A geometric factor theory-based method for formation and cement density inversion in cased hole

Uncertainties in the physical properties of the cement sheath in cased holes significantly impact the accuracy of formation density and porosity evaluation. The presence of casing strings and cement significantly attenuates nuclear logging tool responses, with spatial variations in cement thickness and density under poor cementing conditions introducing additional complexities for density logging and pulsed neutron logging data interpretation. Therefore, determining annular cement density has become critical for the cased hole formation evaluation. To address this need, a unified geometric factor theory-based inversion framework is established. This single framework is applied to two distinct logging scenarios - azimuthal cement density evaluation and simultaneous formation-and-cement density determination - by adapting it to the respective tool configurations. A high-fidelity Monte Carlo modeling program was developed using the Geant4 toolkit to simulate the detector responses of the azimuthal gamma cement density logging tool and the multi-detector cased-hole formation density logging tool, both of which share the same underlying response model. The inversion results of Geant4 simulation and field data demonstrated that the proposed methodology achieves a maximum cement density measurement error of 0.031 g/cm³ and a mean absolute formation density inversion error below 0.025 g/cm³.