Data Assimilation Using Principal Component Analysis and Artificial Neural Network

Data assimilation (DA) for uncertainty reduction using reservoir simulation models normally demands high computational time; it may take days or even weeks to run a single reservoir application, depending on the reservoir model characteristics. Therefore, it is important to accelerate the process to make it more feasible for practical studies, especially those requiring many simulation runs. One possible way is by using proxy models to replace the reservoir simulator in some time-consuming parts of the procedure. However, the main challenge inherent in proxy models is the inclusion of 3D geostatistical realizations (block-to-block grid properties such as porosity and permeability) as uncertain attributes in the proxy construction. In most cases, it is impossible to treat the values of all grid properties explicitly as input to the proxy building process due to the high dimensionality issue. We present a new methodology for DA combining principal component analysis (PCA) with artificial neural networks (ANN) to solve this problem. The PCA technique is applied to reduce the dimension of the problem, making it possible and feasible to use grid properties in proxy modeling. The trained ANN is used as a proxy for the reservoir simulator, with the goal of reducing the total computational time spent on the application. We run three DA processes using a complex real-field reservoir model for validating the methodology. The first (DA1), used as the reference solution, is the conventional process in which the DA method updates all grid property values explicitly. The second (DA2) is only executed to validate the proposed parameterization via PCA. Both DA1 and DA2 use only the reservoir simulator to generate the reservoir outputs. In the third (DA3), the ANN replaces the reservoir simulator to save computational time. It is important to mention that after DA3, the results (the posterior ensemble) are validated with the reservoir simulator. The DA3, although a little bit less accurate than the DA1, allowed good overall results. Therefore, it seems reasonable to offer the decision-makers the possibility of choosing between the conventional approach (DA1), normally more accurate but slower, and the proposed DA3, much faster than DA1 (with overall good results). This choice may depend on the objective of the reservoir study, available resources, and time to perform the study. The key contribution of this paper is a practical methodology for DA combining PCA [for dimensional reduction (DR)] and ANN (for computational time reduction) applicable in real fields, filling a gap in the literature in this research area.