Responses and data inversion of four-detector scattered-gamma-ray logging in cased holes

In cased holes, detector response of scattered-gamma-ray logging tool is subject to casing, cement sheath, and formation density, while the logging result requires four parameters-casing thickness, cement sheath density, cement sheath thickness, and formation density-for cased-hole formation evaluation and cement bond evaluation. Therefore, It is necessary to study the detector response and logging data inversion. We designed a four-detector scattered-gamma-ray logging tool for cased holes and performed Monte Carlo numerical simulations to obtain relationships between the responses of four detectors versus casing, cement sheath, and formation, respectively; on this basis, forward modeling formulas for the detector responses were established, and an optimization inversion method was applied to obtain the casing thickness, cement sheath density and formation density from the forward model. As demonstrated by the result, detector response was a function of formation density, cement sheath thickness, cement sheath density, and casing thickness; the response of detector count rate versus casing thickness was less influenced by ambient conditions, compared to the other parameters. Relatively accurate casing thickness values could be calculated when the condition of the borehole and formation is normal; accurate cement sheath density values could be obtained when the cement sheath was relatively thick; and relatively accurate formation density values could be obtained when the cement sheath has neither of low density nor of great thickness.