Modeling and Inversion with Azimuthal Gamma Ray for a Better Geosteering Decision-Making
Authors: Wang Jiaxin , Crawford Jeffrey , Montgomery Matthew 
Published: October 2020

Abstract
Azimuthal gamma ray (GR) logging-while-drilling (LWD) tools have demonstrated great value for geosteering applications in directional drilling. Their ability to indicate the relative stratigraphic position of the drilling assembly can determine whether the well should be steered up or steered down to stay in the target zone. However, this determination remains rather qualitative and largely depends on the user experience, especially when the quality and amount of real-time data is limited by intrinsic statistical noise, telemetry bandwidth, rate of penetration (ROP), and other drilling conditions. In addition, the commonly used geosteering modeling for azimuthal GR is geometry based only, without considering any measurement physics. Thus, a new forward-modeling and inversion method has been developed to provide an optimized pre-job planning and potentially quantitative real-time decision-making for more accurate geosteering with azimuthal GR.
The geosteering question can be simplified mathematically to a prediction of separation between azimuthal GR curves when approaching or passing a bed boundary in a two-bed formation model. Separation will give an indication of a steering direction change, even in the simplest case of only up- and down-facing GR curves. In this study, a method was developed to solve this question in seconds with only two factors: measurement precision and front-to-back ratio. The theoretical up- and down-facing readings of an azimuthal GR tool can be forward-modeled accurately from this ratio for any bed boundary changes. Combined with measurement precision, the counting statistics effects can be added to the model to mimic the real-world log curves, and this for any pre-selected stratigraphic marker.
The forward model results agree well with industrial standards of full Monte Carlo nuclear simulation and its deterministic nature allow it to run very fast. Thus, various scenarios can be evaluated quickly during either the pre-well phase or the operation. Detection limits achieved by any azimuthal GR tool in any given scenario can be statistically predicted for various confidence levels (e.g., 95% possibility of up/down curve separation). Thus, based on the detection limits, confidence level, and their variation with ROP, .etc. the drilling and geosteering plan can be optimized to reach the best ROP confidently without compromising the steering capability. Also in real time, when a potential separation of up- and down-facing azimuthal GR curves appear on the log, inversion of this model can be carried out to derive the possibility that this separation truly reflects formation changes to offer some quantitative insight to make steering decisions. Inversion of the modeling also has the potential to help recover the true API values of the formation beds and enhance the detection of the bed boundary positions.
The novelty of this approach stems from the statistical nature of nuclear counting statistics and the derivation of front-to-back ratio. Front-to-back ratio, when properly defined, is a factor that fully represents the measurement physics of the tool. In addition to the aforementioned applications, an overall coverage chart can be recalculated as a quick look-up reference to measure the effectiveness of azimuthal GR. The chart reflects the detection limits that an azimuthal GR tool can resolve for geosteering in a 0–200-API sampling space at a certain confidence level. Overall, the paper includes a detailed description of the model and its inversion, applications, and example log demonstrations from early trials.