Monte Carlo simulation of natural gamma-ray oil-well logging tool responses and use in log interpretation

A new specific purpose Monte Carlo code named McNGR has been developed, benchmarked, and demonstrated for the interpretation and design of natural gamma-ray logging tools. This code has several unique features that make it very useful, efficient, and user-friendly. One of these is the use of a pseudo-long detector correlated sampling concept. Another important feature is the use of the Monte Carlo Library Least-Squares (MCLLS) approach which allows the calculation (by Monte Carlo) of individual library spectra for the three natural radioactivities {dollar}sp{lcub}40{rcub}{dollar}K, uranium, and thorium. This feature offers the capability of quantitative characterization of the natural activities {dollar}sp{lcub}40{rcub}{dollar}K, uranium, and thorium in the rock formation as well as the borehole and formation matrix effects by using a complete set of libraries under standard logging conditions. {dollar}sp{lcub}40{rcub}{dollar}K in borehole fluid can also be characterized by using the tool response to {dollar}sp{lcub}40{rcub}{dollar}K activity in borehole fluid as the fourth library spectrum. Three major empirical approaches have been developed for correcting natural gamma-ray log responses for variations in logging conditions such as borehole and tool diameters, tool standoff, borehole fluid type, and formation type. The first approach is the Semi-Empirical (SE) approach and it features the use of the radioisotope concentration correction factor as a function of an effective absorption parameter. The second approach is the Principal Components Analysis (PCA) approach which consists of the generation of a complete set of library spectra over a wide borehole and formation parameter range and the subsequent reduction of this data set by the PCA approach to less than 10% of its original size while still maintaining essentially all of the variance of the original set. The third approach is the Monte Carlo Multiply Scattered Components (MCMSC) approach and it involves the decomposition of the {dollar}sp{lcub}40{rcub}{dollar}K, uranium, and thorium library spectra obtained under standard logging conditions by Monte Carlo simulation to produce individual multiply scattered characteristic components. Empirical expressions for the multiply scattered component coefficients are obtained as a function of formation and borehole fluid parameters including density and composition. The use of the third approach can be easily extended to other nuclear logs containing gamma-ray spectra.