A Surrogate Model for Fast Land Subsidence Prediction and Uncertainty Quantification

Numerical modeling of anthropogenic land subsidence due to the exploitation of subsurface resources is of major interest to anticipate possible environmental impacts on the ground surface. The reliability of predictions depends on different sources of uncertainty introduced into the modeling procedure. In this study, we focus on reduction of model parameter uncertainty via assimilation of land surface displacements. A test case application on a deep hydrocarbon reservoir is considered where land settlements are predicted with the aid of a 3D Finite Element (FE) model. The calibration of the parameters defining the rock constitutive law is obtained by the Ensemble Smoother (ES) technique. The ES convergence is guaranteed with a large number of Monte Carlo simulations that may be computationally infeasible in large scale and complex systems. A surrogate model based on the generalized Polynomial Chaos Expansion (gPCE) is proposed as an approximation of the forward problem. This approach is expected to reduce the overall computational cost of the original ES formulation and enhance the accuracy of the parameter estimation problem. The result is compared with a posterior sampling by Markov Chain Monte Carlo (MCMC) to assess the quality of the assimilation.