Applying the Multilevel Monte Carlo Method for Heterogeneity-Induced Uncertainty Quantification of Surfactant/Polymer Flooding

Reservoir heterogeneity can be detrimental to the success of surfactant/ polymer enhanced-oil-recovery (EOR) processes. Therefore, it is important to evaluate the effect of uncertainty in reservoir heterogeneity on the performance of surfactant/polymer EOR. Usually, a Monte Carlo sampling approach is used, in which a number of stochastic reservoir-model realizations are generated and then numerical simulation is performed to obtain a certain objective function, such as the recovery factor. However, Monte Carlo simulation (MCS) has a slow convergence rate and requires a large number of samples to produce accurate results. This can be computationally expensive when using large complex reservoir models. This study applies a multiscale approach to improve the efficiency of uncertainty quantification. This method is known as the multilevel Monte Carlo (MLMC) method. This method comprises performing a small number of expensive simulations on the fine-scale model and a large number of less-expensive simulations on coarser upscaled models, and then combining the results to produce the quantities of interest. The purpose of this method is to reduce computational cost while maintaining the accuracy of the fine-scale model. The results of this approach are compared with a reference MCS, assuming a large number of simulations on the fine-scale model. Other advantages of the MLMC method are its nonintrusiveness and its scalability to incorporate an increasing number of uncertainties. This study uses the MLMC method to efficiently quantify the effect of uncertainty in heterogeneity on the recovery factor of a chemical EOR process, specifically surfactant/polymer flooding. The permeability field is assumed to be the random input. This method is first demonstrated by use of a Gaussian 3D reservoir model. Different coarsening algorithms are used and compared, such as the renormalization method and the pressure-solver method (PSM). The results are compared with running Monte Carlo for the fine-scale model while equating the computational cost for the MLMC method. Both of these results are then compared with the reference case, which uses a large number of runs of the fine-scale model. The method is then extended to a channelized non-Gaussian generated 3D reservoir model incorporating multiphase upscaling The results show that it is possible to robustly quantify spatial uncertainty for a surfactant/polymer EOR process while greatly reducing the computational requirement, up to two orders of magnitude compared with traditional Monte Carlo for both the Gaussian and non-Gaussian reservoir models. The method can be easily extended to other EOR processes to quantify spatial uncertainty, such as carbon dioxide (CO2) EOR. Other possible extensions of this method are also discussed.