Probabilistic multiscale characterization and modeling of organic-rich shale poroelastic properties

A probabilistic modeling and validation for multiscale poroelastic behavior of organic-rich shale is presented. The methodology is based on the integration of microporomechanics and effective medium theory with uncertainty quantification and propagation from nano- to macroscale. The multiscale model utilizes and improves an existing structural thought model of organic-rich shale material consisting of three levels that span from the nanoscale elementary building blocks of material to the scale of the macroscopic inorganic/organic hard/soft inclusion composite. Major model parameters related to the composition and mechanical properties of shale subscale features are modeled as random variables. Probabilistic description of model input parameters are constructed using the maximum entropy principle (MaxEnt) based on available information. Special care is given to the development of probabilistic description of random elasticity tensor of clay phase exhibiting transversely isotropic symmetry properties by employing the theory of random matrix combined with MaxEnt principle. Having the probabilistic descriptions of uncertain model parameters in hand, a Monte Carlo simulation is carried out to propagate the uncertainty across different scales, which allows us to construct a prior probabilistic descriptions of model outputs. The model predictions at different scales are validated against the available experimental measurements from samples of different formations and relevant information in the literature. Furthermore, a global sensitivity analysis is performed to characterize the contribution of each source of uncertainty in the variation of model predictions with respect to different quantities of interest related to macroscale mechanical properties of shale rocks. The integration of experimental characterization, microporomechanical modeling, and uncertainty quantification and propagation proposed in this work provides valuable insights into understanding the effect of subscale compositions and their variation in the upscaled poroelastic properties of shale rocks and improves the robustness and reliability of predictive models for the shale multiscale behavior.