Uncertainty Quantification Based on Hierarchical Representation of Fractured Reservoirs

In the modeling of fractured reservoirs, the spatial representation plays an important role to enclose the heterogeneities present in the subsurface. The reservoir flow response obtained from simulation in time is determined by the type of method and by the scale of the representation (fine or coarse). As a deterministic model cannot capture the range of possible scenarios, a set of different realizations associated to an ensemble is required to evaluate the variability of flow responses. The challenge is to determine if the coarse scale simulations, practical in terms of performance, can capture the variability present in the set of realizations. This thesis attempts to quantify the uncertainty of different hierarchical levels for fractured reservoirs and determine the possibility of using coarse scale simulations in uncertainty quantification. The uncertainties, associated to the flow response, were estimated via clustering to a representative subgroup for each ensemble and using Multi-Dimensional Scaling (MDS) distance technique for analysis. Uncertainty trajectories were built in order to analyze the effect of coarsening to the spread in flow response. An advanced framework was built which allows generating an ensemble of realizations with different fracture distributions and connectivity. This framework provides a stable numerical model with the conformal unstructured grid for Discrete Fracture and Matrix (DFM) model at high resolution. Based on this high-fidelity model, we created a coarser DFM representation and numerically upscale it to EDFM models to obtain flow responses at different scales. It is shown that the representatives of the ensemble at coarser scale do not behave similarly to the finest scale ensemble solution. While, the intermediate coarse levels show an accurate flow response in some realizations, it does not hold for all of them. We demonstrate that MDS analysis can help in estimation of the accuracy of flow responses at different scales. However, more practical applications of MDS still need to be developed.Petroleum Engineering and Geo-science