Multilevel Monte Carlo Method with Application to Uncertainty Quantification in Reservoir Simulation

Abstract:

The rational management of oil and gas reservoirs requires understanding of their response to existing and planned schemes of exploitation and operation. Such understanding requires analyzing and quantifying the influence of the subsurface uncertainty on predictions of oil and gas production. As the subsurface properties are typically heterogeneous causing a large number of model parameters, the dimension independent Monte Carlo (MC) method is usually used for uncertainty quantification (UQ). However, the standard MC simulation is computationally expensive because a large number of model executions are required and each model execution is costly simulated on a fine scale spatial grid to ensure accuracy. This study describes a multilevel Monte Carlo (MLMC) method for UQ in reservoir simulation. MLMC is a variance reduction technique for the standard MC. It improves computational efficiency by conducting simulations on a geometric sequence of grids, a larger number of simulations on coarse grids and fewer simulations on fine grids. In this study, we applied the MLMC method to a highly heterogeneous reservoir model from the tenth SPE project. We estimated both the expectation and the probability distribution of oil productions to quantify the influence of subsurface uncertainty. The results indicate that MLMC can achieve the same accuracy as standard MC with a significantly reduced cost, e.g., about 80-90% and 70-90% computational savings in estimating expectations and approximating probability distributions, respectively.