Numerical and computational methods for solving the elegant Boltzmann transport equation (BTE), or its approximations, include Monte Carlo (MC), discrete ordinates, and diffusion solutions. These methods, of varying accuracy, are laborious and computationally inefficient for modeling and inversion of borehole nuclear measurements. The concept of adjoint solutions or flux sensitivity functions (FSFs) for estimating detector sensitivities, resulting from formation and borehole perturbations, has proven to be both an accurate and fast method for simulating and understanding nuclear logs. Obtaining a petrophysically significant formation parameter, in lieu of energy dependent nuclear cross sections, for perturbation estimates could prove to be challenging, considering the complexity of particle transport physics. This calculated formation parameter must be robust to account for petrophysical, geometrical, and borehole environmental effects. In gamma-gamma tools, electron density and photoelectric factor govern the basis of bulk density and Pe measurements with a linear relationship. Migration length is an important formation property tightly related to the measurement principle of neutron porosity responses. But as formation lithology and fluid compositions (e.g., formation gas density) vary, the relationship between neutron responses and migration length becomes highly nonlinear. In the presence of borehole and environmental effects, response perturbations increase, further complicating the nonlinearity.

The choice of formation parameter becomes crucial in generalizing detector responses to petrophysical and environmental effects for accurate and robust fastforward modeling of nuclear logs. The inverse of migration length, as the formation parameter, has shown to be problematic in gas formations. In this paper, we develop a new formation parameter, Fp using a combination of relevant petrophysical properties, such as neutron characteristic lengths and bulk density. In conjunction with FSFs and the linear iterative refinement (LIR) technique, the parameterization proved to be robust for rapid simulation of detector responses in any formation lithology, saturating fluid type, water salinity, fluid density, borehole size, well inclination, and mud filtrate invasion, with a 2-porosity unit (pu) accuracy. This tolerance is maintained for azimuthal measurements around the hole in presence of standoff up to 3" for varying stabilizer and borehole sizes — a seemingly reasonable tolerance in view of the borehole and environmental effects.