The McLDL code with subspace weight window-biasing combined with the Monte Carlo multiply scattered components approach for simulation of gamma-gamma litho-density logging tools

Abstract

A new Monte Carlo method for modelling photon transport in the presence of deep-penetration and streaming effects by combining a subspace weight window and biasing schemes has been developed. This method is based on use of an importance map from which an importance subspace is identified for a given particle transport system. Biasing schemes, including direction biasing and the exponential transform, are applied to drive particles into the importance subspace. The subspace weight window approach used consists of splitting and Russian Roulette that acts as a particle weight stabilizer in the subspace to control weight fluctuations caused by the biasing schemes. This approach has been implemented in the optimization of the McLDL code, a specific purpose Monte Carlo code for modelling the spectral response of dual-spaced γ-γ litho-density logging tools, which are highly collimated, deep-penetration, three-dimensional, and low-yield photon transport systems. The McLDL code has been tested on a computational benchmark tool and benchmarked experimentally against laboratory test pit data for a commercial γ-γ litho-density logging tool (the Z-Densilog). The Monte Carlo Multiply Scattered Components (MCMSC) approach has been developed in conjunction with the McLDL code and Library Least-Squares (LLS) analysis. The MCMSC approach consists of constructing component libraries (1-4, 5-8 scatters, etc.) of γ-ray scattered spectra for a reference formation and borehole with the McLDL Monte Carlo code. Then the LLS approach is used with these library spectra to obtain empirical relationships between formation and borehole parameters and the component amounts. These, in turn, can be used to construct the spectra for samples with a range of formation and borehole parameters. This approach should significantly reduce the amount of experimental effort or extent of the Monte Carlo calculations necessary for complete logging tool calibration while maintaining a close physical relationship that allows one to retain intuition about the measurements.