Formation density and photoelectric index calculation using an ultra-slim density tool

Measuring formation density accurately is challenging due to mud accumulated on wellbore and mudcake on the borehole wall, particularly for through-the-bit density tools, which are ultra-slim tools with smaller detector crystals. This work introduces a novel method that overcomes this challenge by utilizing detector response models based on gamma physics principles. These models include the effects of key parameters such as lithology and mudcake on density and Pe (Photoelectric index) measurements. Monte Carlo simulations are employed to create and calibrate the models, ensuring accurate responses for both short- and long-spaced detectors. Various logging scenarios are considered in the modelling process. High-precision forward models are designed to correct the reading of these smaller detectors. Inversion algorithms are then developed to minimize errors and obtain optimal solutions using a quasi-Newton method based on weighted regularization. The highlight of the method is that it allows simultaneous determination of formation density, formation photoelectric index, mudcake density, and mudcake photoelectric index. The method is validated using a recently introduced through-the-bit density tool. The average density error is less than 0.015 g/cm³, and the average formation Pe error is less than 0.2 b/e, proving the effectiveness of the method.