A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects, which is of great significance to the development of oil and gas. However, the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density. In this regard, this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system. The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory, and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions. Combined with the relationship between gamma-ray counts and cement density, a multi-parameter calculation equation system is established, and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density. This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm³ for the cement azimuthal density. This accuracy level is ten times higher compared to density accuracy calculated using calibration equations. Overall, this algorithm enhances the accuracy of cement azimuthal density evaluation, provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.