A Homogenization Approach for Predicting the Elastic Modulus of Oilwell Cement

Summary Oilwell cement stone is a typical multiphase, multiscale, and heterogeneous composite material at the macroscopic scale. The macroscopic elastic modulus is determined by the microstructural composition and elastic modulus at the microscale level. In this study, we establish a multiscale homogenization method for the evaluation of its elastic modulus. To distinguish from the four-scale model of traditional concrete and adapt to the feature of oilwell cement without coarse aggregate, it was divided into three scales: nanometer scale [calcium-silicate-hydrate (C–S–H) matrix], micrometer scale (cement paste), and mesoscopic scale (paste + admixtures). The nanoindentation (to obtain microphase modulus), GEMS simulation (to obtain phase volume fraction), and Mori-Tanaka/self-consistent methods were combined for model construction. The model was verified through ultrasonic testing (error ≤ 4% after 0.8 days) and triaxial compression testing, and the relationship between the predicted elastic modulus (EP) and the static elastic modulus (EM) was established: EM = (1.01 – 1.08) EP − 3.962 (R2 = 0.98). It clarified the influence of water/cement ratio (W/C), curing temperature, and admixture performance on the modulus and achieved quantitative calculation of admixture dosage based on the target modulus. This work bridges the gap between the micro- and macroelastic behaviors of oilwell cement, avoiding the excessive reliance of traditional models on macroscopic empirical parameters and providing a basis for guiding cementing design and optimizing the long-term performance of the cement sheath.