Nonstationary Gaussian process as surrogate for uncertainty and sensitivity analysis in hydraulic fracture problem.

Zio Souleymane¹; Alves Rochinha Fernando¹

¹ Federal university of Rio de Janeiro

doi:10.20906/CPS/USM-2016-0022

Resumo

Complex computer models are widely used to predict the behavior of complex physical phenomena. However, this computer models become too expensive when taking into account variability present in the physical properties. To circumvent this problem, the expensive computer model is replaced by the inexpensive mathematical function, called surrogates. In this work, we use the nonstationary multivariate Gaussian process (MGP) as surrogate to predict the evolution of hydraulic fracture (HF) . To access uncertainty and sensitivity in the fracture evolution, we use the statistical approaches such as the uncertainty quantification and the global sensitivity analysis. The mathematical model of the HF relies on complex non-linear and free boundary problems simulated here, through an implicit level set algorithm. The numerical examples are presented to show the efficiency of the MGP to predict the evolution of the HF in the rock which presents discontinuities and uncertainty in the rock properties. The MGP results are compared to the Monte Carlo method(MC) and the stochastic collocation method (SCM).

Palavras-chave: Gaussian Process; Hydraulic Fracrure; surrogate; Uncertainty Quantification; Global sensitivity Analysis