A New Insight into In Situ Capillary Pressure Curve: Upscaling Nuclear Magnetic Resonance Measurements Using Wavelet Analysis

Abstract

Nuclear magnetic resonance (NMR) measurements have been used widely for constructing pseudo-capillary pressure curves. Generating NMR pseudo-capillary pressure curves entails deriving the transverse relaxation time $\left({T}_{2}\right)$ distribution from the well-known Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence and calibrating the ${T}_{2}$ distribution to laboratory capillary pressure data. A problem with the existing methods using the ${T}_{2}$ distribution to evaluate the capillary pressure curves is that inverting the time-domain CPMG echo decays to the ${T}_{2}$ distribution leads to erroneous results. Noise effects, the ill-posed nature of inversion, and regularization smear the estimated ${T}_{2}$ distribution. Accordingly, this study aimed to furnish a robust and straightforward method to derive in situ capillary pressure curves in water-saturated porous media from the CPMG pulse sequence using wavelet analysis. To this end, the CPMG pulse sequence was divided first into segments of equal length. Then, the discrete wavelet transform (DWT) was employed to upscale each segment to derive ${T}_{2}$ and porosity $\left({\phi }_{\mathrm{NMR}}\right)$. Finally, the cumulative sum of ${T}_{2}$ $\left({T}_{2\mathrm{c}}\right)$ versus the ${\phi }_{\mathrm{NMR}}$ value was plotted. The resulting pseudo capillary pressure curves (${T}_{2\mathrm{c}}$ vs. ${\phi }_{\mathrm{NMR}}$) bear a striking resemblance to the capillary pressure curves measured in the laboratory through the centrifuge method. Normalized pseudo capillary pressure curves closely match normalized capillary pressure curves. Consequently, pseudo capillary pressure curves derived in the DWT domain are converted to laboratory capillary pressures curves using a linear transformation.

Graphical Abstract