Quality Control of NMR Measurements in Unconventional Rocks Using Hilbert Transforms and Semi-Logarithmic Derivatives

Abstract

Abstract Nuclear magnetic resonance (NMR) measurements are extremely valuable in the assessment of fluid-flow properties of rocks. However, inverted transverse-relaxation time (T2) distributions are often biased by positivity constraints and the regularization method. In some cases, it is difficult to determine whether the estimated pore-size distributions are correct or by-products of the inversion. On-site quality-control of inversion results is thus essential to avoid erroneous analyses based on non-physical results across unconventional rocks. We introduce and compare two quality-control approaches based on two different signal processing practices: the semi-logarithmic derivative and the Hilbert transform. Validation of the inverted T2 distribution is performed by applying either processing method to the echo train decay of proton magnetization to estimate a pseudo-T2 distribution that is not affected by inversion artifacts. These two 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. NMR laboratory measurements were performed on a wide variety of rocks, the associated T2 distributions were estimated using linear inversion and the two quality-control methods were applied to the same data. 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 biased noise. By verifying the location of the dominant mode of the T2 distribution, the NMR operator can determine whether more stacking of proton magnetization decays 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, especially at early acquisition times, can completely 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.