1D radial inversion of multidetector logging-while-drilling Sigma measurements

Abstract

Sigma measurements are useful in formation evaluation because they can be used to calculate water saturation independently of resistivity. One of the most advantageous features of the logging-while-drilling (LWD) Sigma tool under study is the use of three detectors to measure time decays from which three Sigmas are calculated: one near thermal-neutron detector, one short-spaced gamma-ray detector, and one long-spaced gamma-ray detector. Each detector has a different volume of investigation. Analogous to array resistivity logs, the multidetector Sigma logs, also called multi-depth of investigation Sigma logs, can indicate the presence of invasion and can be used to estimate true formation Sigma. However, the efficacy of the multidetector Sigma interpretation is conditioned by a high-Sigma contrast between invasion and virgin zones. We used a nonlinear gradient-based fast inversion method that uses the measured three-detector time decays and a reference value for invasion-zone Sigma to estimate the radial length of invasion and virgin formation Sigma. Synthetic logs are generated with realistic noise for numerous realizations that are then used to study the stability of the inversion routine and the estimation of error bars. We used a confidence index derived from the multiple-realization study to define the conditions under which the multiple time-decay problem is not stable. The reliability of the Sigma inversion method was verified in a set of test-pit measurements, two synthetic examples, and a field case. Synthetic results indicate that the inversion of multidetector time decays enables the correction of LWD Sigma measurements for invasion effects and improves the calculation of water saturation whenever there is contrast between invasion- and virgin-zone Sigma of more than 5 capture units. Field example results suggest that the inversion can accurately reproduce three-detector time decays honoring invasion effects evidenced in neutron-density logs while managing the presence of noise.

2D inversion-based interpretation of logging-while-drilling thermal-neutron and gamma-ray time decays

“…The uncertainty in the estimation increases as formation thickness decreases and virgin-and invasion-zone Sigma contrast decreases (Ortega et al, 2014b). Additionally, the 2D inversion algorithm might occasionally converge more rapidly in logging environments in which time decays are smooth due to the lack of strong absorbers, which is the case in hydrocarbon-bearing formations.…”

“…We invoke an inversion scheme similar to that implemented by Ortega et al (2014b) on 1D multidetector decay inversion, and we extend it to two dimensions to simultaneously account for invasion and shoulder-bed effects on particle time decays. A modified version of Occam's inversion algorithm (a gradient-based nonlinear inversion method) is used to iteratively estimate virgin-zone Sigmas, invasion-zone Sigmas, and radial lengths of invasion in each layer that reproduce the raw decay measurements at several depth locations.…”

“…Instead, we make use of a priori knowledge of the sensitivity functions of the detectors and the fastforward model to analytically calculate the derivatives. Extending the work on 1D radial inversion of multidetector time decays introduced by Ortega et al (2014b), the analytical expression for the fast-forward multidetector decay model at measurement point j can be expressed as…”

“…The main difference with respect to the 1D multidetector inversion developed by Ortega et al (2014b) relies on the content of the measurement vector d, the number of formation properties to be estimated m, and, most importantly, on the entries of the Jacobian sensitivity matrix J.…”

“…Allen et al (1965) studied the effect of invasion using multigroup neutron diffusion theory; their study recognizes the significant impact of shallow invasion on Sigma logs and reports the variable depth of investigation of the detector response as a function of radial length of invasion. Recently, Ortega et al (2014aOrtega et al ( , 2014b) developed a rapid simulation algorithm to reproduce multidetector time decays and combined it with a 1D radial inversion algorithm to reduce invasion effects on LWD Sigma logs while taking into consideration detectorspecific borehole and diffusion effects. However, the 1D radial inversion method is not sufficient to reduce shoulder-bed effects on Sigma logs acquired in thinly bedded formations.…”