Robust Quantification of Uncertainty in Heterogeneity for Chemical EOR Processes: Applying the Multi-Level Monte Carlo Method

tial uncertainty for CEOR processes while greatly reducing the computational requirement — up to two orders of magnitude when compared to traditional MC for both the Gaussian and the non-Gaussian reservoir models. The method can be easily extended to other EOR processes to quantify different kinds of spatial uncertainty, such as carbon dioxide (CO 2) EOR. Other possible extensions of this method are also discussed. Reservoir heterogeneity can be detrimental to the success of chemical enhanced oil recovery (CEOR) processes. Therefore, it is important to evaluate the effect of uncertainty in reservoir heterogeneity on the performance of CEOR. Usually, a Monte Carlo (MC) sampling approach is used, where 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. Monte Carlo simulation (MCS), however, has a slow convergence rate and requires a large number of samples to produce accurate results. This can be computationally expensive when using large reservoir models. This study used a multiscale approach to improve the efficiency of uncertainty quantification regarding reservoir heterogeneity. This multiscale approach is known as the multilevel Monte Carlo (MLMC) method. This method is based on performing a small number of ex - pensive simulations on the fine scale model and a large number of less expensive simulations on coarser upscaled models, then combining the results to produce the quantities of interest. The purpose of this method is to reduce computational cost while still maintaining the accuracy of the fine scale model. The re - sults of this approach have been compared with a reference MCS that assumes a large number of simulations on the fine scale model. Other advantages of the MLMC method are its nonintrusiveness and its scalability, which allows it to incorpo - rate an increasing number of uncertainties. This study used MLMC to efficiently quantify the effect of uncertainty in heterogeneity on the recovery factor of CEOR processes. The permeability field was assumed to be the random input. This method was first demonstrated using a Gaussian 3D reservoir model. Different coarsening algorithms, such as the renormalization and pressure solver methods, were used, and the results were compared. The results were next com - pared with running the MC approach for the fine scale model while equating the computational cost for the MLMC method. Both of these results were then compared with the reference case, which is assumed to use a large number of runs of the fine scale model. Finally, the method was extended to a channelized non-Gaussian generated 3D reservoir model. The results show that it is possible to robustly quantify spa -