Surrogate models by means of functional kriging to estimate uncertainty in reservoir and geomechanical simulations

Accurate prediction tools for land subsidence induced by oil/gas production are fundamental for energy companies to identify possible affected areas and to propose measures to counteract its potentially adverse effects. The flow-deformation models are computationally demanding so their use in a data assimilation workflow is unfeasible for large models. The calibration process requires running the simulation for several values of the parameters of the PDE to find the sets that best reproduce the observed data. Parameters are petrophysical but also mechanical properties of the rocks. Observed data are production data (well flow rates and pressures) and geodetic measurements, like data from global positioning system (GPS). We propose an approach for fluid and subsidence estimation based on functional kriging surrogate models to jointly replicate the temporal behavior of fluid production and subsidence with a very low computational cost. Then, using Ensemble Smoother with Multiple Data Assimilation (ES-MDA) it is possible to automatically assimilate multiple data sources rapidly and to predict the forecast uncertainty. The workflow has been applied on two test cases: a synthetic reservoir which is a benchmark in the reservoir modeling community and a real field. In both cases, surrogate models proved to be computationally efficient and data assimilation led to an ensemble of models able to quantify prediction uncertainties accurately.