coefficient of correlation by MLS regression were derived, additionally the coefficients of SDR and Kozeny were reestimated. The prediction models were applied, and the results compared to absolute permeability results from basic core analysis. As expected, the Kozeny model response presented better match to the core permeability values when compared with the optimized SDR.