Monte Carlo simulation of the response of the gamma ray backscatter litho-density tool for oil well logging

A specific purpose Monte Carlo code called McLDL has been designed and tested for the simulation of generic gamma-ray litho-density log responses. The analog estimation method which scores only the photons that physically reach the detector is impractical for the gamma-ray well logging tool because of the very small probability that a photon is detected (10{dollar}sp{lcub}-7{rcub}{dollar}). The primary variance reduction method used in the McLDL code is the combined splitting and biasing through "one-step" and "two-step" schemes. In the one-step scheme an estimation of the score in the detector at each collision site is made by forcing the gamma ray to scatter toward the detector, reach it without interaction, and be detected. In the two-step scheme the gamma ray is first forced to scatter to a region in the formation facing the detector collimation window, reach it without interaction and then scatter directly to the detector, reach it without further interaction, and be detected. Following the score estimation, the gamma ray at the original interaction site is forced to scatter and the process is continued at the next interaction until the lowest allowable energy or a prescribed gamma-ray weight is reached. In the latter case Russian Roulette is played to decide whether or not to kill the history. The final score for each history is estimated as the sum of the individual scores calculated at all the scattering sites of the history.; The code also contains complete composition and density correlated sampling. An additional ten comparison samples with different composition and/or density from that of the reference sample only adds 10% to the computation time. The correlated sampling feature can be used to fill out calibration curves when only a few very well known responses for appropriate samples (either experimental or very long Monte Carlo calculations) are available. Use of a single well known total response for each lithology at a known composition and density as a reference sample results in an accurate density calibration curve by adding ten points to this calibration curve from the responses of the associated ten comparison samples. (Abstract shortened with permission of author.)...