Determination of Relevant Spatial Scale in Reservoir Simulation

Abstract

Under-sampling of the subsurface combined with scale differences in observations causes the estimation of geological parameters to be an ill-posed problem. As a result, only a subset of theoretically possible models can truly depict the reality. In reservoir modeling, we capture complexity and heterogeneity by representing the solution space with a large number of high-resolution models, whose spread represents uncertainties in permeability. It is not immediately evident at which scale the static and dynamic model should be formulated. Therefore, this thesis work attempts to determine a relevant spatial scale in reservoir simulation. The relevant spatial scale is subdivided into a static and dynamic spatial scale. The static one is analyzed using the Discrete Cosine Transform (DCT). A dominant basis-vector is determined which explains the predominant pattern in the reservoir model. The associated dimensions to accurately represent this basis-vector is chosen as relevant static spatial scale. A hierarchical ensemble is established using a flow-based upscaling approach, in an attempt to quantify the coarsening effect.

The hierarchical ensemble of models is simulated forward in time to represent fluid flow and associated uncertainties in its response. Dynamic analysis is done on a reduced representation of the response uncertainty, obtained via Multidimensional Scaling (MDS). An Uncertainty Trajectory is built in order to analyze the effect of time on the response uncertainty. The distance from the finest uncertainty trajectory is used to quantify the coarsening effect on a dynamic level. It is shown that the characteristics of the coarser ensemble scale behave similarly to the finest ensemble scale. This observation has led to the use of coarse information in the prediction of representative fine-scale models. Where representatives refer to using them as a subset to approximate the full fine-scale ensemble statistics.