Coupled Temperature–Density Effects on Acoustic Maturation of HGM-Modified Lightweight Oil Well Cement: Mechanisms and Implications for Sonic Logging Optimization

This study quantitatively investigates the coupled effects of curing temperature and slurry density on the early-age acoustic maturation of ultra-low-density Hollow Glass Microsphere (HGM)-modified oil well cement systems, addressing the critical challenge of determining reliable sonic logging timing under lightweight cementing conditions. Longitudinal wave velocity evolution was systematically characterized across a broad thermo–density domain, revealing a consistent three-stage acoustic trajectory comprising percolation-driven acceleration, transition-controlled consolidation, and acoustic stabilization. The results demonstrate that curing temperature primarily regulates the kinetic rate of acoustic maturation through hydration activation, whereas slurry density modulates the initial structural configuration, HGM-induced acoustic impedance heterogeneity, and development of effective solid connectivity. A derivative-based dual-criterion approach was proposed to define the optimal sonic logging time based on intrinsic acoustic stabilization behavior rather than conventional empirical strength-based thresholds. Furthermore, a thermo–density coupled semi-empirical model incorporating Arrhenius-type thermal activation and density-dependent structural effects was developed, providing reliable prediction of sonic logging timing with clear physical interpretability. The model captures the nonlinear interaction between thermal activation and structural constraints, revealing that acoustic maturation is accelerated under elevated-temperature and higher-density conditions but substantially delayed under low-temperature and ultra-low-density scenarios. This study establishes a physics-informed temperature–density–acoustic coupling framework that links hydration-controlled structural evolution with sonic logging optimization, providing a rational basis for improving cement bond evaluation reliability and operational efficiency under challenging wellbore conditions.