A generalized three-phase impedance equation for gas hydrate quantification

Accurate quantification of gas hydrates depends on reliable rock physics theories that relate hydrate saturation and morphology to elastic properties. However, traditional models often lack consideration of rock consolidation and typically assume a single hydrate morphology, limiting their ability to accurately characterize hydrate-bearing sediments. To address these issues, we derive a Generalized Three-Phase Impedance Equation (GTPIE) that accounts for both the degree of sediment consolidation and the coexistence of pore-filling (PF) and matrix-supporting (MS) hydrates. This model is based on the Wyllie time-average and Wood equations. Using this framework, we comprehensively investigate the effects of hydrate saturation, morphology, porosity, clay content, and consolidation coefficient on the P-wave impedance of host sediments. The applicability of the GTPIE is validated through comparison with four sets of experimental data on synthetic methane and tetrahydrofuran (THF) hydrates formed under “excess-water” conditions. The strong agreement between model predictions and experimental results suggests that the GTPIE effectively captures the acoustic responses of hydrate reservoirs. We further apply a grid-search algorithm to estimate hydrate saturation from P-wave impedance at well sites SH17 and SH02 in the Shenhu area, South China Sea. The results demonstrate that our model yields more accurate hydrate saturation estimates than theoretical models that consider only PF or MS morphology, as validated by reference data including the resistivity-based interpretations, nuclear magnetic resonance (NMR)-density log evaluations, and core measurements. Finally, we compare hydrate saturation estimates derived from the GTPIE with those from the time-average equation, Wood equation, and a weighted equation. The results show that the proposed model outperforms these empirical equations. Overall, this generalized model provides a robust theoretical foundation for modeling elastic responses and supports enhanced seismic characterization of hydrate reservoirs.