Quality Control of Nuclear Magnetic Resonance Measurements Using Pseudo-T2 Distributions

Abstract

Summary Nuclear magnetic resonance (NMR) measurements are extremely valuable in the assessment of fluid-flow properties of rocks. However, inverted NMR transverse-relaxation time (T2) distributions are often biased by positivity constraints and the implementation of regularization (stabilization) methods. In some cases, it is difficult to determine whether the estimated pore-size distributions are reliable or byproducts of the inversion. On-site quality control of NMR inversion results is thus essential to avoid erroneous analyses based on nonphysical interpretations across conventional or unconventional rocks. It is also important to adjust the measurement acquisition process in real time in response to variable signal/noise conditions in the borehole environment. We introduce and compare three quality-control approaches; two of them are based on two different signal processing practices, namely the semilogarithmic derivative and the Hilbert transform, while the third is based on a nonlinear optimization technique. Validation of the inverted T2 distribution is performed by applying either method to the echo train decay of proton magnetization to estimate a pseudo-T2 distribution that is not affected by inversion artifacts. These three methods are data-driven processes for on-site, continuous quality control of borehole NMR measurements. In the first method, a pseudo-T2 distribution is constructed by taking the derivative of the echo train decay with respect to the natural logarithm of the relaxation time. For the second method, the Hilbert transform is applied to the raw proton magnetization decay to approximate the T2 distribution. The latter method consists of an approximation of the derivative of the time decay of magnetization using least-squares minimization. NMR laboratory measurements were performed on a wide variety of rocks, the associated T2 distributions were estimated using linear inversion, and the three quality-control methods were applied for comparison. The reliability of our quality-control procedures was verified by benchmarking them against the inverted T2 distributions. Furthermore, these quality-control methods, when applied continuously to borehole NMR measurements, enable the optimization of the measurements in real time to mitigate the effects of biasing noise. By verifying the location of the dominant mode of the T2 distribution during NMR measurement acquisition, the operator can determine whether (a) more stacking of proton magnetization decays is needed, or (b) longer- or shorter-time sampling is needed to attain a high-quality estimation of the pore-size distribution before performing the T2 inversion. Our work provides the basis of effective quality-control methods for NMR measurements for the petrophysical interpretation of rocks with complex pore-size distributions, especially in unconventional rocks, where noise present in the measurements (notably at early acquisition times), can mask the useful signal originating from pore-size distributions and fluids. The fast and reliable quality control of estimated T2 distributions is not affected by inversion artifacts, relying only on unfiltered, raw data.