BAYESIAN INVERSION USING GLOBAL-LOCAL FORWARD MODELS APPLIED TO FRACTURE PROPAGATION IN POROUS MEDIA

In this work, we are interested in parameter estimation in fractured media using Bayesian inversion. Therein, to reduce the computational costs of the forward model, a nonintrusive global-local approach is employed, rather than using fine-scale high-fidelity simulations. The crack propagates within the local region, and a linearized coarse model is employed in the global region. Here, a predictor-corrector mesh refinement approach is adopted, in which the local domain is dynamically adjusted to the current fracture state. Both subdomains change during the fluid injection time. Our algorithmic developments are substantiated with some numerical tests using phase-field descriptions of hydraulic fractures. The obtained results indicate that the global-local approach is an efficient technique for Bayesian inversion. It has the same accuracy as the full approach; however, the computational time is significantly lower.

Automated summary

In this work, Bayesian inversion is used for parameter estimation in fractured media. A nonintrusive global-local approach is employed to reduce the computational costs of the forward model, and a predictor-corrector mesh refinement approach is adopted for dynamic adjustment. Numerical tests using phase-field descriptions of hydraulic fractures confirm the effectiveness of the global-local approach, which achieves the same accuracy as the full approach but with significantly reduced computational time.