Analysis of the performance of ensemble methods in reservoir simulation history matching
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The establishment of a reliable geological model is the basis of efficient reservoir evaluation, management, and development, as well as a guarantee for the performance prediction of reservoirs and wells. In the history matching process of reservoir simulation, Bayesian theory has been successfully used in automatic history matching algorithms. By replacing partitions with Bayesian estimation, and using prior statistical information of unknown parameters, the history matching problem becomes easier to determine in a statistical sense. The ensemble Kalman filter extended by Bayesian theory has also achieved gratifying results in the application of automatic history matching research. However, when the parameters and measurement errors are not normally distributed, the relationship between the model and the parameters is not linear, or the available data scale is very limited, the strict implementation of Bayesian estimation will become extremely complex and cumbersome. With an unstrict implementation of Bayesian estimation, the quality of the fitting results is also unstable. For conventional reservoirs, the history matching of the permeability field is a hot topic in the research of automatic history matching algorithms. The most important feature of the permeability field history matching problem is the large scale of parameters to be fitted. The huge difference in scale between the data used for history matching and the parameters that need to be fitted can cause serious overfitting problems. This dissertation introduces a novel localized Kalman filter based on singular value decomposition (SVD). it also demonstrates the improvement of over-fitting problems when applicating this algorithm in the automatic history matching process of reservoir simulation. At the same time, this dissertation also analyzes and summarizes the two functions of the covariance localization method at the theoretical level with an analytical solution of the objective function based on SVD. It also compares the performance of the localization methods using different correlation functions in the automatic history matching of the reservoir. With the rapid development of the global economy and the continuous increase in energy consumption and demand, the shortage of conventional oil and gas resources has become a bottleneck restricting economic development. The exploration and development of fractured oil and gas reservoirs have become a research hotspot and have received more and more attention. Compared with conventional oil and gas reservoirs, the distribution of hydraulic fractures and nature fractures in fractured reservoirs, such as shale reservoirs, is extremely complicated. Fractures have a significant impact on fluid flow in the reservoir and need to be correctly described in the simulator. To guide the efficient development of fractured oil and gas reservoirs, first of all, it is necessary to be able to accurately describe the geometric characteristics and distribution of the fracture network in fractured oil and gas reservoirs. This dissertation investigates the use of ensemble methods to invert the position and shape of the fracture network because it is a promising direction. However, the relationship between the position of the fractures is highly non-linear. This dissertation demonstrates the proper prior information as an extremely critical factor for a successful history matching. The methods to generate the initial fields with proper prior information are also discussed. At the same time, the scales of different types of fractures vary greatly in the fractured reservoir. Even if the fractures are the same type, there can be scale differences. The use of dense grids to completely and explicitly present all the fractures will lead to a huge waste of computing resources. The automatic history matching using the ensemble method is computationally intensive. The numerical model may need to be run thousands of times in an automatic history matching process, which requires a higher efficiency for the numerical simulator integrated into the automatic history matching program. However, fractured reservoirs, such as the shale gas reservoir requires a high simulation accuracy to capture the sharp pressure change around the fracture which is caused by the enormous permeability contrast between the fracture and matrix. the trade-off between the ensemble history matching program integrated simulator's efficiency and accuracy will be discussed through several numerical cases.