Fast modeling of gamma-gamma density measurementsvia gamma-ray point-kernel approximations

Abstract

Forward-modeling algorithms based on flux sensitivity functions are commonly recognized as fast, reliable, and the most efficient way to implement inversion-based interpretation algorithms for borehole nuclear measurements. Second-order sensitivity functions enhance the accuracy of fast-forward-modeling algorithms in complex geometries: In the presence of standoff, density accuracy is improved up to 70% compared with first-order approximations. However, second-order sensitivity functions can only be generated with the Monte Carlo [Formula: see text]-Particle code for perturbations in bulk density, material composition, and reaction cross sections; therefore, their use is limited to gamma-gamma borehole density measurements. We have developed an alternative method to second-order approximations in complex 3D geometries. It is the first step toward future improvements to simulate borehole environmental effects across arbitrary well trajectories for nuclear measurements based on coupled neutron and gamma-ray transport. The gamma flux-difference (GFD) method quantifies gamma-ray flux perturbations using exponential point kernels and Rytov approximations. Gamma-ray point kernels are corrected for flux buildup and flux perturbations caused by radial heterogeneities, i.e., standoff. Correction coefficients are calculated by flux-fitting 1D radial sensitivity functions yielded by MCNP to the 1D exponential gamma-ray kernel; they depend on standoff and mud density, but they are negligibly affected by formation properties. The GFD method is benchmarked against Monte Carlo calculations. Compared with first-order approximations, it improves simulated density accuracy across regions of significant contrasting properties, up to [Formula: see text] with 3.18 cm (1.25 in) standoff and freshwater mud. The GFD method yields a maximum density error of [Formula: see text] across complex geometries and up to up to 4.45 cm (1.75 in) standoff, similar to that achieved by second-order forward modeling algorithms. Moreover, the principles behind GFD approximations can be adapted to measurements based on coupled neutron and gamma-ray transport.