Ensemble-Based History Matching for Channelized Petroleum Reservoirs

The oil industry is at the backbone of global economy and, as natural resources are becoming scarce, there is a pressing need for efficient extraction strategies. This has led to the development of reservoir models and simulators, able to predict future field behaviour, when paired with accurate geological information. However, the data obtained through in-situ measurements, such as seismic surveys, is insufficient to represent the large number of unknowns (porosity, permeability, pressure and fluid saturation in each grid cell). In response to this issue, the scientific community designed computer-assisted history matching algorithms, which are able to provide estimates for model parameters by conditioning on the log of observed production data. The Ensemble Kalman Filter, in particular, is becoming the industry standard, because of its ease of implementation and natural ability to handle uncertainty. However, as past studies have pointed out, reservoirs with complex structural features, such as curved or branching channels, raise difficulties because of the higher-order dependencies induced between the state variables. Another important drawback is the appearance of ensemble collapse, which leads to poor estimates and causes the filter to diverge. The Subspace EnKF is a recently developed history matching framework, able to address both of these issues, by using parameterizations to constrain the ensemble members to different subregions of the parameter space. The main goal of the Master's project was to adapt this framework to 2D channelized petroleum reservoirs, composed of two types of rocks (permeable sand and background shale). For this purpose, we studied polynomial kernel Principal Components Analysis and proposed a novel analytical solution to the preimage problem. The experiments showed that our method surpasses the fixed-point iterative scheme, suggested in the literature, especially in terms of scalability and computational expense. Next, we paired the resulting KPCA parameterization with the Iterative Ensemble Smoother and the Subspace EnKF. Our comparative history matching experiment revealed that the latter is able to successfully avoid ensemble collapse. Finally, we suggested training set clustering as a means to accommodate the subspace parameterizations to the prior information and conducted a sensitivity study on the Subspace EnKF, which yielded encouraging results.Risk and Environmental ModellingApplied MathematicsElectrical Engineering, Mathematics and Computer Scienc